Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7600,2,Mod(1,7600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7600.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: | \(60.6863055362\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 4x - 1 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 475) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.65109\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7600.1 |
$q$-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 | ||||||||
\(3\) | −1.65109 | −0.953259 | −0.476630 | − | 0.879104i | \(-0.658142\pi\) | ||||
−0.476630 | + | 0.879104i | \(0.658142\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.65109 | 1.37998 | 0.689992 | − | 0.723817i | \(-0.257614\pi\) | ||||
0.689992 | + | 0.723817i | \(0.257614\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.273891 | −0.0912969 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.65109 | −0.799335 | −0.399667 | − | 0.916660i | \(-0.630874\pi\) | ||||
−0.399667 | + | 0.916660i | \(0.630874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.13161 | −1.70060 | −0.850301 | − | 0.526297i | \(-0.823580\pi\) | ||||
−0.850301 | + | 0.526297i | \(0.823580\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.34891 | −0.569694 | −0.284847 | − | 0.958573i | \(-0.591943\pi\) | ||||
−0.284847 | + | 0.958573i | \(0.591943\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.02830 | −1.31548 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.48052 | 1.14277 | 0.571383 | − | 0.820683i | \(-0.306407\pi\) | ||||
0.571383 | + | 0.820683i | \(0.306407\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.40550 | 1.04029 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.651093 | 0.120905 | 0.0604525 | − | 0.998171i | \(-0.480746\pi\) | ||||
0.0604525 | + | 0.998171i | \(0.480746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.67939 | 1.19965 | 0.599827 | − | 0.800130i | \(-0.295236\pi\) | ||||
0.599827 | + | 0.800130i | \(0.295236\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.37720 | 0.761973 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.70769 | 1.43153 | 0.715767 | − | 0.698339i | \(-0.246077\pi\) | ||||
0.715767 | + | 0.698339i | \(0.246077\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.1239 | 1.62111 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.93273 | 0.301842 | 0.150921 | − | 0.988546i | \(-0.451776\pi\) | ||||
0.150921 | + | 0.988546i | \(0.451776\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.65884 | −0.405470 | −0.202735 | − | 0.979234i | \(-0.564983\pi\) | ||||
−0.202735 | + | 0.979234i | \(0.564983\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.71836 | 0.542378 | 0.271189 | − | 0.962526i | \(-0.412583\pi\) | ||||
0.271189 | + | 0.962526i | \(0.412583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.33048 | 0.904355 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.87826 | 0.543066 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.7544 | −1.88931 | −0.944656 | − | 0.328061i | \(-0.893605\pi\) | ||||
−0.944656 | + | 0.328061i | \(0.893605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.65109 | 0.218693 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.84997 | 1.02198 | 0.510989 | − | 0.859587i | \(-0.329279\pi\) | ||||
0.510989 | + | 0.859587i | \(0.329279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.92498 | −0.246469 | −0.123234 | − | 0.992378i | \(-0.539327\pi\) | ||||
−0.123234 | + | 0.992378i | \(0.539327\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.44447 | −0.542978 | −0.271489 | − | 0.962442i | \(-0.587516\pi\) | ||||
−0.271489 | + | 0.962442i | \(0.587516\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.04884 | −1.08935 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.54778 | −0.421044 | −0.210522 | − | 0.977589i | \(-0.567516\pi\) | ||||
−0.210522 | + | 0.977589i | \(0.567516\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.48052 | 0.290322 | 0.145161 | − | 0.989408i | \(-0.453630\pi\) | ||||
0.145161 | + | 0.989408i | \(0.453630\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.67939 | −1.10307 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1599 | 1.70562 | 0.852811 | − | 0.522219i | \(-0.174896\pi\) | ||||
0.852811 | + | 0.522219i | \(0.174896\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.10331 | −0.900368 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.7282 | −1.61663 | −0.808317 | − | 0.588748i | \(-0.799621\pi\) | ||||
−0.808317 | + | 0.588748i | \(0.799621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.07502 | −0.115254 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.06727 | −0.537129 | −0.268565 | − | 0.963262i | \(-0.586549\pi\) | ||||
−0.268565 | + | 0.963262i | \(0.586549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.3871 | −2.34680 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −11.0283 | −1.14358 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.22717 | −0.327670 | −0.163835 | − | 0.986488i | \(-0.552386\pi\) | ||||
−0.163835 | + | 0.986488i | \(0.552386\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.726109 | 0.0729767 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.8032 | 1.67199 | 0.835993 | − | 0.548740i | \(-0.184892\pi\) | ||||
0.835993 | + | 0.548740i | \(0.184892\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.85772 | −0.971310 | −0.485655 | − | 0.874151i | \(-0.661419\pi\) | ||||
−0.485655 | + | 0.874151i | \(0.661419\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.13936 | −0.496841 | −0.248420 | − | 0.968652i | \(-0.579911\pi\) | ||||
−0.248420 | + | 0.968652i | \(0.579911\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.9738 | 1.33845 | 0.669225 | − | 0.743060i | \(-0.266626\pi\) | ||||
0.669225 | + | 0.743060i | \(0.266626\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14.3772 | −1.36462 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.527235 | 0.0495981 | 0.0247990 | − | 0.999692i | \(-0.492105\pi\) | ||||
0.0247990 | + | 0.999692i | \(0.492105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.67939 | 0.155260 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.57608 | −0.786168 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.97170 | −0.361064 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.19112 | −0.287734 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.8217 | −1.04900 | −0.524502 | − | 0.851409i | \(-0.675748\pi\) | ||||
−0.524502 | + | 0.851409i | \(0.675748\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.39000 | 0.386518 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.12386 | −0.709785 | −0.354892 | − | 0.934907i | \(-0.615483\pi\) | ||||
−0.354892 | + | 0.934907i | \(0.615483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.65109 | −0.316590 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.5761 | −1.50163 | −0.750813 | − | 0.660515i | \(-0.770338\pi\) | ||||
−0.750813 | + | 0.660515i | \(0.770338\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.4154 | −1.56197 | −0.780986 | − | 0.624549i | \(-0.785283\pi\) | ||||
−0.780986 | + | 0.624549i | \(0.785283\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.13936 | −0.517027 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.2555 | 1.35935 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.4522 | −0.862084 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −17.2915 | −1.41658 | −0.708288 | − | 0.705924i | \(-0.750532\pi\) | ||||
−0.708288 | + | 0.705924i | \(0.750532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.58383 | −0.210269 | −0.105134 | − | 0.994458i | \(-0.533527\pi\) | ||||
−0.105134 | + | 0.994458i | \(0.533527\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.643343 | 0.0520112 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9738 | 0.875807 | 0.437903 | − | 0.899022i | \(-0.355721\pi\) | ||||
0.437903 | + | 0.899022i | \(0.355721\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22.7098 | 1.80100 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.0099 | 1.57700 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.6794 | 1.77639 | 0.888193 | − | 0.459470i | \(-0.151961\pi\) | ||||
0.888193 | + | 0.459470i | \(0.151961\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.16283 | −0.399512 | −0.199756 | − | 0.979846i | \(-0.564015\pi\) | ||||
−0.199756 | + | 0.979846i | \(0.564015\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.5966 | 1.89205 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.273891 | 0.0209449 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.2165 | 1.30895 | 0.654473 | − | 0.756085i | \(-0.272891\pi\) | ||||
0.654473 | + | 0.756085i | \(0.272891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.9610 | −0.974211 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.6999 | −0.799751 | −0.399875 | − | 0.916570i | \(-0.630947\pi\) | ||||
−0.399875 | + | 0.916570i | \(0.630947\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7720 | −1.24666 | −0.623328 | − | 0.781961i | \(-0.714220\pi\) | ||||
−0.623328 | + | 0.781961i | \(0.714220\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.17833 | 0.234949 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.22717 | 0.455376 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 19.7360 | 1.43558 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8598 | 1.00286 | 0.501431 | − | 0.865197i | \(-0.332807\pi\) | ||||
0.501431 | + | 0.865197i | \(0.332807\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.0694 | −1.51661 | −0.758304 | − | 0.651901i | \(-0.773972\pi\) | ||||
−0.758304 | + | 0.651901i | \(0.773972\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.2555 | −1.51439 | −0.757195 | − | 0.653189i | \(-0.773431\pi\) | ||||
−0.757195 | + | 0.653189i | \(0.773431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.69006 | 0.545134 | 0.272567 | − | 0.962137i | \(-0.412127\pi\) | ||||
0.272567 | + | 0.962137i | \(0.412127\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.33823 | 0.517599 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.37720 | 0.166847 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.50106 | −0.104331 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.65109 | 0.183380 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.69781 | 0.116882 | 0.0584411 | − | 0.998291i | \(-0.481387\pi\) | ||||
0.0584411 | + | 0.998291i | \(0.481387\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.85772 | 0.401364 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.3871 | 1.65550 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.09556 | −0.276752 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.4026 | 0.968822 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.2632 | −1.69175 | −0.845875 | − | 0.533381i | \(-0.820921\pi\) | ||||
−0.845875 | + | 0.533381i | \(0.820921\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.8217 | −1.11649 | −0.558247 | − | 0.829675i | \(-0.688526\pi\) | ||||
−0.558247 | + | 0.829675i | \(0.688526\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.6249 | −0.966442 | −0.483221 | − | 0.875498i | \(-0.660533\pi\) | ||||
−0.483221 | + | 0.875498i | \(0.660533\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.9816 | 1.05151 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.91431 | −0.583996 | −0.291998 | − | 0.956419i | \(-0.594320\pi\) | ||||
−0.291998 | + | 0.956419i | \(0.594320\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −25.0304 | −1.62590 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.6015 | 1.59134 | 0.795668 | − | 0.605733i | \(-0.207120\pi\) | ||||
0.795668 | + | 0.605733i | \(0.207120\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.6150 | −0.941438 | −0.470719 | − | 0.882283i | \(-0.656005\pi\) | ||||
−0.470719 | + | 0.882283i | \(0.656005\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.83717 | −0.182005 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.13161 | 0.390145 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 24.3177 | 1.54107 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3382 | 0.841902 | 0.420951 | − | 0.907083i | \(-0.361696\pi\) | ||||
0.420951 | + | 0.907083i | \(0.361696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.5294 | −0.913453 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.35103 | 0.209031 | 0.104516 | − | 0.994523i | \(-0.466671\pi\) | ||||
0.104516 | + | 0.994523i | \(0.466671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 31.7926 | 1.97549 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.178328 | −0.0110382 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.8860 | 0.671260 | 0.335630 | − | 0.941994i | \(-0.391051\pi\) | ||||
0.335630 | + | 0.941994i | \(0.391051\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.36653 | 0.512023 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.4338 | 1.12393 | 0.561964 | − | 0.827162i | \(-0.310046\pi\) | ||||
0.561964 | + | 0.827162i | \(0.310046\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4076 | 1.23967 | 0.619837 | − | 0.784730i | \(-0.287199\pi\) | ||||
0.619837 | + | 0.784730i | \(0.287199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 36.9632 | 2.23711 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.69994 | 0.162223 | 0.0811117 | − | 0.996705i | \(-0.474153\pi\) | ||||
0.0811117 | + | 0.996705i | \(0.474153\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.82942 | −0.109525 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.2242 | −0.908202 | −0.454101 | − | 0.890950i | \(-0.650040\pi\) | ||||
−0.454101 | + | 0.890950i | \(0.650040\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.18045 | 0.367390 | 0.183695 | − | 0.982983i | \(-0.441194\pi\) | ||||
0.183695 | + | 0.982983i | \(0.441194\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.05659 | 0.416537 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4826 | −0.675449 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.32836 | 0.312354 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.6893 | −1.79289 | −0.896443 | − | 0.443159i | \(-0.853858\pi\) | ||||
−0.896443 | + | 0.443159i | \(0.853858\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.3305 | −0.831539 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −33.6044 | −1.94339 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.70769 | −0.559542 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.7437 | −1.59384 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.7827 | −0.843693 | −0.421847 | − | 0.906667i | \(-0.638618\pi\) | ||||
−0.421847 | + | 0.906667i | \(0.638618\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.2760 | 0.925910 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.9992 | 1.53098 | 0.765492 | − | 0.643445i | \(-0.222496\pi\) | ||||
0.765492 | + | 0.643445i | \(0.222496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.74666 | 0.550914 | 0.275457 | − | 0.961313i | \(-0.411171\pi\) | ||||
0.275457 | + | 0.961313i | \(0.411171\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.7261 | −1.10793 | −0.553964 | − | 0.832540i | \(-0.686886\pi\) | ||||
−0.553964 | + | 0.832540i | \(0.686886\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.72611 | −0.0966436 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.48556 | 0.473618 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.34891 | 0.130697 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.0721 | −1.27589 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.5761 | 0.748473 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.9426 | −1.09614 | −0.548072 | − | 0.836431i | \(-0.684638\pi\) | ||||
−0.548072 | + | 0.836431i | \(0.684638\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.38495 | −0.130695 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.05952 | −0.112189 | −0.0560945 | − | 0.998425i | \(-0.517865\pi\) | ||||
−0.0560945 | + | 0.998425i | \(0.517865\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.870514 | −0.0472798 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −17.7077 | −0.958925 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.44447 | −0.131989 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.5011 | −0.563727 | −0.281863 | − | 0.959455i | \(-0.590952\pi\) | ||||
−0.281863 | + | 0.959455i | \(0.590952\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5059 | 0.883540 | 0.441770 | − | 0.897128i | \(-0.354351\pi\) | ||||
0.441770 | + | 0.897128i | \(0.354351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −33.1444 | −1.76912 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8860 | −0.845527 | −0.422764 | − | 0.906240i | \(-0.638940\pi\) | ||||
−0.422764 | + | 0.906240i | \(0.638940\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.1599 | 0.749422 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.28376 | −0.0677544 | −0.0338772 | − | 0.999426i | \(-0.510786\pi\) | ||||
−0.0338772 | + | 0.999426i | \(0.510786\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.55765 | 0.344188 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.8804 | −1.03775 | −0.518874 | − | 0.854851i | \(-0.673649\pi\) | ||||
−0.518874 | + | 0.854851i | \(0.673649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.529358 | −0.0275573 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −50.2186 | −2.60722 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.4359 | 0.851020 | 0.425510 | − | 0.904954i | \(-0.360095\pi\) | ||||
0.425510 | + | 0.904954i | \(0.360095\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.99225 | −0.205611 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.338233 | −0.0173739 | −0.00868694 | − | 0.999962i | \(-0.502765\pi\) | ||||
−0.00868694 | + | 0.999962i | \(0.502765\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.5187 | 0.999972 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.7339 | −0.701767 | −0.350884 | − | 0.936419i | \(-0.614119\pi\) | ||||
−0.350884 | + | 0.936419i | \(0.614119\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.728232 | 0.0370181 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.26109 | −0.114642 | −0.0573210 | − | 0.998356i | \(-0.518256\pi\) | ||||
−0.0573210 | + | 0.998356i | \(0.518256\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.8732 | −0.651027 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.4132 | 0.676609 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.82942 | 0.392947 | 0.196474 | − | 0.980509i | \(-0.437051\pi\) | ||||
0.196474 | + | 0.980509i | \(0.437051\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.02830 | 0.301792 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.0510 | −1.75036 | −0.875181 | − | 0.483796i | \(-0.839258\pi\) | ||||
−0.875181 | + | 0.483796i | \(0.839258\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.9554 | −2.04013 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.0849 | −1.14428 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.34811 | −0.412787 | −0.206394 | − | 0.978469i | \(-0.566173\pi\) | ||||
−0.206394 | + | 0.978469i | \(0.566173\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.0197 | 1.43144 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.6610 | 1.41031 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.4055 | 1.48896 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.8705 | 0.970738 | 0.485369 | − | 0.874309i | \(-0.338685\pi\) | ||||
0.485369 | + | 0.874309i | \(0.338685\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.400672 | −0.0195276 | −0.00976379 | − | 0.999952i | \(-0.503108\pi\) | ||||
−0.00976379 | + | 0.999952i | \(0.503108\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.01842 | −0.0495174 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.02830 | −0.340123 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −26.8393 | −1.29581 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.2533 | 0.686559 | 0.343280 | − | 0.939233i | \(-0.388462\pi\) | ||||
0.343280 | + | 0.939233i | \(0.388462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.8393 | −0.617017 | −0.308509 | − | 0.951222i | \(-0.599830\pi\) | ||||
−0.308509 | + | 0.951222i | \(0.599830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.48052 | −0.262169 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2555 | 0.632649 | 0.316324 | − | 0.948651i | \(-0.397551\pi\) | ||||
0.316324 | + | 0.948651i | \(0.397551\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.73386 | −0.0825647 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.72611 | 0.272056 | 0.136028 | − | 0.990705i | \(-0.456566\pi\) | ||||
0.136028 | + | 0.990705i | \(0.456566\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.5499 | 1.35036 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.11399 | 0.146958 | 0.0734790 | − | 0.997297i | \(-0.476590\pi\) | ||||
0.0734790 | + | 0.997297i | \(0.476590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.12386 | −0.241273 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.26614 | 0.200441 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.4535 | −1.28422 | −0.642111 | − | 0.766611i | \(-0.721941\pi\) | ||||
−0.642111 | + | 0.766611i | \(0.721941\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −12.6970 | −0.592646 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.9837 | 0.651286 | 0.325643 | − | 0.945493i | \(-0.394419\pi\) | ||||
0.325643 | + | 0.945493i | \(0.394419\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.9992 | 0.836494 | 0.418247 | − | 0.908333i | \(-0.362645\pi\) | ||||
0.418247 | + | 0.908333i | \(0.362645\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6871 | 0.587091 | 0.293545 | − | 0.955945i | \(-0.405165\pi\) | ||||
0.293545 | + | 0.955945i | \(0.405165\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.2272 | −0.749301 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.1188 | −0.834871 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.04884 | 0.324106 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.76720 | 0.172488 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.7544 | −1.13106 | −0.565529 | − | 0.824729i | \(-0.691328\pi\) | ||||
−0.565529 | + | 0.824729i | \(0.691328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −53.3921 | −2.43447 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −33.0382 | −1.50329 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.08277 | −0.185008 | −0.0925039 | − | 0.995712i | \(-0.529487\pi\) | ||||
−0.0925039 | + | 0.995712i | \(0.529487\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −37.4458 | −1.69336 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.2547 | −1.32024 | −0.660122 | − | 0.751158i | \(-0.729496\pi\) | ||||
−0.660122 | + | 0.751158i | \(0.729496\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.52936 | −0.0688788 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.9533 | −0.581034 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.57315 | −0.0704240 | −0.0352120 | − | 0.999380i | \(-0.511211\pi\) | ||||
−0.0352120 | + | 0.999380i | \(0.511211\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.52431 | 0.380838 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.7819 | 0.926619 | 0.463310 | − | 0.886196i | \(-0.346662\pi\) | ||||
0.463310 | + | 0.886196i | \(0.346662\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.6113 | −1.80361 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.8238 | −1.41056 | −0.705282 | − | 0.708926i | \(-0.749180\pi\) | ||||
−0.705282 | + | 0.708926i | \(0.749180\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.05659 | 0.400640 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.40550 | −0.238659 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.85772 | −0.433542 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.4260 | −1.24776 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.4720 | −1.20357 | −0.601784 | − | 0.798659i | \(-0.705543\pi\) | ||||
−0.601784 | + | 0.798659i | \(0.705543\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.4466 | −0.456798 | −0.228399 | − | 0.973568i | \(-0.573349\pi\) | ||||
−0.228399 | + | 0.973568i | \(0.573349\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.6893 | −0.683435 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.03605 | 0.305915 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.15003 | −0.0933034 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.8508 | −0.513314 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.6666 | 0.762370 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −16.7827 | −0.722882 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.4989 | 0.580365 | 0.290182 | − | 0.956971i | \(-0.406284\pi\) | ||||
0.290182 | + | 0.956971i | \(0.406284\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.6922 | 1.18839 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.54698 | 0.365442 | 0.182721 | − | 0.983165i | \(-0.441509\pi\) | ||||
0.182721 | + | 0.983165i | \(0.441509\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.527235 | 0.0225018 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.651093 | −0.0277375 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.3502 | 2.35373 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −27.2378 | −1.15410 | −0.577052 | − | 0.816707i | \(-0.695797\pi\) | ||||
−0.577052 | + | 0.816707i | \(0.695797\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.3030 | 0.689543 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.2816 | −0.434091 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.44235 | −0.0607876 | −0.0303938 | − | 0.999538i | \(-0.509676\pi\) | ||||
−0.0303938 | + | 0.999538i | \(0.509676\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −29.5860 | −1.24249 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.2632 | −0.597945 | −0.298973 | − | 0.954262i | \(-0.596644\pi\) | ||||
−0.298973 | + | 0.954262i | \(0.596644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.91723 | −0.415023 | −0.207512 | − | 0.978233i | \(-0.566536\pi\) | ||||
−0.207512 | + | 0.978233i | \(0.566536\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.8839 | −0.955988 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.23997 | 0.343034 | 0.171517 | − | 0.985181i | \(-0.445133\pi\) | ||||
0.171517 | + | 0.985181i | \(0.445133\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.7875 | 1.44572 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53.7742 | −2.23093 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.4642 | 1.51019 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.9554 | 1.52531 | 0.762656 | − | 0.646804i | \(-0.223895\pi\) | ||||
0.762656 | + | 0.646804i | \(0.223895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.67939 | −0.275219 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 35.0948 | 1.44361 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.36170 | 0.0559184 | 0.0279592 | − | 0.999609i | \(-0.491099\pi\) | ||||
0.0279592 | + | 0.999609i | \(0.491099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.6970 | −0.519654 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.5753 | −1.37185 | −0.685924 | − | 0.727673i | \(-0.740602\pi\) | ||||
−0.685924 | + | 0.727673i | \(0.740602\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6561 | 0.516255 | 0.258127 | − | 0.966111i | \(-0.416895\pi\) | ||||
0.258127 | + | 0.966111i | \(0.416895\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.21730 | 0.0495722 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.4047 | 0.706435 | 0.353217 | − | 0.935541i | \(-0.385088\pi\) | ||||
0.353217 | + | 0.935541i | \(0.385088\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.92498 | −0.159048 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.7995 | −0.922370 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.2603 | 1.50493 | 0.752465 | − | 0.658633i | \(-0.228865\pi\) | ||||
0.752465 | + | 0.658633i | \(0.228865\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.3764 | 0.739806 | 0.369903 | − | 0.929070i | \(-0.379391\pi\) | ||||
0.369903 | + | 0.929070i | \(0.379391\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.5526 | −0.584919 | −0.292459 | − | 0.956278i | \(-0.594474\pi\) | ||||
−0.292459 | + | 0.956278i | \(0.594474\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.6249 | 1.18881 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.5011 | −0.741229 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.37720 | −0.174809 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.4535 | −0.815536 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.0304 | −0.877017 | −0.438509 | − | 0.898727i | \(-0.644493\pi\) | ||||
−0.438509 | + | 0.898727i | \(0.644493\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.80325 | −0.111419 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −38.8160 | −1.53795 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.971704 | 0.0384400 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.6765 | −1.72512 | −0.862558 | − | 0.505958i | \(-0.831139\pi\) | ||||
−0.862558 | + | 0.505958i | \(0.831139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.9263 | −1.02243 | −0.511217 | − | 0.859452i | \(-0.670805\pi\) | ||||
−0.511217 | + | 0.859452i | \(0.670805\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.1046 | −1.65530 | −0.827652 | − | 0.561242i | \(-0.810324\pi\) | ||||
−0.827652 | + | 0.561242i | \(0.810324\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.8110 | −0.816903 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40.2653 | −1.57812 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.4671 | −1.58360 | −0.791801 | − | 0.610779i | \(-0.790856\pi\) | ||||
−0.791801 | + | 0.610779i | \(0.790856\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.679390 | −0.0265055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.4204 | −1.30187 | −0.650937 | − | 0.759131i | \(-0.725624\pi\) | ||||
−0.650937 | + | 0.759131i | \(0.725624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.4883 | 0.758006 | 0.379003 | − | 0.925396i | \(-0.376267\pi\) | ||||
0.379003 | + | 0.925396i | \(0.376267\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.7800 | −0.923539 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.56833 | 0.138166 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 41.7119 | 1.61268 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.10331 | 0.197011 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.747456 | 0.0288123 | 0.0144062 | − | 0.999896i | \(-0.495414\pi\) | ||||
0.0144062 | + | 0.999896i | \(0.495414\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.0275 | −0.961885 | −0.480942 | − | 0.876752i | \(-0.659705\pi\) | ||||
−0.480942 | + | 0.876752i | \(0.659705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.7827 | −0.452179 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.7742 | 1.06431 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.7253 | −1.40525 | −0.702627 | − | 0.711558i | \(-0.747990\pi\) | ||||
−0.702627 | + | 0.711558i | \(0.747990\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24.1471 | 0.921270 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 84.3366 | 3.21297 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.3177 | 0.810963 | 0.405482 | − | 0.914103i | \(-0.367104\pi\) | ||||
0.405482 | + | 0.914103i | \(0.367104\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.65109 | 0.100707 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.53981 | −0.171958 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.7184 | 0.556699 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.1161 | 1.02416 | 0.512081 | − | 0.858937i | \(-0.328875\pi\) | ||||
0.512081 | + | 0.858937i | \(0.328875\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.70769 | −0.328417 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 61.3502 | 2.30731 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.1161 | −0.379918 | −0.189959 | − | 0.981792i | \(-0.560836\pi\) | ||||
−0.189959 | + | 0.981792i | \(0.560836\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.15215 | −0.155718 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.6065 | 1.37092 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −40.6193 | −1.51696 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.1471 | −0.900535 | −0.450268 | − | 0.892894i | \(-0.648671\pi\) | ||||
−0.450268 | + | 0.892894i | \(0.648671\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.9914 | −1.34039 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 24.1308 | 0.897434 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.8988 | −0.738006 | −0.369003 | − | 0.929428i | \(-0.620301\pi\) | ||||
−0.369003 | + | 0.929428i | \(0.620301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.9944 | 1.07387 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.24537 | 0.230994 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.9455 | −0.736705 | −0.368352 | − | 0.929686i | \(-0.620078\pi\) | ||||
−0.368352 | + | 0.929686i | \(0.620078\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.7827 | 0.434021 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.2624 | 1.40751 | 0.703753 | − | 0.710445i | \(-0.251506\pi\) | ||||
0.703753 | + | 0.710445i | \(0.251506\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.1239 | −0.371909 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.5547 | −0.460588 | −0.230294 | − | 0.973121i | \(-0.573969\pi\) | ||||
−0.230294 | + | 0.973121i | \(0.573969\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.03392 | 0.147594 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.7643 | −0.685632 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.2215 | −0.847366 | −0.423683 | − | 0.905810i | \(-0.639263\pi\) | ||||
−0.423683 | + | 0.905810i | \(0.639263\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.0227 | −0.802551 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.4105 | −0.669143 | −0.334571 | − | 0.942370i | \(-0.608592\pi\) | ||||
−0.334571 | + | 0.942370i | \(0.608592\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.9893 | 0.870757 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7982 | 0.427684 | 0.213842 | − | 0.976868i | \(-0.431402\pi\) | ||||
0.213842 | + | 0.976868i | \(0.431402\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.0197 | 1.84704 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −48.1329 | −1.73798 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.2653 | 1.48807 | 0.744033 | − | 0.668143i | \(-0.232910\pi\) | ||||
0.744033 | + | 0.668143i | \(0.232910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.53286 | −0.199261 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.51736 | −0.198446 | −0.0992229 | − | 0.995065i | \(-0.531636\pi\) | ||||
−0.0992229 | + | 0.995065i | \(0.531636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −52.4925 | −1.88316 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.93273 | −0.0692474 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.40550 | 0.336555 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.51948 | 0.125776 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.7771 | 0.598038 | 0.299019 | − | 0.954247i | \(-0.403341\pi\) | ||||
0.299019 | + | 0.954247i | \(0.403341\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −17.9738 | −0.639885 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.92498 | 0.0684446 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.8032 | 0.419146 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.4260 | 1.04232 | 0.521162 | − | 0.853458i | \(-0.325499\pi\) | ||||
0.521162 | + | 0.853458i | \(0.325499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.73408 | −0.308989 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.38788 | 0.0490382 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.57608 | −0.232065 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.4359 | −1.07140 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.48614 | 0.192883 | 0.0964413 | − | 0.995339i | \(-0.469254\pi\) | ||||
0.0964413 | + | 0.995339i | \(0.469254\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.3927 | −0.575626 | −0.287813 | − | 0.957687i | \(-0.592928\pi\) | ||||
−0.287813 | + | 0.957687i | \(0.592928\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33.6949 | −1.18173 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.65884 | 0.0930212 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.13161 | 0.214256 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.1628 | 0.529186 | 0.264593 | − | 0.964360i | \(-0.414762\pi\) | ||||
0.264593 | + | 0.964360i | \(0.414762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.6094 | 0.578968 | 0.289484 | − | 0.957183i | \(-0.406516\pi\) | ||||
0.289484 | + | 0.957183i | \(0.406516\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.2293 | 0.529574 | 0.264787 | − | 0.964307i | \(-0.414698\pi\) | ||||
0.264787 | + | 0.964307i | \(0.414698\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.4565 | 1.64823 | 0.824116 | − | 0.566422i | \(-0.191673\pi\) | ||||
0.824116 | + | 0.566422i | \(0.191673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.45785 | −0.154641 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.8697 | −0.515205 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.1054 | 1.24799 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.26614 | −0.0782359 | −0.0391179 | − | 0.999235i | \(-0.512455\pi\) | ||||
−0.0391179 | + | 0.999235i | \(0.512455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.5761 | −0.985382 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.1367 | 0.865752 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.5011 | −0.498262 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.2045 | −0.350218 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.7226 | 1.63591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −51.8753 | −1.77618 | −0.888089 | − | 0.459672i | \(-0.847967\pi\) | ||||
−0.888089 | + | 0.459672i | \(0.847967\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.17058 | 0.210783 | 0.105391 | − | 0.994431i | \(-0.466390\pi\) | ||||
0.105391 | + | 0.994431i | \(0.466390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.0635 | 1.05987 | 0.529937 | − | 0.848037i | \(-0.322215\pi\) | ||||
0.529937 | + | 0.848037i | \(0.322215\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6511 | −0.397068 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.24772 | −0.110554 | −0.0552768 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552768 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.9589 | 0.643878 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40.1903 | −1.36336 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.2517 | 0.923390 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.883892 | 0.0299152 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.7042 | 1.40825 | 0.704125 | − | 0.710076i | \(-0.251339\pi\) | ||||
0.704125 | + | 0.710076i | \(0.251339\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50.6708 | 1.70908 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.42392 | 0.250118 | 0.125059 | − | 0.992149i | \(-0.460088\pi\) | ||||
0.125059 | + | 0.992149i | \(0.460088\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.0333 | 1.07801 | 0.539004 | − | 0.842303i | \(-0.318801\pi\) | ||||
0.539004 | + | 0.842303i | \(0.318801\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.0275 | 0.672457 | 0.336229 | − | 0.941780i | \(-0.390848\pi\) | ||||
0.336229 | + | 0.941780i | \(0.390848\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.1620 | −1.44761 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.4826 | 0.719695 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.71836 | −0.124430 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 55.4840 | 1.85256 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.34891 | 0.145044 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.3078 | 1.07633 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.0283 | 0.533388 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.94823 | 0.164303 | 0.0821517 | − | 0.996620i | \(-0.473821\pi\) | ||||
0.0821517 | + | 0.996620i | \(0.473821\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.60225 | −0.152647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.3014 | −1.07019 | −0.535096 | − | 0.844791i | \(-0.679725\pi\) | ||||
−0.535096 | + | 0.844791i | \(0.679725\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.0459 | 1.29223 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.6610 | −0.979491 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.3072 | −0.702861 | −0.351430 | − | 0.936214i | \(-0.614305\pi\) | ||||
−0.351430 | + | 0.936214i | \(0.614305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.4076 | 0.804258 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.7536 | 0.716029 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.69994 | 0.0886775 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.7848 | 0.813164 | 0.406582 | − | 0.913614i | \(-0.366721\pi\) | ||||
0.406582 | + | 0.913614i | \(0.366721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.33048 | −0.207473 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −44.5782 | −1.45942 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.3687 | 1.05744 | 0.528719 | − | 0.848797i | \(-0.322673\pi\) | ||||
0.528719 | + | 0.848797i | \(0.322673\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0926 | −0.525163 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.48264 | −0.0483326 | −0.0241663 | − | 0.999708i | \(-0.507693\pi\) | ||||
−0.0241663 | + | 0.999708i | \(0.507693\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.5924 | 0.344935 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.86064 | −0.287932 | −0.143966 | − | 0.989583i | \(-0.545986\pi\) | ||||
−0.143966 | + | 0.989583i | \(0.545986\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.2095 | −0.493723 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.5696 | 1.05614 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.1239 | −0.327944 | −0.163972 | − | 0.986465i | \(-0.552431\pi\) | ||||
−0.163972 | + | 0.986465i | \(0.552431\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.84997 | 0.0921264 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −64.1719 | −2.07222 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.6142 | 0.439169 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.40762 | 0.0453600 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.8139 | 1.34465 | 0.672323 | − | 0.740258i | \(-0.265297\pi\) | ||||
0.672323 | + | 0.740258i | \(0.265297\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.87826 | −0.124588 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.53016 | 0.177471 | 0.0887356 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887356 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −67.2362 | −2.15549 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.9447 | 1.02200 | 0.511001 | − | 0.859580i | \(-0.329275\pi\) | ||||
0.511001 | + | 0.859580i | \(0.329275\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.4338 | 0.429346 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.82730 | −0.122196 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.82862 | 0.281589 | 0.140795 | − | 0.990039i | \(-0.455034\pi\) | ||||
0.140795 | + | 0.990039i | \(0.455034\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.4154 | −0.713489 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5718 | −0.463357 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.7304 | 1.38914 | 0.694570 | − | 0.719425i | \(-0.255595\pi\) | ||||
0.694570 | + | 0.719425i | \(0.255595\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.9271 | 1.04491 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46.6738 | 1.47817 | 0.739086 | − | 0.673611i | \(-0.235257\pi\) | ||||
0.739086 | + | 0.673611i | \(0.235257\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 47.0694 | 1.48921 |
(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 | 7600.2.a.cc.1.1 | 3 | ||
4.3 | odd | 2 | 475.2.a.e.1.2 | ✓ | 3 | ||
5.4 | even | 2 | 7600.2.a.bh.1.3 | 3 | |||
12.11 | even | 2 | 4275.2.a.bm.1.2 | 3 | |||
20.3 | even | 4 | 475.2.b.b.324.4 | 6 | |||
20.7 | even | 4 | 475.2.b.b.324.3 | 6 | |||
20.19 | odd | 2 | 475.2.a.g.1.2 | yes | 3 | ||
60.59 | even | 2 | 4275.2.a.ba.1.2 | 3 | |||
76.75 | even | 2 | 9025.2.a.bc.1.2 | 3 | |||
380.379 | even | 2 | 9025.2.a.y.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.a.e.1.2 | ✓ | 3 | 4.3 | odd | 2 | ||
475.2.a.g.1.2 | yes | 3 | 20.19 | odd | 2 | ||
475.2.b.b.324.3 | 6 | 20.7 | even | 4 | |||
475.2.b.b.324.4 | 6 | 20.3 | even | 4 | |||
4275.2.a.ba.1.2 | 3 | 60.59 | even | 2 | |||
4275.2.a.bm.1.2 | 3 | 12.11 | even | 2 | |||
7600.2.a.bh.1.3 | 3 | 5.4 | even | 2 | |||
7600.2.a.cc.1.1 | 3 | 1.1 | even | 1 | trivial | ||
9025.2.a.y.1.2 | 3 | 380.379 | even | 2 | |||
9025.2.a.bc.1.2 | 3 | 76.75 | even | 2 |