Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1148,2,Mod(1,1148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1148, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1148 = 2^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1148.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: | \(9.16682615204\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.287349.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 6x^{3} + 7x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.36870\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1148.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.126667 | −0.0731312 | −0.0365656 | − | 0.999331i | \(-0.511642\pi\) | ||||
−0.0365656 | + | 0.999331i | \(0.511642\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.03743 | −1.80559 | −0.902797 | − | 0.430067i | \(-0.858490\pi\) | ||||
−0.902797 | + | 0.430067i | \(0.858490\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98396 | −0.994652 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.52602 | −1.06314 | −0.531568 | − | 0.847016i | \(-0.678397\pi\) | ||||
−0.531568 | + | 0.847016i | \(0.678397\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.41540 | 0.669911 | 0.334956 | − | 0.942234i | \(-0.391279\pi\) | ||||
0.334956 | + | 0.942234i | \(0.391279\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.511409 | 0.132045 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.0534754 | −0.0129697 | −0.00648484 | − | 0.999979i | \(-0.502064\pi\) | ||||
−0.00648484 | + | 0.999979i | \(0.502064\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.51925 | 1.03679 | 0.518393 | − | 0.855142i | \(-0.326530\pi\) | ||||
0.518393 | + | 0.855142i | \(0.326530\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.126667 | 0.0276410 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.50378 | 0.522074 | 0.261037 | − | 0.965329i | \(-0.415936\pi\) | ||||
0.261037 | + | 0.965329i | \(0.415936\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.3008 | 2.26017 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.757969 | 0.145871 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.96338 | 1.66446 | 0.832229 | − | 0.554432i | \(-0.187064\pi\) | ||||
0.832229 | + | 0.554432i | \(0.187064\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.562641 | 0.101053 | 0.0505266 | − | 0.998723i | \(-0.483910\pi\) | ||||
0.0505266 | + | 0.998723i | \(0.483910\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.446630 | 0.0777484 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.03743 | 0.682450 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.34135 | −0.549315 | −0.274657 | − | 0.961542i | \(-0.588564\pi\) | ||||
−0.274657 | + | 0.961542i | \(0.588564\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.305951 | −0.0489914 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96934 | 0.452821 | 0.226410 | − | 0.974032i | \(-0.427301\pi\) | ||||
0.226410 | + | 0.974032i | \(0.427301\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12.0475 | 1.79594 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.57187 | −0.958605 | −0.479303 | − | 0.877650i | \(-0.659110\pi\) | ||||
−0.479303 | + | 0.877650i | \(0.659110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.00677356 | 0.000948488 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.414541 | −0.0569416 | −0.0284708 | − | 0.999595i | \(-0.509064\pi\) | ||||
−0.0284708 | + | 0.999595i | \(0.509064\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.2361 | 1.91959 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.572439 | −0.0758214 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.6898 | −1.39169 | −0.695844 | − | 0.718193i | \(-0.744969\pi\) | ||||
−0.695844 | + | 0.718193i | \(0.744969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.49414 | 0.831490 | 0.415745 | − | 0.909481i | \(-0.363521\pi\) | ||||
0.415745 | + | 0.909481i | \(0.363521\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.98396 | 0.375943 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.75201 | −1.20959 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.1258 | 1.48141 | 0.740704 | − | 0.671832i | \(-0.234492\pi\) | ||||
0.740704 | + | 0.671832i | \(0.234492\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.317146 | −0.0381799 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4897 | 1.24489 | 0.622447 | − | 0.782662i | \(-0.286139\pi\) | ||||
0.622447 | + | 0.782662i | \(0.286139\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.94877 | −0.462168 | −0.231084 | − | 0.972934i | \(-0.574227\pi\) | ||||
−0.231084 | + | 0.972934i | \(0.574227\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.43144 | −0.165289 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.52602 | 0.401827 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.62951 | −1.08340 | −0.541702 | − | 0.840570i | \(-0.682220\pi\) | ||||
−0.541702 | + | 0.840570i | \(0.682220\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.85586 | 0.983984 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.61015 | 0.725559 | 0.362779 | − | 0.931875i | \(-0.381828\pi\) | ||||
0.362779 | + | 0.931875i | \(0.381828\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.215903 | 0.0234180 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.13536 | −0.121724 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.8854 | −1.47185 | −0.735927 | − | 0.677061i | \(-0.763253\pi\) | ||||
−0.735927 | + | 0.677061i | \(0.763253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.41540 | −0.253203 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0712680 | −0.00739014 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.2462 | −1.87202 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.8154 | −1.19967 | −0.599834 | − | 0.800125i | \(-0.704767\pi\) | ||||
−0.599834 | + | 0.800125i | \(0.704767\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.5215 | 1.05745 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.44606 | −0.442399 | −0.221200 | − | 0.975229i | \(-0.570997\pi\) | ||||
−0.221200 | + | 0.975229i | \(0.570997\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.9239 | 1.27343 | 0.636717 | − | 0.771097i | \(-0.280292\pi\) | ||||
0.636717 | + | 0.771097i | \(0.280292\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.511409 | −0.0499084 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.57971 | −0.442737 | −0.221369 | − | 0.975190i | \(-0.571052\pi\) | ||||
−0.221369 | + | 0.975190i | \(0.571052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.1663 | 1.45267 | 0.726336 | − | 0.687340i | \(-0.241222\pi\) | ||||
0.726336 | + | 0.687340i | \(0.241222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.423239 | 0.0401720 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.4185 | 1.35637 | 0.678187 | − | 0.734889i | \(-0.262766\pi\) | ||||
0.678187 | + | 0.734889i | \(0.262766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.1088 | −0.942653 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.20744 | −0.666328 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0534754 | 0.00490208 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.43283 | 0.130257 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.126667 | 0.0114212 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −25.4392 | −2.27535 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.4061 | 1.54454 | 0.772272 | − | 0.635292i | \(-0.219120\pi\) | ||||
0.772272 | + | 0.635292i | \(0.219120\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.376118 | −0.0331153 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.82687 | 0.858578 | 0.429289 | − | 0.903167i | \(-0.358764\pi\) | ||||
0.429289 | + | 0.903167i | \(0.358764\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.51925 | −0.391869 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.06025 | −0.263384 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.39344 | −0.119050 | −0.0595248 | − | 0.998227i | \(-0.518959\pi\) | ||||
−0.0595248 | + | 0.998227i | \(0.518959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8863 | 1.00818 | 0.504092 | − | 0.863650i | \(-0.331827\pi\) | ||||
0.504092 | + | 0.863650i | \(0.331827\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.832438 | 0.0701039 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.51675 | −0.712206 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −36.1890 | −3.00534 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.126667 | −0.0104473 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.1792 | 1.57122 | 0.785609 | − | 0.618723i | \(-0.212350\pi\) | ||||
0.785609 | + | 0.618723i | \(0.212350\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.11703 | −0.335039 | −0.167520 | − | 0.985869i | \(-0.553576\pi\) | ||||
−0.167520 | + | 0.985869i | \(0.553576\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.159568 | 0.0129003 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.27162 | −0.182461 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.55689 | −0.124253 | −0.0621267 | − | 0.998068i | \(-0.519788\pi\) | ||||
−0.0621267 | + | 0.998068i | \(0.519788\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.0525087 | 0.00416421 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.50378 | −0.197325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.62513 | 0.518920 | 0.259460 | − | 0.965754i | \(-0.416455\pi\) | ||||
0.259460 | + | 0.965754i | \(0.416455\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.80324 | −0.140382 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.87052 | −0.454274 | −0.227137 | − | 0.973863i | \(-0.572937\pi\) | ||||
−0.227137 | + | 0.973863i | \(0.572937\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.16585 | −0.551219 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.4852 | −1.03124 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.3062 | −1.69591 | −0.847954 | − | 0.530070i | \(-0.822166\pi\) | ||||
−0.847954 | + | 0.530070i | \(0.822166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.3008 | −0.854264 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.35404 | 0.101776 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.1906 | 1.28489 | 0.642445 | − | 0.766332i | \(-0.277920\pi\) | ||||
0.642445 | + | 0.766332i | \(0.277920\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.6422 | −1.16267 | −0.581337 | − | 0.813663i | \(-0.697470\pi\) | ||||
−0.581337 | + | 0.813663i | \(0.697470\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.822593 | −0.0608079 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.4905 | 0.991839 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.188555 | 0.0137885 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.757969 | −0.0551342 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.1606 | 1.38641 | 0.693207 | − | 0.720739i | \(-0.256197\pi\) | ||||
0.693207 | + | 0.720739i | \(0.256197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9782 | −0.934192 | −0.467096 | − | 0.884207i | \(-0.654700\pi\) | ||||
−0.467096 | + | 0.884207i | \(0.654700\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.23526 | 0.0884586 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.9940 | 1.13953 | 0.569764 | − | 0.821808i | \(-0.307035\pi\) | ||||
0.569764 | + | 0.821808i | \(0.307035\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 21.2277 | 1.50479 | 0.752394 | − | 0.658713i | \(-0.228899\pi\) | ||||
0.752394 | + | 0.658713i | \(0.228899\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.53594 | −0.108337 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.96338 | −0.629106 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.03743 | 0.281986 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.47116 | −0.519282 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.9350 | −1.10224 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.273338 | 0.0188174 | 0.00940869 | − | 0.999956i | \(-0.497005\pi\) | ||||
0.00940869 | + | 0.999956i | \(0.497005\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.32869 | −0.0910405 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.9885 | −0.817610 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.562641 | −0.0381945 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.500178 | 0.0337989 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.129164 | −0.00868853 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.90787 | 0.395620 | 0.197810 | − | 0.980240i | \(-0.436617\pi\) | ||||
0.197810 | + | 0.980240i | \(0.436617\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −33.7212 | −2.24808 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.2532 | 1.60974 | 0.804871 | − | 0.593450i | \(-0.202234\pi\) | ||||
0.804871 | + | 0.593450i | \(0.202234\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.2406 | 1.73403 | 0.867013 | − | 0.498285i | \(-0.166037\pi\) | ||||
0.867013 | + | 0.498285i | \(0.166037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.446630 | −0.0293861 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.47026 | −0.554905 | −0.277453 | − | 0.960739i | \(-0.589490\pi\) | ||||
−0.277453 | + | 0.960739i | \(0.589490\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.5335 | 1.73085 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.21974 | 0.0792307 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.2531 | 0.792586 | 0.396293 | − | 0.918124i | \(-0.370296\pi\) | ||||
0.396293 | + | 0.918124i | \(0.370296\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3179 | −0.793467 | −0.396734 | − | 0.917934i | \(-0.629856\pi\) | ||||
−0.396734 | + | 0.917934i | \(0.629856\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.39565 | −0.217831 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.03743 | −0.257942 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.9158 | 0.694555 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.837288 | −0.0530610 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.1168 | −1.20664 | −0.603322 | − | 0.797498i | \(-0.706156\pi\) | ||||
−0.603322 | + | 0.797498i | \(0.706156\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.82837 | −0.555035 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0273478 | −0.00171258 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.15564 | 0.508735 | 0.254367 | − | 0.967108i | \(-0.418133\pi\) | ||||
0.254367 | + | 0.967108i | \(0.418133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.34135 | 0.207621 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.7463 | −1.65556 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.6372 | −0.779246 | −0.389623 | − | 0.920974i | \(-0.627395\pi\) | ||||
−0.389623 | + | 0.920974i | \(0.627395\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.67368 | 0.102813 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.75883 | 0.107638 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.37216 | 0.327546 | 0.163773 | − | 0.986498i | \(-0.447634\pi\) | ||||
0.163773 | + | 0.986498i | \(0.447634\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.2397 | 1.35096 | 0.675482 | − | 0.737377i | \(-0.263936\pi\) | ||||
0.675482 | + | 0.737377i | \(0.263936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.305951 | 0.0185170 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −39.8470 | −2.40287 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.0233 | 0.722411 | 0.361205 | − | 0.932486i | \(-0.382365\pi\) | ||||
0.361205 | + | 0.932486i | \(0.382365\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.67889 | −0.100513 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.6959 | −1.65220 | −0.826100 | − | 0.563524i | \(-0.809445\pi\) | ||||
−0.826100 | + | 0.563524i | \(0.809445\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.0824 | 1.25322 | 0.626610 | − | 0.779333i | \(-0.284442\pi\) | ||||
0.626610 | + | 0.779333i | \(0.284442\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.31118 | 0.136903 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.00000 | 0.0590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9971 | −0.999832 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.49662 | 0.0877331 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.387194 | 0.0226201 | 0.0113100 | − | 0.999936i | \(-0.496400\pi\) | ||||
0.0113100 | + | 0.999936i | \(0.496400\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 43.1592 | 2.51282 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.67262 | −0.155081 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.04762 | 0.349743 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.96934 | −0.171150 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.563168 | 0.0323532 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.2197 | −1.50133 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.6093 | −1.23331 | −0.616653 | − | 0.787235i | \(-0.711512\pi\) | ||||
−0.616653 | + | 0.787235i | \(0.711512\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.63704 | −0.0931278 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.82981 | 0.330578 | 0.165289 | − | 0.986245i | \(-0.447144\pi\) | ||||
0.165289 | + | 0.986245i | \(0.447144\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.6459 | −1.90178 | −0.950889 | − | 0.309531i | \(-0.899828\pi\) | ||||
−0.950889 | + | 0.309531i | \(0.899828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.0475 | −0.678801 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.05722 | 0.0593796 | 0.0296898 | − | 0.999559i | \(-0.490548\pi\) | ||||
0.0296898 | + | 0.999559i | \(0.490548\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −31.6051 | −1.76954 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.580098 | 0.0323779 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.241668 | −0.0134468 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.2961 | 1.51411 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.92107 | −0.106236 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.57187 | 0.362319 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.54210 | −0.249656 | −0.124828 | − | 0.992178i | \(-0.539838\pi\) | ||||
−0.124828 | + | 0.992178i | \(0.539838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.97044 | 0.546377 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −48.9572 | −2.67482 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.87133 | −0.101938 | −0.0509690 | − | 0.998700i | \(-0.516231\pi\) | ||||
−0.0509690 | + | 0.998700i | \(0.516231\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.82634 | −0.0991933 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.98388 | −0.107433 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.28045 | 0.0689373 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.5851 | −1.48084 | −0.740422 | − | 0.672142i | \(-0.765374\pi\) | ||||
−0.740422 | + | 0.672142i | \(0.765374\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.987265 | −0.0528471 | −0.0264235 | − | 0.999651i | \(-0.508412\pi\) | ||||
−0.0264235 | + | 0.999651i | \(0.508412\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.83080 | 0.0977208 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.4049 | 1.56506 | 0.782532 | − | 0.622610i | \(-0.213928\pi\) | ||||
0.782532 | + | 0.622610i | \(0.213928\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −42.3513 | −2.24777 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.00677356 | −0.000358495 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.11369 | −0.217112 | −0.108556 | − | 0.994090i | \(-0.534623\pi\) | ||||
−0.108556 | + | 0.994090i | \(0.534623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.42360 | 0.0749266 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.181492 | −0.00952587 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.9429 | 0.834488 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.2034 | 0.845810 | 0.422905 | − | 0.906174i | \(-0.361010\pi\) | ||||
0.422905 | + | 0.906174i | \(0.361010\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.98396 | 0.155339 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.414541 | 0.0215219 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.8956 | 1.54794 | 0.773969 | − | 0.633224i | \(-0.218269\pi\) | ||||
0.773969 | + | 0.633224i | \(0.218269\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.22231 | 0.166399 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.6501 | 1.11504 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.7403 | −1.78449 | −0.892245 | − | 0.451551i | \(-0.850871\pi\) | ||||
−0.892245 | + | 0.451551i | \(0.850871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.20478 | −0.112954 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.0199 | −1.02297 | −0.511484 | − | 0.859293i | \(-0.670904\pi\) | ||||
−0.511484 | + | 0.859293i | \(0.670904\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.2361 | −0.725537 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.86039 | −0.450399 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.0731 | 0.967043 | 0.483521 | − | 0.875333i | \(-0.339358\pi\) | ||||
0.483521 | + | 0.875333i | \(0.339358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.133890 | −0.00677113 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.24474 | −0.0627888 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 38.8785 | 1.95619 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.27701 | 0.264845 | 0.132423 | − | 0.991193i | \(-0.457724\pi\) | ||||
0.132423 | + | 0.991193i | \(0.457724\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.572439 | 0.0286578 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.5626 | −1.67604 | −0.838018 | − | 0.545643i | \(-0.816286\pi\) | ||||
−0.838018 | + | 0.545643i | \(0.816286\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.35900 | 0.0676967 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −35.7549 | −1.77668 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.7817 | 0.583996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.67568 | −0.379538 | −0.189769 | − | 0.981829i | \(-0.560774\pi\) | ||||
−0.189769 | + | 0.981829i | \(0.560774\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.176503 | 0.00870624 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.6898 | 0.526009 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.6880 | −1.31006 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.50560 | −0.0737297 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.9653 | 0.779956 | 0.389978 | − | 0.920824i | \(-0.372483\pi\) | ||||
0.389978 | + | 0.920824i | \(0.372483\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.83173 | 0.186747 | 0.0933737 | − | 0.995631i | \(-0.470235\pi\) | ||||
0.0933737 | + | 0.995631i | \(0.470235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.6102 | 0.953478 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.604317 | −0.0293137 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.49414 | −0.314274 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.07879 | 0.0520845 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.6049 | −0.751664 | −0.375832 | − | 0.926688i | \(-0.622643\pi\) | ||||
−0.375832 | + | 0.926688i | \(0.622643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5203 | 0.601689 | 0.300845 | − | 0.953673i | \(-0.402731\pi\) | ||||
0.300845 | + | 0.953673i | \(0.402731\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.58395 | 0.219784 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.3152 | 0.541279 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.29040 | 0.157042 | 0.0785212 | − | 0.996912i | \(-0.474980\pi\) | ||||
0.0785212 | + | 0.996912i | \(0.474980\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.98396 | −0.142093 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.7668 | 1.55680 | 0.778399 | − | 0.627770i | \(-0.216032\pi\) | ||||
0.778399 | + | 0.627770i | \(0.216032\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 56.0615 | 2.65757 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.42937 | −0.114905 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.6287 | 1.58704 | 0.793518 | − | 0.608547i | \(-0.208247\pi\) | ||||
0.793518 | + | 0.608547i | \(0.208247\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.52602 | 0.166034 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.521492 | 0.0245018 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.75201 | 0.457181 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.80973 | −0.178212 | −0.0891058 | − | 0.996022i | \(-0.528401\pi\) | ||||
−0.0891058 | + | 0.996022i | \(0.528401\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.0405327 | −0.00189190 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.17907 | −0.380937 | −0.190469 | − | 0.981693i | \(-0.561001\pi\) | ||||
−0.190469 | + | 0.981693i | \(0.561001\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.7880 | 1.01257 | 0.506287 | − | 0.862365i | \(-0.331018\pi\) | ||||
0.506287 | + | 0.862365i | \(0.331018\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.287739 | 0.0133436 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.9535 | 1.71001 | 0.855003 | − | 0.518624i | \(-0.173555\pi\) | ||||
0.855003 | + | 0.518624i | \(0.173555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.1258 | −0.559919 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.197207 | 0.00908680 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.4700 | −0.481410 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 51.0713 | 2.34331 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.23697 | 0.0566371 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.3900 | −0.840259 | −0.420129 | − | 0.907464i | \(-0.638015\pi\) | ||||
−0.420129 | + | 0.907464i | \(0.638015\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.07069 | −0.367992 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.317146 | 0.0144306 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 47.7037 | 2.16611 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.1947 | 0.733851 | 0.366925 | − | 0.930250i | \(-0.380410\pi\) | ||||
0.366925 | + | 0.930250i | \(0.380410\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.839185 | −0.0379493 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.5702 | 0.838061 | 0.419030 | − | 0.907972i | \(-0.362370\pi\) | ||||
0.419030 | + | 0.907972i | \(0.362370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.479320 | −0.0215875 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −42.4798 | −1.90932 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.4897 | −0.470525 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.23630 | −0.144877 | −0.0724383 | − | 0.997373i | \(-0.523078\pi\) | ||||
−0.0724383 | + | 0.997373i | \(0.523078\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.743600 | 0.0332216 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.9849 | −0.712734 | −0.356367 | − | 0.934346i | \(-0.615985\pi\) | ||||
−0.356367 | + | 0.934346i | \(0.615985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.9506 | 0.798793 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.907676 | 0.0403113 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.1681 | 0.716640 | 0.358320 | − | 0.933599i | \(-0.383350\pi\) | ||||
0.358320 | + | 0.933599i | \(0.383350\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.94877 | 0.174683 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.42545 | 0.151237 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −52.1795 | −2.29931 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.1725 | 1.01913 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.82546 | 0.124024 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.6766 | −0.862048 | −0.431024 | − | 0.902341i | \(-0.641848\pi\) | ||||
−0.431024 | + | 0.902341i | \(0.641848\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.2052 | 0.752332 | 0.376166 | − | 0.926552i | \(-0.377242\pi\) | ||||
0.376166 | + | 0.926552i | \(0.377242\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.43144 | 0.0624733 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.0300874 | −0.00131063 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7311 | −0.727439 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31.8978 | 1.38424 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.41540 | −0.104623 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.4903 | 0.799404 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.17749 | −0.0939655 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.52602 | −0.151877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.0154440 | 0.000663988 0 | 0.000331994 | − | 1.00000i | \(-0.499894\pi\) | ||||
0.000331994 | 1.00000i | \(0.499894\pi\) | ||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.98135 | 0.0850277 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −61.2330 | −2.62294 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.7473 | 1.44293 | 0.721464 | − | 0.692451i | \(-0.243469\pi\) | ||||
0.721464 | + | 0.692451i | \(0.243469\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.3782 | −0.827043 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.5077 | 1.72569 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.62951 | 0.409488 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.70880 | −0.0725344 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.2488 | 1.40880 | 0.704399 | − | 0.709805i | \(-0.251217\pi\) | ||||
0.704399 | + | 0.709805i | \(0.251217\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.17215 | 0.303350 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0238837 | −0.00100837 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.0275 | −0.844059 | −0.422029 | − | 0.906582i | \(-0.638682\pi\) | ||||
−0.422029 | + | 0.906582i | \(0.638682\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −58.2135 | −2.44906 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.85586 | −0.371911 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.3964 | 1.27428 | 0.637141 | − | 0.770747i | \(-0.280117\pi\) | ||||
0.637141 | + | 0.770747i | \(0.280117\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.0843 | −1.09160 | −0.545798 | − | 0.837917i | \(-0.683773\pi\) | ||||
−0.545798 | + | 0.837917i | \(0.683773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.42702 | −0.101390 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 28.2948 | 1.17998 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.3390 | 1.67934 | 0.839668 | − | 0.543101i | \(-0.182750\pi\) | ||||
0.839668 | + | 0.543101i | \(0.182750\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.64391 | 0.0683186 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.61015 | −0.274235 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.46168 | 0.0605367 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29.0996 | 1.20312 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.30040 | 0.0536733 | 0.0268367 | − | 0.999640i | \(-0.491457\pi\) | ||||
0.0268367 | + | 0.999640i | \(0.491457\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.54271 | 0.104771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.02592 | −0.0833351 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.1353 | 1.27857 | 0.639286 | − | 0.768969i | \(-0.279230\pi\) | ||||
0.639286 | + | 0.768969i | \(0.279230\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.215903 | −0.00885116 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.68884 | −0.110047 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3986 | 0.465734 | 0.232867 | − | 0.972509i | \(-0.425189\pi\) | ||||
0.232867 | + | 0.972509i | \(0.425189\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7031 | −0.477380 | −0.238690 | − | 0.971096i | \(-0.576718\pi\) | ||||
−0.238690 | + | 0.971096i | \(0.576718\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −36.1830 | −1.47348 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.78495 | −0.235192 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.8918 | 1.37562 | 0.687812 | − | 0.725888i | \(-0.258571\pi\) | ||||
0.687812 | + | 0.725888i | \(0.258571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.13536 | 0.0460073 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.8737 | −0.642180 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.4202 | −1.51139 | −0.755693 | − | 0.654925i | \(-0.772700\pi\) | ||||
−0.755693 | + | 0.654925i | \(0.772700\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.511409 | −0.0206220 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.1568 | 0.972518 | 0.486259 | − | 0.873815i | \(-0.338361\pi\) | ||||
0.486259 | + | 0.873815i | \(0.338361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.0504 | 0.564732 | 0.282366 | − | 0.959307i | \(-0.408881\pi\) | ||||
0.282366 | + | 0.959307i | \(0.408881\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.89779 | 0.0761556 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.8854 | 0.556309 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 46.2049 | 1.84820 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.01843 | 0.0806085 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.178680 | 0.00712443 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.31402 | 0.370785 | 0.185393 | − | 0.982665i | \(-0.440644\pi\) | ||||
0.185393 | + | 0.982665i | \(0.440644\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.0346229 | −0.00137614 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −70.2760 | −2.78882 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.41540 | 0.0957016 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −31.3007 | −1.23824 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.28680 | 0.287811 | 0.143906 | − | 0.989591i | \(-0.454034\pi\) | ||||
0.143906 | + | 0.989591i | \(0.454034\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.967833 | −0.0381676 | −0.0190838 | − | 0.999818i | \(-0.506075\pi\) | ||||
−0.0190838 | + | 0.999818i | \(0.506075\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.51855 | 0.0597928 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.7171 | 0.421333 | 0.210666 | − | 0.977558i | \(-0.432437\pi\) | ||||
0.210666 | + | 0.977558i | \(0.432437\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.6923 | 1.47955 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0712680 | 0.00279321 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0378 | 0.471077 | 0.235539 | − | 0.971865i | \(-0.424315\pi\) | ||||
0.235539 | + | 0.971865i | \(0.424315\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.6753 | −1.55024 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.7829 | 0.459697 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.3539 | −1.64987 | −0.824936 | − | 0.565226i | \(-0.808789\pi\) | ||||
−0.824936 | + | 0.565226i | \(0.808789\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.16165 | −0.0840783 | −0.0420391 | − | 0.999116i | \(-0.513385\pi\) | ||||
−0.0420391 | + | 0.999116i | \(0.513385\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0163609 | 0.000635403 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.2462 | 0.707555 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.4423 | 0.868970 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.748332 | −0.0289322 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.8985 | −0.883987 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.796393 | −0.0306987 | −0.0153494 | − | 0.999882i | \(-0.504886\pi\) | ||||
−0.0153494 | + | 0.999882i | \(0.504886\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.56570 | 0.329694 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.3629 | 1.12851 | 0.564254 | − | 0.825601i | \(-0.309164\pi\) | ||||
0.564254 | + | 0.825601i | \(0.309164\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.8154 | 0.453432 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.07208 | −0.117722 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.2777 | 1.50292 | 0.751459 | − | 0.659780i | \(-0.229351\pi\) | ||||
0.751459 | + | 0.659780i | \(0.229351\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.62591 | 0.214955 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.32381 | −0.126811 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.00128 | −0.0381458 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.3284 | −1.34396 | −0.671979 | − | 0.740570i | \(-0.734555\pi\) | ||||
−0.671979 | + | 0.740570i | \(0.734555\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.5215 | −0.399678 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −47.9901 | −1.82037 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0534754 | 0.00202552 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.07290 | 0.0405809 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.6523 | −0.515640 | −0.257820 | − | 0.966193i | \(-0.583004\pi\) | ||||
−0.257820 | + | 0.966193i | \(0.583004\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.1004 | −0.569522 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.36091 | −0.126579 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.44606 | 0.167211 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.4663 | −0.430626 | −0.215313 | − | 0.976545i | \(-0.569077\pi\) | ||||
−0.215313 | + | 0.976545i | \(0.569077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28.7340 | 1.07761 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.40873 | 0.0527572 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 34.3858 | 1.28596 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.55206 | −0.0579628 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.0868167 | 0.00323772 | 0.00161886 | − | 0.999999i | \(-0.499485\pi\) | ||||
0.00161886 | + | 0.999999i | \(0.499485\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.9239 | −0.481313 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.56027 | 0.0580272 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 101.294 | 3.76196 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.28840 | −0.159048 | −0.0795239 | − | 0.996833i | \(-0.525340\pi\) | ||||
−0.0795239 | + | 0.996833i | \(0.525340\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.1375 | −0.968054 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.158787 | −0.00587294 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.7270 | −0.765569 | −0.382785 | − | 0.923838i | \(-0.625035\pi\) | ||||
−0.382785 | + | 0.923838i | \(0.625035\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.511409 | 0.0188636 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.7560 | −1.57494 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.79602 | −0.213210 | −0.106605 | − | 0.994301i | \(-0.533998\pi\) | ||||
−0.106605 | + | 0.994301i | \(0.533998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.38267 | −0.0507936 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.74866 | 0.0641520 | 0.0320760 | − | 0.999485i | \(-0.489788\pi\) | ||||
0.0320760 | + | 0.999485i | \(0.489788\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −77.4345 | −2.83698 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −19.7244 | −0.721678 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.57971 | 0.167339 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.113270 | 0.00413330 | 0.00206665 | − | 0.999998i | \(-0.499342\pi\) | ||||
0.00206665 | + | 0.999998i | \(0.499342\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.42147 | 0.0882433 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.6222 | 0.604945 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.7134 | 1.07995 | 0.539976 | − | 0.841680i | \(-0.318433\pi\) | ||||
0.539976 | + | 0.841680i | \(0.318433\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.11826 | 0.0405904 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −45.1150 | −1.63542 | −0.817708 | − | 0.575633i | \(-0.804756\pi\) | ||||
−0.817708 | + | 0.575633i | \(0.804756\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.1663 | −0.549058 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.644245 | −0.0232927 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.8200 | −0.932307 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.2415 | 1.16266 | 0.581329 | − | 0.813669i | \(-0.302533\pi\) | ||||
0.581329 | + | 0.813669i | \(0.302533\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.03305 | −0.0372044 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.6254 | −0.849747 | −0.424874 | − | 0.905253i | \(-0.639682\pi\) | ||||
−0.424874 | + | 0.905253i | \(0.639682\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.35832 | 0.228397 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.423239 | −0.0151836 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.51925 | −0.161919 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.9868 | −1.32349 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.79397 | 0.242797 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.28584 | 0.224351 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.48114 | −0.159735 | −0.0798676 | − | 0.996805i | \(-0.525450\pi\) | ||||
−0.0798676 | + | 0.996805i | \(0.525450\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.60072 | 0.0569872 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.4185 | −0.512661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.6860 | 0.557024 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.212000 | −0.00751887 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.42314 | −0.262941 | −0.131470 | − | 0.991320i | \(-0.541970\pi\) | ||||
−0.131470 | + | 0.991320i | \(0.541970\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.351433 | 0.0124328 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 41.4336 | 1.46398 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.9234 | 0.491348 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.1088 | 0.356289 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.680475 | −0.0239538 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.9314 | 0.524961 | 0.262480 | − | 0.964937i | \(-0.415460\pi\) | ||||
0.262480 | + | 0.964937i | \(0.415460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.8200 | 1.57384 | 0.786922 | − | 0.617052i | \(-0.211673\pi\) | ||||
0.786922 | + | 0.617052i | \(0.211673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.81703 | −0.0987976 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −26.7485 | −0.936959 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.4192 | 0.469478 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.20744 | 0.251848 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.5228 | −0.925654 | −0.462827 | − | 0.886449i | \(-0.653165\pi\) | ||||
−0.462827 | + | 0.886449i | \(0.653165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.9182 | 1.42632 | 0.713160 | − | 0.701002i | \(-0.247263\pi\) | ||||
0.713160 | + | 0.701002i | \(0.247263\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.04730 | 0.175725 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.31952 | 0.150204 | 0.0751022 | − | 0.997176i | \(-0.476072\pi\) | ||||
0.0751022 | + | 0.997176i | \(0.476072\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −51.7234 | −1.79643 | −0.898214 | − | 0.439558i | \(-0.855135\pi\) | ||||
−0.898214 | + | 0.439558i | \(0.855135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.52296 | −0.0528308 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.0534754 | −0.00185281 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.7018 | 0.820235 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.426464 | 0.0147408 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −34.5939 | −1.19431 | −0.597157 | − | 0.802125i | \(-0.703703\pi\) | ||||
−0.597157 | + | 0.802125i | \(0.703703\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51.3422 | 1.77042 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.50816 | 0.120827 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.9316 | 0.995278 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.43283 | −0.0492326 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.67045 | −0.0916494 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.36600 | −0.286783 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.33241 | 0.319536 | 0.159768 | − | 0.987155i | \(-0.448925\pi\) | ||||
0.159768 | + | 0.987155i | \(0.448925\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 54.4457 | 1.86200 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.1930 | −0.997215 | −0.498607 | − | 0.866828i | \(-0.666155\pi\) | ||||
−0.498607 | + | 0.866828i | \(0.666155\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.72856 | −0.331934 | −0.165967 | − | 0.986131i | \(-0.553075\pi\) | ||||
−0.165967 | + | 0.986131i | \(0.553075\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.126667 | −0.00431680 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.606028 | −0.0206294 | −0.0103147 | − | 0.999947i | \(-0.503283\pi\) | ||||
−0.0103147 | + | 0.999947i | \(0.503283\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 90.0597 | 3.06212 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.15298 | 0.0731189 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.9539 | 1.15181 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.2887 | 0.992411 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.2565 | 1.19325 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 25.4392 | 0.860003 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.1441 | −1.32180 | −0.660900 | − | 0.750474i | \(-0.729825\pi\) | ||||
−0.660900 | + | 0.750474i | \(0.729825\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.0490446 | −0.00165423 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.0373 | −1.51735 | −0.758673 | − | 0.651471i | \(-0.774152\pi\) | ||||
−0.758673 | + | 0.651471i | \(0.774152\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.3193 | 1.42416 | 0.712078 | − | 0.702100i | \(-0.247754\pi\) | ||||
0.712078 | + | 0.702100i | \(0.247754\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.46684 | −0.183766 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.2033 | −0.846244 | −0.423122 | − | 0.906073i | \(-0.639066\pi\) | ||||
−0.423122 | + | 0.906073i | \(0.639066\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.4061 | −0.583783 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −31.2259 | −1.04611 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29.6999 | −0.993869 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −69.4060 | −2.31999 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.766034 | −0.0255771 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.04316 | 0.168199 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0221677 | 0.000738515 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.376118 | 0.0125164 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 63.1542 | 2.09932 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.9134 | −0.561602 | −0.280801 | − | 0.959766i | \(-0.590600\pi\) | ||||
−0.280801 | + | 0.959766i | \(0.590600\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.2668 | 0.440033 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.1664 | −0.469355 | −0.234678 | − | 0.972073i | \(-0.575403\pi\) | ||||
−0.234678 | + | 0.972073i | \(0.575403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.3075 | −0.771367 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.32116 | 0.109794 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.82687 | −0.324512 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.9329 | −0.492591 | −0.246296 | − | 0.969195i | \(-0.579213\pi\) | ||||
−0.246296 | + | 0.969195i | \(0.579213\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.73718 | 0.0901931 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.3367 | 0.833968 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −37.7601 | −1.24154 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −38.5645 | −1.26662 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.4443 | 0.572328 | 0.286164 | − | 0.958181i | \(-0.407620\pi\) | ||||
0.286164 | + | 0.958181i | \(0.407620\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.51925 | 0.148112 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.738444 | −0.0241756 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.761279 | −0.0248965 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.1148 | 1.04914 | 0.524572 | − | 0.851366i | \(-0.324225\pi\) | ||||
0.524572 | + | 0.851366i | \(0.324225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.26182 | 0.139079 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.4780 | −0.960955 | −0.480478 | − | 0.877007i | \(-0.659537\pi\) | ||||
−0.480478 | + | 0.877007i | \(0.659537\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.50378 | −0.0815342 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.06025 | 0.0995499 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.8238 | 1.22911 | 0.614554 | − | 0.788875i | \(-0.289336\pi\) | ||||
0.614554 | + | 0.788875i | \(0.289336\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.53785 | −0.309612 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.133915 | −0.00434250 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.3765 | 0.757240 | 0.378620 | − | 0.925552i | \(-0.376399\pi\) | ||||
0.378620 | + | 0.925552i | \(0.376399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −77.3597 | −2.50330 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.00332 | 0.129409 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.39344 | 0.0449965 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6834 | −0.989788 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.6656 | 0.440369 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 52.3986 | 1.68677 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2162 | 0.328530 | 0.164265 | − | 0.986416i | \(-0.447475\pi\) | ||||
0.164265 | + | 0.986416i | \(0.447475\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0306114 | 0.000983380 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.4432 | 0.559779 | 0.279889 | − | 0.960032i | \(-0.409702\pi\) | ||||
0.279889 | + | 0.960032i | \(0.409702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.8863 | −0.381057 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.45751 | −0.110729 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.8180 | 1.40186 | 0.700931 | − | 0.713229i | \(-0.252768\pi\) | ||||
0.700931 | + | 0.713229i | \(0.252768\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.9604 | 1.56478 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.2557 | −1.44490 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.2429 | −1.25166 | −0.625828 | − | 0.779961i | \(-0.715239\pi\) | ||||
−0.625828 | + | 0.779961i | \(0.715239\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −64.5748 | −2.05752 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.832438 | −0.0264968 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.43457 | 0.236406 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.97731 | −0.285174 | −0.142587 | − | 0.989782i | \(-0.545542\pi\) | ||||
−0.142587 | + | 0.989782i | \(0.545542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.575334 | 0.0182577 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −85.7052 | −2.71704 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.6449 | 0.432139 | 0.216070 | − | 0.976378i | \(-0.430676\pi\) | ||||
0.216070 | + | 0.976378i | \(0.430676\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.53264 | −0.0801292 |
(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 | 1148.2.a.d.1.3 | ✓ | 5 | |
4.3 | odd | 2 | 4592.2.a.bc.1.3 | 5 | |||
7.6 | odd | 2 | 8036.2.a.k.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1148.2.a.d.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
4592.2.a.bc.1.3 | 5 | 4.3 | odd | 2 | |||
8036.2.a.k.1.3 | 5 | 7.6 | odd | 2 |