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: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
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 | ||||||||
\(3\) | 0.321033 | 0.185348 | 0.0926741 | − | 0.995696i | \(-0.470459\pi\) | ||||
0.0926741 | + | 0.995696i | \(0.470459\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.321033 | 0.131061 | ||||||||
\(7\) | −2.34471 | −0.886219 | −0.443109 | − | 0.896468i | \(-0.646125\pi\) | ||||
−0.443109 | + | 0.896468i | \(0.646125\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.89694 | −0.965646 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 4.30702 | 1.29862 | 0.649308 | − | 0.760525i | \(-0.275059\pi\) | ||||
0.649308 | + | 0.760525i | \(0.275059\pi\) | |||||||
\(12\) | 0.321033 | 0.0926741 | ||||||||
\(13\) | −0.151560 | −0.0420353 | −0.0210176 | − | 0.999779i | \(-0.506691\pi\) | ||||
−0.0210176 | + | 0.999779i | \(0.506691\pi\) | |||||||
\(14\) | −2.34471 | −0.626651 | ||||||||
\(15\) | −0.321033 | −0.0828903 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.90146 | −0.703708 | −0.351854 | − | 0.936055i | \(-0.614449\pi\) | ||||
−0.351854 | + | 0.936055i | \(0.614449\pi\) | |||||||
\(18\) | −2.89694 | −0.682815 | ||||||||
\(19\) | 0.850025 | 0.195009 | 0.0975046 | − | 0.995235i | \(-0.468914\pi\) | ||||
0.0975046 | + | 0.995235i | \(0.468914\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −0.752730 | −0.164259 | ||||||||
\(22\) | 4.30702 | 0.918260 | ||||||||
\(23\) | 1.17772 | 0.245571 | 0.122786 | − | 0.992433i | \(-0.460817\pi\) | ||||
0.122786 | + | 0.992433i | \(0.460817\pi\) | |||||||
\(24\) | 0.321033 | 0.0655305 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.151560 | −0.0297234 | ||||||||
\(27\) | −1.89311 | −0.364329 | ||||||||
\(28\) | −2.34471 | −0.443109 | ||||||||
\(29\) | −6.06456 | −1.12616 | −0.563081 | − | 0.826402i | \(-0.690384\pi\) | ||||
−0.563081 | + | 0.826402i | \(0.690384\pi\) | |||||||
\(30\) | −0.321033 | −0.0586123 | ||||||||
\(31\) | 3.37842 | 0.606783 | 0.303391 | − | 0.952866i | \(-0.401881\pi\) | ||||
0.303391 | + | 0.952866i | \(0.401881\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.38269 | 0.240696 | ||||||||
\(34\) | −2.90146 | −0.497597 | ||||||||
\(35\) | 2.34471 | 0.396329 | ||||||||
\(36\) | −2.89694 | −0.482823 | ||||||||
\(37\) | 3.84651 | 0.632363 | 0.316181 | − | 0.948699i | \(-0.397599\pi\) | ||||
0.316181 | + | 0.948699i | \(0.397599\pi\) | |||||||
\(38\) | 0.850025 | 0.137892 | ||||||||
\(39\) | −0.0486558 | −0.00779117 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 4.36256 | 0.681318 | 0.340659 | − | 0.940187i | \(-0.389350\pi\) | ||||
0.340659 | + | 0.940187i | \(0.389350\pi\) | |||||||
\(42\) | −0.752730 | −0.116149 | ||||||||
\(43\) | 2.16365 | 0.329953 | 0.164976 | − | 0.986298i | \(-0.447245\pi\) | ||||
0.164976 | + | 0.986298i | \(0.447245\pi\) | |||||||
\(44\) | 4.30702 | 0.649308 | ||||||||
\(45\) | 2.89694 | 0.431850 | ||||||||
\(46\) | 1.17772 | 0.173645 | ||||||||
\(47\) | −3.12847 | −0.456335 | −0.228167 | − | 0.973622i | \(-0.573273\pi\) | ||||
−0.228167 | + | 0.973622i | \(0.573273\pi\) | |||||||
\(48\) | 0.321033 | 0.0463371 | ||||||||
\(49\) | −1.50232 | −0.214617 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −0.931464 | −0.130431 | ||||||||
\(52\) | −0.151560 | −0.0210176 | ||||||||
\(53\) | 12.8478 | 1.76478 | 0.882390 | − | 0.470520i | \(-0.155933\pi\) | ||||
0.882390 | + | 0.470520i | \(0.155933\pi\) | |||||||
\(54\) | −1.89311 | −0.257620 | ||||||||
\(55\) | −4.30702 | −0.580759 | ||||||||
\(56\) | −2.34471 | −0.313326 | ||||||||
\(57\) | 0.272886 | 0.0361446 | ||||||||
\(58\) | −6.06456 | −0.796316 | ||||||||
\(59\) | 8.77318 | 1.14217 | 0.571086 | − | 0.820891i | \(-0.306522\pi\) | ||||
0.571086 | + | 0.820891i | \(0.306522\pi\) | |||||||
\(60\) | −0.321033 | −0.0414451 | ||||||||
\(61\) | 4.12343 | 0.527951 | 0.263976 | − | 0.964529i | \(-0.414966\pi\) | ||||
0.263976 | + | 0.964529i | \(0.414966\pi\) | |||||||
\(62\) | 3.37842 | 0.429060 | ||||||||
\(63\) | 6.79249 | 0.855773 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.151560 | 0.0187988 | ||||||||
\(66\) | 1.38269 | 0.170198 | ||||||||
\(67\) | 11.2919 | 1.37953 | 0.689763 | − | 0.724035i | \(-0.257715\pi\) | ||||
0.689763 | + | 0.724035i | \(0.257715\pi\) | |||||||
\(68\) | −2.90146 | −0.351854 | ||||||||
\(69\) | 0.378086 | 0.0455162 | ||||||||
\(70\) | 2.34471 | 0.280247 | ||||||||
\(71\) | 5.48369 | 0.650794 | 0.325397 | − | 0.945578i | \(-0.394502\pi\) | ||||
0.325397 | + | 0.945578i | \(0.394502\pi\) | |||||||
\(72\) | −2.89694 | −0.341407 | ||||||||
\(73\) | −1.89647 | −0.221965 | −0.110982 | − | 0.993822i | \(-0.535400\pi\) | ||||
−0.110982 | + | 0.993822i | \(0.535400\pi\) | |||||||
\(74\) | 3.84651 | 0.447148 | ||||||||
\(75\) | 0.321033 | 0.0370697 | ||||||||
\(76\) | 0.850025 | 0.0975046 | ||||||||
\(77\) | −10.0987 | −1.15086 | ||||||||
\(78\) | −0.0486558 | −0.00550919 | ||||||||
\(79\) | −7.14621 | −0.804012 | −0.402006 | − | 0.915637i | \(-0.631687\pi\) | ||||
−0.402006 | + | 0.915637i | \(0.631687\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 8.08306 | 0.898118 | ||||||||
\(82\) | 4.36256 | 0.481765 | ||||||||
\(83\) | 12.8931 | 1.41520 | 0.707602 | − | 0.706611i | \(-0.249777\pi\) | ||||
0.707602 | + | 0.706611i | \(0.249777\pi\) | |||||||
\(84\) | −0.752730 | −0.0821295 | ||||||||
\(85\) | 2.90146 | 0.314708 | ||||||||
\(86\) | 2.16365 | 0.233312 | ||||||||
\(87\) | −1.94692 | −0.208732 | ||||||||
\(88\) | 4.30702 | 0.459130 | ||||||||
\(89\) | −3.45632 | −0.366369 | −0.183184 | − | 0.983079i | \(-0.558641\pi\) | ||||
−0.183184 | + | 0.983079i | \(0.558641\pi\) | |||||||
\(90\) | 2.89694 | 0.305364 | ||||||||
\(91\) | 0.355366 | 0.0372525 | ||||||||
\(92\) | 1.17772 | 0.122786 | ||||||||
\(93\) | 1.08458 | 0.112466 | ||||||||
\(94\) | −3.12847 | −0.322678 | ||||||||
\(95\) | −0.850025 | −0.0872108 | ||||||||
\(96\) | 0.321033 | 0.0327653 | ||||||||
\(97\) | −6.67442 | −0.677684 | −0.338842 | − | 0.940843i | \(-0.610035\pi\) | ||||
−0.338842 | + | 0.940843i | \(0.610035\pi\) | |||||||
\(98\) | −1.50232 | −0.151757 | ||||||||
\(99\) | −12.4772 | −1.25400 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.9350 | −1.08807 | −0.544035 | − | 0.839063i | \(-0.683104\pi\) | ||||
−0.544035 | + | 0.839063i | \(0.683104\pi\) | |||||||
\(102\) | −0.931464 | −0.0922287 | ||||||||
\(103\) | 5.20948 | 0.513305 | 0.256652 | − | 0.966504i | \(-0.417380\pi\) | ||||
0.256652 | + | 0.966504i | \(0.417380\pi\) | |||||||
\(104\) | −0.151560 | −0.0148617 | ||||||||
\(105\) | 0.752730 | 0.0734589 | ||||||||
\(106\) | 12.8478 | 1.24789 | ||||||||
\(107\) | −7.53359 | −0.728300 | −0.364150 | − | 0.931340i | \(-0.618640\pi\) | ||||
−0.364150 | + | 0.931340i | \(0.618640\pi\) | |||||||
\(108\) | −1.89311 | −0.182165 | ||||||||
\(109\) | 5.91804 | 0.566845 | 0.283423 | − | 0.958995i | \(-0.408530\pi\) | ||||
0.283423 | + | 0.958995i | \(0.408530\pi\) | |||||||
\(110\) | −4.30702 | −0.410659 | ||||||||
\(111\) | 1.23486 | 0.117207 | ||||||||
\(112\) | −2.34471 | −0.221555 | ||||||||
\(113\) | 6.64989 | 0.625569 | 0.312784 | − | 0.949824i | \(-0.398738\pi\) | ||||
0.312784 | + | 0.949824i | \(0.398738\pi\) | |||||||
\(114\) | 0.272886 | 0.0255581 | ||||||||
\(115\) | −1.17772 | −0.109823 | ||||||||
\(116\) | −6.06456 | −0.563081 | ||||||||
\(117\) | 0.439061 | 0.0405912 | ||||||||
\(118\) | 8.77318 | 0.807637 | ||||||||
\(119\) | 6.80310 | 0.623639 | ||||||||
\(120\) | −0.321033 | −0.0293061 | ||||||||
\(121\) | 7.55045 | 0.686404 | ||||||||
\(122\) | 4.12343 | 0.373318 | ||||||||
\(123\) | 1.40053 | 0.126281 | ||||||||
\(124\) | 3.37842 | 0.303391 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 6.79249 | 0.605123 | ||||||||
\(127\) | 15.9042 | 1.41127 | 0.705633 | − | 0.708578i | \(-0.250663\pi\) | ||||
0.705633 | + | 0.708578i | \(0.250663\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.694601 | 0.0611562 | ||||||||
\(130\) | 0.151560 | 0.0132927 | ||||||||
\(131\) | 13.9823 | 1.22164 | 0.610818 | − | 0.791771i | \(-0.290841\pi\) | ||||
0.610818 | + | 0.791771i | \(0.290841\pi\) | |||||||
\(132\) | 1.38269 | 0.120348 | ||||||||
\(133\) | −1.99307 | −0.172821 | ||||||||
\(134\) | 11.2919 | 0.975472 | ||||||||
\(135\) | 1.89311 | 0.162933 | ||||||||
\(136\) | −2.90146 | −0.248798 | ||||||||
\(137\) | −9.68718 | −0.827632 | −0.413816 | − | 0.910361i | \(-0.635804\pi\) | ||||
−0.413816 | + | 0.910361i | \(0.635804\pi\) | |||||||
\(138\) | 0.378086 | 0.0321848 | ||||||||
\(139\) | 10.2590 | 0.870156 | 0.435078 | − | 0.900393i | \(-0.356721\pi\) | ||||
0.435078 | + | 0.900393i | \(0.356721\pi\) | |||||||
\(140\) | 2.34471 | 0.198165 | ||||||||
\(141\) | −1.00434 | −0.0845809 | ||||||||
\(142\) | 5.48369 | 0.460181 | ||||||||
\(143\) | −0.652774 | −0.0545877 | ||||||||
\(144\) | −2.89694 | −0.241412 | ||||||||
\(145\) | 6.06456 | 0.503635 | ||||||||
\(146\) | −1.89647 | −0.156953 | ||||||||
\(147\) | −0.482293 | −0.0397788 | ||||||||
\(148\) | 3.84651 | 0.316181 | ||||||||
\(149\) | −22.7688 | −1.86529 | −0.932645 | − | 0.360794i | \(-0.882506\pi\) | ||||
−0.932645 | + | 0.360794i | \(0.882506\pi\) | |||||||
\(150\) | 0.321033 | 0.0262122 | ||||||||
\(151\) | −3.64951 | −0.296993 | −0.148496 | − | 0.988913i | \(-0.547443\pi\) | ||||
−0.148496 | + | 0.988913i | \(0.547443\pi\) | |||||||
\(152\) | 0.850025 | 0.0689462 | ||||||||
\(153\) | 8.40536 | 0.679533 | ||||||||
\(154\) | −10.0987 | −0.813779 | ||||||||
\(155\) | −3.37842 | −0.271361 | ||||||||
\(156\) | −0.0486558 | −0.00389558 | ||||||||
\(157\) | 23.1613 | 1.84847 | 0.924236 | − | 0.381821i | \(-0.124703\pi\) | ||||
0.924236 | + | 0.381821i | \(0.124703\pi\) | |||||||
\(158\) | −7.14621 | −0.568522 | ||||||||
\(159\) | 4.12456 | 0.327099 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −2.76141 | −0.217630 | ||||||||
\(162\) | 8.08306 | 0.635066 | ||||||||
\(163\) | −14.6133 | −1.14460 | −0.572302 | − | 0.820043i | \(-0.693949\pi\) | ||||
−0.572302 | + | 0.820043i | \(0.693949\pi\) | |||||||
\(164\) | 4.36256 | 0.340659 | ||||||||
\(165\) | −1.38269 | −0.107643 | ||||||||
\(166\) | 12.8931 | 1.00070 | ||||||||
\(167\) | 18.8141 | 1.45588 | 0.727941 | − | 0.685640i | \(-0.240477\pi\) | ||||
0.727941 | + | 0.685640i | \(0.240477\pi\) | |||||||
\(168\) | −0.752730 | −0.0580744 | ||||||||
\(169\) | −12.9770 | −0.998233 | ||||||||
\(170\) | 2.90146 | 0.222532 | ||||||||
\(171\) | −2.46247 | −0.188310 | ||||||||
\(172\) | 2.16365 | 0.164976 | ||||||||
\(173\) | 21.5517 | 1.63854 | 0.819271 | − | 0.573406i | \(-0.194378\pi\) | ||||
0.819271 | + | 0.573406i | \(0.194378\pi\) | |||||||
\(174\) | −1.94692 | −0.147596 | ||||||||
\(175\) | −2.34471 | −0.177244 | ||||||||
\(176\) | 4.30702 | 0.324654 | ||||||||
\(177\) | 2.81648 | 0.211699 | ||||||||
\(178\) | −3.45632 | −0.259062 | ||||||||
\(179\) | −12.3686 | −0.924470 | −0.462235 | − | 0.886758i | \(-0.652952\pi\) | ||||
−0.462235 | + | 0.886758i | \(0.652952\pi\) | |||||||
\(180\) | 2.89694 | 0.215925 | ||||||||
\(181\) | −4.07510 | −0.302900 | −0.151450 | − | 0.988465i | \(-0.548394\pi\) | ||||
−0.151450 | + | 0.988465i | \(0.548394\pi\) | |||||||
\(182\) | 0.355366 | 0.0263415 | ||||||||
\(183\) | 1.32376 | 0.0978549 | ||||||||
\(184\) | 1.17772 | 0.0868226 | ||||||||
\(185\) | −3.84651 | −0.282801 | ||||||||
\(186\) | 1.08458 | 0.0795255 | ||||||||
\(187\) | −12.4967 | −0.913847 | ||||||||
\(188\) | −3.12847 | −0.228167 | ||||||||
\(189\) | 4.43880 | 0.322875 | ||||||||
\(190\) | −0.850025 | −0.0616673 | ||||||||
\(191\) | 21.3120 | 1.54208 | 0.771042 | − | 0.636785i | \(-0.219736\pi\) | ||||
0.771042 | + | 0.636785i | \(0.219736\pi\) | |||||||
\(192\) | 0.321033 | 0.0231685 | ||||||||
\(193\) | 3.22833 | 0.232380 | 0.116190 | − | 0.993227i | \(-0.462932\pi\) | ||||
0.116190 | + | 0.993227i | \(0.462932\pi\) | |||||||
\(194\) | −6.67442 | −0.479195 | ||||||||
\(195\) | 0.0486558 | 0.00348432 | ||||||||
\(196\) | −1.50232 | −0.107308 | ||||||||
\(197\) | 17.7112 | 1.26187 | 0.630936 | − | 0.775835i | \(-0.282671\pi\) | ||||
0.630936 | + | 0.775835i | \(0.282671\pi\) | |||||||
\(198\) | −12.4772 | −0.886714 | ||||||||
\(199\) | 0.0733493 | 0.00519959 | 0.00259980 | − | 0.999997i | \(-0.499172\pi\) | ||||
0.00259980 | + | 0.999997i | \(0.499172\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 3.62507 | 0.255693 | ||||||||
\(202\) | −10.9350 | −0.769381 | ||||||||
\(203\) | 14.2197 | 0.998025 | ||||||||
\(204\) | −0.931464 | −0.0652156 | ||||||||
\(205\) | −4.36256 | −0.304695 | ||||||||
\(206\) | 5.20948 | 0.362961 | ||||||||
\(207\) | −3.41178 | −0.237135 | ||||||||
\(208\) | −0.151560 | −0.0105088 | ||||||||
\(209\) | 3.66108 | 0.253242 | ||||||||
\(210\) | 0.752730 | 0.0519433 | ||||||||
\(211\) | −6.33949 | −0.436428 | −0.218214 | − | 0.975901i | \(-0.570023\pi\) | ||||
−0.218214 | + | 0.975901i | \(0.570023\pi\) | |||||||
\(212\) | 12.8478 | 0.882390 | ||||||||
\(213\) | 1.76044 | 0.120623 | ||||||||
\(214\) | −7.53359 | −0.514986 | ||||||||
\(215\) | −2.16365 | −0.147559 | ||||||||
\(216\) | −1.89311 | −0.128810 | ||||||||
\(217\) | −7.92143 | −0.537742 | ||||||||
\(218\) | 5.91804 | 0.400820 | ||||||||
\(219\) | −0.608829 | −0.0411408 | ||||||||
\(220\) | −4.30702 | −0.290379 | ||||||||
\(221\) | 0.439747 | 0.0295806 | ||||||||
\(222\) | 1.23486 | 0.0828781 | ||||||||
\(223\) | 10.1762 | 0.681447 | 0.340723 | − | 0.940164i | \(-0.389328\pi\) | ||||
0.340723 | + | 0.940164i | \(0.389328\pi\) | |||||||
\(224\) | −2.34471 | −0.156663 | ||||||||
\(225\) | −2.89694 | −0.193129 | ||||||||
\(226\) | 6.64989 | 0.442344 | ||||||||
\(227\) | 17.1555 | 1.13865 | 0.569326 | − | 0.822112i | \(-0.307204\pi\) | ||||
0.569326 | + | 0.822112i | \(0.307204\pi\) | |||||||
\(228\) | 0.272886 | 0.0180723 | ||||||||
\(229\) | 25.4373 | 1.68094 | 0.840471 | − | 0.541856i | \(-0.182278\pi\) | ||||
0.840471 | + | 0.541856i | \(0.182278\pi\) | |||||||
\(230\) | −1.17772 | −0.0776565 | ||||||||
\(231\) | −3.24202 | −0.213310 | ||||||||
\(232\) | −6.06456 | −0.398158 | ||||||||
\(233\) | −19.7605 | −1.29456 | −0.647278 | − | 0.762254i | \(-0.724093\pi\) | ||||
−0.647278 | + | 0.762254i | \(0.724093\pi\) | |||||||
\(234\) | 0.439061 | 0.0287023 | ||||||||
\(235\) | 3.12847 | 0.204079 | ||||||||
\(236\) | 8.77318 | 0.571086 | ||||||||
\(237\) | −2.29417 | −0.149022 | ||||||||
\(238\) | 6.80310 | 0.440980 | ||||||||
\(239\) | 23.0312 | 1.48976 | 0.744882 | − | 0.667197i | \(-0.232506\pi\) | ||||
0.744882 | + | 0.667197i | \(0.232506\pi\) | |||||||
\(240\) | −0.321033 | −0.0207226 | ||||||||
\(241\) | −21.9418 | −1.41340 | −0.706699 | − | 0.707515i | \(-0.749816\pi\) | ||||
−0.706699 | + | 0.707515i | \(0.749816\pi\) | |||||||
\(242\) | 7.55045 | 0.485361 | ||||||||
\(243\) | 8.27426 | 0.530794 | ||||||||
\(244\) | 4.12343 | 0.263976 | ||||||||
\(245\) | 1.50232 | 0.0959795 | ||||||||
\(246\) | 1.40053 | 0.0892942 | ||||||||
\(247\) | −0.128830 | −0.00819727 | ||||||||
\(248\) | 3.37842 | 0.214530 | ||||||||
\(249\) | 4.13912 | 0.262306 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 21.4800 | 1.35581 | 0.677904 | − | 0.735151i | \(-0.262889\pi\) | ||||
0.677904 | + | 0.735151i | \(0.262889\pi\) | |||||||
\(252\) | 6.79249 | 0.427887 | ||||||||
\(253\) | 5.07246 | 0.318903 | ||||||||
\(254\) | 15.9042 | 0.997916 | ||||||||
\(255\) | 0.931464 | 0.0583306 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.8081 | −1.36035 | −0.680177 | − | 0.733048i | \(-0.738097\pi\) | ||||
−0.680177 | + | 0.733048i | \(0.738097\pi\) | |||||||
\(258\) | 0.694601 | 0.0432440 | ||||||||
\(259\) | −9.01897 | −0.560412 | ||||||||
\(260\) | 0.151560 | 0.00939938 | ||||||||
\(261\) | 17.5687 | 1.08747 | ||||||||
\(262\) | 13.9823 | 0.863827 | ||||||||
\(263\) | 8.82818 | 0.544369 | 0.272185 | − | 0.962245i | \(-0.412254\pi\) | ||||
0.272185 | + | 0.962245i | \(0.412254\pi\) | |||||||
\(264\) | 1.38269 | 0.0850990 | ||||||||
\(265\) | −12.8478 | −0.789233 | ||||||||
\(266\) | −1.99307 | −0.122203 | ||||||||
\(267\) | −1.10959 | −0.0679058 | ||||||||
\(268\) | 11.2919 | 0.689763 | ||||||||
\(269\) | −16.1412 | −0.984145 | −0.492072 | − | 0.870554i | \(-0.663761\pi\) | ||||
−0.492072 | + | 0.870554i | \(0.663761\pi\) | |||||||
\(270\) | 1.89311 | 0.115211 | ||||||||
\(271\) | 11.6232 | 0.706060 | 0.353030 | − | 0.935612i | \(-0.385151\pi\) | ||||
0.353030 | + | 0.935612i | \(0.385151\pi\) | |||||||
\(272\) | −2.90146 | −0.175927 | ||||||||
\(273\) | 0.114084 | 0.00690468 | ||||||||
\(274\) | −9.68718 | −0.585224 | ||||||||
\(275\) | 4.30702 | 0.259723 | ||||||||
\(276\) | 0.378086 | 0.0227581 | ||||||||
\(277\) | −2.00332 | −0.120368 | −0.0601839 | − | 0.998187i | \(-0.519169\pi\) | ||||
−0.0601839 | + | 0.998187i | \(0.519169\pi\) | |||||||
\(278\) | 10.2590 | 0.615293 | ||||||||
\(279\) | −9.78708 | −0.585937 | ||||||||
\(280\) | 2.34471 | 0.140123 | ||||||||
\(281\) | −29.1666 | −1.73994 | −0.869968 | − | 0.493108i | \(-0.835861\pi\) | ||||
−0.869968 | + | 0.493108i | \(0.835861\pi\) | |||||||
\(282\) | −1.00434 | −0.0598077 | ||||||||
\(283\) | −26.2792 | −1.56214 | −0.781068 | − | 0.624445i | \(-0.785325\pi\) | ||||
−0.781068 | + | 0.624445i | \(0.785325\pi\) | |||||||
\(284\) | 5.48369 | 0.325397 | ||||||||
\(285\) | −0.272886 | −0.0161644 | ||||||||
\(286\) | −0.652774 | −0.0385993 | ||||||||
\(287\) | −10.2290 | −0.603797 | ||||||||
\(288\) | −2.89694 | −0.170704 | ||||||||
\(289\) | −8.58151 | −0.504795 | ||||||||
\(290\) | 6.06456 | 0.356123 | ||||||||
\(291\) | −2.14271 | −0.125608 | ||||||||
\(292\) | −1.89647 | −0.110982 | ||||||||
\(293\) | 33.7640 | 1.97252 | 0.986258 | − | 0.165212i | \(-0.0528307\pi\) | ||||
0.986258 | + | 0.165212i | \(0.0528307\pi\) | |||||||
\(294\) | −0.482293 | −0.0281279 | ||||||||
\(295\) | −8.77318 | −0.510794 | ||||||||
\(296\) | 3.84651 | 0.223574 | ||||||||
\(297\) | −8.15367 | −0.473124 | ||||||||
\(298\) | −22.7688 | −1.31896 | ||||||||
\(299\) | −0.178496 | −0.0103227 | ||||||||
\(300\) | 0.321033 | 0.0185348 | ||||||||
\(301\) | −5.07313 | −0.292410 | ||||||||
\(302\) | −3.64951 | −0.210006 | ||||||||
\(303\) | −3.51048 | −0.201672 | ||||||||
\(304\) | 0.850025 | 0.0487523 | ||||||||
\(305\) | −4.12343 | −0.236107 | ||||||||
\(306\) | 8.40536 | 0.480502 | ||||||||
\(307\) | 33.2915 | 1.90005 | 0.950023 | − | 0.312179i | \(-0.101059\pi\) | ||||
0.950023 | + | 0.312179i | \(0.101059\pi\) | |||||||
\(308\) | −10.0987 | −0.575429 | ||||||||
\(309\) | 1.67241 | 0.0951402 | ||||||||
\(310\) | −3.37842 | −0.191881 | ||||||||
\(311\) | −19.7768 | −1.12144 | −0.560720 | − | 0.828006i | \(-0.689475\pi\) | ||||
−0.560720 | + | 0.828006i | \(0.689475\pi\) | |||||||
\(312\) | −0.0486558 | −0.00275459 | ||||||||
\(313\) | 7.51930 | 0.425016 | 0.212508 | − | 0.977159i | \(-0.431837\pi\) | ||||
0.212508 | + | 0.977159i | \(0.431837\pi\) | |||||||
\(314\) | 23.1613 | 1.30707 | ||||||||
\(315\) | −6.79249 | −0.382714 | ||||||||
\(316\) | −7.14621 | −0.402006 | ||||||||
\(317\) | −26.3118 | −1.47782 | −0.738910 | − | 0.673805i | \(-0.764659\pi\) | ||||
−0.738910 | + | 0.673805i | \(0.764659\pi\) | |||||||
\(318\) | 4.12456 | 0.231294 | ||||||||
\(319\) | −26.1202 | −1.46245 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −2.41853 | −0.134989 | ||||||||
\(322\) | −2.76141 | −0.153888 | ||||||||
\(323\) | −2.46632 | −0.137230 | ||||||||
\(324\) | 8.08306 | 0.449059 | ||||||||
\(325\) | −0.151560 | −0.00840706 | ||||||||
\(326\) | −14.6133 | −0.809357 | ||||||||
\(327\) | 1.89988 | 0.105064 | ||||||||
\(328\) | 4.36256 | 0.240882 | ||||||||
\(329\) | 7.33538 | 0.404412 | ||||||||
\(330\) | −1.38269 | −0.0761148 | ||||||||
\(331\) | 34.7556 | 1.91034 | 0.955170 | − | 0.296057i | \(-0.0956720\pi\) | ||||
0.955170 | + | 0.296057i | \(0.0956720\pi\) | |||||||
\(332\) | 12.8931 | 0.707602 | ||||||||
\(333\) | −11.1431 | −0.610639 | ||||||||
\(334\) | 18.8141 | 1.02946 | ||||||||
\(335\) | −11.2919 | −0.616943 | ||||||||
\(336\) | −0.752730 | −0.0410648 | ||||||||
\(337\) | 36.0840 | 1.96562 | 0.982810 | − | 0.184618i | \(-0.0591049\pi\) | ||||
0.982810 | + | 0.184618i | \(0.0591049\pi\) | |||||||
\(338\) | −12.9770 | −0.705857 | ||||||||
\(339\) | 2.13483 | 0.115948 | ||||||||
\(340\) | 2.90146 | 0.157354 | ||||||||
\(341\) | 14.5509 | 0.787978 | ||||||||
\(342\) | −2.46247 | −0.133155 | ||||||||
\(343\) | 19.9355 | 1.07642 | ||||||||
\(344\) | 2.16365 | 0.116656 | ||||||||
\(345\) | −0.378086 | −0.0203555 | ||||||||
\(346\) | 21.5517 | 1.15862 | ||||||||
\(347\) | −10.1447 | −0.544598 | −0.272299 | − | 0.962213i | \(-0.587784\pi\) | ||||
−0.272299 | + | 0.962213i | \(0.587784\pi\) | |||||||
\(348\) | −1.94692 | −0.104366 | ||||||||
\(349\) | 22.0956 | 1.18275 | 0.591374 | − | 0.806397i | \(-0.298586\pi\) | ||||
0.591374 | + | 0.806397i | \(0.298586\pi\) | |||||||
\(350\) | −2.34471 | −0.125330 | ||||||||
\(351\) | 0.286920 | 0.0153147 | ||||||||
\(352\) | 4.30702 | 0.229565 | ||||||||
\(353\) | 8.98398 | 0.478169 | 0.239084 | − | 0.970999i | \(-0.423153\pi\) | ||||
0.239084 | + | 0.970999i | \(0.423153\pi\) | |||||||
\(354\) | 2.81648 | 0.149694 | ||||||||
\(355\) | −5.48369 | −0.291044 | ||||||||
\(356\) | −3.45632 | −0.183184 | ||||||||
\(357\) | 2.18402 | 0.115590 | ||||||||
\(358\) | −12.3686 | −0.653699 | ||||||||
\(359\) | −23.4608 | −1.23821 | −0.619107 | − | 0.785306i | \(-0.712505\pi\) | ||||
−0.619107 | + | 0.785306i | \(0.712505\pi\) | |||||||
\(360\) | 2.89694 | 0.152682 | ||||||||
\(361\) | −18.2775 | −0.961971 | ||||||||
\(362\) | −4.07510 | −0.214183 | ||||||||
\(363\) | 2.42394 | 0.127224 | ||||||||
\(364\) | 0.355366 | 0.0186262 | ||||||||
\(365\) | 1.89647 | 0.0992658 | ||||||||
\(366\) | 1.32376 | 0.0691938 | ||||||||
\(367\) | −21.0118 | −1.09681 | −0.548405 | − | 0.836213i | \(-0.684765\pi\) | ||||
−0.548405 | + | 0.836213i | \(0.684765\pi\) | |||||||
\(368\) | 1.17772 | 0.0613929 | ||||||||
\(369\) | −12.6381 | −0.657912 | ||||||||
\(370\) | −3.84651 | −0.199971 | ||||||||
\(371\) | −30.1244 | −1.56398 | ||||||||
\(372\) | 1.08458 | 0.0562330 | ||||||||
\(373\) | −22.8935 | −1.18538 | −0.592689 | − | 0.805431i | \(-0.701934\pi\) | ||||
−0.592689 | + | 0.805431i | \(0.701934\pi\) | |||||||
\(374\) | −12.4967 | −0.646187 | ||||||||
\(375\) | −0.321033 | −0.0165781 | ||||||||
\(376\) | −3.12847 | −0.161339 | ||||||||
\(377\) | 0.919148 | 0.0473385 | ||||||||
\(378\) | 4.43880 | 0.228307 | ||||||||
\(379\) | 37.1256 | 1.90701 | 0.953507 | − | 0.301372i | \(-0.0974447\pi\) | ||||
0.953507 | + | 0.301372i | \(0.0974447\pi\) | |||||||
\(380\) | −0.850025 | −0.0436054 | ||||||||
\(381\) | 5.10575 | 0.261576 | ||||||||
\(382\) | 21.3120 | 1.09042 | ||||||||
\(383\) | 18.3424 | 0.937253 | 0.468626 | − | 0.883396i | \(-0.344749\pi\) | ||||
0.468626 | + | 0.883396i | \(0.344749\pi\) | |||||||
\(384\) | 0.321033 | 0.0163826 | ||||||||
\(385\) | 10.0987 | 0.514679 | ||||||||
\(386\) | 3.22833 | 0.164317 | ||||||||
\(387\) | −6.26795 | −0.318618 | ||||||||
\(388\) | −6.67442 | −0.338842 | ||||||||
\(389\) | 8.01259 | 0.406254 | 0.203127 | − | 0.979152i | \(-0.434890\pi\) | ||||
0.203127 | + | 0.979152i | \(0.434890\pi\) | |||||||
\(390\) | 0.0486558 | 0.00246378 | ||||||||
\(391\) | −3.41711 | −0.172811 | ||||||||
\(392\) | −1.50232 | −0.0758784 | ||||||||
\(393\) | 4.48876 | 0.226428 | ||||||||
\(394\) | 17.7112 | 0.892279 | ||||||||
\(395\) | 7.14621 | 0.359565 | ||||||||
\(396\) | −12.4772 | −0.627002 | ||||||||
\(397\) | 20.2147 | 1.01455 | 0.507275 | − | 0.861785i | \(-0.330653\pi\) | ||||
0.507275 | + | 0.861785i | \(0.330653\pi\) | |||||||
\(398\) | 0.0733493 | 0.00367667 | ||||||||
\(399\) | −0.639839 | −0.0320320 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −3.11232 | −0.155422 | −0.0777108 | − | 0.996976i | \(-0.524761\pi\) | ||||
−0.0777108 | + | 0.996976i | \(0.524761\pi\) | |||||||
\(402\) | 3.62507 | 0.180802 | ||||||||
\(403\) | −0.512035 | −0.0255063 | ||||||||
\(404\) | −10.9350 | −0.544035 | ||||||||
\(405\) | −8.08306 | −0.401651 | ||||||||
\(406\) | 14.2197 | 0.705710 | ||||||||
\(407\) | 16.5670 | 0.821197 | ||||||||
\(408\) | −0.931464 | −0.0461144 | ||||||||
\(409\) | −27.3963 | −1.35466 | −0.677329 | − | 0.735680i | \(-0.736863\pi\) | ||||
−0.677329 | + | 0.735680i | \(0.736863\pi\) | |||||||
\(410\) | −4.36256 | −0.215452 | ||||||||
\(411\) | −3.10990 | −0.153400 | ||||||||
\(412\) | 5.20948 | 0.256652 | ||||||||
\(413\) | −20.5706 | −1.01221 | ||||||||
\(414\) | −3.41178 | −0.167680 | ||||||||
\(415\) | −12.8931 | −0.632899 | ||||||||
\(416\) | −0.151560 | −0.00743086 | ||||||||
\(417\) | 3.29347 | 0.161282 | ||||||||
\(418\) | 3.66108 | 0.179069 | ||||||||
\(419\) | −3.33288 | −0.162822 | −0.0814110 | − | 0.996681i | \(-0.525943\pi\) | ||||
−0.0814110 | + | 0.996681i | \(0.525943\pi\) | |||||||
\(420\) | 0.752730 | 0.0367294 | ||||||||
\(421\) | 2.01962 | 0.0984300 | 0.0492150 | − | 0.998788i | \(-0.484328\pi\) | ||||
0.0492150 | + | 0.998788i | \(0.484328\pi\) | |||||||
\(422\) | −6.33949 | −0.308601 | ||||||||
\(423\) | 9.06300 | 0.440658 | ||||||||
\(424\) | 12.8478 | 0.623944 | ||||||||
\(425\) | −2.90146 | −0.140742 | ||||||||
\(426\) | 1.76044 | 0.0852937 | ||||||||
\(427\) | −9.66827 | −0.467880 | ||||||||
\(428\) | −7.53359 | −0.364150 | ||||||||
\(429\) | −0.209562 | −0.0101177 | ||||||||
\(430\) | −2.16365 | −0.104340 | ||||||||
\(431\) | −38.1102 | −1.83570 | −0.917851 | − | 0.396925i | \(-0.870077\pi\) | ||||
−0.917851 | + | 0.396925i | \(0.870077\pi\) | |||||||
\(432\) | −1.89311 | −0.0910823 | ||||||||
\(433\) | 7.36690 | 0.354030 | 0.177015 | − | 0.984208i | \(-0.443356\pi\) | ||||
0.177015 | + | 0.984208i | \(0.443356\pi\) | |||||||
\(434\) | −7.92143 | −0.380241 | ||||||||
\(435\) | 1.94692 | 0.0933478 | ||||||||
\(436\) | 5.91804 | 0.283423 | ||||||||
\(437\) | 1.00109 | 0.0478887 | ||||||||
\(438\) | −0.608829 | −0.0290910 | ||||||||
\(439\) | −36.3794 | −1.73630 | −0.868148 | − | 0.496306i | \(-0.834690\pi\) | ||||
−0.868148 | + | 0.496306i | \(0.834690\pi\) | |||||||
\(440\) | −4.30702 | −0.205329 | ||||||||
\(441\) | 4.35212 | 0.207244 | ||||||||
\(442\) | 0.439747 | 0.0209166 | ||||||||
\(443\) | −25.2432 | −1.19934 | −0.599670 | − | 0.800247i | \(-0.704702\pi\) | ||||
−0.599670 | + | 0.800247i | \(0.704702\pi\) | |||||||
\(444\) | 1.23486 | 0.0586037 | ||||||||
\(445\) | 3.45632 | 0.163845 | ||||||||
\(446\) | 10.1762 | 0.481856 | ||||||||
\(447\) | −7.30952 | −0.345728 | ||||||||
\(448\) | −2.34471 | −0.110777 | ||||||||
\(449\) | 12.1827 | 0.574938 | 0.287469 | − | 0.957790i | \(-0.407186\pi\) | ||||
0.287469 | + | 0.957790i | \(0.407186\pi\) | |||||||
\(450\) | −2.89694 | −0.136563 | ||||||||
\(451\) | 18.7897 | 0.884771 | ||||||||
\(452\) | 6.64989 | 0.312784 | ||||||||
\(453\) | −1.17161 | −0.0550471 | ||||||||
\(454\) | 17.1555 | 0.805149 | ||||||||
\(455\) | −0.355366 | −0.0166598 | ||||||||
\(456\) | 0.272886 | 0.0127791 | ||||||||
\(457\) | 33.4459 | 1.56453 | 0.782266 | − | 0.622944i | \(-0.214064\pi\) | ||||
0.782266 | + | 0.622944i | \(0.214064\pi\) | |||||||
\(458\) | 25.4373 | 1.18861 | ||||||||
\(459\) | 5.49279 | 0.256381 | ||||||||
\(460\) | −1.17772 | −0.0549114 | ||||||||
\(461\) | 11.8769 | 0.553162 | 0.276581 | − | 0.960991i | \(-0.410799\pi\) | ||||
0.276581 | + | 0.960991i | \(0.410799\pi\) | |||||||
\(462\) | −3.24202 | −0.150833 | ||||||||
\(463\) | −25.8702 | −1.20229 | −0.601145 | − | 0.799140i | \(-0.705288\pi\) | ||||
−0.601145 | + | 0.799140i | \(0.705288\pi\) | |||||||
\(464\) | −6.06456 | −0.281540 | ||||||||
\(465\) | −1.08458 | −0.0502964 | ||||||||
\(466\) | −19.7605 | −0.915390 | ||||||||
\(467\) | −29.7130 | −1.37495 | −0.687476 | − | 0.726207i | \(-0.741281\pi\) | ||||
−0.687476 | + | 0.726207i | \(0.741281\pi\) | |||||||
\(468\) | 0.439061 | 0.0202956 | ||||||||
\(469\) | −26.4763 | −1.22256 | ||||||||
\(470\) | 3.12847 | 0.144306 | ||||||||
\(471\) | 7.43553 | 0.342611 | ||||||||
\(472\) | 8.77318 | 0.403818 | ||||||||
\(473\) | 9.31887 | 0.428482 | ||||||||
\(474\) | −2.29417 | −0.105375 | ||||||||
\(475\) | 0.850025 | 0.0390018 | ||||||||
\(476\) | 6.80310 | 0.311820 | ||||||||
\(477\) | −37.2192 | −1.70415 | ||||||||
\(478\) | 23.0312 | 1.05342 | ||||||||
\(479\) | −1.19710 | −0.0546969 | −0.0273485 | − | 0.999626i | \(-0.508706\pi\) | ||||
−0.0273485 | + | 0.999626i | \(0.508706\pi\) | |||||||
\(480\) | −0.321033 | −0.0146531 | ||||||||
\(481\) | −0.582979 | −0.0265816 | ||||||||
\(482\) | −21.9418 | −0.999423 | ||||||||
\(483\) | −0.886504 | −0.0403373 | ||||||||
\(484\) | 7.55045 | 0.343202 | ||||||||
\(485\) | 6.67442 | 0.303070 | ||||||||
\(486\) | 8.27426 | 0.375328 | ||||||||
\(487\) | −31.3802 | −1.42197 | −0.710987 | − | 0.703205i | \(-0.751752\pi\) | ||||
−0.710987 | + | 0.703205i | \(0.751752\pi\) | |||||||
\(488\) | 4.12343 | 0.186659 | ||||||||
\(489\) | −4.69135 | −0.212150 | ||||||||
\(490\) | 1.50232 | 0.0678677 | ||||||||
\(491\) | 20.8352 | 0.940278 | 0.470139 | − | 0.882592i | \(-0.344204\pi\) | ||||
0.470139 | + | 0.882592i | \(0.344204\pi\) | |||||||
\(492\) | 1.40053 | 0.0631406 | ||||||||
\(493\) | 17.5961 | 0.792489 | ||||||||
\(494\) | −0.128830 | −0.00579635 | ||||||||
\(495\) | 12.4772 | 0.560807 | ||||||||
\(496\) | 3.37842 | 0.151696 | ||||||||
\(497\) | −12.8577 | −0.576745 | ||||||||
\(498\) | 4.13912 | 0.185478 | ||||||||
\(499\) | 11.1576 | 0.499483 | 0.249741 | − | 0.968313i | \(-0.419654\pi\) | ||||
0.249741 | + | 0.968313i | \(0.419654\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 6.03996 | 0.269845 | ||||||||
\(502\) | 21.4800 | 0.958701 | ||||||||
\(503\) | −30.2780 | −1.35003 | −0.675015 | − | 0.737804i | \(-0.735863\pi\) | ||||
−0.675015 | + | 0.737804i | \(0.735863\pi\) | |||||||
\(504\) | 6.79249 | 0.302562 | ||||||||
\(505\) | 10.9350 | 0.486600 | ||||||||
\(506\) | 5.07246 | 0.225498 | ||||||||
\(507\) | −4.16605 | −0.185021 | ||||||||
\(508\) | 15.9042 | 0.705633 | ||||||||
\(509\) | 17.5268 | 0.776863 | 0.388431 | − | 0.921478i | \(-0.373017\pi\) | ||||
0.388431 | + | 0.921478i | \(0.373017\pi\) | |||||||
\(510\) | 0.931464 | 0.0412459 | ||||||||
\(511\) | 4.44668 | 0.196710 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.60919 | −0.0710475 | ||||||||
\(514\) | −21.8081 | −0.961915 | ||||||||
\(515\) | −5.20948 | −0.229557 | ||||||||
\(516\) | 0.694601 | 0.0305781 | ||||||||
\(517\) | −13.4744 | −0.592604 | ||||||||
\(518\) | −9.01897 | −0.396271 | ||||||||
\(519\) | 6.91879 | 0.303701 | ||||||||
\(520\) | 0.151560 | 0.00664636 | ||||||||
\(521\) | 13.6637 | 0.598617 | 0.299308 | − | 0.954156i | \(-0.403244\pi\) | ||||
0.299308 | + | 0.954156i | \(0.403244\pi\) | |||||||
\(522\) | 17.5687 | 0.768960 | ||||||||
\(523\) | −9.09377 | −0.397643 | −0.198821 | − | 0.980036i | \(-0.563711\pi\) | ||||
−0.198821 | + | 0.980036i | \(0.563711\pi\) | |||||||
\(524\) | 13.9823 | 0.610818 | ||||||||
\(525\) | −0.752730 | −0.0328518 | ||||||||
\(526\) | 8.82818 | 0.384927 | ||||||||
\(527\) | −9.80237 | −0.426998 | ||||||||
\(528\) | 1.38269 | 0.0601741 | ||||||||
\(529\) | −21.6130 | −0.939695 | ||||||||
\(530\) | −12.8478 | −0.558072 | ||||||||
\(531\) | −25.4154 | −1.10293 | ||||||||
\(532\) | −1.99307 | −0.0864104 | ||||||||
\(533\) | −0.661192 | −0.0286394 | ||||||||
\(534\) | −1.10959 | −0.0480167 | ||||||||
\(535\) | 7.53359 | 0.325706 | ||||||||
\(536\) | 11.2919 | 0.487736 | ||||||||
\(537\) | −3.97071 | −0.171349 | ||||||||
\(538\) | −16.1412 | −0.695896 | ||||||||
\(539\) | −6.47051 | −0.278705 | ||||||||
\(540\) | 1.89311 | 0.0814665 | ||||||||
\(541\) | −36.4917 | −1.56890 | −0.784451 | − | 0.620191i | \(-0.787055\pi\) | ||||
−0.784451 | + | 0.620191i | \(0.787055\pi\) | |||||||
\(542\) | 11.6232 | 0.499260 | ||||||||
\(543\) | −1.30824 | −0.0561420 | ||||||||
\(544\) | −2.90146 | −0.124399 | ||||||||
\(545\) | −5.91804 | −0.253501 | ||||||||
\(546\) | 0.114084 | 0.00488235 | ||||||||
\(547\) | −21.6270 | −0.924702 | −0.462351 | − | 0.886697i | \(-0.652994\pi\) | ||||
−0.462351 | + | 0.886697i | \(0.652994\pi\) | |||||||
\(548\) | −9.68718 | −0.413816 | ||||||||
\(549\) | −11.9453 | −0.509814 | ||||||||
\(550\) | 4.30702 | 0.183652 | ||||||||
\(551\) | −5.15503 | −0.219612 | ||||||||
\(552\) | 0.378086 | 0.0160924 | ||||||||
\(553\) | 16.7558 | 0.712530 | ||||||||
\(554\) | −2.00332 | −0.0851128 | ||||||||
\(555\) | −1.23486 | −0.0524167 | ||||||||
\(556\) | 10.2590 | 0.435078 | ||||||||
\(557\) | −6.32452 | −0.267978 | −0.133989 | − | 0.990983i | \(-0.542779\pi\) | ||||
−0.133989 | + | 0.990983i | \(0.542779\pi\) | |||||||
\(558\) | −9.78708 | −0.414320 | ||||||||
\(559\) | −0.327923 | −0.0138697 | ||||||||
\(560\) | 2.34471 | 0.0990823 | ||||||||
\(561\) | −4.01184 | −0.169380 | ||||||||
\(562\) | −29.1666 | −1.23032 | ||||||||
\(563\) | −7.82093 | −0.329613 | −0.164807 | − | 0.986326i | \(-0.552700\pi\) | ||||
−0.164807 | + | 0.986326i | \(0.552700\pi\) | |||||||
\(564\) | −1.00434 | −0.0422904 | ||||||||
\(565\) | −6.64989 | −0.279763 | ||||||||
\(566\) | −26.2792 | −1.10460 | ||||||||
\(567\) | −18.9525 | −0.795929 | ||||||||
\(568\) | 5.48369 | 0.230090 | ||||||||
\(569\) | 7.53621 | 0.315935 | 0.157967 | − | 0.987444i | \(-0.449506\pi\) | ||||
0.157967 | + | 0.987444i | \(0.449506\pi\) | |||||||
\(570\) | −0.272886 | −0.0114299 | ||||||||
\(571\) | 14.5664 | 0.609586 | 0.304793 | − | 0.952419i | \(-0.401413\pi\) | ||||
0.304793 | + | 0.952419i | \(0.401413\pi\) | |||||||
\(572\) | −0.652774 | −0.0272939 | ||||||||
\(573\) | 6.84185 | 0.285822 | ||||||||
\(574\) | −10.2290 | −0.426949 | ||||||||
\(575\) | 1.17772 | 0.0491143 | ||||||||
\(576\) | −2.89694 | −0.120706 | ||||||||
\(577\) | −33.3390 | −1.38792 | −0.693960 | − | 0.720013i | \(-0.744136\pi\) | ||||
−0.693960 | + | 0.720013i | \(0.744136\pi\) | |||||||
\(578\) | −8.58151 | −0.356944 | ||||||||
\(579\) | 1.03640 | 0.0430712 | ||||||||
\(580\) | 6.06456 | 0.251817 | ||||||||
\(581\) | −30.2307 | −1.25418 | ||||||||
\(582\) | −2.14271 | −0.0888180 | ||||||||
\(583\) | 55.3357 | 2.29177 | ||||||||
\(584\) | −1.89647 | −0.0784765 | ||||||||
\(585\) | −0.439061 | −0.0181529 | ||||||||
\(586\) | 33.7640 | 1.39478 | ||||||||
\(587\) | −43.9050 | −1.81215 | −0.906077 | − | 0.423114i | \(-0.860937\pi\) | ||||
−0.906077 | + | 0.423114i | \(0.860937\pi\) | |||||||
\(588\) | −0.482293 | −0.0198894 | ||||||||
\(589\) | 2.87174 | 0.118328 | ||||||||
\(590\) | −8.77318 | −0.361186 | ||||||||
\(591\) | 5.68588 | 0.233886 | ||||||||
\(592\) | 3.84651 | 0.158091 | ||||||||
\(593\) | −16.2032 | −0.665386 | −0.332693 | − | 0.943035i | \(-0.607957\pi\) | ||||
−0.332693 | + | 0.943035i | \(0.607957\pi\) | |||||||
\(594\) | −8.15367 | −0.334549 | ||||||||
\(595\) | −6.80310 | −0.278900 | ||||||||
\(596\) | −22.7688 | −0.932645 | ||||||||
\(597\) | 0.0235475 | 0.000963736 0 | ||||||||
\(598\) | −0.178496 | −0.00729923 | ||||||||
\(599\) | 17.8205 | 0.728126 | 0.364063 | − | 0.931374i | \(-0.381389\pi\) | ||||
0.364063 | + | 0.931374i | \(0.381389\pi\) | |||||||
\(600\) | 0.321033 | 0.0131061 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | −5.07313 | −0.206765 | ||||||||
\(603\) | −32.7119 | −1.33213 | ||||||||
\(604\) | −3.64951 | −0.148496 | ||||||||
\(605\) | −7.55045 | −0.306969 | ||||||||
\(606\) | −3.51048 | −0.142604 | ||||||||
\(607\) | 5.62662 | 0.228378 | 0.114189 | − | 0.993459i | \(-0.463573\pi\) | ||||
0.114189 | + | 0.993459i | \(0.463573\pi\) | |||||||
\(608\) | 0.850025 | 0.0344731 | ||||||||
\(609\) | 4.56498 | 0.184982 | ||||||||
\(610\) | −4.12343 | −0.166953 | ||||||||
\(611\) | 0.474153 | 0.0191822 | ||||||||
\(612\) | 8.40536 | 0.339767 | ||||||||
\(613\) | 17.9431 | 0.724713 | 0.362357 | − | 0.932040i | \(-0.381972\pi\) | ||||
0.362357 | + | 0.932040i | \(0.381972\pi\) | |||||||
\(614\) | 33.2915 | 1.34354 | ||||||||
\(615\) | −1.40053 | −0.0564746 | ||||||||
\(616\) | −10.0987 | −0.406890 | ||||||||
\(617\) | 33.4323 | 1.34593 | 0.672967 | − | 0.739672i | \(-0.265019\pi\) | ||||
0.672967 | + | 0.739672i | \(0.265019\pi\) | |||||||
\(618\) | 1.67241 | 0.0672743 | ||||||||
\(619\) | −2.89611 | −0.116404 | −0.0582022 | − | 0.998305i | \(-0.518537\pi\) | ||||
−0.0582022 | + | 0.998305i | \(0.518537\pi\) | |||||||
\(620\) | −3.37842 | −0.135681 | ||||||||
\(621\) | −2.22955 | −0.0894688 | ||||||||
\(622\) | −19.7768 | −0.792977 | ||||||||
\(623\) | 8.10408 | 0.324683 | ||||||||
\(624\) | −0.0486558 | −0.00194779 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.51930 | 0.300532 | ||||||||
\(627\) | 1.17533 | 0.0469380 | ||||||||
\(628\) | 23.1613 | 0.924236 | ||||||||
\(629\) | −11.1605 | −0.444999 | ||||||||
\(630\) | −6.79249 | −0.270619 | ||||||||
\(631\) | −41.2078 | −1.64046 | −0.820229 | − | 0.572035i | \(-0.806154\pi\) | ||||
−0.820229 | + | 0.572035i | \(0.806154\pi\) | |||||||
\(632\) | −7.14621 | −0.284261 | ||||||||
\(633\) | −2.03518 | −0.0808912 | ||||||||
\(634\) | −26.3118 | −1.04498 | ||||||||
\(635\) | −15.9042 | −0.631137 | ||||||||
\(636\) | 4.12456 | 0.163549 | ||||||||
\(637\) | 0.227692 | 0.00902147 | ||||||||
\(638\) | −26.1202 | −1.03411 | ||||||||
\(639\) | −15.8859 | −0.628436 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −30.7811 | −1.21578 | −0.607890 | − | 0.794022i | \(-0.707984\pi\) | ||||
−0.607890 | + | 0.794022i | \(0.707984\pi\) | |||||||
\(642\) | −2.41853 | −0.0954517 | ||||||||
\(643\) | 5.46225 | 0.215410 | 0.107705 | − | 0.994183i | \(-0.465650\pi\) | ||||
0.107705 | + | 0.994183i | \(0.465650\pi\) | |||||||
\(644\) | −2.76141 | −0.108815 | ||||||||
\(645\) | −0.694601 | −0.0273499 | ||||||||
\(646\) | −2.46632 | −0.0970360 | ||||||||
\(647\) | 14.4120 | 0.566596 | 0.283298 | − | 0.959032i | \(-0.408571\pi\) | ||||
0.283298 | + | 0.959032i | \(0.408571\pi\) | |||||||
\(648\) | 8.08306 | 0.317533 | ||||||||
\(649\) | 37.7863 | 1.48324 | ||||||||
\(650\) | −0.151560 | −0.00594469 | ||||||||
\(651\) | −2.54304 | −0.0996695 | ||||||||
\(652\) | −14.6133 | −0.572302 | ||||||||
\(653\) | 8.47619 | 0.331699 | 0.165849 | − | 0.986151i | \(-0.446963\pi\) | ||||
0.165849 | + | 0.986151i | \(0.446963\pi\) | |||||||
\(654\) | 1.89988 | 0.0742913 | ||||||||
\(655\) | −13.9823 | −0.546332 | ||||||||
\(656\) | 4.36256 | 0.170329 | ||||||||
\(657\) | 5.49396 | 0.214340 | ||||||||
\(658\) | 7.33538 | 0.285963 | ||||||||
\(659\) | 14.3998 | 0.560938 | 0.280469 | − | 0.959863i | \(-0.409510\pi\) | ||||
0.280469 | + | 0.959863i | \(0.409510\pi\) | |||||||
\(660\) | −1.38269 | −0.0538213 | ||||||||
\(661\) | −25.5124 | −0.992316 | −0.496158 | − | 0.868232i | \(-0.665256\pi\) | ||||
−0.496158 | + | 0.868232i | \(0.665256\pi\) | |||||||
\(662\) | 34.7556 | 1.35081 | ||||||||
\(663\) | 0.141173 | 0.00548271 | ||||||||
\(664\) | 12.8931 | 0.500350 | ||||||||
\(665\) | 1.99307 | 0.0772878 | ||||||||
\(666\) | −11.1431 | −0.431787 | ||||||||
\(667\) | −7.14235 | −0.276553 | ||||||||
\(668\) | 18.8141 | 0.727941 | ||||||||
\(669\) | 3.26688 | 0.126305 | ||||||||
\(670\) | −11.2919 | −0.436244 | ||||||||
\(671\) | 17.7597 | 0.685606 | ||||||||
\(672\) | −0.752730 | −0.0290372 | ||||||||
\(673\) | 33.5502 | 1.29326 | 0.646632 | − | 0.762802i | \(-0.276177\pi\) | ||||
0.646632 | + | 0.762802i | \(0.276177\pi\) | |||||||
\(674\) | 36.0840 | 1.38990 | ||||||||
\(675\) | −1.89311 | −0.0728658 | ||||||||
\(676\) | −12.9770 | −0.499117 | ||||||||
\(677\) | 14.1461 | 0.543678 | 0.271839 | − | 0.962343i | \(-0.412368\pi\) | ||||
0.271839 | + | 0.962343i | \(0.412368\pi\) | |||||||
\(678\) | 2.13483 | 0.0819877 | ||||||||
\(679\) | 15.6496 | 0.600576 | ||||||||
\(680\) | 2.90146 | 0.111266 | ||||||||
\(681\) | 5.50749 | 0.211047 | ||||||||
\(682\) | 14.5509 | 0.557184 | ||||||||
\(683\) | −5.35864 | −0.205043 | −0.102521 | − | 0.994731i | \(-0.532691\pi\) | ||||
−0.102521 | + | 0.994731i | \(0.532691\pi\) | |||||||
\(684\) | −2.46247 | −0.0941549 | ||||||||
\(685\) | 9.68718 | 0.370128 | ||||||||
\(686\) | 19.9355 | 0.761141 | ||||||||
\(687\) | 8.16620 | 0.311560 | ||||||||
\(688\) | 2.16365 | 0.0824882 | ||||||||
\(689\) | −1.94722 | −0.0741830 | ||||||||
\(690\) | −0.378086 | −0.0143935 | ||||||||
\(691\) | −24.1494 | −0.918688 | −0.459344 | − | 0.888258i | \(-0.651915\pi\) | ||||
−0.459344 | + | 0.888258i | \(0.651915\pi\) | |||||||
\(692\) | 21.5517 | 0.819271 | ||||||||
\(693\) | 29.2554 | 1.11132 | ||||||||
\(694\) | −10.1447 | −0.385089 | ||||||||
\(695\) | −10.2590 | −0.389146 | ||||||||
\(696\) | −1.94692 | −0.0737979 | ||||||||
\(697\) | −12.6578 | −0.479449 | ||||||||
\(698\) | 22.0956 | 0.836329 | ||||||||
\(699\) | −6.34378 | −0.239944 | ||||||||
\(700\) | −2.34471 | −0.0886219 | ||||||||
\(701\) | 10.3783 | 0.391982 | 0.195991 | − | 0.980606i | \(-0.437208\pi\) | ||||
0.195991 | + | 0.980606i | \(0.437208\pi\) | |||||||
\(702\) | 0.286920 | 0.0108291 | ||||||||
\(703\) | 3.26963 | 0.123317 | ||||||||
\(704\) | 4.30702 | 0.162327 | ||||||||
\(705\) | 1.00434 | 0.0378257 | ||||||||
\(706\) | 8.98398 | 0.338116 | ||||||||
\(707\) | 25.6394 | 0.964268 | ||||||||
\(708\) | 2.81648 | 0.105850 | ||||||||
\(709\) | 16.2357 | 0.609744 | 0.304872 | − | 0.952393i | \(-0.401386\pi\) | ||||
0.304872 | + | 0.952393i | \(0.401386\pi\) | |||||||
\(710\) | −5.48369 | −0.205799 | ||||||||
\(711\) | 20.7021 | 0.776391 | ||||||||
\(712\) | −3.45632 | −0.129531 | ||||||||
\(713\) | 3.97883 | 0.149008 | ||||||||
\(714\) | 2.18402 | 0.0817348 | ||||||||
\(715\) | 0.652774 | 0.0244124 | ||||||||
\(716\) | −12.3686 | −0.462235 | ||||||||
\(717\) | 7.39376 | 0.276125 | ||||||||
\(718\) | −23.4608 | −0.875550 | ||||||||
\(719\) | −11.9936 | −0.447284 | −0.223642 | − | 0.974671i | \(-0.571795\pi\) | ||||
−0.223642 | + | 0.974671i | \(0.571795\pi\) | |||||||
\(720\) | 2.89694 | 0.107963 | ||||||||
\(721\) | −12.2147 | −0.454900 | ||||||||
\(722\) | −18.2775 | −0.680217 | ||||||||
\(723\) | −7.04404 | −0.261971 | ||||||||
\(724\) | −4.07510 | −0.151450 | ||||||||
\(725\) | −6.06456 | −0.225232 | ||||||||
\(726\) | 2.42394 | 0.0899608 | ||||||||
\(727\) | −14.5660 | −0.540221 | −0.270111 | − | 0.962829i | \(-0.587060\pi\) | ||||
−0.270111 | + | 0.962829i | \(0.587060\pi\) | |||||||
\(728\) | 0.355366 | 0.0131707 | ||||||||
\(729\) | −21.5929 | −0.799737 | ||||||||
\(730\) | 1.89647 | 0.0701915 | ||||||||
\(731\) | −6.27774 | −0.232191 | ||||||||
\(732\) | 1.32376 | 0.0489274 | ||||||||
\(733\) | 41.1765 | 1.52089 | 0.760444 | − | 0.649403i | \(-0.224981\pi\) | ||||
0.760444 | + | 0.649403i | \(0.224981\pi\) | |||||||
\(734\) | −21.0118 | −0.775561 | ||||||||
\(735\) | 0.482293 | 0.0177896 | ||||||||
\(736\) | 1.17772 | 0.0434113 | ||||||||
\(737\) | 48.6345 | 1.79147 | ||||||||
\(738\) | −12.6381 | −0.465214 | ||||||||
\(739\) | 5.78885 | 0.212946 | 0.106473 | − | 0.994316i | \(-0.466044\pi\) | ||||
0.106473 | + | 0.994316i | \(0.466044\pi\) | |||||||
\(740\) | −3.84651 | −0.141401 | ||||||||
\(741\) | −0.0413587 | −0.00151935 | ||||||||
\(742\) | −30.1244 | −1.10590 | ||||||||
\(743\) | −18.0317 | −0.661519 | −0.330759 | − | 0.943715i | \(-0.607305\pi\) | ||||
−0.330759 | + | 0.943715i | \(0.607305\pi\) | |||||||
\(744\) | 1.08458 | 0.0397628 | ||||||||
\(745\) | 22.7688 | 0.834183 | ||||||||
\(746\) | −22.8935 | −0.838189 | ||||||||
\(747\) | −37.3506 | −1.36659 | ||||||||
\(748\) | −12.4967 | −0.456923 | ||||||||
\(749\) | 17.6641 | 0.645433 | ||||||||
\(750\) | −0.321033 | −0.0117225 | ||||||||
\(751\) | −13.4161 | −0.489560 | −0.244780 | − | 0.969579i | \(-0.578716\pi\) | ||||
−0.244780 | + | 0.969579i | \(0.578716\pi\) | |||||||
\(752\) | −3.12847 | −0.114084 | ||||||||
\(753\) | 6.89579 | 0.251297 | ||||||||
\(754\) | 0.919148 | 0.0334734 | ||||||||
\(755\) | 3.64951 | 0.132819 | ||||||||
\(756\) | 4.43880 | 0.161438 | ||||||||
\(757\) | 24.8404 | 0.902841 | 0.451421 | − | 0.892311i | \(-0.350917\pi\) | ||||
0.451421 | + | 0.892311i | \(0.350917\pi\) | |||||||
\(758\) | 37.1256 | 1.34846 | ||||||||
\(759\) | 1.62843 | 0.0591081 | ||||||||
\(760\) | −0.850025 | −0.0308337 | ||||||||
\(761\) | −8.78430 | −0.318431 | −0.159215 | − | 0.987244i | \(-0.550896\pi\) | ||||
−0.159215 | + | 0.987244i | \(0.550896\pi\) | |||||||
\(762\) | 5.10575 | 0.184962 | ||||||||
\(763\) | −13.8761 | −0.502349 | ||||||||
\(764\) | 21.3120 | 0.771042 | ||||||||
\(765\) | −8.40536 | −0.303896 | ||||||||
\(766\) | 18.3424 | 0.662738 | ||||||||
\(767\) | −1.32967 | −0.0480115 | ||||||||
\(768\) | 0.321033 | 0.0115843 | ||||||||
\(769\) | 37.7680 | 1.36195 | 0.680975 | − | 0.732306i | \(-0.261556\pi\) | ||||
0.680975 | + | 0.732306i | \(0.261556\pi\) | |||||||
\(770\) | 10.0987 | 0.363933 | ||||||||
\(771\) | −7.00112 | −0.252139 | ||||||||
\(772\) | 3.22833 | 0.116190 | ||||||||
\(773\) | −2.07521 | −0.0746401 | −0.0373201 | − | 0.999303i | \(-0.511882\pi\) | ||||
−0.0373201 | + | 0.999303i | \(0.511882\pi\) | |||||||
\(774\) | −6.26795 | −0.225297 | ||||||||
\(775\) | 3.37842 | 0.121357 | ||||||||
\(776\) | −6.67442 | −0.239598 | ||||||||
\(777\) | −2.89538 | −0.103871 | ||||||||
\(778\) | 8.01259 | 0.287265 | ||||||||
\(779\) | 3.70829 | 0.132863 | ||||||||
\(780\) | 0.0486558 | 0.00174216 | ||||||||
\(781\) | 23.6184 | 0.845131 | ||||||||
\(782\) | −3.41711 | −0.122196 | ||||||||
\(783\) | 11.4809 | 0.410293 | ||||||||
\(784\) | −1.50232 | −0.0536541 | ||||||||
\(785\) | −23.1613 | −0.826662 | ||||||||
\(786\) | 4.48876 | 0.160109 | ||||||||
\(787\) | −15.1359 | −0.539535 | −0.269768 | − | 0.962925i | \(-0.586947\pi\) | ||||
−0.269768 | + | 0.962925i | \(0.586947\pi\) | |||||||
\(788\) | 17.7112 | 0.630936 | ||||||||
\(789\) | 2.83414 | 0.100898 | ||||||||
\(790\) | 7.14621 | 0.254251 | ||||||||
\(791\) | −15.5921 | −0.554391 | ||||||||
\(792\) | −12.4772 | −0.443357 | ||||||||
\(793\) | −0.624949 | −0.0221926 | ||||||||
\(794\) | 20.2147 | 0.717395 | ||||||||
\(795\) | −4.12456 | −0.146283 | ||||||||
\(796\) | 0.0733493 | 0.00259980 | ||||||||
\(797\) | 33.3137 | 1.18003 | 0.590015 | − | 0.807392i | \(-0.299122\pi\) | ||||
0.590015 | + | 0.807392i | \(0.299122\pi\) | |||||||
\(798\) | −0.639839 | −0.0226501 | ||||||||
\(799\) | 9.07715 | 0.321127 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 10.0127 | 0.353783 | ||||||||
\(802\) | −3.11232 | −0.109900 | ||||||||
\(803\) | −8.16814 | −0.288247 | ||||||||
\(804\) | 3.62507 | 0.127846 | ||||||||
\(805\) | 2.76141 | 0.0973271 | ||||||||
\(806\) | −0.512035 | −0.0180357 | ||||||||
\(807\) | −5.18184 | −0.182410 | ||||||||
\(808\) | −10.9350 | −0.384691 | ||||||||
\(809\) | 1.31239 | 0.0461412 | 0.0230706 | − | 0.999734i | \(-0.492656\pi\) | ||||
0.0230706 | + | 0.999734i | \(0.492656\pi\) | |||||||
\(810\) | −8.08306 | −0.284010 | ||||||||
\(811\) | 46.2504 | 1.62407 | 0.812035 | − | 0.583609i | \(-0.198360\pi\) | ||||
0.812035 | + | 0.583609i | \(0.198360\pi\) | |||||||
\(812\) | 14.2197 | 0.499013 | ||||||||
\(813\) | 3.73143 | 0.130867 | ||||||||
\(814\) | 16.5670 | 0.580674 | ||||||||
\(815\) | 14.6133 | 0.511882 | ||||||||
\(816\) | −0.931464 | −0.0326078 | ||||||||
\(817\) | 1.83915 | 0.0643439 | ||||||||
\(818\) | −27.3963 | −0.957888 | ||||||||
\(819\) | −1.02947 | −0.0359727 | ||||||||
\(820\) | −4.36256 | −0.152347 | ||||||||
\(821\) | 2.52277 | 0.0880451 | 0.0440226 | − | 0.999031i | \(-0.485983\pi\) | ||||
0.0440226 | + | 0.999031i | \(0.485983\pi\) | |||||||
\(822\) | −3.10990 | −0.108470 | ||||||||
\(823\) | 27.0537 | 0.943031 | 0.471516 | − | 0.881858i | \(-0.343707\pi\) | ||||
0.471516 | + | 0.881858i | \(0.343707\pi\) | |||||||
\(824\) | 5.20948 | 0.181481 | ||||||||
\(825\) | 1.38269 | 0.0481393 | ||||||||
\(826\) | −20.5706 | −0.715743 | ||||||||
\(827\) | 15.0034 | 0.521720 | 0.260860 | − | 0.965377i | \(-0.415994\pi\) | ||||
0.260860 | + | 0.965377i | \(0.415994\pi\) | |||||||
\(828\) | −3.41178 | −0.118568 | ||||||||
\(829\) | −33.8495 | −1.17564 | −0.587821 | − | 0.808991i | \(-0.700014\pi\) | ||||
−0.587821 | + | 0.808991i | \(0.700014\pi\) | |||||||
\(830\) | −12.8931 | −0.447527 | ||||||||
\(831\) | −0.643131 | −0.0223100 | ||||||||
\(832\) | −0.151560 | −0.00525441 | ||||||||
\(833\) | 4.35892 | 0.151027 | ||||||||
\(834\) | 3.29347 | 0.114044 | ||||||||
\(835\) | −18.8141 | −0.651090 | ||||||||
\(836\) | 3.66108 | 0.126621 | ||||||||
\(837\) | −6.39572 | −0.221069 | ||||||||
\(838\) | −3.33288 | −0.115132 | ||||||||
\(839\) | −1.95845 | −0.0676133 | −0.0338066 | − | 0.999428i | \(-0.510763\pi\) | ||||
−0.0338066 | + | 0.999428i | \(0.510763\pi\) | |||||||
\(840\) | 0.752730 | 0.0259716 | ||||||||
\(841\) | 7.77893 | 0.268239 | ||||||||
\(842\) | 2.01962 | 0.0696005 | ||||||||
\(843\) | −9.36345 | −0.322494 | ||||||||
\(844\) | −6.33949 | −0.218214 | ||||||||
\(845\) | 12.9770 | 0.446423 | ||||||||
\(846\) | 9.06300 | 0.311592 | ||||||||
\(847\) | −17.7036 | −0.608304 | ||||||||
\(848\) | 12.8478 | 0.441195 | ||||||||
\(849\) | −8.43648 | −0.289539 | ||||||||
\(850\) | −2.90146 | −0.0995194 | ||||||||
\(851\) | 4.53011 | 0.155290 | ||||||||
\(852\) | 1.76044 | 0.0603117 | ||||||||
\(853\) | 17.1518 | 0.587268 | 0.293634 | − | 0.955918i | \(-0.405135\pi\) | ||||
0.293634 | + | 0.955918i | \(0.405135\pi\) | |||||||
\(854\) | −9.66827 | −0.330841 | ||||||||
\(855\) | 2.46247 | 0.0842147 | ||||||||
\(856\) | −7.53359 | −0.257493 | ||||||||
\(857\) | −39.9535 | −1.36478 | −0.682392 | − | 0.730986i | \(-0.739060\pi\) | ||||
−0.682392 | + | 0.730986i | \(0.739060\pi\) | |||||||
\(858\) | −0.209562 | −0.00715432 | ||||||||
\(859\) | −46.4688 | −1.58549 | −0.792747 | − | 0.609551i | \(-0.791350\pi\) | ||||
−0.792747 | + | 0.609551i | \(0.791350\pi\) | |||||||
\(860\) | −2.16365 | −0.0737797 | ||||||||
\(861\) | −3.28383 | −0.111913 | ||||||||
\(862\) | −38.1102 | −1.29804 | ||||||||
\(863\) | −13.5713 | −0.461974 | −0.230987 | − | 0.972957i | \(-0.574195\pi\) | ||||
−0.230987 | + | 0.972957i | \(0.574195\pi\) | |||||||
\(864\) | −1.89311 | −0.0644049 | ||||||||
\(865\) | −21.5517 | −0.732779 | ||||||||
\(866\) | 7.36690 | 0.250337 | ||||||||
\(867\) | −2.75494 | −0.0935628 | ||||||||
\(868\) | −7.92143 | −0.268871 | ||||||||
\(869\) | −30.7789 | −1.04410 | ||||||||
\(870\) | 1.94692 | 0.0660069 | ||||||||
\(871\) | −1.71141 | −0.0579888 | ||||||||
\(872\) | 5.91804 | 0.200410 | ||||||||
\(873\) | 19.3354 | 0.654403 | ||||||||
\(874\) | 1.00109 | 0.0338624 | ||||||||
\(875\) | 2.34471 | 0.0792658 | ||||||||
\(876\) | −0.608829 | −0.0205704 | ||||||||
\(877\) | 52.8279 | 1.78387 | 0.891936 | − | 0.452161i | \(-0.149347\pi\) | ||||
0.891936 | + | 0.452161i | \(0.149347\pi\) | |||||||
\(878\) | −36.3794 | −1.22775 | ||||||||
\(879\) | 10.8394 | 0.365602 | ||||||||
\(880\) | −4.30702 | −0.145190 | ||||||||
\(881\) | −49.5291 | −1.66868 | −0.834339 | − | 0.551251i | \(-0.814151\pi\) | ||||
−0.834339 | + | 0.551251i | \(0.814151\pi\) | |||||||
\(882\) | 4.35212 | 0.146543 | ||||||||
\(883\) | −27.1728 | −0.914436 | −0.457218 | − | 0.889355i | \(-0.651154\pi\) | ||||
−0.457218 | + | 0.889355i | \(0.651154\pi\) | |||||||
\(884\) | 0.439747 | 0.0147903 | ||||||||
\(885\) | −2.81648 | −0.0946749 | ||||||||
\(886\) | −25.2432 | −0.848062 | ||||||||
\(887\) | 51.6010 | 1.73259 | 0.866296 | − | 0.499530i | \(-0.166494\pi\) | ||||
0.866296 | + | 0.499530i | \(0.166494\pi\) | |||||||
\(888\) | 1.23486 | 0.0414391 | ||||||||
\(889\) | −37.2907 | −1.25069 | ||||||||
\(890\) | 3.45632 | 0.115856 | ||||||||
\(891\) | 34.8139 | 1.16631 | ||||||||
\(892\) | 10.1762 | 0.340723 | ||||||||
\(893\) | −2.65928 | −0.0889895 | ||||||||
\(894\) | −7.30952 | −0.244467 | ||||||||
\(895\) | 12.3686 | 0.413435 | ||||||||
\(896\) | −2.34471 | −0.0783314 | ||||||||
\(897\) | −0.0573029 | −0.00191329 | ||||||||
\(898\) | 12.1827 | 0.406543 | ||||||||
\(899\) | −20.4887 | −0.683335 | ||||||||
\(900\) | −2.89694 | −0.0965646 | ||||||||
\(901\) | −37.2774 | −1.24189 | ||||||||
\(902\) | 18.7897 | 0.625627 | ||||||||
\(903\) | −1.62864 | −0.0541978 | ||||||||
\(904\) | 6.64989 | 0.221172 | ||||||||
\(905\) | 4.07510 | 0.135461 | ||||||||
\(906\) | −1.17161 | −0.0389242 | ||||||||
\(907\) | 15.8778 | 0.527212 | 0.263606 | − | 0.964630i | \(-0.415088\pi\) | ||||
0.263606 | + | 0.964630i | \(0.415088\pi\) | |||||||
\(908\) | 17.1555 | 0.569326 | ||||||||
\(909\) | 31.6779 | 1.05069 | ||||||||
\(910\) | −0.355366 | −0.0117803 | ||||||||
\(911\) | 25.4708 | 0.843884 | 0.421942 | − | 0.906623i | \(-0.361349\pi\) | ||||
0.421942 | + | 0.906623i | \(0.361349\pi\) | |||||||
\(912\) | 0.272886 | 0.00903616 | ||||||||
\(913\) | 55.5310 | 1.83781 | ||||||||
\(914\) | 33.4459 | 1.10629 | ||||||||
\(915\) | −1.32376 | −0.0437620 | ||||||||
\(916\) | 25.4373 | 0.840471 | ||||||||
\(917\) | −32.7844 | −1.08264 | ||||||||
\(918\) | 5.49279 | 0.181289 | ||||||||
\(919\) | 32.6551 | 1.07719 | 0.538596 | − | 0.842564i | \(-0.318955\pi\) | ||||
0.538596 | + | 0.842564i | \(0.318955\pi\) | |||||||
\(920\) | −1.17772 | −0.0388282 | ||||||||
\(921\) | 10.6877 | 0.352170 | ||||||||
\(922\) | 11.8769 | 0.391145 | ||||||||
\(923\) | −0.831110 | −0.0273563 | ||||||||
\(924\) | −3.24202 | −0.106655 | ||||||||
\(925\) | 3.84651 | 0.126473 | ||||||||
\(926\) | −25.8702 | −0.850147 | ||||||||
\(927\) | −15.0915 | −0.495671 | ||||||||
\(928\) | −6.06456 | −0.199079 | ||||||||
\(929\) | 55.1004 | 1.80779 | 0.903893 | − | 0.427759i | \(-0.140697\pi\) | ||||
0.903893 | + | 0.427759i | \(0.140697\pi\) | |||||||
\(930\) | −1.08458 | −0.0355649 | ||||||||
\(931\) | −1.27701 | −0.0418522 | ||||||||
\(932\) | −19.7605 | −0.647278 | ||||||||
\(933\) | −6.34900 | −0.207857 | ||||||||
\(934\) | −29.7130 | −0.972238 | ||||||||
\(935\) | 12.4967 | 0.408685 | ||||||||
\(936\) | 0.439061 | 0.0143512 | ||||||||
\(937\) | −42.2839 | −1.38136 | −0.690678 | − | 0.723163i | \(-0.742688\pi\) | ||||
−0.690678 | + | 0.723163i | \(0.742688\pi\) | |||||||
\(938\) | −26.4763 | −0.864481 | ||||||||
\(939\) | 2.41394 | 0.0787760 | ||||||||
\(940\) | 3.12847 | 0.102040 | ||||||||
\(941\) | 25.6397 | 0.835829 | 0.417915 | − | 0.908486i | \(-0.362761\pi\) | ||||
0.417915 | + | 0.908486i | \(0.362761\pi\) | |||||||
\(942\) | 7.43553 | 0.242263 | ||||||||
\(943\) | 5.13787 | 0.167312 | ||||||||
\(944\) | 8.77318 | 0.285543 | ||||||||
\(945\) | −4.43880 | −0.144394 | ||||||||
\(946\) | 9.31887 | 0.302983 | ||||||||
\(947\) | −24.5699 | −0.798414 | −0.399207 | − | 0.916861i | \(-0.630715\pi\) | ||||
−0.399207 | + | 0.916861i | \(0.630715\pi\) | |||||||
\(948\) | −2.29417 | −0.0745111 | ||||||||
\(949\) | 0.287430 | 0.00933036 | ||||||||
\(950\) | 0.850025 | 0.0275785 | ||||||||
\(951\) | −8.44695 | −0.273911 | ||||||||
\(952\) | 6.80310 | 0.220490 | ||||||||
\(953\) | −34.2866 | −1.11065 | −0.555326 | − | 0.831632i | \(-0.687407\pi\) | ||||
−0.555326 | + | 0.831632i | \(0.687407\pi\) | |||||||
\(954\) | −37.2192 | −1.20502 | ||||||||
\(955\) | −21.3120 | −0.689640 | ||||||||
\(956\) | 23.0312 | 0.744882 | ||||||||
\(957\) | −8.38544 | −0.271063 | ||||||||
\(958\) | −1.19710 | −0.0386766 | ||||||||
\(959\) | 22.7137 | 0.733463 | ||||||||
\(960\) | −0.321033 | −0.0103613 | ||||||||
\(961\) | −19.5863 | −0.631815 | ||||||||
\(962\) | −0.582979 | −0.0187960 | ||||||||
\(963\) | 21.8244 | 0.703280 | ||||||||
\(964\) | −21.9418 | −0.706699 | ||||||||
\(965\) | −3.22833 | −0.103924 | ||||||||
\(966\) | −0.886504 | −0.0285228 | ||||||||
\(967\) | −52.5731 | −1.69064 | −0.845319 | − | 0.534262i | \(-0.820590\pi\) | ||||
−0.845319 | + | 0.534262i | \(0.820590\pi\) | |||||||
\(968\) | 7.55045 | 0.242681 | ||||||||
\(969\) | −0.791768 | −0.0254353 | ||||||||
\(970\) | 6.67442 | 0.214303 | ||||||||
\(971\) | 14.3289 | 0.459838 | 0.229919 | − | 0.973210i | \(-0.426154\pi\) | ||||
0.229919 | + | 0.973210i | \(0.426154\pi\) | |||||||
\(972\) | 8.27426 | 0.265397 | ||||||||
\(973\) | −24.0544 | −0.771148 | ||||||||
\(974\) | −31.3802 | −1.00549 | ||||||||
\(975\) | −0.0486558 | −0.00155823 | ||||||||
\(976\) | 4.12343 | 0.131988 | ||||||||
\(977\) | −44.4430 | −1.42186 | −0.710929 | − | 0.703263i | \(-0.751725\pi\) | ||||
−0.710929 | + | 0.703263i | \(0.751725\pi\) | |||||||
\(978\) | −4.69135 | −0.150013 | ||||||||
\(979\) | −14.8864 | −0.475773 | ||||||||
\(980\) | 1.50232 | 0.0479897 | ||||||||
\(981\) | −17.1442 | −0.547372 | ||||||||
\(982\) | 20.8352 | 0.664877 | ||||||||
\(983\) | 46.3054 | 1.47691 | 0.738456 | − | 0.674301i | \(-0.235555\pi\) | ||||
0.738456 | + | 0.674301i | \(0.235555\pi\) | |||||||
\(984\) | 1.40053 | 0.0446471 | ||||||||
\(985\) | −17.7112 | −0.564327 | ||||||||
\(986\) | 17.5961 | 0.560374 | ||||||||
\(987\) | 2.35490 | 0.0749572 | ||||||||
\(988\) | −0.128830 | −0.00409864 | ||||||||
\(989\) | 2.54817 | 0.0810270 | ||||||||
\(990\) | 12.4772 | 0.396551 | ||||||||
\(991\) | 23.2970 | 0.740053 | 0.370027 | − | 0.929021i | \(-0.379349\pi\) | ||||
0.370027 | + | 0.929021i | \(0.379349\pi\) | |||||||
\(992\) | 3.37842 | 0.107265 | ||||||||
\(993\) | 11.1577 | 0.354078 | ||||||||
\(994\) | −12.8577 | −0.407821 | ||||||||
\(995\) | −0.0733493 | −0.00232533 | ||||||||
\(996\) | 4.13912 | 0.131153 | ||||||||
\(997\) | 12.9217 | 0.409235 | 0.204617 | − | 0.978842i | \(-0.434405\pi\) | ||||
0.204617 | + | 0.978842i | \(0.434405\pi\) | |||||||
\(998\) | 11.1576 | 0.353188 | ||||||||
\(999\) | −7.28187 | −0.230388 |
(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.h.1.15 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.h.1.15 | ✓ | 28 | 1.1 | even | 1 | trivial |