Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2667,2,Mod(1,2667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2667, 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("2667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2667 = 3 \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2667.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: | \(21.2961022191\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | 7.7.118870813.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 9x^{5} - 3x^{4} + 20x^{3} + 7x^{2} - 13x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.301070\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2667.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.09968 | 1.48470 | 0.742348 | − | 0.670014i | \(-0.233712\pi\) | ||||
0.742348 | + | 0.670014i | \(0.233712\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.40865 | 1.20432 | ||||||||
\(5\) | −3.29054 | −1.47157 | −0.735787 | − | 0.677213i | \(-0.763188\pi\) | ||||
−0.735787 | + | 0.677213i | \(0.763188\pi\) | |||||||
\(6\) | 2.09968 | 0.857190 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.858029 | 0.303359 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −6.90907 | −2.18484 | ||||||||
\(11\) | −3.62521 | −1.09304 | −0.546521 | − | 0.837445i | \(-0.684048\pi\) | ||||
−0.546521 | + | 0.837445i | \(0.684048\pi\) | |||||||
\(12\) | 2.40865 | 0.695317 | ||||||||
\(13\) | −2.16007 | −0.599095 | −0.299547 | − | 0.954081i | \(-0.596836\pi\) | ||||
−0.299547 | + | 0.954081i | \(0.596836\pi\) | |||||||
\(14\) | 2.09968 | 0.561163 | ||||||||
\(15\) | −3.29054 | −0.849614 | ||||||||
\(16\) | −3.01571 | −0.753928 | ||||||||
\(17\) | 2.19233 | 0.531718 | 0.265859 | − | 0.964012i | \(-0.414344\pi\) | ||||
0.265859 | + | 0.964012i | \(0.414344\pi\) | |||||||
\(18\) | 2.09968 | 0.494899 | ||||||||
\(19\) | −6.66601 | −1.52929 | −0.764643 | − | 0.644454i | \(-0.777085\pi\) | ||||
−0.764643 | + | 0.644454i | \(0.777085\pi\) | |||||||
\(20\) | −7.92575 | −1.77225 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −7.61177 | −1.62284 | ||||||||
\(23\) | 2.36522 | 0.493183 | 0.246591 | − | 0.969120i | \(-0.420689\pi\) | ||||
0.246591 | + | 0.969120i | \(0.420689\pi\) | |||||||
\(24\) | 0.858029 | 0.175145 | ||||||||
\(25\) | 5.82765 | 1.16553 | ||||||||
\(26\) | −4.53544 | −0.889474 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.40865 | 0.455192 | ||||||||
\(29\) | 2.06180 | 0.382867 | 0.191433 | − | 0.981506i | \(-0.438686\pi\) | ||||
0.191433 | + | 0.981506i | \(0.438686\pi\) | |||||||
\(30\) | −6.90907 | −1.26142 | ||||||||
\(31\) | −2.19207 | −0.393708 | −0.196854 | − | 0.980433i | \(-0.563072\pi\) | ||||
−0.196854 | + | 0.980433i | \(0.563072\pi\) | |||||||
\(32\) | −8.04808 | −1.42271 | ||||||||
\(33\) | −3.62521 | −0.631068 | ||||||||
\(34\) | 4.60319 | 0.789440 | ||||||||
\(35\) | −3.29054 | −0.556203 | ||||||||
\(36\) | 2.40865 | 0.401441 | ||||||||
\(37\) | −10.1454 | −1.66789 | −0.833947 | − | 0.551845i | \(-0.813924\pi\) | ||||
−0.833947 | + | 0.551845i | \(0.813924\pi\) | |||||||
\(38\) | −13.9965 | −2.27053 | ||||||||
\(39\) | −2.16007 | −0.345887 | ||||||||
\(40\) | −2.82338 | −0.446416 | ||||||||
\(41\) | −0.647495 | −0.101122 | −0.0505608 | − | 0.998721i | \(-0.516101\pi\) | ||||
−0.0505608 | + | 0.998721i | \(0.516101\pi\) | |||||||
\(42\) | 2.09968 | 0.323987 | ||||||||
\(43\) | 3.67859 | 0.560979 | 0.280490 | − | 0.959857i | \(-0.409503\pi\) | ||||
0.280490 | + | 0.959857i | \(0.409503\pi\) | |||||||
\(44\) | −8.73185 | −1.31638 | ||||||||
\(45\) | −3.29054 | −0.490525 | ||||||||
\(46\) | 4.96620 | 0.732227 | ||||||||
\(47\) | −8.59064 | −1.25307 | −0.626537 | − | 0.779392i | \(-0.715528\pi\) | ||||
−0.626537 | + | 0.779392i | \(0.715528\pi\) | |||||||
\(48\) | −3.01571 | −0.435280 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 12.2362 | 1.73046 | ||||||||
\(51\) | 2.19233 | 0.306988 | ||||||||
\(52\) | −5.20284 | −0.721504 | ||||||||
\(53\) | 2.84924 | 0.391373 | 0.195686 | − | 0.980667i | \(-0.437307\pi\) | ||||
0.195686 | + | 0.980667i | \(0.437307\pi\) | |||||||
\(54\) | 2.09968 | 0.285730 | ||||||||
\(55\) | 11.9289 | 1.60849 | ||||||||
\(56\) | 0.858029 | 0.114659 | ||||||||
\(57\) | −6.66601 | −0.882934 | ||||||||
\(58\) | 4.32912 | 0.568441 | ||||||||
\(59\) | −0.592789 | −0.0771745 | −0.0385873 | − | 0.999255i | \(-0.512286\pi\) | ||||
−0.0385873 | + | 0.999255i | \(0.512286\pi\) | |||||||
\(60\) | −7.92575 | −1.02321 | ||||||||
\(61\) | −13.5269 | −1.73195 | −0.865973 | − | 0.500091i | \(-0.833300\pi\) | ||||
−0.865973 | + | 0.500091i | \(0.833300\pi\) | |||||||
\(62\) | −4.60265 | −0.584537 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −10.8670 | −1.35837 | ||||||||
\(65\) | 7.10778 | 0.881612 | ||||||||
\(66\) | −7.61177 | −0.936945 | ||||||||
\(67\) | 0.664083 | 0.0811306 | 0.0405653 | − | 0.999177i | \(-0.487084\pi\) | ||||
0.0405653 | + | 0.999177i | \(0.487084\pi\) | |||||||
\(68\) | 5.28055 | 0.640361 | ||||||||
\(69\) | 2.36522 | 0.284739 | ||||||||
\(70\) | −6.90907 | −0.825792 | ||||||||
\(71\) | −5.65049 | −0.670589 | −0.335295 | − | 0.942113i | \(-0.608836\pi\) | ||||
−0.335295 | + | 0.942113i | \(0.608836\pi\) | |||||||
\(72\) | 0.858029 | 0.101120 | ||||||||
\(73\) | −3.24624 | −0.379943 | −0.189972 | − | 0.981790i | \(-0.560840\pi\) | ||||
−0.189972 | + | 0.981790i | \(0.560840\pi\) | |||||||
\(74\) | −21.3021 | −2.47632 | ||||||||
\(75\) | 5.82765 | 0.672919 | ||||||||
\(76\) | −16.0561 | −1.84176 | ||||||||
\(77\) | −3.62521 | −0.413131 | ||||||||
\(78\) | −4.53544 | −0.513538 | ||||||||
\(79\) | 4.01101 | 0.451274 | 0.225637 | − | 0.974211i | \(-0.427554\pi\) | ||||
0.225637 | + | 0.974211i | \(0.427554\pi\) | |||||||
\(80\) | 9.92332 | 1.10946 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.35953 | −0.150135 | ||||||||
\(83\) | −3.40033 | −0.373235 | −0.186617 | − | 0.982433i | \(-0.559752\pi\) | ||||
−0.186617 | + | 0.982433i | \(0.559752\pi\) | |||||||
\(84\) | 2.40865 | 0.262805 | ||||||||
\(85\) | −7.21395 | −0.782463 | ||||||||
\(86\) | 7.72385 | 0.832884 | ||||||||
\(87\) | 2.06180 | 0.221048 | ||||||||
\(88\) | −3.11054 | −0.331584 | ||||||||
\(89\) | 6.31252 | 0.669126 | 0.334563 | − | 0.942373i | \(-0.391411\pi\) | ||||
0.334563 | + | 0.942373i | \(0.391411\pi\) | |||||||
\(90\) | −6.90907 | −0.728280 | ||||||||
\(91\) | −2.16007 | −0.226436 | ||||||||
\(92\) | 5.69698 | 0.593952 | ||||||||
\(93\) | −2.19207 | −0.227307 | ||||||||
\(94\) | −18.0376 | −1.86043 | ||||||||
\(95\) | 21.9348 | 2.25046 | ||||||||
\(96\) | −8.04808 | −0.821404 | ||||||||
\(97\) | −0.0689323 | −0.00699902 | −0.00349951 | − | 0.999994i | \(-0.501114\pi\) | ||||
−0.00349951 | + | 0.999994i | \(0.501114\pi\) | |||||||
\(98\) | 2.09968 | 0.212100 | ||||||||
\(99\) | −3.62521 | −0.364347 | ||||||||
\(100\) | 14.0368 | 1.40368 | ||||||||
\(101\) | 6.53614 | 0.650370 | 0.325185 | − | 0.945650i | \(-0.394573\pi\) | ||||
0.325185 | + | 0.945650i | \(0.394573\pi\) | |||||||
\(102\) | 4.60319 | 0.455784 | ||||||||
\(103\) | 1.42084 | 0.140000 | 0.0700000 | − | 0.997547i | \(-0.477700\pi\) | ||||
0.0700000 | + | 0.997547i | \(0.477700\pi\) | |||||||
\(104\) | −1.85340 | −0.181741 | ||||||||
\(105\) | −3.29054 | −0.321124 | ||||||||
\(106\) | 5.98248 | 0.581070 | ||||||||
\(107\) | 17.1418 | 1.65716 | 0.828581 | − | 0.559869i | \(-0.189149\pi\) | ||||
0.828581 | + | 0.559869i | \(0.189149\pi\) | |||||||
\(108\) | 2.40865 | 0.231772 | ||||||||
\(109\) | 14.3137 | 1.37100 | 0.685500 | − | 0.728073i | \(-0.259584\pi\) | ||||
0.685500 | + | 0.728073i | \(0.259584\pi\) | |||||||
\(110\) | 25.0468 | 2.38812 | ||||||||
\(111\) | −10.1454 | −0.962959 | ||||||||
\(112\) | −3.01571 | −0.284958 | ||||||||
\(113\) | 9.27873 | 0.872870 | 0.436435 | − | 0.899736i | \(-0.356241\pi\) | ||||
0.436435 | + | 0.899736i | \(0.356241\pi\) | |||||||
\(114\) | −13.9965 | −1.31089 | ||||||||
\(115\) | −7.78285 | −0.725755 | ||||||||
\(116\) | 4.96615 | 0.461095 | ||||||||
\(117\) | −2.16007 | −0.199698 | ||||||||
\(118\) | −1.24467 | −0.114581 | ||||||||
\(119\) | 2.19233 | 0.200971 | ||||||||
\(120\) | −2.82338 | −0.257738 | ||||||||
\(121\) | 2.14215 | 0.194741 | ||||||||
\(122\) | −28.4022 | −2.57141 | ||||||||
\(123\) | −0.647495 | −0.0583826 | ||||||||
\(124\) | −5.27993 | −0.474152 | ||||||||
\(125\) | −2.72342 | −0.243590 | ||||||||
\(126\) | 2.09968 | 0.187054 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −6.72095 | −0.594054 | ||||||||
\(129\) | 3.67859 | 0.323882 | ||||||||
\(130\) | 14.9241 | 1.30893 | ||||||||
\(131\) | 17.8118 | 1.55623 | 0.778113 | − | 0.628124i | \(-0.216177\pi\) | ||||
0.778113 | + | 0.628124i | \(0.216177\pi\) | |||||||
\(132\) | −8.73185 | −0.760010 | ||||||||
\(133\) | −6.66601 | −0.578016 | ||||||||
\(134\) | 1.39436 | 0.120454 | ||||||||
\(135\) | −3.29054 | −0.283205 | ||||||||
\(136\) | 1.88108 | 0.161302 | ||||||||
\(137\) | 7.51288 | 0.641869 | 0.320934 | − | 0.947101i | \(-0.396003\pi\) | ||||
0.320934 | + | 0.947101i | \(0.396003\pi\) | |||||||
\(138\) | 4.96620 | 0.422751 | ||||||||
\(139\) | −4.67226 | −0.396296 | −0.198148 | − | 0.980172i | \(-0.563493\pi\) | ||||
−0.198148 | + | 0.980172i | \(0.563493\pi\) | |||||||
\(140\) | −7.92575 | −0.669848 | ||||||||
\(141\) | −8.59064 | −0.723462 | ||||||||
\(142\) | −11.8642 | −0.995622 | ||||||||
\(143\) | 7.83069 | 0.654836 | ||||||||
\(144\) | −3.01571 | −0.251309 | ||||||||
\(145\) | −6.78443 | −0.563417 | ||||||||
\(146\) | −6.81605 | −0.564101 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −24.4367 | −2.00868 | ||||||||
\(149\) | −12.9632 | −1.06199 | −0.530994 | − | 0.847375i | \(-0.678181\pi\) | ||||
−0.530994 | + | 0.847375i | \(0.678181\pi\) | |||||||
\(150\) | 12.2362 | 0.999081 | ||||||||
\(151\) | 10.9338 | 0.889780 | 0.444890 | − | 0.895585i | \(-0.353243\pi\) | ||||
0.444890 | + | 0.895585i | \(0.353243\pi\) | |||||||
\(152\) | −5.71963 | −0.463923 | ||||||||
\(153\) | 2.19233 | 0.177239 | ||||||||
\(154\) | −7.61177 | −0.613374 | ||||||||
\(155\) | 7.21310 | 0.579370 | ||||||||
\(156\) | −5.20284 | −0.416561 | ||||||||
\(157\) | −20.5157 | −1.63733 | −0.818665 | − | 0.574271i | \(-0.805285\pi\) | ||||
−0.818665 | + | 0.574271i | \(0.805285\pi\) | |||||||
\(158\) | 8.42183 | 0.670005 | ||||||||
\(159\) | 2.84924 | 0.225959 | ||||||||
\(160\) | 26.4825 | 2.09363 | ||||||||
\(161\) | 2.36522 | 0.186406 | ||||||||
\(162\) | 2.09968 | 0.164966 | ||||||||
\(163\) | 1.33340 | 0.104440 | 0.0522199 | − | 0.998636i | \(-0.483370\pi\) | ||||
0.0522199 | + | 0.998636i | \(0.483370\pi\) | |||||||
\(164\) | −1.55959 | −0.121783 | ||||||||
\(165\) | 11.9289 | 0.928663 | ||||||||
\(166\) | −7.13960 | −0.554140 | ||||||||
\(167\) | 0.822111 | 0.0636169 | 0.0318084 | − | 0.999494i | \(-0.489873\pi\) | ||||
0.0318084 | + | 0.999494i | \(0.489873\pi\) | |||||||
\(168\) | 0.858029 | 0.0661984 | ||||||||
\(169\) | −8.33411 | −0.641086 | ||||||||
\(170\) | −15.1470 | −1.16172 | ||||||||
\(171\) | −6.66601 | −0.509762 | ||||||||
\(172\) | 8.86042 | 0.675601 | ||||||||
\(173\) | −22.8603 | −1.73804 | −0.869020 | − | 0.494777i | \(-0.835250\pi\) | ||||
−0.869020 | + | 0.494777i | \(0.835250\pi\) | |||||||
\(174\) | 4.32912 | 0.328189 | ||||||||
\(175\) | 5.82765 | 0.440529 | ||||||||
\(176\) | 10.9326 | 0.824075 | ||||||||
\(177\) | −0.592789 | −0.0445567 | ||||||||
\(178\) | 13.2543 | 0.993449 | ||||||||
\(179\) | 1.52134 | 0.113710 | 0.0568552 | − | 0.998382i | \(-0.481893\pi\) | ||||
0.0568552 | + | 0.998382i | \(0.481893\pi\) | |||||||
\(180\) | −7.92575 | −0.590751 | ||||||||
\(181\) | 14.4514 | 1.07417 | 0.537084 | − | 0.843529i | \(-0.319526\pi\) | ||||
0.537084 | + | 0.843529i | \(0.319526\pi\) | |||||||
\(182\) | −4.53544 | −0.336189 | ||||||||
\(183\) | −13.5269 | −0.999939 | ||||||||
\(184\) | 2.02943 | 0.149611 | ||||||||
\(185\) | 33.3838 | 2.45443 | ||||||||
\(186\) | −4.60265 | −0.337483 | ||||||||
\(187\) | −7.94766 | −0.581190 | ||||||||
\(188\) | −20.6918 | −1.50911 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 46.0559 | 3.34125 | ||||||||
\(191\) | 6.46436 | 0.467744 | 0.233872 | − | 0.972267i | \(-0.424860\pi\) | ||||
0.233872 | + | 0.972267i | \(0.424860\pi\) | |||||||
\(192\) | −10.8670 | −0.784255 | ||||||||
\(193\) | −21.4158 | −1.54154 | −0.770771 | − | 0.637112i | \(-0.780129\pi\) | ||||
−0.770771 | + | 0.637112i | \(0.780129\pi\) | |||||||
\(194\) | −0.144736 | −0.0103914 | ||||||||
\(195\) | 7.10778 | 0.508999 | ||||||||
\(196\) | 2.40865 | 0.172046 | ||||||||
\(197\) | 15.2826 | 1.08884 | 0.544419 | − | 0.838814i | \(-0.316750\pi\) | ||||
0.544419 | + | 0.838814i | \(0.316750\pi\) | |||||||
\(198\) | −7.61177 | −0.540945 | ||||||||
\(199\) | −9.68248 | −0.686373 | −0.343186 | − | 0.939267i | \(-0.611506\pi\) | ||||
−0.343186 | + | 0.939267i | \(0.611506\pi\) | |||||||
\(200\) | 5.00030 | 0.353574 | ||||||||
\(201\) | 0.664083 | 0.0468408 | ||||||||
\(202\) | 13.7238 | 0.965603 | ||||||||
\(203\) | 2.06180 | 0.144710 | ||||||||
\(204\) | 5.28055 | 0.369713 | ||||||||
\(205\) | 2.13061 | 0.148808 | ||||||||
\(206\) | 2.98332 | 0.207857 | ||||||||
\(207\) | 2.36522 | 0.164394 | ||||||||
\(208\) | 6.51414 | 0.451674 | ||||||||
\(209\) | 24.1657 | 1.67157 | ||||||||
\(210\) | −6.90907 | −0.476771 | ||||||||
\(211\) | −22.7122 | −1.56357 | −0.781785 | − | 0.623549i | \(-0.785690\pi\) | ||||
−0.781785 | + | 0.623549i | \(0.785690\pi\) | |||||||
\(212\) | 6.86281 | 0.471340 | ||||||||
\(213\) | −5.65049 | −0.387165 | ||||||||
\(214\) | 35.9923 | 2.46038 | ||||||||
\(215\) | −12.1045 | −0.825523 | ||||||||
\(216\) | 0.858029 | 0.0583815 | ||||||||
\(217\) | −2.19207 | −0.148808 | ||||||||
\(218\) | 30.0541 | 2.03552 | ||||||||
\(219\) | −3.24624 | −0.219360 | ||||||||
\(220\) | 28.7325 | 1.93715 | ||||||||
\(221\) | −4.73558 | −0.318550 | ||||||||
\(222\) | −21.3021 | −1.42970 | ||||||||
\(223\) | 6.33989 | 0.424551 | 0.212275 | − | 0.977210i | \(-0.431913\pi\) | ||||
0.212275 | + | 0.977210i | \(0.431913\pi\) | |||||||
\(224\) | −8.04808 | −0.537735 | ||||||||
\(225\) | 5.82765 | 0.388510 | ||||||||
\(226\) | 19.4824 | 1.29595 | ||||||||
\(227\) | −15.7349 | −1.04436 | −0.522181 | − | 0.852835i | \(-0.674881\pi\) | ||||
−0.522181 | + | 0.852835i | \(0.674881\pi\) | |||||||
\(228\) | −16.0561 | −1.06334 | ||||||||
\(229\) | −0.365275 | −0.0241380 | −0.0120690 | − | 0.999927i | \(-0.503842\pi\) | ||||
−0.0120690 | + | 0.999927i | \(0.503842\pi\) | |||||||
\(230\) | −16.3415 | −1.07753 | ||||||||
\(231\) | −3.62521 | −0.238521 | ||||||||
\(232\) | 1.76908 | 0.116146 | ||||||||
\(233\) | −4.21293 | −0.275998 | −0.137999 | − | 0.990432i | \(-0.544067\pi\) | ||||
−0.137999 | + | 0.990432i | \(0.544067\pi\) | |||||||
\(234\) | −4.53544 | −0.296491 | ||||||||
\(235\) | 28.2678 | 1.84399 | ||||||||
\(236\) | −1.42782 | −0.0929431 | ||||||||
\(237\) | 4.01101 | 0.260543 | ||||||||
\(238\) | 4.60319 | 0.298380 | ||||||||
\(239\) | −3.38821 | −0.219165 | −0.109582 | − | 0.993978i | \(-0.534951\pi\) | ||||
−0.109582 | + | 0.993978i | \(0.534951\pi\) | |||||||
\(240\) | 9.92332 | 0.640547 | ||||||||
\(241\) | −10.0609 | −0.648077 | −0.324039 | − | 0.946044i | \(-0.605041\pi\) | ||||
−0.324039 | + | 0.946044i | \(0.605041\pi\) | |||||||
\(242\) | 4.49782 | 0.289131 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −32.5816 | −2.08582 | ||||||||
\(245\) | −3.29054 | −0.210225 | ||||||||
\(246\) | −1.35953 | −0.0866805 | ||||||||
\(247\) | 14.3990 | 0.916188 | ||||||||
\(248\) | −1.88086 | −0.119435 | ||||||||
\(249\) | −3.40033 | −0.215487 | ||||||||
\(250\) | −5.71830 | −0.361657 | ||||||||
\(251\) | 1.13195 | 0.0714479 | 0.0357240 | − | 0.999362i | \(-0.488626\pi\) | ||||
0.0357240 | + | 0.999362i | \(0.488626\pi\) | |||||||
\(252\) | 2.40865 | 0.151731 | ||||||||
\(253\) | −8.57442 | −0.539069 | ||||||||
\(254\) | −2.09968 | −0.131746 | ||||||||
\(255\) | −7.21395 | −0.451755 | ||||||||
\(256\) | 7.62208 | 0.476380 | ||||||||
\(257\) | −29.2462 | −1.82433 | −0.912165 | − | 0.409824i | \(-0.865590\pi\) | ||||
−0.912165 | + | 0.409824i | \(0.865590\pi\) | |||||||
\(258\) | 7.72385 | 0.480866 | ||||||||
\(259\) | −10.1454 | −0.630404 | ||||||||
\(260\) | 17.1202 | 1.06175 | ||||||||
\(261\) | 2.06180 | 0.127622 | ||||||||
\(262\) | 37.3991 | 2.31052 | ||||||||
\(263\) | 26.3656 | 1.62577 | 0.812887 | − | 0.582422i | \(-0.197895\pi\) | ||||
0.812887 | + | 0.582422i | \(0.197895\pi\) | |||||||
\(264\) | −3.11054 | −0.191440 | ||||||||
\(265\) | −9.37552 | −0.575934 | ||||||||
\(266\) | −13.9965 | −0.858179 | ||||||||
\(267\) | 6.31252 | 0.386320 | ||||||||
\(268\) | 1.59954 | 0.0977076 | ||||||||
\(269\) | −22.2274 | −1.35523 | −0.677613 | − | 0.735419i | \(-0.736986\pi\) | ||||
−0.677613 | + | 0.735419i | \(0.736986\pi\) | |||||||
\(270\) | −6.90907 | −0.420473 | ||||||||
\(271\) | −26.8490 | −1.63096 | −0.815482 | − | 0.578783i | \(-0.803528\pi\) | ||||
−0.815482 | + | 0.578783i | \(0.803528\pi\) | |||||||
\(272\) | −6.61144 | −0.400877 | ||||||||
\(273\) | −2.16007 | −0.130733 | ||||||||
\(274\) | 15.7746 | 0.952981 | ||||||||
\(275\) | −21.1265 | −1.27397 | ||||||||
\(276\) | 5.69698 | 0.342918 | ||||||||
\(277\) | 2.10995 | 0.126775 | 0.0633873 | − | 0.997989i | \(-0.479810\pi\) | ||||
0.0633873 | + | 0.997989i | \(0.479810\pi\) | |||||||
\(278\) | −9.81024 | −0.588379 | ||||||||
\(279\) | −2.19207 | −0.131236 | ||||||||
\(280\) | −2.82338 | −0.168729 | ||||||||
\(281\) | 19.6051 | 1.16954 | 0.584772 | − | 0.811198i | \(-0.301184\pi\) | ||||
0.584772 | + | 0.811198i | \(0.301184\pi\) | |||||||
\(282\) | −18.0376 | −1.07412 | ||||||||
\(283\) | −5.28771 | −0.314322 | −0.157161 | − | 0.987573i | \(-0.550234\pi\) | ||||
−0.157161 | + | 0.987573i | \(0.550234\pi\) | |||||||
\(284\) | −13.6100 | −0.807607 | ||||||||
\(285\) | 21.9348 | 1.29930 | ||||||||
\(286\) | 16.4419 | 0.972232 | ||||||||
\(287\) | −0.647495 | −0.0382204 | ||||||||
\(288\) | −8.04808 | −0.474238 | ||||||||
\(289\) | −12.1937 | −0.717276 | ||||||||
\(290\) | −14.2451 | −0.836503 | ||||||||
\(291\) | −0.0689323 | −0.00404089 | ||||||||
\(292\) | −7.81904 | −0.457575 | ||||||||
\(293\) | 9.05623 | 0.529071 | 0.264535 | − | 0.964376i | \(-0.414781\pi\) | ||||
0.264535 | + | 0.964376i | \(0.414781\pi\) | |||||||
\(294\) | 2.09968 | 0.122456 | ||||||||
\(295\) | 1.95059 | 0.113568 | ||||||||
\(296\) | −8.70505 | −0.505971 | ||||||||
\(297\) | −3.62521 | −0.210356 | ||||||||
\(298\) | −27.2186 | −1.57673 | ||||||||
\(299\) | −5.10903 | −0.295463 | ||||||||
\(300\) | 14.0368 | 0.810413 | ||||||||
\(301\) | 3.67859 | 0.212030 | ||||||||
\(302\) | 22.9575 | 1.32105 | ||||||||
\(303\) | 6.53614 | 0.375492 | ||||||||
\(304\) | 20.1027 | 1.15297 | ||||||||
\(305\) | 44.5109 | 2.54869 | ||||||||
\(306\) | 4.60319 | 0.263147 | ||||||||
\(307\) | 23.4922 | 1.34077 | 0.670386 | − | 0.742012i | \(-0.266128\pi\) | ||||
0.670386 | + | 0.742012i | \(0.266128\pi\) | |||||||
\(308\) | −8.73185 | −0.497544 | ||||||||
\(309\) | 1.42084 | 0.0808290 | ||||||||
\(310\) | 15.1452 | 0.860189 | ||||||||
\(311\) | −0.106610 | −0.00604531 | −0.00302265 | − | 0.999995i | \(-0.500962\pi\) | ||||
−0.00302265 | + | 0.999995i | \(0.500962\pi\) | |||||||
\(312\) | −1.85340 | −0.104928 | ||||||||
\(313\) | 23.6312 | 1.33572 | 0.667858 | − | 0.744289i | \(-0.267211\pi\) | ||||
0.667858 | + | 0.744289i | \(0.267211\pi\) | |||||||
\(314\) | −43.0763 | −2.43094 | ||||||||
\(315\) | −3.29054 | −0.185401 | ||||||||
\(316\) | 9.66112 | 0.543480 | ||||||||
\(317\) | 8.87083 | 0.498236 | 0.249118 | − | 0.968473i | \(-0.419859\pi\) | ||||
0.249118 | + | 0.968473i | \(0.419859\pi\) | |||||||
\(318\) | 5.98248 | 0.335481 | ||||||||
\(319\) | −7.47446 | −0.418489 | ||||||||
\(320\) | 35.7582 | 1.99894 | ||||||||
\(321\) | 17.1418 | 0.956763 | ||||||||
\(322\) | 4.96620 | 0.276756 | ||||||||
\(323\) | −14.6141 | −0.813150 | ||||||||
\(324\) | 2.40865 | 0.133814 | ||||||||
\(325\) | −12.5881 | −0.698263 | ||||||||
\(326\) | 2.79971 | 0.155061 | ||||||||
\(327\) | 14.3137 | 0.791547 | ||||||||
\(328\) | −0.555570 | −0.0306762 | ||||||||
\(329\) | −8.59064 | −0.473617 | ||||||||
\(330\) | 25.0468 | 1.37878 | ||||||||
\(331\) | −27.3847 | −1.50520 | −0.752599 | − | 0.658480i | \(-0.771200\pi\) | ||||
−0.752599 | + | 0.658480i | \(0.771200\pi\) | |||||||
\(332\) | −8.19020 | −0.449496 | ||||||||
\(333\) | −10.1454 | −0.555964 | ||||||||
\(334\) | 1.72617 | 0.0944518 | ||||||||
\(335\) | −2.18519 | −0.119390 | ||||||||
\(336\) | −3.01571 | −0.164521 | ||||||||
\(337\) | 18.4898 | 1.00720 | 0.503601 | − | 0.863936i | \(-0.332008\pi\) | ||||
0.503601 | + | 0.863936i | \(0.332008\pi\) | |||||||
\(338\) | −17.4990 | −0.951818 | ||||||||
\(339\) | 9.27873 | 0.503952 | ||||||||
\(340\) | −17.3759 | −0.942339 | ||||||||
\(341\) | 7.94673 | 0.430339 | ||||||||
\(342\) | −13.9965 | −0.756842 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 3.15634 | 0.170178 | ||||||||
\(345\) | −7.78285 | −0.419015 | ||||||||
\(346\) | −47.9994 | −2.58046 | ||||||||
\(347\) | 24.2408 | 1.30132 | 0.650658 | − | 0.759371i | \(-0.274493\pi\) | ||||
0.650658 | + | 0.759371i | \(0.274493\pi\) | |||||||
\(348\) | 4.96615 | 0.266214 | ||||||||
\(349\) | −7.74084 | −0.414358 | −0.207179 | − | 0.978303i | \(-0.566428\pi\) | ||||
−0.207179 | + | 0.978303i | \(0.566428\pi\) | |||||||
\(350\) | 12.2362 | 0.654052 | ||||||||
\(351\) | −2.16007 | −0.115296 | ||||||||
\(352\) | 29.1760 | 1.55508 | ||||||||
\(353\) | −10.6201 | −0.565253 | −0.282626 | − | 0.959230i | \(-0.591206\pi\) | ||||
−0.282626 | + | 0.959230i | \(0.591206\pi\) | |||||||
\(354\) | −1.24467 | −0.0661532 | ||||||||
\(355\) | 18.5932 | 0.986822 | ||||||||
\(356\) | 15.2046 | 0.805845 | ||||||||
\(357\) | 2.19233 | 0.116030 | ||||||||
\(358\) | 3.19433 | 0.168825 | ||||||||
\(359\) | 11.5939 | 0.611900 | 0.305950 | − | 0.952048i | \(-0.401026\pi\) | ||||
0.305950 | + | 0.952048i | \(0.401026\pi\) | |||||||
\(360\) | −2.82338 | −0.148805 | ||||||||
\(361\) | 25.4357 | 1.33872 | ||||||||
\(362\) | 30.3434 | 1.59481 | ||||||||
\(363\) | 2.14215 | 0.112434 | ||||||||
\(364\) | −5.20284 | −0.272703 | ||||||||
\(365\) | 10.6819 | 0.559115 | ||||||||
\(366\) | −28.4022 | −1.48461 | ||||||||
\(367\) | −19.5505 | −1.02053 | −0.510263 | − | 0.860018i | \(-0.670452\pi\) | ||||
−0.510263 | + | 0.860018i | \(0.670452\pi\) | |||||||
\(368\) | −7.13282 | −0.371824 | ||||||||
\(369\) | −0.647495 | −0.0337072 | ||||||||
\(370\) | 70.0953 | 3.64408 | ||||||||
\(371\) | 2.84924 | 0.147925 | ||||||||
\(372\) | −5.27993 | −0.273752 | ||||||||
\(373\) | 3.95621 | 0.204845 | 0.102423 | − | 0.994741i | \(-0.467341\pi\) | ||||
0.102423 | + | 0.994741i | \(0.467341\pi\) | |||||||
\(374\) | −16.6875 | −0.862891 | ||||||||
\(375\) | −2.72342 | −0.140637 | ||||||||
\(376\) | −7.37102 | −0.380131 | ||||||||
\(377\) | −4.45362 | −0.229373 | ||||||||
\(378\) | 2.09968 | 0.107996 | ||||||||
\(379\) | −26.2433 | −1.34803 | −0.674014 | − | 0.738718i | \(-0.735431\pi\) | ||||
−0.674014 | + | 0.738718i | \(0.735431\pi\) | |||||||
\(380\) | 52.8331 | 2.71028 | ||||||||
\(381\) | −1.00000 | −0.0512316 | ||||||||
\(382\) | 13.5731 | 0.694459 | ||||||||
\(383\) | 2.25979 | 0.115470 | 0.0577349 | − | 0.998332i | \(-0.481612\pi\) | ||||
0.0577349 | + | 0.998332i | \(0.481612\pi\) | |||||||
\(384\) | −6.72095 | −0.342977 | ||||||||
\(385\) | 11.9289 | 0.607953 | ||||||||
\(386\) | −44.9663 | −2.28872 | ||||||||
\(387\) | 3.67859 | 0.186993 | ||||||||
\(388\) | −0.166034 | −0.00842909 | ||||||||
\(389\) | −4.79264 | −0.242997 | −0.121498 | − | 0.992592i | \(-0.538770\pi\) | ||||
−0.121498 | + | 0.992592i | \(0.538770\pi\) | |||||||
\(390\) | 14.9241 | 0.755709 | ||||||||
\(391\) | 5.18535 | 0.262234 | ||||||||
\(392\) | 0.858029 | 0.0433370 | ||||||||
\(393\) | 17.8118 | 0.898488 | ||||||||
\(394\) | 32.0885 | 1.61659 | ||||||||
\(395\) | −13.1984 | −0.664083 | ||||||||
\(396\) | −8.73185 | −0.438792 | ||||||||
\(397\) | 34.5066 | 1.73184 | 0.865919 | − | 0.500185i | \(-0.166735\pi\) | ||||
0.865919 | + | 0.500185i | \(0.166735\pi\) | |||||||
\(398\) | −20.3301 | −1.01906 | ||||||||
\(399\) | −6.66601 | −0.333718 | ||||||||
\(400\) | −17.5745 | −0.878725 | ||||||||
\(401\) | −2.10653 | −0.105195 | −0.0525975 | − | 0.998616i | \(-0.516750\pi\) | ||||
−0.0525975 | + | 0.998616i | \(0.516750\pi\) | |||||||
\(402\) | 1.39436 | 0.0695444 | ||||||||
\(403\) | 4.73502 | 0.235868 | ||||||||
\(404\) | 15.7433 | 0.783257 | ||||||||
\(405\) | −3.29054 | −0.163508 | ||||||||
\(406\) | 4.32912 | 0.214850 | ||||||||
\(407\) | 36.7792 | 1.82308 | ||||||||
\(408\) | 1.88108 | 0.0931276 | ||||||||
\(409\) | 36.8469 | 1.82196 | 0.910981 | − | 0.412449i | \(-0.135327\pi\) | ||||
0.910981 | + | 0.412449i | \(0.135327\pi\) | |||||||
\(410\) | 4.47359 | 0.220935 | ||||||||
\(411\) | 7.51288 | 0.370583 | ||||||||
\(412\) | 3.42231 | 0.168605 | ||||||||
\(413\) | −0.592789 | −0.0291692 | ||||||||
\(414\) | 4.96620 | 0.244076 | ||||||||
\(415\) | 11.1889 | 0.549243 | ||||||||
\(416\) | 17.3844 | 0.852340 | ||||||||
\(417\) | −4.67226 | −0.228801 | ||||||||
\(418\) | 50.7401 | 2.48178 | ||||||||
\(419\) | −23.4163 | −1.14396 | −0.571981 | − | 0.820267i | \(-0.693825\pi\) | ||||
−0.571981 | + | 0.820267i | \(0.693825\pi\) | |||||||
\(420\) | −7.92575 | −0.386737 | ||||||||
\(421\) | 7.19583 | 0.350703 | 0.175352 | − | 0.984506i | \(-0.443894\pi\) | ||||
0.175352 | + | 0.984506i | \(0.443894\pi\) | |||||||
\(422\) | −47.6882 | −2.32143 | ||||||||
\(423\) | −8.59064 | −0.417691 | ||||||||
\(424\) | 2.44473 | 0.118727 | ||||||||
\(425\) | 12.7761 | 0.619734 | ||||||||
\(426\) | −11.8642 | −0.574823 | ||||||||
\(427\) | −13.5269 | −0.654614 | ||||||||
\(428\) | 41.2886 | 1.99576 | ||||||||
\(429\) | 7.83069 | 0.378069 | ||||||||
\(430\) | −25.4156 | −1.22565 | ||||||||
\(431\) | −18.8941 | −0.910098 | −0.455049 | − | 0.890466i | \(-0.650378\pi\) | ||||
−0.455049 | + | 0.890466i | \(0.650378\pi\) | |||||||
\(432\) | −3.01571 | −0.145093 | ||||||||
\(433\) | 18.2660 | 0.877810 | 0.438905 | − | 0.898534i | \(-0.355367\pi\) | ||||
0.438905 | + | 0.898534i | \(0.355367\pi\) | |||||||
\(434\) | −4.60265 | −0.220934 | ||||||||
\(435\) | −6.78443 | −0.325289 | ||||||||
\(436\) | 34.4766 | 1.65113 | ||||||||
\(437\) | −15.7666 | −0.754218 | ||||||||
\(438\) | −6.81605 | −0.325684 | ||||||||
\(439\) | −31.3238 | −1.49501 | −0.747503 | − | 0.664259i | \(-0.768747\pi\) | ||||
−0.747503 | + | 0.664259i | \(0.768747\pi\) | |||||||
\(440\) | 10.2353 | 0.487951 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −9.94319 | −0.472950 | ||||||||
\(443\) | −7.54570 | −0.358507 | −0.179254 | − | 0.983803i | \(-0.557368\pi\) | ||||
−0.179254 | + | 0.983803i | \(0.557368\pi\) | |||||||
\(444\) | −24.4367 | −1.15971 | ||||||||
\(445\) | −20.7716 | −0.984669 | ||||||||
\(446\) | 13.3117 | 0.630329 | ||||||||
\(447\) | −12.9632 | −0.613140 | ||||||||
\(448\) | −10.8670 | −0.513415 | ||||||||
\(449\) | −24.4439 | −1.15358 | −0.576790 | − | 0.816892i | \(-0.695695\pi\) | ||||
−0.576790 | + | 0.816892i | \(0.695695\pi\) | |||||||
\(450\) | 12.2362 | 0.576820 | ||||||||
\(451\) | 2.34730 | 0.110530 | ||||||||
\(452\) | 22.3492 | 1.05122 | ||||||||
\(453\) | 10.9338 | 0.513715 | ||||||||
\(454\) | −33.0382 | −1.55056 | ||||||||
\(455\) | 7.10778 | 0.333218 | ||||||||
\(456\) | −5.71963 | −0.267846 | ||||||||
\(457\) | 10.3236 | 0.482915 | 0.241458 | − | 0.970411i | \(-0.422375\pi\) | ||||
0.241458 | + | 0.970411i | \(0.422375\pi\) | |||||||
\(458\) | −0.766959 | −0.0358377 | ||||||||
\(459\) | 2.19233 | 0.102329 | ||||||||
\(460\) | −18.7462 | −0.874044 | ||||||||
\(461\) | −0.224984 | −0.0104785 | −0.00523927 | − | 0.999986i | \(-0.501668\pi\) | ||||
−0.00523927 | + | 0.999986i | \(0.501668\pi\) | |||||||
\(462\) | −7.61177 | −0.354132 | ||||||||
\(463\) | −21.4269 | −0.995795 | −0.497897 | − | 0.867236i | \(-0.665894\pi\) | ||||
−0.497897 | + | 0.867236i | \(0.665894\pi\) | |||||||
\(464\) | −6.21779 | −0.288654 | ||||||||
\(465\) | 7.21310 | 0.334500 | ||||||||
\(466\) | −8.84580 | −0.409774 | ||||||||
\(467\) | 14.8070 | 0.685186 | 0.342593 | − | 0.939484i | \(-0.388695\pi\) | ||||
0.342593 | + | 0.939484i | \(0.388695\pi\) | |||||||
\(468\) | −5.20284 | −0.240501 | ||||||||
\(469\) | 0.664083 | 0.0306645 | ||||||||
\(470\) | 59.3534 | 2.73777 | ||||||||
\(471\) | −20.5157 | −0.945313 | ||||||||
\(472\) | −0.508630 | −0.0234116 | ||||||||
\(473\) | −13.3357 | −0.613174 | ||||||||
\(474\) | 8.42183 | 0.386828 | ||||||||
\(475\) | −38.8472 | −1.78243 | ||||||||
\(476\) | 5.28055 | 0.242034 | ||||||||
\(477\) | 2.84924 | 0.130458 | ||||||||
\(478\) | −7.11414 | −0.325393 | ||||||||
\(479\) | −10.2074 | −0.466390 | −0.233195 | − | 0.972430i | \(-0.574918\pi\) | ||||
−0.233195 | + | 0.972430i | \(0.574918\pi\) | |||||||
\(480\) | 26.4825 | 1.20876 | ||||||||
\(481\) | 21.9147 | 0.999226 | ||||||||
\(482\) | −21.1246 | −0.962198 | ||||||||
\(483\) | 2.36522 | 0.107621 | ||||||||
\(484\) | 5.15968 | 0.234531 | ||||||||
\(485\) | 0.226825 | 0.0102996 | ||||||||
\(486\) | 2.09968 | 0.0952433 | ||||||||
\(487\) | 16.1543 | 0.732023 | 0.366011 | − | 0.930610i | \(-0.380723\pi\) | ||||
0.366011 | + | 0.930610i | \(0.380723\pi\) | |||||||
\(488\) | −11.6065 | −0.525402 | ||||||||
\(489\) | 1.33340 | 0.0602984 | ||||||||
\(490\) | −6.90907 | −0.312120 | ||||||||
\(491\) | −12.4633 | −0.562459 | −0.281229 | − | 0.959641i | \(-0.590742\pi\) | ||||
−0.281229 | + | 0.959641i | \(0.590742\pi\) | |||||||
\(492\) | −1.55959 | −0.0703116 | ||||||||
\(493\) | 4.52015 | 0.203577 | ||||||||
\(494\) | 30.2333 | 1.36026 | ||||||||
\(495\) | 11.9289 | 0.536164 | ||||||||
\(496\) | 6.61066 | 0.296827 | ||||||||
\(497\) | −5.65049 | −0.253459 | ||||||||
\(498\) | −7.13960 | −0.319933 | ||||||||
\(499\) | −13.4987 | −0.604283 | −0.302142 | − | 0.953263i | \(-0.597702\pi\) | ||||
−0.302142 | + | 0.953263i | \(0.597702\pi\) | |||||||
\(500\) | −6.55976 | −0.293361 | ||||||||
\(501\) | 0.822111 | 0.0367292 | ||||||||
\(502\) | 2.37673 | 0.106078 | ||||||||
\(503\) | 22.8347 | 1.01815 | 0.509074 | − | 0.860723i | \(-0.329988\pi\) | ||||
0.509074 | + | 0.860723i | \(0.329988\pi\) | |||||||
\(504\) | 0.858029 | 0.0382197 | ||||||||
\(505\) | −21.5074 | −0.957068 | ||||||||
\(506\) | −18.0035 | −0.800354 | ||||||||
\(507\) | −8.33411 | −0.370131 | ||||||||
\(508\) | −2.40865 | −0.106866 | ||||||||
\(509\) | −27.5341 | −1.22043 | −0.610214 | − | 0.792237i | \(-0.708916\pi\) | ||||
−0.610214 | + | 0.792237i | \(0.708916\pi\) | |||||||
\(510\) | −15.1470 | −0.670719 | ||||||||
\(511\) | −3.24624 | −0.143605 | ||||||||
\(512\) | 29.4458 | 1.30133 | ||||||||
\(513\) | −6.66601 | −0.294311 | ||||||||
\(514\) | −61.4077 | −2.70858 | ||||||||
\(515\) | −4.67534 | −0.206020 | ||||||||
\(516\) | 8.86042 | 0.390058 | ||||||||
\(517\) | 31.1429 | 1.36966 | ||||||||
\(518\) | −21.3021 | −0.935959 | ||||||||
\(519\) | −22.8603 | −1.00346 | ||||||||
\(520\) | 6.09869 | 0.267445 | ||||||||
\(521\) | 21.7185 | 0.951504 | 0.475752 | − | 0.879580i | \(-0.342176\pi\) | ||||
0.475752 | + | 0.879580i | \(0.342176\pi\) | |||||||
\(522\) | 4.32912 | 0.189480 | ||||||||
\(523\) | −25.3129 | −1.10685 | −0.553427 | − | 0.832898i | \(-0.686680\pi\) | ||||
−0.553427 | + | 0.832898i | \(0.686680\pi\) | |||||||
\(524\) | 42.9024 | 1.87420 | ||||||||
\(525\) | 5.82765 | 0.254340 | ||||||||
\(526\) | 55.3593 | 2.41378 | ||||||||
\(527\) | −4.80575 | −0.209342 | ||||||||
\(528\) | 10.9326 | 0.475780 | ||||||||
\(529\) | −17.4057 | −0.756771 | ||||||||
\(530\) | −19.6856 | −0.855087 | ||||||||
\(531\) | −0.592789 | −0.0257248 | ||||||||
\(532\) | −16.0561 | −0.696119 | ||||||||
\(533\) | 1.39863 | 0.0605815 | ||||||||
\(534\) | 13.2543 | 0.573568 | ||||||||
\(535\) | −56.4058 | −2.43864 | ||||||||
\(536\) | 0.569803 | 0.0246117 | ||||||||
\(537\) | 1.52134 | 0.0656508 | ||||||||
\(538\) | −46.6703 | −2.01210 | ||||||||
\(539\) | −3.62521 | −0.156149 | ||||||||
\(540\) | −7.92575 | −0.341070 | ||||||||
\(541\) | −0.966528 | −0.0415543 | −0.0207771 | − | 0.999784i | \(-0.506614\pi\) | ||||
−0.0207771 | + | 0.999784i | \(0.506614\pi\) | |||||||
\(542\) | −56.3744 | −2.42149 | ||||||||
\(543\) | 14.4514 | 0.620171 | ||||||||
\(544\) | −17.6441 | −0.756483 | ||||||||
\(545\) | −47.0997 | −2.01753 | ||||||||
\(546\) | −4.53544 | −0.194099 | ||||||||
\(547\) | −6.92682 | −0.296170 | −0.148085 | − | 0.988975i | \(-0.547311\pi\) | ||||
−0.148085 | + | 0.988975i | \(0.547311\pi\) | |||||||
\(548\) | 18.0959 | 0.773018 | ||||||||
\(549\) | −13.5269 | −0.577315 | ||||||||
\(550\) | −44.3588 | −1.89146 | ||||||||
\(551\) | −13.7440 | −0.585513 | ||||||||
\(552\) | 2.02943 | 0.0863782 | ||||||||
\(553\) | 4.01101 | 0.170566 | ||||||||
\(554\) | 4.43021 | 0.188222 | ||||||||
\(555\) | 33.3838 | 1.41706 | ||||||||
\(556\) | −11.2538 | −0.477268 | ||||||||
\(557\) | −41.5856 | −1.76204 | −0.881019 | − | 0.473080i | \(-0.843142\pi\) | ||||
−0.881019 | + | 0.473080i | \(0.843142\pi\) | |||||||
\(558\) | −4.60265 | −0.194846 | ||||||||
\(559\) | −7.94600 | −0.336080 | ||||||||
\(560\) | 9.92332 | 0.419337 | ||||||||
\(561\) | −7.94766 | −0.335550 | ||||||||
\(562\) | 41.1645 | 1.73642 | ||||||||
\(563\) | −31.7414 | −1.33774 | −0.668871 | − | 0.743378i | \(-0.733222\pi\) | ||||
−0.668871 | + | 0.743378i | \(0.733222\pi\) | |||||||
\(564\) | −20.6918 | −0.871283 | ||||||||
\(565\) | −30.5320 | −1.28449 | ||||||||
\(566\) | −11.1025 | −0.466673 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −4.84828 | −0.203429 | ||||||||
\(569\) | −0.333729 | −0.0139906 | −0.00699532 | − | 0.999976i | \(-0.502227\pi\) | ||||
−0.00699532 | + | 0.999976i | \(0.502227\pi\) | |||||||
\(570\) | 46.0559 | 1.92907 | ||||||||
\(571\) | 12.9921 | 0.543704 | 0.271852 | − | 0.962339i | \(-0.412364\pi\) | ||||
0.271852 | + | 0.962339i | \(0.412364\pi\) | |||||||
\(572\) | 18.8614 | 0.788634 | ||||||||
\(573\) | 6.46436 | 0.270052 | ||||||||
\(574\) | −1.35953 | −0.0567457 | ||||||||
\(575\) | 13.7837 | 0.574819 | ||||||||
\(576\) | −10.8670 | −0.452790 | ||||||||
\(577\) | 32.0896 | 1.33591 | 0.667954 | − | 0.744203i | \(-0.267170\pi\) | ||||
0.667954 | + | 0.744203i | \(0.267170\pi\) | |||||||
\(578\) | −25.6028 | −1.06494 | ||||||||
\(579\) | −21.4158 | −0.890010 | ||||||||
\(580\) | −16.3413 | −0.678536 | ||||||||
\(581\) | −3.40033 | −0.141070 | ||||||||
\(582\) | −0.144736 | −0.00599949 | ||||||||
\(583\) | −10.3291 | −0.427787 | ||||||||
\(584\) | −2.78537 | −0.115259 | ||||||||
\(585\) | 7.10778 | 0.293871 | ||||||||
\(586\) | 19.0152 | 0.785509 | ||||||||
\(587\) | −40.9497 | −1.69017 | −0.845087 | − | 0.534629i | \(-0.820451\pi\) | ||||
−0.845087 | + | 0.534629i | \(0.820451\pi\) | |||||||
\(588\) | 2.40865 | 0.0993310 | ||||||||
\(589\) | 14.6124 | 0.602093 | ||||||||
\(590\) | 4.09562 | 0.168614 | ||||||||
\(591\) | 15.2826 | 0.628640 | ||||||||
\(592\) | 30.5956 | 1.25747 | ||||||||
\(593\) | 42.4563 | 1.74347 | 0.871735 | − | 0.489978i | \(-0.162995\pi\) | ||||
0.871735 | + | 0.489978i | \(0.162995\pi\) | |||||||
\(594\) | −7.61177 | −0.312315 | ||||||||
\(595\) | −7.21395 | −0.295743 | ||||||||
\(596\) | −31.2238 | −1.27898 | ||||||||
\(597\) | −9.68248 | −0.396277 | ||||||||
\(598\) | −10.7273 | −0.438673 | ||||||||
\(599\) | 26.8144 | 1.09560 | 0.547802 | − | 0.836608i | \(-0.315465\pi\) | ||||
0.547802 | + | 0.836608i | \(0.315465\pi\) | |||||||
\(600\) | 5.00030 | 0.204136 | ||||||||
\(601\) | −32.3520 | −1.31967 | −0.659833 | − | 0.751412i | \(-0.729373\pi\) | ||||
−0.659833 | + | 0.751412i | \(0.729373\pi\) | |||||||
\(602\) | 7.72385 | 0.314801 | ||||||||
\(603\) | 0.664083 | 0.0270435 | ||||||||
\(604\) | 26.3357 | 1.07158 | ||||||||
\(605\) | −7.04882 | −0.286575 | ||||||||
\(606\) | 13.7238 | 0.557491 | ||||||||
\(607\) | −5.75375 | −0.233538 | −0.116769 | − | 0.993159i | \(-0.537254\pi\) | ||||
−0.116769 | + | 0.993159i | \(0.537254\pi\) | |||||||
\(608\) | 53.6486 | 2.17574 | ||||||||
\(609\) | 2.06180 | 0.0835483 | ||||||||
\(610\) | 93.4585 | 3.78402 | ||||||||
\(611\) | 18.5564 | 0.750710 | ||||||||
\(612\) | 5.28055 | 0.213454 | ||||||||
\(613\) | −28.0175 | −1.13162 | −0.565808 | − | 0.824537i | \(-0.691436\pi\) | ||||
−0.565808 | + | 0.824537i | \(0.691436\pi\) | |||||||
\(614\) | 49.3261 | 1.99064 | ||||||||
\(615\) | 2.13061 | 0.0859144 | ||||||||
\(616\) | −3.11054 | −0.125327 | ||||||||
\(617\) | −1.13222 | −0.0455814 | −0.0227907 | − | 0.999740i | \(-0.507255\pi\) | ||||
−0.0227907 | + | 0.999740i | \(0.507255\pi\) | |||||||
\(618\) | 2.98332 | 0.120007 | ||||||||
\(619\) | 14.6756 | 0.589862 | 0.294931 | − | 0.955519i | \(-0.404703\pi\) | ||||
0.294931 | + | 0.955519i | \(0.404703\pi\) | |||||||
\(620\) | 17.3738 | 0.697750 | ||||||||
\(621\) | 2.36522 | 0.0949130 | ||||||||
\(622\) | −0.223847 | −0.00897545 | ||||||||
\(623\) | 6.31252 | 0.252906 | ||||||||
\(624\) | 6.51414 | 0.260774 | ||||||||
\(625\) | −20.1767 | −0.807070 | ||||||||
\(626\) | 49.6180 | 1.98313 | ||||||||
\(627\) | 24.1657 | 0.965084 | ||||||||
\(628\) | −49.4151 | −1.97188 | ||||||||
\(629\) | −22.2421 | −0.886849 | ||||||||
\(630\) | −6.90907 | −0.275264 | ||||||||
\(631\) | −33.4295 | −1.33081 | −0.665404 | − | 0.746483i | \(-0.731741\pi\) | ||||
−0.665404 | + | 0.746483i | \(0.731741\pi\) | |||||||
\(632\) | 3.44157 | 0.136898 | ||||||||
\(633\) | −22.7122 | −0.902727 | ||||||||
\(634\) | 18.6259 | 0.739729 | ||||||||
\(635\) | 3.29054 | 0.130581 | ||||||||
\(636\) | 6.86281 | 0.272128 | ||||||||
\(637\) | −2.16007 | −0.0855850 | ||||||||
\(638\) | −15.6940 | −0.621329 | ||||||||
\(639\) | −5.65049 | −0.223530 | ||||||||
\(640\) | 22.1156 | 0.874194 | ||||||||
\(641\) | 13.4509 | 0.531278 | 0.265639 | − | 0.964073i | \(-0.414417\pi\) | ||||
0.265639 | + | 0.964073i | \(0.414417\pi\) | |||||||
\(642\) | 35.9923 | 1.42050 | ||||||||
\(643\) | 11.7618 | 0.463838 | 0.231919 | − | 0.972735i | \(-0.425499\pi\) | ||||
0.231919 | + | 0.972735i | \(0.425499\pi\) | |||||||
\(644\) | 5.69698 | 0.224493 | ||||||||
\(645\) | −12.1045 | −0.476616 | ||||||||
\(646\) | −30.6849 | −1.20728 | ||||||||
\(647\) | 8.12298 | 0.319347 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(648\) | 0.858029 | 0.0337066 | ||||||||
\(649\) | 2.14898 | 0.0843550 | ||||||||
\(650\) | −26.4310 | −1.03671 | ||||||||
\(651\) | −2.19207 | −0.0859141 | ||||||||
\(652\) | 3.21169 | 0.125779 | ||||||||
\(653\) | −29.8203 | −1.16696 | −0.583479 | − | 0.812128i | \(-0.698309\pi\) | ||||
−0.583479 | + | 0.812128i | \(0.698309\pi\) | |||||||
\(654\) | 30.0541 | 1.17521 | ||||||||
\(655\) | −58.6105 | −2.29010 | ||||||||
\(656\) | 1.95266 | 0.0762384 | ||||||||
\(657\) | −3.24624 | −0.126648 | ||||||||
\(658\) | −18.0376 | −0.703178 | ||||||||
\(659\) | 7.08303 | 0.275916 | 0.137958 | − | 0.990438i | \(-0.455946\pi\) | ||||
0.137958 | + | 0.990438i | \(0.455946\pi\) | |||||||
\(660\) | 28.7325 | 1.11841 | ||||||||
\(661\) | 36.2548 | 1.41015 | 0.705075 | − | 0.709133i | \(-0.250913\pi\) | ||||
0.705075 | + | 0.709133i | \(0.250913\pi\) | |||||||
\(662\) | −57.4990 | −2.23476 | ||||||||
\(663\) | −4.73558 | −0.183915 | ||||||||
\(664\) | −2.91758 | −0.113224 | ||||||||
\(665\) | 21.9348 | 0.850594 | ||||||||
\(666\) | −21.3021 | −0.825439 | ||||||||
\(667\) | 4.87661 | 0.188823 | ||||||||
\(668\) | 1.98018 | 0.0766153 | ||||||||
\(669\) | 6.33989 | 0.245114 | ||||||||
\(670\) | −4.58820 | −0.177258 | ||||||||
\(671\) | 49.0379 | 1.89309 | ||||||||
\(672\) | −8.04808 | −0.310461 | ||||||||
\(673\) | 22.9499 | 0.884656 | 0.442328 | − | 0.896853i | \(-0.354153\pi\) | ||||
0.442328 | + | 0.896853i | \(0.354153\pi\) | |||||||
\(674\) | 38.8226 | 1.49539 | ||||||||
\(675\) | 5.82765 | 0.224306 | ||||||||
\(676\) | −20.0739 | −0.772075 | ||||||||
\(677\) | 3.57237 | 0.137297 | 0.0686486 | − | 0.997641i | \(-0.478131\pi\) | ||||
0.0686486 | + | 0.997641i | \(0.478131\pi\) | |||||||
\(678\) | 19.4824 | 0.748215 | ||||||||
\(679\) | −0.0689323 | −0.00264538 | ||||||||
\(680\) | −6.18978 | −0.237367 | ||||||||
\(681\) | −15.7349 | −0.602962 | ||||||||
\(682\) | 16.6856 | 0.638923 | ||||||||
\(683\) | −22.1918 | −0.849145 | −0.424573 | − | 0.905394i | \(-0.639576\pi\) | ||||
−0.424573 | + | 0.905394i | \(0.639576\pi\) | |||||||
\(684\) | −16.0561 | −0.613919 | ||||||||
\(685\) | −24.7214 | −0.944558 | ||||||||
\(686\) | 2.09968 | 0.0801661 | ||||||||
\(687\) | −0.365275 | −0.0139361 | ||||||||
\(688\) | −11.0936 | −0.422938 | ||||||||
\(689\) | −6.15454 | −0.234469 | ||||||||
\(690\) | −16.3415 | −0.622110 | ||||||||
\(691\) | −27.5328 | −1.04740 | −0.523698 | − | 0.851904i | \(-0.675448\pi\) | ||||
−0.523698 | + | 0.851904i | \(0.675448\pi\) | |||||||
\(692\) | −55.0625 | −2.09316 | ||||||||
\(693\) | −3.62521 | −0.137710 | ||||||||
\(694\) | 50.8979 | 1.93206 | ||||||||
\(695\) | 15.3742 | 0.583178 | ||||||||
\(696\) | 1.76908 | 0.0670570 | ||||||||
\(697\) | −1.41952 | −0.0537683 | ||||||||
\(698\) | −16.2533 | −0.615195 | ||||||||
\(699\) | −4.21293 | −0.159348 | ||||||||
\(700\) | 14.0368 | 0.530540 | ||||||||
\(701\) | −33.7129 | −1.27332 | −0.636659 | − | 0.771146i | \(-0.719684\pi\) | ||||
−0.636659 | + | 0.771146i | \(0.719684\pi\) | |||||||
\(702\) | −4.53544 | −0.171179 | ||||||||
\(703\) | 67.6293 | 2.55069 | ||||||||
\(704\) | 39.3950 | 1.48475 | ||||||||
\(705\) | 28.2678 | 1.06463 | ||||||||
\(706\) | −22.2989 | −0.839229 | ||||||||
\(707\) | 6.53614 | 0.245817 | ||||||||
\(708\) | −1.42782 | −0.0536607 | ||||||||
\(709\) | −43.1638 | −1.62105 | −0.810525 | − | 0.585704i | \(-0.800818\pi\) | ||||
−0.810525 | + | 0.585704i | \(0.800818\pi\) | |||||||
\(710\) | 39.0396 | 1.46513 | ||||||||
\(711\) | 4.01101 | 0.150425 | ||||||||
\(712\) | 5.41633 | 0.202986 | ||||||||
\(713\) | −5.18474 | −0.194170 | ||||||||
\(714\) | 4.60319 | 0.172270 | ||||||||
\(715\) | −25.7672 | −0.963639 | ||||||||
\(716\) | 3.66438 | 0.136944 | ||||||||
\(717\) | −3.38821 | −0.126535 | ||||||||
\(718\) | 24.3434 | 0.908486 | ||||||||
\(719\) | 13.6734 | 0.509931 | 0.254965 | − | 0.966950i | \(-0.417936\pi\) | ||||
0.254965 | + | 0.966950i | \(0.417936\pi\) | |||||||
\(720\) | 9.92332 | 0.369820 | ||||||||
\(721\) | 1.42084 | 0.0529150 | ||||||||
\(722\) | 53.4067 | 1.98759 | ||||||||
\(723\) | −10.0609 | −0.374168 | ||||||||
\(724\) | 34.8085 | 1.29365 | ||||||||
\(725\) | 12.0154 | 0.446243 | ||||||||
\(726\) | 4.49782 | 0.166930 | ||||||||
\(727\) | −32.4355 | −1.20297 | −0.601483 | − | 0.798886i | \(-0.705423\pi\) | ||||
−0.601483 | + | 0.798886i | \(0.705423\pi\) | |||||||
\(728\) | −1.85340 | −0.0686916 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 22.4285 | 0.830116 | ||||||||
\(731\) | 8.06468 | 0.298283 | ||||||||
\(732\) | −32.5816 | −1.20425 | ||||||||
\(733\) | −42.8281 | −1.58189 | −0.790946 | − | 0.611886i | \(-0.790411\pi\) | ||||
−0.790946 | + | 0.611886i | \(0.790411\pi\) | |||||||
\(734\) | −41.0497 | −1.51517 | ||||||||
\(735\) | −3.29054 | −0.121373 | ||||||||
\(736\) | −19.0355 | −0.701657 | ||||||||
\(737\) | −2.40744 | −0.0886792 | ||||||||
\(738\) | −1.35953 | −0.0500450 | ||||||||
\(739\) | 38.7706 | 1.42620 | 0.713099 | − | 0.701063i | \(-0.247291\pi\) | ||||
0.713099 | + | 0.701063i | \(0.247291\pi\) | |||||||
\(740\) | 80.4099 | 2.95593 | ||||||||
\(741\) | 14.3990 | 0.528961 | ||||||||
\(742\) | 5.98248 | 0.219624 | ||||||||
\(743\) | 13.9130 | 0.510418 | 0.255209 | − | 0.966886i | \(-0.417856\pi\) | ||||
0.255209 | + | 0.966886i | \(0.417856\pi\) | |||||||
\(744\) | −1.88086 | −0.0689558 | ||||||||
\(745\) | 42.6560 | 1.56280 | ||||||||
\(746\) | 8.30678 | 0.304133 | ||||||||
\(747\) | −3.40033 | −0.124412 | ||||||||
\(748\) | −19.1431 | −0.699942 | ||||||||
\(749\) | 17.1418 | 0.626348 | ||||||||
\(750\) | −5.71830 | −0.208803 | ||||||||
\(751\) | −0.457421 | −0.0166915 | −0.00834576 | − | 0.999965i | \(-0.502657\pi\) | ||||
−0.00834576 | + | 0.999965i | \(0.502657\pi\) | |||||||
\(752\) | 25.9069 | 0.944727 | ||||||||
\(753\) | 1.13195 | 0.0412505 | ||||||||
\(754\) | −9.35118 | −0.340550 | ||||||||
\(755\) | −35.9781 | −1.30938 | ||||||||
\(756\) | 2.40865 | 0.0876017 | ||||||||
\(757\) | −20.9802 | −0.762539 | −0.381269 | − | 0.924464i | \(-0.624513\pi\) | ||||
−0.381269 | + | 0.924464i | \(0.624513\pi\) | |||||||
\(758\) | −55.1025 | −2.00141 | ||||||||
\(759\) | −8.57442 | −0.311232 | ||||||||
\(760\) | 18.8207 | 0.682697 | ||||||||
\(761\) | −30.4760 | −1.10476 | −0.552378 | − | 0.833594i | \(-0.686279\pi\) | ||||
−0.552378 | + | 0.833594i | \(0.686279\pi\) | |||||||
\(762\) | −2.09968 | −0.0760633 | ||||||||
\(763\) | 14.3137 | 0.518189 | ||||||||
\(764\) | 15.5704 | 0.563316 | ||||||||
\(765\) | −7.21395 | −0.260821 | ||||||||
\(766\) | 4.74483 | 0.171438 | ||||||||
\(767\) | 1.28046 | 0.0462348 | ||||||||
\(768\) | 7.62208 | 0.275038 | ||||||||
\(769\) | −21.8499 | −0.787927 | −0.393963 | − | 0.919126i | \(-0.628896\pi\) | ||||
−0.393963 | + | 0.919126i | \(0.628896\pi\) | |||||||
\(770\) | 25.0468 | 0.902626 | ||||||||
\(771\) | −29.2462 | −1.05328 | ||||||||
\(772\) | −51.5831 | −1.85652 | ||||||||
\(773\) | 19.4525 | 0.699659 | 0.349830 | − | 0.936813i | \(-0.386239\pi\) | ||||
0.349830 | + | 0.936813i | \(0.386239\pi\) | |||||||
\(774\) | 7.72385 | 0.277628 | ||||||||
\(775\) | −12.7746 | −0.458879 | ||||||||
\(776\) | −0.0591460 | −0.00212322 | ||||||||
\(777\) | −10.1454 | −0.363964 | ||||||||
\(778\) | −10.0630 | −0.360776 | ||||||||
\(779\) | 4.31620 | 0.154644 | ||||||||
\(780\) | 17.1202 | 0.613000 | ||||||||
\(781\) | 20.4842 | 0.732982 | ||||||||
\(782\) | 10.8876 | 0.389338 | ||||||||
\(783\) | 2.06180 | 0.0736827 | ||||||||
\(784\) | −3.01571 | −0.107704 | ||||||||
\(785\) | 67.5077 | 2.40945 | ||||||||
\(786\) | 37.3991 | 1.33398 | ||||||||
\(787\) | 41.2974 | 1.47209 | 0.736047 | − | 0.676930i | \(-0.236690\pi\) | ||||
0.736047 | + | 0.676930i | \(0.236690\pi\) | |||||||
\(788\) | 36.8103 | 1.31131 | ||||||||
\(789\) | 26.3656 | 0.938641 | ||||||||
\(790\) | −27.7124 | −0.985962 | ||||||||
\(791\) | 9.27873 | 0.329914 | ||||||||
\(792\) | −3.11054 | −0.110528 | ||||||||
\(793\) | 29.2191 | 1.03760 | ||||||||
\(794\) | 72.4528 | 2.57125 | ||||||||
\(795\) | −9.37552 | −0.332516 | ||||||||
\(796\) | −23.3217 | −0.826615 | ||||||||
\(797\) | −35.1784 | −1.24608 | −0.623042 | − | 0.782188i | \(-0.714103\pi\) | ||||
−0.623042 | + | 0.782188i | \(0.714103\pi\) | |||||||
\(798\) | −13.9965 | −0.495470 | ||||||||
\(799\) | −18.8335 | −0.666282 | ||||||||
\(800\) | −46.9014 | −1.65822 | ||||||||
\(801\) | 6.31252 | 0.223042 | ||||||||
\(802\) | −4.42303 | −0.156183 | ||||||||
\(803\) | 11.7683 | 0.415294 | ||||||||
\(804\) | 1.59954 | 0.0564115 | ||||||||
\(805\) | −7.78285 | −0.274310 | ||||||||
\(806\) | 9.94203 | 0.350193 | ||||||||
\(807\) | −22.2274 | −0.782440 | ||||||||
\(808\) | 5.60820 | 0.197296 | ||||||||
\(809\) | 32.9258 | 1.15761 | 0.578804 | − | 0.815466i | \(-0.303520\pi\) | ||||
0.578804 | + | 0.815466i | \(0.303520\pi\) | |||||||
\(810\) | −6.90907 | −0.242760 | ||||||||
\(811\) | −46.5481 | −1.63453 | −0.817263 | − | 0.576265i | \(-0.804510\pi\) | ||||
−0.817263 | + | 0.576265i | \(0.804510\pi\) | |||||||
\(812\) | 4.96615 | 0.174278 | ||||||||
\(813\) | −26.8490 | −0.941637 | ||||||||
\(814\) | 77.2245 | 2.70672 | ||||||||
\(815\) | −4.38760 | −0.153691 | ||||||||
\(816\) | −6.61144 | −0.231447 | ||||||||
\(817\) | −24.5215 | −0.857899 | ||||||||
\(818\) | 77.3666 | 2.70506 | ||||||||
\(819\) | −2.16007 | −0.0754788 | ||||||||
\(820\) | 5.13188 | 0.179213 | ||||||||
\(821\) | 24.6736 | 0.861114 | 0.430557 | − | 0.902563i | \(-0.358317\pi\) | ||||
0.430557 | + | 0.902563i | \(0.358317\pi\) | |||||||
\(822\) | 15.7746 | 0.550204 | ||||||||
\(823\) | −35.8137 | −1.24839 | −0.624193 | − | 0.781270i | \(-0.714572\pi\) | ||||
−0.624193 | + | 0.781270i | \(0.714572\pi\) | |||||||
\(824\) | 1.21913 | 0.0424703 | ||||||||
\(825\) | −21.1265 | −0.735529 | ||||||||
\(826\) | −1.24467 | −0.0433075 | ||||||||
\(827\) | −43.4022 | −1.50924 | −0.754621 | − | 0.656161i | \(-0.772179\pi\) | ||||
−0.754621 | + | 0.656161i | \(0.772179\pi\) | |||||||
\(828\) | 5.69698 | 0.197984 | ||||||||
\(829\) | −12.6369 | −0.438896 | −0.219448 | − | 0.975624i | \(-0.570426\pi\) | ||||
−0.219448 | + | 0.975624i | \(0.570426\pi\) | |||||||
\(830\) | 23.4931 | 0.815459 | ||||||||
\(831\) | 2.10995 | 0.0731933 | ||||||||
\(832\) | 23.4733 | 0.813792 | ||||||||
\(833\) | 2.19233 | 0.0759598 | ||||||||
\(834\) | −9.81024 | −0.339701 | ||||||||
\(835\) | −2.70519 | −0.0936170 | ||||||||
\(836\) | 58.2066 | 2.01312 | ||||||||
\(837\) | −2.19207 | −0.0757691 | ||||||||
\(838\) | −49.1668 | −1.69844 | ||||||||
\(839\) | 28.0483 | 0.968336 | 0.484168 | − | 0.874975i | \(-0.339122\pi\) | ||||
0.484168 | + | 0.874975i | \(0.339122\pi\) | |||||||
\(840\) | −2.82338 | −0.0974159 | ||||||||
\(841\) | −24.7490 | −0.853413 | ||||||||
\(842\) | 15.1089 | 0.520688 | ||||||||
\(843\) | 19.6051 | 0.675237 | ||||||||
\(844\) | −54.7056 | −1.88304 | ||||||||
\(845\) | 27.4237 | 0.943405 | ||||||||
\(846\) | −18.0376 | −0.620145 | ||||||||
\(847\) | 2.14215 | 0.0736050 | ||||||||
\(848\) | −8.59247 | −0.295067 | ||||||||
\(849\) | −5.28771 | −0.181474 | ||||||||
\(850\) | 26.8258 | 0.920117 | ||||||||
\(851\) | −23.9961 | −0.822576 | ||||||||
\(852\) | −13.6100 | −0.466272 | ||||||||
\(853\) | 19.5717 | 0.670121 | 0.335060 | − | 0.942197i | \(-0.391243\pi\) | ||||
0.335060 | + | 0.942197i | \(0.391243\pi\) | |||||||
\(854\) | −28.4022 | −0.971903 | ||||||||
\(855\) | 21.9348 | 0.750153 | ||||||||
\(856\) | 14.7082 | 0.502715 | ||||||||
\(857\) | 5.60926 | 0.191609 | 0.0958043 | − | 0.995400i | \(-0.469458\pi\) | ||||
0.0958043 | + | 0.995400i | \(0.469458\pi\) | |||||||
\(858\) | 16.4419 | 0.561318 | ||||||||
\(859\) | 9.59070 | 0.327231 | 0.163615 | − | 0.986524i | \(-0.447684\pi\) | ||||
0.163615 | + | 0.986524i | \(0.447684\pi\) | |||||||
\(860\) | −29.1556 | −0.994197 | ||||||||
\(861\) | −0.647495 | −0.0220666 | ||||||||
\(862\) | −39.6716 | −1.35122 | ||||||||
\(863\) | −30.6668 | −1.04391 | −0.521955 | − | 0.852973i | \(-0.674797\pi\) | ||||
−0.521955 | + | 0.852973i | \(0.674797\pi\) | |||||||
\(864\) | −8.04808 | −0.273801 | ||||||||
\(865\) | 75.2229 | 2.55765 | ||||||||
\(866\) | 38.3528 | 1.30328 | ||||||||
\(867\) | −12.1937 | −0.414119 | ||||||||
\(868\) | −5.27993 | −0.179213 | ||||||||
\(869\) | −14.5408 | −0.493262 | ||||||||
\(870\) | −14.2451 | −0.482955 | ||||||||
\(871\) | −1.43446 | −0.0486049 | ||||||||
\(872\) | 12.2815 | 0.415905 | ||||||||
\(873\) | −0.0689323 | −0.00233301 | ||||||||
\(874\) | −33.1047 | −1.11978 | ||||||||
\(875\) | −2.72342 | −0.0920684 | ||||||||
\(876\) | −7.81904 | −0.264181 | ||||||||
\(877\) | −3.44789 | −0.116427 | −0.0582136 | − | 0.998304i | \(-0.518540\pi\) | ||||
−0.0582136 | + | 0.998304i | \(0.518540\pi\) | |||||||
\(878\) | −65.7700 | −2.21963 | ||||||||
\(879\) | 9.05623 | 0.305459 | ||||||||
\(880\) | −35.9741 | −1.21269 | ||||||||
\(881\) | 37.1051 | 1.25010 | 0.625052 | − | 0.780583i | \(-0.285078\pi\) | ||||
0.625052 | + | 0.780583i | \(0.285078\pi\) | |||||||
\(882\) | 2.09968 | 0.0706998 | ||||||||
\(883\) | −18.6304 | −0.626964 | −0.313482 | − | 0.949594i | \(-0.601496\pi\) | ||||
−0.313482 | + | 0.949594i | \(0.601496\pi\) | |||||||
\(884\) | −11.4063 | −0.383637 | ||||||||
\(885\) | 1.95059 | 0.0655685 | ||||||||
\(886\) | −15.8435 | −0.532274 | ||||||||
\(887\) | −4.44415 | −0.149220 | −0.0746100 | − | 0.997213i | \(-0.523771\pi\) | ||||
−0.0746100 | + | 0.997213i | \(0.523771\pi\) | |||||||
\(888\) | −8.70505 | −0.292122 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −43.6137 | −1.46193 | ||||||||
\(891\) | −3.62521 | −0.121449 | ||||||||
\(892\) | 15.2706 | 0.511297 | ||||||||
\(893\) | 57.2653 | 1.91631 | ||||||||
\(894\) | −27.2186 | −0.910326 | ||||||||
\(895\) | −5.00604 | −0.167333 | ||||||||
\(896\) | −6.72095 | −0.224531 | ||||||||
\(897\) | −5.10903 | −0.170586 | ||||||||
\(898\) | −51.3244 | −1.71272 | ||||||||
\(899\) | −4.51962 | −0.150738 | ||||||||
\(900\) | 14.0368 | 0.467892 | ||||||||
\(901\) | 6.24647 | 0.208100 | ||||||||
\(902\) | 4.92858 | 0.164104 | ||||||||
\(903\) | 3.67859 | 0.122416 | ||||||||
\(904\) | 7.96142 | 0.264793 | ||||||||
\(905\) | −47.5531 | −1.58072 | ||||||||
\(906\) | 22.9575 | 0.762711 | ||||||||
\(907\) | 48.7902 | 1.62005 | 0.810026 | − | 0.586393i | \(-0.199453\pi\) | ||||
0.810026 | + | 0.586393i | \(0.199453\pi\) | |||||||
\(908\) | −37.8998 | −1.25775 | ||||||||
\(909\) | 6.53614 | 0.216790 | ||||||||
\(910\) | 14.9241 | 0.494728 | ||||||||
\(911\) | 33.0894 | 1.09630 | 0.548150 | − | 0.836380i | \(-0.315332\pi\) | ||||
0.548150 | + | 0.836380i | \(0.315332\pi\) | |||||||
\(912\) | 20.1027 | 0.665669 | ||||||||
\(913\) | 12.3269 | 0.407961 | ||||||||
\(914\) | 21.6761 | 0.716983 | ||||||||
\(915\) | 44.5109 | 1.47148 | ||||||||
\(916\) | −0.879818 | −0.0290700 | ||||||||
\(917\) | 17.8118 | 0.588198 | ||||||||
\(918\) | 4.60319 | 0.151928 | ||||||||
\(919\) | 4.96601 | 0.163814 | 0.0819068 | − | 0.996640i | \(-0.473899\pi\) | ||||
0.0819068 | + | 0.996640i | \(0.473899\pi\) | |||||||
\(920\) | −6.67792 | −0.220164 | ||||||||
\(921\) | 23.4922 | 0.774095 | ||||||||
\(922\) | −0.472394 | −0.0155575 | ||||||||
\(923\) | 12.2054 | 0.401747 | ||||||||
\(924\) | −8.73185 | −0.287257 | ||||||||
\(925\) | −59.1238 | −1.94398 | ||||||||
\(926\) | −44.9897 | −1.47845 | ||||||||
\(927\) | 1.42084 | 0.0466666 | ||||||||
\(928\) | −16.5935 | −0.544709 | ||||||||
\(929\) | 2.64029 | 0.0866251 | 0.0433125 | − | 0.999062i | \(-0.486209\pi\) | ||||
0.0433125 | + | 0.999062i | \(0.486209\pi\) | |||||||
\(930\) | 15.1452 | 0.496631 | ||||||||
\(931\) | −6.66601 | −0.218470 | ||||||||
\(932\) | −10.1475 | −0.332391 | ||||||||
\(933\) | −0.106610 | −0.00349026 | ||||||||
\(934\) | 31.0899 | 1.01729 | ||||||||
\(935\) | 26.1521 | 0.855265 | ||||||||
\(936\) | −1.85340 | −0.0605803 | ||||||||
\(937\) | −25.1677 | −0.822194 | −0.411097 | − | 0.911592i | \(-0.634854\pi\) | ||||
−0.411097 | + | 0.911592i | \(0.634854\pi\) | |||||||
\(938\) | 1.39436 | 0.0455275 | ||||||||
\(939\) | 23.6312 | 0.771176 | ||||||||
\(940\) | 68.0873 | 2.22076 | ||||||||
\(941\) | 35.0361 | 1.14215 | 0.571073 | − | 0.820899i | \(-0.306527\pi\) | ||||
0.571073 | + | 0.820899i | \(0.306527\pi\) | |||||||
\(942\) | −43.0763 | −1.40350 | ||||||||
\(943\) | −1.53147 | −0.0498715 | ||||||||
\(944\) | 1.78768 | 0.0581840 | ||||||||
\(945\) | −3.29054 | −0.107041 | ||||||||
\(946\) | −28.0006 | −0.910377 | ||||||||
\(947\) | 34.0698 | 1.10712 | 0.553560 | − | 0.832809i | \(-0.313269\pi\) | ||||
0.553560 | + | 0.832809i | \(0.313269\pi\) | |||||||
\(948\) | 9.66112 | 0.313779 | ||||||||
\(949\) | 7.01209 | 0.227622 | ||||||||
\(950\) | −81.5665 | −2.64637 | ||||||||
\(951\) | 8.87083 | 0.287657 | ||||||||
\(952\) | 1.88108 | 0.0609663 | ||||||||
\(953\) | −26.4808 | −0.857796 | −0.428898 | − | 0.903353i | \(-0.641098\pi\) | ||||
−0.428898 | + | 0.903353i | \(0.641098\pi\) | |||||||
\(954\) | 5.98248 | 0.193690 | ||||||||
\(955\) | −21.2712 | −0.688321 | ||||||||
\(956\) | −8.16100 | −0.263945 | ||||||||
\(957\) | −7.47446 | −0.241615 | ||||||||
\(958\) | −21.4323 | −0.692447 | ||||||||
\(959\) | 7.51288 | 0.242604 | ||||||||
\(960\) | 35.7582 | 1.15409 | ||||||||
\(961\) | −26.1948 | −0.844994 | ||||||||
\(962\) | 46.0139 | 1.48355 | ||||||||
\(963\) | 17.1418 | 0.552387 | ||||||||
\(964\) | −24.2331 | −0.780495 | ||||||||
\(965\) | 70.4695 | 2.26849 | ||||||||
\(966\) | 4.96620 | 0.159785 | ||||||||
\(967\) | −10.2513 | −0.329659 | −0.164829 | − | 0.986322i | \(-0.552707\pi\) | ||||
−0.164829 | + | 0.986322i | \(0.552707\pi\) | |||||||
\(968\) | 1.83802 | 0.0590763 | ||||||||
\(969\) | −14.6141 | −0.469472 | ||||||||
\(970\) | 0.476259 | 0.0152917 | ||||||||
\(971\) | 10.1088 | 0.324407 | 0.162203 | − | 0.986757i | \(-0.448140\pi\) | ||||
0.162203 | + | 0.986757i | \(0.448140\pi\) | |||||||
\(972\) | 2.40865 | 0.0772574 | ||||||||
\(973\) | −4.67226 | −0.149786 | ||||||||
\(974\) | 33.9189 | 1.08683 | ||||||||
\(975\) | −12.5881 | −0.403142 | ||||||||
\(976\) | 40.7933 | 1.30576 | ||||||||
\(977\) | 10.4900 | 0.335604 | 0.167802 | − | 0.985821i | \(-0.446333\pi\) | ||||
0.167802 | + | 0.985821i | \(0.446333\pi\) | |||||||
\(978\) | 2.79971 | 0.0895248 | ||||||||
\(979\) | −22.8842 | −0.731383 | ||||||||
\(980\) | −7.92575 | −0.253179 | ||||||||
\(981\) | 14.3137 | 0.457000 | ||||||||
\(982\) | −26.1688 | −0.835081 | ||||||||
\(983\) | 15.4551 | 0.492940 | 0.246470 | − | 0.969150i | \(-0.420729\pi\) | ||||
0.246470 | + | 0.969150i | \(0.420729\pi\) | |||||||
\(984\) | −0.555570 | −0.0177109 | ||||||||
\(985\) | −50.2879 | −1.60230 | ||||||||
\(986\) | 9.49085 | 0.302250 | ||||||||
\(987\) | −8.59064 | −0.273443 | ||||||||
\(988\) | 34.6822 | 1.10339 | ||||||||
\(989\) | 8.70067 | 0.276665 | ||||||||
\(990\) | 25.0468 | 0.796041 | ||||||||
\(991\) | 58.7140 | 1.86511 | 0.932556 | − | 0.361026i | \(-0.117574\pi\) | ||||
0.932556 | + | 0.361026i | \(0.117574\pi\) | |||||||
\(992\) | 17.6420 | 0.560134 | ||||||||
\(993\) | −27.3847 | −0.869026 | ||||||||
\(994\) | −11.8642 | −0.376310 | ||||||||
\(995\) | 31.8606 | 1.01005 | ||||||||
\(996\) | −8.19020 | −0.259516 | ||||||||
\(997\) | −9.14112 | −0.289502 | −0.144751 | − | 0.989468i | \(-0.546238\pi\) | ||||
−0.144751 | + | 0.989468i | \(0.546238\pi\) | |||||||
\(998\) | −28.3428 | −0.897177 | ||||||||
\(999\) | −10.1454 | −0.320986 |
(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 | 2667.2.a.j.1.7 | ✓ | 7 | |
3.2 | odd | 2 | 8001.2.a.l.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2667.2.a.j.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial | |
8001.2.a.l.1.1 | 7 | 3.2 | odd | 2 |