Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4015,2,Mod(1,4015)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4015, 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("4015.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4015 = 5 \cdot 11 \cdot 73 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4015.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: | \(32.0599364115\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4015.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.421939 | −0.298356 | −0.149178 | − | 0.988810i | \(-0.547663\pi\) | ||||
−0.149178 | + | 0.988810i | \(0.547663\pi\) | |||||||
\(3\) | −2.05594 | −1.18700 | −0.593499 | − | 0.804834i | \(-0.702254\pi\) | ||||
−0.593499 | + | 0.804834i | \(0.702254\pi\) | |||||||
\(4\) | −1.82197 | −0.910984 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.867482 | 0.354148 | ||||||||
\(7\) | −0.0580639 | −0.0219461 | −0.0109730 | − | 0.999940i | \(-0.503493\pi\) | ||||
−0.0109730 | + | 0.999940i | \(0.503493\pi\) | |||||||
\(8\) | 1.61264 | 0.570153 | ||||||||
\(9\) | 1.22690 | 0.408967 | ||||||||
\(10\) | −0.421939 | −0.133429 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.74586 | 1.08134 | ||||||||
\(13\) | 6.32922 | 1.75541 | 0.877704 | − | 0.479202i | \(-0.159074\pi\) | ||||
0.877704 | + | 0.479202i | \(0.159074\pi\) | |||||||
\(14\) | 0.0244994 | 0.00654774 | ||||||||
\(15\) | −2.05594 | −0.530842 | ||||||||
\(16\) | 2.96350 | 0.740875 | ||||||||
\(17\) | 5.86865 | 1.42336 | 0.711678 | − | 0.702506i | \(-0.247936\pi\) | ||||
0.711678 | + | 0.702506i | \(0.247936\pi\) | |||||||
\(18\) | −0.517676 | −0.122018 | ||||||||
\(19\) | 0.796345 | 0.182694 | 0.0913470 | − | 0.995819i | \(-0.470883\pi\) | ||||
0.0913470 | + | 0.995819i | \(0.470883\pi\) | |||||||
\(20\) | −1.82197 | −0.407404 | ||||||||
\(21\) | 0.119376 | 0.0260500 | ||||||||
\(22\) | −0.421939 | −0.0899576 | ||||||||
\(23\) | 8.29329 | 1.72927 | 0.864635 | − | 0.502400i | \(-0.167549\pi\) | ||||
0.864635 | + | 0.502400i | \(0.167549\pi\) | |||||||
\(24\) | −3.31549 | −0.676771 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.67054 | −0.523736 | ||||||||
\(27\) | 3.64539 | 0.701556 | ||||||||
\(28\) | 0.105790 | 0.0199925 | ||||||||
\(29\) | −1.17504 | −0.218199 | −0.109099 | − | 0.994031i | \(-0.534797\pi\) | ||||
−0.109099 | + | 0.994031i | \(0.534797\pi\) | |||||||
\(30\) | 0.867482 | 0.158380 | ||||||||
\(31\) | −0.271039 | −0.0486800 | −0.0243400 | − | 0.999704i | \(-0.507748\pi\) | ||||
−0.0243400 | + | 0.999704i | \(0.507748\pi\) | |||||||
\(32\) | −4.47569 | −0.791197 | ||||||||
\(33\) | −2.05594 | −0.357894 | ||||||||
\(34\) | −2.47621 | −0.424666 | ||||||||
\(35\) | −0.0580639 | −0.00981458 | ||||||||
\(36\) | −2.23537 | −0.372562 | ||||||||
\(37\) | 3.31240 | 0.544556 | 0.272278 | − | 0.962219i | \(-0.412223\pi\) | ||||
0.272278 | + | 0.962219i | \(0.412223\pi\) | |||||||
\(38\) | −0.336009 | −0.0545078 | ||||||||
\(39\) | −13.0125 | −2.08367 | ||||||||
\(40\) | 1.61264 | 0.254980 | ||||||||
\(41\) | 1.75836 | 0.274610 | 0.137305 | − | 0.990529i | \(-0.456156\pi\) | ||||
0.137305 | + | 0.990529i | \(0.456156\pi\) | |||||||
\(42\) | −0.0503693 | −0.00777216 | ||||||||
\(43\) | −1.18574 | −0.180823 | −0.0904117 | − | 0.995904i | \(-0.528818\pi\) | ||||
−0.0904117 | + | 0.995904i | \(0.528818\pi\) | |||||||
\(44\) | −1.82197 | −0.274672 | ||||||||
\(45\) | 1.22690 | 0.182895 | ||||||||
\(46\) | −3.49926 | −0.515938 | ||||||||
\(47\) | −11.5364 | −1.68275 | −0.841376 | − | 0.540450i | \(-0.818254\pi\) | ||||
−0.841376 | + | 0.540450i | \(0.818254\pi\) | |||||||
\(48\) | −6.09279 | −0.879418 | ||||||||
\(49\) | −6.99663 | −0.999518 | ||||||||
\(50\) | −0.421939 | −0.0596711 | ||||||||
\(51\) | −12.0656 | −1.68952 | ||||||||
\(52\) | −11.5316 | −1.59915 | ||||||||
\(53\) | 3.80653 | 0.522867 | 0.261433 | − | 0.965222i | \(-0.415805\pi\) | ||||
0.261433 | + | 0.965222i | \(0.415805\pi\) | |||||||
\(54\) | −1.53813 | −0.209313 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | −0.0936359 | −0.0125126 | ||||||||
\(57\) | −1.63724 | −0.216858 | ||||||||
\(58\) | 0.495794 | 0.0651009 | ||||||||
\(59\) | 1.80051 | 0.234406 | 0.117203 | − | 0.993108i | \(-0.462607\pi\) | ||||
0.117203 | + | 0.993108i | \(0.462607\pi\) | |||||||
\(60\) | 3.74586 | 0.483589 | ||||||||
\(61\) | 7.32347 | 0.937674 | 0.468837 | − | 0.883285i | \(-0.344673\pi\) | ||||
0.468837 | + | 0.883285i | \(0.344673\pi\) | |||||||
\(62\) | 0.114362 | 0.0145240 | ||||||||
\(63\) | −0.0712385 | −0.00897521 | ||||||||
\(64\) | −4.03854 | −0.504817 | ||||||||
\(65\) | 6.32922 | 0.785043 | ||||||||
\(66\) | 0.867482 | 0.106780 | ||||||||
\(67\) | 11.5619 | 1.41251 | 0.706257 | − | 0.707955i | \(-0.250382\pi\) | ||||
0.706257 | + | 0.707955i | \(0.250382\pi\) | |||||||
\(68\) | −10.6925 | −1.29665 | ||||||||
\(69\) | −17.0505 | −2.05264 | ||||||||
\(70\) | 0.0244994 | 0.00292824 | ||||||||
\(71\) | −2.43721 | −0.289244 | −0.144622 | − | 0.989487i | \(-0.546197\pi\) | ||||
−0.144622 | + | 0.989487i | \(0.546197\pi\) | |||||||
\(72\) | 1.97854 | 0.233173 | ||||||||
\(73\) | 1.00000 | 0.117041 | ||||||||
\(74\) | −1.39763 | −0.162471 | ||||||||
\(75\) | −2.05594 | −0.237400 | ||||||||
\(76\) | −1.45091 | −0.166431 | ||||||||
\(77\) | −0.0580639 | −0.00661699 | ||||||||
\(78\) | 5.49048 | 0.621674 | ||||||||
\(79\) | 10.1837 | 1.14575 | 0.572876 | − | 0.819642i | \(-0.305828\pi\) | ||||
0.572876 | + | 0.819642i | \(0.305828\pi\) | |||||||
\(80\) | 2.96350 | 0.331330 | ||||||||
\(81\) | −11.1754 | −1.24171 | ||||||||
\(82\) | −0.741920 | −0.0819314 | ||||||||
\(83\) | 1.69280 | 0.185809 | 0.0929043 | − | 0.995675i | \(-0.470385\pi\) | ||||
0.0929043 | + | 0.995675i | \(0.470385\pi\) | |||||||
\(84\) | −0.217499 | −0.0237311 | ||||||||
\(85\) | 5.86865 | 0.636544 | ||||||||
\(86\) | 0.500309 | 0.0539497 | ||||||||
\(87\) | 2.41581 | 0.259002 | ||||||||
\(88\) | 1.61264 | 0.171908 | ||||||||
\(89\) | 10.5321 | 1.11640 | 0.558198 | − | 0.829708i | \(-0.311493\pi\) | ||||
0.558198 | + | 0.829708i | \(0.311493\pi\) | |||||||
\(90\) | −0.517676 | −0.0545679 | ||||||||
\(91\) | −0.367499 | −0.0385243 | ||||||||
\(92\) | −15.1101 | −1.57534 | ||||||||
\(93\) | 0.557240 | 0.0577831 | ||||||||
\(94\) | 4.86764 | 0.502059 | ||||||||
\(95\) | 0.796345 | 0.0817033 | ||||||||
\(96\) | 9.20176 | 0.939151 | ||||||||
\(97\) | −17.3837 | −1.76505 | −0.882524 | − | 0.470268i | \(-0.844157\pi\) | ||||
−0.882524 | + | 0.470268i | \(0.844157\pi\) | |||||||
\(98\) | 2.95215 | 0.298212 | ||||||||
\(99\) | 1.22690 | 0.123308 | ||||||||
\(100\) | −1.82197 | −0.182197 | ||||||||
\(101\) | 17.1524 | 1.70673 | 0.853363 | − | 0.521318i | \(-0.174559\pi\) | ||||
0.853363 | + | 0.521318i | \(0.174559\pi\) | |||||||
\(102\) | 5.09094 | 0.504078 | ||||||||
\(103\) | −7.46160 | −0.735213 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(104\) | 10.2067 | 1.00085 | ||||||||
\(105\) | 0.119376 | 0.0116499 | ||||||||
\(106\) | −1.60612 | −0.156000 | ||||||||
\(107\) | −5.35473 | −0.517661 | −0.258831 | − | 0.965923i | \(-0.583337\pi\) | ||||
−0.258831 | + | 0.965923i | \(0.583337\pi\) | |||||||
\(108\) | −6.64179 | −0.639106 | ||||||||
\(109\) | −3.32627 | −0.318599 | −0.159300 | − | 0.987230i | \(-0.550924\pi\) | ||||
−0.159300 | + | 0.987230i | \(0.550924\pi\) | |||||||
\(110\) | −0.421939 | −0.0402303 | ||||||||
\(111\) | −6.81011 | −0.646387 | ||||||||
\(112\) | −0.172072 | −0.0162593 | ||||||||
\(113\) | −4.97691 | −0.468189 | −0.234094 | − | 0.972214i | \(-0.575212\pi\) | ||||
−0.234094 | + | 0.972214i | \(0.575212\pi\) | |||||||
\(114\) | 0.690815 | 0.0647007 | ||||||||
\(115\) | 8.29329 | 0.773353 | ||||||||
\(116\) | 2.14088 | 0.198776 | ||||||||
\(117\) | 7.76531 | 0.717903 | ||||||||
\(118\) | −0.759705 | −0.0699365 | ||||||||
\(119\) | −0.340756 | −0.0312371 | ||||||||
\(120\) | −3.31549 | −0.302661 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.09006 | −0.279761 | ||||||||
\(123\) | −3.61509 | −0.325961 | ||||||||
\(124\) | 0.493824 | 0.0443467 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.0300583 | 0.00267781 | ||||||||
\(127\) | −9.98530 | −0.886052 | −0.443026 | − | 0.896509i | \(-0.646095\pi\) | ||||
−0.443026 | + | 0.896509i | \(0.646095\pi\) | |||||||
\(128\) | 10.6554 | 0.941813 | ||||||||
\(129\) | 2.43781 | 0.214637 | ||||||||
\(130\) | −2.67054 | −0.234222 | ||||||||
\(131\) | −15.7333 | −1.37463 | −0.687314 | − | 0.726361i | \(-0.741210\pi\) | ||||
−0.687314 | + | 0.726361i | \(0.741210\pi\) | |||||||
\(132\) | 3.74586 | 0.326035 | ||||||||
\(133\) | −0.0462389 | −0.00400942 | ||||||||
\(134\) | −4.87843 | −0.421432 | ||||||||
\(135\) | 3.64539 | 0.313745 | ||||||||
\(136\) | 9.46399 | 0.811530 | ||||||||
\(137\) | −0.359744 | −0.0307350 | −0.0153675 | − | 0.999882i | \(-0.504892\pi\) | ||||
−0.0153675 | + | 0.999882i | \(0.504892\pi\) | |||||||
\(138\) | 7.19428 | 0.612418 | ||||||||
\(139\) | 3.22965 | 0.273935 | 0.136968 | − | 0.990576i | \(-0.456264\pi\) | ||||
0.136968 | + | 0.990576i | \(0.456264\pi\) | |||||||
\(140\) | 0.105790 | 0.00894093 | ||||||||
\(141\) | 23.7181 | 1.99742 | ||||||||
\(142\) | 1.02836 | 0.0862976 | ||||||||
\(143\) | 6.32922 | 0.529276 | ||||||||
\(144\) | 3.63592 | 0.302993 | ||||||||
\(145\) | −1.17504 | −0.0975815 | ||||||||
\(146\) | −0.421939 | −0.0349199 | ||||||||
\(147\) | 14.3847 | 1.18643 | ||||||||
\(148\) | −6.03509 | −0.496082 | ||||||||
\(149\) | −3.54582 | −0.290485 | −0.145242 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145242 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(150\) | 0.867482 | 0.0708296 | ||||||||
\(151\) | −13.4361 | −1.09342 | −0.546709 | − | 0.837323i | \(-0.684120\pi\) | ||||
−0.546709 | + | 0.837323i | \(0.684120\pi\) | |||||||
\(152\) | 1.28421 | 0.104164 | ||||||||
\(153\) | 7.20024 | 0.582105 | ||||||||
\(154\) | 0.0244994 | 0.00197422 | ||||||||
\(155\) | −0.271039 | −0.0217704 | ||||||||
\(156\) | 23.7084 | 1.89819 | ||||||||
\(157\) | 1.13284 | 0.0904102 | 0.0452051 | − | 0.998978i | \(-0.485606\pi\) | ||||
0.0452051 | + | 0.998978i | \(0.485606\pi\) | |||||||
\(158\) | −4.29688 | −0.341841 | ||||||||
\(159\) | −7.82600 | −0.620642 | ||||||||
\(160\) | −4.47569 | −0.353834 | ||||||||
\(161\) | −0.481541 | −0.0379507 | ||||||||
\(162\) | 4.71534 | 0.370472 | ||||||||
\(163\) | 3.66846 | 0.287336 | 0.143668 | − | 0.989626i | \(-0.454110\pi\) | ||||
0.143668 | + | 0.989626i | \(0.454110\pi\) | |||||||
\(164\) | −3.20367 | −0.250165 | ||||||||
\(165\) | −2.05594 | −0.160055 | ||||||||
\(166\) | −0.714256 | −0.0554371 | ||||||||
\(167\) | −13.5067 | −1.04518 | −0.522589 | − | 0.852585i | \(-0.675034\pi\) | ||||
−0.522589 | + | 0.852585i | \(0.675034\pi\) | |||||||
\(168\) | 0.192510 | 0.0148525 | ||||||||
\(169\) | 27.0590 | 2.08146 | ||||||||
\(170\) | −2.47621 | −0.189917 | ||||||||
\(171\) | 0.977035 | 0.0747158 | ||||||||
\(172\) | 2.16038 | 0.164727 | ||||||||
\(173\) | 8.10928 | 0.616537 | 0.308269 | − | 0.951299i | \(-0.400250\pi\) | ||||
0.308269 | + | 0.951299i | \(0.400250\pi\) | |||||||
\(174\) | −1.01932 | −0.0772747 | ||||||||
\(175\) | −0.0580639 | −0.00438922 | ||||||||
\(176\) | 2.96350 | 0.223382 | ||||||||
\(177\) | −3.70174 | −0.278240 | ||||||||
\(178\) | −4.44389 | −0.333083 | ||||||||
\(179\) | −16.7291 | −1.25039 | −0.625196 | − | 0.780467i | \(-0.714981\pi\) | ||||
−0.625196 | + | 0.780467i | \(0.714981\pi\) | |||||||
\(180\) | −2.23537 | −0.166615 | ||||||||
\(181\) | 25.8052 | 1.91809 | 0.959044 | − | 0.283256i | \(-0.0914145\pi\) | ||||
0.959044 | + | 0.283256i | \(0.0914145\pi\) | |||||||
\(182\) | 0.155062 | 0.0114940 | ||||||||
\(183\) | −15.0566 | −1.11302 | ||||||||
\(184\) | 13.3741 | 0.985949 | ||||||||
\(185\) | 3.31240 | 0.243533 | ||||||||
\(186\) | −0.235121 | −0.0172399 | ||||||||
\(187\) | 5.86865 | 0.429158 | ||||||||
\(188\) | 21.0189 | 1.53296 | ||||||||
\(189\) | −0.211666 | −0.0153964 | ||||||||
\(190\) | −0.336009 | −0.0243766 | ||||||||
\(191\) | 21.0196 | 1.52093 | 0.760464 | − | 0.649380i | \(-0.224972\pi\) | ||||
0.760464 | + | 0.649380i | \(0.224972\pi\) | |||||||
\(192\) | 8.30300 | 0.599217 | ||||||||
\(193\) | 12.1296 | 0.873110 | 0.436555 | − | 0.899678i | \(-0.356198\pi\) | ||||
0.436555 | + | 0.899678i | \(0.356198\pi\) | |||||||
\(194\) | 7.33486 | 0.526612 | ||||||||
\(195\) | −13.0125 | −0.931845 | ||||||||
\(196\) | 12.7476 | 0.910545 | ||||||||
\(197\) | −18.0668 | −1.28721 | −0.643605 | − | 0.765358i | \(-0.722562\pi\) | ||||
−0.643605 | + | 0.765358i | \(0.722562\pi\) | |||||||
\(198\) | −0.517676 | −0.0367897 | ||||||||
\(199\) | 11.8000 | 0.836482 | 0.418241 | − | 0.908336i | \(-0.362647\pi\) | ||||
0.418241 | + | 0.908336i | \(0.362647\pi\) | |||||||
\(200\) | 1.61264 | 0.114031 | ||||||||
\(201\) | −23.7707 | −1.67665 | ||||||||
\(202\) | −7.23725 | −0.509211 | ||||||||
\(203\) | 0.0682272 | 0.00478861 | ||||||||
\(204\) | 21.9831 | 1.53913 | ||||||||
\(205\) | 1.75836 | 0.122809 | ||||||||
\(206\) | 3.14834 | 0.219355 | ||||||||
\(207\) | 10.1750 | 0.707214 | ||||||||
\(208\) | 18.7566 | 1.30054 | ||||||||
\(209\) | 0.796345 | 0.0550843 | ||||||||
\(210\) | −0.0503693 | −0.00347581 | ||||||||
\(211\) | −11.5382 | −0.794322 | −0.397161 | − | 0.917749i | \(-0.630005\pi\) | ||||
−0.397161 | + | 0.917749i | \(0.630005\pi\) | |||||||
\(212\) | −6.93537 | −0.476323 | ||||||||
\(213\) | 5.01077 | 0.343332 | ||||||||
\(214\) | 2.25937 | 0.154447 | ||||||||
\(215\) | −1.18574 | −0.0808667 | ||||||||
\(216\) | 5.87869 | 0.399994 | ||||||||
\(217\) | 0.0157376 | 0.00106833 | ||||||||
\(218\) | 1.40348 | 0.0950559 | ||||||||
\(219\) | −2.05594 | −0.138928 | ||||||||
\(220\) | −1.82197 | −0.122837 | ||||||||
\(221\) | 37.1439 | 2.49857 | ||||||||
\(222\) | 2.87345 | 0.192853 | ||||||||
\(223\) | 13.1748 | 0.882252 | 0.441126 | − | 0.897445i | \(-0.354579\pi\) | ||||
0.441126 | + | 0.897445i | \(0.354579\pi\) | |||||||
\(224\) | 0.259876 | 0.0173637 | ||||||||
\(225\) | 1.22690 | 0.0817933 | ||||||||
\(226\) | 2.09995 | 0.139687 | ||||||||
\(227\) | 2.72086 | 0.180590 | 0.0902949 | − | 0.995915i | \(-0.471219\pi\) | ||||
0.0902949 | + | 0.995915i | \(0.471219\pi\) | |||||||
\(228\) | 2.98300 | 0.197554 | ||||||||
\(229\) | −4.38186 | −0.289562 | −0.144781 | − | 0.989464i | \(-0.546248\pi\) | ||||
−0.144781 | + | 0.989464i | \(0.546248\pi\) | |||||||
\(230\) | −3.49926 | −0.230734 | ||||||||
\(231\) | 0.119376 | 0.00785436 | ||||||||
\(232\) | −1.89491 | −0.124407 | ||||||||
\(233\) | −16.0203 | −1.04952 | −0.524761 | − | 0.851250i | \(-0.675845\pi\) | ||||
−0.524761 | + | 0.851250i | \(0.675845\pi\) | |||||||
\(234\) | −3.27649 | −0.214191 | ||||||||
\(235\) | −11.5364 | −0.752550 | ||||||||
\(236\) | −3.28047 | −0.213540 | ||||||||
\(237\) | −20.9370 | −1.36001 | ||||||||
\(238\) | 0.143778 | 0.00931976 | ||||||||
\(239\) | −5.87473 | −0.380004 | −0.190002 | − | 0.981784i | \(-0.560850\pi\) | ||||
−0.190002 | + | 0.981784i | \(0.560850\pi\) | |||||||
\(240\) | −6.09279 | −0.393288 | ||||||||
\(241\) | 18.3559 | 1.18241 | 0.591205 | − | 0.806521i | \(-0.298652\pi\) | ||||
0.591205 | + | 0.806521i | \(0.298652\pi\) | |||||||
\(242\) | −0.421939 | −0.0271232 | ||||||||
\(243\) | 12.0398 | 0.772356 | ||||||||
\(244\) | −13.3431 | −0.854206 | ||||||||
\(245\) | −6.99663 | −0.446998 | ||||||||
\(246\) | 1.52535 | 0.0972524 | ||||||||
\(247\) | 5.04024 | 0.320703 | ||||||||
\(248\) | −0.437087 | −0.0277550 | ||||||||
\(249\) | −3.48029 | −0.220555 | ||||||||
\(250\) | −0.421939 | −0.0266857 | ||||||||
\(251\) | 14.5307 | 0.917167 | 0.458584 | − | 0.888651i | \(-0.348357\pi\) | ||||
0.458584 | + | 0.888651i | \(0.348357\pi\) | |||||||
\(252\) | 0.129794 | 0.00817627 | ||||||||
\(253\) | 8.29329 | 0.521395 | ||||||||
\(254\) | 4.21319 | 0.264359 | ||||||||
\(255\) | −12.0656 | −0.755577 | ||||||||
\(256\) | 3.58115 | 0.223822 | ||||||||
\(257\) | 10.8262 | 0.675318 | 0.337659 | − | 0.941269i | \(-0.390365\pi\) | ||||
0.337659 | + | 0.941269i | \(0.390365\pi\) | |||||||
\(258\) | −1.02861 | −0.0640382 | ||||||||
\(259\) | −0.192331 | −0.0119509 | ||||||||
\(260\) | −11.5316 | −0.715161 | ||||||||
\(261\) | −1.44165 | −0.0892360 | ||||||||
\(262\) | 6.63850 | 0.410128 | ||||||||
\(263\) | 15.7384 | 0.970470 | 0.485235 | − | 0.874384i | \(-0.338734\pi\) | ||||
0.485235 | + | 0.874384i | \(0.338734\pi\) | |||||||
\(264\) | −3.31549 | −0.204054 | ||||||||
\(265\) | 3.80653 | 0.233833 | ||||||||
\(266\) | 0.0195100 | 0.00119623 | ||||||||
\(267\) | −21.6533 | −1.32516 | ||||||||
\(268\) | −21.0655 | −1.28678 | ||||||||
\(269\) | −5.28552 | −0.322264 | −0.161132 | − | 0.986933i | \(-0.551514\pi\) | ||||
−0.161132 | + | 0.986933i | \(0.551514\pi\) | |||||||
\(270\) | −1.53813 | −0.0936077 | ||||||||
\(271\) | −25.1431 | −1.52734 | −0.763668 | − | 0.645610i | \(-0.776603\pi\) | ||||
−0.763668 | + | 0.645610i | \(0.776603\pi\) | |||||||
\(272\) | 17.3917 | 1.05453 | ||||||||
\(273\) | 0.755556 | 0.0457283 | ||||||||
\(274\) | 0.151790 | 0.00916998 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 31.0655 | 1.86992 | ||||||||
\(277\) | 18.6561 | 1.12094 | 0.560468 | − | 0.828176i | \(-0.310621\pi\) | ||||
0.560468 | + | 0.828176i | \(0.310621\pi\) | |||||||
\(278\) | −1.36271 | −0.0817302 | ||||||||
\(279\) | −0.332537 | −0.0199085 | ||||||||
\(280\) | −0.0936359 | −0.00559581 | ||||||||
\(281\) | 14.3401 | 0.855457 | 0.427729 | − | 0.903907i | \(-0.359314\pi\) | ||||
0.427729 | + | 0.903907i | \(0.359314\pi\) | |||||||
\(282\) | −10.0076 | −0.595943 | ||||||||
\(283\) | −16.0739 | −0.955496 | −0.477748 | − | 0.878497i | \(-0.658547\pi\) | ||||
−0.477748 | + | 0.878497i | \(0.658547\pi\) | |||||||
\(284\) | 4.44053 | 0.263497 | ||||||||
\(285\) | −1.63724 | −0.0969817 | ||||||||
\(286\) | −2.67054 | −0.157912 | ||||||||
\(287\) | −0.102097 | −0.00602660 | ||||||||
\(288\) | −5.49122 | −0.323573 | ||||||||
\(289\) | 17.4410 | 1.02594 | ||||||||
\(290\) | 0.495794 | 0.0291140 | ||||||||
\(291\) | 35.7399 | 2.09511 | ||||||||
\(292\) | −1.82197 | −0.106623 | ||||||||
\(293\) | −2.29458 | −0.134051 | −0.0670254 | − | 0.997751i | \(-0.521351\pi\) | ||||
−0.0670254 | + | 0.997751i | \(0.521351\pi\) | |||||||
\(294\) | −6.06945 | −0.353977 | ||||||||
\(295\) | 1.80051 | 0.104830 | ||||||||
\(296\) | 5.34170 | 0.310480 | ||||||||
\(297\) | 3.64539 | 0.211527 | ||||||||
\(298\) | 1.49612 | 0.0866678 | ||||||||
\(299\) | 52.4900 | 3.03558 | ||||||||
\(300\) | 3.74586 | 0.216267 | ||||||||
\(301\) | 0.0688485 | 0.00396836 | ||||||||
\(302\) | 5.66923 | 0.326228 | ||||||||
\(303\) | −35.2643 | −2.02588 | ||||||||
\(304\) | 2.35997 | 0.135354 | ||||||||
\(305\) | 7.32347 | 0.419341 | ||||||||
\(306\) | −3.03806 | −0.173674 | ||||||||
\(307\) | −29.5989 | −1.68930 | −0.844650 | − | 0.535318i | \(-0.820192\pi\) | ||||
−0.844650 | + | 0.535318i | \(0.820192\pi\) | |||||||
\(308\) | 0.105790 | 0.00602797 | ||||||||
\(309\) | 15.3406 | 0.872697 | ||||||||
\(310\) | 0.114362 | 0.00649531 | ||||||||
\(311\) | 7.86269 | 0.445852 | 0.222926 | − | 0.974835i | \(-0.428439\pi\) | ||||
0.222926 | + | 0.974835i | \(0.428439\pi\) | |||||||
\(312\) | −20.9844 | −1.18801 | ||||||||
\(313\) | 17.4585 | 0.986815 | 0.493408 | − | 0.869798i | \(-0.335751\pi\) | ||||
0.493408 | + | 0.869798i | \(0.335751\pi\) | |||||||
\(314\) | −0.477988 | −0.0269744 | ||||||||
\(315\) | −0.0712385 | −0.00401384 | ||||||||
\(316\) | −18.5543 | −1.04376 | ||||||||
\(317\) | −0.269093 | −0.0151138 | −0.00755689 | − | 0.999971i | \(-0.502405\pi\) | ||||
−0.00755689 | + | 0.999971i | \(0.502405\pi\) | |||||||
\(318\) | 3.30209 | 0.185172 | ||||||||
\(319\) | −1.17504 | −0.0657894 | ||||||||
\(320\) | −4.03854 | −0.225761 | ||||||||
\(321\) | 11.0090 | 0.614463 | ||||||||
\(322\) | 0.203181 | 0.0113228 | ||||||||
\(323\) | 4.67347 | 0.260039 | ||||||||
\(324\) | 20.3612 | 1.13118 | ||||||||
\(325\) | 6.32922 | 0.351082 | ||||||||
\(326\) | −1.54787 | −0.0857283 | ||||||||
\(327\) | 6.83862 | 0.378177 | ||||||||
\(328\) | 2.83559 | 0.156570 | ||||||||
\(329\) | 0.669846 | 0.0369298 | ||||||||
\(330\) | 0.867482 | 0.0477533 | ||||||||
\(331\) | 23.9116 | 1.31430 | 0.657149 | − | 0.753760i | \(-0.271762\pi\) | ||||
0.657149 | + | 0.753760i | \(0.271762\pi\) | |||||||
\(332\) | −3.08422 | −0.169269 | ||||||||
\(333\) | 4.06399 | 0.222705 | ||||||||
\(334\) | 5.69899 | 0.311835 | ||||||||
\(335\) | 11.5619 | 0.631696 | ||||||||
\(336\) | 0.353771 | 0.0192998 | ||||||||
\(337\) | 24.3953 | 1.32890 | 0.664448 | − | 0.747334i | \(-0.268667\pi\) | ||||
0.664448 | + | 0.747334i | \(0.268667\pi\) | |||||||
\(338\) | −11.4172 | −0.621016 | ||||||||
\(339\) | 10.2322 | 0.555739 | ||||||||
\(340\) | −10.6925 | −0.579881 | ||||||||
\(341\) | −0.271039 | −0.0146776 | ||||||||
\(342\) | −0.412249 | −0.0222919 | ||||||||
\(343\) | 0.812698 | 0.0438816 | ||||||||
\(344\) | −1.91216 | −0.103097 | ||||||||
\(345\) | −17.0505 | −0.917970 | ||||||||
\(346\) | −3.42162 | −0.183947 | ||||||||
\(347\) | −6.25222 | −0.335637 | −0.167818 | − | 0.985818i | \(-0.553672\pi\) | ||||
−0.167818 | + | 0.985818i | \(0.553672\pi\) | |||||||
\(348\) | −4.40152 | −0.235946 | ||||||||
\(349\) | −0.727597 | −0.0389474 | −0.0194737 | − | 0.999810i | \(-0.506199\pi\) | ||||
−0.0194737 | + | 0.999810i | \(0.506199\pi\) | |||||||
\(350\) | 0.0244994 | 0.00130955 | ||||||||
\(351\) | 23.0725 | 1.23152 | ||||||||
\(352\) | −4.47569 | −0.238555 | ||||||||
\(353\) | 2.69860 | 0.143632 | 0.0718160 | − | 0.997418i | \(-0.477121\pi\) | ||||
0.0718160 | + | 0.997418i | \(0.477121\pi\) | |||||||
\(354\) | 1.56191 | 0.0830145 | ||||||||
\(355\) | −2.43721 | −0.129354 | ||||||||
\(356\) | −19.1891 | −1.01702 | ||||||||
\(357\) | 0.700575 | 0.0370784 | ||||||||
\(358\) | 7.05866 | 0.373062 | ||||||||
\(359\) | −8.46936 | −0.446996 | −0.223498 | − | 0.974704i | \(-0.571748\pi\) | ||||
−0.223498 | + | 0.974704i | \(0.571748\pi\) | |||||||
\(360\) | 1.97854 | 0.104278 | ||||||||
\(361\) | −18.3658 | −0.966623 | ||||||||
\(362\) | −10.8882 | −0.572273 | ||||||||
\(363\) | −2.05594 | −0.107909 | ||||||||
\(364\) | 0.669571 | 0.0350950 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 6.35298 | 0.332075 | ||||||||
\(367\) | −12.1939 | −0.636515 | −0.318257 | − | 0.948004i | \(-0.603098\pi\) | ||||
−0.318257 | + | 0.948004i | \(0.603098\pi\) | |||||||
\(368\) | 24.5772 | 1.28117 | ||||||||
\(369\) | 2.15733 | 0.112306 | ||||||||
\(370\) | −1.39763 | −0.0726594 | ||||||||
\(371\) | −0.221022 | −0.0114749 | ||||||||
\(372\) | −1.01527 | −0.0526395 | ||||||||
\(373\) | 26.5346 | 1.37391 | 0.686955 | − | 0.726700i | \(-0.258947\pi\) | ||||
0.686955 | + | 0.726700i | \(0.258947\pi\) | |||||||
\(374\) | −2.47621 | −0.128042 | ||||||||
\(375\) | −2.05594 | −0.106168 | ||||||||
\(376\) | −18.6040 | −0.959426 | ||||||||
\(377\) | −7.43706 | −0.383028 | ||||||||
\(378\) | 0.0893099 | 0.00459361 | ||||||||
\(379\) | −11.4594 | −0.588629 | −0.294314 | − | 0.955709i | \(-0.595091\pi\) | ||||
−0.294314 | + | 0.955709i | \(0.595091\pi\) | |||||||
\(380\) | −1.45091 | −0.0744304 | ||||||||
\(381\) | 20.5292 | 1.05174 | ||||||||
\(382\) | −8.86900 | −0.453778 | ||||||||
\(383\) | −12.5491 | −0.641230 | −0.320615 | − | 0.947210i | \(-0.603890\pi\) | ||||
−0.320615 | + | 0.947210i | \(0.603890\pi\) | |||||||
\(384\) | −21.9069 | −1.11793 | ||||||||
\(385\) | −0.0580639 | −0.00295921 | ||||||||
\(386\) | −5.11796 | −0.260497 | ||||||||
\(387\) | −1.45478 | −0.0739507 | ||||||||
\(388\) | 31.6725 | 1.60793 | ||||||||
\(389\) | −25.3120 | −1.28337 | −0.641683 | − | 0.766970i | \(-0.721764\pi\) | ||||
−0.641683 | + | 0.766970i | \(0.721764\pi\) | |||||||
\(390\) | 5.49048 | 0.278021 | ||||||||
\(391\) | 48.6704 | 2.46137 | ||||||||
\(392\) | −11.2830 | −0.569878 | ||||||||
\(393\) | 32.3468 | 1.63168 | ||||||||
\(394\) | 7.62310 | 0.384046 | ||||||||
\(395\) | 10.1837 | 0.512396 | ||||||||
\(396\) | −2.23537 | −0.112332 | ||||||||
\(397\) | −20.5408 | −1.03092 | −0.515458 | − | 0.856915i | \(-0.672378\pi\) | ||||
−0.515458 | + | 0.856915i | \(0.672378\pi\) | |||||||
\(398\) | −4.97889 | −0.249569 | ||||||||
\(399\) | 0.0950645 | 0.00475918 | ||||||||
\(400\) | 2.96350 | 0.148175 | ||||||||
\(401\) | 2.76198 | 0.137927 | 0.0689633 | − | 0.997619i | \(-0.478031\pi\) | ||||
0.0689633 | + | 0.997619i | \(0.478031\pi\) | |||||||
\(402\) | 10.0298 | 0.500239 | ||||||||
\(403\) | −1.71546 | −0.0854533 | ||||||||
\(404\) | −31.2511 | −1.55480 | ||||||||
\(405\) | −11.1754 | −0.555311 | ||||||||
\(406\) | −0.0287877 | −0.00142871 | ||||||||
\(407\) | 3.31240 | 0.164190 | ||||||||
\(408\) | −19.4574 | −0.963286 | ||||||||
\(409\) | 12.6883 | 0.627397 | 0.313698 | − | 0.949523i | \(-0.398432\pi\) | ||||
0.313698 | + | 0.949523i | \(0.398432\pi\) | |||||||
\(410\) | −0.741920 | −0.0366408 | ||||||||
\(411\) | 0.739614 | 0.0364825 | ||||||||
\(412\) | 13.5948 | 0.669767 | ||||||||
\(413\) | −0.104545 | −0.00514430 | ||||||||
\(414\) | −4.29324 | −0.211001 | ||||||||
\(415\) | 1.69280 | 0.0830961 | ||||||||
\(416\) | −28.3276 | −1.38888 | ||||||||
\(417\) | −6.63998 | −0.325161 | ||||||||
\(418\) | −0.336009 | −0.0164347 | ||||||||
\(419\) | −9.15123 | −0.447067 | −0.223533 | − | 0.974696i | \(-0.571759\pi\) | ||||
−0.223533 | + | 0.974696i | \(0.571759\pi\) | |||||||
\(420\) | −0.217499 | −0.0106129 | ||||||||
\(421\) | −13.8899 | −0.676950 | −0.338475 | − | 0.940975i | \(-0.609911\pi\) | ||||
−0.338475 | + | 0.940975i | \(0.609911\pi\) | |||||||
\(422\) | 4.86841 | 0.236991 | ||||||||
\(423\) | −14.1540 | −0.688189 | ||||||||
\(424\) | 6.13854 | 0.298114 | ||||||||
\(425\) | 5.86865 | 0.284671 | ||||||||
\(426\) | −2.11424 | −0.102435 | ||||||||
\(427\) | −0.425229 | −0.0205783 | ||||||||
\(428\) | 9.75614 | 0.471581 | ||||||||
\(429\) | −13.0125 | −0.628250 | ||||||||
\(430\) | 0.500309 | 0.0241270 | ||||||||
\(431\) | −9.50354 | −0.457769 | −0.228885 | − | 0.973454i | \(-0.573508\pi\) | ||||
−0.228885 | + | 0.973454i | \(0.573508\pi\) | |||||||
\(432\) | 10.8031 | 0.519766 | ||||||||
\(433\) | −34.4609 | −1.65609 | −0.828043 | − | 0.560664i | \(-0.810546\pi\) | ||||
−0.828043 | + | 0.560664i | \(0.810546\pi\) | |||||||
\(434\) | −0.00664028 | −0.000318744 0 | ||||||||
\(435\) | 2.41581 | 0.115829 | ||||||||
\(436\) | 6.06036 | 0.290239 | ||||||||
\(437\) | 6.60432 | 0.315928 | ||||||||
\(438\) | 0.867482 | 0.0414499 | ||||||||
\(439\) | −24.1079 | −1.15061 | −0.575303 | − | 0.817940i | \(-0.695116\pi\) | ||||
−0.575303 | + | 0.817940i | \(0.695116\pi\) | |||||||
\(440\) | 1.61264 | 0.0768794 | ||||||||
\(441\) | −8.58416 | −0.408770 | ||||||||
\(442\) | −15.6725 | −0.745463 | ||||||||
\(443\) | 30.4108 | 1.44486 | 0.722430 | − | 0.691444i | \(-0.243025\pi\) | ||||
0.722430 | + | 0.691444i | \(0.243025\pi\) | |||||||
\(444\) | 12.4078 | 0.588848 | ||||||||
\(445\) | 10.5321 | 0.499268 | ||||||||
\(446\) | −5.55897 | −0.263225 | ||||||||
\(447\) | 7.29000 | 0.344805 | ||||||||
\(448\) | 0.234493 | 0.0110788 | ||||||||
\(449\) | 8.93383 | 0.421614 | 0.210807 | − | 0.977528i | \(-0.432391\pi\) | ||||
0.210807 | + | 0.977528i | \(0.432391\pi\) | |||||||
\(450\) | −0.517676 | −0.0244035 | ||||||||
\(451\) | 1.75836 | 0.0827979 | ||||||||
\(452\) | 9.06777 | 0.426512 | ||||||||
\(453\) | 27.6239 | 1.29789 | ||||||||
\(454\) | −1.14804 | −0.0538800 | ||||||||
\(455\) | −0.367499 | −0.0172286 | ||||||||
\(456\) | −2.64027 | −0.123642 | ||||||||
\(457\) | −18.0465 | −0.844178 | −0.422089 | − | 0.906554i | \(-0.638703\pi\) | ||||
−0.422089 | + | 0.906554i | \(0.638703\pi\) | |||||||
\(458\) | 1.84888 | 0.0863924 | ||||||||
\(459\) | 21.3935 | 0.998564 | ||||||||
\(460\) | −15.1101 | −0.704513 | ||||||||
\(461\) | −21.9323 | −1.02149 | −0.510744 | − | 0.859733i | \(-0.670630\pi\) | ||||
−0.510744 | + | 0.859733i | \(0.670630\pi\) | |||||||
\(462\) | −0.0503693 | −0.00234339 | ||||||||
\(463\) | 11.7722 | 0.547100 | 0.273550 | − | 0.961858i | \(-0.411802\pi\) | ||||
0.273550 | + | 0.961858i | \(0.411802\pi\) | |||||||
\(464\) | −3.48222 | −0.161658 | ||||||||
\(465\) | 0.557240 | 0.0258414 | ||||||||
\(466\) | 6.75957 | 0.313131 | ||||||||
\(467\) | −7.31958 | −0.338710 | −0.169355 | − | 0.985555i | \(-0.554168\pi\) | ||||
−0.169355 | + | 0.985555i | \(0.554168\pi\) | |||||||
\(468\) | −14.1482 | −0.653998 | ||||||||
\(469\) | −0.671330 | −0.0309992 | ||||||||
\(470\) | 4.86764 | 0.224527 | ||||||||
\(471\) | −2.32905 | −0.107317 | ||||||||
\(472\) | 2.90357 | 0.133647 | ||||||||
\(473\) | −1.18574 | −0.0545203 | ||||||||
\(474\) | 8.83414 | 0.405765 | ||||||||
\(475\) | 0.796345 | 0.0365388 | ||||||||
\(476\) | 0.620847 | 0.0284565 | ||||||||
\(477\) | 4.67023 | 0.213835 | ||||||||
\(478\) | 2.47877 | 0.113376 | ||||||||
\(479\) | 32.6962 | 1.49393 | 0.746964 | − | 0.664864i | \(-0.231511\pi\) | ||||
0.746964 | + | 0.664864i | \(0.231511\pi\) | |||||||
\(480\) | 9.20176 | 0.420001 | ||||||||
\(481\) | 20.9649 | 0.955918 | ||||||||
\(482\) | −7.74508 | −0.352779 | ||||||||
\(483\) | 0.990020 | 0.0450475 | ||||||||
\(484\) | −1.82197 | −0.0828167 | ||||||||
\(485\) | −17.3837 | −0.789353 | ||||||||
\(486\) | −5.08007 | −0.230437 | ||||||||
\(487\) | 30.1482 | 1.36615 | 0.683074 | − | 0.730350i | \(-0.260643\pi\) | ||||
0.683074 | + | 0.730350i | \(0.260643\pi\) | |||||||
\(488\) | 11.8101 | 0.534618 | ||||||||
\(489\) | −7.54214 | −0.341068 | ||||||||
\(490\) | 2.95215 | 0.133364 | ||||||||
\(491\) | 39.3210 | 1.77453 | 0.887267 | − | 0.461256i | \(-0.152601\pi\) | ||||
0.887267 | + | 0.461256i | \(0.152601\pi\) | |||||||
\(492\) | 6.58657 | 0.296946 | ||||||||
\(493\) | −6.89587 | −0.310575 | ||||||||
\(494\) | −2.12667 | −0.0956835 | ||||||||
\(495\) | 1.22690 | 0.0551450 | ||||||||
\(496\) | −0.803224 | −0.0360658 | ||||||||
\(497\) | 0.141514 | 0.00634777 | ||||||||
\(498\) | 1.46847 | 0.0658037 | ||||||||
\(499\) | −7.48890 | −0.335249 | −0.167625 | − | 0.985851i | \(-0.553610\pi\) | ||||
−0.167625 | + | 0.985851i | \(0.553610\pi\) | |||||||
\(500\) | −1.82197 | −0.0814809 | ||||||||
\(501\) | 27.7690 | 1.24063 | ||||||||
\(502\) | −6.13105 | −0.273642 | ||||||||
\(503\) | −9.35534 | −0.417134 | −0.208567 | − | 0.978008i | \(-0.566880\pi\) | ||||
−0.208567 | + | 0.978008i | \(0.566880\pi\) | |||||||
\(504\) | −0.114882 | −0.00511724 | ||||||||
\(505\) | 17.1524 | 0.763271 | ||||||||
\(506\) | −3.49926 | −0.155561 | ||||||||
\(507\) | −55.6317 | −2.47069 | ||||||||
\(508\) | 18.1929 | 0.807179 | ||||||||
\(509\) | 13.4172 | 0.594707 | 0.297353 | − | 0.954768i | \(-0.403896\pi\) | ||||
0.297353 | + | 0.954768i | \(0.403896\pi\) | |||||||
\(510\) | 5.09094 | 0.225431 | ||||||||
\(511\) | −0.0580639 | −0.00256859 | ||||||||
\(512\) | −22.8218 | −1.00859 | ||||||||
\(513\) | 2.90299 | 0.128170 | ||||||||
\(514\) | −4.56798 | −0.201485 | ||||||||
\(515\) | −7.46160 | −0.328797 | ||||||||
\(516\) | −4.44161 | −0.195531 | ||||||||
\(517\) | −11.5364 | −0.507369 | ||||||||
\(518\) | 0.0811519 | 0.00356561 | ||||||||
\(519\) | −16.6722 | −0.731829 | ||||||||
\(520\) | 10.2067 | 0.447594 | ||||||||
\(521\) | −5.77327 | −0.252932 | −0.126466 | − | 0.991971i | \(-0.540363\pi\) | ||||
−0.126466 | + | 0.991971i | \(0.540363\pi\) | |||||||
\(522\) | 0.608289 | 0.0266241 | ||||||||
\(523\) | −10.3779 | −0.453793 | −0.226896 | − | 0.973919i | \(-0.572858\pi\) | ||||
−0.226896 | + | 0.973919i | \(0.572858\pi\) | |||||||
\(524\) | 28.6656 | 1.25226 | ||||||||
\(525\) | 0.119376 | 0.00520999 | ||||||||
\(526\) | −6.64063 | −0.289545 | ||||||||
\(527\) | −1.59063 | −0.0692889 | ||||||||
\(528\) | −6.09279 | −0.265155 | ||||||||
\(529\) | 45.7787 | 1.99038 | ||||||||
\(530\) | −1.60612 | −0.0697654 | ||||||||
\(531\) | 2.20904 | 0.0958644 | ||||||||
\(532\) | 0.0842457 | 0.00365252 | ||||||||
\(533\) | 11.1290 | 0.482052 | ||||||||
\(534\) | 9.13637 | 0.395370 | ||||||||
\(535\) | −5.35473 | −0.231505 | ||||||||
\(536\) | 18.6452 | 0.805349 | ||||||||
\(537\) | 34.3941 | 1.48421 | ||||||||
\(538\) | 2.23017 | 0.0961493 | ||||||||
\(539\) | −6.99663 | −0.301366 | ||||||||
\(540\) | −6.64179 | −0.285817 | ||||||||
\(541\) | −3.11922 | −0.134106 | −0.0670529 | − | 0.997749i | \(-0.521360\pi\) | ||||
−0.0670529 | + | 0.997749i | \(0.521360\pi\) | |||||||
\(542\) | 10.6089 | 0.455689 | ||||||||
\(543\) | −53.0541 | −2.27677 | ||||||||
\(544\) | −26.2662 | −1.12616 | ||||||||
\(545\) | −3.32627 | −0.142482 | ||||||||
\(546\) | −0.318798 | −0.0136433 | ||||||||
\(547\) | −33.8721 | −1.44827 | −0.724134 | − | 0.689659i | \(-0.757760\pi\) | ||||
−0.724134 | + | 0.689659i | \(0.757760\pi\) | |||||||
\(548\) | 0.655443 | 0.0279991 | ||||||||
\(549\) | 8.98516 | 0.383477 | ||||||||
\(550\) | −0.421939 | −0.0179915 | ||||||||
\(551\) | −0.935735 | −0.0398636 | ||||||||
\(552\) | −27.4963 | −1.17032 | ||||||||
\(553\) | −0.591303 | −0.0251447 | ||||||||
\(554\) | −7.87173 | −0.334438 | ||||||||
\(555\) | −6.81011 | −0.289073 | ||||||||
\(556\) | −5.88432 | −0.249551 | ||||||||
\(557\) | 7.61945 | 0.322847 | 0.161423 | − | 0.986885i | \(-0.448392\pi\) | ||||
0.161423 | + | 0.986885i | \(0.448392\pi\) | |||||||
\(558\) | 0.140310 | 0.00593981 | ||||||||
\(559\) | −7.50479 | −0.317419 | ||||||||
\(560\) | −0.172072 | −0.00727138 | ||||||||
\(561\) | −12.0656 | −0.509410 | ||||||||
\(562\) | −6.05063 | −0.255231 | ||||||||
\(563\) | −12.1437 | −0.511797 | −0.255899 | − | 0.966704i | \(-0.582371\pi\) | ||||
−0.255899 | + | 0.966704i | \(0.582371\pi\) | |||||||
\(564\) | −43.2136 | −1.81962 | ||||||||
\(565\) | −4.97691 | −0.209380 | ||||||||
\(566\) | 6.78221 | 0.285078 | ||||||||
\(567\) | 0.648888 | 0.0272507 | ||||||||
\(568\) | −3.93034 | −0.164913 | ||||||||
\(569\) | −42.0698 | −1.76366 | −0.881830 | − | 0.471568i | \(-0.843688\pi\) | ||||
−0.881830 | + | 0.471568i | \(0.843688\pi\) | |||||||
\(570\) | 0.690815 | 0.0289350 | ||||||||
\(571\) | 1.39958 | 0.0585708 | 0.0292854 | − | 0.999571i | \(-0.490677\pi\) | ||||
0.0292854 | + | 0.999571i | \(0.490677\pi\) | |||||||
\(572\) | −11.5316 | −0.482162 | ||||||||
\(573\) | −43.2152 | −1.80534 | ||||||||
\(574\) | 0.0430787 | 0.00179807 | ||||||||
\(575\) | 8.29329 | 0.345854 | ||||||||
\(576\) | −4.95488 | −0.206453 | ||||||||
\(577\) | 28.8807 | 1.20232 | 0.601159 | − | 0.799129i | \(-0.294706\pi\) | ||||
0.601159 | + | 0.799129i | \(0.294706\pi\) | |||||||
\(578\) | −7.35903 | −0.306095 | ||||||||
\(579\) | −24.9378 | −1.03638 | ||||||||
\(580\) | 2.14088 | 0.0888952 | ||||||||
\(581\) | −0.0982903 | −0.00407777 | ||||||||
\(582\) | −15.0800 | −0.625088 | ||||||||
\(583\) | 3.80653 | 0.157650 | ||||||||
\(584\) | 1.61264 | 0.0667314 | ||||||||
\(585\) | 7.76531 | 0.321056 | ||||||||
\(586\) | 0.968172 | 0.0399948 | ||||||||
\(587\) | −33.1395 | −1.36781 | −0.683907 | − | 0.729569i | \(-0.739721\pi\) | ||||
−0.683907 | + | 0.729569i | \(0.739721\pi\) | |||||||
\(588\) | −26.2084 | −1.08082 | ||||||||
\(589\) | −0.215840 | −0.00889355 | ||||||||
\(590\) | −0.759705 | −0.0312765 | ||||||||
\(591\) | 37.1444 | 1.52792 | ||||||||
\(592\) | 9.81631 | 0.403448 | ||||||||
\(593\) | −20.3765 | −0.836763 | −0.418382 | − | 0.908271i | \(-0.637403\pi\) | ||||
−0.418382 | + | 0.908271i | \(0.637403\pi\) | |||||||
\(594\) | −1.53813 | −0.0631103 | ||||||||
\(595\) | −0.340756 | −0.0139696 | ||||||||
\(596\) | 6.46036 | 0.264627 | ||||||||
\(597\) | −24.2602 | −0.992903 | ||||||||
\(598\) | −22.1476 | −0.905682 | ||||||||
\(599\) | −36.4738 | −1.49028 | −0.745140 | − | 0.666908i | \(-0.767618\pi\) | ||||
−0.745140 | + | 0.666908i | \(0.767618\pi\) | |||||||
\(600\) | −3.31549 | −0.135354 | ||||||||
\(601\) | 1.23151 | 0.0502345 | 0.0251172 | − | 0.999685i | \(-0.492004\pi\) | ||||
0.0251172 | + | 0.999685i | \(0.492004\pi\) | |||||||
\(602\) | −0.0290499 | −0.00118398 | ||||||||
\(603\) | 14.1853 | 0.577671 | ||||||||
\(604\) | 24.4802 | 0.996086 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 14.8794 | 0.604433 | ||||||||
\(607\) | −45.9718 | −1.86594 | −0.932968 | − | 0.359958i | \(-0.882791\pi\) | ||||
−0.932968 | + | 0.359958i | \(0.882791\pi\) | |||||||
\(608\) | −3.56419 | −0.144547 | ||||||||
\(609\) | −0.140271 | −0.00568407 | ||||||||
\(610\) | −3.09006 | −0.125113 | ||||||||
\(611\) | −73.0162 | −2.95392 | ||||||||
\(612\) | −13.1186 | −0.530288 | ||||||||
\(613\) | 12.5456 | 0.506710 | 0.253355 | − | 0.967373i | \(-0.418466\pi\) | ||||
0.253355 | + | 0.967373i | \(0.418466\pi\) | |||||||
\(614\) | 12.4889 | 0.504013 | ||||||||
\(615\) | −3.61509 | −0.145774 | ||||||||
\(616\) | −0.0936359 | −0.00377270 | ||||||||
\(617\) | 12.3123 | 0.495674 | 0.247837 | − | 0.968802i | \(-0.420280\pi\) | ||||
0.247837 | + | 0.968802i | \(0.420280\pi\) | |||||||
\(618\) | −6.47280 | −0.260374 | ||||||||
\(619\) | 26.5602 | 1.06754 | 0.533772 | − | 0.845629i | \(-0.320774\pi\) | ||||
0.533772 | + | 0.845629i | \(0.320774\pi\) | |||||||
\(620\) | 0.493824 | 0.0198324 | ||||||||
\(621\) | 30.2323 | 1.21318 | ||||||||
\(622\) | −3.31757 | −0.133023 | ||||||||
\(623\) | −0.611532 | −0.0245005 | ||||||||
\(624\) | −38.5626 | −1.54374 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −7.36644 | −0.294422 | ||||||||
\(627\) | −1.63724 | −0.0653851 | ||||||||
\(628\) | −2.06399 | −0.0823623 | ||||||||
\(629\) | 19.4393 | 0.775097 | ||||||||
\(630\) | 0.0300583 | 0.00119755 | ||||||||
\(631\) | −23.2148 | −0.924166 | −0.462083 | − | 0.886837i | \(-0.652898\pi\) | ||||
−0.462083 | + | 0.886837i | \(0.652898\pi\) | |||||||
\(632\) | 16.4225 | 0.653254 | ||||||||
\(633\) | 23.7219 | 0.942860 | ||||||||
\(634\) | 0.113541 | 0.00450928 | ||||||||
\(635\) | −9.98530 | −0.396255 | ||||||||
\(636\) | 14.2587 | 0.565395 | ||||||||
\(637\) | −44.2832 | −1.75456 | ||||||||
\(638\) | 0.495794 | 0.0196287 | ||||||||
\(639\) | −2.99022 | −0.118291 | ||||||||
\(640\) | 10.6554 | 0.421191 | ||||||||
\(641\) | −2.79433 | −0.110369 | −0.0551847 | − | 0.998476i | \(-0.517575\pi\) | ||||
−0.0551847 | + | 0.998476i | \(0.517575\pi\) | |||||||
\(642\) | −4.64513 | −0.183329 | ||||||||
\(643\) | −47.9516 | −1.89103 | −0.945513 | − | 0.325586i | \(-0.894439\pi\) | ||||
−0.945513 | + | 0.325586i | \(0.894439\pi\) | |||||||
\(644\) | 0.877351 | 0.0345725 | ||||||||
\(645\) | 2.43781 | 0.0959887 | ||||||||
\(646\) | −1.97192 | −0.0775840 | ||||||||
\(647\) | 42.0348 | 1.65256 | 0.826279 | − | 0.563261i | \(-0.190453\pi\) | ||||
0.826279 | + | 0.563261i | \(0.190453\pi\) | |||||||
\(648\) | −18.0219 | −0.707966 | ||||||||
\(649\) | 1.80051 | 0.0706762 | ||||||||
\(650\) | −2.67054 | −0.104747 | ||||||||
\(651\) | −0.0323555 | −0.00126811 | ||||||||
\(652\) | −6.68382 | −0.261758 | ||||||||
\(653\) | 32.3619 | 1.26642 | 0.633209 | − | 0.773981i | \(-0.281738\pi\) | ||||
0.633209 | + | 0.773981i | \(0.281738\pi\) | |||||||
\(654\) | −2.88548 | −0.112831 | ||||||||
\(655\) | −15.7333 | −0.614752 | ||||||||
\(656\) | 5.21090 | 0.203452 | ||||||||
\(657\) | 1.22690 | 0.0478659 | ||||||||
\(658\) | −0.282634 | −0.0110182 | ||||||||
\(659\) | −13.5290 | −0.527014 | −0.263507 | − | 0.964657i | \(-0.584879\pi\) | ||||
−0.263507 | + | 0.964657i | \(0.584879\pi\) | |||||||
\(660\) | 3.74586 | 0.145807 | ||||||||
\(661\) | 10.6160 | 0.412915 | 0.206457 | − | 0.978456i | \(-0.433807\pi\) | ||||
0.206457 | + | 0.978456i | \(0.433807\pi\) | |||||||
\(662\) | −10.0892 | −0.392129 | ||||||||
\(663\) | −76.3658 | −2.96580 | ||||||||
\(664\) | 2.72987 | 0.105939 | ||||||||
\(665\) | −0.0462389 | −0.00179307 | ||||||||
\(666\) | −1.71475 | −0.0664453 | ||||||||
\(667\) | −9.74492 | −0.377325 | ||||||||
\(668\) | 24.6087 | 0.952141 | ||||||||
\(669\) | −27.0867 | −1.04723 | ||||||||
\(670\) | −4.87843 | −0.188470 | ||||||||
\(671\) | 7.32347 | 0.282719 | ||||||||
\(672\) | −0.534290 | −0.0206107 | ||||||||
\(673\) | −27.0125 | −1.04125 | −0.520627 | − | 0.853784i | \(-0.674302\pi\) | ||||
−0.520627 | + | 0.853784i | \(0.674302\pi\) | |||||||
\(674\) | −10.2933 | −0.396484 | ||||||||
\(675\) | 3.64539 | 0.140311 | ||||||||
\(676\) | −49.3006 | −1.89618 | ||||||||
\(677\) | 1.25101 | 0.0480803 | 0.0240402 | − | 0.999711i | \(-0.492347\pi\) | ||||
0.0240402 | + | 0.999711i | \(0.492347\pi\) | |||||||
\(678\) | −4.31738 | −0.165808 | ||||||||
\(679\) | 1.00936 | 0.0387359 | ||||||||
\(680\) | 9.46399 | 0.362927 | ||||||||
\(681\) | −5.59393 | −0.214360 | ||||||||
\(682\) | 0.114362 | 0.00437914 | ||||||||
\(683\) | 27.9142 | 1.06811 | 0.534053 | − | 0.845451i | \(-0.320668\pi\) | ||||
0.534053 | + | 0.845451i | \(0.320668\pi\) | |||||||
\(684\) | −1.78013 | −0.0680649 | ||||||||
\(685\) | −0.359744 | −0.0137451 | ||||||||
\(686\) | −0.342909 | −0.0130923 | ||||||||
\(687\) | 9.00886 | 0.343709 | ||||||||
\(688\) | −3.51394 | −0.133968 | ||||||||
\(689\) | 24.0923 | 0.917845 | ||||||||
\(690\) | 7.19428 | 0.273882 | ||||||||
\(691\) | 10.0972 | 0.384115 | 0.192057 | − | 0.981384i | \(-0.438484\pi\) | ||||
0.192057 | + | 0.981384i | \(0.438484\pi\) | |||||||
\(692\) | −14.7748 | −0.561655 | ||||||||
\(693\) | −0.0712385 | −0.00270613 | ||||||||
\(694\) | 2.63805 | 0.100139 | ||||||||
\(695\) | 3.22965 | 0.122508 | ||||||||
\(696\) | 3.89582 | 0.147671 | ||||||||
\(697\) | 10.3192 | 0.390867 | ||||||||
\(698\) | 0.307001 | 0.0116202 | ||||||||
\(699\) | 32.9367 | 1.24578 | ||||||||
\(700\) | 0.105790 | 0.00399850 | ||||||||
\(701\) | 24.0837 | 0.909630 | 0.454815 | − | 0.890586i | \(-0.349705\pi\) | ||||
0.454815 | + | 0.890586i | \(0.349705\pi\) | |||||||
\(702\) | −9.73517 | −0.367430 | ||||||||
\(703\) | 2.63782 | 0.0994871 | ||||||||
\(704\) | −4.03854 | −0.152208 | ||||||||
\(705\) | 23.7181 | 0.893275 | ||||||||
\(706\) | −1.13864 | −0.0428535 | ||||||||
\(707\) | −0.995933 | −0.0374559 | ||||||||
\(708\) | 6.74446 | 0.253472 | ||||||||
\(709\) | 18.6612 | 0.700834 | 0.350417 | − | 0.936594i | \(-0.386040\pi\) | ||||
0.350417 | + | 0.936594i | \(0.386040\pi\) | |||||||
\(710\) | 1.02836 | 0.0385935 | ||||||||
\(711\) | 12.4943 | 0.468574 | ||||||||
\(712\) | 16.9844 | 0.636517 | ||||||||
\(713\) | −2.24780 | −0.0841809 | ||||||||
\(714\) | −0.295600 | −0.0110625 | ||||||||
\(715\) | 6.32922 | 0.236699 | ||||||||
\(716\) | 30.4799 | 1.13909 | ||||||||
\(717\) | 12.0781 | 0.451065 | ||||||||
\(718\) | 3.57355 | 0.133364 | ||||||||
\(719\) | −41.7871 | −1.55839 | −0.779197 | − | 0.626779i | \(-0.784373\pi\) | ||||
−0.779197 | + | 0.626779i | \(0.784373\pi\) | |||||||
\(720\) | 3.63592 | 0.135503 | ||||||||
\(721\) | 0.433249 | 0.0161350 | ||||||||
\(722\) | 7.74926 | 0.288397 | ||||||||
\(723\) | −37.7388 | −1.40352 | ||||||||
\(724\) | −47.0163 | −1.74735 | ||||||||
\(725\) | −1.17504 | −0.0436398 | ||||||||
\(726\) | 0.867482 | 0.0321953 | ||||||||
\(727\) | −4.24284 | −0.157358 | −0.0786791 | − | 0.996900i | \(-0.525070\pi\) | ||||
−0.0786791 | + | 0.996900i | \(0.525070\pi\) | |||||||
\(728\) | −0.592642 | −0.0219648 | ||||||||
\(729\) | 8.77304 | 0.324927 | ||||||||
\(730\) | −0.421939 | −0.0156167 | ||||||||
\(731\) | −6.95868 | −0.257376 | ||||||||
\(732\) | 27.4327 | 1.01394 | ||||||||
\(733\) | −1.98876 | −0.0734566 | −0.0367283 | − | 0.999325i | \(-0.511694\pi\) | ||||
−0.0367283 | + | 0.999325i | \(0.511694\pi\) | |||||||
\(734\) | 5.14507 | 0.189908 | ||||||||
\(735\) | 14.3847 | 0.530586 | ||||||||
\(736\) | −37.1182 | −1.36819 | ||||||||
\(737\) | 11.5619 | 0.425889 | ||||||||
\(738\) | −0.910261 | −0.0335072 | ||||||||
\(739\) | 36.6734 | 1.34905 | 0.674526 | − | 0.738251i | \(-0.264348\pi\) | ||||
0.674526 | + | 0.738251i | \(0.264348\pi\) | |||||||
\(740\) | −6.03509 | −0.221854 | ||||||||
\(741\) | −10.3624 | −0.380674 | ||||||||
\(742\) | 0.0932576 | 0.00342359 | ||||||||
\(743\) | 20.5285 | 0.753116 | 0.376558 | − | 0.926393i | \(-0.377108\pi\) | ||||
0.376558 | + | 0.926393i | \(0.377108\pi\) | |||||||
\(744\) | 0.898625 | 0.0329452 | ||||||||
\(745\) | −3.54582 | −0.129909 | ||||||||
\(746\) | −11.1960 | −0.409914 | ||||||||
\(747\) | 2.07689 | 0.0759895 | ||||||||
\(748\) | −10.6925 | −0.390956 | ||||||||
\(749\) | 0.310916 | 0.0113606 | ||||||||
\(750\) | 0.867482 | 0.0316760 | ||||||||
\(751\) | 28.2983 | 1.03262 | 0.516310 | − | 0.856402i | \(-0.327305\pi\) | ||||
0.516310 | + | 0.856402i | \(0.327305\pi\) | |||||||
\(752\) | −34.1880 | −1.24671 | ||||||||
\(753\) | −29.8742 | −1.08868 | ||||||||
\(754\) | 3.13798 | 0.114279 | ||||||||
\(755\) | −13.4361 | −0.488991 | ||||||||
\(756\) | 0.385648 | 0.0140259 | ||||||||
\(757\) | −20.7624 | −0.754622 | −0.377311 | − | 0.926087i | \(-0.623151\pi\) | ||||
−0.377311 | + | 0.926087i | \(0.623151\pi\) | |||||||
\(758\) | 4.83515 | 0.175621 | ||||||||
\(759\) | −17.0505 | −0.618895 | ||||||||
\(760\) | 1.28421 | 0.0465834 | ||||||||
\(761\) | −7.83255 | −0.283930 | −0.141965 | − | 0.989872i | \(-0.545342\pi\) | ||||
−0.141965 | + | 0.989872i | \(0.545342\pi\) | |||||||
\(762\) | −8.66207 | −0.313794 | ||||||||
\(763\) | 0.193136 | 0.00699200 | ||||||||
\(764\) | −38.2971 | −1.38554 | ||||||||
\(765\) | 7.20024 | 0.260325 | ||||||||
\(766\) | 5.29496 | 0.191315 | ||||||||
\(767\) | 11.3958 | 0.411479 | ||||||||
\(768\) | −7.36264 | −0.265676 | ||||||||
\(769\) | 5.47033 | 0.197265 | 0.0986326 | − | 0.995124i | \(-0.468553\pi\) | ||||
0.0986326 | + | 0.995124i | \(0.468553\pi\) | |||||||
\(770\) | 0.0244994 | 0.000882897 0 | ||||||||
\(771\) | −22.2580 | −0.801602 | ||||||||
\(772\) | −22.0998 | −0.795389 | ||||||||
\(773\) | 1.72694 | 0.0621139 | 0.0310569 | − | 0.999518i | \(-0.490113\pi\) | ||||
0.0310569 | + | 0.999518i | \(0.490113\pi\) | |||||||
\(774\) | 0.613829 | 0.0220636 | ||||||||
\(775\) | −0.271039 | −0.00973600 | ||||||||
\(776\) | −28.0336 | −1.00635 | ||||||||
\(777\) | 0.395421 | 0.0141857 | ||||||||
\(778\) | 10.6801 | 0.382900 | ||||||||
\(779\) | 1.40026 | 0.0501696 | ||||||||
\(780\) | 23.7084 | 0.848896 | ||||||||
\(781\) | −2.43721 | −0.0872104 | ||||||||
\(782\) | −20.5359 | −0.734363 | ||||||||
\(783\) | −4.28347 | −0.153079 | ||||||||
\(784\) | −20.7345 | −0.740519 | ||||||||
\(785\) | 1.13284 | 0.0404327 | ||||||||
\(786\) | −13.6484 | −0.486822 | ||||||||
\(787\) | −44.3928 | −1.58243 | −0.791216 | − | 0.611537i | \(-0.790551\pi\) | ||||
−0.791216 | + | 0.611537i | \(0.790551\pi\) | |||||||
\(788\) | 32.9172 | 1.17263 | ||||||||
\(789\) | −32.3572 | −1.15195 | ||||||||
\(790\) | −4.29688 | −0.152876 | ||||||||
\(791\) | 0.288979 | 0.0102749 | ||||||||
\(792\) | 1.97854 | 0.0703045 | ||||||||
\(793\) | 46.3518 | 1.64600 | ||||||||
\(794\) | 8.66698 | 0.307579 | ||||||||
\(795\) | −7.82600 | −0.277560 | ||||||||
\(796\) | −21.4993 | −0.762021 | ||||||||
\(797\) | 31.4065 | 1.11247 | 0.556237 | − | 0.831024i | \(-0.312245\pi\) | ||||
0.556237 | + | 0.831024i | \(0.312245\pi\) | |||||||
\(798\) | −0.0401114 | −0.00141993 | ||||||||
\(799\) | −67.7028 | −2.39515 | ||||||||
\(800\) | −4.47569 | −0.158239 | ||||||||
\(801\) | 12.9218 | 0.456569 | ||||||||
\(802\) | −1.16539 | −0.0411512 | ||||||||
\(803\) | 1.00000 | 0.0352892 | ||||||||
\(804\) | 43.3094 | 1.52740 | ||||||||
\(805\) | −0.481541 | −0.0169721 | ||||||||
\(806\) | 0.723820 | 0.0254955 | ||||||||
\(807\) | 10.8667 | 0.382527 | ||||||||
\(808\) | 27.6605 | 0.973095 | ||||||||
\(809\) | 0.367867 | 0.0129335 | 0.00646675 | − | 0.999979i | \(-0.497942\pi\) | ||||
0.00646675 | + | 0.999979i | \(0.497942\pi\) | |||||||
\(810\) | 4.71534 | 0.165680 | ||||||||
\(811\) | −13.9338 | −0.489283 | −0.244642 | − | 0.969614i | \(-0.578670\pi\) | ||||
−0.244642 | + | 0.969614i | \(0.578670\pi\) | |||||||
\(812\) | −0.124308 | −0.00436235 | ||||||||
\(813\) | 51.6928 | 1.81295 | ||||||||
\(814\) | −1.39763 | −0.0489870 | ||||||||
\(815\) | 3.66846 | 0.128501 | ||||||||
\(816\) | −35.7564 | −1.25173 | ||||||||
\(817\) | −0.944257 | −0.0330354 | ||||||||
\(818\) | −5.35369 | −0.187187 | ||||||||
\(819\) | −0.450884 | −0.0157552 | ||||||||
\(820\) | −3.20367 | −0.111877 | ||||||||
\(821\) | −6.97646 | −0.243480 | −0.121740 | − | 0.992562i | \(-0.538847\pi\) | ||||
−0.121740 | + | 0.992562i | \(0.538847\pi\) | |||||||
\(822\) | −0.312072 | −0.0108848 | ||||||||
\(823\) | 25.5197 | 0.889561 | 0.444781 | − | 0.895640i | \(-0.353282\pi\) | ||||
0.444781 | + | 0.895640i | \(0.353282\pi\) | |||||||
\(824\) | −12.0328 | −0.419184 | ||||||||
\(825\) | −2.05594 | −0.0715787 | ||||||||
\(826\) | 0.0441114 | 0.00153483 | ||||||||
\(827\) | −13.1983 | −0.458951 | −0.229476 | − | 0.973314i | \(-0.573701\pi\) | ||||
−0.229476 | + | 0.973314i | \(0.573701\pi\) | |||||||
\(828\) | −18.5386 | −0.644260 | ||||||||
\(829\) | −18.0657 | −0.627448 | −0.313724 | − | 0.949514i | \(-0.601577\pi\) | ||||
−0.313724 | + | 0.949514i | \(0.601577\pi\) | |||||||
\(830\) | −0.714256 | −0.0247922 | ||||||||
\(831\) | −38.3558 | −1.33055 | ||||||||
\(832\) | −25.5608 | −0.886161 | ||||||||
\(833\) | −41.0607 | −1.42267 | ||||||||
\(834\) | 2.80166 | 0.0970137 | ||||||||
\(835\) | −13.5067 | −0.467418 | ||||||||
\(836\) | −1.45091 | −0.0501809 | ||||||||
\(837\) | −0.988043 | −0.0341517 | ||||||||
\(838\) | 3.86126 | 0.133385 | ||||||||
\(839\) | 0.449001 | 0.0155012 | 0.00775062 | − | 0.999970i | \(-0.497533\pi\) | ||||
0.00775062 | + | 0.999970i | \(0.497533\pi\) | |||||||
\(840\) | 0.192510 | 0.00664223 | ||||||||
\(841\) | −27.6193 | −0.952389 | ||||||||
\(842\) | 5.86067 | 0.201972 | ||||||||
\(843\) | −29.4824 | −1.01543 | ||||||||
\(844\) | 21.0222 | 0.723615 | ||||||||
\(845\) | 27.0590 | 0.930857 | ||||||||
\(846\) | 5.97210 | 0.205325 | ||||||||
\(847\) | −0.0580639 | −0.00199510 | ||||||||
\(848\) | 11.2806 | 0.387379 | ||||||||
\(849\) | 33.0471 | 1.13417 | ||||||||
\(850\) | −2.47621 | −0.0849333 | ||||||||
\(851\) | 27.4707 | 0.941685 | ||||||||
\(852\) | −9.12946 | −0.312770 | ||||||||
\(853\) | −15.9855 | −0.547335 | −0.273667 | − | 0.961824i | \(-0.588237\pi\) | ||||
−0.273667 | + | 0.961824i | \(0.588237\pi\) | |||||||
\(854\) | 0.179421 | 0.00613965 | ||||||||
\(855\) | 0.977035 | 0.0334139 | ||||||||
\(856\) | −8.63523 | −0.295146 | ||||||||
\(857\) | 9.41864 | 0.321735 | 0.160867 | − | 0.986976i | \(-0.448571\pi\) | ||||
0.160867 | + | 0.986976i | \(0.448571\pi\) | |||||||
\(858\) | 5.49048 | 0.187442 | ||||||||
\(859\) | −30.8026 | −1.05097 | −0.525485 | − | 0.850803i | \(-0.676116\pi\) | ||||
−0.525485 | + | 0.850803i | \(0.676116\pi\) | |||||||
\(860\) | 2.16038 | 0.0736682 | ||||||||
\(861\) | 0.209906 | 0.00715357 | ||||||||
\(862\) | 4.00991 | 0.136578 | ||||||||
\(863\) | 36.6797 | 1.24859 | 0.624295 | − | 0.781189i | \(-0.285386\pi\) | ||||
0.624295 | + | 0.781189i | \(0.285386\pi\) | |||||||
\(864\) | −16.3156 | −0.555069 | ||||||||
\(865\) | 8.10928 | 0.275724 | ||||||||
\(866\) | 14.5404 | 0.494103 | ||||||||
\(867\) | −35.8577 | −1.21779 | ||||||||
\(868\) | −0.0286733 | −0.000973236 0 | ||||||||
\(869\) | 10.1837 | 0.345457 | ||||||||
\(870\) | −1.01932 | −0.0345583 | ||||||||
\(871\) | 73.1780 | 2.47954 | ||||||||
\(872\) | −5.36407 | −0.181650 | ||||||||
\(873\) | −21.3281 | −0.721845 | ||||||||
\(874\) | −2.78662 | −0.0942588 | ||||||||
\(875\) | −0.0580639 | −0.00196292 | ||||||||
\(876\) | 3.74586 | 0.126561 | ||||||||
\(877\) | 7.05155 | 0.238114 | 0.119057 | − | 0.992887i | \(-0.462013\pi\) | ||||
0.119057 | + | 0.992887i | \(0.462013\pi\) | |||||||
\(878\) | 10.1720 | 0.343290 | ||||||||
\(879\) | 4.71753 | 0.159118 | ||||||||
\(880\) | 2.96350 | 0.0998996 | ||||||||
\(881\) | −10.9248 | −0.368067 | −0.184034 | − | 0.982920i | \(-0.558916\pi\) | ||||
−0.184034 | + | 0.982920i | \(0.558916\pi\) | |||||||
\(882\) | 3.62199 | 0.121959 | ||||||||
\(883\) | 43.6605 | 1.46929 | 0.734646 | − | 0.678451i | \(-0.237348\pi\) | ||||
0.734646 | + | 0.678451i | \(0.237348\pi\) | |||||||
\(884\) | −67.6750 | −2.27616 | ||||||||
\(885\) | −3.70174 | −0.124433 | ||||||||
\(886\) | −12.8315 | −0.431082 | ||||||||
\(887\) | −25.6433 | −0.861018 | −0.430509 | − | 0.902586i | \(-0.641666\pi\) | ||||
−0.430509 | + | 0.902586i | \(0.641666\pi\) | |||||||
\(888\) | −10.9822 | −0.368540 | ||||||||
\(889\) | 0.579785 | 0.0194454 | ||||||||
\(890\) | −4.44389 | −0.148959 | ||||||||
\(891\) | −11.1754 | −0.374391 | ||||||||
\(892\) | −24.0041 | −0.803718 | ||||||||
\(893\) | −9.18693 | −0.307429 | ||||||||
\(894\) | −3.07593 | −0.102875 | ||||||||
\(895\) | −16.7291 | −0.559193 | ||||||||
\(896\) | −0.618693 | −0.0206691 | ||||||||
\(897\) | −107.917 | −3.60323 | ||||||||
\(898\) | −3.76953 | −0.125791 | ||||||||
\(899\) | 0.318480 | 0.0106219 | ||||||||
\(900\) | −2.23537 | −0.0745124 | ||||||||
\(901\) | 22.3392 | 0.744225 | ||||||||
\(902\) | −0.741920 | −0.0247032 | ||||||||
\(903\) | −0.141549 | −0.00471044 | ||||||||
\(904\) | −8.02595 | −0.266939 | ||||||||
\(905\) | 25.8052 | 0.857795 | ||||||||
\(906\) | −11.6556 | −0.387232 | ||||||||
\(907\) | 29.5453 | 0.981034 | 0.490517 | − | 0.871432i | \(-0.336808\pi\) | ||||
0.490517 | + | 0.871432i | \(0.336808\pi\) | |||||||
\(908\) | −4.95732 | −0.164514 | ||||||||
\(909\) | 21.0442 | 0.697994 | ||||||||
\(910\) | 0.155062 | 0.00514025 | ||||||||
\(911\) | 26.3096 | 0.871677 | 0.435838 | − | 0.900025i | \(-0.356452\pi\) | ||||
0.435838 | + | 0.900025i | \(0.356452\pi\) | |||||||
\(912\) | −4.85196 | −0.160665 | ||||||||
\(913\) | 1.69280 | 0.0560234 | ||||||||
\(914\) | 7.61450 | 0.251865 | ||||||||
\(915\) | −15.0566 | −0.497757 | ||||||||
\(916\) | 7.98362 | 0.263786 | ||||||||
\(917\) | 0.913538 | 0.0301677 | ||||||||
\(918\) | −9.02675 | −0.297927 | ||||||||
\(919\) | 53.2713 | 1.75726 | 0.878629 | − | 0.477505i | \(-0.158459\pi\) | ||||
0.878629 | + | 0.477505i | \(0.158459\pi\) | |||||||
\(920\) | 13.3741 | 0.440930 | ||||||||
\(921\) | 60.8537 | 2.00520 | ||||||||
\(922\) | 9.25408 | 0.304767 | ||||||||
\(923\) | −15.4257 | −0.507742 | ||||||||
\(924\) | −0.217499 | −0.00715520 | ||||||||
\(925\) | 3.31240 | 0.108911 | ||||||||
\(926\) | −4.96714 | −0.163230 | ||||||||
\(927\) | −9.15463 | −0.300678 | ||||||||
\(928\) | 5.25910 | 0.172638 | ||||||||
\(929\) | 38.9317 | 1.27731 | 0.638654 | − | 0.769494i | \(-0.279492\pi\) | ||||
0.638654 | + | 0.769494i | \(0.279492\pi\) | |||||||
\(930\) | −0.235121 | −0.00770993 | ||||||||
\(931\) | −5.57173 | −0.182606 | ||||||||
\(932\) | 29.1884 | 0.956098 | ||||||||
\(933\) | −16.1652 | −0.529226 | ||||||||
\(934\) | 3.08842 | 0.101056 | ||||||||
\(935\) | 5.86865 | 0.191925 | ||||||||
\(936\) | 12.5226 | 0.409315 | ||||||||
\(937\) | 46.6511 | 1.52403 | 0.762013 | − | 0.647562i | \(-0.224211\pi\) | ||||
0.762013 | + | 0.647562i | \(0.224211\pi\) | |||||||
\(938\) | 0.283260 | 0.00924878 | ||||||||
\(939\) | −35.8938 | −1.17135 | ||||||||
\(940\) | 21.0189 | 0.685560 | ||||||||
\(941\) | 50.3438 | 1.64116 | 0.820581 | − | 0.571530i | \(-0.193650\pi\) | ||||
0.820581 | + | 0.571530i | \(0.193650\pi\) | |||||||
\(942\) | 0.982716 | 0.0320186 | ||||||||
\(943\) | 14.5826 | 0.474875 | ||||||||
\(944\) | 5.33581 | 0.173666 | ||||||||
\(945\) | −0.211666 | −0.00688548 | ||||||||
\(946\) | 0.500309 | 0.0162664 | ||||||||
\(947\) | 25.3314 | 0.823162 | 0.411581 | − | 0.911373i | \(-0.364977\pi\) | ||||
0.411581 | + | 0.911373i | \(0.364977\pi\) | |||||||
\(948\) | 38.1466 | 1.23894 | ||||||||
\(949\) | 6.32922 | 0.205455 | ||||||||
\(950\) | −0.336009 | −0.0109016 | ||||||||
\(951\) | 0.553240 | 0.0179400 | ||||||||
\(952\) | −0.549516 | −0.0178099 | ||||||||
\(953\) | 39.2750 | 1.27224 | 0.636120 | − | 0.771590i | \(-0.280538\pi\) | ||||
0.636120 | + | 0.771590i | \(0.280538\pi\) | |||||||
\(954\) | −1.97055 | −0.0637989 | ||||||||
\(955\) | 21.0196 | 0.680180 | ||||||||
\(956\) | 10.7036 | 0.346178 | ||||||||
\(957\) | 2.41581 | 0.0780920 | ||||||||
\(958\) | −13.7958 | −0.445722 | ||||||||
\(959\) | 0.0208881 | 0.000674514 0 | ||||||||
\(960\) | 8.30300 | 0.267978 | ||||||||
\(961\) | −30.9265 | −0.997630 | ||||||||
\(962\) | −8.84591 | −0.285204 | ||||||||
\(963\) | −6.56972 | −0.211706 | ||||||||
\(964\) | −33.4439 | −1.07716 | ||||||||
\(965\) | 12.1296 | 0.390467 | ||||||||
\(966\) | −0.417728 | −0.0134402 | ||||||||
\(967\) | 35.6000 | 1.14482 | 0.572409 | − | 0.819968i | \(-0.306009\pi\) | ||||
0.572409 | + | 0.819968i | \(0.306009\pi\) | |||||||
\(968\) | 1.61264 | 0.0518321 | ||||||||
\(969\) | −9.60838 | −0.308666 | ||||||||
\(970\) | 7.33486 | 0.235508 | ||||||||
\(971\) | 5.02580 | 0.161286 | 0.0806428 | − | 0.996743i | \(-0.474303\pi\) | ||||
0.0806428 | + | 0.996743i | \(0.474303\pi\) | |||||||
\(972\) | −21.9362 | −0.703604 | ||||||||
\(973\) | −0.187526 | −0.00601181 | ||||||||
\(974\) | −12.7207 | −0.407598 | ||||||||
\(975\) | −13.0125 | −0.416734 | ||||||||
\(976\) | 21.7031 | 0.694700 | ||||||||
\(977\) | −18.9735 | −0.607015 | −0.303507 | − | 0.952829i | \(-0.598158\pi\) | ||||
−0.303507 | + | 0.952829i | \(0.598158\pi\) | |||||||
\(978\) | 3.18232 | 0.101759 | ||||||||
\(979\) | 10.5321 | 0.336606 | ||||||||
\(980\) | 12.7476 | 0.407208 | ||||||||
\(981\) | −4.08100 | −0.130296 | ||||||||
\(982\) | −16.5911 | −0.529442 | ||||||||
\(983\) | −31.2871 | −0.997904 | −0.498952 | − | 0.866630i | \(-0.666282\pi\) | ||||
−0.498952 | + | 0.866630i | \(0.666282\pi\) | |||||||
\(984\) | −5.82982 | −0.185848 | ||||||||
\(985\) | −18.0668 | −0.575657 | ||||||||
\(986\) | 2.90964 | 0.0926617 | ||||||||
\(987\) | −1.37716 | −0.0438356 | ||||||||
\(988\) | −9.18316 | −0.292155 | ||||||||
\(989\) | −9.83367 | −0.312693 | ||||||||
\(990\) | −0.517676 | −0.0164528 | ||||||||
\(991\) | −20.8298 | −0.661680 | −0.330840 | − | 0.943687i | \(-0.607332\pi\) | ||||
−0.330840 | + | 0.943687i | \(0.607332\pi\) | |||||||
\(992\) | 1.21308 | 0.0385155 | ||||||||
\(993\) | −49.1608 | −1.56007 | ||||||||
\(994\) | −0.0597103 | −0.00189389 | ||||||||
\(995\) | 11.8000 | 0.374086 | ||||||||
\(996\) | 6.34098 | 0.200922 | ||||||||
\(997\) | −34.4365 | −1.09061 | −0.545307 | − | 0.838236i | \(-0.683587\pi\) | ||||
−0.545307 | + | 0.838236i | \(0.683587\pi\) | |||||||
\(998\) | 3.15986 | 0.100023 | ||||||||
\(999\) | 12.0750 | 0.382036 |
(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 | 4015.2.a.h.1.16 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4015.2.a.h.1.16 | ✓ | 37 | 1.1 | even | 1 | trivial |