Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4527,2,Mod(1,4527)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4527, 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("4527.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4527 = 3^{2} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4527.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: | \(36.1482769950\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.07636\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4527.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37178 | 0.969995 | 0.484998 | − | 0.874515i | \(-0.338820\pi\) | ||||
0.484998 | + | 0.874515i | \(0.338820\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.118218 | −0.0591089 | ||||||||
\(5\) | −1.17276 | −0.524472 | −0.262236 | − | 0.965004i | \(-0.584460\pi\) | ||||
−0.262236 | + | 0.965004i | \(0.584460\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.469303 | 0.177380 | 0.0886899 | − | 0.996059i | \(-0.471732\pi\) | ||||
0.0886899 | + | 0.996059i | \(0.471732\pi\) | |||||||
\(8\) | −2.90573 | −1.02733 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.60876 | −0.508736 | ||||||||
\(11\) | 5.74596 | 1.73247 | 0.866237 | − | 0.499634i | \(-0.166532\pi\) | ||||
0.866237 | + | 0.499634i | \(0.166532\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.85873 | −0.515518 | −0.257759 | − | 0.966209i | \(-0.582984\pi\) | ||||
−0.257759 | + | 0.966209i | \(0.582984\pi\) | |||||||
\(14\) | 0.643780 | 0.172058 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.74959 | −0.937397 | ||||||||
\(17\) | −5.22916 | −1.26826 | −0.634129 | − | 0.773228i | \(-0.718641\pi\) | ||||
−0.634129 | + | 0.773228i | \(0.718641\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.12602 | 0.487743 | 0.243872 | − | 0.969808i | \(-0.421582\pi\) | ||||
0.243872 | + | 0.969808i | \(0.421582\pi\) | |||||||
\(20\) | 0.138641 | 0.0310010 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.88220 | 1.68049 | ||||||||
\(23\) | −0.171951 | −0.0358543 | −0.0179271 | − | 0.999839i | \(-0.505707\pi\) | ||||
−0.0179271 | + | 0.999839i | \(0.505707\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.62464 | −0.724929 | ||||||||
\(26\) | −2.54977 | −0.500050 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0554799 | −0.0104847 | ||||||||
\(29\) | 6.19149 | 1.14973 | 0.574865 | − | 0.818248i | \(-0.305054\pi\) | ||||
0.574865 | + | 0.818248i | \(0.305054\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.396234 | −0.0711658 | −0.0355829 | − | 0.999367i | \(-0.511329\pi\) | ||||
−0.0355829 | + | 0.999367i | \(0.511329\pi\) | |||||||
\(32\) | 0.667846 | 0.118060 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.17326 | −1.23020 | ||||||||
\(35\) | −0.550377 | −0.0930307 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.17999 | −1.34478 | −0.672391 | − | 0.740196i | \(-0.734733\pi\) | ||||
−0.672391 | + | 0.740196i | \(0.734733\pi\) | |||||||
\(38\) | 2.91644 | 0.473109 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.40771 | 0.538807 | ||||||||
\(41\) | 12.4282 | 1.94095 | 0.970477 | − | 0.241193i | \(-0.0775388\pi\) | ||||
0.970477 | + | 0.241193i | \(0.0775388\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.97920 | −0.759321 | −0.379661 | − | 0.925126i | \(-0.623959\pi\) | ||||
−0.379661 | + | 0.925126i | \(0.623959\pi\) | |||||||
\(44\) | −0.679275 | −0.102405 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.235879 | −0.0347785 | ||||||||
\(47\) | 0.521599 | 0.0760831 | 0.0380415 | − | 0.999276i | \(-0.487888\pi\) | ||||
0.0380415 | + | 0.999276i | \(0.487888\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.77976 | −0.968536 | ||||||||
\(50\) | −4.97222 | −0.703178 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.219735 | 0.0304717 | ||||||||
\(53\) | −8.76106 | −1.20342 | −0.601712 | − | 0.798713i | \(-0.705514\pi\) | ||||
−0.601712 | + | 0.798713i | \(0.705514\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.73861 | −0.908634 | ||||||||
\(56\) | −1.36367 | −0.182228 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.49336 | 1.11523 | ||||||||
\(59\) | −3.35297 | −0.436519 | −0.218260 | − | 0.975891i | \(-0.570038\pi\) | ||||
−0.218260 | + | 0.975891i | \(0.570038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.38243 | −0.689150 | −0.344575 | − | 0.938759i | \(-0.611977\pi\) | ||||
−0.344575 | + | 0.938759i | \(0.611977\pi\) | |||||||
\(62\) | −0.543546 | −0.0690305 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.41532 | 1.05191 | ||||||||
\(65\) | 2.17983 | 0.270375 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.42823 | 1.02967 | 0.514836 | − | 0.857289i | \(-0.327853\pi\) | ||||
0.514836 | + | 0.857289i | \(0.327853\pi\) | |||||||
\(68\) | 0.618179 | 0.0749653 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.754997 | −0.0902394 | ||||||||
\(71\) | −7.47643 | −0.887289 | −0.443644 | − | 0.896203i | \(-0.646315\pi\) | ||||
−0.443644 | + | 0.896203i | \(0.646315\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.60009 | −0.538400 | −0.269200 | − | 0.963084i | \(-0.586759\pi\) | ||||
−0.269200 | + | 0.963084i | \(0.586759\pi\) | |||||||
\(74\) | −11.2212 | −1.30443 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.251334 | −0.0288299 | ||||||||
\(77\) | 2.69660 | 0.307306 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.1992 | −1.93506 | −0.967530 | − | 0.252758i | \(-0.918662\pi\) | ||||
−0.967530 | + | 0.252758i | \(0.918662\pi\) | |||||||
\(80\) | 4.39735 | 0.491639 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 17.0487 | 1.88272 | ||||||||
\(83\) | −5.97721 | −0.656084 | −0.328042 | − | 0.944663i | \(-0.606389\pi\) | ||||
−0.328042 | + | 0.944663i | \(0.606389\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.13253 | 0.665166 | ||||||||
\(86\) | −6.83038 | −0.736538 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −16.6962 | −1.77982 | ||||||||
\(89\) | 4.25595 | 0.451130 | 0.225565 | − | 0.974228i | \(-0.427577\pi\) | ||||
0.225565 | + | 0.974228i | \(0.427577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.872306 | −0.0914425 | ||||||||
\(92\) | 0.0203277 | 0.00211930 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.715520 | 0.0738002 | ||||||||
\(95\) | −2.49331 | −0.255808 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.64532 | −0.268592 | −0.134296 | − | 0.990941i | \(-0.542877\pi\) | ||||
−0.134296 | + | 0.990941i | \(0.542877\pi\) | |||||||
\(98\) | −9.30034 | −0.939476 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.428497 | 0.0428497 | ||||||||
\(101\) | −6.39045 | −0.635873 | −0.317937 | − | 0.948112i | \(-0.602990\pi\) | ||||
−0.317937 | + | 0.948112i | \(0.602990\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.6014 | −1.63578 | −0.817890 | − | 0.575375i | \(-0.804856\pi\) | ||||
−0.817890 | + | 0.575375i | \(0.804856\pi\) | |||||||
\(104\) | 5.40096 | 0.529608 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.0182 | −1.16732 | ||||||||
\(107\) | −9.15760 | −0.885299 | −0.442649 | − | 0.896695i | \(-0.645961\pi\) | ||||
−0.442649 | + | 0.896695i | \(0.645961\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.51891 | 0.624398 | 0.312199 | − | 0.950017i | \(-0.398934\pi\) | ||||
0.312199 | + | 0.950017i | \(0.398934\pi\) | |||||||
\(110\) | −9.24390 | −0.881371 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.75969 | −0.166275 | ||||||||
\(113\) | −1.36694 | −0.128591 | −0.0642954 | − | 0.997931i | \(-0.520480\pi\) | ||||
−0.0642954 | + | 0.997931i | \(0.520480\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.201656 | 0.0188046 | ||||||||
\(116\) | −0.731944 | −0.0679593 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.59954 | −0.423422 | ||||||||
\(119\) | −2.45406 | −0.224963 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22.0161 | 2.00146 | ||||||||
\(122\) | −7.38352 | −0.668473 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0468419 | 0.00420653 | ||||||||
\(125\) | 10.1146 | 0.904677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.77469 | 0.601157 | 0.300578 | − | 0.953757i | \(-0.402820\pi\) | ||||
0.300578 | + | 0.953757i | \(0.402820\pi\) | |||||||
\(128\) | 10.2083 | 0.902293 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.99025 | 0.262263 | ||||||||
\(131\) | −16.6839 | −1.45768 | −0.728838 | − | 0.684687i | \(-0.759939\pi\) | ||||
−0.728838 | + | 0.684687i | \(0.759939\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.997748 | 0.0865158 | ||||||||
\(134\) | 11.5617 | 0.998777 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.1945 | 1.30292 | ||||||||
\(137\) | −13.0662 | −1.11632 | −0.558162 | − | 0.829732i | \(-0.688493\pi\) | ||||
−0.558162 | + | 0.829732i | \(0.688493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8468 | −0.920017 | −0.460008 | − | 0.887915i | \(-0.652154\pi\) | ||||
−0.460008 | + | 0.887915i | \(0.652154\pi\) | |||||||
\(140\) | 0.0650644 | 0.00549894 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.2560 | −0.860666 | ||||||||
\(143\) | −10.6802 | −0.893122 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.26110 | −0.603002 | ||||||||
\(146\) | −6.31032 | −0.522245 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.967020 | 0.0794886 | ||||||||
\(149\) | −0.0210826 | −0.00172716 | −0.000863578 | − | 1.00000i | \(-0.500275\pi\) | ||||
−0.000863578 | 1.00000i | \(0.500275\pi\) | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.1704 | 1.23455 | 0.617276 | − | 0.786746i | \(-0.288236\pi\) | ||||
0.617276 | + | 0.786746i | \(0.288236\pi\) | |||||||
\(152\) | −6.17765 | −0.501074 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.69914 | 0.298085 | ||||||||
\(155\) | 0.464686 | 0.0373245 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.1437 | 0.889367 | 0.444684 | − | 0.895688i | \(-0.353316\pi\) | ||||
0.444684 | + | 0.895688i | \(0.353316\pi\) | |||||||
\(158\) | −23.5935 | −1.87700 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.783221 | −0.0619190 | ||||||||
\(161\) | −0.0806970 | −0.00635982 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3388 | −0.809797 | −0.404899 | − | 0.914362i | \(-0.632693\pi\) | ||||
−0.404899 | + | 0.914362i | \(0.632693\pi\) | |||||||
\(164\) | −1.46923 | −0.114728 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.19942 | −0.636398 | ||||||||
\(167\) | 15.6444 | 1.21060 | 0.605300 | − | 0.795998i | \(-0.293053\pi\) | ||||
0.605300 | + | 0.795998i | \(0.293053\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.54513 | −0.734241 | ||||||||
\(170\) | 8.41248 | 0.645208 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.588630 | 0.0448826 | ||||||||
\(173\) | 5.69316 | 0.432843 | 0.216422 | − | 0.976300i | \(-0.430561\pi\) | ||||
0.216422 | + | 0.976300i | \(0.430561\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.70105 | −0.128588 | ||||||||
\(176\) | −21.5450 | −1.62402 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.83823 | 0.437594 | ||||||||
\(179\) | −10.8571 | −0.811495 | −0.405748 | − | 0.913985i | \(-0.632989\pi\) | ||||
−0.405748 | + | 0.913985i | \(0.632989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.26595 | 0.465744 | 0.232872 | − | 0.972507i | \(-0.425188\pi\) | ||||
0.232872 | + | 0.972507i | \(0.425188\pi\) | |||||||
\(182\) | −1.19661 | −0.0886988 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.499643 | 0.0368342 | ||||||||
\(185\) | 9.59313 | 0.705301 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.0466 | −2.19722 | ||||||||
\(188\) | −0.0616623 | −0.00449718 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.42027 | −0.248132 | ||||||||
\(191\) | −8.26296 | −0.597887 | −0.298943 | − | 0.954271i | \(-0.596634\pi\) | ||||
−0.298943 | + | 0.954271i | \(0.596634\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.8469 | −1.42861 | −0.714306 | − | 0.699833i | \(-0.753258\pi\) | ||||
−0.714306 | + | 0.699833i | \(0.753258\pi\) | |||||||
\(194\) | −3.62880 | −0.260533 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.801487 | 0.0572491 | ||||||||
\(197\) | 4.24866 | 0.302704 | 0.151352 | − | 0.988480i | \(-0.451637\pi\) | ||||
0.151352 | + | 0.988480i | \(0.451637\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.63286 | 0.328415 | 0.164207 | − | 0.986426i | \(-0.447493\pi\) | ||||
0.164207 | + | 0.986426i | \(0.447493\pi\) | |||||||
\(200\) | 10.5322 | 0.744742 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.76630 | −0.616794 | ||||||||
\(203\) | 2.90568 | 0.203939 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −14.5752 | −1.01798 | ||||||||
\(206\) | −22.7734 | −1.58670 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.96947 | 0.483246 | ||||||||
\(209\) | 12.2161 | 0.845002 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.2699 | 0.707007 | 0.353503 | − | 0.935433i | \(-0.384990\pi\) | ||||
0.353503 | + | 0.935433i | \(0.384990\pi\) | |||||||
\(212\) | 1.03571 | 0.0711330 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.5622 | −0.858736 | ||||||||
\(215\) | 5.83939 | 0.398243 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.185954 | −0.0126234 | ||||||||
\(218\) | 8.94251 | 0.605663 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.796624 | 0.0537083 | ||||||||
\(221\) | 9.71958 | 0.653810 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7887 | 0.990326 | 0.495163 | − | 0.868800i | \(-0.335108\pi\) | ||||
0.495163 | + | 0.868800i | \(0.335108\pi\) | |||||||
\(224\) | 0.313422 | 0.0209414 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.87514 | −0.124732 | ||||||||
\(227\) | −14.9154 | −0.989969 | −0.494984 | − | 0.868902i | \(-0.664826\pi\) | ||||
−0.494984 | + | 0.868902i | \(0.664826\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.2488 | −1.20592 | −0.602959 | − | 0.797772i | \(-0.706012\pi\) | ||||
−0.602959 | + | 0.797772i | \(0.706012\pi\) | |||||||
\(230\) | 0.276628 | 0.0182403 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.9908 | −1.18115 | ||||||||
\(233\) | 16.6741 | 1.09235 | 0.546177 | − | 0.837670i | \(-0.316082\pi\) | ||||
0.546177 | + | 0.837670i | \(0.316082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.611708 | −0.0399035 | ||||||||
\(236\) | 0.396380 | 0.0258022 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.36643 | −0.218213 | ||||||||
\(239\) | −24.3691 | −1.57631 | −0.788153 | − | 0.615479i | \(-0.788963\pi\) | ||||
−0.788153 | + | 0.615479i | \(0.788963\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1071 | 1.16638 | 0.583190 | − | 0.812336i | \(-0.301804\pi\) | ||||
0.583190 | + | 0.812336i | \(0.301804\pi\) | |||||||
\(242\) | 30.2013 | 1.94141 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.636299 | 0.0407349 | ||||||||
\(245\) | 7.95100 | 0.507971 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.95170 | −0.251441 | ||||||||
\(248\) | 1.15135 | 0.0731108 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.8750 | 0.877533 | ||||||||
\(251\) | −26.9687 | −1.70225 | −0.851124 | − | 0.524965i | \(-0.824078\pi\) | ||||
−0.851124 | + | 0.524965i | \(0.824078\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.988024 | −0.0621165 | ||||||||
\(254\) | 9.29340 | 0.583119 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.82712 | −0.176695 | ||||||||
\(257\) | −20.3022 | −1.26642 | −0.633208 | − | 0.773982i | \(-0.718262\pi\) | ||||
−0.633208 | + | 0.773982i | \(0.718262\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.83889 | −0.238537 | ||||||||
\(260\) | −0.257695 | −0.0159816 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −22.8866 | −1.41394 | ||||||||
\(263\) | 12.0595 | 0.743622 | 0.371811 | − | 0.928309i | \(-0.378737\pi\) | ||||
0.371811 | + | 0.928309i | \(0.378737\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.2746 | 0.631162 | ||||||||
\(266\) | 1.36869 | 0.0839199 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.996366 | −0.0608628 | ||||||||
\(269\) | 25.0120 | 1.52501 | 0.762506 | − | 0.646982i | \(-0.223969\pi\) | ||||
0.762506 | + | 0.646982i | \(0.223969\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.0354 | −1.09557 | −0.547787 | − | 0.836618i | \(-0.684530\pi\) | ||||
−0.547787 | + | 0.836618i | \(0.684530\pi\) | |||||||
\(272\) | 19.6072 | 1.18886 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.9240 | −1.08283 | ||||||||
\(275\) | −20.8271 | −1.25592 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.3688 | −1.76460 | −0.882301 | − | 0.470686i | \(-0.844006\pi\) | ||||
−0.882301 | + | 0.470686i | \(0.844006\pi\) | |||||||
\(278\) | −14.8795 | −0.892412 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.59925 | 0.0955733 | ||||||||
\(281\) | −12.0977 | −0.721686 | −0.360843 | − | 0.932626i | \(-0.617511\pi\) | ||||
−0.360843 | + | 0.932626i | \(0.617511\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.04149 | −0.478017 | −0.239009 | − | 0.971017i | \(-0.576822\pi\) | ||||
−0.239009 | + | 0.971017i | \(0.576822\pi\) | |||||||
\(284\) | 0.883846 | 0.0524466 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.6509 | −0.866324 | ||||||||
\(287\) | 5.83257 | 0.344286 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3441 | 0.608477 | ||||||||
\(290\) | −9.96064 | −0.584909 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.543812 | 0.0318242 | ||||||||
\(293\) | 13.5236 | 0.790056 | 0.395028 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395028 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.93221 | 0.228942 | ||||||||
\(296\) | 23.7688 | 1.38154 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.0289207 | −0.00167533 | ||||||||
\(299\) | 0.319610 | 0.0184835 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.33675 | −0.134688 | ||||||||
\(302\) | 20.8105 | 1.19751 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7.97171 | −0.457209 | ||||||||
\(305\) | 6.31228 | 0.361440 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.60632 | 0.205824 | 0.102912 | − | 0.994690i | \(-0.467184\pi\) | ||||
0.102912 | + | 0.994690i | \(0.467184\pi\) | |||||||
\(308\) | −0.318785 | −0.0181645 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.637447 | 0.0362046 | ||||||||
\(311\) | 27.5438 | 1.56187 | 0.780934 | − | 0.624613i | \(-0.214743\pi\) | ||||
0.780934 | + | 0.624613i | \(0.214743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.2190 | −1.70808 | −0.854039 | − | 0.520209i | \(-0.825854\pi\) | ||||
−0.854039 | + | 0.520209i | \(0.825854\pi\) | |||||||
\(314\) | 15.2868 | 0.862682 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.03325 | 0.114379 | ||||||||
\(317\) | 5.23152 | 0.293831 | 0.146916 | − | 0.989149i | \(-0.453065\pi\) | ||||
0.146916 | + | 0.989149i | \(0.453065\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.5761 | 1.99188 | ||||||||
\(320\) | −9.86911 | −0.551700 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.110699 | −0.00616899 | ||||||||
\(323\) | −11.1173 | −0.618584 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.73723 | 0.373714 | ||||||||
\(326\) | −14.1826 | −0.785500 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −36.1129 | −1.99400 | ||||||||
\(329\) | 0.244788 | 0.0134956 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.56111 | −0.305666 | −0.152833 | − | 0.988252i | \(-0.548840\pi\) | ||||
−0.152833 | + | 0.988252i | \(0.548840\pi\) | |||||||
\(332\) | 0.706612 | 0.0387804 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 21.4607 | 1.17428 | ||||||||
\(335\) | −9.88426 | −0.540035 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.20314 | 0.0655392 | 0.0327696 | − | 0.999463i | \(-0.489567\pi\) | ||||
0.0327696 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(338\) | −13.0938 | −0.712210 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.724973 | −0.0393172 | ||||||||
\(341\) | −2.27675 | −0.123293 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.46688 | −0.349178 | ||||||||
\(344\) | 14.4682 | 0.780074 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.80977 | 0.419856 | ||||||||
\(347\) | −18.8760 | −1.01332 | −0.506659 | − | 0.862147i | \(-0.669120\pi\) | ||||
−0.506659 | + | 0.862147i | \(0.669120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.3633 | 0.982966 | 0.491483 | − | 0.870887i | \(-0.336455\pi\) | ||||
0.491483 | + | 0.870887i | \(0.336455\pi\) | |||||||
\(350\) | −2.33347 | −0.124729 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.83742 | 0.204535 | ||||||||
\(353\) | 2.06519 | 0.109919 | 0.0549596 | − | 0.998489i | \(-0.482497\pi\) | ||||
0.0549596 | + | 0.998489i | \(0.482497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.76802 | 0.465358 | ||||||||
\(356\) | −0.503129 | −0.0266658 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.8935 | −0.787147 | ||||||||
\(359\) | 7.83605 | 0.413571 | 0.206786 | − | 0.978386i | \(-0.433700\pi\) | ||||
0.206786 | + | 0.978386i | \(0.433700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4800 | −0.762107 | ||||||||
\(362\) | 8.59550 | 0.451770 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.103122 | 0.00540506 | ||||||||
\(365\) | 5.39478 | 0.282376 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.3479 | 1.42755 | 0.713775 | − | 0.700375i | \(-0.246984\pi\) | ||||
0.713775 | + | 0.700375i | \(0.246984\pi\) | |||||||
\(368\) | 0.644745 | 0.0336097 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 13.1597 | 0.684139 | ||||||||
\(371\) | −4.11159 | −0.213463 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.3381 | 1.62263 | 0.811313 | − | 0.584612i | \(-0.198753\pi\) | ||||
0.811313 | + | 0.584612i | \(0.198753\pi\) | |||||||
\(374\) | −41.2173 | −2.13130 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.51563 | −0.0781625 | ||||||||
\(377\) | −11.5083 | −0.592707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.97192 | −0.101291 | −0.0506454 | − | 0.998717i | \(-0.516128\pi\) | ||||
−0.0506454 | + | 0.998717i | \(0.516128\pi\) | |||||||
\(380\) | 0.294753 | 0.0151205 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.3350 | −0.579948 | ||||||||
\(383\) | 24.9455 | 1.27466 | 0.637328 | − | 0.770593i | \(-0.280040\pi\) | ||||
0.637328 | + | 0.770593i | \(0.280040\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.16245 | −0.161173 | ||||||||
\(386\) | −27.2256 | −1.38575 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.312724 | 0.0158761 | ||||||||
\(389\) | 8.98152 | 0.455381 | 0.227691 | − | 0.973734i | \(-0.426883\pi\) | ||||
0.227691 | + | 0.973734i | \(0.426883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.899159 | 0.0454724 | ||||||||
\(392\) | 19.7001 | 0.995007 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.82822 | 0.293622 | ||||||||
\(395\) | 20.1704 | 1.01488 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3125 | −0.517569 | −0.258784 | − | 0.965935i | \(-0.583322\pi\) | ||||
−0.258784 | + | 0.965935i | \(0.583322\pi\) | |||||||
\(398\) | 6.35527 | 0.318561 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.5909 | 0.679546 | ||||||||
\(401\) | 22.2691 | 1.11207 | 0.556033 | − | 0.831160i | \(-0.312323\pi\) | ||||
0.556033 | + | 0.831160i | \(0.312323\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.736492 | 0.0366873 | ||||||||
\(404\) | 0.755464 | 0.0375858 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.98596 | 0.197820 | ||||||||
\(407\) | −47.0019 | −2.32980 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.36108 | −0.462876 | −0.231438 | − | 0.972850i | \(-0.574343\pi\) | ||||
−0.231438 | + | 0.972850i | \(0.574343\pi\) | |||||||
\(410\) | −19.9940 | −0.987433 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.96257 | 0.0966891 | ||||||||
\(413\) | −1.57356 | −0.0774297 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.00980 | 0.344098 | ||||||||
\(416\) | −1.24134 | −0.0608619 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.7578 | 0.819648 | ||||||||
\(419\) | 34.9797 | 1.70887 | 0.854436 | − | 0.519557i | \(-0.173903\pi\) | ||||
0.854436 | + | 0.519557i | \(0.173903\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.9244 | 0.776107 | 0.388054 | − | 0.921637i | \(-0.373147\pi\) | ||||
0.388054 | + | 0.921637i | \(0.373147\pi\) | |||||||
\(422\) | 14.0880 | 0.685793 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 25.4573 | 1.23631 | ||||||||
\(425\) | 18.9538 | 0.919396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.52599 | −0.122241 | ||||||||
\(428\) | 1.08259 | 0.0523290 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.01036 | 0.386294 | ||||||||
\(431\) | 37.5257 | 1.80755 | 0.903775 | − | 0.428008i | \(-0.140785\pi\) | ||||
0.903775 | + | 0.428008i | \(0.140785\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.7776 | 1.33491 | 0.667454 | − | 0.744651i | \(-0.267384\pi\) | ||||
0.667454 | + | 0.744651i | \(0.267384\pi\) | |||||||
\(434\) | −0.255088 | −0.0122446 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.770651 | −0.0369075 | ||||||||
\(437\) | −0.365572 | −0.0174877 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.3507 | 1.78265 | 0.891327 | − | 0.453362i | \(-0.149775\pi\) | ||||
0.891327 | + | 0.453362i | \(0.149775\pi\) | |||||||
\(440\) | 19.5806 | 0.933468 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 13.3331 | 0.634193 | ||||||||
\(443\) | −15.8245 | −0.751844 | −0.375922 | − | 0.926651i | \(-0.622674\pi\) | ||||
−0.375922 | + | 0.926651i | \(0.622674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.99119 | −0.236605 | ||||||||
\(446\) | 20.2869 | 0.960612 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.94933 | 0.186588 | ||||||||
\(449\) | 33.0395 | 1.55923 | 0.779616 | − | 0.626258i | \(-0.215414\pi\) | ||||
0.779616 | + | 0.626258i | \(0.215414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 71.4118 | 3.36265 | ||||||||
\(452\) | 0.161596 | 0.00760086 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20.4606 | −0.960265 | ||||||||
\(455\) | 1.02300 | 0.0479591 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.38585 | −0.298717 | −0.149359 | − | 0.988783i | \(-0.547721\pi\) | ||||
−0.149359 | + | 0.988783i | \(0.547721\pi\) | |||||||
\(458\) | −25.0334 | −1.16973 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0238394 | −0.00111152 | ||||||||
\(461\) | −4.10510 | −0.191193 | −0.0955967 | − | 0.995420i | \(-0.530476\pi\) | ||||
−0.0955967 | + | 0.995420i | \(0.530476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.9482 | −1.02002 | −0.510011 | − | 0.860168i | \(-0.670359\pi\) | ||||
−0.510011 | + | 0.860168i | \(0.670359\pi\) | |||||||
\(464\) | −23.2155 | −1.07775 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.8732 | 1.05958 | ||||||||
\(467\) | 20.9539 | 0.969633 | 0.484816 | − | 0.874616i | \(-0.338886\pi\) | ||||
0.484816 | + | 0.874616i | \(0.338886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.95539 | 0.182643 | ||||||||
\(470\) | −0.839130 | −0.0387062 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.74282 | 0.448450 | ||||||||
\(473\) | −28.6103 | −1.31550 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.70608 | −0.353579 | ||||||||
\(476\) | 0.290113 | 0.0132973 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −33.4291 | −1.52901 | ||||||||
\(479\) | −40.1617 | −1.83503 | −0.917517 | − | 0.397698i | \(-0.869809\pi\) | ||||
−0.917517 | + | 0.397698i | \(0.869809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.2044 | 0.693260 | ||||||||
\(482\) | 24.8389 | 1.13138 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.60269 | −0.118304 | ||||||||
\(485\) | 3.10232 | 0.140869 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.56804 | −0.0710547 | −0.0355273 | − | 0.999369i | \(-0.511311\pi\) | ||||
−0.0355273 | + | 0.999369i | \(0.511311\pi\) | |||||||
\(488\) | 15.6399 | 0.707985 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.9070 | 0.492729 | ||||||||
\(491\) | −9.66243 | −0.436059 | −0.218030 | − | 0.975942i | \(-0.569963\pi\) | ||||
−0.218030 | + | 0.975942i | \(0.569963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.3763 | −1.45815 | ||||||||
\(494\) | −5.42086 | −0.243896 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.48572 | 0.0667106 | ||||||||
\(497\) | −3.50871 | −0.157387 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.6363 | −0.923810 | −0.461905 | − | 0.886930i | \(-0.652834\pi\) | ||||
−0.461905 | + | 0.886930i | \(0.652834\pi\) | |||||||
\(500\) | −1.19573 | −0.0534745 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −36.9951 | −1.65117 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.49444 | 0.333498 | ||||||||
\(506\) | −1.35535 | −0.0602528 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.800889 | −0.0355337 | ||||||||
\(509\) | 23.3284 | 1.03401 | 0.517006 | − | 0.855982i | \(-0.327047\pi\) | ||||
0.517006 | + | 0.855982i | \(0.327047\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.15883 | −0.0955012 | ||||||||
\(512\) | −24.2947 | −1.07369 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.8501 | −1.22842 | ||||||||
\(515\) | 19.4693 | 0.857921 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.99709 | 0.131812 | ||||||||
\(518\) | −5.26612 | −0.231380 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.33401 | −0.277765 | ||||||||
\(521\) | 43.2647 | 1.89546 | 0.947730 | − | 0.319073i | \(-0.103371\pi\) | ||||
0.947730 | + | 0.319073i | \(0.103371\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.4082 | −1.89811 | −0.949054 | − | 0.315112i | \(-0.897958\pi\) | ||||
−0.949054 | + | 0.315112i | \(0.897958\pi\) | |||||||
\(524\) | 1.97233 | 0.0861615 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.5430 | 0.721310 | ||||||||
\(527\) | 2.07197 | 0.0902565 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9704 | −0.998714 | ||||||||
\(530\) | 14.0945 | 0.612225 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.117952 | −0.00511385 | ||||||||
\(533\) | −23.1006 | −1.00060 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.7396 | 0.464315 | ||||||||
\(536\) | −24.4902 | −1.05781 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.3110 | 1.47925 | ||||||||
\(539\) | −38.9562 | −1.67796 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.5657 | 1.40011 | 0.700054 | − | 0.714090i | \(-0.253159\pi\) | ||||
0.700054 | + | 0.714090i | \(0.253159\pi\) | |||||||
\(542\) | −24.7406 | −1.06270 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.49228 | −0.149730 | ||||||||
\(545\) | −7.64509 | −0.327480 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.8377 | 1.19025 | 0.595127 | − | 0.803631i | \(-0.297102\pi\) | ||||
0.595127 | + | 0.803631i | \(0.297102\pi\) | |||||||
\(548\) | 1.54466 | 0.0659847 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −28.5702 | −1.21824 | ||||||||
\(551\) | 13.1633 | 0.560773 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.07162 | −0.343240 | ||||||||
\(554\) | −40.2876 | −1.71166 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.28229 | 0.0543811 | ||||||||
\(557\) | −15.7225 | −0.666182 | −0.333091 | − | 0.942895i | \(-0.608092\pi\) | ||||
−0.333091 | + | 0.942895i | \(0.608092\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.25498 | 0.391444 | ||||||||
\(560\) | 2.06369 | 0.0872068 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.5953 | −0.700033 | ||||||||
\(563\) | 24.7817 | 1.04442 | 0.522212 | − | 0.852816i | \(-0.325107\pi\) | ||||
0.522212 | + | 0.852816i | \(0.325107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.60309 | 0.0674423 | ||||||||
\(566\) | −11.0312 | −0.463674 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.7245 | 0.911539 | ||||||||
\(569\) | −2.95346 | −0.123816 | −0.0619078 | − | 0.998082i | \(-0.519718\pi\) | ||||
−0.0619078 | + | 0.998082i | \(0.519718\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.7926 | −0.451656 | −0.225828 | − | 0.974167i | \(-0.572509\pi\) | ||||
−0.225828 | + | 0.974167i | \(0.572509\pi\) | |||||||
\(572\) | 1.26259 | 0.0527914 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.00101 | 0.333956 | ||||||||
\(575\) | 0.623261 | 0.0259918 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.92593 | −0.246700 | −0.123350 | − | 0.992363i | \(-0.539364\pi\) | ||||
−0.123350 | + | 0.992363i | \(0.539364\pi\) | |||||||
\(578\) | 14.1898 | 0.590220 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.858391 | 0.0356428 | ||||||||
\(581\) | −2.80512 | −0.116376 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −50.3407 | −2.08490 | ||||||||
\(584\) | 13.3666 | 0.553115 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.5514 | 0.766350 | ||||||||
\(587\) | 14.8090 | 0.611234 | 0.305617 | − | 0.952155i | \(-0.401137\pi\) | ||||
0.305617 | + | 0.952155i | \(0.401137\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.842403 | −0.0347106 | ||||||||
\(590\) | 5.39414 | 0.222073 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 30.6716 | 1.26060 | ||||||||
\(593\) | −33.4465 | −1.37348 | −0.686741 | − | 0.726902i | \(-0.740959\pi\) | ||||
−0.686741 | + | 0.726902i | \(0.740959\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.87801 | 0.117987 | ||||||||
\(596\) | 0.00249234 | 0.000102090 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.438435 | 0.0179289 | ||||||||
\(599\) | −9.35823 | −0.382367 | −0.191183 | − | 0.981554i | \(-0.561233\pi\) | ||||
−0.191183 | + | 0.981554i | \(0.561233\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.16182 | −0.251346 | −0.125673 | − | 0.992072i | \(-0.540109\pi\) | ||||
−0.125673 | + | 0.992072i | \(0.540109\pi\) | |||||||
\(602\) | −3.20551 | −0.130647 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.79341 | −0.0729730 | ||||||||
\(605\) | −25.8195 | −1.04971 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.7361 | 1.45048 | 0.725242 | − | 0.688494i | \(-0.241728\pi\) | ||||
0.725242 | + | 0.688494i | \(0.241728\pi\) | |||||||
\(608\) | 1.41986 | 0.0575828 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.65907 | 0.350595 | ||||||||
\(611\) | −0.969511 | −0.0392222 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.96528 | −0.0793771 | −0.0396885 | − | 0.999212i | \(-0.512637\pi\) | ||||
−0.0396885 | + | 0.999212i | \(0.512637\pi\) | |||||||
\(614\) | 4.94708 | 0.199648 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.83558 | −0.315705 | ||||||||
\(617\) | 35.4461 | 1.42701 | 0.713503 | − | 0.700652i | \(-0.247107\pi\) | ||||
0.713503 | + | 0.700652i | \(0.247107\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.4643 | −1.38524 | −0.692618 | − | 0.721304i | \(-0.743543\pi\) | ||||
−0.692618 | + | 0.721304i | \(0.743543\pi\) | |||||||
\(620\) | −0.0549341 | −0.00220621 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 37.7841 | 1.51501 | ||||||||
\(623\) | 1.99733 | 0.0800213 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.26126 | 0.250451 | ||||||||
\(626\) | −41.4538 | −1.65683 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.31739 | −0.0525695 | ||||||||
\(629\) | 42.7745 | 1.70553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.7560 | −1.18457 | −0.592284 | − | 0.805729i | \(-0.701774\pi\) | ||||
−0.592284 | + | 0.805729i | \(0.701774\pi\) | |||||||
\(632\) | 49.9762 | 1.98795 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.17650 | 0.285015 | ||||||||
\(635\) | −7.94506 | −0.315290 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.6017 | 0.499298 | ||||||||
\(638\) | 48.8026 | 1.93211 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.9718 | −0.473228 | ||||||||
\(641\) | 32.9327 | 1.30077 | 0.650383 | − | 0.759607i | \(-0.274609\pi\) | ||||
0.650383 | + | 0.759607i | \(0.274609\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.492253 | −0.0194126 | −0.00970628 | − | 0.999953i | \(-0.503090\pi\) | ||||
−0.00970628 | + | 0.999953i | \(0.503090\pi\) | |||||||
\(644\) | 0.00953982 | 0.000375922 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.2505 | −0.600024 | ||||||||
\(647\) | −3.76376 | −0.147969 | −0.0739844 | − | 0.997259i | \(-0.523571\pi\) | ||||
−0.0739844 | + | 0.997259i | \(0.523571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.2660 | −0.756258 | ||||||||
\(650\) | 9.24200 | 0.362501 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.22223 | 0.0478662 | ||||||||
\(653\) | −18.5728 | −0.726809 | −0.363404 | − | 0.931631i | \(-0.618386\pi\) | ||||
−0.363404 | + | 0.931631i | \(0.618386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.5661 | 0.764510 | ||||||||
\(656\) | −46.6005 | −1.81945 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.335795 | 0.0130907 | ||||||||
\(659\) | 34.1930 | 1.33197 | 0.665985 | − | 0.745965i | \(-0.268012\pi\) | ||||
0.665985 | + | 0.745965i | \(0.268012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.5439 | 1.14912 | 0.574562 | − | 0.818461i | \(-0.305173\pi\) | ||||
0.574562 | + | 0.818461i | \(0.305173\pi\) | |||||||
\(662\) | −7.62862 | −0.296495 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.3682 | 0.674015 | ||||||||
\(665\) | −1.17012 | −0.0453751 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.06463 | −0.0412227 | ||||||||
\(668\) | −1.84944 | −0.0715572 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.5590 | −0.523831 | ||||||||
\(671\) | −30.9273 | −1.19393 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.15185 | −0.352778 | −0.176389 | − | 0.984321i | \(-0.556442\pi\) | ||||
−0.176389 | + | 0.984321i | \(0.556442\pi\) | |||||||
\(674\) | 1.65045 | 0.0635728 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.12840 | 0.0434001 | ||||||||
\(677\) | 33.1256 | 1.27312 | 0.636561 | − | 0.771227i | \(-0.280356\pi\) | ||||
0.636561 | + | 0.771227i | \(0.280356\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.24146 | −0.0476427 | ||||||||
\(680\) | −17.8195 | −0.683345 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.12320 | −0.119593 | ||||||||
\(683\) | −49.1452 | −1.88049 | −0.940245 | − | 0.340498i | \(-0.889404\pi\) | ||||
−0.940245 | + | 0.340498i | \(0.889404\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.3235 | 0.585481 | ||||||||
\(686\) | −8.87113 | −0.338701 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.6700 | 0.711786 | ||||||||
\(689\) | 16.2844 | 0.620387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.1013 | 1.29727 | 0.648637 | − | 0.761098i | \(-0.275339\pi\) | ||||
0.648637 | + | 0.761098i | \(0.275339\pi\) | |||||||
\(692\) | −0.673033 | −0.0255849 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −25.8938 | −0.982914 | ||||||||
\(695\) | 12.7207 | 0.482523 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −64.9889 | −2.46163 | ||||||||
\(698\) | 25.1904 | 0.953473 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.201095 | 0.00760067 | ||||||||
\(701\) | −26.2590 | −0.991787 | −0.495894 | − | 0.868383i | \(-0.665159\pi\) | ||||
−0.495894 | + | 0.868383i | \(0.665159\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.3909 | −0.655909 | ||||||||
\(704\) | 48.3541 | 1.82241 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.83299 | 0.106621 | ||||||||
\(707\) | −2.99905 | −0.112791 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.4811 | 1.06963 | 0.534815 | − | 0.844969i | \(-0.320381\pi\) | ||||
0.534815 | + | 0.844969i | \(0.320381\pi\) | |||||||
\(710\) | 12.0278 | 0.451395 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.3666 | −0.463460 | ||||||||
\(713\) | 0.0681329 | 0.00255160 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.5252 | 0.468418 | ||||||||
\(716\) | 1.28350 | 0.0479666 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.7493 | 0.401162 | ||||||||
\(719\) | −13.8368 | −0.516024 | −0.258012 | − | 0.966142i | \(-0.583067\pi\) | ||||
−0.258012 | + | 0.966142i | \(0.583067\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.79106 | −0.290154 | ||||||||
\(722\) | −19.8634 | −0.739240 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.740746 | −0.0275296 | ||||||||
\(725\) | −22.4419 | −0.833473 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.61759 | 0.356697 | 0.178348 | − | 0.983967i | \(-0.442925\pi\) | ||||
0.178348 | + | 0.983967i | \(0.442925\pi\) | |||||||
\(728\) | 2.53469 | 0.0939417 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.40046 | 0.273903 | ||||||||
\(731\) | 26.0370 | 0.963015 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.9530 | −0.626175 | −0.313087 | − | 0.949724i | \(-0.601363\pi\) | ||||
−0.313087 | + | 0.949724i | \(0.601363\pi\) | |||||||
\(734\) | 37.5153 | 1.38472 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.114837 | −0.00423294 | ||||||||
\(737\) | 48.4283 | 1.78388 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.82452 | 0.361401 | 0.180700 | − | 0.983538i | \(-0.442164\pi\) | ||||
0.180700 | + | 0.983538i | \(0.442164\pi\) | |||||||
\(740\) | −1.13408 | −0.0416895 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.64019 | −0.207058 | ||||||||
\(743\) | −28.8650 | −1.05896 | −0.529478 | − | 0.848324i | \(-0.677612\pi\) | ||||
−0.529478 | + | 0.848324i | \(0.677612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.0247248 | 0.000905845 0 | ||||||||
\(746\) | 42.9890 | 1.57394 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.55204 | 0.129875 | ||||||||
\(749\) | −4.29769 | −0.157034 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.70834 | −0.354262 | −0.177131 | − | 0.984187i | \(-0.556682\pi\) | ||||
−0.177131 | + | 0.984187i | \(0.556682\pi\) | |||||||
\(752\) | −1.95578 | −0.0713200 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −15.7869 | −0.574923 | ||||||||
\(755\) | −17.7912 | −0.647489 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.99476 | −0.217883 | −0.108942 | − | 0.994048i | \(-0.534746\pi\) | ||||
−0.108942 | + | 0.994048i | \(0.534746\pi\) | |||||||
\(758\) | −2.70505 | −0.0982517 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.24488 | 0.262799 | ||||||||
\(761\) | −15.4793 | −0.561123 | −0.280562 | − | 0.959836i | \(-0.590521\pi\) | ||||
−0.280562 | + | 0.959836i | \(0.590521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.05934 | 0.110756 | ||||||||
\(764\) | 0.976829 | 0.0353404 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34.2198 | 1.23641 | ||||||||
\(767\) | 6.23226 | 0.225034 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.9740 | −1.00877 | −0.504384 | − | 0.863480i | \(-0.668280\pi\) | ||||
−0.504384 | + | 0.863480i | \(0.668280\pi\) | |||||||
\(770\) | −4.33819 | −0.156337 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.34626 | 0.0844436 | ||||||||
\(773\) | −31.7330 | −1.14136 | −0.570679 | − | 0.821173i | \(-0.693320\pi\) | ||||
−0.570679 | + | 0.821173i | \(0.693320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.43621 | 0.0515901 | ||||||||
\(776\) | 7.68659 | 0.275932 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.3207 | 0.441718 | ||||||||
\(779\) | 26.4226 | 0.946687 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.9593 | −1.53720 | ||||||||
\(782\) | 1.23345 | 0.0441080 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25.4213 | 0.907903 | ||||||||
\(785\) | −13.0689 | −0.466448 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.1339 | 0.682051 | 0.341025 | − | 0.940054i | \(-0.389226\pi\) | ||||
0.341025 | + | 0.940054i | \(0.389226\pi\) | |||||||
\(788\) | −0.502266 | −0.0178925 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 27.6694 | 0.984434 | ||||||||
\(791\) | −0.641508 | −0.0228094 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0045 | 0.355270 | ||||||||
\(794\) | −14.1465 | −0.502039 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.547686 | −0.0194122 | ||||||||
\(797\) | 2.45993 | 0.0871352 | 0.0435676 | − | 0.999050i | \(-0.486128\pi\) | ||||
0.0435676 | + | 0.999050i | \(0.486128\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.72752 | −0.0964929 | ||||||||
\(800\) | −2.42071 | −0.0855849 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 30.5483 | 1.07870 | ||||||||
\(803\) | −26.4320 | −0.932764 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0946379 | 0.00333555 | ||||||||
\(806\) | 1.01031 | 0.0355865 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 18.5689 | 0.653252 | ||||||||
\(809\) | −16.9350 | −0.595404 | −0.297702 | − | 0.954659i | \(-0.596220\pi\) | ||||
−0.297702 | + | 0.954659i | \(0.596220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.7584 | −0.834269 | −0.417135 | − | 0.908845i | \(-0.636966\pi\) | ||||
−0.417135 | + | 0.908845i | \(0.636966\pi\) | |||||||
\(812\) | −0.343503 | −0.0120546 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −64.4764 | −2.25990 | ||||||||
\(815\) | 12.1249 | 0.424716 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.5859 | −0.370354 | ||||||||
\(818\) | −12.8413 | −0.448987 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.72305 | 0.0601714 | ||||||||
\(821\) | −19.2765 | −0.672755 | −0.336378 | − | 0.941727i | \(-0.609202\pi\) | ||||
−0.336378 | + | 0.941727i | \(0.609202\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.8192 | 1.84116 | 0.920580 | − | 0.390553i | \(-0.127716\pi\) | ||||
0.920580 | + | 0.390553i | \(0.127716\pi\) | |||||||
\(824\) | 48.2390 | 1.68049 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.15858 | −0.0751064 | ||||||||
\(827\) | 25.7144 | 0.894176 | 0.447088 | − | 0.894490i | \(-0.352461\pi\) | ||||
0.447088 | + | 0.894490i | \(0.352461\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.3380 | 0.810562 | 0.405281 | − | 0.914192i | \(-0.367174\pi\) | ||||
0.405281 | + | 0.914192i | \(0.367174\pi\) | |||||||
\(830\) | 9.61591 | 0.333773 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.6418 | −0.542281 | ||||||||
\(833\) | 35.4524 | 1.22835 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.3471 | −0.634926 | ||||||||
\(836\) | −1.44415 | −0.0499471 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 47.9845 | 1.65760 | ||||||||
\(839\) | −18.8028 | −0.649144 | −0.324572 | − | 0.945861i | \(-0.605220\pi\) | ||||
−0.324572 | + | 0.945861i | \(0.605220\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.33453 | 0.321880 | ||||||||
\(842\) | 21.8448 | 0.752821 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.21408 | −0.0417904 | ||||||||
\(845\) | 11.1941 | 0.385089 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.3322 | 0.355019 | ||||||||
\(848\) | 32.8504 | 1.12809 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 26.0005 | 0.891810 | ||||||||
\(851\) | 1.40656 | 0.0482162 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.0553 | −1.54266 | −0.771332 | − | 0.636433i | \(-0.780409\pi\) | ||||
−0.771332 | + | 0.636433i | \(0.780409\pi\) | |||||||
\(854\) | −3.46511 | −0.118573 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.6095 | 0.909495 | ||||||||
\(857\) | 33.4362 | 1.14216 | 0.571079 | − | 0.820895i | \(-0.306525\pi\) | ||||
0.571079 | + | 0.820895i | \(0.306525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.4483 | 0.663567 | 0.331784 | − | 0.943355i | \(-0.392350\pi\) | ||||
0.331784 | + | 0.943355i | \(0.392350\pi\) | |||||||
\(860\) | −0.690319 | −0.0235397 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 51.4770 | 1.75332 | ||||||||
\(863\) | 16.1628 | 0.550186 | 0.275093 | − | 0.961418i | \(-0.411291\pi\) | ||||
0.275093 | + | 0.961418i | \(0.411291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.67669 | −0.227014 | ||||||||
\(866\) | 38.1048 | 1.29485 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.0219830 | 0.000746153 0 | ||||||||
\(869\) | −98.8259 | −3.35244 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.6658 | −0.530815 | ||||||||
\(872\) | −18.9422 | −0.641463 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.501484 | −0.0169630 | ||||||||
\(875\) | 4.74681 | 0.160471 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.3959 | −0.756255 | −0.378127 | − | 0.925754i | \(-0.623432\pi\) | ||||
−0.378127 | + | 0.925754i | \(0.623432\pi\) | |||||||
\(878\) | 51.2370 | 1.72917 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 25.2670 | 0.851751 | ||||||||
\(881\) | −10.4074 | −0.350633 | −0.175316 | − | 0.984512i | \(-0.556095\pi\) | ||||
−0.175316 | + | 0.984512i | \(0.556095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.3582 | −0.617803 | −0.308902 | − | 0.951094i | \(-0.599961\pi\) | ||||
−0.308902 | + | 0.951094i | \(0.599961\pi\) | |||||||
\(884\) | −1.14903 | −0.0386460 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −21.7077 | −0.729286 | ||||||||
\(887\) | 22.9758 | 0.771453 | 0.385726 | − | 0.922613i | \(-0.373951\pi\) | ||||
0.385726 | + | 0.922613i | \(0.373951\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.17938 | 0.106633 | ||||||||
\(890\) | −6.84682 | −0.229506 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.74829 | −0.0585370 | ||||||||
\(893\) | 1.10893 | 0.0371090 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.7327 | 0.425607 | ||||||||
\(896\) | 4.79077 | 0.160048 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 45.3230 | 1.51245 | ||||||||
\(899\) | −2.45328 | −0.0818215 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.8130 | 1.52625 | ||||||||
\(902\) | 97.9614 | 3.26176 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.97196 | 0.132105 | ||||||||
\(905\) | −7.34843 | −0.244270 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.415835 | 0.0138076 | 0.00690378 | − | 0.999976i | \(-0.497802\pi\) | ||||
0.00690378 | + | 0.999976i | \(0.497802\pi\) | |||||||
\(908\) | 1.76326 | 0.0585159 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.40333 | 0.0465201 | ||||||||
\(911\) | 13.6089 | 0.450881 | 0.225441 | − | 0.974257i | \(-0.427618\pi\) | ||||
0.225441 | + | 0.974257i | \(0.427618\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −34.3448 | −1.13665 | ||||||||
\(914\) | −8.75998 | −0.289754 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.15734 | 0.0712804 | ||||||||
\(917\) | −7.82978 | −0.258562 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.8913 | −0.491218 | −0.245609 | − | 0.969369i | \(-0.578988\pi\) | ||||
−0.245609 | + | 0.969369i | \(0.578988\pi\) | |||||||
\(920\) | −0.585959 | −0.0193185 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.63129 | −0.185457 | ||||||||
\(923\) | 13.8966 | 0.457414 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.6496 | 0.974871 | ||||||||
\(926\) | −30.1082 | −0.989416 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.13496 | 0.135737 | ||||||||
\(929\) | 19.4977 | 0.639699 | 0.319850 | − | 0.947468i | \(-0.396368\pi\) | ||||
0.319850 | + | 0.947468i | \(0.396368\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.4139 | −0.472397 | ||||||||
\(932\) | −1.97117 | −0.0645678 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.7442 | 0.940539 | ||||||||
\(935\) | 35.2373 | 1.15238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.5125 | 0.408764 | 0.204382 | − | 0.978891i | \(-0.434481\pi\) | ||||
0.204382 | + | 0.978891i | \(0.434481\pi\) | |||||||
\(938\) | 5.42593 | 0.177163 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.0723148 | 0.00235865 | ||||||||
\(941\) | −4.08256 | −0.133088 | −0.0665439 | − | 0.997783i | \(-0.521197\pi\) | ||||
−0.0665439 | + | 0.997783i | \(0.521197\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.13704 | −0.0695915 | ||||||||
\(944\) | 12.5723 | 0.409192 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39.2471 | −1.27603 | ||||||||
\(947\) | 0.698574 | 0.0227006 | 0.0113503 | − | 0.999936i | \(-0.496387\pi\) | ||||
0.0113503 | + | 0.999936i | \(0.496387\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.55032 | 0.277555 | ||||||||
\(950\) | −10.5710 | −0.342970 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.13083 | 0.231112 | ||||||||
\(953\) | −7.31223 | −0.236866 | −0.118433 | − | 0.992962i | \(-0.537787\pi\) | ||||
−0.118433 | + | 0.992962i | \(0.537787\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.69044 | 0.313575 | ||||||||
\(956\) | 2.88086 | 0.0931737 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −55.0930 | −1.77997 | ||||||||
\(959\) | −6.13202 | −0.198013 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8430 | −0.994935 | ||||||||
\(962\) | 20.8571 | 0.672459 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.14058 | −0.0689434 | ||||||||
\(965\) | 23.2756 | 0.749267 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.1107 | 1.22556 | 0.612778 | − | 0.790255i | \(-0.290052\pi\) | ||||
0.612778 | + | 0.790255i | \(0.290052\pi\) | |||||||
\(968\) | −63.9729 | −2.05617 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.25570 | 0.136642 | ||||||||
\(971\) | 51.0424 | 1.63803 | 0.819014 | − | 0.573773i | \(-0.194521\pi\) | ||||
0.819014 | + | 0.573773i | \(0.194521\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.09045 | −0.163192 | ||||||||
\(974\) | −2.15101 | −0.0689227 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.1819 | 0.646007 | ||||||||
\(977\) | −53.4134 | −1.70885 | −0.854424 | − | 0.519577i | \(-0.826090\pi\) | ||||
−0.854424 | + | 0.519577i | \(0.826090\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.4546 | 0.781571 | ||||||||
\(980\) | −0.939949 | −0.0300256 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.2547 | −0.422976 | ||||||||
\(983\) | −1.20932 | −0.0385714 | −0.0192857 | − | 0.999814i | \(-0.506139\pi\) | ||||
−0.0192857 | + | 0.999814i | \(0.506139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.98264 | −0.158760 | ||||||||
\(986\) | −44.4132 | −1.41440 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.467161 | 0.0148624 | ||||||||
\(989\) | 0.856179 | 0.0272249 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3298 | −0.423433 | −0.211717 | − | 0.977331i | \(-0.567905\pi\) | ||||
−0.211717 | + | 0.977331i | \(0.567905\pi\) | |||||||
\(992\) | −0.264624 | −0.00840181 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.81318 | −0.152665 | ||||||||
\(995\) | −5.43321 | −0.172244 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.2475 | −1.24298 | −0.621490 | − | 0.783422i | \(-0.713472\pi\) | ||||
−0.621490 | + | 0.783422i | \(0.713472\pi\) | |||||||
\(998\) | −28.3085 | −0.896091 | ||||||||
\(999\) | 0 | 0 |
(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 | 4527.2.a.k.1.7 | 10 | ||
3.2 | odd | 2 | 503.2.a.e.1.4 | ✓ | 10 | ||
12.11 | even | 2 | 8048.2.a.p.1.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.4 | ✓ | 10 | 3.2 | odd | 2 | ||
4527.2.a.k.1.7 | 10 | 1.1 | even | 1 | trivial | ||
8048.2.a.p.1.4 | 10 | 12.11 | even | 2 |