Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5225,2,Mod(1,5225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5225, 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("5225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5225 = 5^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5225.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: | \(41.7218350561\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 11 x^{13} + 87 x^{12} - 4 x^{11} - 545 x^{10} + 431 x^{9} + 1480 x^{8} - 1763 x^{7} + \cdots + 15 \) |
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 | 1.5 | ||
Root | \(-0.527123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.527123 | −0.372732 | −0.186366 | − | 0.982480i | \(-0.559671\pi\) | ||||
−0.186366 | + | 0.982480i | \(0.559671\pi\) | |||||||
\(3\) | 1.24468 | 0.718614 | 0.359307 | − | 0.933219i | \(-0.383013\pi\) | ||||
0.359307 | + | 0.933219i | \(0.383013\pi\) | |||||||
\(4\) | −1.72214 | −0.861071 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.656097 | −0.267850 | ||||||||
\(7\) | 3.22241 | 1.21796 | 0.608978 | − | 0.793187i | \(-0.291580\pi\) | ||||
0.608978 | + | 0.793187i | \(0.291580\pi\) | |||||||
\(8\) | 1.96203 | 0.693681 | ||||||||
\(9\) | −1.45078 | −0.483594 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −2.14351 | −0.618777 | ||||||||
\(13\) | −4.87506 | −1.35210 | −0.676050 | − | 0.736856i | \(-0.736310\pi\) | ||||
−0.676050 | + | 0.736856i | \(0.736310\pi\) | |||||||
\(14\) | −1.69861 | −0.453971 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.41005 | 0.602513 | ||||||||
\(17\) | 7.11649 | 1.72600 | 0.863002 | − | 0.505201i | \(-0.168582\pi\) | ||||
0.863002 | + | 0.505201i | \(0.168582\pi\) | |||||||
\(18\) | 0.764741 | 0.180251 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.01085 | 0.875240 | ||||||||
\(22\) | −0.527123 | −0.112383 | ||||||||
\(23\) | 1.12671 | 0.234935 | 0.117467 | − | 0.993077i | \(-0.462522\pi\) | ||||
0.117467 | + | 0.993077i | \(0.462522\pi\) | |||||||
\(24\) | 2.44209 | 0.498489 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.56976 | 0.503971 | ||||||||
\(27\) | −5.53978 | −1.06613 | ||||||||
\(28\) | −5.54944 | −1.04875 | ||||||||
\(29\) | 8.47231 | 1.57327 | 0.786634 | − | 0.617420i | \(-0.211822\pi\) | ||||
0.786634 | + | 0.617420i | \(0.211822\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.926610 | −0.166424 | −0.0832121 | − | 0.996532i | \(-0.526518\pi\) | ||||
−0.0832121 | + | 0.996532i | \(0.526518\pi\) | |||||||
\(32\) | −5.19445 | −0.918257 | ||||||||
\(33\) | 1.24468 | 0.216670 | ||||||||
\(34\) | −3.75127 | −0.643337 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.49845 | 0.416409 | ||||||||
\(37\) | −10.7386 | −1.76542 | −0.882709 | − | 0.469920i | \(-0.844283\pi\) | ||||
−0.882709 | + | 0.469920i | \(0.844283\pi\) | |||||||
\(38\) | −0.527123 | −0.0855106 | ||||||||
\(39\) | −6.06787 | −0.971637 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.49805 | 1.17100 | 0.585499 | − | 0.810673i | \(-0.300898\pi\) | ||||
0.585499 | + | 0.810673i | \(0.300898\pi\) | |||||||
\(42\) | −2.11421 | −0.326230 | ||||||||
\(43\) | −7.22055 | −1.10112 | −0.550562 | − | 0.834794i | \(-0.685586\pi\) | ||||
−0.550562 | + | 0.834794i | \(0.685586\pi\) | |||||||
\(44\) | −1.72214 | −0.259623 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.593913 | −0.0875678 | ||||||||
\(47\) | 12.4483 | 1.81577 | 0.907886 | − | 0.419217i | \(-0.137695\pi\) | ||||
0.907886 | + | 0.419217i | \(0.137695\pi\) | |||||||
\(48\) | 2.99973 | 0.432974 | ||||||||
\(49\) | 3.38391 | 0.483416 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.85772 | 1.24033 | ||||||||
\(52\) | 8.39555 | 1.16425 | ||||||||
\(53\) | 7.92848 | 1.08906 | 0.544530 | − | 0.838741i | \(-0.316708\pi\) | ||||
0.544530 | + | 0.838741i | \(0.316708\pi\) | |||||||
\(54\) | 2.92015 | 0.397381 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.32245 | 0.844873 | ||||||||
\(57\) | 1.24468 | 0.164861 | ||||||||
\(58\) | −4.46595 | −0.586408 | ||||||||
\(59\) | 1.91691 | 0.249561 | 0.124780 | − | 0.992184i | \(-0.460177\pi\) | ||||
0.124780 | + | 0.992184i | \(0.460177\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.5308 | −1.47637 | −0.738185 | − | 0.674599i | \(-0.764317\pi\) | ||||
−0.738185 | + | 0.674599i | \(0.764317\pi\) | |||||||
\(62\) | 0.488438 | 0.0620316 | ||||||||
\(63\) | −4.67502 | −0.588997 | ||||||||
\(64\) | −2.08199 | −0.260249 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.656097 | −0.0807600 | ||||||||
\(67\) | 10.2103 | 1.24739 | 0.623693 | − | 0.781669i | \(-0.285631\pi\) | ||||
0.623693 | + | 0.781669i | \(0.285631\pi\) | |||||||
\(68\) | −12.2556 | −1.48621 | ||||||||
\(69\) | 1.40239 | 0.168827 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.979715 | 0.116271 | 0.0581354 | − | 0.998309i | \(-0.481484\pi\) | ||||
0.0581354 | + | 0.998309i | \(0.481484\pi\) | |||||||
\(72\) | −2.84647 | −0.335460 | ||||||||
\(73\) | −15.3116 | −1.79209 | −0.896044 | − | 0.443965i | \(-0.853571\pi\) | ||||
−0.896044 | + | 0.443965i | \(0.853571\pi\) | |||||||
\(74\) | 5.66057 | 0.658028 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.72214 | −0.197543 | ||||||||
\(77\) | 3.22241 | 0.367227 | ||||||||
\(78\) | 3.19852 | 0.362161 | ||||||||
\(79\) | −3.05834 | −0.344091 | −0.172045 | − | 0.985089i | \(-0.555038\pi\) | ||||
−0.172045 | + | 0.985089i | \(0.555038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.54288 | −0.282542 | ||||||||
\(82\) | −3.95240 | −0.436469 | ||||||||
\(83\) | −2.60802 | −0.286268 | −0.143134 | − | 0.989703i | \(-0.545718\pi\) | ||||
−0.143134 | + | 0.989703i | \(0.545718\pi\) | |||||||
\(84\) | −6.90725 | −0.753643 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.80612 | 0.410424 | ||||||||
\(87\) | 10.5453 | 1.13057 | ||||||||
\(88\) | 1.96203 | 0.209153 | ||||||||
\(89\) | 5.38303 | 0.570600 | 0.285300 | − | 0.958438i | \(-0.407907\pi\) | ||||
0.285300 | + | 0.958438i | \(0.407907\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.7094 | −1.64680 | ||||||||
\(92\) | −1.94035 | −0.202295 | ||||||||
\(93\) | −1.15333 | −0.119595 | ||||||||
\(94\) | −6.56179 | −0.676797 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −6.46540 | −0.659872 | ||||||||
\(97\) | 15.6399 | 1.58799 | 0.793995 | − | 0.607924i | \(-0.207997\pi\) | ||||
0.793995 | + | 0.607924i | \(0.207997\pi\) | |||||||
\(98\) | −1.78374 | −0.180185 | ||||||||
\(99\) | −1.45078 | −0.145809 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5602 | 1.44879 | 0.724396 | − | 0.689384i | \(-0.242119\pi\) | ||||
0.724396 | + | 0.689384i | \(0.242119\pi\) | |||||||
\(102\) | −4.66911 | −0.462311 | ||||||||
\(103\) | 10.2341 | 1.00839 | 0.504197 | − | 0.863589i | \(-0.331789\pi\) | ||||
0.504197 | + | 0.863589i | \(0.331789\pi\) | |||||||
\(104\) | −9.56501 | −0.937926 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.17928 | −0.405928 | ||||||||
\(107\) | 5.30542 | 0.512895 | 0.256447 | − | 0.966558i | \(-0.417448\pi\) | ||||
0.256447 | + | 0.966558i | \(0.417448\pi\) | |||||||
\(108\) | 9.54028 | 0.918014 | ||||||||
\(109\) | −6.54304 | −0.626709 | −0.313355 | − | 0.949636i | \(-0.601453\pi\) | ||||
−0.313355 | + | 0.949636i | \(0.601453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.3661 | −1.26865 | ||||||||
\(112\) | 7.76618 | 0.733835 | ||||||||
\(113\) | −5.52729 | −0.519963 | −0.259982 | − | 0.965614i | \(-0.583717\pi\) | ||||
−0.259982 | + | 0.965614i | \(0.583717\pi\) | |||||||
\(114\) | −0.656097 | −0.0614491 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −14.5905 | −1.35470 | ||||||||
\(117\) | 7.07266 | 0.653868 | ||||||||
\(118\) | −1.01045 | −0.0930194 | ||||||||
\(119\) | 22.9322 | 2.10220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 6.07816 | 0.550291 | ||||||||
\(123\) | 9.33264 | 0.841496 | ||||||||
\(124\) | 1.59575 | 0.143303 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.46431 | 0.219538 | ||||||||
\(127\) | 2.97437 | 0.263932 | 0.131966 | − | 0.991254i | \(-0.457871\pi\) | ||||
0.131966 | + | 0.991254i | \(0.457871\pi\) | |||||||
\(128\) | 11.4864 | 1.01526 | ||||||||
\(129\) | −8.98724 | −0.791283 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1638 | 0.975388 | 0.487694 | − | 0.873015i | \(-0.337838\pi\) | ||||
0.487694 | + | 0.873015i | \(0.337838\pi\) | |||||||
\(132\) | −2.14351 | −0.186568 | ||||||||
\(133\) | 3.22241 | 0.279418 | ||||||||
\(134\) | −5.38208 | −0.464941 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.9627 | 1.19730 | ||||||||
\(137\) | −13.3569 | −1.14116 | −0.570580 | − | 0.821242i | \(-0.693282\pi\) | ||||
−0.570580 | + | 0.821242i | \(0.693282\pi\) | |||||||
\(138\) | −0.739229 | −0.0629274 | ||||||||
\(139\) | 17.5311 | 1.48697 | 0.743485 | − | 0.668753i | \(-0.233171\pi\) | ||||
0.743485 | + | 0.668753i | \(0.233171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.4941 | 1.30484 | ||||||||
\(142\) | −0.516430 | −0.0433379 | ||||||||
\(143\) | −4.87506 | −0.407673 | ||||||||
\(144\) | −3.49647 | −0.291372 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.07110 | 0.667969 | ||||||||
\(147\) | 4.21187 | 0.347389 | ||||||||
\(148\) | 18.4934 | 1.52015 | ||||||||
\(149\) | −9.45886 | −0.774900 | −0.387450 | − | 0.921891i | \(-0.626644\pi\) | ||||
−0.387450 | + | 0.921891i | \(0.626644\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0675175 | −0.00549449 | −0.00274725 | − | 0.999996i | \(-0.500874\pi\) | ||||
−0.00274725 | + | 0.999996i | \(0.500874\pi\) | |||||||
\(152\) | 1.96203 | 0.159141 | ||||||||
\(153\) | −10.3245 | −0.834685 | ||||||||
\(154\) | −1.69861 | −0.136878 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.4497 | 0.836648 | ||||||||
\(157\) | 13.6996 | 1.09334 | 0.546672 | − | 0.837347i | \(-0.315894\pi\) | ||||
0.546672 | + | 0.837347i | \(0.315894\pi\) | |||||||
\(158\) | 1.61212 | 0.128254 | ||||||||
\(159\) | 9.86838 | 0.782613 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.63071 | 0.286140 | ||||||||
\(162\) | 1.34041 | 0.105313 | ||||||||
\(163\) | 9.50798 | 0.744722 | 0.372361 | − | 0.928088i | \(-0.378548\pi\) | ||||
0.372361 | + | 0.928088i | \(0.378548\pi\) | |||||||
\(164\) | −12.9127 | −1.00831 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.37475 | 0.106701 | ||||||||
\(167\) | −3.51330 | −0.271868 | −0.135934 | − | 0.990718i | \(-0.543403\pi\) | ||||
−0.135934 | + | 0.990718i | \(0.543403\pi\) | |||||||
\(168\) | 7.86940 | 0.607137 | ||||||||
\(169\) | 10.7663 | 0.828174 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.45078 | −0.110944 | ||||||||
\(172\) | 12.4348 | 0.948145 | ||||||||
\(173\) | −3.64800 | −0.277352 | −0.138676 | − | 0.990338i | \(-0.544285\pi\) | ||||
−0.138676 | + | 0.990338i | \(0.544285\pi\) | |||||||
\(174\) | −5.55866 | −0.421401 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.41005 | 0.181665 | ||||||||
\(177\) | 2.38594 | 0.179338 | ||||||||
\(178\) | −2.83752 | −0.212681 | ||||||||
\(179\) | −18.2698 | −1.36555 | −0.682773 | − | 0.730630i | \(-0.739226\pi\) | ||||
−0.682773 | + | 0.730630i | \(0.739226\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.87683 | 0.362492 | 0.181246 | − | 0.983438i | \(-0.441987\pi\) | ||||
0.181246 | + | 0.983438i | \(0.441987\pi\) | |||||||
\(182\) | 8.28081 | 0.613815 | ||||||||
\(183\) | −14.3521 | −1.06094 | ||||||||
\(184\) | 2.21063 | 0.162970 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.607946 | 0.0445768 | ||||||||
\(187\) | 7.11649 | 0.520409 | ||||||||
\(188\) | −21.4377 | −1.56351 | ||||||||
\(189\) | −17.8514 | −1.29850 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.01617 | −0.218242 | −0.109121 | − | 0.994028i | \(-0.534804\pi\) | ||||
−0.109121 | + | 0.994028i | \(0.534804\pi\) | |||||||
\(192\) | −2.59141 | −0.187019 | ||||||||
\(193\) | 11.8494 | 0.852940 | 0.426470 | − | 0.904502i | \(-0.359757\pi\) | ||||
0.426470 | + | 0.904502i | \(0.359757\pi\) | |||||||
\(194\) | −8.24415 | −0.591895 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.82758 | −0.416256 | ||||||||
\(197\) | 22.9156 | 1.63267 | 0.816333 | − | 0.577581i | \(-0.196003\pi\) | ||||
0.816333 | + | 0.577581i | \(0.196003\pi\) | |||||||
\(198\) | 0.764741 | 0.0543478 | ||||||||
\(199\) | −16.6587 | −1.18090 | −0.590452 | − | 0.807072i | \(-0.701051\pi\) | ||||
−0.590452 | + | 0.807072i | \(0.701051\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.7085 | 0.896389 | ||||||||
\(202\) | −7.67500 | −0.540011 | ||||||||
\(203\) | 27.3012 | 1.91617 | ||||||||
\(204\) | −15.2543 | −1.06801 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.39462 | −0.375861 | ||||||||
\(207\) | −1.63461 | −0.113613 | ||||||||
\(208\) | −11.7492 | −0.814658 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0707 | −0.762138 | −0.381069 | − | 0.924547i | \(-0.624444\pi\) | ||||
−0.381069 | + | 0.924547i | \(0.624444\pi\) | |||||||
\(212\) | −13.6540 | −0.937757 | ||||||||
\(213\) | 1.21943 | 0.0835538 | ||||||||
\(214\) | −2.79661 | −0.191172 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.8692 | −0.739555 | ||||||||
\(217\) | −2.98592 | −0.202697 | ||||||||
\(218\) | 3.44898 | 0.233595 | ||||||||
\(219\) | −19.0580 | −1.28782 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −34.6934 | −2.33373 | ||||||||
\(222\) | 7.04558 | 0.472868 | ||||||||
\(223\) | −2.30152 | −0.154121 | −0.0770606 | − | 0.997026i | \(-0.524553\pi\) | ||||
−0.0770606 | + | 0.997026i | \(0.524553\pi\) | |||||||
\(224\) | −16.7386 | −1.11840 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.91356 | 0.193807 | ||||||||
\(227\) | −15.8244 | −1.05030 | −0.525152 | − | 0.851008i | \(-0.675992\pi\) | ||||
−0.525152 | + | 0.851008i | \(0.675992\pi\) | |||||||
\(228\) | −2.14351 | −0.141957 | ||||||||
\(229\) | 21.0470 | 1.39082 | 0.695412 | − | 0.718612i | \(-0.255222\pi\) | ||||
0.695412 | + | 0.718612i | \(0.255222\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.01085 | 0.263895 | ||||||||
\(232\) | 16.6229 | 1.09135 | ||||||||
\(233\) | −1.45166 | −0.0951017 | −0.0475508 | − | 0.998869i | \(-0.515142\pi\) | ||||
−0.0475508 | + | 0.998869i | \(0.515142\pi\) | |||||||
\(234\) | −3.72816 | −0.243718 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.30120 | −0.214890 | ||||||||
\(237\) | −3.80665 | −0.247268 | ||||||||
\(238\) | −12.0881 | −0.783556 | ||||||||
\(239\) | 3.11689 | 0.201615 | 0.100807 | − | 0.994906i | \(-0.467857\pi\) | ||||
0.100807 | + | 0.994906i | \(0.467857\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.3469 | −1.63274 | −0.816369 | − | 0.577531i | \(-0.804016\pi\) | ||||
−0.816369 | + | 0.577531i | \(0.804016\pi\) | |||||||
\(242\) | −0.527123 | −0.0338847 | ||||||||
\(243\) | 13.4543 | 0.863093 | ||||||||
\(244\) | 19.8577 | 1.27126 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.91945 | −0.313653 | ||||||||
\(247\) | −4.87506 | −0.310193 | ||||||||
\(248\) | −1.81803 | −0.115445 | ||||||||
\(249\) | −3.24614 | −0.205716 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0511 | 0.760656 | 0.380328 | − | 0.924852i | \(-0.375811\pi\) | ||||
0.380328 | + | 0.924852i | \(0.375811\pi\) | |||||||
\(252\) | 8.05104 | 0.507168 | ||||||||
\(253\) | 1.12671 | 0.0708355 | ||||||||
\(254\) | −1.56786 | −0.0983761 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.89074 | −0.118171 | ||||||||
\(257\) | 17.1129 | 1.06747 | 0.533737 | − | 0.845651i | \(-0.320787\pi\) | ||||
0.533737 | + | 0.845651i | \(0.320787\pi\) | |||||||
\(258\) | 4.73738 | 0.294937 | ||||||||
\(259\) | −34.6042 | −2.15020 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.2915 | −0.760824 | ||||||||
\(262\) | −5.88471 | −0.363559 | ||||||||
\(263\) | 23.8861 | 1.47288 | 0.736440 | − | 0.676503i | \(-0.236505\pi\) | ||||
0.736440 | + | 0.676503i | \(0.236505\pi\) | |||||||
\(264\) | 2.44209 | 0.150300 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.69861 | −0.104148 | ||||||||
\(267\) | 6.70012 | 0.410041 | ||||||||
\(268\) | −17.5836 | −1.07409 | ||||||||
\(269\) | −5.15565 | −0.314346 | −0.157173 | − | 0.987571i | \(-0.550238\pi\) | ||||
−0.157173 | + | 0.987571i | \(0.550238\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.25556 | 0.562235 | 0.281118 | − | 0.959673i | \(-0.409295\pi\) | ||||
0.281118 | + | 0.959673i | \(0.409295\pi\) | |||||||
\(272\) | 17.1511 | 1.03994 | ||||||||
\(273\) | −19.5532 | −1.18341 | ||||||||
\(274\) | 7.04075 | 0.425347 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.41511 | −0.145372 | ||||||||
\(277\) | −7.65078 | −0.459691 | −0.229845 | − | 0.973227i | \(-0.573822\pi\) | ||||
−0.229845 | + | 0.973227i | \(0.573822\pi\) | |||||||
\(278\) | −9.24106 | −0.554242 | ||||||||
\(279\) | 1.34431 | 0.0804818 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.4752 | 0.982829 | 0.491415 | − | 0.870926i | \(-0.336480\pi\) | ||||
0.491415 | + | 0.870926i | \(0.336480\pi\) | |||||||
\(282\) | −8.16730 | −0.486355 | ||||||||
\(283\) | 10.5470 | 0.626953 | 0.313476 | − | 0.949596i | \(-0.398506\pi\) | ||||
0.313476 | + | 0.949596i | \(0.398506\pi\) | |||||||
\(284\) | −1.68721 | −0.100117 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.56976 | 0.151953 | ||||||||
\(287\) | 24.1618 | 1.42622 | ||||||||
\(288\) | 7.53602 | 0.444064 | ||||||||
\(289\) | 33.6445 | 1.97909 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.4666 | 1.14115 | ||||||||
\(292\) | 26.3688 | 1.54311 | ||||||||
\(293\) | 27.1073 | 1.58362 | 0.791811 | − | 0.610766i | \(-0.209138\pi\) | ||||
0.791811 | + | 0.610766i | \(0.209138\pi\) | |||||||
\(294\) | −2.22018 | −0.129483 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −21.0695 | −1.22464 | ||||||||
\(297\) | −5.53978 | −0.321451 | ||||||||
\(298\) | 4.98598 | 0.288830 | ||||||||
\(299\) | −5.49277 | −0.317655 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.2676 | −1.34112 | ||||||||
\(302\) | 0.0355900 | 0.00204798 | ||||||||
\(303\) | 18.1227 | 1.04112 | ||||||||
\(304\) | 2.41005 | 0.138226 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.44227 | 0.311114 | ||||||||
\(307\) | 15.9437 | 0.909957 | 0.454978 | − | 0.890503i | \(-0.349647\pi\) | ||||
0.454978 | + | 0.890503i | \(0.349647\pi\) | |||||||
\(308\) | −5.54944 | −0.316209 | ||||||||
\(309\) | 12.7381 | 0.724645 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.0972 | 1.30972 | 0.654862 | − | 0.755749i | \(-0.272727\pi\) | ||||
0.654862 | + | 0.755749i | \(0.272727\pi\) | |||||||
\(312\) | −11.9053 | −0.674006 | ||||||||
\(313\) | 19.7892 | 1.11855 | 0.559275 | − | 0.828982i | \(-0.311079\pi\) | ||||
0.559275 | + | 0.828982i | \(0.311079\pi\) | |||||||
\(314\) | −7.22135 | −0.407525 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.26690 | 0.296286 | ||||||||
\(317\) | −6.50111 | −0.365139 | −0.182569 | − | 0.983193i | \(-0.558441\pi\) | ||||
−0.182569 | + | 0.983193i | \(0.558441\pi\) | |||||||
\(318\) | −5.20185 | −0.291705 | ||||||||
\(319\) | 8.47231 | 0.474358 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.60353 | 0.368573 | ||||||||
\(322\) | −1.91383 | −0.106654 | ||||||||
\(323\) | 7.11649 | 0.395972 | ||||||||
\(324\) | 4.37920 | 0.243289 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.01187 | −0.277582 | ||||||||
\(327\) | −8.14396 | −0.450362 | ||||||||
\(328\) | 14.7114 | 0.812300 | ||||||||
\(329\) | 40.1135 | 2.21153 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.931117 | 0.0511788 | 0.0255894 | − | 0.999673i | \(-0.491854\pi\) | ||||
0.0255894 | + | 0.999673i | \(0.491854\pi\) | |||||||
\(332\) | 4.49139 | 0.246497 | ||||||||
\(333\) | 15.5794 | 0.853746 | ||||||||
\(334\) | 1.85194 | 0.101334 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.66637 | 0.527344 | ||||||||
\(337\) | 13.9841 | 0.761761 | 0.380881 | − | 0.924624i | \(-0.375621\pi\) | ||||
0.380881 | + | 0.924624i | \(0.375621\pi\) | |||||||
\(338\) | −5.67514 | −0.308687 | ||||||||
\(339\) | −6.87968 | −0.373653 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.926610 | −0.0501788 | ||||||||
\(342\) | 0.764741 | 0.0413525 | ||||||||
\(343\) | −11.6525 | −0.629176 | ||||||||
\(344\) | −14.1669 | −0.763829 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.92294 | 0.103378 | ||||||||
\(347\) | −30.7347 | −1.64992 | −0.824961 | − | 0.565189i | \(-0.808803\pi\) | ||||
−0.824961 | + | 0.565189i | \(0.808803\pi\) | |||||||
\(348\) | −18.1605 | −0.973502 | ||||||||
\(349\) | −12.9948 | −0.695595 | −0.347798 | − | 0.937570i | \(-0.613070\pi\) | ||||
−0.347798 | + | 0.937570i | \(0.613070\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.0068 | 1.44152 | ||||||||
\(352\) | −5.19445 | −0.276865 | ||||||||
\(353\) | 18.3337 | 0.975803 | 0.487901 | − | 0.872899i | \(-0.337763\pi\) | ||||
0.487901 | + | 0.872899i | \(0.337763\pi\) | |||||||
\(354\) | −1.25768 | −0.0668450 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.27033 | −0.491327 | ||||||||
\(357\) | 28.5432 | 1.51067 | ||||||||
\(358\) | 9.63041 | 0.508983 | ||||||||
\(359\) | −7.55341 | −0.398654 | −0.199327 | − | 0.979933i | \(-0.563876\pi\) | ||||
−0.199327 | + | 0.979933i | \(0.563876\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −2.57069 | −0.135113 | ||||||||
\(363\) | 1.24468 | 0.0653285 | ||||||||
\(364\) | 27.0539 | 1.41801 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.56533 | 0.395446 | ||||||||
\(367\) | 6.80846 | 0.355399 | 0.177699 | − | 0.984085i | \(-0.443135\pi\) | ||||
0.177699 | + | 0.984085i | \(0.443135\pi\) | |||||||
\(368\) | 2.71543 | 0.141551 | ||||||||
\(369\) | −10.8780 | −0.566289 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.5488 | 1.32643 | ||||||||
\(372\) | 1.98620 | 0.102979 | ||||||||
\(373\) | −0.104052 | −0.00538763 | −0.00269381 | − | 0.999996i | \(-0.500857\pi\) | ||||
−0.00269381 | + | 0.999996i | \(0.500857\pi\) | |||||||
\(374\) | −3.75127 | −0.193973 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24.4239 | 1.25957 | ||||||||
\(377\) | −41.3031 | −2.12722 | ||||||||
\(378\) | 9.40990 | 0.483993 | ||||||||
\(379\) | −29.4765 | −1.51411 | −0.757053 | − | 0.653353i | \(-0.773362\pi\) | ||||
−0.757053 | + | 0.653353i | \(0.773362\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.70212 | 0.189665 | ||||||||
\(382\) | 1.58989 | 0.0813460 | ||||||||
\(383\) | −15.0758 | −0.770337 | −0.385169 | − | 0.922846i | \(-0.625857\pi\) | ||||
−0.385169 | + | 0.922846i | \(0.625857\pi\) | |||||||
\(384\) | 14.2968 | 0.729580 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.24610 | −0.317918 | ||||||||
\(387\) | 10.4755 | 0.532497 | ||||||||
\(388\) | −26.9341 | −1.36737 | ||||||||
\(389\) | −8.16895 | −0.414182 | −0.207091 | − | 0.978322i | \(-0.566400\pi\) | ||||
−0.207091 | + | 0.978322i | \(0.566400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.01821 | 0.405498 | ||||||||
\(392\) | 6.63933 | 0.335337 | ||||||||
\(393\) | 13.8953 | 0.700927 | ||||||||
\(394\) | −12.0793 | −0.608548 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.49845 | 0.125552 | ||||||||
\(397\) | 14.6856 | 0.737050 | 0.368525 | − | 0.929618i | \(-0.379863\pi\) | ||||
0.368525 | + | 0.929618i | \(0.379863\pi\) | |||||||
\(398\) | 8.78119 | 0.440161 | ||||||||
\(399\) | 4.01085 | 0.200794 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.14341 | 0.0570994 | 0.0285497 | − | 0.999592i | \(-0.490911\pi\) | ||||
0.0285497 | + | 0.999592i | \(0.490911\pi\) | |||||||
\(402\) | −6.69895 | −0.334113 | ||||||||
\(403\) | 4.51729 | 0.225022 | ||||||||
\(404\) | −25.0747 | −1.24751 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.3911 | −0.714219 | ||||||||
\(407\) | −10.7386 | −0.532294 | ||||||||
\(408\) | 17.3791 | 0.860393 | ||||||||
\(409\) | 34.6619 | 1.71392 | 0.856961 | − | 0.515381i | \(-0.172350\pi\) | ||||
0.856961 | + | 0.515381i | \(0.172350\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.6250 | −0.820053 | ||||||||
\(412\) | −17.6245 | −0.868298 | ||||||||
\(413\) | 6.17708 | 0.303954 | ||||||||
\(414\) | 0.861640 | 0.0423473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 25.3233 | 1.24158 | ||||||||
\(417\) | 21.8206 | 1.06856 | ||||||||
\(418\) | −0.527123 | −0.0257824 | ||||||||
\(419\) | −19.8862 | −0.971505 | −0.485752 | − | 0.874096i | \(-0.661454\pi\) | ||||
−0.485752 | + | 0.874096i | \(0.661454\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.9388 | 1.60534 | 0.802669 | − | 0.596424i | \(-0.203412\pi\) | ||||
0.802669 | + | 0.596424i | \(0.203412\pi\) | |||||||
\(422\) | 5.83562 | 0.284073 | ||||||||
\(423\) | −18.0598 | −0.878097 | ||||||||
\(424\) | 15.5559 | 0.755460 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.642788 | −0.0311432 | ||||||||
\(427\) | −37.1570 | −1.79815 | ||||||||
\(428\) | −9.13669 | −0.441639 | ||||||||
\(429\) | −6.06787 | −0.292960 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.4153 | −1.03154 | −0.515770 | − | 0.856727i | \(-0.672494\pi\) | ||||
−0.515770 | + | 0.856727i | \(0.672494\pi\) | |||||||
\(432\) | −13.3512 | −0.642358 | ||||||||
\(433\) | −31.7437 | −1.52551 | −0.762753 | − | 0.646690i | \(-0.776153\pi\) | ||||
−0.762753 | + | 0.646690i | \(0.776153\pi\) | |||||||
\(434\) | 1.57395 | 0.0755518 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.2680 | 0.539641 | ||||||||
\(437\) | 1.12671 | 0.0538977 | ||||||||
\(438\) | 10.0459 | 0.480012 | ||||||||
\(439\) | 9.40014 | 0.448644 | 0.224322 | − | 0.974515i | \(-0.427983\pi\) | ||||
0.224322 | + | 0.974515i | \(0.427983\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.90932 | −0.233777 | ||||||||
\(442\) | 18.2877 | 0.869856 | ||||||||
\(443\) | 21.5223 | 1.02256 | 0.511278 | − | 0.859415i | \(-0.329172\pi\) | ||||
0.511278 | + | 0.859415i | \(0.329172\pi\) | |||||||
\(444\) | 23.0183 | 1.09240 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.21318 | 0.0574459 | ||||||||
\(447\) | −11.7732 | −0.556854 | ||||||||
\(448\) | −6.70904 | −0.316972 | ||||||||
\(449\) | 30.7497 | 1.45117 | 0.725583 | − | 0.688134i | \(-0.241570\pi\) | ||||
0.725583 | + | 0.688134i | \(0.241570\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.49805 | 0.353069 | ||||||||
\(452\) | 9.51877 | 0.447725 | ||||||||
\(453\) | −0.0840373 | −0.00394842 | ||||||||
\(454\) | 8.34142 | 0.391482 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.44209 | 0.114361 | ||||||||
\(457\) | −0.507061 | −0.0237193 | −0.0118596 | − | 0.999930i | \(-0.503775\pi\) | ||||
−0.0118596 | + | 0.999930i | \(0.503775\pi\) | |||||||
\(458\) | −11.0943 | −0.518405 | ||||||||
\(459\) | −39.4238 | −1.84015 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.60128 | 0.260878 | 0.130439 | − | 0.991456i | \(-0.458361\pi\) | ||||
0.130439 | + | 0.991456i | \(0.458361\pi\) | |||||||
\(462\) | −2.11421 | −0.0983621 | ||||||||
\(463\) | 22.5309 | 1.04710 | 0.523550 | − | 0.851995i | \(-0.324607\pi\) | ||||
0.523550 | + | 0.851995i | \(0.324607\pi\) | |||||||
\(464\) | 20.4187 | 0.947915 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.765205 | 0.0354475 | ||||||||
\(467\) | −15.1056 | −0.699003 | −0.349502 | − | 0.936936i | \(-0.613649\pi\) | ||||
−0.349502 | + | 0.936936i | \(0.613649\pi\) | |||||||
\(468\) | −12.1801 | −0.563026 | ||||||||
\(469\) | 32.9018 | 1.51926 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.0515 | 0.785692 | ||||||||
\(472\) | 3.76103 | 0.173116 | ||||||||
\(473\) | −7.22055 | −0.332001 | ||||||||
\(474\) | 2.00657 | 0.0921648 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −39.4926 | −1.81014 | ||||||||
\(477\) | −11.5025 | −0.526663 | ||||||||
\(478\) | −1.64298 | −0.0751482 | ||||||||
\(479\) | −1.97446 | −0.0902153 | −0.0451076 | − | 0.998982i | \(-0.514363\pi\) | ||||
−0.0451076 | + | 0.998982i | \(0.514363\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52.3515 | 2.38702 | ||||||||
\(482\) | 13.3609 | 0.608574 | ||||||||
\(483\) | 4.51906 | 0.205624 | ||||||||
\(484\) | −1.72214 | −0.0782792 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.09206 | −0.321702 | ||||||||
\(487\) | −6.23748 | −0.282647 | −0.141324 | − | 0.989963i | \(-0.545136\pi\) | ||||
−0.141324 | + | 0.989963i | \(0.545136\pi\) | |||||||
\(488\) | −22.6238 | −1.02413 | ||||||||
\(489\) | 11.8343 | 0.535168 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.4073 | 1.32713 | 0.663566 | − | 0.748117i | \(-0.269042\pi\) | ||||
0.663566 | + | 0.748117i | \(0.269042\pi\) | |||||||
\(492\) | −16.0721 | −0.724587 | ||||||||
\(493\) | 60.2931 | 2.71547 | ||||||||
\(494\) | 2.56976 | 0.115619 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.23318 | −0.100273 | ||||||||
\(497\) | 3.15704 | 0.141613 | ||||||||
\(498\) | 1.71112 | 0.0766770 | ||||||||
\(499\) | −8.33612 | −0.373176 | −0.186588 | − | 0.982438i | \(-0.559743\pi\) | ||||
−0.186588 | + | 0.982438i | \(0.559743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.37292 | −0.195368 | ||||||||
\(502\) | −6.35239 | −0.283521 | ||||||||
\(503\) | 36.9242 | 1.64637 | 0.823184 | − | 0.567774i | \(-0.192195\pi\) | ||||
0.823184 | + | 0.567774i | \(0.192195\pi\) | |||||||
\(504\) | −9.17250 | −0.408576 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.593913 | −0.0264027 | ||||||||
\(507\) | 13.4005 | 0.595137 | ||||||||
\(508\) | −5.12228 | −0.227265 | ||||||||
\(509\) | −14.0280 | −0.621782 | −0.310891 | − | 0.950446i | \(-0.600627\pi\) | ||||
−0.310891 | + | 0.950446i | \(0.600627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −49.3402 | −2.18268 | ||||||||
\(512\) | −21.9761 | −0.971214 | ||||||||
\(513\) | −5.53978 | −0.244587 | ||||||||
\(514\) | −9.02061 | −0.397882 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 15.4773 | 0.681350 | ||||||||
\(517\) | 12.4483 | 0.547476 | ||||||||
\(518\) | 18.2407 | 0.801449 | ||||||||
\(519\) | −4.54057 | −0.199309 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.56794 | 0.287747 | 0.143873 | − | 0.989596i | \(-0.454044\pi\) | ||||
0.143873 | + | 0.989596i | \(0.454044\pi\) | |||||||
\(522\) | 6.47912 | 0.283583 | ||||||||
\(523\) | 6.72747 | 0.294172 | 0.147086 | − | 0.989124i | \(-0.453011\pi\) | ||||
0.147086 | + | 0.989124i | \(0.453011\pi\) | |||||||
\(524\) | −19.2257 | −0.839878 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.5909 | −0.548990 | ||||||||
\(527\) | −6.59422 | −0.287249 | ||||||||
\(528\) | 2.99973 | 0.130547 | ||||||||
\(529\) | −21.7305 | −0.944806 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.78103 | −0.120686 | ||||||||
\(532\) | −5.54944 | −0.240599 | ||||||||
\(533\) | −36.5535 | −1.58331 | ||||||||
\(534\) | −3.53179 | −0.152835 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20.0329 | 0.865288 | ||||||||
\(537\) | −22.7399 | −0.981300 | ||||||||
\(538\) | 2.71766 | 0.117167 | ||||||||
\(539\) | 3.38391 | 0.145755 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.50043 | −0.236482 | −0.118241 | − | 0.992985i | \(-0.537726\pi\) | ||||
−0.118241 | + | 0.992985i | \(0.537726\pi\) | |||||||
\(542\) | −4.87882 | −0.209563 | ||||||||
\(543\) | 6.07008 | 0.260492 | ||||||||
\(544\) | −36.9662 | −1.58491 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.3069 | 0.441096 | ||||||||
\(547\) | 30.6112 | 1.30884 | 0.654420 | − | 0.756131i | \(-0.272913\pi\) | ||||
0.654420 | + | 0.756131i | \(0.272913\pi\) | |||||||
\(548\) | 23.0025 | 0.982619 | ||||||||
\(549\) | 16.7287 | 0.713964 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.47231 | 0.360932 | ||||||||
\(552\) | 2.75152 | 0.117112 | ||||||||
\(553\) | −9.85523 | −0.419087 | ||||||||
\(554\) | 4.03290 | 0.171342 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −30.1911 | −1.28039 | ||||||||
\(557\) | −14.5219 | −0.615313 | −0.307656 | − | 0.951498i | \(-0.599545\pi\) | ||||
−0.307656 | + | 0.951498i | \(0.599545\pi\) | |||||||
\(558\) | −0.708617 | −0.0299982 | ||||||||
\(559\) | 35.2007 | 1.48883 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.85772 | 0.373973 | ||||||||
\(562\) | −8.68447 | −0.366332 | ||||||||
\(563\) | 18.6917 | 0.787762 | 0.393881 | − | 0.919161i | \(-0.371132\pi\) | ||||
0.393881 | + | 0.919161i | \(0.371132\pi\) | |||||||
\(564\) | −26.6830 | −1.12356 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.55955 | −0.233685 | ||||||||
\(567\) | −8.19419 | −0.344124 | ||||||||
\(568\) | 1.92223 | 0.0806549 | ||||||||
\(569\) | 4.12594 | 0.172968 | 0.0864842 | − | 0.996253i | \(-0.472437\pi\) | ||||
0.0864842 | + | 0.996253i | \(0.472437\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.6081 | −0.862422 | −0.431211 | − | 0.902251i | \(-0.641913\pi\) | ||||
−0.431211 | + | 0.902251i | \(0.641913\pi\) | |||||||
\(572\) | 8.39555 | 0.351036 | ||||||||
\(573\) | −3.75415 | −0.156832 | ||||||||
\(574\) | −12.7362 | −0.531600 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.02052 | 0.125855 | ||||||||
\(577\) | 18.0882 | 0.753020 | 0.376510 | − | 0.926413i | \(-0.377124\pi\) | ||||
0.376510 | + | 0.926413i | \(0.377124\pi\) | |||||||
\(578\) | −17.7348 | −0.737669 | ||||||||
\(579\) | 14.7487 | 0.612934 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.40412 | −0.348662 | ||||||||
\(582\) | −10.2613 | −0.425344 | ||||||||
\(583\) | 7.92848 | 0.328364 | ||||||||
\(584\) | −30.0418 | −1.24314 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.2889 | −0.590267 | ||||||||
\(587\) | −31.2026 | −1.28787 | −0.643934 | − | 0.765081i | \(-0.722699\pi\) | ||||
−0.643934 | + | 0.765081i | \(0.722699\pi\) | |||||||
\(588\) | −7.25344 | −0.299127 | ||||||||
\(589\) | −0.926610 | −0.0381803 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.5224 | 1.17326 | ||||||||
\(592\) | −25.8806 | −1.06369 | ||||||||
\(593\) | 31.0847 | 1.27649 | 0.638247 | − | 0.769831i | \(-0.279660\pi\) | ||||
0.638247 | + | 0.769831i | \(0.279660\pi\) | |||||||
\(594\) | 2.92015 | 0.119815 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.2895 | 0.667244 | ||||||||
\(597\) | −20.7347 | −0.848614 | ||||||||
\(598\) | 2.89537 | 0.118400 | ||||||||
\(599\) | −3.46676 | −0.141648 | −0.0708240 | − | 0.997489i | \(-0.522563\pi\) | ||||
−0.0708240 | + | 0.997489i | \(0.522563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.6643 | −0.924498 | −0.462249 | − | 0.886750i | \(-0.652957\pi\) | ||||
−0.462249 | + | 0.886750i | \(0.652957\pi\) | |||||||
\(602\) | 12.2649 | 0.499879 | ||||||||
\(603\) | −14.8129 | −0.603229 | ||||||||
\(604\) | 0.116275 | 0.00473115 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.55289 | −0.388060 | ||||||||
\(607\) | −45.2747 | −1.83764 | −0.918821 | − | 0.394675i | \(-0.870857\pi\) | ||||
−0.918821 | + | 0.394675i | \(0.870857\pi\) | |||||||
\(608\) | −5.19445 | −0.210663 | ||||||||
\(609\) | 33.9812 | 1.37699 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −60.6863 | −2.45511 | ||||||||
\(612\) | 17.7802 | 0.718723 | ||||||||
\(613\) | 32.5470 | 1.31456 | 0.657280 | − | 0.753646i | \(-0.271707\pi\) | ||||
0.657280 | + | 0.753646i | \(0.271707\pi\) | |||||||
\(614\) | −8.40431 | −0.339170 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.32245 | 0.254739 | ||||||||
\(617\) | 0.114512 | 0.00461007 | 0.00230503 | − | 0.999997i | \(-0.499266\pi\) | ||||
0.00230503 | + | 0.999997i | \(0.499266\pi\) | |||||||
\(618\) | −6.71455 | −0.270099 | ||||||||
\(619\) | −21.7981 | −0.876139 | −0.438069 | − | 0.898941i | \(-0.644338\pi\) | ||||
−0.438069 | + | 0.898941i | \(0.644338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.24171 | −0.250471 | ||||||||
\(622\) | −12.1751 | −0.488176 | ||||||||
\(623\) | 17.3463 | 0.694965 | ||||||||
\(624\) | −14.6239 | −0.585425 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.4313 | −0.416920 | ||||||||
\(627\) | 1.24468 | 0.0497075 | ||||||||
\(628\) | −23.5926 | −0.941447 | ||||||||
\(629\) | −76.4213 | −3.04712 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.64209 | −0.304227 | −0.152113 | − | 0.988363i | \(-0.548608\pi\) | ||||
−0.152113 | + | 0.988363i | \(0.548608\pi\) | |||||||
\(632\) | −6.00055 | −0.238689 | ||||||||
\(633\) | −13.7794 | −0.547683 | ||||||||
\(634\) | 3.42688 | 0.136099 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −16.9947 | −0.673885 | ||||||||
\(637\) | −16.4968 | −0.653627 | ||||||||
\(638\) | −4.46595 | −0.176809 | ||||||||
\(639\) | −1.42135 | −0.0562279 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.6286 | −0.617291 | −0.308646 | − | 0.951177i | \(-0.599876\pi\) | ||||
−0.308646 | + | 0.951177i | \(0.599876\pi\) | |||||||
\(642\) | −3.48087 | −0.137379 | ||||||||
\(643\) | −21.8689 | −0.862425 | −0.431213 | − | 0.902250i | \(-0.641914\pi\) | ||||
−0.431213 | + | 0.902250i | \(0.641914\pi\) | |||||||
\(644\) | −6.25260 | −0.246387 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.75127 | −0.147592 | ||||||||
\(647\) | 44.3165 | 1.74226 | 0.871131 | − | 0.491051i | \(-0.163387\pi\) | ||||
0.871131 | + | 0.491051i | \(0.163387\pi\) | |||||||
\(648\) | −4.98919 | −0.195994 | ||||||||
\(649\) | 1.91691 | 0.0752454 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.71650 | −0.145661 | ||||||||
\(652\) | −16.3741 | −0.641259 | ||||||||
\(653\) | −23.2868 | −0.911284 | −0.455642 | − | 0.890163i | \(-0.650590\pi\) | ||||
−0.455642 | + | 0.890163i | \(0.650590\pi\) | |||||||
\(654\) | 4.29287 | 0.167864 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 18.0707 | 0.705543 | ||||||||
\(657\) | 22.2138 | 0.866644 | ||||||||
\(658\) | −21.1448 | −0.824309 | ||||||||
\(659\) | −33.4706 | −1.30383 | −0.651914 | − | 0.758293i | \(-0.726034\pi\) | ||||
−0.651914 | + | 0.758293i | \(0.726034\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.30725 | 0.167533 | 0.0837663 | − | 0.996485i | \(-0.473305\pi\) | ||||
0.0837663 | + | 0.996485i | \(0.473305\pi\) | |||||||
\(662\) | −0.490813 | −0.0190760 | ||||||||
\(663\) | −43.1820 | −1.67705 | ||||||||
\(664\) | −5.11701 | −0.198579 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.21226 | −0.318219 | ||||||||
\(667\) | 9.54581 | 0.369615 | ||||||||
\(668\) | 6.05041 | 0.234097 | ||||||||
\(669\) | −2.86464 | −0.110754 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.5308 | −0.445142 | ||||||||
\(672\) | −20.8342 | −0.803695 | ||||||||
\(673\) | −43.9621 | −1.69461 | −0.847307 | − | 0.531103i | \(-0.821778\pi\) | ||||
−0.847307 | + | 0.531103i | \(0.821778\pi\) | |||||||
\(674\) | −7.37133 | −0.283933 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.5410 | −0.713116 | ||||||||
\(677\) | 19.9483 | 0.766676 | 0.383338 | − | 0.923608i | \(-0.374774\pi\) | ||||
0.383338 | + | 0.923608i | \(0.374774\pi\) | |||||||
\(678\) | 3.62644 | 0.139272 | ||||||||
\(679\) | 50.3981 | 1.93410 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.6963 | −0.754763 | ||||||||
\(682\) | 0.488438 | 0.0187032 | ||||||||
\(683\) | −41.1720 | −1.57540 | −0.787701 | − | 0.616058i | \(-0.788729\pi\) | ||||
−0.787701 | + | 0.616058i | \(0.788729\pi\) | |||||||
\(684\) | 2.49845 | 0.0955308 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.14230 | 0.234514 | ||||||||
\(687\) | 26.1967 | 0.999465 | ||||||||
\(688\) | −17.4019 | −0.663442 | ||||||||
\(689\) | −38.6518 | −1.47252 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.48838 | −0.284872 | −0.142436 | − | 0.989804i | \(-0.545493\pi\) | ||||
−0.142436 | + | 0.989804i | \(0.545493\pi\) | |||||||
\(692\) | 6.28237 | 0.238820 | ||||||||
\(693\) | −4.67502 | −0.177589 | ||||||||
\(694\) | 16.2009 | 0.614979 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 20.6901 | 0.784256 | ||||||||
\(697\) | 53.3598 | 2.02115 | ||||||||
\(698\) | 6.84985 | 0.259271 | ||||||||
\(699\) | −1.80685 | −0.0683414 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.9421 | 0.677666 | 0.338833 | − | 0.940847i | \(-0.389968\pi\) | ||||
0.338833 | + | 0.940847i | \(0.389968\pi\) | |||||||
\(702\) | −14.2359 | −0.537299 | ||||||||
\(703\) | −10.7386 | −0.405015 | ||||||||
\(704\) | −2.08199 | −0.0784681 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.66410 | −0.363713 | ||||||||
\(707\) | 46.9188 | 1.76456 | ||||||||
\(708\) | −4.10892 | −0.154423 | ||||||||
\(709\) | 12.2738 | 0.460954 | 0.230477 | − | 0.973078i | \(-0.425971\pi\) | ||||
0.230477 | + | 0.973078i | \(0.425971\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.43699 | 0.166400 | ||||||||
\(712\) | 10.5616 | 0.395814 | ||||||||
\(713\) | −1.04402 | −0.0390988 | ||||||||
\(714\) | −15.0458 | −0.563074 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 31.4631 | 1.17583 | ||||||||
\(717\) | 3.87951 | 0.144883 | ||||||||
\(718\) | 3.98158 | 0.148591 | ||||||||
\(719\) | 34.2879 | 1.27872 | 0.639361 | − | 0.768907i | \(-0.279199\pi\) | ||||
0.639361 | + | 0.768907i | \(0.279199\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.9784 | 1.22818 | ||||||||
\(722\) | −0.527123 | −0.0196175 | ||||||||
\(723\) | −31.5487 | −1.17331 | ||||||||
\(724\) | −8.39860 | −0.312131 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.656097 | −0.0243500 | ||||||||
\(727\) | 15.7447 | 0.583939 | 0.291970 | − | 0.956428i | \(-0.405689\pi\) | ||||
0.291970 | + | 0.956428i | \(0.405689\pi\) | |||||||
\(728\) | −30.8223 | −1.14235 | ||||||||
\(729\) | 24.3748 | 0.902772 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −51.3850 | −1.90054 | ||||||||
\(732\) | 24.7164 | 0.913544 | ||||||||
\(733\) | 51.1191 | 1.88813 | 0.944063 | − | 0.329765i | \(-0.106970\pi\) | ||||
0.944063 | + | 0.329765i | \(0.106970\pi\) | |||||||
\(734\) | −3.58890 | −0.132469 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.85262 | −0.215731 | ||||||||
\(737\) | 10.2103 | 0.376101 | ||||||||
\(738\) | 5.73407 | 0.211074 | ||||||||
\(739\) | −50.3516 | −1.85221 | −0.926107 | − | 0.377260i | \(-0.876866\pi\) | ||||
−0.926107 | + | 0.377260i | \(0.876866\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.06787 | −0.222909 | ||||||||
\(742\) | −13.4673 | −0.494402 | ||||||||
\(743\) | 2.11671 | 0.0776544 | 0.0388272 | − | 0.999246i | \(-0.487638\pi\) | ||||
0.0388272 | + | 0.999246i | \(0.487638\pi\) | |||||||
\(744\) | −2.26286 | −0.0829606 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.0548484 | 0.00200814 | ||||||||
\(747\) | 3.78368 | 0.138438 | ||||||||
\(748\) | −12.2556 | −0.448109 | ||||||||
\(749\) | 17.0962 | 0.624683 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.61971 | −0.278047 | −0.139024 | − | 0.990289i | \(-0.544396\pi\) | ||||
−0.139024 | + | 0.990289i | \(0.544396\pi\) | |||||||
\(752\) | 30.0011 | 1.09403 | ||||||||
\(753\) | 14.9997 | 0.546618 | ||||||||
\(754\) | 21.7718 | 0.792882 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 30.7427 | 1.11810 | ||||||||
\(757\) | −45.4268 | −1.65107 | −0.825533 | − | 0.564354i | \(-0.809125\pi\) | ||||
−0.825533 | + | 0.564354i | \(0.809125\pi\) | |||||||
\(758\) | 15.5377 | 0.564356 | ||||||||
\(759\) | 1.40239 | 0.0509034 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.78459 | 0.137191 | 0.0685957 | − | 0.997645i | \(-0.478148\pi\) | ||||
0.0685957 | + | 0.997645i | \(0.478148\pi\) | |||||||
\(762\) | −1.95147 | −0.0706944 | ||||||||
\(763\) | −21.0843 | −0.763304 | ||||||||
\(764\) | 5.19427 | 0.187922 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.94680 | 0.287130 | ||||||||
\(767\) | −9.34508 | −0.337431 | ||||||||
\(768\) | −2.35335 | −0.0849193 | ||||||||
\(769\) | 12.0500 | 0.434534 | 0.217267 | − | 0.976112i | \(-0.430286\pi\) | ||||
0.217267 | + | 0.976112i | \(0.430286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.3000 | 0.767101 | ||||||||
\(772\) | −20.4064 | −0.734441 | ||||||||
\(773\) | 5.54555 | 0.199460 | 0.0997298 | − | 0.995015i | \(-0.468202\pi\) | ||||
0.0997298 | + | 0.995015i | \(0.468202\pi\) | |||||||
\(774\) | −5.52185 | −0.198479 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 30.6859 | 1.10156 | ||||||||
\(777\) | −43.0710 | −1.54516 | ||||||||
\(778\) | 4.30604 | 0.154379 | ||||||||
\(779\) | 7.49805 | 0.268646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.979715 | 0.0350570 | ||||||||
\(782\) | −4.22658 | −0.151142 | ||||||||
\(783\) | −46.9347 | −1.67731 | ||||||||
\(784\) | 8.15541 | 0.291265 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7.32456 | −0.261258 | ||||||||
\(787\) | −46.5114 | −1.65795 | −0.828976 | − | 0.559284i | \(-0.811076\pi\) | ||||
−0.828976 | + | 0.559284i | \(0.811076\pi\) | |||||||
\(788\) | −39.4639 | −1.40584 | ||||||||
\(789\) | 29.7304 | 1.05843 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.8112 | −0.633292 | ||||||||
\(792\) | −2.84647 | −0.101145 | ||||||||
\(793\) | 56.2135 | 1.99620 | ||||||||
\(794\) | −7.74113 | −0.274722 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.6887 | 1.01684 | ||||||||
\(797\) | 3.60512 | 0.127700 | 0.0638500 | − | 0.997960i | \(-0.479662\pi\) | ||||
0.0638500 | + | 0.997960i | \(0.479662\pi\) | |||||||
\(798\) | −2.11421 | −0.0748423 | ||||||||
\(799\) | 88.5883 | 3.13403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.80960 | −0.275939 | ||||||||
\(802\) | −0.602720 | −0.0212828 | ||||||||
\(803\) | −15.3116 | −0.540335 | ||||||||
\(804\) | −21.8858 | −0.771854 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.38117 | −0.0838730 | ||||||||
\(807\) | −6.41712 | −0.225893 | ||||||||
\(808\) | 28.5674 | 1.00500 | ||||||||
\(809\) | 32.1749 | 1.13121 | 0.565605 | − | 0.824676i | \(-0.308643\pi\) | ||||
0.565605 | + | 0.824676i | \(0.308643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.8016 | −1.53808 | −0.769041 | − | 0.639200i | \(-0.779266\pi\) | ||||
−0.769041 | + | 0.639200i | \(0.779266\pi\) | |||||||
\(812\) | −47.0166 | −1.64996 | ||||||||
\(813\) | 11.5202 | 0.404030 | ||||||||
\(814\) | 5.66057 | 0.198403 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 21.3476 | 0.747315 | ||||||||
\(817\) | −7.22055 | −0.252615 | ||||||||
\(818\) | −18.2711 | −0.638834 | ||||||||
\(819\) | 22.7910 | 0.796382 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.6149 | −1.31277 | −0.656385 | − | 0.754426i | \(-0.727915\pi\) | ||||
−0.656385 | + | 0.754426i | \(0.727915\pi\) | |||||||
\(822\) | 8.76345 | 0.305660 | ||||||||
\(823\) | 8.52852 | 0.297285 | 0.148643 | − | 0.988891i | \(-0.452510\pi\) | ||||
0.148643 | + | 0.988891i | \(0.452510\pi\) | |||||||
\(824\) | 20.0795 | 0.699503 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.25608 | −0.113293 | ||||||||
\(827\) | 43.5444 | 1.51419 | 0.757093 | − | 0.653307i | \(-0.226619\pi\) | ||||
0.757093 | + | 0.653307i | \(0.226619\pi\) | |||||||
\(828\) | 2.81503 | 0.0978289 | ||||||||
\(829\) | −1.16979 | −0.0406286 | −0.0203143 | − | 0.999794i | \(-0.506467\pi\) | ||||
−0.0203143 | + | 0.999794i | \(0.506467\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.52273 | −0.330340 | ||||||||
\(832\) | 10.1499 | 0.351883 | ||||||||
\(833\) | 24.0816 | 0.834378 | ||||||||
\(834\) | −11.5021 | −0.398286 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.72214 | −0.0595615 | ||||||||
\(837\) | 5.13322 | 0.177430 | ||||||||
\(838\) | 10.4825 | 0.362111 | ||||||||
\(839\) | −45.7360 | −1.57898 | −0.789491 | − | 0.613762i | \(-0.789656\pi\) | ||||
−0.789491 | + | 0.613762i | \(0.789656\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7800 | 1.47517 | ||||||||
\(842\) | −17.3628 | −0.598362 | ||||||||
\(843\) | 20.5063 | 0.706275 | ||||||||
\(844\) | 19.0653 | 0.656255 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.51973 | 0.327295 | ||||||||
\(847\) | 3.22241 | 0.110723 | ||||||||
\(848\) | 19.1081 | 0.656173 | ||||||||
\(849\) | 13.1276 | 0.450537 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.0993 | −0.414758 | ||||||||
\(852\) | −2.10003 | −0.0719457 | ||||||||
\(853\) | −56.7867 | −1.94434 | −0.972170 | − | 0.234277i | \(-0.924728\pi\) | ||||
−0.972170 | + | 0.234277i | \(0.924728\pi\) | |||||||
\(854\) | 19.5863 | 0.670230 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.4094 | 0.355785 | ||||||||
\(857\) | −24.0415 | −0.821241 | −0.410620 | − | 0.911806i | \(-0.634688\pi\) | ||||
−0.410620 | + | 0.911806i | \(0.634688\pi\) | |||||||
\(858\) | 3.19852 | 0.109196 | ||||||||
\(859\) | −21.4533 | −0.731978 | −0.365989 | − | 0.930619i | \(-0.619269\pi\) | ||||
−0.365989 | + | 0.930619i | \(0.619269\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 30.0736 | 1.02490 | ||||||||
\(862\) | 11.2885 | 0.384488 | ||||||||
\(863\) | −25.3546 | −0.863082 | −0.431541 | − | 0.902093i | \(-0.642030\pi\) | ||||
−0.431541 | + | 0.902093i | \(0.642030\pi\) | |||||||
\(864\) | 28.7761 | 0.978983 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.7329 | 0.568606 | ||||||||
\(867\) | 41.8764 | 1.42220 | ||||||||
\(868\) | 5.14217 | 0.174537 | ||||||||
\(869\) | −3.05834 | −0.103747 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −49.7759 | −1.68659 | ||||||||
\(872\) | −12.8376 | −0.434736 | ||||||||
\(873\) | −22.6901 | −0.767944 | ||||||||
\(874\) | −0.593913 | −0.0200894 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 32.8205 | 1.10890 | ||||||||
\(877\) | −39.1208 | −1.32102 | −0.660508 | − | 0.750819i | \(-0.729659\pi\) | ||||
−0.660508 | + | 0.750819i | \(0.729659\pi\) | |||||||
\(878\) | −4.95503 | −0.167224 | ||||||||
\(879\) | 33.7397 | 1.13801 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.4388 | −0.621219 | −0.310610 | − | 0.950538i | \(-0.600533\pi\) | ||||
−0.310610 | + | 0.950538i | \(0.600533\pi\) | |||||||
\(882\) | 2.58782 | 0.0871364 | ||||||||
\(883\) | −4.68809 | −0.157767 | −0.0788834 | − | 0.996884i | \(-0.525135\pi\) | ||||
−0.0788834 | + | 0.996884i | \(0.525135\pi\) | |||||||
\(884\) | 59.7469 | 2.00950 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.3449 | −0.381140 | ||||||||
\(887\) | −29.0079 | −0.973990 | −0.486995 | − | 0.873405i | \(-0.661907\pi\) | ||||
−0.486995 | + | 0.873405i | \(0.661907\pi\) | |||||||
\(888\) | −26.2246 | −0.880041 | ||||||||
\(889\) | 9.58463 | 0.321458 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.54288 | −0.0851896 | ||||||||
\(892\) | 3.96354 | 0.132709 | ||||||||
\(893\) | 12.4483 | 0.416567 | ||||||||
\(894\) | 6.20593 | 0.207557 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 37.0137 | 1.23654 | ||||||||
\(897\) | −6.83672 | −0.228271 | ||||||||
\(898\) | −16.2089 | −0.540897 | ||||||||
\(899\) | −7.85053 | −0.261830 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.4229 | 1.87972 | ||||||||
\(902\) | −3.95240 | −0.131600 | ||||||||
\(903\) | −28.9606 | −0.963747 | ||||||||
\(904\) | −10.8447 | −0.360689 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.0442980 | 0.00147170 | ||||||||
\(907\) | −31.2319 | −1.03704 | −0.518519 | − | 0.855066i | \(-0.673516\pi\) | ||||
−0.518519 | + | 0.855066i | \(0.673516\pi\) | |||||||
\(908\) | 27.2519 | 0.904386 | ||||||||
\(909\) | −21.1237 | −0.700628 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.0740 | −0.400031 | −0.200015 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200015 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(912\) | 2.99973 | 0.0993311 | ||||||||
\(913\) | −2.60802 | −0.0863130 | ||||||||
\(914\) | 0.267283 | 0.00884095 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36.2459 | −1.19760 | ||||||||
\(917\) | 35.9744 | 1.18798 | ||||||||
\(918\) | 20.7812 | 0.685882 | ||||||||
\(919\) | −28.9331 | −0.954416 | −0.477208 | − | 0.878790i | \(-0.658351\pi\) | ||||
−0.477208 | + | 0.878790i | \(0.658351\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.8448 | 0.653907 | ||||||||
\(922\) | −2.95257 | −0.0972376 | ||||||||
\(923\) | −4.77618 | −0.157210 | ||||||||
\(924\) | −6.90725 | −0.227232 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −11.8766 | −0.390288 | ||||||||
\(927\) | −14.8474 | −0.487653 | ||||||||
\(928\) | −44.0090 | −1.44466 | ||||||||
\(929\) | −45.6501 | −1.49773 | −0.748866 | − | 0.662722i | \(-0.769401\pi\) | ||||
−0.748866 | + | 0.662722i | \(0.769401\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.38391 | 0.110903 | ||||||||
\(932\) | 2.49997 | 0.0818893 | ||||||||
\(933\) | 28.7485 | 0.941185 | ||||||||
\(934\) | 7.96250 | 0.260541 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.8767 | 0.453576 | ||||||||
\(937\) | −16.6566 | −0.544146 | −0.272073 | − | 0.962277i | \(-0.587709\pi\) | ||||
−0.272073 | + | 0.962277i | \(0.587709\pi\) | |||||||
\(938\) | −17.3433 | −0.566278 | ||||||||
\(939\) | 24.6311 | 0.803806 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.6743 | 0.576165 | 0.288082 | − | 0.957606i | \(-0.406982\pi\) | ||||
0.288082 | + | 0.957606i | \(0.406982\pi\) | |||||||
\(942\) | −8.98824 | −0.292853 | ||||||||
\(943\) | 8.44811 | 0.275108 | ||||||||
\(944\) | 4.61986 | 0.150364 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.80612 | 0.123748 | ||||||||
\(947\) | 18.3019 | 0.594731 | 0.297366 | − | 0.954764i | \(-0.403892\pi\) | ||||
0.297366 | + | 0.954764i | \(0.403892\pi\) | |||||||
\(948\) | 6.55558 | 0.212915 | ||||||||
\(949\) | 74.6451 | 2.42308 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.09177 | −0.262394 | ||||||||
\(952\) | 44.9937 | 1.45825 | ||||||||
\(953\) | 11.9242 | 0.386261 | 0.193131 | − | 0.981173i | \(-0.438136\pi\) | ||||
0.193131 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(954\) | 6.06323 | 0.196304 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.36772 | −0.173604 | ||||||||
\(957\) | 10.5453 | 0.340880 | ||||||||
\(958\) | 1.04078 | 0.0336261 | ||||||||
\(959\) | −43.0415 | −1.38988 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.1414 | −0.972303 | ||||||||
\(962\) | −27.5957 | −0.889720 | ||||||||
\(963\) | −7.69702 | −0.248033 | ||||||||
\(964\) | 43.6510 | 1.40590 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.38210 | −0.0766428 | ||||||||
\(967\) | −9.97275 | −0.320702 | −0.160351 | − | 0.987060i | \(-0.551263\pi\) | ||||
−0.160351 | + | 0.987060i | \(0.551263\pi\) | |||||||
\(968\) | 1.96203 | 0.0630619 | ||||||||
\(969\) | 8.85772 | 0.284551 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.4714 | −0.656960 | −0.328480 | − | 0.944511i | \(-0.606536\pi\) | ||||
−0.328480 | + | 0.944511i | \(0.606536\pi\) | |||||||
\(972\) | −23.1702 | −0.743184 | ||||||||
\(973\) | 56.4924 | 1.81106 | ||||||||
\(974\) | 3.28792 | 0.105352 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.7899 | −0.889533 | ||||||||
\(977\) | −15.9786 | −0.511202 | −0.255601 | − | 0.966782i | \(-0.582273\pi\) | ||||
−0.255601 | + | 0.966782i | \(0.582273\pi\) | |||||||
\(978\) | −6.23816 | −0.199474 | ||||||||
\(979\) | 5.38303 | 0.172042 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.49253 | 0.303073 | ||||||||
\(982\) | −15.5013 | −0.494665 | ||||||||
\(983\) | 10.3802 | 0.331077 | 0.165538 | − | 0.986203i | \(-0.447064\pi\) | ||||
0.165538 | + | 0.986203i | \(0.447064\pi\) | |||||||
\(984\) | 18.3109 | 0.583730 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −31.7819 | −1.01214 | ||||||||
\(987\) | 49.9283 | 1.58924 | ||||||||
\(988\) | 8.39555 | 0.267098 | ||||||||
\(989\) | −8.13545 | −0.258692 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.3252 | 1.50334 | 0.751668 | − | 0.659542i | \(-0.229250\pi\) | ||||
0.751668 | + | 0.659542i | \(0.229250\pi\) | |||||||
\(992\) | 4.81323 | 0.152820 | ||||||||
\(993\) | 1.15894 | 0.0367778 | ||||||||
\(994\) | −1.66415 | −0.0527836 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.59032 | 0.177136 | ||||||||
\(997\) | 1.92478 | 0.0609584 | 0.0304792 | − | 0.999535i | \(-0.490297\pi\) | ||||
0.0304792 | + | 0.999535i | \(0.490297\pi\) | |||||||
\(998\) | 4.39416 | 0.139095 | ||||||||
\(999\) | 59.4896 | 1.88217 |
(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 | 5225.2.a.y.1.5 | yes | 15 | |
5.4 | even | 2 | 5225.2.a.r.1.11 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5225.2.a.r.1.11 | ✓ | 15 | 5.4 | even | 2 | ||
5225.2.a.y.1.5 | yes | 15 | 1.1 | even | 1 | trivial |