Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [201,2,Mod(1,201)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(201, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("201.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 201 = 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 201.a (trivial) |
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: | yes |
Analytic conductor: | \(1.60499308063\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.1025428.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 8x^{3} + 13x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.33760\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 201.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.33760 | 1.65293 | 0.826467 | − | 0.562985i | \(-0.190347\pi\) | ||||
0.826467 | + | 0.562985i | \(0.190347\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 3.46438 | 1.73219 | ||||||||
\(5\) | −1.73837 | −0.777423 | −0.388711 | − | 0.921360i | \(-0.627080\pi\) | ||||
−0.388711 | + | 0.921360i | \(0.627080\pi\) | |||||||
\(6\) | 2.33760 | 0.954322 | ||||||||
\(7\) | −3.14916 | −1.19027 | −0.595136 | − | 0.803625i | \(-0.702902\pi\) | ||||
−0.595136 | + | 0.803625i | \(0.702902\pi\) | |||||||
\(8\) | 3.42315 | 1.21027 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.06362 | −1.28503 | ||||||||
\(11\) | 1.08555 | 0.327305 | 0.163652 | − | 0.986518i | \(-0.447672\pi\) | ||||
0.163652 | + | 0.986518i | \(0.447672\pi\) | |||||||
\(12\) | 3.46438 | 1.00008 | ||||||||
\(13\) | 3.08555 | 0.855777 | 0.427888 | − | 0.903832i | \(-0.359258\pi\) | ||||
0.427888 | + | 0.903832i | \(0.359258\pi\) | |||||||
\(14\) | −7.36149 | −1.96744 | ||||||||
\(15\) | −1.73837 | −0.448845 | ||||||||
\(16\) | 1.07319 | 0.268298 | ||||||||
\(17\) | −7.83394 | −1.90001 | −0.950005 | − | 0.312234i | \(-0.898923\pi\) | ||||
−0.950005 | + | 0.312234i | \(0.898923\pi\) | |||||||
\(18\) | 2.33760 | 0.550978 | ||||||||
\(19\) | 0.987645 | 0.226581 | 0.113291 | − | 0.993562i | \(-0.463861\pi\) | ||||
0.113291 | + | 0.993562i | \(0.463861\pi\) | |||||||
\(20\) | −6.02238 | −1.34665 | ||||||||
\(21\) | −3.14916 | −0.687204 | ||||||||
\(22\) | 2.53758 | 0.541013 | ||||||||
\(23\) | 1.81156 | 0.377737 | 0.188868 | − | 0.982002i | \(-0.439518\pi\) | ||||
0.188868 | + | 0.982002i | \(0.439518\pi\) | |||||||
\(24\) | 3.42315 | 0.698747 | ||||||||
\(25\) | −1.97807 | −0.395614 | ||||||||
\(26\) | 7.21278 | 1.41454 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −10.9099 | −2.06178 | ||||||||
\(29\) | 8.47870 | 1.57446 | 0.787228 | − | 0.616663i | \(-0.211516\pi\) | ||||
0.787228 | + | 0.616663i | \(0.211516\pi\) | |||||||
\(30\) | −4.06362 | −0.741912 | ||||||||
\(31\) | 2.86515 | 0.514597 | 0.257298 | − | 0.966332i | \(-0.417168\pi\) | ||||
0.257298 | + | 0.966332i | \(0.417168\pi\) | |||||||
\(32\) | −4.33760 | −0.766787 | ||||||||
\(33\) | 1.08555 | 0.188969 | ||||||||
\(34\) | −18.3126 | −3.14059 | ||||||||
\(35\) | 5.47441 | 0.925344 | ||||||||
\(36\) | 3.46438 | 0.577397 | ||||||||
\(37\) | 9.75118 | 1.60308 | 0.801542 | − | 0.597939i | \(-0.204013\pi\) | ||||
0.801542 | + | 0.597939i | \(0.204013\pi\) | |||||||
\(38\) | 2.30872 | 0.374524 | ||||||||
\(39\) | 3.08555 | 0.494083 | ||||||||
\(40\) | −5.95070 | −0.940888 | ||||||||
\(41\) | −6.02238 | −0.940538 | −0.470269 | − | 0.882523i | \(-0.655843\pi\) | ||||
−0.470269 | + | 0.882523i | \(0.655843\pi\) | |||||||
\(42\) | −7.36149 | −1.13590 | ||||||||
\(43\) | 3.81005 | 0.581028 | 0.290514 | − | 0.956871i | \(-0.406174\pi\) | ||||
0.290514 | + | 0.956871i | \(0.406174\pi\) | |||||||
\(44\) | 3.76075 | 0.566955 | ||||||||
\(45\) | −1.73837 | −0.259141 | ||||||||
\(46\) | 4.23471 | 0.624374 | ||||||||
\(47\) | −0.987645 | −0.144063 | −0.0720314 | − | 0.997402i | \(-0.522948\pi\) | ||||
−0.0720314 | + | 0.997402i | \(0.522948\pi\) | |||||||
\(48\) | 1.07319 | 0.154902 | ||||||||
\(49\) | 2.91723 | 0.416748 | ||||||||
\(50\) | −4.62394 | −0.653924 | ||||||||
\(51\) | −7.83394 | −1.09697 | ||||||||
\(52\) | 10.6895 | 1.48237 | ||||||||
\(53\) | −11.8991 | −1.63446 | −0.817231 | − | 0.576310i | \(-0.804492\pi\) | ||||
−0.817231 | + | 0.576310i | \(0.804492\pi\) | |||||||
\(54\) | 2.33760 | 0.318107 | ||||||||
\(55\) | −1.88708 | −0.254454 | ||||||||
\(56\) | −10.7801 | −1.44055 | ||||||||
\(57\) | 0.987645 | 0.130817 | ||||||||
\(58\) | 19.8198 | 2.60247 | ||||||||
\(59\) | 4.34914 | 0.566210 | 0.283105 | − | 0.959089i | \(-0.408636\pi\) | ||||
0.283105 | + | 0.959089i | \(0.408636\pi\) | |||||||
\(60\) | −6.02238 | −0.777486 | ||||||||
\(61\) | 6.70867 | 0.858957 | 0.429479 | − | 0.903077i | \(-0.358697\pi\) | ||||
0.429479 | + | 0.903077i | \(0.358697\pi\) | |||||||
\(62\) | 6.69759 | 0.850594 | ||||||||
\(63\) | −3.14916 | −0.396757 | ||||||||
\(64\) | −12.2860 | −1.53575 | ||||||||
\(65\) | −5.36382 | −0.665300 | ||||||||
\(66\) | 2.53758 | 0.312354 | ||||||||
\(67\) | −1.00000 | −0.122169 | ||||||||
\(68\) | −27.1398 | −3.29118 | ||||||||
\(69\) | 1.81156 | 0.218086 | ||||||||
\(70\) | 12.7970 | 1.52953 | ||||||||
\(71\) | 1.02163 | 0.121246 | 0.0606228 | − | 0.998161i | \(-0.480691\pi\) | ||||
0.0606228 | + | 0.998161i | \(0.480691\pi\) | |||||||
\(72\) | 3.42315 | 0.403422 | ||||||||
\(73\) | 4.74810 | 0.555723 | 0.277862 | − | 0.960621i | \(-0.410374\pi\) | ||||
0.277862 | + | 0.960621i | \(0.410374\pi\) | |||||||
\(74\) | 22.7944 | 2.64979 | ||||||||
\(75\) | −1.97807 | −0.228408 | ||||||||
\(76\) | 3.42158 | 0.392482 | ||||||||
\(77\) | −3.41856 | −0.389582 | ||||||||
\(78\) | 7.21278 | 0.816687 | ||||||||
\(79\) | 15.0968 | 1.69853 | 0.849264 | − | 0.527969i | \(-0.177046\pi\) | ||||
0.849264 | + | 0.527969i | \(0.177046\pi\) | |||||||
\(80\) | −1.86560 | −0.208581 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −14.0779 | −1.55465 | ||||||||
\(83\) | −16.5551 | −1.81716 | −0.908581 | − | 0.417710i | \(-0.862833\pi\) | ||||
−0.908581 | + | 0.417710i | \(0.862833\pi\) | |||||||
\(84\) | −10.9099 | −1.19037 | ||||||||
\(85\) | 13.6183 | 1.47711 | ||||||||
\(86\) | 8.90639 | 0.960400 | ||||||||
\(87\) | 8.47870 | 0.909012 | ||||||||
\(88\) | 3.71599 | 0.396126 | ||||||||
\(89\) | 2.38191 | 0.252482 | 0.126241 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126241 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(90\) | −4.06362 | −0.428343 | ||||||||
\(91\) | −9.71689 | −1.01861 | ||||||||
\(92\) | 6.27595 | 0.654313 | ||||||||
\(93\) | 2.86515 | 0.297102 | ||||||||
\(94\) | −2.30872 | −0.238126 | ||||||||
\(95\) | −1.71689 | −0.176149 | ||||||||
\(96\) | −4.33760 | −0.442705 | ||||||||
\(97\) | −6.12150 | −0.621544 | −0.310772 | − | 0.950485i | \(-0.600588\pi\) | ||||
−0.310772 | + | 0.950485i | \(0.600588\pi\) | |||||||
\(98\) | 6.81933 | 0.688857 | ||||||||
\(99\) | 1.08555 | 0.109102 | ||||||||
\(100\) | −6.85280 | −0.685280 | ||||||||
\(101\) | −7.86793 | −0.782889 | −0.391444 | − | 0.920202i | \(-0.628024\pi\) | ||||
−0.391444 | + | 0.920202i | \(0.628024\pi\) | |||||||
\(102\) | −18.3126 | −1.81322 | ||||||||
\(103\) | −7.66215 | −0.754974 | −0.377487 | − | 0.926015i | \(-0.623212\pi\) | ||||
−0.377487 | + | 0.926015i | \(0.623212\pi\) | |||||||
\(104\) | 10.5623 | 1.03572 | ||||||||
\(105\) | 5.47441 | 0.534248 | ||||||||
\(106\) | −27.8153 | −2.70166 | ||||||||
\(107\) | 8.86688 | 0.857193 | 0.428597 | − | 0.903496i | \(-0.359008\pi\) | ||||
0.428597 | + | 0.903496i | \(0.359008\pi\) | |||||||
\(108\) | 3.46438 | 0.333361 | ||||||||
\(109\) | 6.34792 | 0.608021 | 0.304010 | − | 0.952669i | \(-0.401674\pi\) | ||||
0.304010 | + | 0.952669i | \(0.401674\pi\) | |||||||
\(110\) | −4.41125 | −0.420596 | ||||||||
\(111\) | 9.75118 | 0.925541 | ||||||||
\(112\) | −3.37966 | −0.319348 | ||||||||
\(113\) | −17.4472 | −1.64129 | −0.820647 | − | 0.571435i | \(-0.806387\pi\) | ||||
−0.820647 | + | 0.571435i | \(0.806387\pi\) | |||||||
\(114\) | 2.30872 | 0.216232 | ||||||||
\(115\) | −3.14916 | −0.293661 | ||||||||
\(116\) | 29.3735 | 2.72726 | ||||||||
\(117\) | 3.08555 | 0.285259 | ||||||||
\(118\) | 10.1666 | 0.935907 | ||||||||
\(119\) | 24.6704 | 2.26153 | ||||||||
\(120\) | −5.95070 | −0.543222 | ||||||||
\(121\) | −9.82159 | −0.892872 | ||||||||
\(122\) | 15.6822 | 1.41980 | ||||||||
\(123\) | −6.02238 | −0.543020 | ||||||||
\(124\) | 9.92599 | 0.891380 | ||||||||
\(125\) | 12.1305 | 1.08498 | ||||||||
\(126\) | −7.36149 | −0.655814 | ||||||||
\(127\) | 14.7466 | 1.30855 | 0.654274 | − | 0.756258i | \(-0.272974\pi\) | ||||
0.654274 | + | 0.756258i | \(0.272974\pi\) | |||||||
\(128\) | −20.0445 | −1.77170 | ||||||||
\(129\) | 3.81005 | 0.335456 | ||||||||
\(130\) | −12.5385 | −1.09970 | ||||||||
\(131\) | 2.15445 | 0.188235 | 0.0941176 | − | 0.995561i | \(-0.469997\pi\) | ||||
0.0941176 | + | 0.995561i | \(0.469997\pi\) | |||||||
\(132\) | 3.76075 | 0.327331 | ||||||||
\(133\) | −3.11026 | −0.269693 | ||||||||
\(134\) | −2.33760 | −0.201938 | ||||||||
\(135\) | −1.73837 | −0.149615 | ||||||||
\(136\) | −26.8168 | −2.29952 | ||||||||
\(137\) | 6.51036 | 0.556218 | 0.278109 | − | 0.960550i | \(-0.410292\pi\) | ||||
0.278109 | + | 0.960550i | \(0.410292\pi\) | |||||||
\(138\) | 4.23471 | 0.360483 | ||||||||
\(139\) | −15.5547 | −1.31933 | −0.659665 | − | 0.751560i | \(-0.729302\pi\) | ||||
−0.659665 | + | 0.751560i | \(0.729302\pi\) | |||||||
\(140\) | 18.9655 | 1.60287 | ||||||||
\(141\) | −0.987645 | −0.0831747 | ||||||||
\(142\) | 2.38817 | 0.200411 | ||||||||
\(143\) | 3.34951 | 0.280100 | ||||||||
\(144\) | 1.07319 | 0.0894327 | ||||||||
\(145\) | −14.7391 | −1.22402 | ||||||||
\(146\) | 11.0992 | 0.918574 | ||||||||
\(147\) | 2.91723 | 0.240609 | ||||||||
\(148\) | 33.7818 | 2.77685 | ||||||||
\(149\) | −14.0932 | −1.15456 | −0.577282 | − | 0.816545i | \(-0.695887\pi\) | ||||
−0.577282 | + | 0.816545i | \(0.695887\pi\) | |||||||
\(150\) | −4.62394 | −0.377543 | ||||||||
\(151\) | 15.5834 | 1.26816 | 0.634079 | − | 0.773268i | \(-0.281379\pi\) | ||||
0.634079 | + | 0.773268i | \(0.281379\pi\) | |||||||
\(152\) | 3.38086 | 0.274224 | ||||||||
\(153\) | −7.83394 | −0.633337 | ||||||||
\(154\) | −7.99124 | −0.643953 | ||||||||
\(155\) | −4.98069 | −0.400059 | ||||||||
\(156\) | 10.6895 | 0.855847 | ||||||||
\(157\) | −18.1021 | −1.44471 | −0.722353 | − | 0.691524i | \(-0.756939\pi\) | ||||
−0.722353 | + | 0.691524i | \(0.756939\pi\) | |||||||
\(158\) | 35.2904 | 2.80756 | ||||||||
\(159\) | −11.8991 | −0.943658 | ||||||||
\(160\) | 7.54036 | 0.596118 | ||||||||
\(161\) | −5.70490 | −0.449609 | ||||||||
\(162\) | 2.33760 | 0.183659 | ||||||||
\(163\) | 19.3058 | 1.51215 | 0.756075 | − | 0.654484i | \(-0.227114\pi\) | ||||
0.756075 | + | 0.654484i | \(0.227114\pi\) | |||||||
\(164\) | −20.8638 | −1.62919 | ||||||||
\(165\) | −1.88708 | −0.146909 | ||||||||
\(166\) | −38.6993 | −3.00365 | ||||||||
\(167\) | 14.5408 | 1.12520 | 0.562601 | − | 0.826729i | \(-0.309801\pi\) | ||||
0.562601 | + | 0.826729i | \(0.309801\pi\) | |||||||
\(168\) | −10.7801 | −0.831699 | ||||||||
\(169\) | −3.47940 | −0.267646 | ||||||||
\(170\) | 31.8341 | 2.44157 | ||||||||
\(171\) | 0.987645 | 0.0755271 | ||||||||
\(172\) | 13.1995 | 1.00645 | ||||||||
\(173\) | 13.1049 | 0.996347 | 0.498174 | − | 0.867077i | \(-0.334004\pi\) | ||||
0.498174 | + | 0.867077i | \(0.334004\pi\) | |||||||
\(174\) | 19.8198 | 1.50254 | ||||||||
\(175\) | 6.22927 | 0.470888 | ||||||||
\(176\) | 1.16500 | 0.0878152 | ||||||||
\(177\) | 4.34914 | 0.326901 | ||||||||
\(178\) | 5.56797 | 0.417337 | ||||||||
\(179\) | 22.6457 | 1.69262 | 0.846308 | − | 0.532694i | \(-0.178820\pi\) | ||||
0.846308 | + | 0.532694i | \(0.178820\pi\) | |||||||
\(180\) | −6.02238 | −0.448882 | ||||||||
\(181\) | −23.3799 | −1.73781 | −0.868906 | − | 0.494978i | \(-0.835176\pi\) | ||||
−0.868906 | + | 0.494978i | \(0.835176\pi\) | |||||||
\(182\) | −22.7142 | −1.68369 | ||||||||
\(183\) | 6.70867 | 0.495919 | ||||||||
\(184\) | 6.20125 | 0.457162 | ||||||||
\(185\) | −16.9512 | −1.24627 | ||||||||
\(186\) | 6.69759 | 0.491091 | ||||||||
\(187\) | −8.50411 | −0.621882 | ||||||||
\(188\) | −3.42158 | −0.249545 | ||||||||
\(189\) | −3.14916 | −0.229068 | ||||||||
\(190\) | −4.01341 | −0.291163 | ||||||||
\(191\) | −27.2366 | −1.97077 | −0.985385 | − | 0.170343i | \(-0.945513\pi\) | ||||
−0.985385 | + | 0.170343i | \(0.945513\pi\) | |||||||
\(192\) | −12.2860 | −0.886664 | ||||||||
\(193\) | −19.9913 | −1.43901 | −0.719504 | − | 0.694489i | \(-0.755631\pi\) | ||||
−0.719504 | + | 0.694489i | \(0.755631\pi\) | |||||||
\(194\) | −14.3096 | −1.02737 | ||||||||
\(195\) | −5.36382 | −0.384111 | ||||||||
\(196\) | 10.1064 | 0.721887 | ||||||||
\(197\) | −12.5542 | −0.894451 | −0.447226 | − | 0.894421i | \(-0.647588\pi\) | ||||
−0.447226 | + | 0.894421i | \(0.647588\pi\) | |||||||
\(198\) | 2.53758 | 0.180338 | ||||||||
\(199\) | 5.17305 | 0.366708 | 0.183354 | − | 0.983047i | \(-0.441305\pi\) | ||||
0.183354 | + | 0.983047i | \(0.441305\pi\) | |||||||
\(200\) | −6.77123 | −0.478798 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | −18.3921 | −1.29406 | ||||||||
\(203\) | −26.7008 | −1.87403 | ||||||||
\(204\) | −27.1398 | −1.90017 | ||||||||
\(205\) | 10.4691 | 0.731195 | ||||||||
\(206\) | −17.9111 | −1.24792 | ||||||||
\(207\) | 1.81156 | 0.125912 | ||||||||
\(208\) | 3.31138 | 0.229603 | ||||||||
\(209\) | 1.07213 | 0.0741611 | ||||||||
\(210\) | 12.7970 | 0.883077 | ||||||||
\(211\) | −17.3952 | −1.19753 | −0.598767 | − | 0.800924i | \(-0.704342\pi\) | ||||
−0.598767 | + | 0.800924i | \(0.704342\pi\) | |||||||
\(212\) | −41.2230 | −2.83120 | ||||||||
\(213\) | 1.02163 | 0.0700012 | ||||||||
\(214\) | 20.7272 | 1.41688 | ||||||||
\(215\) | −6.62328 | −0.451704 | ||||||||
\(216\) | 3.42315 | 0.232916 | ||||||||
\(217\) | −9.02283 | −0.612510 | ||||||||
\(218\) | 14.8389 | 1.00502 | ||||||||
\(219\) | 4.74810 | 0.320847 | ||||||||
\(220\) | −6.53758 | −0.440763 | ||||||||
\(221\) | −24.1720 | −1.62598 | ||||||||
\(222\) | 22.7944 | 1.52986 | ||||||||
\(223\) | −9.07143 | −0.607468 | −0.303734 | − | 0.952757i | \(-0.598233\pi\) | ||||
−0.303734 | + | 0.952757i | \(0.598233\pi\) | |||||||
\(224\) | 13.6598 | 0.912685 | ||||||||
\(225\) | −1.97807 | −0.131871 | ||||||||
\(226\) | −40.7846 | −2.71295 | ||||||||
\(227\) | −8.49716 | −0.563976 | −0.281988 | − | 0.959418i | \(-0.590994\pi\) | ||||
−0.281988 | + | 0.959418i | \(0.590994\pi\) | |||||||
\(228\) | 3.42158 | 0.226600 | ||||||||
\(229\) | −15.7368 | −1.03991 | −0.519957 | − | 0.854192i | \(-0.674052\pi\) | ||||
−0.519957 | + | 0.854192i | \(0.674052\pi\) | |||||||
\(230\) | −7.36149 | −0.485402 | ||||||||
\(231\) | −3.41856 | −0.224925 | ||||||||
\(232\) | 29.0239 | 1.90551 | ||||||||
\(233\) | 14.3350 | 0.939119 | 0.469559 | − | 0.882901i | \(-0.344413\pi\) | ||||
0.469559 | + | 0.882901i | \(0.344413\pi\) | |||||||
\(234\) | 7.21278 | 0.471514 | ||||||||
\(235\) | 1.71689 | 0.111998 | ||||||||
\(236\) | 15.0671 | 0.980784 | ||||||||
\(237\) | 15.0968 | 0.980645 | ||||||||
\(238\) | 57.6695 | 3.73816 | ||||||||
\(239\) | 5.30565 | 0.343194 | 0.171597 | − | 0.985167i | \(-0.445107\pi\) | ||||
0.171597 | + | 0.985167i | \(0.445107\pi\) | |||||||
\(240\) | −1.86560 | −0.120424 | ||||||||
\(241\) | 19.2318 | 1.23883 | 0.619416 | − | 0.785063i | \(-0.287370\pi\) | ||||
0.619416 | + | 0.785063i | \(0.287370\pi\) | |||||||
\(242\) | −22.9590 | −1.47586 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 23.2414 | 1.48788 | ||||||||
\(245\) | −5.07123 | −0.323989 | ||||||||
\(246\) | −14.0779 | −0.897576 | ||||||||
\(247\) | 3.04743 | 0.193903 | ||||||||
\(248\) | 9.80784 | 0.622799 | ||||||||
\(249\) | −16.5551 | −1.04914 | ||||||||
\(250\) | 28.3562 | 1.79340 | ||||||||
\(251\) | 26.6500 | 1.68213 | 0.841066 | − | 0.540932i | \(-0.181928\pi\) | ||||
0.841066 | + | 0.540932i | \(0.181928\pi\) | |||||||
\(252\) | −10.9099 | −0.687260 | ||||||||
\(253\) | 1.96653 | 0.123635 | ||||||||
\(254\) | 34.4716 | 2.16294 | ||||||||
\(255\) | 13.6183 | 0.852810 | ||||||||
\(256\) | −22.2842 | −1.39276 | ||||||||
\(257\) | −3.35636 | −0.209364 | −0.104682 | − | 0.994506i | \(-0.533382\pi\) | ||||
−0.104682 | + | 0.994506i | \(0.533382\pi\) | |||||||
\(258\) | 8.90639 | 0.554487 | ||||||||
\(259\) | −30.7081 | −1.90811 | ||||||||
\(260\) | −18.5823 | −1.15243 | ||||||||
\(261\) | 8.47870 | 0.524818 | ||||||||
\(262\) | 5.03625 | 0.311140 | ||||||||
\(263\) | 13.4905 | 0.831862 | 0.415931 | − | 0.909396i | \(-0.363456\pi\) | ||||
0.415931 | + | 0.909396i | \(0.363456\pi\) | |||||||
\(264\) | 3.71599 | 0.228703 | ||||||||
\(265\) | 20.6850 | 1.27067 | ||||||||
\(266\) | −7.27054 | −0.445786 | ||||||||
\(267\) | 2.38191 | 0.145771 | ||||||||
\(268\) | −3.46438 | −0.211621 | ||||||||
\(269\) | 0.978366 | 0.0596520 | 0.0298260 | − | 0.999555i | \(-0.490505\pi\) | ||||
0.0298260 | + | 0.999555i | \(0.490505\pi\) | |||||||
\(270\) | −4.06362 | −0.247304 | ||||||||
\(271\) | −2.39995 | −0.145786 | −0.0728932 | − | 0.997340i | \(-0.523223\pi\) | ||||
−0.0728932 | + | 0.997340i | \(0.523223\pi\) | |||||||
\(272\) | −8.40732 | −0.509769 | ||||||||
\(273\) | −9.71689 | −0.588093 | ||||||||
\(274\) | 15.2186 | 0.919391 | ||||||||
\(275\) | −2.14729 | −0.129486 | ||||||||
\(276\) | 6.27595 | 0.377768 | ||||||||
\(277\) | −15.4674 | −0.929344 | −0.464672 | − | 0.885483i | \(-0.653828\pi\) | ||||
−0.464672 | + | 0.885483i | \(0.653828\pi\) | |||||||
\(278\) | −36.3606 | −2.18077 | ||||||||
\(279\) | 2.86515 | 0.171532 | ||||||||
\(280\) | 18.7397 | 1.11991 | ||||||||
\(281\) | −6.69254 | −0.399243 | −0.199622 | − | 0.979873i | \(-0.563971\pi\) | ||||
−0.199622 | + | 0.979873i | \(0.563971\pi\) | |||||||
\(282\) | −2.30872 | −0.137482 | ||||||||
\(283\) | 20.1770 | 1.19940 | 0.599700 | − | 0.800225i | \(-0.295287\pi\) | ||||
0.599700 | + | 0.800225i | \(0.295287\pi\) | |||||||
\(284\) | 3.53933 | 0.210021 | ||||||||
\(285\) | −1.71689 | −0.101700 | ||||||||
\(286\) | 7.82981 | 0.462986 | ||||||||
\(287\) | 18.9655 | 1.11950 | ||||||||
\(288\) | −4.33760 | −0.255596 | ||||||||
\(289\) | 44.3707 | 2.61004 | ||||||||
\(290\) | −34.4542 | −2.02322 | ||||||||
\(291\) | −6.12150 | −0.358849 | ||||||||
\(292\) | 16.4492 | 0.962620 | ||||||||
\(293\) | 22.3656 | 1.30661 | 0.653305 | − | 0.757095i | \(-0.273382\pi\) | ||||
0.653305 | + | 0.757095i | \(0.273382\pi\) | |||||||
\(294\) | 6.81933 | 0.397712 | ||||||||
\(295\) | −7.56041 | −0.440184 | ||||||||
\(296\) | 33.3797 | 1.94016 | ||||||||
\(297\) | 1.08555 | 0.0629898 | ||||||||
\(298\) | −32.9444 | −1.90842 | ||||||||
\(299\) | 5.58966 | 0.323258 | ||||||||
\(300\) | −6.85280 | −0.395646 | ||||||||
\(301\) | −11.9985 | −0.691581 | ||||||||
\(302\) | 36.4278 | 2.09618 | ||||||||
\(303\) | −7.86793 | −0.452001 | ||||||||
\(304\) | 1.05993 | 0.0607913 | ||||||||
\(305\) | −11.6621 | −0.667773 | ||||||||
\(306\) | −18.3126 | −1.04686 | ||||||||
\(307\) | −12.8565 | −0.733758 | −0.366879 | − | 0.930269i | \(-0.619574\pi\) | ||||
−0.366879 | + | 0.930269i | \(0.619574\pi\) | |||||||
\(308\) | −11.8432 | −0.674830 | ||||||||
\(309\) | −7.66215 | −0.435884 | ||||||||
\(310\) | −11.6429 | −0.661271 | ||||||||
\(311\) | −2.33735 | −0.132539 | −0.0662696 | − | 0.997802i | \(-0.521110\pi\) | ||||
−0.0662696 | + | 0.997802i | \(0.521110\pi\) | |||||||
\(312\) | 10.5623 | 0.597972 | ||||||||
\(313\) | 3.73768 | 0.211266 | 0.105633 | − | 0.994405i | \(-0.466313\pi\) | ||||
0.105633 | + | 0.994405i | \(0.466313\pi\) | |||||||
\(314\) | −42.3156 | −2.38800 | ||||||||
\(315\) | 5.47441 | 0.308448 | ||||||||
\(316\) | 52.3013 | 2.94218 | ||||||||
\(317\) | −5.08947 | −0.285853 | −0.142927 | − | 0.989733i | \(-0.545651\pi\) | ||||
−0.142927 | + | 0.989733i | \(0.545651\pi\) | |||||||
\(318\) | −27.8153 | −1.55980 | ||||||||
\(319\) | 9.20403 | 0.515327 | ||||||||
\(320\) | 21.3576 | 1.19392 | ||||||||
\(321\) | 8.86688 | 0.494901 | ||||||||
\(322\) | −13.3358 | −0.743175 | ||||||||
\(323\) | −7.73716 | −0.430507 | ||||||||
\(324\) | 3.46438 | 0.192466 | ||||||||
\(325\) | −6.10343 | −0.338557 | ||||||||
\(326\) | 45.1294 | 2.49949 | ||||||||
\(327\) | 6.34792 | 0.351041 | ||||||||
\(328\) | −20.6155 | −1.13830 | ||||||||
\(329\) | 3.11026 | 0.171474 | ||||||||
\(330\) | −4.41125 | −0.242831 | ||||||||
\(331\) | 22.6794 | 1.24657 | 0.623287 | − | 0.781993i | \(-0.285797\pi\) | ||||
0.623287 | + | 0.781993i | \(0.285797\pi\) | |||||||
\(332\) | −57.3533 | −3.14767 | ||||||||
\(333\) | 9.75118 | 0.534361 | ||||||||
\(334\) | 33.9906 | 1.85988 | ||||||||
\(335\) | 1.73837 | 0.0949773 | ||||||||
\(336\) | −3.37966 | −0.184375 | ||||||||
\(337\) | −17.5952 | −0.958473 | −0.479236 | − | 0.877686i | \(-0.659086\pi\) | ||||
−0.479236 | + | 0.877686i | \(0.659086\pi\) | |||||||
\(338\) | −8.13346 | −0.442402 | ||||||||
\(339\) | −17.4472 | −0.947602 | ||||||||
\(340\) | 47.1790 | 2.55864 | ||||||||
\(341\) | 3.11026 | 0.168430 | ||||||||
\(342\) | 2.30872 | 0.124841 | ||||||||
\(343\) | 12.8573 | 0.694229 | ||||||||
\(344\) | 13.0424 | 0.703198 | ||||||||
\(345\) | −3.14916 | −0.169545 | ||||||||
\(346\) | 30.6340 | 1.64690 | ||||||||
\(347\) | 5.81035 | 0.311916 | 0.155958 | − | 0.987764i | \(-0.450154\pi\) | ||||
0.155958 | + | 0.987764i | \(0.450154\pi\) | |||||||
\(348\) | 29.3735 | 1.57458 | ||||||||
\(349\) | 21.4083 | 1.14596 | 0.572980 | − | 0.819570i | \(-0.305787\pi\) | ||||
0.572980 | + | 0.819570i | \(0.305787\pi\) | |||||||
\(350\) | 14.5616 | 0.778348 | ||||||||
\(351\) | 3.08555 | 0.164694 | ||||||||
\(352\) | −4.70867 | −0.250973 | ||||||||
\(353\) | −0.696269 | −0.0370586 | −0.0185293 | − | 0.999828i | \(-0.505898\pi\) | ||||
−0.0185293 | + | 0.999828i | \(0.505898\pi\) | |||||||
\(354\) | 10.1666 | 0.540346 | ||||||||
\(355\) | −1.77598 | −0.0942591 | ||||||||
\(356\) | 8.25186 | 0.437348 | ||||||||
\(357\) | 24.6704 | 1.30569 | ||||||||
\(358\) | 52.9366 | 2.79778 | ||||||||
\(359\) | 14.1437 | 0.746475 | 0.373237 | − | 0.927736i | \(-0.378248\pi\) | ||||
0.373237 | + | 0.927736i | \(0.378248\pi\) | |||||||
\(360\) | −5.95070 | −0.313629 | ||||||||
\(361\) | −18.0246 | −0.948661 | ||||||||
\(362\) | −54.6528 | −2.87249 | ||||||||
\(363\) | −9.82159 | −0.515500 | ||||||||
\(364\) | −33.6631 | −1.76442 | ||||||||
\(365\) | −8.25396 | −0.432032 | ||||||||
\(366\) | 15.6822 | 0.819722 | ||||||||
\(367\) | −8.41862 | −0.439448 | −0.219724 | − | 0.975562i | \(-0.570516\pi\) | ||||
−0.219724 | + | 0.975562i | \(0.570516\pi\) | |||||||
\(368\) | 1.94415 | 0.101346 | ||||||||
\(369\) | −6.02238 | −0.313513 | ||||||||
\(370\) | −39.6251 | −2.06001 | ||||||||
\(371\) | 37.4721 | 1.94546 | ||||||||
\(372\) | 9.92599 | 0.514639 | ||||||||
\(373\) | 2.44594 | 0.126646 | 0.0633229 | − | 0.997993i | \(-0.479830\pi\) | ||||
0.0633229 | + | 0.997993i | \(0.479830\pi\) | |||||||
\(374\) | −19.8792 | −1.02793 | ||||||||
\(375\) | 12.1305 | 0.626415 | ||||||||
\(376\) | −3.38086 | −0.174354 | ||||||||
\(377\) | 26.1614 | 1.34738 | ||||||||
\(378\) | −7.36149 | −0.378634 | ||||||||
\(379\) | −29.8978 | −1.53574 | −0.767872 | − | 0.640603i | \(-0.778685\pi\) | ||||
−0.767872 | + | 0.640603i | \(0.778685\pi\) | |||||||
\(380\) | −5.94798 | −0.305125 | ||||||||
\(381\) | 14.7466 | 0.755490 | ||||||||
\(382\) | −63.6683 | −3.25755 | ||||||||
\(383\) | −17.8360 | −0.911375 | −0.455688 | − | 0.890140i | \(-0.650607\pi\) | ||||
−0.455688 | + | 0.890140i | \(0.650607\pi\) | |||||||
\(384\) | −20.0445 | −1.02289 | ||||||||
\(385\) | 5.94273 | 0.302870 | ||||||||
\(386\) | −46.7318 | −2.37858 | ||||||||
\(387\) | 3.81005 | 0.193676 | ||||||||
\(388\) | −21.2072 | −1.07663 | ||||||||
\(389\) | −5.78292 | −0.293206 | −0.146603 | − | 0.989195i | \(-0.546834\pi\) | ||||
−0.146603 | + | 0.989195i | \(0.546834\pi\) | |||||||
\(390\) | −12.5385 | −0.634911 | ||||||||
\(391\) | −14.1917 | −0.717704 | ||||||||
\(392\) | 9.98613 | 0.504375 | ||||||||
\(393\) | 2.15445 | 0.108678 | ||||||||
\(394\) | −29.3468 | −1.47847 | ||||||||
\(395\) | −26.2439 | −1.32047 | ||||||||
\(396\) | 3.76075 | 0.188985 | ||||||||
\(397\) | 20.7917 | 1.04350 | 0.521752 | − | 0.853097i | \(-0.325279\pi\) | ||||
0.521752 | + | 0.853097i | \(0.325279\pi\) | |||||||
\(398\) | 12.0925 | 0.606144 | ||||||||
\(399\) | −3.11026 | −0.155708 | ||||||||
\(400\) | −2.12285 | −0.106142 | ||||||||
\(401\) | 15.4905 | 0.773561 | 0.386780 | − | 0.922172i | \(-0.373587\pi\) | ||||
0.386780 | + | 0.922172i | \(0.373587\pi\) | |||||||
\(402\) | −2.33760 | −0.116589 | ||||||||
\(403\) | 8.84056 | 0.440380 | ||||||||
\(404\) | −27.2575 | −1.35611 | ||||||||
\(405\) | −1.73837 | −0.0863803 | ||||||||
\(406\) | −62.4159 | −3.09765 | ||||||||
\(407\) | 10.5854 | 0.524697 | ||||||||
\(408\) | −26.8168 | −1.32763 | ||||||||
\(409\) | 23.1838 | 1.14637 | 0.573183 | − | 0.819427i | \(-0.305708\pi\) | ||||
0.573183 | + | 0.819427i | \(0.305708\pi\) | |||||||
\(410\) | 24.4727 | 1.20862 | ||||||||
\(411\) | 6.51036 | 0.321132 | ||||||||
\(412\) | −26.5446 | −1.30776 | ||||||||
\(413\) | −13.6961 | −0.673943 | ||||||||
\(414\) | 4.23471 | 0.208125 | ||||||||
\(415\) | 28.7789 | 1.41270 | ||||||||
\(416\) | −13.3839 | −0.656198 | ||||||||
\(417\) | −15.5547 | −0.761716 | ||||||||
\(418\) | 2.50623 | 0.122583 | ||||||||
\(419\) | 3.70438 | 0.180971 | 0.0904854 | − | 0.995898i | \(-0.471158\pi\) | ||||
0.0904854 | + | 0.995898i | \(0.471158\pi\) | |||||||
\(420\) | 18.9655 | 0.925420 | ||||||||
\(421\) | 5.02231 | 0.244772 | 0.122386 | − | 0.992483i | \(-0.460945\pi\) | ||||
0.122386 | + | 0.992483i | \(0.460945\pi\) | |||||||
\(422\) | −40.6630 | −1.97944 | ||||||||
\(423\) | −0.987645 | −0.0480209 | ||||||||
\(424\) | −40.7323 | −1.97813 | ||||||||
\(425\) | 15.4961 | 0.751671 | ||||||||
\(426\) | 2.38817 | 0.115707 | ||||||||
\(427\) | −21.1267 | −1.02239 | ||||||||
\(428\) | 30.7183 | 1.48482 | ||||||||
\(429\) | 3.34951 | 0.161716 | ||||||||
\(430\) | −15.4826 | −0.746637 | ||||||||
\(431\) | 4.57015 | 0.220136 | 0.110068 | − | 0.993924i | \(-0.464893\pi\) | ||||
0.110068 | + | 0.993924i | \(0.464893\pi\) | |||||||
\(432\) | 1.07319 | 0.0516340 | ||||||||
\(433\) | 0.218875 | 0.0105184 | 0.00525922 | − | 0.999986i | \(-0.498326\pi\) | ||||
0.00525922 | + | 0.999986i | \(0.498326\pi\) | |||||||
\(434\) | −21.0918 | −1.01244 | ||||||||
\(435\) | −14.7391 | −0.706687 | ||||||||
\(436\) | 21.9917 | 1.05321 | ||||||||
\(437\) | 1.78918 | 0.0855881 | ||||||||
\(438\) | 11.0992 | 0.530339 | ||||||||
\(439\) | 4.34453 | 0.207353 | 0.103676 | − | 0.994611i | \(-0.466939\pi\) | ||||
0.103676 | + | 0.994611i | \(0.466939\pi\) | |||||||
\(440\) | −6.45976 | −0.307957 | ||||||||
\(441\) | 2.91723 | 0.138916 | ||||||||
\(442\) | −56.5045 | −2.68765 | ||||||||
\(443\) | 20.5054 | 0.974242 | 0.487121 | − | 0.873334i | \(-0.338047\pi\) | ||||
0.487121 | + | 0.873334i | \(0.338047\pi\) | |||||||
\(444\) | 33.7818 | 1.60321 | ||||||||
\(445\) | −4.14065 | −0.196285 | ||||||||
\(446\) | −21.2054 | −1.00411 | ||||||||
\(447\) | −14.0932 | −0.666588 | ||||||||
\(448\) | 38.6905 | 1.82796 | ||||||||
\(449\) | 12.8291 | 0.605440 | 0.302720 | − | 0.953079i | \(-0.402105\pi\) | ||||
0.302720 | + | 0.953079i | \(0.402105\pi\) | |||||||
\(450\) | −4.62394 | −0.217975 | ||||||||
\(451\) | −6.53758 | −0.307842 | ||||||||
\(452\) | −60.4438 | −2.84304 | ||||||||
\(453\) | 15.5834 | 0.732172 | ||||||||
\(454\) | −19.8630 | −0.932216 | ||||||||
\(455\) | 16.8916 | 0.791888 | ||||||||
\(456\) | 3.38086 | 0.158323 | ||||||||
\(457\) | 28.9481 | 1.35414 | 0.677068 | − | 0.735920i | \(-0.263250\pi\) | ||||
0.677068 | + | 0.735920i | \(0.263250\pi\) | |||||||
\(458\) | −36.7863 | −1.71891 | ||||||||
\(459\) | −7.83394 | −0.365657 | ||||||||
\(460\) | −10.9099 | −0.508677 | ||||||||
\(461\) | 6.81172 | 0.317253 | 0.158627 | − | 0.987339i | \(-0.449293\pi\) | ||||
0.158627 | + | 0.987339i | \(0.449293\pi\) | |||||||
\(462\) | −7.99124 | −0.371786 | ||||||||
\(463\) | −20.2404 | −0.940653 | −0.470327 | − | 0.882492i | \(-0.655864\pi\) | ||||
−0.470327 | + | 0.882492i | \(0.655864\pi\) | |||||||
\(464\) | 9.09927 | 0.422423 | ||||||||
\(465\) | −4.98069 | −0.230974 | ||||||||
\(466\) | 33.5096 | 1.55230 | ||||||||
\(467\) | −13.1287 | −0.607522 | −0.303761 | − | 0.952748i | \(-0.598243\pi\) | ||||
−0.303761 | + | 0.952748i | \(0.598243\pi\) | |||||||
\(468\) | 10.6895 | 0.494123 | ||||||||
\(469\) | 3.14916 | 0.145415 | ||||||||
\(470\) | 4.01341 | 0.185125 | ||||||||
\(471\) | −18.1021 | −0.834102 | ||||||||
\(472\) | 14.8877 | 0.685264 | ||||||||
\(473\) | 4.13599 | 0.190173 | ||||||||
\(474\) | 35.2904 | 1.62094 | ||||||||
\(475\) | −1.95363 | −0.0896388 | ||||||||
\(476\) | 85.4677 | 3.91740 | ||||||||
\(477\) | −11.8991 | −0.544821 | ||||||||
\(478\) | 12.4025 | 0.567277 | ||||||||
\(479\) | 5.64065 | 0.257728 | 0.128864 | − | 0.991662i | \(-0.458867\pi\) | ||||
0.128864 | + | 0.991662i | \(0.458867\pi\) | |||||||
\(480\) | 7.54036 | 0.344169 | ||||||||
\(481\) | 30.0877 | 1.37188 | ||||||||
\(482\) | 44.9564 | 2.04771 | ||||||||
\(483\) | −5.70490 | −0.259582 | ||||||||
\(484\) | −34.0258 | −1.54663 | ||||||||
\(485\) | 10.6414 | 0.483202 | ||||||||
\(486\) | 2.33760 | 0.106036 | ||||||||
\(487\) | −22.3820 | −1.01423 | −0.507113 | − | 0.861880i | \(-0.669287\pi\) | ||||
−0.507113 | + | 0.861880i | \(0.669287\pi\) | |||||||
\(488\) | 22.9648 | 1.03957 | ||||||||
\(489\) | 19.3058 | 0.873041 | ||||||||
\(490\) | −11.8545 | −0.535533 | ||||||||
\(491\) | 7.82286 | 0.353041 | 0.176520 | − | 0.984297i | \(-0.443516\pi\) | ||||
0.176520 | + | 0.984297i | \(0.443516\pi\) | |||||||
\(492\) | −20.8638 | −0.940615 | ||||||||
\(493\) | −66.4217 | −2.99148 | ||||||||
\(494\) | 7.12367 | 0.320509 | ||||||||
\(495\) | −1.88708 | −0.0848180 | ||||||||
\(496\) | 3.07486 | 0.138065 | ||||||||
\(497\) | −3.21729 | −0.144315 | ||||||||
\(498\) | −38.6993 | −1.73416 | ||||||||
\(499\) | 34.1870 | 1.53042 | 0.765211 | − | 0.643779i | \(-0.222635\pi\) | ||||
0.765211 | + | 0.643779i | \(0.222635\pi\) | |||||||
\(500\) | 42.0246 | 1.87940 | ||||||||
\(501\) | 14.5408 | 0.649635 | ||||||||
\(502\) | 62.2971 | 2.78046 | ||||||||
\(503\) | −25.3215 | −1.12903 | −0.564514 | − | 0.825424i | \(-0.690936\pi\) | ||||
−0.564514 | + | 0.825424i | \(0.690936\pi\) | |||||||
\(504\) | −10.7801 | −0.480182 | ||||||||
\(505\) | 13.6774 | 0.608635 | ||||||||
\(506\) | 4.59698 | 0.204361 | ||||||||
\(507\) | −3.47940 | −0.154526 | ||||||||
\(508\) | 51.0878 | 2.26666 | ||||||||
\(509\) | 20.7214 | 0.918460 | 0.459230 | − | 0.888317i | \(-0.348125\pi\) | ||||
0.459230 | + | 0.888317i | \(0.348125\pi\) | |||||||
\(510\) | 31.8341 | 1.40964 | ||||||||
\(511\) | −14.9525 | −0.661462 | ||||||||
\(512\) | −12.0025 | −0.530439 | ||||||||
\(513\) | 0.987645 | 0.0436056 | ||||||||
\(514\) | −7.84583 | −0.346065 | ||||||||
\(515\) | 13.3196 | 0.586934 | ||||||||
\(516\) | 13.1995 | 0.581075 | ||||||||
\(517\) | −1.07213 | −0.0471524 | ||||||||
\(518\) | −71.7832 | −3.15397 | ||||||||
\(519\) | 13.1049 | 0.575241 | ||||||||
\(520\) | −18.3612 | −0.805190 | ||||||||
\(521\) | −6.52760 | −0.285979 | −0.142990 | − | 0.989724i | \(-0.545672\pi\) | ||||
−0.142990 | + | 0.989724i | \(0.545672\pi\) | |||||||
\(522\) | 19.8198 | 0.867490 | ||||||||
\(523\) | 28.4978 | 1.24612 | 0.623062 | − | 0.782173i | \(-0.285888\pi\) | ||||
0.623062 | + | 0.782173i | \(0.285888\pi\) | |||||||
\(524\) | 7.46384 | 0.326059 | ||||||||
\(525\) | 6.22927 | 0.271868 | ||||||||
\(526\) | 31.5355 | 1.37501 | ||||||||
\(527\) | −22.4454 | −0.977739 | ||||||||
\(528\) | 1.16500 | 0.0507001 | ||||||||
\(529\) | −19.7182 | −0.857315 | ||||||||
\(530\) | 48.3533 | 2.10033 | ||||||||
\(531\) | 4.34914 | 0.188737 | ||||||||
\(532\) | −10.7751 | −0.467161 | ||||||||
\(533\) | −18.5823 | −0.804890 | ||||||||
\(534\) | 5.56797 | 0.240949 | ||||||||
\(535\) | −15.4139 | −0.666401 | ||||||||
\(536\) | −3.42315 | −0.147858 | ||||||||
\(537\) | 22.6457 | 0.977232 | ||||||||
\(538\) | 2.28703 | 0.0986009 | ||||||||
\(539\) | 3.16679 | 0.136403 | ||||||||
\(540\) | −6.02238 | −0.259162 | ||||||||
\(541\) | −10.8749 | −0.467550 | −0.233775 | − | 0.972291i | \(-0.575108\pi\) | ||||
−0.233775 | + | 0.972291i | \(0.575108\pi\) | |||||||
\(542\) | −5.61012 | −0.240975 | ||||||||
\(543\) | −23.3799 | −1.00333 | ||||||||
\(544\) | 33.9805 | 1.45690 | ||||||||
\(545\) | −11.0350 | −0.472689 | ||||||||
\(546\) | −22.7142 | −0.972079 | ||||||||
\(547\) | −23.1923 | −0.991631 | −0.495815 | − | 0.868428i | \(-0.665131\pi\) | ||||
−0.495815 | + | 0.868428i | \(0.665131\pi\) | |||||||
\(548\) | 22.5544 | 0.963476 | ||||||||
\(549\) | 6.70867 | 0.286319 | ||||||||
\(550\) | −5.01951 | −0.214032 | ||||||||
\(551\) | 8.37395 | 0.356742 | ||||||||
\(552\) | 6.20125 | 0.263943 | ||||||||
\(553\) | −47.5424 | −2.02171 | ||||||||
\(554\) | −36.1566 | −1.53614 | ||||||||
\(555\) | −16.9512 | −0.719536 | ||||||||
\(556\) | −53.8874 | −2.28533 | ||||||||
\(557\) | 17.9172 | 0.759176 | 0.379588 | − | 0.925156i | \(-0.376066\pi\) | ||||
0.379588 | + | 0.925156i | \(0.376066\pi\) | |||||||
\(558\) | 6.69759 | 0.283531 | ||||||||
\(559\) | 11.7561 | 0.497230 | ||||||||
\(560\) | 5.87509 | 0.248268 | ||||||||
\(561\) | −8.50411 | −0.359044 | ||||||||
\(562\) | −15.6445 | −0.659923 | ||||||||
\(563\) | −7.97511 | −0.336111 | −0.168055 | − | 0.985778i | \(-0.553749\pi\) | ||||
−0.168055 | + | 0.985778i | \(0.553749\pi\) | |||||||
\(564\) | −3.42158 | −0.144075 | ||||||||
\(565\) | 30.3297 | 1.27598 | ||||||||
\(566\) | 47.1659 | 1.98253 | ||||||||
\(567\) | −3.14916 | −0.132252 | ||||||||
\(568\) | 3.49721 | 0.146740 | ||||||||
\(569\) | 33.1240 | 1.38863 | 0.694316 | − | 0.719670i | \(-0.255707\pi\) | ||||
0.694316 | + | 0.719670i | \(0.255707\pi\) | |||||||
\(570\) | −4.01341 | −0.168103 | ||||||||
\(571\) | −5.25178 | −0.219780 | −0.109890 | − | 0.993944i | \(-0.535050\pi\) | ||||
−0.109890 | + | 0.993944i | \(0.535050\pi\) | |||||||
\(572\) | 11.6040 | 0.485187 | ||||||||
\(573\) | −27.2366 | −1.13782 | ||||||||
\(574\) | 44.3337 | 1.85045 | ||||||||
\(575\) | −3.58340 | −0.149438 | ||||||||
\(576\) | −12.2860 | −0.511916 | ||||||||
\(577\) | −11.3645 | −0.473112 | −0.236556 | − | 0.971618i | \(-0.576019\pi\) | ||||
−0.236556 | + | 0.971618i | \(0.576019\pi\) | |||||||
\(578\) | 103.721 | 4.31422 | ||||||||
\(579\) | −19.9913 | −0.830811 | ||||||||
\(580\) | −51.0620 | −2.12023 | ||||||||
\(581\) | 52.1348 | 2.16292 | ||||||||
\(582\) | −14.3096 | −0.593153 | ||||||||
\(583\) | −12.9170 | −0.534967 | ||||||||
\(584\) | 16.2535 | 0.672573 | ||||||||
\(585\) | −5.36382 | −0.221767 | ||||||||
\(586\) | 52.2818 | 2.15974 | ||||||||
\(587\) | 5.66033 | 0.233627 | 0.116813 | − | 0.993154i | \(-0.462732\pi\) | ||||
0.116813 | + | 0.993154i | \(0.462732\pi\) | |||||||
\(588\) | 10.1064 | 0.416782 | ||||||||
\(589\) | 2.82975 | 0.116598 | ||||||||
\(590\) | −17.6732 | −0.727595 | ||||||||
\(591\) | −12.5542 | −0.516412 | ||||||||
\(592\) | 10.4649 | 0.430104 | ||||||||
\(593\) | −13.4864 | −0.553822 | −0.276911 | − | 0.960896i | \(-0.589311\pi\) | ||||
−0.276911 | + | 0.960896i | \(0.589311\pi\) | |||||||
\(594\) | 2.53758 | 0.104118 | ||||||||
\(595\) | −42.8862 | −1.75816 | ||||||||
\(596\) | −48.8244 | −1.99993 | ||||||||
\(597\) | 5.17305 | 0.211719 | ||||||||
\(598\) | 13.0664 | 0.534325 | ||||||||
\(599\) | −0.375966 | −0.0153616 | −0.00768078 | − | 0.999971i | \(-0.502445\pi\) | ||||
−0.00768078 | + | 0.999971i | \(0.502445\pi\) | |||||||
\(600\) | −6.77123 | −0.276434 | ||||||||
\(601\) | 0.287554 | 0.0117296 | 0.00586478 | − | 0.999983i | \(-0.498133\pi\) | ||||
0.00586478 | + | 0.999983i | \(0.498133\pi\) | |||||||
\(602\) | −28.0477 | −1.14314 | ||||||||
\(603\) | −1.00000 | −0.0407231 | ||||||||
\(604\) | 53.9869 | 2.19670 | ||||||||
\(605\) | 17.0736 | 0.694139 | ||||||||
\(606\) | −18.3921 | −0.747128 | ||||||||
\(607\) | 8.89680 | 0.361110 | 0.180555 | − | 0.983565i | \(-0.442211\pi\) | ||||
0.180555 | + | 0.983565i | \(0.442211\pi\) | |||||||
\(608\) | −4.28401 | −0.173740 | ||||||||
\(609\) | −26.7008 | −1.08197 | ||||||||
\(610\) | −27.2615 | −1.10378 | ||||||||
\(611\) | −3.04743 | −0.123286 | ||||||||
\(612\) | −27.1398 | −1.09706 | ||||||||
\(613\) | 19.1981 | 0.775402 | 0.387701 | − | 0.921785i | \(-0.373269\pi\) | ||||
0.387701 | + | 0.921785i | \(0.373269\pi\) | |||||||
\(614\) | −30.0533 | −1.21285 | ||||||||
\(615\) | 10.4691 | 0.422156 | ||||||||
\(616\) | −11.7023 | −0.471497 | ||||||||
\(617\) | −4.26972 | −0.171893 | −0.0859463 | − | 0.996300i | \(-0.527391\pi\) | ||||
−0.0859463 | + | 0.996300i | \(0.527391\pi\) | |||||||
\(618\) | −17.9111 | −0.720488 | ||||||||
\(619\) | 14.4053 | 0.578999 | 0.289500 | − | 0.957178i | \(-0.406511\pi\) | ||||
0.289500 | + | 0.957178i | \(0.406511\pi\) | |||||||
\(620\) | −17.2550 | −0.692979 | ||||||||
\(621\) | 1.81156 | 0.0726955 | ||||||||
\(622\) | −5.46380 | −0.219079 | ||||||||
\(623\) | −7.50104 | −0.300523 | ||||||||
\(624\) | 3.31138 | 0.132561 | ||||||||
\(625\) | −11.1969 | −0.447875 | ||||||||
\(626\) | 8.73721 | 0.349209 | ||||||||
\(627\) | 1.07213 | 0.0428169 | ||||||||
\(628\) | −62.7127 | −2.50251 | ||||||||
\(629\) | −76.3902 | −3.04588 | ||||||||
\(630\) | 12.7970 | 0.509845 | ||||||||
\(631\) | 21.3988 | 0.851872 | 0.425936 | − | 0.904753i | \(-0.359945\pi\) | ||||
0.425936 | + | 0.904753i | \(0.359945\pi\) | |||||||
\(632\) | 51.6787 | 2.05567 | ||||||||
\(633\) | −17.3952 | −0.691396 | ||||||||
\(634\) | −11.8972 | −0.472496 | ||||||||
\(635\) | −25.6350 | −1.01729 | ||||||||
\(636\) | −41.2230 | −1.63460 | ||||||||
\(637\) | 9.00126 | 0.356643 | ||||||||
\(638\) | 21.5154 | 0.851801 | ||||||||
\(639\) | 1.02163 | 0.0404152 | ||||||||
\(640\) | 34.8448 | 1.37736 | ||||||||
\(641\) | 3.40675 | 0.134559 | 0.0672793 | − | 0.997734i | \(-0.478568\pi\) | ||||
0.0672793 | + | 0.997734i | \(0.478568\pi\) | |||||||
\(642\) | 20.7272 | 0.818038 | ||||||||
\(643\) | 33.5267 | 1.32217 | 0.661083 | − | 0.750313i | \(-0.270097\pi\) | ||||
0.661083 | + | 0.750313i | \(0.270097\pi\) | |||||||
\(644\) | −19.7640 | −0.778810 | ||||||||
\(645\) | −6.62328 | −0.260791 | ||||||||
\(646\) | −18.0864 | −0.711600 | ||||||||
\(647\) | 5.05600 | 0.198772 | 0.0993860 | − | 0.995049i | \(-0.468312\pi\) | ||||
0.0993860 | + | 0.995049i | \(0.468312\pi\) | |||||||
\(648\) | 3.42315 | 0.134474 | ||||||||
\(649\) | 4.72119 | 0.185323 | ||||||||
\(650\) | −14.2674 | −0.559613 | ||||||||
\(651\) | −9.02283 | −0.353633 | ||||||||
\(652\) | 66.8829 | 2.61934 | ||||||||
\(653\) | −37.7646 | −1.47784 | −0.738921 | − | 0.673792i | \(-0.764664\pi\) | ||||
−0.738921 | + | 0.673792i | \(0.764664\pi\) | |||||||
\(654\) | 14.8389 | 0.580248 | ||||||||
\(655\) | −3.74523 | −0.146338 | ||||||||
\(656\) | −6.46317 | −0.252344 | ||||||||
\(657\) | 4.74810 | 0.185241 | ||||||||
\(658\) | 7.27054 | 0.283435 | ||||||||
\(659\) | −7.86631 | −0.306428 | −0.153214 | − | 0.988193i | \(-0.548962\pi\) | ||||
−0.153214 | + | 0.988193i | \(0.548962\pi\) | |||||||
\(660\) | −6.53758 | −0.254475 | ||||||||
\(661\) | 43.1580 | 1.67865 | 0.839326 | − | 0.543628i | \(-0.182950\pi\) | ||||
0.839326 | + | 0.543628i | \(0.182950\pi\) | |||||||
\(662\) | 53.0155 | 2.06050 | ||||||||
\(663\) | −24.1720 | −0.938763 | ||||||||
\(664\) | −56.6707 | −2.19925 | ||||||||
\(665\) | 5.40678 | 0.209666 | ||||||||
\(666\) | 22.7944 | 0.883264 | ||||||||
\(667\) | 15.3597 | 0.594730 | ||||||||
\(668\) | 50.3750 | 1.94907 | ||||||||
\(669\) | −9.07143 | −0.350722 | ||||||||
\(670\) | 4.06362 | 0.156991 | ||||||||
\(671\) | 7.28257 | 0.281141 | ||||||||
\(672\) | 13.6598 | 0.526939 | ||||||||
\(673\) | −23.1525 | −0.892462 | −0.446231 | − | 0.894918i | \(-0.647234\pi\) | ||||
−0.446231 | + | 0.894918i | \(0.647234\pi\) | |||||||
\(674\) | −41.1306 | −1.58429 | ||||||||
\(675\) | −1.97807 | −0.0761360 | ||||||||
\(676\) | −12.0540 | −0.463615 | ||||||||
\(677\) | −19.6663 | −0.755837 | −0.377918 | − | 0.925839i | \(-0.623360\pi\) | ||||
−0.377918 | + | 0.925839i | \(0.623360\pi\) | |||||||
\(678\) | −40.7846 | −1.56632 | ||||||||
\(679\) | 19.2776 | 0.739806 | ||||||||
\(680\) | 46.6174 | 1.78770 | ||||||||
\(681\) | −8.49716 | −0.325612 | ||||||||
\(682\) | 7.27054 | 0.278403 | ||||||||
\(683\) | −42.8560 | −1.63984 | −0.819919 | − | 0.572480i | \(-0.805981\pi\) | ||||
−0.819919 | + | 0.572480i | \(0.805981\pi\) | |||||||
\(684\) | 3.42158 | 0.130827 | ||||||||
\(685\) | −11.3174 | −0.432416 | ||||||||
\(686\) | 30.0553 | 1.14752 | ||||||||
\(687\) | −15.7368 | −0.600395 | ||||||||
\(688\) | 4.08892 | 0.155889 | ||||||||
\(689\) | −36.7151 | −1.39874 | ||||||||
\(690\) | −7.36149 | −0.280247 | ||||||||
\(691\) | −51.2504 | −1.94966 | −0.974828 | − | 0.222958i | \(-0.928429\pi\) | ||||
−0.974828 | + | 0.222958i | \(0.928429\pi\) | |||||||
\(692\) | 45.4004 | 1.72586 | ||||||||
\(693\) | −3.41856 | −0.129861 | ||||||||
\(694\) | 13.5823 | 0.515576 | ||||||||
\(695\) | 27.0398 | 1.02568 | ||||||||
\(696\) | 29.0239 | 1.10015 | ||||||||
\(697\) | 47.1790 | 1.78703 | ||||||||
\(698\) | 50.0441 | 1.89420 | ||||||||
\(699\) | 14.3350 | 0.542200 | ||||||||
\(700\) | 21.5806 | 0.815669 | ||||||||
\(701\) | −48.4487 | −1.82988 | −0.914941 | − | 0.403589i | \(-0.867763\pi\) | ||||
−0.914941 | + | 0.403589i | \(0.867763\pi\) | |||||||
\(702\) | 7.21278 | 0.272229 | ||||||||
\(703\) | 9.63070 | 0.363229 | ||||||||
\(704\) | −13.3370 | −0.502657 | ||||||||
\(705\) | 1.71689 | 0.0646619 | ||||||||
\(706\) | −1.62760 | −0.0612555 | ||||||||
\(707\) | 24.7774 | 0.931850 | ||||||||
\(708\) | 15.0671 | 0.566256 | ||||||||
\(709\) | 37.1475 | 1.39510 | 0.697551 | − | 0.716535i | \(-0.254273\pi\) | ||||
0.697551 | + | 0.716535i | \(0.254273\pi\) | |||||||
\(710\) | −4.15153 | −0.155804 | ||||||||
\(711\) | 15.0968 | 0.566176 | ||||||||
\(712\) | 8.15364 | 0.305571 | ||||||||
\(713\) | 5.19040 | 0.194382 | ||||||||
\(714\) | 57.6695 | 2.15823 | ||||||||
\(715\) | −5.82268 | −0.217756 | ||||||||
\(716\) | 78.4533 | 2.93194 | ||||||||
\(717\) | 5.30565 | 0.198143 | ||||||||
\(718\) | 33.0623 | 1.23387 | ||||||||
\(719\) | 33.6911 | 1.25646 | 0.628232 | − | 0.778026i | \(-0.283779\pi\) | ||||
0.628232 | + | 0.778026i | \(0.283779\pi\) | |||||||
\(720\) | −1.86560 | −0.0695270 | ||||||||
\(721\) | 24.1294 | 0.898624 | ||||||||
\(722\) | −42.1342 | −1.56807 | ||||||||
\(723\) | 19.2318 | 0.715240 | ||||||||
\(724\) | −80.9968 | −3.01022 | ||||||||
\(725\) | −16.7715 | −0.622877 | ||||||||
\(726\) | −22.9590 | −0.852087 | ||||||||
\(727\) | 21.6307 | 0.802237 | 0.401119 | − | 0.916026i | \(-0.368622\pi\) | ||||
0.401119 | + | 0.916026i | \(0.368622\pi\) | |||||||
\(728\) | −33.2624 | −1.23279 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −19.2945 | −0.714120 | ||||||||
\(731\) | −29.8477 | −1.10396 | ||||||||
\(732\) | 23.2414 | 0.859027 | ||||||||
\(733\) | 8.90406 | 0.328879 | 0.164439 | − | 0.986387i | \(-0.447418\pi\) | ||||
0.164439 | + | 0.986387i | \(0.447418\pi\) | |||||||
\(734\) | −19.6794 | −0.726380 | ||||||||
\(735\) | −5.07123 | −0.187055 | ||||||||
\(736\) | −7.85783 | −0.289644 | ||||||||
\(737\) | −1.08555 | −0.0399866 | ||||||||
\(738\) | −14.0779 | −0.518216 | ||||||||
\(739\) | 5.22982 | 0.192382 | 0.0961910 | − | 0.995363i | \(-0.469334\pi\) | ||||
0.0961910 | + | 0.995363i | \(0.469334\pi\) | |||||||
\(740\) | −58.7253 | −2.15879 | ||||||||
\(741\) | 3.04743 | 0.111950 | ||||||||
\(742\) | 87.5949 | 3.21571 | ||||||||
\(743\) | −5.50983 | −0.202136 | −0.101068 | − | 0.994880i | \(-0.532226\pi\) | ||||
−0.101068 | + | 0.994880i | \(0.532226\pi\) | |||||||
\(744\) | 9.80784 | 0.359573 | ||||||||
\(745\) | 24.4993 | 0.897584 | ||||||||
\(746\) | 5.71763 | 0.209337 | ||||||||
\(747\) | −16.5551 | −0.605720 | ||||||||
\(748\) | −29.4615 | −1.07722 | ||||||||
\(749\) | −27.9232 | −1.02029 | ||||||||
\(750\) | 28.3562 | 1.03542 | ||||||||
\(751\) | 4.09731 | 0.149513 | 0.0747565 | − | 0.997202i | \(-0.476182\pi\) | ||||
0.0747565 | + | 0.997202i | \(0.476182\pi\) | |||||||
\(752\) | −1.05993 | −0.0386518 | ||||||||
\(753\) | 26.6500 | 0.971180 | ||||||||
\(754\) | 61.1550 | 2.22713 | ||||||||
\(755\) | −27.0897 | −0.985895 | ||||||||
\(756\) | −10.9099 | −0.396790 | ||||||||
\(757\) | −5.73586 | −0.208474 | −0.104237 | − | 0.994553i | \(-0.533240\pi\) | ||||
−0.104237 | + | 0.994553i | \(0.533240\pi\) | |||||||
\(758\) | −69.8891 | −2.53849 | ||||||||
\(759\) | 1.96653 | 0.0713807 | ||||||||
\(760\) | −5.87718 | −0.213188 | ||||||||
\(761\) | 29.3667 | 1.06454 | 0.532272 | − | 0.846574i | \(-0.321338\pi\) | ||||
0.532272 | + | 0.846574i | \(0.321338\pi\) | |||||||
\(762\) | 34.4716 | 1.24878 | ||||||||
\(763\) | −19.9907 | −0.723710 | ||||||||
\(764\) | −94.3580 | −3.41375 | ||||||||
\(765\) | 13.6183 | 0.492370 | ||||||||
\(766\) | −41.6934 | −1.50644 | ||||||||
\(767\) | 13.4195 | 0.484549 | ||||||||
\(768\) | −22.2842 | −0.804110 | ||||||||
\(769\) | −11.4403 | −0.412546 | −0.206273 | − | 0.978494i | \(-0.566134\pi\) | ||||
−0.206273 | + | 0.978494i | \(0.566134\pi\) | |||||||
\(770\) | 13.8917 | 0.500623 | ||||||||
\(771\) | −3.35636 | −0.120876 | ||||||||
\(772\) | −69.2577 | −2.49264 | ||||||||
\(773\) | 29.1548 | 1.04863 | 0.524313 | − | 0.851526i | \(-0.324322\pi\) | ||||
0.524313 | + | 0.851526i | \(0.324322\pi\) | |||||||
\(774\) | 8.90639 | 0.320133 | ||||||||
\(775\) | −5.66747 | −0.203582 | ||||||||
\(776\) | −20.9548 | −0.752233 | ||||||||
\(777\) | −30.7081 | −1.10165 | ||||||||
\(778\) | −13.5182 | −0.484650 | ||||||||
\(779\) | −5.94798 | −0.213108 | ||||||||
\(780\) | −18.5823 | −0.665354 | ||||||||
\(781\) | 1.10903 | 0.0396843 | ||||||||
\(782\) | −33.1745 | −1.18632 | ||||||||
\(783\) | 8.47870 | 0.303004 | ||||||||
\(784\) | 3.13075 | 0.111813 | ||||||||
\(785\) | 31.4682 | 1.12315 | ||||||||
\(786\) | 5.03625 | 0.179637 | ||||||||
\(787\) | −26.9321 | −0.960025 | −0.480013 | − | 0.877262i | \(-0.659368\pi\) | ||||
−0.480013 | + | 0.877262i | \(0.659368\pi\) | |||||||
\(788\) | −43.4926 | −1.54936 | ||||||||
\(789\) | 13.4905 | 0.480276 | ||||||||
\(790\) | −61.3478 | −2.18266 | ||||||||
\(791\) | 54.9441 | 1.95359 | ||||||||
\(792\) | 3.71599 | 0.132042 | ||||||||
\(793\) | 20.6999 | 0.735076 | ||||||||
\(794\) | 48.6026 | 1.72484 | ||||||||
\(795\) | 20.6850 | 0.733621 | ||||||||
\(796\) | 17.9215 | 0.635209 | ||||||||
\(797\) | −25.5458 | −0.904879 | −0.452439 | − | 0.891795i | \(-0.649446\pi\) | ||||
−0.452439 | + | 0.891795i | \(0.649446\pi\) | |||||||
\(798\) | −7.27054 | −0.257374 | ||||||||
\(799\) | 7.73716 | 0.273721 | ||||||||
\(800\) | 8.58008 | 0.303352 | ||||||||
\(801\) | 2.38191 | 0.0841608 | ||||||||
\(802\) | 36.2107 | 1.27865 | ||||||||
\(803\) | 5.15429 | 0.181891 | ||||||||
\(804\) | −3.46438 | −0.122179 | ||||||||
\(805\) | 9.91723 | 0.349537 | ||||||||
\(806\) | 20.6657 | 0.727919 | ||||||||
\(807\) | 0.978366 | 0.0344401 | ||||||||
\(808\) | −26.9331 | −0.947503 | ||||||||
\(809\) | −25.5600 | −0.898642 | −0.449321 | − | 0.893370i | \(-0.648334\pi\) | ||||
−0.449321 | + | 0.893370i | \(0.648334\pi\) | |||||||
\(810\) | −4.06362 | −0.142781 | ||||||||
\(811\) | −21.5151 | −0.755499 | −0.377750 | − | 0.925908i | \(-0.623302\pi\) | ||||
−0.377750 | + | 0.925908i | \(0.623302\pi\) | |||||||
\(812\) | −92.5019 | −3.24618 | ||||||||
\(813\) | −2.39995 | −0.0841699 | ||||||||
\(814\) | 24.7444 | 0.867289 | ||||||||
\(815\) | −33.5607 | −1.17558 | ||||||||
\(816\) | −8.40732 | −0.294315 | ||||||||
\(817\) | 3.76298 | 0.131650 | ||||||||
\(818\) | 54.1946 | 1.89487 | ||||||||
\(819\) | −9.71689 | −0.339536 | ||||||||
\(820\) | 36.2691 | 1.26657 | ||||||||
\(821\) | −26.7518 | −0.933646 | −0.466823 | − | 0.884351i | \(-0.654601\pi\) | ||||
−0.466823 | + | 0.884351i | \(0.654601\pi\) | |||||||
\(822\) | 15.2186 | 0.530811 | ||||||||
\(823\) | −47.0767 | −1.64099 | −0.820495 | − | 0.571654i | \(-0.806302\pi\) | ||||
−0.820495 | + | 0.571654i | \(0.806302\pi\) | |||||||
\(824\) | −26.2287 | −0.913719 | ||||||||
\(825\) | −2.14729 | −0.0747590 | ||||||||
\(826\) | −32.0161 | −1.11398 | ||||||||
\(827\) | −6.63909 | −0.230864 | −0.115432 | − | 0.993315i | \(-0.536825\pi\) | ||||
−0.115432 | + | 0.993315i | \(0.536825\pi\) | |||||||
\(828\) | 6.27595 | 0.218104 | ||||||||
\(829\) | −54.1098 | −1.87931 | −0.939655 | − | 0.342123i | \(-0.888854\pi\) | ||||
−0.939655 | + | 0.342123i | \(0.888854\pi\) | |||||||
\(830\) | 67.2737 | 2.33510 | ||||||||
\(831\) | −15.4674 | −0.536557 | ||||||||
\(832\) | −37.9089 | −1.31426 | ||||||||
\(833\) | −22.8534 | −0.791825 | ||||||||
\(834\) | −36.3606 | −1.25907 | ||||||||
\(835\) | −25.2773 | −0.874757 | ||||||||
\(836\) | 3.71429 | 0.128461 | ||||||||
\(837\) | 2.86515 | 0.0990341 | ||||||||
\(838\) | 8.65937 | 0.299133 | ||||||||
\(839\) | 57.3714 | 1.98068 | 0.990340 | − | 0.138659i | \(-0.0442791\pi\) | ||||
0.990340 | + | 0.138659i | \(0.0442791\pi\) | |||||||
\(840\) | 18.7397 | 0.646582 | ||||||||
\(841\) | 42.8884 | 1.47891 | ||||||||
\(842\) | 11.7402 | 0.404593 | ||||||||
\(843\) | −6.69254 | −0.230503 | ||||||||
\(844\) | −60.2636 | −2.07436 | ||||||||
\(845\) | 6.04849 | 0.208074 | ||||||||
\(846\) | −2.30872 | −0.0793755 | ||||||||
\(847\) | 30.9298 | 1.06276 | ||||||||
\(848\) | −12.7700 | −0.438523 | ||||||||
\(849\) | 20.1770 | 0.692474 | ||||||||
\(850\) | 36.2237 | 1.24246 | ||||||||
\(851\) | 17.6649 | 0.605544 | ||||||||
\(852\) | 3.53933 | 0.121256 | ||||||||
\(853\) | 19.5977 | 0.671013 | 0.335506 | − | 0.942038i | \(-0.391093\pi\) | ||||
0.335506 | + | 0.942038i | \(0.391093\pi\) | |||||||
\(854\) | −49.3858 | −1.68995 | ||||||||
\(855\) | −1.71689 | −0.0587165 | ||||||||
\(856\) | 30.3526 | 1.03743 | ||||||||
\(857\) | 41.6015 | 1.42108 | 0.710540 | − | 0.703657i | \(-0.248451\pi\) | ||||
0.710540 | + | 0.703657i | \(0.248451\pi\) | |||||||
\(858\) | 7.82981 | 0.267305 | ||||||||
\(859\) | −2.98279 | −0.101771 | −0.0508857 | − | 0.998704i | \(-0.516204\pi\) | ||||
−0.0508857 | + | 0.998704i | \(0.516204\pi\) | |||||||
\(860\) | −22.9456 | −0.782438 | ||||||||
\(861\) | 18.9655 | 0.646341 | ||||||||
\(862\) | 10.6832 | 0.363871 | ||||||||
\(863\) | −15.0457 | −0.512162 | −0.256081 | − | 0.966655i | \(-0.582431\pi\) | ||||
−0.256081 | + | 0.966655i | \(0.582431\pi\) | |||||||
\(864\) | −4.33760 | −0.147568 | ||||||||
\(865\) | −22.7812 | −0.774583 | ||||||||
\(866\) | 0.511642 | 0.0173863 | ||||||||
\(867\) | 44.3707 | 1.50691 | ||||||||
\(868\) | −31.2586 | −1.06098 | ||||||||
\(869\) | 16.3883 | 0.555936 | ||||||||
\(870\) | −34.4542 | −1.16811 | ||||||||
\(871\) | −3.08555 | −0.104550 | ||||||||
\(872\) | 21.7299 | 0.735867 | ||||||||
\(873\) | −6.12150 | −0.207181 | ||||||||
\(874\) | 4.18239 | 0.141471 | ||||||||
\(875\) | −38.2008 | −1.29142 | ||||||||
\(876\) | 16.4492 | 0.555769 | ||||||||
\(877\) | −10.5987 | −0.357894 | −0.178947 | − | 0.983859i | \(-0.557269\pi\) | ||||
−0.178947 | + | 0.983859i | \(0.557269\pi\) | |||||||
\(878\) | 10.1558 | 0.342741 | ||||||||
\(879\) | 22.3656 | 0.754372 | ||||||||
\(880\) | −2.02520 | −0.0682695 | ||||||||
\(881\) | 23.5147 | 0.792229 | 0.396114 | − | 0.918201i | \(-0.370358\pi\) | ||||
0.396114 | + | 0.918201i | \(0.370358\pi\) | |||||||
\(882\) | 6.81933 | 0.229619 | ||||||||
\(883\) | −49.9816 | −1.68201 | −0.841007 | − | 0.541025i | \(-0.818036\pi\) | ||||
−0.841007 | + | 0.541025i | \(0.818036\pi\) | |||||||
\(884\) | −83.7411 | −2.81652 | ||||||||
\(885\) | −7.56041 | −0.254140 | ||||||||
\(886\) | 47.9335 | 1.61036 | ||||||||
\(887\) | −19.0088 | −0.638253 | −0.319127 | − | 0.947712i | \(-0.603390\pi\) | ||||
−0.319127 | + | 0.947712i | \(0.603390\pi\) | |||||||
\(888\) | 33.3797 | 1.12015 | ||||||||
\(889\) | −46.4394 | −1.55753 | ||||||||
\(890\) | −9.67918 | −0.324447 | ||||||||
\(891\) | 1.08555 | 0.0363672 | ||||||||
\(892\) | −31.4269 | −1.05225 | ||||||||
\(893\) | −0.975443 | −0.0326420 | ||||||||
\(894\) | −32.9444 | −1.10183 | ||||||||
\(895\) | −39.3665 | −1.31588 | ||||||||
\(896\) | 63.1235 | 2.10881 | ||||||||
\(897\) | 5.58966 | 0.186633 | ||||||||
\(898\) | 29.9892 | 1.00075 | ||||||||
\(899\) | 24.2928 | 0.810209 | ||||||||
\(900\) | −6.85280 | −0.228427 | ||||||||
\(901\) | 93.2166 | 3.10550 | ||||||||
\(902\) | −15.2823 | −0.508843 | ||||||||
\(903\) | −11.9985 | −0.399284 | ||||||||
\(904\) | −59.7244 | −1.98640 | ||||||||
\(905\) | 40.6428 | 1.35101 | ||||||||
\(906\) | 36.4278 | 1.21023 | ||||||||
\(907\) | −45.3796 | −1.50680 | −0.753402 | − | 0.657560i | \(-0.771588\pi\) | ||||
−0.753402 | + | 0.657560i | \(0.771588\pi\) | |||||||
\(908\) | −29.4374 | −0.976915 | ||||||||
\(909\) | −7.86793 | −0.260963 | ||||||||
\(910\) | 39.4857 | 1.30894 | ||||||||
\(911\) | 50.7167 | 1.68032 | 0.840160 | − | 0.542339i | \(-0.182461\pi\) | ||||
0.840160 | + | 0.542339i | \(0.182461\pi\) | |||||||
\(912\) | 1.05993 | 0.0350979 | ||||||||
\(913\) | −17.9714 | −0.594765 | ||||||||
\(914\) | 67.6692 | 2.23830 | ||||||||
\(915\) | −11.6621 | −0.385539 | ||||||||
\(916\) | −54.5182 | −1.80133 | ||||||||
\(917\) | −6.78471 | −0.224051 | ||||||||
\(918\) | −18.3126 | −0.604407 | ||||||||
\(919\) | 28.1853 | 0.929747 | 0.464873 | − | 0.885377i | \(-0.346100\pi\) | ||||
0.464873 | + | 0.885377i | \(0.346100\pi\) | |||||||
\(920\) | −10.7801 | −0.355408 | ||||||||
\(921\) | −12.8565 | −0.423635 | ||||||||
\(922\) | 15.9231 | 0.524399 | ||||||||
\(923\) | 3.15230 | 0.103759 | ||||||||
\(924\) | −11.8432 | −0.389613 | ||||||||
\(925\) | −19.2885 | −0.634202 | ||||||||
\(926\) | −47.3141 | −1.55484 | ||||||||
\(927\) | −7.66215 | −0.251658 | ||||||||
\(928\) | −36.7772 | −1.20727 | ||||||||
\(929\) | −16.2587 | −0.533431 | −0.266716 | − | 0.963775i | \(-0.585938\pi\) | ||||
−0.266716 | + | 0.963775i | \(0.585938\pi\) | |||||||
\(930\) | −11.6429 | −0.381785 | ||||||||
\(931\) | 2.88119 | 0.0944272 | ||||||||
\(932\) | 49.6620 | 1.62673 | ||||||||
\(933\) | −2.33735 | −0.0765215 | ||||||||
\(934\) | −30.6896 | −1.00419 | ||||||||
\(935\) | 14.7833 | 0.483465 | ||||||||
\(936\) | 10.5623 | 0.345239 | ||||||||
\(937\) | −13.6287 | −0.445229 | −0.222615 | − | 0.974906i | \(-0.571459\pi\) | ||||
−0.222615 | + | 0.974906i | \(0.571459\pi\) | |||||||
\(938\) | 7.36149 | 0.240361 | ||||||||
\(939\) | 3.73768 | 0.121975 | ||||||||
\(940\) | 5.94798 | 0.194002 | ||||||||
\(941\) | 53.9031 | 1.75719 | 0.878596 | − | 0.477566i | \(-0.158481\pi\) | ||||
0.878596 | + | 0.477566i | \(0.158481\pi\) | |||||||
\(942\) | −42.3156 | −1.37872 | ||||||||
\(943\) | −10.9099 | −0.355276 | ||||||||
\(944\) | 4.66746 | 0.151913 | ||||||||
\(945\) | 5.47441 | 0.178083 | ||||||||
\(946\) | 9.66830 | 0.314344 | ||||||||
\(947\) | −12.4115 | −0.403321 | −0.201661 | − | 0.979455i | \(-0.564634\pi\) | ||||
−0.201661 | + | 0.979455i | \(0.564634\pi\) | |||||||
\(948\) | 52.3013 | 1.69867 | ||||||||
\(949\) | 14.6505 | 0.475575 | ||||||||
\(950\) | −4.56681 | −0.148167 | ||||||||
\(951\) | −5.08947 | −0.165037 | ||||||||
\(952\) | 84.4504 | 2.73705 | ||||||||
\(953\) | 2.05797 | 0.0666640 | 0.0333320 | − | 0.999444i | \(-0.489388\pi\) | ||||
0.0333320 | + | 0.999444i | \(0.489388\pi\) | |||||||
\(954\) | −27.8153 | −0.900553 | ||||||||
\(955\) | 47.3472 | 1.53212 | ||||||||
\(956\) | 18.3808 | 0.594478 | ||||||||
\(957\) | 9.20403 | 0.297524 | ||||||||
\(958\) | 13.1856 | 0.426007 | ||||||||
\(959\) | −20.5022 | −0.662050 | ||||||||
\(960\) | 21.3576 | 0.689312 | ||||||||
\(961\) | −22.7909 | −0.735190 | ||||||||
\(962\) | 70.3331 | 2.26763 | ||||||||
\(963\) | 8.86688 | 0.285731 | ||||||||
\(964\) | 66.6265 | 2.14589 | ||||||||
\(965\) | 34.7523 | 1.11872 | ||||||||
\(966\) | −13.3358 | −0.429072 | ||||||||
\(967\) | −3.78938 | −0.121858 | −0.0609292 | − | 0.998142i | \(-0.519406\pi\) | ||||
−0.0609292 | + | 0.998142i | \(0.519406\pi\) | |||||||
\(968\) | −33.6208 | −1.08061 | ||||||||
\(969\) | −7.73716 | −0.248553 | ||||||||
\(970\) | 24.8754 | 0.798702 | ||||||||
\(971\) | −48.7908 | −1.56577 | −0.782886 | − | 0.622165i | \(-0.786253\pi\) | ||||
−0.782886 | + | 0.622165i | \(0.786253\pi\) | |||||||
\(972\) | 3.46438 | 0.111120 | ||||||||
\(973\) | 48.9842 | 1.57036 | ||||||||
\(974\) | −52.3202 | −1.67645 | ||||||||
\(975\) | −6.10343 | −0.195466 | ||||||||
\(976\) | 7.19969 | 0.230456 | ||||||||
\(977\) | −6.74735 | −0.215867 | −0.107933 | − | 0.994158i | \(-0.534423\pi\) | ||||
−0.107933 | + | 0.994158i | \(0.534423\pi\) | |||||||
\(978\) | 45.1294 | 1.44308 | ||||||||
\(979\) | 2.58568 | 0.0826386 | ||||||||
\(980\) | −17.5687 | −0.561211 | ||||||||
\(981\) | 6.34792 | 0.202674 | ||||||||
\(982\) | 18.2867 | 0.583553 | ||||||||
\(983\) | −8.27198 | −0.263835 | −0.131918 | − | 0.991261i | \(-0.542113\pi\) | ||||
−0.131918 | + | 0.991261i | \(0.542113\pi\) | |||||||
\(984\) | −20.6155 | −0.657198 | ||||||||
\(985\) | 21.8239 | 0.695367 | ||||||||
\(986\) | −155.267 | −4.94472 | ||||||||
\(987\) | 3.11026 | 0.0990006 | ||||||||
\(988\) | 10.5575 | 0.335877 | ||||||||
\(989\) | 6.90214 | 0.219475 | ||||||||
\(990\) | −4.41125 | −0.140199 | ||||||||
\(991\) | −33.9736 | −1.07921 | −0.539604 | − | 0.841919i | \(-0.681426\pi\) | ||||
−0.539604 | + | 0.841919i | \(0.681426\pi\) | |||||||
\(992\) | −12.4279 | −0.394586 | ||||||||
\(993\) | 22.6794 | 0.719710 | ||||||||
\(994\) | −7.52075 | −0.238544 | ||||||||
\(995\) | −8.99268 | −0.285087 | ||||||||
\(996\) | −57.3533 | −1.81731 | ||||||||
\(997\) | 24.0155 | 0.760579 | 0.380290 | − | 0.924868i | \(-0.375824\pi\) | ||||
0.380290 | + | 0.924868i | \(0.375824\pi\) | |||||||
\(998\) | 79.9157 | 2.52969 | ||||||||
\(999\) | 9.75118 | 0.308514 |
(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 | 201.2.a.e.1.5 | ✓ | 5 | |
3.2 | odd | 2 | 603.2.a.k.1.1 | 5 | |||
4.3 | odd | 2 | 3216.2.a.y.1.2 | 5 | |||
5.4 | even | 2 | 5025.2.a.x.1.1 | 5 | |||
7.6 | odd | 2 | 9849.2.a.bb.1.5 | 5 | |||
12.11 | even | 2 | 9648.2.a.cd.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
201.2.a.e.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
603.2.a.k.1.1 | 5 | 3.2 | odd | 2 | |||
3216.2.a.y.1.2 | 5 | 4.3 | odd | 2 | |||
5025.2.a.x.1.1 | 5 | 5.4 | even | 2 | |||
9648.2.a.cd.1.4 | 5 | 12.11 | even | 2 | |||
9849.2.a.bb.1.5 | 5 | 7.6 | odd | 2 |