Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + \cdots + 2048 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.676512\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.676512 | −0.302546 | −0.151273 | − | 0.988492i | \(-0.548337\pi\) | ||||
−0.151273 | + | 0.988492i | \(0.548337\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.72085 | −1.02838 | −0.514191 | − | 0.857675i | \(-0.671908\pi\) | ||||
−0.514191 | + | 0.857675i | \(0.671908\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.676512 | −0.213932 | ||||||||
\(11\) | −5.27216 | −1.58962 | −0.794809 | − | 0.606860i | \(-0.792429\pi\) | ||||
−0.794809 | + | 0.606860i | \(0.792429\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −2.72085 | −0.727176 | ||||||||
\(15\) | 0.676512 | 0.174675 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.01679 | 0.246609 | 0.123304 | − | 0.992369i | \(-0.460651\pi\) | ||||
0.123304 | + | 0.992369i | \(0.460651\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.84704 | 1.11199 | 0.555994 | − | 0.831186i | \(-0.312338\pi\) | ||||
0.555994 | + | 0.831186i | \(0.312338\pi\) | |||||||
\(20\) | −0.676512 | −0.151273 | ||||||||
\(21\) | 2.72085 | 0.593737 | ||||||||
\(22\) | −5.27216 | −1.12403 | ||||||||
\(23\) | −5.02811 | −1.04843 | −0.524217 | − | 0.851585i | \(-0.675642\pi\) | ||||
−0.524217 | + | 0.851585i | \(0.675642\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.54233 | −0.908466 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.72085 | −0.514191 | ||||||||
\(29\) | 6.30498 | 1.17081 | 0.585403 | − | 0.810743i | \(-0.300936\pi\) | ||||
0.585403 | + | 0.810743i | \(0.300936\pi\) | |||||||
\(30\) | 0.676512 | 0.123514 | ||||||||
\(31\) | −3.04264 | −0.546474 | −0.273237 | − | 0.961947i | \(-0.588094\pi\) | ||||
−0.273237 | + | 0.961947i | \(0.588094\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.27216 | 0.917766 | ||||||||
\(34\) | 1.01679 | 0.174379 | ||||||||
\(35\) | 1.84069 | 0.311133 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.00182 | −0.164698 | −0.0823489 | − | 0.996604i | \(-0.526242\pi\) | ||||
−0.0823489 | + | 0.996604i | \(0.526242\pi\) | |||||||
\(38\) | 4.84704 | 0.786294 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −0.676512 | −0.106966 | ||||||||
\(41\) | 9.67843 | 1.51152 | 0.755759 | − | 0.654850i | \(-0.227268\pi\) | ||||
0.755759 | + | 0.654850i | \(0.227268\pi\) | |||||||
\(42\) | 2.72085 | 0.419836 | ||||||||
\(43\) | −8.83597 | −1.34747 | −0.673737 | − | 0.738972i | \(-0.735312\pi\) | ||||
−0.673737 | + | 0.738972i | \(0.735312\pi\) | |||||||
\(44\) | −5.27216 | −0.794809 | ||||||||
\(45\) | −0.676512 | −0.100849 | ||||||||
\(46\) | −5.02811 | −0.741355 | ||||||||
\(47\) | −8.64110 | −1.26043 | −0.630217 | − | 0.776419i | \(-0.717034\pi\) | ||||
−0.630217 | + | 0.776419i | \(0.717034\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0.402999 | 0.0575712 | ||||||||
\(50\) | −4.54233 | −0.642383 | ||||||||
\(51\) | −1.01679 | −0.142380 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −2.36350 | −0.324652 | −0.162326 | − | 0.986737i | \(-0.551900\pi\) | ||||
−0.162326 | + | 0.986737i | \(0.551900\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 3.56668 | 0.480932 | ||||||||
\(56\) | −2.72085 | −0.363588 | ||||||||
\(57\) | −4.84704 | −0.642006 | ||||||||
\(58\) | 6.30498 | 0.827884 | ||||||||
\(59\) | −13.7006 | −1.78367 | −0.891833 | − | 0.452365i | \(-0.850580\pi\) | ||||
−0.891833 | + | 0.452365i | \(0.850580\pi\) | |||||||
\(60\) | 0.676512 | 0.0873374 | ||||||||
\(61\) | 11.9378 | 1.52848 | 0.764242 | − | 0.644930i | \(-0.223113\pi\) | ||||
0.764242 | + | 0.644930i | \(0.223113\pi\) | |||||||
\(62\) | −3.04264 | −0.386416 | ||||||||
\(63\) | −2.72085 | −0.342794 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.676512 | 0.0839110 | ||||||||
\(66\) | 5.27216 | 0.648959 | ||||||||
\(67\) | 2.97048 | 0.362902 | 0.181451 | − | 0.983400i | \(-0.441921\pi\) | ||||
0.181451 | + | 0.983400i | \(0.441921\pi\) | |||||||
\(68\) | 1.01679 | 0.123304 | ||||||||
\(69\) | 5.02811 | 0.605314 | ||||||||
\(70\) | 1.84069 | 0.220004 | ||||||||
\(71\) | 15.6217 | 1.85395 | 0.926977 | − | 0.375119i | \(-0.122398\pi\) | ||||
0.926977 | + | 0.375119i | \(0.122398\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 1.34277 | 0.157159 | 0.0785796 | − | 0.996908i | \(-0.474962\pi\) | ||||
0.0785796 | + | 0.996908i | \(0.474962\pi\) | |||||||
\(74\) | −1.00182 | −0.116459 | ||||||||
\(75\) | 4.54233 | 0.524503 | ||||||||
\(76\) | 4.84704 | 0.555994 | ||||||||
\(77\) | 14.3447 | 1.63474 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −5.10293 | −0.574125 | −0.287062 | − | 0.957912i | \(-0.592679\pi\) | ||||
−0.287062 | + | 0.957912i | \(0.592679\pi\) | |||||||
\(80\) | −0.676512 | −0.0756364 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 9.67843 | 1.06880 | ||||||||
\(83\) | −0.744233 | −0.0816902 | −0.0408451 | − | 0.999165i | \(-0.513005\pi\) | ||||
−0.0408451 | + | 0.999165i | \(0.513005\pi\) | |||||||
\(84\) | 2.72085 | 0.296869 | ||||||||
\(85\) | −0.687874 | −0.0746104 | ||||||||
\(86\) | −8.83597 | −0.952807 | ||||||||
\(87\) | −6.30498 | −0.675965 | ||||||||
\(88\) | −5.27216 | −0.562015 | ||||||||
\(89\) | 13.8862 | 1.47194 | 0.735969 | − | 0.677016i | \(-0.236727\pi\) | ||||
0.735969 | + | 0.677016i | \(0.236727\pi\) | |||||||
\(90\) | −0.676512 | −0.0713107 | ||||||||
\(91\) | 2.72085 | 0.285222 | ||||||||
\(92\) | −5.02811 | −0.524217 | ||||||||
\(93\) | 3.04264 | 0.315507 | ||||||||
\(94\) | −8.64110 | −0.891262 | ||||||||
\(95\) | −3.27908 | −0.336427 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −2.57742 | −0.261697 | −0.130849 | − | 0.991402i | \(-0.541770\pi\) | ||||
−0.130849 | + | 0.991402i | \(0.541770\pi\) | |||||||
\(98\) | 0.402999 | 0.0407090 | ||||||||
\(99\) | −5.27216 | −0.529873 | ||||||||
\(100\) | −4.54233 | −0.454233 | ||||||||
\(101\) | 8.50857 | 0.846634 | 0.423317 | − | 0.905982i | \(-0.360866\pi\) | ||||
0.423317 | + | 0.905982i | \(0.360866\pi\) | |||||||
\(102\) | −1.01679 | −0.100678 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | −1.84069 | −0.179633 | ||||||||
\(106\) | −2.36350 | −0.229564 | ||||||||
\(107\) | −17.8523 | −1.72585 | −0.862925 | − | 0.505332i | \(-0.831370\pi\) | ||||
−0.862925 | + | 0.505332i | \(0.831370\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −0.493205 | −0.0472405 | −0.0236202 | − | 0.999721i | \(-0.507519\pi\) | ||||
−0.0236202 | + | 0.999721i | \(0.507519\pi\) | |||||||
\(110\) | 3.56668 | 0.340070 | ||||||||
\(111\) | 1.00182 | 0.0950883 | ||||||||
\(112\) | −2.72085 | −0.257096 | ||||||||
\(113\) | −10.3192 | −0.970746 | −0.485373 | − | 0.874307i | \(-0.661316\pi\) | ||||
−0.485373 | + | 0.874307i | \(0.661316\pi\) | |||||||
\(114\) | −4.84704 | −0.453967 | ||||||||
\(115\) | 3.40158 | 0.317199 | ||||||||
\(116\) | 6.30498 | 0.585403 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −13.7006 | −1.26124 | ||||||||
\(119\) | −2.76654 | −0.253608 | ||||||||
\(120\) | 0.676512 | 0.0617568 | ||||||||
\(121\) | 16.7957 | 1.52688 | ||||||||
\(122\) | 11.9378 | 1.08080 | ||||||||
\(123\) | −9.67843 | −0.872675 | ||||||||
\(124\) | −3.04264 | −0.273237 | ||||||||
\(125\) | 6.45551 | 0.577398 | ||||||||
\(126\) | −2.72085 | −0.242392 | ||||||||
\(127\) | 14.1251 | 1.25340 | 0.626698 | − | 0.779262i | \(-0.284406\pi\) | ||||
0.626698 | + | 0.779262i | \(0.284406\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.83597 | 0.777964 | ||||||||
\(130\) | 0.676512 | 0.0593341 | ||||||||
\(131\) | −6.29354 | −0.549870 | −0.274935 | − | 0.961463i | \(-0.588656\pi\) | ||||
−0.274935 | + | 0.961463i | \(0.588656\pi\) | |||||||
\(132\) | 5.27216 | 0.458883 | ||||||||
\(133\) | −13.1881 | −1.14355 | ||||||||
\(134\) | 2.97048 | 0.256611 | ||||||||
\(135\) | 0.676512 | 0.0582249 | ||||||||
\(136\) | 1.01679 | 0.0871893 | ||||||||
\(137\) | −6.42562 | −0.548978 | −0.274489 | − | 0.961590i | \(-0.588509\pi\) | ||||
−0.274489 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(138\) | 5.02811 | 0.428021 | ||||||||
\(139\) | 18.3900 | 1.55982 | 0.779909 | − | 0.625893i | \(-0.215265\pi\) | ||||
0.779909 | + | 0.625893i | \(0.215265\pi\) | |||||||
\(140\) | 1.84069 | 0.155566 | ||||||||
\(141\) | 8.64110 | 0.727712 | ||||||||
\(142\) | 15.6217 | 1.31094 | ||||||||
\(143\) | 5.27216 | 0.440881 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.26540 | −0.354222 | ||||||||
\(146\) | 1.34277 | 0.111128 | ||||||||
\(147\) | −0.402999 | −0.0332388 | ||||||||
\(148\) | −1.00182 | −0.0823489 | ||||||||
\(149\) | 14.0749 | 1.15306 | 0.576531 | − | 0.817075i | \(-0.304406\pi\) | ||||
0.576531 | + | 0.817075i | \(0.304406\pi\) | |||||||
\(150\) | 4.54233 | 0.370880 | ||||||||
\(151\) | 23.4183 | 1.90575 | 0.952877 | − | 0.303358i | \(-0.0981077\pi\) | ||||
0.952877 | + | 0.303358i | \(0.0981077\pi\) | |||||||
\(152\) | 4.84704 | 0.393147 | ||||||||
\(153\) | 1.01679 | 0.0822029 | ||||||||
\(154\) | 14.3447 | 1.15593 | ||||||||
\(155\) | 2.05838 | 0.165333 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | 4.71578 | 0.376360 | 0.188180 | − | 0.982135i | \(-0.439741\pi\) | ||||
0.188180 | + | 0.982135i | \(0.439741\pi\) | |||||||
\(158\) | −5.10293 | −0.405967 | ||||||||
\(159\) | 2.36350 | 0.187438 | ||||||||
\(160\) | −0.676512 | −0.0534830 | ||||||||
\(161\) | 13.6807 | 1.07819 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 14.3157 | 1.12129 | 0.560647 | − | 0.828055i | \(-0.310552\pi\) | ||||
0.560647 | + | 0.828055i | \(0.310552\pi\) | |||||||
\(164\) | 9.67843 | 0.755759 | ||||||||
\(165\) | −3.56668 | −0.277666 | ||||||||
\(166\) | −0.744233 | −0.0577637 | ||||||||
\(167\) | 5.09109 | 0.393960 | 0.196980 | − | 0.980407i | \(-0.436887\pi\) | ||||
0.196980 | + | 0.980407i | \(0.436887\pi\) | |||||||
\(168\) | 2.72085 | 0.209918 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.687874 | −0.0527575 | ||||||||
\(171\) | 4.84704 | 0.370663 | ||||||||
\(172\) | −8.83597 | −0.673737 | ||||||||
\(173\) | 8.23408 | 0.626025 | 0.313013 | − | 0.949749i | \(-0.398662\pi\) | ||||
0.313013 | + | 0.949749i | \(0.398662\pi\) | |||||||
\(174\) | −6.30498 | −0.477979 | ||||||||
\(175\) | 12.3590 | 0.934251 | ||||||||
\(176\) | −5.27216 | −0.397404 | ||||||||
\(177\) | 13.7006 | 1.02980 | ||||||||
\(178\) | 13.8862 | 1.04082 | ||||||||
\(179\) | 21.3025 | 1.59223 | 0.796113 | − | 0.605148i | \(-0.206886\pi\) | ||||
0.796113 | + | 0.605148i | \(0.206886\pi\) | |||||||
\(180\) | −0.676512 | −0.0504243 | ||||||||
\(181\) | 8.88993 | 0.660783 | 0.330392 | − | 0.943844i | \(-0.392819\pi\) | ||||
0.330392 | + | 0.943844i | \(0.392819\pi\) | |||||||
\(182\) | 2.72085 | 0.201682 | ||||||||
\(183\) | −11.9378 | −0.882471 | ||||||||
\(184\) | −5.02811 | −0.370677 | ||||||||
\(185\) | 0.677742 | 0.0498286 | ||||||||
\(186\) | 3.04264 | 0.223097 | ||||||||
\(187\) | −5.36070 | −0.392014 | ||||||||
\(188\) | −8.64110 | −0.630217 | ||||||||
\(189\) | 2.72085 | 0.197912 | ||||||||
\(190\) | −3.27908 | −0.237890 | ||||||||
\(191\) | −11.8651 | −0.858532 | −0.429266 | − | 0.903178i | \(-0.641228\pi\) | ||||
−0.429266 | + | 0.903178i | \(0.641228\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 10.6974 | 0.770019 | 0.385009 | − | 0.922913i | \(-0.374198\pi\) | ||||
0.385009 | + | 0.922913i | \(0.374198\pi\) | |||||||
\(194\) | −2.57742 | −0.185048 | ||||||||
\(195\) | −0.676512 | −0.0484461 | ||||||||
\(196\) | 0.402999 | 0.0287856 | ||||||||
\(197\) | −27.1432 | −1.93387 | −0.966936 | − | 0.255021i | \(-0.917918\pi\) | ||||
−0.966936 | + | 0.255021i | \(0.917918\pi\) | |||||||
\(198\) | −5.27216 | −0.374676 | ||||||||
\(199\) | 16.0741 | 1.13946 | 0.569731 | − | 0.821831i | \(-0.307047\pi\) | ||||
0.569731 | + | 0.821831i | \(0.307047\pi\) | |||||||
\(200\) | −4.54233 | −0.321191 | ||||||||
\(201\) | −2.97048 | −0.209522 | ||||||||
\(202\) | 8.50857 | 0.598661 | ||||||||
\(203\) | −17.1549 | −1.20404 | ||||||||
\(204\) | −1.01679 | −0.0711898 | ||||||||
\(205\) | −6.54758 | −0.457303 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −5.02811 | −0.349478 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −25.5544 | −1.76764 | ||||||||
\(210\) | −1.84069 | −0.127019 | ||||||||
\(211\) | 13.8759 | 0.955258 | 0.477629 | − | 0.878562i | \(-0.341496\pi\) | ||||
0.477629 | + | 0.878562i | \(0.341496\pi\) | |||||||
\(212\) | −2.36350 | −0.162326 | ||||||||
\(213\) | −15.6217 | −1.07038 | ||||||||
\(214\) | −17.8523 | −1.22036 | ||||||||
\(215\) | 5.97765 | 0.407672 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 8.27855 | 0.561985 | ||||||||
\(218\) | −0.493205 | −0.0334041 | ||||||||
\(219\) | −1.34277 | −0.0907359 | ||||||||
\(220\) | 3.56668 | 0.240466 | ||||||||
\(221\) | −1.01679 | −0.0683969 | ||||||||
\(222\) | 1.00182 | 0.0672376 | ||||||||
\(223\) | 3.62805 | 0.242952 | 0.121476 | − | 0.992594i | \(-0.461237\pi\) | ||||
0.121476 | + | 0.992594i | \(0.461237\pi\) | |||||||
\(224\) | −2.72085 | −0.181794 | ||||||||
\(225\) | −4.54233 | −0.302822 | ||||||||
\(226\) | −10.3192 | −0.686421 | ||||||||
\(227\) | 12.8428 | 0.852406 | 0.426203 | − | 0.904627i | \(-0.359851\pi\) | ||||
0.426203 | + | 0.904627i | \(0.359851\pi\) | |||||||
\(228\) | −4.84704 | −0.321003 | ||||||||
\(229\) | 16.1697 | 1.06852 | 0.534261 | − | 0.845320i | \(-0.320590\pi\) | ||||
0.534261 | + | 0.845320i | \(0.320590\pi\) | |||||||
\(230\) | 3.40158 | 0.224294 | ||||||||
\(231\) | −14.3447 | −0.943815 | ||||||||
\(232\) | 6.30498 | 0.413942 | ||||||||
\(233\) | −3.08086 | −0.201834 | −0.100917 | − | 0.994895i | \(-0.532178\pi\) | ||||
−0.100917 | + | 0.994895i | \(0.532178\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 5.84581 | 0.381339 | ||||||||
\(236\) | −13.7006 | −0.891833 | ||||||||
\(237\) | 5.10293 | 0.331471 | ||||||||
\(238\) | −2.76654 | −0.179328 | ||||||||
\(239\) | 16.9163 | 1.09422 | 0.547111 | − | 0.837060i | \(-0.315728\pi\) | ||||
0.547111 | + | 0.837060i | \(0.315728\pi\) | |||||||
\(240\) | 0.676512 | 0.0436687 | ||||||||
\(241\) | −29.6909 | −1.91256 | −0.956281 | − | 0.292450i | \(-0.905530\pi\) | ||||
−0.956281 | + | 0.292450i | \(0.905530\pi\) | |||||||
\(242\) | 16.7957 | 1.07967 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.9378 | 0.764242 | ||||||||
\(245\) | −0.272634 | −0.0174179 | ||||||||
\(246\) | −9.67843 | −0.617074 | ||||||||
\(247\) | −4.84704 | −0.308410 | ||||||||
\(248\) | −3.04264 | −0.193208 | ||||||||
\(249\) | 0.744233 | 0.0471638 | ||||||||
\(250\) | 6.45551 | 0.408282 | ||||||||
\(251\) | −3.96047 | −0.249983 | −0.124991 | − | 0.992158i | \(-0.539890\pi\) | ||||
−0.124991 | + | 0.992158i | \(0.539890\pi\) | |||||||
\(252\) | −2.72085 | −0.171397 | ||||||||
\(253\) | 26.5090 | 1.66661 | ||||||||
\(254\) | 14.1251 | 0.886285 | ||||||||
\(255\) | 0.687874 | 0.0430763 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.3377 | 1.76766 | 0.883828 | − | 0.467812i | \(-0.154957\pi\) | ||||
0.883828 | + | 0.467812i | \(0.154957\pi\) | |||||||
\(258\) | 8.83597 | 0.550104 | ||||||||
\(259\) | 2.72579 | 0.169372 | ||||||||
\(260\) | 0.676512 | 0.0419555 | ||||||||
\(261\) | 6.30498 | 0.390268 | ||||||||
\(262\) | −6.29354 | −0.388817 | ||||||||
\(263\) | −5.13158 | −0.316427 | −0.158213 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158213 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(264\) | 5.27216 | 0.324479 | ||||||||
\(265\) | 1.59894 | 0.0982221 | ||||||||
\(266\) | −13.1881 | −0.808611 | ||||||||
\(267\) | −13.8862 | −0.849823 | ||||||||
\(268\) | 2.97048 | 0.181451 | ||||||||
\(269\) | 4.33267 | 0.264168 | 0.132084 | − | 0.991239i | \(-0.457833\pi\) | ||||
0.132084 | + | 0.991239i | \(0.457833\pi\) | |||||||
\(270\) | 0.676512 | 0.0411712 | ||||||||
\(271\) | −15.4148 | −0.936385 | −0.468193 | − | 0.883626i | \(-0.655095\pi\) | ||||
−0.468193 | + | 0.883626i | \(0.655095\pi\) | |||||||
\(272\) | 1.01679 | 0.0616522 | ||||||||
\(273\) | −2.72085 | −0.164673 | ||||||||
\(274\) | −6.42562 | −0.388186 | ||||||||
\(275\) | 23.9479 | 1.44411 | ||||||||
\(276\) | 5.02811 | 0.302657 | ||||||||
\(277\) | −26.4488 | −1.58915 | −0.794576 | − | 0.607164i | \(-0.792307\pi\) | ||||
−0.794576 | + | 0.607164i | \(0.792307\pi\) | |||||||
\(278\) | 18.3900 | 1.10296 | ||||||||
\(279\) | −3.04264 | −0.182158 | ||||||||
\(280\) | 1.84069 | 0.110002 | ||||||||
\(281\) | −1.70942 | −0.101976 | −0.0509879 | − | 0.998699i | \(-0.516237\pi\) | ||||
−0.0509879 | + | 0.998699i | \(0.516237\pi\) | |||||||
\(282\) | 8.64110 | 0.514570 | ||||||||
\(283\) | −4.39481 | −0.261244 | −0.130622 | − | 0.991432i | \(-0.541697\pi\) | ||||
−0.130622 | + | 0.991432i | \(0.541697\pi\) | |||||||
\(284\) | 15.6217 | 0.926977 | ||||||||
\(285\) | 3.27908 | 0.194236 | ||||||||
\(286\) | 5.27216 | 0.311750 | ||||||||
\(287\) | −26.3335 | −1.55442 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.9661 | −0.939184 | ||||||||
\(290\) | −4.26540 | −0.250473 | ||||||||
\(291\) | 2.57742 | 0.151091 | ||||||||
\(292\) | 1.34277 | 0.0785796 | ||||||||
\(293\) | −2.45624 | −0.143495 | −0.0717475 | − | 0.997423i | \(-0.522858\pi\) | ||||
−0.0717475 | + | 0.997423i | \(0.522858\pi\) | |||||||
\(294\) | −0.402999 | −0.0235034 | ||||||||
\(295\) | 9.26862 | 0.539640 | ||||||||
\(296\) | −1.00182 | −0.0582295 | ||||||||
\(297\) | 5.27216 | 0.305922 | ||||||||
\(298\) | 14.0749 | 0.815338 | ||||||||
\(299\) | 5.02811 | 0.290783 | ||||||||
\(300\) | 4.54233 | 0.262252 | ||||||||
\(301\) | 24.0413 | 1.38572 | ||||||||
\(302\) | 23.4183 | 1.34757 | ||||||||
\(303\) | −8.50857 | −0.488804 | ||||||||
\(304\) | 4.84704 | 0.277997 | ||||||||
\(305\) | −8.07610 | −0.462436 | ||||||||
\(306\) | 1.01679 | 0.0581262 | ||||||||
\(307\) | −11.7261 | −0.669242 | −0.334621 | − | 0.942353i | \(-0.608608\pi\) | ||||
−0.334621 | + | 0.942353i | \(0.608608\pi\) | |||||||
\(308\) | 14.3447 | 0.817368 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 2.05838 | 0.116908 | ||||||||
\(311\) | −1.75340 | −0.0994264 | −0.0497132 | − | 0.998764i | \(-0.515831\pi\) | ||||
−0.0497132 | + | 0.998764i | \(0.515831\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 21.0420 | 1.18936 | 0.594681 | − | 0.803962i | \(-0.297278\pi\) | ||||
0.594681 | + | 0.803962i | \(0.297278\pi\) | |||||||
\(314\) | 4.71578 | 0.266127 | ||||||||
\(315\) | 1.84069 | 0.103711 | ||||||||
\(316\) | −5.10293 | −0.287062 | ||||||||
\(317\) | 25.9164 | 1.45561 | 0.727804 | − | 0.685785i | \(-0.240541\pi\) | ||||
0.727804 | + | 0.685785i | \(0.240541\pi\) | |||||||
\(318\) | 2.36350 | 0.132539 | ||||||||
\(319\) | −33.2409 | −1.86113 | ||||||||
\(320\) | −0.676512 | −0.0378182 | ||||||||
\(321\) | 17.8523 | 0.996420 | ||||||||
\(322\) | 13.6807 | 0.762397 | ||||||||
\(323\) | 4.92844 | 0.274226 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.54233 | 0.251963 | ||||||||
\(326\) | 14.3157 | 0.792875 | ||||||||
\(327\) | 0.493205 | 0.0272743 | ||||||||
\(328\) | 9.67843 | 0.534402 | ||||||||
\(329\) | 23.5111 | 1.29621 | ||||||||
\(330\) | −3.56668 | −0.196340 | ||||||||
\(331\) | −18.0656 | −0.992974 | −0.496487 | − | 0.868044i | \(-0.665377\pi\) | ||||
−0.496487 | + | 0.868044i | \(0.665377\pi\) | |||||||
\(332\) | −0.744233 | −0.0408451 | ||||||||
\(333\) | −1.00182 | −0.0548993 | ||||||||
\(334\) | 5.09109 | 0.278572 | ||||||||
\(335\) | −2.00957 | −0.109794 | ||||||||
\(336\) | 2.72085 | 0.148434 | ||||||||
\(337\) | 1.94031 | 0.105696 | 0.0528478 | − | 0.998603i | \(-0.483170\pi\) | ||||
0.0528478 | + | 0.998603i | \(0.483170\pi\) | |||||||
\(338\) | 1.00000 | 0.0543928 | ||||||||
\(339\) | 10.3192 | 0.560460 | ||||||||
\(340\) | −0.687874 | −0.0373052 | ||||||||
\(341\) | 16.0413 | 0.868685 | ||||||||
\(342\) | 4.84704 | 0.262098 | ||||||||
\(343\) | 17.9494 | 0.969178 | ||||||||
\(344\) | −8.83597 | −0.476404 | ||||||||
\(345\) | −3.40158 | −0.183135 | ||||||||
\(346\) | 8.23408 | 0.442667 | ||||||||
\(347\) | 0.229716 | 0.0123318 | 0.00616590 | − | 0.999981i | \(-0.498037\pi\) | ||||
0.00616590 | + | 0.999981i | \(0.498037\pi\) | |||||||
\(348\) | −6.30498 | −0.337982 | ||||||||
\(349\) | 19.8807 | 1.06419 | 0.532095 | − | 0.846684i | \(-0.321405\pi\) | ||||
0.532095 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(350\) | 12.3590 | 0.660615 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −5.27216 | −0.281007 | ||||||||
\(353\) | −10.2245 | −0.544195 | −0.272098 | − | 0.962270i | \(-0.587717\pi\) | ||||
−0.272098 | + | 0.962270i | \(0.587717\pi\) | |||||||
\(354\) | 13.7006 | 0.728178 | ||||||||
\(355\) | −10.5683 | −0.560905 | ||||||||
\(356\) | 13.8862 | 0.735969 | ||||||||
\(357\) | 2.76654 | 0.146421 | ||||||||
\(358\) | 21.3025 | 1.12587 | ||||||||
\(359\) | −4.10661 | −0.216739 | −0.108369 | − | 0.994111i | \(-0.534563\pi\) | ||||
−0.108369 | + | 0.994111i | \(0.534563\pi\) | |||||||
\(360\) | −0.676512 | −0.0356553 | ||||||||
\(361\) | 4.49382 | 0.236517 | ||||||||
\(362\) | 8.88993 | 0.467244 | ||||||||
\(363\) | −16.7957 | −0.881547 | ||||||||
\(364\) | 2.72085 | 0.142611 | ||||||||
\(365\) | −0.908400 | −0.0475478 | ||||||||
\(366\) | −11.9378 | −0.624001 | ||||||||
\(367\) | 24.2806 | 1.26744 | 0.633718 | − | 0.773564i | \(-0.281528\pi\) | ||||
0.633718 | + | 0.773564i | \(0.281528\pi\) | |||||||
\(368\) | −5.02811 | −0.262109 | ||||||||
\(369\) | 9.67843 | 0.503839 | ||||||||
\(370\) | 0.677742 | 0.0352341 | ||||||||
\(371\) | 6.43073 | 0.333867 | ||||||||
\(372\) | 3.04264 | 0.157754 | ||||||||
\(373\) | −2.09879 | −0.108671 | −0.0543355 | − | 0.998523i | \(-0.517304\pi\) | ||||
−0.0543355 | + | 0.998523i | \(0.517304\pi\) | |||||||
\(374\) | −5.36070 | −0.277195 | ||||||||
\(375\) | −6.45551 | −0.333361 | ||||||||
\(376\) | −8.64110 | −0.445631 | ||||||||
\(377\) | −6.30498 | −0.324723 | ||||||||
\(378\) | 2.72085 | 0.139945 | ||||||||
\(379\) | −2.52123 | −0.129507 | −0.0647534 | − | 0.997901i | \(-0.520626\pi\) | ||||
−0.0647534 | + | 0.997901i | \(0.520626\pi\) | |||||||
\(380\) | −3.27908 | −0.168213 | ||||||||
\(381\) | −14.1251 | −0.723649 | ||||||||
\(382\) | −11.8651 | −0.607074 | ||||||||
\(383\) | 2.79825 | 0.142984 | 0.0714918 | − | 0.997441i | \(-0.477224\pi\) | ||||
0.0714918 | + | 0.997441i | \(0.477224\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −9.70440 | −0.494582 | ||||||||
\(386\) | 10.6974 | 0.544485 | ||||||||
\(387\) | −8.83597 | −0.449158 | ||||||||
\(388\) | −2.57742 | −0.130849 | ||||||||
\(389\) | −21.9755 | −1.11420 | −0.557102 | − | 0.830444i | \(-0.688087\pi\) | ||||
−0.557102 | + | 0.830444i | \(0.688087\pi\) | |||||||
\(390\) | −0.676512 | −0.0342565 | ||||||||
\(391\) | −5.11255 | −0.258553 | ||||||||
\(392\) | 0.402999 | 0.0203545 | ||||||||
\(393\) | 6.29354 | 0.317467 | ||||||||
\(394\) | −27.1432 | −1.36745 | ||||||||
\(395\) | 3.45220 | 0.173699 | ||||||||
\(396\) | −5.27216 | −0.264936 | ||||||||
\(397\) | −18.4038 | −0.923658 | −0.461829 | − | 0.886969i | \(-0.652807\pi\) | ||||
−0.461829 | + | 0.886969i | \(0.652807\pi\) | |||||||
\(398\) | 16.0741 | 0.805721 | ||||||||
\(399\) | 13.1881 | 0.660228 | ||||||||
\(400\) | −4.54233 | −0.227117 | ||||||||
\(401\) | 9.25701 | 0.462273 | 0.231136 | − | 0.972921i | \(-0.425756\pi\) | ||||
0.231136 | + | 0.972921i | \(0.425756\pi\) | |||||||
\(402\) | −2.97048 | −0.148154 | ||||||||
\(403\) | 3.04264 | 0.151565 | ||||||||
\(404\) | 8.50857 | 0.423317 | ||||||||
\(405\) | −0.676512 | −0.0336162 | ||||||||
\(406\) | −17.1549 | −0.851382 | ||||||||
\(407\) | 5.28175 | 0.261807 | ||||||||
\(408\) | −1.01679 | −0.0503388 | ||||||||
\(409\) | −6.19590 | −0.306367 | −0.153184 | − | 0.988198i | \(-0.548953\pi\) | ||||
−0.153184 | + | 0.988198i | \(0.548953\pi\) | |||||||
\(410\) | −6.54758 | −0.323362 | ||||||||
\(411\) | 6.42562 | 0.316952 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 37.2772 | 1.83429 | ||||||||
\(414\) | −5.02811 | −0.247118 | ||||||||
\(415\) | 0.503483 | 0.0247150 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | −18.3900 | −0.900562 | ||||||||
\(418\) | −25.5544 | −1.24991 | ||||||||
\(419\) | 15.4153 | 0.753087 | 0.376543 | − | 0.926399i | \(-0.377113\pi\) | ||||
0.376543 | + | 0.926399i | \(0.377113\pi\) | |||||||
\(420\) | −1.84069 | −0.0898163 | ||||||||
\(421\) | −25.8241 | −1.25859 | −0.629294 | − | 0.777167i | \(-0.716656\pi\) | ||||
−0.629294 | + | 0.777167i | \(0.716656\pi\) | |||||||
\(422\) | 13.8759 | 0.675469 | ||||||||
\(423\) | −8.64110 | −0.420145 | ||||||||
\(424\) | −2.36350 | −0.114782 | ||||||||
\(425\) | −4.61861 | −0.224036 | ||||||||
\(426\) | −15.6217 | −0.756873 | ||||||||
\(427\) | −32.4810 | −1.57187 | ||||||||
\(428\) | −17.8523 | −0.862925 | ||||||||
\(429\) | −5.27216 | −0.254543 | ||||||||
\(430\) | 5.97765 | 0.288268 | ||||||||
\(431\) | −7.57974 | −0.365103 | −0.182552 | − | 0.983196i | \(-0.558436\pi\) | ||||
−0.182552 | + | 0.983196i | \(0.558436\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −16.0633 | −0.771954 | −0.385977 | − | 0.922508i | \(-0.626136\pi\) | ||||
−0.385977 | + | 0.922508i | \(0.626136\pi\) | |||||||
\(434\) | 8.27855 | 0.397383 | ||||||||
\(435\) | 4.26540 | 0.204510 | ||||||||
\(436\) | −0.493205 | −0.0236202 | ||||||||
\(437\) | −24.3715 | −1.16585 | ||||||||
\(438\) | −1.34277 | −0.0641600 | ||||||||
\(439\) | 34.5792 | 1.65037 | 0.825187 | − | 0.564859i | \(-0.191069\pi\) | ||||
0.825187 | + | 0.564859i | \(0.191069\pi\) | |||||||
\(440\) | 3.56668 | 0.170035 | ||||||||
\(441\) | 0.402999 | 0.0191904 | ||||||||
\(442\) | −1.01679 | −0.0483639 | ||||||||
\(443\) | 21.2435 | 1.00931 | 0.504654 | − | 0.863322i | \(-0.331620\pi\) | ||||
0.504654 | + | 0.863322i | \(0.331620\pi\) | |||||||
\(444\) | 1.00182 | 0.0475442 | ||||||||
\(445\) | −9.39420 | −0.445328 | ||||||||
\(446\) | 3.62805 | 0.171793 | ||||||||
\(447\) | −14.0749 | −0.665720 | ||||||||
\(448\) | −2.72085 | −0.128548 | ||||||||
\(449\) | 35.5472 | 1.67757 | 0.838787 | − | 0.544460i | \(-0.183265\pi\) | ||||
0.838787 | + | 0.544460i | \(0.183265\pi\) | |||||||
\(450\) | −4.54233 | −0.214128 | ||||||||
\(451\) | −51.0263 | −2.40273 | ||||||||
\(452\) | −10.3192 | −0.485373 | ||||||||
\(453\) | −23.4183 | −1.10029 | ||||||||
\(454\) | 12.8428 | 0.602742 | ||||||||
\(455\) | −1.84069 | −0.0862927 | ||||||||
\(456\) | −4.84704 | −0.226984 | ||||||||
\(457\) | 24.4777 | 1.14502 | 0.572509 | − | 0.819898i | \(-0.305970\pi\) | ||||
0.572509 | + | 0.819898i | \(0.305970\pi\) | |||||||
\(458\) | 16.1697 | 0.755559 | ||||||||
\(459\) | −1.01679 | −0.0474599 | ||||||||
\(460\) | 3.40158 | 0.158600 | ||||||||
\(461\) | −26.6751 | −1.24238 | −0.621191 | − | 0.783659i | \(-0.713351\pi\) | ||||
−0.621191 | + | 0.783659i | \(0.713351\pi\) | |||||||
\(462\) | −14.3447 | −0.667378 | ||||||||
\(463\) | 7.77420 | 0.361298 | 0.180649 | − | 0.983548i | \(-0.442180\pi\) | ||||
0.180649 | + | 0.983548i | \(0.442180\pi\) | |||||||
\(464\) | 6.30498 | 0.292701 | ||||||||
\(465\) | −2.05838 | −0.0954553 | ||||||||
\(466\) | −3.08086 | −0.142718 | ||||||||
\(467\) | 22.4004 | 1.03657 | 0.518283 | − | 0.855209i | \(-0.326571\pi\) | ||||
0.518283 | + | 0.855209i | \(0.326571\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −8.08222 | −0.373202 | ||||||||
\(470\) | 5.84581 | 0.269647 | ||||||||
\(471\) | −4.71578 | −0.217292 | ||||||||
\(472\) | −13.7006 | −0.630621 | ||||||||
\(473\) | 46.5847 | 2.14197 | ||||||||
\(474\) | 5.10293 | 0.234385 | ||||||||
\(475\) | −22.0169 | −1.01020 | ||||||||
\(476\) | −2.76654 | −0.126804 | ||||||||
\(477\) | −2.36350 | −0.108217 | ||||||||
\(478\) | 16.9163 | 0.773731 | ||||||||
\(479\) | −38.0641 | −1.73919 | −0.869597 | − | 0.493762i | \(-0.835621\pi\) | ||||
−0.869597 | + | 0.493762i | \(0.835621\pi\) | |||||||
\(480\) | 0.676512 | 0.0308784 | ||||||||
\(481\) | 1.00182 | 0.0456790 | ||||||||
\(482\) | −29.6909 | −1.35239 | ||||||||
\(483\) | −13.6807 | −0.622494 | ||||||||
\(484\) | 16.7957 | 0.763442 | ||||||||
\(485\) | 1.74366 | 0.0791754 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 17.7607 | 0.804815 | 0.402408 | − | 0.915461i | \(-0.368173\pi\) | ||||
0.402408 | + | 0.915461i | \(0.368173\pi\) | |||||||
\(488\) | 11.9378 | 0.540401 | ||||||||
\(489\) | −14.3157 | −0.647380 | ||||||||
\(490\) | −0.272634 | −0.0123163 | ||||||||
\(491\) | −31.1190 | −1.40438 | −0.702191 | − | 0.711989i | \(-0.747795\pi\) | ||||
−0.702191 | + | 0.711989i | \(0.747795\pi\) | |||||||
\(492\) | −9.67843 | −0.436337 | ||||||||
\(493\) | 6.41086 | 0.288731 | ||||||||
\(494\) | −4.84704 | −0.218079 | ||||||||
\(495\) | 3.56668 | 0.160311 | ||||||||
\(496\) | −3.04264 | −0.136619 | ||||||||
\(497\) | −42.5042 | −1.90657 | ||||||||
\(498\) | 0.744233 | 0.0333499 | ||||||||
\(499\) | 15.2463 | 0.682517 | 0.341258 | − | 0.939970i | \(-0.389147\pi\) | ||||
0.341258 | + | 0.939970i | \(0.389147\pi\) | |||||||
\(500\) | 6.45551 | 0.288699 | ||||||||
\(501\) | −5.09109 | −0.227453 | ||||||||
\(502\) | −3.96047 | −0.176764 | ||||||||
\(503\) | −42.7565 | −1.90642 | −0.953210 | − | 0.302310i | \(-0.902242\pi\) | ||||
−0.953210 | + | 0.302310i | \(0.902242\pi\) | |||||||
\(504\) | −2.72085 | −0.121196 | ||||||||
\(505\) | −5.75615 | −0.256145 | ||||||||
\(506\) | 26.5090 | 1.17847 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 14.1251 | 0.626698 | ||||||||
\(509\) | −11.1467 | −0.494069 | −0.247035 | − | 0.969007i | \(-0.579456\pi\) | ||||
−0.247035 | + | 0.969007i | \(0.579456\pi\) | |||||||
\(510\) | 0.687874 | 0.0304596 | ||||||||
\(511\) | −3.65347 | −0.161620 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.84704 | −0.214002 | ||||||||
\(514\) | 28.3377 | 1.24992 | ||||||||
\(515\) | 0.676512 | 0.0298107 | ||||||||
\(516\) | 8.83597 | 0.388982 | ||||||||
\(517\) | 45.5573 | 2.00361 | ||||||||
\(518\) | 2.72579 | 0.119764 | ||||||||
\(519\) | −8.23408 | −0.361436 | ||||||||
\(520\) | 0.676512 | 0.0296670 | ||||||||
\(521\) | 31.2470 | 1.36896 | 0.684479 | − | 0.729033i | \(-0.260030\pi\) | ||||
0.684479 | + | 0.729033i | \(0.260030\pi\) | |||||||
\(522\) | 6.30498 | 0.275961 | ||||||||
\(523\) | 8.46338 | 0.370078 | 0.185039 | − | 0.982731i | \(-0.440759\pi\) | ||||
0.185039 | + | 0.982731i | \(0.440759\pi\) | |||||||
\(524\) | −6.29354 | −0.274935 | ||||||||
\(525\) | −12.3590 | −0.539390 | ||||||||
\(526\) | −5.13158 | −0.223748 | ||||||||
\(527\) | −3.09374 | −0.134765 | ||||||||
\(528\) | 5.27216 | 0.229442 | ||||||||
\(529\) | 2.28192 | 0.0992141 | ||||||||
\(530\) | 1.59894 | 0.0694535 | ||||||||
\(531\) | −13.7006 | −0.594555 | ||||||||
\(532\) | −13.1881 | −0.571775 | ||||||||
\(533\) | −9.67843 | −0.419219 | ||||||||
\(534\) | −13.8862 | −0.600916 | ||||||||
\(535\) | 12.0773 | 0.522148 | ||||||||
\(536\) | 2.97048 | 0.128305 | ||||||||
\(537\) | −21.3025 | −0.919272 | ||||||||
\(538\) | 4.33267 | 0.186795 | ||||||||
\(539\) | −2.12468 | −0.0915162 | ||||||||
\(540\) | 0.676512 | 0.0291125 | ||||||||
\(541\) | −12.8504 | −0.552480 | −0.276240 | − | 0.961089i | \(-0.589088\pi\) | ||||
−0.276240 | + | 0.961089i | \(0.589088\pi\) | |||||||
\(542\) | −15.4148 | −0.662124 | ||||||||
\(543\) | −8.88993 | −0.381503 | ||||||||
\(544\) | 1.01679 | 0.0435947 | ||||||||
\(545\) | 0.333659 | 0.0142924 | ||||||||
\(546\) | −2.72085 | −0.116441 | ||||||||
\(547\) | −11.5043 | −0.491888 | −0.245944 | − | 0.969284i | \(-0.579098\pi\) | ||||
−0.245944 | + | 0.969284i | \(0.579098\pi\) | |||||||
\(548\) | −6.42562 | −0.274489 | ||||||||
\(549\) | 11.9378 | 0.509495 | ||||||||
\(550\) | 23.9479 | 1.02114 | ||||||||
\(551\) | 30.5605 | 1.30192 | ||||||||
\(552\) | 5.02811 | 0.214011 | ||||||||
\(553\) | 13.8843 | 0.590420 | ||||||||
\(554\) | −26.4488 | −1.12370 | ||||||||
\(555\) | −0.677742 | −0.0287686 | ||||||||
\(556\) | 18.3900 | 0.779909 | ||||||||
\(557\) | −37.2435 | −1.57806 | −0.789028 | − | 0.614357i | \(-0.789416\pi\) | ||||
−0.789028 | + | 0.614357i | \(0.789416\pi\) | |||||||
\(558\) | −3.04264 | −0.128805 | ||||||||
\(559\) | 8.83597 | 0.373722 | ||||||||
\(560\) | 1.84069 | 0.0777832 | ||||||||
\(561\) | 5.36070 | 0.226329 | ||||||||
\(562\) | −1.70942 | −0.0721077 | ||||||||
\(563\) | −13.2837 | −0.559841 | −0.279920 | − | 0.960023i | \(-0.590308\pi\) | ||||
−0.279920 | + | 0.960023i | \(0.590308\pi\) | |||||||
\(564\) | 8.64110 | 0.363856 | ||||||||
\(565\) | 6.98104 | 0.293695 | ||||||||
\(566\) | −4.39481 | −0.184728 | ||||||||
\(567\) | −2.72085 | −0.114265 | ||||||||
\(568\) | 15.6217 | 0.655472 | ||||||||
\(569\) | −4.29722 | −0.180149 | −0.0900745 | − | 0.995935i | \(-0.528711\pi\) | ||||
−0.0900745 | + | 0.995935i | \(0.528711\pi\) | |||||||
\(570\) | 3.27908 | 0.137346 | ||||||||
\(571\) | 43.0999 | 1.80368 | 0.901838 | − | 0.432074i | \(-0.142218\pi\) | ||||
0.901838 | + | 0.432074i | \(0.142218\pi\) | |||||||
\(572\) | 5.27216 | 0.220440 | ||||||||
\(573\) | 11.8651 | 0.495674 | ||||||||
\(574\) | −26.3335 | −1.09914 | ||||||||
\(575\) | 22.8394 | 0.952467 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 17.0048 | 0.707918 | 0.353959 | − | 0.935261i | \(-0.384835\pi\) | ||||
0.353959 | + | 0.935261i | \(0.384835\pi\) | |||||||
\(578\) | −15.9661 | −0.664103 | ||||||||
\(579\) | −10.6974 | −0.444570 | ||||||||
\(580\) | −4.26540 | −0.177111 | ||||||||
\(581\) | 2.02494 | 0.0840088 | ||||||||
\(582\) | 2.57742 | 0.106838 | ||||||||
\(583\) | 12.4608 | 0.516073 | ||||||||
\(584\) | 1.34277 | 0.0555642 | ||||||||
\(585\) | 0.676512 | 0.0279703 | ||||||||
\(586\) | −2.45624 | −0.101466 | ||||||||
\(587\) | −0.310300 | −0.0128075 | −0.00640373 | − | 0.999979i | \(-0.502038\pi\) | ||||
−0.00640373 | + | 0.999979i | \(0.502038\pi\) | |||||||
\(588\) | −0.402999 | −0.0166194 | ||||||||
\(589\) | −14.7478 | −0.607673 | ||||||||
\(590\) | 9.26862 | 0.381583 | ||||||||
\(591\) | 27.1432 | 1.11652 | ||||||||
\(592\) | −1.00182 | −0.0411745 | ||||||||
\(593\) | 34.7530 | 1.42714 | 0.713568 | − | 0.700586i | \(-0.247078\pi\) | ||||
0.713568 | + | 0.700586i | \(0.247078\pi\) | |||||||
\(594\) | 5.27216 | 0.216320 | ||||||||
\(595\) | 1.87160 | 0.0767280 | ||||||||
\(596\) | 14.0749 | 0.576531 | ||||||||
\(597\) | −16.0741 | −0.657868 | ||||||||
\(598\) | 5.02811 | 0.205615 | ||||||||
\(599\) | −19.2572 | −0.786827 | −0.393414 | − | 0.919362i | \(-0.628706\pi\) | ||||
−0.393414 | + | 0.919362i | \(0.628706\pi\) | |||||||
\(600\) | 4.54233 | 0.185440 | ||||||||
\(601\) | −16.5213 | −0.673917 | −0.336959 | − | 0.941519i | \(-0.609398\pi\) | ||||
−0.336959 | + | 0.941519i | \(0.609398\pi\) | |||||||
\(602\) | 24.0413 | 0.979851 | ||||||||
\(603\) | 2.97048 | 0.120967 | ||||||||
\(604\) | 23.4183 | 0.952877 | ||||||||
\(605\) | −11.3625 | −0.461952 | ||||||||
\(606\) | −8.50857 | −0.345637 | ||||||||
\(607\) | −1.62313 | −0.0658809 | −0.0329404 | − | 0.999457i | \(-0.510487\pi\) | ||||
−0.0329404 | + | 0.999457i | \(0.510487\pi\) | |||||||
\(608\) | 4.84704 | 0.196574 | ||||||||
\(609\) | 17.1549 | 0.695151 | ||||||||
\(610\) | −8.07610 | −0.326992 | ||||||||
\(611\) | 8.64110 | 0.349582 | ||||||||
\(612\) | 1.01679 | 0.0411015 | ||||||||
\(613\) | 29.4693 | 1.19025 | 0.595127 | − | 0.803632i | \(-0.297102\pi\) | ||||
0.595127 | + | 0.803632i | \(0.297102\pi\) | |||||||
\(614\) | −11.7261 | −0.473225 | ||||||||
\(615\) | 6.54758 | 0.264024 | ||||||||
\(616\) | 14.3447 | 0.577966 | ||||||||
\(617\) | −9.07021 | −0.365153 | −0.182576 | − | 0.983192i | \(-0.558444\pi\) | ||||
−0.182576 | + | 0.983192i | \(0.558444\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −4.18897 | −0.168369 | −0.0841845 | − | 0.996450i | \(-0.526829\pi\) | ||||
−0.0841845 | + | 0.996450i | \(0.526829\pi\) | |||||||
\(620\) | 2.05838 | 0.0826667 | ||||||||
\(621\) | 5.02811 | 0.201771 | ||||||||
\(622\) | −1.75340 | −0.0703051 | ||||||||
\(623\) | −37.7823 | −1.51371 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 18.3444 | 0.733777 | ||||||||
\(626\) | 21.0420 | 0.841006 | ||||||||
\(627\) | 25.5544 | 1.02054 | ||||||||
\(628\) | 4.71578 | 0.188180 | ||||||||
\(629\) | −1.01864 | −0.0406159 | ||||||||
\(630\) | 1.84069 | 0.0733347 | ||||||||
\(631\) | −15.6492 | −0.622986 | −0.311493 | − | 0.950248i | \(-0.600829\pi\) | ||||
−0.311493 | + | 0.950248i | \(0.600829\pi\) | |||||||
\(632\) | −5.10293 | −0.202984 | ||||||||
\(633\) | −13.8759 | −0.551519 | ||||||||
\(634\) | 25.9164 | 1.02927 | ||||||||
\(635\) | −9.55578 | −0.379210 | ||||||||
\(636\) | 2.36350 | 0.0937191 | ||||||||
\(637\) | −0.402999 | −0.0159674 | ||||||||
\(638\) | −33.2409 | −1.31602 | ||||||||
\(639\) | 15.6217 | 0.617985 | ||||||||
\(640\) | −0.676512 | −0.0267415 | ||||||||
\(641\) | −6.08581 | −0.240375 | −0.120187 | − | 0.992751i | \(-0.538350\pi\) | ||||
−0.120187 | + | 0.992751i | \(0.538350\pi\) | |||||||
\(642\) | 17.8523 | 0.704575 | ||||||||
\(643\) | 20.2998 | 0.800545 | 0.400273 | − | 0.916396i | \(-0.368915\pi\) | ||||
0.400273 | + | 0.916396i | \(0.368915\pi\) | |||||||
\(644\) | 13.6807 | 0.539096 | ||||||||
\(645\) | −5.97765 | −0.235370 | ||||||||
\(646\) | 4.92844 | 0.193907 | ||||||||
\(647\) | −40.1434 | −1.57820 | −0.789100 | − | 0.614264i | \(-0.789453\pi\) | ||||
−0.789100 | + | 0.614264i | \(0.789453\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 72.2318 | 2.83535 | ||||||||
\(650\) | 4.54233 | 0.178165 | ||||||||
\(651\) | −8.27855 | −0.324462 | ||||||||
\(652\) | 14.3157 | 0.560647 | ||||||||
\(653\) | −9.92143 | −0.388256 | −0.194128 | − | 0.980976i | \(-0.562188\pi\) | ||||
−0.194128 | + | 0.980976i | \(0.562188\pi\) | |||||||
\(654\) | 0.493205 | 0.0192858 | ||||||||
\(655\) | 4.25766 | 0.166361 | ||||||||
\(656\) | 9.67843 | 0.377879 | ||||||||
\(657\) | 1.34277 | 0.0523864 | ||||||||
\(658\) | 23.5111 | 0.916558 | ||||||||
\(659\) | −3.80652 | −0.148281 | −0.0741405 | − | 0.997248i | \(-0.523621\pi\) | ||||
−0.0741405 | + | 0.997248i | \(0.523621\pi\) | |||||||
\(660\) | −3.56668 | −0.138833 | ||||||||
\(661\) | −0.560567 | −0.0218035 | −0.0109018 | − | 0.999941i | \(-0.503470\pi\) | ||||
−0.0109018 | + | 0.999941i | \(0.503470\pi\) | |||||||
\(662\) | −18.0656 | −0.702138 | ||||||||
\(663\) | 1.01679 | 0.0394890 | ||||||||
\(664\) | −0.744233 | −0.0288818 | ||||||||
\(665\) | 8.92188 | 0.345976 | ||||||||
\(666\) | −1.00182 | −0.0388197 | ||||||||
\(667\) | −31.7022 | −1.22751 | ||||||||
\(668\) | 5.09109 | 0.196980 | ||||||||
\(669\) | −3.62805 | −0.140269 | ||||||||
\(670\) | −2.00957 | −0.0776364 | ||||||||
\(671\) | −62.9383 | −2.42970 | ||||||||
\(672\) | 2.72085 | 0.104959 | ||||||||
\(673\) | 13.2680 | 0.511444 | 0.255722 | − | 0.966750i | \(-0.417687\pi\) | ||||
0.255722 | + | 0.966750i | \(0.417687\pi\) | |||||||
\(674\) | 1.94031 | 0.0747381 | ||||||||
\(675\) | 4.54233 | 0.174834 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 28.8453 | 1.10861 | 0.554307 | − | 0.832312i | \(-0.312983\pi\) | ||||
0.554307 | + | 0.832312i | \(0.312983\pi\) | |||||||
\(678\) | 10.3192 | 0.396305 | ||||||||
\(679\) | 7.01276 | 0.269125 | ||||||||
\(680\) | −0.687874 | −0.0263787 | ||||||||
\(681\) | −12.8428 | −0.492137 | ||||||||
\(682\) | 16.0413 | 0.614253 | ||||||||
\(683\) | 6.72659 | 0.257386 | 0.128693 | − | 0.991684i | \(-0.458922\pi\) | ||||
0.128693 | + | 0.991684i | \(0.458922\pi\) | |||||||
\(684\) | 4.84704 | 0.185331 | ||||||||
\(685\) | 4.34701 | 0.166091 | ||||||||
\(686\) | 17.9494 | 0.685312 | ||||||||
\(687\) | −16.1697 | −0.616911 | ||||||||
\(688\) | −8.83597 | −0.336868 | ||||||||
\(689\) | 2.36350 | 0.0900424 | ||||||||
\(690\) | −3.40158 | −0.129496 | ||||||||
\(691\) | 11.4509 | 0.435612 | 0.217806 | − | 0.975992i | \(-0.430110\pi\) | ||||
0.217806 | + | 0.975992i | \(0.430110\pi\) | |||||||
\(692\) | 8.23408 | 0.313013 | ||||||||
\(693\) | 14.3447 | 0.544912 | ||||||||
\(694\) | 0.229716 | 0.00871990 | ||||||||
\(695\) | −12.4411 | −0.471916 | ||||||||
\(696\) | −6.30498 | −0.238990 | ||||||||
\(697\) | 9.84097 | 0.372753 | ||||||||
\(698\) | 19.8807 | 0.752497 | ||||||||
\(699\) | 3.08086 | 0.116529 | ||||||||
\(700\) | 12.3590 | 0.467126 | ||||||||
\(701\) | 41.0431 | 1.55018 | 0.775088 | − | 0.631853i | \(-0.217705\pi\) | ||||
0.775088 | + | 0.631853i | \(0.217705\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −4.85585 | −0.183142 | ||||||||
\(704\) | −5.27216 | −0.198702 | ||||||||
\(705\) | −5.84581 | −0.220166 | ||||||||
\(706\) | −10.2245 | −0.384804 | ||||||||
\(707\) | −23.1505 | −0.870664 | ||||||||
\(708\) | 13.7006 | 0.514900 | ||||||||
\(709\) | 25.2166 | 0.947030 | 0.473515 | − | 0.880786i | \(-0.342985\pi\) | ||||
0.473515 | + | 0.880786i | \(0.342985\pi\) | |||||||
\(710\) | −10.5683 | −0.396620 | ||||||||
\(711\) | −5.10293 | −0.191375 | ||||||||
\(712\) | 13.8862 | 0.520408 | ||||||||
\(713\) | 15.2987 | 0.572942 | ||||||||
\(714\) | 2.76654 | 0.103535 | ||||||||
\(715\) | −3.56668 | −0.133386 | ||||||||
\(716\) | 21.3025 | 0.796113 | ||||||||
\(717\) | −16.9163 | −0.631749 | ||||||||
\(718\) | −4.10661 | −0.153257 | ||||||||
\(719\) | −22.2351 | −0.829231 | −0.414616 | − | 0.909997i | \(-0.636084\pi\) | ||||
−0.414616 | + | 0.909997i | \(0.636084\pi\) | |||||||
\(720\) | −0.676512 | −0.0252121 | ||||||||
\(721\) | 2.72085 | 0.101330 | ||||||||
\(722\) | 4.49382 | 0.167243 | ||||||||
\(723\) | 29.6909 | 1.10422 | ||||||||
\(724\) | 8.88993 | 0.330392 | ||||||||
\(725\) | −28.6393 | −1.06364 | ||||||||
\(726\) | −16.7957 | −0.623348 | ||||||||
\(727\) | −30.4872 | −1.13071 | −0.565354 | − | 0.824848i | \(-0.691260\pi\) | ||||
−0.565354 | + | 0.824848i | \(0.691260\pi\) | |||||||
\(728\) | 2.72085 | 0.100841 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.908400 | −0.0336214 | ||||||||
\(731\) | −8.98436 | −0.332299 | ||||||||
\(732\) | −11.9378 | −0.441235 | ||||||||
\(733\) | −41.4654 | −1.53156 | −0.765780 | − | 0.643103i | \(-0.777647\pi\) | ||||
−0.765780 | + | 0.643103i | \(0.777647\pi\) | |||||||
\(734\) | 24.2806 | 0.896212 | ||||||||
\(735\) | 0.272634 | 0.0100562 | ||||||||
\(736\) | −5.02811 | −0.185339 | ||||||||
\(737\) | −15.6609 | −0.576876 | ||||||||
\(738\) | 9.67843 | 0.356268 | ||||||||
\(739\) | 50.7684 | 1.86755 | 0.933773 | − | 0.357866i | \(-0.116495\pi\) | ||||
0.933773 | + | 0.357866i | \(0.116495\pi\) | |||||||
\(740\) | 0.677742 | 0.0249143 | ||||||||
\(741\) | 4.84704 | 0.178061 | ||||||||
\(742\) | 6.43073 | 0.236080 | ||||||||
\(743\) | 15.2433 | 0.559223 | 0.279611 | − | 0.960113i | \(-0.409794\pi\) | ||||
0.279611 | + | 0.960113i | \(0.409794\pi\) | |||||||
\(744\) | 3.04264 | 0.111549 | ||||||||
\(745\) | −9.52185 | −0.348854 | ||||||||
\(746\) | −2.09879 | −0.0768421 | ||||||||
\(747\) | −0.744233 | −0.0272301 | ||||||||
\(748\) | −5.36070 | −0.196007 | ||||||||
\(749\) | 48.5734 | 1.77483 | ||||||||
\(750\) | −6.45551 | −0.235722 | ||||||||
\(751\) | 12.7402 | 0.464898 | 0.232449 | − | 0.972609i | \(-0.425326\pi\) | ||||
0.232449 | + | 0.972609i | \(0.425326\pi\) | |||||||
\(752\) | −8.64110 | −0.315109 | ||||||||
\(753\) | 3.96047 | 0.144328 | ||||||||
\(754\) | −6.30498 | −0.229614 | ||||||||
\(755\) | −15.8428 | −0.576577 | ||||||||
\(756\) | 2.72085 | 0.0989562 | ||||||||
\(757\) | 15.1143 | 0.549337 | 0.274668 | − | 0.961539i | \(-0.411432\pi\) | ||||
0.274668 | + | 0.961539i | \(0.411432\pi\) | |||||||
\(758\) | −2.52123 | −0.0915752 | ||||||||
\(759\) | −26.5090 | −0.962217 | ||||||||
\(760\) | −3.27908 | −0.118945 | ||||||||
\(761\) | 7.05638 | 0.255794 | 0.127897 | − | 0.991787i | \(-0.459177\pi\) | ||||
0.127897 | + | 0.991787i | \(0.459177\pi\) | |||||||
\(762\) | −14.1251 | −0.511697 | ||||||||
\(763\) | 1.34193 | 0.0485813 | ||||||||
\(764\) | −11.8651 | −0.429266 | ||||||||
\(765\) | −0.687874 | −0.0248701 | ||||||||
\(766\) | 2.79825 | 0.101105 | ||||||||
\(767\) | 13.7006 | 0.494700 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 15.4429 | 0.556887 | 0.278443 | − | 0.960453i | \(-0.410182\pi\) | ||||
0.278443 | + | 0.960453i | \(0.410182\pi\) | |||||||
\(770\) | −9.70440 | −0.349722 | ||||||||
\(771\) | −28.3377 | −1.02056 | ||||||||
\(772\) | 10.6974 | 0.385009 | ||||||||
\(773\) | −8.93806 | −0.321480 | −0.160740 | − | 0.986997i | \(-0.551388\pi\) | ||||
−0.160740 | + | 0.986997i | \(0.551388\pi\) | |||||||
\(774\) | −8.83597 | −0.317602 | ||||||||
\(775\) | 13.8207 | 0.496453 | ||||||||
\(776\) | −2.57742 | −0.0925240 | ||||||||
\(777\) | −2.72579 | −0.0977872 | ||||||||
\(778\) | −21.9755 | −0.787861 | ||||||||
\(779\) | 46.9118 | 1.68079 | ||||||||
\(780\) | −0.676512 | −0.0242230 | ||||||||
\(781\) | −82.3601 | −2.94708 | ||||||||
\(782\) | −5.11255 | −0.182825 | ||||||||
\(783\) | −6.30498 | −0.225322 | ||||||||
\(784\) | 0.402999 | 0.0143928 | ||||||||
\(785\) | −3.19028 | −0.113866 | ||||||||
\(786\) | 6.29354 | 0.224483 | ||||||||
\(787\) | 54.3035 | 1.93571 | 0.967856 | − | 0.251507i | \(-0.0809261\pi\) | ||||
0.967856 | + | 0.251507i | \(0.0809261\pi\) | |||||||
\(788\) | −27.1432 | −0.966936 | ||||||||
\(789\) | 5.13158 | 0.182689 | ||||||||
\(790\) | 3.45220 | 0.122824 | ||||||||
\(791\) | 28.0769 | 0.998298 | ||||||||
\(792\) | −5.27216 | −0.187338 | ||||||||
\(793\) | −11.9378 | −0.423925 | ||||||||
\(794\) | −18.4038 | −0.653125 | ||||||||
\(795\) | −1.59894 | −0.0567086 | ||||||||
\(796\) | 16.0741 | 0.569731 | ||||||||
\(797\) | 38.1146 | 1.35009 | 0.675044 | − | 0.737778i | \(-0.264125\pi\) | ||||
0.675044 | + | 0.737778i | \(0.264125\pi\) | |||||||
\(798\) | 13.1881 | 0.466852 | ||||||||
\(799\) | −8.78622 | −0.310834 | ||||||||
\(800\) | −4.54233 | −0.160596 | ||||||||
\(801\) | 13.8862 | 0.490646 | ||||||||
\(802\) | 9.25701 | 0.326876 | ||||||||
\(803\) | −7.07930 | −0.249823 | ||||||||
\(804\) | −2.97048 | −0.104761 | ||||||||
\(805\) | −9.25518 | −0.326202 | ||||||||
\(806\) | 3.04264 | 0.107172 | ||||||||
\(807\) | −4.33267 | −0.152517 | ||||||||
\(808\) | 8.50857 | 0.299330 | ||||||||
\(809\) | −39.7580 | −1.39782 | −0.698909 | − | 0.715211i | \(-0.746331\pi\) | ||||
−0.698909 | + | 0.715211i | \(0.746331\pi\) | |||||||
\(810\) | −0.676512 | −0.0237702 | ||||||||
\(811\) | 37.2157 | 1.30682 | 0.653410 | − | 0.757004i | \(-0.273338\pi\) | ||||
0.653410 | + | 0.757004i | \(0.273338\pi\) | |||||||
\(812\) | −17.1549 | −0.602018 | ||||||||
\(813\) | 15.4148 | 0.540622 | ||||||||
\(814\) | 5.28175 | 0.185125 | ||||||||
\(815\) | −9.68477 | −0.339243 | ||||||||
\(816\) | −1.01679 | −0.0355949 | ||||||||
\(817\) | −42.8283 | −1.49837 | ||||||||
\(818\) | −6.19590 | −0.216635 | ||||||||
\(819\) | 2.72085 | 0.0950740 | ||||||||
\(820\) | −6.54758 | −0.228651 | ||||||||
\(821\) | 21.1159 | 0.736952 | 0.368476 | − | 0.929637i | \(-0.379880\pi\) | ||||
0.368476 | + | 0.929637i | \(0.379880\pi\) | |||||||
\(822\) | 6.42562 | 0.224119 | ||||||||
\(823\) | −33.4694 | −1.16667 | −0.583335 | − | 0.812232i | \(-0.698252\pi\) | ||||
−0.583335 | + | 0.812232i | \(0.698252\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | −23.9479 | −0.833759 | ||||||||
\(826\) | 37.2772 | 1.29704 | ||||||||
\(827\) | −25.7208 | −0.894401 | −0.447201 | − | 0.894434i | \(-0.647579\pi\) | ||||
−0.447201 | + | 0.894434i | \(0.647579\pi\) | |||||||
\(828\) | −5.02811 | −0.174739 | ||||||||
\(829\) | −22.7542 | −0.790286 | −0.395143 | − | 0.918620i | \(-0.629305\pi\) | ||||
−0.395143 | + | 0.918620i | \(0.629305\pi\) | |||||||
\(830\) | 0.503483 | 0.0174761 | ||||||||
\(831\) | 26.4488 | 0.917498 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 0.409766 | 0.0141976 | ||||||||
\(834\) | −18.3900 | −0.636793 | ||||||||
\(835\) | −3.44419 | −0.119191 | ||||||||
\(836\) | −25.5544 | −0.883818 | ||||||||
\(837\) | 3.04264 | 0.105169 | ||||||||
\(838\) | 15.4153 | 0.532513 | ||||||||
\(839\) | 19.5982 | 0.676605 | 0.338303 | − | 0.941037i | \(-0.390147\pi\) | ||||
0.338303 | + | 0.941037i | \(0.390147\pi\) | |||||||
\(840\) | −1.84069 | −0.0635097 | ||||||||
\(841\) | 10.7528 | 0.370785 | ||||||||
\(842\) | −25.8241 | −0.889957 | ||||||||
\(843\) | 1.70942 | 0.0588757 | ||||||||
\(844\) | 13.8759 | 0.477629 | ||||||||
\(845\) | −0.676512 | −0.0232727 | ||||||||
\(846\) | −8.64110 | −0.297087 | ||||||||
\(847\) | −45.6986 | −1.57022 | ||||||||
\(848\) | −2.36350 | −0.0811631 | ||||||||
\(849\) | 4.39481 | 0.150829 | ||||||||
\(850\) | −4.61861 | −0.158417 | ||||||||
\(851\) | 5.03725 | 0.172675 | ||||||||
\(852\) | −15.6217 | −0.535190 | ||||||||
\(853\) | 39.9423 | 1.36760 | 0.683799 | − | 0.729670i | \(-0.260327\pi\) | ||||
0.683799 | + | 0.729670i | \(0.260327\pi\) | |||||||
\(854\) | −32.4810 | −1.11148 | ||||||||
\(855\) | −3.27908 | −0.112142 | ||||||||
\(856\) | −17.8523 | −0.610180 | ||||||||
\(857\) | −54.7153 | −1.86904 | −0.934519 | − | 0.355912i | \(-0.884170\pi\) | ||||
−0.934519 | + | 0.355912i | \(0.884170\pi\) | |||||||
\(858\) | −5.27216 | −0.179989 | ||||||||
\(859\) | −30.0969 | −1.02689 | −0.513446 | − | 0.858122i | \(-0.671632\pi\) | ||||
−0.513446 | + | 0.858122i | \(0.671632\pi\) | |||||||
\(860\) | 5.97765 | 0.203836 | ||||||||
\(861\) | 26.3335 | 0.897444 | ||||||||
\(862\) | −7.57974 | −0.258167 | ||||||||
\(863\) | 30.9324 | 1.05295 | 0.526475 | − | 0.850191i | \(-0.323513\pi\) | ||||
0.526475 | + | 0.850191i | \(0.323513\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −5.57046 | −0.189401 | ||||||||
\(866\) | −16.0633 | −0.545854 | ||||||||
\(867\) | 15.9661 | 0.542238 | ||||||||
\(868\) | 8.27855 | 0.280992 | ||||||||
\(869\) | 26.9035 | 0.912639 | ||||||||
\(870\) | 4.26540 | 0.144610 | ||||||||
\(871\) | −2.97048 | −0.100651 | ||||||||
\(872\) | −0.493205 | −0.0167020 | ||||||||
\(873\) | −2.57742 | −0.0872325 | ||||||||
\(874\) | −24.3715 | −0.824378 | ||||||||
\(875\) | −17.5644 | −0.593786 | ||||||||
\(876\) | −1.34277 | −0.0453680 | ||||||||
\(877\) | 32.5460 | 1.09900 | 0.549500 | − | 0.835494i | \(-0.314818\pi\) | ||||
0.549500 | + | 0.835494i | \(0.314818\pi\) | |||||||
\(878\) | 34.5792 | 1.16699 | ||||||||
\(879\) | 2.45624 | 0.0828469 | ||||||||
\(880\) | 3.56668 | 0.120233 | ||||||||
\(881\) | 7.14872 | 0.240847 | 0.120423 | − | 0.992723i | \(-0.461575\pi\) | ||||
0.120423 | + | 0.992723i | \(0.461575\pi\) | |||||||
\(882\) | 0.402999 | 0.0135697 | ||||||||
\(883\) | −7.51123 | −0.252773 | −0.126387 | − | 0.991981i | \(-0.540338\pi\) | ||||
−0.126387 | + | 0.991981i | \(0.540338\pi\) | |||||||
\(884\) | −1.01679 | −0.0341985 | ||||||||
\(885\) | −9.26862 | −0.311561 | ||||||||
\(886\) | 21.2435 | 0.713688 | ||||||||
\(887\) | 7.79271 | 0.261654 | 0.130827 | − | 0.991405i | \(-0.458237\pi\) | ||||
0.130827 | + | 0.991405i | \(0.458237\pi\) | |||||||
\(888\) | 1.00182 | 0.0336188 | ||||||||
\(889\) | −38.4321 | −1.28897 | ||||||||
\(890\) | −9.39420 | −0.314894 | ||||||||
\(891\) | −5.27216 | −0.176624 | ||||||||
\(892\) | 3.62805 | 0.121476 | ||||||||
\(893\) | −41.8838 | −1.40159 | ||||||||
\(894\) | −14.0749 | −0.470735 | ||||||||
\(895\) | −14.4114 | −0.481721 | ||||||||
\(896\) | −2.72085 | −0.0908971 | ||||||||
\(897\) | −5.02811 | −0.167884 | ||||||||
\(898\) | 35.5472 | 1.18622 | ||||||||
\(899\) | −19.1838 | −0.639815 | ||||||||
\(900\) | −4.54233 | −0.151411 | ||||||||
\(901\) | −2.40320 | −0.0800621 | ||||||||
\(902\) | −51.0263 | −1.69899 | ||||||||
\(903\) | −24.0413 | −0.800045 | ||||||||
\(904\) | −10.3192 | −0.343210 | ||||||||
\(905\) | −6.01415 | −0.199917 | ||||||||
\(906\) | −23.4183 | −0.778021 | ||||||||
\(907\) | −2.50049 | −0.0830273 | −0.0415136 | − | 0.999138i | \(-0.513218\pi\) | ||||
−0.0415136 | + | 0.999138i | \(0.513218\pi\) | |||||||
\(908\) | 12.8428 | 0.426203 | ||||||||
\(909\) | 8.50857 | 0.282211 | ||||||||
\(910\) | −1.84069 | −0.0610181 | ||||||||
\(911\) | −23.9600 | −0.793831 | −0.396915 | − | 0.917855i | \(-0.629919\pi\) | ||||
−0.396915 | + | 0.917855i | \(0.629919\pi\) | |||||||
\(912\) | −4.84704 | −0.160502 | ||||||||
\(913\) | 3.92372 | 0.129856 | ||||||||
\(914\) | 24.4777 | 0.809650 | ||||||||
\(915\) | 8.07610 | 0.266988 | ||||||||
\(916\) | 16.1697 | 0.534261 | ||||||||
\(917\) | 17.1238 | 0.565476 | ||||||||
\(918\) | −1.01679 | −0.0335592 | ||||||||
\(919\) | −52.1127 | −1.71904 | −0.859519 | − | 0.511104i | \(-0.829237\pi\) | ||||
−0.859519 | + | 0.511104i | \(0.829237\pi\) | |||||||
\(920\) | 3.40158 | 0.112147 | ||||||||
\(921\) | 11.7261 | 0.386387 | ||||||||
\(922\) | −26.6751 | −0.878496 | ||||||||
\(923\) | −15.6217 | −0.514194 | ||||||||
\(924\) | −14.3447 | −0.471907 | ||||||||
\(925\) | 4.55059 | 0.149622 | ||||||||
\(926\) | 7.77420 | 0.255476 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | 6.30498 | 0.206971 | ||||||||
\(929\) | 16.1845 | 0.530995 | 0.265498 | − | 0.964112i | \(-0.414464\pi\) | ||||
0.265498 | + | 0.964112i | \(0.414464\pi\) | |||||||
\(930\) | −2.05838 | −0.0674971 | ||||||||
\(931\) | 1.95335 | 0.0640185 | ||||||||
\(932\) | −3.08086 | −0.100917 | ||||||||
\(933\) | 1.75340 | 0.0574039 | ||||||||
\(934\) | 22.4004 | 0.732963 | ||||||||
\(935\) | 3.62658 | 0.118602 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 12.5147 | 0.408837 | 0.204419 | − | 0.978884i | \(-0.434470\pi\) | ||||
0.204419 | + | 0.978884i | \(0.434470\pi\) | |||||||
\(938\) | −8.08222 | −0.263894 | ||||||||
\(939\) | −21.0420 | −0.686679 | ||||||||
\(940\) | 5.84581 | 0.190669 | ||||||||
\(941\) | −51.5353 | −1.68000 | −0.840002 | − | 0.542583i | \(-0.817446\pi\) | ||||
−0.840002 | + | 0.542583i | \(0.817446\pi\) | |||||||
\(942\) | −4.71578 | −0.153648 | ||||||||
\(943\) | −48.6643 | −1.58473 | ||||||||
\(944\) | −13.7006 | −0.445916 | ||||||||
\(945\) | −1.84069 | −0.0598775 | ||||||||
\(946\) | 46.5847 | 1.51460 | ||||||||
\(947\) | −42.8955 | −1.39392 | −0.696959 | − | 0.717111i | \(-0.745464\pi\) | ||||
−0.696959 | + | 0.717111i | \(0.745464\pi\) | |||||||
\(948\) | 5.10293 | 0.165736 | ||||||||
\(949\) | −1.34277 | −0.0435881 | ||||||||
\(950\) | −22.0169 | −0.714322 | ||||||||
\(951\) | −25.9164 | −0.840396 | ||||||||
\(952\) | −2.76654 | −0.0896640 | ||||||||
\(953\) | 13.4076 | 0.434314 | 0.217157 | − | 0.976137i | \(-0.430322\pi\) | ||||
0.217157 | + | 0.976137i | \(0.430322\pi\) | |||||||
\(954\) | −2.36350 | −0.0765213 | ||||||||
\(955\) | 8.02692 | 0.259745 | ||||||||
\(956\) | 16.9163 | 0.547111 | ||||||||
\(957\) | 33.2409 | 1.07453 | ||||||||
\(958\) | −38.0641 | −1.22980 | ||||||||
\(959\) | 17.4831 | 0.564559 | ||||||||
\(960\) | 0.676512 | 0.0218343 | ||||||||
\(961\) | −21.7423 | −0.701366 | ||||||||
\(962\) | 1.00182 | 0.0322999 | ||||||||
\(963\) | −17.8523 | −0.575283 | ||||||||
\(964\) | −29.6909 | −0.956281 | ||||||||
\(965\) | −7.23695 | −0.232966 | ||||||||
\(966\) | −13.6807 | −0.440170 | ||||||||
\(967\) | 44.3002 | 1.42460 | 0.712299 | − | 0.701876i | \(-0.247654\pi\) | ||||
0.712299 | + | 0.701876i | \(0.247654\pi\) | |||||||
\(968\) | 16.7957 | 0.539835 | ||||||||
\(969\) | −4.92844 | −0.158324 | ||||||||
\(970\) | 1.74366 | 0.0559855 | ||||||||
\(971\) | 4.94382 | 0.158655 | 0.0793274 | − | 0.996849i | \(-0.474723\pi\) | ||||
0.0793274 | + | 0.996849i | \(0.474723\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −50.0363 | −1.60409 | ||||||||
\(974\) | 17.7607 | 0.569090 | ||||||||
\(975\) | −4.54233 | −0.145471 | ||||||||
\(976\) | 11.9378 | 0.382121 | ||||||||
\(977\) | 44.7955 | 1.43313 | 0.716567 | − | 0.697518i | \(-0.245712\pi\) | ||||
0.716567 | + | 0.697518i | \(0.245712\pi\) | |||||||
\(978\) | −14.3157 | −0.457767 | ||||||||
\(979\) | −73.2105 | −2.33982 | ||||||||
\(980\) | −0.272634 | −0.00870896 | ||||||||
\(981\) | −0.493205 | −0.0157468 | ||||||||
\(982\) | −31.1190 | −0.993048 | ||||||||
\(983\) | 8.01746 | 0.255717 | 0.127859 | − | 0.991792i | \(-0.459190\pi\) | ||||
0.127859 | + | 0.991792i | \(0.459190\pi\) | |||||||
\(984\) | −9.67843 | −0.308537 | ||||||||
\(985\) | 18.3627 | 0.585084 | ||||||||
\(986\) | 6.41086 | 0.204163 | ||||||||
\(987\) | −23.5111 | −0.748367 | ||||||||
\(988\) | −4.84704 | −0.154205 | ||||||||
\(989\) | 44.4283 | 1.41274 | ||||||||
\(990\) | 3.56668 | 0.113357 | ||||||||
\(991\) | −46.1093 | −1.46471 | −0.732356 | − | 0.680922i | \(-0.761579\pi\) | ||||
−0.732356 | + | 0.680922i | \(0.761579\pi\) | |||||||
\(992\) | −3.04264 | −0.0966039 | ||||||||
\(993\) | 18.0656 | 0.573294 | ||||||||
\(994\) | −42.5042 | −1.34815 | ||||||||
\(995\) | −10.8743 | −0.344739 | ||||||||
\(996\) | 0.744233 | 0.0235819 | ||||||||
\(997\) | 6.11084 | 0.193532 | 0.0967662 | − | 0.995307i | \(-0.469150\pi\) | ||||
0.0967662 | + | 0.995307i | \(0.469150\pi\) | |||||||
\(998\) | 15.2463 | 0.482612 | ||||||||
\(999\) | 1.00182 | 0.0316961 |
(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 | 8034.2.a.bc.1.7 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.bc.1.7 | ✓ | 15 | 1.1 | even | 1 | trivial |