Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8015,2,Mod(1,8015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8015, 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("8015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8015 = 5 \cdot 7 \cdot 229 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8015.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: | \(64.0000972201\) |
Analytic rank: | \(1\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0912753 | −0.0645414 | −0.0322707 | − | 0.999479i | \(-0.510274\pi\) | ||||
−0.0322707 | + | 0.999479i | \(0.510274\pi\) | |||||||
\(3\) | 1.39308 | 0.804294 | 0.402147 | − | 0.915575i | \(-0.368264\pi\) | ||||
0.402147 | + | 0.915575i | \(0.368264\pi\) | |||||||
\(4\) | −1.99167 | −0.995834 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.127154 | −0.0519102 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.364341 | 0.128814 | ||||||||
\(9\) | −1.05934 | −0.353112 | ||||||||
\(10\) | −0.0912753 | −0.0288638 | ||||||||
\(11\) | −3.28459 | −0.990341 | −0.495171 | − | 0.868796i | \(-0.664894\pi\) | ||||
−0.495171 | + | 0.868796i | \(0.664894\pi\) | |||||||
\(12\) | −2.77455 | −0.800943 | ||||||||
\(13\) | −4.46665 | −1.23883 | −0.619413 | − | 0.785066i | \(-0.712629\pi\) | ||||
−0.619413 | + | 0.785066i | \(0.712629\pi\) | |||||||
\(14\) | −0.0912753 | −0.0243943 | ||||||||
\(15\) | 1.39308 | 0.359691 | ||||||||
\(16\) | 3.95008 | 0.987521 | ||||||||
\(17\) | 3.13663 | 0.760744 | 0.380372 | − | 0.924834i | \(-0.375796\pi\) | ||||
0.380372 | + | 0.924834i | \(0.375796\pi\) | |||||||
\(18\) | 0.0966912 | 0.0227903 | ||||||||
\(19\) | 5.44163 | 1.24840 | 0.624198 | − | 0.781266i | \(-0.285426\pi\) | ||||
0.624198 | + | 0.781266i | \(0.285426\pi\) | |||||||
\(20\) | −1.99167 | −0.445351 | ||||||||
\(21\) | 1.39308 | 0.303994 | ||||||||
\(22\) | 0.299802 | 0.0639180 | ||||||||
\(23\) | 6.43325 | 1.34143 | 0.670713 | − | 0.741717i | \(-0.265988\pi\) | ||||
0.670713 | + | 0.741717i | \(0.265988\pi\) | |||||||
\(24\) | 0.507555 | 0.103604 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.407695 | 0.0799555 | ||||||||
\(27\) | −5.65497 | −1.08830 | ||||||||
\(28\) | −1.99167 | −0.376390 | ||||||||
\(29\) | −8.98145 | −1.66781 | −0.833906 | − | 0.551906i | \(-0.813901\pi\) | ||||
−0.833906 | + | 0.551906i | \(0.813901\pi\) | |||||||
\(30\) | −0.127154 | −0.0232150 | ||||||||
\(31\) | −0.433335 | −0.0778292 | −0.0389146 | − | 0.999243i | \(-0.512390\pi\) | ||||
−0.0389146 | + | 0.999243i | \(0.512390\pi\) | |||||||
\(32\) | −1.08923 | −0.192550 | ||||||||
\(33\) | −4.57569 | −0.796525 | ||||||||
\(34\) | −0.286297 | −0.0490995 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 2.10985 | 0.351641 | ||||||||
\(37\) | 6.99614 | 1.15016 | 0.575079 | − | 0.818098i | \(-0.304971\pi\) | ||||
0.575079 | + | 0.818098i | \(0.304971\pi\) | |||||||
\(38\) | −0.496687 | −0.0805732 | ||||||||
\(39\) | −6.22239 | −0.996379 | ||||||||
\(40\) | 0.364341 | 0.0576073 | ||||||||
\(41\) | −2.90353 | −0.453455 | −0.226728 | − | 0.973958i | \(-0.572803\pi\) | ||||
−0.226728 | + | 0.973958i | \(0.572803\pi\) | |||||||
\(42\) | −0.127154 | −0.0196202 | ||||||||
\(43\) | −6.71898 | −1.02464 | −0.512318 | − | 0.858796i | \(-0.671213\pi\) | ||||
−0.512318 | + | 0.858796i | \(0.671213\pi\) | |||||||
\(44\) | 6.54182 | 0.986216 | ||||||||
\(45\) | −1.05934 | −0.157916 | ||||||||
\(46\) | −0.587197 | −0.0865774 | ||||||||
\(47\) | −3.74451 | −0.546193 | −0.273097 | − | 0.961987i | \(-0.588048\pi\) | ||||
−0.273097 | + | 0.961987i | \(0.588048\pi\) | |||||||
\(48\) | 5.50277 | 0.794256 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.0912753 | −0.0129083 | ||||||||
\(51\) | 4.36956 | 0.611861 | ||||||||
\(52\) | 8.89608 | 1.23366 | ||||||||
\(53\) | 3.27811 | 0.450283 | 0.225142 | − | 0.974326i | \(-0.427716\pi\) | ||||
0.225142 | + | 0.974326i | \(0.427716\pi\) | |||||||
\(54\) | 0.516159 | 0.0702403 | ||||||||
\(55\) | −3.28459 | −0.442894 | ||||||||
\(56\) | 0.364341 | 0.0486871 | ||||||||
\(57\) | 7.58061 | 1.00408 | ||||||||
\(58\) | 0.819784 | 0.107643 | ||||||||
\(59\) | 7.47012 | 0.972526 | 0.486263 | − | 0.873812i | \(-0.338360\pi\) | ||||
0.486263 | + | 0.873812i | \(0.338360\pi\) | |||||||
\(60\) | −2.77455 | −0.358193 | ||||||||
\(61\) | 2.99535 | 0.383515 | 0.191757 | − | 0.981442i | \(-0.438581\pi\) | ||||
0.191757 | + | 0.981442i | \(0.438581\pi\) | |||||||
\(62\) | 0.0395527 | 0.00502320 | ||||||||
\(63\) | −1.05934 | −0.133464 | ||||||||
\(64\) | −7.80075 | −0.975093 | ||||||||
\(65\) | −4.46665 | −0.554019 | ||||||||
\(66\) | 0.417647 | 0.0514088 | ||||||||
\(67\) | −1.29381 | −0.158064 | −0.0790321 | − | 0.996872i | \(-0.525183\pi\) | ||||
−0.0790321 | + | 0.996872i | \(0.525183\pi\) | |||||||
\(68\) | −6.24712 | −0.757575 | ||||||||
\(69\) | 8.96201 | 1.07890 | ||||||||
\(70\) | −0.0912753 | −0.0109095 | ||||||||
\(71\) | −12.0108 | −1.42542 | −0.712712 | − | 0.701457i | \(-0.752533\pi\) | ||||
−0.712712 | + | 0.701457i | \(0.752533\pi\) | |||||||
\(72\) | −0.385959 | −0.0454857 | ||||||||
\(73\) | −10.8202 | −1.26641 | −0.633203 | − | 0.773986i | \(-0.718260\pi\) | ||||
−0.633203 | + | 0.773986i | \(0.718260\pi\) | |||||||
\(74\) | −0.638575 | −0.0742328 | ||||||||
\(75\) | 1.39308 | 0.160859 | ||||||||
\(76\) | −10.8379 | −1.24320 | ||||||||
\(77\) | −3.28459 | −0.374314 | ||||||||
\(78\) | 0.567950 | 0.0643077 | ||||||||
\(79\) | 4.21285 | 0.473983 | 0.236991 | − | 0.971512i | \(-0.423839\pi\) | ||||
0.236991 | + | 0.971512i | \(0.423839\pi\) | |||||||
\(80\) | 3.95008 | 0.441633 | ||||||||
\(81\) | −4.69980 | −0.522200 | ||||||||
\(82\) | 0.265021 | 0.0292666 | ||||||||
\(83\) | 12.2113 | 1.34036 | 0.670181 | − | 0.742197i | \(-0.266216\pi\) | ||||
0.670181 | + | 0.742197i | \(0.266216\pi\) | |||||||
\(84\) | −2.77455 | −0.302728 | ||||||||
\(85\) | 3.13663 | 0.340215 | ||||||||
\(86\) | 0.613277 | 0.0661314 | ||||||||
\(87\) | −12.5118 | −1.34141 | ||||||||
\(88\) | −1.19671 | −0.127570 | ||||||||
\(89\) | 9.61205 | 1.01887 | 0.509437 | − | 0.860508i | \(-0.329854\pi\) | ||||
0.509437 | + | 0.860508i | \(0.329854\pi\) | |||||||
\(90\) | 0.0966912 | 0.0101921 | ||||||||
\(91\) | −4.46665 | −0.468232 | ||||||||
\(92\) | −12.8129 | −1.33584 | ||||||||
\(93\) | −0.603669 | −0.0625975 | ||||||||
\(94\) | 0.341781 | 0.0352521 | ||||||||
\(95\) | 5.44163 | 0.558300 | ||||||||
\(96\) | −1.51738 | −0.154867 | ||||||||
\(97\) | 3.55578 | 0.361035 | 0.180517 | − | 0.983572i | \(-0.442223\pi\) | ||||
0.180517 | + | 0.983572i | \(0.442223\pi\) | |||||||
\(98\) | −0.0912753 | −0.00922020 | ||||||||
\(99\) | 3.47948 | 0.349701 | ||||||||
\(100\) | −1.99167 | −0.199167 | ||||||||
\(101\) | −12.2115 | −1.21509 | −0.607547 | − | 0.794284i | \(-0.707846\pi\) | ||||
−0.607547 | + | 0.794284i | \(0.707846\pi\) | |||||||
\(102\) | −0.398833 | −0.0394904 | ||||||||
\(103\) | −9.11033 | −0.897667 | −0.448834 | − | 0.893615i | \(-0.648160\pi\) | ||||
−0.448834 | + | 0.893615i | \(0.648160\pi\) | |||||||
\(104\) | −1.62738 | −0.159578 | ||||||||
\(105\) | 1.39308 | 0.135950 | ||||||||
\(106\) | −0.299211 | −0.0290619 | ||||||||
\(107\) | 11.5115 | 1.11285 | 0.556427 | − | 0.830896i | \(-0.312172\pi\) | ||||
0.556427 | + | 0.830896i | \(0.312172\pi\) | |||||||
\(108\) | 11.2628 | 1.08377 | ||||||||
\(109\) | −0.737245 | −0.0706153 | −0.0353077 | − | 0.999376i | \(-0.511241\pi\) | ||||
−0.0353077 | + | 0.999376i | \(0.511241\pi\) | |||||||
\(110\) | 0.299802 | 0.0285850 | ||||||||
\(111\) | 9.74617 | 0.925065 | ||||||||
\(112\) | 3.95008 | 0.373248 | ||||||||
\(113\) | −18.8082 | −1.76932 | −0.884662 | − | 0.466232i | \(-0.845611\pi\) | ||||
−0.884662 | + | 0.466232i | \(0.845611\pi\) | |||||||
\(114\) | −0.691923 | −0.0648045 | ||||||||
\(115\) | 6.43325 | 0.599904 | ||||||||
\(116\) | 17.8881 | 1.66087 | ||||||||
\(117\) | 4.73168 | 0.437444 | ||||||||
\(118\) | −0.681837 | −0.0627682 | ||||||||
\(119\) | 3.13663 | 0.287534 | ||||||||
\(120\) | 0.507555 | 0.0463332 | ||||||||
\(121\) | −0.211465 | −0.0192241 | ||||||||
\(122\) | −0.273401 | −0.0247526 | ||||||||
\(123\) | −4.04484 | −0.364711 | ||||||||
\(124\) | 0.863059 | 0.0775050 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.0966912 | 0.00861393 | ||||||||
\(127\) | −13.7778 | −1.22258 | −0.611290 | − | 0.791406i | \(-0.709349\pi\) | ||||
−0.611290 | + | 0.791406i | \(0.709349\pi\) | |||||||
\(128\) | 2.89047 | 0.255484 | ||||||||
\(129\) | −9.36006 | −0.824107 | ||||||||
\(130\) | 0.407695 | 0.0357572 | ||||||||
\(131\) | −22.6986 | −1.98319 | −0.991594 | − | 0.129388i | \(-0.958699\pi\) | ||||
−0.991594 | + | 0.129388i | \(0.958699\pi\) | |||||||
\(132\) | 9.11326 | 0.793207 | ||||||||
\(133\) | 5.44163 | 0.471849 | ||||||||
\(134\) | 0.118093 | 0.0102017 | ||||||||
\(135\) | −5.65497 | −0.486702 | ||||||||
\(136\) | 1.14280 | 0.0979944 | ||||||||
\(137\) | −2.21283 | −0.189055 | −0.0945273 | − | 0.995522i | \(-0.530134\pi\) | ||||
−0.0945273 | + | 0.995522i | \(0.530134\pi\) | |||||||
\(138\) | −0.818011 | −0.0696337 | ||||||||
\(139\) | −2.36781 | −0.200835 | −0.100417 | − | 0.994945i | \(-0.532018\pi\) | ||||
−0.100417 | + | 0.994945i | \(0.532018\pi\) | |||||||
\(140\) | −1.99167 | −0.168327 | ||||||||
\(141\) | −5.21639 | −0.439300 | ||||||||
\(142\) | 1.09629 | 0.0919988 | ||||||||
\(143\) | 14.6711 | 1.22686 | ||||||||
\(144\) | −4.18446 | −0.348705 | ||||||||
\(145\) | −8.98145 | −0.745869 | ||||||||
\(146\) | 0.987615 | 0.0817356 | ||||||||
\(147\) | 1.39308 | 0.114899 | ||||||||
\(148\) | −13.9340 | −1.14537 | ||||||||
\(149\) | 12.1250 | 0.993319 | 0.496659 | − | 0.867946i | \(-0.334560\pi\) | ||||
0.496659 | + | 0.867946i | \(0.334560\pi\) | |||||||
\(150\) | −0.127154 | −0.0103820 | ||||||||
\(151\) | −11.2656 | −0.916778 | −0.458389 | − | 0.888752i | \(-0.651573\pi\) | ||||
−0.458389 | + | 0.888752i | \(0.651573\pi\) | |||||||
\(152\) | 1.98261 | 0.160811 | ||||||||
\(153\) | −3.32274 | −0.268628 | ||||||||
\(154\) | 0.299802 | 0.0241587 | ||||||||
\(155\) | −0.433335 | −0.0348063 | ||||||||
\(156\) | 12.3929 | 0.992229 | ||||||||
\(157\) | −5.94740 | −0.474654 | −0.237327 | − | 0.971430i | \(-0.576271\pi\) | ||||
−0.237327 | + | 0.971430i | \(0.576271\pi\) | |||||||
\(158\) | −0.384529 | −0.0305915 | ||||||||
\(159\) | 4.56666 | 0.362160 | ||||||||
\(160\) | −1.08923 | −0.0861109 | ||||||||
\(161\) | 6.43325 | 0.507011 | ||||||||
\(162\) | 0.428976 | 0.0337035 | ||||||||
\(163\) | −10.7955 | −0.845571 | −0.422786 | − | 0.906230i | \(-0.638948\pi\) | ||||
−0.422786 | + | 0.906230i | \(0.638948\pi\) | |||||||
\(164\) | 5.78287 | 0.451566 | ||||||||
\(165\) | −4.57569 | −0.356217 | ||||||||
\(166\) | −1.11459 | −0.0865088 | ||||||||
\(167\) | −12.2343 | −0.946720 | −0.473360 | − | 0.880869i | \(-0.656959\pi\) | ||||
−0.473360 | + | 0.880869i | \(0.656959\pi\) | |||||||
\(168\) | 0.507555 | 0.0391587 | ||||||||
\(169\) | 6.95094 | 0.534688 | ||||||||
\(170\) | −0.286297 | −0.0219579 | ||||||||
\(171\) | −5.76451 | −0.440823 | ||||||||
\(172\) | 13.3820 | 1.02037 | ||||||||
\(173\) | 17.8022 | 1.35348 | 0.676739 | − | 0.736223i | \(-0.263393\pi\) | ||||
0.676739 | + | 0.736223i | \(0.263393\pi\) | |||||||
\(174\) | 1.14202 | 0.0865765 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −12.9744 | −0.977982 | ||||||||
\(177\) | 10.4065 | 0.782197 | ||||||||
\(178\) | −0.877342 | −0.0657596 | ||||||||
\(179\) | −3.24467 | −0.242518 | −0.121259 | − | 0.992621i | \(-0.538693\pi\) | ||||
−0.121259 | + | 0.992621i | \(0.538693\pi\) | |||||||
\(180\) | 2.10985 | 0.157259 | ||||||||
\(181\) | −7.18720 | −0.534220 | −0.267110 | − | 0.963666i | \(-0.586069\pi\) | ||||
−0.267110 | + | 0.963666i | \(0.586069\pi\) | |||||||
\(182\) | 0.407695 | 0.0302203 | ||||||||
\(183\) | 4.17275 | 0.308459 | ||||||||
\(184\) | 2.34390 | 0.172794 | ||||||||
\(185\) | 6.99614 | 0.514367 | ||||||||
\(186\) | 0.0551000 | 0.00404013 | ||||||||
\(187\) | −10.3025 | −0.753396 | ||||||||
\(188\) | 7.45783 | 0.543918 | ||||||||
\(189\) | −5.65497 | −0.411338 | ||||||||
\(190\) | −0.496687 | −0.0360334 | ||||||||
\(191\) | 17.3783 | 1.25745 | 0.628723 | − | 0.777629i | \(-0.283578\pi\) | ||||
0.628723 | + | 0.777629i | \(0.283578\pi\) | |||||||
\(192\) | −10.8670 | −0.784261 | ||||||||
\(193\) | −5.72987 | −0.412445 | −0.206223 | − | 0.978505i | \(-0.566117\pi\) | ||||
−0.206223 | + | 0.978505i | \(0.566117\pi\) | |||||||
\(194\) | −0.324555 | −0.0233017 | ||||||||
\(195\) | −6.22239 | −0.445594 | ||||||||
\(196\) | −1.99167 | −0.142262 | ||||||||
\(197\) | −19.3061 | −1.37550 | −0.687752 | − | 0.725946i | \(-0.741402\pi\) | ||||
−0.687752 | + | 0.725946i | \(0.741402\pi\) | |||||||
\(198\) | −0.317591 | −0.0225702 | ||||||||
\(199\) | −13.0622 | −0.925954 | −0.462977 | − | 0.886370i | \(-0.653219\pi\) | ||||
−0.462977 | + | 0.886370i | \(0.653219\pi\) | |||||||
\(200\) | 0.364341 | 0.0257628 | ||||||||
\(201\) | −1.80238 | −0.127130 | ||||||||
\(202\) | 1.11461 | 0.0784238 | ||||||||
\(203\) | −8.98145 | −0.630374 | ||||||||
\(204\) | −8.70272 | −0.609313 | ||||||||
\(205\) | −2.90353 | −0.202791 | ||||||||
\(206\) | 0.831548 | 0.0579367 | ||||||||
\(207\) | −6.81497 | −0.473673 | ||||||||
\(208\) | −17.6436 | −1.22337 | ||||||||
\(209\) | −17.8735 | −1.23634 | ||||||||
\(210\) | −0.127154 | −0.00877443 | ||||||||
\(211\) | −17.1104 | −1.17793 | −0.588964 | − | 0.808159i | \(-0.700464\pi\) | ||||
−0.588964 | + | 0.808159i | \(0.700464\pi\) | |||||||
\(212\) | −6.52891 | −0.448407 | ||||||||
\(213\) | −16.7320 | −1.14646 | ||||||||
\(214\) | −1.05071 | −0.0718251 | ||||||||
\(215\) | −6.71898 | −0.458231 | ||||||||
\(216\) | −2.06034 | −0.140188 | ||||||||
\(217\) | −0.433335 | −0.0294167 | ||||||||
\(218\) | 0.0672923 | 0.00455761 | ||||||||
\(219\) | −15.0733 | −1.01856 | ||||||||
\(220\) | 6.54182 | 0.441049 | ||||||||
\(221\) | −14.0102 | −0.942428 | ||||||||
\(222\) | −0.889584 | −0.0597050 | ||||||||
\(223\) | 23.5983 | 1.58026 | 0.790129 | − | 0.612940i | \(-0.210013\pi\) | ||||
0.790129 | + | 0.612940i | \(0.210013\pi\) | |||||||
\(224\) | −1.08923 | −0.0727770 | ||||||||
\(225\) | −1.05934 | −0.0706224 | ||||||||
\(226\) | 1.71672 | 0.114195 | ||||||||
\(227\) | −24.8162 | −1.64711 | −0.823553 | − | 0.567239i | \(-0.808012\pi\) | ||||
−0.823553 | + | 0.567239i | \(0.808012\pi\) | |||||||
\(228\) | −15.0981 | −0.999894 | ||||||||
\(229\) | −1.00000 | −0.0660819 | ||||||||
\(230\) | −0.587197 | −0.0387186 | ||||||||
\(231\) | −4.57569 | −0.301058 | ||||||||
\(232\) | −3.27231 | −0.214837 | ||||||||
\(233\) | −16.1950 | −1.06097 | −0.530485 | − | 0.847695i | \(-0.677990\pi\) | ||||
−0.530485 | + | 0.847695i | \(0.677990\pi\) | |||||||
\(234\) | −0.431885 | −0.0282332 | ||||||||
\(235\) | −3.74451 | −0.244265 | ||||||||
\(236\) | −14.8780 | −0.968475 | ||||||||
\(237\) | 5.86883 | 0.381221 | ||||||||
\(238\) | −0.286297 | −0.0185578 | ||||||||
\(239\) | 2.75362 | 0.178117 | 0.0890585 | − | 0.996026i | \(-0.471614\pi\) | ||||
0.0890585 | + | 0.996026i | \(0.471614\pi\) | |||||||
\(240\) | 5.50277 | 0.355202 | ||||||||
\(241\) | 1.96725 | 0.126721 | 0.0633607 | − | 0.997991i | \(-0.479818\pi\) | ||||
0.0633607 | + | 0.997991i | \(0.479818\pi\) | |||||||
\(242\) | 0.0193015 | 0.00124075 | ||||||||
\(243\) | 10.4177 | 0.668297 | ||||||||
\(244\) | −5.96574 | −0.381917 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0.369194 | 0.0235390 | ||||||||
\(247\) | −24.3059 | −1.54654 | ||||||||
\(248\) | −0.157881 | −0.0100255 | ||||||||
\(249\) | 17.0113 | 1.07804 | ||||||||
\(250\) | −0.0912753 | −0.00577276 | ||||||||
\(251\) | −17.2723 | −1.09022 | −0.545108 | − | 0.838366i | \(-0.683512\pi\) | ||||
−0.545108 | + | 0.838366i | \(0.683512\pi\) | |||||||
\(252\) | 2.10985 | 0.132908 | ||||||||
\(253\) | −21.1306 | −1.32847 | ||||||||
\(254\) | 1.25757 | 0.0789070 | ||||||||
\(255\) | 4.36956 | 0.273633 | ||||||||
\(256\) | 15.3377 | 0.958604 | ||||||||
\(257\) | −30.3905 | −1.89571 | −0.947853 | − | 0.318707i | \(-0.896751\pi\) | ||||
−0.947853 | + | 0.318707i | \(0.896751\pi\) | |||||||
\(258\) | 0.854342 | 0.0531890 | ||||||||
\(259\) | 6.99614 | 0.434719 | ||||||||
\(260\) | 8.89608 | 0.551712 | ||||||||
\(261\) | 9.51436 | 0.588924 | ||||||||
\(262\) | 2.07182 | 0.127998 | ||||||||
\(263\) | −10.6496 | −0.656682 | −0.328341 | − | 0.944559i | \(-0.606490\pi\) | ||||
−0.328341 | + | 0.944559i | \(0.606490\pi\) | |||||||
\(264\) | −1.66711 | −0.102604 | ||||||||
\(265\) | 3.27811 | 0.201373 | ||||||||
\(266\) | −0.496687 | −0.0304538 | ||||||||
\(267\) | 13.3903 | 0.819475 | ||||||||
\(268\) | 2.57684 | 0.157406 | ||||||||
\(269\) | −23.9865 | −1.46248 | −0.731242 | − | 0.682118i | \(-0.761059\pi\) | ||||
−0.731242 | + | 0.682118i | \(0.761059\pi\) | |||||||
\(270\) | 0.516159 | 0.0314124 | ||||||||
\(271\) | 3.42192 | 0.207867 | 0.103933 | − | 0.994584i | \(-0.466857\pi\) | ||||
0.103933 | + | 0.994584i | \(0.466857\pi\) | |||||||
\(272\) | 12.3899 | 0.751250 | ||||||||
\(273\) | −6.22239 | −0.376596 | ||||||||
\(274\) | 0.201976 | 0.0122018 | ||||||||
\(275\) | −3.28459 | −0.198068 | ||||||||
\(276\) | −17.8494 | −1.07441 | ||||||||
\(277\) | 7.97404 | 0.479113 | 0.239557 | − | 0.970882i | \(-0.422998\pi\) | ||||
0.239557 | + | 0.970882i | \(0.422998\pi\) | |||||||
\(278\) | 0.216122 | 0.0129622 | ||||||||
\(279\) | 0.459047 | 0.0274824 | ||||||||
\(280\) | 0.364341 | 0.0217735 | ||||||||
\(281\) | 16.7408 | 0.998674 | 0.499337 | − | 0.866408i | \(-0.333577\pi\) | ||||
0.499337 | + | 0.866408i | \(0.333577\pi\) | |||||||
\(282\) | 0.476128 | 0.0283530 | ||||||||
\(283\) | 17.8651 | 1.06197 | 0.530985 | − | 0.847381i | \(-0.321822\pi\) | ||||
0.530985 | + | 0.847381i | \(0.321822\pi\) | |||||||
\(284\) | 23.9216 | 1.41949 | ||||||||
\(285\) | 7.58061 | 0.449037 | ||||||||
\(286\) | −1.33911 | −0.0791832 | ||||||||
\(287\) | −2.90353 | −0.171390 | ||||||||
\(288\) | 1.15386 | 0.0679916 | ||||||||
\(289\) | −7.16157 | −0.421269 | ||||||||
\(290\) | 0.819784 | 0.0481394 | ||||||||
\(291\) | 4.95348 | 0.290378 | ||||||||
\(292\) | 21.5502 | 1.26113 | ||||||||
\(293\) | 31.0443 | 1.81363 | 0.906814 | − | 0.421531i | \(-0.138507\pi\) | ||||
0.906814 | + | 0.421531i | \(0.138507\pi\) | |||||||
\(294\) | −0.127154 | −0.00741575 | ||||||||
\(295\) | 7.47012 | 0.434927 | ||||||||
\(296\) | 2.54898 | 0.148156 | ||||||||
\(297\) | 18.5743 | 1.07779 | ||||||||
\(298\) | −1.10671 | −0.0641102 | ||||||||
\(299\) | −28.7351 | −1.66179 | ||||||||
\(300\) | −2.77455 | −0.160189 | ||||||||
\(301\) | −6.71898 | −0.387276 | ||||||||
\(302\) | 1.02827 | 0.0591701 | ||||||||
\(303\) | −17.0116 | −0.977292 | ||||||||
\(304\) | 21.4949 | 1.23282 | ||||||||
\(305\) | 2.99535 | 0.171513 | ||||||||
\(306\) | 0.303284 | 0.0173376 | ||||||||
\(307\) | −11.9045 | −0.679427 | −0.339714 | − | 0.940529i | \(-0.610330\pi\) | ||||
−0.339714 | + | 0.940529i | \(0.610330\pi\) | |||||||
\(308\) | 6.54182 | 0.372755 | ||||||||
\(309\) | −12.6914 | −0.721988 | ||||||||
\(310\) | 0.0395527 | 0.00224645 | ||||||||
\(311\) | 14.7307 | 0.835303 | 0.417652 | − | 0.908607i | \(-0.362853\pi\) | ||||
0.417652 | + | 0.908607i | \(0.362853\pi\) | |||||||
\(312\) | −2.26707 | −0.128347 | ||||||||
\(313\) | −0.0212285 | −0.00119991 | −0.000599953 | − | 1.00000i | \(-0.500191\pi\) | ||||
−0.000599953 | 1.00000i | \(0.500191\pi\) | ||||||||
\(314\) | 0.542851 | 0.0306349 | ||||||||
\(315\) | −1.05934 | −0.0596868 | ||||||||
\(316\) | −8.39061 | −0.472009 | ||||||||
\(317\) | −21.5915 | −1.21270 | −0.606349 | − | 0.795198i | \(-0.707367\pi\) | ||||
−0.606349 | + | 0.795198i | \(0.707367\pi\) | |||||||
\(318\) | −0.416823 | −0.0233743 | ||||||||
\(319\) | 29.5004 | 1.65170 | ||||||||
\(320\) | −7.80075 | −0.436075 | ||||||||
\(321\) | 16.0363 | 0.895061 | ||||||||
\(322\) | −0.587197 | −0.0327232 | ||||||||
\(323\) | 17.0684 | 0.949709 | ||||||||
\(324\) | 9.36045 | 0.520025 | ||||||||
\(325\) | −4.46665 | −0.247765 | ||||||||
\(326\) | 0.985366 | 0.0545744 | ||||||||
\(327\) | −1.02704 | −0.0567954 | ||||||||
\(328\) | −1.05787 | −0.0584113 | ||||||||
\(329\) | −3.74451 | −0.206442 | ||||||||
\(330\) | 0.417647 | 0.0229907 | ||||||||
\(331\) | −2.81199 | −0.154561 | −0.0772804 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772804 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(332\) | −24.3208 | −1.33478 | ||||||||
\(333\) | −7.41126 | −0.406135 | ||||||||
\(334\) | 1.11669 | 0.0611026 | ||||||||
\(335\) | −1.29381 | −0.0706885 | ||||||||
\(336\) | 5.50277 | 0.300201 | ||||||||
\(337\) | 25.8382 | 1.40750 | 0.703748 | − | 0.710450i | \(-0.251508\pi\) | ||||
0.703748 | + | 0.710450i | \(0.251508\pi\) | |||||||
\(338\) | −0.634449 | −0.0345095 | ||||||||
\(339\) | −26.2012 | −1.42306 | ||||||||
\(340\) | −6.24712 | −0.338798 | ||||||||
\(341\) | 1.42333 | 0.0770775 | ||||||||
\(342\) | 0.526158 | 0.0284514 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.44800 | −0.131987 | ||||||||
\(345\) | 8.96201 | 0.482499 | ||||||||
\(346\) | −1.62490 | −0.0873553 | ||||||||
\(347\) | 16.0173 | 0.859856 | 0.429928 | − | 0.902863i | \(-0.358539\pi\) | ||||
0.429928 | + | 0.902863i | \(0.358539\pi\) | |||||||
\(348\) | 24.9195 | 1.33582 | ||||||||
\(349\) | 3.02232 | 0.161781 | 0.0808907 | − | 0.996723i | \(-0.474224\pi\) | ||||
0.0808907 | + | 0.996723i | \(0.474224\pi\) | |||||||
\(350\) | −0.0912753 | −0.00487887 | ||||||||
\(351\) | 25.2587 | 1.34821 | ||||||||
\(352\) | 3.57766 | 0.190690 | ||||||||
\(353\) | 25.3920 | 1.35148 | 0.675741 | − | 0.737139i | \(-0.263824\pi\) | ||||
0.675741 | + | 0.737139i | \(0.263824\pi\) | |||||||
\(354\) | −0.949852 | −0.0504841 | ||||||||
\(355\) | −12.0108 | −0.637469 | ||||||||
\(356\) | −19.1440 | −1.01463 | ||||||||
\(357\) | 4.36956 | 0.231262 | ||||||||
\(358\) | 0.296158 | 0.0156524 | ||||||||
\(359\) | 20.9385 | 1.10509 | 0.552545 | − | 0.833483i | \(-0.313657\pi\) | ||||
0.552545 | + | 0.833483i | \(0.313657\pi\) | |||||||
\(360\) | −0.385959 | −0.0203418 | ||||||||
\(361\) | 10.6114 | 0.558493 | ||||||||
\(362\) | 0.656013 | 0.0344793 | ||||||||
\(363\) | −0.294587 | −0.0154618 | ||||||||
\(364\) | 8.89608 | 0.466281 | ||||||||
\(365\) | −10.8202 | −0.566354 | ||||||||
\(366\) | −0.380869 | −0.0199083 | ||||||||
\(367\) | −24.7169 | −1.29021 | −0.645105 | − | 0.764094i | \(-0.723186\pi\) | ||||
−0.645105 | + | 0.764094i | \(0.723186\pi\) | |||||||
\(368\) | 25.4119 | 1.32469 | ||||||||
\(369\) | 3.07581 | 0.160120 | ||||||||
\(370\) | −0.638575 | −0.0331979 | ||||||||
\(371\) | 3.27811 | 0.170191 | ||||||||
\(372\) | 1.20231 | 0.0623368 | ||||||||
\(373\) | −36.3444 | −1.88184 | −0.940922 | − | 0.338623i | \(-0.890039\pi\) | ||||
−0.940922 | + | 0.338623i | \(0.890039\pi\) | |||||||
\(374\) | 0.940367 | 0.0486252 | ||||||||
\(375\) | 1.39308 | 0.0719382 | ||||||||
\(376\) | −1.36428 | −0.0703573 | ||||||||
\(377\) | 40.1170 | 2.06613 | ||||||||
\(378\) | 0.516159 | 0.0265484 | ||||||||
\(379\) | 29.0024 | 1.48975 | 0.744877 | − | 0.667201i | \(-0.232508\pi\) | ||||
0.744877 | + | 0.667201i | \(0.232508\pi\) | |||||||
\(380\) | −10.8379 | −0.555974 | ||||||||
\(381\) | −19.1935 | −0.983314 | ||||||||
\(382\) | −1.58621 | −0.0811574 | ||||||||
\(383\) | −26.5586 | −1.35708 | −0.678540 | − | 0.734564i | \(-0.737387\pi\) | ||||
−0.678540 | + | 0.734564i | \(0.737387\pi\) | |||||||
\(384\) | 4.02665 | 0.205484 | ||||||||
\(385\) | −3.28459 | −0.167398 | ||||||||
\(386\) | 0.522996 | 0.0266198 | ||||||||
\(387\) | 7.11766 | 0.361811 | ||||||||
\(388\) | −7.08194 | −0.359531 | ||||||||
\(389\) | 36.4517 | 1.84818 | 0.924088 | − | 0.382180i | \(-0.124827\pi\) | ||||
0.924088 | + | 0.382180i | \(0.124827\pi\) | |||||||
\(390\) | 0.567950 | 0.0287593 | ||||||||
\(391\) | 20.1787 | 1.02048 | ||||||||
\(392\) | 0.364341 | 0.0184020 | ||||||||
\(393\) | −31.6209 | −1.59507 | ||||||||
\(394\) | 1.76217 | 0.0887769 | ||||||||
\(395\) | 4.21285 | 0.211972 | ||||||||
\(396\) | −6.92998 | −0.348245 | ||||||||
\(397\) | −36.6704 | −1.84044 | −0.920218 | − | 0.391406i | \(-0.871989\pi\) | ||||
−0.920218 | + | 0.391406i | \(0.871989\pi\) | |||||||
\(398\) | 1.19225 | 0.0597623 | ||||||||
\(399\) | 7.58061 | 0.379505 | ||||||||
\(400\) | 3.95008 | 0.197504 | ||||||||
\(401\) | 37.0380 | 1.84959 | 0.924795 | − | 0.380466i | \(-0.124236\pi\) | ||||
0.924795 | + | 0.380466i | \(0.124236\pi\) | |||||||
\(402\) | 0.164513 | 0.00820515 | ||||||||
\(403\) | 1.93555 | 0.0964168 | ||||||||
\(404\) | 24.3213 | 1.21003 | ||||||||
\(405\) | −4.69980 | −0.233535 | ||||||||
\(406\) | 0.819784 | 0.0406852 | ||||||||
\(407\) | −22.9795 | −1.13905 | ||||||||
\(408\) | 1.59201 | 0.0788162 | ||||||||
\(409\) | 23.3971 | 1.15691 | 0.578457 | − | 0.815713i | \(-0.303655\pi\) | ||||
0.578457 | + | 0.815713i | \(0.303655\pi\) | |||||||
\(410\) | 0.265021 | 0.0130884 | ||||||||
\(411\) | −3.08264 | −0.152055 | ||||||||
\(412\) | 18.1448 | 0.893928 | ||||||||
\(413\) | 7.47012 | 0.367580 | ||||||||
\(414\) | 0.622038 | 0.0305715 | ||||||||
\(415\) | 12.2113 | 0.599428 | ||||||||
\(416\) | 4.86519 | 0.238536 | ||||||||
\(417\) | −3.29854 | −0.161530 | ||||||||
\(418\) | 1.63141 | 0.0797950 | ||||||||
\(419\) | −25.5908 | −1.25019 | −0.625096 | − | 0.780548i | \(-0.714940\pi\) | ||||
−0.625096 | + | 0.780548i | \(0.714940\pi\) | |||||||
\(420\) | −2.77455 | −0.135384 | ||||||||
\(421\) | 12.4192 | 0.605273 | 0.302637 | − | 0.953106i | \(-0.402133\pi\) | ||||
0.302637 | + | 0.953106i | \(0.402133\pi\) | |||||||
\(422\) | 1.56176 | 0.0760251 | ||||||||
\(423\) | 3.96669 | 0.192867 | ||||||||
\(424\) | 1.19435 | 0.0580027 | ||||||||
\(425\) | 3.13663 | 0.152149 | ||||||||
\(426\) | 1.52722 | 0.0739940 | ||||||||
\(427\) | 2.99535 | 0.144955 | ||||||||
\(428\) | −22.9270 | −1.10822 | ||||||||
\(429\) | 20.4380 | 0.986755 | ||||||||
\(430\) | 0.613277 | 0.0295748 | ||||||||
\(431\) | −19.2717 | −0.928284 | −0.464142 | − | 0.885761i | \(-0.653637\pi\) | ||||
−0.464142 | + | 0.885761i | \(0.653637\pi\) | |||||||
\(432\) | −22.3376 | −1.07472 | ||||||||
\(433\) | −25.5135 | −1.22610 | −0.613051 | − | 0.790043i | \(-0.710058\pi\) | ||||
−0.613051 | + | 0.790043i | \(0.710058\pi\) | |||||||
\(434\) | 0.0395527 | 0.00189859 | ||||||||
\(435\) | −12.5118 | −0.599897 | ||||||||
\(436\) | 1.46835 | 0.0703211 | ||||||||
\(437\) | 35.0074 | 1.67463 | ||||||||
\(438\) | 1.37582 | 0.0657394 | ||||||||
\(439\) | 15.6435 | 0.746622 | 0.373311 | − | 0.927706i | \(-0.378222\pi\) | ||||
0.373311 | + | 0.927706i | \(0.378222\pi\) | |||||||
\(440\) | −1.19671 | −0.0570509 | ||||||||
\(441\) | −1.05934 | −0.0504445 | ||||||||
\(442\) | 1.27879 | 0.0608256 | ||||||||
\(443\) | −3.67763 | −0.174730 | −0.0873648 | − | 0.996176i | \(-0.527845\pi\) | ||||
−0.0873648 | + | 0.996176i | \(0.527845\pi\) | |||||||
\(444\) | −19.4111 | −0.921212 | ||||||||
\(445\) | 9.61205 | 0.455655 | ||||||||
\(446\) | −2.15394 | −0.101992 | ||||||||
\(447\) | 16.8911 | 0.798920 | ||||||||
\(448\) | −7.80075 | −0.368551 | ||||||||
\(449\) | 11.8358 | 0.558565 | 0.279283 | − | 0.960209i | \(-0.409903\pi\) | ||||
0.279283 | + | 0.960209i | \(0.409903\pi\) | |||||||
\(450\) | 0.0966912 | 0.00455807 | ||||||||
\(451\) | 9.53691 | 0.449075 | ||||||||
\(452\) | 37.4597 | 1.76195 | ||||||||
\(453\) | −15.6938 | −0.737358 | ||||||||
\(454\) | 2.26510 | 0.106307 | ||||||||
\(455\) | −4.46665 | −0.209400 | ||||||||
\(456\) | 2.76193 | 0.129339 | ||||||||
\(457\) | 4.55566 | 0.213105 | 0.106552 | − | 0.994307i | \(-0.466019\pi\) | ||||
0.106552 | + | 0.994307i | \(0.466019\pi\) | |||||||
\(458\) | 0.0912753 | 0.00426501 | ||||||||
\(459\) | −17.7375 | −0.827917 | ||||||||
\(460\) | −12.8129 | −0.597405 | ||||||||
\(461\) | −2.03862 | −0.0949478 | −0.0474739 | − | 0.998872i | \(-0.515117\pi\) | ||||
−0.0474739 | + | 0.998872i | \(0.515117\pi\) | |||||||
\(462\) | 0.417647 | 0.0194307 | ||||||||
\(463\) | 2.98899 | 0.138910 | 0.0694550 | − | 0.997585i | \(-0.477874\pi\) | ||||
0.0694550 | + | 0.997585i | \(0.477874\pi\) | |||||||
\(464\) | −35.4775 | −1.64700 | ||||||||
\(465\) | −0.603669 | −0.0279945 | ||||||||
\(466\) | 1.47820 | 0.0684764 | ||||||||
\(467\) | −4.23492 | −0.195969 | −0.0979844 | − | 0.995188i | \(-0.531240\pi\) | ||||
−0.0979844 | + | 0.995188i | \(0.531240\pi\) | |||||||
\(468\) | −9.42394 | −0.435622 | ||||||||
\(469\) | −1.29381 | −0.0597427 | ||||||||
\(470\) | 0.341781 | 0.0157652 | ||||||||
\(471\) | −8.28519 | −0.381762 | ||||||||
\(472\) | 2.72167 | 0.125275 | ||||||||
\(473\) | 22.0691 | 1.01474 | ||||||||
\(474\) | −0.535679 | −0.0246046 | ||||||||
\(475\) | 5.44163 | 0.249679 | ||||||||
\(476\) | −6.24712 | −0.286336 | ||||||||
\(477\) | −3.47262 | −0.159000 | ||||||||
\(478\) | −0.251338 | −0.0114959 | ||||||||
\(479\) | 24.8177 | 1.13395 | 0.566975 | − | 0.823735i | \(-0.308113\pi\) | ||||
0.566975 | + | 0.823735i | \(0.308113\pi\) | |||||||
\(480\) | −1.51738 | −0.0692585 | ||||||||
\(481\) | −31.2493 | −1.42485 | ||||||||
\(482\) | −0.179561 | −0.00817878 | ||||||||
\(483\) | 8.96201 | 0.407786 | ||||||||
\(484\) | 0.421168 | 0.0191440 | ||||||||
\(485\) | 3.55578 | 0.161460 | ||||||||
\(486\) | −0.950880 | −0.0431328 | ||||||||
\(487\) | −19.5912 | −0.887762 | −0.443881 | − | 0.896086i | \(-0.646399\pi\) | ||||
−0.443881 | + | 0.896086i | \(0.646399\pi\) | |||||||
\(488\) | 1.09133 | 0.0494020 | ||||||||
\(489\) | −15.0390 | −0.680088 | ||||||||
\(490\) | −0.0912753 | −0.00412340 | ||||||||
\(491\) | −36.6177 | −1.65253 | −0.826266 | − | 0.563280i | \(-0.809539\pi\) | ||||
−0.826266 | + | 0.563280i | \(0.809539\pi\) | |||||||
\(492\) | 8.05598 | 0.363192 | ||||||||
\(493\) | −28.1714 | −1.26878 | ||||||||
\(494\) | 2.21852 | 0.0998161 | ||||||||
\(495\) | 3.47948 | 0.156391 | ||||||||
\(496\) | −1.71171 | −0.0768579 | ||||||||
\(497\) | −12.0108 | −0.538759 | ||||||||
\(498\) | −1.55271 | −0.0695785 | ||||||||
\(499\) | −36.6564 | −1.64096 | −0.820482 | − | 0.571672i | \(-0.806295\pi\) | ||||
−0.820482 | + | 0.571672i | \(0.806295\pi\) | |||||||
\(500\) | −1.99167 | −0.0890701 | ||||||||
\(501\) | −17.0433 | −0.761440 | ||||||||
\(502\) | 1.57653 | 0.0703641 | ||||||||
\(503\) | −14.0056 | −0.624478 | −0.312239 | − | 0.950004i | \(-0.601079\pi\) | ||||
−0.312239 | + | 0.950004i | \(0.601079\pi\) | |||||||
\(504\) | −0.385959 | −0.0171920 | ||||||||
\(505\) | −12.2115 | −0.543406 | ||||||||
\(506\) | 1.92870 | 0.0857412 | ||||||||
\(507\) | 9.68319 | 0.430046 | ||||||||
\(508\) | 27.4408 | 1.21749 | ||||||||
\(509\) | −10.1324 | −0.449113 | −0.224556 | − | 0.974461i | \(-0.572093\pi\) | ||||
−0.224556 | + | 0.974461i | \(0.572093\pi\) | |||||||
\(510\) | −0.398833 | −0.0176606 | ||||||||
\(511\) | −10.8202 | −0.478657 | ||||||||
\(512\) | −7.18089 | −0.317353 | ||||||||
\(513\) | −30.7723 | −1.35863 | ||||||||
\(514\) | 2.77390 | 0.122352 | ||||||||
\(515\) | −9.11033 | −0.401449 | ||||||||
\(516\) | 18.6421 | 0.820675 | ||||||||
\(517\) | 12.2992 | 0.540918 | ||||||||
\(518\) | −0.638575 | −0.0280574 | ||||||||
\(519\) | 24.7999 | 1.08859 | ||||||||
\(520\) | −1.62738 | −0.0713654 | ||||||||
\(521\) | −35.6218 | −1.56062 | −0.780310 | − | 0.625392i | \(-0.784939\pi\) | ||||
−0.780310 | + | 0.625392i | \(0.784939\pi\) | |||||||
\(522\) | −0.868426 | −0.0380100 | ||||||||
\(523\) | 3.91862 | 0.171349 | 0.0856746 | − | 0.996323i | \(-0.472695\pi\) | ||||
0.0856746 | + | 0.996323i | \(0.472695\pi\) | |||||||
\(524\) | 45.2081 | 1.97493 | ||||||||
\(525\) | 1.39308 | 0.0607989 | ||||||||
\(526\) | 0.972045 | 0.0423832 | ||||||||
\(527\) | −1.35921 | −0.0592081 | ||||||||
\(528\) | −18.0743 | −0.786585 | ||||||||
\(529\) | 18.3867 | 0.799422 | ||||||||
\(530\) | −0.299211 | −0.0129969 | ||||||||
\(531\) | −7.91336 | −0.343411 | ||||||||
\(532\) | −10.8379 | −0.469884 | ||||||||
\(533\) | 12.9690 | 0.561752 | ||||||||
\(534\) | −1.22221 | −0.0528900 | ||||||||
\(535\) | 11.5115 | 0.497684 | ||||||||
\(536\) | −0.471388 | −0.0203609 | ||||||||
\(537\) | −4.52007 | −0.195055 | ||||||||
\(538\) | 2.18938 | 0.0943907 | ||||||||
\(539\) | −3.28459 | −0.141477 | ||||||||
\(540\) | 11.2628 | 0.484675 | ||||||||
\(541\) | 32.3998 | 1.39298 | 0.696489 | − | 0.717568i | \(-0.254745\pi\) | ||||
0.696489 | + | 0.717568i | \(0.254745\pi\) | |||||||
\(542\) | −0.312337 | −0.0134160 | ||||||||
\(543\) | −10.0123 | −0.429670 | ||||||||
\(544\) | −3.41650 | −0.146481 | ||||||||
\(545\) | −0.737245 | −0.0315801 | ||||||||
\(546\) | 0.567950 | 0.0243060 | ||||||||
\(547\) | 18.2757 | 0.781414 | 0.390707 | − | 0.920515i | \(-0.372231\pi\) | ||||
0.390707 | + | 0.920515i | \(0.372231\pi\) | |||||||
\(548\) | 4.40722 | 0.188267 | ||||||||
\(549\) | −3.17308 | −0.135424 | ||||||||
\(550\) | 0.299802 | 0.0127836 | ||||||||
\(551\) | −48.8737 | −2.08209 | ||||||||
\(552\) | 3.26523 | 0.138977 | ||||||||
\(553\) | 4.21285 | 0.179149 | ||||||||
\(554\) | −0.727832 | −0.0309226 | ||||||||
\(555\) | 9.74617 | 0.413702 | ||||||||
\(556\) | 4.71589 | 0.199998 | ||||||||
\(557\) | −15.3175 | −0.649022 | −0.324511 | − | 0.945882i | \(-0.605200\pi\) | ||||
−0.324511 | + | 0.945882i | \(0.605200\pi\) | |||||||
\(558\) | −0.0418996 | −0.00177375 | ||||||||
\(559\) | 30.0113 | 1.26934 | ||||||||
\(560\) | 3.95008 | 0.166921 | ||||||||
\(561\) | −14.3522 | −0.605952 | ||||||||
\(562\) | −1.52802 | −0.0644558 | ||||||||
\(563\) | −39.3470 | −1.65828 | −0.829140 | − | 0.559041i | \(-0.811169\pi\) | ||||
−0.829140 | + | 0.559041i | \(0.811169\pi\) | |||||||
\(564\) | 10.3893 | 0.437470 | ||||||||
\(565\) | −18.8082 | −0.791266 | ||||||||
\(566\) | −1.63064 | −0.0685411 | ||||||||
\(567\) | −4.69980 | −0.197373 | ||||||||
\(568\) | −4.37603 | −0.183614 | ||||||||
\(569\) | 28.0906 | 1.17762 | 0.588809 | − | 0.808272i | \(-0.299597\pi\) | ||||
0.588809 | + | 0.808272i | \(0.299597\pi\) | |||||||
\(570\) | −0.691923 | −0.0289815 | ||||||||
\(571\) | 2.07078 | 0.0866593 | 0.0433297 | − | 0.999061i | \(-0.486203\pi\) | ||||
0.0433297 | + | 0.999061i | \(0.486203\pi\) | |||||||
\(572\) | −29.2200 | −1.22175 | ||||||||
\(573\) | 24.2093 | 1.01136 | ||||||||
\(574\) | 0.265021 | 0.0110617 | ||||||||
\(575\) | 6.43325 | 0.268285 | ||||||||
\(576\) | 8.26361 | 0.344317 | ||||||||
\(577\) | −26.9641 | −1.12253 | −0.561266 | − | 0.827635i | \(-0.689686\pi\) | ||||
−0.561266 | + | 0.827635i | \(0.689686\pi\) | |||||||
\(578\) | 0.653675 | 0.0271893 | ||||||||
\(579\) | −7.98215 | −0.331727 | ||||||||
\(580\) | 17.8881 | 0.742762 | ||||||||
\(581\) | 12.2113 | 0.506609 | ||||||||
\(582\) | −0.452130 | −0.0187414 | ||||||||
\(583\) | −10.7673 | −0.445934 | ||||||||
\(584\) | −3.94223 | −0.163131 | ||||||||
\(585\) | 4.73168 | 0.195631 | ||||||||
\(586\) | −2.83358 | −0.117054 | ||||||||
\(587\) | −26.3491 | −1.08754 | −0.543772 | − | 0.839233i | \(-0.683005\pi\) | ||||
−0.543772 | + | 0.839233i | \(0.683005\pi\) | |||||||
\(588\) | −2.77455 | −0.114420 | ||||||||
\(589\) | −2.35805 | −0.0971617 | ||||||||
\(590\) | −0.681837 | −0.0280708 | ||||||||
\(591\) | −26.8949 | −1.10631 | ||||||||
\(592\) | 27.6353 | 1.13581 | ||||||||
\(593\) | −0.461528 | −0.0189527 | −0.00947635 | − | 0.999955i | \(-0.503016\pi\) | ||||
−0.00947635 | + | 0.999955i | \(0.503016\pi\) | |||||||
\(594\) | −1.69537 | −0.0695619 | ||||||||
\(595\) | 3.13663 | 0.128589 | ||||||||
\(596\) | −24.1490 | −0.989181 | ||||||||
\(597\) | −18.1966 | −0.744739 | ||||||||
\(598\) | 2.62280 | 0.107254 | ||||||||
\(599\) | −34.2624 | −1.39992 | −0.699961 | − | 0.714181i | \(-0.746799\pi\) | ||||
−0.699961 | + | 0.714181i | \(0.746799\pi\) | |||||||
\(600\) | 0.507555 | 0.0207208 | ||||||||
\(601\) | 4.82272 | 0.196723 | 0.0983614 | − | 0.995151i | \(-0.468640\pi\) | ||||
0.0983614 | + | 0.995151i | \(0.468640\pi\) | |||||||
\(602\) | 0.613277 | 0.0249953 | ||||||||
\(603\) | 1.37058 | 0.0558143 | ||||||||
\(604\) | 22.4373 | 0.912959 | ||||||||
\(605\) | −0.211465 | −0.00859726 | ||||||||
\(606\) | 1.55274 | 0.0630758 | ||||||||
\(607\) | −13.2768 | −0.538887 | −0.269443 | − | 0.963016i | \(-0.586840\pi\) | ||||
−0.269443 | + | 0.963016i | \(0.586840\pi\) | |||||||
\(608\) | −5.92717 | −0.240378 | ||||||||
\(609\) | −12.5118 | −0.507006 | ||||||||
\(610\) | −0.273401 | −0.0110697 | ||||||||
\(611\) | 16.7254 | 0.676638 | ||||||||
\(612\) | 6.61780 | 0.267509 | ||||||||
\(613\) | −25.1532 | −1.01593 | −0.507965 | − | 0.861378i | \(-0.669602\pi\) | ||||
−0.507965 | + | 0.861378i | \(0.669602\pi\) | |||||||
\(614\) | 1.08659 | 0.0438512 | ||||||||
\(615\) | −4.04484 | −0.163104 | ||||||||
\(616\) | −1.19671 | −0.0482168 | ||||||||
\(617\) | 17.9264 | 0.721690 | 0.360845 | − | 0.932626i | \(-0.382488\pi\) | ||||
0.360845 | + | 0.932626i | \(0.382488\pi\) | |||||||
\(618\) | 1.15841 | 0.0465981 | ||||||||
\(619\) | 40.7720 | 1.63877 | 0.819383 | − | 0.573247i | \(-0.194316\pi\) | ||||
0.819383 | + | 0.573247i | \(0.194316\pi\) | |||||||
\(620\) | 0.863059 | 0.0346613 | ||||||||
\(621\) | −36.3798 | −1.45987 | ||||||||
\(622\) | −1.34455 | −0.0539116 | ||||||||
\(623\) | 9.61205 | 0.385099 | ||||||||
\(624\) | −24.5789 | −0.983945 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.00193764 | 7.74436e−5 0 | ||||||||
\(627\) | −24.8992 | −0.994379 | ||||||||
\(628\) | 11.8453 | 0.472677 | ||||||||
\(629\) | 21.9443 | 0.874976 | ||||||||
\(630\) | 0.0966912 | 0.00385227 | ||||||||
\(631\) | −12.7986 | −0.509506 | −0.254753 | − | 0.967006i | \(-0.581994\pi\) | ||||
−0.254753 | + | 0.967006i | \(0.581994\pi\) | |||||||
\(632\) | 1.53491 | 0.0610556 | ||||||||
\(633\) | −23.8361 | −0.947400 | ||||||||
\(634\) | 1.97077 | 0.0782693 | ||||||||
\(635\) | −13.7778 | −0.546755 | ||||||||
\(636\) | −9.09528 | −0.360651 | ||||||||
\(637\) | −4.46665 | −0.176975 | ||||||||
\(638\) | −2.69266 | −0.106603 | ||||||||
\(639\) | 12.7235 | 0.503334 | ||||||||
\(640\) | 2.89047 | 0.114256 | ||||||||
\(641\) | −29.7696 | −1.17583 | −0.587914 | − | 0.808923i | \(-0.700051\pi\) | ||||
−0.587914 | + | 0.808923i | \(0.700051\pi\) | |||||||
\(642\) | −1.46372 | −0.0577685 | ||||||||
\(643\) | −14.9518 | −0.589642 | −0.294821 | − | 0.955553i | \(-0.595260\pi\) | ||||
−0.294821 | + | 0.955553i | \(0.595260\pi\) | |||||||
\(644\) | −12.8129 | −0.504899 | ||||||||
\(645\) | −9.36006 | −0.368552 | ||||||||
\(646\) | −1.55792 | −0.0612956 | ||||||||
\(647\) | −10.9196 | −0.429293 | −0.214646 | − | 0.976692i | \(-0.568860\pi\) | ||||
−0.214646 | + | 0.976692i | \(0.568860\pi\) | |||||||
\(648\) | −1.71233 | −0.0672667 | ||||||||
\(649\) | −24.5363 | −0.963133 | ||||||||
\(650\) | 0.407695 | 0.0159911 | ||||||||
\(651\) | −0.603669 | −0.0236596 | ||||||||
\(652\) | 21.5011 | 0.842049 | ||||||||
\(653\) | 25.1484 | 0.984135 | 0.492067 | − | 0.870557i | \(-0.336241\pi\) | ||||
0.492067 | + | 0.870557i | \(0.336241\pi\) | |||||||
\(654\) | 0.0937434 | 0.00366566 | ||||||||
\(655\) | −22.6986 | −0.886909 | ||||||||
\(656\) | −11.4692 | −0.447796 | ||||||||
\(657\) | 11.4622 | 0.447183 | ||||||||
\(658\) | 0.341781 | 0.0133240 | ||||||||
\(659\) | 22.6846 | 0.883668 | 0.441834 | − | 0.897097i | \(-0.354328\pi\) | ||||
0.441834 | + | 0.897097i | \(0.354328\pi\) | |||||||
\(660\) | 9.11326 | 0.354733 | ||||||||
\(661\) | 3.87538 | 0.150735 | 0.0753674 | − | 0.997156i | \(-0.475987\pi\) | ||||
0.0753674 | + | 0.997156i | \(0.475987\pi\) | |||||||
\(662\) | 0.256665 | 0.00997556 | ||||||||
\(663\) | −19.5173 | −0.757989 | ||||||||
\(664\) | 4.44907 | 0.172657 | ||||||||
\(665\) | 5.44163 | 0.211017 | ||||||||
\(666\) | 0.676465 | 0.0262125 | ||||||||
\(667\) | −57.7799 | −2.23725 | ||||||||
\(668\) | 24.3667 | 0.942776 | ||||||||
\(669\) | 32.8743 | 1.27099 | ||||||||
\(670\) | 0.118093 | 0.00456233 | ||||||||
\(671\) | −9.83849 | −0.379811 | ||||||||
\(672\) | −1.51738 | −0.0585341 | ||||||||
\(673\) | −4.27162 | −0.164659 | −0.0823294 | − | 0.996605i | \(-0.526236\pi\) | ||||
−0.0823294 | + | 0.996605i | \(0.526236\pi\) | |||||||
\(674\) | −2.35839 | −0.0908417 | ||||||||
\(675\) | −5.65497 | −0.217660 | ||||||||
\(676\) | −13.8440 | −0.532460 | ||||||||
\(677\) | 4.56127 | 0.175304 | 0.0876518 | − | 0.996151i | \(-0.472064\pi\) | ||||
0.0876518 | + | 0.996151i | \(0.472064\pi\) | |||||||
\(678\) | 2.39153 | 0.0918460 | ||||||||
\(679\) | 3.55578 | 0.136458 | ||||||||
\(680\) | 1.14280 | 0.0438244 | ||||||||
\(681\) | −34.5708 | −1.32476 | ||||||||
\(682\) | −0.129915 | −0.00497469 | ||||||||
\(683\) | −18.2544 | −0.698487 | −0.349244 | − | 0.937032i | \(-0.613561\pi\) | ||||
−0.349244 | + | 0.937032i | \(0.613561\pi\) | |||||||
\(684\) | 11.4810 | 0.438987 | ||||||||
\(685\) | −2.21283 | −0.0845478 | ||||||||
\(686\) | −0.0912753 | −0.00348491 | ||||||||
\(687\) | −1.39308 | −0.0531492 | ||||||||
\(688\) | −26.5405 | −1.01185 | ||||||||
\(689\) | −14.6422 | −0.557822 | ||||||||
\(690\) | −0.818011 | −0.0311411 | ||||||||
\(691\) | 28.6186 | 1.08870 | 0.544352 | − | 0.838857i | \(-0.316776\pi\) | ||||
0.544352 | + | 0.838857i | \(0.316776\pi\) | |||||||
\(692\) | −35.4561 | −1.34784 | ||||||||
\(693\) | 3.47948 | 0.132175 | ||||||||
\(694\) | −1.46199 | −0.0554963 | ||||||||
\(695\) | −2.36781 | −0.0898160 | ||||||||
\(696\) | −4.55858 | −0.172792 | ||||||||
\(697\) | −9.10729 | −0.344963 | ||||||||
\(698\) | −0.275864 | −0.0104416 | ||||||||
\(699\) | −22.5609 | −0.853331 | ||||||||
\(700\) | −1.99167 | −0.0752780 | ||||||||
\(701\) | 35.0867 | 1.32521 | 0.662603 | − | 0.748970i | \(-0.269452\pi\) | ||||
0.662603 | + | 0.748970i | \(0.269452\pi\) | |||||||
\(702\) | −2.30550 | −0.0870155 | ||||||||
\(703\) | 38.0704 | 1.43585 | ||||||||
\(704\) | 25.6223 | 0.965675 | ||||||||
\(705\) | −5.21639 | −0.196461 | ||||||||
\(706\) | −2.31767 | −0.0872265 | ||||||||
\(707\) | −12.2115 | −0.459262 | ||||||||
\(708\) | −20.7262 | −0.778938 | ||||||||
\(709\) | 6.56374 | 0.246506 | 0.123253 | − | 0.992375i | \(-0.460667\pi\) | ||||
0.123253 | + | 0.992375i | \(0.460667\pi\) | |||||||
\(710\) | 1.09629 | 0.0411431 | ||||||||
\(711\) | −4.46282 | −0.167369 | ||||||||
\(712\) | 3.50206 | 0.131245 | ||||||||
\(713\) | −2.78775 | −0.104402 | ||||||||
\(714\) | −0.398833 | −0.0149260 | ||||||||
\(715\) | 14.6711 | 0.548668 | ||||||||
\(716\) | 6.46230 | 0.241508 | ||||||||
\(717\) | 3.83601 | 0.143258 | ||||||||
\(718\) | −1.91116 | −0.0713240 | ||||||||
\(719\) | −38.0218 | −1.41798 | −0.708988 | − | 0.705221i | \(-0.750848\pi\) | ||||
−0.708988 | + | 0.705221i | \(0.750848\pi\) | |||||||
\(720\) | −4.18446 | −0.155946 | ||||||||
\(721\) | −9.11033 | −0.339286 | ||||||||
\(722\) | −0.968555 | −0.0360459 | ||||||||
\(723\) | 2.74053 | 0.101921 | ||||||||
\(724\) | 14.3145 | 0.531995 | ||||||||
\(725\) | −8.98145 | −0.333563 | ||||||||
\(726\) | 0.0268885 | 0.000997925 0 | ||||||||
\(727\) | 0.957673 | 0.0355181 | 0.0177591 | − | 0.999842i | \(-0.494347\pi\) | ||||
0.0177591 | + | 0.999842i | \(0.494347\pi\) | |||||||
\(728\) | −1.62738 | −0.0603148 | ||||||||
\(729\) | 28.6121 | 1.05971 | ||||||||
\(730\) | 0.987615 | 0.0365533 | ||||||||
\(731\) | −21.0749 | −0.779485 | ||||||||
\(732\) | −8.31073 | −0.307174 | ||||||||
\(733\) | −15.7838 | −0.582988 | −0.291494 | − | 0.956573i | \(-0.594152\pi\) | ||||
−0.291494 | + | 0.956573i | \(0.594152\pi\) | |||||||
\(734\) | 2.25604 | 0.0832719 | ||||||||
\(735\) | 1.39308 | 0.0513844 | ||||||||
\(736\) | −7.00727 | −0.258291 | ||||||||
\(737\) | 4.24964 | 0.156538 | ||||||||
\(738\) | −0.280746 | −0.0103344 | ||||||||
\(739\) | −43.5255 | −1.60111 | −0.800556 | − | 0.599259i | \(-0.795462\pi\) | ||||
−0.800556 | + | 0.599259i | \(0.795462\pi\) | |||||||
\(740\) | −13.9340 | −0.512224 | ||||||||
\(741\) | −33.8599 | −1.24388 | ||||||||
\(742\) | −0.299211 | −0.0109844 | ||||||||
\(743\) | 16.2523 | 0.596239 | 0.298120 | − | 0.954529i | \(-0.403641\pi\) | ||||
0.298120 | + | 0.954529i | \(0.403641\pi\) | |||||||
\(744\) | −0.219941 | −0.00806343 | ||||||||
\(745\) | 12.1250 | 0.444226 | ||||||||
\(746\) | 3.31735 | 0.121457 | ||||||||
\(747\) | −12.9358 | −0.473298 | ||||||||
\(748\) | 20.5192 | 0.750258 | ||||||||
\(749\) | 11.5115 | 0.420619 | ||||||||
\(750\) | −0.127154 | −0.00464299 | ||||||||
\(751\) | −16.2769 | −0.593951 | −0.296976 | − | 0.954885i | \(-0.595978\pi\) | ||||
−0.296976 | + | 0.954885i | \(0.595978\pi\) | |||||||
\(752\) | −14.7911 | −0.539377 | ||||||||
\(753\) | −24.0616 | −0.876855 | ||||||||
\(754\) | −3.66169 | −0.133351 | ||||||||
\(755\) | −11.2656 | −0.409995 | ||||||||
\(756\) | 11.2628 | 0.409625 | ||||||||
\(757\) | 20.0155 | 0.727476 | 0.363738 | − | 0.931501i | \(-0.381500\pi\) | ||||
0.363738 | + | 0.931501i | \(0.381500\pi\) | |||||||
\(758\) | −2.64721 | −0.0961508 | ||||||||
\(759\) | −29.4365 | −1.06848 | ||||||||
\(760\) | 1.98261 | 0.0719168 | ||||||||
\(761\) | 0.439370 | 0.0159271 | 0.00796357 | − | 0.999968i | \(-0.497465\pi\) | ||||
0.00796357 | + | 0.999968i | \(0.497465\pi\) | |||||||
\(762\) | 1.75189 | 0.0634644 | ||||||||
\(763\) | −0.737245 | −0.0266901 | ||||||||
\(764\) | −34.6117 | −1.25221 | ||||||||
\(765\) | −3.32274 | −0.120134 | ||||||||
\(766\) | 2.42414 | 0.0875878 | ||||||||
\(767\) | −33.3664 | −1.20479 | ||||||||
\(768\) | 21.3665 | 0.770999 | ||||||||
\(769\) | −25.4850 | −0.919014 | −0.459507 | − | 0.888174i | \(-0.651974\pi\) | ||||
−0.459507 | + | 0.888174i | \(0.651974\pi\) | |||||||
\(770\) | 0.299802 | 0.0108041 | ||||||||
\(771\) | −42.3363 | −1.52470 | ||||||||
\(772\) | 11.4120 | 0.410727 | ||||||||
\(773\) | 22.2581 | 0.800567 | 0.400283 | − | 0.916391i | \(-0.368912\pi\) | ||||
0.400283 | + | 0.916391i | \(0.368912\pi\) | |||||||
\(774\) | −0.649666 | −0.0233518 | ||||||||
\(775\) | −0.433335 | −0.0155658 | ||||||||
\(776\) | 1.29552 | 0.0465063 | ||||||||
\(777\) | 9.74617 | 0.349642 | ||||||||
\(778\) | −3.32714 | −0.119284 | ||||||||
\(779\) | −15.7999 | −0.566092 | ||||||||
\(780\) | 12.3929 | 0.443738 | ||||||||
\(781\) | 39.4507 | 1.41166 | ||||||||
\(782\) | −1.84182 | −0.0658632 | ||||||||
\(783\) | 50.7898 | 1.81508 | ||||||||
\(784\) | 3.95008 | 0.141074 | ||||||||
\(785\) | −5.94740 | −0.212272 | ||||||||
\(786\) | 2.88621 | 0.102948 | ||||||||
\(787\) | 38.0516 | 1.35639 | 0.678197 | − | 0.734880i | \(-0.262762\pi\) | ||||
0.678197 | + | 0.734880i | \(0.262762\pi\) | |||||||
\(788\) | 38.4514 | 1.36977 | ||||||||
\(789\) | −14.8357 | −0.528165 | ||||||||
\(790\) | −0.384529 | −0.0136809 | ||||||||
\(791\) | −18.8082 | −0.668742 | ||||||||
\(792\) | 1.26772 | 0.0450464 | ||||||||
\(793\) | −13.3792 | −0.475108 | ||||||||
\(794\) | 3.34710 | 0.118784 | ||||||||
\(795\) | 4.56666 | 0.161963 | ||||||||
\(796\) | 26.0155 | 0.922096 | ||||||||
\(797\) | −1.93650 | −0.0685944 | −0.0342972 | − | 0.999412i | \(-0.510919\pi\) | ||||
−0.0342972 | + | 0.999412i | \(0.510919\pi\) | |||||||
\(798\) | −0.691923 | −0.0244938 | ||||||||
\(799\) | −11.7451 | −0.415513 | ||||||||
\(800\) | −1.08923 | −0.0385100 | ||||||||
\(801\) | −10.1824 | −0.359777 | ||||||||
\(802\) | −3.38066 | −0.119375 | ||||||||
\(803\) | 35.5399 | 1.25417 | ||||||||
\(804\) | 3.58974 | 0.126600 | ||||||||
\(805\) | 6.43325 | 0.226742 | ||||||||
\(806\) | −0.176668 | −0.00622287 | ||||||||
\(807\) | −33.4151 | −1.17627 | ||||||||
\(808\) | −4.44916 | −0.156521 | ||||||||
\(809\) | 33.1191 | 1.16441 | 0.582203 | − | 0.813043i | \(-0.302191\pi\) | ||||
0.582203 | + | 0.813043i | \(0.302191\pi\) | |||||||
\(810\) | 0.428976 | 0.0150727 | ||||||||
\(811\) | −36.1465 | −1.26927 | −0.634637 | − | 0.772810i | \(-0.718850\pi\) | ||||
−0.634637 | + | 0.772810i | \(0.718850\pi\) | |||||||
\(812\) | 17.8881 | 0.627748 | ||||||||
\(813\) | 4.76700 | 0.167186 | ||||||||
\(814\) | 2.09746 | 0.0735158 | ||||||||
\(815\) | −10.7955 | −0.378151 | ||||||||
\(816\) | 17.2601 | 0.604226 | ||||||||
\(817\) | −36.5622 | −1.27915 | ||||||||
\(818\) | −2.13558 | −0.0746688 | ||||||||
\(819\) | 4.73168 | 0.165338 | ||||||||
\(820\) | 5.78287 | 0.201947 | ||||||||
\(821\) | −18.7664 | −0.654951 | −0.327475 | − | 0.944860i | \(-0.606198\pi\) | ||||
−0.327475 | + | 0.944860i | \(0.606198\pi\) | |||||||
\(822\) | 0.281369 | 0.00981386 | ||||||||
\(823\) | 21.1442 | 0.737039 | 0.368520 | − | 0.929620i | \(-0.379865\pi\) | ||||
0.368520 | + | 0.929620i | \(0.379865\pi\) | |||||||
\(824\) | −3.31926 | −0.115632 | ||||||||
\(825\) | −4.57569 | −0.159305 | ||||||||
\(826\) | −0.681837 | −0.0237241 | ||||||||
\(827\) | 35.3225 | 1.22828 | 0.614142 | − | 0.789196i | \(-0.289502\pi\) | ||||
0.614142 | + | 0.789196i | \(0.289502\pi\) | |||||||
\(828\) | 13.5732 | 0.471700 | ||||||||
\(829\) | 4.60932 | 0.160088 | 0.0800442 | − | 0.996791i | \(-0.474494\pi\) | ||||
0.0800442 | + | 0.996791i | \(0.474494\pi\) | |||||||
\(830\) | −1.11459 | −0.0386879 | ||||||||
\(831\) | 11.1084 | 0.385348 | ||||||||
\(832\) | 34.8432 | 1.20797 | ||||||||
\(833\) | 3.13663 | 0.108678 | ||||||||
\(834\) | 0.301075 | 0.0104254 | ||||||||
\(835\) | −12.2343 | −0.423386 | ||||||||
\(836\) | 35.5982 | 1.23119 | ||||||||
\(837\) | 2.45049 | 0.0847014 | ||||||||
\(838\) | 2.33581 | 0.0806891 | ||||||||
\(839\) | 52.8725 | 1.82536 | 0.912681 | − | 0.408673i | \(-0.134008\pi\) | ||||
0.912681 | + | 0.408673i | \(0.134008\pi\) | |||||||
\(840\) | 0.507555 | 0.0175123 | ||||||||
\(841\) | 51.6664 | 1.78160 | ||||||||
\(842\) | −1.13356 | −0.0390652 | ||||||||
\(843\) | 23.3213 | 0.803227 | ||||||||
\(844\) | 34.0783 | 1.17302 | ||||||||
\(845\) | 6.95094 | 0.239120 | ||||||||
\(846\) | −0.362061 | −0.0124479 | ||||||||
\(847\) | −0.211465 | −0.00726601 | ||||||||
\(848\) | 12.9488 | 0.444664 | ||||||||
\(849\) | 24.8875 | 0.854136 | ||||||||
\(850\) | −0.286297 | −0.00981989 | ||||||||
\(851\) | 45.0079 | 1.54285 | ||||||||
\(852\) | 33.3246 | 1.14168 | ||||||||
\(853\) | 12.4694 | 0.426945 | 0.213473 | − | 0.976949i | \(-0.431523\pi\) | ||||
0.213473 | + | 0.976949i | \(0.431523\pi\) | |||||||
\(854\) | −0.273401 | −0.00935559 | ||||||||
\(855\) | −5.76451 | −0.197142 | ||||||||
\(856\) | 4.19409 | 0.143351 | ||||||||
\(857\) | 29.8351 | 1.01915 | 0.509575 | − | 0.860427i | \(-0.329803\pi\) | ||||
0.509575 | + | 0.860427i | \(0.329803\pi\) | |||||||
\(858\) | −1.86548 | −0.0636866 | ||||||||
\(859\) | 40.3673 | 1.37731 | 0.688657 | − | 0.725088i | \(-0.258201\pi\) | ||||
0.688657 | + | 0.725088i | \(0.258201\pi\) | |||||||
\(860\) | 13.3820 | 0.456322 | ||||||||
\(861\) | −4.04484 | −0.137848 | ||||||||
\(862\) | 1.75903 | 0.0599128 | ||||||||
\(863\) | 7.89203 | 0.268648 | 0.134324 | − | 0.990937i | \(-0.457114\pi\) | ||||
0.134324 | + | 0.990937i | \(0.457114\pi\) | |||||||
\(864\) | 6.15954 | 0.209552 | ||||||||
\(865\) | 17.8022 | 0.605293 | ||||||||
\(866\) | 2.32876 | 0.0791344 | ||||||||
\(867\) | −9.97662 | −0.338824 | ||||||||
\(868\) | 0.863059 | 0.0292941 | ||||||||
\(869\) | −13.8375 | −0.469405 | ||||||||
\(870\) | 1.14202 | 0.0387182 | ||||||||
\(871\) | 5.77900 | 0.195814 | ||||||||
\(872\) | −0.268609 | −0.00909623 | ||||||||
\(873\) | −3.76677 | −0.127486 | ||||||||
\(874\) | −3.19531 | −0.108083 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 30.0211 | 1.01432 | ||||||||
\(877\) | 10.0721 | 0.340110 | 0.170055 | − | 0.985435i | \(-0.445606\pi\) | ||||
0.170055 | + | 0.985435i | \(0.445606\pi\) | |||||||
\(878\) | −1.42786 | −0.0481880 | ||||||||
\(879\) | 43.2471 | 1.45869 | ||||||||
\(880\) | −12.9744 | −0.437367 | ||||||||
\(881\) | −54.8146 | −1.84675 | −0.923376 | − | 0.383897i | \(-0.874582\pi\) | ||||
−0.923376 | + | 0.383897i | \(0.874582\pi\) | |||||||
\(882\) | 0.0966912 | 0.00325576 | ||||||||
\(883\) | −36.8268 | −1.23932 | −0.619660 | − | 0.784870i | \(-0.712729\pi\) | ||||
−0.619660 | + | 0.784870i | \(0.712729\pi\) | |||||||
\(884\) | 27.9037 | 0.938503 | ||||||||
\(885\) | 10.4065 | 0.349809 | ||||||||
\(886\) | 0.335677 | 0.0112773 | ||||||||
\(887\) | 15.1972 | 0.510271 | 0.255136 | − | 0.966905i | \(-0.417880\pi\) | ||||
0.255136 | + | 0.966905i | \(0.417880\pi\) | |||||||
\(888\) | 3.55093 | 0.119161 | ||||||||
\(889\) | −13.7778 | −0.462092 | ||||||||
\(890\) | −0.877342 | −0.0294086 | ||||||||
\(891\) | 15.4369 | 0.517156 | ||||||||
\(892\) | −47.0000 | −1.57368 | ||||||||
\(893\) | −20.3763 | −0.681865 | ||||||||
\(894\) | −1.54174 | −0.0515634 | ||||||||
\(895\) | −3.24467 | −0.108457 | ||||||||
\(896\) | 2.89047 | 0.0965638 | ||||||||
\(897\) | −40.0302 | −1.33657 | ||||||||
\(898\) | −1.08032 | −0.0360506 | ||||||||
\(899\) | 3.89197 | 0.129805 | ||||||||
\(900\) | 2.10985 | 0.0703282 | ||||||||
\(901\) | 10.2822 | 0.342550 | ||||||||
\(902\) | −0.870484 | −0.0289839 | ||||||||
\(903\) | −9.36006 | −0.311483 | ||||||||
\(904\) | −6.85259 | −0.227914 | ||||||||
\(905\) | −7.18720 | −0.238910 | ||||||||
\(906\) | 1.43246 | 0.0475901 | ||||||||
\(907\) | −30.6546 | −1.01787 | −0.508934 | − | 0.860805i | \(-0.669960\pi\) | ||||
−0.508934 | + | 0.860805i | \(0.669960\pi\) | |||||||
\(908\) | 49.4256 | 1.64025 | ||||||||
\(909\) | 12.9361 | 0.429064 | ||||||||
\(910\) | 0.407695 | 0.0135149 | ||||||||
\(911\) | −5.55492 | −0.184043 | −0.0920214 | − | 0.995757i | \(-0.529333\pi\) | ||||
−0.0920214 | + | 0.995757i | \(0.529333\pi\) | |||||||
\(912\) | 29.9441 | 0.991547 | ||||||||
\(913\) | −40.1091 | −1.32742 | ||||||||
\(914\) | −0.415819 | −0.0137541 | ||||||||
\(915\) | 4.17275 | 0.137947 | ||||||||
\(916\) | 1.99167 | 0.0658066 | ||||||||
\(917\) | −22.6986 | −0.749575 | ||||||||
\(918\) | 1.61900 | 0.0534349 | ||||||||
\(919\) | 46.6722 | 1.53958 | 0.769788 | − | 0.638300i | \(-0.220362\pi\) | ||||
0.769788 | + | 0.638300i | \(0.220362\pi\) | |||||||
\(920\) | 2.34390 | 0.0772759 | ||||||||
\(921\) | −16.5839 | −0.546459 | ||||||||
\(922\) | 0.186075 | 0.00612806 | ||||||||
\(923\) | 53.6481 | 1.76585 | ||||||||
\(924\) | 9.11326 | 0.299804 | ||||||||
\(925\) | 6.99614 | 0.230032 | ||||||||
\(926\) | −0.272821 | −0.00896544 | ||||||||
\(927\) | 9.65090 | 0.316977 | ||||||||
\(928\) | 9.78283 | 0.321137 | ||||||||
\(929\) | 14.1732 | 0.465008 | 0.232504 | − | 0.972595i | \(-0.425308\pi\) | ||||
0.232504 | + | 0.972595i | \(0.425308\pi\) | |||||||
\(930\) | 0.0551000 | 0.00180680 | ||||||||
\(931\) | 5.44163 | 0.178342 | ||||||||
\(932\) | 32.2551 | 1.05655 | ||||||||
\(933\) | 20.5211 | 0.671829 | ||||||||
\(934\) | 0.386544 | 0.0126481 | ||||||||
\(935\) | −10.3025 | −0.336929 | ||||||||
\(936\) | 1.72394 | 0.0563488 | ||||||||
\(937\) | 13.2822 | 0.433912 | 0.216956 | − | 0.976181i | \(-0.430387\pi\) | ||||
0.216956 | + | 0.976181i | \(0.430387\pi\) | |||||||
\(938\) | 0.118093 | 0.00385587 | ||||||||
\(939\) | −0.0295729 | −0.000965076 0 | ||||||||
\(940\) | 7.45783 | 0.243247 | ||||||||
\(941\) | −18.4555 | −0.601633 | −0.300816 | − | 0.953682i | \(-0.597259\pi\) | ||||
−0.300816 | + | 0.953682i | \(0.597259\pi\) | |||||||
\(942\) | 0.756233 | 0.0246394 | ||||||||
\(943\) | −18.6791 | −0.608276 | ||||||||
\(944\) | 29.5076 | 0.960390 | ||||||||
\(945\) | −5.65497 | −0.183956 | ||||||||
\(946\) | −2.01436 | −0.0654926 | ||||||||
\(947\) | 50.3752 | 1.63697 | 0.818486 | − | 0.574526i | \(-0.194814\pi\) | ||||
0.818486 | + | 0.574526i | \(0.194814\pi\) | |||||||
\(948\) | −11.6888 | −0.379633 | ||||||||
\(949\) | 48.3299 | 1.56886 | ||||||||
\(950\) | −0.496687 | −0.0161146 | ||||||||
\(951\) | −30.0786 | −0.975366 | ||||||||
\(952\) | 1.14280 | 0.0370384 | ||||||||
\(953\) | −30.4291 | −0.985694 | −0.492847 | − | 0.870116i | \(-0.664044\pi\) | ||||
−0.492847 | + | 0.870116i | \(0.664044\pi\) | |||||||
\(954\) | 0.316964 | 0.0102621 | ||||||||
\(955\) | 17.3783 | 0.562347 | ||||||||
\(956\) | −5.48430 | −0.177375 | ||||||||
\(957\) | 41.0963 | 1.32845 | ||||||||
\(958\) | −2.26525 | −0.0731868 | ||||||||
\(959\) | −2.21283 | −0.0714559 | ||||||||
\(960\) | −10.8670 | −0.350732 | ||||||||
\(961\) | −30.8122 | −0.993943 | ||||||||
\(962\) | 2.85229 | 0.0919615 | ||||||||
\(963\) | −12.1945 | −0.392962 | ||||||||
\(964\) | −3.91810 | −0.126194 | ||||||||
\(965\) | −5.72987 | −0.184451 | ||||||||
\(966\) | −0.818011 | −0.0263191 | ||||||||
\(967\) | 23.1148 | 0.743321 | 0.371661 | − | 0.928369i | \(-0.378789\pi\) | ||||
0.371661 | + | 0.928369i | \(0.378789\pi\) | |||||||
\(968\) | −0.0770452 | −0.00247633 | ||||||||
\(969\) | 23.7776 | 0.763845 | ||||||||
\(970\) | −0.324555 | −0.0104208 | ||||||||
\(971\) | 14.6673 | 0.470695 | 0.235347 | − | 0.971911i | \(-0.424377\pi\) | ||||
0.235347 | + | 0.971911i | \(0.424377\pi\) | |||||||
\(972\) | −20.7486 | −0.665513 | ||||||||
\(973\) | −2.36781 | −0.0759084 | ||||||||
\(974\) | 1.78819 | 0.0572974 | ||||||||
\(975\) | −6.22239 | −0.199276 | ||||||||
\(976\) | 11.8319 | 0.378729 | ||||||||
\(977\) | 7.00864 | 0.224226 | 0.112113 | − | 0.993695i | \(-0.464238\pi\) | ||||
0.112113 | + | 0.993695i | \(0.464238\pi\) | |||||||
\(978\) | 1.37269 | 0.0438938 | ||||||||
\(979\) | −31.5716 | −1.00903 | ||||||||
\(980\) | −1.99167 | −0.0636215 | ||||||||
\(981\) | 0.780990 | 0.0249351 | ||||||||
\(982\) | 3.34229 | 0.106657 | ||||||||
\(983\) | −55.8845 | −1.78244 | −0.891220 | − | 0.453571i | \(-0.850150\pi\) | ||||
−0.891220 | + | 0.453571i | \(0.850150\pi\) | |||||||
\(984\) | −1.47370 | −0.0469799 | ||||||||
\(985\) | −19.3061 | −0.615144 | ||||||||
\(986\) | 2.57136 | 0.0818887 | ||||||||
\(987\) | −5.21639 | −0.166040 | ||||||||
\(988\) | 48.4092 | 1.54010 | ||||||||
\(989\) | −43.2249 | −1.37447 | ||||||||
\(990\) | −0.317591 | −0.0100937 | ||||||||
\(991\) | −55.3542 | −1.75838 | −0.879192 | − | 0.476468i | \(-0.841917\pi\) | ||||
−0.879192 | + | 0.476468i | \(0.841917\pi\) | |||||||
\(992\) | 0.472000 | 0.0149860 | ||||||||
\(993\) | −3.91731 | −0.124312 | ||||||||
\(994\) | 1.09629 | 0.0347723 | ||||||||
\(995\) | −13.0622 | −0.414099 | ||||||||
\(996\) | −33.8808 | −1.07355 | ||||||||
\(997\) | 1.93241 | 0.0611999 | 0.0306000 | − | 0.999532i | \(-0.490258\pi\) | ||||
0.0306000 | + | 0.999532i | \(0.490258\pi\) | |||||||
\(998\) | 3.34582 | 0.105910 | ||||||||
\(999\) | −39.5630 | −1.25172 |
(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 | 8015.2.a.h.1.19 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8015.2.a.h.1.19 | ✓ | 38 | 1.1 | even | 1 | trivial |