Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 \) |
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 | 1.5 | ||
Root | \(0.924862\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.924862 | −0.413611 | −0.206805 | − | 0.978382i | \(-0.566307\pi\) | ||||
−0.206805 | + | 0.978382i | \(0.566307\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.24556 | −1.60467 | −0.802335 | − | 0.596874i | \(-0.796409\pi\) | ||||
−0.802335 | + | 0.596874i | \(0.796409\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.924862 | 0.292467 | ||||||||
\(11\) | 2.47789 | 0.747113 | 0.373556 | − | 0.927608i | \(-0.378138\pi\) | ||||
0.373556 | + | 0.927608i | \(0.378138\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 4.24556 | 1.13467 | ||||||||
\(15\) | 0.924862 | 0.238798 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.549056 | 0.133166 | 0.0665828 | − | 0.997781i | \(-0.478790\pi\) | ||||
0.0665828 | + | 0.997781i | \(0.478790\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.66906 | −1.07116 | −0.535578 | − | 0.844486i | \(-0.679906\pi\) | ||||
−0.535578 | + | 0.844486i | \(0.679906\pi\) | |||||||
\(20\) | −0.924862 | −0.206805 | ||||||||
\(21\) | 4.24556 | 0.926457 | ||||||||
\(22\) | −2.47789 | −0.528288 | ||||||||
\(23\) | −2.37974 | −0.496210 | −0.248105 | − | 0.968733i | \(-0.579808\pi\) | ||||
−0.248105 | + | 0.968733i | \(0.579808\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −4.14463 | −0.828926 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.24556 | −0.802335 | ||||||||
\(29\) | 7.33896 | 1.36281 | 0.681406 | − | 0.731906i | \(-0.261369\pi\) | ||||
0.681406 | + | 0.731906i | \(0.261369\pi\) | |||||||
\(30\) | −0.924862 | −0.168856 | ||||||||
\(31\) | 8.34581 | 1.49895 | 0.749476 | − | 0.662032i | \(-0.230306\pi\) | ||||
0.749476 | + | 0.662032i | \(0.230306\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.47789 | −0.431346 | ||||||||
\(34\) | −0.549056 | −0.0941623 | ||||||||
\(35\) | 3.92656 | 0.663709 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.19443 | −1.51155 | −0.755777 | − | 0.654829i | \(-0.772741\pi\) | ||||
−0.755777 | + | 0.654829i | \(0.772741\pi\) | |||||||
\(38\) | 4.66906 | 0.757422 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0.924862 | 0.146234 | ||||||||
\(41\) | −0.968492 | −0.151253 | −0.0756265 | − | 0.997136i | \(-0.524096\pi\) | ||||
−0.0756265 | + | 0.997136i | \(0.524096\pi\) | |||||||
\(42\) | −4.24556 | −0.655104 | ||||||||
\(43\) | −11.3612 | −1.73257 | −0.866284 | − | 0.499553i | \(-0.833498\pi\) | ||||
−0.866284 | + | 0.499553i | \(0.833498\pi\) | |||||||
\(44\) | 2.47789 | 0.373556 | ||||||||
\(45\) | −0.924862 | −0.137870 | ||||||||
\(46\) | 2.37974 | 0.350874 | ||||||||
\(47\) | 2.40638 | 0.351007 | 0.175503 | − | 0.984479i | \(-0.443845\pi\) | ||||
0.175503 | + | 0.984479i | \(0.443845\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 11.0248 | 1.57497 | ||||||||
\(50\) | 4.14463 | 0.586139 | ||||||||
\(51\) | −0.549056 | −0.0768832 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −10.3792 | −1.42570 | −0.712850 | − | 0.701317i | \(-0.752596\pi\) | ||||
−0.712850 | + | 0.701317i | \(0.752596\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.29171 | −0.309014 | ||||||||
\(56\) | 4.24556 | 0.567337 | ||||||||
\(57\) | 4.66906 | 0.618433 | ||||||||
\(58\) | −7.33896 | −0.963653 | ||||||||
\(59\) | 3.20528 | 0.417293 | 0.208646 | − | 0.977991i | \(-0.433094\pi\) | ||||
0.208646 | + | 0.977991i | \(0.433094\pi\) | |||||||
\(60\) | 0.924862 | 0.119399 | ||||||||
\(61\) | −6.92554 | −0.886725 | −0.443363 | − | 0.896342i | \(-0.646215\pi\) | ||||
−0.443363 | + | 0.896342i | \(0.646215\pi\) | |||||||
\(62\) | −8.34581 | −1.05992 | ||||||||
\(63\) | −4.24556 | −0.534890 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.924862 | 0.114715 | ||||||||
\(66\) | 2.47789 | 0.305007 | ||||||||
\(67\) | −2.85465 | −0.348751 | −0.174376 | − | 0.984679i | \(-0.555791\pi\) | ||||
−0.174376 | + | 0.984679i | \(0.555791\pi\) | |||||||
\(68\) | 0.549056 | 0.0665828 | ||||||||
\(69\) | 2.37974 | 0.286487 | ||||||||
\(70\) | −3.92656 | −0.469313 | ||||||||
\(71\) | −7.09939 | −0.842543 | −0.421271 | − | 0.906935i | \(-0.638416\pi\) | ||||
−0.421271 | + | 0.906935i | \(0.638416\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 7.73116 | 0.904863 | 0.452432 | − | 0.891799i | \(-0.350557\pi\) | ||||
0.452432 | + | 0.891799i | \(0.350557\pi\) | |||||||
\(74\) | 9.19443 | 1.06883 | ||||||||
\(75\) | 4.14463 | 0.478581 | ||||||||
\(76\) | −4.66906 | −0.535578 | ||||||||
\(77\) | −10.5200 | −1.19887 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 11.8927 | 1.33804 | 0.669018 | − | 0.743246i | \(-0.266715\pi\) | ||||
0.669018 | + | 0.743246i | \(0.266715\pi\) | |||||||
\(80\) | −0.924862 | −0.103403 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.968492 | 0.106952 | ||||||||
\(83\) | 7.46254 | 0.819120 | 0.409560 | − | 0.912283i | \(-0.365682\pi\) | ||||
0.409560 | + | 0.912283i | \(0.365682\pi\) | |||||||
\(84\) | 4.24556 | 0.463228 | ||||||||
\(85\) | −0.507801 | −0.0550788 | ||||||||
\(86\) | 11.3612 | 1.22511 | ||||||||
\(87\) | −7.33896 | −0.786819 | ||||||||
\(88\) | −2.47789 | −0.264144 | ||||||||
\(89\) | −0.591240 | −0.0626713 | −0.0313357 | − | 0.999509i | \(-0.509976\pi\) | ||||
−0.0313357 | + | 0.999509i | \(0.509976\pi\) | |||||||
\(90\) | 0.924862 | 0.0974890 | ||||||||
\(91\) | 4.24556 | 0.445056 | ||||||||
\(92\) | −2.37974 | −0.248105 | ||||||||
\(93\) | −8.34581 | −0.865420 | ||||||||
\(94\) | −2.40638 | −0.248199 | ||||||||
\(95\) | 4.31824 | 0.443042 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.00078 | −0.710821 | −0.355411 | − | 0.934710i | \(-0.615659\pi\) | ||||
−0.355411 | + | 0.934710i | \(0.615659\pi\) | |||||||
\(98\) | −11.0248 | −1.11367 | ||||||||
\(99\) | 2.47789 | 0.249038 | ||||||||
\(100\) | −4.14463 | −0.414463 | ||||||||
\(101\) | −16.7023 | −1.66194 | −0.830971 | − | 0.556316i | \(-0.812215\pi\) | ||||
−0.830971 | + | 0.556316i | \(0.812215\pi\) | |||||||
\(102\) | 0.549056 | 0.0543646 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −3.92656 | −0.383193 | ||||||||
\(106\) | 10.3792 | 1.00812 | ||||||||
\(107\) | −15.5404 | −1.50234 | −0.751172 | − | 0.660107i | \(-0.770511\pi\) | ||||
−0.751172 | + | 0.660107i | \(0.770511\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −2.53988 | −0.243277 | −0.121638 | − | 0.992574i | \(-0.538815\pi\) | ||||
−0.121638 | + | 0.992574i | \(0.538815\pi\) | |||||||
\(110\) | 2.29171 | 0.218506 | ||||||||
\(111\) | 9.19443 | 0.872697 | ||||||||
\(112\) | −4.24556 | −0.401168 | ||||||||
\(113\) | −0.761050 | −0.0715936 | −0.0357968 | − | 0.999359i | \(-0.511397\pi\) | ||||
−0.0357968 | + | 0.999359i | \(0.511397\pi\) | |||||||
\(114\) | −4.66906 | −0.437298 | ||||||||
\(115\) | 2.20093 | 0.205238 | ||||||||
\(116\) | 7.33896 | 0.681406 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −3.20528 | −0.295070 | ||||||||
\(119\) | −2.33105 | −0.213687 | ||||||||
\(120\) | −0.924862 | −0.0844280 | ||||||||
\(121\) | −4.86005 | −0.441823 | ||||||||
\(122\) | 6.92554 | 0.627009 | ||||||||
\(123\) | 0.968492 | 0.0873260 | ||||||||
\(124\) | 8.34581 | 0.749476 | ||||||||
\(125\) | 8.45752 | 0.756464 | ||||||||
\(126\) | 4.24556 | 0.378224 | ||||||||
\(127\) | 7.62232 | 0.676372 | 0.338186 | − | 0.941079i | \(-0.390187\pi\) | ||||
0.338186 | + | 0.941079i | \(0.390187\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.3612 | 1.00030 | ||||||||
\(130\) | −0.924862 | −0.0811158 | ||||||||
\(131\) | −17.1454 | −1.49800 | −0.749002 | − | 0.662567i | \(-0.769467\pi\) | ||||
−0.749002 | + | 0.662567i | \(0.769467\pi\) | |||||||
\(132\) | −2.47789 | −0.215673 | ||||||||
\(133\) | 19.8228 | 1.71885 | ||||||||
\(134\) | 2.85465 | 0.246604 | ||||||||
\(135\) | 0.924862 | 0.0795994 | ||||||||
\(136\) | −0.549056 | −0.0470812 | ||||||||
\(137\) | −2.30953 | −0.197316 | −0.0986581 | − | 0.995121i | \(-0.531455\pi\) | ||||
−0.0986581 | + | 0.995121i | \(0.531455\pi\) | |||||||
\(138\) | −2.37974 | −0.202577 | ||||||||
\(139\) | −5.43429 | −0.460931 | −0.230465 | − | 0.973081i | \(-0.574025\pi\) | ||||
−0.230465 | + | 0.973081i | \(0.574025\pi\) | |||||||
\(140\) | 3.92656 | 0.331855 | ||||||||
\(141\) | −2.40638 | −0.202654 | ||||||||
\(142\) | 7.09939 | 0.595768 | ||||||||
\(143\) | −2.47789 | −0.207212 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.78753 | −0.563674 | ||||||||
\(146\) | −7.73116 | −0.639835 | ||||||||
\(147\) | −11.0248 | −0.909308 | ||||||||
\(148\) | −9.19443 | −0.755777 | ||||||||
\(149\) | −18.1116 | −1.48376 | −0.741879 | − | 0.670533i | \(-0.766065\pi\) | ||||
−0.741879 | + | 0.670533i | \(0.766065\pi\) | |||||||
\(150\) | −4.14463 | −0.338408 | ||||||||
\(151\) | 18.4752 | 1.50349 | 0.751745 | − | 0.659454i | \(-0.229213\pi\) | ||||
0.751745 | + | 0.659454i | \(0.229213\pi\) | |||||||
\(152\) | 4.66906 | 0.378711 | ||||||||
\(153\) | 0.549056 | 0.0443885 | ||||||||
\(154\) | 10.5200 | 0.847729 | ||||||||
\(155\) | −7.71872 | −0.619983 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −2.42290 | −0.193368 | −0.0966840 | − | 0.995315i | \(-0.530824\pi\) | ||||
−0.0966840 | + | 0.995315i | \(0.530824\pi\) | |||||||
\(158\) | −11.8927 | −0.946135 | ||||||||
\(159\) | 10.3792 | 0.823128 | ||||||||
\(160\) | 0.924862 | 0.0731168 | ||||||||
\(161\) | 10.1033 | 0.796254 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −0.347587 | −0.0272251 | −0.0136126 | − | 0.999907i | \(-0.504333\pi\) | ||||
−0.0136126 | + | 0.999907i | \(0.504333\pi\) | |||||||
\(164\) | −0.968492 | −0.0756265 | ||||||||
\(165\) | 2.29171 | 0.178409 | ||||||||
\(166\) | −7.46254 | −0.579206 | ||||||||
\(167\) | −2.09894 | −0.162421 | −0.0812106 | − | 0.996697i | \(-0.525879\pi\) | ||||
−0.0812106 | + | 0.996697i | \(0.525879\pi\) | |||||||
\(168\) | −4.24556 | −0.327552 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0.507801 | 0.0389466 | ||||||||
\(171\) | −4.66906 | −0.357052 | ||||||||
\(172\) | −11.3612 | −0.866284 | ||||||||
\(173\) | −6.76812 | −0.514570 | −0.257285 | − | 0.966336i | \(-0.582828\pi\) | ||||
−0.257285 | + | 0.966336i | \(0.582828\pi\) | |||||||
\(174\) | 7.33896 | 0.556365 | ||||||||
\(175\) | 17.5963 | 1.33015 | ||||||||
\(176\) | 2.47789 | 0.186778 | ||||||||
\(177\) | −3.20528 | −0.240924 | ||||||||
\(178\) | 0.591240 | 0.0443153 | ||||||||
\(179\) | 18.8614 | 1.40976 | 0.704882 | − | 0.709325i | \(-0.251000\pi\) | ||||
0.704882 | + | 0.709325i | \(0.251000\pi\) | |||||||
\(180\) | −0.924862 | −0.0689351 | ||||||||
\(181\) | −21.5859 | −1.60447 | −0.802234 | − | 0.597010i | \(-0.796355\pi\) | ||||
−0.802234 | + | 0.597010i | \(0.796355\pi\) | |||||||
\(182\) | −4.24556 | −0.314702 | ||||||||
\(183\) | 6.92554 | 0.511951 | ||||||||
\(184\) | 2.37974 | 0.175437 | ||||||||
\(185\) | 8.50358 | 0.625195 | ||||||||
\(186\) | 8.34581 | 0.611945 | ||||||||
\(187\) | 1.36050 | 0.0994897 | ||||||||
\(188\) | 2.40638 | 0.175503 | ||||||||
\(189\) | 4.24556 | 0.308819 | ||||||||
\(190\) | −4.31824 | −0.313278 | ||||||||
\(191\) | 5.01170 | 0.362634 | 0.181317 | − | 0.983425i | \(-0.441964\pi\) | ||||
0.181317 | + | 0.983425i | \(0.441964\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 8.23014 | 0.592418 | 0.296209 | − | 0.955123i | \(-0.404277\pi\) | ||||
0.296209 | + | 0.955123i | \(0.404277\pi\) | |||||||
\(194\) | 7.00078 | 0.502626 | ||||||||
\(195\) | −0.924862 | −0.0662307 | ||||||||
\(196\) | 11.0248 | 0.787484 | ||||||||
\(197\) | −0.479465 | −0.0341605 | −0.0170802 | − | 0.999854i | \(-0.505437\pi\) | ||||
−0.0170802 | + | 0.999854i | \(0.505437\pi\) | |||||||
\(198\) | −2.47789 | −0.176096 | ||||||||
\(199\) | −12.7103 | −0.901007 | −0.450504 | − | 0.892775i | \(-0.648756\pi\) | ||||
−0.450504 | + | 0.892775i | \(0.648756\pi\) | |||||||
\(200\) | 4.14463 | 0.293070 | ||||||||
\(201\) | 2.85465 | 0.201352 | ||||||||
\(202\) | 16.7023 | 1.17517 | ||||||||
\(203\) | −31.1580 | −2.18686 | ||||||||
\(204\) | −0.549056 | −0.0384416 | ||||||||
\(205\) | 0.895721 | 0.0625599 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | −2.37974 | −0.165403 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | −11.5694 | −0.800275 | ||||||||
\(210\) | 3.92656 | 0.270958 | ||||||||
\(211\) | 10.6225 | 0.731286 | 0.365643 | − | 0.930755i | \(-0.380849\pi\) | ||||
0.365643 | + | 0.930755i | \(0.380849\pi\) | |||||||
\(212\) | −10.3792 | −0.712850 | ||||||||
\(213\) | 7.09939 | 0.486442 | ||||||||
\(214\) | 15.5404 | 1.06232 | ||||||||
\(215\) | 10.5075 | 0.716609 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −35.4326 | −2.40532 | ||||||||
\(218\) | 2.53988 | 0.172023 | ||||||||
\(219\) | −7.73116 | −0.522423 | ||||||||
\(220\) | −2.29171 | −0.154507 | ||||||||
\(221\) | −0.549056 | −0.0369335 | ||||||||
\(222\) | −9.19443 | −0.617090 | ||||||||
\(223\) | 19.4059 | 1.29951 | 0.649756 | − | 0.760143i | \(-0.274871\pi\) | ||||
0.649756 | + | 0.760143i | \(0.274871\pi\) | |||||||
\(224\) | 4.24556 | 0.283668 | ||||||||
\(225\) | −4.14463 | −0.276309 | ||||||||
\(226\) | 0.761050 | 0.0506243 | ||||||||
\(227\) | −7.36686 | −0.488956 | −0.244478 | − | 0.969655i | \(-0.578617\pi\) | ||||
−0.244478 | + | 0.969655i | \(0.578617\pi\) | |||||||
\(228\) | 4.66906 | 0.309216 | ||||||||
\(229\) | 2.87706 | 0.190122 | 0.0950608 | − | 0.995471i | \(-0.469695\pi\) | ||||
0.0950608 | + | 0.995471i | \(0.469695\pi\) | |||||||
\(230\) | −2.20093 | −0.145125 | ||||||||
\(231\) | 10.5200 | 0.692168 | ||||||||
\(232\) | −7.33896 | −0.481827 | ||||||||
\(233\) | 21.3454 | 1.39838 | 0.699190 | − | 0.714936i | \(-0.253544\pi\) | ||||
0.699190 | + | 0.714936i | \(0.253544\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | −2.22557 | −0.145180 | ||||||||
\(236\) | 3.20528 | 0.208646 | ||||||||
\(237\) | −11.8927 | −0.772516 | ||||||||
\(238\) | 2.33105 | 0.151100 | ||||||||
\(239\) | −4.40691 | −0.285059 | −0.142530 | − | 0.989791i | \(-0.545524\pi\) | ||||
−0.142530 | + | 0.989791i | \(0.545524\pi\) | |||||||
\(240\) | 0.924862 | 0.0596996 | ||||||||
\(241\) | 3.62912 | 0.233772 | 0.116886 | − | 0.993145i | \(-0.462709\pi\) | ||||
0.116886 | + | 0.993145i | \(0.462709\pi\) | |||||||
\(242\) | 4.86005 | 0.312416 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.92554 | −0.443363 | ||||||||
\(245\) | −10.1964 | −0.651424 | ||||||||
\(246\) | −0.968492 | −0.0617488 | ||||||||
\(247\) | 4.66906 | 0.297085 | ||||||||
\(248\) | −8.34581 | −0.529960 | ||||||||
\(249\) | −7.46254 | −0.472919 | ||||||||
\(250\) | −8.45752 | −0.534901 | ||||||||
\(251\) | 15.8324 | 0.999332 | 0.499666 | − | 0.866218i | \(-0.333456\pi\) | ||||
0.499666 | + | 0.866218i | \(0.333456\pi\) | |||||||
\(252\) | −4.24556 | −0.267445 | ||||||||
\(253\) | −5.89674 | −0.370725 | ||||||||
\(254\) | −7.62232 | −0.478267 | ||||||||
\(255\) | 0.507801 | 0.0317997 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −27.4973 | −1.71523 | −0.857617 | − | 0.514289i | \(-0.828056\pi\) | ||||
−0.857617 | + | 0.514289i | \(0.828056\pi\) | |||||||
\(258\) | −11.3612 | −0.707318 | ||||||||
\(259\) | 39.0355 | 2.42555 | ||||||||
\(260\) | 0.924862 | 0.0573575 | ||||||||
\(261\) | 7.33896 | 0.454270 | ||||||||
\(262\) | 17.1454 | 1.05925 | ||||||||
\(263\) | −16.7345 | −1.03190 | −0.515948 | − | 0.856620i | \(-0.672560\pi\) | ||||
−0.515948 | + | 0.856620i | \(0.672560\pi\) | |||||||
\(264\) | 2.47789 | 0.152504 | ||||||||
\(265\) | 9.59937 | 0.589685 | ||||||||
\(266\) | −19.8228 | −1.21541 | ||||||||
\(267\) | 0.591240 | 0.0361833 | ||||||||
\(268\) | −2.85465 | −0.174376 | ||||||||
\(269\) | 10.8418 | 0.661035 | 0.330517 | − | 0.943800i | \(-0.392777\pi\) | ||||
0.330517 | + | 0.943800i | \(0.392777\pi\) | |||||||
\(270\) | −0.924862 | −0.0562853 | ||||||||
\(271\) | 17.9774 | 1.09205 | 0.546026 | − | 0.837769i | \(-0.316140\pi\) | ||||
0.546026 | + | 0.837769i | \(0.316140\pi\) | |||||||
\(272\) | 0.549056 | 0.0332914 | ||||||||
\(273\) | −4.24556 | −0.256953 | ||||||||
\(274\) | 2.30953 | 0.139524 | ||||||||
\(275\) | −10.2699 | −0.619301 | ||||||||
\(276\) | 2.37974 | 0.143244 | ||||||||
\(277\) | 25.6652 | 1.54207 | 0.771036 | − | 0.636792i | \(-0.219739\pi\) | ||||
0.771036 | + | 0.636792i | \(0.219739\pi\) | |||||||
\(278\) | 5.43429 | 0.325927 | ||||||||
\(279\) | 8.34581 | 0.499651 | ||||||||
\(280\) | −3.92656 | −0.234657 | ||||||||
\(281\) | 23.1458 | 1.38076 | 0.690380 | − | 0.723447i | \(-0.257443\pi\) | ||||
0.690380 | + | 0.723447i | \(0.257443\pi\) | |||||||
\(282\) | 2.40638 | 0.143298 | ||||||||
\(283\) | −16.1782 | −0.961694 | −0.480847 | − | 0.876805i | \(-0.659671\pi\) | ||||
−0.480847 | + | 0.876805i | \(0.659671\pi\) | |||||||
\(284\) | −7.09939 | −0.421271 | ||||||||
\(285\) | −4.31824 | −0.255790 | ||||||||
\(286\) | 2.47789 | 0.146521 | ||||||||
\(287\) | 4.11179 | 0.242711 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.6985 | −0.982267 | ||||||||
\(290\) | 6.78753 | 0.398577 | ||||||||
\(291\) | 7.00078 | 0.410393 | ||||||||
\(292\) | 7.73116 | 0.452432 | ||||||||
\(293\) | 25.8709 | 1.51139 | 0.755696 | − | 0.654923i | \(-0.227299\pi\) | ||||
0.755696 | + | 0.654923i | \(0.227299\pi\) | |||||||
\(294\) | 11.0248 | 0.642978 | ||||||||
\(295\) | −2.96445 | −0.172597 | ||||||||
\(296\) | 9.19443 | 0.534415 | ||||||||
\(297\) | −2.47789 | −0.143782 | ||||||||
\(298\) | 18.1116 | 1.04918 | ||||||||
\(299\) | 2.37974 | 0.137624 | ||||||||
\(300\) | 4.14463 | 0.239290 | ||||||||
\(301\) | 48.2347 | 2.78020 | ||||||||
\(302\) | −18.4752 | −1.06313 | ||||||||
\(303\) | 16.7023 | 0.959523 | ||||||||
\(304\) | −4.66906 | −0.267789 | ||||||||
\(305\) | 6.40517 | 0.366759 | ||||||||
\(306\) | −0.549056 | −0.0313874 | ||||||||
\(307\) | 3.15586 | 0.180114 | 0.0900572 | − | 0.995937i | \(-0.471295\pi\) | ||||
0.0900572 | + | 0.995937i | \(0.471295\pi\) | |||||||
\(308\) | −10.5200 | −0.599435 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 7.71872 | 0.438394 | ||||||||
\(311\) | 6.63267 | 0.376104 | 0.188052 | − | 0.982159i | \(-0.439783\pi\) | ||||
0.188052 | + | 0.982159i | \(0.439783\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −8.29547 | −0.468888 | −0.234444 | − | 0.972130i | \(-0.575327\pi\) | ||||
−0.234444 | + | 0.972130i | \(0.575327\pi\) | |||||||
\(314\) | 2.42290 | 0.136732 | ||||||||
\(315\) | 3.92656 | 0.221236 | ||||||||
\(316\) | 11.8927 | 0.669018 | ||||||||
\(317\) | 1.19753 | 0.0672602 | 0.0336301 | − | 0.999434i | \(-0.489293\pi\) | ||||
0.0336301 | + | 0.999434i | \(0.489293\pi\) | |||||||
\(318\) | −10.3792 | −0.582039 | ||||||||
\(319\) | 18.1852 | 1.01817 | ||||||||
\(320\) | −0.924862 | −0.0517014 | ||||||||
\(321\) | 15.5404 | 0.867378 | ||||||||
\(322\) | −10.1033 | −0.563037 | ||||||||
\(323\) | −2.56358 | −0.142641 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.14463 | 0.229903 | ||||||||
\(326\) | 0.347587 | 0.0192511 | ||||||||
\(327\) | 2.53988 | 0.140456 | ||||||||
\(328\) | 0.968492 | 0.0534760 | ||||||||
\(329\) | −10.2164 | −0.563250 | ||||||||
\(330\) | −2.29171 | −0.126154 | ||||||||
\(331\) | 15.5698 | 0.855791 | 0.427896 | − | 0.903828i | \(-0.359255\pi\) | ||||
0.427896 | + | 0.903828i | \(0.359255\pi\) | |||||||
\(332\) | 7.46254 | 0.409560 | ||||||||
\(333\) | −9.19443 | −0.503852 | ||||||||
\(334\) | 2.09894 | 0.114849 | ||||||||
\(335\) | 2.64016 | 0.144247 | ||||||||
\(336\) | 4.24556 | 0.231614 | ||||||||
\(337\) | −12.9559 | −0.705752 | −0.352876 | − | 0.935670i | \(-0.614796\pi\) | ||||
−0.352876 | + | 0.935670i | \(0.614796\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 0.761050 | 0.0413346 | ||||||||
\(340\) | −0.507801 | −0.0275394 | ||||||||
\(341\) | 20.6800 | 1.11989 | ||||||||
\(342\) | 4.66906 | 0.252474 | ||||||||
\(343\) | −17.0874 | −0.922633 | ||||||||
\(344\) | 11.3612 | 0.612555 | ||||||||
\(345\) | −2.20093 | −0.118494 | ||||||||
\(346\) | 6.76812 | 0.363856 | ||||||||
\(347\) | 30.5303 | 1.63895 | 0.819476 | − | 0.573113i | \(-0.194264\pi\) | ||||
0.819476 | + | 0.573113i | \(0.194264\pi\) | |||||||
\(348\) | −7.33896 | −0.393410 | ||||||||
\(349\) | 5.81081 | 0.311046 | 0.155523 | − | 0.987832i | \(-0.450294\pi\) | ||||
0.155523 | + | 0.987832i | \(0.450294\pi\) | |||||||
\(350\) | −17.5963 | −0.940560 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | −2.47789 | −0.132072 | ||||||||
\(353\) | −21.3783 | −1.13785 | −0.568926 | − | 0.822389i | \(-0.692641\pi\) | ||||
−0.568926 | + | 0.822389i | \(0.692641\pi\) | |||||||
\(354\) | 3.20528 | 0.170359 | ||||||||
\(355\) | 6.56596 | 0.348485 | ||||||||
\(356\) | −0.591240 | −0.0313357 | ||||||||
\(357\) | 2.33105 | 0.123372 | ||||||||
\(358\) | −18.8614 | −0.996854 | ||||||||
\(359\) | 6.87350 | 0.362769 | 0.181385 | − | 0.983412i | \(-0.441942\pi\) | ||||
0.181385 | + | 0.983412i | \(0.441942\pi\) | |||||||
\(360\) | 0.924862 | 0.0487445 | ||||||||
\(361\) | 2.80016 | 0.147377 | ||||||||
\(362\) | 21.5859 | 1.13453 | ||||||||
\(363\) | 4.86005 | 0.255087 | ||||||||
\(364\) | 4.24556 | 0.222528 | ||||||||
\(365\) | −7.15025 | −0.374261 | ||||||||
\(366\) | −6.92554 | −0.362004 | ||||||||
\(367\) | 23.9000 | 1.24757 | 0.623786 | − | 0.781595i | \(-0.285594\pi\) | ||||
0.623786 | + | 0.781595i | \(0.285594\pi\) | |||||||
\(368\) | −2.37974 | −0.124053 | ||||||||
\(369\) | −0.968492 | −0.0504177 | ||||||||
\(370\) | −8.50358 | −0.442080 | ||||||||
\(371\) | 44.0657 | 2.28778 | ||||||||
\(372\) | −8.34581 | −0.432710 | ||||||||
\(373\) | −19.9817 | −1.03461 | −0.517307 | − | 0.855800i | \(-0.673066\pi\) | ||||
−0.517307 | + | 0.855800i | \(0.673066\pi\) | |||||||
\(374\) | −1.36050 | −0.0703499 | ||||||||
\(375\) | −8.45752 | −0.436745 | ||||||||
\(376\) | −2.40638 | −0.124100 | ||||||||
\(377\) | −7.33896 | −0.377976 | ||||||||
\(378\) | −4.24556 | −0.218368 | ||||||||
\(379\) | −9.19649 | −0.472392 | −0.236196 | − | 0.971705i | \(-0.575901\pi\) | ||||
−0.236196 | + | 0.971705i | \(0.575901\pi\) | |||||||
\(380\) | 4.31824 | 0.221521 | ||||||||
\(381\) | −7.62232 | −0.390503 | ||||||||
\(382\) | −5.01170 | −0.256421 | ||||||||
\(383\) | −20.1021 | −1.02717 | −0.513586 | − | 0.858038i | \(-0.671683\pi\) | ||||
−0.513586 | + | 0.858038i | \(0.671683\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 9.72958 | 0.495865 | ||||||||
\(386\) | −8.23014 | −0.418903 | ||||||||
\(387\) | −11.3612 | −0.577522 | ||||||||
\(388\) | −7.00078 | −0.355411 | ||||||||
\(389\) | 21.9274 | 1.11176 | 0.555882 | − | 0.831261i | \(-0.312381\pi\) | ||||
0.555882 | + | 0.831261i | \(0.312381\pi\) | |||||||
\(390\) | 0.924862 | 0.0468322 | ||||||||
\(391\) | −1.30661 | −0.0660782 | ||||||||
\(392\) | −11.0248 | −0.556835 | ||||||||
\(393\) | 17.1454 | 0.864874 | ||||||||
\(394\) | 0.479465 | 0.0241551 | ||||||||
\(395\) | −10.9991 | −0.553426 | ||||||||
\(396\) | 2.47789 | 0.124519 | ||||||||
\(397\) | 28.3446 | 1.42258 | 0.711288 | − | 0.702900i | \(-0.248112\pi\) | ||||
0.711288 | + | 0.702900i | \(0.248112\pi\) | |||||||
\(398\) | 12.7103 | 0.637108 | ||||||||
\(399\) | −19.8228 | −0.992381 | ||||||||
\(400\) | −4.14463 | −0.207232 | ||||||||
\(401\) | −21.8488 | −1.09108 | −0.545539 | − | 0.838086i | \(-0.683675\pi\) | ||||
−0.545539 | + | 0.838086i | \(0.683675\pi\) | |||||||
\(402\) | −2.85465 | −0.142377 | ||||||||
\(403\) | −8.34581 | −0.415734 | ||||||||
\(404\) | −16.7023 | −0.830971 | ||||||||
\(405\) | −0.924862 | −0.0459568 | ||||||||
\(406\) | 31.1580 | 1.54635 | ||||||||
\(407\) | −22.7828 | −1.12930 | ||||||||
\(408\) | 0.549056 | 0.0271823 | ||||||||
\(409\) | 2.98848 | 0.147771 | 0.0738854 | − | 0.997267i | \(-0.476460\pi\) | ||||
0.0738854 | + | 0.997267i | \(0.476460\pi\) | |||||||
\(410\) | −0.895721 | −0.0442365 | ||||||||
\(411\) | 2.30953 | 0.113921 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −13.6082 | −0.669617 | ||||||||
\(414\) | 2.37974 | 0.116958 | ||||||||
\(415\) | −6.90182 | −0.338797 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 5.43429 | 0.266118 | ||||||||
\(418\) | 11.5694 | 0.565880 | ||||||||
\(419\) | 7.64382 | 0.373425 | 0.186713 | − | 0.982415i | \(-0.440217\pi\) | ||||
0.186713 | + | 0.982415i | \(0.440217\pi\) | |||||||
\(420\) | −3.92656 | −0.191596 | ||||||||
\(421\) | 6.62472 | 0.322869 | 0.161435 | − | 0.986883i | \(-0.448388\pi\) | ||||
0.161435 | + | 0.986883i | \(0.448388\pi\) | |||||||
\(422\) | −10.6225 | −0.517097 | ||||||||
\(423\) | 2.40638 | 0.117002 | ||||||||
\(424\) | 10.3792 | 0.504061 | ||||||||
\(425\) | −2.27563 | −0.110384 | ||||||||
\(426\) | −7.09939 | −0.343967 | ||||||||
\(427\) | 29.4028 | 1.42290 | ||||||||
\(428\) | −15.5404 | −0.751172 | ||||||||
\(429\) | 2.47789 | 0.119634 | ||||||||
\(430\) | −10.5075 | −0.506719 | ||||||||
\(431\) | −23.7953 | −1.14618 | −0.573089 | − | 0.819493i | \(-0.694255\pi\) | ||||
−0.573089 | + | 0.819493i | \(0.694255\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 9.20725 | 0.442472 | 0.221236 | − | 0.975220i | \(-0.428991\pi\) | ||||
0.221236 | + | 0.975220i | \(0.428991\pi\) | |||||||
\(434\) | 35.4326 | 1.70082 | ||||||||
\(435\) | 6.78753 | 0.325437 | ||||||||
\(436\) | −2.53988 | −0.121638 | ||||||||
\(437\) | 11.1112 | 0.531519 | ||||||||
\(438\) | 7.73116 | 0.369409 | ||||||||
\(439\) | −1.68419 | −0.0803819 | −0.0401910 | − | 0.999192i | \(-0.512797\pi\) | ||||
−0.0401910 | + | 0.999192i | \(0.512797\pi\) | |||||||
\(440\) | 2.29171 | 0.109253 | ||||||||
\(441\) | 11.0248 | 0.524989 | ||||||||
\(442\) | 0.549056 | 0.0261159 | ||||||||
\(443\) | −4.58842 | −0.218003 | −0.109001 | − | 0.994042i | \(-0.534765\pi\) | ||||
−0.109001 | + | 0.994042i | \(0.534765\pi\) | |||||||
\(444\) | 9.19443 | 0.436348 | ||||||||
\(445\) | 0.546816 | 0.0259215 | ||||||||
\(446\) | −19.4059 | −0.918894 | ||||||||
\(447\) | 18.1116 | 0.856648 | ||||||||
\(448\) | −4.24556 | −0.200584 | ||||||||
\(449\) | 5.14126 | 0.242631 | 0.121316 | − | 0.992614i | \(-0.461289\pi\) | ||||
0.121316 | + | 0.992614i | \(0.461289\pi\) | |||||||
\(450\) | 4.14463 | 0.195380 | ||||||||
\(451\) | −2.39982 | −0.113003 | ||||||||
\(452\) | −0.761050 | −0.0357968 | ||||||||
\(453\) | −18.4752 | −0.868040 | ||||||||
\(454\) | 7.36686 | 0.345744 | ||||||||
\(455\) | −3.92656 | −0.184080 | ||||||||
\(456\) | −4.66906 | −0.218649 | ||||||||
\(457\) | 20.4298 | 0.955665 | 0.477833 | − | 0.878451i | \(-0.341423\pi\) | ||||
0.477833 | + | 0.878451i | \(0.341423\pi\) | |||||||
\(458\) | −2.87706 | −0.134436 | ||||||||
\(459\) | −0.549056 | −0.0256277 | ||||||||
\(460\) | 2.20093 | 0.102619 | ||||||||
\(461\) | −6.15593 | −0.286710 | −0.143355 | − | 0.989671i | \(-0.545789\pi\) | ||||
−0.143355 | + | 0.989671i | \(0.545789\pi\) | |||||||
\(462\) | −10.5200 | −0.489436 | ||||||||
\(463\) | 15.7448 | 0.731722 | 0.365861 | − | 0.930670i | \(-0.380775\pi\) | ||||
0.365861 | + | 0.930670i | \(0.380775\pi\) | |||||||
\(464\) | 7.33896 | 0.340703 | ||||||||
\(465\) | 7.71872 | 0.357947 | ||||||||
\(466\) | −21.3454 | −0.988804 | ||||||||
\(467\) | 32.0932 | 1.48510 | 0.742549 | − | 0.669791i | \(-0.233617\pi\) | ||||
0.742549 | + | 0.669791i | \(0.233617\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 12.1196 | 0.559631 | ||||||||
\(470\) | 2.22557 | 0.102658 | ||||||||
\(471\) | 2.42290 | 0.111641 | ||||||||
\(472\) | −3.20528 | −0.147535 | ||||||||
\(473\) | −28.1518 | −1.29442 | ||||||||
\(474\) | 11.8927 | 0.546251 | ||||||||
\(475\) | 19.3515 | 0.887910 | ||||||||
\(476\) | −2.33105 | −0.106843 | ||||||||
\(477\) | −10.3792 | −0.475233 | ||||||||
\(478\) | 4.40691 | 0.201567 | ||||||||
\(479\) | 41.1788 | 1.88151 | 0.940753 | − | 0.339093i | \(-0.110120\pi\) | ||||
0.940753 | + | 0.339093i | \(0.110120\pi\) | |||||||
\(480\) | −0.924862 | −0.0422140 | ||||||||
\(481\) | 9.19443 | 0.419230 | ||||||||
\(482\) | −3.62912 | −0.165302 | ||||||||
\(483\) | −10.1033 | −0.459718 | ||||||||
\(484\) | −4.86005 | −0.220911 | ||||||||
\(485\) | 6.47475 | 0.294003 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 5.83363 | 0.264347 | 0.132174 | − | 0.991227i | \(-0.457804\pi\) | ||||
0.132174 | + | 0.991227i | \(0.457804\pi\) | |||||||
\(488\) | 6.92554 | 0.313505 | ||||||||
\(489\) | 0.347587 | 0.0157184 | ||||||||
\(490\) | 10.1964 | 0.460626 | ||||||||
\(491\) | 8.06550 | 0.363991 | 0.181995 | − | 0.983299i | \(-0.441744\pi\) | ||||
0.181995 | + | 0.983299i | \(0.441744\pi\) | |||||||
\(492\) | 0.968492 | 0.0436630 | ||||||||
\(493\) | 4.02950 | 0.181480 | ||||||||
\(494\) | −4.66906 | −0.210071 | ||||||||
\(495\) | −2.29171 | −0.103005 | ||||||||
\(496\) | 8.34581 | 0.374738 | ||||||||
\(497\) | 30.1409 | 1.35200 | ||||||||
\(498\) | 7.46254 | 0.334404 | ||||||||
\(499\) | −1.14142 | −0.0510970 | −0.0255485 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255485 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(500\) | 8.45752 | 0.378232 | ||||||||
\(501\) | 2.09894 | 0.0937739 | ||||||||
\(502\) | −15.8324 | −0.706635 | ||||||||
\(503\) | −31.0106 | −1.38270 | −0.691348 | − | 0.722522i | \(-0.742983\pi\) | ||||
−0.691348 | + | 0.722522i | \(0.742983\pi\) | |||||||
\(504\) | 4.24556 | 0.189112 | ||||||||
\(505\) | 15.4473 | 0.687397 | ||||||||
\(506\) | 5.89674 | 0.262142 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 7.62232 | 0.338186 | ||||||||
\(509\) | −8.44767 | −0.374436 | −0.187218 | − | 0.982318i | \(-0.559947\pi\) | ||||
−0.187218 | + | 0.982318i | \(0.559947\pi\) | |||||||
\(510\) | −0.507801 | −0.0224858 | ||||||||
\(511\) | −32.8231 | −1.45201 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.66906 | 0.206144 | ||||||||
\(514\) | 27.4973 | 1.21285 | ||||||||
\(515\) | −0.924862 | −0.0407543 | ||||||||
\(516\) | 11.3612 | 0.500149 | ||||||||
\(517\) | 5.96275 | 0.262241 | ||||||||
\(518\) | −39.0355 | −1.71512 | ||||||||
\(519\) | 6.76812 | 0.297087 | ||||||||
\(520\) | −0.924862 | −0.0405579 | ||||||||
\(521\) | −12.4275 | −0.544459 | −0.272230 | − | 0.962232i | \(-0.587761\pi\) | ||||
−0.272230 | + | 0.962232i | \(0.587761\pi\) | |||||||
\(522\) | −7.33896 | −0.321218 | ||||||||
\(523\) | 19.8778 | 0.869195 | 0.434597 | − | 0.900625i | \(-0.356891\pi\) | ||||
0.434597 | + | 0.900625i | \(0.356891\pi\) | |||||||
\(524\) | −17.1454 | −0.749002 | ||||||||
\(525\) | −17.5963 | −0.767964 | ||||||||
\(526\) | 16.7345 | 0.729660 | ||||||||
\(527\) | 4.58232 | 0.199609 | ||||||||
\(528\) | −2.47789 | −0.107836 | ||||||||
\(529\) | −17.3368 | −0.753775 | ||||||||
\(530\) | −9.59937 | −0.416970 | ||||||||
\(531\) | 3.20528 | 0.139098 | ||||||||
\(532\) | 19.8228 | 0.859427 | ||||||||
\(533\) | 0.968492 | 0.0419500 | ||||||||
\(534\) | −0.591240 | −0.0255855 | ||||||||
\(535\) | 14.3727 | 0.621386 | ||||||||
\(536\) | 2.85465 | 0.123302 | ||||||||
\(537\) | −18.8614 | −0.813928 | ||||||||
\(538\) | −10.8418 | −0.467422 | ||||||||
\(539\) | 27.3182 | 1.17668 | ||||||||
\(540\) | 0.924862 | 0.0397997 | ||||||||
\(541\) | −22.9394 | −0.986243 | −0.493122 | − | 0.869960i | \(-0.664144\pi\) | ||||
−0.493122 | + | 0.869960i | \(0.664144\pi\) | |||||||
\(542\) | −17.9774 | −0.772197 | ||||||||
\(543\) | 21.5859 | 0.926340 | ||||||||
\(544\) | −0.549056 | −0.0235406 | ||||||||
\(545\) | 2.34904 | 0.100622 | ||||||||
\(546\) | 4.24556 | 0.181693 | ||||||||
\(547\) | −29.0471 | −1.24196 | −0.620981 | − | 0.783825i | \(-0.713266\pi\) | ||||
−0.620981 | + | 0.783825i | \(0.713266\pi\) | |||||||
\(548\) | −2.30953 | −0.0986581 | ||||||||
\(549\) | −6.92554 | −0.295575 | ||||||||
\(550\) | 10.2699 | 0.437912 | ||||||||
\(551\) | −34.2661 | −1.45978 | ||||||||
\(552\) | −2.37974 | −0.101289 | ||||||||
\(553\) | −50.4913 | −2.14711 | ||||||||
\(554\) | −25.6652 | −1.09041 | ||||||||
\(555\) | −8.50358 | −0.360957 | ||||||||
\(556\) | −5.43429 | −0.230465 | ||||||||
\(557\) | −1.52392 | −0.0645706 | −0.0322853 | − | 0.999479i | \(-0.510279\pi\) | ||||
−0.0322853 | + | 0.999479i | \(0.510279\pi\) | |||||||
\(558\) | −8.34581 | −0.353306 | ||||||||
\(559\) | 11.3612 | 0.480528 | ||||||||
\(560\) | 3.92656 | 0.165927 | ||||||||
\(561\) | −1.36050 | −0.0574404 | ||||||||
\(562\) | −23.1458 | −0.976345 | ||||||||
\(563\) | −28.0389 | −1.18170 | −0.590850 | − | 0.806781i | \(-0.701207\pi\) | ||||
−0.590850 | + | 0.806781i | \(0.701207\pi\) | |||||||
\(564\) | −2.40638 | −0.101327 | ||||||||
\(565\) | 0.703866 | 0.0296119 | ||||||||
\(566\) | 16.1782 | 0.680020 | ||||||||
\(567\) | −4.24556 | −0.178297 | ||||||||
\(568\) | 7.09939 | 0.297884 | ||||||||
\(569\) | −32.8020 | −1.37513 | −0.687566 | − | 0.726122i | \(-0.741321\pi\) | ||||
−0.687566 | + | 0.726122i | \(0.741321\pi\) | |||||||
\(570\) | 4.31824 | 0.180871 | ||||||||
\(571\) | 42.3562 | 1.77255 | 0.886277 | − | 0.463156i | \(-0.153283\pi\) | ||||
0.886277 | + | 0.463156i | \(0.153283\pi\) | |||||||
\(572\) | −2.47789 | −0.103606 | ||||||||
\(573\) | −5.01170 | −0.209367 | ||||||||
\(574\) | −4.11179 | −0.171623 | ||||||||
\(575\) | 9.86315 | 0.411322 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 30.3341 | 1.26283 | 0.631413 | − | 0.775447i | \(-0.282475\pi\) | ||||
0.631413 | + | 0.775447i | \(0.282475\pi\) | |||||||
\(578\) | 16.6985 | 0.694568 | ||||||||
\(579\) | −8.23014 | −0.342033 | ||||||||
\(580\) | −6.78753 | −0.281837 | ||||||||
\(581\) | −31.6827 | −1.31442 | ||||||||
\(582\) | −7.00078 | −0.290191 | ||||||||
\(583\) | −25.7187 | −1.06516 | ||||||||
\(584\) | −7.73116 | −0.319918 | ||||||||
\(585\) | 0.924862 | 0.0382383 | ||||||||
\(586\) | −25.8709 | −1.06872 | ||||||||
\(587\) | 12.0373 | 0.496834 | 0.248417 | − | 0.968653i | \(-0.420090\pi\) | ||||
0.248417 | + | 0.968653i | \(0.420090\pi\) | |||||||
\(588\) | −11.0248 | −0.454654 | ||||||||
\(589\) | −38.9671 | −1.60561 | ||||||||
\(590\) | 2.96445 | 0.122044 | ||||||||
\(591\) | 0.479465 | 0.0197226 | ||||||||
\(592\) | −9.19443 | −0.377889 | ||||||||
\(593\) | 13.7264 | 0.563676 | 0.281838 | − | 0.959462i | \(-0.409056\pi\) | ||||
0.281838 | + | 0.959462i | \(0.409056\pi\) | |||||||
\(594\) | 2.47789 | 0.101669 | ||||||||
\(595\) | 2.15590 | 0.0883833 | ||||||||
\(596\) | −18.1116 | −0.741879 | ||||||||
\(597\) | 12.7103 | 0.520197 | ||||||||
\(598\) | −2.37974 | −0.0973149 | ||||||||
\(599\) | −7.25685 | −0.296507 | −0.148253 | − | 0.988949i | \(-0.547365\pi\) | ||||
−0.148253 | + | 0.988949i | \(0.547365\pi\) | |||||||
\(600\) | −4.14463 | −0.169204 | ||||||||
\(601\) | 23.7190 | 0.967517 | 0.483758 | − | 0.875202i | \(-0.339271\pi\) | ||||
0.483758 | + | 0.875202i | \(0.339271\pi\) | |||||||
\(602\) | −48.2347 | −1.96590 | ||||||||
\(603\) | −2.85465 | −0.116250 | ||||||||
\(604\) | 18.4752 | 0.751745 | ||||||||
\(605\) | 4.49488 | 0.182743 | ||||||||
\(606\) | −16.7023 | −0.678485 | ||||||||
\(607\) | 24.7564 | 1.00483 | 0.502416 | − | 0.864626i | \(-0.332445\pi\) | ||||
0.502416 | + | 0.864626i | \(0.332445\pi\) | |||||||
\(608\) | 4.66906 | 0.189356 | ||||||||
\(609\) | 31.1580 | 1.26259 | ||||||||
\(610\) | −6.40517 | −0.259338 | ||||||||
\(611\) | −2.40638 | −0.0973517 | ||||||||
\(612\) | 0.549056 | 0.0221943 | ||||||||
\(613\) | 37.8561 | 1.52899 | 0.764496 | − | 0.644629i | \(-0.222988\pi\) | ||||
0.764496 | + | 0.644629i | \(0.222988\pi\) | |||||||
\(614\) | −3.15586 | −0.127360 | ||||||||
\(615\) | −0.895721 | −0.0361190 | ||||||||
\(616\) | 10.5200 | 0.423864 | ||||||||
\(617\) | 6.05777 | 0.243877 | 0.121938 | − | 0.992538i | \(-0.461089\pi\) | ||||
0.121938 | + | 0.992538i | \(0.461089\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −30.3573 | −1.22016 | −0.610081 | − | 0.792339i | \(-0.708863\pi\) | ||||
−0.610081 | + | 0.792339i | \(0.708863\pi\) | |||||||
\(620\) | −7.71872 | −0.309991 | ||||||||
\(621\) | 2.37974 | 0.0954958 | ||||||||
\(622\) | −6.63267 | −0.265946 | ||||||||
\(623\) | 2.51015 | 0.100567 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 12.9011 | 0.516044 | ||||||||
\(626\) | 8.29547 | 0.331554 | ||||||||
\(627\) | 11.5694 | 0.462039 | ||||||||
\(628\) | −2.42290 | −0.0966840 | ||||||||
\(629\) | −5.04826 | −0.201287 | ||||||||
\(630\) | −3.92656 | −0.156438 | ||||||||
\(631\) | −0.227520 | −0.00905741 | −0.00452871 | − | 0.999990i | \(-0.501442\pi\) | ||||
−0.00452871 | + | 0.999990i | \(0.501442\pi\) | |||||||
\(632\) | −11.8927 | −0.473067 | ||||||||
\(633\) | −10.6225 | −0.422208 | ||||||||
\(634\) | −1.19753 | −0.0475601 | ||||||||
\(635\) | −7.04960 | −0.279755 | ||||||||
\(636\) | 10.3792 | 0.411564 | ||||||||
\(637\) | −11.0248 | −0.436817 | ||||||||
\(638\) | −18.1852 | −0.719957 | ||||||||
\(639\) | −7.09939 | −0.280848 | ||||||||
\(640\) | 0.924862 | 0.0365584 | ||||||||
\(641\) | −32.0388 | −1.26546 | −0.632728 | − | 0.774374i | \(-0.718065\pi\) | ||||
−0.632728 | + | 0.774374i | \(0.718065\pi\) | |||||||
\(642\) | −15.5404 | −0.613329 | ||||||||
\(643\) | 10.9375 | 0.431334 | 0.215667 | − | 0.976467i | \(-0.430807\pi\) | ||||
0.215667 | + | 0.976467i | \(0.430807\pi\) | |||||||
\(644\) | 10.1033 | 0.398127 | ||||||||
\(645\) | −10.5075 | −0.413734 | ||||||||
\(646\) | 2.56358 | 0.100863 | ||||||||
\(647\) | 0.956751 | 0.0376137 | 0.0188069 | − | 0.999823i | \(-0.494013\pi\) | ||||
0.0188069 | + | 0.999823i | \(0.494013\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 7.94235 | 0.311764 | ||||||||
\(650\) | −4.14463 | −0.162566 | ||||||||
\(651\) | 35.4326 | 1.38871 | ||||||||
\(652\) | −0.347587 | −0.0136126 | ||||||||
\(653\) | 40.7145 | 1.59328 | 0.796641 | − | 0.604453i | \(-0.206608\pi\) | ||||
0.796641 | + | 0.604453i | \(0.206608\pi\) | |||||||
\(654\) | −2.53988 | −0.0993173 | ||||||||
\(655\) | 15.8572 | 0.619591 | ||||||||
\(656\) | −0.968492 | −0.0378133 | ||||||||
\(657\) | 7.73116 | 0.301621 | ||||||||
\(658\) | 10.2164 | 0.398278 | ||||||||
\(659\) | 1.62392 | 0.0632589 | 0.0316295 | − | 0.999500i | \(-0.489930\pi\) | ||||
0.0316295 | + | 0.999500i | \(0.489930\pi\) | |||||||
\(660\) | 2.29171 | 0.0892046 | ||||||||
\(661\) | −28.9108 | −1.12450 | −0.562251 | − | 0.826967i | \(-0.690064\pi\) | ||||
−0.562251 | + | 0.826967i | \(0.690064\pi\) | |||||||
\(662\) | −15.5698 | −0.605136 | ||||||||
\(663\) | 0.549056 | 0.0213236 | ||||||||
\(664\) | −7.46254 | −0.289603 | ||||||||
\(665\) | −18.3333 | −0.710937 | ||||||||
\(666\) | 9.19443 | 0.356277 | ||||||||
\(667\) | −17.4648 | −0.676241 | ||||||||
\(668\) | −2.09894 | −0.0812106 | ||||||||
\(669\) | −19.4059 | −0.750274 | ||||||||
\(670\) | −2.64016 | −0.101998 | ||||||||
\(671\) | −17.1608 | −0.662483 | ||||||||
\(672\) | −4.24556 | −0.163776 | ||||||||
\(673\) | 28.5791 | 1.10164 | 0.550821 | − | 0.834624i | \(-0.314315\pi\) | ||||
0.550821 | + | 0.834624i | \(0.314315\pi\) | |||||||
\(674\) | 12.9559 | 0.499042 | ||||||||
\(675\) | 4.14463 | 0.159527 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −7.90647 | −0.303870 | −0.151935 | − | 0.988390i | \(-0.548550\pi\) | ||||
−0.151935 | + | 0.988390i | \(0.548550\pi\) | |||||||
\(678\) | −0.761050 | −0.0292279 | ||||||||
\(679\) | 29.7222 | 1.14063 | ||||||||
\(680\) | 0.507801 | 0.0194733 | ||||||||
\(681\) | 7.36686 | 0.282299 | ||||||||
\(682\) | −20.6800 | −0.791879 | ||||||||
\(683\) | 29.6214 | 1.13343 | 0.566716 | − | 0.823913i | \(-0.308214\pi\) | ||||
0.566716 | + | 0.823913i | \(0.308214\pi\) | |||||||
\(684\) | −4.66906 | −0.178526 | ||||||||
\(685\) | 2.13599 | 0.0816121 | ||||||||
\(686\) | 17.0874 | 0.652400 | ||||||||
\(687\) | −2.87706 | −0.109767 | ||||||||
\(688\) | −11.3612 | −0.433142 | ||||||||
\(689\) | 10.3792 | 0.395418 | ||||||||
\(690\) | 2.20093 | 0.0837881 | ||||||||
\(691\) | −7.71057 | −0.293324 | −0.146662 | − | 0.989187i | \(-0.546853\pi\) | ||||
−0.146662 | + | 0.989187i | \(0.546853\pi\) | |||||||
\(692\) | −6.76812 | −0.257285 | ||||||||
\(693\) | −10.5200 | −0.399623 | ||||||||
\(694\) | −30.5303 | −1.15891 | ||||||||
\(695\) | 5.02597 | 0.190646 | ||||||||
\(696\) | 7.33896 | 0.278183 | ||||||||
\(697\) | −0.531756 | −0.0201417 | ||||||||
\(698\) | −5.81081 | −0.219942 | ||||||||
\(699\) | −21.3454 | −0.807355 | ||||||||
\(700\) | 17.5963 | 0.665077 | ||||||||
\(701\) | 25.3023 | 0.955654 | 0.477827 | − | 0.878454i | \(-0.341425\pi\) | ||||
0.477827 | + | 0.878454i | \(0.341425\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 42.9294 | 1.61911 | ||||||||
\(704\) | 2.47789 | 0.0933891 | ||||||||
\(705\) | 2.22557 | 0.0838198 | ||||||||
\(706\) | 21.3783 | 0.804582 | ||||||||
\(707\) | 70.9107 | 2.66687 | ||||||||
\(708\) | −3.20528 | −0.120462 | ||||||||
\(709\) | −13.7359 | −0.515861 | −0.257930 | − | 0.966164i | \(-0.583041\pi\) | ||||
−0.257930 | + | 0.966164i | \(0.583041\pi\) | |||||||
\(710\) | −6.56596 | −0.246416 | ||||||||
\(711\) | 11.8927 | 0.446012 | ||||||||
\(712\) | 0.591240 | 0.0221577 | ||||||||
\(713\) | −19.8609 | −0.743796 | ||||||||
\(714\) | −2.33105 | −0.0872373 | ||||||||
\(715\) | 2.29171 | 0.0857050 | ||||||||
\(716\) | 18.8614 | 0.704882 | ||||||||
\(717\) | 4.40691 | 0.164579 | ||||||||
\(718\) | −6.87350 | −0.256517 | ||||||||
\(719\) | −8.94794 | −0.333702 | −0.166851 | − | 0.985982i | \(-0.553360\pi\) | ||||
−0.166851 | + | 0.985982i | \(0.553360\pi\) | |||||||
\(720\) | −0.924862 | −0.0344676 | ||||||||
\(721\) | −4.24556 | −0.158113 | ||||||||
\(722\) | −2.80016 | −0.104211 | ||||||||
\(723\) | −3.62912 | −0.134968 | ||||||||
\(724\) | −21.5859 | −0.802234 | ||||||||
\(725\) | −30.4173 | −1.12967 | ||||||||
\(726\) | −4.86005 | −0.180373 | ||||||||
\(727\) | 40.1106 | 1.48762 | 0.743809 | − | 0.668392i | \(-0.233017\pi\) | ||||
0.743809 | + | 0.668392i | \(0.233017\pi\) | |||||||
\(728\) | −4.24556 | −0.157351 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.15025 | 0.264643 | ||||||||
\(731\) | −6.23794 | −0.230718 | ||||||||
\(732\) | 6.92554 | 0.255975 | ||||||||
\(733\) | 30.3820 | 1.12219 | 0.561093 | − | 0.827753i | \(-0.310381\pi\) | ||||
0.561093 | + | 0.827753i | \(0.310381\pi\) | |||||||
\(734\) | −23.9000 | −0.882166 | ||||||||
\(735\) | 10.1964 | 0.376100 | ||||||||
\(736\) | 2.37974 | 0.0877185 | ||||||||
\(737\) | −7.07352 | −0.260557 | ||||||||
\(738\) | 0.968492 | 0.0356507 | ||||||||
\(739\) | 48.9164 | 1.79942 | 0.899710 | − | 0.436489i | \(-0.143778\pi\) | ||||
0.899710 | + | 0.436489i | \(0.143778\pi\) | |||||||
\(740\) | 8.50358 | 0.312598 | ||||||||
\(741\) | −4.66906 | −0.171522 | ||||||||
\(742\) | −44.0657 | −1.61770 | ||||||||
\(743\) | 6.61259 | 0.242592 | 0.121296 | − | 0.992616i | \(-0.461295\pi\) | ||||
0.121296 | + | 0.992616i | \(0.461295\pi\) | |||||||
\(744\) | 8.34581 | 0.305972 | ||||||||
\(745\) | 16.7507 | 0.613699 | ||||||||
\(746\) | 19.9817 | 0.731583 | ||||||||
\(747\) | 7.46254 | 0.273040 | ||||||||
\(748\) | 1.36050 | 0.0497449 | ||||||||
\(749\) | 65.9775 | 2.41077 | ||||||||
\(750\) | 8.45752 | 0.308825 | ||||||||
\(751\) | 32.7253 | 1.19416 | 0.597081 | − | 0.802181i | \(-0.296327\pi\) | ||||
0.597081 | + | 0.802181i | \(0.296327\pi\) | |||||||
\(752\) | 2.40638 | 0.0877517 | ||||||||
\(753\) | −15.8324 | −0.576965 | ||||||||
\(754\) | 7.33896 | 0.267269 | ||||||||
\(755\) | −17.0870 | −0.621860 | ||||||||
\(756\) | 4.24556 | 0.154409 | ||||||||
\(757\) | −30.9809 | −1.12602 | −0.563010 | − | 0.826450i | \(-0.690357\pi\) | ||||
−0.563010 | + | 0.826450i | \(0.690357\pi\) | |||||||
\(758\) | 9.19649 | 0.334032 | ||||||||
\(759\) | 5.89674 | 0.214038 | ||||||||
\(760\) | −4.31824 | −0.156639 | ||||||||
\(761\) | 0.601756 | 0.0218136 | 0.0109068 | − | 0.999941i | \(-0.496528\pi\) | ||||
0.0109068 | + | 0.999941i | \(0.496528\pi\) | |||||||
\(762\) | 7.62232 | 0.276128 | ||||||||
\(763\) | 10.7832 | 0.390379 | ||||||||
\(764\) | 5.01170 | 0.181317 | ||||||||
\(765\) | −0.507801 | −0.0183596 | ||||||||
\(766\) | 20.1021 | 0.726320 | ||||||||
\(767\) | −3.20528 | −0.115736 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 25.4331 | 0.917142 | 0.458571 | − | 0.888658i | \(-0.348361\pi\) | ||||
0.458571 | + | 0.888658i | \(0.348361\pi\) | |||||||
\(770\) | −9.72958 | −0.350630 | ||||||||
\(771\) | 27.4973 | 0.990291 | ||||||||
\(772\) | 8.23014 | 0.296209 | ||||||||
\(773\) | 2.97235 | 0.106908 | 0.0534540 | − | 0.998570i | \(-0.482977\pi\) | ||||
0.0534540 | + | 0.998570i | \(0.482977\pi\) | |||||||
\(774\) | 11.3612 | 0.408370 | ||||||||
\(775\) | −34.5903 | −1.24252 | ||||||||
\(776\) | 7.00078 | 0.251313 | ||||||||
\(777\) | −39.0355 | −1.40039 | ||||||||
\(778\) | −21.9274 | −0.786136 | ||||||||
\(779\) | 4.52195 | 0.162016 | ||||||||
\(780\) | −0.924862 | −0.0331154 | ||||||||
\(781\) | −17.5915 | −0.629474 | ||||||||
\(782\) | 1.30661 | 0.0467243 | ||||||||
\(783\) | −7.33896 | −0.262273 | ||||||||
\(784\) | 11.0248 | 0.393742 | ||||||||
\(785\) | 2.24084 | 0.0799791 | ||||||||
\(786\) | −17.1454 | −0.611558 | ||||||||
\(787\) | 49.4887 | 1.76408 | 0.882041 | − | 0.471173i | \(-0.156169\pi\) | ||||
0.882041 | + | 0.471173i | \(0.156169\pi\) | |||||||
\(788\) | −0.479465 | −0.0170802 | ||||||||
\(789\) | 16.7345 | 0.595765 | ||||||||
\(790\) | 10.9991 | 0.391332 | ||||||||
\(791\) | 3.23108 | 0.114884 | ||||||||
\(792\) | −2.47789 | −0.0880481 | ||||||||
\(793\) | 6.92554 | 0.245933 | ||||||||
\(794\) | −28.3446 | −1.00591 | ||||||||
\(795\) | −9.59937 | −0.340455 | ||||||||
\(796\) | −12.7103 | −0.450504 | ||||||||
\(797\) | 24.3948 | 0.864107 | 0.432054 | − | 0.901848i | \(-0.357789\pi\) | ||||
0.432054 | + | 0.901848i | \(0.357789\pi\) | |||||||
\(798\) | 19.8228 | 0.701719 | ||||||||
\(799\) | 1.32124 | 0.0467420 | ||||||||
\(800\) | 4.14463 | 0.146535 | ||||||||
\(801\) | −0.591240 | −0.0208904 | ||||||||
\(802\) | 21.8488 | 0.771508 | ||||||||
\(803\) | 19.1570 | 0.676035 | ||||||||
\(804\) | 2.85465 | 0.100676 | ||||||||
\(805\) | −9.34419 | −0.329339 | ||||||||
\(806\) | 8.34581 | 0.293969 | ||||||||
\(807\) | −10.8418 | −0.381649 | ||||||||
\(808\) | 16.7023 | 0.587585 | ||||||||
\(809\) | −16.6019 | −0.583692 | −0.291846 | − | 0.956465i | \(-0.594270\pi\) | ||||
−0.291846 | + | 0.956465i | \(0.594270\pi\) | |||||||
\(810\) | 0.924862 | 0.0324963 | ||||||||
\(811\) | −28.0278 | −0.984189 | −0.492094 | − | 0.870542i | \(-0.663769\pi\) | ||||
−0.492094 | + | 0.870542i | \(0.663769\pi\) | |||||||
\(812\) | −31.1580 | −1.09343 | ||||||||
\(813\) | −17.9774 | −0.630496 | ||||||||
\(814\) | 22.7828 | 0.798537 | ||||||||
\(815\) | 0.321470 | 0.0112606 | ||||||||
\(816\) | −0.549056 | −0.0192208 | ||||||||
\(817\) | 53.0462 | 1.85585 | ||||||||
\(818\) | −2.98848 | −0.104490 | ||||||||
\(819\) | 4.24556 | 0.148352 | ||||||||
\(820\) | 0.895721 | 0.0312799 | ||||||||
\(821\) | −8.96226 | −0.312785 | −0.156393 | − | 0.987695i | \(-0.549987\pi\) | ||||
−0.156393 | + | 0.987695i | \(0.549987\pi\) | |||||||
\(822\) | −2.30953 | −0.0805540 | ||||||||
\(823\) | 29.9469 | 1.04388 | 0.521942 | − | 0.852981i | \(-0.325208\pi\) | ||||
0.521942 | + | 0.852981i | \(0.325208\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 10.2699 | 0.357554 | ||||||||
\(826\) | 13.6082 | 0.473491 | ||||||||
\(827\) | −26.2269 | −0.911999 | −0.455999 | − | 0.889980i | \(-0.650718\pi\) | ||||
−0.455999 | + | 0.889980i | \(0.650718\pi\) | |||||||
\(828\) | −2.37974 | −0.0827017 | ||||||||
\(829\) | −36.2795 | −1.26004 | −0.630020 | − | 0.776579i | \(-0.716953\pi\) | ||||
−0.630020 | + | 0.776579i | \(0.716953\pi\) | |||||||
\(830\) | 6.90182 | 0.239566 | ||||||||
\(831\) | −25.6652 | −0.890315 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 6.05322 | 0.209732 | ||||||||
\(834\) | −5.43429 | −0.188174 | ||||||||
\(835\) | 1.94123 | 0.0671791 | ||||||||
\(836\) | −11.5694 | −0.400137 | ||||||||
\(837\) | −8.34581 | −0.288473 | ||||||||
\(838\) | −7.64382 | −0.264051 | ||||||||
\(839\) | 43.7783 | 1.51139 | 0.755697 | − | 0.654921i | \(-0.227298\pi\) | ||||
0.755697 | + | 0.654921i | \(0.227298\pi\) | |||||||
\(840\) | 3.92656 | 0.135479 | ||||||||
\(841\) | 24.8604 | 0.857255 | ||||||||
\(842\) | −6.62472 | −0.228303 | ||||||||
\(843\) | −23.1458 | −0.797182 | ||||||||
\(844\) | 10.6225 | 0.365643 | ||||||||
\(845\) | −0.924862 | −0.0318162 | ||||||||
\(846\) | −2.40638 | −0.0827331 | ||||||||
\(847\) | 20.6336 | 0.708980 | ||||||||
\(848\) | −10.3792 | −0.356425 | ||||||||
\(849\) | 16.1782 | 0.555234 | ||||||||
\(850\) | 2.27563 | 0.0780536 | ||||||||
\(851\) | 21.8804 | 0.750049 | ||||||||
\(852\) | 7.09939 | 0.243221 | ||||||||
\(853\) | 24.6685 | 0.844632 | 0.422316 | − | 0.906449i | \(-0.361217\pi\) | ||||
0.422316 | + | 0.906449i | \(0.361217\pi\) | |||||||
\(854\) | −29.4028 | −1.00614 | ||||||||
\(855\) | 4.31824 | 0.147681 | ||||||||
\(856\) | 15.5404 | 0.531159 | ||||||||
\(857\) | 35.4427 | 1.21070 | 0.605350 | − | 0.795959i | \(-0.293033\pi\) | ||||
0.605350 | + | 0.795959i | \(0.293033\pi\) | |||||||
\(858\) | −2.47789 | −0.0845938 | ||||||||
\(859\) | −5.55366 | −0.189488 | −0.0947442 | − | 0.995502i | \(-0.530203\pi\) | ||||
−0.0947442 | + | 0.995502i | \(0.530203\pi\) | |||||||
\(860\) | 10.5075 | 0.358304 | ||||||||
\(861\) | −4.11179 | −0.140129 | ||||||||
\(862\) | 23.7953 | 0.810470 | ||||||||
\(863\) | −45.0178 | −1.53242 | −0.766211 | − | 0.642589i | \(-0.777860\pi\) | ||||
−0.766211 | + | 0.642589i | \(0.777860\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 6.25957 | 0.212832 | ||||||||
\(866\) | −9.20725 | −0.312875 | ||||||||
\(867\) | 16.6985 | 0.567112 | ||||||||
\(868\) | −35.4326 | −1.20266 | ||||||||
\(869\) | 29.4689 | 0.999664 | ||||||||
\(870\) | −6.78753 | −0.230119 | ||||||||
\(871\) | 2.85465 | 0.0967262 | ||||||||
\(872\) | 2.53988 | 0.0860113 | ||||||||
\(873\) | −7.00078 | −0.236940 | ||||||||
\(874\) | −11.1112 | −0.375841 | ||||||||
\(875\) | −35.9069 | −1.21387 | ||||||||
\(876\) | −7.73116 | −0.261212 | ||||||||
\(877\) | 22.3613 | 0.755089 | 0.377545 | − | 0.925991i | \(-0.376769\pi\) | ||||
0.377545 | + | 0.925991i | \(0.376769\pi\) | |||||||
\(878\) | 1.68419 | 0.0568386 | ||||||||
\(879\) | −25.8709 | −0.872602 | ||||||||
\(880\) | −2.29171 | −0.0772535 | ||||||||
\(881\) | 16.0301 | 0.540067 | 0.270033 | − | 0.962851i | \(-0.412965\pi\) | ||||
0.270033 | + | 0.962851i | \(0.412965\pi\) | |||||||
\(882\) | −11.0248 | −0.371223 | ||||||||
\(883\) | −11.1985 | −0.376859 | −0.188429 | − | 0.982087i | \(-0.560340\pi\) | ||||
−0.188429 | + | 0.982087i | \(0.560340\pi\) | |||||||
\(884\) | −0.549056 | −0.0184668 | ||||||||
\(885\) | 2.96445 | 0.0996488 | ||||||||
\(886\) | 4.58842 | 0.154151 | ||||||||
\(887\) | 34.0707 | 1.14398 | 0.571992 | − | 0.820259i | \(-0.306171\pi\) | ||||
0.571992 | + | 0.820259i | \(0.306171\pi\) | |||||||
\(888\) | −9.19443 | −0.308545 | ||||||||
\(889\) | −32.3610 | −1.08535 | ||||||||
\(890\) | −0.546816 | −0.0183293 | ||||||||
\(891\) | 2.47789 | 0.0830125 | ||||||||
\(892\) | 19.4059 | 0.649756 | ||||||||
\(893\) | −11.2355 | −0.375983 | ||||||||
\(894\) | −18.1116 | −0.605742 | ||||||||
\(895\) | −17.4442 | −0.583094 | ||||||||
\(896\) | 4.24556 | 0.141834 | ||||||||
\(897\) | −2.37974 | −0.0794573 | ||||||||
\(898\) | −5.14126 | −0.171566 | ||||||||
\(899\) | 61.2496 | 2.04279 | ||||||||
\(900\) | −4.14463 | −0.138154 | ||||||||
\(901\) | −5.69879 | −0.189854 | ||||||||
\(902\) | 2.39982 | 0.0799052 | ||||||||
\(903\) | −48.2347 | −1.60515 | ||||||||
\(904\) | 0.761050 | 0.0253121 | ||||||||
\(905\) | 19.9640 | 0.663625 | ||||||||
\(906\) | 18.4752 | 0.613797 | ||||||||
\(907\) | 10.0554 | 0.333885 | 0.166943 | − | 0.985967i | \(-0.446610\pi\) | ||||
0.166943 | + | 0.985967i | \(0.446610\pi\) | |||||||
\(908\) | −7.36686 | −0.244478 | ||||||||
\(909\) | −16.7023 | −0.553981 | ||||||||
\(910\) | 3.92656 | 0.130164 | ||||||||
\(911\) | 9.21796 | 0.305405 | 0.152702 | − | 0.988272i | \(-0.451202\pi\) | ||||
0.152702 | + | 0.988272i | \(0.451202\pi\) | |||||||
\(912\) | 4.66906 | 0.154608 | ||||||||
\(913\) | 18.4914 | 0.611975 | ||||||||
\(914\) | −20.4298 | −0.675758 | ||||||||
\(915\) | −6.40517 | −0.211748 | ||||||||
\(916\) | 2.87706 | 0.0950608 | ||||||||
\(917\) | 72.7920 | 2.40380 | ||||||||
\(918\) | 0.549056 | 0.0181215 | ||||||||
\(919\) | 51.7380 | 1.70668 | 0.853339 | − | 0.521356i | \(-0.174574\pi\) | ||||
0.853339 | + | 0.521356i | \(0.174574\pi\) | |||||||
\(920\) | −2.20093 | −0.0725626 | ||||||||
\(921\) | −3.15586 | −0.103989 | ||||||||
\(922\) | 6.15593 | 0.202735 | ||||||||
\(923\) | 7.09939 | 0.233679 | ||||||||
\(924\) | 10.5200 | 0.346084 | ||||||||
\(925\) | 38.1075 | 1.25297 | ||||||||
\(926\) | −15.7448 | −0.517406 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −7.33896 | −0.240913 | ||||||||
\(929\) | 15.4283 | 0.506185 | 0.253092 | − | 0.967442i | \(-0.418552\pi\) | ||||
0.253092 | + | 0.967442i | \(0.418552\pi\) | |||||||
\(930\) | −7.71872 | −0.253107 | ||||||||
\(931\) | −51.4754 | −1.68704 | ||||||||
\(932\) | 21.3454 | 0.699190 | ||||||||
\(933\) | −6.63267 | −0.217144 | ||||||||
\(934\) | −32.0932 | −1.05012 | ||||||||
\(935\) | −1.25828 | −0.0411500 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | −24.8677 | −0.812392 | −0.406196 | − | 0.913786i | \(-0.633145\pi\) | ||||
−0.406196 | + | 0.913786i | \(0.633145\pi\) | |||||||
\(938\) | −12.1196 | −0.395719 | ||||||||
\(939\) | 8.29547 | 0.270713 | ||||||||
\(940\) | −2.22557 | −0.0725901 | ||||||||
\(941\) | 20.6871 | 0.674379 | 0.337189 | − | 0.941437i | \(-0.390524\pi\) | ||||
0.337189 | + | 0.941437i | \(0.390524\pi\) | |||||||
\(942\) | −2.42290 | −0.0789422 | ||||||||
\(943\) | 2.30476 | 0.0750533 | ||||||||
\(944\) | 3.20528 | 0.104323 | ||||||||
\(945\) | −3.92656 | −0.127731 | ||||||||
\(946\) | 28.1518 | 0.915295 | ||||||||
\(947\) | −56.3540 | −1.83126 | −0.915629 | − | 0.402024i | \(-0.868307\pi\) | ||||
−0.915629 | + | 0.402024i | \(0.868307\pi\) | |||||||
\(948\) | −11.8927 | −0.386258 | ||||||||
\(949\) | −7.73116 | −0.250964 | ||||||||
\(950\) | −19.3515 | −0.627847 | ||||||||
\(951\) | −1.19753 | −0.0388327 | ||||||||
\(952\) | 2.33105 | 0.0755498 | ||||||||
\(953\) | 16.3780 | 0.530537 | 0.265268 | − | 0.964175i | \(-0.414539\pi\) | ||||
0.265268 | + | 0.964175i | \(0.414539\pi\) | |||||||
\(954\) | 10.3792 | 0.336041 | ||||||||
\(955\) | −4.63513 | −0.149989 | ||||||||
\(956\) | −4.40691 | −0.142530 | ||||||||
\(957\) | −18.1852 | −0.587843 | ||||||||
\(958\) | −41.1788 | −1.33043 | ||||||||
\(959\) | 9.80523 | 0.316627 | ||||||||
\(960\) | 0.924862 | 0.0298498 | ||||||||
\(961\) | 38.6526 | 1.24686 | ||||||||
\(962\) | −9.19443 | −0.296440 | ||||||||
\(963\) | −15.5404 | −0.500781 | ||||||||
\(964\) | 3.62912 | 0.116886 | ||||||||
\(965\) | −7.61174 | −0.245031 | ||||||||
\(966\) | 10.1033 | 0.325069 | ||||||||
\(967\) | −6.28152 | −0.202000 | −0.101000 | − | 0.994886i | \(-0.532204\pi\) | ||||
−0.101000 | + | 0.994886i | \(0.532204\pi\) | |||||||
\(968\) | 4.86005 | 0.156208 | ||||||||
\(969\) | 2.56358 | 0.0823540 | ||||||||
\(970\) | −6.47475 | −0.207892 | ||||||||
\(971\) | −16.8905 | −0.542042 | −0.271021 | − | 0.962573i | \(-0.587361\pi\) | ||||
−0.271021 | + | 0.962573i | \(0.587361\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 23.0716 | 0.739642 | ||||||||
\(974\) | −5.83363 | −0.186922 | ||||||||
\(975\) | −4.14463 | −0.132734 | ||||||||
\(976\) | −6.92554 | −0.221681 | ||||||||
\(977\) | 52.3227 | 1.67395 | 0.836976 | − | 0.547240i | \(-0.184321\pi\) | ||||
0.836976 | + | 0.547240i | \(0.184321\pi\) | |||||||
\(978\) | −0.347587 | −0.0111146 | ||||||||
\(979\) | −1.46503 | −0.0468226 | ||||||||
\(980\) | −10.1964 | −0.325712 | ||||||||
\(981\) | −2.53988 | −0.0810922 | ||||||||
\(982\) | −8.06550 | −0.257380 | ||||||||
\(983\) | −13.1119 | −0.418205 | −0.209102 | − | 0.977894i | \(-0.567054\pi\) | ||||
−0.209102 | + | 0.977894i | \(0.567054\pi\) | |||||||
\(984\) | −0.968492 | −0.0308744 | ||||||||
\(985\) | 0.443439 | 0.0141291 | ||||||||
\(986\) | −4.02950 | −0.128325 | ||||||||
\(987\) | 10.2164 | 0.325193 | ||||||||
\(988\) | 4.66906 | 0.148543 | ||||||||
\(989\) | 27.0367 | 0.859718 | ||||||||
\(990\) | 2.29171 | 0.0728353 | ||||||||
\(991\) | 23.5113 | 0.746861 | 0.373430 | − | 0.927658i | \(-0.378181\pi\) | ||||
0.373430 | + | 0.927658i | \(0.378181\pi\) | |||||||
\(992\) | −8.34581 | −0.264980 | ||||||||
\(993\) | −15.5698 | −0.494091 | ||||||||
\(994\) | −30.1409 | −0.956011 | ||||||||
\(995\) | 11.7552 | 0.372666 | ||||||||
\(996\) | −7.46254 | −0.236460 | ||||||||
\(997\) | −23.0393 | −0.729662 | −0.364831 | − | 0.931074i | \(-0.618873\pi\) | ||||
−0.364831 | + | 0.931074i | \(0.618873\pi\) | |||||||
\(998\) | 1.14142 | 0.0361311 | ||||||||
\(999\) | 9.19443 | 0.290899 |
(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 | 8034.2.a.ba.1.5 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.ba.1.5 | ✓ | 14 | 1.1 | even | 1 | trivial |