Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, 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("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-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 | ||||||||
\(3\) | 2.82843 | 1.63299 | 0.816497 | − | 0.577350i | \(-0.195913\pi\) | ||||
0.816497 | + | 0.577350i | \(0.195913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.00000 | 1.66667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.82843 | 1.89386 | 0.946932 | − | 0.321433i | \(-0.104164\pi\) | ||||
0.946932 | + | 0.321433i | \(0.104164\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.17157 | −0.284148 | −0.142074 | − | 0.989856i | \(-0.545377\pi\) | ||||
−0.142074 | + | 0.989856i | \(0.545377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.65685 | −1.23443 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.65685 | 1.42184 | 0.710921 | − | 0.703272i | \(-0.248278\pi\) | ||||
0.710921 | + | 0.703272i | \(0.248278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.82843 | −0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.65685 | −0.601183 | −0.300592 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300592 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19.3137 | 3.09267 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.82843 | −0.412568 | −0.206284 | − | 0.978492i | \(-0.566137\pi\) | ||||
−0.206284 | + | 0.978492i | \(0.566137\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.31371 | −0.464012 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.343146 | −0.0471347 | −0.0235673 | − | 0.999722i | \(-0.507502\pi\) | ||||
−0.0235673 | + | 0.999722i | \(0.507502\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.65685 | 1.25722 | 0.628608 | − | 0.777723i | \(-0.283625\pi\) | ||||
0.628608 | + | 0.777723i | \(0.283625\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3137 | 1.70465 | 0.852323 | − | 0.523016i | \(-0.175193\pi\) | ||||
0.852323 | + | 0.523016i | \(0.175193\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.0000 | −1.25988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.48528 | −0.547964 | −0.273982 | − | 0.961735i | \(-0.588341\pi\) | ||||
−0.273982 | + | 0.961735i | \(0.588341\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3137 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.82843 | 0.799207 | 0.399603 | − | 0.916688i | \(-0.369148\pi\) | ||||
0.399603 | + | 0.916688i | \(0.369148\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.6569 | 2.32186 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.31371 | 0.987251 | 0.493626 | − | 0.869675i | \(-0.335671\pi\) | ||||
0.493626 | + | 0.869675i | \(0.335671\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.6569 | −1.43163 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.65685 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.3137 | −1.32476 | −0.662382 | − | 0.749166i | \(-0.730454\pi\) | ||||
−0.662382 | + | 0.749166i | \(0.730454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.17157 | 0.115439 | 0.0577193 | − | 0.998333i | \(-0.481617\pi\) | ||||
0.0577193 | + | 0.998333i | \(0.481617\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.65685 | −0.353521 | −0.176761 | − | 0.984254i | \(-0.556562\pi\) | ||||
−0.176761 | + | 0.984254i | \(0.556562\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.65685 | 0.350263 | 0.175132 | − | 0.984545i | \(-0.443965\pi\) | ||||
0.175132 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.3431 | −0.981728 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.34315 | −0.784857 | −0.392429 | − | 0.919782i | \(-0.628365\pi\) | ||||
−0.392429 | + | 0.919782i | \(0.628365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 34.1421 | 3.15644 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.34315 | 0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.9706 | 1.53018 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.6569 | 1.38932 | 0.694661 | − | 0.719338i | \(-0.255555\pi\) | ||||
0.694661 | + | 0.719338i | \(0.255555\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.9706 | −1.49417 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.3137 | −0.988483 | −0.494242 | − | 0.869325i | \(-0.664554\pi\) | ||||
−0.494242 | + | 0.869325i | \(0.664554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.9706 | −1.96251 | −0.981254 | − | 0.192720i | \(-0.938269\pi\) | ||||
−0.981254 | + | 0.192720i | \(0.938269\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.82843 | −0.571022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.48528 | −0.699854 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6569 | 0.954967 | 0.477483 | − | 0.878641i | \(-0.341549\pi\) | ||||
0.477483 | + | 0.878641i | \(0.341549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.85786 | −0.473580 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.970563 | −0.0769706 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.65685 | −0.445823 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.485281 | −0.0380102 | −0.0190051 | − | 0.999819i | \(-0.506050\pi\) | ||||
−0.0190051 | + | 0.999819i | \(0.506050\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.9706 | 0.848928 | 0.424464 | − | 0.905445i | \(-0.360463\pi\) | ||||
0.424464 | + | 0.905445i | \(0.360463\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.6274 | 2.58672 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.14214 | −0.466978 | −0.233489 | − | 0.972359i | \(-0.575014\pi\) | ||||
−0.233489 | + | 0.972359i | \(0.575014\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.3137 | 2.05302 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.65685 | 0.123839 | 0.0619196 | − | 0.998081i | \(-0.480278\pi\) | ||||
0.0619196 | + | 0.998081i | \(0.480278\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.31371 | −0.0976472 | −0.0488236 | − | 0.998807i | \(-0.515547\pi\) | ||||
−0.0488236 | + | 0.998807i | \(0.515547\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 37.6569 | 2.78367 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.17157 | 0.0856739 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.3137 | −0.822951 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3137 | 1.39749 | 0.698745 | − | 0.715370i | \(-0.253742\pi\) | ||||
0.698745 | + | 0.715370i | \(0.253742\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.82843 | 0.491521 | 0.245760 | − | 0.969331i | \(-0.420962\pi\) | ||||
0.245760 | + | 0.969331i | \(0.420962\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.17157 | 0.368459 | 0.184230 | − | 0.982883i | \(-0.441021\pi\) | ||||
0.184230 | + | 0.982883i | \(0.441021\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.6569 | −1.53521 | −0.767607 | − | 0.640921i | \(-0.778553\pi\) | ||||
−0.767607 | + | 0.640921i | \(0.778553\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.6863 | −0.894822 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.3137 | −1.07481 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.1421 | 0.982946 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 32.0000 | 2.19260 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.3137 | 1.30510 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.17157 | −0.346314 | −0.173157 | − | 0.984894i | \(-0.555397\pi\) | ||||
−0.173157 | + | 0.984894i | \(0.555397\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.68629 | 0.178295 | 0.0891477 | − | 0.996018i | \(-0.471586\pi\) | ||||
0.0891477 | + | 0.996018i | \(0.471586\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.3137 | −1.40845 | −0.704225 | − | 0.709977i | \(-0.748705\pi\) | ||||
−0.704225 | + | 0.709977i | \(0.748705\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.65685 | 0.372194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.1421 | −1.45058 | −0.725290 | − | 0.688444i | \(-0.758294\pi\) | ||||
−0.725290 | + | 0.688444i | \(0.758294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.3137 | −0.734904 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.686292 | 0.0443925 | 0.0221963 | − | 0.999754i | \(-0.492934\pi\) | ||||
0.0221963 | + | 0.999754i | \(0.492934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1421 | −0.907218 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.9706 | −1.07547 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.82843 | −0.177822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.3137 | −0.830486 | −0.415243 | − | 0.909710i | \(-0.636304\pi\) | ||||
−0.415243 | + | 0.909710i | \(0.636304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.31371 | 0.454452 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 38.2843 | 2.36974 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.9706 | 1.41643 | 0.708213 | − | 0.705999i | \(-0.249502\pi\) | ||||
0.708213 | + | 0.705999i | \(0.249502\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.3431 | 1.61217 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.31371 | −0.323983 | −0.161991 | − | 0.986792i | \(-0.551792\pi\) | ||||
−0.161991 | + | 0.986792i | \(0.551792\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3137 | 0.930242 | 0.465121 | − | 0.885247i | \(-0.346011\pi\) | ||||
0.465121 | + | 0.885247i | \(0.346011\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −38.6274 | −2.33784 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.17157 | −0.0703930 | −0.0351965 | − | 0.999380i | \(-0.511206\pi\) | ||||
−0.0351965 | + | 0.999380i | \(0.511206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.31371 | −0.316989 | −0.158495 | − | 0.987360i | \(-0.550664\pi\) | ||||
−0.158495 | + | 0.987360i | \(0.550664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.6274 | −0.750622 | −0.375311 | − | 0.926899i | \(-0.622464\pi\) | ||||
−0.375311 | + | 0.926899i | \(0.622464\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.6274 | −0.919260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.6569 | 1.26955 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.8284 | 0.866286 | 0.433143 | − | 0.901325i | \(-0.357405\pi\) | ||||
0.433143 | + | 0.901325i | \(0.357405\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.65685 | −0.328244 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.3137 | 1.11694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | 0.691669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −37.6569 | −2.16333 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.6569 | −1.57846 | −0.789230 | − | 0.614098i | \(-0.789520\pi\) | ||||
−0.789230 | + | 0.614098i | \(0.789520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.31371 | 0.188510 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.3137 | −1.54882 | −0.774409 | − | 0.632685i | \(-0.781953\pi\) | ||||
−0.774409 | + | 0.632685i | \(0.781953\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.3137 | −1.20472 | −0.602361 | − | 0.798224i | \(-0.705773\pi\) | ||||
−0.602361 | + | 0.798224i | \(0.705773\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.3137 | −1.19710 | −0.598549 | − | 0.801087i | \(-0.704256\pi\) | ||||
−0.598549 | + | 0.801087i | \(0.704256\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.65685 | −0.428702 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3431 | −0.577298 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.3431 | 0.571977 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.65685 | 0.311872 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.3137 | −0.841718 | −0.420859 | − | 0.907126i | \(-0.638271\pi\) | ||||
−0.420859 | + | 0.907126i | \(0.638271\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −18.2843 | −1.00197 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.51472 | 0.191459 | 0.0957295 | − | 0.995407i | \(-0.469482\pi\) | ||||
0.0957295 | + | 0.995407i | \(0.469482\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.5980 | −1.28167 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.9706 | −1.23312 | −0.616562 | − | 0.787306i | \(-0.711475\pi\) | ||||
−0.616562 | + | 0.787306i | \(0.711475\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.97056 | −0.373126 | −0.186563 | − | 0.982443i | \(-0.559735\pi\) | ||||
−0.186563 | + | 0.982443i | \(0.559735\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 38.6274 | 2.06178 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.31371 | 0.0699216 | 0.0349608 | − | 0.999389i | \(-0.488869\pi\) | ||||
0.0349608 | + | 0.999389i | \(0.488869\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.62742 | 0.350760 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.3137 | −1.23045 | −0.615225 | − | 0.788351i | \(-0.710935\pi\) | ||||
−0.615225 | + | 0.788351i | \(0.710935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.82843 | 0.148454 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.48528 | 0.442928 | 0.221464 | − | 0.975169i | \(-0.428916\pi\) | ||||
0.221464 | + | 0.975169i | \(0.428916\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30.0000 | 1.56174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.686292 | 0.0356305 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.79899 | 0.196704 | 0.0983521 | − | 0.995152i | \(-0.468643\pi\) | ||||
0.0983521 | + | 0.995152i | \(0.468643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 52.2843 | 2.69278 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3431 | −1.14769 | −0.573845 | − | 0.818964i | \(-0.694549\pi\) | ||||
−0.573845 | + | 0.818964i | \(0.694549\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 44.2843 | 2.26875 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.1421 | −1.74458 | −0.872291 | − | 0.488987i | \(-0.837366\pi\) | ||||
−0.872291 | + | 0.488987i | \(0.837366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.0000 | −1.52499 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.6274 | −1.24866 | −0.624330 | − | 0.781161i | \(-0.714628\pi\) | ||||
−0.624330 | + | 0.781161i | \(0.714628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.31371 | −0.167581 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −32.0000 | −1.61419 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3137 | −0.668196 | −0.334098 | − | 0.942538i | \(-0.608432\pi\) | ||||
−0.334098 | + | 0.942538i | \(0.608432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3137 | 0.864605 | 0.432303 | − | 0.901729i | \(-0.357701\pi\) | ||||
0.432303 | + | 0.901729i | \(0.357701\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.65685 | 0.181264 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.9706 | 1.72918 | 0.864592 | − | 0.502475i | \(-0.167577\pi\) | ||||
0.864592 | + | 0.502475i | \(0.167577\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −64.9706 | −3.20476 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.3137 | −0.950365 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.3137 | 0.554035 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.3431 | 0.700709 | 0.350354 | − | 0.936617i | \(-0.386061\pi\) | ||||
0.350354 | + | 0.936617i | \(0.386061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.1421 | −0.687614 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.6274 | −1.28859 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.3137 | −0.932475 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.3137 | −0.544962 | −0.272481 | − | 0.962161i | \(-0.587844\pi\) | ||||
−0.272481 | + | 0.962161i | \(0.587844\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.65685 | −0.175737 | −0.0878686 | − | 0.996132i | \(-0.528006\pi\) | ||||
−0.0878686 | + | 0.996132i | \(0.528006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | −0.714286 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.1716 | −1.00589 | −0.502946 | − | 0.864318i | \(-0.667751\pi\) | ||||
−0.502946 | + | 0.864318i | \(0.667751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 32.9706 | 1.55945 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.6274 | −0.784696 | −0.392348 | − | 0.919817i | \(-0.628337\pi\) | ||||
−0.392348 | + | 0.919817i | \(0.628337\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 33.9411 | 1.59469 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.4853 | 0.771149 | 0.385574 | − | 0.922677i | \(-0.374003\pi\) | ||||
0.385574 | + | 0.922677i | \(0.374003\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.62742 | −0.309341 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.6274 | −1.51961 | −0.759805 | − | 0.650151i | \(-0.774706\pi\) | ||||
−0.759805 | + | 0.650151i | \(0.774706\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.1421 | 1.02903 | 0.514516 | − | 0.857481i | \(-0.327972\pi\) | ||||
0.514516 | + | 0.857481i | \(0.327972\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.17157 | −0.424410 | −0.212205 | − | 0.977225i | \(-0.568064\pi\) | ||||
−0.212205 | + | 0.977225i | \(0.568064\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.97056 | 0.414222 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39.5980 | 1.82458 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.71573 | −0.0785578 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.0000 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.9706 | −1.13856 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.0000 | −0.728025 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.51472 | −0.340524 | −0.170262 | − | 0.985399i | \(-0.554461\pi\) | ||||
−0.170262 | + | 0.985399i | \(0.554461\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.37258 | −0.0620703 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.3137 | 1.05213 | 0.526066 | − | 0.850443i | \(-0.323666\pi\) | ||||
0.526066 | + | 0.850443i | \(0.323666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.97056 | −0.404014 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.6274 | −1.01498 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.65685 | 0.0741710 | 0.0370855 | − | 0.999312i | \(-0.488193\pi\) | ||||
0.0370855 | + | 0.999312i | \(0.488193\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.0294 | 1.38629 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.6274 | −1.27643 | −0.638217 | − | 0.769857i | \(-0.720328\pi\) | ||||
−0.638217 | + | 0.769857i | \(0.720328\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 95.1127 | 4.22410 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.31371 | 0.412823 | 0.206411 | − | 0.978465i | \(-0.433821\pi\) | ||||
0.206411 | + | 0.978465i | \(0.433821\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.6569 | −0.604144 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.82843 | 0.124394 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.3726 | −0.762572 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.68629 | 0.117689 | 0.0588443 | − | 0.998267i | \(-0.481258\pi\) | ||||
0.0588443 | + | 0.998267i | \(0.481258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.5980 | 1.64404 | 0.822022 | − | 0.569455i | \(-0.192846\pi\) | ||||
0.822022 | + | 0.569455i | \(0.192846\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 48.2843 | 2.09536 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 40.9706 | 1.77463 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.68629 | 0.202228 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.71573 | −0.159457 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 66.5685 | 2.84108 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.1421 | −1.61613 | −0.808067 | − | 0.589090i | \(-0.799486\pi\) | ||||
−0.808067 | + | 0.589090i | \(0.799486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −40.9706 | −1.73287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.31371 | 0.139905 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.6569 | 0.491278 | 0.245639 | − | 0.969361i | \(-0.421002\pi\) | ||||
0.245639 | + | 0.969361i | \(0.421002\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.3431 | 0.852829 | 0.426415 | − | 0.904528i | \(-0.359776\pi\) | ||||
0.426415 | + | 0.904528i | \(0.359776\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.9411 | −1.92258 | −0.961288 | − | 0.275545i | \(-0.911142\pi\) | ||||
−0.961288 | + | 0.275545i | \(0.911142\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 54.6274 | 2.28209 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.97056 | −0.290188 | −0.145094 | − | 0.989418i | \(-0.546349\pi\) | ||||
−0.145094 | + | 0.989418i | \(0.546349\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.3137 | 0.802650 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.343146 | 0.0142116 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.1421 | 1.07900 | 0.539501 | − | 0.841985i | \(-0.318613\pi\) | ||||
0.539501 | + | 0.841985i | \(0.318613\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.6274 | 0.601692 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.4853 | −0.841230 | −0.420615 | − | 0.907239i | \(-0.638186\pi\) | ||||
−0.420615 | + | 0.907239i | \(0.638186\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −61.2548 | −2.50699 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.65685 | −0.231133 | −0.115566 | − | 0.993300i | \(-0.536868\pi\) | ||||
−0.115566 | + | 0.993300i | \(0.536868\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.9411 | −1.79240 | −0.896198 | − | 0.443654i | \(-0.853682\pi\) | ||||
−0.896198 | + | 0.443654i | \(0.853682\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.4264 | −0.913274 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.2843 | −0.742136 | −0.371068 | − | 0.928606i | \(-0.621008\pi\) | ||||
−0.371068 | + | 0.928606i | \(0.621008\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −43.3137 | −1.75516 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −19.3137 | −0.781349 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.4558 | −1.02815 | −0.514076 | − | 0.857745i | \(-0.671865\pi\) | ||||
−0.514076 | + | 0.857745i | \(0.671865\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.6569 | −0.469287 | −0.234644 | − | 0.972081i | \(-0.575392\pi\) | ||||
−0.234644 | + | 0.972081i | \(0.575392\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.6569 | 1.03124 | 0.515618 | − | 0.856819i | \(-0.327562\pi\) | ||||
0.515618 | + | 0.856819i | \(0.327562\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.0000 | 0.642058 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.6274 | −0.746292 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.28427 | 0.170825 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 45.2548 | 1.79872 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.4853 | −0.811656 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 56.5685 | 2.23782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 49.4558 | 1.95035 | 0.975174 | − | 0.221440i | \(-0.0710756\pi\) | ||||
0.975174 | + | 0.221440i | \(0.0710756\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.1127 | −1.38042 | −0.690211 | − | 0.723608i | \(-0.742482\pi\) | ||||
−0.690211 | + | 0.723608i | \(0.742482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.65685 | −0.379065 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.343146 | −0.0134283 | −0.00671417 | − | 0.999977i | \(-0.502137\pi\) | ||||
−0.00671417 | + | 0.999977i | \(0.502137\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 34.1421 | 1.33201 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9411 | 0.854705 | 0.427352 | − | 0.904085i | \(-0.359446\pi\) | ||||
0.427352 | + | 0.904085i | \(0.359446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.627417 | −0.0244037 | −0.0122018 | − | 0.999926i | \(-0.503884\pi\) | ||||
−0.0122018 | + | 0.999926i | \(0.503884\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −22.6274 | −0.878776 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.6569 | 0.838557 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.6274 | −0.565529 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.3137 | −0.513970 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.48528 | −0.172895 | −0.0864474 | − | 0.996256i | \(-0.527551\pi\) | ||||
−0.0864474 | + | 0.996256i | \(0.527551\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.1716 | −0.659957 | −0.329979 | − | 0.943988i | \(-0.607042\pi\) | ||||
−0.329979 | + | 0.943988i | \(0.607042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.3137 | −0.587686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.59798 | 0.291155 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.7990 | 1.21675 | 0.608377 | − | 0.793648i | \(-0.291821\pi\) | ||||
0.608377 | + | 0.793648i | \(0.291821\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −60.2843 | −2.29999 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.34315 | −0.0892667 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6863 | 0.634776 | 0.317388 | − | 0.948296i | \(-0.397194\pi\) | ||||
0.317388 | + | 0.948296i | \(0.397194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.0000 | 0.379869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.02944 | −0.266259 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −62.6274 | −2.36879 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.6274 | 1.23232 | 0.616160 | − | 0.787621i | \(-0.288687\pi\) | ||||
0.616160 | + | 0.787621i | \(0.288687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.6274 | 1.00143 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.6274 | −0.774679 | −0.387339 | − | 0.921937i | \(-0.626606\pi\) | ||||
−0.387339 | + | 0.921937i | \(0.626606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.0000 | −0.750059 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.94113 | 0.0724927 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.6569 | −1.10601 | −0.553007 | − | 0.833177i | \(-0.686520\pi\) | ||||
−0.553007 | + | 0.833177i | \(0.686520\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.34315 | −0.0872633 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.9706 | 0.631142 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.4853 | −1.35316 | −0.676582 | − | 0.736367i | \(-0.736540\pi\) | ||||
−0.676582 | + | 0.736367i | \(0.736540\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.0000 | −1.59259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.02944 | 0.259993 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.4558 | −1.23572 | −0.617860 | − | 0.786288i | \(-0.712000\pi\) | ||||
−0.617860 | + | 0.786288i | \(0.712000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.48528 | 0.165217 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.9411 | 1.39569 | 0.697843 | − | 0.716250i | \(-0.254143\pi\) | ||||
0.697843 | + | 0.716250i | \(0.254143\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.5980 | 1.08584 | 0.542922 | − | 0.839783i | \(-0.317318\pi\) | ||||
0.542922 | + | 0.839783i | \(0.317318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.0000 | −1.09764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.31371 | 0.267237 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | 0.583848 | 0.291924 | − | 0.956441i | \(-0.405705\pi\) | ||||
0.291924 | + | 0.956441i | \(0.405705\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −33.9411 | −1.23688 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.31371 | 0.338512 | 0.169256 | − | 0.985572i | \(-0.445863\pi\) | ||||
0.169256 | + | 0.985572i | \(0.445863\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.31371 | −0.264774 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 65.9411 | 2.38100 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.9706 | 0.539852 | 0.269926 | − | 0.962881i | \(-0.413001\pi\) | ||||
0.269926 | + | 0.962881i | \(0.413001\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.6569 | −1.35618 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.2843 | 1.08925 | 0.544625 | − | 0.838680i | \(-0.316672\pi\) | ||||
0.544625 | + | 0.838680i | \(0.316672\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.6863 | 0.742117 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.3137 | −0.404836 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43.3137 | 1.54791 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.9706 | 0.676228 | 0.338114 | − | 0.941105i | \(-0.390211\pi\) | ||||
0.338114 | + | 0.941105i | \(0.390211\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 64.9706 | 2.31301 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.6863 | 0.593296 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 90.9117 | 3.22837 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.6274 | 0.447286 | 0.223643 | − | 0.974671i | \(-0.428205\pi\) | ||||
0.223643 | + | 0.974671i | \(0.428205\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.31371 | 0.117231 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 46.5685 | 1.64542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.82843 | −0.240970 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.0294 | −0.529061 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.9706 | 0.807602 | 0.403801 | − | 0.914847i | \(-0.367689\pi\) | ||||
0.403801 | + | 0.914847i | \(0.367689\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9411 | 0.489539 | 0.244770 | − | 0.969581i | \(-0.421288\pi\) | ||||
0.244770 | + | 0.969581i | \(0.421288\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 43.3137 | 1.51908 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −68.2843 | −2.38605 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.6863 | −0.652156 | −0.326078 | − | 0.945343i | \(-0.605727\pi\) | ||||
−0.326078 | + | 0.945343i | \(0.605727\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.4853 | 1.27180 | 0.635898 | − | 0.771773i | \(-0.280630\pi\) | ||||
0.635898 | + | 0.771773i | \(0.280630\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.2843 | −1.19218 | −0.596090 | − | 0.802917i | \(-0.703280\pi\) | ||||
−0.596090 | + | 0.802917i | \(0.703280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.31371 | −0.114951 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.51472 | 0.121778 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −37.6569 | −1.30006 | −0.650029 | − | 0.759909i | \(-0.725243\pi\) | ||||
−0.650029 | + | 0.759909i | \(0.725243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.0294 | −0.517641 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −35.7157 | −1.22576 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.3431 | −0.354558 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.4853 | 1.11227 | 0.556137 | − | 0.831090i | \(-0.312283\pi\) | ||||
0.556137 | + | 0.831090i | \(0.312283\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 48.7696 | 1.66594 | 0.832968 | − | 0.553321i | \(-0.186640\pi\) | ||||
0.832968 | + | 0.553321i | \(0.186640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.2843 | 1.10153 | 0.550763 | − | 0.834662i | \(-0.314337\pi\) | ||||
0.550763 | + | 0.834662i | \(0.314337\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −33.9411 | −1.15671 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.8284 | −0.504766 | −0.252383 | − | 0.967627i | \(-0.581214\pi\) | ||||
−0.252383 | + | 0.967627i | \(0.581214\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.2010 | −1.50115 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.00000 | 0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.6274 | −1.03777 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 38.2843 | 1.29573 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.45584 | −0.0491604 | −0.0245802 | − | 0.999698i | \(-0.507825\pi\) | ||||
−0.0245802 | + | 0.999698i | \(0.507825\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 41.9411 | 1.41464 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.6274 | −1.77306 | −0.886531 | − | 0.462668i | \(-0.846892\pi\) | ||||
−0.886531 | + | 0.462668i | \(0.846892\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.8284 | 1.44129 | 0.720646 | − | 0.693304i | \(-0.243845\pi\) | ||||
0.720646 | + | 0.693304i | \(0.243845\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.2843 | −0.613926 | −0.306963 | − | 0.951721i | \(-0.599313\pi\) | ||||
−0.306963 | + | 0.951721i | \(0.599313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −31.3137 | −1.05023 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 54.6274 | 1.82396 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.402020 | 0.0133932 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.9411 | 1.12949 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.4853 | −1.47711 | −0.738555 | − | 0.674193i | \(-0.764491\pi\) | ||||
−0.738555 | + | 0.674193i | \(0.764491\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −66.5685 | −2.20794 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.9411 | −1.91968 | −0.959838 | − | 0.280556i | \(-0.909481\pi\) | ||||
−0.959838 | + | 0.280556i | \(0.909481\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.6274 | 0.747223 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000 | 1.05558 | 0.527791 | − | 0.849374i | \(-0.323020\pi\) | ||||
0.527791 | + | 0.849374i | \(0.323020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −78.2254 | −2.57761 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 77.2548 | 2.54287 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.85786 | 0.192398 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.3137 | −0.568044 | −0.284022 | − | 0.958818i | \(-0.591669\pi\) | ||||
−0.284022 | + | 0.958818i | \(0.591669\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −77.2548 | −2.52921 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.4558 | −1.61565 | −0.807826 | − | 0.589421i | \(-0.799356\pi\) | ||||
−0.807826 | + | 0.589421i | \(0.799356\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −60.2843 | −1.96730 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.3137 | −0.955600 | −0.477800 | − | 0.878469i | \(-0.658566\pi\) | ||||
−0.477800 | + | 0.878469i | \(0.658566\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9706 | 0.552638 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.8284 | 1.52172 | 0.760860 | − | 0.648916i | \(-0.224778\pi\) | ||||
0.760860 | + | 0.648916i | \(0.224778\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46.6274 | 1.51359 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −60.2843 | −1.95485 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.8284 | −1.90564 | −0.952820 | − | 0.303536i | \(-0.901833\pi\) | ||||
−0.952820 | + | 0.303536i | \(0.901833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.6569 | −0.700067 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.9411 | 1.48352 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18.2843 | −0.589202 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.9706 | 0.610052 | 0.305026 | − | 0.952344i | \(-0.401335\pi\) | ||||
0.305026 | + | 0.952344i | \(0.401335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.3137 | 1.00490 | 0.502452 | − | 0.864605i | \(-0.332431\pi\) | ||||
0.502452 | + | 0.864605i | \(0.332431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.6569 | −1.39671 | −0.698353 | − | 0.715753i | \(-0.746084\pi\) | ||||
−0.698353 | + | 0.715753i | \(0.746084\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.31371 | −0.297667 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.2843 | 0.583772 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.1421 | −1.59929 | −0.799643 | − | 0.600476i | \(-0.794978\pi\) | ||||
−0.799643 | + | 0.600476i | \(0.794978\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.0000 | 0.509286 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16.9706 | −0.539633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.94113 | −0.315790 | −0.157895 | − | 0.987456i | \(-0.550471\pi\) | ||||
−0.157895 | + | 0.987456i | \(0.550471\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −43.3137 | −1.37452 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.45584 | −0.299470 | −0.149735 | − | 0.988726i | \(-0.547842\pi\) | ||||
−0.149735 | + | 0.988726i | \(0.547842\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −20.6863 | −0.654485 |
(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 | 4400.2.a.bn.1.2 | 2 | ||
4.3 | odd | 2 | 275.2.a.c.1.2 | 2 | |||
5.2 | odd | 4 | 4400.2.b.q.4049.1 | 4 | |||
5.3 | odd | 4 | 4400.2.b.q.4049.4 | 4 | |||
5.4 | even | 2 | 880.2.a.m.1.1 | 2 | |||
12.11 | even | 2 | 2475.2.a.x.1.1 | 2 | |||
15.14 | odd | 2 | 7920.2.a.ch.1.1 | 2 | |||
20.3 | even | 4 | 275.2.b.d.199.2 | 4 | |||
20.7 | even | 4 | 275.2.b.d.199.3 | 4 | |||
20.19 | odd | 2 | 55.2.a.b.1.1 | ✓ | 2 | ||
40.19 | odd | 2 | 3520.2.a.bn.1.1 | 2 | |||
40.29 | even | 2 | 3520.2.a.bo.1.2 | 2 | |||
44.43 | even | 2 | 3025.2.a.o.1.1 | 2 | |||
55.54 | odd | 2 | 9680.2.a.bn.1.1 | 2 | |||
60.23 | odd | 4 | 2475.2.c.l.199.3 | 4 | |||
60.47 | odd | 4 | 2475.2.c.l.199.2 | 4 | |||
60.59 | even | 2 | 495.2.a.b.1.2 | 2 | |||
140.139 | even | 2 | 2695.2.a.f.1.1 | 2 | |||
220.19 | even | 10 | 605.2.g.l.251.2 | 8 | |||
220.39 | even | 10 | 605.2.g.l.366.1 | 8 | |||
220.59 | odd | 10 | 605.2.g.f.511.1 | 8 | |||
220.79 | even | 10 | 605.2.g.l.81.1 | 8 | |||
220.119 | odd | 10 | 605.2.g.f.81.2 | 8 | |||
220.139 | even | 10 | 605.2.g.l.511.2 | 8 | |||
220.159 | odd | 10 | 605.2.g.f.366.2 | 8 | |||
220.179 | odd | 10 | 605.2.g.f.251.1 | 8 | |||
220.219 | even | 2 | 605.2.a.d.1.2 | 2 | |||
260.259 | odd | 2 | 9295.2.a.g.1.2 | 2 | |||
660.659 | odd | 2 | 5445.2.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.a.b.1.1 | ✓ | 2 | 20.19 | odd | 2 | ||
275.2.a.c.1.2 | 2 | 4.3 | odd | 2 | |||
275.2.b.d.199.2 | 4 | 20.3 | even | 4 | |||
275.2.b.d.199.3 | 4 | 20.7 | even | 4 | |||
495.2.a.b.1.2 | 2 | 60.59 | even | 2 | |||
605.2.a.d.1.2 | 2 | 220.219 | even | 2 | |||
605.2.g.f.81.2 | 8 | 220.119 | odd | 10 | |||
605.2.g.f.251.1 | 8 | 220.179 | odd | 10 | |||
605.2.g.f.366.2 | 8 | 220.159 | odd | 10 | |||
605.2.g.f.511.1 | 8 | 220.59 | odd | 10 | |||
605.2.g.l.81.1 | 8 | 220.79 | even | 10 | |||
605.2.g.l.251.2 | 8 | 220.19 | even | 10 | |||
605.2.g.l.366.1 | 8 | 220.39 | even | 10 | |||
605.2.g.l.511.2 | 8 | 220.139 | even | 10 | |||
880.2.a.m.1.1 | 2 | 5.4 | even | 2 | |||
2475.2.a.x.1.1 | 2 | 12.11 | even | 2 | |||
2475.2.c.l.199.2 | 4 | 60.47 | odd | 4 | |||
2475.2.c.l.199.3 | 4 | 60.23 | odd | 4 | |||
2695.2.a.f.1.1 | 2 | 140.139 | even | 2 | |||
3025.2.a.o.1.1 | 2 | 44.43 | even | 2 | |||
3520.2.a.bn.1.1 | 2 | 40.19 | odd | 2 | |||
3520.2.a.bo.1.2 | 2 | 40.29 | even | 2 | |||
4400.2.a.bn.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4400.2.b.q.4049.1 | 4 | 5.2 | odd | 4 | |||
4400.2.b.q.4049.4 | 4 | 5.3 | odd | 4 | |||
5445.2.a.y.1.1 | 2 | 660.659 | odd | 2 | |||
7920.2.a.ch.1.1 | 2 | 15.14 | odd | 2 | |||
9295.2.a.g.1.2 | 2 | 260.259 | odd | 2 | |||
9680.2.a.bn.1.1 | 2 | 55.54 | odd | 2 |