Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(1.84416\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.844163 | 0.487378 | 0.243689 | − | 0.969853i | \(-0.421642\pi\) | ||||
0.243689 | + | 0.969853i | \(0.421642\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.844163 | 0.344628 | ||||||||
\(7\) | −0.532701 | −0.201342 | −0.100671 | − | 0.994920i | \(-0.532099\pi\) | ||||
−0.100671 | + | 0.994920i | \(0.532099\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.28739 | −0.762463 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.961430 | −0.289882 | −0.144941 | − | 0.989440i | \(-0.546299\pi\) | ||||
−0.144941 | + | 0.989440i | \(0.546299\pi\) | |||||||
\(12\) | 0.844163 | 0.243689 | ||||||||
\(13\) | −1.20269 | −0.333566 | −0.166783 | − | 0.985994i | \(-0.553338\pi\) | ||||
−0.166783 | + | 0.985994i | \(0.553338\pi\) | |||||||
\(14\) | −0.532701 | −0.142370 | ||||||||
\(15\) | 0.844163 | 0.217962 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.49260 | −1.33215 | −0.666076 | − | 0.745884i | \(-0.732027\pi\) | ||||
−0.666076 | + | 0.745884i | \(0.732027\pi\) | |||||||
\(18\) | −2.28739 | −0.539143 | ||||||||
\(19\) | −4.34072 | −0.995829 | −0.497914 | − | 0.867226i | \(-0.665901\pi\) | ||||
−0.497914 | + | 0.867226i | \(0.665901\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −0.449687 | −0.0981297 | ||||||||
\(22\) | −0.961430 | −0.204978 | ||||||||
\(23\) | 6.60521 | 1.37728 | 0.688641 | − | 0.725103i | \(-0.258208\pi\) | ||||
0.688641 | + | 0.725103i | \(0.258208\pi\) | |||||||
\(24\) | 0.844163 | 0.172314 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.20269 | −0.235867 | ||||||||
\(27\) | −4.46342 | −0.858985 | ||||||||
\(28\) | −0.532701 | −0.100671 | ||||||||
\(29\) | −7.33783 | −1.36260 | −0.681300 | − | 0.732004i | \(-0.738585\pi\) | ||||
−0.681300 | + | 0.732004i | \(0.738585\pi\) | |||||||
\(30\) | 0.844163 | 0.154122 | ||||||||
\(31\) | 7.02057 | 1.26093 | 0.630466 | − | 0.776217i | \(-0.282864\pi\) | ||||
0.630466 | + | 0.776217i | \(0.282864\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.811604 | −0.141282 | ||||||||
\(34\) | −5.49260 | −0.941974 | ||||||||
\(35\) | −0.532701 | −0.0900429 | ||||||||
\(36\) | −2.28739 | −0.381231 | ||||||||
\(37\) | −5.84241 | −0.960486 | −0.480243 | − | 0.877136i | \(-0.659451\pi\) | ||||
−0.480243 | + | 0.877136i | \(0.659451\pi\) | |||||||
\(38\) | −4.34072 | −0.704157 | ||||||||
\(39\) | −1.01527 | −0.162573 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 9.20135 | 1.43701 | 0.718504 | − | 0.695522i | \(-0.244827\pi\) | ||||
0.718504 | + | 0.695522i | \(0.244827\pi\) | |||||||
\(42\) | −0.449687 | −0.0693881 | ||||||||
\(43\) | −9.44089 | −1.43972 | −0.719861 | − | 0.694118i | \(-0.755795\pi\) | ||||
−0.719861 | + | 0.694118i | \(0.755795\pi\) | |||||||
\(44\) | −0.961430 | −0.144941 | ||||||||
\(45\) | −2.28739 | −0.340984 | ||||||||
\(46\) | 6.60521 | 0.973885 | ||||||||
\(47\) | −7.28325 | −1.06237 | −0.531186 | − | 0.847255i | \(-0.678253\pi\) | ||||
−0.531186 | + | 0.847255i | \(0.678253\pi\) | |||||||
\(48\) | 0.844163 | 0.121844 | ||||||||
\(49\) | −6.71623 | −0.959461 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −4.63665 | −0.649261 | ||||||||
\(52\) | −1.20269 | −0.166783 | ||||||||
\(53\) | 6.24445 | 0.857742 | 0.428871 | − | 0.903366i | \(-0.358912\pi\) | ||||
0.428871 | + | 0.903366i | \(0.358912\pi\) | |||||||
\(54\) | −4.46342 | −0.607394 | ||||||||
\(55\) | −0.961430 | −0.129639 | ||||||||
\(56\) | −0.532701 | −0.0711852 | ||||||||
\(57\) | −3.66427 | −0.485345 | ||||||||
\(58\) | −7.33783 | −0.963504 | ||||||||
\(59\) | −9.77782 | −1.27296 | −0.636482 | − | 0.771292i | \(-0.719611\pi\) | ||||
−0.636482 | + | 0.771292i | \(0.719611\pi\) | |||||||
\(60\) | 0.844163 | 0.108981 | ||||||||
\(61\) | −5.61164 | −0.718497 | −0.359249 | − | 0.933242i | \(-0.616967\pi\) | ||||
−0.359249 | + | 0.933242i | \(0.616967\pi\) | |||||||
\(62\) | 7.02057 | 0.891614 | ||||||||
\(63\) | 1.21849 | 0.153516 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.20269 | −0.149175 | ||||||||
\(66\) | −0.811604 | −0.0999015 | ||||||||
\(67\) | 11.5528 | 1.41140 | 0.705700 | − | 0.708511i | \(-0.250633\pi\) | ||||
0.705700 | + | 0.708511i | \(0.250633\pi\) | |||||||
\(68\) | −5.49260 | −0.666076 | ||||||||
\(69\) | 5.57587 | 0.671256 | ||||||||
\(70\) | −0.532701 | −0.0636700 | ||||||||
\(71\) | −3.84683 | −0.456534 | −0.228267 | − | 0.973599i | \(-0.573306\pi\) | ||||
−0.228267 | + | 0.973599i | \(0.573306\pi\) | |||||||
\(72\) | −2.28739 | −0.269571 | ||||||||
\(73\) | 7.54343 | 0.882891 | 0.441446 | − | 0.897288i | \(-0.354466\pi\) | ||||
0.441446 | + | 0.897288i | \(0.354466\pi\) | |||||||
\(74\) | −5.84241 | −0.679166 | ||||||||
\(75\) | 0.844163 | 0.0974755 | ||||||||
\(76\) | −4.34072 | −0.497914 | ||||||||
\(77\) | 0.512155 | 0.0583655 | ||||||||
\(78\) | −1.01527 | −0.114956 | ||||||||
\(79\) | −0.0908517 | −0.0102216 | −0.00511081 | − | 0.999987i | \(-0.501627\pi\) | ||||
−0.00511081 | + | 0.999987i | \(0.501627\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 3.09431 | 0.343813 | ||||||||
\(82\) | 9.20135 | 1.01612 | ||||||||
\(83\) | −13.2425 | −1.45355 | −0.726775 | − | 0.686876i | \(-0.758982\pi\) | ||||
−0.726775 | + | 0.686876i | \(0.758982\pi\) | |||||||
\(84\) | −0.449687 | −0.0490648 | ||||||||
\(85\) | −5.49260 | −0.595756 | ||||||||
\(86\) | −9.44089 | −1.01804 | ||||||||
\(87\) | −6.19432 | −0.664101 | ||||||||
\(88\) | −0.961430 | −0.102489 | ||||||||
\(89\) | −14.0969 | −1.49426 | −0.747132 | − | 0.664675i | \(-0.768570\pi\) | ||||
−0.747132 | + | 0.664675i | \(0.768570\pi\) | |||||||
\(90\) | −2.28739 | −0.241112 | ||||||||
\(91\) | 0.640674 | 0.0671609 | ||||||||
\(92\) | 6.60521 | 0.688641 | ||||||||
\(93\) | 5.92651 | 0.614550 | ||||||||
\(94\) | −7.28325 | −0.751210 | ||||||||
\(95\) | −4.34072 | −0.445348 | ||||||||
\(96\) | 0.844163 | 0.0861570 | ||||||||
\(97\) | 8.35252 | 0.848070 | 0.424035 | − | 0.905646i | \(-0.360613\pi\) | ||||
0.424035 | + | 0.905646i | \(0.360613\pi\) | |||||||
\(98\) | −6.71623 | −0.678442 | ||||||||
\(99\) | 2.19917 | 0.221024 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.85205 | 0.980315 | 0.490158 | − | 0.871634i | \(-0.336939\pi\) | ||||
0.490158 | + | 0.871634i | \(0.336939\pi\) | |||||||
\(102\) | −4.63665 | −0.459097 | ||||||||
\(103\) | −15.3763 | −1.51507 | −0.757534 | − | 0.652795i | \(-0.773596\pi\) | ||||
−0.757534 | + | 0.652795i | \(0.773596\pi\) | |||||||
\(104\) | −1.20269 | −0.117933 | ||||||||
\(105\) | −0.449687 | −0.0438849 | ||||||||
\(106\) | 6.24445 | 0.606515 | ||||||||
\(107\) | −4.15714 | −0.401886 | −0.200943 | − | 0.979603i | \(-0.564401\pi\) | ||||
−0.200943 | + | 0.979603i | \(0.564401\pi\) | |||||||
\(108\) | −4.46342 | −0.429493 | ||||||||
\(109\) | −0.609510 | −0.0583805 | −0.0291902 | − | 0.999574i | \(-0.509293\pi\) | ||||
−0.0291902 | + | 0.999574i | \(0.509293\pi\) | |||||||
\(110\) | −0.961430 | −0.0916688 | ||||||||
\(111\) | −4.93194 | −0.468119 | ||||||||
\(112\) | −0.532701 | −0.0503355 | ||||||||
\(113\) | −5.36554 | −0.504748 | −0.252374 | − | 0.967630i | \(-0.581211\pi\) | ||||
−0.252374 | + | 0.967630i | \(0.581211\pi\) | |||||||
\(114\) | −3.66427 | −0.343191 | ||||||||
\(115\) | 6.60521 | 0.615939 | ||||||||
\(116\) | −7.33783 | −0.681300 | ||||||||
\(117\) | 2.75102 | 0.254332 | ||||||||
\(118\) | −9.77782 | −0.900121 | ||||||||
\(119\) | 2.92592 | 0.268218 | ||||||||
\(120\) | 0.844163 | 0.0770612 | ||||||||
\(121\) | −10.0757 | −0.915968 | ||||||||
\(122\) | −5.61164 | −0.508054 | ||||||||
\(123\) | 7.76744 | 0.700366 | ||||||||
\(124\) | 7.02057 | 0.630466 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 1.21849 | 0.108552 | ||||||||
\(127\) | −5.62604 | −0.499231 | −0.249615 | − | 0.968345i | \(-0.580304\pi\) | ||||
−0.249615 | + | 0.968345i | \(0.580304\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.96965 | −0.701689 | ||||||||
\(130\) | −1.20269 | −0.105483 | ||||||||
\(131\) | 0.518832 | 0.0453306 | 0.0226653 | − | 0.999743i | \(-0.492785\pi\) | ||||
0.0226653 | + | 0.999743i | \(0.492785\pi\) | |||||||
\(132\) | −0.811604 | −0.0706411 | ||||||||
\(133\) | 2.31231 | 0.200502 | ||||||||
\(134\) | 11.5528 | 0.998011 | ||||||||
\(135\) | −4.46342 | −0.384150 | ||||||||
\(136\) | −5.49260 | −0.470987 | ||||||||
\(137\) | −4.41924 | −0.377561 | −0.188780 | − | 0.982019i | \(-0.560453\pi\) | ||||
−0.188780 | + | 0.982019i | \(0.560453\pi\) | |||||||
\(138\) | 5.57587 | 0.474650 | ||||||||
\(139\) | −22.4968 | −1.90815 | −0.954076 | − | 0.299563i | \(-0.903159\pi\) | ||||
−0.954076 | + | 0.299563i | \(0.903159\pi\) | |||||||
\(140\) | −0.532701 | −0.0450215 | ||||||||
\(141\) | −6.14825 | −0.517776 | ||||||||
\(142\) | −3.84683 | −0.322819 | ||||||||
\(143\) | 1.15630 | 0.0966948 | ||||||||
\(144\) | −2.28739 | −0.190616 | ||||||||
\(145\) | −7.33783 | −0.609373 | ||||||||
\(146\) | 7.54343 | 0.624298 | ||||||||
\(147\) | −5.66959 | −0.467620 | ||||||||
\(148\) | −5.84241 | −0.480243 | ||||||||
\(149\) | 19.7775 | 1.62023 | 0.810117 | − | 0.586268i | \(-0.199403\pi\) | ||||
0.810117 | + | 0.586268i | \(0.199403\pi\) | |||||||
\(150\) | 0.844163 | 0.0689256 | ||||||||
\(151\) | −6.89037 | −0.560730 | −0.280365 | − | 0.959893i | \(-0.590456\pi\) | ||||
−0.280365 | + | 0.959893i | \(0.590456\pi\) | |||||||
\(152\) | −4.34072 | −0.352079 | ||||||||
\(153\) | 12.5637 | 1.01572 | ||||||||
\(154\) | 0.512155 | 0.0412706 | ||||||||
\(155\) | 7.02057 | 0.563906 | ||||||||
\(156\) | −1.01527 | −0.0812863 | ||||||||
\(157\) | −6.83852 | −0.545774 | −0.272887 | − | 0.962046i | \(-0.587978\pi\) | ||||
−0.272887 | + | 0.962046i | \(0.587978\pi\) | |||||||
\(158\) | −0.0908517 | −0.00722777 | ||||||||
\(159\) | 5.27134 | 0.418044 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −3.51860 | −0.277305 | ||||||||
\(162\) | 3.09431 | 0.243112 | ||||||||
\(163\) | −2.76885 | −0.216873 | −0.108437 | − | 0.994103i | \(-0.534584\pi\) | ||||
−0.108437 | + | 0.994103i | \(0.534584\pi\) | |||||||
\(164\) | 9.20135 | 0.718504 | ||||||||
\(165\) | −0.811604 | −0.0631833 | ||||||||
\(166\) | −13.2425 | −1.02782 | ||||||||
\(167\) | −4.26084 | −0.329714 | −0.164857 | − | 0.986317i | \(-0.552716\pi\) | ||||
−0.164857 | + | 0.986317i | \(0.552716\pi\) | |||||||
\(168\) | −0.449687 | −0.0346941 | ||||||||
\(169\) | −11.5535 | −0.888734 | ||||||||
\(170\) | −5.49260 | −0.421263 | ||||||||
\(171\) | 9.92891 | 0.759283 | ||||||||
\(172\) | −9.44089 | −0.719861 | ||||||||
\(173\) | 8.79251 | 0.668482 | 0.334241 | − | 0.942488i | \(-0.391520\pi\) | ||||
0.334241 | + | 0.942488i | \(0.391520\pi\) | |||||||
\(174\) | −6.19432 | −0.469590 | ||||||||
\(175\) | −0.532701 | −0.0402684 | ||||||||
\(176\) | −0.961430 | −0.0724705 | ||||||||
\(177\) | −8.25407 | −0.620414 | ||||||||
\(178\) | −14.0969 | −1.05660 | ||||||||
\(179\) | 11.7877 | 0.881051 | 0.440525 | − | 0.897740i | \(-0.354792\pi\) | ||||
0.440525 | + | 0.897740i | \(0.354792\pi\) | |||||||
\(180\) | −2.28739 | −0.170492 | ||||||||
\(181\) | 24.3416 | 1.80930 | 0.904648 | − | 0.426159i | \(-0.140133\pi\) | ||||
0.904648 | + | 0.426159i | \(0.140133\pi\) | |||||||
\(182\) | 0.640674 | 0.0474899 | ||||||||
\(183\) | −4.73714 | −0.350180 | ||||||||
\(184\) | 6.60521 | 0.486942 | ||||||||
\(185\) | −5.84241 | −0.429542 | ||||||||
\(186\) | 5.92651 | 0.434553 | ||||||||
\(187\) | 5.28076 | 0.386167 | ||||||||
\(188\) | −7.28325 | −0.531186 | ||||||||
\(189\) | 2.37767 | 0.172950 | ||||||||
\(190\) | −4.34072 | −0.314909 | ||||||||
\(191\) | 12.8086 | 0.926796 | 0.463398 | − | 0.886150i | \(-0.346630\pi\) | ||||
0.463398 | + | 0.886150i | \(0.346630\pi\) | |||||||
\(192\) | 0.844163 | 0.0609222 | ||||||||
\(193\) | 20.6520 | 1.48657 | 0.743283 | − | 0.668978i | \(-0.233268\pi\) | ||||
0.743283 | + | 0.668978i | \(0.233268\pi\) | |||||||
\(194\) | 8.35252 | 0.599676 | ||||||||
\(195\) | −1.01527 | −0.0727047 | ||||||||
\(196\) | −6.71623 | −0.479731 | ||||||||
\(197\) | −12.6133 | −0.898659 | −0.449329 | − | 0.893366i | \(-0.648337\pi\) | ||||
−0.449329 | + | 0.893366i | \(0.648337\pi\) | |||||||
\(198\) | 2.19917 | 0.156288 | ||||||||
\(199\) | 22.9659 | 1.62801 | 0.814005 | − | 0.580858i | \(-0.197283\pi\) | ||||
0.814005 | + | 0.580858i | \(0.197283\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 9.75245 | 0.687885 | ||||||||
\(202\) | 9.85205 | 0.693188 | ||||||||
\(203\) | 3.90887 | 0.274349 | ||||||||
\(204\) | −4.63665 | −0.324631 | ||||||||
\(205\) | 9.20135 | 0.642650 | ||||||||
\(206\) | −15.3763 | −1.07132 | ||||||||
\(207\) | −15.1087 | −1.05013 | ||||||||
\(208\) | −1.20269 | −0.0833915 | ||||||||
\(209\) | 4.17330 | 0.288673 | ||||||||
\(210\) | −0.449687 | −0.0310313 | ||||||||
\(211\) | −20.3893 | −1.40366 | −0.701830 | − | 0.712344i | \(-0.747633\pi\) | ||||
−0.701830 | + | 0.712344i | \(0.747633\pi\) | |||||||
\(212\) | 6.24445 | 0.428871 | ||||||||
\(213\) | −3.24735 | −0.222505 | ||||||||
\(214\) | −4.15714 | −0.284176 | ||||||||
\(215\) | −9.44089 | −0.643863 | ||||||||
\(216\) | −4.46342 | −0.303697 | ||||||||
\(217\) | −3.73987 | −0.253879 | ||||||||
\(218\) | −0.609510 | −0.0412812 | ||||||||
\(219\) | 6.36788 | 0.430302 | ||||||||
\(220\) | −0.961430 | −0.0648196 | ||||||||
\(221\) | 6.60589 | 0.444360 | ||||||||
\(222\) | −4.93194 | −0.331010 | ||||||||
\(223\) | −18.2859 | −1.22452 | −0.612258 | − | 0.790658i | \(-0.709739\pi\) | ||||
−0.612258 | + | 0.790658i | \(0.709739\pi\) | |||||||
\(224\) | −0.532701 | −0.0355926 | ||||||||
\(225\) | −2.28739 | −0.152493 | ||||||||
\(226\) | −5.36554 | −0.356911 | ||||||||
\(227\) | 23.9381 | 1.58883 | 0.794414 | − | 0.607376i | \(-0.207778\pi\) | ||||
0.794414 | + | 0.607376i | \(0.207778\pi\) | |||||||
\(228\) | −3.66427 | −0.242672 | ||||||||
\(229\) | 23.1069 | 1.52695 | 0.763473 | − | 0.645840i | \(-0.223493\pi\) | ||||
0.763473 | + | 0.645840i | \(0.223493\pi\) | |||||||
\(230\) | 6.60521 | 0.435534 | ||||||||
\(231\) | 0.432342 | 0.0284460 | ||||||||
\(232\) | −7.33783 | −0.481752 | ||||||||
\(233\) | 10.5496 | 0.691125 | 0.345562 | − | 0.938396i | \(-0.387688\pi\) | ||||
0.345562 | + | 0.938396i | \(0.387688\pi\) | |||||||
\(234\) | 2.75102 | 0.179840 | ||||||||
\(235\) | −7.28325 | −0.475107 | ||||||||
\(236\) | −9.77782 | −0.636482 | ||||||||
\(237\) | −0.0766937 | −0.00498179 | ||||||||
\(238\) | 2.92592 | 0.189659 | ||||||||
\(239\) | 2.97603 | 0.192503 | 0.0962515 | − | 0.995357i | \(-0.469315\pi\) | ||||
0.0962515 | + | 0.995357i | \(0.469315\pi\) | |||||||
\(240\) | 0.844163 | 0.0544905 | ||||||||
\(241\) | −22.2492 | −1.43320 | −0.716600 | − | 0.697484i | \(-0.754303\pi\) | ||||
−0.716600 | + | 0.697484i | \(0.754303\pi\) | |||||||
\(242\) | −10.0757 | −0.647687 | ||||||||
\(243\) | 16.0024 | 1.02655 | ||||||||
\(244\) | −5.61164 | −0.359249 | ||||||||
\(245\) | −6.71623 | −0.429084 | ||||||||
\(246\) | 7.76744 | 0.495234 | ||||||||
\(247\) | 5.22053 | 0.332175 | ||||||||
\(248\) | 7.02057 | 0.445807 | ||||||||
\(249\) | −11.1788 | −0.708428 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −12.4001 | −0.782689 | −0.391344 | − | 0.920244i | \(-0.627990\pi\) | ||||
−0.391344 | + | 0.920244i | \(0.627990\pi\) | |||||||
\(252\) | 1.21849 | 0.0767579 | ||||||||
\(253\) | −6.35045 | −0.399249 | ||||||||
\(254\) | −5.62604 | −0.353009 | ||||||||
\(255\) | −4.63665 | −0.290358 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.07976 | −0.129732 | −0.0648659 | − | 0.997894i | \(-0.520662\pi\) | ||||
−0.0648659 | + | 0.997894i | \(0.520662\pi\) | |||||||
\(258\) | −7.96965 | −0.496169 | ||||||||
\(259\) | 3.11226 | 0.193386 | ||||||||
\(260\) | −1.20269 | −0.0745876 | ||||||||
\(261\) | 16.7845 | 1.03893 | ||||||||
\(262\) | 0.518832 | 0.0320536 | ||||||||
\(263\) | 4.98966 | 0.307675 | 0.153838 | − | 0.988096i | \(-0.450837\pi\) | ||||
0.153838 | + | 0.988096i | \(0.450837\pi\) | |||||||
\(264\) | −0.811604 | −0.0499508 | ||||||||
\(265\) | 6.24445 | 0.383594 | ||||||||
\(266\) | 2.31231 | 0.141777 | ||||||||
\(267\) | −11.9001 | −0.728271 | ||||||||
\(268\) | 11.5528 | 0.705700 | ||||||||
\(269\) | 0.908252 | 0.0553771 | 0.0276886 | − | 0.999617i | \(-0.491185\pi\) | ||||
0.0276886 | + | 0.999617i | \(0.491185\pi\) | |||||||
\(270\) | −4.46342 | −0.271635 | ||||||||
\(271\) | 16.6795 | 1.01321 | 0.506603 | − | 0.862180i | \(-0.330901\pi\) | ||||
0.506603 | + | 0.862180i | \(0.330901\pi\) | |||||||
\(272\) | −5.49260 | −0.333038 | ||||||||
\(273\) | 0.540833 | 0.0327327 | ||||||||
\(274\) | −4.41924 | −0.266976 | ||||||||
\(275\) | −0.961430 | −0.0579764 | ||||||||
\(276\) | 5.57587 | 0.335628 | ||||||||
\(277\) | 27.1449 | 1.63098 | 0.815489 | − | 0.578772i | \(-0.196468\pi\) | ||||
0.815489 | + | 0.578772i | \(0.196468\pi\) | |||||||
\(278\) | −22.4968 | −1.34927 | ||||||||
\(279\) | −16.0588 | −0.961414 | ||||||||
\(280\) | −0.532701 | −0.0318350 | ||||||||
\(281\) | −15.7002 | −0.936595 | −0.468297 | − | 0.883571i | \(-0.655132\pi\) | ||||
−0.468297 | + | 0.883571i | \(0.655132\pi\) | |||||||
\(282\) | −6.14825 | −0.366123 | ||||||||
\(283\) | 17.5279 | 1.04192 | 0.520962 | − | 0.853580i | \(-0.325573\pi\) | ||||
0.520962 | + | 0.853580i | \(0.325573\pi\) | |||||||
\(284\) | −3.84683 | −0.228267 | ||||||||
\(285\) | −3.66427 | −0.217053 | ||||||||
\(286\) | 1.15630 | 0.0683736 | ||||||||
\(287\) | −4.90157 | −0.289330 | ||||||||
\(288\) | −2.28739 | −0.134786 | ||||||||
\(289\) | 13.1687 | 0.774628 | ||||||||
\(290\) | −7.33783 | −0.430892 | ||||||||
\(291\) | 7.05089 | 0.413330 | ||||||||
\(292\) | 7.54343 | 0.441446 | ||||||||
\(293\) | −27.7763 | −1.62271 | −0.811355 | − | 0.584553i | \(-0.801270\pi\) | ||||
−0.811355 | + | 0.584553i | \(0.801270\pi\) | |||||||
\(294\) | −5.66959 | −0.330657 | ||||||||
\(295\) | −9.77782 | −0.569287 | ||||||||
\(296\) | −5.84241 | −0.339583 | ||||||||
\(297\) | 4.29127 | 0.249005 | ||||||||
\(298\) | 19.7775 | 1.14568 | ||||||||
\(299\) | −7.94401 | −0.459414 | ||||||||
\(300\) | 0.844163 | 0.0487378 | ||||||||
\(301\) | 5.02917 | 0.289877 | ||||||||
\(302\) | −6.89037 | −0.396496 | ||||||||
\(303\) | 8.31673 | 0.477784 | ||||||||
\(304\) | −4.34072 | −0.248957 | ||||||||
\(305\) | −5.61164 | −0.321322 | ||||||||
\(306\) | 12.5637 | 0.718220 | ||||||||
\(307\) | 30.2322 | 1.72545 | 0.862723 | − | 0.505677i | \(-0.168757\pi\) | ||||
0.862723 | + | 0.505677i | \(0.168757\pi\) | |||||||
\(308\) | 0.512155 | 0.0291827 | ||||||||
\(309\) | −12.9801 | −0.738411 | ||||||||
\(310\) | 7.02057 | 0.398742 | ||||||||
\(311\) | 12.3450 | 0.700021 | 0.350011 | − | 0.936746i | \(-0.386178\pi\) | ||||
0.350011 | + | 0.936746i | \(0.386178\pi\) | |||||||
\(312\) | −1.01527 | −0.0574781 | ||||||||
\(313\) | −31.9710 | −1.80711 | −0.903554 | − | 0.428474i | \(-0.859051\pi\) | ||||
−0.903554 | + | 0.428474i | \(0.859051\pi\) | |||||||
\(314\) | −6.83852 | −0.385920 | ||||||||
\(315\) | 1.21849 | 0.0686544 | ||||||||
\(316\) | −0.0908517 | −0.00511081 | ||||||||
\(317\) | −8.44300 | −0.474206 | −0.237103 | − | 0.971485i | \(-0.576198\pi\) | ||||
−0.237103 | + | 0.971485i | \(0.576198\pi\) | |||||||
\(318\) | 5.27134 | 0.295602 | ||||||||
\(319\) | 7.05481 | 0.394993 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −3.50930 | −0.195870 | ||||||||
\(322\) | −3.51860 | −0.196084 | ||||||||
\(323\) | 23.8418 | 1.32660 | ||||||||
\(324\) | 3.09431 | 0.171906 | ||||||||
\(325\) | −1.20269 | −0.0667132 | ||||||||
\(326\) | −2.76885 | −0.153352 | ||||||||
\(327\) | −0.514526 | −0.0284533 | ||||||||
\(328\) | 9.20135 | 0.508059 | ||||||||
\(329\) | 3.87980 | 0.213900 | ||||||||
\(330\) | −0.811604 | −0.0446773 | ||||||||
\(331\) | 16.6072 | 0.912815 | 0.456408 | − | 0.889771i | \(-0.349136\pi\) | ||||
0.456408 | + | 0.889771i | \(0.349136\pi\) | |||||||
\(332\) | −13.2425 | −0.726775 | ||||||||
\(333\) | 13.3639 | 0.732335 | ||||||||
\(334\) | −4.26084 | −0.233143 | ||||||||
\(335\) | 11.5528 | 0.631197 | ||||||||
\(336\) | −0.449687 | −0.0245324 | ||||||||
\(337\) | −14.1086 | −0.768543 | −0.384272 | − | 0.923220i | \(-0.625547\pi\) | ||||
−0.384272 | + | 0.923220i | \(0.625547\pi\) | |||||||
\(338\) | −11.5535 | −0.628430 | ||||||||
\(339\) | −4.52939 | −0.246003 | ||||||||
\(340\) | −5.49260 | −0.297878 | ||||||||
\(341\) | −6.74979 | −0.365522 | ||||||||
\(342\) | 9.92891 | 0.536894 | ||||||||
\(343\) | 7.30665 | 0.394522 | ||||||||
\(344\) | −9.44089 | −0.509019 | ||||||||
\(345\) | 5.57587 | 0.300195 | ||||||||
\(346\) | 8.79251 | 0.472688 | ||||||||
\(347\) | −33.9642 | −1.82329 | −0.911647 | − | 0.410975i | \(-0.865188\pi\) | ||||
−0.911647 | + | 0.410975i | \(0.865188\pi\) | |||||||
\(348\) | −6.19432 | −0.332050 | ||||||||
\(349\) | 13.0855 | 0.700453 | 0.350227 | − | 0.936665i | \(-0.386105\pi\) | ||||
0.350227 | + | 0.936665i | \(0.386105\pi\) | |||||||
\(350\) | −0.532701 | −0.0284741 | ||||||||
\(351\) | 5.36810 | 0.286528 | ||||||||
\(352\) | −0.961430 | −0.0512444 | ||||||||
\(353\) | −16.0428 | −0.853873 | −0.426936 | − | 0.904282i | \(-0.640407\pi\) | ||||
−0.426936 | + | 0.904282i | \(0.640407\pi\) | |||||||
\(354\) | −8.25407 | −0.438699 | ||||||||
\(355\) | −3.84683 | −0.204168 | ||||||||
\(356\) | −14.0969 | −0.747132 | ||||||||
\(357\) | 2.46995 | 0.130724 | ||||||||
\(358\) | 11.7877 | 0.622997 | ||||||||
\(359\) | 0.802407 | 0.0423494 | 0.0211747 | − | 0.999776i | \(-0.493259\pi\) | ||||
0.0211747 | + | 0.999776i | \(0.493259\pi\) | |||||||
\(360\) | −2.28739 | −0.120556 | ||||||||
\(361\) | −0.158171 | −0.00832478 | ||||||||
\(362\) | 24.3416 | 1.27937 | ||||||||
\(363\) | −8.50549 | −0.446423 | ||||||||
\(364\) | 0.640674 | 0.0335804 | ||||||||
\(365\) | 7.54343 | 0.394841 | ||||||||
\(366\) | −4.73714 | −0.247614 | ||||||||
\(367\) | 7.01696 | 0.366282 | 0.183141 | − | 0.983087i | \(-0.441373\pi\) | ||||
0.183141 | + | 0.983087i | \(0.441373\pi\) | |||||||
\(368\) | 6.60521 | 0.344320 | ||||||||
\(369\) | −21.0471 | −1.09567 | ||||||||
\(370\) | −5.84241 | −0.303732 | ||||||||
\(371\) | −3.32643 | −0.172700 | ||||||||
\(372\) | 5.92651 | 0.307275 | ||||||||
\(373\) | 14.4241 | 0.746854 | 0.373427 | − | 0.927660i | \(-0.378183\pi\) | ||||
0.373427 | + | 0.927660i | \(0.378183\pi\) | |||||||
\(374\) | 5.28076 | 0.273061 | ||||||||
\(375\) | 0.844163 | 0.0435924 | ||||||||
\(376\) | −7.28325 | −0.375605 | ||||||||
\(377\) | 8.82512 | 0.454517 | ||||||||
\(378\) | 2.37767 | 0.122294 | ||||||||
\(379\) | −0.642511 | −0.0330036 | −0.0165018 | − | 0.999864i | \(-0.505253\pi\) | ||||
−0.0165018 | + | 0.999864i | \(0.505253\pi\) | |||||||
\(380\) | −4.34072 | −0.222674 | ||||||||
\(381\) | −4.74930 | −0.243314 | ||||||||
\(382\) | 12.8086 | 0.655344 | ||||||||
\(383\) | −8.96481 | −0.458080 | −0.229040 | − | 0.973417i | \(-0.573559\pi\) | ||||
−0.229040 | + | 0.973417i | \(0.573559\pi\) | |||||||
\(384\) | 0.844163 | 0.0430785 | ||||||||
\(385\) | 0.512155 | 0.0261018 | ||||||||
\(386\) | 20.6520 | 1.05116 | ||||||||
\(387\) | 21.5950 | 1.09773 | ||||||||
\(388\) | 8.35252 | 0.424035 | ||||||||
\(389\) | 37.1210 | 1.88211 | 0.941054 | − | 0.338257i | \(-0.109837\pi\) | ||||
0.941054 | + | 0.338257i | \(0.109837\pi\) | |||||||
\(390\) | −1.01527 | −0.0514100 | ||||||||
\(391\) | −36.2798 | −1.83475 | ||||||||
\(392\) | −6.71623 | −0.339221 | ||||||||
\(393\) | 0.437979 | 0.0220931 | ||||||||
\(394\) | −12.6133 | −0.635448 | ||||||||
\(395\) | −0.0908517 | −0.00457125 | ||||||||
\(396\) | 2.19917 | 0.110512 | ||||||||
\(397\) | −19.5965 | −0.983522 | −0.491761 | − | 0.870730i | \(-0.663647\pi\) | ||||
−0.491761 | + | 0.870730i | \(0.663647\pi\) | |||||||
\(398\) | 22.9659 | 1.15118 | ||||||||
\(399\) | 1.95196 | 0.0977203 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −15.5264 | −0.775351 | −0.387676 | − | 0.921796i | \(-0.626722\pi\) | ||||
−0.387676 | + | 0.921796i | \(0.626722\pi\) | |||||||
\(402\) | 9.75245 | 0.486408 | ||||||||
\(403\) | −8.44357 | −0.420604 | ||||||||
\(404\) | 9.85205 | 0.490158 | ||||||||
\(405\) | 3.09431 | 0.153758 | ||||||||
\(406\) | 3.90887 | 0.193994 | ||||||||
\(407\) | 5.61707 | 0.278428 | ||||||||
\(408\) | −4.63665 | −0.229548 | ||||||||
\(409\) | −24.6582 | −1.21927 | −0.609636 | − | 0.792682i | \(-0.708684\pi\) | ||||
−0.609636 | + | 0.792682i | \(0.708684\pi\) | |||||||
\(410\) | 9.20135 | 0.454422 | ||||||||
\(411\) | −3.73056 | −0.184015 | ||||||||
\(412\) | −15.3763 | −0.757534 | ||||||||
\(413\) | 5.20866 | 0.256301 | ||||||||
\(414\) | −15.1087 | −0.742551 | ||||||||
\(415\) | −13.2425 | −0.650047 | ||||||||
\(416\) | −1.20269 | −0.0589667 | ||||||||
\(417\) | −18.9910 | −0.929991 | ||||||||
\(418\) | 4.17330 | 0.204123 | ||||||||
\(419\) | −17.9818 | −0.878470 | −0.439235 | − | 0.898372i | \(-0.644750\pi\) | ||||
−0.439235 | + | 0.898372i | \(0.644750\pi\) | |||||||
\(420\) | −0.449687 | −0.0219425 | ||||||||
\(421\) | 0.752344 | 0.0366670 | 0.0183335 | − | 0.999832i | \(-0.494164\pi\) | ||||
0.0183335 | + | 0.999832i | \(0.494164\pi\) | |||||||
\(422\) | −20.3893 | −0.992538 | ||||||||
\(423\) | 16.6596 | 0.810019 | ||||||||
\(424\) | 6.24445 | 0.303258 | ||||||||
\(425\) | −5.49260 | −0.266430 | ||||||||
\(426\) | −3.24735 | −0.157335 | ||||||||
\(427\) | 2.98933 | 0.144664 | ||||||||
\(428\) | −4.15714 | −0.200943 | ||||||||
\(429\) | 0.976107 | 0.0471269 | ||||||||
\(430\) | −9.44089 | −0.455280 | ||||||||
\(431\) | 20.3211 | 0.978832 | 0.489416 | − | 0.872050i | \(-0.337210\pi\) | ||||
0.489416 | + | 0.872050i | \(0.337210\pi\) | |||||||
\(432\) | −4.46342 | −0.214746 | ||||||||
\(433\) | −33.7894 | −1.62381 | −0.811907 | − | 0.583787i | \(-0.801570\pi\) | ||||
−0.811907 | + | 0.583787i | \(0.801570\pi\) | |||||||
\(434\) | −3.73987 | −0.179519 | ||||||||
\(435\) | −6.19432 | −0.296995 | ||||||||
\(436\) | −0.609510 | −0.0291902 | ||||||||
\(437\) | −28.6713 | −1.37154 | ||||||||
\(438\) | 6.36788 | 0.304269 | ||||||||
\(439\) | −22.3552 | −1.06696 | −0.533478 | − | 0.845814i | \(-0.679115\pi\) | ||||
−0.533478 | + | 0.845814i | \(0.679115\pi\) | |||||||
\(440\) | −0.961430 | −0.0458344 | ||||||||
\(441\) | 15.3626 | 0.731554 | ||||||||
\(442\) | 6.60589 | 0.314210 | ||||||||
\(443\) | 21.2089 | 1.00766 | 0.503832 | − | 0.863802i | \(-0.331923\pi\) | ||||
0.503832 | + | 0.863802i | \(0.331923\pi\) | |||||||
\(444\) | −4.93194 | −0.234060 | ||||||||
\(445\) | −14.0969 | −0.668256 | ||||||||
\(446\) | −18.2859 | −0.865863 | ||||||||
\(447\) | 16.6954 | 0.789666 | ||||||||
\(448\) | −0.532701 | −0.0251678 | ||||||||
\(449\) | −24.8674 | −1.17356 | −0.586782 | − | 0.809745i | \(-0.699606\pi\) | ||||
−0.586782 | + | 0.809745i | \(0.699606\pi\) | |||||||
\(450\) | −2.28739 | −0.107829 | ||||||||
\(451\) | −8.84645 | −0.416563 | ||||||||
\(452\) | −5.36554 | −0.252374 | ||||||||
\(453\) | −5.81659 | −0.273287 | ||||||||
\(454\) | 23.9381 | 1.12347 | ||||||||
\(455\) | 0.640674 | 0.0300352 | ||||||||
\(456\) | −3.66427 | −0.171595 | ||||||||
\(457\) | 38.5370 | 1.80268 | 0.901342 | − | 0.433109i | \(-0.142583\pi\) | ||||
0.901342 | + | 0.433109i | \(0.142583\pi\) | |||||||
\(458\) | 23.1069 | 1.07971 | ||||||||
\(459\) | 24.5158 | 1.14430 | ||||||||
\(460\) | 6.60521 | 0.307969 | ||||||||
\(461\) | 14.0184 | 0.652903 | 0.326451 | − | 0.945214i | \(-0.394147\pi\) | ||||
0.326451 | + | 0.945214i | \(0.394147\pi\) | |||||||
\(462\) | 0.432342 | 0.0201144 | ||||||||
\(463\) | 33.7519 | 1.56858 | 0.784291 | − | 0.620393i | \(-0.213027\pi\) | ||||
0.784291 | + | 0.620393i | \(0.213027\pi\) | |||||||
\(464\) | −7.33783 | −0.340650 | ||||||||
\(465\) | 5.92651 | 0.274835 | ||||||||
\(466\) | 10.5496 | 0.488699 | ||||||||
\(467\) | 37.4995 | 1.73527 | 0.867635 | − | 0.497201i | \(-0.165639\pi\) | ||||
0.867635 | + | 0.497201i | \(0.165639\pi\) | |||||||
\(468\) | 2.75102 | 0.127166 | ||||||||
\(469\) | −6.15419 | −0.284174 | ||||||||
\(470\) | −7.28325 | −0.335951 | ||||||||
\(471\) | −5.77283 | −0.265998 | ||||||||
\(472\) | −9.77782 | −0.450061 | ||||||||
\(473\) | 9.07676 | 0.417350 | ||||||||
\(474\) | −0.0766937 | −0.00352266 | ||||||||
\(475\) | −4.34072 | −0.199166 | ||||||||
\(476\) | 2.92592 | 0.134109 | ||||||||
\(477\) | −14.2835 | −0.653996 | ||||||||
\(478\) | 2.97603 | 0.136120 | ||||||||
\(479\) | −31.2817 | −1.42930 | −0.714648 | − | 0.699484i | \(-0.753413\pi\) | ||||
−0.714648 | + | 0.699484i | \(0.753413\pi\) | |||||||
\(480\) | 0.844163 | 0.0385306 | ||||||||
\(481\) | 7.02660 | 0.320385 | ||||||||
\(482\) | −22.2492 | −1.01343 | ||||||||
\(483\) | −2.97027 | −0.135152 | ||||||||
\(484\) | −10.0757 | −0.457984 | ||||||||
\(485\) | 8.35252 | 0.379268 | ||||||||
\(486\) | 16.0024 | 0.725882 | ||||||||
\(487\) | 9.32490 | 0.422552 | 0.211276 | − | 0.977426i | \(-0.432238\pi\) | ||||
0.211276 | + | 0.977426i | \(0.432238\pi\) | |||||||
\(488\) | −5.61164 | −0.254027 | ||||||||
\(489\) | −2.33736 | −0.105699 | ||||||||
\(490\) | −6.71623 | −0.303408 | ||||||||
\(491\) | 34.9844 | 1.57882 | 0.789412 | − | 0.613863i | \(-0.210385\pi\) | ||||
0.789412 | + | 0.613863i | \(0.210385\pi\) | |||||||
\(492\) | 7.76744 | 0.350183 | ||||||||
\(493\) | 40.3038 | 1.81519 | ||||||||
\(494\) | 5.22053 | 0.234883 | ||||||||
\(495\) | 2.19917 | 0.0988451 | ||||||||
\(496\) | 7.02057 | 0.315233 | ||||||||
\(497\) | 2.04921 | 0.0919196 | ||||||||
\(498\) | −11.1788 | −0.500934 | ||||||||
\(499\) | −37.5728 | −1.68199 | −0.840995 | − | 0.541043i | \(-0.818030\pi\) | ||||
−0.840995 | + | 0.541043i | \(0.818030\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −3.59685 | −0.160695 | ||||||||
\(502\) | −12.4001 | −0.553445 | ||||||||
\(503\) | 19.0226 | 0.848176 | 0.424088 | − | 0.905621i | \(-0.360595\pi\) | ||||
0.424088 | + | 0.905621i | \(0.360595\pi\) | |||||||
\(504\) | 1.21849 | 0.0542761 | ||||||||
\(505\) | 9.85205 | 0.438410 | ||||||||
\(506\) | −6.35045 | −0.282312 | ||||||||
\(507\) | −9.75307 | −0.433149 | ||||||||
\(508\) | −5.62604 | −0.249615 | ||||||||
\(509\) | 28.1930 | 1.24963 | 0.624816 | − | 0.780772i | \(-0.285174\pi\) | ||||
0.624816 | + | 0.780772i | \(0.285174\pi\) | |||||||
\(510\) | −4.63665 | −0.205314 | ||||||||
\(511\) | −4.01839 | −0.177763 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 19.3744 | 0.855402 | ||||||||
\(514\) | −2.07976 | −0.0917342 | ||||||||
\(515\) | −15.3763 | −0.677559 | ||||||||
\(516\) | −7.96965 | −0.350844 | ||||||||
\(517\) | 7.00234 | 0.307963 | ||||||||
\(518\) | 3.11226 | 0.136745 | ||||||||
\(519\) | 7.42231 | 0.325803 | ||||||||
\(520\) | −1.20269 | −0.0527414 | ||||||||
\(521\) | −13.1659 | −0.576808 | −0.288404 | − | 0.957509i | \(-0.593125\pi\) | ||||
−0.288404 | + | 0.957509i | \(0.593125\pi\) | |||||||
\(522\) | 16.7845 | 0.734636 | ||||||||
\(523\) | 16.5833 | 0.725136 | 0.362568 | − | 0.931957i | \(-0.381900\pi\) | ||||
0.362568 | + | 0.931957i | \(0.381900\pi\) | |||||||
\(524\) | 0.518832 | 0.0226653 | ||||||||
\(525\) | −0.449687 | −0.0196259 | ||||||||
\(526\) | 4.98966 | 0.217559 | ||||||||
\(527\) | −38.5612 | −1.67975 | ||||||||
\(528\) | −0.811604 | −0.0353205 | ||||||||
\(529\) | 20.6288 | 0.896903 | ||||||||
\(530\) | 6.24445 | 0.271242 | ||||||||
\(531\) | 22.3657 | 0.970588 | ||||||||
\(532\) | 2.31231 | 0.100251 | ||||||||
\(533\) | −11.0664 | −0.479337 | ||||||||
\(534\) | −11.9001 | −0.514966 | ||||||||
\(535\) | −4.15714 | −0.179729 | ||||||||
\(536\) | 11.5528 | 0.499005 | ||||||||
\(537\) | 9.95070 | 0.429404 | ||||||||
\(538\) | 0.908252 | 0.0391575 | ||||||||
\(539\) | 6.45719 | 0.278131 | ||||||||
\(540\) | −4.46342 | −0.192075 | ||||||||
\(541\) | −5.59725 | −0.240644 | −0.120322 | − | 0.992735i | \(-0.538393\pi\) | ||||
−0.120322 | + | 0.992735i | \(0.538393\pi\) | |||||||
\(542\) | 16.6795 | 0.716445 | ||||||||
\(543\) | 20.5483 | 0.881811 | ||||||||
\(544\) | −5.49260 | −0.235493 | ||||||||
\(545\) | −0.609510 | −0.0261085 | ||||||||
\(546\) | 0.540833 | 0.0231455 | ||||||||
\(547\) | 30.5086 | 1.30445 | 0.652227 | − | 0.758024i | \(-0.273835\pi\) | ||||
0.652227 | + | 0.758024i | \(0.273835\pi\) | |||||||
\(548\) | −4.41924 | −0.188780 | ||||||||
\(549\) | 12.8360 | 0.547827 | ||||||||
\(550\) | −0.961430 | −0.0409955 | ||||||||
\(551\) | 31.8514 | 1.35692 | ||||||||
\(552\) | 5.57587 | 0.237325 | ||||||||
\(553\) | 0.0483968 | 0.00205804 | ||||||||
\(554\) | 27.1449 | 1.15328 | ||||||||
\(555\) | −4.93194 | −0.209349 | ||||||||
\(556\) | −22.4968 | −0.954076 | ||||||||
\(557\) | −15.7133 | −0.665793 | −0.332896 | − | 0.942963i | \(-0.608026\pi\) | ||||
−0.332896 | + | 0.942963i | \(0.608026\pi\) | |||||||
\(558\) | −16.0588 | −0.679822 | ||||||||
\(559\) | 11.3545 | 0.480242 | ||||||||
\(560\) | −0.532701 | −0.0225107 | ||||||||
\(561\) | 4.45782 | 0.188209 | ||||||||
\(562\) | −15.7002 | −0.662273 | ||||||||
\(563\) | −31.9893 | −1.34819 | −0.674093 | − | 0.738646i | \(-0.735465\pi\) | ||||
−0.674093 | + | 0.738646i | \(0.735465\pi\) | |||||||
\(564\) | −6.14825 | −0.258888 | ||||||||
\(565\) | −5.36554 | −0.225730 | ||||||||
\(566\) | 17.5279 | 0.736751 | ||||||||
\(567\) | −1.64834 | −0.0692240 | ||||||||
\(568\) | −3.84683 | −0.161409 | ||||||||
\(569\) | −18.2157 | −0.763643 | −0.381821 | − | 0.924236i | \(-0.624703\pi\) | ||||
−0.381821 | + | 0.924236i | \(0.624703\pi\) | |||||||
\(570\) | −3.66427 | −0.153480 | ||||||||
\(571\) | 28.0809 | 1.17515 | 0.587575 | − | 0.809170i | \(-0.300083\pi\) | ||||
0.587575 | + | 0.809170i | \(0.300083\pi\) | |||||||
\(572\) | 1.15630 | 0.0483474 | ||||||||
\(573\) | 10.8125 | 0.451700 | ||||||||
\(574\) | −4.90157 | −0.204587 | ||||||||
\(575\) | 6.60521 | 0.275456 | ||||||||
\(576\) | −2.28739 | −0.0953079 | ||||||||
\(577\) | −16.4558 | −0.685062 | −0.342531 | − | 0.939506i | \(-0.611284\pi\) | ||||
−0.342531 | + | 0.939506i | \(0.611284\pi\) | |||||||
\(578\) | 13.1687 | 0.547745 | ||||||||
\(579\) | 17.4337 | 0.724519 | ||||||||
\(580\) | −7.33783 | −0.304687 | ||||||||
\(581\) | 7.05428 | 0.292661 | ||||||||
\(582\) | 7.05089 | 0.292269 | ||||||||
\(583\) | −6.00361 | −0.248644 | ||||||||
\(584\) | 7.54343 | 0.312149 | ||||||||
\(585\) | 2.75102 | 0.113741 | ||||||||
\(586\) | −27.7763 | −1.14743 | ||||||||
\(587\) | −2.02510 | −0.0835848 | −0.0417924 | − | 0.999126i | \(-0.513307\pi\) | ||||
−0.0417924 | + | 0.999126i | \(0.513307\pi\) | |||||||
\(588\) | −5.66959 | −0.233810 | ||||||||
\(589\) | −30.4743 | −1.25567 | ||||||||
\(590\) | −9.77782 | −0.402547 | ||||||||
\(591\) | −10.6477 | −0.437986 | ||||||||
\(592\) | −5.84241 | −0.240121 | ||||||||
\(593\) | 8.40701 | 0.345234 | 0.172617 | − | 0.984989i | \(-0.444778\pi\) | ||||
0.172617 | + | 0.984989i | \(0.444778\pi\) | |||||||
\(594\) | 4.29127 | 0.176073 | ||||||||
\(595\) | 2.92592 | 0.119951 | ||||||||
\(596\) | 19.7775 | 0.810117 | ||||||||
\(597\) | 19.3870 | 0.793456 | ||||||||
\(598\) | −7.94401 | −0.324855 | ||||||||
\(599\) | 20.3150 | 0.830049 | 0.415024 | − | 0.909810i | \(-0.363773\pi\) | ||||
0.415024 | + | 0.909810i | \(0.363773\pi\) | |||||||
\(600\) | 0.844163 | 0.0344628 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | 5.02917 | 0.204974 | ||||||||
\(603\) | −26.4258 | −1.07614 | ||||||||
\(604\) | −6.89037 | −0.280365 | ||||||||
\(605\) | −10.0757 | −0.409633 | ||||||||
\(606\) | 8.31673 | 0.337844 | ||||||||
\(607\) | −5.70283 | −0.231471 | −0.115735 | − | 0.993280i | \(-0.536922\pi\) | ||||
−0.115735 | + | 0.993280i | \(0.536922\pi\) | |||||||
\(608\) | −4.34072 | −0.176039 | ||||||||
\(609\) | 3.29972 | 0.133711 | ||||||||
\(610\) | −5.61164 | −0.227209 | ||||||||
\(611\) | 8.75949 | 0.354371 | ||||||||
\(612\) | 12.5637 | 0.507858 | ||||||||
\(613\) | −32.3291 | −1.30576 | −0.652880 | − | 0.757461i | \(-0.726440\pi\) | ||||
−0.652880 | + | 0.757461i | \(0.726440\pi\) | |||||||
\(614\) | 30.2322 | 1.22007 | ||||||||
\(615\) | 7.76744 | 0.313213 | ||||||||
\(616\) | 0.512155 | 0.0206353 | ||||||||
\(617\) | −32.7379 | −1.31798 | −0.658990 | − | 0.752152i | \(-0.729016\pi\) | ||||
−0.658990 | + | 0.752152i | \(0.729016\pi\) | |||||||
\(618\) | −12.9801 | −0.522135 | ||||||||
\(619\) | 15.0430 | 0.604629 | 0.302315 | − | 0.953208i | \(-0.402241\pi\) | ||||
0.302315 | + | 0.953208i | \(0.402241\pi\) | |||||||
\(620\) | 7.02057 | 0.281953 | ||||||||
\(621\) | −29.4818 | −1.18306 | ||||||||
\(622\) | 12.3450 | 0.494990 | ||||||||
\(623\) | 7.50942 | 0.300858 | ||||||||
\(624\) | −1.01527 | −0.0406431 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −31.9710 | −1.27782 | ||||||||
\(627\) | 3.52294 | 0.140693 | ||||||||
\(628\) | −6.83852 | −0.272887 | ||||||||
\(629\) | 32.0900 | 1.27951 | ||||||||
\(630\) | 1.21849 | 0.0485460 | ||||||||
\(631\) | −6.39353 | −0.254522 | −0.127261 | − | 0.991869i | \(-0.540619\pi\) | ||||
−0.127261 | + | 0.991869i | \(0.540619\pi\) | |||||||
\(632\) | −0.0908517 | −0.00361389 | ||||||||
\(633\) | −17.2119 | −0.684113 | ||||||||
\(634\) | −8.44300 | −0.335314 | ||||||||
\(635\) | −5.62604 | −0.223263 | ||||||||
\(636\) | 5.27134 | 0.209022 | ||||||||
\(637\) | 8.07753 | 0.320044 | ||||||||
\(638\) | 7.05481 | 0.279303 | ||||||||
\(639\) | 8.79919 | 0.348091 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −0.779702 | −0.0307964 | −0.0153982 | − | 0.999881i | \(-0.504902\pi\) | ||||
−0.0153982 | + | 0.999881i | \(0.504902\pi\) | |||||||
\(642\) | −3.50930 | −0.138501 | ||||||||
\(643\) | −4.27884 | −0.168741 | −0.0843705 | − | 0.996434i | \(-0.526888\pi\) | ||||
−0.0843705 | + | 0.996434i | \(0.526888\pi\) | |||||||
\(644\) | −3.51860 | −0.138652 | ||||||||
\(645\) | −7.96965 | −0.313805 | ||||||||
\(646\) | 23.8418 | 0.938045 | ||||||||
\(647\) | 19.4922 | 0.766316 | 0.383158 | − | 0.923683i | \(-0.374836\pi\) | ||||
0.383158 | + | 0.923683i | \(0.374836\pi\) | |||||||
\(648\) | 3.09431 | 0.121556 | ||||||||
\(649\) | 9.40069 | 0.369010 | ||||||||
\(650\) | −1.20269 | −0.0471733 | ||||||||
\(651\) | −3.15706 | −0.123735 | ||||||||
\(652\) | −2.76885 | −0.108437 | ||||||||
\(653\) | −39.2685 | −1.53669 | −0.768347 | − | 0.640034i | \(-0.778920\pi\) | ||||
−0.768347 | + | 0.640034i | \(0.778920\pi\) | |||||||
\(654\) | −0.514526 | −0.0201196 | ||||||||
\(655\) | 0.518832 | 0.0202725 | ||||||||
\(656\) | 9.20135 | 0.359252 | ||||||||
\(657\) | −17.2548 | −0.673172 | ||||||||
\(658\) | 3.87980 | 0.151250 | ||||||||
\(659\) | 27.5689 | 1.07393 | 0.536966 | − | 0.843604i | \(-0.319570\pi\) | ||||
0.536966 | + | 0.843604i | \(0.319570\pi\) | |||||||
\(660\) | −0.811604 | −0.0315916 | ||||||||
\(661\) | 10.0809 | 0.392101 | 0.196050 | − | 0.980594i | \(-0.437188\pi\) | ||||
0.196050 | + | 0.980594i | \(0.437188\pi\) | |||||||
\(662\) | 16.6072 | 0.645458 | ||||||||
\(663\) | 5.57645 | 0.216571 | ||||||||
\(664\) | −13.2425 | −0.513908 | ||||||||
\(665\) | 2.31231 | 0.0896673 | ||||||||
\(666\) | 13.3639 | 0.517839 | ||||||||
\(667\) | −48.4679 | −1.87668 | ||||||||
\(668\) | −4.26084 | −0.164857 | ||||||||
\(669\) | −15.4363 | −0.596802 | ||||||||
\(670\) | 11.5528 | 0.446324 | ||||||||
\(671\) | 5.39520 | 0.208280 | ||||||||
\(672\) | −0.449687 | −0.0173470 | ||||||||
\(673\) | −20.8497 | −0.803698 | −0.401849 | − | 0.915706i | \(-0.631632\pi\) | ||||
−0.401849 | + | 0.915706i | \(0.631632\pi\) | |||||||
\(674\) | −14.1086 | −0.543442 | ||||||||
\(675\) | −4.46342 | −0.171797 | ||||||||
\(676\) | −11.5535 | −0.444367 | ||||||||
\(677\) | 32.6106 | 1.25333 | 0.626664 | − | 0.779290i | \(-0.284420\pi\) | ||||
0.626664 | + | 0.779290i | \(0.284420\pi\) | |||||||
\(678\) | −4.52939 | −0.173950 | ||||||||
\(679\) | −4.44940 | −0.170752 | ||||||||
\(680\) | −5.49260 | −0.210632 | ||||||||
\(681\) | 20.2077 | 0.774360 | ||||||||
\(682\) | −6.74979 | −0.258463 | ||||||||
\(683\) | −37.6401 | −1.44026 | −0.720129 | − | 0.693840i | \(-0.755917\pi\) | ||||
−0.720129 | + | 0.693840i | \(0.755917\pi\) | |||||||
\(684\) | 9.92891 | 0.379641 | ||||||||
\(685\) | −4.41924 | −0.168850 | ||||||||
\(686\) | 7.30665 | 0.278969 | ||||||||
\(687\) | 19.5060 | 0.744200 | ||||||||
\(688\) | −9.44089 | −0.359931 | ||||||||
\(689\) | −7.51014 | −0.286113 | ||||||||
\(690\) | 5.57587 | 0.212270 | ||||||||
\(691\) | −43.6848 | −1.66185 | −0.830923 | − | 0.556387i | \(-0.812187\pi\) | ||||
−0.830923 | + | 0.556387i | \(0.812187\pi\) | |||||||
\(692\) | 8.79251 | 0.334241 | ||||||||
\(693\) | −1.17150 | −0.0445015 | ||||||||
\(694\) | −33.9642 | −1.28926 | ||||||||
\(695\) | −22.4968 | −0.853352 | ||||||||
\(696\) | −6.19432 | −0.234795 | ||||||||
\(697\) | −50.5393 | −1.91431 | ||||||||
\(698\) | 13.0855 | 0.495295 | ||||||||
\(699\) | 8.90555 | 0.336839 | ||||||||
\(700\) | −0.532701 | −0.0201342 | ||||||||
\(701\) | −46.4998 | −1.75627 | −0.878137 | − | 0.478410i | \(-0.841213\pi\) | ||||
−0.878137 | + | 0.478410i | \(0.841213\pi\) | |||||||
\(702\) | 5.36810 | 0.202606 | ||||||||
\(703\) | 25.3602 | 0.956480 | ||||||||
\(704\) | −0.961430 | −0.0362353 | ||||||||
\(705\) | −6.14825 | −0.231557 | ||||||||
\(706\) | −16.0428 | −0.603779 | ||||||||
\(707\) | −5.24820 | −0.197379 | ||||||||
\(708\) | −8.25407 | −0.310207 | ||||||||
\(709\) | 31.5037 | 1.18315 | 0.591574 | − | 0.806251i | \(-0.298507\pi\) | ||||
0.591574 | + | 0.806251i | \(0.298507\pi\) | |||||||
\(710\) | −3.84683 | −0.144369 | ||||||||
\(711\) | 0.207813 | 0.00779360 | ||||||||
\(712\) | −14.0969 | −0.528302 | ||||||||
\(713\) | 46.3723 | 1.73666 | ||||||||
\(714\) | 2.46995 | 0.0924355 | ||||||||
\(715\) | 1.15630 | 0.0432432 | ||||||||
\(716\) | 11.7877 | 0.440525 | ||||||||
\(717\) | 2.51225 | 0.0938217 | ||||||||
\(718\) | 0.802407 | 0.0299455 | ||||||||
\(719\) | −40.2451 | −1.50089 | −0.750444 | − | 0.660934i | \(-0.770160\pi\) | ||||
−0.750444 | + | 0.660934i | \(0.770160\pi\) | |||||||
\(720\) | −2.28739 | −0.0852459 | ||||||||
\(721\) | 8.19096 | 0.305047 | ||||||||
\(722\) | −0.158171 | −0.00588651 | ||||||||
\(723\) | −18.7820 | −0.698510 | ||||||||
\(724\) | 24.3416 | 0.904648 | ||||||||
\(725\) | −7.33783 | −0.272520 | ||||||||
\(726\) | −8.50549 | −0.315668 | ||||||||
\(727\) | 29.2020 | 1.08304 | 0.541522 | − | 0.840687i | \(-0.317848\pi\) | ||||
0.541522 | + | 0.840687i | \(0.317848\pi\) | |||||||
\(728\) | 0.640674 | 0.0237449 | ||||||||
\(729\) | 4.22566 | 0.156506 | ||||||||
\(730\) | 7.54343 | 0.279195 | ||||||||
\(731\) | 51.8551 | 1.91793 | ||||||||
\(732\) | −4.73714 | −0.175090 | ||||||||
\(733\) | −42.4811 | −1.56908 | −0.784538 | − | 0.620080i | \(-0.787100\pi\) | ||||
−0.784538 | + | 0.620080i | \(0.787100\pi\) | |||||||
\(734\) | 7.01696 | 0.259001 | ||||||||
\(735\) | −5.66959 | −0.209126 | ||||||||
\(736\) | 6.60521 | 0.243471 | ||||||||
\(737\) | −11.1072 | −0.409140 | ||||||||
\(738\) | −21.0471 | −0.774753 | ||||||||
\(739\) | 11.0192 | 0.405346 | 0.202673 | − | 0.979246i | \(-0.435037\pi\) | ||||
0.202673 | + | 0.979246i | \(0.435037\pi\) | |||||||
\(740\) | −5.84241 | −0.214771 | ||||||||
\(741\) | 4.40698 | 0.161894 | ||||||||
\(742\) | −3.32643 | −0.122117 | ||||||||
\(743\) | 35.5120 | 1.30281 | 0.651404 | − | 0.758731i | \(-0.274180\pi\) | ||||
0.651404 | + | 0.758731i | \(0.274180\pi\) | |||||||
\(744\) | 5.92651 | 0.217276 | ||||||||
\(745\) | 19.7775 | 0.724591 | ||||||||
\(746\) | 14.4241 | 0.528106 | ||||||||
\(747\) | 30.2907 | 1.10828 | ||||||||
\(748\) | 5.28076 | 0.193084 | ||||||||
\(749\) | 2.21451 | 0.0809165 | ||||||||
\(750\) | 0.844163 | 0.0308245 | ||||||||
\(751\) | −44.2767 | −1.61568 | −0.807840 | − | 0.589402i | \(-0.799364\pi\) | ||||
−0.807840 | + | 0.589402i | \(0.799364\pi\) | |||||||
\(752\) | −7.28325 | −0.265593 | ||||||||
\(753\) | −10.4677 | −0.381465 | ||||||||
\(754\) | 8.82512 | 0.321392 | ||||||||
\(755\) | −6.89037 | −0.250766 | ||||||||
\(756\) | 2.37767 | 0.0864749 | ||||||||
\(757\) | 17.9051 | 0.650771 | 0.325386 | − | 0.945581i | \(-0.394506\pi\) | ||||
0.325386 | + | 0.945581i | \(0.394506\pi\) | |||||||
\(758\) | −0.642511 | −0.0233371 | ||||||||
\(759\) | −5.36081 | −0.194585 | ||||||||
\(760\) | −4.34072 | −0.157454 | ||||||||
\(761\) | −6.96672 | −0.252543 | −0.126272 | − | 0.991996i | \(-0.540301\pi\) | ||||
−0.126272 | + | 0.991996i | \(0.540301\pi\) | |||||||
\(762\) | −4.74930 | −0.172049 | ||||||||
\(763\) | 0.324687 | 0.0117544 | ||||||||
\(764\) | 12.8086 | 0.463398 | ||||||||
\(765\) | 12.5637 | 0.454242 | ||||||||
\(766\) | −8.96481 | −0.323912 | ||||||||
\(767\) | 11.7597 | 0.424617 | ||||||||
\(768\) | 0.844163 | 0.0304611 | ||||||||
\(769\) | −22.6634 | −0.817265 | −0.408632 | − | 0.912699i | \(-0.633994\pi\) | ||||
−0.408632 | + | 0.912699i | \(0.633994\pi\) | |||||||
\(770\) | 0.512155 | 0.0184568 | ||||||||
\(771\) | −1.75565 | −0.0632284 | ||||||||
\(772\) | 20.6520 | 0.743283 | ||||||||
\(773\) | 40.9769 | 1.47384 | 0.736918 | − | 0.675982i | \(-0.236280\pi\) | ||||
0.736918 | + | 0.675982i | \(0.236280\pi\) | |||||||
\(774\) | 21.5950 | 0.776216 | ||||||||
\(775\) | 7.02057 | 0.252186 | ||||||||
\(776\) | 8.35252 | 0.299838 | ||||||||
\(777\) | 2.62725 | 0.0942521 | ||||||||
\(778\) | 37.1210 | 1.33085 | ||||||||
\(779\) | −39.9404 | −1.43101 | ||||||||
\(780\) | −1.01527 | −0.0363523 | ||||||||
\(781\) | 3.69846 | 0.132341 | ||||||||
\(782\) | −36.2798 | −1.29736 | ||||||||
\(783\) | 32.7518 | 1.17045 | ||||||||
\(784\) | −6.71623 | −0.239865 | ||||||||
\(785\) | −6.83852 | −0.244077 | ||||||||
\(786\) | 0.437979 | 0.0156222 | ||||||||
\(787\) | 0.254953 | 0.00908809 | 0.00454404 | − | 0.999990i | \(-0.498554\pi\) | ||||
0.00454404 | + | 0.999990i | \(0.498554\pi\) | |||||||
\(788\) | −12.6133 | −0.449329 | ||||||||
\(789\) | 4.21208 | 0.149954 | ||||||||
\(790\) | −0.0908517 | −0.00323236 | ||||||||
\(791\) | 2.85823 | 0.101627 | ||||||||
\(792\) | 2.19917 | 0.0781439 | ||||||||
\(793\) | 6.74906 | 0.239666 | ||||||||
\(794\) | −19.5965 | −0.695455 | ||||||||
\(795\) | 5.27134 | 0.186955 | ||||||||
\(796\) | 22.9659 | 0.814005 | ||||||||
\(797\) | 30.3945 | 1.07663 | 0.538313 | − | 0.842745i | \(-0.319062\pi\) | ||||
0.538313 | + | 0.842745i | \(0.319062\pi\) | |||||||
\(798\) | 1.95196 | 0.0690987 | ||||||||
\(799\) | 40.0040 | 1.41524 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 32.2450 | 1.13932 | ||||||||
\(802\) | −15.5264 | −0.548256 | ||||||||
\(803\) | −7.25248 | −0.255934 | ||||||||
\(804\) | 9.75245 | 0.343942 | ||||||||
\(805\) | −3.51860 | −0.124014 | ||||||||
\(806\) | −8.44357 | −0.297412 | ||||||||
\(807\) | 0.766713 | 0.0269896 | ||||||||
\(808\) | 9.85205 | 0.346594 | ||||||||
\(809\) | −54.6837 | −1.92258 | −0.961289 | − | 0.275543i | \(-0.911142\pi\) | ||||
−0.961289 | + | 0.275543i | \(0.911142\pi\) | |||||||
\(810\) | 3.09431 | 0.108723 | ||||||||
\(811\) | −25.5682 | −0.897819 | −0.448910 | − | 0.893577i | \(-0.648188\pi\) | ||||
−0.448910 | + | 0.893577i | \(0.648188\pi\) | |||||||
\(812\) | 3.90887 | 0.137174 | ||||||||
\(813\) | 14.0802 | 0.493814 | ||||||||
\(814\) | 5.61707 | 0.196878 | ||||||||
\(815\) | −2.76885 | −0.0969886 | ||||||||
\(816\) | −4.63665 | −0.162315 | ||||||||
\(817\) | 40.9802 | 1.43372 | ||||||||
\(818\) | −24.6582 | −0.862155 | ||||||||
\(819\) | −1.46547 | −0.0512077 | ||||||||
\(820\) | 9.20135 | 0.321325 | ||||||||
\(821\) | −19.6687 | −0.686441 | −0.343221 | − | 0.939255i | \(-0.611518\pi\) | ||||
−0.343221 | + | 0.939255i | \(0.611518\pi\) | |||||||
\(822\) | −3.73056 | −0.130118 | ||||||||
\(823\) | −1.93117 | −0.0673163 | −0.0336582 | − | 0.999433i | \(-0.510716\pi\) | ||||
−0.0336582 | + | 0.999433i | \(0.510716\pi\) | |||||||
\(824\) | −15.3763 | −0.535658 | ||||||||
\(825\) | −0.811604 | −0.0282564 | ||||||||
\(826\) | 5.20866 | 0.181232 | ||||||||
\(827\) | −40.2192 | −1.39856 | −0.699280 | − | 0.714848i | \(-0.746496\pi\) | ||||
−0.699280 | + | 0.714848i | \(0.746496\pi\) | |||||||
\(828\) | −15.1087 | −0.525063 | ||||||||
\(829\) | 20.8718 | 0.724907 | 0.362454 | − | 0.932002i | \(-0.381939\pi\) | ||||
0.362454 | + | 0.932002i | \(0.381939\pi\) | |||||||
\(830\) | −13.2425 | −0.459653 | ||||||||
\(831\) | 22.9147 | 0.794903 | ||||||||
\(832\) | −1.20269 | −0.0416957 | ||||||||
\(833\) | 36.8896 | 1.27815 | ||||||||
\(834\) | −18.9910 | −0.657603 | ||||||||
\(835\) | −4.26084 | −0.147453 | ||||||||
\(836\) | 4.17330 | 0.144337 | ||||||||
\(837\) | −31.3358 | −1.08312 | ||||||||
\(838\) | −17.9818 | −0.621172 | ||||||||
\(839\) | −13.1018 | −0.452325 | −0.226162 | − | 0.974090i | \(-0.572618\pi\) | ||||
−0.226162 | + | 0.974090i | \(0.572618\pi\) | |||||||
\(840\) | −0.449687 | −0.0155157 | ||||||||
\(841\) | 24.8437 | 0.856679 | ||||||||
\(842\) | 0.752344 | 0.0259275 | ||||||||
\(843\) | −13.2535 | −0.456476 | ||||||||
\(844\) | −20.3893 | −0.701830 | ||||||||
\(845\) | −11.5535 | −0.397454 | ||||||||
\(846\) | 16.6596 | 0.572770 | ||||||||
\(847\) | 5.36731 | 0.184423 | ||||||||
\(848\) | 6.24445 | 0.214435 | ||||||||
\(849\) | 14.7964 | 0.507810 | ||||||||
\(850\) | −5.49260 | −0.188395 | ||||||||
\(851\) | −38.5903 | −1.32286 | ||||||||
\(852\) | −3.24735 | −0.111252 | ||||||||
\(853\) | 10.5851 | 0.362426 | 0.181213 | − | 0.983444i | \(-0.441998\pi\) | ||||
0.181213 | + | 0.983444i | \(0.441998\pi\) | |||||||
\(854\) | 2.98933 | 0.102293 | ||||||||
\(855\) | 9.92891 | 0.339562 | ||||||||
\(856\) | −4.15714 | −0.142088 | ||||||||
\(857\) | −49.1792 | −1.67993 | −0.839964 | − | 0.542642i | \(-0.817424\pi\) | ||||
−0.839964 | + | 0.542642i | \(0.817424\pi\) | |||||||
\(858\) | 0.976107 | 0.0333237 | ||||||||
\(859\) | −6.37161 | −0.217397 | −0.108698 | − | 0.994075i | \(-0.534668\pi\) | ||||
−0.108698 | + | 0.994075i | \(0.534668\pi\) | |||||||
\(860\) | −9.44089 | −0.321932 | ||||||||
\(861\) | −4.13772 | −0.141013 | ||||||||
\(862\) | 20.3211 | 0.692139 | ||||||||
\(863\) | 27.6061 | 0.939723 | 0.469861 | − | 0.882740i | \(-0.344304\pi\) | ||||
0.469861 | + | 0.882740i | \(0.344304\pi\) | |||||||
\(864\) | −4.46342 | −0.151849 | ||||||||
\(865\) | 8.79251 | 0.298954 | ||||||||
\(866\) | −33.7894 | −1.14821 | ||||||||
\(867\) | 11.1165 | 0.377537 | ||||||||
\(868\) | −3.73987 | −0.126939 | ||||||||
\(869\) | 0.0873476 | 0.00296306 | ||||||||
\(870\) | −6.19432 | −0.210007 | ||||||||
\(871\) | −13.8944 | −0.470795 | ||||||||
\(872\) | −0.609510 | −0.0206406 | ||||||||
\(873\) | −19.1055 | −0.646622 | ||||||||
\(874\) | −28.6713 | −0.969823 | ||||||||
\(875\) | −0.532701 | −0.0180086 | ||||||||
\(876\) | 6.36788 | 0.215151 | ||||||||
\(877\) | 14.0886 | 0.475737 | 0.237869 | − | 0.971297i | \(-0.423551\pi\) | ||||
0.237869 | + | 0.971297i | \(0.423551\pi\) | |||||||
\(878\) | −22.3552 | −0.754451 | ||||||||
\(879\) | −23.4478 | −0.790873 | ||||||||
\(880\) | −0.961430 | −0.0324098 | ||||||||
\(881\) | 24.2259 | 0.816190 | 0.408095 | − | 0.912939i | \(-0.366193\pi\) | ||||
0.408095 | + | 0.912939i | \(0.366193\pi\) | |||||||
\(882\) | 15.3626 | 0.517287 | ||||||||
\(883\) | 37.8604 | 1.27410 | 0.637052 | − | 0.770821i | \(-0.280154\pi\) | ||||
0.637052 | + | 0.770821i | \(0.280154\pi\) | |||||||
\(884\) | 6.60589 | 0.222180 | ||||||||
\(885\) | −8.25407 | −0.277458 | ||||||||
\(886\) | 21.2089 | 0.712526 | ||||||||
\(887\) | −40.0641 | −1.34522 | −0.672611 | − | 0.739996i | \(-0.734827\pi\) | ||||
−0.672611 | + | 0.739996i | \(0.734827\pi\) | |||||||
\(888\) | −4.93194 | −0.165505 | ||||||||
\(889\) | 2.99700 | 0.100516 | ||||||||
\(890\) | −14.0969 | −0.472528 | ||||||||
\(891\) | −2.97497 | −0.0996652 | ||||||||
\(892\) | −18.2859 | −0.612258 | ||||||||
\(893\) | 31.6145 | 1.05794 | ||||||||
\(894\) | 16.6954 | 0.558378 | ||||||||
\(895\) | 11.7877 | 0.394018 | ||||||||
\(896\) | −0.532701 | −0.0177963 | ||||||||
\(897\) | −6.70604 | −0.223908 | ||||||||
\(898\) | −24.8674 | −0.829835 | ||||||||
\(899\) | −51.5157 | −1.71815 | ||||||||
\(900\) | −2.28739 | −0.0762463 | ||||||||
\(901\) | −34.2983 | −1.14264 | ||||||||
\(902\) | −8.84645 | −0.294555 | ||||||||
\(903\) | 4.24544 | 0.141279 | ||||||||
\(904\) | −5.36554 | −0.178455 | ||||||||
\(905\) | 24.3416 | 0.809142 | ||||||||
\(906\) | −5.81659 | −0.193243 | ||||||||
\(907\) | 47.2600 | 1.56924 | 0.784621 | − | 0.619975i | \(-0.212857\pi\) | ||||
0.784621 | + | 0.619975i | \(0.212857\pi\) | |||||||
\(908\) | 23.9381 | 0.794414 | ||||||||
\(909\) | −22.5355 | −0.747454 | ||||||||
\(910\) | 0.640674 | 0.0212381 | ||||||||
\(911\) | 10.6548 | 0.353008 | 0.176504 | − | 0.984300i | \(-0.443521\pi\) | ||||
0.176504 | + | 0.984300i | \(0.443521\pi\) | |||||||
\(912\) | −3.66427 | −0.121336 | ||||||||
\(913\) | 12.7317 | 0.421358 | ||||||||
\(914\) | 38.5370 | 1.27469 | ||||||||
\(915\) | −4.73714 | −0.156605 | ||||||||
\(916\) | 23.1069 | 0.763473 | ||||||||
\(917\) | −0.276383 | −0.00912696 | ||||||||
\(918\) | 24.5158 | 0.809141 | ||||||||
\(919\) | −4.25145 | −0.140242 | −0.0701212 | − | 0.997538i | \(-0.522339\pi\) | ||||
−0.0701212 | + | 0.997538i | \(0.522339\pi\) | |||||||
\(920\) | 6.60521 | 0.217767 | ||||||||
\(921\) | 25.5209 | 0.840944 | ||||||||
\(922\) | 14.0184 | 0.461672 | ||||||||
\(923\) | 4.62654 | 0.152284 | ||||||||
\(924\) | 0.432342 | 0.0142230 | ||||||||
\(925\) | −5.84241 | −0.192097 | ||||||||
\(926\) | 33.7519 | 1.10915 | ||||||||
\(927\) | 35.1715 | 1.15518 | ||||||||
\(928\) | −7.33783 | −0.240876 | ||||||||
\(929\) | 44.4081 | 1.45698 | 0.728492 | − | 0.685055i | \(-0.240222\pi\) | ||||
0.728492 | + | 0.685055i | \(0.240222\pi\) | |||||||
\(930\) | 5.92651 | 0.194338 | ||||||||
\(931\) | 29.1533 | 0.955459 | ||||||||
\(932\) | 10.5496 | 0.345562 | ||||||||
\(933\) | 10.4212 | 0.341175 | ||||||||
\(934\) | 37.4995 | 1.22702 | ||||||||
\(935\) | 5.28076 | 0.172699 | ||||||||
\(936\) | 2.75102 | 0.0899198 | ||||||||
\(937\) | 5.47272 | 0.178786 | 0.0893930 | − | 0.995996i | \(-0.471507\pi\) | ||||
0.0893930 | + | 0.995996i | \(0.471507\pi\) | |||||||
\(938\) | −6.15419 | −0.200942 | ||||||||
\(939\) | −26.9887 | −0.880744 | ||||||||
\(940\) | −7.28325 | −0.237554 | ||||||||
\(941\) | −50.5208 | −1.64693 | −0.823466 | − | 0.567366i | \(-0.807963\pi\) | ||||
−0.823466 | + | 0.567366i | \(0.807963\pi\) | |||||||
\(942\) | −5.77283 | −0.188089 | ||||||||
\(943\) | 60.7768 | 1.97916 | ||||||||
\(944\) | −9.77782 | −0.318241 | ||||||||
\(945\) | 2.37767 | 0.0773455 | ||||||||
\(946\) | 9.07676 | 0.295111 | ||||||||
\(947\) | 32.7854 | 1.06538 | 0.532691 | − | 0.846310i | \(-0.321181\pi\) | ||||
0.532691 | + | 0.846310i | \(0.321181\pi\) | |||||||
\(948\) | −0.0766937 | −0.00249089 | ||||||||
\(949\) | −9.07240 | −0.294502 | ||||||||
\(950\) | −4.34072 | −0.140831 | ||||||||
\(951\) | −7.12726 | −0.231117 | ||||||||
\(952\) | 2.92592 | 0.0948295 | ||||||||
\(953\) | −13.6612 | −0.442528 | −0.221264 | − | 0.975214i | \(-0.571018\pi\) | ||||
−0.221264 | + | 0.975214i | \(0.571018\pi\) | |||||||
\(954\) | −14.2835 | −0.462445 | ||||||||
\(955\) | 12.8086 | 0.414476 | ||||||||
\(956\) | 2.97603 | 0.0962515 | ||||||||
\(957\) | 5.95541 | 0.192511 | ||||||||
\(958\) | −31.2817 | −1.01066 | ||||||||
\(959\) | 2.35413 | 0.0760189 | ||||||||
\(960\) | 0.844163 | 0.0272452 | ||||||||
\(961\) | 18.2884 | 0.589950 | ||||||||
\(962\) | 7.02660 | 0.226547 | ||||||||
\(963\) | 9.50899 | 0.306423 | ||||||||
\(964\) | −22.2492 | −0.716600 | ||||||||
\(965\) | 20.6520 | 0.664812 | ||||||||
\(966\) | −2.97027 | −0.0955670 | ||||||||
\(967\) | −8.52830 | −0.274252 | −0.137126 | − | 0.990554i | \(-0.543786\pi\) | ||||
−0.137126 | + | 0.990554i | \(0.543786\pi\) | |||||||
\(968\) | −10.0757 | −0.323844 | ||||||||
\(969\) | 20.1264 | 0.646553 | ||||||||
\(970\) | 8.35252 | 0.268183 | ||||||||
\(971\) | −19.4931 | −0.625562 | −0.312781 | − | 0.949825i | \(-0.601261\pi\) | ||||
−0.312781 | + | 0.949825i | \(0.601261\pi\) | |||||||
\(972\) | 16.0024 | 0.513276 | ||||||||
\(973\) | 11.9841 | 0.384191 | ||||||||
\(974\) | 9.32490 | 0.298789 | ||||||||
\(975\) | −1.01527 | −0.0325145 | ||||||||
\(976\) | −5.61164 | −0.179624 | ||||||||
\(977\) | −14.6151 | −0.467578 | −0.233789 | − | 0.972287i | \(-0.575112\pi\) | ||||
−0.233789 | + | 0.972287i | \(0.575112\pi\) | |||||||
\(978\) | −2.33736 | −0.0747405 | ||||||||
\(979\) | 13.5532 | 0.433161 | ||||||||
\(980\) | −6.71623 | −0.214542 | ||||||||
\(981\) | 1.39419 | 0.0445129 | ||||||||
\(982\) | 34.9844 | 1.11640 | ||||||||
\(983\) | 33.2877 | 1.06171 | 0.530856 | − | 0.847462i | \(-0.321871\pi\) | ||||
0.530856 | + | 0.847462i | \(0.321871\pi\) | |||||||
\(984\) | 7.76744 | 0.247617 | ||||||||
\(985\) | −12.6133 | −0.401892 | ||||||||
\(986\) | 40.3038 | 1.28353 | ||||||||
\(987\) | 3.27518 | 0.104250 | ||||||||
\(988\) | 5.22053 | 0.166087 | ||||||||
\(989\) | −62.3590 | −1.98290 | ||||||||
\(990\) | 2.19917 | 0.0698941 | ||||||||
\(991\) | 37.9919 | 1.20685 | 0.603426 | − | 0.797419i | \(-0.293802\pi\) | ||||
0.603426 | + | 0.797419i | \(0.293802\pi\) | |||||||
\(992\) | 7.02057 | 0.222903 | ||||||||
\(993\) | 14.0192 | 0.444886 | ||||||||
\(994\) | 2.04921 | 0.0649970 | ||||||||
\(995\) | 22.9659 | 0.728068 | ||||||||
\(996\) | −11.1788 | −0.354214 | ||||||||
\(997\) | −47.0677 | −1.49065 | −0.745325 | − | 0.666701i | \(-0.767706\pi\) | ||||
−0.745325 | + | 0.666701i | \(0.767706\pi\) | |||||||
\(998\) | −37.5728 | −1.18935 | ||||||||
\(999\) | 26.0771 | 0.825043 |
(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 | 6010.2.a.c.1.13 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.13 | ✓ | 16 | 1.1 | even | 1 | trivial |