Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,26,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(19.7998389976\) |
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: | \( x^{12} + 71168091 x^{10} + \cdots + 10\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{44}\cdot 3^{20}\cdot 5^{29} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.3 | ||
Root | \(-3156.95i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.26.b.a.4.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 6313.90i | − | 1.08999i | −0.838439 | − | 0.544995i | \(-0.816531\pi\) | ||
0.838439 | − | 0.544995i | \(-0.183469\pi\) | |||||||
\(3\) | − | 71116.0i | − | 0.0772595i | −0.999254 | − | 0.0386297i | \(-0.987701\pi\) | ||
0.999254 | − | 0.0386297i | \(-0.0122993\pi\) | |||||||
\(4\) | −6.31093e6 | −0.188080 | ||||||||
\(5\) | 3.25528e8 | − | 4.38241e8i | 0.596298 | − | 0.802763i | ||||
\(6\) | −4.49019e8 | −0.0842121 | ||||||||
\(7\) | 3.34630e10i | 0.913774i | 0.889525 | + | 0.456887i | \(0.151036\pi\) | ||||
−0.889525 | + | 0.456887i | \(0.848964\pi\) | |||||||
\(8\) | − | 1.72013e11i | − | 0.884985i | ||||||
\(9\) | 8.42231e11 | 0.994031 | ||||||||
\(10\) | −2.76701e12 | − | 2.05535e12i | −0.875005 | − | 0.649959i | ||||
\(11\) | 1.82144e13 | 1.74987 | 0.874936 | − | 0.484239i | \(-0.160903\pi\) | ||||
0.874936 | + | 0.484239i | \(0.160903\pi\) | |||||||
\(12\) | 4.48808e11i | 0.0145310i | ||||||||
\(13\) | − | 9.99300e13i | − | 1.18961i | −0.803871 | − | 0.594804i | \(-0.797230\pi\) | ||
0.803871 | − | 0.594804i | \(-0.202770\pi\) | |||||||
\(14\) | 2.11282e14 | 0.996005 | ||||||||
\(15\) | −3.11659e13 | − | 2.31502e13i | −0.0620211 | − | 0.0460696i | ||||
\(16\) | −1.29783e15 | −1.15271 | ||||||||
\(17\) | 2.20067e15i | 0.916100i | 0.888926 | + | 0.458050i | \(0.151452\pi\) | ||||
−0.888926 | + | 0.458050i | \(0.848548\pi\) | |||||||
\(18\) | − | 5.31776e15i | − | 1.08348i | ||||||
\(19\) | −1.27990e16 | −1.32665 | −0.663323 | − | 0.748333i | \(-0.730854\pi\) | ||||
−0.663323 | + | 0.748333i | \(0.730854\pi\) | |||||||
\(20\) | −2.05438e15 | + | 2.76570e15i | −0.112152 | + | 0.150984i | ||||
\(21\) | 2.37975e15 | 0.0705977 | ||||||||
\(22\) | − | 1.15004e17i | − | 1.90734i | ||||||
\(23\) | − | 7.08167e16i | − | 0.673810i | −0.941539 | − | 0.336905i | \(-0.890620\pi\) | ||
0.941539 | − | 0.336905i | \(-0.109380\pi\) | |||||||
\(24\) | −1.22329e16 | −0.0683735 | ||||||||
\(25\) | −8.60865e16 | − | 2.85319e17i | −0.288858 | − | 0.957372i | ||||
\(26\) | −6.30948e17 | −1.29666 | ||||||||
\(27\) | − | 1.20152e17i | − | 0.154058i | ||||||
\(28\) | − | 2.11182e17i | − | 0.171863i | ||||||
\(29\) | −2.12993e18 | −1.11787 | −0.558935 | − | 0.829212i | \(-0.688790\pi\) | ||||
−0.558935 | + | 0.829212i | \(0.688790\pi\) | |||||||
\(30\) | −1.46168e17 | + | 1.96779e17i | −0.0502155 | + | 0.0676024i | ||||
\(31\) | 4.58579e18 | 1.04567 | 0.522833 | − | 0.852435i | \(-0.324875\pi\) | ||||
0.522833 | + | 0.852435i | \(0.324875\pi\) | |||||||
\(32\) | 2.42259e18i | 0.371454i | ||||||||
\(33\) | − | 1.29534e18i | − | 0.135194i | ||||||
\(34\) | 1.38948e19 | 0.998541 | ||||||||
\(35\) | 1.46648e19 | + | 1.08931e19i | 0.733544 | + | 0.544881i | ||||
\(36\) | −5.31526e18 | −0.186958 | ||||||||
\(37\) | 1.67895e19i | 0.419292i | 0.977777 | + | 0.209646i | \(0.0672311\pi\) | ||||
−0.977777 | + | 0.209646i | \(0.932769\pi\) | |||||||
\(38\) | 8.08114e19i | 1.44603i | ||||||||
\(39\) | −7.10662e18 | −0.0919085 | ||||||||
\(40\) | −7.53830e19 | − | 5.59950e19i | −0.710434 | − | 0.527715i | ||||
\(41\) | 4.79379e19 | 0.331804 | 0.165902 | − | 0.986142i | \(-0.446947\pi\) | ||||
0.165902 | + | 0.986142i | \(0.446947\pi\) | |||||||
\(42\) | − | 1.50255e19i | − | 0.0769508i | ||||||
\(43\) | − | 1.55532e20i | − | 0.593558i | −0.954946 | − | 0.296779i | \(-0.904087\pi\) | ||
0.954946 | − | 0.296779i | \(-0.0959125\pi\) | |||||||
\(44\) | −1.14950e20 | −0.329116 | ||||||||
\(45\) | 2.74170e20 | − | 3.69100e20i | 0.592738 | − | 0.797972i | ||||
\(46\) | −4.47129e20 | −0.734447 | ||||||||
\(47\) | − | 8.97966e20i | − | 1.12729i | −0.826016 | − | 0.563646i | \(-0.809398\pi\) | ||
0.826016 | − | 0.563646i | \(-0.190602\pi\) | |||||||
\(48\) | 9.22966e19i | 0.0890574i | ||||||||
\(49\) | 2.21299e20 | 0.165017 | ||||||||
\(50\) | −1.80148e21 | + | 5.43542e20i | −1.04353 | + | 0.314853i | ||||
\(51\) | 1.56503e20 | 0.0707774 | ||||||||
\(52\) | 6.30651e20i | 0.223742i | ||||||||
\(53\) | 6.78665e21i | 1.89761i | 0.315863 | + | 0.948805i | \(0.397706\pi\) | ||||
−0.315863 | + | 0.948805i | \(0.602294\pi\) | |||||||
\(54\) | −7.58627e20 | −0.167922 | ||||||||
\(55\) | 5.92929e21 | − | 7.98229e21i | 1.04344 | − | 1.40473i | ||||
\(56\) | 5.75606e21 | 0.808677 | ||||||||
\(57\) | 9.10211e20i | 0.102496i | ||||||||
\(58\) | 1.34482e22i | 1.21847i | ||||||||
\(59\) | 8.34744e21 | 0.610806 | 0.305403 | − | 0.952223i | \(-0.401209\pi\) | ||||
0.305403 | + | 0.952223i | \(0.401209\pi\) | |||||||
\(60\) | 1.96686e20 | + | 1.46099e20i | 0.0116649 | + | 0.00866479i | ||||
\(61\) | −8.24148e21 | −0.397541 | −0.198771 | − | 0.980046i | \(-0.563695\pi\) | ||||
−0.198771 | + | 0.980046i | \(0.563695\pi\) | |||||||
\(62\) | − | 2.89542e22i | − | 1.13977i | ||||||
\(63\) | 2.81835e22i | 0.908320i | ||||||||
\(64\) | −2.82520e22 | −0.747825 | ||||||||
\(65\) | −4.37934e22 | − | 3.25300e22i | −0.954974 | − | 0.709361i | ||||
\(66\) | −8.17862e21 | −0.147360 | ||||||||
\(67\) | − | 8.00779e21i | − | 0.119558i | −0.998212 | − | 0.0597789i | \(-0.980960\pi\) | ||
0.998212 | − | 0.0597789i | \(-0.0190396\pi\) | |||||||
\(68\) | − | 1.38883e22i | − | 0.172300i | ||||||
\(69\) | −5.03620e21 | −0.0520582 | ||||||||
\(70\) | 6.87781e22 | − | 9.25923e22i | 0.593916 | − | 0.799557i | ||||
\(71\) | 8.71591e21 | 0.0630352 | 0.0315176 | − | 0.999503i | \(-0.489966\pi\) | ||||
0.0315176 | + | 0.999503i | \(0.489966\pi\) | |||||||
\(72\) | − | 1.44875e23i | − | 0.879703i | ||||||
\(73\) | 1.89109e23i | 0.966444i | 0.875498 | + | 0.483222i | \(0.160534\pi\) | ||||
−0.875498 | + | 0.483222i | \(0.839466\pi\) | |||||||
\(74\) | 1.06007e23 | 0.457024 | ||||||||
\(75\) | −2.02907e22 | + | 6.12213e21i | −0.0739660 | + | 0.0223170i | ||||
\(76\) | 8.07733e22 | 0.249516 | ||||||||
\(77\) | 6.09508e23i | 1.59899i | ||||||||
\(78\) | 4.48705e22i | 0.100179i | ||||||||
\(79\) | −1.13990e23 | −0.217034 | −0.108517 | − | 0.994095i | \(-0.534610\pi\) | ||||
−0.108517 | + | 0.994095i | \(0.534610\pi\) | |||||||
\(80\) | −4.22480e23 | + | 5.68763e23i | −0.687356 | + | 0.925350i | ||||
\(81\) | 7.05068e23 | 0.982129 | ||||||||
\(82\) | − | 3.02675e23i | − | 0.361663i | ||||||
\(83\) | − | 9.87203e23i | − | 1.01375i | −0.862020 | − | 0.506874i | \(-0.830801\pi\) | ||
0.862020 | − | 0.506874i | \(-0.169199\pi\) | |||||||
\(84\) | −1.50184e22 | −0.0132780 | ||||||||
\(85\) | 9.64422e23 | + | 7.16379e23i | 0.735412 | + | 0.546268i | ||||
\(86\) | −9.82012e23 | −0.646973 | ||||||||
\(87\) | 1.51472e23i | 0.0863660i | ||||||||
\(88\) | − | 3.13311e24i | − | 1.54861i | ||||||
\(89\) | −9.13656e23 | −0.392110 | −0.196055 | − | 0.980593i | \(-0.562813\pi\) | ||||
−0.196055 | + | 0.980593i | \(0.562813\pi\) | |||||||
\(90\) | −2.33046e24 | − | 1.73108e24i | −0.869782 | − | 0.646079i | ||||
\(91\) | 3.34395e24 | 1.08703 | ||||||||
\(92\) | 4.46919e23i | 0.126730i | ||||||||
\(93\) | − | 3.26123e23i | − | 0.0807876i | ||||||
\(94\) | −5.66967e24 | −1.22874 | ||||||||
\(95\) | −4.16642e24 | + | 5.60903e24i | −0.791075 | + | 1.06498i | ||||
\(96\) | 1.72285e23 | 0.0286983 | ||||||||
\(97\) | 1.03288e24i | 0.151149i | 0.997140 | + | 0.0755745i | \(0.0240791\pi\) | ||||
−0.997140 | + | 0.0755745i | \(0.975921\pi\) | |||||||
\(98\) | − | 1.39726e24i | − | 0.179867i | ||||||
\(99\) | 1.53407e25 | 1.73943 | ||||||||
\(100\) | 5.43286e23 | + | 1.80063e24i | 0.0543286 | + | 0.180063i | ||||
\(101\) | 9.50077e24 | 0.838960 | 0.419480 | − | 0.907765i | \(-0.362212\pi\) | ||||
0.419480 | + | 0.907765i | \(0.362212\pi\) | |||||||
\(102\) | − | 9.88143e23i | − | 0.0771467i | ||||||
\(103\) | 7.31026e24i | 0.505205i | 0.967570 | + | 0.252602i | \(0.0812864\pi\) | ||||
−0.967570 | + | 0.252602i | \(0.918714\pi\) | |||||||
\(104\) | −1.71892e25 | −1.05279 | ||||||||
\(105\) | 7.74675e23 | − | 1.04290e24i | 0.0420972 | − | 0.0566732i | ||||
\(106\) | 4.28502e25 | 2.06838 | ||||||||
\(107\) | 1.98063e25i | 0.850171i | 0.905153 | + | 0.425085i | \(0.139756\pi\) | ||||
−0.905153 | + | 0.425085i | \(0.860244\pi\) | |||||||
\(108\) | 7.58270e23i | 0.0289752i | ||||||||
\(109\) | −2.78064e25 | −0.946922 | −0.473461 | − | 0.880815i | \(-0.656996\pi\) | ||||
−0.473461 | + | 0.880815i | \(0.656996\pi\) | |||||||
\(110\) | −5.03994e25 | − | 3.74370e25i | −1.53115 | − | 1.13734i | ||||
\(111\) | 1.19400e24 | 0.0323943 | ||||||||
\(112\) | − | 4.34293e25i | − | 1.05331i | ||||||
\(113\) | 8.19644e25i | 1.77887i | 0.457059 | + | 0.889436i | \(0.348903\pi\) | ||||
−0.457059 | + | 0.889436i | \(0.651097\pi\) | |||||||
\(114\) | 5.74698e24 | 0.111720 | ||||||||
\(115\) | −3.10347e25 | − | 2.30528e25i | −0.540910 | − | 0.401791i | ||||
\(116\) | 1.34419e25 | 0.210249 | ||||||||
\(117\) | − | 8.41642e25i | − | 1.18251i | ||||||
\(118\) | − | 5.27049e25i | − | 0.665773i | ||||||
\(119\) | −7.36409e25 | −0.837109 | ||||||||
\(120\) | −3.98214e24 | + | 5.36094e24i | −0.0407709 | + | 0.0548877i | ||||
\(121\) | 2.23417e26 | 2.06205 | ||||||||
\(122\) | 5.20359e25i | 0.433316i | ||||||||
\(123\) | − | 3.40915e24i | − | 0.0256350i | ||||||
\(124\) | −2.89406e25 | −0.196669 | ||||||||
\(125\) | −1.53062e26 | − | 5.51527e25i | −0.940789 | − | 0.338994i | ||||
\(126\) | 1.77948e26 | 0.990060 | ||||||||
\(127\) | 2.00659e26i | 1.01137i | 0.862717 | + | 0.505686i | \(0.168761\pi\) | ||||
−0.862717 | + | 0.505686i | \(0.831239\pi\) | |||||||
\(128\) | 2.59669e26i | 1.18658i | ||||||||
\(129\) | −1.10608e25 | −0.0458580 | ||||||||
\(130\) | −2.05391e26 | + | 2.76507e26i | −0.773197 | + | 1.04091i | ||||
\(131\) | 1.88307e26 | 0.644133 | 0.322066 | − | 0.946717i | \(-0.395623\pi\) | ||||
0.322066 | + | 0.946717i | \(0.395623\pi\) | |||||||
\(132\) | 8.17476e24i | 0.0254273i | ||||||||
\(133\) | − | 4.28291e26i | − | 1.21225i | ||||||
\(134\) | −5.05604e25 | −0.130317 | ||||||||
\(135\) | −5.26554e25 | − | 3.91128e25i | −0.123672 | − | 0.0918643i | ||||
\(136\) | 3.78543e26 | 0.810735 | ||||||||
\(137\) | − | 1.93039e26i | − | 0.377257i | −0.982048 | − | 0.188629i | \(-0.939596\pi\) | ||
0.982048 | − | 0.188629i | \(-0.0604042\pi\) | |||||||
\(138\) | 3.17981e25i | 0.0567430i | ||||||||
\(139\) | −2.35098e25 | −0.0383321 | −0.0191661 | − | 0.999816i | \(-0.506101\pi\) | ||||
−0.0191661 | + | 0.999816i | \(0.506101\pi\) | |||||||
\(140\) | −9.25487e25 | − | 6.87457e25i | −0.137965 | − | 0.102481i | ||||
\(141\) | −6.38598e25 | −0.0870940 | ||||||||
\(142\) | − | 5.50314e25i | − | 0.0687078i | ||||||
\(143\) | − | 1.82017e27i | − | 2.08166i | ||||||
\(144\) | −1.09307e27 | −1.14583 | ||||||||
\(145\) | −6.93353e26 | + | 9.33424e26i | −0.666583 | + | 0.897385i | ||||
\(146\) | 1.19402e27 | 1.05342 | ||||||||
\(147\) | − | 1.57379e25i | − | 0.0127491i | ||||||
\(148\) | − | 1.05957e26i | − | 0.0788605i | ||||||
\(149\) | −8.08718e26 | −0.553310 | −0.276655 | − | 0.960969i | \(-0.589226\pi\) | ||||
−0.276655 | + | 0.960969i | \(0.589226\pi\) | |||||||
\(150\) | 3.86545e25 | + | 1.28114e26i | 0.0243254 | + | 0.0806223i | ||||
\(151\) | −1.94023e27 | −1.12368 | −0.561838 | − | 0.827247i | \(-0.689906\pi\) | ||||
−0.561838 | + | 0.827247i | \(0.689906\pi\) | |||||||
\(152\) | 2.20159e27i | 1.17406i | ||||||||
\(153\) | 1.85347e27i | 0.910632i | ||||||||
\(154\) | 3.84837e27 | 1.74288 | ||||||||
\(155\) | 1.49280e27 | − | 2.00968e27i | 0.623528 | − | 0.839423i | ||||
\(156\) | 4.48494e25 | 0.0172862 | ||||||||
\(157\) | − | 7.20403e26i | − | 0.256348i | −0.991752 | − | 0.128174i | \(-0.959088\pi\) | ||
0.991752 | − | 0.128174i | \(-0.0409116\pi\) | |||||||
\(158\) | 7.19721e26i | 0.236565i | ||||||||
\(159\) | 4.82639e26 | 0.146608 | ||||||||
\(160\) | 1.06168e27 | + | 7.88620e26i | 0.298190 | + | 0.221497i | ||||
\(161\) | 2.36973e27 | 0.615710 | ||||||||
\(162\) | − | 4.45173e27i | − | 1.07051i | ||||||
\(163\) | 7.26372e27i | 1.61739i | 0.588229 | + | 0.808694i | \(0.299825\pi\) | ||||
−0.588229 | + | 0.808694i | \(0.700175\pi\) | |||||||
\(164\) | −3.02533e26 | −0.0624057 | ||||||||
\(165\) | −5.67668e26 | − | 4.21668e26i | −0.108529 | − | 0.0806159i | ||||
\(166\) | −6.23310e27 | −1.10498 | ||||||||
\(167\) | 8.01662e25i | 0.0131836i | 0.999978 | + | 0.00659182i | \(0.00209826\pi\) | ||||
−0.999978 | + | 0.00659182i | \(0.997902\pi\) | |||||||
\(168\) | − | 4.09348e26i | − | 0.0624779i | ||||||
\(169\) | −2.92960e27 | −0.415168 | ||||||||
\(170\) | 4.52314e27 | − | 6.08927e27i | 0.595428 | − | 0.801592i | ||||
\(171\) | −1.07797e28 | −1.31873 | ||||||||
\(172\) | 9.81549e26i | 0.111637i | ||||||||
\(173\) | − | 7.99251e27i | − | 0.845486i | −0.906249 | − | 0.422743i | \(-0.861067\pi\) | ||
0.906249 | − | 0.422743i | \(-0.138933\pi\) | |||||||
\(174\) | 9.56382e26 | 0.0941382 | ||||||||
\(175\) | 9.54762e27 | − | 2.88071e27i | 0.874822 | − | 0.263951i | ||||
\(176\) | −2.36392e28 | −2.01709 | ||||||||
\(177\) | − | 5.93636e26i | − | 0.0471905i | ||||||
\(178\) | 5.76873e27i | 0.427396i | ||||||||
\(179\) | 2.21151e28 | 1.52766 | 0.763829 | − | 0.645419i | \(-0.223317\pi\) | ||||
0.763829 | + | 0.645419i | \(0.223317\pi\) | |||||||
\(180\) | −1.73026e27 | + | 2.32936e27i | −0.111482 | + | 0.150083i | ||||
\(181\) | 1.90946e28 | 1.14796 | 0.573982 | − | 0.818868i | \(-0.305398\pi\) | ||||
0.573982 | + | 0.818868i | \(0.305398\pi\) | |||||||
\(182\) | − | 2.11134e28i | − | 1.18486i | ||||||
\(183\) | 5.86101e26i | 0.0307138i | ||||||||
\(184\) | −1.21814e28 | −0.596312 | ||||||||
\(185\) | 7.35784e27 | + | 5.46545e27i | 0.336592 | + | 0.250023i | ||||
\(186\) | −2.05911e27 | −0.0880578 | ||||||||
\(187\) | 4.00838e28i | 1.60306i | ||||||||
\(188\) | 5.66700e27i | 0.212021i | ||||||||
\(189\) | 4.02064e27 | 0.140774 | ||||||||
\(190\) | 3.54148e28 | + | 2.63064e28i | 1.16082 | + | 0.862265i | ||||
\(191\) | −5.19174e28 | −1.59366 | −0.796830 | − | 0.604204i | \(-0.793491\pi\) | ||||
−0.796830 | + | 0.604204i | \(0.793491\pi\) | |||||||
\(192\) | 2.00917e27i | 0.0577765i | ||||||||
\(193\) | − | 4.44868e27i | − | 0.119885i | −0.998202 | − | 0.0599425i | \(-0.980908\pi\) | ||
0.998202 | − | 0.0599425i | \(-0.0190917\pi\) | |||||||
\(194\) | 6.52153e27 | 0.164751 | ||||||||
\(195\) | −2.31340e27 | + | 3.11441e27i | −0.0548048 | + | 0.0737808i | ||||
\(196\) | −1.39660e27 | −0.0310364 | ||||||||
\(197\) | 5.37613e28i | 1.12109i | 0.828122 | + | 0.560547i | \(0.189409\pi\) | ||||
−0.828122 | + | 0.560547i | \(0.810591\pi\) | |||||||
\(198\) | − | 9.68599e28i | − | 1.89596i | ||||||
\(199\) | 5.29552e28 | 0.973297 | 0.486649 | − | 0.873598i | \(-0.338219\pi\) | ||||
0.486649 | + | 0.873598i | \(0.338219\pi\) | |||||||
\(200\) | −4.90785e28 | + | 1.48080e28i | −0.847260 | + | 0.255635i | ||||
\(201\) | −5.69482e26 | −0.00923697 | ||||||||
\(202\) | − | 5.99869e28i | − | 0.914459i | ||||||
\(203\) | − | 7.12739e28i | − | 1.02148i | ||||||
\(204\) | −9.87677e26 | −0.0133118 | ||||||||
\(205\) | 1.56051e28 | − | 2.10084e28i | 0.197854 | − | 0.266360i | ||||
\(206\) | 4.61562e28 | 0.550668 | ||||||||
\(207\) | − | 5.96440e28i | − | 0.669788i | ||||||
\(208\) | 1.29692e29i | 1.37127i | ||||||||
\(209\) | −2.33125e29 | −2.32146 | ||||||||
\(210\) | −6.58479e27 | − | 4.89122e27i | −0.0617733 | − | 0.0458856i | ||||
\(211\) | 3.70619e28 | 0.327640 | 0.163820 | − | 0.986490i | \(-0.447618\pi\) | ||||
0.163820 | + | 0.986490i | \(0.447618\pi\) | |||||||
\(212\) | − | 4.28300e28i | − | 0.356903i | ||||||
\(213\) | − | 6.19840e26i | − | 0.00487007i | ||||||
\(214\) | 1.25055e29 | 0.926678 | ||||||||
\(215\) | −6.81603e28 | − | 5.06299e28i | −0.476487 | − | 0.353937i | ||||
\(216\) | −2.06677e28 | −0.136339 | ||||||||
\(217\) | 1.53454e29i | 0.955503i | ||||||||
\(218\) | 1.75567e29i | 1.03214i | ||||||||
\(219\) | 1.34487e28 | 0.0746670 | ||||||||
\(220\) | −3.74193e28 | + | 5.03756e28i | −0.196251 | + | 0.264203i | ||||
\(221\) | 2.19913e29 | 1.08980 | ||||||||
\(222\) | − | 7.53882e27i | − | 0.0353094i | ||||||
\(223\) | 2.00308e29i | 0.886926i | 0.896293 | + | 0.443463i | \(0.146250\pi\) | ||||
−0.896293 | + | 0.443463i | \(0.853750\pi\) | |||||||
\(224\) | −8.10670e28 | −0.339425 | ||||||||
\(225\) | −7.25047e28 | − | 2.40305e29i | −0.287134 | − | 0.951657i | ||||
\(226\) | 5.17515e29 | 1.93895 | ||||||||
\(227\) | − | 2.72579e29i | − | 0.966427i | −0.875503 | − | 0.483214i | \(-0.839469\pi\) | ||
0.875503 | − | 0.483214i | \(-0.160531\pi\) | |||||||
\(228\) | − | 5.74428e27i | − | 0.0192775i | ||||||
\(229\) | 2.35864e29 | 0.749408 | 0.374704 | − | 0.927145i | \(-0.377744\pi\) | ||||
0.374704 | + | 0.927145i | \(0.377744\pi\) | |||||||
\(230\) | −1.45553e29 | + | 1.95950e29i | −0.437949 | + | 0.589587i | ||||
\(231\) | 4.33457e28 | 0.123537 | ||||||||
\(232\) | 3.66376e29i | 0.989298i | ||||||||
\(233\) | − | 2.85511e29i | − | 0.730591i | −0.930892 | − | 0.365295i | \(-0.880968\pi\) | ||
0.930892 | − | 0.365295i | \(-0.119032\pi\) | |||||||
\(234\) | −5.31404e29 | −1.28892 | ||||||||
\(235\) | −3.93525e29 | − | 2.92313e29i | −0.904949 | − | 0.672202i | ||||
\(236\) | −5.26801e28 | −0.114880 | ||||||||
\(237\) | 8.10650e27i | 0.0167679i | ||||||||
\(238\) | 4.64961e29i | 0.912441i | ||||||||
\(239\) | −3.11095e29 | −0.579321 | −0.289660 | − | 0.957130i | \(-0.593542\pi\) | ||||
−0.289660 | + | 0.957130i | \(0.593542\pi\) | |||||||
\(240\) | 4.04481e28 | + | 3.00451e28i | 0.0714921 | + | 0.0531047i | ||||
\(241\) | −1.05064e29 | −0.176295 | −0.0881475 | − | 0.996107i | \(-0.528095\pi\) | ||||
−0.0881475 | + | 0.996107i | \(0.528095\pi\) | |||||||
\(242\) | − | 1.41063e30i | − | 2.24762i | ||||||
\(243\) | − | 1.51945e29i | − | 0.229936i | ||||||
\(244\) | 5.20114e28 | 0.0747697 | ||||||||
\(245\) | 7.20390e28 | − | 9.69822e28i | 0.0983992 | − | 0.132470i | ||||
\(246\) | −2.15251e28 | −0.0279419 | ||||||||
\(247\) | 1.27900e30i | 1.57819i | ||||||||
\(248\) | − | 7.88815e29i | − | 0.925399i | ||||||
\(249\) | −7.02059e28 | −0.0783217 | ||||||||
\(250\) | −3.48229e29 | + | 9.66418e29i | −0.369500 | + | 1.02545i | ||||
\(251\) | 1.05031e30 | 1.06022 | 0.530111 | − | 0.847928i | \(-0.322150\pi\) | ||||
0.530111 | + | 0.847928i | \(0.322150\pi\) | |||||||
\(252\) | − | 1.77864e29i | − | 0.170837i | ||||||
\(253\) | − | 1.28988e30i | − | 1.17908i | ||||||
\(254\) | 1.26694e30 | 1.10239 | ||||||||
\(255\) | 5.09460e28 | − | 6.85859e28i | 0.0422044 | − | 0.0568175i | ||||
\(256\) | 6.91545e29 | 0.545533 | ||||||||
\(257\) | 2.63115e30i | 1.97688i | 0.151599 | + | 0.988442i | \(0.451558\pi\) | ||||
−0.151599 | + | 0.988442i | \(0.548442\pi\) | |||||||
\(258\) | 6.98368e28i | 0.0499848i | ||||||||
\(259\) | −5.61827e29 | −0.383138 | ||||||||
\(260\) | 2.76377e29 | + | 2.05294e29i | 0.179612 | + | 0.133417i | ||||
\(261\) | −1.79390e30 | −1.11120 | ||||||||
\(262\) | − | 1.18895e30i | − | 0.702099i | ||||||
\(263\) | 9.52475e29i | 0.536298i | 0.963377 | + | 0.268149i | \(0.0864120\pi\) | ||||
−0.963377 | + | 0.268149i | \(0.913588\pi\) | |||||||
\(264\) | −2.22814e29 | −0.119645 | ||||||||
\(265\) | 2.97418e30 | + | 2.20924e30i | 1.52333 | + | 1.13154i | ||||
\(266\) | −2.70419e30 | −1.32135 | ||||||||
\(267\) | 6.49755e28i | 0.0302942i | ||||||||
\(268\) | 5.05366e28i | 0.0224865i | ||||||||
\(269\) | 1.14301e30 | 0.485452 | 0.242726 | − | 0.970095i | \(-0.421958\pi\) | ||||
0.242726 | + | 0.970095i | \(0.421958\pi\) | |||||||
\(270\) | −2.46954e29 | + | 3.32461e29i | −0.100131 | + | 0.134801i | ||||
\(271\) | −9.46451e29 | −0.366422 | −0.183211 | − | 0.983074i | \(-0.558649\pi\) | ||||
−0.183211 | + | 0.983074i | \(0.558649\pi\) | |||||||
\(272\) | − | 2.85610e30i | − | 1.05599i | ||||||
\(273\) | − | 2.37809e29i | − | 0.0839836i | ||||||
\(274\) | −1.21883e30 | −0.411207 | ||||||||
\(275\) | −1.56801e30 | − | 5.19691e30i | −0.505465 | − | 1.67528i | ||||
\(276\) | 3.17831e28 | 0.00979112 | ||||||||
\(277\) | − | 7.31941e29i | − | 0.215516i | −0.994177 | − | 0.107758i | \(-0.965633\pi\) | ||
0.994177 | − | 0.107758i | \(-0.0343671\pi\) | |||||||
\(278\) | 1.48438e29i | 0.0417817i | ||||||||
\(279\) | 3.86230e30 | 1.03943 | ||||||||
\(280\) | 1.87376e30 | − | 2.52254e30i | 0.482212 | − | 0.649176i | ||||
\(281\) | −7.88433e29 | −0.194060 | −0.0970299 | − | 0.995281i | \(-0.530934\pi\) | ||||
−0.0970299 | + | 0.995281i | \(0.530934\pi\) | |||||||
\(282\) | 4.03204e29i | 0.0949317i | ||||||||
\(283\) | 6.09023e29i | 0.137184i | 0.997645 | + | 0.0685920i | \(0.0218507\pi\) | ||||
−0.997645 | + | 0.0685920i | \(0.978149\pi\) | |||||||
\(284\) | −5.50054e28 | −0.0118557 | ||||||||
\(285\) | 3.98892e29 | + | 2.96299e29i | 0.0822800 | + | 0.0611181i | ||||
\(286\) | −1.14923e31 | −2.26899 | ||||||||
\(287\) | 1.60415e30i | 0.303194i | ||||||||
\(288\) | 2.04038e30i | 0.369237i | ||||||||
\(289\) | 9.27687e29 | 0.160760 | ||||||||
\(290\) | 5.89355e30 | + | 4.37776e30i | 0.978142 | + | 0.726570i | ||||
\(291\) | 7.34546e28 | 0.0116777 | ||||||||
\(292\) | − | 1.19345e30i | − | 0.181769i | ||||||
\(293\) | 6.89904e30i | 1.00680i | 0.864053 | + | 0.503400i | \(0.167918\pi\) | ||||
−0.864053 | + | 0.503400i | \(0.832082\pi\) | |||||||
\(294\) | −9.93675e28 | −0.0138964 | ||||||||
\(295\) | 2.71732e30 | − | 3.65819e30i | 0.364222 | − | 0.490332i | ||||
\(296\) | 2.88801e30 | 0.371067 | ||||||||
\(297\) | − | 2.18849e30i | − | 0.269581i | ||||||
\(298\) | 5.10617e30i | 0.603103i | ||||||||
\(299\) | −7.07671e30 | −0.801570 | ||||||||
\(300\) | 1.28053e29 | − | 3.86363e28i | 0.0139115 | − | 0.00419740i | ||||
\(301\) | 5.20455e30 | 0.542378 | ||||||||
\(302\) | 1.22504e31i | 1.22480i | ||||||||
\(303\) | − | 6.75656e29i | − | 0.0648176i | ||||||
\(304\) | 1.66109e31 | 1.52923 | ||||||||
\(305\) | −2.68283e30 | + | 3.61175e30i | −0.237053 | + | 0.319132i | ||||
\(306\) | 1.17026e31 | 0.992581 | ||||||||
\(307\) | − | 1.77035e31i | − | 1.44155i | −0.693171 | − | 0.720773i | \(-0.743787\pi\) | ||
0.693171 | − | 0.720773i | \(-0.256213\pi\) | |||||||
\(308\) | − | 3.84656e30i | − | 0.300738i | ||||||
\(309\) | 5.19876e29 | 0.0390318 | ||||||||
\(310\) | −1.26889e31 | − | 9.42541e30i | −0.914963 | − | 0.679640i | ||||
\(311\) | −1.86741e31 | −1.29340 | −0.646701 | − | 0.762743i | \(-0.723852\pi\) | ||||
−0.646701 | + | 0.762743i | \(0.723852\pi\) | |||||||
\(312\) | 1.22243e30i | 0.0813377i | ||||||||
\(313\) | − | 1.97244e31i | − | 1.26096i | −0.776207 | − | 0.630479i | \(-0.782859\pi\) | ||
0.776207 | − | 0.630479i | \(-0.217141\pi\) | |||||||
\(314\) | −4.54855e30 | −0.279417 | ||||||||
\(315\) | 1.23512e31 | + | 9.17453e30i | 0.729166 | + | 0.541629i | ||||
\(316\) | 7.19381e29 | 0.0408198 | ||||||||
\(317\) | 2.26583e31i | 1.23591i | 0.786214 | + | 0.617954i | \(0.212038\pi\) | ||||
−0.786214 | + | 0.617954i | \(0.787962\pi\) | |||||||
\(318\) | − | 3.04734e30i | − | 0.159802i | ||||||
\(319\) | −3.87955e31 | −1.95613 | ||||||||
\(320\) | −9.19682e30 | + | 1.23812e31i | −0.445926 | + | 0.600326i | ||||
\(321\) | 1.40854e30 | 0.0656837 | ||||||||
\(322\) | − | 1.49623e31i | − | 0.671118i | ||||||
\(323\) | − | 2.81663e31i | − | 1.21534i | ||||||
\(324\) | −4.44963e30 | −0.184719 | ||||||||
\(325\) | −2.85119e31 | + | 8.60263e30i | −1.13890 | + | 0.343628i | ||||
\(326\) | 4.58624e31 | 1.76294 | ||||||||
\(327\) | 1.97748e30i | 0.0731587i | ||||||||
\(328\) | − | 8.24594e30i | − | 0.293641i | ||||||
\(329\) | 3.00486e31 | 1.03009 | ||||||||
\(330\) | −2.66237e30 | + | 3.58420e30i | −0.0878706 | + | 0.118296i | ||||
\(331\) | 2.49464e31 | 0.792789 | 0.396394 | − | 0.918080i | \(-0.370261\pi\) | ||||
0.396394 | + | 0.918080i | \(0.370261\pi\) | |||||||
\(332\) | 6.23017e30i | 0.190666i | ||||||||
\(333\) | 1.41406e31i | 0.416789i | ||||||||
\(334\) | 5.06162e29 | 0.0143701 | ||||||||
\(335\) | −3.50934e30 | − | 2.60676e30i | −0.0959766 | − | 0.0712920i | ||||
\(336\) | −3.08852e30 | −0.0813784 | ||||||||
\(337\) | − | 1.07256e31i | − | 0.272300i | −0.990688 | − | 0.136150i | \(-0.956527\pi\) | ||
0.990688 | − | 0.136150i | \(-0.0434730\pi\) | |||||||
\(338\) | 1.84972e31i | 0.452530i | ||||||||
\(339\) | 5.82898e30 | 0.137435 | ||||||||
\(340\) | −6.08640e30 | − | 4.52101e30i | −0.138316 | − | 0.102742i | ||||
\(341\) | 8.35275e31 | 1.82978 | ||||||||
\(342\) | 6.80619e31i | 1.43740i | ||||||||
\(343\) | 5.22814e31i | 1.06456i | ||||||||
\(344\) | −2.67535e31 | −0.525290 | ||||||||
\(345\) | −1.63942e30 | + | 2.20707e30i | −0.0310422 | + | 0.0417904i | ||||
\(346\) | −5.04639e31 | −0.921573 | ||||||||
\(347\) | − | 8.48517e31i | − | 1.49466i | −0.664453 | − | 0.747330i | \(-0.731336\pi\) | ||
0.664453 | − | 0.747330i | \(-0.268664\pi\) | |||||||
\(348\) | − | 9.55931e29i | − | 0.0162437i | ||||||
\(349\) | −2.89637e31 | −0.474829 | −0.237414 | − | 0.971408i | \(-0.576300\pi\) | ||||
−0.237414 | + | 0.971408i | \(0.576300\pi\) | |||||||
\(350\) | −1.81885e31 | − | 6.02827e31i | −0.287705 | − | 0.953548i | ||||
\(351\) | −1.20068e31 | −0.183268 | ||||||||
\(352\) | 4.41260e31i | 0.649997i | ||||||||
\(353\) | 8.84461e31i | 1.25746i | 0.777623 | + | 0.628731i | \(0.216425\pi\) | ||||
−0.777623 | + | 0.628731i | \(0.783575\pi\) | |||||||
\(354\) | −3.74816e30 | −0.0514372 | ||||||||
\(355\) | 2.83727e30 | − | 3.81966e30i | 0.0375877 | − | 0.0506024i | ||||
\(356\) | 5.76601e30 | 0.0737481 | ||||||||
\(357\) | 5.23704e30i | 0.0646746i | ||||||||
\(358\) | − | 1.39633e32i | − | 1.66513i | ||||||
\(359\) | −2.72715e31 | −0.314072 | −0.157036 | − | 0.987593i | \(-0.550194\pi\) | ||||
−0.157036 | + | 0.987593i | \(0.550194\pi\) | |||||||
\(360\) | −6.34899e31 | − | 4.71607e31i | −0.706193 | − | 0.524565i | ||||
\(361\) | 7.07370e31 | 0.759988 | ||||||||
\(362\) | − | 1.20561e32i | − | 1.25127i | ||||||
\(363\) | − | 1.58885e31i | − | 0.159313i | ||||||
\(364\) | −2.11034e31 | −0.204450 | ||||||||
\(365\) | 8.28753e31 | + | 6.15603e31i | 0.775826 | + | 0.576288i | ||||
\(366\) | 3.70059e30 | 0.0334778 | ||||||||
\(367\) | − | 1.20849e32i | − | 1.05661i | −0.849054 | − | 0.528306i | \(-0.822827\pi\) | ||
0.849054 | − | 0.528306i | \(-0.177173\pi\) | |||||||
\(368\) | 9.19081e31i | 0.776705i | ||||||||
\(369\) | 4.03748e31 | 0.329823 | ||||||||
\(370\) | 3.45083e31 | − | 4.64567e31i | 0.272522 | − | 0.366882i | ||||
\(371\) | −2.27101e32 | −1.73399 | ||||||||
\(372\) | 2.05814e30i | 0.0151946i | ||||||||
\(373\) | 1.72298e32i | 1.23004i | 0.788512 | + | 0.615020i | \(0.210852\pi\) | ||||
−0.788512 | + | 0.615020i | \(0.789148\pi\) | |||||||
\(374\) | 2.53085e32 | 1.74732 | ||||||||
\(375\) | −3.92224e30 | + | 1.08852e31i | −0.0261905 | + | 0.0726848i | ||||
\(376\) | −1.54462e32 | −0.997637 | ||||||||
\(377\) | 2.12844e32i | 1.32983i | ||||||||
\(378\) | − | 2.53859e31i | − | 0.153442i | ||||||
\(379\) | −7.65880e31 | −0.447889 | −0.223945 | − | 0.974602i | \(-0.571893\pi\) | ||||
−0.223945 | + | 0.974602i | \(0.571893\pi\) | |||||||
\(380\) | 2.62940e31 | − | 3.53982e31i | 0.148786 | − | 0.200302i | ||||
\(381\) | 1.42700e31 | 0.0781381 | ||||||||
\(382\) | 3.27801e32i | 1.73707i | ||||||||
\(383\) | − | 2.34216e32i | − | 1.20125i | −0.799532 | − | 0.600623i | \(-0.794919\pi\) | ||
0.799532 | − | 0.600623i | \(-0.205081\pi\) | |||||||
\(384\) | 1.84666e31 | 0.0916742 | ||||||||
\(385\) | 2.67111e32 | + | 1.98412e32i | 1.28361 | + | 0.953472i | ||||
\(386\) | −2.80885e31 | −0.130674 | ||||||||
\(387\) | − | 1.30994e32i | − | 0.590015i | ||||||
\(388\) | − | 6.51846e30i | − | 0.0284281i | ||||||
\(389\) | −1.78957e32 | −0.755752 | −0.377876 | − | 0.925856i | \(-0.623345\pi\) | ||||
−0.377876 | + | 0.925856i | \(0.623345\pi\) | |||||||
\(390\) | 1.96641e31 | + | 1.46066e31i | 0.0804204 | + | 0.0597368i | ||||
\(391\) | 1.55844e32 | 0.617278 | ||||||||
\(392\) | − | 3.80663e31i | − | 0.146037i | ||||||
\(393\) | − | 1.33916e31i | − | 0.0497653i | ||||||
\(394\) | 3.39444e32 | 1.22198 | ||||||||
\(395\) | −3.71069e31 | + | 4.99550e31i | −0.129417 | + | 0.174227i | ||||
\(396\) | −9.68142e31 | −0.327152 | ||||||||
\(397\) | − | 2.80991e32i | − | 0.920048i | −0.887906 | − | 0.460024i | \(-0.847841\pi\) | ||
0.887906 | − | 0.460024i | \(-0.152159\pi\) | |||||||
\(398\) | − | 3.34354e32i | − | 1.06089i | ||||||
\(399\) | −3.04584e31 | −0.0936581 | ||||||||
\(400\) | 1.11726e32 | + | 3.70296e32i | 0.332969 | + | 1.10357i | ||||
\(401\) | −6.22371e32 | −1.79781 | −0.898907 | − | 0.438140i | \(-0.855637\pi\) | ||||
−0.898907 | + | 0.438140i | \(0.855637\pi\) | |||||||
\(402\) | 3.59565e30i | 0.0100682i | ||||||||
\(403\) | − | 4.58258e32i | − | 1.24393i | ||||||
\(404\) | −5.99586e31 | −0.157792 | ||||||||
\(405\) | 2.29519e32 | − | 3.08990e32i | 0.585641 | − | 0.788417i | ||||
\(406\) | −4.50016e32 | −1.11340 | ||||||||
\(407\) | 3.05811e32i | 0.733707i | ||||||||
\(408\) | − | 2.69205e31i | − | 0.0626370i | ||||||
\(409\) | 2.80739e32 | 0.633521 | 0.316760 | − | 0.948506i | \(-0.397405\pi\) | ||||
0.316760 | + | 0.948506i | \(0.397405\pi\) | |||||||
\(410\) | −1.32645e32 | − | 9.85293e31i | −0.290330 | − | 0.215659i | ||||
\(411\) | −1.37281e31 | −0.0291467 | ||||||||
\(412\) | − | 4.61345e31i | − | 0.0950190i | ||||||
\(413\) | 2.79330e32i | 0.558138i | ||||||||
\(414\) | −3.76586e32 | −0.730063 | ||||||||
\(415\) | −4.32633e32 | − | 3.21362e32i | −0.813801 | − | 0.604496i | ||||
\(416\) | 2.42089e32 | 0.441885 | ||||||||
\(417\) | 1.67192e30i | 0.00296152i | ||||||||
\(418\) | 1.47193e33i | 2.53037i | ||||||||
\(419\) | −8.22274e32 | −1.37196 | −0.685980 | − | 0.727620i | \(-0.740626\pi\) | ||||
−0.685980 | + | 0.727620i | \(0.740626\pi\) | |||||||
\(420\) | −4.88892e30 | + | 6.58169e30i | −0.00791766 | + | 0.0106591i | ||||
\(421\) | 1.22311e33 | 1.92282 | 0.961410 | − | 0.275121i | \(-0.0887180\pi\) | ||||
0.961410 | + | 0.275121i | \(0.0887180\pi\) | |||||||
\(422\) | − | 2.34005e32i | − | 0.357125i | ||||||
\(423\) | − | 7.56295e32i | − | 1.12056i | ||||||
\(424\) | 1.16739e33 | 1.67936 | ||||||||
\(425\) | 6.27893e32 | − | 1.89448e32i | 0.877049 | − | 0.264623i | ||||
\(426\) | −3.91361e30 | −0.00530833 | ||||||||
\(427\) | − | 2.75784e32i | − | 0.363263i | ||||||
\(428\) | − | 1.24996e32i | − | 0.159900i | ||||||
\(429\) | −1.29443e32 | −0.160828 | ||||||||
\(430\) | −3.19672e32 | + | 4.30358e32i | −0.385789 | + | 0.519366i | ||||
\(431\) | 3.42455e30 | 0.00401456 | 0.00200728 | − | 0.999998i | \(-0.499361\pi\) | ||||
0.00200728 | + | 0.999998i | \(0.499361\pi\) | |||||||
\(432\) | 1.55937e32i | 0.177583i | ||||||||
\(433\) | 1.57159e33i | 1.73876i | 0.494141 | + | 0.869382i | \(0.335483\pi\) | ||||
−0.494141 | + | 0.869382i | \(0.664517\pi\) | |||||||
\(434\) | 9.68895e32 | 1.04149 | ||||||||
\(435\) | 6.63814e31 | + | 4.93085e31i | 0.0693315 | + | 0.0514998i | ||||
\(436\) | 1.75484e32 | 0.178097 | ||||||||
\(437\) | 9.06380e32i | 0.893907i | ||||||||
\(438\) | − | 8.49137e31i | − | 0.0813863i | ||||||
\(439\) | −1.28443e33 | −1.19648 | −0.598240 | − | 0.801317i | \(-0.704133\pi\) | ||||
−0.598240 | + | 0.801317i | \(0.704133\pi\) | |||||||
\(440\) | −1.37306e33 | − | 1.01991e33i | −1.24317 | − | 0.923433i | ||||
\(441\) | 1.86385e32 | 0.164032 | ||||||||
\(442\) | − | 1.38851e33i | − | 1.18787i | ||||||
\(443\) | 2.78771e32i | 0.231847i | 0.993258 | + | 0.115923i | \(0.0369827\pi\) | ||||
−0.993258 | + | 0.115923i | \(0.963017\pi\) | |||||||
\(444\) | −7.53526e30 | −0.00609272 | ||||||||
\(445\) | −2.97420e32 | + | 4.00401e32i | −0.233814 | + | 0.314771i | ||||
\(446\) | 1.26472e33 | 0.966741 | ||||||||
\(447\) | 5.75128e31i | 0.0427484i | ||||||||
\(448\) | − | 9.45396e32i | − | 0.683343i | ||||||
\(449\) | −1.77478e33 | −1.24757 | −0.623785 | − | 0.781596i | \(-0.714406\pi\) | ||||
−0.623785 | + | 0.781596i | \(0.714406\pi\) | |||||||
\(450\) | −1.51726e33 | + | 4.57788e32i | −1.03730 | + | 0.312974i | ||||
\(451\) | 8.73161e32 | 0.580614 | ||||||||
\(452\) | − | 5.17271e32i | − | 0.334571i | ||||||
\(453\) | 1.37981e32i | 0.0868147i | ||||||||
\(454\) | −1.72104e33 | −1.05340 | ||||||||
\(455\) | 1.08855e33 | − | 1.46546e33i | 0.648195 | − | 0.872631i | ||||
\(456\) | 1.56568e32 | 0.0907073 | ||||||||
\(457\) | 5.67070e32i | 0.319657i | 0.987145 | + | 0.159829i | \(0.0510942\pi\) | ||||
−0.987145 | + | 0.159829i | \(0.948906\pi\) | |||||||
\(458\) | − | 1.48922e33i | − | 0.816848i | ||||||
\(459\) | 2.64414e32 | 0.141132 | ||||||||
\(460\) | 1.95858e32 | + | 1.45484e32i | 0.101735 | + | 0.0755690i | ||||
\(461\) | 2.05579e33 | 1.03924 | 0.519622 | − | 0.854397i | \(-0.326073\pi\) | ||||
0.519622 | + | 0.854397i | \(0.326073\pi\) | |||||||
\(462\) | − | 2.73681e32i | − | 0.134654i | ||||||
\(463\) | − | 1.15042e33i | − | 0.550929i | −0.961311 | − | 0.275465i | \(-0.911168\pi\) | ||
0.961311 | − | 0.275465i | \(-0.0888317\pi\) | |||||||
\(464\) | 2.76430e33 | 1.28858 | ||||||||
\(465\) | −1.42920e32 | − | 1.06162e32i | −0.0648534 | − | 0.0481735i | ||||
\(466\) | −1.80269e33 | −0.796337 | ||||||||
\(467\) | 1.30592e33i | 0.561639i | 0.959761 | + | 0.280819i | \(0.0906061\pi\) | ||||
−0.959761 | + | 0.280819i | \(0.909394\pi\) | |||||||
\(468\) | 5.31154e32i | 0.222406i | ||||||||
\(469\) | 2.67964e32 | 0.109249 | ||||||||
\(470\) | −1.84564e33 | + | 2.48468e33i | −0.732694 | + | 0.986387i | ||||
\(471\) | −5.12322e31 | −0.0198053 | ||||||||
\(472\) | − | 1.43587e33i | − | 0.540554i | ||||||
\(473\) | − | 2.83292e33i | − | 1.03865i | ||||||
\(474\) | 5.11837e31 | 0.0182769 | ||||||||
\(475\) | 1.10182e33 | + | 3.65179e33i | 0.383213 | + | 1.27009i | ||||
\(476\) | 4.64742e32 | 0.157444 | ||||||||
\(477\) | 5.71593e33i | 1.88628i | ||||||||
\(478\) | 1.96422e33i | 0.631454i | ||||||||
\(479\) | −4.71822e32 | −0.147769 | −0.0738847 | − | 0.997267i | \(-0.523540\pi\) | ||||
−0.0738847 | + | 0.997267i | \(0.523540\pi\) | |||||||
\(480\) | 5.60835e31 | − | 7.55022e31i | 0.0171127 | − | 0.0230380i | ||||
\(481\) | 1.67778e33 | 0.498793 | ||||||||
\(482\) | 6.63362e32i | 0.192160i | ||||||||
\(483\) | − | 1.68526e32i | − | 0.0475694i | ||||||
\(484\) | −1.40997e33 | −0.387831 | ||||||||
\(485\) | 4.52652e32 | + | 3.36233e32i | 0.121337 | + | 0.0901297i | ||||
\(486\) | −9.59365e32 | −0.250629 | ||||||||
\(487\) | − | 3.91800e33i | − | 0.997591i | −0.866720 | − | 0.498796i | \(-0.833776\pi\) | ||
0.866720 | − | 0.498796i | \(-0.166224\pi\) | |||||||
\(488\) | 1.41764e33i | 0.351818i | ||||||||
\(489\) | 5.16567e32 | 0.124959 | ||||||||
\(490\) | −6.12336e32 | − | 4.54847e32i | −0.144391 | − | 0.107254i | ||||
\(491\) | −1.49234e33 | −0.343043 | −0.171521 | − | 0.985180i | \(-0.554868\pi\) | ||||
−0.171521 | + | 0.985180i | \(0.554868\pi\) | |||||||
\(492\) | 2.15149e31i | 0.00482143i | ||||||||
\(493\) | − | 4.68728e33i | − | 1.02408i | ||||||
\(494\) | 8.07549e33 | 1.72021 | ||||||||
\(495\) | 4.99383e33 | − | 6.72293e33i | 1.03722 | − | 1.39635i | ||||
\(496\) | −5.95159e33 | −1.20535 | ||||||||
\(497\) | 2.91660e32i | 0.0575999i | ||||||||
\(498\) | 4.43273e32i | 0.0853699i | ||||||||
\(499\) | −7.73935e33 | −1.45361 | −0.726805 | − | 0.686844i | \(-0.758996\pi\) | ||||
−0.726805 | + | 0.686844i | \(0.758996\pi\) | |||||||
\(500\) | 9.65963e32 | + | 3.48064e32i | 0.176944 | + | 0.0637580i | ||||
\(501\) | 5.70110e30 | 0.00101856 | ||||||||
\(502\) | − | 6.63157e33i | − | 1.15563i | ||||||
\(503\) | 8.35964e33i | 1.42098i | 0.703708 | + | 0.710489i | \(0.251526\pi\) | ||||
−0.703708 | + | 0.710489i | \(0.748474\pi\) | |||||||
\(504\) | 4.84793e33 | 0.803850 | ||||||||
\(505\) | 3.09276e33 | − | 4.16362e33i | 0.500270 | − | 0.673487i | ||||
\(506\) | −8.14419e33 | −1.28519 | ||||||||
\(507\) | 2.08341e32i | 0.0320757i | ||||||||
\(508\) | − | 1.26634e33i | − | 0.190219i | ||||||
\(509\) | −1.26637e34 | −1.85605 | −0.928023 | − | 0.372522i | \(-0.878493\pi\) | ||||
−0.928023 | + | 0.372522i | \(0.878493\pi\) | |||||||
\(510\) | −4.33044e32 | − | 3.21668e32i | −0.0619306 | − | 0.0460024i | ||||
\(511\) | −6.32815e33 | −0.883112 | ||||||||
\(512\) | 4.34670e33i | 0.591950i | ||||||||
\(513\) | 1.53782e33i | 0.204380i | ||||||||
\(514\) | 1.66128e34 | 2.15479 | ||||||||
\(515\) | 3.20365e33 | + | 2.37969e33i | 0.405560 | + | 0.301252i | ||||
\(516\) | 6.98039e31 | 0.00862498 | ||||||||
\(517\) | − | 1.63559e34i | − | 1.97262i | ||||||
\(518\) | 3.54732e33i | 0.417617i | ||||||||
\(519\) | −5.68395e32 | −0.0653218 | ||||||||
\(520\) | −5.59558e33 | + | 7.53303e33i | −0.627774 | + | 0.845138i | ||||
\(521\) | −2.92449e33 | −0.320316 | −0.160158 | − | 0.987091i | \(-0.551200\pi\) | ||||
−0.160158 | + | 0.987091i | \(0.551200\pi\) | |||||||
\(522\) | 1.13265e34i | 1.21119i | ||||||||
\(523\) | 7.60851e33i | 0.794380i | 0.917736 | + | 0.397190i | \(0.130015\pi\) | ||||
−0.917736 | + | 0.397190i | \(0.869985\pi\) | |||||||
\(524\) | −1.18839e33 | −0.121149 | ||||||||
\(525\) | −2.04865e32 | − | 6.78988e32i | −0.0203927 | − | 0.0675882i | ||||
\(526\) | 6.01383e33 | 0.584560 | ||||||||
\(527\) | 1.00918e34i | 0.957936i | ||||||||
\(528\) | 1.68113e33i | 0.155839i | ||||||||
\(529\) | 6.03077e33 | 0.545980 | ||||||||
\(530\) | 1.39489e34 | − | 1.87787e34i | 1.23337 | − | 1.66042i | ||||
\(531\) | 7.03047e33 | 0.607160 | ||||||||
\(532\) | 2.70291e33i | 0.228001i | ||||||||
\(533\) | − | 4.79044e33i | − | 0.394716i | ||||||
\(534\) | 4.10249e32 | 0.0330204 | ||||||||
\(535\) | 8.67992e33 | + | 6.44750e33i | 0.682486 | + | 0.506955i | ||||
\(536\) | −1.37744e33 | −0.105807 | ||||||||
\(537\) | − | 1.57274e33i | − | 0.118026i | ||||||
\(538\) | − | 7.21685e33i | − | 0.529138i | ||||||
\(539\) | 4.03083e33 | 0.288758 | ||||||||
\(540\) | 3.32305e32 | + | 2.46838e32i | 0.0232602 | + | 0.0172779i | ||||
\(541\) | −1.94229e34 | −1.32846 | −0.664230 | − | 0.747528i | \(-0.731241\pi\) | ||||
−0.664230 | + | 0.747528i | \(0.731241\pi\) | |||||||
\(542\) | 5.97580e33i | 0.399397i | ||||||||
\(543\) | − | 1.35793e33i | − | 0.0886910i | ||||||
\(544\) | −5.33132e33 | −0.340289 | ||||||||
\(545\) | −9.05177e33 | + | 1.21859e34i | −0.564647 | + | 0.760154i | ||||
\(546\) | −1.50150e33 | −0.0915414 | ||||||||
\(547\) | − | 1.91244e34i | − | 1.13958i | −0.821790 | − | 0.569791i | \(-0.807024\pi\) | ||
0.821790 | − | 0.569791i | \(-0.192976\pi\) | |||||||
\(548\) | 1.21825e33i | 0.0709546i | ||||||||
\(549\) | −6.94123e33 | −0.395168 | ||||||||
\(550\) | −3.28128e34 | + | 9.90029e33i | −1.82604 | + | 0.550952i | ||||
\(551\) | 2.72610e34 | 1.48302 | ||||||||
\(552\) | 8.66290e32i | 0.0460707i | ||||||||
\(553\) | − | 3.81444e33i | − | 0.198320i | ||||||
\(554\) | −4.62140e33 | −0.234910 | ||||||||
\(555\) | 3.88681e32 | − | 5.23260e32i | 0.0193166 | − | 0.0260049i | ||||
\(556\) | 1.48368e32 | 0.00720952 | ||||||||
\(557\) | − | 4.52903e33i | − | 0.215187i | −0.994195 | − | 0.107593i | \(-0.965686\pi\) | ||
0.994195 | − | 0.107593i | \(-0.0343144\pi\) | |||||||
\(558\) | − | 2.43862e34i | − | 1.13296i | ||||||
\(559\) | −1.55423e34 | −0.706102 | ||||||||
\(560\) | −1.90325e34 | − | 1.41374e34i | −0.845561 | − | 0.628088i | ||||
\(561\) | 2.85060e33 | 0.123851 | ||||||||
\(562\) | 4.97809e33i | 0.211523i | ||||||||
\(563\) | − | 3.42883e34i | − | 1.42492i | −0.701712 | − | 0.712461i | \(-0.747581\pi\) | ||
0.701712 | − | 0.712461i | \(-0.252419\pi\) | |||||||
\(564\) | 4.03014e32 | 0.0163807 | ||||||||
\(565\) | 3.59201e34 | + | 2.66817e34i | 1.42801 | + | 1.06074i | ||||
\(566\) | 3.84531e33 | 0.149529 | ||||||||
\(567\) | 2.35937e34i | 0.897444i | ||||||||
\(568\) | − | 1.49925e33i | − | 0.0557852i | ||||||
\(569\) | −1.19665e34 | −0.435577 | −0.217788 | − | 0.975996i | \(-0.569884\pi\) | ||||
−0.217788 | + | 0.975996i | \(0.569884\pi\) | |||||||
\(570\) | 1.87080e33 | − | 2.51856e33i | 0.0666181 | − | 0.0896844i | ||||
\(571\) | 5.39502e34 | 1.87950 | 0.939749 | − | 0.341864i | \(-0.111058\pi\) | ||||
0.939749 | + | 0.341864i | \(0.111058\pi\) | |||||||
\(572\) | 1.14869e34i | 0.391520i | ||||||||
\(573\) | 3.69216e33i | 0.123125i | ||||||||
\(574\) | 1.01284e34 | 0.330478 | ||||||||
\(575\) | −2.02053e34 | + | 6.09636e33i | −0.645087 | + | 0.194636i | ||||
\(576\) | −2.37947e34 | −0.743361 | ||||||||
\(577\) | − | 3.46528e34i | − | 1.05935i | −0.848200 | − | 0.529677i | \(-0.822313\pi\) | ||
0.848200 | − | 0.529677i | \(-0.177687\pi\) | |||||||
\(578\) | − | 5.85732e33i | − | 0.175227i | ||||||
\(579\) | −3.16372e32 | −0.00926225 | ||||||||
\(580\) | 4.37570e33 | − | 5.89077e33i | 0.125371 | − | 0.168780i | ||||
\(581\) | 3.30347e34 | 0.926338 | ||||||||
\(582\) | − | 4.63785e32i | − | 0.0127286i | ||||||
\(583\) | 1.23615e35i | 3.32057i | ||||||||
\(584\) | 3.25292e34 | 0.855289 | ||||||||
\(585\) | −3.68842e34 | − | 2.73978e34i | −0.949274 | − | 0.705126i | ||||
\(586\) | 4.35599e34 | 1.09740 | ||||||||
\(587\) | 5.34642e34i | 1.31852i | 0.751915 | + | 0.659260i | \(0.229130\pi\) | ||||
−0.751915 | + | 0.659260i | \(0.770870\pi\) | |||||||
\(588\) | 9.93207e31i | 0.00239786i | ||||||||
\(589\) | −5.86934e34 | −1.38723 | ||||||||
\(590\) | −2.30974e34 | − | 1.71569e34i | −0.534458 | − | 0.396999i | ||||
\(591\) | 3.82329e33 | 0.0866151 | ||||||||
\(592\) | − | 2.17900e34i | − | 0.483320i | ||||||
\(593\) | − | 3.72971e34i | − | 0.810012i | −0.914314 | − | 0.405006i | \(-0.867269\pi\) | ||
0.914314 | − | 0.405006i | \(-0.132731\pi\) | |||||||
\(594\) | −1.38179e34 | −0.293841 | ||||||||
\(595\) | −2.39722e34 | + | 3.22724e34i | −0.499166 | + | 0.672000i | ||||
\(596\) | 5.10376e33 | 0.104067 | ||||||||
\(597\) | − | 3.76596e33i | − | 0.0751964i | ||||||
\(598\) | 4.46816e34i | 0.873704i | ||||||||
\(599\) | 5.17432e34 | 0.990874 | 0.495437 | − | 0.868644i | \(-0.335008\pi\) | ||||
0.495437 | + | 0.868644i | \(0.335008\pi\) | |||||||
\(600\) | 1.05308e33 | + | 3.49027e33i | 0.0197503 | + | 0.0654588i | ||||
\(601\) | −5.13702e34 | −0.943584 | −0.471792 | − | 0.881710i | \(-0.656393\pi\) | ||||
−0.471792 | + | 0.881710i | \(0.656393\pi\) | |||||||
\(602\) | − | 3.28610e34i | − | 0.591187i | ||||||
\(603\) | − | 6.74441e33i | − | 0.118844i | ||||||
\(604\) | 1.22447e34 | 0.211341 | ||||||||
\(605\) | 7.27285e34 | − | 9.79105e34i | 1.22960 | − | 1.65534i | ||||
\(606\) | −4.26603e33 | −0.0706506 | ||||||||
\(607\) | − | 8.79446e34i | − | 1.42676i | −0.700778 | − | 0.713379i | \(-0.747164\pi\) | ||
0.700778 | − | 0.713379i | \(-0.252836\pi\) | |||||||
\(608\) | − | 3.10066e34i | − | 0.492788i | ||||||
\(609\) | −5.06871e33 | −0.0789190 | ||||||||
\(610\) | 2.28042e34 | + | 1.69391e34i | 0.347851 | + | 0.258386i | ||||
\(611\) | −8.97338e34 | −1.34104 | ||||||||
\(612\) | − | 1.16971e34i | − | 0.171272i | ||||||
\(613\) | − | 1.70622e33i | − | 0.0244782i | −0.999925 | − | 0.0122391i | \(-0.996104\pi\) | ||
0.999925 | − | 0.0122391i | \(-0.00389593\pi\) | |||||||
\(614\) | −1.11778e35 | −1.57127 | ||||||||
\(615\) | −1.49403e33 | − | 1.10977e33i | −0.0205788 | − | 0.0152861i | ||||
\(616\) | 1.04843e35 | 1.41508 | ||||||||
\(617\) | 1.12122e34i | 0.148295i | 0.997247 | + | 0.0741475i | \(0.0236236\pi\) | ||||
−0.997247 | + | 0.0741475i | \(0.976376\pi\) | |||||||
\(618\) | − | 3.28245e33i | − | 0.0425443i | ||||||
\(619\) | 7.85440e34 | 0.997654 | 0.498827 | − | 0.866701i | \(-0.333764\pi\) | ||||
0.498827 | + | 0.866701i | \(0.333764\pi\) | |||||||
\(620\) | −9.42097e33 | + | 1.26829e34i | −0.117273 | + | 0.157879i | ||||
\(621\) | −8.50875e33 | −0.103806 | ||||||||
\(622\) | 1.17906e35i | 1.40980i | ||||||||
\(623\) | − | 3.05736e34i | − | 0.358300i | ||||||
\(624\) | 9.22320e33 | 0.105943 | ||||||||
\(625\) | −7.39961e34 | + | 4.91242e34i | −0.833122 | + | 0.553090i | ||||
\(626\) | −1.24538e35 | −1.37443 | ||||||||
\(627\) | 1.65789e34i | 0.179355i | ||||||||
\(628\) | 4.54641e33i | 0.0482140i | ||||||||
\(629\) | −3.69481e34 | −0.384113 | ||||||||
\(630\) | 5.79271e34 | − | 7.79841e34i | 0.590371 | − | 0.794784i | ||||
\(631\) | −6.73578e34 | −0.673009 | −0.336504 | − | 0.941682i | \(-0.609245\pi\) | ||||
−0.336504 | + | 0.941682i | \(0.609245\pi\) | |||||||
\(632\) | 1.96077e34i | 0.192072i | ||||||||
\(633\) | − | 2.63569e33i | − | 0.0253133i | ||||||
\(634\) | 1.43062e35 | 1.34713 | ||||||||
\(635\) | 8.79367e34 | + | 6.53199e34i | 0.811893 | + | 0.603079i | ||||
\(636\) | −3.04590e33 | −0.0275741 | ||||||||
\(637\) | − | 2.21144e34i | − | 0.196305i | ||||||
\(638\) | 2.44951e35i | 2.13216i | ||||||||
\(639\) | 7.34081e33 | 0.0626590 | ||||||||
\(640\) | 1.13798e35 | + | 8.45295e34i | 0.952540 | + | 0.707552i | ||||
\(641\) | 7.31472e34 | 0.600444 | 0.300222 | − | 0.953869i | \(-0.402939\pi\) | ||||
0.300222 | + | 0.953869i | \(0.402939\pi\) | |||||||
\(642\) | − | 8.89341e33i | − | 0.0715946i | ||||||
\(643\) | − | 2.10086e35i | − | 1.65867i | −0.558749 | − | 0.829337i | \(-0.688719\pi\) | ||
0.558749 | − | 0.829337i | \(-0.311281\pi\) | |||||||
\(644\) | −1.49552e34 | −0.115803 | ||||||||
\(645\) | −3.60060e33 | + | 4.84729e33i | −0.0273450 | + | 0.0368131i | ||||
\(646\) | −1.77839e35 | −1.32471 | ||||||||
\(647\) | 1.38944e34i | 0.101516i | 0.998711 | + | 0.0507582i | \(0.0161638\pi\) | ||||
−0.998711 | + | 0.0507582i | \(0.983836\pi\) | |||||||
\(648\) | − | 1.21281e35i | − | 0.869169i | ||||||
\(649\) | 1.52044e35 | 1.06883 | ||||||||
\(650\) | 5.43161e34 | + | 1.80022e35i | 0.374552 | + | 1.24139i | ||||
\(651\) | 1.09130e34 | 0.0738216 | ||||||||
\(652\) | − | 4.58408e34i | − | 0.304199i | ||||||
\(653\) | − | 6.94252e34i | − | 0.451962i | −0.974132 | − | 0.225981i | \(-0.927441\pi\) | ||
0.974132 | − | 0.225981i | \(-0.0725588\pi\) | |||||||
\(654\) | 1.24856e34 | 0.0797423 | ||||||||
\(655\) | 6.12992e34 | − | 8.25238e34i | 0.384095 | − | 0.517086i | ||||
\(656\) | −6.22154e34 | −0.382472 | ||||||||
\(657\) | 1.59274e35i | 0.960676i | ||||||||
\(658\) | − | 1.89724e35i | − | 1.12279i | ||||||
\(659\) | −5.89779e34 | −0.342469 | −0.171235 | − | 0.985230i | \(-0.554776\pi\) | ||||
−0.171235 | + | 0.985230i | \(0.554776\pi\) | |||||||
\(660\) | 3.58251e33 | + | 2.66111e33i | 0.0204121 | + | 0.0151623i | ||||
\(661\) | −1.44684e35 | −0.808913 | −0.404457 | − | 0.914557i | \(-0.632539\pi\) | ||||
−0.404457 | + | 0.914557i | \(0.632539\pi\) | |||||||
\(662\) | − | 1.57509e35i | − | 0.864132i | ||||||
\(663\) | − | 1.56393e34i | − | 0.0841974i | ||||||
\(664\) | −1.69812e35 | −0.897153 | ||||||||
\(665\) | −1.87695e35 | − | 1.39421e35i | −0.973153 | − | 0.722864i | ||||
\(666\) | 8.92826e34 | 0.454296 | ||||||||
\(667\) | 1.50835e35i | 0.753232i | ||||||||
\(668\) | − | 5.05923e32i | − | 0.00247958i | ||||||
\(669\) | 1.42451e34 | 0.0685234 | ||||||||
\(670\) | −1.64588e34 | + | 2.21576e34i | −0.0777076 | + | 0.104614i | ||||
\(671\) | −1.50114e35 | −0.695646 | ||||||||
\(672\) | 5.76516e33i | 0.0262238i | ||||||||
\(673\) | 2.30536e35i | 1.02932i | 0.857394 | + | 0.514661i | \(0.172082\pi\) | ||||
−0.857394 | + | 0.514661i | \(0.827918\pi\) | |||||||
\(674\) | −6.77204e34 | −0.296805 | ||||||||
\(675\) | −3.42816e34 | + | 1.03435e34i | −0.147491 | + | 0.0445009i | ||||
\(676\) | 1.84885e34 | 0.0780850 | ||||||||
\(677\) | 7.48456e34i | 0.310319i | 0.987889 | + | 0.155159i | \(0.0495891\pi\) | ||||
−0.987889 | + | 0.155159i | \(0.950411\pi\) | |||||||
\(678\) | − | 3.68036e34i | − | 0.149803i | ||||||
\(679\) | −3.45634e34 | −0.138116 | ||||||||
\(680\) | 1.23226e35 | − | 1.65893e35i | 0.483439 | − | 0.650829i | ||||
\(681\) | −1.93847e34 | −0.0746656 | ||||||||
\(682\) | − | 5.27384e35i | − | 1.99445i | ||||||
\(683\) | 7.67141e34i | 0.284850i | 0.989806 | + | 0.142425i | \(0.0454900\pi\) | ||||
−0.989806 | + | 0.142425i | \(0.954510\pi\) | |||||||
\(684\) | 6.80298e34 | 0.248026 | ||||||||
\(685\) | −8.45975e34 | − | 6.28395e34i | −0.302848 | − | 0.224958i | ||||
\(686\) | 3.30100e35 | 1.16036 | ||||||||
\(687\) | − | 1.67737e34i | − | 0.0578988i | ||||||
\(688\) | 2.01854e35i | 0.684198i | ||||||||
\(689\) | 6.78190e35 | 2.25741 | ||||||||
\(690\) | 1.39352e34 | + | 1.03512e34i | 0.0455512 | + | 0.0338357i | ||||
\(691\) | 1.00480e35 | 0.322555 | 0.161278 | − | 0.986909i | \(-0.448439\pi\) | ||||
0.161278 | + | 0.986909i | \(0.448439\pi\) | |||||||
\(692\) | 5.04401e34i | 0.159019i | ||||||||
\(693\) | 5.13346e35i | 1.58944i | ||||||||
\(694\) | −5.35746e35 | −1.62917 | ||||||||
\(695\) | −7.65308e33 | + | 1.03029e34i | −0.0228574 | + | 0.0307716i | ||||
\(696\) | 2.60552e34 | 0.0764326 | ||||||||
\(697\) | 1.05495e35i | 0.303965i | ||||||||
\(698\) | 1.82874e35i | 0.517559i | ||||||||
\(699\) | −2.03044e34 | −0.0564450 | ||||||||
\(700\) | −6.02543e34 | + | 1.81799e34i | −0.164537 | + | 0.0496440i | ||||
\(701\) | 5.43593e35 | 1.45814 | 0.729070 | − | 0.684440i | \(-0.239953\pi\) | ||||
0.729070 | + | 0.684440i | \(0.239953\pi\) | |||||||
\(702\) | 7.58096e34i | 0.199761i | ||||||||
\(703\) | − | 2.14888e35i | − | 0.556252i | ||||||
\(704\) | −5.14593e35 | −1.30860 | ||||||||
\(705\) | −2.07881e34 | + | 2.79859e34i | −0.0519339 | + | 0.0699159i | ||||
\(706\) | 5.58440e35 | 1.37062 | ||||||||
\(707\) | 3.17924e35i | 0.766620i | ||||||||
\(708\) | 3.74639e33i | 0.00887560i | ||||||||
\(709\) | −2.08778e35 | −0.485967 | −0.242984 | − | 0.970030i | \(-0.578126\pi\) | ||||
−0.242984 | + | 0.970030i | \(0.578126\pi\) | |||||||
\(710\) | −2.41170e34 | − | 1.79142e34i | −0.0551561 | − | 0.0409703i | ||||
\(711\) | −9.60058e34 | −0.215738 | ||||||||
\(712\) | 1.57160e35i | 0.347011i | ||||||||
\(713\) | − | 3.24750e35i | − | 0.704581i | ||||||
\(714\) | 3.30662e34 | 0.0704947 | ||||||||
\(715\) | −7.97670e35 | − | 5.92514e35i | −1.67108 | − | 1.24129i | ||||
\(716\) | −1.39567e35 | −0.287322 | ||||||||
\(717\) | 2.21238e34i | 0.0447580i | ||||||||
\(718\) | 1.72190e35i | 0.342335i | ||||||||
\(719\) | 4.27958e35 | 0.836162 | 0.418081 | − | 0.908410i | \(-0.362703\pi\) | ||||
0.418081 | + | 0.908410i | \(0.362703\pi\) | |||||||
\(720\) | −3.55826e35 | + | 4.79030e35i | −0.683253 | + | 0.919827i | ||||
\(721\) | −2.44623e35 | −0.461643 | ||||||||
\(722\) | − | 4.46627e35i | − | 0.828380i | ||||||
\(723\) | 7.47171e33i | 0.0136204i | ||||||||
\(724\) | −1.20505e35 | −0.215909 | ||||||||
\(725\) | 1.83359e35 | + | 6.07711e35i | 0.322906 | + | 1.07022i | ||||
\(726\) | −1.00319e35 | −0.173650 | ||||||||
\(727\) | − | 8.01009e35i | − | 1.36288i | −0.731875 | − | 0.681439i | \(-0.761354\pi\) | ||
0.731875 | − | 0.681439i | \(-0.238646\pi\) | |||||||
\(728\) | − | 5.75203e35i | − | 0.962008i | ||||||
\(729\) | 5.86590e35 | 0.964364 | ||||||||
\(730\) | 3.88686e35 | − | 5.23267e35i | 0.628149 | − | 0.845644i | ||||
\(731\) | 3.42274e35 | 0.543759 | ||||||||
\(732\) | − | 3.69884e33i | − | 0.00577666i | ||||||
\(733\) | − | 4.73921e35i | − | 0.727622i | −0.931473 | − | 0.363811i | \(-0.881475\pi\) | ||
0.931473 | − | 0.363811i | \(-0.118525\pi\) | |||||||
\(734\) | −7.63026e35 | −1.15170 | ||||||||
\(735\) | −6.89699e33 | − | 5.12312e33i | −0.0102345 | − | 0.00760227i | ||||
\(736\) | 1.71560e35 | 0.250289 | ||||||||
\(737\) | − | 1.45857e35i | − | 0.209211i | ||||||
\(738\) | − | 2.54923e35i | − | 0.359504i | ||||||
\(739\) | −4.23795e35 | −0.587626 | −0.293813 | − | 0.955863i | \(-0.594924\pi\) | ||||
−0.293813 | + | 0.955863i | \(0.594924\pi\) | |||||||
\(740\) | −4.64348e34 | − | 3.44921e34i | −0.0633063 | − | 0.0470243i | ||||
\(741\) | 9.09574e34 | 0.121930 | ||||||||
\(742\) | 1.43390e36i | 1.89003i | ||||||||
\(743\) | 2.79773e35i | 0.362614i | 0.983427 | + | 0.181307i | \(0.0580328\pi\) | ||||
−0.983427 | + | 0.181307i | \(0.941967\pi\) | |||||||
\(744\) | −5.60974e34 | −0.0714959 | ||||||||
\(745\) | −2.63260e35 | + | 3.54413e35i | −0.329938 | + | 0.444177i | ||||
\(746\) | 1.08787e36 | 1.34073 | ||||||||
\(747\) | − | 8.31453e35i | − | 1.00770i | ||||||
\(748\) | − | 2.52966e35i | − | 0.301504i | ||||||
\(749\) | −6.62777e35 | −0.776864 | ||||||||
\(750\) | 6.87278e34 | + | 2.47646e34i | 0.0792258 | + | 0.0285474i | ||||
\(751\) | −4.10259e35 | −0.465114 | −0.232557 | − | 0.972583i | \(-0.574709\pi\) | ||||
−0.232557 | + | 0.972583i | \(0.574709\pi\) | |||||||
\(752\) | 1.16541e36i | 1.29944i | ||||||||
\(753\) | − | 7.46940e34i | − | 0.0819122i | ||||||
\(754\) | 1.34388e36 | 1.44950 | ||||||||
\(755\) | −6.31599e35 | + | 8.50288e35i | −0.670046 | + | 0.902047i | ||||
\(756\) | −2.53739e34 | −0.0264768 | ||||||||
\(757\) | 1.01875e36i | 1.04561i | 0.852451 | + | 0.522807i | \(0.175115\pi\) | ||||
−0.852451 | + | 0.522807i | \(0.824885\pi\) | |||||||
\(758\) | 4.83569e35i | 0.488195i | ||||||||
\(759\) | −9.17313e34 | −0.0910952 | ||||||||
\(760\) | 9.64825e35 | + | 7.16678e35i | 0.942494 | + | 0.700090i | ||||
\(761\) | −1.41828e36 | −1.36287 | −0.681434 | − | 0.731879i | \(-0.738644\pi\) | ||||
−0.681434 | + | 0.731879i | \(0.738644\pi\) | |||||||
\(762\) | − | 9.00996e34i | − | 0.0851698i | ||||||
\(763\) | − | 9.30486e35i | − | 0.865273i | ||||||
\(764\) | 3.27647e35 | 0.299736 | ||||||||
\(765\) | 8.12266e35 | + | 6.03356e35i | 0.731022 | + | 0.543008i | ||||
\(766\) | −1.47882e36 | −1.30935 | ||||||||
\(767\) | − | 8.34159e35i | − | 0.726619i | ||||||
\(768\) | − | 4.91799e34i | − | 0.0421475i | ||||||
\(769\) | 2.13487e36 | 1.80008 | 0.900040 | − | 0.435808i | \(-0.143537\pi\) | ||||
0.900040 | + | 0.435808i | \(0.143537\pi\) | |||||||
\(770\) | 1.25275e36 | − | 1.68651e36i | 1.03928 | − | 1.39912i | ||||
\(771\) | 1.87117e35 | 0.152733 | ||||||||
\(772\) | 2.80753e34i | 0.0225480i | ||||||||
\(773\) | 5.07472e35i | 0.401022i | 0.979691 | + | 0.200511i | \(0.0642603\pi\) | ||||
−0.979691 | + | 0.200511i | \(0.935740\pi\) | |||||||
\(774\) | −8.27081e35 | −0.643111 | ||||||||
\(775\) | −3.94775e35 | − | 1.30841e36i | −0.302050 | − | 1.00109i | ||||
\(776\) | 1.77669e35 | 0.133765 | ||||||||
\(777\) | 3.99549e34i | 0.0296010i | ||||||||
\(778\) | 1.12992e36i | 0.823763i | ||||||||
\(779\) | −6.13556e35 | −0.440186 | ||||||||
\(780\) | 1.45997e34 | − | 1.96548e34i | 0.0103077 | − | 0.0138767i | ||||
\(781\) | 1.58755e35 | 0.110304 | ||||||||
\(782\) | − | 9.83983e35i | − | 0.672827i | ||||||
\(783\) | 2.55916e35i | 0.172217i | ||||||||
\(784\) | −2.87209e35 | −0.190216 | ||||||||
\(785\) | −3.15710e35 | − | 2.34511e35i | −0.205787 | − | 0.152860i | ||||
\(786\) | −8.45535e34 | −0.0542438 | ||||||||
\(787\) | − | 4.72481e35i | − | 0.298332i | −0.988812 | − | 0.149166i | \(-0.952341\pi\) | ||
0.988812 | − | 0.149166i | \(-0.0476589\pi\) | |||||||
\(788\) | − | 3.39284e35i | − | 0.210856i | ||||||
\(789\) | 6.77362e34 | 0.0414341 | ||||||||
\(790\) | 3.15411e35 | + | 2.34289e35i | 0.189906 | + | 0.141063i | ||||
\(791\) | −2.74277e36 | −1.62549 | ||||||||
\(792\) | − | 2.63880e36i | − | 1.53937i | ||||||
\(793\) | 8.23571e35i | 0.472919i | ||||||||
\(794\) | −1.77415e36 | −1.00284 | ||||||||
\(795\) | 1.57112e35 | − | 2.11512e35i | 0.0874222 | − | 0.117692i | ||||
\(796\) | −3.34197e35 | −0.183058 | ||||||||
\(797\) | − | 1.69149e36i | − | 0.912096i | −0.889955 | − | 0.456048i | \(-0.849265\pi\) | ||
0.889955 | − | 0.456048i | \(-0.150735\pi\) | |||||||
\(798\) | 1.92311e35i | 0.102086i | ||||||||
\(799\) | 1.97613e36 | 1.03271 | ||||||||
\(800\) | 6.91211e35 | − | 2.08552e35i | 0.355620 | − | 0.107298i | ||||
\(801\) | −7.69509e35 | −0.389769 | ||||||||
\(802\) | 3.92959e36i | 1.95960i | ||||||||
\(803\) | 3.44451e36i | 1.69115i | ||||||||
\(804\) | 3.59396e33 | 0.00173729 | ||||||||
\(805\) | 7.71415e35 | − | 1.03851e36i | 0.367146 | − | 0.494270i | ||||
\(806\) | −2.89340e36 | −1.35588 | ||||||||
\(807\) | − | 8.12863e34i | − | 0.0375058i | ||||||
\(808\) | − | 1.63425e36i | − | 0.742467i | ||||||
\(809\) | 1.61569e34 | 0.00722771 | 0.00361386 | − | 0.999993i | \(-0.498850\pi\) | ||||
0.00361386 | + | 0.999993i | \(0.498850\pi\) | |||||||
\(810\) | −1.95093e36 | − | 1.44916e36i | −0.859367 | − | 0.638343i | ||||
\(811\) | 8.38978e35 | 0.363907 | 0.181953 | − | 0.983307i | \(-0.441758\pi\) | ||||
0.181953 | + | 0.983307i | \(0.441758\pi\) | |||||||
\(812\) | 4.49804e35i | 0.192120i | ||||||||
\(813\) | 6.73078e34i | 0.0283096i | ||||||||
\(814\) | 1.93086e36 | 0.799734 | ||||||||
\(815\) | 3.18326e36 | + | 2.36454e36i | 1.29838 | + | 0.964445i | ||||
\(816\) | −2.03114e35 | −0.0815856 | ||||||||
\(817\) | 1.99065e36i | 0.787441i | ||||||||
\(818\) | − | 1.77256e36i | − | 0.690532i | ||||||
\(819\) | 2.81638e36 | 1.08054 | ||||||||
\(820\) | −9.84828e34 | + | 1.32582e35i | −0.0372124 | + | 0.0500970i | ||||
\(821\) | 4.82346e36 | 1.79502 | 0.897510 | − | 0.440993i | \(-0.145374\pi\) | ||||
0.897510 | + | 0.440993i | \(0.145374\pi\) | |||||||
\(822\) | 8.66782e34i | 0.0317696i | ||||||||
\(823\) | − | 2.05555e36i | − | 0.742046i | −0.928624 | − | 0.371023i | \(-0.879007\pi\) | ||
0.928624 | − | 0.371023i | \(-0.120993\pi\) | |||||||
\(824\) | 1.25746e36 | 0.447099 | ||||||||
\(825\) | −3.69584e35 | + | 1.11511e35i | −0.129431 | + | 0.0390520i | ||||
\(826\) | 1.76366e36 | 0.608366 | ||||||||
\(827\) | − | 1.61138e36i | − | 0.547494i | −0.961802 | − | 0.273747i | \(-0.911737\pi\) | ||
0.961802 | − | 0.273747i | \(-0.0882631\pi\) | |||||||
\(828\) | 3.76409e35i | 0.125974i | ||||||||
\(829\) | −5.88426e36 | −1.93982 | −0.969908 | − | 0.243472i | \(-0.921714\pi\) | ||||
−0.969908 | + | 0.243472i | \(0.921714\pi\) | |||||||
\(830\) | −2.02905e36 | + | 2.73160e36i | −0.658895 | + | 0.887035i | ||||
\(831\) | −5.20527e34 | −0.0166506 | ||||||||
\(832\) | 2.82322e36i | 0.889618i | ||||||||
\(833\) | 4.87006e35i | 0.151172i | ||||||||
\(834\) | 1.05563e34 | 0.00322803 | ||||||||
\(835\) | 3.51321e34 | + | 2.60963e34i | 0.0105833 | + | 0.00786137i | ||||
\(836\) | 1.47124e36 | 0.436621 | ||||||||
\(837\) | − | 5.50992e35i | − | 0.161093i | ||||||
\(838\) | 5.19176e36i | 1.49542i | ||||||||
\(839\) | −2.56435e36 | −0.727702 | −0.363851 | − | 0.931457i | \(-0.618538\pi\) | ||||
−0.363851 | + | 0.931457i | \(0.618538\pi\) | |||||||
\(840\) | −1.79393e35 | − | 1.33254e35i | −0.0501550 | − | 0.0372554i | ||||
\(841\) | 9.06258e35 | 0.249633 | ||||||||
\(842\) | − | 7.72258e36i | − | 2.09586i | ||||||
\(843\) | 5.60702e34i | 0.0149930i | ||||||||
\(844\) | −2.33895e35 | −0.0616226 | ||||||||
\(845\) | −9.53666e35 | + | 1.28387e36i | −0.247564 | + | 0.333282i | ||||
\(846\) | −4.77517e36 | −1.22140 | ||||||||
\(847\) | 7.47620e36i | 1.88425i | ||||||||
\(848\) | − | 8.80792e36i | − | 2.18739i | ||||||
\(849\) | 4.33113e34 | 0.0105988 | ||||||||
\(850\) | −1.19616e36 | − | 3.96445e36i | −0.288437 | − | 0.955975i | ||||
\(851\) | 1.18898e36 | 0.282523 | ||||||||
\(852\) | 3.91177e33i | 0.000915963i | ||||||||
\(853\) | − | 5.96355e36i | − | 1.37607i | −0.725675 | − | 0.688037i | \(-0.758472\pi\) | ||
0.725675 | − | 0.688037i | \(-0.241528\pi\) | |||||||
\(854\) | −1.74128e36 | −0.395953 | ||||||||
\(855\) | −3.50909e36 | + | 4.72410e36i | −0.786353 | + | 1.05863i | ||||
\(856\) | 3.40694e36 | 0.752388 | ||||||||
\(857\) | − | 4.07011e35i | − | 0.0885820i | −0.999019 | − | 0.0442910i | \(-0.985897\pi\) | ||
0.999019 | − | 0.0442910i | \(-0.0141029\pi\) | |||||||
\(858\) | 8.17289e35i | 0.175301i | ||||||||
\(859\) | −4.17556e35 | −0.0882673 | −0.0441336 | − | 0.999026i | \(-0.514053\pi\) | ||||
−0.0441336 | + | 0.999026i | \(0.514053\pi\) | |||||||
\(860\) | 4.30155e35 | + | 3.19522e35i | 0.0896178 | + | 0.0665686i | ||||
\(861\) | 1.14080e35 | 0.0234246 | ||||||||
\(862\) | − | 2.16223e34i | − | 0.00437583i | ||||||
\(863\) | − | 2.97664e36i | − | 0.593734i | −0.954919 | − | 0.296867i | \(-0.904058\pi\) | ||
0.954919 | − | 0.296867i | \(-0.0959418\pi\) | |||||||
\(864\) | 2.91079e35 | 0.0572254 | ||||||||
\(865\) | −3.50264e36 | − | 2.60178e36i | −0.678726 | − | 0.504162i | ||||
\(866\) | 9.92286e36 | 1.89524 | ||||||||
\(867\) | − | 6.59734e34i | − | 0.0124202i | ||||||
\(868\) | − | 9.68438e35i | − | 0.179711i | ||||||
\(869\) | −2.07626e36 | −0.379781 | ||||||||
\(870\) | 3.11329e35 | − | 4.19125e35i | 0.0561344 | − | 0.0755707i | ||||
\(871\) | −8.00219e35 | −0.142227 | ||||||||
\(872\) | 4.78306e36i | 0.838012i | ||||||||
\(873\) | 8.69927e35i | 0.150247i | ||||||||
\(874\) | 5.72279e36 | 0.974350 | ||||||||
\(875\) | 1.84557e36 | − | 5.12191e36i | 0.309763 | − | 0.859668i | ||||
\(876\) | −8.48737e34 | −0.0140434 | ||||||||
\(877\) | − | 1.00528e37i | − | 1.63980i | −0.572508 | − | 0.819899i | \(-0.694030\pi\) | ||
0.572508 | − | 0.819899i | \(-0.305970\pi\) | |||||||
\(878\) | 8.10980e36i | 1.30415i | ||||||||
\(879\) | 4.90632e35 | 0.0777849 | ||||||||
\(880\) | −7.69522e36 | + | 1.03597e37i | −1.20278 | + | 1.61924i | ||||
\(881\) | 2.24336e36 | 0.345700 | 0.172850 | − | 0.984948i | \(-0.444702\pi\) | ||||
0.172850 | + | 0.984948i | \(0.444702\pi\) | |||||||
\(882\) | − | 1.17682e36i | − | 0.178793i | ||||||
\(883\) | 3.14992e36i | 0.471835i | 0.971773 | + | 0.235918i | \(0.0758095\pi\) | ||||
−0.971773 | + | 0.235918i | \(0.924190\pi\) | |||||||
\(884\) | −1.38785e36 | −0.204970 | ||||||||
\(885\) | −2.60156e35 | − | 1.93245e35i | −0.0378828 | − | 0.0281396i | ||||
\(886\) | 1.76013e36 | 0.252711 | ||||||||
\(887\) | 9.57382e36i | 1.35531i | 0.735378 | + | 0.677657i | \(0.237004\pi\) | ||||
−0.735378 | + | 0.677657i | \(0.762996\pi\) | |||||||
\(888\) | − | 2.05384e35i | − | 0.0286684i | ||||||
\(889\) | −6.71463e36 | −0.924166 | ||||||||
\(890\) | 2.52809e36 | + | 1.87788e36i | 0.343098 | + | 0.254855i | ||||
\(891\) | 1.28424e37 | 1.71860 | ||||||||
\(892\) | − | 1.26413e36i | − | 0.166813i | ||||||
\(893\) | 1.14930e37i | 1.49552i | ||||||||
\(894\) | 3.63130e35 | 0.0465954 | ||||||||
\(895\) | 7.19908e36 | − | 9.69174e36i | 0.910939 | − | 1.22635i | ||||
\(896\) | −8.68929e36 | −1.08426 | ||||||||
\(897\) | 5.03267e35i | 0.0619289i | ||||||||
\(898\) | 1.12058e37i | 1.35984i | ||||||||
\(899\) | −9.76744e36 | −1.16892 | ||||||||
\(900\) | 4.57572e35 | + | 1.51654e36i | 0.0540043 | + | 0.178988i | ||||
\(901\) | −1.49352e37 | −1.73840 | ||||||||
\(902\) | − | 5.51305e36i | − | 0.632864i | ||||||
\(903\) | − | 3.70127e35i | − | 0.0419038i | ||||||
\(904\) | 1.40989e37 | 1.57428 | ||||||||
\(905\) | 6.21582e36 | − | 8.36803e36i | 0.684528 | − | 0.921543i | ||||
\(906\) | 8.71201e35 | 0.0946272 | ||||||||
\(907\) | − | 3.90194e36i | − | 0.418013i | −0.977914 | − | 0.209007i | \(-0.932977\pi\) | ||
0.977914 | − | 0.209007i | \(-0.0670230\pi\) | |||||||
\(908\) | 1.72023e36i | 0.181766i | ||||||||
\(909\) | 8.00184e36 | 0.833953 | ||||||||
\(910\) | −9.25275e36 | − | 6.87300e36i | −0.951160 | − | 0.706527i | ||||
\(911\) | 3.83962e36 | 0.389322 | 0.194661 | − | 0.980871i | \(-0.437639\pi\) | ||||
0.194661 | + | 0.980871i | \(0.437639\pi\) | |||||||
\(912\) | − | 1.18130e36i | − | 0.118148i | ||||||
\(913\) | − | 1.79813e37i | − | 1.77393i | ||||||
\(914\) | 3.58043e36 | 0.348423 | ||||||||
\(915\) | 2.56853e35 | + | 1.90792e35i | 0.0246559 | + | 0.0183146i | ||||
\(916\) | −1.48852e36 | −0.140949 | ||||||||
\(917\) | 6.30131e36i | 0.588592i | ||||||||
\(918\) | − | 1.66949e36i | − | 0.153833i | ||||||
\(919\) | −5.06195e36 | −0.460123 | −0.230062 | − | 0.973176i | \(-0.573893\pi\) | ||||
−0.230062 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(920\) | −3.96538e36 | + | 5.33837e36i | −0.355579 | + | 0.478697i | ||||
\(921\) | −1.25900e36 | −0.111373 | ||||||||
\(922\) | − | 1.29801e37i | − | 1.13277i | ||||||
\(923\) | − | 8.70981e35i | − | 0.0749872i | ||||||
\(924\) | −2.73552e35 | −0.0232349 | ||||||||
\(925\) | 4.79037e36 | − | 1.44535e36i | 0.401418 | − | 0.121116i | ||||
\(926\) | −7.26367e36 | −0.600508 | ||||||||
\(927\) | 6.15693e36i | 0.502189i | ||||||||
\(928\) | − | 5.15996e36i | − | 0.415237i | ||||||
\(929\) | −1.60110e37 | −1.27122 | −0.635612 | − | 0.772008i | \(-0.719252\pi\) | ||||
−0.635612 | + | 0.772008i | \(0.719252\pi\) | |||||||
\(930\) | −6.70298e35 | + | 9.02386e35i | −0.0525086 | + | 0.0706896i | ||||
\(931\) | −2.83240e36 | −0.218919 | ||||||||
\(932\) | 1.80184e36i | 0.137410i | ||||||||
\(933\) | 1.32802e36i | 0.0999276i | ||||||||
\(934\) | 8.24548e36 | 0.612181 | ||||||||
\(935\) | 1.75664e37 | + | 1.30484e37i | 1.28688 | + | 0.955900i | ||||
\(936\) | −1.44773e37 | −1.04650 | ||||||||
\(937\) | − | 5.78467e36i | − | 0.412604i | −0.978488 | − | 0.206302i | \(-0.933857\pi\) | ||
0.978488 | − | 0.206302i | \(-0.0661430\pi\) | |||||||
\(938\) | − | 1.69190e36i | − | 0.119080i | ||||||
\(939\) | −1.40272e36 | −0.0974209 | ||||||||
\(940\) | 2.48351e36 | + | 1.84477e36i | 0.170203 | + | 0.126428i | ||||
\(941\) | −8.61297e36 | −0.582483 | −0.291241 | − | 0.956650i | \(-0.594068\pi\) | ||||
−0.291241 | + | 0.956650i | \(0.594068\pi\) | |||||||
\(942\) | 3.23475e35i | 0.0215876i | ||||||||
\(943\) | − | 3.39480e36i | − | 0.223573i | ||||||
\(944\) | −1.08336e37 | −0.704079 | ||||||||
\(945\) | 1.30883e36 | − | 1.76201e36i | 0.0839432 | − | 0.113008i | ||||
\(946\) | −1.78868e37 | −1.13212 | ||||||||
\(947\) | 1.81921e37i | 1.13634i | 0.822911 | + | 0.568171i | \(0.192349\pi\) | ||||
−0.822911 | + | 0.568171i | \(0.807651\pi\) | |||||||
\(948\) | − | 5.11595e34i | − | 0.00315371i | ||||||
\(949\) | 1.88977e37 | 1.14969 | ||||||||
\(950\) | 2.30570e37 | − | 6.95677e36i | 1.38439 | − | 0.417698i | ||||
\(951\) | 1.61137e36 | 0.0954856 | ||||||||
\(952\) | 1.26672e37i | 0.740829i | ||||||||
\(953\) | − | 4.55923e35i | − | 0.0263166i | −0.999913 | − | 0.0131583i | \(-0.995811\pi\) | ||
0.999913 | − | 0.0131583i | \(-0.00418854\pi\) | |||||||
\(954\) | 3.60898e37 | 2.05603 | ||||||||
\(955\) | −1.69005e37 | + | 2.27523e37i | −0.950296 | + | 1.27933i | ||||
\(956\) | 1.96330e36 | 0.108959 | ||||||||
\(957\) | 2.75898e36i | 0.151129i | ||||||||
\(958\) | 2.97904e36i | 0.161067i | ||||||||
\(959\) | 6.45965e36 | 0.344728 | ||||||||
\(960\) | 8.80500e35 | + | 6.54041e35i | 0.0463809 | + | 0.0344520i | ||||
\(961\) | 1.79670e36 | 0.0934187 | ||||||||
\(962\) | − | 1.05933e37i | − | 0.543680i | ||||||
\(963\) | 1.66815e37i | 0.845096i | ||||||||
\(964\) | 6.63049e35 | 0.0331576 | ||||||||
\(965\) | −1.94959e36 | − | 1.44817e36i | −0.0962393 | − | 0.0714872i | ||||
\(966\) | −1.06406e36 | −0.0518502 | ||||||||
\(967\) | − | 1.18549e37i | − | 0.570251i | −0.958490 | − | 0.285125i | \(-0.907965\pi\) | ||
0.958490 | − | 0.285125i | \(-0.0920352\pi\) | |||||||
\(968\) | − | 3.84306e37i | − | 1.82488i | ||||||
\(969\) | −2.00307e36 | −0.0938965 | ||||||||
\(970\) | 2.12294e36 | − | 2.85800e36i | 0.0982406 | − | 0.132256i | ||||
\(971\) | 3.31536e37 | 1.51458 | 0.757288 | − | 0.653081i | \(-0.226524\pi\) | ||||
0.757288 | + | 0.653081i | \(0.226524\pi\) | |||||||
\(972\) | 9.58913e35i | 0.0432465i | ||||||||
\(973\) | − | 7.86706e35i | − | 0.0350269i | ||||||
\(974\) | −2.47379e37 | −1.08737 | ||||||||
\(975\) | 6.11784e35 | + | 2.02765e36i | 0.0265485 | + | 0.0879906i | ||||
\(976\) | 1.06961e37 | 0.458248 | ||||||||
\(977\) | 1.59575e37i | 0.674966i | 0.941332 | + | 0.337483i | \(0.109576\pi\) | ||||
−0.941332 | + | 0.337483i | \(0.890424\pi\) | |||||||
\(978\) | − | 3.26155e36i | − | 0.136204i | ||||||
\(979\) | −1.66417e37 | −0.686142 | ||||||||
\(980\) | −4.54633e35 | + | 6.12048e35i | −0.0185069 | + | 0.0249149i | ||||
\(981\) | −2.34195e37 | −0.941270 | ||||||||
\(982\) | 9.42247e36i | 0.373913i | ||||||||
\(983\) | − | 5.23038e36i | − | 0.204934i | −0.994736 | − | 0.102467i | \(-0.967326\pi\) | ||
0.994736 | − | 0.102467i | \(-0.0326736\pi\) | |||||||
\(984\) | −5.86418e35 | −0.0226866 | ||||||||
\(985\) | 2.35604e37 | + | 1.75008e37i | 0.899974 | + | 0.668506i | ||||
\(986\) | −2.95950e37 | −1.11624 | ||||||||
\(987\) | − | 2.13694e36i | − | 0.0795843i | ||||||
\(988\) | − | 8.07168e36i | − | 0.296826i | ||||||
\(989\) | −1.10142e37 | −0.399946 | ||||||||
\(990\) | −4.24479e37 | − | 3.15306e37i | −1.52201 | − | 1.13056i | ||||
\(991\) | −4.04463e37 | −1.43205 | −0.716025 | − | 0.698075i | \(-0.754040\pi\) | ||||
−0.716025 | + | 0.698075i | \(0.754040\pi\) | |||||||
\(992\) | 1.11095e37i | 0.388417i | ||||||||
\(993\) | − | 1.77409e36i | − | 0.0612504i | ||||||
\(994\) | 1.84151e36 | 0.0627834 | ||||||||
\(995\) | 1.72384e37 | − | 2.32071e37i | 0.580375 | − | 0.781327i | ||||
\(996\) | 4.43065e35 | 0.0147308 | ||||||||
\(997\) | − | 4.79135e37i | − | 1.57315i | −0.617498 | − | 0.786573i | \(-0.711854\pi\) | ||
0.617498 | − | 0.786573i | \(-0.288146\pi\) | |||||||
\(998\) | 4.88655e37i | 1.58442i | ||||||||
\(999\) | 2.01729e36 | 0.0645952 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 5.26.b.a.4.3 | ✓ | 12 | |
3.2 | odd | 2 | 45.26.b.b.19.10 | 12 | |||
5.2 | odd | 4 | 25.26.a.f.1.10 | 12 | |||
5.3 | odd | 4 | 25.26.a.f.1.3 | 12 | |||
5.4 | even | 2 | inner | 5.26.b.a.4.10 | yes | 12 | |
15.14 | odd | 2 | 45.26.b.b.19.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.26.b.a.4.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
5.26.b.a.4.10 | yes | 12 | 5.4 | even | 2 | inner | |
25.26.a.f.1.3 | 12 | 5.3 | odd | 4 | |||
25.26.a.f.1.10 | 12 | 5.2 | odd | 4 | |||
45.26.b.b.19.3 | 12 | 15.14 | odd | 2 | |||
45.26.b.b.19.10 | 12 | 3.2 | odd | 2 |