Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [667,2,Mod(1,667)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(667, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("667.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 667 = 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 667.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: | \(5.32602181482\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} - 547 x^{4} + 352 x^{3} + 219 x^{2} - 88 x - 40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.22202\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 667.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.22202 | −1.57121 | −0.785604 | − | 0.618729i | \(-0.787648\pi\) | ||||
−0.785604 | + | 0.618729i | \(0.787648\pi\) | |||||||
\(3\) | 0.328413 | 0.189609 | 0.0948047 | − | 0.995496i | \(-0.469777\pi\) | ||||
0.0948047 | + | 0.995496i | \(0.469777\pi\) | |||||||
\(4\) | 2.93739 | 1.46870 | ||||||||
\(5\) | 2.84468 | 1.27218 | 0.636090 | − | 0.771615i | \(-0.280551\pi\) | ||||
0.636090 | + | 0.771615i | \(0.280551\pi\) | |||||||
\(6\) | −0.729742 | −0.297916 | ||||||||
\(7\) | −1.80107 | −0.680740 | −0.340370 | − | 0.940292i | \(-0.610552\pi\) | ||||
−0.340370 | + | 0.940292i | \(0.610552\pi\) | |||||||
\(8\) | −2.08291 | −0.736418 | ||||||||
\(9\) | −2.89214 | −0.964048 | ||||||||
\(10\) | −6.32095 | −1.99886 | ||||||||
\(11\) | 1.40952 | 0.424985 | 0.212493 | − | 0.977163i | \(-0.431842\pi\) | ||||
0.212493 | + | 0.977163i | \(0.431842\pi\) | |||||||
\(12\) | 0.964678 | 0.278479 | ||||||||
\(13\) | 5.09892 | 1.41419 | 0.707093 | − | 0.707120i | \(-0.250006\pi\) | ||||
0.707093 | + | 0.707120i | \(0.250006\pi\) | |||||||
\(14\) | 4.00202 | 1.06958 | ||||||||
\(15\) | 0.934230 | 0.241217 | ||||||||
\(16\) | −1.24652 | −0.311629 | ||||||||
\(17\) | −0.501226 | −0.121565 | −0.0607825 | − | 0.998151i | \(-0.519360\pi\) | ||||
−0.0607825 | + | 0.998151i | \(0.519360\pi\) | |||||||
\(18\) | 6.42642 | 1.51472 | ||||||||
\(19\) | 7.81418 | 1.79270 | 0.896348 | − | 0.443351i | \(-0.146210\pi\) | ||||
0.896348 | + | 0.443351i | \(0.146210\pi\) | |||||||
\(20\) | 8.35594 | 1.86844 | ||||||||
\(21\) | −0.591495 | −0.129075 | ||||||||
\(22\) | −3.13198 | −0.667741 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −0.684054 | −0.139632 | ||||||||
\(25\) | 3.09220 | 0.618441 | ||||||||
\(26\) | −11.3299 | −2.22198 | ||||||||
\(27\) | −1.93506 | −0.372402 | ||||||||
\(28\) | −5.29044 | −0.999800 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −2.07588 | −0.379003 | ||||||||
\(31\) | −7.79469 | −1.39997 | −0.699984 | − | 0.714159i | \(-0.746809\pi\) | ||||
−0.699984 | + | 0.714159i | \(0.746809\pi\) | |||||||
\(32\) | 6.93560 | 1.22605 | ||||||||
\(33\) | 0.462904 | 0.0805813 | ||||||||
\(34\) | 1.11374 | 0.191004 | ||||||||
\(35\) | −5.12346 | −0.866024 | ||||||||
\(36\) | −8.49536 | −1.41589 | ||||||||
\(37\) | 6.33384 | 1.04128 | 0.520639 | − | 0.853777i | \(-0.325694\pi\) | ||||
0.520639 | + | 0.853777i | \(0.325694\pi\) | |||||||
\(38\) | −17.3633 | −2.81670 | ||||||||
\(39\) | 1.67455 | 0.268143 | ||||||||
\(40\) | −5.92520 | −0.936856 | ||||||||
\(41\) | 4.39300 | 0.686071 | 0.343035 | − | 0.939322i | \(-0.388545\pi\) | ||||
0.343035 | + | 0.939322i | \(0.388545\pi\) | |||||||
\(42\) | 1.31432 | 0.202803 | ||||||||
\(43\) | −8.99740 | −1.37209 | −0.686046 | − | 0.727559i | \(-0.740655\pi\) | ||||
−0.686046 | + | 0.727559i | \(0.740655\pi\) | |||||||
\(44\) | 4.14030 | 0.624174 | ||||||||
\(45\) | −8.22723 | −1.22644 | ||||||||
\(46\) | 2.22202 | 0.327620 | ||||||||
\(47\) | 11.9950 | 1.74965 | 0.874826 | − | 0.484437i | \(-0.160975\pi\) | ||||
0.874826 | + | 0.484437i | \(0.160975\pi\) | |||||||
\(48\) | −0.409372 | −0.0590878 | ||||||||
\(49\) | −3.75615 | −0.536593 | ||||||||
\(50\) | −6.87095 | −0.971699 | ||||||||
\(51\) | −0.164609 | −0.0230499 | ||||||||
\(52\) | 14.9775 | 2.07701 | ||||||||
\(53\) | 8.71106 | 1.19656 | 0.598278 | − | 0.801289i | \(-0.295852\pi\) | ||||
0.598278 | + | 0.801289i | \(0.295852\pi\) | |||||||
\(54\) | 4.29975 | 0.585121 | ||||||||
\(55\) | 4.00962 | 0.540658 | ||||||||
\(56\) | 3.75146 | 0.501310 | ||||||||
\(57\) | 2.56628 | 0.339912 | ||||||||
\(58\) | −2.22202 | −0.291766 | ||||||||
\(59\) | 11.5319 | 1.50133 | 0.750664 | − | 0.660685i | \(-0.229734\pi\) | ||||
0.750664 | + | 0.660685i | \(0.229734\pi\) | |||||||
\(60\) | 2.74420 | 0.354275 | ||||||||
\(61\) | −7.18620 | −0.920099 | −0.460049 | − | 0.887893i | \(-0.652168\pi\) | ||||
−0.460049 | + | 0.887893i | \(0.652168\pi\) | |||||||
\(62\) | 17.3200 | 2.19964 | ||||||||
\(63\) | 5.20895 | 0.656266 | ||||||||
\(64\) | −12.9180 | −1.61475 | ||||||||
\(65\) | 14.5048 | 1.79910 | ||||||||
\(66\) | −1.02858 | −0.126610 | ||||||||
\(67\) | 9.87757 | 1.20674 | 0.603369 | − | 0.797462i | \(-0.293825\pi\) | ||||
0.603369 | + | 0.797462i | \(0.293825\pi\) | |||||||
\(68\) | −1.47230 | −0.178542 | ||||||||
\(69\) | −0.328413 | −0.0395363 | ||||||||
\(70\) | 11.3845 | 1.36070 | ||||||||
\(71\) | −0.384807 | −0.0456682 | −0.0228341 | − | 0.999739i | \(-0.507269\pi\) | ||||
−0.0228341 | + | 0.999739i | \(0.507269\pi\) | |||||||
\(72\) | 6.02407 | 0.709943 | ||||||||
\(73\) | 9.35756 | 1.09522 | 0.547610 | − | 0.836734i | \(-0.315538\pi\) | ||||
0.547610 | + | 0.836734i | \(0.315538\pi\) | |||||||
\(74\) | −14.0740 | −1.63606 | ||||||||
\(75\) | 1.01552 | 0.117262 | ||||||||
\(76\) | 22.9533 | 2.63293 | ||||||||
\(77\) | −2.53864 | −0.289305 | ||||||||
\(78\) | −3.72090 | −0.421309 | ||||||||
\(79\) | −4.12358 | −0.463939 | −0.231969 | − | 0.972723i | \(-0.574517\pi\) | ||||
−0.231969 | + | 0.972723i | \(0.574517\pi\) | |||||||
\(80\) | −3.54594 | −0.396448 | ||||||||
\(81\) | 8.04094 | 0.893437 | ||||||||
\(82\) | −9.76134 | −1.07796 | ||||||||
\(83\) | −10.6700 | −1.17118 | −0.585591 | − | 0.810607i | \(-0.699137\pi\) | ||||
−0.585591 | + | 0.810607i | \(0.699137\pi\) | |||||||
\(84\) | −1.73745 | −0.189572 | ||||||||
\(85\) | −1.42583 | −0.154653 | ||||||||
\(86\) | 19.9924 | 2.15584 | ||||||||
\(87\) | 0.328413 | 0.0352096 | ||||||||
\(88\) | −2.93589 | −0.312967 | ||||||||
\(89\) | 5.51277 | 0.584352 | 0.292176 | − | 0.956365i | \(-0.405621\pi\) | ||||
0.292176 | + | 0.956365i | \(0.405621\pi\) | |||||||
\(90\) | 18.2811 | 1.92700 | ||||||||
\(91\) | −9.18351 | −0.962694 | ||||||||
\(92\) | −2.93739 | −0.306244 | ||||||||
\(93\) | −2.55988 | −0.265447 | ||||||||
\(94\) | −26.6532 | −2.74907 | ||||||||
\(95\) | 22.2288 | 2.28063 | ||||||||
\(96\) | 2.27774 | 0.232471 | ||||||||
\(97\) | 9.04550 | 0.918431 | 0.459216 | − | 0.888325i | \(-0.348131\pi\) | ||||
0.459216 | + | 0.888325i | \(0.348131\pi\) | |||||||
\(98\) | 8.34626 | 0.843099 | ||||||||
\(99\) | −4.07653 | −0.409706 | ||||||||
\(100\) | 9.08301 | 0.908301 | ||||||||
\(101\) | 18.4647 | 1.83731 | 0.918654 | − | 0.395063i | \(-0.129277\pi\) | ||||
0.918654 | + | 0.395063i | \(0.129277\pi\) | |||||||
\(102\) | 0.365765 | 0.0362162 | ||||||||
\(103\) | 0.820569 | 0.0808530 | 0.0404265 | − | 0.999183i | \(-0.487128\pi\) | ||||
0.0404265 | + | 0.999183i | \(0.487128\pi\) | |||||||
\(104\) | −10.6206 | −1.04143 | ||||||||
\(105\) | −1.68261 | −0.164206 | ||||||||
\(106\) | −19.3562 | −1.88004 | ||||||||
\(107\) | −11.0507 | −1.06831 | −0.534157 | − | 0.845385i | \(-0.679371\pi\) | ||||
−0.534157 | + | 0.845385i | \(0.679371\pi\) | |||||||
\(108\) | −5.68402 | −0.546945 | ||||||||
\(109\) | −12.5958 | −1.20646 | −0.603230 | − | 0.797567i | \(-0.706120\pi\) | ||||
−0.603230 | + | 0.797567i | \(0.706120\pi\) | |||||||
\(110\) | −8.90948 | −0.849486 | ||||||||
\(111\) | 2.08012 | 0.197436 | ||||||||
\(112\) | 2.24506 | 0.212138 | ||||||||
\(113\) | 9.91984 | 0.933180 | 0.466590 | − | 0.884474i | \(-0.345482\pi\) | ||||
0.466590 | + | 0.884474i | \(0.345482\pi\) | |||||||
\(114\) | −5.70234 | −0.534073 | ||||||||
\(115\) | −2.84468 | −0.265268 | ||||||||
\(116\) | 2.93739 | 0.272730 | ||||||||
\(117\) | −14.7468 | −1.36334 | ||||||||
\(118\) | −25.6242 | −2.35890 | ||||||||
\(119\) | 0.902742 | 0.0827542 | ||||||||
\(120\) | −1.94591 | −0.177637 | ||||||||
\(121\) | −9.01326 | −0.819387 | ||||||||
\(122\) | 15.9679 | 1.44567 | ||||||||
\(123\) | 1.44272 | 0.130085 | ||||||||
\(124\) | −22.8960 | −2.05613 | ||||||||
\(125\) | −5.42707 | −0.485412 | ||||||||
\(126\) | −11.5744 | −1.03113 | ||||||||
\(127\) | 8.01333 | 0.711068 | 0.355534 | − | 0.934663i | \(-0.384299\pi\) | ||||
0.355534 | + | 0.934663i | \(0.384299\pi\) | |||||||
\(128\) | 14.8330 | 1.31106 | ||||||||
\(129\) | −2.95487 | −0.260161 | ||||||||
\(130\) | −32.2300 | −2.82676 | ||||||||
\(131\) | 0.372674 | 0.0325607 | 0.0162804 | − | 0.999867i | \(-0.494818\pi\) | ||||
0.0162804 | + | 0.999867i | \(0.494818\pi\) | |||||||
\(132\) | 1.35973 | 0.118349 | ||||||||
\(133\) | −14.0739 | −1.22036 | ||||||||
\(134\) | −21.9482 | −1.89604 | ||||||||
\(135\) | −5.50462 | −0.473762 | ||||||||
\(136\) | 1.04401 | 0.0895227 | ||||||||
\(137\) | 11.6518 | 0.995481 | 0.497740 | − | 0.867326i | \(-0.334163\pi\) | ||||
0.497740 | + | 0.867326i | \(0.334163\pi\) | |||||||
\(138\) | 0.729742 | 0.0621198 | ||||||||
\(139\) | −11.6120 | −0.984914 | −0.492457 | − | 0.870337i | \(-0.663901\pi\) | ||||
−0.492457 | + | 0.870337i | \(0.663901\pi\) | |||||||
\(140\) | −15.0496 | −1.27192 | ||||||||
\(141\) | 3.93932 | 0.331751 | ||||||||
\(142\) | 0.855051 | 0.0717543 | ||||||||
\(143\) | 7.18702 | 0.601009 | ||||||||
\(144\) | 3.60510 | 0.300425 | ||||||||
\(145\) | 2.84468 | 0.236238 | ||||||||
\(146\) | −20.7927 | −1.72082 | ||||||||
\(147\) | −1.23357 | −0.101743 | ||||||||
\(148\) | 18.6050 | 1.52932 | ||||||||
\(149\) | 17.5192 | 1.43523 | 0.717613 | − | 0.696442i | \(-0.245235\pi\) | ||||
0.717613 | + | 0.696442i | \(0.245235\pi\) | |||||||
\(150\) | −2.25651 | −0.184243 | ||||||||
\(151\) | −19.4111 | −1.57965 | −0.789827 | − | 0.613330i | \(-0.789829\pi\) | ||||
−0.789827 | + | 0.613330i | \(0.789829\pi\) | |||||||
\(152\) | −16.2762 | −1.32017 | ||||||||
\(153\) | 1.44962 | 0.117195 | ||||||||
\(154\) | 5.64091 | 0.454558 | ||||||||
\(155\) | −22.1734 | −1.78101 | ||||||||
\(156\) | 4.91882 | 0.393821 | ||||||||
\(157\) | 14.5093 | 1.15797 | 0.578984 | − | 0.815339i | \(-0.303449\pi\) | ||||
0.578984 | + | 0.815339i | \(0.303449\pi\) | |||||||
\(158\) | 9.16269 | 0.728945 | ||||||||
\(159\) | 2.86083 | 0.226878 | ||||||||
\(160\) | 19.7296 | 1.55976 | ||||||||
\(161\) | 1.80107 | 0.141944 | ||||||||
\(162\) | −17.8672 | −1.40378 | ||||||||
\(163\) | 0.723953 | 0.0567044 | 0.0283522 | − | 0.999598i | \(-0.490974\pi\) | ||||
0.0283522 | + | 0.999598i | \(0.490974\pi\) | |||||||
\(164\) | 12.9039 | 1.00763 | ||||||||
\(165\) | 1.31681 | 0.102514 | ||||||||
\(166\) | 23.7089 | 1.84017 | ||||||||
\(167\) | −1.18921 | −0.0920239 | −0.0460120 | − | 0.998941i | \(-0.514651\pi\) | ||||
−0.0460120 | + | 0.998941i | \(0.514651\pi\) | |||||||
\(168\) | 1.23203 | 0.0950530 | ||||||||
\(169\) | 12.9990 | 0.999924 | ||||||||
\(170\) | 3.16822 | 0.242991 | ||||||||
\(171\) | −22.5997 | −1.72825 | ||||||||
\(172\) | −26.4289 | −2.01518 | ||||||||
\(173\) | −22.6406 | −1.72133 | −0.860666 | − | 0.509171i | \(-0.829952\pi\) | ||||
−0.860666 | + | 0.509171i | \(0.829952\pi\) | |||||||
\(174\) | −0.729742 | −0.0553216 | ||||||||
\(175\) | −5.56927 | −0.420997 | ||||||||
\(176\) | −1.75698 | −0.132438 | ||||||||
\(177\) | 3.78723 | 0.284666 | ||||||||
\(178\) | −12.2495 | −0.918139 | ||||||||
\(179\) | 3.57152 | 0.266948 | 0.133474 | − | 0.991052i | \(-0.457387\pi\) | ||||
0.133474 | + | 0.991052i | \(0.457387\pi\) | |||||||
\(180\) | −24.1666 | −1.80127 | ||||||||
\(181\) | 3.21511 | 0.238978 | 0.119489 | − | 0.992836i | \(-0.461874\pi\) | ||||
0.119489 | + | 0.992836i | \(0.461874\pi\) | |||||||
\(182\) | 20.4060 | 1.51259 | ||||||||
\(183\) | −2.36004 | −0.174459 | ||||||||
\(184\) | 2.08291 | 0.153554 | ||||||||
\(185\) | 18.0178 | 1.32469 | ||||||||
\(186\) | 5.68811 | 0.417073 | ||||||||
\(187\) | −0.706486 | −0.0516634 | ||||||||
\(188\) | 35.2341 | 2.56971 | ||||||||
\(189\) | 3.48517 | 0.253509 | ||||||||
\(190\) | −49.3930 | −3.58335 | ||||||||
\(191\) | −20.7504 | −1.50145 | −0.750724 | − | 0.660617i | \(-0.770295\pi\) | ||||
−0.750724 | + | 0.660617i | \(0.770295\pi\) | |||||||
\(192\) | −4.24245 | −0.306173 | ||||||||
\(193\) | −2.47792 | −0.178364 | −0.0891822 | − | 0.996015i | \(-0.528425\pi\) | ||||
−0.0891822 | + | 0.996015i | \(0.528425\pi\) | |||||||
\(194\) | −20.0993 | −1.44305 | ||||||||
\(195\) | 4.76357 | 0.341126 | ||||||||
\(196\) | −11.0333 | −0.788092 | ||||||||
\(197\) | −4.27137 | −0.304323 | −0.152161 | − | 0.988356i | \(-0.548623\pi\) | ||||
−0.152161 | + | 0.988356i | \(0.548623\pi\) | |||||||
\(198\) | 9.05814 | 0.643734 | ||||||||
\(199\) | −20.3914 | −1.44551 | −0.722754 | − | 0.691105i | \(-0.757124\pi\) | ||||
−0.722754 | + | 0.691105i | \(0.757124\pi\) | |||||||
\(200\) | −6.44077 | −0.455431 | ||||||||
\(201\) | 3.24392 | 0.228809 | ||||||||
\(202\) | −41.0290 | −2.88679 | ||||||||
\(203\) | −1.80107 | −0.126410 | ||||||||
\(204\) | −0.483521 | −0.0338533 | ||||||||
\(205\) | 12.4967 | 0.872805 | ||||||||
\(206\) | −1.82332 | −0.127037 | ||||||||
\(207\) | 2.89214 | 0.201018 | ||||||||
\(208\) | −6.35588 | −0.440701 | ||||||||
\(209\) | 11.0142 | 0.761870 | ||||||||
\(210\) | 3.73881 | 0.258002 | ||||||||
\(211\) | 2.74660 | 0.189084 | 0.0945420 | − | 0.995521i | \(-0.469861\pi\) | ||||
0.0945420 | + | 0.995521i | \(0.469861\pi\) | |||||||
\(212\) | 25.5878 | 1.75738 | ||||||||
\(213\) | −0.126376 | −0.00865912 | ||||||||
\(214\) | 24.5550 | 1.67854 | ||||||||
\(215\) | −25.5947 | −1.74555 | ||||||||
\(216\) | 4.03054 | 0.274244 | ||||||||
\(217\) | 14.0388 | 0.953014 | ||||||||
\(218\) | 27.9882 | 1.89560 | ||||||||
\(219\) | 3.07315 | 0.207664 | ||||||||
\(220\) | 11.7778 | 0.794062 | ||||||||
\(221\) | −2.55571 | −0.171916 | ||||||||
\(222\) | −4.62207 | −0.310213 | ||||||||
\(223\) | 3.05964 | 0.204889 | 0.102444 | − | 0.994739i | \(-0.467334\pi\) | ||||
0.102444 | + | 0.994739i | \(0.467334\pi\) | |||||||
\(224\) | −12.4915 | −0.834623 | ||||||||
\(225\) | −8.94310 | −0.596207 | ||||||||
\(226\) | −22.0421 | −1.46622 | ||||||||
\(227\) | −27.5136 | −1.82614 | −0.913071 | − | 0.407801i | \(-0.866296\pi\) | ||||
−0.913071 | + | 0.407801i | \(0.866296\pi\) | |||||||
\(228\) | 7.53817 | 0.499227 | ||||||||
\(229\) | −28.8643 | −1.90740 | −0.953702 | − | 0.300753i | \(-0.902762\pi\) | ||||
−0.953702 | + | 0.300753i | \(0.902762\pi\) | |||||||
\(230\) | 6.32095 | 0.416791 | ||||||||
\(231\) | −0.833722 | −0.0548549 | ||||||||
\(232\) | −2.08291 | −0.136749 | ||||||||
\(233\) | −21.1884 | −1.38810 | −0.694049 | − | 0.719928i | \(-0.744175\pi\) | ||||
−0.694049 | + | 0.719928i | \(0.744175\pi\) | |||||||
\(234\) | 32.7678 | 2.14210 | ||||||||
\(235\) | 34.1220 | 2.22587 | ||||||||
\(236\) | 33.8737 | 2.20499 | ||||||||
\(237\) | −1.35424 | −0.0879672 | ||||||||
\(238\) | −2.00591 | −0.130024 | ||||||||
\(239\) | 19.4543 | 1.25839 | 0.629197 | − | 0.777246i | \(-0.283384\pi\) | ||||
0.629197 | + | 0.777246i | \(0.283384\pi\) | |||||||
\(240\) | −1.16453 | −0.0751702 | ||||||||
\(241\) | −6.87026 | −0.442552 | −0.221276 | − | 0.975211i | \(-0.571022\pi\) | ||||
−0.221276 | + | 0.975211i | \(0.571022\pi\) | |||||||
\(242\) | 20.0277 | 1.28743 | ||||||||
\(243\) | 8.44592 | 0.541806 | ||||||||
\(244\) | −21.1087 | −1.35134 | ||||||||
\(245\) | −10.6850 | −0.682643 | ||||||||
\(246\) | −3.20575 | −0.204391 | ||||||||
\(247\) | 39.8439 | 2.53521 | ||||||||
\(248\) | 16.2356 | 1.03096 | ||||||||
\(249\) | −3.50416 | −0.222067 | ||||||||
\(250\) | 12.0591 | 0.762683 | ||||||||
\(251\) | −18.4447 | −1.16422 | −0.582109 | − | 0.813111i | \(-0.697772\pi\) | ||||
−0.582109 | + | 0.813111i | \(0.697772\pi\) | |||||||
\(252\) | 15.3007 | 0.963855 | ||||||||
\(253\) | −1.40952 | −0.0886156 | ||||||||
\(254\) | −17.8058 | −1.11724 | ||||||||
\(255\) | −0.468260 | −0.0293236 | ||||||||
\(256\) | −7.12319 | −0.445200 | ||||||||
\(257\) | 5.21225 | 0.325131 | 0.162566 | − | 0.986698i | \(-0.448023\pi\) | ||||
0.162566 | + | 0.986698i | \(0.448023\pi\) | |||||||
\(258\) | 6.56578 | 0.408768 | ||||||||
\(259\) | −11.4077 | −0.708839 | ||||||||
\(260\) | 42.6063 | 2.64233 | ||||||||
\(261\) | −2.89214 | −0.179019 | ||||||||
\(262\) | −0.828092 | −0.0511597 | ||||||||
\(263\) | 13.9972 | 0.863103 | 0.431552 | − | 0.902088i | \(-0.357966\pi\) | ||||
0.431552 | + | 0.902088i | \(0.357966\pi\) | |||||||
\(264\) | −0.964186 | −0.0593415 | ||||||||
\(265\) | 24.7802 | 1.52223 | ||||||||
\(266\) | 31.2725 | 1.91744 | ||||||||
\(267\) | 1.81047 | 0.110799 | ||||||||
\(268\) | 29.0143 | 1.77233 | ||||||||
\(269\) | −7.68969 | −0.468848 | −0.234424 | − | 0.972134i | \(-0.575320\pi\) | ||||
−0.234424 | + | 0.972134i | \(0.575320\pi\) | |||||||
\(270\) | 12.2314 | 0.744379 | ||||||||
\(271\) | −25.3993 | −1.54290 | −0.771448 | − | 0.636292i | \(-0.780467\pi\) | ||||
−0.771448 | + | 0.636292i | \(0.780467\pi\) | |||||||
\(272\) | 0.624785 | 0.0378832 | ||||||||
\(273\) | −3.01599 | −0.182536 | ||||||||
\(274\) | −25.8906 | −1.56411 | ||||||||
\(275\) | 4.35851 | 0.262828 | ||||||||
\(276\) | −0.964678 | −0.0580668 | ||||||||
\(277\) | 13.8691 | 0.833312 | 0.416656 | − | 0.909064i | \(-0.363202\pi\) | ||||
0.416656 | + | 0.909064i | \(0.363202\pi\) | |||||||
\(278\) | 25.8021 | 1.54751 | ||||||||
\(279\) | 22.5434 | 1.34964 | ||||||||
\(280\) | 10.6717 | 0.637756 | ||||||||
\(281\) | −6.93041 | −0.413433 | −0.206717 | − | 0.978401i | \(-0.566278\pi\) | ||||
−0.206717 | + | 0.978401i | \(0.566278\pi\) | |||||||
\(282\) | −8.75327 | −0.521250 | ||||||||
\(283\) | 20.0345 | 1.19092 | 0.595462 | − | 0.803383i | \(-0.296969\pi\) | ||||
0.595462 | + | 0.803383i | \(0.296969\pi\) | |||||||
\(284\) | −1.13033 | −0.0670727 | ||||||||
\(285\) | 7.30025 | 0.432429 | ||||||||
\(286\) | −15.9697 | −0.944310 | ||||||||
\(287\) | −7.91209 | −0.467036 | ||||||||
\(288\) | −20.0588 | −1.18197 | ||||||||
\(289\) | −16.7488 | −0.985222 | ||||||||
\(290\) | −6.32095 | −0.371179 | ||||||||
\(291\) | 2.97066 | 0.174143 | ||||||||
\(292\) | 27.4868 | 1.60854 | ||||||||
\(293\) | −5.85153 | −0.341850 | −0.170925 | − | 0.985284i | \(-0.554676\pi\) | ||||
−0.170925 | + | 0.985284i | \(0.554676\pi\) | |||||||
\(294\) | 2.74102 | 0.159860 | ||||||||
\(295\) | 32.8046 | 1.90996 | ||||||||
\(296\) | −13.1928 | −0.766816 | ||||||||
\(297\) | −2.72750 | −0.158265 | ||||||||
\(298\) | −38.9280 | −2.25504 | ||||||||
\(299\) | −5.09892 | −0.294878 | ||||||||
\(300\) | 2.98298 | 0.172222 | ||||||||
\(301\) | 16.2049 | 0.934037 | ||||||||
\(302\) | 43.1319 | 2.48196 | ||||||||
\(303\) | 6.06406 | 0.348371 | ||||||||
\(304\) | −9.74050 | −0.558656 | ||||||||
\(305\) | −20.4424 | −1.17053 | ||||||||
\(306\) | −3.22108 | −0.184137 | ||||||||
\(307\) | −7.86578 | −0.448924 | −0.224462 | − | 0.974483i | \(-0.572062\pi\) | ||||
−0.224462 | + | 0.974483i | \(0.572062\pi\) | |||||||
\(308\) | −7.45697 | −0.424900 | ||||||||
\(309\) | 0.269486 | 0.0153305 | ||||||||
\(310\) | 49.2698 | 2.79834 | ||||||||
\(311\) | −20.2996 | −1.15109 | −0.575543 | − | 0.817772i | \(-0.695209\pi\) | ||||
−0.575543 | + | 0.817772i | \(0.695209\pi\) | |||||||
\(312\) | −3.48794 | −0.197466 | ||||||||
\(313\) | −24.4505 | −1.38203 | −0.691013 | − | 0.722843i | \(-0.742835\pi\) | ||||
−0.691013 | + | 0.722843i | \(0.742835\pi\) | |||||||
\(314\) | −32.2400 | −1.81941 | ||||||||
\(315\) | 14.8178 | 0.834888 | ||||||||
\(316\) | −12.1126 | −0.681385 | ||||||||
\(317\) | 7.43875 | 0.417802 | 0.208901 | − | 0.977937i | \(-0.433011\pi\) | ||||
0.208901 | + | 0.977937i | \(0.433011\pi\) | |||||||
\(318\) | −6.35682 | −0.356473 | ||||||||
\(319\) | 1.40952 | 0.0789178 | ||||||||
\(320\) | −36.7477 | −2.05426 | ||||||||
\(321\) | −3.62921 | −0.202563 | ||||||||
\(322\) | −4.00202 | −0.223024 | ||||||||
\(323\) | −3.91667 | −0.217929 | ||||||||
\(324\) | 23.6194 | 1.31219 | ||||||||
\(325\) | 15.7669 | 0.874591 | ||||||||
\(326\) | −1.60864 | −0.0890944 | ||||||||
\(327\) | −4.13663 | −0.228756 | ||||||||
\(328\) | −9.15020 | −0.505235 | ||||||||
\(329\) | −21.6038 | −1.19106 | ||||||||
\(330\) | −2.92599 | −0.161071 | ||||||||
\(331\) | −6.99061 | −0.384239 | −0.192119 | − | 0.981372i | \(-0.561536\pi\) | ||||
−0.192119 | + | 0.981372i | \(0.561536\pi\) | |||||||
\(332\) | −31.3419 | −1.72011 | ||||||||
\(333\) | −18.3184 | −1.00384 | ||||||||
\(334\) | 2.64246 | 0.144589 | ||||||||
\(335\) | 28.0985 | 1.53519 | ||||||||
\(336\) | 0.737307 | 0.0402234 | ||||||||
\(337\) | 17.4221 | 0.949041 | 0.474520 | − | 0.880245i | \(-0.342622\pi\) | ||||
0.474520 | + | 0.880245i | \(0.342622\pi\) | |||||||
\(338\) | −28.8841 | −1.57109 | ||||||||
\(339\) | 3.25781 | 0.176940 | ||||||||
\(340\) | −4.18821 | −0.227138 | ||||||||
\(341\) | −10.9867 | −0.594966 | ||||||||
\(342\) | 50.2172 | 2.71543 | ||||||||
\(343\) | 19.3726 | 1.04602 | ||||||||
\(344\) | 18.7407 | 1.01043 | ||||||||
\(345\) | −0.934230 | −0.0502973 | ||||||||
\(346\) | 50.3079 | 2.70457 | ||||||||
\(347\) | −10.8202 | −0.580858 | −0.290429 | − | 0.956897i | \(-0.593798\pi\) | ||||
−0.290429 | + | 0.956897i | \(0.593798\pi\) | |||||||
\(348\) | 0.964678 | 0.0517122 | ||||||||
\(349\) | 24.1066 | 1.29039 | 0.645197 | − | 0.764016i | \(-0.276775\pi\) | ||||
0.645197 | + | 0.764016i | \(0.276775\pi\) | |||||||
\(350\) | 12.3751 | 0.661474 | ||||||||
\(351\) | −9.86671 | −0.526646 | ||||||||
\(352\) | 9.77584 | 0.521054 | ||||||||
\(353\) | 36.3842 | 1.93653 | 0.968267 | − | 0.249916i | \(-0.0804032\pi\) | ||||
0.968267 | + | 0.249916i | \(0.0804032\pi\) | |||||||
\(354\) | −8.41532 | −0.447269 | ||||||||
\(355\) | −1.09465 | −0.0580982 | ||||||||
\(356\) | 16.1931 | 0.858235 | ||||||||
\(357\) | 0.296472 | 0.0156910 | ||||||||
\(358\) | −7.93601 | −0.419431 | ||||||||
\(359\) | −3.15217 | −0.166365 | −0.0831826 | − | 0.996534i | \(-0.526508\pi\) | ||||
−0.0831826 | + | 0.996534i | \(0.526508\pi\) | |||||||
\(360\) | 17.1365 | 0.903175 | ||||||||
\(361\) | 42.0614 | 2.21376 | ||||||||
\(362\) | −7.14406 | −0.375484 | ||||||||
\(363\) | −2.96007 | −0.155364 | ||||||||
\(364\) | −26.9756 | −1.41390 | ||||||||
\(365\) | 26.6193 | 1.39332 | ||||||||
\(366\) | 5.24407 | 0.274112 | ||||||||
\(367\) | −0.0743026 | −0.00387856 | −0.00193928 | − | 0.999998i | \(-0.500617\pi\) | ||||
−0.00193928 | + | 0.999998i | \(0.500617\pi\) | |||||||
\(368\) | 1.24652 | 0.0649791 | ||||||||
\(369\) | −12.7052 | −0.661405 | ||||||||
\(370\) | −40.0359 | −2.08137 | ||||||||
\(371\) | −15.6892 | −0.814543 | ||||||||
\(372\) | −7.51936 | −0.389861 | ||||||||
\(373\) | −23.7526 | −1.22986 | −0.614931 | − | 0.788581i | \(-0.710816\pi\) | ||||
−0.614931 | + | 0.788581i | \(0.710816\pi\) | |||||||
\(374\) | 1.56983 | 0.0811739 | ||||||||
\(375\) | −1.78232 | −0.0920387 | ||||||||
\(376\) | −24.9845 | −1.28848 | ||||||||
\(377\) | 5.09892 | 0.262608 | ||||||||
\(378\) | −7.74414 | −0.398316 | ||||||||
\(379\) | 9.28844 | 0.477115 | 0.238558 | − | 0.971128i | \(-0.423325\pi\) | ||||
0.238558 | + | 0.971128i | \(0.423325\pi\) | |||||||
\(380\) | 65.2948 | 3.34955 | ||||||||
\(381\) | 2.63168 | 0.134825 | ||||||||
\(382\) | 46.1079 | 2.35909 | ||||||||
\(383\) | 2.87551 | 0.146932 | 0.0734659 | − | 0.997298i | \(-0.476594\pi\) | ||||
0.0734659 | + | 0.997298i | \(0.476594\pi\) | |||||||
\(384\) | 4.87135 | 0.248590 | ||||||||
\(385\) | −7.22161 | −0.368047 | ||||||||
\(386\) | 5.50599 | 0.280248 | ||||||||
\(387\) | 26.0218 | 1.32276 | ||||||||
\(388\) | 26.5702 | 1.34890 | ||||||||
\(389\) | −10.5562 | −0.535219 | −0.267610 | − | 0.963527i | \(-0.586234\pi\) | ||||
−0.267610 | + | 0.963527i | \(0.586234\pi\) | |||||||
\(390\) | −10.5848 | −0.535980 | ||||||||
\(391\) | 0.501226 | 0.0253481 | ||||||||
\(392\) | 7.82371 | 0.395157 | ||||||||
\(393\) | 0.122391 | 0.00617382 | ||||||||
\(394\) | 9.49109 | 0.478154 | ||||||||
\(395\) | −11.7303 | −0.590214 | ||||||||
\(396\) | −11.9744 | −0.601734 | ||||||||
\(397\) | −39.5081 | −1.98286 | −0.991428 | − | 0.130657i | \(-0.958291\pi\) | ||||
−0.991428 | + | 0.130657i | \(0.958291\pi\) | |||||||
\(398\) | 45.3102 | 2.27119 | ||||||||
\(399\) | −4.62205 | −0.231392 | ||||||||
\(400\) | −3.85448 | −0.192724 | ||||||||
\(401\) | 1.17595 | 0.0587240 | 0.0293620 | − | 0.999569i | \(-0.490652\pi\) | ||||
0.0293620 | + | 0.999569i | \(0.490652\pi\) | |||||||
\(402\) | −7.20808 | −0.359506 | ||||||||
\(403\) | −39.7445 | −1.97981 | ||||||||
\(404\) | 54.2381 | 2.69845 | ||||||||
\(405\) | 22.8739 | 1.13661 | ||||||||
\(406\) | 4.00202 | 0.198617 | ||||||||
\(407\) | 8.92766 | 0.442528 | ||||||||
\(408\) | 0.342865 | 0.0169744 | ||||||||
\(409\) | 15.8860 | 0.785514 | 0.392757 | − | 0.919642i | \(-0.371521\pi\) | ||||
0.392757 | + | 0.919642i | \(0.371521\pi\) | |||||||
\(410\) | −27.7679 | −1.37136 | ||||||||
\(411\) | 3.82661 | 0.188753 | ||||||||
\(412\) | 2.41033 | 0.118748 | ||||||||
\(413\) | −20.7698 | −1.02201 | ||||||||
\(414\) | −6.42642 | −0.315841 | ||||||||
\(415\) | −30.3527 | −1.48995 | ||||||||
\(416\) | 35.3641 | 1.73387 | ||||||||
\(417\) | −3.81352 | −0.186749 | ||||||||
\(418\) | −24.4739 | −1.19706 | ||||||||
\(419\) | −4.67871 | −0.228570 | −0.114285 | − | 0.993448i | \(-0.536458\pi\) | ||||
−0.114285 | + | 0.993448i | \(0.536458\pi\) | |||||||
\(420\) | −4.94249 | −0.241169 | ||||||||
\(421\) | 1.42283 | 0.0693447 | 0.0346724 | − | 0.999399i | \(-0.488961\pi\) | ||||
0.0346724 | + | 0.999399i | \(0.488961\pi\) | |||||||
\(422\) | −6.10302 | −0.297090 | ||||||||
\(423\) | −34.6913 | −1.68675 | ||||||||
\(424\) | −18.1443 | −0.881166 | ||||||||
\(425\) | −1.54989 | −0.0751808 | ||||||||
\(426\) | 0.280810 | 0.0136053 | ||||||||
\(427\) | 12.9428 | 0.626348 | ||||||||
\(428\) | −32.4603 | −1.56903 | ||||||||
\(429\) | 2.36031 | 0.113957 | ||||||||
\(430\) | 56.8721 | 2.74262 | ||||||||
\(431\) | −21.0267 | −1.01282 | −0.506409 | − | 0.862293i | \(-0.669027\pi\) | ||||
−0.506409 | + | 0.862293i | \(0.669027\pi\) | |||||||
\(432\) | 2.41208 | 0.116051 | ||||||||
\(433\) | −11.1203 | −0.534406 | −0.267203 | − | 0.963640i | \(-0.586099\pi\) | ||||
−0.267203 | + | 0.963640i | \(0.586099\pi\) | |||||||
\(434\) | −31.1945 | −1.49738 | ||||||||
\(435\) | 0.934230 | 0.0447929 | ||||||||
\(436\) | −36.9988 | −1.77192 | ||||||||
\(437\) | −7.81418 | −0.373803 | ||||||||
\(438\) | −6.82860 | −0.326283 | ||||||||
\(439\) | −17.7462 | −0.846978 | −0.423489 | − | 0.905901i | \(-0.639195\pi\) | ||||
−0.423489 | + | 0.905901i | \(0.639195\pi\) | |||||||
\(440\) | −8.35167 | −0.398150 | ||||||||
\(441\) | 10.8633 | 0.517302 | ||||||||
\(442\) | 5.67885 | 0.270115 | ||||||||
\(443\) | −21.6709 | −1.02962 | −0.514808 | − | 0.857305i | \(-0.672137\pi\) | ||||
−0.514808 | + | 0.857305i | \(0.672137\pi\) | |||||||
\(444\) | 6.11012 | 0.289973 | ||||||||
\(445\) | 15.6821 | 0.743401 | ||||||||
\(446\) | −6.79860 | −0.321923 | ||||||||
\(447\) | 5.75353 | 0.272132 | ||||||||
\(448\) | 23.2663 | 1.09923 | ||||||||
\(449\) | −18.1103 | −0.854679 | −0.427339 | − | 0.904091i | \(-0.640549\pi\) | ||||
−0.427339 | + | 0.904091i | \(0.640549\pi\) | |||||||
\(450\) | 19.8718 | 0.936765 | ||||||||
\(451\) | 6.19200 | 0.291570 | ||||||||
\(452\) | 29.1384 | 1.37056 | ||||||||
\(453\) | −6.37486 | −0.299517 | ||||||||
\(454\) | 61.1359 | 2.86925 | ||||||||
\(455\) | −26.1241 | −1.22472 | ||||||||
\(456\) | −5.34532 | −0.250318 | ||||||||
\(457\) | −23.0751 | −1.07941 | −0.539704 | − | 0.841855i | \(-0.681464\pi\) | ||||
−0.539704 | + | 0.841855i | \(0.681464\pi\) | |||||||
\(458\) | 64.1371 | 2.99693 | ||||||||
\(459\) | 0.969901 | 0.0452711 | ||||||||
\(460\) | −8.35594 | −0.389598 | ||||||||
\(461\) | −4.00828 | −0.186684 | −0.0933421 | − | 0.995634i | \(-0.529755\pi\) | ||||
−0.0933421 | + | 0.995634i | \(0.529755\pi\) | |||||||
\(462\) | 1.85255 | 0.0861885 | ||||||||
\(463\) | 12.0196 | 0.558597 | 0.279298 | − | 0.960204i | \(-0.409898\pi\) | ||||
0.279298 | + | 0.960204i | \(0.409898\pi\) | |||||||
\(464\) | −1.24652 | −0.0578680 | ||||||||
\(465\) | −7.28203 | −0.337696 | ||||||||
\(466\) | 47.0811 | 2.18099 | ||||||||
\(467\) | 28.1869 | 1.30433 | 0.652167 | − | 0.758075i | \(-0.273860\pi\) | ||||
0.652167 | + | 0.758075i | \(0.273860\pi\) | |||||||
\(468\) | −43.3172 | −2.00234 | ||||||||
\(469\) | −17.7902 | −0.821474 | ||||||||
\(470\) | −75.8199 | −3.49731 | ||||||||
\(471\) | 4.76504 | 0.219562 | ||||||||
\(472\) | −24.0199 | −1.10560 | ||||||||
\(473\) | −12.6820 | −0.583119 | ||||||||
\(474\) | 3.00915 | 0.138215 | ||||||||
\(475\) | 24.1630 | 1.10868 | ||||||||
\(476\) | 2.65171 | 0.121541 | ||||||||
\(477\) | −25.1936 | −1.15354 | ||||||||
\(478\) | −43.2279 | −1.97720 | ||||||||
\(479\) | −17.7258 | −0.809912 | −0.404956 | − | 0.914336i | \(-0.632713\pi\) | ||||
−0.404956 | + | 0.914336i | \(0.632713\pi\) | |||||||
\(480\) | 6.47945 | 0.295745 | ||||||||
\(481\) | 32.2958 | 1.47256 | ||||||||
\(482\) | 15.2659 | 0.695342 | ||||||||
\(483\) | 0.591495 | 0.0269139 | ||||||||
\(484\) | −26.4755 | −1.20343 | ||||||||
\(485\) | 25.7315 | 1.16841 | ||||||||
\(486\) | −18.7670 | −0.851291 | ||||||||
\(487\) | 19.0479 | 0.863143 | 0.431571 | − | 0.902079i | \(-0.357959\pi\) | ||||
0.431571 | + | 0.902079i | \(0.357959\pi\) | |||||||
\(488\) | 14.9682 | 0.677578 | ||||||||
\(489\) | 0.237756 | 0.0107517 | ||||||||
\(490\) | 23.7424 | 1.07257 | ||||||||
\(491\) | −12.8644 | −0.580563 | −0.290281 | − | 0.956941i | \(-0.593749\pi\) | ||||
−0.290281 | + | 0.956941i | \(0.593749\pi\) | |||||||
\(492\) | 4.23783 | 0.191056 | ||||||||
\(493\) | −0.501226 | −0.0225741 | ||||||||
\(494\) | −88.5341 | −3.98334 | ||||||||
\(495\) | −11.5964 | −0.521220 | ||||||||
\(496\) | 9.71620 | 0.436270 | ||||||||
\(497\) | 0.693064 | 0.0310882 | ||||||||
\(498\) | 7.78633 | 0.348914 | ||||||||
\(499\) | 5.35211 | 0.239593 | 0.119797 | − | 0.992798i | \(-0.461776\pi\) | ||||
0.119797 | + | 0.992798i | \(0.461776\pi\) | |||||||
\(500\) | −15.9414 | −0.712922 | ||||||||
\(501\) | −0.390553 | −0.0174486 | ||||||||
\(502\) | 40.9845 | 1.82923 | ||||||||
\(503\) | −6.72802 | −0.299987 | −0.149994 | − | 0.988687i | \(-0.547925\pi\) | ||||
−0.149994 | + | 0.988687i | \(0.547925\pi\) | |||||||
\(504\) | −10.8498 | −0.483287 | ||||||||
\(505\) | 52.5262 | 2.33739 | ||||||||
\(506\) | 3.13198 | 0.139234 | ||||||||
\(507\) | 4.26905 | 0.189595 | ||||||||
\(508\) | 23.5383 | 1.04434 | ||||||||
\(509\) | −3.24589 | −0.143871 | −0.0719357 | − | 0.997409i | \(-0.522918\pi\) | ||||
−0.0719357 | + | 0.997409i | \(0.522918\pi\) | |||||||
\(510\) | 1.04049 | 0.0460735 | ||||||||
\(511\) | −16.8536 | −0.745560 | ||||||||
\(512\) | −13.8381 | −0.611562 | ||||||||
\(513\) | −15.1209 | −0.667604 | ||||||||
\(514\) | −11.5818 | −0.510849 | ||||||||
\(515\) | 2.33426 | 0.102860 | ||||||||
\(516\) | −8.67960 | −0.382098 | ||||||||
\(517\) | 16.9072 | 0.743577 | ||||||||
\(518\) | 25.3482 | 1.11373 | ||||||||
\(519\) | −7.43547 | −0.326381 | ||||||||
\(520\) | −30.2121 | −1.32489 | ||||||||
\(521\) | −1.97409 | −0.0864863 | −0.0432432 | − | 0.999065i | \(-0.513769\pi\) | ||||
−0.0432432 | + | 0.999065i | \(0.513769\pi\) | |||||||
\(522\) | 6.42642 | 0.281277 | ||||||||
\(523\) | −23.5368 | −1.02919 | −0.514597 | − | 0.857432i | \(-0.672058\pi\) | ||||
−0.514597 | + | 0.857432i | \(0.672058\pi\) | |||||||
\(524\) | 1.09469 | 0.0478218 | ||||||||
\(525\) | −1.82902 | −0.0798251 | ||||||||
\(526\) | −31.1021 | −1.35611 | ||||||||
\(527\) | 3.90690 | 0.170187 | ||||||||
\(528\) | −0.577017 | −0.0251114 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −55.0621 | −2.39175 | ||||||||
\(531\) | −33.3520 | −1.44735 | ||||||||
\(532\) | −41.3405 | −1.79234 | ||||||||
\(533\) | 22.3995 | 0.970232 | ||||||||
\(534\) | −4.02290 | −0.174088 | ||||||||
\(535\) | −31.4358 | −1.35909 | ||||||||
\(536\) | −20.5740 | −0.888664 | ||||||||
\(537\) | 1.17294 | 0.0506159 | ||||||||
\(538\) | 17.0867 | 0.736659 | ||||||||
\(539\) | −5.29436 | −0.228044 | ||||||||
\(540\) | −16.1692 | −0.695813 | ||||||||
\(541\) | 8.64825 | 0.371817 | 0.185909 | − | 0.982567i | \(-0.440477\pi\) | ||||
0.185909 | + | 0.982567i | \(0.440477\pi\) | |||||||
\(542\) | 56.4378 | 2.42421 | ||||||||
\(543\) | 1.05589 | 0.0453124 | ||||||||
\(544\) | −3.47630 | −0.149045 | ||||||||
\(545\) | −35.8310 | −1.53483 | ||||||||
\(546\) | 6.70159 | 0.286802 | ||||||||
\(547\) | −9.69255 | −0.414423 | −0.207212 | − | 0.978296i | \(-0.566439\pi\) | ||||
−0.207212 | + | 0.978296i | \(0.566439\pi\) | |||||||
\(548\) | 34.2259 | 1.46206 | ||||||||
\(549\) | 20.7835 | 0.887020 | ||||||||
\(550\) | −9.68472 | −0.412958 | ||||||||
\(551\) | 7.81418 | 0.332895 | ||||||||
\(552\) | 0.684054 | 0.0291153 | ||||||||
\(553\) | 7.42685 | 0.315822 | ||||||||
\(554\) | −30.8174 | −1.30931 | ||||||||
\(555\) | 5.91727 | 0.251174 | ||||||||
\(556\) | −34.1089 | −1.44654 | ||||||||
\(557\) | 13.3947 | 0.567551 | 0.283775 | − | 0.958891i | \(-0.408413\pi\) | ||||
0.283775 | + | 0.958891i | \(0.408413\pi\) | |||||||
\(558\) | −50.0919 | −2.12056 | ||||||||
\(559\) | −45.8771 | −1.94039 | ||||||||
\(560\) | 6.38648 | 0.269878 | ||||||||
\(561\) | −0.232019 | −0.00979586 | ||||||||
\(562\) | 15.3995 | 0.649590 | ||||||||
\(563\) | −13.4723 | −0.567789 | −0.283894 | − | 0.958856i | \(-0.591627\pi\) | ||||
−0.283894 | + | 0.958856i | \(0.591627\pi\) | |||||||
\(564\) | 11.5713 | 0.487241 | ||||||||
\(565\) | 28.2188 | 1.18717 | ||||||||
\(566\) | −44.5170 | −1.87119 | ||||||||
\(567\) | −14.4823 | −0.608199 | ||||||||
\(568\) | 0.801517 | 0.0336309 | ||||||||
\(569\) | 24.5456 | 1.02901 | 0.514503 | − | 0.857489i | \(-0.327977\pi\) | ||||
0.514503 | + | 0.857489i | \(0.327977\pi\) | |||||||
\(570\) | −16.2213 | −0.679436 | ||||||||
\(571\) | 25.9329 | 1.08526 | 0.542630 | − | 0.839972i | \(-0.317429\pi\) | ||||
0.542630 | + | 0.839972i | \(0.317429\pi\) | |||||||
\(572\) | 21.1111 | 0.882699 | ||||||||
\(573\) | −6.81471 | −0.284689 | ||||||||
\(574\) | 17.5809 | 0.733811 | ||||||||
\(575\) | −3.09220 | −0.128954 | ||||||||
\(576\) | 37.3608 | 1.55670 | ||||||||
\(577\) | −19.2044 | −0.799491 | −0.399745 | − | 0.916626i | \(-0.630901\pi\) | ||||
−0.399745 | + | 0.916626i | \(0.630901\pi\) | |||||||
\(578\) | 37.2162 | 1.54799 | ||||||||
\(579\) | −0.813781 | −0.0338196 | ||||||||
\(580\) | 8.35594 | 0.346961 | ||||||||
\(581\) | 19.2174 | 0.797270 | ||||||||
\(582\) | −6.60088 | −0.273615 | ||||||||
\(583\) | 12.2784 | 0.508519 | ||||||||
\(584\) | −19.4909 | −0.806540 | ||||||||
\(585\) | −41.9500 | −1.73442 | ||||||||
\(586\) | 13.0022 | 0.537118 | ||||||||
\(587\) | 25.5057 | 1.05273 | 0.526367 | − | 0.850258i | \(-0.323554\pi\) | ||||
0.526367 | + | 0.850258i | \(0.323554\pi\) | |||||||
\(588\) | −3.62348 | −0.149430 | ||||||||
\(589\) | −60.9091 | −2.50972 | ||||||||
\(590\) | −72.8926 | −3.00094 | ||||||||
\(591\) | −1.40277 | −0.0577024 | ||||||||
\(592\) | −7.89523 | −0.324492 | ||||||||
\(593\) | 17.1281 | 0.703368 | 0.351684 | − | 0.936119i | \(-0.385609\pi\) | ||||
0.351684 | + | 0.936119i | \(0.385609\pi\) | |||||||
\(594\) | 6.06057 | 0.248668 | ||||||||
\(595\) | 2.56801 | 0.105278 | ||||||||
\(596\) | 51.4607 | 2.10791 | ||||||||
\(597\) | −6.69681 | −0.274082 | ||||||||
\(598\) | 11.3299 | 0.463315 | ||||||||
\(599\) | 5.44669 | 0.222546 | 0.111273 | − | 0.993790i | \(-0.464507\pi\) | ||||
0.111273 | + | 0.993790i | \(0.464507\pi\) | |||||||
\(600\) | −2.11523 | −0.0863540 | ||||||||
\(601\) | −35.1853 | −1.43524 | −0.717619 | − | 0.696436i | \(-0.754768\pi\) | ||||
−0.717619 | + | 0.696436i | \(0.754768\pi\) | |||||||
\(602\) | −36.0078 | −1.46757 | ||||||||
\(603\) | −28.5674 | −1.16335 | ||||||||
\(604\) | −57.0180 | −2.32003 | ||||||||
\(605\) | −25.6398 | −1.04241 | ||||||||
\(606\) | −13.4745 | −0.547363 | ||||||||
\(607\) | −30.3496 | −1.23185 | −0.615926 | − | 0.787804i | \(-0.711218\pi\) | ||||
−0.615926 | + | 0.787804i | \(0.711218\pi\) | |||||||
\(608\) | 54.1960 | 2.19794 | ||||||||
\(609\) | −0.591495 | −0.0239686 | ||||||||
\(610\) | 45.4236 | 1.83915 | ||||||||
\(611\) | 61.1617 | 2.47434 | ||||||||
\(612\) | 4.25809 | 0.172123 | ||||||||
\(613\) | 18.2357 | 0.736534 | 0.368267 | − | 0.929720i | \(-0.379951\pi\) | ||||
0.368267 | + | 0.929720i | \(0.379951\pi\) | |||||||
\(614\) | 17.4780 | 0.705353 | ||||||||
\(615\) | 4.10407 | 0.165492 | ||||||||
\(616\) | 5.28774 | 0.213049 | ||||||||
\(617\) | −11.1167 | −0.447542 | −0.223771 | − | 0.974642i | \(-0.571837\pi\) | ||||
−0.223771 | + | 0.974642i | \(0.571837\pi\) | |||||||
\(618\) | −0.598803 | −0.0240874 | ||||||||
\(619\) | 23.8373 | 0.958101 | 0.479051 | − | 0.877787i | \(-0.340981\pi\) | ||||
0.479051 | + | 0.877787i | \(0.340981\pi\) | |||||||
\(620\) | −65.1319 | −2.61576 | ||||||||
\(621\) | 1.93506 | 0.0776512 | ||||||||
\(622\) | 45.1062 | 1.80859 | ||||||||
\(623\) | −9.92887 | −0.397792 | ||||||||
\(624\) | −2.08736 | −0.0835611 | ||||||||
\(625\) | −30.8993 | −1.23597 | ||||||||
\(626\) | 54.3297 | 2.17145 | ||||||||
\(627\) | 3.61722 | 0.144458 | ||||||||
\(628\) | 42.6195 | 1.70070 | ||||||||
\(629\) | −3.17468 | −0.126583 | ||||||||
\(630\) | −32.9255 | −1.31178 | ||||||||
\(631\) | 20.4200 | 0.812907 | 0.406454 | − | 0.913671i | \(-0.366765\pi\) | ||||
0.406454 | + | 0.913671i | \(0.366765\pi\) | |||||||
\(632\) | 8.58903 | 0.341653 | ||||||||
\(633\) | 0.902021 | 0.0358521 | ||||||||
\(634\) | −16.5291 | −0.656454 | ||||||||
\(635\) | 22.7953 | 0.904606 | ||||||||
\(636\) | 8.40336 | 0.333215 | ||||||||
\(637\) | −19.1523 | −0.758843 | ||||||||
\(638\) | −3.13198 | −0.123996 | ||||||||
\(639\) | 1.11292 | 0.0440264 | ||||||||
\(640\) | 42.1951 | 1.66791 | ||||||||
\(641\) | 29.0930 | 1.14911 | 0.574553 | − | 0.818468i | \(-0.305176\pi\) | ||||
0.574553 | + | 0.818468i | \(0.305176\pi\) | |||||||
\(642\) | 8.06418 | 0.318268 | ||||||||
\(643\) | −0.376790 | −0.0148592 | −0.00742958 | − | 0.999972i | \(-0.502365\pi\) | ||||
−0.00742958 | + | 0.999972i | \(0.502365\pi\) | |||||||
\(644\) | 5.29044 | 0.208473 | ||||||||
\(645\) | −8.40565 | −0.330972 | ||||||||
\(646\) | 8.70293 | 0.342412 | ||||||||
\(647\) | 29.5176 | 1.16046 | 0.580228 | − | 0.814454i | \(-0.302963\pi\) | ||||
0.580228 | + | 0.814454i | \(0.302963\pi\) | |||||||
\(648\) | −16.7485 | −0.657944 | ||||||||
\(649\) | 16.2544 | 0.638042 | ||||||||
\(650\) | −35.0344 | −1.37416 | ||||||||
\(651\) | 4.61052 | 0.180700 | ||||||||
\(652\) | 2.12653 | 0.0832815 | ||||||||
\(653\) | −14.7520 | −0.577289 | −0.288645 | − | 0.957436i | \(-0.593205\pi\) | ||||
−0.288645 | + | 0.957436i | \(0.593205\pi\) | |||||||
\(654\) | 9.19169 | 0.359424 | ||||||||
\(655\) | 1.06014 | 0.0414231 | ||||||||
\(656\) | −5.47594 | −0.213799 | ||||||||
\(657\) | −27.0634 | −1.05584 | ||||||||
\(658\) | 48.0043 | 1.87140 | ||||||||
\(659\) | −20.0983 | −0.782920 | −0.391460 | − | 0.920195i | \(-0.628030\pi\) | ||||
−0.391460 | + | 0.920195i | \(0.628030\pi\) | |||||||
\(660\) | 3.86800 | 0.150562 | ||||||||
\(661\) | 20.8457 | 0.810803 | 0.405401 | − | 0.914139i | \(-0.367132\pi\) | ||||
0.405401 | + | 0.914139i | \(0.367132\pi\) | |||||||
\(662\) | 15.5333 | 0.603719 | ||||||||
\(663\) | −0.839329 | −0.0325968 | ||||||||
\(664\) | 22.2245 | 0.862480 | ||||||||
\(665\) | −40.0357 | −1.55252 | ||||||||
\(666\) | 40.7039 | 1.57724 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −3.49318 | −0.135155 | ||||||||
\(669\) | 1.00483 | 0.0388489 | ||||||||
\(670\) | −62.4356 | −2.41210 | ||||||||
\(671\) | −10.1291 | −0.391029 | ||||||||
\(672\) | −4.10237 | −0.158252 | ||||||||
\(673\) | 31.2830 | 1.20587 | 0.602935 | − | 0.797790i | \(-0.293998\pi\) | ||||
0.602935 | + | 0.797790i | \(0.293998\pi\) | |||||||
\(674\) | −38.7123 | −1.49114 | ||||||||
\(675\) | −5.98359 | −0.230309 | ||||||||
\(676\) | 38.1832 | 1.46858 | ||||||||
\(677\) | −6.86906 | −0.263999 | −0.132000 | − | 0.991250i | \(-0.542140\pi\) | ||||
−0.132000 | + | 0.991250i | \(0.542140\pi\) | |||||||
\(678\) | −7.23892 | −0.278009 | ||||||||
\(679\) | −16.2916 | −0.625213 | ||||||||
\(680\) | 2.96986 | 0.113889 | ||||||||
\(681\) | −9.03583 | −0.346254 | ||||||||
\(682\) | 24.4128 | 0.934815 | ||||||||
\(683\) | 21.0191 | 0.804275 | 0.402137 | − | 0.915579i | \(-0.368267\pi\) | ||||
0.402137 | + | 0.915579i | \(0.368267\pi\) | |||||||
\(684\) | −66.3843 | −2.53827 | ||||||||
\(685\) | 33.1456 | 1.26643 | ||||||||
\(686\) | −43.0463 | −1.64352 | ||||||||
\(687\) | −9.47941 | −0.361662 | ||||||||
\(688\) | 11.2154 | 0.427583 | ||||||||
\(689\) | 44.4170 | 1.69215 | ||||||||
\(690\) | 2.07588 | 0.0790275 | ||||||||
\(691\) | −42.9608 | −1.63431 | −0.817153 | − | 0.576421i | \(-0.804449\pi\) | ||||
−0.817153 | + | 0.576421i | \(0.804449\pi\) | |||||||
\(692\) | −66.5042 | −2.52811 | ||||||||
\(693\) | 7.34211 | 0.278904 | ||||||||
\(694\) | 24.0427 | 0.912649 | ||||||||
\(695\) | −33.0323 | −1.25299 | ||||||||
\(696\) | −0.684054 | −0.0259290 | ||||||||
\(697\) | −2.20188 | −0.0834022 | ||||||||
\(698\) | −53.5654 | −2.02748 | ||||||||
\(699\) | −6.95855 | −0.263197 | ||||||||
\(700\) | −16.3591 | −0.618317 | ||||||||
\(701\) | 16.1787 | 0.611062 | 0.305531 | − | 0.952182i | \(-0.401166\pi\) | ||||
0.305531 | + | 0.952182i | \(0.401166\pi\) | |||||||
\(702\) | 21.9241 | 0.827471 | ||||||||
\(703\) | 49.4938 | 1.86669 | ||||||||
\(704\) | −18.2082 | −0.686247 | ||||||||
\(705\) | 11.2061 | 0.422046 | ||||||||
\(706\) | −80.8465 | −3.04270 | ||||||||
\(707\) | −33.2562 | −1.25073 | ||||||||
\(708\) | 11.1246 | 0.418087 | ||||||||
\(709\) | 46.3214 | 1.73964 | 0.869818 | − | 0.493373i | \(-0.164236\pi\) | ||||
0.869818 | + | 0.493373i | \(0.164236\pi\) | |||||||
\(710\) | 2.43235 | 0.0912843 | ||||||||
\(711\) | 11.9260 | 0.447260 | ||||||||
\(712\) | −11.4826 | −0.430328 | ||||||||
\(713\) | 7.79469 | 0.291913 | ||||||||
\(714\) | −0.658769 | −0.0246538 | ||||||||
\(715\) | 20.4448 | 0.764591 | ||||||||
\(716\) | 10.4910 | 0.392066 | ||||||||
\(717\) | 6.38905 | 0.238603 | ||||||||
\(718\) | 7.00420 | 0.261394 | ||||||||
\(719\) | 41.8530 | 1.56085 | 0.780426 | − | 0.625248i | \(-0.215002\pi\) | ||||
0.780426 | + | 0.625248i | \(0.215002\pi\) | |||||||
\(720\) | 10.2554 | 0.382195 | ||||||||
\(721\) | −1.47790 | −0.0550399 | ||||||||
\(722\) | −93.4615 | −3.47828 | ||||||||
\(723\) | −2.25628 | −0.0839121 | ||||||||
\(724\) | 9.44405 | 0.350985 | ||||||||
\(725\) | 3.09220 | 0.114842 | ||||||||
\(726\) | 6.57736 | 0.244109 | ||||||||
\(727\) | −8.41082 | −0.311940 | −0.155970 | − | 0.987762i | \(-0.549850\pi\) | ||||
−0.155970 | + | 0.987762i | \(0.549850\pi\) | |||||||
\(728\) | 19.1284 | 0.708945 | ||||||||
\(729\) | −21.3491 | −0.790706 | ||||||||
\(730\) | −59.1486 | −2.18919 | ||||||||
\(731\) | 4.50973 | 0.166798 | ||||||||
\(732\) | −6.93237 | −0.256228 | ||||||||
\(733\) | −10.4264 | −0.385106 | −0.192553 | − | 0.981287i | \(-0.561677\pi\) | ||||
−0.192553 | + | 0.981287i | \(0.561677\pi\) | |||||||
\(734\) | 0.165102 | 0.00609403 | ||||||||
\(735\) | −3.50911 | −0.129435 | ||||||||
\(736\) | −6.93560 | −0.255650 | ||||||||
\(737\) | 13.9226 | 0.512846 | ||||||||
\(738\) | 28.2312 | 1.03921 | ||||||||
\(739\) | 29.2951 | 1.07764 | 0.538819 | − | 0.842421i | \(-0.318871\pi\) | ||||
0.538819 | + | 0.842421i | \(0.318871\pi\) | |||||||
\(740\) | 52.9252 | 1.94557 | ||||||||
\(741\) | 13.0853 | 0.480699 | ||||||||
\(742\) | 34.8618 | 1.27982 | ||||||||
\(743\) | 19.0857 | 0.700186 | 0.350093 | − | 0.936715i | \(-0.386150\pi\) | ||||
0.350093 | + | 0.936715i | \(0.386150\pi\) | |||||||
\(744\) | 5.33199 | 0.195480 | ||||||||
\(745\) | 49.8364 | 1.82587 | ||||||||
\(746\) | 52.7788 | 1.93237 | ||||||||
\(747\) | 30.8591 | 1.12908 | ||||||||
\(748\) | −2.07523 | −0.0758778 | ||||||||
\(749\) | 19.9031 | 0.727244 | ||||||||
\(750\) | 3.96036 | 0.144612 | ||||||||
\(751\) | 47.7446 | 1.74222 | 0.871112 | − | 0.491084i | \(-0.163399\pi\) | ||||
0.871112 | + | 0.491084i | \(0.163399\pi\) | |||||||
\(752\) | −14.9520 | −0.545242 | ||||||||
\(753\) | −6.05747 | −0.220747 | ||||||||
\(754\) | −11.3299 | −0.412612 | ||||||||
\(755\) | −55.2184 | −2.00960 | ||||||||
\(756\) | 10.2373 | 0.372328 | ||||||||
\(757\) | 35.8215 | 1.30196 | 0.650978 | − | 0.759097i | \(-0.274359\pi\) | ||||
0.650978 | + | 0.759097i | \(0.274359\pi\) | |||||||
\(758\) | −20.6391 | −0.749647 | ||||||||
\(759\) | −0.462904 | −0.0168024 | ||||||||
\(760\) | −46.3006 | −1.67950 | ||||||||
\(761\) | 18.4287 | 0.668039 | 0.334019 | − | 0.942566i | \(-0.391595\pi\) | ||||
0.334019 | + | 0.942566i | \(0.391595\pi\) | |||||||
\(762\) | −5.84766 | −0.211838 | ||||||||
\(763\) | 22.6859 | 0.821285 | ||||||||
\(764\) | −60.9521 | −2.20517 | ||||||||
\(765\) | 4.12370 | 0.149093 | ||||||||
\(766\) | −6.38945 | −0.230860 | ||||||||
\(767\) | 58.8003 | 2.12316 | ||||||||
\(768\) | −2.33935 | −0.0844141 | ||||||||
\(769\) | −12.7262 | −0.458920 | −0.229460 | − | 0.973318i | \(-0.573696\pi\) | ||||
−0.229460 | + | 0.973318i | \(0.573696\pi\) | |||||||
\(770\) | 16.0466 | 0.578279 | ||||||||
\(771\) | 1.71177 | 0.0616480 | ||||||||
\(772\) | −7.27861 | −0.261963 | ||||||||
\(773\) | −6.64414 | −0.238973 | −0.119487 | − | 0.992836i | \(-0.538125\pi\) | ||||
−0.119487 | + | 0.992836i | \(0.538125\pi\) | |||||||
\(774\) | −57.8211 | −2.07833 | ||||||||
\(775\) | −24.1028 | −0.865796 | ||||||||
\(776\) | −18.8409 | −0.676350 | ||||||||
\(777\) | −3.74644 | −0.134403 | ||||||||
\(778\) | 23.4561 | 0.840941 | ||||||||
\(779\) | 34.3277 | 1.22992 | ||||||||
\(780\) | 13.9925 | 0.501011 | ||||||||
\(781\) | −0.542392 | −0.0194083 | ||||||||
\(782\) | −1.11374 | −0.0398271 | ||||||||
\(783\) | −1.93506 | −0.0691533 | ||||||||
\(784\) | 4.68210 | 0.167218 | ||||||||
\(785\) | 41.2743 | 1.47314 | ||||||||
\(786\) | −0.271956 | −0.00970036 | ||||||||
\(787\) | 1.15831 | 0.0412893 | 0.0206446 | − | 0.999787i | \(-0.493428\pi\) | ||||
0.0206446 | + | 0.999787i | \(0.493428\pi\) | |||||||
\(788\) | −12.5467 | −0.446957 | ||||||||
\(789\) | 4.59686 | 0.163653 | ||||||||
\(790\) | 26.0649 | 0.927349 | ||||||||
\(791\) | −17.8663 | −0.635253 | ||||||||
\(792\) | 8.49102 | 0.301715 | ||||||||
\(793\) | −36.6419 | −1.30119 | ||||||||
\(794\) | 87.7880 | 3.11548 | ||||||||
\(795\) | 8.13813 | 0.288630 | ||||||||
\(796\) | −59.8975 | −2.12301 | ||||||||
\(797\) | 26.5128 | 0.939131 | 0.469566 | − | 0.882898i | \(-0.344411\pi\) | ||||
0.469566 | + | 0.882898i | \(0.344411\pi\) | |||||||
\(798\) | 10.2703 | 0.363565 | ||||||||
\(799\) | −6.01221 | −0.212697 | ||||||||
\(800\) | 21.4463 | 0.758240 | ||||||||
\(801\) | −15.9437 | −0.563344 | ||||||||
\(802\) | −2.61298 | −0.0922676 | ||||||||
\(803\) | 13.1896 | 0.465452 | ||||||||
\(804\) | 9.52868 | 0.336050 | ||||||||
\(805\) | 5.12346 | 0.180578 | ||||||||
\(806\) | 88.3133 | 3.11070 | ||||||||
\(807\) | −2.52539 | −0.0888981 | ||||||||
\(808\) | −38.4603 | −1.35303 | ||||||||
\(809\) | −2.83108 | −0.0995355 | −0.0497678 | − | 0.998761i | \(-0.515848\pi\) | ||||
−0.0497678 | + | 0.998761i | \(0.515848\pi\) | |||||||
\(810\) | −50.8263 | −1.78586 | ||||||||
\(811\) | −16.8762 | −0.592605 | −0.296303 | − | 0.955094i | \(-0.595754\pi\) | ||||
−0.296303 | + | 0.955094i | \(0.595754\pi\) | |||||||
\(812\) | −5.29044 | −0.185658 | ||||||||
\(813\) | −8.34146 | −0.292548 | ||||||||
\(814\) | −19.8375 | −0.695303 | ||||||||
\(815\) | 2.05942 | 0.0721382 | ||||||||
\(816\) | 0.205188 | 0.00718301 | ||||||||
\(817\) | −70.3073 | −2.45974 | ||||||||
\(818\) | −35.2991 | −1.23421 | ||||||||
\(819\) | 26.5600 | 0.928083 | ||||||||
\(820\) | 36.7076 | 1.28189 | ||||||||
\(821\) | −43.9573 | −1.53412 | −0.767060 | − | 0.641575i | \(-0.778281\pi\) | ||||
−0.767060 | + | 0.641575i | \(0.778281\pi\) | |||||||
\(822\) | −8.50281 | −0.296570 | ||||||||
\(823\) | −37.7144 | −1.31464 | −0.657321 | − | 0.753610i | \(-0.728311\pi\) | ||||
−0.657321 | + | 0.753610i | \(0.728311\pi\) | |||||||
\(824\) | −1.70917 | −0.0595417 | ||||||||
\(825\) | 1.43139 | 0.0498347 | ||||||||
\(826\) | 46.1509 | 1.60580 | ||||||||
\(827\) | −12.6140 | −0.438633 | −0.219317 | − | 0.975654i | \(-0.570383\pi\) | ||||
−0.219317 | + | 0.975654i | \(0.570383\pi\) | |||||||
\(828\) | 8.49536 | 0.295234 | ||||||||
\(829\) | 37.1288 | 1.28954 | 0.644768 | − | 0.764378i | \(-0.276954\pi\) | ||||
0.644768 | + | 0.764378i | \(0.276954\pi\) | |||||||
\(830\) | 67.4443 | 2.34103 | ||||||||
\(831\) | 4.55479 | 0.158004 | ||||||||
\(832\) | −65.8681 | −2.28356 | ||||||||
\(833\) | 1.88268 | 0.0652310 | ||||||||
\(834\) | 8.47374 | 0.293422 | ||||||||
\(835\) | −3.38293 | −0.117071 | ||||||||
\(836\) | 32.3531 | 1.11895 | ||||||||
\(837\) | 15.0832 | 0.521351 | ||||||||
\(838\) | 10.3962 | 0.359131 | ||||||||
\(839\) | 8.77668 | 0.303005 | 0.151502 | − | 0.988457i | \(-0.451589\pi\) | ||||
0.151502 | + | 0.988457i | \(0.451589\pi\) | |||||||
\(840\) | 3.50473 | 0.120925 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −3.16157 | −0.108955 | ||||||||
\(843\) | −2.27604 | −0.0783909 | ||||||||
\(844\) | 8.06785 | 0.277707 | ||||||||
\(845\) | 36.9780 | 1.27208 | ||||||||
\(846\) | 77.0850 | 2.65024 | ||||||||
\(847\) | 16.2335 | 0.557790 | ||||||||
\(848\) | −10.8585 | −0.372881 | ||||||||
\(849\) | 6.57958 | 0.225811 | ||||||||
\(850\) | 3.44390 | 0.118125 | ||||||||
\(851\) | −6.33384 | −0.217121 | ||||||||
\(852\) | −0.371215 | −0.0127176 | ||||||||
\(853\) | −10.9924 | −0.376374 | −0.188187 | − | 0.982133i | \(-0.560261\pi\) | ||||
−0.188187 | + | 0.982133i | \(0.560261\pi\) | |||||||
\(854\) | −28.7593 | −0.984123 | ||||||||
\(855\) | −64.2890 | −2.19864 | ||||||||
\(856\) | 23.0176 | 0.786726 | ||||||||
\(857\) | −21.7731 | −0.743754 | −0.371877 | − | 0.928282i | \(-0.621286\pi\) | ||||
−0.371877 | + | 0.928282i | \(0.621286\pi\) | |||||||
\(858\) | −5.24467 | −0.179050 | ||||||||
\(859\) | 23.3166 | 0.795552 | 0.397776 | − | 0.917483i | \(-0.369782\pi\) | ||||
0.397776 | + | 0.917483i | \(0.369782\pi\) | |||||||
\(860\) | −75.1817 | −2.56368 | ||||||||
\(861\) | −2.59843 | −0.0885544 | ||||||||
\(862\) | 46.7217 | 1.59135 | ||||||||
\(863\) | −33.2592 | −1.13216 | −0.566078 | − | 0.824351i | \(-0.691540\pi\) | ||||
−0.566078 | + | 0.824351i | \(0.691540\pi\) | |||||||
\(864\) | −13.4208 | −0.456584 | ||||||||
\(865\) | −64.4052 | −2.18984 | ||||||||
\(866\) | 24.7095 | 0.839663 | ||||||||
\(867\) | −5.50052 | −0.186807 | ||||||||
\(868\) | 41.2374 | 1.39969 | ||||||||
\(869\) | −5.81226 | −0.197167 | ||||||||
\(870\) | −2.07588 | −0.0703790 | ||||||||
\(871\) | 50.3650 | 1.70655 | ||||||||
\(872\) | 26.2359 | 0.888459 | ||||||||
\(873\) | −26.1609 | −0.885412 | ||||||||
\(874\) | 17.3633 | 0.587322 | ||||||||
\(875\) | 9.77453 | 0.330439 | ||||||||
\(876\) | 9.02703 | 0.304995 | ||||||||
\(877\) | 11.2534 | 0.380001 | 0.190000 | − | 0.981784i | \(-0.439151\pi\) | ||||
0.190000 | + | 0.981784i | \(0.439151\pi\) | |||||||
\(878\) | 39.4324 | 1.33078 | ||||||||
\(879\) | −1.92172 | −0.0648180 | ||||||||
\(880\) | −4.99806 | −0.168485 | ||||||||
\(881\) | −14.9883 | −0.504969 | −0.252484 | − | 0.967601i | \(-0.581248\pi\) | ||||
−0.252484 | + | 0.967601i | \(0.581248\pi\) | |||||||
\(882\) | −24.1386 | −0.812788 | ||||||||
\(883\) | −35.7353 | −1.20259 | −0.601294 | − | 0.799028i | \(-0.705348\pi\) | ||||
−0.601294 | + | 0.799028i | \(0.705348\pi\) | |||||||
\(884\) | −7.50712 | −0.252492 | ||||||||
\(885\) | 10.7735 | 0.362146 | ||||||||
\(886\) | 48.1533 | 1.61774 | ||||||||
\(887\) | −13.8883 | −0.466322 | −0.233161 | − | 0.972438i | \(-0.574907\pi\) | ||||
−0.233161 | + | 0.972438i | \(0.574907\pi\) | |||||||
\(888\) | −4.33269 | −0.145396 | ||||||||
\(889\) | −14.4326 | −0.484052 | ||||||||
\(890\) | −34.8459 | −1.16804 | ||||||||
\(891\) | 11.3338 | 0.379698 | ||||||||
\(892\) | 8.98737 | 0.300919 | ||||||||
\(893\) | 93.7312 | 3.13660 | ||||||||
\(894\) | −12.7845 | −0.427577 | ||||||||
\(895\) | 10.1598 | 0.339606 | ||||||||
\(896\) | −26.7152 | −0.892494 | ||||||||
\(897\) | −1.67455 | −0.0559117 | ||||||||
\(898\) | 40.2416 | 1.34288 | ||||||||
\(899\) | −7.79469 | −0.259967 | ||||||||
\(900\) | −26.2694 | −0.875646 | ||||||||
\(901\) | −4.36620 | −0.145459 | ||||||||
\(902\) | −13.7588 | −0.458117 | ||||||||
\(903\) | 5.32192 | 0.177102 | ||||||||
\(904\) | −20.6621 | −0.687211 | ||||||||
\(905\) | 9.14597 | 0.304022 | ||||||||
\(906\) | 14.1651 | 0.470604 | ||||||||
\(907\) | −46.1230 | −1.53149 | −0.765745 | − | 0.643145i | \(-0.777629\pi\) | ||||
−0.765745 | + | 0.643145i | \(0.777629\pi\) | |||||||
\(908\) | −80.8182 | −2.68205 | ||||||||
\(909\) | −53.4026 | −1.77125 | ||||||||
\(910\) | 58.0485 | 1.92429 | ||||||||
\(911\) | 44.3915 | 1.47076 | 0.735378 | − | 0.677657i | \(-0.237004\pi\) | ||||
0.735378 | + | 0.677657i | \(0.237004\pi\) | |||||||
\(912\) | −3.19891 | −0.105926 | ||||||||
\(913\) | −15.0395 | −0.497735 | ||||||||
\(914\) | 51.2735 | 1.69598 | ||||||||
\(915\) | −6.71357 | −0.221944 | ||||||||
\(916\) | −84.7856 | −2.80140 | ||||||||
\(917\) | −0.671212 | −0.0221654 | ||||||||
\(918\) | −2.15514 | −0.0711303 | ||||||||
\(919\) | 34.6558 | 1.14319 | 0.571595 | − | 0.820536i | \(-0.306325\pi\) | ||||
0.571595 | + | 0.820536i | \(0.306325\pi\) | |||||||
\(920\) | 5.92520 | 0.195348 | ||||||||
\(921\) | −2.58323 | −0.0851202 | ||||||||
\(922\) | 8.90649 | 0.293320 | ||||||||
\(923\) | −1.96210 | −0.0645834 | ||||||||
\(924\) | −2.44897 | −0.0805651 | ||||||||
\(925\) | 19.5855 | 0.643968 | ||||||||
\(926\) | −26.7078 | −0.877671 | ||||||||
\(927\) | −2.37320 | −0.0779462 | ||||||||
\(928\) | 6.93560 | 0.227672 | ||||||||
\(929\) | 15.0404 | 0.493459 | 0.246729 | − | 0.969084i | \(-0.420644\pi\) | ||||
0.246729 | + | 0.969084i | \(0.420644\pi\) | |||||||
\(930\) | 16.1809 | 0.530591 | ||||||||
\(931\) | −29.3512 | −0.961948 | ||||||||
\(932\) | −62.2386 | −2.03869 | ||||||||
\(933\) | −6.66666 | −0.218257 | ||||||||
\(934\) | −62.6320 | −2.04938 | ||||||||
\(935\) | −2.00973 | −0.0657251 | ||||||||
\(936\) | 30.7162 | 1.00399 | ||||||||
\(937\) | 47.2748 | 1.54440 | 0.772201 | − | 0.635378i | \(-0.219156\pi\) | ||||
0.772201 | + | 0.635378i | \(0.219156\pi\) | |||||||
\(938\) | 39.5302 | 1.29071 | ||||||||
\(939\) | −8.02988 | −0.262045 | ||||||||
\(940\) | 100.230 | 3.26913 | ||||||||
\(941\) | 4.38264 | 0.142870 | 0.0714351 | − | 0.997445i | \(-0.477242\pi\) | ||||
0.0714351 | + | 0.997445i | \(0.477242\pi\) | |||||||
\(942\) | −10.5880 | −0.344977 | ||||||||
\(943\) | −4.39300 | −0.143056 | ||||||||
\(944\) | −14.3747 | −0.467857 | ||||||||
\(945\) | 9.91420 | 0.322509 | ||||||||
\(946\) | 28.1797 | 0.916201 | ||||||||
\(947\) | −53.8299 | −1.74924 | −0.874619 | − | 0.484811i | \(-0.838888\pi\) | ||||
−0.874619 | + | 0.484811i | \(0.838888\pi\) | |||||||
\(948\) | −3.97793 | −0.129197 | ||||||||
\(949\) | 47.7135 | 1.54884 | ||||||||
\(950\) | −53.6908 | −1.74196 | ||||||||
\(951\) | 2.44298 | 0.0792192 | ||||||||
\(952\) | −1.88033 | −0.0609417 | ||||||||
\(953\) | −31.2581 | −1.01255 | −0.506275 | − | 0.862372i | \(-0.668978\pi\) | ||||
−0.506275 | + | 0.862372i | \(0.668978\pi\) | |||||||
\(954\) | 55.9809 | 1.81245 | ||||||||
\(955\) | −59.0283 | −1.91011 | ||||||||
\(956\) | 57.1449 | 1.84820 | ||||||||
\(957\) | 0.462904 | 0.0149636 | ||||||||
\(958\) | 39.3871 | 1.27254 | ||||||||
\(959\) | −20.9857 | −0.677664 | ||||||||
\(960\) | −12.0684 | −0.389507 | ||||||||
\(961\) | 29.7571 | 0.959908 | ||||||||
\(962\) | −71.7620 | −2.31370 | ||||||||
\(963\) | 31.9603 | 1.02991 | ||||||||
\(964\) | −20.1806 | −0.649974 | ||||||||
\(965\) | −7.04888 | −0.226912 | ||||||||
\(966\) | −1.31432 | −0.0422874 | ||||||||
\(967\) | 10.1582 | 0.326665 | 0.163332 | − | 0.986571i | \(-0.447776\pi\) | ||||
0.163332 | + | 0.986571i | \(0.447776\pi\) | |||||||
\(968\) | 18.7738 | 0.603412 | ||||||||
\(969\) | −1.28629 | −0.0413214 | ||||||||
\(970\) | −57.1761 | −1.83581 | ||||||||
\(971\) | −52.2495 | −1.67677 | −0.838383 | − | 0.545082i | \(-0.816499\pi\) | ||||
−0.838383 | + | 0.545082i | \(0.816499\pi\) | |||||||
\(972\) | 24.8090 | 0.795749 | ||||||||
\(973\) | 20.9139 | 0.670470 | ||||||||
\(974\) | −42.3249 | −1.35618 | ||||||||
\(975\) | 5.17806 | 0.165831 | ||||||||
\(976\) | 8.95771 | 0.286729 | ||||||||
\(977\) | 5.14710 | 0.164670 | 0.0823352 | − | 0.996605i | \(-0.473762\pi\) | ||||
0.0823352 | + | 0.996605i | \(0.473762\pi\) | |||||||
\(978\) | −0.528299 | −0.0168931 | ||||||||
\(979\) | 7.77034 | 0.248341 | ||||||||
\(980\) | −31.3862 | −1.00259 | ||||||||
\(981\) | 36.4289 | 1.16309 | ||||||||
\(982\) | 28.5850 | 0.912185 | ||||||||
\(983\) | 34.7181 | 1.10734 | 0.553668 | − | 0.832737i | \(-0.313228\pi\) | ||||
0.553668 | + | 0.832737i | \(0.313228\pi\) | |||||||
\(984\) | −3.00505 | −0.0957974 | ||||||||
\(985\) | −12.1507 | −0.387153 | ||||||||
\(986\) | 1.11374 | 0.0354686 | ||||||||
\(987\) | −7.09499 | −0.225836 | ||||||||
\(988\) | 117.037 | 3.72345 | ||||||||
\(989\) | 8.99740 | 0.286101 | ||||||||
\(990\) | 25.7675 | 0.818945 | ||||||||
\(991\) | −38.1511 | −1.21191 | −0.605954 | − | 0.795499i | \(-0.707209\pi\) | ||||
−0.605954 | + | 0.795499i | \(0.707209\pi\) | |||||||
\(992\) | −54.0608 | −1.71643 | ||||||||
\(993\) | −2.29581 | −0.0728553 | ||||||||
\(994\) | −1.54001 | −0.0488460 | ||||||||
\(995\) | −58.0070 | −1.83895 | ||||||||
\(996\) | −10.2931 | −0.326149 | ||||||||
\(997\) | −53.7247 | −1.70148 | −0.850740 | − | 0.525588i | \(-0.823846\pi\) | ||||
−0.850740 | + | 0.525588i | \(0.823846\pi\) | |||||||
\(998\) | −11.8925 | −0.376451 | ||||||||
\(999\) | −12.2564 | −0.387774 |
(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 | 667.2.a.c.1.2 | ✓ | 13 | |
3.2 | odd | 2 | 6003.2.a.o.1.12 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.c.1.2 | ✓ | 13 | 1.1 | even | 1 | trivial | |
6003.2.a.o.1.12 | 13 | 3.2 | odd | 2 |