Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1519,2,Mod(1,1519)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1519, 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("1519.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1519 = 7^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1519.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: | \(12.1292760670\) |
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: | \( x^{13} - 5 x^{12} - 9 x^{11} + 76 x^{10} - 17 x^{9} - 387 x^{8} + 332 x^{7} + 758 x^{6} - 875 x^{5} + \cdots + 21 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 217) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.47057\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1519.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.47057 | −1.03985 | −0.519925 | − | 0.854212i | \(-0.674040\pi\) | ||||
−0.519925 | + | 0.854212i | \(0.674040\pi\) | |||||||
\(3\) | 1.55945 | 0.900351 | 0.450175 | − | 0.892940i | \(-0.351361\pi\) | ||||
0.450175 | + | 0.892940i | \(0.351361\pi\) | |||||||
\(4\) | 0.162576 | 0.0812879 | ||||||||
\(5\) | −4.37105 | −1.95479 | −0.977397 | − | 0.211410i | \(-0.932194\pi\) | ||||
−0.977397 | + | 0.211410i | \(0.932194\pi\) | |||||||
\(6\) | −2.29329 | −0.936230 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.70206 | 0.955323 | ||||||||
\(9\) | −0.568105 | −0.189368 | ||||||||
\(10\) | 6.42794 | 2.03269 | ||||||||
\(11\) | 0.334425 | 0.100833 | 0.0504164 | − | 0.998728i | \(-0.483945\pi\) | ||||
0.0504164 | + | 0.998728i | \(0.483945\pi\) | |||||||
\(12\) | 0.253529 | 0.0731877 | ||||||||
\(13\) | −5.80839 | −1.61096 | −0.805479 | − | 0.592625i | \(-0.798092\pi\) | ||||
−0.805479 | + | 0.592625i | \(0.798092\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.81646 | −1.76000 | ||||||||
\(16\) | −4.29872 | −1.07468 | ||||||||
\(17\) | −2.86861 | −0.695740 | −0.347870 | − | 0.937543i | \(-0.613095\pi\) | ||||
−0.347870 | + | 0.937543i | \(0.613095\pi\) | |||||||
\(18\) | 0.835438 | 0.196915 | ||||||||
\(19\) | −0.421184 | −0.0966262 | −0.0483131 | − | 0.998832i | \(-0.515385\pi\) | ||||
−0.0483131 | + | 0.998832i | \(0.515385\pi\) | |||||||
\(20\) | −0.710628 | −0.158901 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.491795 | −0.104851 | ||||||||
\(23\) | 2.00865 | 0.418833 | 0.209416 | − | 0.977827i | \(-0.432844\pi\) | ||||
0.209416 | + | 0.977827i | \(0.432844\pi\) | |||||||
\(24\) | 4.21374 | 0.860126 | ||||||||
\(25\) | 14.1061 | 2.82122 | ||||||||
\(26\) | 8.54164 | 1.67515 | ||||||||
\(27\) | −5.56429 | −1.07085 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.99544 | 0.927629 | 0.463814 | − | 0.885932i | \(-0.346480\pi\) | ||||
0.463814 | + | 0.885932i | \(0.346480\pi\) | |||||||
\(30\) | 10.0241 | 1.83014 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 0.917448 | 0.162183 | ||||||||
\(33\) | 0.521520 | 0.0907850 | ||||||||
\(34\) | 4.21849 | 0.723465 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0923602 | −0.0153934 | ||||||||
\(37\) | −4.42560 | −0.727564 | −0.363782 | − | 0.931484i | \(-0.618515\pi\) | ||||
−0.363782 | + | 0.931484i | \(0.618515\pi\) | |||||||
\(38\) | 0.619380 | 0.100477 | ||||||||
\(39\) | −9.05791 | −1.45043 | ||||||||
\(40\) | −11.8109 | −1.86746 | ||||||||
\(41\) | 10.1180 | 1.58016 | 0.790081 | − | 0.613002i | \(-0.210038\pi\) | ||||
0.790081 | + | 0.613002i | \(0.210038\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.91910 | −0.750155 | −0.375078 | − | 0.926993i | \(-0.622384\pi\) | ||||
−0.375078 | + | 0.926993i | \(0.622384\pi\) | |||||||
\(44\) | 0.0543694 | 0.00819650 | ||||||||
\(45\) | 2.48322 | 0.370176 | ||||||||
\(46\) | −2.95386 | −0.435523 | ||||||||
\(47\) | 1.20240 | 0.175388 | 0.0876940 | − | 0.996147i | \(-0.472050\pi\) | ||||
0.0876940 | + | 0.996147i | \(0.472050\pi\) | |||||||
\(48\) | −6.70365 | −0.967589 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −20.7440 | −2.93365 | ||||||||
\(51\) | −4.47346 | −0.626410 | ||||||||
\(52\) | −0.944304 | −0.130951 | ||||||||
\(53\) | −5.10760 | −0.701583 | −0.350792 | − | 0.936454i | \(-0.614087\pi\) | ||||
−0.350792 | + | 0.936454i | \(0.614087\pi\) | |||||||
\(54\) | 8.18268 | 1.11352 | ||||||||
\(55\) | −1.46179 | −0.197108 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.656816 | −0.0869974 | ||||||||
\(58\) | −7.34614 | −0.964595 | ||||||||
\(59\) | 7.94464 | 1.03430 | 0.517152 | − | 0.855893i | \(-0.326992\pi\) | ||||
0.517152 | + | 0.855893i | \(0.326992\pi\) | |||||||
\(60\) | −1.10819 | −0.143067 | ||||||||
\(61\) | 1.02514 | 0.131256 | 0.0656280 | − | 0.997844i | \(-0.479095\pi\) | ||||
0.0656280 | + | 0.997844i | \(0.479095\pi\) | |||||||
\(62\) | 1.47057 | 0.186763 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.24827 | 0.906034 | ||||||||
\(65\) | 25.3888 | 3.14909 | ||||||||
\(66\) | −0.766932 | −0.0944028 | ||||||||
\(67\) | 7.16201 | 0.874979 | 0.437490 | − | 0.899224i | \(-0.355868\pi\) | ||||
0.437490 | + | 0.899224i | \(0.355868\pi\) | |||||||
\(68\) | −0.466367 | −0.0565553 | ||||||||
\(69\) | 3.13240 | 0.377096 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.51205 | 0.179447 | 0.0897237 | − | 0.995967i | \(-0.471402\pi\) | ||||
0.0897237 | + | 0.995967i | \(0.471402\pi\) | |||||||
\(72\) | −1.53505 | −0.180908 | ||||||||
\(73\) | −10.3665 | −1.21331 | −0.606653 | − | 0.794967i | \(-0.707488\pi\) | ||||
−0.606653 | + | 0.794967i | \(0.707488\pi\) | |||||||
\(74\) | 6.50815 | 0.756557 | ||||||||
\(75\) | 21.9978 | 2.54009 | ||||||||
\(76\) | −0.0684743 | −0.00785454 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 13.3203 | 1.50823 | ||||||||
\(79\) | 7.74342 | 0.871203 | 0.435601 | − | 0.900140i | \(-0.356536\pi\) | ||||
0.435601 | + | 0.900140i | \(0.356536\pi\) | |||||||
\(80\) | 18.7899 | 2.10078 | ||||||||
\(81\) | −6.97294 | −0.774771 | ||||||||
\(82\) | −14.8792 | −1.64313 | ||||||||
\(83\) | 12.5211 | 1.37437 | 0.687184 | − | 0.726483i | \(-0.258847\pi\) | ||||
0.687184 | + | 0.726483i | \(0.258847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.5388 | 1.36003 | ||||||||
\(86\) | 7.23387 | 0.780049 | ||||||||
\(87\) | 7.79015 | 0.835192 | ||||||||
\(88\) | 0.903636 | 0.0963279 | ||||||||
\(89\) | −2.43545 | −0.258157 | −0.129078 | − | 0.991634i | \(-0.541202\pi\) | ||||
−0.129078 | + | 0.991634i | \(0.541202\pi\) | |||||||
\(90\) | −3.65175 | −0.384928 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.326558 | 0.0340461 | ||||||||
\(93\) | −1.55945 | −0.161708 | ||||||||
\(94\) | −1.76821 | −0.182377 | ||||||||
\(95\) | 1.84102 | 0.188884 | ||||||||
\(96\) | 1.43072 | 0.146022 | ||||||||
\(97\) | −4.26302 | −0.432844 | −0.216422 | − | 0.976300i | \(-0.569439\pi\) | ||||
−0.216422 | + | 0.976300i | \(0.569439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.189988 | −0.0190946 | ||||||||
\(100\) | 2.29331 | 0.229331 | ||||||||
\(101\) | −1.21018 | −0.120417 | −0.0602086 | − | 0.998186i | \(-0.519177\pi\) | ||||
−0.0602086 | + | 0.998186i | \(0.519177\pi\) | |||||||
\(102\) | 6.57854 | 0.651372 | ||||||||
\(103\) | 16.5647 | 1.63217 | 0.816086 | − | 0.577931i | \(-0.196140\pi\) | ||||
0.816086 | + | 0.577931i | \(0.196140\pi\) | |||||||
\(104\) | −15.6946 | −1.53898 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.51109 | 0.729541 | ||||||||
\(107\) | 15.9724 | 1.54411 | 0.772053 | − | 0.635558i | \(-0.219230\pi\) | ||||
0.772053 | + | 0.635558i | \(0.219230\pi\) | |||||||
\(108\) | −0.904620 | −0.0870471 | ||||||||
\(109\) | 5.22794 | 0.500746 | 0.250373 | − | 0.968149i | \(-0.419447\pi\) | ||||
0.250373 | + | 0.968149i | \(0.419447\pi\) | |||||||
\(110\) | 2.14966 | 0.204962 | ||||||||
\(111\) | −6.90151 | −0.655063 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.16180 | 0.861870 | 0.430935 | − | 0.902383i | \(-0.358184\pi\) | ||||
0.430935 | + | 0.902383i | \(0.358184\pi\) | |||||||
\(114\) | 0.965894 | 0.0904643 | ||||||||
\(115\) | −8.77993 | −0.818732 | ||||||||
\(116\) | 0.812137 | 0.0754050 | ||||||||
\(117\) | 3.29978 | 0.305064 | ||||||||
\(118\) | −11.6832 | −1.07552 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −18.4185 | −1.68137 | ||||||||
\(121\) | −10.8882 | −0.989833 | ||||||||
\(122\) | −1.50754 | −0.136487 | ||||||||
\(123\) | 15.7785 | 1.42270 | ||||||||
\(124\) | −0.162576 | −0.0145997 | ||||||||
\(125\) | −39.8033 | −3.56012 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.84670 | −0.341339 | −0.170670 | − | 0.985328i | \(-0.554593\pi\) | ||||
−0.170670 | + | 0.985328i | \(0.554593\pi\) | |||||||
\(128\) | −12.4940 | −1.10432 | ||||||||
\(129\) | −7.67110 | −0.675403 | ||||||||
\(130\) | −37.3360 | −3.27458 | ||||||||
\(131\) | −2.97936 | −0.260308 | −0.130154 | − | 0.991494i | \(-0.541547\pi\) | ||||
−0.130154 | + | 0.991494i | \(0.541547\pi\) | |||||||
\(132\) | 0.0847866 | 0.00737972 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.5322 | −0.909847 | ||||||||
\(135\) | 24.3218 | 2.09329 | ||||||||
\(136\) | −7.75116 | −0.664656 | ||||||||
\(137\) | 12.6454 | 1.08037 | 0.540184 | − | 0.841547i | \(-0.318355\pi\) | ||||
0.540184 | + | 0.841547i | \(0.318355\pi\) | |||||||
\(138\) | −4.60641 | −0.392124 | ||||||||
\(139\) | 9.18944 | 0.779438 | 0.389719 | − | 0.920934i | \(-0.372572\pi\) | ||||
0.389719 | + | 0.920934i | \(0.372572\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.87509 | 0.157911 | ||||||||
\(142\) | −2.22358 | −0.186598 | ||||||||
\(143\) | −1.94247 | −0.162438 | ||||||||
\(144\) | 2.44213 | 0.203510 | ||||||||
\(145\) | −21.8353 | −1.81332 | ||||||||
\(146\) | 15.2446 | 1.26166 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.719495 | −0.0591421 | ||||||||
\(149\) | 8.23664 | 0.674772 | 0.337386 | − | 0.941366i | \(-0.390457\pi\) | ||||
0.337386 | + | 0.941366i | \(0.390457\pi\) | |||||||
\(150\) | −32.3493 | −2.64131 | ||||||||
\(151\) | −6.49472 | −0.528533 | −0.264266 | − | 0.964450i | \(-0.585130\pi\) | ||||
−0.264266 | + | 0.964450i | \(0.585130\pi\) | |||||||
\(152\) | −1.13806 | −0.0923092 | ||||||||
\(153\) | 1.62967 | 0.131751 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.37105 | 0.351092 | ||||||||
\(156\) | −1.47260 | −0.117902 | ||||||||
\(157\) | −17.0392 | −1.35988 | −0.679938 | − | 0.733270i | \(-0.737993\pi\) | ||||
−0.679938 | + | 0.733270i | \(0.737993\pi\) | |||||||
\(158\) | −11.3872 | −0.905920 | ||||||||
\(159\) | −7.96507 | −0.631671 | ||||||||
\(160\) | −4.01022 | −0.317035 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 10.2542 | 0.805646 | ||||||||
\(163\) | 3.54835 | 0.277928 | 0.138964 | − | 0.990297i | \(-0.455623\pi\) | ||||
0.138964 | + | 0.990297i | \(0.455623\pi\) | |||||||
\(164\) | 1.64494 | 0.128448 | ||||||||
\(165\) | −2.27959 | −0.177466 | ||||||||
\(166\) | −18.4131 | −1.42914 | ||||||||
\(167\) | 24.6131 | 1.90462 | 0.952310 | − | 0.305133i | \(-0.0987008\pi\) | ||||
0.952310 | + | 0.305133i | \(0.0987008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20.7374 | 1.59518 | ||||||||
\(170\) | −18.4393 | −1.41423 | ||||||||
\(171\) | 0.239277 | 0.0182979 | ||||||||
\(172\) | −0.799726 | −0.0609786 | ||||||||
\(173\) | −15.4342 | −1.17344 | −0.586721 | − | 0.809789i | \(-0.699582\pi\) | ||||
−0.586721 | + | 0.809789i | \(0.699582\pi\) | |||||||
\(174\) | −11.4560 | −0.868474 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.43760 | −0.108363 | ||||||||
\(177\) | 12.3893 | 0.931237 | ||||||||
\(178\) | 3.58149 | 0.268444 | ||||||||
\(179\) | 19.6717 | 1.47033 | 0.735165 | − | 0.677889i | \(-0.237105\pi\) | ||||
0.735165 | + | 0.677889i | \(0.237105\pi\) | |||||||
\(180\) | 0.403711 | 0.0300909 | ||||||||
\(181\) | −12.4376 | −0.924477 | −0.462239 | − | 0.886756i | \(-0.652954\pi\) | ||||
−0.462239 | + | 0.886756i | \(0.652954\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.59866 | 0.118176 | ||||||||
\(184\) | 5.42750 | 0.400121 | ||||||||
\(185\) | 19.3445 | 1.42224 | ||||||||
\(186\) | 2.29329 | 0.168152 | ||||||||
\(187\) | −0.959334 | −0.0701535 | ||||||||
\(188\) | 0.195481 | 0.0142569 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.70734 | −0.196411 | ||||||||
\(191\) | −4.72288 | −0.341736 | −0.170868 | − | 0.985294i | \(-0.554657\pi\) | ||||
−0.170868 | + | 0.985294i | \(0.554657\pi\) | |||||||
\(192\) | 11.3033 | 0.815748 | ||||||||
\(193\) | −2.10268 | −0.151354 | −0.0756771 | − | 0.997132i | \(-0.524112\pi\) | ||||
−0.0756771 | + | 0.997132i | \(0.524112\pi\) | |||||||
\(194\) | 6.26907 | 0.450093 | ||||||||
\(195\) | 39.5926 | 2.83529 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.31625 | −0.307520 | −0.153760 | − | 0.988108i | \(-0.549138\pi\) | ||||
−0.153760 | + | 0.988108i | \(0.549138\pi\) | |||||||
\(198\) | 0.279391 | 0.0198555 | ||||||||
\(199\) | 6.25485 | 0.443394 | 0.221697 | − | 0.975116i | \(-0.428840\pi\) | ||||
0.221697 | + | 0.975116i | \(0.428840\pi\) | |||||||
\(200\) | 38.1156 | 2.69518 | ||||||||
\(201\) | 11.1688 | 0.787788 | ||||||||
\(202\) | 1.77965 | 0.125216 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.727277 | −0.0509196 | ||||||||
\(205\) | −44.2262 | −3.08889 | ||||||||
\(206\) | −24.3596 | −1.69721 | ||||||||
\(207\) | −1.14113 | −0.0793137 | ||||||||
\(208\) | 24.9686 | 1.73126 | ||||||||
\(209\) | −0.140854 | −0.00974309 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.12522 | 0.0774631 | 0.0387316 | − | 0.999250i | \(-0.487668\pi\) | ||||
0.0387316 | + | 0.999250i | \(0.487668\pi\) | |||||||
\(212\) | −0.830373 | −0.0570302 | ||||||||
\(213\) | 2.35797 | 0.161566 | ||||||||
\(214\) | −23.4885 | −1.60564 | ||||||||
\(215\) | 21.5016 | 1.46640 | ||||||||
\(216\) | −15.0351 | −1.02301 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −7.68805 | −0.520700 | ||||||||
\(219\) | −16.1661 | −1.09240 | ||||||||
\(220\) | −0.237652 | −0.0160225 | ||||||||
\(221\) | 16.6620 | 1.12081 | ||||||||
\(222\) | 10.1492 | 0.681167 | ||||||||
\(223\) | 26.0719 | 1.74590 | 0.872952 | − | 0.487806i | \(-0.162203\pi\) | ||||
0.872952 | + | 0.487806i | \(0.162203\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.01376 | −0.534250 | ||||||||
\(226\) | −13.4731 | −0.896215 | ||||||||
\(227\) | −15.5167 | −1.02988 | −0.514941 | − | 0.857226i | \(-0.672186\pi\) | ||||
−0.514941 | + | 0.857226i | \(0.672186\pi\) | |||||||
\(228\) | −0.106782 | −0.00707184 | ||||||||
\(229\) | −17.7363 | −1.17205 | −0.586025 | − | 0.810293i | \(-0.699308\pi\) | ||||
−0.586025 | + | 0.810293i | \(0.699308\pi\) | |||||||
\(230\) | 12.9115 | 0.851359 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 13.4980 | 0.886185 | ||||||||
\(233\) | −0.155388 | −0.0101798 | −0.00508991 | − | 0.999987i | \(-0.501620\pi\) | ||||
−0.00508991 | + | 0.999987i | \(0.501620\pi\) | |||||||
\(234\) | −4.85255 | −0.317221 | ||||||||
\(235\) | −5.25576 | −0.342848 | ||||||||
\(236\) | 1.29161 | 0.0840765 | ||||||||
\(237\) | 12.0755 | 0.784388 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.2663 | 1.18155 | 0.590773 | − | 0.806838i | \(-0.298823\pi\) | ||||
0.590773 | + | 0.806838i | \(0.298823\pi\) | |||||||
\(240\) | 29.3020 | 1.89144 | ||||||||
\(241\) | 18.5803 | 1.19686 | 0.598431 | − | 0.801175i | \(-0.295791\pi\) | ||||
0.598431 | + | 0.801175i | \(0.295791\pi\) | |||||||
\(242\) | 16.0118 | 1.02928 | ||||||||
\(243\) | 5.81890 | 0.373283 | ||||||||
\(244\) | 0.166663 | 0.0106695 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −23.2034 | −1.47940 | ||||||||
\(247\) | 2.44640 | 0.155661 | ||||||||
\(248\) | −2.70206 | −0.171581 | ||||||||
\(249\) | 19.5261 | 1.23741 | ||||||||
\(250\) | 58.5336 | 3.70199 | ||||||||
\(251\) | −17.8295 | −1.12539 | −0.562693 | − | 0.826666i | \(-0.690235\pi\) | ||||
−0.562693 | + | 0.826666i | \(0.690235\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.671743 | 0.0422321 | ||||||||
\(254\) | 5.65684 | 0.354942 | ||||||||
\(255\) | 19.5537 | 1.22450 | ||||||||
\(256\) | 3.87674 | 0.242296 | ||||||||
\(257\) | −9.25708 | −0.577441 | −0.288720 | − | 0.957413i | \(-0.593230\pi\) | ||||
−0.288720 | + | 0.957413i | \(0.593230\pi\) | |||||||
\(258\) | 11.2809 | 0.702318 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.12760 | 0.255983 | ||||||||
\(261\) | −2.83793 | −0.175664 | ||||||||
\(262\) | 4.38136 | 0.270681 | ||||||||
\(263\) | −18.8778 | −1.16405 | −0.582027 | − | 0.813169i | \(-0.697740\pi\) | ||||
−0.582027 | + | 0.813169i | \(0.697740\pi\) | |||||||
\(264\) | 1.40918 | 0.0867289 | ||||||||
\(265\) | 22.3256 | 1.37145 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.79797 | −0.232432 | ||||||||
\(268\) | 1.16437 | 0.0711252 | ||||||||
\(269\) | 18.4723 | 1.12628 | 0.563138 | − | 0.826363i | \(-0.309594\pi\) | ||||
0.563138 | + | 0.826363i | \(0.309594\pi\) | |||||||
\(270\) | −35.7670 | −2.17671 | ||||||||
\(271\) | −30.5777 | −1.85746 | −0.928731 | − | 0.370753i | \(-0.879099\pi\) | ||||
−0.928731 | + | 0.370753i | \(0.879099\pi\) | |||||||
\(272\) | 12.3314 | 0.747698 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.5959 | −1.12342 | ||||||||
\(275\) | 4.71744 | 0.284472 | ||||||||
\(276\) | 0.509252 | 0.0306534 | ||||||||
\(277\) | −27.2746 | −1.63877 | −0.819387 | − | 0.573240i | \(-0.805686\pi\) | ||||
−0.819387 | + | 0.573240i | \(0.805686\pi\) | |||||||
\(278\) | −13.5137 | −0.810499 | ||||||||
\(279\) | 0.568105 | 0.0340116 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.9872 | 0.953716 | 0.476858 | − | 0.878980i | \(-0.341776\pi\) | ||||
0.476858 | + | 0.878980i | \(0.341776\pi\) | |||||||
\(282\) | −2.75745 | −0.164204 | ||||||||
\(283\) | 11.7377 | 0.697733 | 0.348867 | − | 0.937172i | \(-0.386567\pi\) | ||||
0.348867 | + | 0.937172i | \(0.386567\pi\) | |||||||
\(284\) | 0.245823 | 0.0145869 | ||||||||
\(285\) | 2.87098 | 0.170062 | ||||||||
\(286\) | 2.85654 | 0.168911 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.521207 | −0.0307124 | ||||||||
\(289\) | −8.77108 | −0.515946 | ||||||||
\(290\) | 32.1104 | 1.88559 | ||||||||
\(291\) | −6.64798 | −0.389712 | ||||||||
\(292\) | −1.68534 | −0.0986271 | ||||||||
\(293\) | −4.91819 | −0.287324 | −0.143662 | − | 0.989627i | \(-0.545888\pi\) | ||||
−0.143662 | + | 0.989627i | \(0.545888\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −34.7265 | −2.02185 | ||||||||
\(296\) | −11.9582 | −0.695058 | ||||||||
\(297\) | −1.86084 | −0.107977 | ||||||||
\(298\) | −12.1126 | −0.701662 | ||||||||
\(299\) | −11.6670 | −0.674722 | ||||||||
\(300\) | 3.57632 | 0.206479 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.55094 | 0.549595 | ||||||||
\(303\) | −1.88722 | −0.108418 | ||||||||
\(304\) | 1.81055 | 0.103842 | ||||||||
\(305\) | −4.48095 | −0.256579 | ||||||||
\(306\) | −2.39655 | −0.137001 | ||||||||
\(307\) | −17.5101 | −0.999355 | −0.499677 | − | 0.866212i | \(-0.666548\pi\) | ||||
−0.499677 | + | 0.866212i | \(0.666548\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.8319 | 1.46953 | ||||||||
\(310\) | −6.42794 | −0.365083 | ||||||||
\(311\) | −11.2651 | −0.638786 | −0.319393 | − | 0.947622i | \(-0.603479\pi\) | ||||
−0.319393 | + | 0.947622i | \(0.603479\pi\) | |||||||
\(312\) | −24.4750 | −1.38563 | ||||||||
\(313\) | 24.7326 | 1.39797 | 0.698983 | − | 0.715138i | \(-0.253636\pi\) | ||||
0.698983 | + | 0.715138i | \(0.253636\pi\) | |||||||
\(314\) | 25.0573 | 1.41407 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.25889 | 0.0708183 | ||||||||
\(317\) | −27.2078 | −1.52814 | −0.764071 | − | 0.645132i | \(-0.776802\pi\) | ||||
−0.764071 | + | 0.645132i | \(0.776802\pi\) | |||||||
\(318\) | 11.7132 | 0.656843 | ||||||||
\(319\) | 1.67060 | 0.0935355 | ||||||||
\(320\) | −31.6826 | −1.77111 | ||||||||
\(321\) | 24.9081 | 1.39024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.20821 | 0.0672267 | ||||||||
\(324\) | −1.13363 | −0.0629795 | ||||||||
\(325\) | −81.9338 | −4.54487 | ||||||||
\(326\) | −5.21810 | −0.289004 | ||||||||
\(327\) | 8.15273 | 0.450847 | ||||||||
\(328\) | 27.3394 | 1.50957 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.35230 | 0.184538 | ||||||||
\(331\) | 26.2818 | 1.44458 | 0.722289 | − | 0.691591i | \(-0.243090\pi\) | ||||
0.722289 | + | 0.691591i | \(0.243090\pi\) | |||||||
\(332\) | 2.03563 | 0.111720 | ||||||||
\(333\) | 2.51420 | 0.137778 | ||||||||
\(334\) | −36.1953 | −1.98052 | ||||||||
\(335\) | −31.3055 | −1.71040 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.5855 | −0.685576 | −0.342788 | − | 0.939413i | \(-0.611371\pi\) | ||||
−0.342788 | + | 0.939413i | \(0.611371\pi\) | |||||||
\(338\) | −30.4958 | −1.65875 | ||||||||
\(339\) | 14.2874 | 0.775985 | ||||||||
\(340\) | 2.03851 | 0.110554 | ||||||||
\(341\) | −0.334425 | −0.0181101 | ||||||||
\(342\) | −0.351873 | −0.0190271 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −13.2917 | −0.716640 | ||||||||
\(345\) | −13.6919 | −0.737146 | ||||||||
\(346\) | 22.6971 | 1.22020 | ||||||||
\(347\) | 10.1617 | 0.545509 | 0.272755 | − | 0.962084i | \(-0.412065\pi\) | ||||
0.272755 | + | 0.962084i | \(0.412065\pi\) | |||||||
\(348\) | 1.26649 | 0.0678910 | ||||||||
\(349\) | −2.58840 | −0.138554 | −0.0692769 | − | 0.997597i | \(-0.522069\pi\) | ||||
−0.0692769 | + | 0.997597i | \(0.522069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 32.3196 | 1.72509 | ||||||||
\(352\) | 0.306817 | 0.0163534 | ||||||||
\(353\) | 2.76436 | 0.147132 | 0.0735659 | − | 0.997290i | \(-0.476562\pi\) | ||||
0.0735659 | + | 0.997290i | \(0.476562\pi\) | |||||||
\(354\) | −18.2193 | −0.968347 | ||||||||
\(355\) | −6.60925 | −0.350783 | ||||||||
\(356\) | −0.395945 | −0.0209850 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.9286 | −1.52892 | ||||||||
\(359\) | 22.1626 | 1.16970 | 0.584848 | − | 0.811143i | \(-0.301154\pi\) | ||||
0.584848 | + | 0.811143i | \(0.301154\pi\) | |||||||
\(360\) | 6.70981 | 0.353638 | ||||||||
\(361\) | −18.8226 | −0.990663 | ||||||||
\(362\) | 18.2903 | 0.961318 | ||||||||
\(363\) | −16.9796 | −0.891197 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 45.3125 | 2.37176 | ||||||||
\(366\) | −2.35094 | −0.122886 | ||||||||
\(367\) | −6.89463 | −0.359897 | −0.179948 | − | 0.983676i | \(-0.557593\pi\) | ||||
−0.179948 | + | 0.983676i | \(0.557593\pi\) | |||||||
\(368\) | −8.63463 | −0.450111 | ||||||||
\(369\) | −5.74808 | −0.299233 | ||||||||
\(370\) | −28.4475 | −1.47891 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.253529 | −0.0131449 | ||||||||
\(373\) | −10.1121 | −0.523585 | −0.261792 | − | 0.965124i | \(-0.584314\pi\) | ||||
−0.261792 | + | 0.965124i | \(0.584314\pi\) | |||||||
\(374\) | 1.41077 | 0.0729491 | ||||||||
\(375\) | −62.0714 | −3.20536 | ||||||||
\(376\) | 3.24896 | 0.167552 | ||||||||
\(377\) | −29.0154 | −1.49437 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.654720 | −0.0336307 | −0.0168154 | − | 0.999859i | \(-0.505353\pi\) | ||||
−0.0168154 | + | 0.999859i | \(0.505353\pi\) | |||||||
\(380\) | 0.299305 | 0.0153540 | ||||||||
\(381\) | −5.99875 | −0.307325 | ||||||||
\(382\) | 6.94533 | 0.355354 | ||||||||
\(383\) | 17.3588 | 0.886995 | 0.443498 | − | 0.896276i | \(-0.353737\pi\) | ||||
0.443498 | + | 0.896276i | \(0.353737\pi\) | |||||||
\(384\) | −19.4838 | −0.994278 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.09214 | 0.157386 | ||||||||
\(387\) | 2.79456 | 0.142056 | ||||||||
\(388\) | −0.693064 | −0.0351850 | ||||||||
\(389\) | 17.9331 | 0.909247 | 0.454623 | − | 0.890684i | \(-0.349774\pi\) | ||||
0.454623 | + | 0.890684i | \(0.349774\pi\) | |||||||
\(390\) | −58.2237 | −2.94827 | ||||||||
\(391\) | −5.76204 | −0.291399 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.64618 | −0.234369 | ||||||||
\(394\) | 6.34734 | 0.319775 | ||||||||
\(395\) | −33.8469 | −1.70302 | ||||||||
\(396\) | −0.0308875 | −0.00155216 | ||||||||
\(397\) | −2.34293 | −0.117588 | −0.0587942 | − | 0.998270i | \(-0.518726\pi\) | ||||
−0.0587942 | + | 0.998270i | \(0.518726\pi\) | |||||||
\(398\) | −9.19819 | −0.461064 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −60.6383 | −3.03191 | ||||||||
\(401\) | −2.67963 | −0.133815 | −0.0669073 | − | 0.997759i | \(-0.521313\pi\) | ||||
−0.0669073 | + | 0.997759i | \(0.521313\pi\) | |||||||
\(402\) | −16.4245 | −0.819181 | ||||||||
\(403\) | 5.80839 | 0.289337 | ||||||||
\(404\) | −0.196746 | −0.00978847 | ||||||||
\(405\) | 30.4791 | 1.51452 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.48003 | −0.0733623 | ||||||||
\(408\) | −12.0876 | −0.598424 | ||||||||
\(409\) | 25.7060 | 1.27108 | 0.635539 | − | 0.772069i | \(-0.280778\pi\) | ||||
0.635539 | + | 0.772069i | \(0.280778\pi\) | |||||||
\(410\) | 65.0378 | 3.21199 | ||||||||
\(411\) | 19.7199 | 0.972710 | ||||||||
\(412\) | 2.69303 | 0.132676 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.67810 | 0.0824743 | ||||||||
\(415\) | −54.7304 | −2.68661 | ||||||||
\(416\) | −5.32890 | −0.261271 | ||||||||
\(417\) | 14.3305 | 0.701768 | ||||||||
\(418\) | 0.207136 | 0.0101314 | ||||||||
\(419\) | 10.5209 | 0.513979 | 0.256989 | − | 0.966414i | \(-0.417269\pi\) | ||||
0.256989 | + | 0.966414i | \(0.417269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.38713 | 0.408764 | 0.204382 | − | 0.978891i | \(-0.434482\pi\) | ||||
0.204382 | + | 0.978891i | \(0.434482\pi\) | |||||||
\(422\) | −1.65471 | −0.0805500 | ||||||||
\(423\) | −0.683090 | −0.0332129 | ||||||||
\(424\) | −13.8011 | −0.670238 | ||||||||
\(425\) | −40.4649 | −1.96284 | ||||||||
\(426\) | −3.46756 | −0.168004 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.59672 | 0.125517 | ||||||||
\(429\) | −3.02919 | −0.146251 | ||||||||
\(430\) | −31.6197 | −1.52484 | ||||||||
\(431\) | −8.68680 | −0.418429 | −0.209214 | − | 0.977870i | \(-0.567091\pi\) | ||||
−0.209214 | + | 0.977870i | \(0.567091\pi\) | |||||||
\(432\) | 23.9193 | 1.15082 | ||||||||
\(433\) | 31.1680 | 1.49784 | 0.748918 | − | 0.662663i | \(-0.230574\pi\) | ||||
0.748918 | + | 0.662663i | \(0.230574\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34.0512 | −1.63263 | ||||||||
\(436\) | 0.849937 | 0.0407046 | ||||||||
\(437\) | −0.846011 | −0.0404702 | ||||||||
\(438\) | 23.7733 | 1.13593 | ||||||||
\(439\) | 5.38928 | 0.257216 | 0.128608 | − | 0.991695i | \(-0.458949\pi\) | ||||
0.128608 | + | 0.991695i | \(0.458949\pi\) | |||||||
\(440\) | −3.94984 | −0.188301 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.5026 | −1.16547 | ||||||||
\(443\) | −13.6858 | −0.650231 | −0.325115 | − | 0.945674i | \(-0.605403\pi\) | ||||
−0.325115 | + | 0.945674i | \(0.605403\pi\) | |||||||
\(444\) | −1.12202 | −0.0532487 | ||||||||
\(445\) | 10.6455 | 0.504644 | ||||||||
\(446\) | −38.3406 | −1.81548 | ||||||||
\(447\) | 12.8447 | 0.607532 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.7774 | −0.933352 | −0.466676 | − | 0.884428i | \(-0.654549\pi\) | ||||
−0.466676 | + | 0.884428i | \(0.654549\pi\) | |||||||
\(450\) | 11.7848 | 0.555540 | ||||||||
\(451\) | 3.38370 | 0.159332 | ||||||||
\(452\) | 1.48949 | 0.0700596 | ||||||||
\(453\) | −10.1282 | −0.475865 | ||||||||
\(454\) | 22.8185 | 1.07092 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.77476 | −0.0831106 | ||||||||
\(457\) | −1.60745 | −0.0751933 | −0.0375967 | − | 0.999293i | \(-0.511970\pi\) | ||||
−0.0375967 | + | 0.999293i | \(0.511970\pi\) | |||||||
\(458\) | 26.0825 | 1.21876 | ||||||||
\(459\) | 15.9618 | 0.745032 | ||||||||
\(460\) | −1.42740 | −0.0665531 | ||||||||
\(461\) | −0.957604 | −0.0446001 | −0.0223000 | − | 0.999751i | \(-0.507099\pi\) | ||||
−0.0223000 | + | 0.999751i | \(0.507099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.3693 | −0.667798 | −0.333899 | − | 0.942609i | \(-0.608365\pi\) | ||||
−0.333899 | + | 0.942609i | \(0.608365\pi\) | |||||||
\(464\) | −21.4740 | −0.996905 | ||||||||
\(465\) | 6.81646 | 0.316106 | ||||||||
\(466\) | 0.228509 | 0.0105855 | ||||||||
\(467\) | 12.8116 | 0.592850 | 0.296425 | − | 0.955056i | \(-0.404206\pi\) | ||||
0.296425 | + | 0.955056i | \(0.404206\pi\) | |||||||
\(468\) | 0.536464 | 0.0247981 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.72896 | 0.356510 | ||||||||
\(471\) | −26.5718 | −1.22437 | ||||||||
\(472\) | 21.4669 | 0.988095 | ||||||||
\(473\) | −1.64507 | −0.0756403 | ||||||||
\(474\) | −17.7579 | −0.815646 | ||||||||
\(475\) | −5.94127 | −0.272604 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.90166 | 0.132858 | ||||||||
\(478\) | −26.8618 | −1.22863 | ||||||||
\(479\) | 12.1914 | 0.557039 | 0.278519 | − | 0.960431i | \(-0.410156\pi\) | ||||
0.278519 | + | 0.960431i | \(0.410156\pi\) | |||||||
\(480\) | −6.25374 | −0.285443 | ||||||||
\(481\) | 25.7056 | 1.17207 | ||||||||
\(482\) | −27.3236 | −1.24456 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.77015 | −0.0804615 | ||||||||
\(485\) | 18.6339 | 0.846122 | ||||||||
\(486\) | −8.55711 | −0.388158 | ||||||||
\(487\) | 39.5308 | 1.79131 | 0.895656 | − | 0.444747i | \(-0.146706\pi\) | ||||
0.895656 | + | 0.444747i | \(0.146706\pi\) | |||||||
\(488\) | 2.77000 | 0.125392 | ||||||||
\(489\) | 5.53349 | 0.250233 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.77830 | −0.260771 | −0.130386 | − | 0.991463i | \(-0.541622\pi\) | ||||
−0.130386 | + | 0.991463i | \(0.541622\pi\) | |||||||
\(492\) | 2.56521 | 0.115648 | ||||||||
\(493\) | −14.3300 | −0.645389 | ||||||||
\(494\) | −3.59760 | −0.161864 | ||||||||
\(495\) | 0.830450 | 0.0373260 | ||||||||
\(496\) | 4.29872 | 0.193018 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −28.7144 | −1.28672 | ||||||||
\(499\) | 5.57172 | 0.249424 | 0.124712 | − | 0.992193i | \(-0.460199\pi\) | ||||
0.124712 | + | 0.992193i | \(0.460199\pi\) | |||||||
\(500\) | −6.47106 | −0.289395 | ||||||||
\(501\) | 38.3830 | 1.71483 | ||||||||
\(502\) | 26.2195 | 1.17023 | ||||||||
\(503\) | −8.93145 | −0.398234 | −0.199117 | − | 0.979976i | \(-0.563807\pi\) | ||||
−0.199117 | + | 0.979976i | \(0.563807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.28976 | 0.235391 | ||||||||
\(506\) | −0.987845 | −0.0439151 | ||||||||
\(507\) | 32.3390 | 1.43623 | ||||||||
\(508\) | −0.625381 | −0.0277468 | ||||||||
\(509\) | −30.4587 | −1.35006 | −0.675030 | − | 0.737790i | \(-0.735869\pi\) | ||||
−0.675030 | + | 0.737790i | \(0.735869\pi\) | |||||||
\(510\) | −28.7552 | −1.27330 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.2870 | 0.852371 | ||||||||
\(513\) | 2.34359 | 0.103472 | ||||||||
\(514\) | 13.6132 | 0.600452 | ||||||||
\(515\) | −72.4054 | −3.19056 | ||||||||
\(516\) | −1.24714 | −0.0549021 | ||||||||
\(517\) | 0.402112 | 0.0176849 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.0690 | −1.05651 | ||||||||
\(520\) | 68.6021 | 3.00840 | ||||||||
\(521\) | −40.5530 | −1.77666 | −0.888331 | − | 0.459204i | \(-0.848135\pi\) | ||||
−0.888331 | + | 0.459204i | \(0.848135\pi\) | |||||||
\(522\) | 4.17338 | 0.182664 | ||||||||
\(523\) | 31.5736 | 1.38062 | 0.690308 | − | 0.723515i | \(-0.257475\pi\) | ||||
0.690308 | + | 0.723515i | \(0.257475\pi\) | |||||||
\(524\) | −0.484372 | −0.0211599 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.7611 | 1.21044 | ||||||||
\(527\) | 2.86861 | 0.124959 | ||||||||
\(528\) | −2.24187 | −0.0975648 | ||||||||
\(529\) | −18.9653 | −0.824579 | ||||||||
\(530\) | −32.8314 | −1.42610 | ||||||||
\(531\) | −4.51339 | −0.195865 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −58.7692 | −2.54558 | ||||||||
\(534\) | 5.58517 | 0.241694 | ||||||||
\(535\) | −69.8160 | −3.01841 | ||||||||
\(536\) | 19.3522 | 0.835887 | ||||||||
\(537\) | 30.6770 | 1.32381 | ||||||||
\(538\) | −27.1648 | −1.17116 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.95414 | 0.170159 | ||||||||
\(541\) | 1.68274 | 0.0723466 | 0.0361733 | − | 0.999346i | \(-0.488483\pi\) | ||||
0.0361733 | + | 0.999346i | \(0.488483\pi\) | |||||||
\(542\) | 44.9666 | 1.93148 | ||||||||
\(543\) | −19.3958 | −0.832354 | ||||||||
\(544\) | −2.63180 | −0.112838 | ||||||||
\(545\) | −22.8516 | −0.978855 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.227486 | −0.00972661 | −0.00486331 | − | 0.999988i | \(-0.501548\pi\) | ||||
−0.00486331 | + | 0.999988i | \(0.501548\pi\) | |||||||
\(548\) | 2.05583 | 0.0878209 | ||||||||
\(549\) | −0.582388 | −0.0248557 | ||||||||
\(550\) | −6.93732 | −0.295808 | ||||||||
\(551\) | −2.10400 | −0.0896332 | ||||||||
\(552\) | 8.46393 | 0.360249 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 40.1093 | 1.70408 | ||||||||
\(555\) | 30.1669 | 1.28051 | ||||||||
\(556\) | 1.49398 | 0.0633589 | ||||||||
\(557\) | −7.88211 | −0.333976 | −0.166988 | − | 0.985959i | \(-0.553404\pi\) | ||||
−0.166988 | + | 0.985959i | \(0.553404\pi\) | |||||||
\(558\) | −0.835438 | −0.0353669 | ||||||||
\(559\) | 28.5720 | 1.20847 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.49604 | −0.0631627 | ||||||||
\(562\) | −23.5103 | −0.991721 | ||||||||
\(563\) | −20.5424 | −0.865760 | −0.432880 | − | 0.901451i | \(-0.642503\pi\) | ||||
−0.432880 | + | 0.901451i | \(0.642503\pi\) | |||||||
\(564\) | 0.304844 | 0.0128362 | ||||||||
\(565\) | −40.0467 | −1.68478 | ||||||||
\(566\) | −17.2611 | −0.725538 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.08565 | 0.171430 | ||||||||
\(569\) | 26.0926 | 1.09386 | 0.546930 | − | 0.837178i | \(-0.315796\pi\) | ||||
0.546930 | + | 0.837178i | \(0.315796\pi\) | |||||||
\(570\) | −4.22198 | −0.176839 | ||||||||
\(571\) | −12.6705 | −0.530243 | −0.265122 | − | 0.964215i | \(-0.585412\pi\) | ||||
−0.265122 | + | 0.964215i | \(0.585412\pi\) | |||||||
\(572\) | −0.315799 | −0.0132042 | ||||||||
\(573\) | −7.36511 | −0.307682 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.3343 | 1.18162 | ||||||||
\(576\) | −4.11778 | −0.171574 | ||||||||
\(577\) | −0.893748 | −0.0372072 | −0.0186036 | − | 0.999827i | \(-0.505922\pi\) | ||||
−0.0186036 | + | 0.999827i | \(0.505922\pi\) | |||||||
\(578\) | 12.8985 | 0.536506 | ||||||||
\(579\) | −3.27903 | −0.136272 | ||||||||
\(580\) | −3.54990 | −0.147401 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9.77632 | 0.405242 | ||||||||
\(583\) | −1.70811 | −0.0707427 | ||||||||
\(584\) | −28.0109 | −1.15910 | ||||||||
\(585\) | −14.4235 | −0.596338 | ||||||||
\(586\) | 7.23254 | 0.298773 | ||||||||
\(587\) | 24.3556 | 1.00526 | 0.502631 | − | 0.864501i | \(-0.332365\pi\) | ||||
0.502631 | + | 0.864501i | \(0.332365\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.421184 | 0.0173546 | ||||||||
\(590\) | 51.0677 | 2.10242 | ||||||||
\(591\) | −6.73099 | −0.276876 | ||||||||
\(592\) | 19.0244 | 0.781898 | ||||||||
\(593\) | 13.3120 | 0.546660 | 0.273330 | − | 0.961920i | \(-0.411875\pi\) | ||||
0.273330 | + | 0.961920i | \(0.411875\pi\) | |||||||
\(594\) | 2.73649 | 0.112280 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.33908 | 0.0548508 | ||||||||
\(597\) | 9.75414 | 0.399211 | ||||||||
\(598\) | 17.1572 | 0.701610 | ||||||||
\(599\) | 8.92277 | 0.364574 | 0.182287 | − | 0.983245i | \(-0.441650\pi\) | ||||
0.182287 | + | 0.983245i | \(0.441650\pi\) | |||||||
\(600\) | 59.4395 | 2.42661 | ||||||||
\(601\) | −23.3119 | −0.950911 | −0.475455 | − | 0.879740i | \(-0.657717\pi\) | ||||
−0.475455 | + | 0.879740i | \(0.657717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.06878 | −0.165693 | ||||||||
\(604\) | −1.05588 | −0.0429633 | ||||||||
\(605\) | 47.5927 | 1.93492 | ||||||||
\(606\) | 2.77528 | 0.112738 | ||||||||
\(607\) | 14.7724 | 0.599592 | 0.299796 | − | 0.954003i | \(-0.403081\pi\) | ||||
0.299796 | + | 0.954003i | \(0.403081\pi\) | |||||||
\(608\) | −0.386414 | −0.0156712 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.58955 | 0.266803 | ||||||||
\(611\) | −6.98401 | −0.282543 | ||||||||
\(612\) | 0.264945 | 0.0107098 | ||||||||
\(613\) | −11.0055 | −0.444507 | −0.222254 | − | 0.974989i | \(-0.571341\pi\) | ||||
−0.222254 | + | 0.974989i | \(0.571341\pi\) | |||||||
\(614\) | 25.7498 | 1.03918 | ||||||||
\(615\) | −68.9688 | −2.78109 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.9673 | 1.04540 | 0.522701 | − | 0.852516i | \(-0.324924\pi\) | ||||
0.522701 | + | 0.852516i | \(0.324924\pi\) | |||||||
\(618\) | −37.9877 | −1.52809 | ||||||||
\(619\) | 21.9804 | 0.883468 | 0.441734 | − | 0.897146i | \(-0.354363\pi\) | ||||
0.441734 | + | 0.897146i | \(0.354363\pi\) | |||||||
\(620\) | 0.710628 | 0.0285395 | ||||||||
\(621\) | −11.1767 | −0.448507 | ||||||||
\(622\) | 16.5661 | 0.664242 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 38.9374 | 1.55875 | ||||||||
\(625\) | 103.452 | 4.13808 | ||||||||
\(626\) | −36.3709 | −1.45368 | ||||||||
\(627\) | −0.219656 | −0.00877220 | ||||||||
\(628\) | −2.77016 | −0.110541 | ||||||||
\(629\) | 12.6953 | 0.506195 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.6583 | 1.69820 | 0.849100 | − | 0.528232i | \(-0.177145\pi\) | ||||
0.849100 | + | 0.528232i | \(0.177145\pi\) | |||||||
\(632\) | 20.9232 | 0.832280 | ||||||||
\(633\) | 1.75472 | 0.0697440 | ||||||||
\(634\) | 40.0110 | 1.58904 | ||||||||
\(635\) | 16.8141 | 0.667249 | ||||||||
\(636\) | −1.29493 | −0.0513472 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.45673 | −0.0972629 | ||||||||
\(639\) | −0.859004 | −0.0339817 | ||||||||
\(640\) | 54.6119 | 2.15872 | ||||||||
\(641\) | −3.95319 | −0.156142 | −0.0780709 | − | 0.996948i | \(-0.524876\pi\) | ||||
−0.0780709 | + | 0.996948i | \(0.524876\pi\) | |||||||
\(642\) | −36.6292 | −1.44564 | ||||||||
\(643\) | −7.43895 | −0.293364 | −0.146682 | − | 0.989184i | \(-0.546859\pi\) | ||||
−0.146682 | + | 0.989184i | \(0.546859\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33.5308 | 1.32027 | ||||||||
\(646\) | −1.77676 | −0.0699057 | ||||||||
\(647\) | −11.3252 | −0.445241 | −0.222621 | − | 0.974905i | \(-0.571461\pi\) | ||||
−0.222621 | + | 0.974905i | \(0.571461\pi\) | |||||||
\(648\) | −18.8413 | −0.740157 | ||||||||
\(649\) | 2.65689 | 0.104292 | ||||||||
\(650\) | 120.489 | 4.72598 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.576876 | 0.0225922 | ||||||||
\(653\) | 40.3302 | 1.57824 | 0.789122 | − | 0.614237i | \(-0.210536\pi\) | ||||
0.789122 | + | 0.614237i | \(0.210536\pi\) | |||||||
\(654\) | −11.9892 | −0.468813 | ||||||||
\(655\) | 13.0230 | 0.508849 | ||||||||
\(656\) | −43.4944 | −1.69817 | ||||||||
\(657\) | 5.88926 | 0.229762 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.42326 | −0.0554424 | −0.0277212 | − | 0.999616i | \(-0.508825\pi\) | ||||
−0.0277212 | + | 0.999616i | \(0.508825\pi\) | |||||||
\(660\) | −0.370607 | −0.0144258 | ||||||||
\(661\) | 36.1402 | 1.40569 | 0.702845 | − | 0.711343i | \(-0.251913\pi\) | ||||
0.702845 | + | 0.711343i | \(0.251913\pi\) | |||||||
\(662\) | −38.6492 | −1.50214 | ||||||||
\(663\) | 25.9836 | 1.00912 | ||||||||
\(664\) | 33.8327 | 1.31296 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.69731 | −0.143268 | ||||||||
\(667\) | 10.0341 | 0.388521 | ||||||||
\(668\) | 4.00150 | 0.154823 | ||||||||
\(669\) | 40.6579 | 1.57193 | ||||||||
\(670\) | 46.0370 | 1.77856 | ||||||||
\(671\) | 0.342833 | 0.0132349 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.3356 | −1.05371 | −0.526855 | − | 0.849955i | \(-0.676629\pi\) | ||||
−0.526855 | + | 0.849955i | \(0.676629\pi\) | |||||||
\(674\) | 18.5079 | 0.712896 | ||||||||
\(675\) | −78.4906 | −3.02110 | ||||||||
\(676\) | 3.37140 | 0.129669 | ||||||||
\(677\) | 38.4725 | 1.47862 | 0.739309 | − | 0.673366i | \(-0.235152\pi\) | ||||
0.739309 | + | 0.673366i | \(0.235152\pi\) | |||||||
\(678\) | −21.0106 | −0.806908 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 33.8807 | 1.29927 | ||||||||
\(681\) | −24.1976 | −0.927255 | ||||||||
\(682\) | 0.491795 | 0.0188318 | ||||||||
\(683\) | −23.8648 | −0.913161 | −0.456580 | − | 0.889682i | \(-0.650926\pi\) | ||||
−0.456580 | + | 0.889682i | \(0.650926\pi\) | |||||||
\(684\) | 0.0389006 | 0.00148740 | ||||||||
\(685\) | −55.2736 | −2.11190 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.6590 | −1.05526 | ||||||||
\(688\) | 21.1458 | 0.806177 | ||||||||
\(689\) | 29.6670 | 1.13022 | ||||||||
\(690\) | 20.1349 | 0.766522 | ||||||||
\(691\) | 15.1546 | 0.576508 | 0.288254 | − | 0.957554i | \(-0.406925\pi\) | ||||
0.288254 | + | 0.957554i | \(0.406925\pi\) | |||||||
\(692\) | −2.50923 | −0.0953867 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.9435 | −0.567248 | ||||||||
\(695\) | −40.1675 | −1.52364 | ||||||||
\(696\) | 21.0495 | 0.797877 | ||||||||
\(697\) | −29.0245 | −1.09938 | ||||||||
\(698\) | 3.80642 | 0.144075 | ||||||||
\(699\) | −0.242321 | −0.00916541 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.5410 | −0.926900 | −0.463450 | − | 0.886123i | \(-0.653389\pi\) | ||||
−0.463450 | + | 0.886123i | \(0.653389\pi\) | |||||||
\(702\) | −47.5282 | −1.79384 | ||||||||
\(703\) | 1.86399 | 0.0703017 | ||||||||
\(704\) | 2.42400 | 0.0913580 | ||||||||
\(705\) | −8.19611 | −0.308683 | ||||||||
\(706\) | −4.06518 | −0.152995 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.01420 | 0.0756983 | ||||||||
\(709\) | −16.7029 | −0.627290 | −0.313645 | − | 0.949540i | \(-0.601550\pi\) | ||||
−0.313645 | + | 0.949540i | \(0.601550\pi\) | |||||||
\(710\) | 9.71937 | 0.364762 | ||||||||
\(711\) | −4.39908 | −0.164978 | ||||||||
\(712\) | −6.58072 | −0.246623 | ||||||||
\(713\) | −2.00865 | −0.0752246 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.49064 | 0.317532 | ||||||||
\(716\) | 3.19814 | 0.119520 | ||||||||
\(717\) | 28.4854 | 1.06381 | ||||||||
\(718\) | −32.5916 | −1.21631 | ||||||||
\(719\) | 0.150659 | 0.00561864 | 0.00280932 | − | 0.999996i | \(-0.499106\pi\) | ||||
0.00280932 | + | 0.999996i | \(0.499106\pi\) | |||||||
\(720\) | −10.6747 | −0.397821 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 27.6800 | 1.03014 | ||||||||
\(723\) | 28.9751 | 1.07760 | ||||||||
\(724\) | −2.02205 | −0.0751489 | ||||||||
\(725\) | 70.4662 | 2.61705 | ||||||||
\(726\) | 24.9697 | 0.926711 | ||||||||
\(727\) | 8.32486 | 0.308752 | 0.154376 | − | 0.988012i | \(-0.450663\pi\) | ||||
0.154376 | + | 0.988012i | \(0.450663\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9931 | 1.11086 | ||||||||
\(730\) | −66.6352 | −2.46628 | ||||||||
\(731\) | 14.1110 | 0.521913 | ||||||||
\(732\) | 0.259904 | 0.00960632 | ||||||||
\(733\) | −21.8943 | −0.808685 | −0.404343 | − | 0.914608i | \(-0.632500\pi\) | ||||
−0.404343 | + | 0.914608i | \(0.632500\pi\) | |||||||
\(734\) | 10.1390 | 0.374239 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.84283 | 0.0679278 | ||||||||
\(737\) | 2.39515 | 0.0882267 | ||||||||
\(738\) | 8.45295 | 0.311157 | ||||||||
\(739\) | −1.64886 | −0.0606542 | −0.0303271 | − | 0.999540i | \(-0.509655\pi\) | ||||
−0.0303271 | + | 0.999540i | \(0.509655\pi\) | |||||||
\(740\) | 3.14495 | 0.115611 | ||||||||
\(741\) | 3.81505 | 0.140149 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.14880 | 0.188891 | 0.0944455 | − | 0.995530i | \(-0.469892\pi\) | ||||
0.0944455 | + | 0.995530i | \(0.469892\pi\) | |||||||
\(744\) | −4.21374 | −0.154483 | ||||||||
\(745\) | −36.0028 | −1.31904 | ||||||||
\(746\) | 14.8706 | 0.544450 | ||||||||
\(747\) | −7.11329 | −0.260262 | ||||||||
\(748\) | −0.155965 | −0.00570263 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 91.2804 | 3.33309 | ||||||||
\(751\) | 34.8988 | 1.27347 | 0.636737 | − | 0.771081i | \(-0.280284\pi\) | ||||
0.636737 | + | 0.771081i | \(0.280284\pi\) | |||||||
\(752\) | −5.16878 | −0.188486 | ||||||||
\(753\) | −27.8042 | −1.01324 | ||||||||
\(754\) | 42.6692 | 1.55392 | ||||||||
\(755\) | 28.3888 | 1.03317 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.3537 | −0.885150 | −0.442575 | − | 0.896732i | \(-0.645935\pi\) | ||||
−0.442575 | + | 0.896732i | \(0.645935\pi\) | |||||||
\(758\) | 0.962812 | 0.0349709 | ||||||||
\(759\) | 1.04755 | 0.0380237 | ||||||||
\(760\) | 4.97454 | 0.180445 | ||||||||
\(761\) | 32.9130 | 1.19310 | 0.596548 | − | 0.802577i | \(-0.296539\pi\) | ||||
0.596548 | + | 0.802577i | \(0.296539\pi\) | |||||||
\(762\) | 8.82158 | 0.319572 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.767827 | −0.0277790 | ||||||||
\(765\) | −7.12338 | −0.257546 | ||||||||
\(766\) | −25.5274 | −0.922342 | ||||||||
\(767\) | −46.1456 | −1.66622 | ||||||||
\(768\) | 6.04559 | 0.218151 | ||||||||
\(769\) | 29.1096 | 1.04972 | 0.524859 | − | 0.851189i | \(-0.324118\pi\) | ||||
0.524859 | + | 0.851189i | \(0.324118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.4360 | −0.519899 | ||||||||
\(772\) | −0.341845 | −0.0123033 | ||||||||
\(773\) | 15.1138 | 0.543605 | 0.271803 | − | 0.962353i | \(-0.412380\pi\) | ||||
0.271803 | + | 0.962353i | \(0.412380\pi\) | |||||||
\(774\) | −4.10960 | −0.147717 | ||||||||
\(775\) | −14.1061 | −0.506707 | ||||||||
\(776\) | −11.5189 | −0.413506 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26.3719 | −0.945480 | ||||||||
\(779\) | −4.26153 | −0.152685 | ||||||||
\(780\) | 6.43681 | 0.230475 | ||||||||
\(781\) | 0.505667 | 0.0180942 | ||||||||
\(782\) | 8.47348 | 0.303011 | ||||||||
\(783\) | −27.7961 | −0.993350 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 74.4792 | 2.65828 | ||||||||
\(786\) | 6.83253 | 0.243708 | ||||||||
\(787\) | 43.2670 | 1.54230 | 0.771151 | − | 0.636653i | \(-0.219681\pi\) | ||||
0.771151 | + | 0.636653i | \(0.219681\pi\) | |||||||
\(788\) | −0.701718 | −0.0249977 | ||||||||
\(789\) | −29.4390 | −1.04806 | ||||||||
\(790\) | 49.7742 | 1.77089 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.513360 | −0.0182415 | ||||||||
\(793\) | −5.95443 | −0.211448 | ||||||||
\(794\) | 3.44545 | 0.122274 | ||||||||
\(795\) | 34.8157 | 1.23479 | ||||||||
\(796\) | 1.01689 | 0.0360426 | ||||||||
\(797\) | 9.61790 | 0.340683 | 0.170342 | − | 0.985385i | \(-0.445513\pi\) | ||||
0.170342 | + | 0.985385i | \(0.445513\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.44922 | −0.122024 | ||||||||
\(800\) | 12.9416 | 0.457556 | ||||||||
\(801\) | 1.38359 | 0.0488867 | ||||||||
\(802\) | 3.94059 | 0.139147 | ||||||||
\(803\) | −3.46681 | −0.122341 | ||||||||
\(804\) | 1.81578 | 0.0640377 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.54164 | −0.300867 | ||||||||
\(807\) | 28.8067 | 1.01404 | ||||||||
\(808\) | −3.26998 | −0.115037 | ||||||||
\(809\) | 18.0374 | 0.634161 | 0.317080 | − | 0.948399i | \(-0.397297\pi\) | ||||
0.317080 | + | 0.948399i | \(0.397297\pi\) | |||||||
\(810\) | −44.8217 | −1.57487 | ||||||||
\(811\) | 28.6423 | 1.00577 | 0.502884 | − | 0.864354i | \(-0.332272\pi\) | ||||
0.502884 | + | 0.864354i | \(0.332272\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −47.6845 | −1.67237 | ||||||||
\(814\) | 2.17649 | 0.0762858 | ||||||||
\(815\) | −15.5100 | −0.543293 | ||||||||
\(816\) | 19.2302 | 0.673191 | ||||||||
\(817\) | 2.07184 | 0.0724846 | ||||||||
\(818\) | −37.8024 | −1.32173 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.19012 | −0.251090 | ||||||||
\(821\) | −14.6425 | −0.511025 | −0.255513 | − | 0.966806i | \(-0.582244\pi\) | ||||
−0.255513 | + | 0.966806i | \(0.582244\pi\) | |||||||
\(822\) | −28.9995 | −1.01147 | ||||||||
\(823\) | −21.6422 | −0.754400 | −0.377200 | − | 0.926132i | \(-0.623113\pi\) | ||||
−0.377200 | + | 0.926132i | \(0.623113\pi\) | |||||||
\(824\) | 44.7589 | 1.55925 | ||||||||
\(825\) | 7.35662 | 0.256125 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.94455 | 0.206712 | 0.103356 | − | 0.994644i | \(-0.467042\pi\) | ||||
0.103356 | + | 0.994644i | \(0.467042\pi\) | |||||||
\(828\) | −0.185519 | −0.00644725 | ||||||||
\(829\) | −10.0735 | −0.349868 | −0.174934 | − | 0.984580i | \(-0.555971\pi\) | ||||
−0.174934 | + | 0.984580i | \(0.555971\pi\) | |||||||
\(830\) | 80.4848 | 2.79367 | ||||||||
\(831\) | −42.5335 | −1.47547 | ||||||||
\(832\) | −42.1008 | −1.45958 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −21.0740 | −0.729733 | ||||||||
\(835\) | −107.585 | −3.72314 | ||||||||
\(836\) | −0.0228995 | −0.000791996 0 | ||||||||
\(837\) | 5.56429 | 0.192330 | ||||||||
\(838\) | −15.4717 | −0.534461 | ||||||||
\(839\) | −14.2644 | −0.492461 | −0.246231 | − | 0.969211i | \(-0.579192\pi\) | ||||
−0.246231 | + | 0.969211i | \(0.579192\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.04563 | −0.139504 | ||||||||
\(842\) | −12.3339 | −0.425053 | ||||||||
\(843\) | 24.9313 | 0.858679 | ||||||||
\(844\) | 0.182933 | 0.00629682 | ||||||||
\(845\) | −90.6443 | −3.11826 | ||||||||
\(846\) | 1.00453 | 0.0345365 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 21.9562 | 0.753978 | ||||||||
\(849\) | 18.3044 | 0.628205 | ||||||||
\(850\) | 59.5065 | 2.04106 | ||||||||
\(851\) | −8.88948 | −0.304728 | ||||||||
\(852\) | 0.383349 | 0.0131333 | ||||||||
\(853\) | −3.41266 | −0.116847 | −0.0584236 | − | 0.998292i | \(-0.518607\pi\) | ||||
−0.0584236 | + | 0.998292i | \(0.518607\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.04589 | −0.0357687 | ||||||||
\(856\) | 43.1583 | 1.47512 | ||||||||
\(857\) | 0.980031 | 0.0334772 | 0.0167386 | − | 0.999860i | \(-0.494672\pi\) | ||||
0.0167386 | + | 0.999860i | \(0.494672\pi\) | |||||||
\(858\) | 4.45464 | 0.152079 | ||||||||
\(859\) | 44.5634 | 1.52048 | 0.760242 | − | 0.649640i | \(-0.225080\pi\) | ||||
0.760242 | + | 0.649640i | \(0.225080\pi\) | |||||||
\(860\) | 3.49565 | 0.119201 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.7746 | 0.435103 | ||||||||
\(863\) | 44.8459 | 1.52657 | 0.763286 | − | 0.646061i | \(-0.223585\pi\) | ||||
0.763286 | + | 0.646061i | \(0.223585\pi\) | |||||||
\(864\) | −5.10495 | −0.173674 | ||||||||
\(865\) | 67.4638 | 2.29384 | ||||||||
\(866\) | −45.8347 | −1.55752 | ||||||||
\(867\) | −13.6781 | −0.464532 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.58959 | 0.0878459 | ||||||||
\(870\) | 50.0746 | 1.69769 | ||||||||
\(871\) | −41.5998 | −1.40955 | ||||||||
\(872\) | 14.1262 | 0.478374 | ||||||||
\(873\) | 2.42184 | 0.0819670 | ||||||||
\(874\) | 1.24412 | 0.0420829 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.62821 | −0.0887990 | ||||||||
\(877\) | 17.4548 | 0.589407 | 0.294704 | − | 0.955589i | \(-0.404779\pi\) | ||||
0.294704 | + | 0.955589i | \(0.404779\pi\) | |||||||
\(878\) | −7.92531 | −0.267466 | ||||||||
\(879\) | −7.66968 | −0.258692 | ||||||||
\(880\) | 6.28382 | 0.211828 | ||||||||
\(881\) | 6.27922 | 0.211552 | 0.105776 | − | 0.994390i | \(-0.466267\pi\) | ||||
0.105776 | + | 0.994390i | \(0.466267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.89048 | 0.299189 | 0.149594 | − | 0.988747i | \(-0.452203\pi\) | ||||
0.149594 | + | 0.988747i | \(0.452203\pi\) | |||||||
\(884\) | 2.70884 | 0.0911081 | ||||||||
\(885\) | −54.1543 | −1.82038 | ||||||||
\(886\) | 20.1259 | 0.676143 | ||||||||
\(887\) | 21.7374 | 0.729870 | 0.364935 | − | 0.931033i | \(-0.381091\pi\) | ||||
0.364935 | + | 0.931033i | \(0.381091\pi\) | |||||||
\(888\) | −18.6483 | −0.625796 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −15.6549 | −0.524754 | ||||||||
\(891\) | −2.33192 | −0.0781224 | ||||||||
\(892\) | 4.23866 | 0.141921 | ||||||||
\(893\) | −0.506431 | −0.0169471 | ||||||||
\(894\) | −18.8890 | −0.631742 | ||||||||
\(895\) | −85.9859 | −2.87419 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.1942 | −0.607486 | ||||||||
\(898\) | 29.0840 | 0.970546 | ||||||||
\(899\) | −4.99544 | −0.166607 | ||||||||
\(900\) | −1.30284 | −0.0434281 | ||||||||
\(901\) | 14.6517 | 0.488119 | ||||||||
\(902\) | −4.97597 | −0.165682 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.7557 | 0.823364 | ||||||||
\(905\) | 54.3653 | 1.80716 | ||||||||
\(906\) | 14.8942 | 0.494828 | ||||||||
\(907\) | 7.17151 | 0.238126 | 0.119063 | − | 0.992887i | \(-0.462011\pi\) | ||||
0.119063 | + | 0.992887i | \(0.462011\pi\) | |||||||
\(908\) | −2.52265 | −0.0837170 | ||||||||
\(909\) | 0.687509 | 0.0228032 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.7540 | 1.15145 | 0.575726 | − | 0.817643i | \(-0.304720\pi\) | ||||
0.575726 | + | 0.817643i | \(0.304720\pi\) | |||||||
\(912\) | 2.82347 | 0.0934944 | ||||||||
\(913\) | 4.18736 | 0.138581 | ||||||||
\(914\) | 2.36387 | 0.0781898 | ||||||||
\(915\) | −6.98784 | −0.231011 | ||||||||
\(916\) | −2.88350 | −0.0952736 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −23.4729 | −0.774722 | ||||||||
\(919\) | 51.0930 | 1.68540 | 0.842700 | − | 0.538383i | \(-0.180964\pi\) | ||||
0.842700 | + | 0.538383i | \(0.180964\pi\) | |||||||
\(920\) | −23.7239 | −0.782154 | ||||||||
\(921\) | −27.3062 | −0.899770 | ||||||||
\(922\) | 1.40822 | 0.0463774 | ||||||||
\(923\) | −8.78258 | −0.289082 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −62.4280 | −2.05262 | ||||||||
\(926\) | 21.1311 | 0.694410 | ||||||||
\(927\) | −9.41051 | −0.309082 | ||||||||
\(928\) | 4.58305 | 0.150446 | ||||||||
\(929\) | 28.3627 | 0.930550 | 0.465275 | − | 0.885166i | \(-0.345955\pi\) | ||||
0.465275 | + | 0.885166i | \(0.345955\pi\) | |||||||
\(930\) | −10.0241 | −0.328702 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.0252624 | −0.000827497 0 | ||||||||
\(933\) | −17.5674 | −0.575132 | ||||||||
\(934\) | −18.8403 | −0.616475 | ||||||||
\(935\) | 4.19330 | 0.137136 | ||||||||
\(936\) | 8.91620 | 0.291435 | ||||||||
\(937\) | −43.8732 | −1.43328 | −0.716638 | − | 0.697446i | \(-0.754320\pi\) | ||||
−0.716638 | + | 0.697446i | \(0.754320\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.5693 | 1.25866 | ||||||||
\(940\) | −0.854459 | −0.0278694 | ||||||||
\(941\) | −15.9227 | −0.519066 | −0.259533 | − | 0.965734i | \(-0.583569\pi\) | ||||
−0.259533 | + | 0.965734i | \(0.583569\pi\) | |||||||
\(942\) | 39.0757 | 1.27316 | ||||||||
\(943\) | 20.3235 | 0.661824 | ||||||||
\(944\) | −34.1518 | −1.11155 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.41919 | 0.0786546 | ||||||||
\(947\) | 11.6994 | 0.380181 | 0.190090 | − | 0.981767i | \(-0.439122\pi\) | ||||
0.190090 | + | 0.981767i | \(0.439122\pi\) | |||||||
\(948\) | 1.96319 | 0.0637613 | ||||||||
\(949\) | 60.2126 | 1.95458 | ||||||||
\(950\) | 8.73705 | 0.283467 | ||||||||
\(951\) | −42.4293 | −1.37586 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.1045 | −1.72022 | −0.860112 | − | 0.510105i | \(-0.829606\pi\) | ||||
−0.860112 | + | 0.510105i | \(0.829606\pi\) | |||||||
\(954\) | −4.26709 | −0.138152 | ||||||||
\(955\) | 20.6440 | 0.668023 | ||||||||
\(956\) | 2.96965 | 0.0960455 | ||||||||
\(957\) | 2.60522 | 0.0842148 | ||||||||
\(958\) | −17.9283 | −0.579237 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −49.4075 | −1.59462 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −37.8019 | −1.21878 | ||||||||
\(963\) | −9.07398 | −0.292405 | ||||||||
\(964\) | 3.02071 | 0.0972904 | ||||||||
\(965\) | 9.19093 | 0.295866 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.5960 | 0.823112 | 0.411556 | − | 0.911385i | \(-0.364985\pi\) | ||||
0.411556 | + | 0.911385i | \(0.364985\pi\) | |||||||
\(968\) | −29.4205 | −0.945610 | ||||||||
\(969\) | 1.88415 | 0.0605276 | ||||||||
\(970\) | −27.4024 | −0.879839 | ||||||||
\(971\) | 54.0563 | 1.73475 | 0.867375 | − | 0.497655i | \(-0.165806\pi\) | ||||
0.867375 | + | 0.497655i | \(0.165806\pi\) | |||||||
\(972\) | 0.946013 | 0.0303434 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −58.1328 | −1.86270 | ||||||||
\(975\) | −127.772 | −4.09198 | ||||||||
\(976\) | −4.40680 | −0.141058 | ||||||||
\(977\) | −17.3425 | −0.554834 | −0.277417 | − | 0.960750i | \(-0.589478\pi\) | ||||
−0.277417 | + | 0.960750i | \(0.589478\pi\) | |||||||
\(978\) | −8.13738 | −0.260205 | ||||||||
\(979\) | −0.814474 | −0.0260307 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.97002 | −0.0948254 | ||||||||
\(982\) | 8.49740 | 0.271163 | ||||||||
\(983\) | 46.7270 | 1.49036 | 0.745181 | − | 0.666863i | \(-0.232363\pi\) | ||||
0.745181 | + | 0.666863i | \(0.232363\pi\) | |||||||
\(984\) | 42.6345 | 1.35914 | ||||||||
\(985\) | 18.8666 | 0.601138 | ||||||||
\(986\) | 21.0732 | 0.671107 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.397725 | 0.0126533 | ||||||||
\(989\) | −9.88075 | −0.314190 | ||||||||
\(990\) | −1.22123 | −0.0388134 | ||||||||
\(991\) | −57.0083 | −1.81093 | −0.905464 | − | 0.424423i | \(-0.860477\pi\) | ||||
−0.905464 | + | 0.424423i | \(0.860477\pi\) | |||||||
\(992\) | −0.917448 | −0.0291290 | ||||||||
\(993\) | 40.9852 | 1.30063 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.3403 | −0.866745 | ||||||||
\(996\) | 3.17446 | 0.100587 | ||||||||
\(997\) | −30.6155 | −0.969601 | −0.484801 | − | 0.874625i | \(-0.661108\pi\) | ||||
−0.484801 | + | 0.874625i | \(0.661108\pi\) | |||||||
\(998\) | −8.19360 | −0.259364 | ||||||||
\(999\) | 24.6253 | 0.779111 |
(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 | 1519.2.a.j.1.3 | 13 | ||
7.3 | odd | 6 | 217.2.f.b.156.11 | yes | 26 | ||
7.5 | odd | 6 | 217.2.f.b.32.11 | ✓ | 26 | ||
7.6 | odd | 2 | 1519.2.a.k.1.3 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
217.2.f.b.32.11 | ✓ | 26 | 7.5 | odd | 6 | ||
217.2.f.b.156.11 | yes | 26 | 7.3 | odd | 6 | ||
1519.2.a.j.1.3 | 13 | 1.1 | even | 1 | trivial | ||
1519.2.a.k.1.3 | 13 | 7.6 | odd | 2 |