Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(1,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, 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("975.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.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: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.21432 | −0.858654 | −0.429327 | − | 0.903149i | \(-0.641249\pi\) | ||||
−0.429327 | + | 0.903149i | \(0.641249\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.525428 | −0.262714 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.21432 | −0.495744 | ||||||||
\(7\) | −2.59210 | −0.979723 | −0.489862 | − | 0.871800i | \(-0.662953\pi\) | ||||
−0.489862 | + | 0.871800i | \(0.662953\pi\) | |||||||
\(8\) | 3.06668 | 1.08423 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.11753 | −1.84451 | −0.922253 | − | 0.386588i | \(-0.873654\pi\) | ||||
−0.922253 | + | 0.386588i | \(0.873654\pi\) | |||||||
\(12\) | −0.525428 | −0.151678 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 3.14764 | 0.841243 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.67307 | −0.668268 | ||||||||
\(17\) | 4.37778 | 1.06177 | 0.530884 | − | 0.847444i | \(-0.321860\pi\) | ||||
0.530884 | + | 0.847444i | \(0.321860\pi\) | |||||||
\(18\) | −1.21432 | −0.286218 | ||||||||
\(19\) | 4.14764 | 0.951535 | 0.475767 | − | 0.879571i | \(-0.342170\pi\) | ||||
0.475767 | + | 0.879571i | \(0.342170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.59210 | −0.565643 | ||||||||
\(22\) | 7.42864 | 1.58379 | ||||||||
\(23\) | 7.95407 | 1.65854 | 0.829269 | − | 0.558850i | \(-0.188757\pi\) | ||||
0.829269 | + | 0.558850i | \(0.188757\pi\) | |||||||
\(24\) | 3.06668 | 0.625983 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.21432 | 0.238148 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.36196 | 0.257387 | ||||||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.36196 | 0.963037 | 0.481518 | − | 0.876436i | \(-0.340085\pi\) | ||||
0.481518 | + | 0.876436i | \(0.340085\pi\) | |||||||
\(32\) | −2.88739 | −0.510423 | ||||||||
\(33\) | −6.11753 | −1.06493 | ||||||||
\(34\) | −5.31603 | −0.911692 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.525428 | −0.0875713 | ||||||||
\(37\) | 6.90321 | 1.13488 | 0.567441 | − | 0.823414i | \(-0.307934\pi\) | ||||
0.567441 | + | 0.823414i | \(0.307934\pi\) | |||||||
\(38\) | −5.03657 | −0.817039 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.19850 | −1.43656 | −0.718282 | − | 0.695752i | \(-0.755071\pi\) | ||||
−0.718282 | + | 0.695752i | \(0.755071\pi\) | |||||||
\(42\) | 3.14764 | 0.485692 | ||||||||
\(43\) | 11.1383 | 1.69857 | 0.849286 | − | 0.527934i | \(-0.177033\pi\) | ||||
0.849286 | + | 0.527934i | \(0.177033\pi\) | |||||||
\(44\) | 3.21432 | 0.484577 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.65878 | −1.42411 | ||||||||
\(47\) | −1.21432 | −0.177127 | −0.0885634 | − | 0.996071i | \(-0.528228\pi\) | ||||
−0.0885634 | + | 0.996071i | \(0.528228\pi\) | |||||||
\(48\) | −2.67307 | −0.385825 | ||||||||
\(49\) | −0.280996 | −0.0401423 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.37778 | 0.613012 | ||||||||
\(52\) | 0.525428 | 0.0728637 | ||||||||
\(53\) | 4.95407 | 0.680493 | 0.340247 | − | 0.940336i | \(-0.389489\pi\) | ||||
0.340247 | + | 0.940336i | \(0.389489\pi\) | |||||||
\(54\) | −1.21432 | −0.165248 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.94914 | −1.06225 | ||||||||
\(57\) | 4.14764 | 0.549369 | ||||||||
\(58\) | 3.64296 | 0.478344 | ||||||||
\(59\) | 5.44938 | 0.709449 | 0.354725 | − | 0.934971i | \(-0.384575\pi\) | ||||
0.354725 | + | 0.934971i | \(0.384575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.99063 | 1.27917 | 0.639585 | − | 0.768721i | \(-0.279106\pi\) | ||||
0.639585 | + | 0.768721i | \(0.279106\pi\) | |||||||
\(62\) | −6.51114 | −0.826915 | ||||||||
\(63\) | −2.59210 | −0.326574 | ||||||||
\(64\) | 8.85236 | 1.10654 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.42864 | 0.914402 | ||||||||
\(67\) | −4.87310 | −0.595344 | −0.297672 | − | 0.954668i | \(-0.596210\pi\) | ||||
−0.297672 | + | 0.954668i | \(0.596210\pi\) | |||||||
\(68\) | −2.30021 | −0.278941 | ||||||||
\(69\) | 7.95407 | 0.957557 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.39207 | 0.165209 | 0.0826044 | − | 0.996582i | \(-0.473676\pi\) | ||||
0.0826044 | + | 0.996582i | \(0.473676\pi\) | |||||||
\(72\) | 3.06668 | 0.361411 | ||||||||
\(73\) | 13.1383 | 1.53772 | 0.768859 | − | 0.639418i | \(-0.220825\pi\) | ||||
0.768859 | + | 0.639418i | \(0.220825\pi\) | |||||||
\(74\) | −8.38271 | −0.974470 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.17929 | −0.249981 | ||||||||
\(77\) | 15.8573 | 1.80710 | ||||||||
\(78\) | 1.21432 | 0.137495 | ||||||||
\(79\) | −12.3827 | −1.39316 | −0.696582 | − | 0.717478i | \(-0.745297\pi\) | ||||
−0.696582 | + | 0.717478i | \(0.745297\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 11.1699 | 1.23351 | ||||||||
\(83\) | −13.2558 | −1.45501 | −0.727507 | − | 0.686100i | \(-0.759321\pi\) | ||||
−0.727507 | + | 0.686100i | \(0.759321\pi\) | |||||||
\(84\) | 1.36196 | 0.148602 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −13.5254 | −1.45848 | ||||||||
\(87\) | −3.00000 | −0.321634 | ||||||||
\(88\) | −18.7605 | −1.99988 | ||||||||
\(89\) | 8.04149 | 0.852396 | 0.426198 | − | 0.904630i | \(-0.359853\pi\) | ||||
0.426198 | + | 0.904630i | \(0.359853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.59210 | 0.271726 | ||||||||
\(92\) | −4.17929 | −0.435721 | ||||||||
\(93\) | 5.36196 | 0.556010 | ||||||||
\(94\) | 1.47457 | 0.152091 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.88739 | −0.294693 | ||||||||
\(97\) | 15.3778 | 1.56138 | 0.780689 | − | 0.624920i | \(-0.214868\pi\) | ||||
0.780689 | + | 0.624920i | \(0.214868\pi\) | |||||||
\(98\) | 0.341219 | 0.0344684 | ||||||||
\(99\) | −6.11753 | −0.614835 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.33185 | 0.630043 | 0.315021 | − | 0.949085i | \(-0.397988\pi\) | ||||
0.315021 | + | 0.949085i | \(0.397988\pi\) | |||||||
\(102\) | −5.31603 | −0.526365 | ||||||||
\(103\) | 1.23014 | 0.121209 | 0.0606047 | − | 0.998162i | \(-0.480697\pi\) | ||||
0.0606047 | + | 0.998162i | \(0.480697\pi\) | |||||||
\(104\) | −3.06668 | −0.300712 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.01582 | −0.584308 | ||||||||
\(107\) | −10.4286 | −1.00817 | −0.504087 | − | 0.863653i | \(-0.668171\pi\) | ||||
−0.504087 | + | 0.863653i | \(0.668171\pi\) | |||||||
\(108\) | −0.525428 | −0.0505593 | ||||||||
\(109\) | 8.94470 | 0.856747 | 0.428373 | − | 0.903602i | \(-0.359087\pi\) | ||||
0.428373 | + | 0.903602i | \(0.359087\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.90321 | 0.655224 | ||||||||
\(112\) | 6.92888 | 0.654717 | ||||||||
\(113\) | 5.57136 | 0.524110 | 0.262055 | − | 0.965053i | \(-0.415600\pi\) | ||||
0.262055 | + | 0.965053i | \(0.415600\pi\) | |||||||
\(114\) | −5.03657 | −0.471718 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.57628 | 0.146354 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −6.61729 | −0.609171 | ||||||||
\(119\) | −11.3477 | −1.04024 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 26.4242 | 2.40220 | ||||||||
\(122\) | −12.1318 | −1.09836 | ||||||||
\(123\) | −9.19850 | −0.829401 | ||||||||
\(124\) | −2.81732 | −0.253003 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.14764 | 0.280414 | ||||||||
\(127\) | 3.65878 | 0.324664 | 0.162332 | − | 0.986736i | \(-0.448098\pi\) | ||||
0.162332 | + | 0.986736i | \(0.448098\pi\) | |||||||
\(128\) | −4.97481 | −0.439715 | ||||||||
\(129\) | 11.1383 | 0.980670 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.60793 | 0.227856 | 0.113928 | − | 0.993489i | \(-0.463657\pi\) | ||||
0.113928 | + | 0.993489i | \(0.463657\pi\) | |||||||
\(132\) | 3.21432 | 0.279771 | ||||||||
\(133\) | −10.7511 | −0.932241 | ||||||||
\(134\) | 5.91750 | 0.511194 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.4252 | 1.15121 | ||||||||
\(137\) | −11.4795 | −0.980759 | −0.490380 | − | 0.871509i | \(-0.663142\pi\) | ||||
−0.490380 | + | 0.871509i | \(0.663142\pi\) | |||||||
\(138\) | −9.65878 | −0.822210 | ||||||||
\(139\) | 11.8064 | 1.00141 | 0.500704 | − | 0.865619i | \(-0.333075\pi\) | ||||
0.500704 | + | 0.865619i | \(0.333075\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.21432 | −0.102264 | ||||||||
\(142\) | −1.69042 | −0.141857 | ||||||||
\(143\) | 6.11753 | 0.511574 | ||||||||
\(144\) | −2.67307 | −0.222756 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.9541 | −1.32037 | ||||||||
\(147\) | −0.280996 | −0.0231762 | ||||||||
\(148\) | −3.62714 | −0.298149 | ||||||||
\(149\) | −9.86665 | −0.808307 | −0.404154 | − | 0.914691i | \(-0.632434\pi\) | ||||
−0.404154 | + | 0.914691i | \(0.632434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0207 | 0.896855 | 0.448428 | − | 0.893819i | \(-0.351984\pi\) | ||||
0.448428 | + | 0.893819i | \(0.351984\pi\) | |||||||
\(152\) | 12.7195 | 1.03169 | ||||||||
\(153\) | 4.37778 | 0.353923 | ||||||||
\(154\) | −19.2558 | −1.55168 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.525428 | 0.0420679 | ||||||||
\(157\) | −12.6271 | −1.00776 | −0.503878 | − | 0.863775i | \(-0.668094\pi\) | ||||
−0.503878 | + | 0.863775i | \(0.668094\pi\) | |||||||
\(158\) | 15.0366 | 1.19624 | ||||||||
\(159\) | 4.95407 | 0.392883 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.6178 | −1.62491 | ||||||||
\(162\) | −1.21432 | −0.0954060 | ||||||||
\(163\) | 3.19850 | 0.250526 | 0.125263 | − | 0.992124i | \(-0.460023\pi\) | ||||
0.125263 | + | 0.992124i | \(0.460023\pi\) | |||||||
\(164\) | 4.83314 | 0.377405 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.0968 | 1.24935 | ||||||||
\(167\) | −14.7699 | −1.14293 | −0.571463 | − | 0.820628i | \(-0.693624\pi\) | ||||
−0.571463 | + | 0.820628i | \(0.693624\pi\) | |||||||
\(168\) | −7.94914 | −0.613290 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.14764 | 0.317178 | ||||||||
\(172\) | −5.85236 | −0.446238 | ||||||||
\(173\) | 6.13828 | 0.466684 | 0.233342 | − | 0.972395i | \(-0.425034\pi\) | ||||
0.233342 | + | 0.972395i | \(0.425034\pi\) | |||||||
\(174\) | 3.64296 | 0.276172 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 16.3526 | 1.23262 | ||||||||
\(177\) | 5.44938 | 0.409601 | ||||||||
\(178\) | −9.76494 | −0.731913 | ||||||||
\(179\) | 14.6494 | 1.09495 | 0.547474 | − | 0.836823i | \(-0.315589\pi\) | ||||
0.547474 | + | 0.836823i | \(0.315589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.16992 | −0.309948 | −0.154974 | − | 0.987919i | \(-0.549529\pi\) | ||||
−0.154974 | + | 0.987919i | \(0.549529\pi\) | |||||||
\(182\) | −3.14764 | −0.233319 | ||||||||
\(183\) | 9.99063 | 0.738529 | ||||||||
\(184\) | 24.3926 | 1.79824 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.51114 | −0.477420 | ||||||||
\(187\) | −26.7812 | −1.95844 | ||||||||
\(188\) | 0.638037 | 0.0465336 | ||||||||
\(189\) | −2.59210 | −0.188548 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.19358 | 0.303437 | 0.151718 | − | 0.988424i | \(-0.451519\pi\) | ||||
0.151718 | + | 0.988424i | \(0.451519\pi\) | |||||||
\(192\) | 8.85236 | 0.638864 | ||||||||
\(193\) | 12.4746 | 0.897939 | 0.448970 | − | 0.893547i | \(-0.351791\pi\) | ||||
0.448970 | + | 0.893547i | \(0.351791\pi\) | |||||||
\(194\) | −18.6735 | −1.34068 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.147643 | 0.0105459 | ||||||||
\(197\) | 0.903212 | 0.0643512 | 0.0321756 | − | 0.999482i | \(-0.489756\pi\) | ||||
0.0321756 | + | 0.999482i | \(0.489756\pi\) | |||||||
\(198\) | 7.42864 | 0.527930 | ||||||||
\(199\) | −14.8573 | −1.05320 | −0.526602 | − | 0.850112i | \(-0.676534\pi\) | ||||
−0.526602 | + | 0.850112i | \(0.676534\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.87310 | −0.343722 | ||||||||
\(202\) | −7.68889 | −0.540989 | ||||||||
\(203\) | 7.77631 | 0.545790 | ||||||||
\(204\) | −2.30021 | −0.161047 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.49378 | −0.104077 | ||||||||
\(207\) | 7.95407 | 0.552846 | ||||||||
\(208\) | 2.67307 | 0.185344 | ||||||||
\(209\) | −25.3733 | −1.75511 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.4242 | −1.40606 | −0.703030 | − | 0.711160i | \(-0.748170\pi\) | ||||
−0.703030 | + | 0.711160i | \(0.748170\pi\) | |||||||
\(212\) | −2.60300 | −0.178775 | ||||||||
\(213\) | 1.39207 | 0.0953834 | ||||||||
\(214\) | 12.6637 | 0.865673 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.06668 | 0.208661 | ||||||||
\(217\) | −13.8988 | −0.943510 | ||||||||
\(218\) | −10.8617 | −0.735649 | ||||||||
\(219\) | 13.1383 | 0.887802 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.37778 | −0.294482 | ||||||||
\(222\) | −8.38271 | −0.562610 | ||||||||
\(223\) | −2.90321 | −0.194413 | −0.0972067 | − | 0.995264i | \(-0.530991\pi\) | ||||
−0.0972067 | + | 0.995264i | \(0.530991\pi\) | |||||||
\(224\) | 7.48442 | 0.500074 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.76541 | −0.450029 | ||||||||
\(227\) | −3.10816 | −0.206296 | −0.103148 | − | 0.994666i | \(-0.532892\pi\) | ||||
−0.103148 | + | 0.994666i | \(0.532892\pi\) | |||||||
\(228\) | −2.17929 | −0.144327 | ||||||||
\(229\) | −21.2257 | −1.40263 | −0.701317 | − | 0.712850i | \(-0.747404\pi\) | ||||
−0.701317 | + | 0.712850i | \(0.747404\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.8573 | 1.04333 | ||||||||
\(232\) | −9.20003 | −0.604012 | ||||||||
\(233\) | 6.04149 | 0.395791 | 0.197895 | − | 0.980223i | \(-0.436589\pi\) | ||||
0.197895 | + | 0.980223i | \(0.436589\pi\) | |||||||
\(234\) | 1.21432 | 0.0793826 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.86326 | −0.186382 | ||||||||
\(237\) | −12.3827 | −0.804343 | ||||||||
\(238\) | 13.7797 | 0.893205 | ||||||||
\(239\) | −20.9605 | −1.35582 | −0.677912 | − | 0.735143i | \(-0.737115\pi\) | ||||
−0.677912 | + | 0.735143i | \(0.737115\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5763 | 0.681278 | 0.340639 | − | 0.940194i | \(-0.389357\pi\) | ||||
0.340639 | + | 0.940194i | \(0.389357\pi\) | |||||||
\(242\) | −32.0874 | −2.06266 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.24935 | −0.336055 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.1699 | 0.712168 | ||||||||
\(247\) | −4.14764 | −0.263908 | ||||||||
\(248\) | 16.4434 | 1.04416 | ||||||||
\(249\) | −13.2558 | −0.840053 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.2810 | −1.02765 | −0.513824 | − | 0.857896i | \(-0.671771\pi\) | ||||
−0.513824 | + | 0.857896i | \(0.671771\pi\) | |||||||
\(252\) | 1.36196 | 0.0857956 | ||||||||
\(253\) | −48.6593 | −3.05918 | ||||||||
\(254\) | −4.44293 | −0.278774 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.6637 | −0.728981 | ||||||||
\(257\) | 20.0049 | 1.24787 | 0.623936 | − | 0.781475i | \(-0.285532\pi\) | ||||
0.623936 | + | 0.781475i | \(0.285532\pi\) | |||||||
\(258\) | −13.5254 | −0.842056 | ||||||||
\(259\) | −17.8938 | −1.11187 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.00000 | −0.185695 | ||||||||
\(262\) | −3.16686 | −0.195649 | ||||||||
\(263\) | 3.15701 | 0.194670 | 0.0973348 | − | 0.995252i | \(-0.468968\pi\) | ||||
0.0973348 | + | 0.995252i | \(0.468968\pi\) | |||||||
\(264\) | −18.7605 | −1.15463 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 13.0553 | 0.800472 | ||||||||
\(267\) | 8.04149 | 0.492131 | ||||||||
\(268\) | 2.56046 | 0.156405 | ||||||||
\(269\) | −17.7971 | −1.08511 | −0.542553 | − | 0.840022i | \(-0.682542\pi\) | ||||
−0.542553 | + | 0.840022i | \(0.682542\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.3575 | −1.54036 | −0.770180 | − | 0.637827i | \(-0.779834\pi\) | ||||
−0.770180 | + | 0.637827i | \(0.779834\pi\) | |||||||
\(272\) | −11.7021 | −0.709546 | ||||||||
\(273\) | 2.59210 | 0.156881 | ||||||||
\(274\) | 13.9398 | 0.842133 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.17929 | −0.251563 | ||||||||
\(277\) | −0.235063 | −0.0141236 | −0.00706179 | − | 0.999975i | \(-0.502248\pi\) | ||||
−0.00706179 | + | 0.999975i | \(0.502248\pi\) | |||||||
\(278\) | −14.3368 | −0.859863 | ||||||||
\(279\) | 5.36196 | 0.321012 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.1338 | 1.73798 | 0.868989 | − | 0.494831i | \(-0.164770\pi\) | ||||
0.868989 | + | 0.494831i | \(0.164770\pi\) | |||||||
\(282\) | 1.47457 | 0.0878095 | ||||||||
\(283\) | −20.5718 | −1.22287 | −0.611434 | − | 0.791295i | \(-0.709407\pi\) | ||||
−0.611434 | + | 0.791295i | \(0.709407\pi\) | |||||||
\(284\) | −0.731434 | −0.0434026 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.42864 | −0.439265 | ||||||||
\(287\) | 23.8435 | 1.40744 | ||||||||
\(288\) | −2.88739 | −0.170141 | ||||||||
\(289\) | 2.16500 | 0.127353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.3778 | 0.901462 | ||||||||
\(292\) | −6.90321 | −0.403980 | ||||||||
\(293\) | 3.12399 | 0.182505 | 0.0912526 | − | 0.995828i | \(-0.470913\pi\) | ||||
0.0912526 | + | 0.995828i | \(0.470913\pi\) | |||||||
\(294\) | 0.341219 | 0.0199003 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 21.1699 | 1.23048 | ||||||||
\(297\) | −6.11753 | −0.354975 | ||||||||
\(298\) | 11.9813 | 0.694056 | ||||||||
\(299\) | −7.95407 | −0.459996 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.8716 | −1.66413 | ||||||||
\(302\) | −13.3827 | −0.770088 | ||||||||
\(303\) | 6.33185 | 0.363755 | ||||||||
\(304\) | −11.0869 | −0.635880 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.31603 | −0.303897 | ||||||||
\(307\) | −14.0874 | −0.804012 | −0.402006 | − | 0.915637i | \(-0.631687\pi\) | ||||
−0.402006 | + | 0.915637i | \(0.631687\pi\) | |||||||
\(308\) | −8.33185 | −0.474751 | ||||||||
\(309\) | 1.23014 | 0.0699803 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.6128 | 0.998733 | 0.499366 | − | 0.866391i | \(-0.333566\pi\) | ||||
0.499366 | + | 0.866391i | \(0.333566\pi\) | |||||||
\(312\) | −3.06668 | −0.173616 | ||||||||
\(313\) | 17.2810 | 0.976780 | 0.488390 | − | 0.872626i | \(-0.337584\pi\) | ||||
0.488390 | + | 0.872626i | \(0.337584\pi\) | |||||||
\(314\) | 15.3334 | 0.865313 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.50622 | 0.366003 | ||||||||
\(317\) | 0.668149 | 0.0375270 | 0.0187635 | − | 0.999824i | \(-0.494027\pi\) | ||||
0.0187635 | + | 0.999824i | \(0.494027\pi\) | |||||||
\(318\) | −6.01582 | −0.337351 | ||||||||
\(319\) | 18.3526 | 1.02755 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.4286 | −0.582070 | ||||||||
\(322\) | 25.0366 | 1.39523 | ||||||||
\(323\) | 18.1575 | 1.01031 | ||||||||
\(324\) | −0.525428 | −0.0291904 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.88400 | −0.215115 | ||||||||
\(327\) | 8.94470 | 0.494643 | ||||||||
\(328\) | −28.2088 | −1.55757 | ||||||||
\(329\) | 3.14764 | 0.173535 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.3921 | 1.17581 | 0.587907 | − | 0.808928i | \(-0.299952\pi\) | ||||
0.587907 | + | 0.808928i | \(0.299952\pi\) | |||||||
\(332\) | 6.96497 | 0.382252 | ||||||||
\(333\) | 6.90321 | 0.378294 | ||||||||
\(334\) | 17.9353 | 0.981378 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.92888 | 0.378001 | ||||||||
\(337\) | 27.5259 | 1.49943 | 0.749716 | − | 0.661760i | \(-0.230190\pi\) | ||||
0.749716 | + | 0.661760i | \(0.230190\pi\) | |||||||
\(338\) | −1.21432 | −0.0660503 | ||||||||
\(339\) | 5.57136 | 0.302595 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.8020 | −1.77633 | ||||||||
\(342\) | −5.03657 | −0.272346 | ||||||||
\(343\) | 18.8731 | 1.01905 | ||||||||
\(344\) | 34.1575 | 1.84165 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.45383 | −0.400720 | ||||||||
\(347\) | 3.53972 | 0.190022 | 0.0950110 | − | 0.995476i | \(-0.469711\pi\) | ||||
0.0950110 | + | 0.995476i | \(0.469711\pi\) | |||||||
\(348\) | 1.57628 | 0.0844976 | ||||||||
\(349\) | −3.46520 | −0.185488 | −0.0927441 | − | 0.995690i | \(-0.529564\pi\) | ||||
−0.0927441 | + | 0.995690i | \(0.529564\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 17.6637 | 0.941479 | ||||||||
\(353\) | 16.6365 | 0.885472 | 0.442736 | − | 0.896652i | \(-0.354008\pi\) | ||||
0.442736 | + | 0.896652i | \(0.354008\pi\) | |||||||
\(354\) | −6.61729 | −0.351705 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.22522 | −0.223936 | ||||||||
\(357\) | −11.3477 | −0.600583 | ||||||||
\(358\) | −17.7891 | −0.940182 | ||||||||
\(359\) | −30.2652 | −1.59733 | −0.798667 | − | 0.601773i | \(-0.794461\pi\) | ||||
−0.798667 | + | 0.601773i | \(0.794461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.79706 | −0.0945819 | ||||||||
\(362\) | 5.06361 | 0.266138 | ||||||||
\(363\) | 26.4242 | 1.38691 | ||||||||
\(364\) | −1.36196 | −0.0713863 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.1318 | −0.634140 | ||||||||
\(367\) | 21.1240 | 1.10266 | 0.551332 | − | 0.834286i | \(-0.314120\pi\) | ||||
0.551332 | + | 0.834286i | \(0.314120\pi\) | |||||||
\(368\) | −21.2618 | −1.10835 | ||||||||
\(369\) | −9.19850 | −0.478855 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.8415 | −0.666695 | ||||||||
\(372\) | −2.81732 | −0.146071 | ||||||||
\(373\) | 16.9541 | 0.877848 | 0.438924 | − | 0.898524i | \(-0.355360\pi\) | ||||
0.438924 | + | 0.898524i | \(0.355360\pi\) | |||||||
\(374\) | 32.5210 | 1.68162 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.72393 | −0.192047 | ||||||||
\(377\) | 3.00000 | 0.154508 | ||||||||
\(378\) | 3.14764 | 0.161897 | ||||||||
\(379\) | −8.27946 | −0.425288 | −0.212644 | − | 0.977130i | \(-0.568207\pi\) | ||||
−0.212644 | + | 0.977130i | \(0.568207\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.65878 | 0.187445 | ||||||||
\(382\) | −5.09234 | −0.260547 | ||||||||
\(383\) | −21.7418 | −1.11095 | −0.555476 | − | 0.831533i | \(-0.687464\pi\) | ||||
−0.555476 | + | 0.831533i | \(0.687464\pi\) | |||||||
\(384\) | −4.97481 | −0.253870 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.1481 | −0.771019 | ||||||||
\(387\) | 11.1383 | 0.566190 | ||||||||
\(388\) | −8.07991 | −0.410195 | ||||||||
\(389\) | 21.7748 | 1.10403 | 0.552013 | − | 0.833836i | \(-0.313860\pi\) | ||||
0.552013 | + | 0.833836i | \(0.313860\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.8212 | 1.76098 | ||||||||
\(392\) | −0.861725 | −0.0435237 | ||||||||
\(393\) | 2.60793 | 0.131552 | ||||||||
\(394\) | −1.09679 | −0.0552554 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.21432 | 0.161526 | ||||||||
\(397\) | 4.91750 | 0.246802 | 0.123401 | − | 0.992357i | \(-0.460620\pi\) | ||||
0.123401 | + | 0.992357i | \(0.460620\pi\) | |||||||
\(398\) | 18.0415 | 0.904338 | ||||||||
\(399\) | −10.7511 | −0.538229 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.60793 | 0.130234 | 0.0651168 | − | 0.997878i | \(-0.479258\pi\) | ||||
0.0651168 | + | 0.997878i | \(0.479258\pi\) | |||||||
\(402\) | 5.91750 | 0.295138 | ||||||||
\(403\) | −5.36196 | −0.267098 | ||||||||
\(404\) | −3.32693 | −0.165521 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.44293 | −0.468645 | ||||||||
\(407\) | −42.2306 | −2.09329 | ||||||||
\(408\) | 13.4252 | 0.664649 | ||||||||
\(409\) | 18.7096 | 0.925132 | 0.462566 | − | 0.886585i | \(-0.346929\pi\) | ||||
0.462566 | + | 0.886585i | \(0.346929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.4795 | −0.566242 | ||||||||
\(412\) | −0.646350 | −0.0318434 | ||||||||
\(413\) | −14.1254 | −0.695064 | ||||||||
\(414\) | −9.65878 | −0.474703 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.88739 | 0.141566 | ||||||||
\(417\) | 11.8064 | 0.578163 | ||||||||
\(418\) | 30.8113 | 1.50703 | ||||||||
\(419\) | 14.2623 | 0.696757 | 0.348379 | − | 0.937354i | \(-0.386732\pi\) | ||||
0.348379 | + | 0.937354i | \(0.386732\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.8064 | −1.06278 | −0.531390 | − | 0.847127i | \(-0.678330\pi\) | ||||
−0.531390 | + | 0.847127i | \(0.678330\pi\) | |||||||
\(422\) | 24.8015 | 1.20732 | ||||||||
\(423\) | −1.21432 | −0.0590422 | ||||||||
\(424\) | 15.1925 | 0.737814 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.69042 | −0.0819013 | ||||||||
\(427\) | −25.8968 | −1.25323 | ||||||||
\(428\) | 5.47949 | 0.264861 | ||||||||
\(429\) | 6.11753 | 0.295357 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.53480 | −0.218433 | −0.109217 | − | 0.994018i | \(-0.534834\pi\) | ||||
−0.109217 | + | 0.994018i | \(0.534834\pi\) | |||||||
\(432\) | −2.67307 | −0.128608 | ||||||||
\(433\) | −19.4608 | −0.935224 | −0.467612 | − | 0.883934i | \(-0.654886\pi\) | ||||
−0.467612 | + | 0.883934i | \(0.654886\pi\) | |||||||
\(434\) | 16.8775 | 0.810148 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.69979 | −0.225079 | ||||||||
\(437\) | 32.9906 | 1.57816 | ||||||||
\(438\) | −15.9541 | −0.762315 | ||||||||
\(439\) | −3.17976 | −0.151762 | −0.0758809 | − | 0.997117i | \(-0.524177\pi\) | ||||
−0.0758809 | + | 0.997117i | \(0.524177\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.280996 | −0.0133808 | ||||||||
\(442\) | 5.31603 | 0.252858 | ||||||||
\(443\) | −32.6780 | −1.55258 | −0.776289 | − | 0.630377i | \(-0.782900\pi\) | ||||
−0.776289 | + | 0.630377i | \(0.782900\pi\) | |||||||
\(444\) | −3.62714 | −0.172136 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.52543 | 0.166934 | ||||||||
\(447\) | −9.86665 | −0.466676 | ||||||||
\(448\) | −22.9462 | −1.08411 | ||||||||
\(449\) | −20.1748 | −0.952110 | −0.476055 | − | 0.879416i | \(-0.657934\pi\) | ||||
−0.476055 | + | 0.879416i | \(0.657934\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 56.2721 | 2.64975 | ||||||||
\(452\) | −2.92735 | −0.137691 | ||||||||
\(453\) | 11.0207 | 0.517800 | ||||||||
\(454\) | 3.77430 | 0.177137 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.7195 | 0.595644 | ||||||||
\(457\) | −19.5669 | −0.915302 | −0.457651 | − | 0.889132i | \(-0.651309\pi\) | ||||
−0.457651 | + | 0.889132i | \(0.651309\pi\) | |||||||
\(458\) | 25.7748 | 1.20438 | ||||||||
\(459\) | 4.37778 | 0.204337 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.1338 | 1.54320 | 0.771598 | − | 0.636110i | \(-0.219458\pi\) | ||||
0.771598 | + | 0.636110i | \(0.219458\pi\) | |||||||
\(462\) | −19.2558 | −0.895861 | ||||||||
\(463\) | 11.1684 | 0.519039 | 0.259519 | − | 0.965738i | \(-0.416436\pi\) | ||||
0.259519 | + | 0.965738i | \(0.416436\pi\) | |||||||
\(464\) | 8.01921 | 0.372283 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.33630 | −0.339847 | ||||||||
\(467\) | 39.2672 | 1.81707 | 0.908534 | − | 0.417810i | \(-0.137202\pi\) | ||||
0.908534 | + | 0.417810i | \(0.137202\pi\) | |||||||
\(468\) | 0.525428 | 0.0242879 | ||||||||
\(469\) | 12.6316 | 0.583272 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.6271 | −0.581828 | ||||||||
\(472\) | 16.7115 | 0.769209 | ||||||||
\(473\) | −68.1388 | −3.13302 | ||||||||
\(474\) | 15.0366 | 0.690652 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.96238 | 0.273285 | ||||||||
\(477\) | 4.95407 | 0.226831 | ||||||||
\(478\) | 25.4528 | 1.16418 | ||||||||
\(479\) | −12.8000 | −0.584846 | −0.292423 | − | 0.956289i | \(-0.594461\pi\) | ||||
−0.292423 | + | 0.956289i | \(0.594461\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.90321 | −0.314759 | ||||||||
\(482\) | −12.8430 | −0.584982 | ||||||||
\(483\) | −20.6178 | −0.938141 | ||||||||
\(484\) | −13.8840 | −0.631091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.21432 | −0.0550827 | ||||||||
\(487\) | 3.06668 | 0.138964 | 0.0694822 | − | 0.997583i | \(-0.477865\pi\) | ||||
0.0694822 | + | 0.997583i | \(0.477865\pi\) | |||||||
\(488\) | 30.6380 | 1.38692 | ||||||||
\(489\) | 3.19850 | 0.144641 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.17130 | 0.0528601 | 0.0264300 | − | 0.999651i | \(-0.491586\pi\) | ||||
0.0264300 | + | 0.999651i | \(0.491586\pi\) | |||||||
\(492\) | 4.83314 | 0.217895 | ||||||||
\(493\) | −13.1334 | −0.591496 | ||||||||
\(494\) | 5.03657 | 0.226606 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.3329 | −0.643566 | ||||||||
\(497\) | −3.60840 | −0.161859 | ||||||||
\(498\) | 16.0968 | 0.721314 | ||||||||
\(499\) | 38.4499 | 1.72125 | 0.860626 | − | 0.509237i | \(-0.170073\pi\) | ||||
0.860626 | + | 0.509237i | \(0.170073\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.7699 | −0.659869 | ||||||||
\(502\) | 19.7703 | 0.882393 | ||||||||
\(503\) | 11.1985 | 0.499316 | 0.249658 | − | 0.968334i | \(-0.419682\pi\) | ||||
0.249658 | + | 0.968334i | \(0.419682\pi\) | |||||||
\(504\) | −7.94914 | −0.354083 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 59.0879 | 2.62678 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −1.92242 | −0.0852938 | ||||||||
\(509\) | −6.48442 | −0.287417 | −0.143708 | − | 0.989620i | \(-0.545903\pi\) | ||||
−0.143708 | + | 0.989620i | \(0.545903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.0558 | −1.50654 | ||||||||
\(512\) | 24.1131 | 1.06566 | ||||||||
\(513\) | 4.14764 | 0.183123 | ||||||||
\(514\) | −24.2924 | −1.07149 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.85236 | −0.257636 | ||||||||
\(517\) | 7.42864 | 0.326711 | ||||||||
\(518\) | 21.7288 | 0.954711 | ||||||||
\(519\) | 6.13828 | 0.269440 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.75557 | 0.383588 | 0.191794 | − | 0.981435i | \(-0.438569\pi\) | ||||
0.191794 | + | 0.981435i | \(0.438569\pi\) | |||||||
\(522\) | 3.64296 | 0.159448 | ||||||||
\(523\) | 0.447375 | 0.0195624 | 0.00978118 | − | 0.999952i | \(-0.496887\pi\) | ||||
0.00978118 | + | 0.999952i | \(0.496887\pi\) | |||||||
\(524\) | −1.37028 | −0.0598608 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.83362 | −0.167154 | ||||||||
\(527\) | 23.4735 | 1.02252 | ||||||||
\(528\) | 16.3526 | 0.711655 | ||||||||
\(529\) | 40.2672 | 1.75075 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.44938 | 0.236483 | ||||||||
\(532\) | 5.64894 | 0.244912 | ||||||||
\(533\) | 9.19850 | 0.398431 | ||||||||
\(534\) | −9.76494 | −0.422570 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.9442 | −0.645492 | ||||||||
\(537\) | 14.6494 | 0.632169 | ||||||||
\(538\) | 21.6113 | 0.931730 | ||||||||
\(539\) | 1.71900 | 0.0740427 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.9733 | −1.67559 | −0.837796 | − | 0.545983i | \(-0.816156\pi\) | ||||
−0.837796 | + | 0.545983i | \(0.816156\pi\) | |||||||
\(542\) | 30.7921 | 1.32264 | ||||||||
\(543\) | −4.16992 | −0.178948 | ||||||||
\(544\) | −12.6404 | −0.541952 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.14764 | −0.134707 | ||||||||
\(547\) | 13.1669 | 0.562974 | 0.281487 | − | 0.959565i | \(-0.409172\pi\) | ||||
0.281487 | + | 0.959565i | \(0.409172\pi\) | |||||||
\(548\) | 6.03164 | 0.257659 | ||||||||
\(549\) | 9.99063 | 0.426390 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.4429 | −0.530087 | ||||||||
\(552\) | 24.3926 | 1.03822 | ||||||||
\(553\) | 32.0973 | 1.36491 | ||||||||
\(554\) | 0.285442 | 0.0121273 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.20342 | −0.263084 | ||||||||
\(557\) | 34.3926 | 1.45726 | 0.728630 | − | 0.684908i | \(-0.240158\pi\) | ||||
0.728630 | + | 0.684908i | \(0.240158\pi\) | |||||||
\(558\) | −6.51114 | −0.275638 | ||||||||
\(559\) | −11.1383 | −0.471099 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.7812 | −1.13070 | ||||||||
\(562\) | −35.3778 | −1.49232 | ||||||||
\(563\) | −15.3921 | −0.648699 | −0.324349 | − | 0.945937i | \(-0.605145\pi\) | ||||
−0.324349 | + | 0.945937i | \(0.605145\pi\) | |||||||
\(564\) | 0.638037 | 0.0268662 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 24.9808 | 1.05002 | ||||||||
\(567\) | −2.59210 | −0.108858 | ||||||||
\(568\) | 4.26904 | 0.179125 | ||||||||
\(569\) | 17.6049 | 0.738034 | 0.369017 | − | 0.929423i | \(-0.379694\pi\) | ||||
0.369017 | + | 0.929423i | \(0.379694\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.8336 | 1.49959 | 0.749795 | − | 0.661670i | \(-0.230152\pi\) | ||||
0.749795 | + | 0.661670i | \(0.230152\pi\) | |||||||
\(572\) | −3.21432 | −0.134397 | ||||||||
\(573\) | 4.19358 | 0.175189 | ||||||||
\(574\) | −28.9536 | −1.20850 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.85236 | 0.368848 | ||||||||
\(577\) | 27.3145 | 1.13712 | 0.568559 | − | 0.822643i | \(-0.307501\pi\) | ||||
0.568559 | + | 0.822643i | \(0.307501\pi\) | |||||||
\(578\) | −2.62900 | −0.109352 | ||||||||
\(579\) | 12.4746 | 0.518426 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.3604 | 1.42551 | ||||||||
\(582\) | −18.6735 | −0.774043 | ||||||||
\(583\) | −30.3067 | −1.25517 | ||||||||
\(584\) | 40.2908 | 1.66725 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.79352 | −0.156709 | ||||||||
\(587\) | 6.21924 | 0.256696 | 0.128348 | − | 0.991729i | \(-0.459033\pi\) | ||||
0.128348 | + | 0.991729i | \(0.459033\pi\) | |||||||
\(588\) | 0.147643 | 0.00608870 | ||||||||
\(589\) | 22.2395 | 0.916363 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.903212 | 0.0371532 | ||||||||
\(592\) | −18.4528 | −0.758404 | ||||||||
\(593\) | 12.3970 | 0.509084 | 0.254542 | − | 0.967062i | \(-0.418075\pi\) | ||||
0.254542 | + | 0.967062i | \(0.418075\pi\) | |||||||
\(594\) | 7.42864 | 0.304801 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.18421 | 0.212353 | ||||||||
\(597\) | −14.8573 | −0.608068 | ||||||||
\(598\) | 9.65878 | 0.394977 | ||||||||
\(599\) | 44.2306 | 1.80721 | 0.903607 | − | 0.428362i | \(-0.140909\pi\) | ||||
0.903607 | + | 0.428362i | \(0.140909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.7003 | −1.74178 | −0.870890 | − | 0.491478i | \(-0.836457\pi\) | ||||
−0.870890 | + | 0.491478i | \(0.836457\pi\) | |||||||
\(602\) | 35.0593 | 1.42891 | ||||||||
\(603\) | −4.87310 | −0.198448 | ||||||||
\(604\) | −5.79060 | −0.235616 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.68889 | −0.312340 | ||||||||
\(607\) | −37.5625 | −1.52461 | −0.762307 | − | 0.647216i | \(-0.775933\pi\) | ||||
−0.762307 | + | 0.647216i | \(0.775933\pi\) | |||||||
\(608\) | −11.9759 | −0.485685 | ||||||||
\(609\) | 7.77631 | 0.315112 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.21432 | 0.0491261 | ||||||||
\(612\) | −2.30021 | −0.0929804 | ||||||||
\(613\) | 29.1052 | 1.17555 | 0.587775 | − | 0.809024i | \(-0.300004\pi\) | ||||
0.587775 | + | 0.809024i | \(0.300004\pi\) | |||||||
\(614\) | 17.1066 | 0.690367 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.6291 | 1.95932 | ||||||||
\(617\) | 38.4286 | 1.54708 | 0.773539 | − | 0.633748i | \(-0.218484\pi\) | ||||
0.773539 | + | 0.633748i | \(0.218484\pi\) | |||||||
\(618\) | −1.49378 | −0.0600888 | ||||||||
\(619\) | −28.0143 | −1.12599 | −0.562995 | − | 0.826461i | \(-0.690351\pi\) | ||||
−0.562995 | + | 0.826461i | \(0.690351\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.95407 | 0.319186 | ||||||||
\(622\) | −21.3876 | −0.857566 | ||||||||
\(623\) | −20.8444 | −0.835112 | ||||||||
\(624\) | 2.67307 | 0.107008 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −20.9847 | −0.838715 | ||||||||
\(627\) | −25.3733 | −1.01331 | ||||||||
\(628\) | 6.63465 | 0.264751 | ||||||||
\(629\) | 30.2208 | 1.20498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.7610 | −1.22457 | −0.612287 | − | 0.790635i | \(-0.709750\pi\) | ||||
−0.612287 | + | 0.790635i | \(0.709750\pi\) | |||||||
\(632\) | −37.9738 | −1.51051 | ||||||||
\(633\) | −20.4242 | −0.811789 | ||||||||
\(634\) | −0.811346 | −0.0322227 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.60300 | −0.103216 | ||||||||
\(637\) | 0.280996 | 0.0111335 | ||||||||
\(638\) | −22.2859 | −0.882308 | ||||||||
\(639\) | 1.39207 | 0.0550696 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.2351 | 0.601749 | 0.300874 | − | 0.953664i | \(-0.402722\pi\) | ||||
0.300874 | + | 0.953664i | \(0.402722\pi\) | |||||||
\(642\) | 12.6637 | 0.499796 | ||||||||
\(643\) | 4.88448 | 0.192625 | 0.0963125 | − | 0.995351i | \(-0.469295\pi\) | ||||
0.0963125 | + | 0.995351i | \(0.469295\pi\) | |||||||
\(644\) | 10.8331 | 0.426886 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.0490 | −0.867506 | ||||||||
\(647\) | −41.1655 | −1.61838 | −0.809191 | − | 0.587546i | \(-0.800094\pi\) | ||||
−0.809191 | + | 0.587546i | \(0.800094\pi\) | |||||||
\(648\) | 3.06668 | 0.120470 | ||||||||
\(649\) | −33.3368 | −1.30858 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.8988 | −0.544736 | ||||||||
\(652\) | −1.68058 | −0.0658166 | ||||||||
\(653\) | −20.7748 | −0.812980 | −0.406490 | − | 0.913655i | \(-0.633247\pi\) | ||||
−0.406490 | + | 0.913655i | \(0.633247\pi\) | |||||||
\(654\) | −10.8617 | −0.424727 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 24.5882 | 0.960009 | ||||||||
\(657\) | 13.1383 | 0.512573 | ||||||||
\(658\) | −3.82225 | −0.149007 | ||||||||
\(659\) | −37.4148 | −1.45747 | −0.728737 | − | 0.684793i | \(-0.759892\pi\) | ||||
−0.728737 | + | 0.684793i | \(0.759892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7605 | −0.690803 | −0.345402 | − | 0.938455i | \(-0.612257\pi\) | ||||
−0.345402 | + | 0.938455i | \(0.612257\pi\) | |||||||
\(662\) | −25.9768 | −1.00962 | ||||||||
\(663\) | −4.37778 | −0.170019 | ||||||||
\(664\) | −40.6513 | −1.57758 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.38271 | −0.324823 | ||||||||
\(667\) | −23.8622 | −0.923948 | ||||||||
\(668\) | 7.76049 | 0.300262 | ||||||||
\(669\) | −2.90321 | −0.112245 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −61.1180 | −2.35943 | ||||||||
\(672\) | 7.48442 | 0.288718 | ||||||||
\(673\) | 26.9353 | 1.03828 | 0.519140 | − | 0.854689i | \(-0.326252\pi\) | ||||
0.519140 | + | 0.854689i | \(0.326252\pi\) | |||||||
\(674\) | −33.4252 | −1.28749 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.525428 | −0.0202088 | ||||||||
\(677\) | 4.46028 | 0.171423 | 0.0857113 | − | 0.996320i | \(-0.472684\pi\) | ||||
0.0857113 | + | 0.996320i | \(0.472684\pi\) | |||||||
\(678\) | −6.76541 | −0.259824 | ||||||||
\(679\) | −39.8608 | −1.52972 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.10816 | −0.119105 | ||||||||
\(682\) | 39.8321 | 1.52525 | ||||||||
\(683\) | −9.62867 | −0.368431 | −0.184215 | − | 0.982886i | \(-0.558974\pi\) | ||||
−0.184215 | + | 0.982886i | \(0.558974\pi\) | |||||||
\(684\) | −2.17929 | −0.0833271 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −22.9180 | −0.875012 | ||||||||
\(687\) | −21.2257 | −0.809811 | ||||||||
\(688\) | −29.7734 | −1.13510 | ||||||||
\(689\) | −4.95407 | −0.188735 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.9605 | 1.25388 | 0.626939 | − | 0.779069i | \(-0.284308\pi\) | ||||
0.626939 | + | 0.779069i | \(0.284308\pi\) | |||||||
\(692\) | −3.22522 | −0.122604 | ||||||||
\(693\) | 15.8573 | 0.602368 | ||||||||
\(694\) | −4.29835 | −0.163163 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.20003 | −0.348726 | ||||||||
\(697\) | −40.2690 | −1.52530 | ||||||||
\(698\) | 4.20787 | 0.159270 | ||||||||
\(699\) | 6.04149 | 0.228510 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.8385 | −0.749291 | −0.374646 | − | 0.927168i | \(-0.622236\pi\) | ||||
−0.374646 | + | 0.927168i | \(0.622236\pi\) | |||||||
\(702\) | 1.21432 | 0.0458315 | ||||||||
\(703\) | 28.6321 | 1.07988 | ||||||||
\(704\) | −54.1546 | −2.04103 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.2020 | −0.760314 | ||||||||
\(707\) | −16.4128 | −0.617268 | ||||||||
\(708\) | −2.86326 | −0.107608 | ||||||||
\(709\) | 16.7828 | 0.630290 | 0.315145 | − | 0.949044i | \(-0.397947\pi\) | ||||
0.315145 | + | 0.949044i | \(0.397947\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.3827 | −0.464388 | ||||||||
\(712\) | 24.6606 | 0.924197 | ||||||||
\(713\) | 42.6494 | 1.59723 | ||||||||
\(714\) | 13.7797 | 0.515692 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.69721 | −0.287658 | ||||||||
\(717\) | −20.9605 | −0.782785 | ||||||||
\(718\) | 36.7516 | 1.37156 | ||||||||
\(719\) | −7.89384 | −0.294391 | −0.147195 | − | 0.989107i | \(-0.547025\pi\) | ||||
−0.147195 | + | 0.989107i | \(0.547025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.18865 | −0.118752 | ||||||||
\(722\) | 2.18220 | 0.0812131 | ||||||||
\(723\) | 10.5763 | 0.393336 | ||||||||
\(724\) | 2.19099 | 0.0814275 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −32.0874 | −1.19088 | ||||||||
\(727\) | 47.6182 | 1.76606 | 0.883031 | − | 0.469314i | \(-0.155499\pi\) | ||||
0.883031 | + | 0.469314i | \(0.155499\pi\) | |||||||
\(728\) | 7.94914 | 0.294615 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48.7610 | 1.80349 | ||||||||
\(732\) | −5.24935 | −0.194022 | ||||||||
\(733\) | 10.3970 | 0.384022 | 0.192011 | − | 0.981393i | \(-0.438499\pi\) | ||||
0.192011 | + | 0.981393i | \(0.438499\pi\) | |||||||
\(734\) | −25.6513 | −0.946806 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.9665 | −0.846556 | ||||||||
\(737\) | 29.8113 | 1.09812 | ||||||||
\(738\) | 11.1699 | 0.411170 | ||||||||
\(739\) | 40.1175 | 1.47575 | 0.737874 | − | 0.674939i | \(-0.235830\pi\) | ||||
0.737874 | + | 0.674939i | \(0.235830\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.14764 | −0.152367 | ||||||||
\(742\) | 15.5936 | 0.572460 | ||||||||
\(743\) | −41.1497 | −1.50963 | −0.754817 | − | 0.655935i | \(-0.772274\pi\) | ||||
−0.754817 | + | 0.655935i | \(0.772274\pi\) | |||||||
\(744\) | 16.4434 | 0.602845 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.5877 | −0.753768 | ||||||||
\(747\) | −13.2558 | −0.485005 | ||||||||
\(748\) | 14.0716 | 0.514509 | ||||||||
\(749\) | 27.0321 | 0.987732 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.6178 | 1.70111 | 0.850553 | − | 0.525889i | \(-0.176267\pi\) | ||||
0.850553 | + | 0.525889i | \(0.176267\pi\) | |||||||
\(752\) | 3.24596 | 0.118368 | ||||||||
\(753\) | −16.2810 | −0.593312 | ||||||||
\(754\) | −3.64296 | −0.132669 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.36196 | 0.0495341 | ||||||||
\(757\) | 11.1748 | 0.406156 | 0.203078 | − | 0.979163i | \(-0.434905\pi\) | ||||
0.203078 | + | 0.979163i | \(0.434905\pi\) | |||||||
\(758\) | 10.0539 | 0.365175 | ||||||||
\(759\) | −48.6593 | −1.76622 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.9260 | −1.33857 | −0.669283 | − | 0.743008i | \(-0.733398\pi\) | ||||
−0.669283 | + | 0.743008i | \(0.733398\pi\) | |||||||
\(762\) | −4.44293 | −0.160950 | ||||||||
\(763\) | −23.1856 | −0.839375 | ||||||||
\(764\) | −2.20342 | −0.0797170 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.4014 | 0.953923 | ||||||||
\(767\) | −5.44938 | −0.196766 | ||||||||
\(768\) | −11.6637 | −0.420878 | ||||||||
\(769\) | 32.9273 | 1.18739 | 0.593695 | − | 0.804690i | \(-0.297668\pi\) | ||||
0.593695 | + | 0.804690i | \(0.297668\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0049 | 0.720460 | ||||||||
\(772\) | −6.55448 | −0.235901 | ||||||||
\(773\) | −11.7649 | −0.423155 | −0.211578 | − | 0.977361i | \(-0.567860\pi\) | ||||
−0.211578 | + | 0.977361i | \(0.567860\pi\) | |||||||
\(774\) | −13.5254 | −0.486161 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 47.1587 | 1.69290 | ||||||||
\(777\) | −17.8938 | −0.641938 | ||||||||
\(778\) | −26.4415 | −0.947975 | ||||||||
\(779\) | −38.1521 | −1.36694 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.51606 | −0.304729 | ||||||||
\(782\) | −42.2841 | −1.51207 | ||||||||
\(783\) | −3.00000 | −0.107211 | ||||||||
\(784\) | 0.751123 | 0.0268258 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.16686 | −0.112958 | ||||||||
\(787\) | −11.2888 | −0.402403 | −0.201202 | − | 0.979550i | \(-0.564485\pi\) | ||||
−0.201202 | + | 0.979550i | \(0.564485\pi\) | |||||||
\(788\) | −0.474572 | −0.0169059 | ||||||||
\(789\) | 3.15701 | 0.112393 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.4415 | −0.513482 | ||||||||
\(792\) | −18.7605 | −0.666625 | ||||||||
\(793\) | −9.99063 | −0.354778 | ||||||||
\(794\) | −5.97142 | −0.211918 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.80642 | 0.276691 | ||||||||
\(797\) | 10.6030 | 0.375578 | 0.187789 | − | 0.982209i | \(-0.439868\pi\) | ||||
0.187789 | + | 0.982209i | \(0.439868\pi\) | |||||||
\(798\) | 13.0553 | 0.462153 | ||||||||
\(799\) | −5.31603 | −0.188068 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.04149 | 0.284132 | ||||||||
\(802\) | −3.16686 | −0.111826 | ||||||||
\(803\) | −80.3738 | −2.83633 | ||||||||
\(804\) | 2.56046 | 0.0903005 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.51114 | 0.229345 | ||||||||
\(807\) | −17.7971 | −0.626486 | ||||||||
\(808\) | 19.4177 | 0.683114 | ||||||||
\(809\) | −22.9906 | −0.808308 | −0.404154 | − | 0.914691i | \(-0.632434\pi\) | ||||
−0.404154 | + | 0.914691i | \(0.632434\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.71255 | −0.305939 | −0.152970 | − | 0.988231i | \(-0.548884\pi\) | ||||
−0.152970 | + | 0.988231i | \(0.548884\pi\) | |||||||
\(812\) | −4.08589 | −0.143387 | ||||||||
\(813\) | −25.3575 | −0.889327 | ||||||||
\(814\) | 51.2815 | 1.79741 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −11.7021 | −0.409656 | ||||||||
\(817\) | 46.1976 | 1.61625 | ||||||||
\(818\) | −22.7195 | −0.794368 | ||||||||
\(819\) | 2.59210 | 0.0905754 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.7828 | −0.795124 | −0.397562 | − | 0.917575i | \(-0.630144\pi\) | ||||
−0.397562 | + | 0.917575i | \(0.630144\pi\) | |||||||
\(822\) | 13.9398 | 0.486206 | ||||||||
\(823\) | 28.8988 | 1.00735 | 0.503674 | − | 0.863894i | \(-0.331981\pi\) | ||||
0.503674 | + | 0.863894i | \(0.331981\pi\) | |||||||
\(824\) | 3.77245 | 0.131419 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.1527 | 0.596819 | ||||||||
\(827\) | 1.09832 | 0.0381923 | 0.0190962 | − | 0.999818i | \(-0.493921\pi\) | ||||
0.0190962 | + | 0.999818i | \(0.493921\pi\) | |||||||
\(828\) | −4.17929 | −0.145240 | ||||||||
\(829\) | −54.3689 | −1.88831 | −0.944155 | − | 0.329502i | \(-0.893119\pi\) | ||||
−0.944155 | + | 0.329502i | \(0.893119\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.235063 | −0.00815426 | ||||||||
\(832\) | −8.85236 | −0.306900 | ||||||||
\(833\) | −1.23014 | −0.0426219 | ||||||||
\(834\) | −14.3368 | −0.496442 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.3319 | 0.461092 | ||||||||
\(837\) | 5.36196 | 0.185337 | ||||||||
\(838\) | −17.3189 | −0.598273 | ||||||||
\(839\) | −21.2716 | −0.734378 | −0.367189 | − | 0.930146i | \(-0.619680\pi\) | ||||
−0.367189 | + | 0.930146i | \(0.619680\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 26.4800 | 0.912560 | ||||||||
\(843\) | 29.1338 | 1.00342 | ||||||||
\(844\) | 10.7314 | 0.369391 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.47457 | 0.0506968 | ||||||||
\(847\) | −68.4943 | −2.35349 | ||||||||
\(848\) | −13.2426 | −0.454752 | ||||||||
\(849\) | −20.5718 | −0.706024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 54.9086 | 1.88224 | ||||||||
\(852\) | −0.731434 | −0.0250585 | ||||||||
\(853\) | −5.04101 | −0.172601 | −0.0863005 | − | 0.996269i | \(-0.527505\pi\) | ||||
−0.0863005 | + | 0.996269i | \(0.527505\pi\) | |||||||
\(854\) | 31.4469 | 1.07609 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.9813 | −1.09310 | ||||||||
\(857\) | −26.3497 | −0.900088 | −0.450044 | − | 0.893006i | \(-0.648592\pi\) | ||||
−0.450044 | + | 0.893006i | \(0.648592\pi\) | |||||||
\(858\) | −7.42864 | −0.253610 | ||||||||
\(859\) | −12.5575 | −0.428458 | −0.214229 | − | 0.976783i | \(-0.568724\pi\) | ||||
−0.214229 | + | 0.976783i | \(0.568724\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.8435 | 0.812583 | ||||||||
\(862\) | 5.50669 | 0.187559 | ||||||||
\(863\) | 42.5788 | 1.44940 | 0.724699 | − | 0.689066i | \(-0.241979\pi\) | ||||
0.724699 | + | 0.689066i | \(0.241979\pi\) | |||||||
\(864\) | −2.88739 | −0.0982310 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.6316 | 0.803034 | ||||||||
\(867\) | 2.16500 | 0.0735271 | ||||||||
\(868\) | 7.30279 | 0.247873 | ||||||||
\(869\) | 75.7516 | 2.56970 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.87310 | 0.165119 | ||||||||
\(872\) | 27.4305 | 0.928914 | ||||||||
\(873\) | 15.3778 | 0.520459 | ||||||||
\(874\) | −40.0612 | −1.35509 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.90321 | −0.233238 | ||||||||
\(877\) | −39.3590 | −1.32906 | −0.664530 | − | 0.747261i | \(-0.731368\pi\) | ||||
−0.664530 | + | 0.747261i | \(0.731368\pi\) | |||||||
\(878\) | 3.86125 | 0.130311 | ||||||||
\(879\) | 3.12399 | 0.105369 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.8845 | 1.14160 | 0.570799 | − | 0.821090i | \(-0.306634\pi\) | ||||
0.570799 | + | 0.821090i | \(0.306634\pi\) | |||||||
\(882\) | 0.341219 | 0.0114895 | ||||||||
\(883\) | −40.6035 | −1.36642 | −0.683208 | − | 0.730224i | \(-0.739416\pi\) | ||||
−0.683208 | + | 0.730224i | \(0.739416\pi\) | |||||||
\(884\) | 2.30021 | 0.0773644 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 39.6815 | 1.33313 | ||||||||
\(887\) | −56.9733 | −1.91298 | −0.956488 | − | 0.291772i | \(-0.905755\pi\) | ||||
−0.956488 | + | 0.291772i | \(0.905755\pi\) | |||||||
\(888\) | 21.1699 | 0.710416 | ||||||||
\(889\) | −9.48394 | −0.318081 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.11753 | −0.204945 | ||||||||
\(892\) | 1.52543 | 0.0510751 | ||||||||
\(893\) | −5.03657 | −0.168542 | ||||||||
\(894\) | 11.9813 | 0.400713 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.8952 | 0.430799 | ||||||||
\(897\) | −7.95407 | −0.265579 | ||||||||
\(898\) | 24.4987 | 0.817532 | ||||||||
\(899\) | −16.0859 | −0.536494 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.6878 | 0.722527 | ||||||||
\(902\) | −68.3323 | −2.27522 | ||||||||
\(903\) | −28.8716 | −0.960786 | ||||||||
\(904\) | 17.0856 | 0.568257 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.3827 | −0.444611 | ||||||||
\(907\) | 21.4479 | 0.712164 | 0.356082 | − | 0.934455i | \(-0.384112\pi\) | ||||
0.356082 | + | 0.934455i | \(0.384112\pi\) | |||||||
\(908\) | 1.63311 | 0.0541968 | ||||||||
\(909\) | 6.33185 | 0.210014 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.0781 | 0.565821 | 0.282911 | − | 0.959146i | \(-0.408700\pi\) | ||||
0.282911 | + | 0.959146i | \(0.408700\pi\) | |||||||
\(912\) | −11.0869 | −0.367125 | ||||||||
\(913\) | 81.0928 | 2.68378 | ||||||||
\(914\) | 23.7605 | 0.785927 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.1526 | 0.368491 | ||||||||
\(917\) | −6.76001 | −0.223235 | ||||||||
\(918\) | −5.31603 | −0.175455 | ||||||||
\(919\) | 22.8069 | 0.752330 | 0.376165 | − | 0.926553i | \(-0.377243\pi\) | ||||
0.376165 | + | 0.926553i | \(0.377243\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.0874 | −0.464196 | ||||||||
\(922\) | −40.2351 | −1.32507 | ||||||||
\(923\) | −1.39207 | −0.0458207 | ||||||||
\(924\) | −8.33185 | −0.274098 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.5620 | −0.445675 | ||||||||
\(927\) | 1.23014 | 0.0404031 | ||||||||
\(928\) | 8.66217 | 0.284350 | ||||||||
\(929\) | −22.7654 | −0.746909 | −0.373454 | − | 0.927649i | \(-0.621827\pi\) | ||||
−0.373454 | + | 0.927649i | \(0.621827\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.16547 | −0.0381968 | ||||||||
\(932\) | −3.17436 | −0.103980 | ||||||||
\(933\) | 17.6128 | 0.576619 | ||||||||
\(934\) | −47.6829 | −1.56023 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.06668 | −0.100237 | ||||||||
\(937\) | −29.2065 | −0.954134 | −0.477067 | − | 0.878867i | \(-0.658300\pi\) | ||||
−0.477067 | + | 0.878867i | \(0.658300\pi\) | |||||||
\(938\) | −15.3388 | −0.500829 | ||||||||
\(939\) | 17.2810 | 0.563944 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.189130 | 0.00616547 | 0.00308274 | − | 0.999995i | \(-0.499019\pi\) | ||||
0.00308274 | + | 0.999995i | \(0.499019\pi\) | |||||||
\(942\) | 15.3334 | 0.499589 | ||||||||
\(943\) | −73.1655 | −2.38260 | ||||||||
\(944\) | −14.5666 | −0.474102 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 82.7422 | 2.69018 | ||||||||
\(947\) | −30.7812 | −1.00026 | −0.500128 | − | 0.865952i | \(-0.666714\pi\) | ||||
−0.500128 | + | 0.865952i | \(0.666714\pi\) | |||||||
\(948\) | 6.50622 | 0.211312 | ||||||||
\(949\) | −13.1383 | −0.426486 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.668149 | 0.0216662 | ||||||||
\(952\) | −34.7996 | −1.12786 | ||||||||
\(953\) | −52.2400 | −1.69222 | −0.846110 | − | 0.533009i | \(-0.821061\pi\) | ||||
−0.846110 | + | 0.533009i | \(0.821061\pi\) | |||||||
\(954\) | −6.01582 | −0.194769 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.0132 | 0.356193 | ||||||||
\(957\) | 18.3526 | 0.593255 | ||||||||
\(958\) | 15.5433 | 0.502180 | ||||||||
\(959\) | 29.7560 | 0.960873 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.24935 | −0.0725598 | ||||||||
\(962\) | 8.38271 | 0.270269 | ||||||||
\(963\) | −10.4286 | −0.336058 | ||||||||
\(964\) | −5.55707 | −0.178981 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 25.0366 | 0.805538 | ||||||||
\(967\) | 47.5279 | 1.52839 | 0.764197 | − | 0.644983i | \(-0.223135\pi\) | ||||
0.764197 | + | 0.644983i | \(0.223135\pi\) | |||||||
\(968\) | 81.0345 | 2.60455 | ||||||||
\(969\) | 18.1575 | 0.583303 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.6445 | −0.502056 | −0.251028 | − | 0.967980i | \(-0.580769\pi\) | ||||
−0.251028 | + | 0.967980i | \(0.580769\pi\) | |||||||
\(972\) | −0.525428 | −0.0168531 | ||||||||
\(973\) | −30.6035 | −0.981103 | ||||||||
\(974\) | −3.72393 | −0.119322 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −26.7057 | −0.854828 | ||||||||
\(977\) | 14.3398 | 0.458772 | 0.229386 | − | 0.973336i | \(-0.426328\pi\) | ||||
0.229386 | + | 0.973336i | \(0.426328\pi\) | |||||||
\(978\) | −3.88400 | −0.124197 | ||||||||
\(979\) | −49.1941 | −1.57225 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.94470 | 0.285582 | ||||||||
\(982\) | −1.42233 | −0.0453885 | ||||||||
\(983\) | 6.95206 | 0.221736 | 0.110868 | − | 0.993835i | \(-0.464637\pi\) | ||||
0.110868 | + | 0.993835i | \(0.464637\pi\) | |||||||
\(984\) | −28.2088 | −0.899264 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 15.9481 | 0.507891 | ||||||||
\(987\) | 3.14764 | 0.100191 | ||||||||
\(988\) | 2.17929 | 0.0693323 | ||||||||
\(989\) | 88.5946 | 2.81714 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.5768 | 0.431280 | 0.215640 | − | 0.976473i | \(-0.430816\pi\) | ||||
0.215640 | + | 0.976473i | \(0.430816\pi\) | |||||||
\(992\) | −15.4821 | −0.491557 | ||||||||
\(993\) | 21.3921 | 0.678857 | ||||||||
\(994\) | 4.38175 | 0.138981 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.96497 | 0.220693 | ||||||||
\(997\) | −13.6953 | −0.433736 | −0.216868 | − | 0.976201i | \(-0.569584\pi\) | ||||
−0.216868 | + | 0.976201i | \(0.569584\pi\) | |||||||
\(998\) | −46.6904 | −1.47796 | ||||||||
\(999\) | 6.90321 | 0.218408 |
(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 | 975.2.a.q.1.1 | yes | 3 | |
3.2 | odd | 2 | 2925.2.a.be.1.3 | 3 | |||
5.2 | odd | 4 | 975.2.c.k.274.3 | 6 | |||
5.3 | odd | 4 | 975.2.c.k.274.4 | 6 | |||
5.4 | even | 2 | 975.2.a.m.1.3 | ✓ | 3 | ||
15.2 | even | 4 | 2925.2.c.y.2224.4 | 6 | |||
15.8 | even | 4 | 2925.2.c.y.2224.3 | 6 | |||
15.14 | odd | 2 | 2925.2.a.bk.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
975.2.a.m.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
975.2.a.q.1.1 | yes | 3 | 1.1 | even | 1 | trivial | |
975.2.c.k.274.3 | 6 | 5.2 | odd | 4 | |||
975.2.c.k.274.4 | 6 | 5.3 | odd | 4 | |||
2925.2.a.be.1.3 | 3 | 3.2 | odd | 2 | |||
2925.2.a.bk.1.1 | 3 | 15.14 | odd | 2 | |||
2925.2.c.y.2224.3 | 6 | 15.8 | even | 4 | |||
2925.2.c.y.2224.4 | 6 | 15.2 | even | 4 |