Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.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: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 10x^{6} + 9x^{5} + 28x^{4} - 22x^{3} - 16x^{2} + 7x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.18675\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.18675 | 1.54627 | 0.773134 | − | 0.634243i | \(-0.218688\pi\) | ||||
0.773134 | + | 0.634243i | \(0.218688\pi\) | |||||||
\(3\) | −2.66680 | −1.53968 | −0.769838 | − | 0.638239i | \(-0.779663\pi\) | ||||
−0.769838 | + | 0.638239i | \(0.779663\pi\) | |||||||
\(4\) | 2.78189 | 1.39094 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.83163 | −2.38075 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.70979 | 0.604503 | ||||||||
\(9\) | 4.11181 | 1.37060 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.38662 | −1.02110 | −0.510551 | − | 0.859847i | \(-0.670559\pi\) | ||||
−0.510551 | + | 0.859847i | \(0.670559\pi\) | |||||||
\(12\) | −7.41873 | −2.14160 | ||||||||
\(13\) | 0.0686513 | 0.0190405 | 0.00952023 | − | 0.999955i | \(-0.496970\pi\) | ||||
0.00952023 | + | 0.999955i | \(0.496970\pi\) | |||||||
\(14\) | 2.18675 | 0.584434 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.82488 | −0.456220 | ||||||||
\(17\) | 2.64995 | 0.642707 | 0.321354 | − | 0.946959i | \(-0.395862\pi\) | ||||
0.321354 | + | 0.946959i | \(0.395862\pi\) | |||||||
\(18\) | 8.99151 | 2.11932 | ||||||||
\(19\) | 3.27497 | 0.751329 | 0.375665 | − | 0.926756i | \(-0.377414\pi\) | ||||
0.375665 | + | 0.926756i | \(0.377414\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.66680 | −0.581943 | ||||||||
\(22\) | −7.40569 | −1.57890 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −4.55967 | −0.930738 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.150124 | 0.0294416 | ||||||||
\(27\) | −2.96497 | −0.570608 | ||||||||
\(28\) | 2.78189 | 0.525727 | ||||||||
\(29\) | −0.498885 | −0.0926406 | −0.0463203 | − | 0.998927i | \(-0.514749\pi\) | ||||
−0.0463203 | + | 0.998927i | \(0.514749\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.846864 | −0.152101 | −0.0760507 | − | 0.997104i | \(-0.524231\pi\) | ||||
−0.0760507 | + | 0.997104i | \(0.524231\pi\) | |||||||
\(32\) | −7.41015 | −1.30994 | ||||||||
\(33\) | 9.03142 | 1.57217 | ||||||||
\(34\) | 5.79479 | 0.993798 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 11.4386 | 1.90643 | ||||||||
\(37\) | −2.34362 | −0.385289 | −0.192645 | − | 0.981269i | \(-0.561706\pi\) | ||||
−0.192645 | + | 0.981269i | \(0.561706\pi\) | |||||||
\(38\) | 7.16155 | 1.16176 | ||||||||
\(39\) | −0.183079 | −0.0293161 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.68516 | −0.419351 | −0.209675 | − | 0.977771i | \(-0.567241\pi\) | ||||
−0.209675 | + | 0.977771i | \(0.567241\pi\) | |||||||
\(42\) | −5.83163 | −0.899839 | ||||||||
\(43\) | −9.07605 | −1.38408 | −0.692042 | − | 0.721857i | \(-0.743289\pi\) | ||||
−0.692042 | + | 0.721857i | \(0.743289\pi\) | |||||||
\(44\) | −9.42118 | −1.42030 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.18675 | −0.322419 | ||||||||
\(47\) | −6.92879 | −1.01067 | −0.505334 | − | 0.862924i | \(-0.668631\pi\) | ||||
−0.505334 | + | 0.862924i | \(0.668631\pi\) | |||||||
\(48\) | 4.86659 | 0.702431 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.06688 | −0.989561 | ||||||||
\(52\) | 0.190980 | 0.0264842 | ||||||||
\(53\) | 0.0435836 | 0.00598667 | 0.00299334 | − | 0.999996i | \(-0.499047\pi\) | ||||
0.00299334 | + | 0.999996i | \(0.499047\pi\) | |||||||
\(54\) | −6.48365 | −0.882312 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.70979 | 0.228481 | ||||||||
\(57\) | −8.73368 | −1.15680 | ||||||||
\(58\) | −1.09094 | −0.143247 | ||||||||
\(59\) | 4.71871 | 0.614324 | 0.307162 | − | 0.951657i | \(-0.400621\pi\) | ||||
0.307162 | + | 0.951657i | \(0.400621\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.53139 | 1.09233 | 0.546166 | − | 0.837677i | \(-0.316087\pi\) | ||||
0.546166 | + | 0.837677i | \(0.316087\pi\) | |||||||
\(62\) | −1.85188 | −0.235189 | ||||||||
\(63\) | 4.11181 | 0.518039 | ||||||||
\(64\) | −12.5544 | −1.56930 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 19.7495 | 2.43099 | ||||||||
\(67\) | −8.46553 | −1.03423 | −0.517114 | − | 0.855916i | \(-0.672994\pi\) | ||||
−0.517114 | + | 0.855916i | \(0.672994\pi\) | |||||||
\(68\) | 7.37186 | 0.893970 | ||||||||
\(69\) | 2.66680 | 0.321045 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.438487 | −0.0520388 | −0.0260194 | − | 0.999661i | \(-0.508283\pi\) | ||||
−0.0260194 | + | 0.999661i | \(0.508283\pi\) | |||||||
\(72\) | 7.03034 | 0.828533 | ||||||||
\(73\) | −7.74306 | −0.906256 | −0.453128 | − | 0.891445i | \(-0.649692\pi\) | ||||
−0.453128 | + | 0.891445i | \(0.649692\pi\) | |||||||
\(74\) | −5.12493 | −0.595761 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.11059 | 1.04506 | ||||||||
\(77\) | −3.38662 | −0.385941 | ||||||||
\(78\) | −0.400349 | −0.0453306 | ||||||||
\(79\) | −9.44444 | −1.06258 | −0.531291 | − | 0.847189i | \(-0.678293\pi\) | ||||
−0.531291 | + | 0.847189i | \(0.678293\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.42846 | −0.492051 | ||||||||
\(82\) | −5.87177 | −0.648429 | ||||||||
\(83\) | −4.36410 | −0.479022 | −0.239511 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239511 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(84\) | −7.41873 | −0.809449 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.8471 | −2.14016 | ||||||||
\(87\) | 1.33042 | 0.142636 | ||||||||
\(88\) | −5.79041 | −0.617259 | ||||||||
\(89\) | −6.14427 | −0.651292 | −0.325646 | − | 0.945492i | \(-0.605582\pi\) | ||||
−0.325646 | + | 0.945492i | \(0.605582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0686513 | 0.00719662 | ||||||||
\(92\) | −2.78189 | −0.290032 | ||||||||
\(93\) | 2.25842 | 0.234187 | ||||||||
\(94\) | −15.1515 | −1.56276 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 19.7614 | 2.01689 | ||||||||
\(97\) | −6.71968 | −0.682280 | −0.341140 | − | 0.940012i | \(-0.610813\pi\) | ||||
−0.341140 | + | 0.940012i | \(0.610813\pi\) | |||||||
\(98\) | 2.18675 | 0.220895 | ||||||||
\(99\) | −13.9251 | −1.39953 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.6748 | 1.26119 | 0.630594 | − | 0.776113i | \(-0.282811\pi\) | ||||
0.630594 | + | 0.776113i | \(0.282811\pi\) | |||||||
\(102\) | −15.4535 | −1.53013 | ||||||||
\(103\) | −1.67902 | −0.165439 | −0.0827196 | − | 0.996573i | \(-0.526361\pi\) | ||||
−0.0827196 | + | 0.996573i | \(0.526361\pi\) | |||||||
\(104\) | 0.117380 | 0.0115100 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.0953066 | 0.00925700 | ||||||||
\(107\) | −1.83599 | −0.177492 | −0.0887459 | − | 0.996054i | \(-0.528286\pi\) | ||||
−0.0887459 | + | 0.996054i | \(0.528286\pi\) | |||||||
\(108\) | −8.24820 | −0.793683 | ||||||||
\(109\) | 15.3677 | 1.47195 | 0.735977 | − | 0.677006i | \(-0.236723\pi\) | ||||
0.735977 | + | 0.677006i | \(0.236723\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.24997 | 0.593221 | ||||||||
\(112\) | −1.82488 | −0.172435 | ||||||||
\(113\) | −12.0189 | −1.13065 | −0.565323 | − | 0.824870i | \(-0.691248\pi\) | ||||
−0.565323 | + | 0.824870i | \(0.691248\pi\) | |||||||
\(114\) | −19.0984 | −1.78873 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.38784 | −0.128858 | ||||||||
\(117\) | 0.282281 | 0.0260969 | ||||||||
\(118\) | 10.3187 | 0.949909 | ||||||||
\(119\) | 2.64995 | 0.242921 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.469162 | 0.0426511 | ||||||||
\(122\) | 18.6560 | 1.68904 | ||||||||
\(123\) | 7.16076 | 0.645664 | ||||||||
\(124\) | −2.35588 | −0.211564 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.99151 | 0.801027 | ||||||||
\(127\) | −11.4855 | −1.01917 | −0.509587 | − | 0.860419i | \(-0.670202\pi\) | ||||
−0.509587 | + | 0.860419i | \(0.670202\pi\) | |||||||
\(128\) | −12.6331 | −1.11662 | ||||||||
\(129\) | 24.2040 | 2.13104 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.79086 | −0.418579 | −0.209290 | − | 0.977854i | \(-0.567115\pi\) | ||||
−0.209290 | + | 0.977854i | \(0.567115\pi\) | |||||||
\(132\) | 25.1244 | 2.18680 | ||||||||
\(133\) | 3.27497 | 0.283976 | ||||||||
\(134\) | −18.5120 | −1.59919 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.53086 | 0.388518 | ||||||||
\(137\) | −14.5227 | −1.24076 | −0.620378 | − | 0.784303i | \(-0.713021\pi\) | ||||
−0.620378 | + | 0.784303i | \(0.713021\pi\) | |||||||
\(138\) | 5.83163 | 0.496421 | ||||||||
\(139\) | −15.7239 | −1.33369 | −0.666844 | − | 0.745198i | \(-0.732355\pi\) | ||||
−0.666844 | + | 0.745198i | \(0.732355\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.4777 | 1.55610 | ||||||||
\(142\) | −0.958862 | −0.0804659 | ||||||||
\(143\) | −0.232496 | −0.0194423 | ||||||||
\(144\) | −7.50356 | −0.625297 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −16.9321 | −1.40131 | ||||||||
\(147\) | −2.66680 | −0.219954 | ||||||||
\(148\) | −6.51970 | −0.535916 | ||||||||
\(149\) | −3.25848 | −0.266945 | −0.133472 | − | 0.991053i | \(-0.542613\pi\) | ||||
−0.133472 | + | 0.991053i | \(0.542613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.41686 | 0.278060 | 0.139030 | − | 0.990288i | \(-0.455602\pi\) | ||||
0.139030 | + | 0.990288i | \(0.455602\pi\) | |||||||
\(152\) | 5.59952 | 0.454181 | ||||||||
\(153\) | 10.8961 | 0.880896 | ||||||||
\(154\) | −7.40569 | −0.596767 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.509306 | −0.0407771 | ||||||||
\(157\) | −14.7913 | −1.18047 | −0.590236 | − | 0.807231i | \(-0.700965\pi\) | ||||
−0.590236 | + | 0.807231i | \(0.700965\pi\) | |||||||
\(158\) | −20.6527 | −1.64304 | ||||||||
\(159\) | −0.116229 | −0.00921754 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −9.68395 | −0.760843 | ||||||||
\(163\) | −23.5301 | −1.84302 | −0.921512 | − | 0.388351i | \(-0.873045\pi\) | ||||
−0.921512 | + | 0.388351i | \(0.873045\pi\) | |||||||
\(164\) | −7.46980 | −0.583293 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.54321 | −0.740697 | ||||||||
\(167\) | 20.8784 | 1.61562 | 0.807810 | − | 0.589442i | \(-0.200653\pi\) | ||||
0.807810 | + | 0.589442i | \(0.200653\pi\) | |||||||
\(168\) | −4.55967 | −0.351786 | ||||||||
\(169\) | −12.9953 | −0.999637 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.4660 | 1.02977 | ||||||||
\(172\) | −25.2485 | −1.92518 | ||||||||
\(173\) | −10.5021 | −0.798463 | −0.399231 | − | 0.916850i | \(-0.630723\pi\) | ||||
−0.399231 | + | 0.916850i | \(0.630723\pi\) | |||||||
\(174\) | 2.90931 | 0.220554 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.18017 | 0.465848 | ||||||||
\(177\) | −12.5838 | −0.945860 | ||||||||
\(178\) | −13.4360 | −1.00707 | ||||||||
\(179\) | 22.0735 | 1.64985 | 0.824927 | − | 0.565239i | \(-0.191216\pi\) | ||||
0.824927 | + | 0.565239i | \(0.191216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.41151 | 0.327905 | 0.163952 | − | 0.986468i | \(-0.447576\pi\) | ||||
0.163952 | + | 0.986468i | \(0.447576\pi\) | |||||||
\(182\) | 0.150124 | 0.0111279 | ||||||||
\(183\) | −22.7515 | −1.68184 | ||||||||
\(184\) | −1.70979 | −0.126048 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.93860 | 0.362115 | ||||||||
\(187\) | −8.97436 | −0.656270 | ||||||||
\(188\) | −19.2751 | −1.40578 | ||||||||
\(189\) | −2.96497 | −0.215670 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.98892 | −0.433343 | −0.216672 | − | 0.976245i | \(-0.569520\pi\) | ||||
−0.216672 | + | 0.976245i | \(0.569520\pi\) | |||||||
\(192\) | 33.4800 | 2.41621 | ||||||||
\(193\) | 12.5614 | 0.904186 | 0.452093 | − | 0.891971i | \(-0.350677\pi\) | ||||
0.452093 | + | 0.891971i | \(0.350677\pi\) | |||||||
\(194\) | −14.6943 | −1.05499 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.78189 | 0.198706 | ||||||||
\(197\) | 2.61220 | 0.186112 | 0.0930558 | − | 0.995661i | \(-0.470337\pi\) | ||||
0.0930558 | + | 0.995661i | \(0.470337\pi\) | |||||||
\(198\) | −30.4508 | −2.16404 | ||||||||
\(199\) | 9.74423 | 0.690750 | 0.345375 | − | 0.938465i | \(-0.387752\pi\) | ||||
0.345375 | + | 0.938465i | \(0.387752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.5758 | 1.59238 | ||||||||
\(202\) | 27.7166 | 1.95013 | ||||||||
\(203\) | −0.498885 | −0.0350148 | ||||||||
\(204\) | −19.6593 | −1.37642 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.67161 | −0.255813 | ||||||||
\(207\) | −4.11181 | −0.285790 | ||||||||
\(208\) | −0.125281 | −0.00868664 | ||||||||
\(209\) | −11.0911 | −0.767185 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.69331 | −0.185415 | −0.0927077 | − | 0.995693i | \(-0.529552\pi\) | ||||
−0.0927077 | + | 0.995693i | \(0.529552\pi\) | |||||||
\(212\) | 0.121245 | 0.00832712 | ||||||||
\(213\) | 1.16936 | 0.0801229 | ||||||||
\(214\) | −4.01485 | −0.274450 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.06947 | −0.344934 | ||||||||
\(217\) | −0.846864 | −0.0574889 | ||||||||
\(218\) | 33.6053 | 2.27604 | ||||||||
\(219\) | 20.6492 | 1.39534 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.181923 | 0.0122374 | ||||||||
\(222\) | 13.6671 | 0.917278 | ||||||||
\(223\) | −5.41743 | −0.362778 | −0.181389 | − | 0.983411i | \(-0.558059\pi\) | ||||
−0.181389 | + | 0.983411i | \(0.558059\pi\) | |||||||
\(224\) | −7.41015 | −0.495111 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −26.2824 | −1.74828 | ||||||||
\(227\) | −5.86988 | −0.389598 | −0.194799 | − | 0.980843i | \(-0.562405\pi\) | ||||
−0.194799 | + | 0.980843i | \(0.562405\pi\) | |||||||
\(228\) | −24.2961 | −1.60905 | ||||||||
\(229\) | 25.0481 | 1.65522 | 0.827612 | − | 0.561301i | \(-0.189699\pi\) | ||||
0.827612 | + | 0.561301i | \(0.189699\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.03142 | 0.594224 | ||||||||
\(232\) | −0.852989 | −0.0560015 | ||||||||
\(233\) | 12.5329 | 0.821057 | 0.410528 | − | 0.911848i | \(-0.365344\pi\) | ||||
0.410528 | + | 0.911848i | \(0.365344\pi\) | |||||||
\(234\) | 0.617279 | 0.0403528 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.1269 | 0.854489 | ||||||||
\(237\) | 25.1864 | 1.63603 | ||||||||
\(238\) | 5.79479 | 0.375620 | ||||||||
\(239\) | −14.2246 | −0.920111 | −0.460056 | − | 0.887890i | \(-0.652171\pi\) | ||||
−0.460056 | + | 0.887890i | \(0.652171\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.95273 | −0.190202 | −0.0951011 | − | 0.995468i | \(-0.530317\pi\) | ||||
−0.0951011 | + | 0.995468i | \(0.530317\pi\) | |||||||
\(242\) | 1.02594 | 0.0659500 | ||||||||
\(243\) | 20.7047 | 1.32821 | ||||||||
\(244\) | 23.7334 | 1.51937 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.6588 | 0.998370 | ||||||||
\(247\) | 0.224831 | 0.0143057 | ||||||||
\(248\) | −1.44796 | −0.0919457 | ||||||||
\(249\) | 11.6382 | 0.737539 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.3474 | −1.66303 | −0.831517 | − | 0.555499i | \(-0.812527\pi\) | ||||
−0.831517 | + | 0.555499i | \(0.812527\pi\) | |||||||
\(252\) | 11.4386 | 0.720563 | ||||||||
\(253\) | 3.38662 | 0.212915 | ||||||||
\(254\) | −25.1160 | −1.57592 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.51659 | −0.157287 | ||||||||
\(257\) | −7.76198 | −0.484179 | −0.242089 | − | 0.970254i | \(-0.577833\pi\) | ||||
−0.242089 | + | 0.970254i | \(0.577833\pi\) | |||||||
\(258\) | 52.9281 | 3.29516 | ||||||||
\(259\) | −2.34362 | −0.145626 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.05132 | −0.126973 | ||||||||
\(262\) | −10.4764 | −0.647235 | ||||||||
\(263\) | 10.1109 | 0.623462 | 0.311731 | − | 0.950170i | \(-0.399091\pi\) | ||||
0.311731 | + | 0.950170i | \(0.399091\pi\) | |||||||
\(264\) | 15.4418 | 0.950380 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.16155 | 0.439103 | ||||||||
\(267\) | 16.3855 | 1.00278 | ||||||||
\(268\) | −23.5501 | −1.43855 | ||||||||
\(269\) | 15.1067 | 0.921074 | 0.460537 | − | 0.887641i | \(-0.347657\pi\) | ||||
0.460537 | + | 0.887641i | \(0.347657\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.27056 | −0.198672 | −0.0993362 | − | 0.995054i | \(-0.531672\pi\) | ||||
−0.0993362 | + | 0.995054i | \(0.531672\pi\) | |||||||
\(272\) | −4.83584 | −0.293216 | ||||||||
\(273\) | −0.183079 | −0.0110805 | ||||||||
\(274\) | −31.7575 | −1.91854 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.41873 | 0.446555 | ||||||||
\(277\) | 9.29013 | 0.558190 | 0.279095 | − | 0.960264i | \(-0.409966\pi\) | ||||
0.279095 | + | 0.960264i | \(0.409966\pi\) | |||||||
\(278\) | −34.3844 | −2.06224 | ||||||||
\(279\) | −3.48214 | −0.208470 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.4571 | −1.51864 | −0.759321 | − | 0.650716i | \(-0.774469\pi\) | ||||
−0.759321 | + | 0.650716i | \(0.774469\pi\) | |||||||
\(282\) | 40.4061 | 2.40615 | ||||||||
\(283\) | 2.89396 | 0.172028 | 0.0860140 | − | 0.996294i | \(-0.472587\pi\) | ||||
0.0860140 | + | 0.996294i | \(0.472587\pi\) | |||||||
\(284\) | −1.21982 | −0.0723830 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.508411 | −0.0300629 | ||||||||
\(287\) | −2.68516 | −0.158500 | ||||||||
\(288\) | −30.4691 | −1.79541 | ||||||||
\(289\) | −9.97776 | −0.586927 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.9200 | 1.05049 | ||||||||
\(292\) | −21.5403 | −1.26055 | ||||||||
\(293\) | 22.0396 | 1.28757 | 0.643785 | − | 0.765207i | \(-0.277363\pi\) | ||||
0.643785 | + | 0.765207i | \(0.277363\pi\) | |||||||
\(294\) | −5.83163 | −0.340107 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.00711 | −0.232909 | ||||||||
\(297\) | 10.0412 | 0.582649 | ||||||||
\(298\) | −7.12548 | −0.412768 | ||||||||
\(299\) | −0.0686513 | −0.00397021 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.07605 | −0.523135 | ||||||||
\(302\) | 7.47183 | 0.429956 | ||||||||
\(303\) | −33.8011 | −1.94182 | ||||||||
\(304\) | −5.97643 | −0.342772 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 23.8270 | 1.36210 | ||||||||
\(307\) | −11.8220 | −0.674715 | −0.337357 | − | 0.941377i | \(-0.609533\pi\) | ||||
−0.337357 | + | 0.941377i | \(0.609533\pi\) | |||||||
\(308\) | −9.42118 | −0.536821 | ||||||||
\(309\) | 4.47762 | 0.254723 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.8962 | −0.787981 | −0.393990 | − | 0.919115i | \(-0.628906\pi\) | ||||
−0.393990 | + | 0.919115i | \(0.628906\pi\) | |||||||
\(312\) | −0.313027 | −0.0177217 | ||||||||
\(313\) | −5.82462 | −0.329227 | −0.164614 | − | 0.986358i | \(-0.552638\pi\) | ||||
−0.164614 | + | 0.986358i | \(0.552638\pi\) | |||||||
\(314\) | −32.3449 | −1.82533 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −26.2734 | −1.47799 | ||||||||
\(317\) | 27.7561 | 1.55894 | 0.779468 | − | 0.626442i | \(-0.215490\pi\) | ||||
0.779468 | + | 0.626442i | \(0.215490\pi\) | |||||||
\(318\) | −0.254164 | −0.0142528 | ||||||||
\(319\) | 1.68953 | 0.0945956 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.89621 | 0.273280 | ||||||||
\(322\) | −2.18675 | −0.121863 | ||||||||
\(323\) | 8.67851 | 0.482885 | ||||||||
\(324\) | −12.3195 | −0.684415 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −51.4546 | −2.84981 | ||||||||
\(327\) | −40.9824 | −2.26633 | ||||||||
\(328\) | −4.59106 | −0.253499 | ||||||||
\(329\) | −6.92879 | −0.381996 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.41366 | −0.517421 | −0.258711 | − | 0.965955i | \(-0.583298\pi\) | ||||
−0.258711 | + | 0.965955i | \(0.583298\pi\) | |||||||
\(332\) | −12.1404 | −0.666293 | ||||||||
\(333\) | −9.63653 | −0.528079 | ||||||||
\(334\) | 45.6559 | 2.49818 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.86659 | 0.265494 | ||||||||
\(337\) | 9.80625 | 0.534181 | 0.267090 | − | 0.963672i | \(-0.413938\pi\) | ||||
0.267090 | + | 0.963672i | \(0.413938\pi\) | |||||||
\(338\) | −28.4175 | −1.54571 | ||||||||
\(339\) | 32.0520 | 1.74083 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.86800 | 0.155311 | ||||||||
\(342\) | 29.4469 | 1.59231 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −15.5182 | −0.836683 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.9656 | −1.23464 | ||||||||
\(347\) | 12.9279 | 0.694008 | 0.347004 | − | 0.937864i | \(-0.387199\pi\) | ||||
0.347004 | + | 0.937864i | \(0.387199\pi\) | |||||||
\(348\) | 3.70109 | 0.198399 | ||||||||
\(349\) | −19.7938 | −1.05954 | −0.529769 | − | 0.848142i | \(-0.677722\pi\) | ||||
−0.529769 | + | 0.848142i | \(0.677722\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.203549 | −0.0108646 | ||||||||
\(352\) | 25.0953 | 1.33758 | ||||||||
\(353\) | 21.5440 | 1.14667 | 0.573335 | − | 0.819321i | \(-0.305650\pi\) | ||||
0.573335 | + | 0.819321i | \(0.305650\pi\) | |||||||
\(354\) | −27.5178 | −1.46255 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −17.0927 | −0.905910 | ||||||||
\(357\) | −7.06688 | −0.374019 | ||||||||
\(358\) | 48.2694 | 2.55112 | ||||||||
\(359\) | 29.8229 | 1.57399 | 0.786996 | − | 0.616958i | \(-0.211635\pi\) | ||||
0.786996 | + | 0.616958i | \(0.211635\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.27458 | −0.435504 | ||||||||
\(362\) | 9.64688 | 0.507029 | ||||||||
\(363\) | −1.25116 | −0.0656689 | ||||||||
\(364\) | 0.190980 | 0.0100101 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −49.7519 | −2.60057 | ||||||||
\(367\) | −12.5327 | −0.654203 | −0.327102 | − | 0.944989i | \(-0.606072\pi\) | ||||
−0.327102 | + | 0.944989i | \(0.606072\pi\) | |||||||
\(368\) | 1.82488 | 0.0951285 | ||||||||
\(369\) | −11.0408 | −0.574763 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0435836 | 0.00226275 | ||||||||
\(372\) | 6.28266 | 0.325741 | ||||||||
\(373\) | −24.4351 | −1.26520 | −0.632600 | − | 0.774479i | \(-0.718012\pi\) | ||||
−0.632600 | + | 0.774479i | \(0.718012\pi\) | |||||||
\(374\) | −19.6247 | −1.01477 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.8468 | −0.610951 | ||||||||
\(377\) | −0.0342491 | −0.00176392 | ||||||||
\(378\) | −6.48365 | −0.333483 | ||||||||
\(379\) | 28.0657 | 1.44164 | 0.720820 | − | 0.693122i | \(-0.243765\pi\) | ||||
0.720820 | + | 0.693122i | \(0.243765\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 30.6295 | 1.56920 | ||||||||
\(382\) | −13.0963 | −0.670065 | ||||||||
\(383\) | 13.8519 | 0.707799 | 0.353900 | − | 0.935283i | \(-0.384855\pi\) | ||||
0.353900 | + | 0.935283i | \(0.384855\pi\) | |||||||
\(384\) | 33.6898 | 1.71923 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 27.4686 | 1.39811 | ||||||||
\(387\) | −37.3190 | −1.89703 | ||||||||
\(388\) | −18.6934 | −0.949013 | ||||||||
\(389\) | −0.469165 | −0.0237876 | −0.0118938 | − | 0.999929i | \(-0.503786\pi\) | ||||
−0.0118938 | + | 0.999929i | \(0.503786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.64995 | −0.134014 | ||||||||
\(392\) | 1.70979 | 0.0863575 | ||||||||
\(393\) | 12.7762 | 0.644476 | ||||||||
\(394\) | 5.71224 | 0.287778 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −38.7381 | −1.94666 | ||||||||
\(397\) | −11.8028 | −0.592364 | −0.296182 | − | 0.955132i | \(-0.595713\pi\) | ||||
−0.296182 | + | 0.955132i | \(0.595713\pi\) | |||||||
\(398\) | 21.3082 | 1.06808 | ||||||||
\(399\) | −8.73368 | −0.437231 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.06276 | −0.152947 | −0.0764735 | − | 0.997072i | \(-0.524366\pi\) | ||||
−0.0764735 | + | 0.997072i | \(0.524366\pi\) | |||||||
\(402\) | 49.3678 | 2.46224 | ||||||||
\(403\) | −0.0581384 | −0.00289608 | ||||||||
\(404\) | 35.2598 | 1.75424 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.09094 | −0.0541423 | ||||||||
\(407\) | 7.93695 | 0.393420 | ||||||||
\(408\) | −12.0829 | −0.598193 | ||||||||
\(409\) | 34.8685 | 1.72414 | 0.862068 | − | 0.506792i | \(-0.169169\pi\) | ||||
0.862068 | + | 0.506792i | \(0.169169\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 38.7290 | 1.91036 | ||||||||
\(412\) | −4.67085 | −0.230116 | ||||||||
\(413\) | 4.71871 | 0.232193 | ||||||||
\(414\) | −8.99151 | −0.441908 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.508717 | −0.0249419 | ||||||||
\(417\) | 41.9326 | 2.05345 | ||||||||
\(418\) | −24.2534 | −1.18627 | ||||||||
\(419\) | 14.2917 | 0.698193 | 0.349096 | − | 0.937087i | \(-0.386489\pi\) | ||||
0.349096 | + | 0.937087i | \(0.386489\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5522 | 1.00165 | 0.500827 | − | 0.865548i | \(-0.333029\pi\) | ||||
0.500827 | + | 0.865548i | \(0.333029\pi\) | |||||||
\(422\) | −5.88961 | −0.286702 | ||||||||
\(423\) | −28.4898 | −1.38522 | ||||||||
\(424\) | 0.0745190 | 0.00361896 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.55709 | 0.123891 | ||||||||
\(427\) | 8.53139 | 0.412863 | ||||||||
\(428\) | −5.10751 | −0.246881 | ||||||||
\(429\) | 0.620019 | 0.0299348 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.3898 | −0.885806 | −0.442903 | − | 0.896569i | \(-0.646051\pi\) | ||||
−0.442903 | + | 0.896569i | \(0.646051\pi\) | |||||||
\(432\) | 5.41071 | 0.260323 | ||||||||
\(433\) | 15.1621 | 0.728645 | 0.364323 | − | 0.931273i | \(-0.381301\pi\) | ||||
0.364323 | + | 0.931273i | \(0.381301\pi\) | |||||||
\(434\) | −1.85188 | −0.0888932 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 42.7511 | 2.04741 | ||||||||
\(437\) | −3.27497 | −0.156663 | ||||||||
\(438\) | 45.1546 | 2.15757 | ||||||||
\(439\) | −37.5351 | −1.79145 | −0.895727 | − | 0.444604i | \(-0.853344\pi\) | ||||
−0.895727 | + | 0.444604i | \(0.853344\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.11181 | 0.195800 | ||||||||
\(442\) | 0.397820 | 0.0189224 | ||||||||
\(443\) | −25.7620 | −1.22399 | −0.611995 | − | 0.790861i | \(-0.709633\pi\) | ||||
−0.611995 | + | 0.790861i | \(0.709633\pi\) | |||||||
\(444\) | 17.3867 | 0.825137 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11.8466 | −0.560952 | ||||||||
\(447\) | 8.68969 | 0.411008 | ||||||||
\(448\) | −12.5544 | −0.593139 | ||||||||
\(449\) | 35.3393 | 1.66777 | 0.833883 | − | 0.551942i | \(-0.186113\pi\) | ||||
0.833883 | + | 0.551942i | \(0.186113\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.09359 | 0.428200 | ||||||||
\(452\) | −33.4353 | −1.57266 | ||||||||
\(453\) | −9.11208 | −0.428123 | ||||||||
\(454\) | −12.8360 | −0.602422 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −14.9328 | −0.699291 | ||||||||
\(457\) | −8.30606 | −0.388541 | −0.194271 | − | 0.980948i | \(-0.562234\pi\) | ||||
−0.194271 | + | 0.980948i | \(0.562234\pi\) | |||||||
\(458\) | 54.7739 | 2.55942 | ||||||||
\(459\) | −7.85701 | −0.366734 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.6213 | 0.960431 | 0.480216 | − | 0.877150i | \(-0.340558\pi\) | ||||
0.480216 | + | 0.877150i | \(0.340558\pi\) | |||||||
\(462\) | 19.7495 | 0.918829 | ||||||||
\(463\) | −13.7920 | −0.640968 | −0.320484 | − | 0.947254i | \(-0.603845\pi\) | ||||
−0.320484 | + | 0.947254i | \(0.603845\pi\) | |||||||
\(464\) | 0.910405 | 0.0422645 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.4063 | 1.26957 | ||||||||
\(467\) | 16.7233 | 0.773860 | 0.386930 | − | 0.922109i | \(-0.373535\pi\) | ||||
0.386930 | + | 0.922109i | \(0.373535\pi\) | |||||||
\(468\) | 0.785274 | 0.0362993 | ||||||||
\(469\) | −8.46553 | −0.390902 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 39.4453 | 1.81754 | ||||||||
\(472\) | 8.06801 | 0.371360 | ||||||||
\(473\) | 30.7371 | 1.41329 | ||||||||
\(474\) | 55.0765 | 2.52975 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.37186 | 0.337889 | ||||||||
\(477\) | 0.179208 | 0.00820535 | ||||||||
\(478\) | −31.1056 | −1.42274 | ||||||||
\(479\) | 36.9462 | 1.68812 | 0.844058 | − | 0.536252i | \(-0.180160\pi\) | ||||
0.844058 | + | 0.536252i | \(0.180160\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.160893 | −0.00733609 | ||||||||
\(482\) | −6.45690 | −0.294104 | ||||||||
\(483\) | 2.66680 | 0.121343 | ||||||||
\(484\) | 1.30516 | 0.0593252 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 45.2761 | 2.05376 | ||||||||
\(487\) | −1.03549 | −0.0469224 | −0.0234612 | − | 0.999725i | \(-0.507469\pi\) | ||||
−0.0234612 | + | 0.999725i | \(0.507469\pi\) | |||||||
\(488\) | 14.5869 | 0.660318 | ||||||||
\(489\) | 62.7501 | 2.83766 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.49792 | 0.157859 | 0.0789294 | − | 0.996880i | \(-0.474850\pi\) | ||||
0.0789294 | + | 0.996880i | \(0.474850\pi\) | |||||||
\(492\) | 19.9204 | 0.898083 | ||||||||
\(493\) | −1.32202 | −0.0595408 | ||||||||
\(494\) | 0.491650 | 0.0221204 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.54543 | 0.0693917 | ||||||||
\(497\) | −0.438487 | −0.0196688 | ||||||||
\(498\) | 25.4498 | 1.14043 | ||||||||
\(499\) | 12.9687 | 0.580559 | 0.290279 | − | 0.956942i | \(-0.406252\pi\) | ||||
0.290279 | + | 0.956942i | \(0.406252\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −55.6785 | −2.48753 | ||||||||
\(502\) | −57.6153 | −2.57150 | ||||||||
\(503\) | −6.09468 | −0.271748 | −0.135874 | − | 0.990726i | \(-0.543384\pi\) | ||||
−0.135874 | + | 0.990726i | \(0.543384\pi\) | |||||||
\(504\) | 7.03034 | 0.313156 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.40569 | 0.329223 | ||||||||
\(507\) | 34.6558 | 1.53912 | ||||||||
\(508\) | −31.9514 | −1.41761 | ||||||||
\(509\) | 28.0398 | 1.24284 | 0.621420 | − | 0.783478i | \(-0.286556\pi\) | ||||
0.621420 | + | 0.783478i | \(0.286556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.74306 | −0.342533 | ||||||||
\(512\) | 19.7630 | 0.873408 | ||||||||
\(513\) | −9.71017 | −0.428715 | ||||||||
\(514\) | −16.9735 | −0.748670 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 67.3327 | 2.96416 | ||||||||
\(517\) | 23.4651 | 1.03200 | ||||||||
\(518\) | −5.12493 | −0.225176 | ||||||||
\(519\) | 28.0071 | 1.22937 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.7913 | −0.560396 | −0.280198 | − | 0.959942i | \(-0.590400\pi\) | ||||
−0.280198 | + | 0.959942i | \(0.590400\pi\) | |||||||
\(522\) | −4.48573 | −0.196335 | ||||||||
\(523\) | −26.9318 | −1.17765 | −0.588823 | − | 0.808262i | \(-0.700409\pi\) | ||||
−0.588823 | + | 0.808262i | \(0.700409\pi\) | |||||||
\(524\) | −13.3276 | −0.582220 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.1099 | 0.964039 | ||||||||
\(527\) | −2.24415 | −0.0977567 | ||||||||
\(528\) | −16.4813 | −0.717255 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.4024 | 0.841994 | ||||||||
\(532\) | 9.11059 | 0.394994 | ||||||||
\(533\) | −0.184340 | −0.00798463 | ||||||||
\(534\) | 35.8311 | 1.55056 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.4743 | −0.625194 | ||||||||
\(537\) | −58.8657 | −2.54024 | ||||||||
\(538\) | 33.0347 | 1.42423 | ||||||||
\(539\) | −3.38662 | −0.145872 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.0305 | 1.59207 | 0.796033 | − | 0.605253i | \(-0.206928\pi\) | ||||
0.796033 | + | 0.605253i | \(0.206928\pi\) | |||||||
\(542\) | −7.15191 | −0.307201 | ||||||||
\(543\) | −11.7646 | −0.504867 | ||||||||
\(544\) | −19.6365 | −0.841909 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.400349 | −0.0171334 | ||||||||
\(547\) | 14.7399 | 0.630232 | 0.315116 | − | 0.949053i | \(-0.397957\pi\) | ||||
0.315116 | + | 0.949053i | \(0.397957\pi\) | |||||||
\(548\) | −40.4004 | −1.72582 | ||||||||
\(549\) | 35.0794 | 1.49715 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.63383 | −0.0696036 | ||||||||
\(552\) | 4.55967 | 0.194072 | ||||||||
\(553\) | −9.44444 | −0.401619 | ||||||||
\(554\) | 20.3152 | 0.863111 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −43.7422 | −1.85508 | ||||||||
\(557\) | −27.7047 | −1.17388 | −0.586942 | − | 0.809629i | \(-0.699668\pi\) | ||||
−0.586942 | + | 0.809629i | \(0.699668\pi\) | |||||||
\(558\) | −7.61459 | −0.322351 | ||||||||
\(559\) | −0.623083 | −0.0263536 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.9328 | 1.01044 | ||||||||
\(562\) | −55.6684 | −2.34823 | ||||||||
\(563\) | 14.9839 | 0.631498 | 0.315749 | − | 0.948843i | \(-0.397744\pi\) | ||||
0.315749 | + | 0.948843i | \(0.397744\pi\) | |||||||
\(564\) | 51.4028 | 2.16445 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.32837 | 0.266001 | ||||||||
\(567\) | −4.42846 | −0.185978 | ||||||||
\(568\) | −0.749721 | −0.0314576 | ||||||||
\(569\) | −25.2881 | −1.06013 | −0.530067 | − | 0.847956i | \(-0.677833\pi\) | ||||
−0.530067 | + | 0.847956i | \(0.677833\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.7514 | 0.784721 | 0.392360 | − | 0.919812i | \(-0.371659\pi\) | ||||
0.392360 | + | 0.919812i | \(0.371659\pi\) | |||||||
\(572\) | −0.646777 | −0.0270431 | ||||||||
\(573\) | 15.9712 | 0.667208 | ||||||||
\(574\) | −5.87177 | −0.245083 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −51.6213 | −2.15089 | ||||||||
\(577\) | −16.3012 | −0.678626 | −0.339313 | − | 0.940673i | \(-0.610195\pi\) | ||||
−0.339313 | + | 0.940673i | \(0.610195\pi\) | |||||||
\(578\) | −21.8189 | −0.907546 | ||||||||
\(579\) | −33.4986 | −1.39215 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.36410 | −0.181053 | ||||||||
\(582\) | 39.1867 | 1.62434 | ||||||||
\(583\) | −0.147601 | −0.00611301 | ||||||||
\(584\) | −13.2390 | −0.547834 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 48.1952 | 1.99093 | ||||||||
\(587\) | 8.75631 | 0.361412 | 0.180706 | − | 0.983537i | \(-0.442162\pi\) | ||||
0.180706 | + | 0.983537i | \(0.442162\pi\) | |||||||
\(588\) | −7.41873 | −0.305943 | ||||||||
\(589\) | −2.77345 | −0.114278 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.96621 | −0.286552 | ||||||||
\(592\) | 4.27684 | 0.175777 | ||||||||
\(593\) | −16.0251 | −0.658071 | −0.329036 | − | 0.944317i | \(-0.606724\pi\) | ||||
−0.329036 | + | 0.944317i | \(0.606724\pi\) | |||||||
\(594\) | 21.9576 | 0.900932 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.06471 | −0.371305 | ||||||||
\(597\) | −25.9859 | −1.06353 | ||||||||
\(598\) | −0.150124 | −0.00613901 | ||||||||
\(599\) | 0.892426 | 0.0364635 | 0.0182318 | − | 0.999834i | \(-0.494196\pi\) | ||||
0.0182318 | + | 0.999834i | \(0.494196\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.7711 | −1.54072 | −0.770358 | − | 0.637611i | \(-0.779923\pi\) | ||||
−0.770358 | + | 0.637611i | \(0.779923\pi\) | |||||||
\(602\) | −19.8471 | −0.808906 | ||||||||
\(603\) | −34.8086 | −1.41752 | ||||||||
\(604\) | 9.50532 | 0.386766 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −73.9146 | −3.00257 | ||||||||
\(607\) | −26.4468 | −1.07344 | −0.536722 | − | 0.843759i | \(-0.680338\pi\) | ||||
−0.536722 | + | 0.843759i | \(0.680338\pi\) | |||||||
\(608\) | −24.2680 | −0.984197 | ||||||||
\(609\) | 1.33042 | 0.0539115 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.475671 | −0.0192436 | ||||||||
\(612\) | 30.3117 | 1.22528 | ||||||||
\(613\) | 32.7728 | 1.32368 | 0.661841 | − | 0.749644i | \(-0.269775\pi\) | ||||
0.661841 | + | 0.749644i | \(0.269775\pi\) | |||||||
\(614\) | −25.8517 | −1.04329 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.79041 | −0.233302 | ||||||||
\(617\) | 29.5205 | 1.18845 | 0.594226 | − | 0.804298i | \(-0.297459\pi\) | ||||
0.594226 | + | 0.804298i | \(0.297459\pi\) | |||||||
\(618\) | 9.79144 | 0.393869 | ||||||||
\(619\) | 45.4373 | 1.82628 | 0.913139 | − | 0.407649i | \(-0.133651\pi\) | ||||
0.913139 | + | 0.407649i | \(0.133651\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.96497 | 0.118980 | ||||||||
\(622\) | −30.3875 | −1.21843 | ||||||||
\(623\) | −6.14427 | −0.246165 | ||||||||
\(624\) | 0.334098 | 0.0133746 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.7370 | −0.509073 | ||||||||
\(627\) | 29.5776 | 1.18122 | ||||||||
\(628\) | −41.1476 | −1.64197 | ||||||||
\(629\) | −6.21049 | −0.247628 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.03836 | 0.240383 | 0.120192 | − | 0.992751i | \(-0.461649\pi\) | ||||
0.120192 | + | 0.992751i | \(0.461649\pi\) | |||||||
\(632\) | −16.1480 | −0.642334 | ||||||||
\(633\) | 7.18252 | 0.285480 | ||||||||
\(634\) | 60.6956 | 2.41053 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.323335 | −0.0128211 | ||||||||
\(637\) | 0.0686513 | 0.00272007 | ||||||||
\(638\) | 3.69459 | 0.146270 | ||||||||
\(639\) | −1.80297 | −0.0713245 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.1481 | 1.03279 | 0.516394 | − | 0.856351i | \(-0.327274\pi\) | ||||
0.516394 | + | 0.856351i | \(0.327274\pi\) | |||||||
\(642\) | 10.7068 | 0.422564 | ||||||||
\(643\) | 23.3377 | 0.920350 | 0.460175 | − | 0.887828i | \(-0.347787\pi\) | ||||
0.460175 | + | 0.887828i | \(0.347787\pi\) | |||||||
\(644\) | −2.78189 | −0.109622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.9777 | 0.746669 | ||||||||
\(647\) | 28.5192 | 1.12121 | 0.560603 | − | 0.828085i | \(-0.310569\pi\) | ||||
0.560603 | + | 0.828085i | \(0.310569\pi\) | |||||||
\(648\) | −7.57175 | −0.297446 | ||||||||
\(649\) | −15.9805 | −0.627288 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.25842 | 0.0885143 | ||||||||
\(652\) | −65.4582 | −2.56354 | ||||||||
\(653\) | 22.4429 | 0.878258 | 0.439129 | − | 0.898424i | \(-0.355287\pi\) | ||||
0.439129 | + | 0.898424i | \(0.355287\pi\) | |||||||
\(654\) | −89.6184 | −3.50436 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.90009 | 0.191316 | ||||||||
\(657\) | −31.8380 | −1.24212 | ||||||||
\(658\) | −15.1515 | −0.590669 | ||||||||
\(659\) | −31.9129 | −1.24315 | −0.621576 | − | 0.783354i | \(-0.713507\pi\) | ||||
−0.621576 | + | 0.783354i | \(0.713507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.5132 | 1.73136 | 0.865681 | − | 0.500596i | \(-0.166886\pi\) | ||||
0.865681 | + | 0.500596i | \(0.166886\pi\) | |||||||
\(662\) | −20.5853 | −0.800072 | ||||||||
\(663\) | −0.485151 | −0.0188417 | ||||||||
\(664\) | −7.46171 | −0.289570 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −21.0727 | −0.816551 | ||||||||
\(667\) | 0.498885 | 0.0193169 | ||||||||
\(668\) | 58.0814 | 2.24724 | ||||||||
\(669\) | 14.4472 | 0.558561 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.8925 | −1.11538 | ||||||||
\(672\) | 19.7614 | 0.762311 | ||||||||
\(673\) | 31.5630 | 1.21667 | 0.608333 | − | 0.793682i | \(-0.291839\pi\) | ||||
0.608333 | + | 0.793682i | \(0.291839\pi\) | |||||||
\(674\) | 21.4438 | 0.825986 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −36.1514 | −1.39044 | ||||||||
\(677\) | 27.7525 | 1.06662 | 0.533308 | − | 0.845921i | \(-0.320949\pi\) | ||||
0.533308 | + | 0.845921i | \(0.320949\pi\) | |||||||
\(678\) | 70.0899 | 2.69179 | ||||||||
\(679\) | −6.71968 | −0.257878 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.6538 | 0.599854 | ||||||||
\(682\) | 6.27161 | 0.240153 | ||||||||
\(683\) | −35.4743 | −1.35739 | −0.678694 | − | 0.734421i | \(-0.737454\pi\) | ||||
−0.678694 | + | 0.734421i | \(0.737454\pi\) | |||||||
\(684\) | 37.4610 | 1.43236 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.18675 | 0.0834906 | ||||||||
\(687\) | −66.7981 | −2.54851 | ||||||||
\(688\) | 16.5627 | 0.631447 | ||||||||
\(689\) | 0.00299208 | 0.000113989 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.1938 | −1.56709 | −0.783543 | − | 0.621338i | \(-0.786590\pi\) | ||||
−0.783543 | + | 0.621338i | \(0.786590\pi\) | |||||||
\(692\) | −29.2158 | −1.11062 | ||||||||
\(693\) | −13.9251 | −0.528971 | ||||||||
\(694\) | 28.2702 | 1.07312 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.27475 | 0.0862241 | ||||||||
\(697\) | −7.11553 | −0.269520 | ||||||||
\(698\) | −43.2842 | −1.63833 | ||||||||
\(699\) | −33.4227 | −1.26416 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.69638 | 0.328458 | 0.164229 | − | 0.986422i | \(-0.447486\pi\) | ||||
0.164229 | + | 0.986422i | \(0.447486\pi\) | |||||||
\(702\) | −0.445111 | −0.0167996 | ||||||||
\(703\) | −7.67530 | −0.289479 | ||||||||
\(704\) | 42.5169 | 1.60242 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 47.1113 | 1.77306 | ||||||||
\(707\) | 12.6748 | 0.476684 | ||||||||
\(708\) | −35.0068 | −1.31564 | ||||||||
\(709\) | −43.8845 | −1.64812 | −0.824059 | − | 0.566503i | \(-0.808296\pi\) | ||||
−0.824059 | + | 0.566503i | \(0.808296\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −38.8337 | −1.45638 | ||||||||
\(712\) | −10.5054 | −0.393708 | ||||||||
\(713\) | 0.846864 | 0.0317153 | ||||||||
\(714\) | −15.4535 | −0.578333 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 61.4061 | 2.29485 | ||||||||
\(717\) | 37.9341 | 1.41667 | ||||||||
\(718\) | 65.2153 | 2.43381 | ||||||||
\(719\) | −18.6846 | −0.696819 | −0.348410 | − | 0.937342i | \(-0.613278\pi\) | ||||
−0.348410 | + | 0.937342i | \(0.613278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.67902 | −0.0625301 | ||||||||
\(722\) | −18.0945 | −0.673406 | ||||||||
\(723\) | 7.87434 | 0.292850 | ||||||||
\(724\) | 12.2723 | 0.456097 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.73598 | −0.101542 | ||||||||
\(727\) | −31.5659 | −1.17071 | −0.585357 | − | 0.810776i | \(-0.699046\pi\) | ||||
−0.585357 | + | 0.810776i | \(0.699046\pi\) | |||||||
\(728\) | 0.117380 | 0.00435037 | ||||||||
\(729\) | −41.9299 | −1.55296 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.0511 | −0.889561 | ||||||||
\(732\) | −63.2921 | −2.33934 | ||||||||
\(733\) | 29.9205 | 1.10514 | 0.552569 | − | 0.833467i | \(-0.313648\pi\) | ||||
0.552569 | + | 0.833467i | \(0.313648\pi\) | |||||||
\(734\) | −27.4060 | −1.01157 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.41015 | 0.273142 | ||||||||
\(737\) | 28.6695 | 1.05605 | ||||||||
\(738\) | −24.1436 | −0.888738 | ||||||||
\(739\) | 12.1667 | 0.447560 | 0.223780 | − | 0.974640i | \(-0.428160\pi\) | ||||
0.223780 | + | 0.974640i | \(0.428160\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.599579 | −0.0220261 | ||||||||
\(742\) | 0.0953066 | 0.00349882 | ||||||||
\(743\) | −36.1379 | −1.32577 | −0.662886 | − | 0.748720i | \(-0.730669\pi\) | ||||
−0.662886 | + | 0.748720i | \(0.730669\pi\) | |||||||
\(744\) | 3.86142 | 0.141567 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −53.4335 | −1.95634 | ||||||||
\(747\) | −17.9443 | −0.656549 | ||||||||
\(748\) | −24.9657 | −0.912835 | ||||||||
\(749\) | −1.83599 | −0.0670856 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.5432 | 1.00507 | 0.502533 | − | 0.864558i | \(-0.332401\pi\) | ||||
0.502533 | + | 0.864558i | \(0.332401\pi\) | |||||||
\(752\) | 12.6442 | 0.461087 | ||||||||
\(753\) | 70.2632 | 2.56053 | ||||||||
\(754\) | −0.0748943 | −0.00272749 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.24820 | −0.299984 | ||||||||
\(757\) | −19.1764 | −0.696977 | −0.348489 | − | 0.937313i | \(-0.613305\pi\) | ||||
−0.348489 | + | 0.937313i | \(0.613305\pi\) | |||||||
\(758\) | 61.3728 | 2.22916 | ||||||||
\(759\) | −9.03142 | −0.327820 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.83852 | −0.175396 | −0.0876981 | − | 0.996147i | \(-0.527951\pi\) | ||||
−0.0876981 | + | 0.996147i | \(0.527951\pi\) | |||||||
\(762\) | 66.9792 | 2.42640 | ||||||||
\(763\) | 15.3677 | 0.556347 | ||||||||
\(764\) | −16.6605 | −0.602756 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.2907 | 1.09445 | ||||||||
\(767\) | 0.323946 | 0.0116970 | ||||||||
\(768\) | 6.71122 | 0.242170 | ||||||||
\(769\) | −40.2108 | −1.45004 | −0.725019 | − | 0.688728i | \(-0.758169\pi\) | ||||
−0.725019 | + | 0.688728i | \(0.758169\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.6996 | 0.745479 | ||||||||
\(772\) | 34.9443 | 1.25767 | ||||||||
\(773\) | 15.1467 | 0.544790 | 0.272395 | − | 0.962186i | \(-0.412184\pi\) | ||||
0.272395 | + | 0.962186i | \(0.412184\pi\) | |||||||
\(774\) | −81.6073 | −2.93332 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.4893 | −0.412440 | ||||||||
\(777\) | 6.24997 | 0.224216 | ||||||||
\(778\) | −1.02595 | −0.0367820 | ||||||||
\(779\) | −8.79380 | −0.315071 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.48499 | 0.0531370 | ||||||||
\(782\) | −5.79479 | −0.207221 | ||||||||
\(783\) | 1.47918 | 0.0528614 | ||||||||
\(784\) | −1.82488 | −0.0651743 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27.9385 | 0.996533 | ||||||||
\(787\) | −43.3536 | −1.54539 | −0.772695 | − | 0.634778i | \(-0.781092\pi\) | ||||
−0.772695 | + | 0.634778i | \(0.781092\pi\) | |||||||
\(788\) | 7.26685 | 0.258871 | ||||||||
\(789\) | −26.9636 | −0.959930 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0189 | −0.427344 | ||||||||
\(792\) | −23.8090 | −0.846017 | ||||||||
\(793\) | 0.585692 | 0.0207985 | ||||||||
\(794\) | −25.8097 | −0.915953 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.1073 | 0.960794 | ||||||||
\(797\) | −31.6543 | −1.12125 | −0.560626 | − | 0.828069i | \(-0.689440\pi\) | ||||
−0.560626 | + | 0.828069i | \(0.689440\pi\) | |||||||
\(798\) | −19.0984 | −0.676076 | ||||||||
\(799\) | −18.3609 | −0.649564 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25.2641 | −0.892662 | ||||||||
\(802\) | −6.69750 | −0.236497 | ||||||||
\(803\) | 26.2228 | 0.925381 | ||||||||
\(804\) | 62.8034 | 2.21491 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.127134 | −0.00447811 | ||||||||
\(807\) | −40.2866 | −1.41816 | ||||||||
\(808\) | 21.6712 | 0.762392 | ||||||||
\(809\) | 9.67754 | 0.340244 | 0.170122 | − | 0.985423i | \(-0.445584\pi\) | ||||
0.170122 | + | 0.985423i | \(0.445584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.68358 | −0.129348 | −0.0646740 | − | 0.997906i | \(-0.520601\pi\) | ||||
−0.0646740 | + | 0.997906i | \(0.520601\pi\) | |||||||
\(812\) | −1.38784 | −0.0487037 | ||||||||
\(813\) | 8.72192 | 0.305891 | ||||||||
\(814\) | 17.3562 | 0.608333 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.8962 | 0.451458 | ||||||||
\(817\) | −29.7238 | −1.03990 | ||||||||
\(818\) | 76.2488 | 2.66598 | ||||||||
\(819\) | 0.282281 | 0.00986370 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.0592 | 0.700072 | 0.350036 | − | 0.936736i | \(-0.386169\pi\) | ||||
0.350036 | + | 0.936736i | \(0.386169\pi\) | |||||||
\(822\) | 84.6908 | 2.95393 | ||||||||
\(823\) | −41.2668 | −1.43847 | −0.719236 | − | 0.694766i | \(-0.755508\pi\) | ||||
−0.719236 | + | 0.694766i | \(0.755508\pi\) | |||||||
\(824\) | −2.87078 | −0.100008 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.3187 | 0.359032 | ||||||||
\(827\) | 6.03898 | 0.209996 | 0.104998 | − | 0.994472i | \(-0.466516\pi\) | ||||
0.104998 | + | 0.994472i | \(0.466516\pi\) | |||||||
\(828\) | −11.4386 | −0.397518 | ||||||||
\(829\) | −15.7649 | −0.547536 | −0.273768 | − | 0.961796i | \(-0.588270\pi\) | ||||
−0.273768 | + | 0.961796i | \(0.588270\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.7749 | −0.859431 | ||||||||
\(832\) | −0.861876 | −0.0298802 | ||||||||
\(833\) | 2.64995 | 0.0918154 | ||||||||
\(834\) | 91.6961 | 3.17518 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −30.8541 | −1.06711 | ||||||||
\(837\) | 2.51092 | 0.0867902 | ||||||||
\(838\) | 31.2523 | 1.07959 | ||||||||
\(839\) | −40.0524 | −1.38276 | −0.691381 | − | 0.722490i | \(-0.742997\pi\) | ||||
−0.691381 | + | 0.722490i | \(0.742997\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7511 | −0.991418 | ||||||||
\(842\) | 44.9426 | 1.54882 | ||||||||
\(843\) | 67.8889 | 2.33822 | ||||||||
\(844\) | −7.49249 | −0.257902 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −62.3002 | −2.14193 | ||||||||
\(847\) | 0.469162 | 0.0161206 | ||||||||
\(848\) | −0.0795350 | −0.00273124 | ||||||||
\(849\) | −7.71760 | −0.264867 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.34362 | 0.0803384 | ||||||||
\(852\) | 3.25301 | 0.111446 | ||||||||
\(853\) | 39.8281 | 1.36369 | 0.681844 | − | 0.731498i | \(-0.261178\pi\) | ||||
0.681844 | + | 0.731498i | \(0.261178\pi\) | |||||||
\(854\) | 18.6560 | 0.638397 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.13916 | −0.107294 | ||||||||
\(857\) | 15.6310 | 0.533945 | 0.266972 | − | 0.963704i | \(-0.413977\pi\) | ||||
0.266972 | + | 0.963704i | \(0.413977\pi\) | |||||||
\(858\) | 1.35583 | 0.0462872 | ||||||||
\(859\) | 9.42293 | 0.321506 | 0.160753 | − | 0.986995i | \(-0.448608\pi\) | ||||
0.160753 | + | 0.986995i | \(0.448608\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.16076 | 0.244038 | ||||||||
\(862\) | −40.2140 | −1.36969 | ||||||||
\(863\) | −9.46081 | −0.322050 | −0.161025 | − | 0.986950i | \(-0.551480\pi\) | ||||
−0.161025 | + | 0.986950i | \(0.551480\pi\) | |||||||
\(864\) | 21.9708 | 0.747463 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 33.1558 | 1.12668 | ||||||||
\(867\) | 26.6087 | 0.903678 | ||||||||
\(868\) | −2.35588 | −0.0799638 | ||||||||
\(869\) | 31.9847 | 1.08501 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.581170 | −0.0196922 | ||||||||
\(872\) | 26.2755 | 0.889801 | ||||||||
\(873\) | −27.6300 | −0.935135 | ||||||||
\(874\) | −7.16155 | −0.242243 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 57.4436 | 1.94084 | ||||||||
\(877\) | −41.0285 | −1.38544 | −0.692718 | − | 0.721209i | \(-0.743587\pi\) | ||||
−0.692718 | + | 0.721209i | \(0.743587\pi\) | |||||||
\(878\) | −82.0801 | −2.77007 | ||||||||
\(879\) | −58.7752 | −1.98244 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.1627 | 1.45419 | 0.727093 | − | 0.686538i | \(-0.240871\pi\) | ||||
0.727093 | + | 0.686538i | \(0.240871\pi\) | |||||||
\(882\) | 8.99151 | 0.302760 | ||||||||
\(883\) | 11.3463 | 0.381835 | 0.190917 | − | 0.981606i | \(-0.438854\pi\) | ||||
0.190917 | + | 0.981606i | \(0.438854\pi\) | |||||||
\(884\) | 0.506088 | 0.0170216 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −56.3352 | −1.89262 | ||||||||
\(887\) | 20.7827 | 0.697813 | 0.348907 | − | 0.937157i | \(-0.386553\pi\) | ||||
0.348907 | + | 0.937157i | \(0.386553\pi\) | |||||||
\(888\) | 10.6861 | 0.358604 | ||||||||
\(889\) | −11.4855 | −0.385212 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.9975 | 0.502435 | ||||||||
\(892\) | −15.0707 | −0.504604 | ||||||||
\(893\) | −22.6916 | −0.759344 | ||||||||
\(894\) | 19.0022 | 0.635529 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −12.6331 | −0.422041 | ||||||||
\(897\) | 0.183079 | 0.00611284 | ||||||||
\(898\) | 77.2783 | 2.57881 | ||||||||
\(899\) | 0.422488 | 0.0140908 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.115495 | 0.00384768 | ||||||||
\(902\) | 19.8854 | 0.662112 | ||||||||
\(903\) | 24.2040 | 0.805458 | ||||||||
\(904\) | −20.5499 | −0.683478 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −19.9259 | −0.661992 | ||||||||
\(907\) | 20.4570 | 0.679264 | 0.339632 | − | 0.940558i | \(-0.389697\pi\) | ||||
0.339632 | + | 0.940558i | \(0.389697\pi\) | |||||||
\(908\) | −16.3293 | −0.541908 | ||||||||
\(909\) | 52.1163 | 1.72859 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.8765 | 1.15551 | 0.577755 | − | 0.816210i | \(-0.303929\pi\) | ||||
0.577755 | + | 0.816210i | \(0.303929\pi\) | |||||||
\(912\) | 15.9379 | 0.527757 | ||||||||
\(913\) | 14.7795 | 0.489131 | ||||||||
\(914\) | −18.1633 | −0.600789 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 69.6809 | 2.30232 | ||||||||
\(917\) | −4.79086 | −0.158208 | ||||||||
\(918\) | −17.1813 | −0.567069 | ||||||||
\(919\) | −45.0649 | −1.48655 | −0.743277 | − | 0.668984i | \(-0.766730\pi\) | ||||
−0.743277 | + | 0.668984i | \(0.766730\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.5268 | 1.03884 | ||||||||
\(922\) | 45.0938 | 1.48508 | ||||||||
\(923\) | −0.0301027 | −0.000990843 0 | ||||||||
\(924\) | 25.1244 | 0.826531 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −30.1596 | −0.991107 | ||||||||
\(927\) | −6.90382 | −0.226751 | ||||||||
\(928\) | 3.69681 | 0.121354 | ||||||||
\(929\) | 30.5061 | 1.00087 | 0.500436 | − | 0.865774i | \(-0.333173\pi\) | ||||
0.500436 | + | 0.865774i | \(0.333173\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.27497 | 0.107333 | ||||||||
\(932\) | 34.8651 | 1.14204 | ||||||||
\(933\) | 37.0583 | 1.21324 | ||||||||
\(934\) | 36.5696 | 1.19659 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.482642 | 0.0157756 | ||||||||
\(937\) | −5.72001 | −0.186865 | −0.0934323 | − | 0.995626i | \(-0.529784\pi\) | ||||
−0.0934323 | + | 0.995626i | \(0.529784\pi\) | |||||||
\(938\) | −18.5120 | −0.604439 | ||||||||
\(939\) | 15.5331 | 0.506903 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.6577 | −1.06461 | −0.532305 | − | 0.846553i | \(-0.678674\pi\) | ||||
−0.532305 | + | 0.846553i | \(0.678674\pi\) | |||||||
\(942\) | 86.2572 | 2.81041 | ||||||||
\(943\) | 2.68516 | 0.0874407 | ||||||||
\(944\) | −8.61108 | −0.280267 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 67.2144 | 2.18533 | ||||||||
\(947\) | 9.01828 | 0.293055 | 0.146527 | − | 0.989207i | \(-0.453190\pi\) | ||||
0.146527 | + | 0.989207i | \(0.453190\pi\) | |||||||
\(948\) | 70.0657 | 2.27563 | ||||||||
\(949\) | −0.531571 | −0.0172555 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −74.0198 | −2.40026 | ||||||||
\(952\) | 4.53086 | 0.146846 | ||||||||
\(953\) | 14.4232 | 0.467212 | 0.233606 | − | 0.972331i | \(-0.424947\pi\) | ||||
0.233606 | + | 0.972331i | \(0.424947\pi\) | |||||||
\(954\) | 0.391883 | 0.0126877 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −39.5712 | −1.27982 | ||||||||
\(957\) | −4.50564 | −0.145647 | ||||||||
\(958\) | 80.7922 | 2.61028 | ||||||||
\(959\) | −14.5227 | −0.468962 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2828 | −0.976865 | ||||||||
\(962\) | −0.351833 | −0.0113436 | ||||||||
\(963\) | −7.54923 | −0.243271 | ||||||||
\(964\) | −8.21417 | −0.264561 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.83163 | 0.187629 | ||||||||
\(967\) | 22.8714 | 0.735493 | 0.367747 | − | 0.929926i | \(-0.380129\pi\) | ||||
0.367747 | + | 0.929926i | \(0.380129\pi\) | |||||||
\(968\) | 0.802169 | 0.0257827 | ||||||||
\(969\) | −23.1438 | −0.743487 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.18825 | −0.198590 | −0.0992952 | − | 0.995058i | \(-0.531659\pi\) | ||||
−0.0992952 | + | 0.995058i | \(0.531659\pi\) | |||||||
\(972\) | 57.5981 | 1.84746 | ||||||||
\(973\) | −15.7239 | −0.504086 | ||||||||
\(974\) | −2.26435 | −0.0725545 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.5688 | −0.498344 | ||||||||
\(977\) | −1.03108 | −0.0329871 | −0.0164936 | − | 0.999864i | \(-0.505250\pi\) | ||||
−0.0164936 | + | 0.999864i | \(0.505250\pi\) | |||||||
\(978\) | 137.219 | 4.38778 | ||||||||
\(979\) | 20.8083 | 0.665036 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 63.1889 | 2.01747 | ||||||||
\(982\) | 7.64908 | 0.244092 | ||||||||
\(983\) | −57.5700 | −1.83620 | −0.918098 | − | 0.396352i | \(-0.870276\pi\) | ||||
−0.918098 | + | 0.396352i | \(0.870276\pi\) | |||||||
\(984\) | 12.2434 | 0.390306 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.89093 | −0.0920660 | ||||||||
\(987\) | 18.4777 | 0.588151 | ||||||||
\(988\) | 0.625454 | 0.0198984 | ||||||||
\(989\) | 9.07605 | 0.288602 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.2309 | 0.547359 | 0.273680 | − | 0.961821i | \(-0.411759\pi\) | ||||
0.273680 | + | 0.961821i | \(0.411759\pi\) | |||||||
\(992\) | 6.27539 | 0.199244 | ||||||||
\(993\) | 25.1043 | 0.796661 | ||||||||
\(994\) | −0.958862 | −0.0304133 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 32.3761 | 1.02588 | ||||||||
\(997\) | 4.57213 | 0.144801 | 0.0724004 | − | 0.997376i | \(-0.476934\pi\) | ||||
0.0724004 | + | 0.997376i | \(0.476934\pi\) | |||||||
\(998\) | 28.3593 | 0.897699 | ||||||||
\(999\) | 6.94877 | 0.219849 |
(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 | 4025.2.a.u.1.8 | ✓ | 8 | |
5.4 | even | 2 | 4025.2.a.v.1.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4025.2.a.u.1.8 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4025.2.a.v.1.1 | yes | 8 | 5.4 | even | 2 |