Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 30 x^{17} + 132 x^{16} + 332 x^{15} - 1714 x^{14} - 1598 x^{13} + 11179 x^{12} + 2544 x^{11} - 38897 x^{10} + 3416 x^{9} + 71354 x^{8} - 10941 x^{7} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Root | \(-2.85652\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 | ||||||||
\(3\) | 2.85652 | 1.64921 | 0.824606 | − | 0.565708i | \(-0.191397\pi\) | ||||
0.824606 | + | 0.565708i | \(0.191397\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0885731 | −0.0396111 | −0.0198055 | − | 0.999804i | \(-0.506305\pi\) | ||||
−0.0198055 | + | 0.999804i | \(0.506305\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.03776 | −0.392238 | −0.196119 | − | 0.980580i | \(-0.562834\pi\) | ||||
−0.196119 | + | 0.980580i | \(0.562834\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.15970 | 1.71990 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.21731 | −0.970057 | −0.485028 | − | 0.874498i | \(-0.661191\pi\) | ||||
−0.485028 | + | 0.874498i | \(0.661191\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.70422 | −0.472665 | −0.236333 | − | 0.971672i | \(-0.575945\pi\) | ||||
−0.236333 | + | 0.971672i | \(0.575945\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.253011 | −0.0653270 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.37063 | −1.78764 | −0.893820 | − | 0.448427i | \(-0.851985\pi\) | ||||
−0.893820 | + | 0.448427i | \(0.851985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.96439 | −0.646883 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.03892 | −1.67623 | −0.838115 | − | 0.545493i | \(-0.816342\pi\) | ||||
−0.838115 | + | 0.545493i | \(0.816342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99215 | −0.998431 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.16921 | 1.18726 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.83179 | 1.08294 | 0.541468 | − | 0.840721i | \(-0.317869\pi\) | ||||
0.541468 | + | 0.840721i | \(0.317869\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.90929 | 0.881734 | 0.440867 | − | 0.897573i | \(-0.354671\pi\) | ||||
0.440867 | + | 0.897573i | \(0.354671\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.19032 | −1.59983 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0919179 | 0.0155370 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.56946 | −0.751214 | −0.375607 | − | 0.926779i | \(-0.622566\pi\) | ||||
−0.375607 | + | 0.926779i | \(0.622566\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.86813 | −0.779525 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.12531 | 0.644265 | 0.322132 | − | 0.946695i | \(-0.395600\pi\) | ||||
0.322132 | + | 0.946695i | \(0.395600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.33634 | −0.813784 | −0.406892 | − | 0.913476i | \(-0.633387\pi\) | ||||
−0.406892 | + | 0.913476i | \(0.633387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.457010 | −0.0681270 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.46858 | −0.214215 | −0.107107 | − | 0.994247i | \(-0.534159\pi\) | ||||
−0.107107 | + | 0.994247i | \(0.534159\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.92305 | −0.846149 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −21.0543 | −2.94820 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.284967 | 0.0384250 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.85652 | −0.378355 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3962 | 1.35347 | 0.676733 | − | 0.736228i | \(-0.263395\pi\) | ||||
0.676733 | + | 0.736228i | \(0.263395\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.61138 | −1.23061 | −0.615306 | − | 0.788289i | \(-0.710967\pi\) | ||||
−0.615306 | + | 0.788289i | \(0.710967\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.35455 | −0.674609 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.150948 | 0.0187228 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.16429 | 0.508749 | 0.254374 | − | 0.967106i | \(-0.418130\pi\) | ||||
0.254374 | + | 0.967106i | \(0.418130\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −22.9633 | −2.76446 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.1829 | −1.92056 | −0.960278 | − | 0.279044i | \(-0.909982\pi\) | ||||
−0.960278 | + | 0.279044i | \(0.909982\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.73490 | 0.905301 | 0.452651 | − | 0.891688i | \(-0.350478\pi\) | ||||
0.452651 | + | 0.891688i | \(0.350478\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.2602 | −1.64662 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.33881 | 0.380493 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.03842 | 0.116832 | 0.0584159 | − | 0.998292i | \(-0.481395\pi\) | ||||
0.0584159 | + | 0.998292i | \(0.481395\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.14337 | 0.238152 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.95170 | 0.323991 | 0.161996 | − | 0.986791i | \(-0.448207\pi\) | ||||
0.161996 | + | 0.986791i | \(0.448207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.652839 | 0.0708103 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.6586 | 1.78599 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.28961 | −0.348698 | −0.174349 | − | 0.984684i | \(-0.555782\pi\) | ||||
−0.174349 | + | 0.984684i | \(0.555782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.76858 | 0.185397 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.0235 | 1.45417 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0885731 | 0.00908741 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.36984 | −0.443690 | −0.221845 | − | 0.975082i | \(-0.571208\pi\) | ||||
−0.221845 | + | 0.975082i | \(0.571208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.6004 | −1.66840 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0603 | 1.20004 | 0.600022 | − | 0.799984i | \(-0.295159\pi\) | ||||
0.600022 | + | 0.799984i | \(0.295159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.36874 | −0.331932 | −0.165966 | − | 0.986132i | \(-0.553074\pi\) | ||||
−0.165966 | + | 0.986132i | \(0.553074\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.262565 | 0.0256237 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.33757 | −0.612676 | −0.306338 | − | 0.951923i | \(-0.599104\pi\) | ||||
−0.306338 | + | 0.951923i | \(0.599104\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.26610 | 0.887531 | 0.443766 | − | 0.896143i | \(-0.353642\pi\) | ||||
0.443766 | + | 0.896143i | \(0.353642\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.0527 | −1.23891 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.2220 | 1.33790 | 0.668948 | − | 0.743309i | \(-0.266745\pi\) | ||||
0.668948 | + | 0.743309i | \(0.266745\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.712032 | 0.0663973 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.79325 | −0.812936 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.64897 | 0.701180 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.648889 | −0.0589899 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.7840 | 1.06253 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.885036 | 0.0791600 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.75517 | −0.688160 | −0.344080 | − | 0.938940i | \(-0.611809\pi\) | ||||
−0.344080 | + | 0.938940i | \(0.611809\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.2433 | −1.34210 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.27890 | 0.810701 | 0.405351 | − | 0.914161i | \(-0.367149\pi\) | ||||
0.405351 | + | 0.914161i | \(0.367149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.03776 | 0.0899855 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.546426 | −0.0470288 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.4985 | 1.06782 | 0.533909 | − | 0.845542i | \(-0.320722\pi\) | ||||
0.533909 | + | 0.845542i | \(0.320722\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.7974 | 1.42474 | 0.712370 | − | 0.701804i | \(-0.247622\pi\) | ||||
0.712370 | + | 0.701804i | \(0.247622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.19503 | −0.353286 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.48301 | 0.458512 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.516539 | −0.0428962 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.9193 | −1.39548 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.2187 | 1.49253 | 0.746265 | − | 0.665648i | \(-0.231845\pi\) | ||||
0.746265 | + | 0.665648i | \(0.231845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.79632 | −0.553076 | −0.276538 | − | 0.961003i | \(-0.589187\pi\) | ||||
−0.276538 | + | 0.961003i | \(0.589187\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −38.0302 | −3.07456 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.434831 | −0.0349264 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.24443 | −0.657977 | −0.328989 | − | 0.944334i | \(-0.606708\pi\) | ||||
−0.328989 | + | 0.944334i | \(0.606708\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.85652 | 0.226537 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.34250 | 0.657481 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.07188 | −0.0839565 | −0.0419782 | − | 0.999119i | \(-0.513366\pi\) | ||||
−0.0419782 | + | 0.999119i | \(0.513366\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.814015 | 0.0633709 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.2284 | −1.79747 | −0.898735 | − | 0.438492i | \(-0.855513\pi\) | ||||
−0.898735 | + | 0.438492i | \(0.855513\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0956 | −0.776588 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.15970 | −0.394572 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.29216 | −0.478384 | −0.239192 | − | 0.970972i | \(-0.576882\pi\) | ||||
−0.239192 | + | 0.970972i | \(0.576882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.18068 | 0.391622 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.6969 | 2.23215 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.2652 | 1.51469 | 0.757347 | − | 0.653012i | \(-0.226495\pi\) | ||||
0.757347 | + | 0.653012i | \(0.226495\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.39564 | −0.624043 | −0.312022 | − | 0.950075i | \(-0.601006\pi\) | ||||
−0.312022 | + | 0.950075i | \(0.601006\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27.4551 | −2.02954 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.404731 | 0.0297564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 23.7136 | 1.73411 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.40218 | −0.465690 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.03597 | −0.219675 | −0.109838 | − | 0.993950i | \(-0.535033\pi\) | ||||
−0.109838 | + | 0.993950i | \(0.535033\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.1680 | 0.875873 | 0.437937 | − | 0.899006i | \(-0.355709\pi\) | ||||
0.437937 | + | 0.899006i | \(0.355709\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.431185 | 0.0308778 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.33865 | −0.380363 | −0.190182 | − | 0.981749i | \(-0.560908\pi\) | ||||
−0.190182 | + | 0.981749i | \(0.560908\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2965 | 1.01345 | 0.506727 | − | 0.862107i | \(-0.330855\pi\) | ||||
0.506727 | + | 0.862107i | \(0.330855\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.8954 | 0.839034 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.05202 | −0.424768 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.365391 | −0.0255200 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −41.4784 | −2.88295 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.21731 | 0.222546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.9466 | −1.57971 | −0.789853 | − | 0.613296i | \(-0.789843\pi\) | ||||
−0.789853 | + | 0.613296i | \(0.789843\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −46.2267 | −3.16740 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.472656 | 0.0322349 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.09468 | −0.345849 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.0949 | 1.49303 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.5612 | 0.844955 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.4394 | −1.77051 | −0.885256 | − | 0.465104i | \(-0.846017\pi\) | ||||
−0.885256 | + | 0.465104i | \(0.846017\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.7580 | −1.71720 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.9138 | −0.923493 | −0.461747 | − | 0.887012i | \(-0.652777\pi\) | ||||
−0.461747 | + | 0.887012i | \(0.652777\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.45337 | −0.624696 | −0.312348 | − | 0.949968i | \(-0.601116\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601116\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.53738 | 0.627513 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.77299 | −0.247177 | −0.123589 | − | 0.992334i | \(-0.539440\pi\) | ||||
−0.123589 | + | 0.992334i | \(0.539440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.130077 | 0.00848528 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.96628 | 0.192680 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3884 | 1.38350 | 0.691752 | − | 0.722135i | \(-0.256839\pi\) | ||||
0.691752 | + | 0.722135i | \(0.256839\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8013 | −0.695771 | −0.347885 | − | 0.937537i | \(-0.613100\pi\) | ||||
−0.347885 | + | 0.937537i | \(0.613100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.3850 | −0.794501 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.524622 | 0.0335169 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.70422 | 0.108437 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.43159 | 0.534330 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.4478 | 1.79561 | 0.897803 | − | 0.440396i | \(-0.145162\pi\) | ||||
0.897803 | + | 0.440396i | \(0.145162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.8637 | 1.62604 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.86485 | 0.116781 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.27628 | −0.329125 | −0.164563 | − | 0.986367i | \(-0.552621\pi\) | ||||
−0.164563 | + | 0.986367i | \(0.552621\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.74202 | 0.294655 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 30.0902 | 1.86254 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.58348 | −0.0976416 | −0.0488208 | − | 0.998808i | \(-0.515546\pi\) | ||||
−0.0488208 | + | 0.998808i | \(0.515546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.0885731 | −0.00544100 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.39682 | −0.575076 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.60812 | 0.280962 | 0.140481 | − | 0.990083i | \(-0.455135\pi\) | ||||
0.140481 | + | 0.990083i | \(0.455135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.79800 | 0.230712 | 0.115356 | − | 0.993324i | \(-0.463199\pi\) | ||||
0.115356 | + | 0.993324i | \(0.463199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.05197 | 0.305759 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.0613 | 0.968535 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.4205 | −0.746278 | −0.373139 | − | 0.927775i | \(-0.621719\pi\) | ||||
−0.373139 | + | 0.927775i | \(0.621719\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.3304 | 1.51649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.97777 | −0.117984 | −0.0589920 | − | 0.998258i | \(-0.518789\pi\) | ||||
−0.0589920 | + | 0.998258i | \(0.518789\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.55942 | −0.211585 | −0.105793 | − | 0.994388i | \(-0.533738\pi\) | ||||
−0.105793 | + | 0.994388i | \(0.533738\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.253011 | 0.0149871 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.28110 | −0.252705 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 37.3261 | 2.19565 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.4825 | −0.731739 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.16113 | 0.301516 | 0.150758 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150758 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.920821 | −0.0536123 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.8483 | −1.15171 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.7001 | 0.792296 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.53786 | 0.319197 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 34.4504 | 1.97913 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.851310 | 0.0487458 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.4802 | −0.826431 | −0.413215 | − | 0.910633i | \(-0.635594\pi\) | ||||
−0.413215 | + | 0.910633i | \(0.635594\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.62286 | −0.547425 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.49798 | 0.538581 | 0.269290 | − | 0.963059i | \(-0.413211\pi\) | ||||
0.269290 | + | 0.963059i | \(0.413211\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.4175 | −1.15406 | −0.577032 | − | 0.816722i | \(-0.695789\pi\) | ||||
−0.577032 | + | 0.816722i | \(0.695789\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.474268 | 0.0267220 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.90019 | −0.443719 | −0.221859 | − | 0.975079i | \(-0.571213\pi\) | ||||
−0.221859 | + | 0.975079i | \(0.571213\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.7627 | −1.05051 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.1034 | −1.01043 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.37063 | 0.410113 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.50772 | 0.471923 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.4688 | 1.46373 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.52404 | 0.0840232 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.0082 | 1.26464 | 0.632322 | − | 0.774706i | \(-0.282102\pi\) | ||||
0.632322 | + | 0.774706i | \(0.282102\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −23.5770 | −1.29201 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.368844 | −0.0201521 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.00185 | 0.490362 | 0.245181 | − | 0.969477i | \(-0.421153\pi\) | ||||
0.245181 | + | 0.969477i | \(0.421153\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 40.6255 | 2.20648 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.7947 | −0.855332 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.4111 | 0.724130 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.03393 | 0.109503 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.39084 | 0.504127 | 0.252063 | − | 0.967711i | \(-0.418891\pi\) | ||||
0.252063 | + | 0.967711i | \(0.418891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.8648 | −1.49157 | −0.745785 | − | 0.666187i | \(-0.767925\pi\) | ||||
−0.745785 | + | 0.666187i | \(0.767925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.5137 | −0.561179 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.2736 | −1.02583 | −0.512914 | − | 0.858440i | \(-0.671434\pi\) | ||||
−0.512914 | + | 0.858440i | \(0.671434\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.43337 | 0.0760753 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.8494 | 1.15639 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.90579 | −0.522807 | −0.261404 | − | 0.965230i | \(-0.584185\pi\) | ||||
−0.261404 | + | 0.965230i | \(0.584185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.85356 | −0.0972868 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.685104 | −0.0358600 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.46826 | 0.389840 | 0.194920 | − | 0.980819i | \(-0.437555\pi\) | ||||
0.194920 | + | 0.980819i | \(0.437555\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.2853 | 1.10807 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.03776 | −0.0538780 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0939 | −0.677974 | −0.338987 | − | 0.940791i | \(-0.610084\pi\) | ||||
−0.338987 | + | 0.940791i | \(0.610084\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.52812 | 0.130552 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.93864 | −0.511866 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3309 | 1.35253 | 0.676264 | − | 0.736659i | \(-0.263598\pi\) | ||||
0.676264 | + | 0.736659i | \(0.263598\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −22.1528 | −1.13492 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.8993 | −1.62998 | −0.814990 | − | 0.579475i | \(-0.803258\pi\) | ||||
−0.814990 | + | 0.579475i | \(0.803258\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.295729 | −0.0150717 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −27.5339 | −1.39963 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −34.0638 | −1.72710 | −0.863550 | − | 0.504263i | \(-0.831764\pi\) | ||||
−0.863550 | + | 0.504263i | \(0.831764\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 59.2519 | 2.99650 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.5054 | 1.33702 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.0919764 | −0.00462783 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.76277 | 0.138659 | 0.0693296 | − | 0.997594i | \(-0.477914\pi\) | ||||
0.0693296 | + | 0.997594i | \(0.477914\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.96439 | 0.148405 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.3761 | 0.618031 | 0.309016 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309016 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.36649 | −0.416765 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.189845 | −0.00943347 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.7014 | 0.728721 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.9713 | −0.641390 | −0.320695 | − | 0.947183i | \(-0.603916\pi\) | ||||
−0.320695 | + | 0.947183i | \(0.603916\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.7022 | 1.76106 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.7888 | −0.530881 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.261441 | −0.0128336 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 47.9822 | 2.34970 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.5359 | −1.63833 | −0.819167 | − | 0.573555i | \(-0.805564\pi\) | ||||
−0.819167 | + | 0.573555i | \(0.805564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6229 | 0.663940 | 0.331970 | − | 0.943290i | \(-0.392287\pi\) | ||||
0.331970 | + | 0.943290i | \(0.392287\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.57744 | −0.368428 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 36.7953 | 1.78483 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.97434 | 0.482692 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.6623 | 0.756183 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.7866 | −1.43477 | −0.717385 | − | 0.696677i | \(-0.754661\pi\) | ||||
−0.717385 | + | 0.696677i | \(0.754661\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.1599 | 1.01688 | 0.508440 | − | 0.861098i | \(-0.330223\pi\) | ||||
0.508440 | + | 0.861098i | \(0.330223\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.47550 | −0.0707450 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.03892 | 0.384554 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0324 | −0.765184 | −0.382592 | − | 0.923917i | \(-0.624968\pi\) | ||||
−0.382592 | + | 0.923917i | \(0.624968\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −30.5611 | −1.45529 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.35806 | 0.159546 | 0.0797731 | − | 0.996813i | \(-0.474580\pi\) | ||||
0.0797731 | + | 0.996813i | \(0.474580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.291371 | 0.0138123 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 52.0419 | 2.46150 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −39.1830 | −1.84916 | −0.924581 | − | 0.380986i | \(-0.875585\pi\) | ||||
−0.924581 | + | 0.380986i | \(0.875585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.2724 | −0.624973 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.4138 | −0.912140 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.156648 | −0.00734378 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.2503 | 1.41505 | 0.707524 | − | 0.706689i | \(-0.249812\pi\) | ||||
0.707524 | + | 0.706689i | \(0.249812\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −45.4709 | −2.12240 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.3657 | 0.669079 | 0.334540 | − | 0.942382i | \(-0.391419\pi\) | ||||
0.334540 | + | 0.942382i | \(0.391419\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.1330 | −0.610344 | −0.305172 | − | 0.952297i | \(-0.598714\pi\) | ||||
−0.305172 | + | 0.952297i | \(0.598714\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.24210 | −0.0576011 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.0546 | −0.974289 | −0.487145 | − | 0.873321i | \(-0.661962\pi\) | ||||
−0.487145 | + | 0.873321i | \(0.661962\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.32155 | −0.199550 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.5504 | −1.08514 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.1687 | 0.789417 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.99215 | 0.229056 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.15970 | 0.236246 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.5659 | 0.848300 | 0.424150 | − | 0.905592i | \(-0.360573\pi\) | ||||
0.424150 | + | 0.905592i | \(0.360573\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.78736 | 0.355073 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 23.8305 | 1.08433 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.387050 | 0.0175750 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5515 | 0.478132 | 0.239066 | − | 0.971003i | \(-0.423159\pi\) | ||||
0.239066 | + | 0.971003i | \(0.423159\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.06186 | −0.138462 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.9409 | 1.39634 | 0.698171 | − | 0.715931i | \(-0.253997\pi\) | ||||
0.698171 | + | 0.715931i | \(0.253997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.9839 | −1.93590 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.47035 | 0.0660871 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.7940 | 0.753315 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.86676 | −0.352165 | −0.176082 | − | 0.984375i | \(-0.556342\pi\) | ||||
−0.176082 | + | 0.984375i | \(0.556342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −66.3525 | −2.96441 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.8432 | −1.64275 | −0.821377 | − | 0.570385i | \(-0.806794\pi\) | ||||
−0.821377 | + | 0.570385i | \(0.806794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.06822 | −0.0475350 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.8384 | −1.28076 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0462 | 0.622586 | 0.311293 | − | 0.950314i | \(-0.399238\pi\) | ||||
0.311293 | + | 0.950314i | \(0.399238\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.02700 | −0.355093 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.16921 | −0.272377 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.298379 | 0.0131482 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.72489 | 0.207801 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.9737 | −0.788956 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8705 | 1.26484 | 0.632419 | − | 0.774626i | \(-0.282062\pi\) | ||||
0.632419 | + | 0.774626i | \(0.282062\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.42273 | 0.324573 | 0.162287 | − | 0.986744i | \(-0.448113\pi\) | ||||
0.162287 | + | 0.986744i | \(0.448113\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.7987 | 0.645868 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.1845 | −1.57622 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.6242 | 1.80975 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 53.6411 | 2.32783 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.03043 | −0.304522 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.561338 | 0.0242688 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 57.8880 | 2.49805 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.0563 | 0.820813 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.9867 | −0.644328 | −0.322164 | − | 0.946684i | \(-0.604410\pi\) | ||||
−0.322164 | + | 0.946684i | \(0.604410\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −23.9823 | −1.02918 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.820727 | −0.0351561 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.85339 | 0.293030 | 0.146515 | − | 0.989208i | \(-0.453194\pi\) | ||||
0.146515 | + | 0.989208i | \(0.453194\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −49.5918 | −2.11653 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.83179 | −0.248442 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.07764 | −0.0458258 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.15612 | 0.0490746 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.71004 | −0.114828 | −0.0574139 | − | 0.998350i | \(-0.518285\pi\) | ||||
−0.0574139 | + | 0.998350i | \(0.518285\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.09429 | 0.384647 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 67.7384 | 2.85992 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.10309 | −0.0886348 | −0.0443174 | − | 0.999018i | \(-0.514111\pi\) | ||||
−0.0443174 | + | 0.999018i | \(0.514111\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.25969 | −0.0529955 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.22431 | −0.0934124 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.39698 | 0.268175 | 0.134088 | − | 0.990969i | \(-0.457190\pi\) | ||||
0.134088 | + | 0.990969i | \(0.457190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.82945 | 0.0765599 | 0.0382800 | − | 0.999267i | \(-0.487812\pi\) | ||||
0.0382800 | + | 0.999267i | \(0.487812\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.67231 | −0.362291 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.1315 | 1.67360 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.85154 | 0.368494 | 0.184247 | − | 0.982880i | \(-0.441015\pi\) | ||||
0.184247 | + | 0.982880i | \(0.441015\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.7582 | 1.44450 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.06317 | −0.127082 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.21731 | −0.133248 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.778845 | 0.0322013 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.8109 | −0.487490 | −0.243745 | − | 0.969839i | \(-0.578376\pi\) | ||||
−0.243745 | + | 0.969839i | \(0.578376\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.90929 | −0.202284 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.2500 | −0.627299 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.1874 | −1.11645 | −0.558226 | − | 0.829689i | \(-0.688518\pi\) | ||||
−0.558226 | + | 0.829689i | \(0.688518\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.677493 | −0.0277745 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 40.8383 | 1.67140 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.3426 | −0.586025 | −0.293012 | − | 0.956109i | \(-0.594658\pi\) | ||||
−0.293012 | + | 0.956109i | \(0.594658\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.3965 | 1.56622 | 0.783112 | − | 0.621881i | \(-0.213631\pi\) | ||||
0.783112 | + | 0.621881i | \(0.213631\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 21.4865 | 0.874996 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0574741 | 0.00233665 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.9277 | 0.484130 | 0.242065 | − | 0.970260i | \(-0.422175\pi\) | ||||
0.242065 | + | 0.970260i | \(0.422175\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.2877 | −0.700533 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.50279 | 0.101252 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.0479 | −0.809727 | −0.404864 | − | 0.914377i | \(-0.632681\pi\) | ||||
−0.404864 | + | 0.914377i | \(0.632681\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.04375 | −0.0420879 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.9788 | 0.844574 | 0.422287 | − | 0.906462i | \(-0.361227\pi\) | ||||
0.422287 | + | 0.906462i | \(0.361227\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.2131 | −0.490884 | −0.245442 | − | 0.969411i | \(-0.578933\pi\) | ||||
−0.245442 | + | 0.969411i | \(0.578933\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −49.5938 | −1.99013 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.41383 | 0.136772 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8824 | 0.995295 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.19032 | 0.367026 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.6798 | 1.34290 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.2634 | −1.48343 | −0.741716 | − | 0.670714i | \(-0.765988\pi\) | ||||
−0.741716 | + | 0.670714i | \(0.765988\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −65.5473 | −2.60527 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.686900 | 0.0272588 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.0942 | 0.399945 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −83.4988 | −3.30316 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.8250 | −0.822537 | −0.411268 | − | 0.911514i | \(-0.634914\pi\) | ||||
−0.411268 | + | 0.911514i | \(0.634914\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −50.0434 | −1.97352 | −0.986759 | − | 0.162193i | \(-0.948143\pi\) | ||||
−0.986759 | + | 0.162193i | \(0.948143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.35015 | 0.0531621 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.6868 | 0.695340 | 0.347670 | − | 0.937617i | \(-0.386973\pi\) | ||||
0.347670 | + | 0.937617i | \(0.386973\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.4478 | −1.31294 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.5530 | −0.570379 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.0964 | 1.52996 | 0.764981 | − | 0.644053i | \(-0.222749\pi\) | ||||
0.764981 | + | 0.644053i | \(0.222749\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.821861 | −0.0321128 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 39.9097 | 1.55703 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.52628 | −0.293182 | −0.146591 | − | 0.989197i | \(-0.546830\pi\) | ||||
−0.146591 | + | 0.989197i | \(0.546830\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.7980 | −1.74244 | −0.871220 | − | 0.490893i | \(-0.836671\pi\) | ||||
−0.871220 | + | 0.490893i | \(0.836671\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.8812 | 1.39351 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0919179 | −0.00356442 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46.8813 | −1.81525 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −75.5246 | −2.91995 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 30.9228 | 1.19376 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.93385 | 0.344375 | 0.172187 | − | 0.985064i | \(-0.444917\pi\) | ||||
0.172187 | + | 0.985064i | \(0.444917\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −30.7976 | −1.18540 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.3985 | 1.55264 | 0.776320 | − | 0.630339i | \(-0.217084\pi\) | ||||
0.776320 | + | 0.630339i | \(0.217084\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.53486 | 0.174032 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.7451 | −1.52304 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.7635 | 1.06234 | 0.531171 | − | 0.847264i | \(-0.321752\pi\) | ||||
0.531171 | + | 0.847264i | \(0.321752\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.10703 | −0.0422974 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −27.0037 | −1.03026 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.70422 | −0.0649255 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.5104 | −1.12263 | −0.561315 | − | 0.827602i | \(-0.689704\pi\) | ||||
−0.561315 | + | 0.827602i | \(0.689704\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.2273 | 0.654409 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.48780 | −0.0564355 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.4061 | −1.15171 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.7776 | −0.407647 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.0356 | −0.718966 | −0.359483 | − | 0.933152i | \(-0.617047\pi\) | ||||
−0.359483 | + | 0.933152i | \(0.617047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.56946 | 0.172340 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.371567 | 0.0139940 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.5157 | −0.470702 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.2727 | 0.385798 | 0.192899 | − | 0.981219i | \(-0.438211\pi\) | ||||
0.192899 | + | 0.981219i | \(0.438211\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.35795 | 0.200939 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.4654 | −1.47799 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.485647 | −0.0181622 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 61.0965 | 2.28169 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −52.4911 | −1.95759 | −0.978794 | − | 0.204847i | \(-0.934330\pi\) | ||||
−0.978794 | + | 0.204847i | \(0.934330\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.49595 | 0.130196 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.8540 | −1.14747 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29.1132 | −1.08124 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −44.1990 | −1.63925 | −0.819624 | − | 0.572901i | \(-0.805818\pi\) | ||||
−0.819624 | + | 0.572901i | \(0.805818\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.8082 | −1.54845 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.3322 | 1.45475 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.7174 | 1.79942 | 0.899709 | − | 0.436489i | \(-0.143778\pi\) | ||||
0.899709 | + | 0.436489i | \(0.143778\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.49859 | 0.0552764 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.3978 | −0.493515 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.3238 | −0.416552 | −0.208276 | − | 0.978070i | \(-0.566785\pi\) | ||||
−0.208276 | + | 0.978070i | \(0.566785\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.86813 | 0.178835 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.69013 | 0.355496 | 0.177748 | − | 0.984076i | \(-0.443119\pi\) | ||||
0.177748 | + | 0.984076i | \(0.443119\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.61368 | −0.0591208 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.2299 | 0.557232 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.57690 | 0.240315 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.1889 | −0.481268 | −0.240634 | − | 0.970616i | \(-0.577355\pi\) | ||||
−0.240634 | + | 0.970616i | \(0.577355\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 81.2615 | 2.96134 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.601971 | 0.0219080 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.6045 | −0.712537 | −0.356269 | − | 0.934384i | \(-0.615951\pi\) | ||||
−0.356269 | + | 0.934384i | \(0.615951\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 73.8802 | 2.68168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.1170 | −1.27299 | −0.636494 | − | 0.771281i | \(-0.719616\pi\) | ||||
−0.636494 | + | 0.771281i | \(0.719616\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.61602 | −0.348123 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.36845 | 0.121787 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.7173 | −0.639736 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.63677 | 0.311450 | 0.155725 | − | 0.987800i | \(-0.450229\pi\) | ||||
0.155725 | + | 0.987800i | \(0.450229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.0718 | −0.542797 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.2541 | −0.728489 | −0.364245 | − | 0.931303i | \(-0.618673\pi\) | ||||
−0.364245 | + | 0.931303i | \(0.618673\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.5079 | −0.880350 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.5457 | 0.485948 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.12531 | −0.147804 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.0655 | 1.86305 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 35.9775 | 1.28573 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.730235 | 0.0260632 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.56732 | 0.0915152 | 0.0457576 | − | 0.998953i | \(-0.485430\pi\) | ||||
0.0457576 | + | 0.998953i | \(0.485430\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.52324 | −0.161032 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.7591 | −0.524774 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.3799 | 0.581667 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.253011 | −0.00897336 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.0570 | −0.852142 | −0.426071 | − | 0.904690i | \(-0.640103\pi\) | ||||
−0.426071 | + | 0.904690i | \(0.640103\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.8244 | 0.382939 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.9734 | −0.599724 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.8856 | −0.878194 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.738921 | −0.0260435 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.1632 | 0.463365 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.9163 | 0.981486 | 0.490743 | − | 0.871304i | \(-0.336725\pi\) | ||||
0.490743 | + | 0.871304i | \(0.336725\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.9634 | −1.26285 | −0.631423 | − | 0.775439i | \(-0.717529\pi\) | ||||
−0.631423 | + | 0.775439i | \(0.717529\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.8491 | 0.380493 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.0949401 | 0.00332561 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.33634 | 0.186695 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.12531 | 0.318864 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.3921 | 1.68889 | 0.844447 | − | 0.535639i | \(-0.179929\pi\) | ||||
0.844447 | + | 0.535639i | \(0.179929\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.2755 | −1.26449 | −0.632243 | − | 0.774770i | \(-0.717866\pi\) | ||||
−0.632243 | + | 0.774770i | \(0.717866\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 45.8795 | 1.59732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.80648 | 0.341005 | 0.170502 | − | 0.985357i | \(-0.445461\pi\) | ||||
0.170502 | + | 0.985357i | \(0.445461\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.5270 | 0.990784 | 0.495392 | − | 0.868669i | \(-0.335024\pi\) | ||||
0.495392 | + | 0.868669i | \(0.335024\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.4795 | −1.23077 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 43.6566 | 1.51261 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.05741 | 0.0711997 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.2864 | 1.04685 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.84903 | 0.132883 | 0.0664417 | − | 0.997790i | \(-0.478835\pi\) | ||||
0.0664417 | + | 0.997790i | \(0.478835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.00974 | 0.172749 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.64955 | −0.194581 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.894202 | 0.0307615 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.673394 | 0.0231381 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.1675 | −0.348949 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.7335 | 1.25921 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.5811 | 1.01284 | 0.506419 | − | 0.862287i | \(-0.330969\pi\) | ||||
0.506419 | + | 0.862287i | \(0.330969\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.457010 | 0.0156294 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.9147 | 1.63673 | 0.818367 | − | 0.574696i | \(-0.194880\pi\) | ||||
0.818367 | + | 0.574696i | \(0.194880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.9344 | 0.884869 | 0.442435 | − | 0.896801i | \(-0.354115\pi\) | ||||
0.442435 | + | 0.896801i | \(0.354115\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.2290 | −0.416764 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.4891 | 1.13998 | 0.569991 | − | 0.821651i | \(-0.306947\pi\) | ||||
0.569991 | + | 0.821651i | \(0.306947\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.557316 | 0.0189493 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 106.623 | 3.62110 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.34094 | −0.113333 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.09685 | −0.240468 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −22.5471 | −0.763102 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.918458 | −0.0310496 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.3017 | −1.36089 | −0.680445 | − | 0.732799i | \(-0.738214\pi\) | ||||
−0.680445 | + | 0.732799i | \(0.738214\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.7429 | 0.497264 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.1204 | 1.01478 | 0.507390 | − | 0.861716i | \(-0.330610\pi\) | ||||
0.507390 | + | 0.861716i | \(0.330610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.0269 | −1.41432 | −0.707159 | − | 0.707054i | \(-0.750024\pi\) | ||||
−0.707159 | + | 0.707054i | \(0.750024\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.63034 | −0.0884180 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.57071 | −0.119893 | −0.0599464 | − | 0.998202i | \(-0.519093\pi\) | ||||
−0.0599464 | + | 0.998202i | \(0.519093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.04804 | 0.269923 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.89590 | −0.231021 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.46858 | 0.0491443 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.79495 | −0.0599987 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 39.1345 | 1.30666 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 28.6299 | 0.954861 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.37063 | −0.245551 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.8190 | 0.526423 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.743628 | 0.0247190 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.83728 | 0.127415 | 0.0637075 | − | 0.997969i | \(-0.479708\pi\) | ||||
0.0637075 | + | 0.997969i | \(0.479708\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 62.2274 | 2.06395 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −56.0715 | −1.85773 | −0.928865 | − | 0.370417i | \(-0.879215\pi\) | ||||
−0.928865 | + | 0.370417i | \(0.879215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.49655 | −0.314290 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.43178 | 0.0803922 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.62931 | −0.317988 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.4512 | −0.575662 | −0.287831 | − | 0.957681i | \(-0.592934\pi\) | ||||
−0.287831 | + | 0.957681i | \(0.592934\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −41.3630 | −1.36296 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.5792 | 0.907780 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.8114 | 0.750036 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.3817 | −0.570889 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.2513 | 0.598805 | 0.299403 | − | 0.954127i | \(-0.403213\pi\) | ||||
0.299403 | + | 0.954127i | \(0.403213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.92305 | 0.194120 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.1311 | 0.888234 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.10039 | −0.0686900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.0007 | 1.01275 | 0.506374 | − | 0.862314i | \(-0.330985\pi\) | ||||
0.506374 | + | 0.862314i | \(0.330985\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −58.3229 | −1.90329 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.79842 | −0.319419 | −0.159710 | − | 0.987164i | \(-0.551056\pi\) | ||||
−0.159710 | + | 0.987164i | \(0.551056\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.1630 | −1.07994 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.567061 | 0.0184465 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.3777 | 0.857159 | 0.428579 | − | 0.903504i | \(-0.359014\pi\) | ||||
0.428579 | + | 0.903504i | \(0.359014\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.1820 | −0.427904 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.5670 | −0.731786 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.36599 | −0.206215 | −0.103107 | − | 0.994670i | \(-0.532879\pi\) | ||||
−0.103107 | + | 0.994670i | \(0.532879\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.268905 | 0.00870157 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −53.5960 | −1.73251 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.9705 | −0.418839 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.89891 | −0.222546 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32.6999 | −1.05374 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.07776 | −0.0346943 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.1282 | 0.518647 | 0.259323 | − | 0.965791i | \(-0.416500\pi\) | ||||
0.259323 | + | 0.965791i | \(0.416500\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.0543 | 0.676362 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.3086 | 1.61448 | 0.807239 | − | 0.590224i | \(-0.200961\pi\) | ||||
0.807239 | + | 0.590224i | \(0.200961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.4318 | −0.558837 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24.3025 | 0.778302 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.1982 | −1.31805 | −0.659024 | − | 0.752122i | \(-0.729031\pi\) | ||||
−0.659024 | + | 0.752122i | \(0.729031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.5837 | 0.338256 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 47.8102 | 1.52646 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.8963 | −0.666487 | −0.333244 | − | 0.942841i | \(-0.608143\pi\) | ||||
−0.333244 | + | 0.942841i | \(0.608143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.472861 | 0.0150666 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.35345 | 0.138572 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 42.8984 | 1.36409 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.2955 | −0.422345 | −0.211173 | − | 0.977449i | \(-0.567728\pi\) | ||||
−0.211173 | + | 0.977449i | \(0.567728\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 65.7233 | 2.08567 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.26629 | −0.0401440 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.2409 | 1.49613 | 0.748067 | − | 0.663623i | \(-0.230982\pi\) | ||||
0.748067 | + | 0.663623i | \(0.230982\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −28.1899 | −0.891891 |
(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 | 4028.2.a.d.1.18 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.d.1.18 | ✓ | 19 | 1.1 | even | 1 | trivial |