Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(1,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, 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("187.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.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: | \(1.49320251780\) |
Analytic rank: | \(1\) |
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 | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 187.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.17009 | 0.827376 | 0.413688 | − | 0.910419i | \(-0.364240\pi\) | ||||
0.413688 | + | 0.910419i | \(0.364240\pi\) | |||||||
\(3\) | −1.53919 | −0.888651 | −0.444326 | − | 0.895865i | \(-0.646557\pi\) | ||||
−0.444326 | + | 0.895865i | \(0.646557\pi\) | |||||||
\(4\) | −0.630898 | −0.315449 | ||||||||
\(5\) | −4.17009 | −1.86492 | −0.932460 | − | 0.361274i | \(-0.882342\pi\) | ||||
−0.932460 | + | 0.361274i | \(0.882342\pi\) | |||||||
\(6\) | −1.80098 | −0.735249 | ||||||||
\(7\) | 1.07838 | 0.407588 | 0.203794 | − | 0.979014i | \(-0.434673\pi\) | ||||
0.203794 | + | 0.979014i | \(0.434673\pi\) | |||||||
\(8\) | −3.07838 | −1.08837 | ||||||||
\(9\) | −0.630898 | −0.210299 | ||||||||
\(10\) | −4.87936 | −1.54299 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.971071 | 0.280324 | ||||||||
\(13\) | 5.51026 | 1.52827 | 0.764136 | − | 0.645056i | \(-0.223166\pi\) | ||||
0.764136 | + | 0.645056i | \(0.223166\pi\) | |||||||
\(14\) | 1.26180 | 0.337229 | ||||||||
\(15\) | 6.41855 | 1.65726 | ||||||||
\(16\) | −2.34017 | −0.585043 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.738205 | −0.173997 | ||||||||
\(19\) | −4.58864 | −1.05271 | −0.526353 | − | 0.850266i | \(-0.676441\pi\) | ||||
−0.526353 | + | 0.850266i | \(0.676441\pi\) | |||||||
\(20\) | 2.63090 | 0.588287 | ||||||||
\(21\) | −1.65983 | −0.362204 | ||||||||
\(22\) | −1.17009 | −0.249463 | ||||||||
\(23\) | −5.53919 | −1.15500 | −0.577500 | − | 0.816390i | \(-0.695972\pi\) | ||||
−0.577500 | + | 0.816390i | \(0.695972\pi\) | |||||||
\(24\) | 4.73820 | 0.967182 | ||||||||
\(25\) | 12.3896 | 2.47792 | ||||||||
\(26\) | 6.44748 | 1.26445 | ||||||||
\(27\) | 5.58864 | 1.07553 | ||||||||
\(28\) | −0.680346 | −0.128573 | ||||||||
\(29\) | −8.87936 | −1.64886 | −0.824428 | − | 0.565967i | \(-0.808503\pi\) | ||||
−0.824428 | + | 0.565967i | \(0.808503\pi\) | |||||||
\(30\) | 7.51026 | 1.37118 | ||||||||
\(31\) | 3.58864 | 0.644538 | 0.322269 | − | 0.946648i | \(-0.395554\pi\) | ||||
0.322269 | + | 0.946648i | \(0.395554\pi\) | |||||||
\(32\) | 3.41855 | 0.604320 | ||||||||
\(33\) | 1.53919 | 0.267938 | ||||||||
\(34\) | −1.17009 | −0.200668 | ||||||||
\(35\) | −4.49693 | −0.760120 | ||||||||
\(36\) | 0.398032 | 0.0663386 | ||||||||
\(37\) | −10.0361 | −1.64993 | −0.824964 | − | 0.565186i | \(-0.808805\pi\) | ||||
−0.824964 | + | 0.565186i | \(0.808805\pi\) | |||||||
\(38\) | −5.36910 | −0.870983 | ||||||||
\(39\) | −8.48133 | −1.35810 | ||||||||
\(40\) | 12.8371 | 2.02972 | ||||||||
\(41\) | 1.07838 | 0.168414 | 0.0842072 | − | 0.996448i | \(-0.473164\pi\) | ||||
0.0842072 | + | 0.996448i | \(0.473164\pi\) | |||||||
\(42\) | −1.94214 | −0.299679 | ||||||||
\(43\) | −6.83710 | −1.04265 | −0.521324 | − | 0.853359i | \(-0.674562\pi\) | ||||
−0.521324 | + | 0.853359i | \(0.674562\pi\) | |||||||
\(44\) | 0.630898 | 0.0951114 | ||||||||
\(45\) | 2.63090 | 0.392191 | ||||||||
\(46\) | −6.48133 | −0.955620 | ||||||||
\(47\) | 8.78765 | 1.28181 | 0.640905 | − | 0.767620i | \(-0.278559\pi\) | ||||
0.640905 | + | 0.767620i | \(0.278559\pi\) | |||||||
\(48\) | 3.60197 | 0.519899 | ||||||||
\(49\) | −5.83710 | −0.833872 | ||||||||
\(50\) | 14.4969 | 2.05018 | ||||||||
\(51\) | 1.53919 | 0.215530 | ||||||||
\(52\) | −3.47641 | −0.482091 | ||||||||
\(53\) | −3.95055 | −0.542650 | −0.271325 | − | 0.962488i | \(-0.587462\pi\) | ||||
−0.271325 | + | 0.962488i | \(0.587462\pi\) | |||||||
\(54\) | 6.53919 | 0.889871 | ||||||||
\(55\) | 4.17009 | 0.562294 | ||||||||
\(56\) | −3.31965 | −0.443607 | ||||||||
\(57\) | 7.06278 | 0.935488 | ||||||||
\(58\) | −10.3896 | −1.36422 | ||||||||
\(59\) | 8.31124 | 1.08203 | 0.541016 | − | 0.841012i | \(-0.318040\pi\) | ||||
0.541016 | + | 0.841012i | \(0.318040\pi\) | |||||||
\(60\) | −4.04945 | −0.522782 | ||||||||
\(61\) | −3.07838 | −0.394146 | −0.197073 | − | 0.980389i | \(-0.563144\pi\) | ||||
−0.197073 | + | 0.980389i | \(0.563144\pi\) | |||||||
\(62\) | 4.19902 | 0.533276 | ||||||||
\(63\) | −0.680346 | −0.0857155 | ||||||||
\(64\) | 8.68035 | 1.08504 | ||||||||
\(65\) | −22.9783 | −2.85010 | ||||||||
\(66\) | 1.80098 | 0.221686 | ||||||||
\(67\) | 1.49693 | 0.182879 | 0.0914395 | − | 0.995811i | \(-0.470853\pi\) | ||||
0.0914395 | + | 0.995811i | \(0.470853\pi\) | |||||||
\(68\) | 0.630898 | 0.0765076 | ||||||||
\(69\) | 8.52586 | 1.02639 | ||||||||
\(70\) | −5.26180 | −0.628905 | ||||||||
\(71\) | 4.51026 | 0.535269 | 0.267635 | − | 0.963520i | \(-0.413758\pi\) | ||||
0.267635 | + | 0.963520i | \(0.413758\pi\) | |||||||
\(72\) | 1.94214 | 0.228884 | ||||||||
\(73\) | −4.53919 | −0.531272 | −0.265636 | − | 0.964073i | \(-0.585582\pi\) | ||||
−0.265636 | + | 0.964073i | \(0.585582\pi\) | |||||||
\(74\) | −11.7431 | −1.36511 | ||||||||
\(75\) | −19.0700 | −2.20201 | ||||||||
\(76\) | 2.89496 | 0.332075 | ||||||||
\(77\) | −1.07838 | −0.122893 | ||||||||
\(78\) | −9.92389 | −1.12366 | ||||||||
\(79\) | 7.80098 | 0.877679 | 0.438840 | − | 0.898565i | \(-0.355390\pi\) | ||||
0.438840 | + | 0.898565i | \(0.355390\pi\) | |||||||
\(80\) | 9.75872 | 1.09106 | ||||||||
\(81\) | −6.70928 | −0.745475 | ||||||||
\(82\) | 1.26180 | 0.139342 | ||||||||
\(83\) | −4.68035 | −0.513735 | −0.256867 | − | 0.966447i | \(-0.582690\pi\) | ||||
−0.256867 | + | 0.966447i | \(0.582690\pi\) | |||||||
\(84\) | 1.04718 | 0.114257 | ||||||||
\(85\) | 4.17009 | 0.452309 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 13.6670 | 1.46526 | ||||||||
\(88\) | 3.07838 | 0.328156 | ||||||||
\(89\) | −1.18342 | −0.125442 | −0.0627210 | − | 0.998031i | \(-0.519978\pi\) | ||||
−0.0627210 | + | 0.998031i | \(0.519978\pi\) | |||||||
\(90\) | 3.07838 | 0.324490 | ||||||||
\(91\) | 5.94214 | 0.622906 | ||||||||
\(92\) | 3.49466 | 0.364344 | ||||||||
\(93\) | −5.52359 | −0.572770 | ||||||||
\(94\) | 10.2823 | 1.06054 | ||||||||
\(95\) | 19.1350 | 1.96321 | ||||||||
\(96\) | −5.26180 | −0.537030 | ||||||||
\(97\) | −8.80098 | −0.893605 | −0.446802 | − | 0.894633i | \(-0.647437\pi\) | ||||
−0.446802 | + | 0.894633i | \(0.647437\pi\) | |||||||
\(98\) | −6.82991 | −0.689925 | ||||||||
\(99\) | 0.630898 | 0.0634076 | ||||||||
\(100\) | −7.81658 | −0.781658 | ||||||||
\(101\) | −4.43188 | −0.440989 | −0.220494 | − | 0.975388i | \(-0.570767\pi\) | ||||
−0.220494 | + | 0.975388i | \(0.570767\pi\) | |||||||
\(102\) | 1.80098 | 0.178324 | ||||||||
\(103\) | −11.4947 | −1.13260 | −0.566301 | − | 0.824198i | \(-0.691626\pi\) | ||||
−0.566301 | + | 0.824198i | \(0.691626\pi\) | |||||||
\(104\) | −16.9627 | −1.66333 | ||||||||
\(105\) | 6.92162 | 0.675481 | ||||||||
\(106\) | −4.62249 | −0.448976 | ||||||||
\(107\) | −0.0422604 | −0.00408547 | −0.00204273 | − | 0.999998i | \(-0.500650\pi\) | ||||
−0.00204273 | + | 0.999998i | \(0.500650\pi\) | |||||||
\(108\) | −3.52586 | −0.339276 | ||||||||
\(109\) | 8.97826 | 0.859961 | 0.429981 | − | 0.902838i | \(-0.358520\pi\) | ||||
0.429981 | + | 0.902838i | \(0.358520\pi\) | |||||||
\(110\) | 4.87936 | 0.465229 | ||||||||
\(111\) | 15.4475 | 1.46621 | ||||||||
\(112\) | −2.52359 | −0.238457 | ||||||||
\(113\) | −4.85043 | −0.456290 | −0.228145 | − | 0.973627i | \(-0.573266\pi\) | ||||
−0.228145 | + | 0.973627i | \(0.573266\pi\) | |||||||
\(114\) | 8.26406 | 0.774000 | ||||||||
\(115\) | 23.0989 | 2.15398 | ||||||||
\(116\) | 5.60197 | 0.520130 | ||||||||
\(117\) | −3.47641 | −0.321394 | ||||||||
\(118\) | 9.72487 | 0.895247 | ||||||||
\(119\) | −1.07838 | −0.0988547 | ||||||||
\(120\) | −19.7587 | −1.80372 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −3.60197 | −0.326107 | ||||||||
\(123\) | −1.65983 | −0.149662 | ||||||||
\(124\) | −2.26406 | −0.203319 | ||||||||
\(125\) | −30.8154 | −2.75621 | ||||||||
\(126\) | −0.796064 | −0.0709190 | ||||||||
\(127\) | −4.83710 | −0.429223 | −0.214612 | − | 0.976699i | \(-0.568849\pi\) | ||||
−0.214612 | + | 0.976699i | \(0.568849\pi\) | |||||||
\(128\) | 3.31965 | 0.293419 | ||||||||
\(129\) | 10.5236 | 0.926550 | ||||||||
\(130\) | −26.8865 | −2.35811 | ||||||||
\(131\) | 6.36683 | 0.556273 | 0.278136 | − | 0.960542i | \(-0.410283\pi\) | ||||
0.278136 | + | 0.960542i | \(0.410283\pi\) | |||||||
\(132\) | −0.971071 | −0.0845208 | ||||||||
\(133\) | −4.94828 | −0.429071 | ||||||||
\(134\) | 1.75154 | 0.151310 | ||||||||
\(135\) | −23.3051 | −2.00578 | ||||||||
\(136\) | 3.07838 | 0.263969 | ||||||||
\(137\) | −2.50307 | −0.213852 | −0.106926 | − | 0.994267i | \(-0.534101\pi\) | ||||
−0.106926 | + | 0.994267i | \(0.534101\pi\) | |||||||
\(138\) | 9.97599 | 0.849213 | ||||||||
\(139\) | −3.21953 | −0.273077 | −0.136539 | − | 0.990635i | \(-0.543598\pi\) | ||||
−0.136539 | + | 0.990635i | \(0.543598\pi\) | |||||||
\(140\) | 2.83710 | 0.239779 | ||||||||
\(141\) | −13.5259 | −1.13908 | ||||||||
\(142\) | 5.27739 | 0.442869 | ||||||||
\(143\) | −5.51026 | −0.460791 | ||||||||
\(144\) | 1.47641 | 0.123034 | ||||||||
\(145\) | 37.0277 | 3.07498 | ||||||||
\(146\) | −5.31124 | −0.439562 | ||||||||
\(147\) | 8.98440 | 0.741021 | ||||||||
\(148\) | 6.33176 | 0.520468 | ||||||||
\(149\) | −12.4319 | −1.01846 | −0.509230 | − | 0.860631i | \(-0.670070\pi\) | ||||
−0.509230 | + | 0.860631i | \(0.670070\pi\) | |||||||
\(150\) | −22.3135 | −1.82189 | ||||||||
\(151\) | 3.41136 | 0.277613 | 0.138806 | − | 0.990320i | \(-0.455673\pi\) | ||||
0.138806 | + | 0.990320i | \(0.455673\pi\) | |||||||
\(152\) | 14.1256 | 1.14573 | ||||||||
\(153\) | 0.630898 | 0.0510050 | ||||||||
\(154\) | −1.26180 | −0.101678 | ||||||||
\(155\) | −14.9649 | −1.20201 | ||||||||
\(156\) | 5.35085 | 0.428411 | ||||||||
\(157\) | −2.23513 | −0.178383 | −0.0891915 | − | 0.996014i | \(-0.528428\pi\) | ||||
−0.0891915 | + | 0.996014i | \(0.528428\pi\) | |||||||
\(158\) | 9.12783 | 0.726171 | ||||||||
\(159\) | 6.08065 | 0.482227 | ||||||||
\(160\) | −14.2557 | −1.12701 | ||||||||
\(161\) | −5.97334 | −0.470765 | ||||||||
\(162\) | −7.85043 | −0.616788 | ||||||||
\(163\) | 13.9421 | 1.09203 | 0.546016 | − | 0.837774i | \(-0.316144\pi\) | ||||
0.546016 | + | 0.837774i | \(0.316144\pi\) | |||||||
\(164\) | −0.680346 | −0.0531261 | ||||||||
\(165\) | −6.41855 | −0.499683 | ||||||||
\(166\) | −5.47641 | −0.425052 | ||||||||
\(167\) | 13.7165 | 1.06141 | 0.530706 | − | 0.847556i | \(-0.321927\pi\) | ||||
0.530706 | + | 0.847556i | \(0.321927\pi\) | |||||||
\(168\) | 5.10957 | 0.394212 | ||||||||
\(169\) | 17.3630 | 1.33561 | ||||||||
\(170\) | 4.87936 | 0.374230 | ||||||||
\(171\) | 2.89496 | 0.221383 | ||||||||
\(172\) | 4.31351 | 0.328902 | ||||||||
\(173\) | 6.65368 | 0.505870 | 0.252935 | − | 0.967483i | \(-0.418604\pi\) | ||||
0.252935 | + | 0.967483i | \(0.418604\pi\) | |||||||
\(174\) | 15.9916 | 1.21232 | ||||||||
\(175\) | 13.3607 | 1.00997 | ||||||||
\(176\) | 2.34017 | 0.176397 | ||||||||
\(177\) | −12.7926 | −0.961549 | ||||||||
\(178\) | −1.38470 | −0.103788 | ||||||||
\(179\) | 3.42469 | 0.255974 | 0.127987 | − | 0.991776i | \(-0.459148\pi\) | ||||
0.127987 | + | 0.991776i | \(0.459148\pi\) | |||||||
\(180\) | −1.65983 | −0.123716 | ||||||||
\(181\) | −0.460811 | −0.0342518 | −0.0171259 | − | 0.999853i | \(-0.505452\pi\) | ||||
−0.0171259 | + | 0.999853i | \(0.505452\pi\) | |||||||
\(182\) | 6.95282 | 0.515377 | ||||||||
\(183\) | 4.73820 | 0.350258 | ||||||||
\(184\) | 17.0517 | 1.25707 | ||||||||
\(185\) | 41.8515 | 3.07698 | ||||||||
\(186\) | −6.46308 | −0.473896 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −5.54411 | −0.404346 | ||||||||
\(189\) | 6.02666 | 0.438375 | ||||||||
\(190\) | 22.3896 | 1.62431 | ||||||||
\(191\) | −5.83710 | −0.422358 | −0.211179 | − | 0.977447i | \(-0.567730\pi\) | ||||
−0.211179 | + | 0.977447i | \(0.567730\pi\) | |||||||
\(192\) | −13.3607 | −0.964225 | ||||||||
\(193\) | 15.2195 | 1.09553 | 0.547763 | − | 0.836634i | \(-0.315480\pi\) | ||||
0.547763 | + | 0.836634i | \(0.315480\pi\) | |||||||
\(194\) | −10.2979 | −0.739347 | ||||||||
\(195\) | 35.3679 | 2.53275 | ||||||||
\(196\) | 3.68261 | 0.263044 | ||||||||
\(197\) | −21.0628 | −1.50066 | −0.750330 | − | 0.661063i | \(-0.770106\pi\) | ||||
−0.750330 | + | 0.661063i | \(0.770106\pi\) | |||||||
\(198\) | 0.738205 | 0.0524619 | ||||||||
\(199\) | 14.1256 | 1.00133 | 0.500667 | − | 0.865640i | \(-0.333088\pi\) | ||||
0.500667 | + | 0.865640i | \(0.333088\pi\) | |||||||
\(200\) | −38.1399 | −2.69690 | ||||||||
\(201\) | −2.30406 | −0.162516 | ||||||||
\(202\) | −5.18568 | −0.364864 | ||||||||
\(203\) | −9.57531 | −0.672055 | ||||||||
\(204\) | −0.971071 | −0.0679885 | ||||||||
\(205\) | −4.49693 | −0.314079 | ||||||||
\(206\) | −13.4497 | −0.937088 | ||||||||
\(207\) | 3.49466 | 0.242896 | ||||||||
\(208\) | −12.8950 | −0.894105 | ||||||||
\(209\) | 4.58864 | 0.317403 | ||||||||
\(210\) | 8.09890 | 0.558877 | ||||||||
\(211\) | 7.36069 | 0.506731 | 0.253365 | − | 0.967371i | \(-0.418462\pi\) | ||||
0.253365 | + | 0.967371i | \(0.418462\pi\) | |||||||
\(212\) | 2.49239 | 0.171178 | ||||||||
\(213\) | −6.94214 | −0.475668 | ||||||||
\(214\) | −0.0494483 | −0.00338022 | ||||||||
\(215\) | 28.5113 | 1.94445 | ||||||||
\(216\) | −17.2039 | −1.17058 | ||||||||
\(217\) | 3.86991 | 0.262706 | ||||||||
\(218\) | 10.5053 | 0.711511 | ||||||||
\(219\) | 6.98667 | 0.472115 | ||||||||
\(220\) | −2.63090 | −0.177375 | ||||||||
\(221\) | −5.51026 | −0.370660 | ||||||||
\(222\) | 18.0749 | 1.21311 | ||||||||
\(223\) | −21.9711 | −1.47129 | −0.735646 | − | 0.677366i | \(-0.763121\pi\) | ||||
−0.735646 | + | 0.677366i | \(0.763121\pi\) | |||||||
\(224\) | 3.68649 | 0.246314 | ||||||||
\(225\) | −7.81658 | −0.521106 | ||||||||
\(226\) | −5.67543 | −0.377524 | ||||||||
\(227\) | −21.7431 | −1.44314 | −0.721571 | − | 0.692340i | \(-0.756580\pi\) | ||||
−0.721571 | + | 0.692340i | \(0.756580\pi\) | |||||||
\(228\) | −4.45589 | −0.295099 | ||||||||
\(229\) | −20.4101 | −1.34874 | −0.674370 | − | 0.738394i | \(-0.735585\pi\) | ||||
−0.674370 | + | 0.738394i | \(0.735585\pi\) | |||||||
\(230\) | 27.0277 | 1.78215 | ||||||||
\(231\) | 1.65983 | 0.109209 | ||||||||
\(232\) | 27.3340 | 1.79457 | ||||||||
\(233\) | 2.39803 | 0.157100 | 0.0785501 | − | 0.996910i | \(-0.474971\pi\) | ||||
0.0785501 | + | 0.996910i | \(0.474971\pi\) | |||||||
\(234\) | −4.06770 | −0.265914 | ||||||||
\(235\) | −36.6453 | −2.39047 | ||||||||
\(236\) | −5.24354 | −0.341326 | ||||||||
\(237\) | −12.0072 | −0.779951 | ||||||||
\(238\) | −1.26180 | −0.0817900 | ||||||||
\(239\) | −6.40522 | −0.414319 | −0.207160 | − | 0.978307i | \(-0.566422\pi\) | ||||
−0.207160 | + | 0.978307i | \(0.566422\pi\) | |||||||
\(240\) | −15.0205 | −0.969570 | ||||||||
\(241\) | 16.7792 | 1.08085 | 0.540423 | − | 0.841393i | \(-0.318264\pi\) | ||||
0.540423 | + | 0.841393i | \(0.318264\pi\) | |||||||
\(242\) | 1.17009 | 0.0752160 | ||||||||
\(243\) | −6.43907 | −0.413067 | ||||||||
\(244\) | 1.94214 | 0.124333 | ||||||||
\(245\) | 24.3412 | 1.55510 | ||||||||
\(246\) | −1.94214 | −0.123826 | ||||||||
\(247\) | −25.2846 | −1.60882 | ||||||||
\(248\) | −11.0472 | −0.701497 | ||||||||
\(249\) | 7.20394 | 0.456531 | ||||||||
\(250\) | −36.0566 | −2.28042 | ||||||||
\(251\) | 24.6020 | 1.55286 | 0.776431 | − | 0.630202i | \(-0.217028\pi\) | ||||
0.776431 | + | 0.630202i | \(0.217028\pi\) | |||||||
\(252\) | 0.429229 | 0.0270389 | ||||||||
\(253\) | 5.53919 | 0.348246 | ||||||||
\(254\) | −5.65983 | −0.355129 | ||||||||
\(255\) | −6.41855 | −0.401945 | ||||||||
\(256\) | −13.4764 | −0.842276 | ||||||||
\(257\) | 22.4885 | 1.40280 | 0.701398 | − | 0.712770i | \(-0.252560\pi\) | ||||
0.701398 | + | 0.712770i | \(0.252560\pi\) | |||||||
\(258\) | 12.3135 | 0.766606 | ||||||||
\(259\) | −10.8227 | −0.672491 | ||||||||
\(260\) | 14.4969 | 0.899061 | ||||||||
\(261\) | 5.60197 | 0.346753 | ||||||||
\(262\) | 7.44975 | 0.460247 | ||||||||
\(263\) | −17.8238 | −1.09906 | −0.549530 | − | 0.835474i | \(-0.685193\pi\) | ||||
−0.549530 | + | 0.835474i | \(0.685193\pi\) | |||||||
\(264\) | −4.73820 | −0.291616 | ||||||||
\(265\) | 16.4741 | 1.01200 | ||||||||
\(266\) | −5.78992 | −0.355003 | ||||||||
\(267\) | 1.82150 | 0.111474 | ||||||||
\(268\) | −0.944409 | −0.0576889 | ||||||||
\(269\) | 19.0784 | 1.16323 | 0.581615 | − | 0.813464i | \(-0.302421\pi\) | ||||
0.581615 | + | 0.813464i | \(0.302421\pi\) | |||||||
\(270\) | −27.2690 | −1.65954 | ||||||||
\(271\) | −20.2557 | −1.23044 | −0.615222 | − | 0.788354i | \(-0.710933\pi\) | ||||
−0.615222 | + | 0.788354i | \(0.710933\pi\) | |||||||
\(272\) | 2.34017 | 0.141894 | ||||||||
\(273\) | −9.14608 | −0.553546 | ||||||||
\(274\) | −2.92881 | −0.176936 | ||||||||
\(275\) | −12.3896 | −0.747122 | ||||||||
\(276\) | −5.37894 | −0.323774 | ||||||||
\(277\) | −17.3874 | −1.04470 | −0.522352 | − | 0.852730i | \(-0.674945\pi\) | ||||
−0.522352 | + | 0.852730i | \(0.674945\pi\) | |||||||
\(278\) | −3.76713 | −0.225938 | ||||||||
\(279\) | −2.26406 | −0.135546 | ||||||||
\(280\) | 13.8432 | 0.827292 | ||||||||
\(281\) | −1.32684 | −0.0791528 | −0.0395764 | − | 0.999217i | \(-0.512601\pi\) | ||||
−0.0395764 | + | 0.999217i | \(0.512601\pi\) | |||||||
\(282\) | −15.8264 | −0.942450 | ||||||||
\(283\) | −13.6442 | −0.811065 | −0.405533 | − | 0.914081i | \(-0.632914\pi\) | ||||
−0.405533 | + | 0.914081i | \(0.632914\pi\) | |||||||
\(284\) | −2.84551 | −0.168850 | ||||||||
\(285\) | −29.4524 | −1.74461 | ||||||||
\(286\) | −6.44748 | −0.381247 | ||||||||
\(287\) | 1.16290 | 0.0686437 | ||||||||
\(288\) | −2.15676 | −0.127088 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 43.3256 | 2.54417 | ||||||||
\(291\) | 13.5464 | 0.794103 | ||||||||
\(292\) | 2.86376 | 0.167589 | ||||||||
\(293\) | −6.73820 | −0.393650 | −0.196825 | − | 0.980439i | \(-0.563063\pi\) | ||||
−0.196825 | + | 0.980439i | \(0.563063\pi\) | |||||||
\(294\) | 10.5125 | 0.613103 | ||||||||
\(295\) | −34.6586 | −2.01790 | ||||||||
\(296\) | 30.8950 | 1.79573 | ||||||||
\(297\) | −5.58864 | −0.324286 | ||||||||
\(298\) | −14.5464 | −0.842649 | ||||||||
\(299\) | −30.5224 | −1.76515 | ||||||||
\(300\) | 12.0312 | 0.694621 | ||||||||
\(301\) | −7.37298 | −0.424971 | ||||||||
\(302\) | 3.99159 | 0.229690 | ||||||||
\(303\) | 6.82150 | 0.391885 | ||||||||
\(304\) | 10.7382 | 0.615878 | ||||||||
\(305\) | 12.8371 | 0.735050 | ||||||||
\(306\) | 0.738205 | 0.0422004 | ||||||||
\(307\) | 19.3268 | 1.10304 | 0.551521 | − | 0.834161i | \(-0.314048\pi\) | ||||
0.551521 | + | 0.834161i | \(0.314048\pi\) | |||||||
\(308\) | 0.680346 | 0.0387663 | ||||||||
\(309\) | 17.6925 | 1.00649 | ||||||||
\(310\) | −17.5103 | −0.994516 | ||||||||
\(311\) | −18.2557 | −1.03518 | −0.517592 | − | 0.855628i | \(-0.673171\pi\) | ||||
−0.517592 | + | 0.855628i | \(0.673171\pi\) | |||||||
\(312\) | 26.1087 | 1.47812 | ||||||||
\(313\) | −12.8238 | −0.724842 | −0.362421 | − | 0.932014i | \(-0.618050\pi\) | ||||
−0.362421 | + | 0.932014i | \(0.618050\pi\) | |||||||
\(314\) | −2.61530 | −0.147590 | ||||||||
\(315\) | 2.83710 | 0.159853 | ||||||||
\(316\) | −4.92162 | −0.276863 | ||||||||
\(317\) | −21.2485 | −1.19343 | −0.596716 | − | 0.802452i | \(-0.703528\pi\) | ||||
−0.596716 | + | 0.802452i | \(0.703528\pi\) | |||||||
\(318\) | 7.11488 | 0.398983 | ||||||||
\(319\) | 8.87936 | 0.497149 | ||||||||
\(320\) | −36.1978 | −2.02352 | ||||||||
\(321\) | 0.0650468 | 0.00363056 | ||||||||
\(322\) | −6.98932 | −0.389500 | ||||||||
\(323\) | 4.58864 | 0.255319 | ||||||||
\(324\) | 4.23287 | 0.235159 | ||||||||
\(325\) | 68.2700 | 3.78694 | ||||||||
\(326\) | 16.3135 | 0.903522 | ||||||||
\(327\) | −13.8192 | −0.764205 | ||||||||
\(328\) | −3.31965 | −0.183297 | ||||||||
\(329\) | 9.47641 | 0.522451 | ||||||||
\(330\) | −7.51026 | −0.413426 | ||||||||
\(331\) | −15.7070 | −0.863335 | −0.431668 | − | 0.902033i | \(-0.642075\pi\) | ||||
−0.431668 | + | 0.902033i | \(0.642075\pi\) | |||||||
\(332\) | 2.95282 | 0.162057 | ||||||||
\(333\) | 6.33176 | 0.346978 | ||||||||
\(334\) | 16.0494 | 0.878187 | ||||||||
\(335\) | −6.24232 | −0.341054 | ||||||||
\(336\) | 3.88428 | 0.211905 | ||||||||
\(337\) | 9.57531 | 0.521600 | 0.260800 | − | 0.965393i | \(-0.416014\pi\) | ||||
0.260800 | + | 0.965393i | \(0.416014\pi\) | |||||||
\(338\) | 20.3162 | 1.10505 | ||||||||
\(339\) | 7.46573 | 0.405483 | ||||||||
\(340\) | −2.63090 | −0.142680 | ||||||||
\(341\) | −3.58864 | −0.194336 | ||||||||
\(342\) | 3.38735 | 0.183167 | ||||||||
\(343\) | −13.8432 | −0.747465 | ||||||||
\(344\) | 21.0472 | 1.13479 | ||||||||
\(345\) | −35.5536 | −1.91414 | ||||||||
\(346\) | 7.78539 | 0.418545 | ||||||||
\(347\) | −19.0928 | −1.02495 | −0.512476 | − | 0.858701i | \(-0.671272\pi\) | ||||
−0.512476 | + | 0.858701i | \(0.671272\pi\) | |||||||
\(348\) | −8.62249 | −0.462214 | ||||||||
\(349\) | −28.5958 | −1.53070 | −0.765350 | − | 0.643615i | \(-0.777434\pi\) | ||||
−0.765350 | + | 0.643615i | \(0.777434\pi\) | |||||||
\(350\) | 15.6332 | 0.835628 | ||||||||
\(351\) | 30.7948 | 1.64371 | ||||||||
\(352\) | −3.41855 | −0.182209 | ||||||||
\(353\) | −17.3051 | −0.921058 | −0.460529 | − | 0.887645i | \(-0.652340\pi\) | ||||
−0.460529 | + | 0.887645i | \(0.652340\pi\) | |||||||
\(354\) | −14.9684 | −0.795562 | ||||||||
\(355\) | −18.8082 | −0.998234 | ||||||||
\(356\) | 0.746615 | 0.0395705 | ||||||||
\(357\) | 1.65983 | 0.0878474 | ||||||||
\(358\) | 4.00719 | 0.211786 | ||||||||
\(359\) | 16.3207 | 0.861374 | 0.430687 | − | 0.902501i | \(-0.358271\pi\) | ||||
0.430687 | + | 0.902501i | \(0.358271\pi\) | |||||||
\(360\) | −8.09890 | −0.426849 | ||||||||
\(361\) | 2.05559 | 0.108189 | ||||||||
\(362\) | −0.539189 | −0.0283391 | ||||||||
\(363\) | −1.53919 | −0.0807865 | ||||||||
\(364\) | −3.74888 | −0.196495 | ||||||||
\(365\) | 18.9288 | 0.990779 | ||||||||
\(366\) | 5.54411 | 0.289795 | ||||||||
\(367\) | −0.196748 | −0.0102702 | −0.00513509 | − | 0.999987i | \(-0.501635\pi\) | ||||
−0.00513509 | + | 0.999987i | \(0.501635\pi\) | |||||||
\(368\) | 12.9627 | 0.675725 | ||||||||
\(369\) | −0.680346 | −0.0354174 | ||||||||
\(370\) | 48.9698 | 2.54582 | ||||||||
\(371\) | −4.26019 | −0.221178 | ||||||||
\(372\) | 3.48482 | 0.180680 | ||||||||
\(373\) | −5.45240 | −0.282315 | −0.141157 | − | 0.989987i | \(-0.545082\pi\) | ||||
−0.141157 | + | 0.989987i | \(0.545082\pi\) | |||||||
\(374\) | 1.17009 | 0.0605037 | ||||||||
\(375\) | 47.4307 | 2.44931 | ||||||||
\(376\) | −27.0517 | −1.39509 | ||||||||
\(377\) | −48.9276 | −2.51990 | ||||||||
\(378\) | 7.05172 | 0.362701 | ||||||||
\(379\) | 15.9021 | 0.816838 | 0.408419 | − | 0.912794i | \(-0.366080\pi\) | ||||
0.408419 | + | 0.912794i | \(0.366080\pi\) | |||||||
\(380\) | −12.0722 | −0.619293 | ||||||||
\(381\) | 7.44521 | 0.381430 | ||||||||
\(382\) | −6.82991 | −0.349449 | ||||||||
\(383\) | 20.2762 | 1.03606 | 0.518032 | − | 0.855361i | \(-0.326665\pi\) | ||||
0.518032 | + | 0.855361i | \(0.326665\pi\) | |||||||
\(384\) | −5.10957 | −0.260747 | ||||||||
\(385\) | 4.49693 | 0.229185 | ||||||||
\(386\) | 17.8082 | 0.906412 | ||||||||
\(387\) | 4.31351 | 0.219268 | ||||||||
\(388\) | 5.55252 | 0.281886 | ||||||||
\(389\) | −13.7298 | −0.696128 | −0.348064 | − | 0.937471i | \(-0.613161\pi\) | ||||
−0.348064 | + | 0.937471i | \(0.613161\pi\) | |||||||
\(390\) | 41.3835 | 2.09553 | ||||||||
\(391\) | 5.53919 | 0.280129 | ||||||||
\(392\) | 17.9688 | 0.907562 | ||||||||
\(393\) | −9.79976 | −0.494333 | ||||||||
\(394\) | −24.6453 | −1.24161 | ||||||||
\(395\) | −32.5308 | −1.63680 | ||||||||
\(396\) | −0.398032 | −0.0200019 | ||||||||
\(397\) | −24.8020 | −1.24478 | −0.622389 | − | 0.782708i | \(-0.713838\pi\) | ||||
−0.622389 | + | 0.782708i | \(0.713838\pi\) | |||||||
\(398\) | 16.5281 | 0.828480 | ||||||||
\(399\) | 7.61634 | 0.381294 | ||||||||
\(400\) | −28.9939 | −1.44969 | ||||||||
\(401\) | 6.91321 | 0.345229 | 0.172615 | − | 0.984989i | \(-0.444778\pi\) | ||||
0.172615 | + | 0.984989i | \(0.444778\pi\) | |||||||
\(402\) | −2.69594 | −0.134461 | ||||||||
\(403\) | 19.7743 | 0.985029 | ||||||||
\(404\) | 2.79606 | 0.139109 | ||||||||
\(405\) | 27.9783 | 1.39025 | ||||||||
\(406\) | −11.2039 | −0.556042 | ||||||||
\(407\) | 10.0361 | 0.497472 | ||||||||
\(408\) | −4.73820 | −0.234576 | ||||||||
\(409\) | −19.0277 | −0.940860 | −0.470430 | − | 0.882437i | \(-0.655901\pi\) | ||||
−0.470430 | + | 0.882437i | \(0.655901\pi\) | |||||||
\(410\) | −5.26180 | −0.259862 | ||||||||
\(411\) | 3.85270 | 0.190040 | ||||||||
\(412\) | 7.25195 | 0.357278 | ||||||||
\(413\) | 8.96266 | 0.441024 | ||||||||
\(414\) | 4.08906 | 0.200966 | ||||||||
\(415\) | 19.5174 | 0.958074 | ||||||||
\(416\) | 18.8371 | 0.923565 | ||||||||
\(417\) | 4.95547 | 0.242671 | ||||||||
\(418\) | 5.36910 | 0.262611 | ||||||||
\(419\) | 35.0205 | 1.71086 | 0.855432 | − | 0.517915i | \(-0.173292\pi\) | ||||
0.855432 | + | 0.517915i | \(0.173292\pi\) | |||||||
\(420\) | −4.36683 | −0.213080 | ||||||||
\(421\) | −26.0905 | −1.27157 | −0.635786 | − | 0.771865i | \(-0.719324\pi\) | ||||
−0.635786 | + | 0.771865i | \(0.719324\pi\) | |||||||
\(422\) | 8.61265 | 0.419257 | ||||||||
\(423\) | −5.54411 | −0.269564 | ||||||||
\(424\) | 12.1613 | 0.590604 | ||||||||
\(425\) | −12.3896 | −0.600985 | ||||||||
\(426\) | −8.12291 | −0.393556 | ||||||||
\(427\) | −3.31965 | −0.160649 | ||||||||
\(428\) | 0.0266620 | 0.00128876 | ||||||||
\(429\) | 8.48133 | 0.409482 | ||||||||
\(430\) | 33.3607 | 1.60880 | ||||||||
\(431\) | −12.5659 | −0.605276 | −0.302638 | − | 0.953106i | \(-0.597867\pi\) | ||||
−0.302638 | + | 0.953106i | \(0.597867\pi\) | |||||||
\(432\) | −13.0784 | −0.629234 | ||||||||
\(433\) | 29.4040 | 1.41307 | 0.706533 | − | 0.707680i | \(-0.250258\pi\) | ||||
0.706533 | + | 0.707680i | \(0.250258\pi\) | |||||||
\(434\) | 4.52813 | 0.217357 | ||||||||
\(435\) | −56.9926 | −2.73259 | ||||||||
\(436\) | −5.66436 | −0.271274 | ||||||||
\(437\) | 25.4173 | 1.21588 | ||||||||
\(438\) | 8.17501 | 0.390617 | ||||||||
\(439\) | 32.6069 | 1.55624 | 0.778121 | − | 0.628114i | \(-0.216173\pi\) | ||||
0.778121 | + | 0.628114i | \(0.216173\pi\) | |||||||
\(440\) | −12.8371 | −0.611985 | ||||||||
\(441\) | 3.68261 | 0.175363 | ||||||||
\(442\) | −6.44748 | −0.306675 | ||||||||
\(443\) | 15.6765 | 0.744812 | 0.372406 | − | 0.928070i | \(-0.378533\pi\) | ||||
0.372406 | + | 0.928070i | \(0.378533\pi\) | |||||||
\(444\) | −9.74578 | −0.462514 | ||||||||
\(445\) | 4.93495 | 0.233939 | ||||||||
\(446\) | −25.7081 | −1.21731 | ||||||||
\(447\) | 19.1350 | 0.905055 | ||||||||
\(448\) | 9.36069 | 0.442251 | ||||||||
\(449\) | −2.02174 | −0.0954119 | −0.0477059 | − | 0.998861i | \(-0.515191\pi\) | ||||
−0.0477059 | + | 0.998861i | \(0.515191\pi\) | |||||||
\(450\) | −9.14608 | −0.431150 | ||||||||
\(451\) | −1.07838 | −0.0507788 | ||||||||
\(452\) | 3.06013 | 0.143936 | ||||||||
\(453\) | −5.25073 | −0.246701 | ||||||||
\(454\) | −25.4413 | −1.19402 | ||||||||
\(455\) | −24.7792 | −1.16167 | ||||||||
\(456\) | −21.7419 | −1.01816 | ||||||||
\(457\) | −0.463079 | −0.0216619 | −0.0108310 | − | 0.999941i | \(-0.503448\pi\) | ||||
−0.0108310 | + | 0.999941i | \(0.503448\pi\) | |||||||
\(458\) | −23.8816 | −1.11592 | ||||||||
\(459\) | −5.58864 | −0.260855 | ||||||||
\(460\) | −14.5730 | −0.679471 | ||||||||
\(461\) | 22.5236 | 1.04903 | 0.524514 | − | 0.851402i | \(-0.324247\pi\) | ||||
0.524514 | + | 0.851402i | \(0.324247\pi\) | |||||||
\(462\) | 1.94214 | 0.0903566 | ||||||||
\(463\) | 6.73594 | 0.313046 | 0.156523 | − | 0.987674i | \(-0.449972\pi\) | ||||
0.156523 | + | 0.987674i | \(0.449972\pi\) | |||||||
\(464\) | 20.7792 | 0.964652 | ||||||||
\(465\) | 23.0338 | 1.06817 | ||||||||
\(466\) | 2.80590 | 0.129981 | ||||||||
\(467\) | −2.08225 | −0.0963552 | −0.0481776 | − | 0.998839i | \(-0.515341\pi\) | ||||
−0.0481776 | + | 0.998839i | \(0.515341\pi\) | |||||||
\(468\) | 2.19326 | 0.101383 | ||||||||
\(469\) | 1.61425 | 0.0745393 | ||||||||
\(470\) | −42.8781 | −1.97782 | ||||||||
\(471\) | 3.44029 | 0.158520 | ||||||||
\(472\) | −25.5851 | −1.17765 | ||||||||
\(473\) | 6.83710 | 0.314370 | ||||||||
\(474\) | −14.0494 | −0.645313 | ||||||||
\(475\) | −56.8515 | −2.60852 | ||||||||
\(476\) | 0.680346 | 0.0311836 | ||||||||
\(477\) | 2.49239 | 0.114119 | ||||||||
\(478\) | −7.49466 | −0.342798 | ||||||||
\(479\) | −27.6163 | −1.26182 | −0.630911 | − | 0.775855i | \(-0.717319\pi\) | ||||
−0.630911 | + | 0.775855i | \(0.717319\pi\) | |||||||
\(480\) | 21.9421 | 1.00152 | ||||||||
\(481\) | −55.3016 | −2.52154 | ||||||||
\(482\) | 19.6332 | 0.894266 | ||||||||
\(483\) | 9.19410 | 0.418346 | ||||||||
\(484\) | −0.630898 | −0.0286772 | ||||||||
\(485\) | 36.7009 | 1.66650 | ||||||||
\(486\) | −7.53427 | −0.341761 | ||||||||
\(487\) | −42.5018 | −1.92594 | −0.962971 | − | 0.269604i | \(-0.913107\pi\) | ||||
−0.962971 | + | 0.269604i | \(0.913107\pi\) | |||||||
\(488\) | 9.47641 | 0.428977 | ||||||||
\(489\) | −21.4596 | −0.970436 | ||||||||
\(490\) | 28.4813 | 1.28666 | ||||||||
\(491\) | 35.8069 | 1.61595 | 0.807973 | − | 0.589220i | \(-0.200565\pi\) | ||||
0.807973 | + | 0.589220i | \(0.200565\pi\) | |||||||
\(492\) | 1.04718 | 0.0472106 | ||||||||
\(493\) | 8.87936 | 0.399906 | ||||||||
\(494\) | −29.5851 | −1.33110 | ||||||||
\(495\) | −2.63090 | −0.118250 | ||||||||
\(496\) | −8.39803 | −0.377083 | ||||||||
\(497\) | 4.86376 | 0.218170 | ||||||||
\(498\) | 8.42923 | 0.377723 | ||||||||
\(499\) | 4.26406 | 0.190886 | 0.0954428 | − | 0.995435i | \(-0.469573\pi\) | ||||
0.0954428 | + | 0.995435i | \(0.469573\pi\) | |||||||
\(500\) | 19.4413 | 0.869443 | ||||||||
\(501\) | −21.1122 | −0.943225 | ||||||||
\(502\) | 28.7864 | 1.28480 | ||||||||
\(503\) | 28.4235 | 1.26734 | 0.633670 | − | 0.773603i | \(-0.281548\pi\) | ||||
0.633670 | + | 0.773603i | \(0.281548\pi\) | |||||||
\(504\) | 2.09436 | 0.0932903 | ||||||||
\(505\) | 18.4813 | 0.822408 | ||||||||
\(506\) | 6.48133 | 0.288130 | ||||||||
\(507\) | −26.7249 | −1.18689 | ||||||||
\(508\) | 3.05172 | 0.135398 | ||||||||
\(509\) | 40.4740 | 1.79398 | 0.896988 | − | 0.442054i | \(-0.145750\pi\) | ||||
0.896988 | + | 0.442054i | \(0.145750\pi\) | |||||||
\(510\) | −7.51026 | −0.332560 | ||||||||
\(511\) | −4.89496 | −0.216540 | ||||||||
\(512\) | −22.4079 | −0.990297 | ||||||||
\(513\) | −25.6442 | −1.13222 | ||||||||
\(514\) | 26.3135 | 1.16064 | ||||||||
\(515\) | 47.9337 | 2.11221 | ||||||||
\(516\) | −6.63931 | −0.292279 | ||||||||
\(517\) | −8.78765 | −0.386481 | ||||||||
\(518\) | −12.6635 | −0.556403 | ||||||||
\(519\) | −10.2413 | −0.449542 | ||||||||
\(520\) | 70.7358 | 3.10197 | ||||||||
\(521\) | −2.59478 | −0.113679 | −0.0568397 | − | 0.998383i | \(-0.518102\pi\) | ||||
−0.0568397 | + | 0.998383i | \(0.518102\pi\) | |||||||
\(522\) | 6.55479 | 0.286895 | ||||||||
\(523\) | −16.2823 | −0.711976 | −0.355988 | − | 0.934491i | \(-0.615856\pi\) | ||||
−0.355988 | + | 0.934491i | \(0.615856\pi\) | |||||||
\(524\) | −4.01682 | −0.175476 | ||||||||
\(525\) | −20.5646 | −0.897514 | ||||||||
\(526\) | −20.8554 | −0.909337 | ||||||||
\(527\) | −3.58864 | −0.156323 | ||||||||
\(528\) | −3.60197 | −0.156756 | ||||||||
\(529\) | 7.68261 | 0.334027 | ||||||||
\(530\) | 19.2762 | 0.837303 | ||||||||
\(531\) | −5.24354 | −0.227550 | ||||||||
\(532\) | 3.12186 | 0.135350 | ||||||||
\(533\) | 5.94214 | 0.257383 | ||||||||
\(534\) | 2.13132 | 0.0922311 | ||||||||
\(535\) | 0.176230 | 0.00761907 | ||||||||
\(536\) | −4.60811 | −0.199040 | ||||||||
\(537\) | −5.27125 | −0.227471 | ||||||||
\(538\) | 22.3234 | 0.962428 | ||||||||
\(539\) | 5.83710 | 0.251422 | ||||||||
\(540\) | 14.7031 | 0.632722 | ||||||||
\(541\) | 15.4030 | 0.662225 | 0.331112 | − | 0.943591i | \(-0.392576\pi\) | ||||
0.331112 | + | 0.943591i | \(0.392576\pi\) | |||||||
\(542\) | −23.7009 | −1.01804 | ||||||||
\(543\) | 0.709275 | 0.0304379 | ||||||||
\(544\) | −3.41855 | −0.146569 | ||||||||
\(545\) | −37.4401 | −1.60376 | ||||||||
\(546\) | −10.7017 | −0.457991 | ||||||||
\(547\) | 21.9311 | 0.937705 | 0.468853 | − | 0.883276i | \(-0.344668\pi\) | ||||
0.468853 | + | 0.883276i | \(0.344668\pi\) | |||||||
\(548\) | 1.57918 | 0.0674593 | ||||||||
\(549\) | 1.94214 | 0.0828886 | ||||||||
\(550\) | −14.4969 | −0.618151 | ||||||||
\(551\) | 40.7442 | 1.73576 | ||||||||
\(552\) | −26.2458 | −1.11710 | ||||||||
\(553\) | 8.41241 | 0.357732 | ||||||||
\(554\) | −20.3447 | −0.864364 | ||||||||
\(555\) | −64.4173 | −2.73436 | ||||||||
\(556\) | 2.03120 | 0.0861419 | ||||||||
\(557\) | −38.1568 | −1.61675 | −0.808377 | − | 0.588665i | \(-0.799654\pi\) | ||||
−0.808377 | + | 0.588665i | \(0.799654\pi\) | |||||||
\(558\) | −2.64915 | −0.112147 | ||||||||
\(559\) | −37.6742 | −1.59345 | ||||||||
\(560\) | 10.5236 | 0.444703 | ||||||||
\(561\) | −1.53919 | −0.0649846 | ||||||||
\(562\) | −1.55252 | −0.0654891 | ||||||||
\(563\) | 29.3945 | 1.23883 | 0.619416 | − | 0.785063i | \(-0.287369\pi\) | ||||
0.619416 | + | 0.785063i | \(0.287369\pi\) | |||||||
\(564\) | 8.53343 | 0.359322 | ||||||||
\(565\) | 20.2267 | 0.850945 | ||||||||
\(566\) | −15.9649 | −0.671056 | ||||||||
\(567\) | −7.23513 | −0.303847 | ||||||||
\(568\) | −13.8843 | −0.582572 | ||||||||
\(569\) | −14.1568 | −0.593482 | −0.296741 | − | 0.954958i | \(-0.595900\pi\) | ||||
−0.296741 | + | 0.954958i | \(0.595900\pi\) | |||||||
\(570\) | −34.4619 | −1.44345 | ||||||||
\(571\) | 20.0300 | 0.838228 | 0.419114 | − | 0.907934i | \(-0.362341\pi\) | ||||
0.419114 | + | 0.907934i | \(0.362341\pi\) | |||||||
\(572\) | 3.47641 | 0.145356 | ||||||||
\(573\) | 8.98440 | 0.375329 | ||||||||
\(574\) | 1.36069 | 0.0567942 | ||||||||
\(575\) | −68.6285 | −2.86200 | ||||||||
\(576\) | −5.47641 | −0.228184 | ||||||||
\(577\) | 15.8904 | 0.661527 | 0.330764 | − | 0.943714i | \(-0.392694\pi\) | ||||
0.330764 | + | 0.943714i | \(0.392694\pi\) | |||||||
\(578\) | 1.17009 | 0.0486692 | ||||||||
\(579\) | −23.4257 | −0.973540 | ||||||||
\(580\) | −23.3607 | −0.970000 | ||||||||
\(581\) | −5.04718 | −0.209392 | ||||||||
\(582\) | 15.8504 | 0.657022 | ||||||||
\(583\) | 3.95055 | 0.163615 | ||||||||
\(584\) | 13.9733 | 0.578221 | ||||||||
\(585\) | 14.4969 | 0.599374 | ||||||||
\(586\) | −7.88428 | −0.325697 | ||||||||
\(587\) | −9.10116 | −0.375645 | −0.187823 | − | 0.982203i | \(-0.560143\pi\) | ||||
−0.187823 | + | 0.982203i | \(0.560143\pi\) | |||||||
\(588\) | −5.66824 | −0.233754 | ||||||||
\(589\) | −16.4670 | −0.678509 | ||||||||
\(590\) | −40.5536 | −1.66956 | ||||||||
\(591\) | 32.4196 | 1.33356 | ||||||||
\(592\) | 23.4863 | 0.965279 | ||||||||
\(593\) | −44.6875 | −1.83510 | −0.917549 | − | 0.397624i | \(-0.869835\pi\) | ||||
−0.917549 | + | 0.397624i | \(0.869835\pi\) | |||||||
\(594\) | −6.53919 | −0.268306 | ||||||||
\(595\) | 4.49693 | 0.184356 | ||||||||
\(596\) | 7.84324 | 0.321272 | ||||||||
\(597\) | −21.7419 | −0.889837 | ||||||||
\(598\) | −35.7138 | −1.46045 | ||||||||
\(599\) | 8.51971 | 0.348106 | 0.174053 | − | 0.984736i | \(-0.444314\pi\) | ||||
0.174053 | + | 0.984736i | \(0.444314\pi\) | |||||||
\(600\) | 58.7046 | 2.39660 | ||||||||
\(601\) | 22.8104 | 0.930457 | 0.465229 | − | 0.885191i | \(-0.345972\pi\) | ||||
0.465229 | + | 0.885191i | \(0.345972\pi\) | |||||||
\(602\) | −8.62702 | −0.351611 | ||||||||
\(603\) | −0.944409 | −0.0384593 | ||||||||
\(604\) | −2.15222 | −0.0875726 | ||||||||
\(605\) | −4.17009 | −0.169538 | ||||||||
\(606\) | 7.98175 | 0.324236 | ||||||||
\(607\) | −9.15061 | −0.371412 | −0.185706 | − | 0.982605i | \(-0.559457\pi\) | ||||
−0.185706 | + | 0.982605i | \(0.559457\pi\) | |||||||
\(608\) | −15.6865 | −0.636171 | ||||||||
\(609\) | 14.7382 | 0.597222 | ||||||||
\(610\) | 15.0205 | 0.608163 | ||||||||
\(611\) | 48.4222 | 1.95895 | ||||||||
\(612\) | −0.398032 | −0.0160895 | ||||||||
\(613\) | 14.0456 | 0.567295 | 0.283648 | − | 0.958929i | \(-0.408455\pi\) | ||||
0.283648 | + | 0.958929i | \(0.408455\pi\) | |||||||
\(614\) | 22.6141 | 0.912630 | ||||||||
\(615\) | 6.92162 | 0.279107 | ||||||||
\(616\) | 3.31965 | 0.133753 | ||||||||
\(617\) | 24.9360 | 1.00389 | 0.501943 | − | 0.864901i | \(-0.332619\pi\) | ||||
0.501943 | + | 0.864901i | \(0.332619\pi\) | |||||||
\(618\) | 20.7017 | 0.832745 | ||||||||
\(619\) | 22.5246 | 0.905342 | 0.452671 | − | 0.891678i | \(-0.350471\pi\) | ||||
0.452671 | + | 0.891678i | \(0.350471\pi\) | |||||||
\(620\) | 9.44134 | 0.379173 | ||||||||
\(621\) | −30.9565 | −1.24224 | ||||||||
\(622\) | −21.3607 | −0.856486 | ||||||||
\(623\) | −1.27617 | −0.0511287 | ||||||||
\(624\) | 19.8478 | 0.794547 | ||||||||
\(625\) | 66.5546 | 2.66218 | ||||||||
\(626\) | −15.0049 | −0.599717 | ||||||||
\(627\) | −7.06278 | −0.282060 | ||||||||
\(628\) | 1.41014 | 0.0562707 | ||||||||
\(629\) | 10.0361 | 0.400166 | ||||||||
\(630\) | 3.31965 | 0.132258 | ||||||||
\(631\) | −28.9299 | −1.15168 | −0.575840 | − | 0.817563i | \(-0.695325\pi\) | ||||
−0.575840 | + | 0.817563i | \(0.695325\pi\) | |||||||
\(632\) | −24.0144 | −0.955241 | ||||||||
\(633\) | −11.3295 | −0.450307 | ||||||||
\(634\) | −24.8625 | −0.987418 | ||||||||
\(635\) | 20.1711 | 0.800467 | ||||||||
\(636\) | −3.83626 | −0.152118 | ||||||||
\(637\) | −32.1639 | −1.27438 | ||||||||
\(638\) | 10.3896 | 0.411329 | ||||||||
\(639\) | −2.84551 | −0.112567 | ||||||||
\(640\) | −13.8432 | −0.547202 | ||||||||
\(641\) | −2.13501 | −0.0843280 | −0.0421640 | − | 0.999111i | \(-0.513425\pi\) | ||||
−0.0421640 | + | 0.999111i | \(0.513425\pi\) | |||||||
\(642\) | 0.0761103 | 0.00300383 | ||||||||
\(643\) | 9.72261 | 0.383422 | 0.191711 | − | 0.981451i | \(-0.438596\pi\) | ||||
0.191711 | + | 0.981451i | \(0.438596\pi\) | |||||||
\(644\) | 3.76856 | 0.148502 | ||||||||
\(645\) | −43.8843 | −1.72794 | ||||||||
\(646\) | 5.36910 | 0.211245 | ||||||||
\(647\) | −44.2990 | −1.74157 | −0.870786 | − | 0.491662i | \(-0.836389\pi\) | ||||
−0.870786 | + | 0.491662i | \(0.836389\pi\) | |||||||
\(648\) | 20.6537 | 0.811353 | ||||||||
\(649\) | −8.31124 | −0.326245 | ||||||||
\(650\) | 79.8818 | 3.13322 | ||||||||
\(651\) | −5.95652 | −0.233454 | ||||||||
\(652\) | −8.79606 | −0.344480 | ||||||||
\(653\) | −30.3002 | −1.18574 | −0.592869 | − | 0.805299i | \(-0.702005\pi\) | ||||
−0.592869 | + | 0.805299i | \(0.702005\pi\) | |||||||
\(654\) | −16.1697 | −0.632285 | ||||||||
\(655\) | −26.5503 | −1.03740 | ||||||||
\(656\) | −2.52359 | −0.0985297 | ||||||||
\(657\) | 2.86376 | 0.111726 | ||||||||
\(658\) | 11.0882 | 0.432264 | ||||||||
\(659\) | 28.1373 | 1.09607 | 0.548036 | − | 0.836454i | \(-0.315376\pi\) | ||||
0.548036 | + | 0.836454i | \(0.315376\pi\) | |||||||
\(660\) | 4.04945 | 0.157625 | ||||||||
\(661\) | 22.1857 | 0.862923 | 0.431462 | − | 0.902131i | \(-0.357998\pi\) | ||||
0.431462 | + | 0.902131i | \(0.357998\pi\) | |||||||
\(662\) | −18.3786 | −0.714303 | ||||||||
\(663\) | 8.48133 | 0.329388 | ||||||||
\(664\) | 14.4079 | 0.559134 | ||||||||
\(665\) | 20.6348 | 0.800182 | ||||||||
\(666\) | 7.40871 | 0.287082 | ||||||||
\(667\) | 49.1845 | 1.90443 | ||||||||
\(668\) | −8.65368 | −0.334821 | ||||||||
\(669\) | 33.8176 | 1.30747 | ||||||||
\(670\) | −7.30406 | −0.282180 | ||||||||
\(671\) | 3.07838 | 0.118839 | ||||||||
\(672\) | −5.67420 | −0.218887 | ||||||||
\(673\) | 34.3701 | 1.32487 | 0.662436 | − | 0.749119i | \(-0.269523\pi\) | ||||
0.662436 | + | 0.749119i | \(0.269523\pi\) | |||||||
\(674\) | 11.2039 | 0.431560 | ||||||||
\(675\) | 69.2411 | 2.66509 | ||||||||
\(676\) | −10.9542 | −0.421317 | ||||||||
\(677\) | 37.3184 | 1.43426 | 0.717132 | − | 0.696937i | \(-0.245454\pi\) | ||||
0.717132 | + | 0.696937i | \(0.245454\pi\) | |||||||
\(678\) | 8.73555 | 0.335487 | ||||||||
\(679\) | −9.49079 | −0.364223 | ||||||||
\(680\) | −12.8371 | −0.492280 | ||||||||
\(681\) | 33.4668 | 1.28245 | ||||||||
\(682\) | −4.19902 | −0.160789 | ||||||||
\(683\) | −39.6475 | −1.51707 | −0.758535 | − | 0.651632i | \(-0.774085\pi\) | ||||
−0.758535 | + | 0.651632i | \(0.774085\pi\) | |||||||
\(684\) | −1.82642 | −0.0698350 | ||||||||
\(685\) | 10.4380 | 0.398816 | ||||||||
\(686\) | −16.1978 | −0.618435 | ||||||||
\(687\) | 31.4151 | 1.19856 | ||||||||
\(688\) | 16.0000 | 0.609994 | ||||||||
\(689\) | −21.7686 | −0.829316 | ||||||||
\(690\) | −41.6007 | −1.58371 | ||||||||
\(691\) | −13.4007 | −0.509786 | −0.254893 | − | 0.966969i | \(-0.582040\pi\) | ||||
−0.254893 | + | 0.966969i | \(0.582040\pi\) | |||||||
\(692\) | −4.19779 | −0.159576 | ||||||||
\(693\) | 0.680346 | 0.0258442 | ||||||||
\(694\) | −22.3402 | −0.848021 | ||||||||
\(695\) | 13.4257 | 0.509267 | ||||||||
\(696\) | −42.0722 | −1.59474 | ||||||||
\(697\) | −1.07838 | −0.0408465 | ||||||||
\(698\) | −33.4596 | −1.26646 | ||||||||
\(699\) | −3.69102 | −0.139607 | ||||||||
\(700\) | −8.42923 | −0.318595 | ||||||||
\(701\) | 16.6803 | 0.630008 | 0.315004 | − | 0.949090i | \(-0.397994\pi\) | ||||
0.315004 | + | 0.949090i | \(0.397994\pi\) | |||||||
\(702\) | 36.0326 | 1.35996 | ||||||||
\(703\) | 46.0521 | 1.73689 | ||||||||
\(704\) | −8.68035 | −0.327153 | ||||||||
\(705\) | 56.4040 | 2.12430 | ||||||||
\(706\) | −20.2485 | −0.762061 | ||||||||
\(707\) | −4.77924 | −0.179742 | ||||||||
\(708\) | 8.07080 | 0.303319 | ||||||||
\(709\) | 12.1350 | 0.455740 | 0.227870 | − | 0.973692i | \(-0.426824\pi\) | ||||
0.227870 | + | 0.973692i | \(0.426824\pi\) | |||||||
\(710\) | −22.0072 | −0.825915 | ||||||||
\(711\) | −4.92162 | −0.184575 | ||||||||
\(712\) | 3.64301 | 0.136527 | ||||||||
\(713\) | −19.8781 | −0.744442 | ||||||||
\(714\) | 1.94214 | 0.0726828 | ||||||||
\(715\) | 22.9783 | 0.859338 | ||||||||
\(716\) | −2.16063 | −0.0807466 | ||||||||
\(717\) | 9.85884 | 0.368185 | ||||||||
\(718\) | 19.0966 | 0.712680 | ||||||||
\(719\) | −12.6754 | −0.472714 | −0.236357 | − | 0.971666i | \(-0.575953\pi\) | ||||
−0.236357 | + | 0.971666i | \(0.575953\pi\) | |||||||
\(720\) | −6.15676 | −0.229449 | ||||||||
\(721\) | −12.3956 | −0.461636 | ||||||||
\(722\) | 2.40522 | 0.0895130 | ||||||||
\(723\) | −25.8264 | −0.960495 | ||||||||
\(724\) | 0.290725 | 0.0108047 | ||||||||
\(725\) | −110.012 | −4.08574 | ||||||||
\(726\) | −1.80098 | −0.0668408 | ||||||||
\(727\) | −6.10957 | −0.226592 | −0.113296 | − | 0.993561i | \(-0.536141\pi\) | ||||
−0.113296 | + | 0.993561i | \(0.536141\pi\) | |||||||
\(728\) | −18.2922 | −0.677952 | ||||||||
\(729\) | 30.0388 | 1.11255 | ||||||||
\(730\) | 22.1483 | 0.819747 | ||||||||
\(731\) | 6.83710 | 0.252879 | ||||||||
\(732\) | −2.98932 | −0.110489 | ||||||||
\(733\) | −8.86830 | −0.327558 | −0.163779 | − | 0.986497i | \(-0.552368\pi\) | ||||
−0.163779 | + | 0.986497i | \(0.552368\pi\) | |||||||
\(734\) | −0.230213 | −0.00849731 | ||||||||
\(735\) | −37.4657 | −1.38194 | ||||||||
\(736\) | −18.9360 | −0.697990 | ||||||||
\(737\) | −1.49693 | −0.0551401 | ||||||||
\(738\) | −0.796064 | −0.0293035 | ||||||||
\(739\) | −27.1845 | −0.999997 | −0.499998 | − | 0.866026i | \(-0.666666\pi\) | ||||
−0.499998 | + | 0.866026i | \(0.666666\pi\) | |||||||
\(740\) | −26.4040 | −0.970630 | ||||||||
\(741\) | 38.9177 | 1.42968 | ||||||||
\(742\) | −4.98479 | −0.182997 | ||||||||
\(743\) | 25.8120 | 0.946952 | 0.473476 | − | 0.880807i | \(-0.342999\pi\) | ||||
0.473476 | + | 0.880807i | \(0.342999\pi\) | |||||||
\(744\) | 17.0037 | 0.623386 | ||||||||
\(745\) | 51.8420 | 1.89934 | ||||||||
\(746\) | −6.37978 | −0.233580 | ||||||||
\(747\) | 2.95282 | 0.108038 | ||||||||
\(748\) | −0.630898 | −0.0230679 | ||||||||
\(749\) | −0.0455727 | −0.00166519 | ||||||||
\(750\) | 55.4980 | 2.02650 | ||||||||
\(751\) | 7.07942 | 0.258332 | 0.129166 | − | 0.991623i | \(-0.458770\pi\) | ||||
0.129166 | + | 0.991623i | \(0.458770\pi\) | |||||||
\(752\) | −20.5646 | −0.749915 | ||||||||
\(753\) | −37.8671 | −1.37995 | ||||||||
\(754\) | −57.2495 | −2.08490 | ||||||||
\(755\) | −14.2257 | −0.517725 | ||||||||
\(756\) | −3.80221 | −0.138285 | ||||||||
\(757\) | −8.24128 | −0.299534 | −0.149767 | − | 0.988721i | \(-0.547852\pi\) | ||||
−0.149767 | + | 0.988721i | \(0.547852\pi\) | |||||||
\(758\) | 18.6069 | 0.675833 | ||||||||
\(759\) | −8.52586 | −0.309469 | ||||||||
\(760\) | −58.9048 | −2.13670 | ||||||||
\(761\) | 14.0338 | 0.508727 | 0.254363 | − | 0.967109i | \(-0.418134\pi\) | ||||
0.254363 | + | 0.967109i | \(0.418134\pi\) | |||||||
\(762\) | 8.71154 | 0.315586 | ||||||||
\(763\) | 9.68195 | 0.350510 | ||||||||
\(764\) | 3.68261 | 0.133232 | ||||||||
\(765\) | −2.63090 | −0.0951203 | ||||||||
\(766\) | 23.7249 | 0.857215 | ||||||||
\(767\) | 45.7971 | 1.65364 | ||||||||
\(768\) | 20.7427 | 0.748489 | ||||||||
\(769\) | −35.4063 | −1.27678 | −0.638391 | − | 0.769712i | \(-0.720400\pi\) | ||||
−0.638391 | + | 0.769712i | \(0.720400\pi\) | |||||||
\(770\) | 5.26180 | 0.189622 | ||||||||
\(771\) | −34.6141 | −1.24660 | ||||||||
\(772\) | −9.60197 | −0.345582 | ||||||||
\(773\) | −3.65142 | −0.131332 | −0.0656662 | − | 0.997842i | \(-0.520917\pi\) | ||||
−0.0656662 | + | 0.997842i | \(0.520917\pi\) | |||||||
\(774\) | 5.04718 | 0.181417 | ||||||||
\(775\) | 44.4619 | 1.59712 | ||||||||
\(776\) | 27.0928 | 0.972573 | ||||||||
\(777\) | 16.6582 | 0.597610 | ||||||||
\(778\) | −16.0650 | −0.575960 | ||||||||
\(779\) | −4.94828 | −0.177291 | ||||||||
\(780\) | −22.3135 | −0.798952 | ||||||||
\(781\) | −4.51026 | −0.161390 | ||||||||
\(782\) | 6.48133 | 0.231772 | ||||||||
\(783\) | −49.6235 | −1.77340 | ||||||||
\(784\) | 13.6598 | 0.487851 | ||||||||
\(785\) | 9.32070 | 0.332670 | ||||||||
\(786\) | −11.4666 | −0.408999 | ||||||||
\(787\) | 41.7308 | 1.48754 | 0.743772 | − | 0.668434i | \(-0.233035\pi\) | ||||
0.743772 | + | 0.668434i | \(0.233035\pi\) | |||||||
\(788\) | 13.2885 | 0.473382 | ||||||||
\(789\) | 27.4341 | 0.976682 | ||||||||
\(790\) | −38.0638 | −1.35425 | ||||||||
\(791\) | −5.23060 | −0.185979 | ||||||||
\(792\) | −1.94214 | −0.0690110 | ||||||||
\(793\) | −16.9627 | −0.602362 | ||||||||
\(794\) | −29.0205 | −1.02990 | ||||||||
\(795\) | −25.3568 | −0.899314 | ||||||||
\(796\) | −8.91178 | −0.315870 | ||||||||
\(797\) | 43.9504 | 1.55680 | 0.778401 | − | 0.627767i | \(-0.216031\pi\) | ||||
0.778401 | + | 0.627767i | \(0.216031\pi\) | |||||||
\(798\) | 8.91178 | 0.315474 | ||||||||
\(799\) | −8.78765 | −0.310885 | ||||||||
\(800\) | 42.3545 | 1.49746 | ||||||||
\(801\) | 0.746615 | 0.0263804 | ||||||||
\(802\) | 8.08906 | 0.285634 | ||||||||
\(803\) | 4.53919 | 0.160184 | ||||||||
\(804\) | 1.45362 | 0.0512653 | ||||||||
\(805\) | 24.9093 | 0.877939 | ||||||||
\(806\) | 23.1377 | 0.814990 | ||||||||
\(807\) | −29.3652 | −1.03370 | ||||||||
\(808\) | 13.6430 | 0.479959 | ||||||||
\(809\) | −13.0894 | −0.460200 | −0.230100 | − | 0.973167i | \(-0.573905\pi\) | ||||
−0.230100 | + | 0.973167i | \(0.573905\pi\) | |||||||
\(810\) | 32.7370 | 1.15026 | ||||||||
\(811\) | 6.75380 | 0.237158 | 0.118579 | − | 0.992945i | \(-0.462166\pi\) | ||||
0.118579 | + | 0.992945i | \(0.462166\pi\) | |||||||
\(812\) | 6.04104 | 0.211999 | ||||||||
\(813\) | 31.1773 | 1.09343 | ||||||||
\(814\) | 11.7431 | 0.411596 | ||||||||
\(815\) | −58.1399 | −2.03655 | ||||||||
\(816\) | −3.60197 | −0.126094 | ||||||||
\(817\) | 31.3730 | 1.09760 | ||||||||
\(818\) | −22.2641 | −0.778445 | ||||||||
\(819\) | −3.74888 | −0.130997 | ||||||||
\(820\) | 2.83710 | 0.0990759 | ||||||||
\(821\) | 30.9471 | 1.08006 | 0.540030 | − | 0.841646i | \(-0.318413\pi\) | ||||
0.540030 | + | 0.841646i | \(0.318413\pi\) | |||||||
\(822\) | 4.50799 | 0.157234 | ||||||||
\(823\) | −50.9104 | −1.77462 | −0.887312 | − | 0.461169i | \(-0.847430\pi\) | ||||
−0.887312 | + | 0.461169i | \(0.847430\pi\) | |||||||
\(824\) | 35.3849 | 1.23269 | ||||||||
\(825\) | 19.0700 | 0.663931 | ||||||||
\(826\) | 10.4871 | 0.364892 | ||||||||
\(827\) | 42.6791 | 1.48410 | 0.742049 | − | 0.670345i | \(-0.233854\pi\) | ||||
0.742049 | + | 0.670345i | \(0.233854\pi\) | |||||||
\(828\) | −2.20477 | −0.0766212 | ||||||||
\(829\) | 16.2495 | 0.564369 | 0.282184 | − | 0.959360i | \(-0.408941\pi\) | ||||
0.282184 | + | 0.959360i | \(0.408941\pi\) | |||||||
\(830\) | 22.8371 | 0.792687 | ||||||||
\(831\) | 26.7624 | 0.928378 | ||||||||
\(832\) | 47.8310 | 1.65824 | ||||||||
\(833\) | 5.83710 | 0.202244 | ||||||||
\(834\) | 5.79833 | 0.200780 | ||||||||
\(835\) | −57.1988 | −1.97945 | ||||||||
\(836\) | −2.89496 | −0.100124 | ||||||||
\(837\) | 20.0556 | 0.693223 | ||||||||
\(838\) | 40.9770 | 1.41553 | ||||||||
\(839\) | 6.19287 | 0.213802 | 0.106901 | − | 0.994270i | \(-0.465907\pi\) | ||||
0.106901 | + | 0.994270i | \(0.465907\pi\) | |||||||
\(840\) | −21.3074 | −0.735174 | ||||||||
\(841\) | 49.8431 | 1.71873 | ||||||||
\(842\) | −30.5281 | −1.05207 | ||||||||
\(843\) | 2.04226 | 0.0703392 | ||||||||
\(844\) | −4.64384 | −0.159848 | ||||||||
\(845\) | −72.4050 | −2.49081 | ||||||||
\(846\) | −6.48709 | −0.223031 | ||||||||
\(847\) | 1.07838 | 0.0370535 | ||||||||
\(848\) | 9.24497 | 0.317474 | ||||||||
\(849\) | 21.0010 | 0.720754 | ||||||||
\(850\) | −14.4969 | −0.497241 | ||||||||
\(851\) | 55.5919 | 1.90567 | ||||||||
\(852\) | 4.37978 | 0.150049 | ||||||||
\(853\) | −27.9721 | −0.957747 | −0.478873 | − | 0.877884i | \(-0.658955\pi\) | ||||
−0.478873 | + | 0.877884i | \(0.658955\pi\) | |||||||
\(854\) | −3.88428 | −0.132917 | ||||||||
\(855\) | −12.0722 | −0.412862 | ||||||||
\(856\) | 0.130094 | 0.00444650 | ||||||||
\(857\) | 13.7743 | 0.470522 | 0.235261 | − | 0.971932i | \(-0.424406\pi\) | ||||
0.235261 | + | 0.971932i | \(0.424406\pi\) | |||||||
\(858\) | 9.92389 | 0.338796 | ||||||||
\(859\) | −6.51148 | −0.222169 | −0.111084 | − | 0.993811i | \(-0.535432\pi\) | ||||
−0.111084 | + | 0.993811i | \(0.535432\pi\) | |||||||
\(860\) | −17.9877 | −0.613376 | ||||||||
\(861\) | −1.78992 | −0.0610003 | ||||||||
\(862\) | −14.7031 | −0.500791 | ||||||||
\(863\) | −40.1217 | −1.36576 | −0.682879 | − | 0.730532i | \(-0.739272\pi\) | ||||
−0.682879 | + | 0.730532i | \(0.739272\pi\) | |||||||
\(864\) | 19.1050 | 0.649967 | ||||||||
\(865\) | −27.7464 | −0.943407 | ||||||||
\(866\) | 34.4052 | 1.16914 | ||||||||
\(867\) | −1.53919 | −0.0522736 | ||||||||
\(868\) | −2.44151 | −0.0828704 | ||||||||
\(869\) | −7.80098 | −0.264630 | ||||||||
\(870\) | −66.6863 | −2.26088 | ||||||||
\(871\) | 8.24846 | 0.279489 | ||||||||
\(872\) | −27.6385 | −0.935957 | ||||||||
\(873\) | 5.55252 | 0.187924 | ||||||||
\(874\) | 29.7405 | 1.00599 | ||||||||
\(875\) | −33.2306 | −1.12340 | ||||||||
\(876\) | −4.40787 | −0.148928 | ||||||||
\(877\) | 18.9348 | 0.639382 | 0.319691 | − | 0.947522i | \(-0.396421\pi\) | ||||
0.319691 | + | 0.947522i | \(0.396421\pi\) | |||||||
\(878\) | 38.1529 | 1.28760 | ||||||||
\(879\) | 10.3714 | 0.349818 | ||||||||
\(880\) | −9.75872 | −0.328967 | ||||||||
\(881\) | 3.74539 | 0.126185 | 0.0630927 | − | 0.998008i | \(-0.479904\pi\) | ||||
0.0630927 | + | 0.998008i | \(0.479904\pi\) | |||||||
\(882\) | 4.30898 | 0.145091 | ||||||||
\(883\) | 5.84324 | 0.196641 | 0.0983204 | − | 0.995155i | \(-0.468653\pi\) | ||||
0.0983204 | + | 0.995155i | \(0.468653\pi\) | |||||||
\(884\) | 3.47641 | 0.116924 | ||||||||
\(885\) | 53.3461 | 1.79321 | ||||||||
\(886\) | 18.3428 | 0.616239 | ||||||||
\(887\) | −25.2306 | −0.847161 | −0.423580 | − | 0.905859i | \(-0.639227\pi\) | ||||
−0.423580 | + | 0.905859i | \(0.639227\pi\) | |||||||
\(888\) | −47.5532 | −1.59578 | ||||||||
\(889\) | −5.21622 | −0.174946 | ||||||||
\(890\) | 5.77432 | 0.193556 | ||||||||
\(891\) | 6.70928 | 0.224769 | ||||||||
\(892\) | 13.8615 | 0.464117 | ||||||||
\(893\) | −40.3234 | −1.34937 | ||||||||
\(894\) | 22.3896 | 0.748821 | ||||||||
\(895\) | −14.2813 | −0.477370 | ||||||||
\(896\) | 3.57984 | 0.119594 | ||||||||
\(897\) | 46.9797 | 1.56861 | ||||||||
\(898\) | −2.36561 | −0.0789415 | ||||||||
\(899\) | −31.8648 | −1.06275 | ||||||||
\(900\) | 4.93146 | 0.164382 | ||||||||
\(901\) | 3.95055 | 0.131612 | ||||||||
\(902\) | −1.26180 | −0.0420132 | ||||||||
\(903\) | 11.3484 | 0.377651 | ||||||||
\(904\) | 14.9315 | 0.496613 | ||||||||
\(905\) | 1.92162 | 0.0638769 | ||||||||
\(906\) | −6.14381 | −0.204114 | ||||||||
\(907\) | −49.9877 | −1.65981 | −0.829907 | − | 0.557901i | \(-0.811607\pi\) | ||||
−0.829907 | + | 0.557901i | \(0.811607\pi\) | |||||||
\(908\) | 13.7177 | 0.455237 | ||||||||
\(909\) | 2.79606 | 0.0927396 | ||||||||
\(910\) | −28.9939 | −0.961137 | ||||||||
\(911\) | −31.5213 | −1.04435 | −0.522174 | − | 0.852839i | \(-0.674879\pi\) | ||||
−0.522174 | + | 0.852839i | \(0.674879\pi\) | |||||||
\(912\) | −16.5281 | −0.547301 | ||||||||
\(913\) | 4.68035 | 0.154897 | ||||||||
\(914\) | −0.541842 | −0.0179225 | ||||||||
\(915\) | −19.7587 | −0.653203 | ||||||||
\(916\) | 12.8767 | 0.425458 | ||||||||
\(917\) | 6.86585 | 0.226730 | ||||||||
\(918\) | −6.53919 | −0.215825 | ||||||||
\(919\) | −42.5913 | −1.40496 | −0.702479 | − | 0.711705i | \(-0.747923\pi\) | ||||
−0.702479 | + | 0.711705i | \(0.747923\pi\) | |||||||
\(920\) | −71.1071 | −2.34433 | ||||||||
\(921\) | −29.7477 | −0.980219 | ||||||||
\(922\) | 26.3545 | 0.867941 | ||||||||
\(923\) | 24.8527 | 0.818037 | ||||||||
\(924\) | −1.04718 | −0.0344497 | ||||||||
\(925\) | −124.344 | −4.08840 | ||||||||
\(926\) | 7.88163 | 0.259006 | ||||||||
\(927\) | 7.25195 | 0.238185 | ||||||||
\(928\) | −30.3545 | −0.996437 | ||||||||
\(929\) | −21.5630 | −0.707460 | −0.353730 | − | 0.935348i | \(-0.615087\pi\) | ||||
−0.353730 | + | 0.935348i | \(0.615087\pi\) | |||||||
\(930\) | 26.9516 | 0.883778 | ||||||||
\(931\) | 26.7843 | 0.877821 | ||||||||
\(932\) | −1.51291 | −0.0495571 | ||||||||
\(933\) | 28.0989 | 0.919917 | ||||||||
\(934\) | −2.43642 | −0.0797220 | ||||||||
\(935\) | −4.17009 | −0.136376 | ||||||||
\(936\) | 10.7017 | 0.349796 | ||||||||
\(937\) | −42.4417 | −1.38651 | −0.693255 | − | 0.720692i | \(-0.743824\pi\) | ||||
−0.693255 | + | 0.720692i | \(0.743824\pi\) | |||||||
\(938\) | 1.88882 | 0.0616721 | ||||||||
\(939\) | 19.7382 | 0.644132 | ||||||||
\(940\) | 23.1194 | 0.754072 | ||||||||
\(941\) | −16.7526 | −0.546119 | −0.273059 | − | 0.961997i | \(-0.588036\pi\) | ||||
−0.273059 | + | 0.961997i | \(0.588036\pi\) | |||||||
\(942\) | 4.02544 | 0.131156 | ||||||||
\(943\) | −5.97334 | −0.194519 | ||||||||
\(944\) | −19.4497 | −0.633035 | ||||||||
\(945\) | −25.1317 | −0.817534 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | −52.7035 | −1.71263 | −0.856317 | − | 0.516450i | \(-0.827253\pi\) | ||||
−0.856317 | + | 0.516450i | \(0.827253\pi\) | |||||||
\(948\) | 7.57531 | 0.246035 | ||||||||
\(949\) | −25.0121 | −0.811927 | ||||||||
\(950\) | −66.5211 | −2.15823 | ||||||||
\(951\) | 32.7054 | 1.06055 | ||||||||
\(952\) | 3.31965 | 0.107591 | ||||||||
\(953\) | 27.6742 | 0.896455 | 0.448228 | − | 0.893919i | \(-0.352055\pi\) | ||||
0.448228 | + | 0.893919i | \(0.352055\pi\) | |||||||
\(954\) | 2.91632 | 0.0944192 | ||||||||
\(955\) | 24.3412 | 0.787663 | ||||||||
\(956\) | 4.04104 | 0.130697 | ||||||||
\(957\) | −13.6670 | −0.441792 | ||||||||
\(958\) | −32.3135 | −1.04400 | ||||||||
\(959\) | −2.69926 | −0.0871635 | ||||||||
\(960\) | 55.7152 | 1.79820 | ||||||||
\(961\) | −18.1217 | −0.584570 | ||||||||
\(962\) | −64.7077 | −2.08626 | ||||||||
\(963\) | 0.0266620 | 0.000859171 0 | ||||||||
\(964\) | −10.5860 | −0.340952 | ||||||||
\(965\) | −63.4668 | −2.04307 | ||||||||
\(966\) | 10.7579 | 0.346129 | ||||||||
\(967\) | 42.3207 | 1.36094 | 0.680471 | − | 0.732775i | \(-0.261775\pi\) | ||||
0.680471 | + | 0.732775i | \(0.261775\pi\) | |||||||
\(968\) | −3.07838 | −0.0989428 | ||||||||
\(969\) | −7.06278 | −0.226889 | ||||||||
\(970\) | 42.9432 | 1.37882 | ||||||||
\(971\) | −2.96493 | −0.0951491 | −0.0475745 | − | 0.998868i | \(-0.515149\pi\) | ||||
−0.0475745 | + | 0.998868i | \(0.515149\pi\) | |||||||
\(972\) | 4.06239 | 0.130301 | ||||||||
\(973\) | −3.47187 | −0.111303 | ||||||||
\(974\) | −49.7308 | −1.59348 | ||||||||
\(975\) | −105.080 | −3.36527 | ||||||||
\(976\) | 7.20394 | 0.230592 | ||||||||
\(977\) | −38.2267 | −1.22298 | −0.611491 | − | 0.791252i | \(-0.709430\pi\) | ||||
−0.611491 | + | 0.791252i | \(0.709430\pi\) | |||||||
\(978\) | −25.1096 | −0.802916 | ||||||||
\(979\) | 1.18342 | 0.0378222 | ||||||||
\(980\) | −15.3568 | −0.490556 | ||||||||
\(981\) | −5.66436 | −0.180849 | ||||||||
\(982\) | 41.8972 | 1.33699 | ||||||||
\(983\) | −1.48974 | −0.0475153 | −0.0237577 | − | 0.999718i | \(-0.507563\pi\) | ||||
−0.0237577 | + | 0.999718i | \(0.507563\pi\) | |||||||
\(984\) | 5.10957 | 0.162887 | ||||||||
\(985\) | 87.8336 | 2.79861 | ||||||||
\(986\) | 10.3896 | 0.330873 | ||||||||
\(987\) | −14.5860 | −0.464277 | ||||||||
\(988\) | 15.9520 | 0.507500 | ||||||||
\(989\) | 37.8720 | 1.20426 | ||||||||
\(990\) | −3.07838 | −0.0978373 | ||||||||
\(991\) | −26.4391 | −0.839865 | −0.419932 | − | 0.907555i | \(-0.637946\pi\) | ||||
−0.419932 | + | 0.907555i | \(0.637946\pi\) | |||||||
\(992\) | 12.2679 | 0.389507 | ||||||||
\(993\) | 24.1761 | 0.767204 | ||||||||
\(994\) | 5.69102 | 0.180508 | ||||||||
\(995\) | −58.9048 | −1.86741 | ||||||||
\(996\) | −4.54495 | −0.144012 | ||||||||
\(997\) | 18.9060 | 0.598760 | 0.299380 | − | 0.954134i | \(-0.403220\pi\) | ||||
0.299380 | + | 0.954134i | \(0.403220\pi\) | |||||||
\(998\) | 4.98932 | 0.157934 | ||||||||
\(999\) | −56.0882 | −1.77455 |
(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 | 187.2.a.e.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 1683.2.a.v.1.1 | 3 | |||
4.3 | odd | 2 | 2992.2.a.r.1.2 | 3 | |||
5.4 | even | 2 | 4675.2.a.bc.1.1 | 3 | |||
7.6 | odd | 2 | 9163.2.a.j.1.3 | 3 | |||
11.10 | odd | 2 | 2057.2.a.p.1.1 | 3 | |||
17.16 | even | 2 | 3179.2.a.t.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.a.e.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1683.2.a.v.1.1 | 3 | 3.2 | odd | 2 | |||
2057.2.a.p.1.1 | 3 | 11.10 | odd | 2 | |||
2992.2.a.r.1.2 | 3 | 4.3 | odd | 2 | |||
3179.2.a.t.1.3 | 3 | 17.16 | even | 2 | |||
4675.2.a.bc.1.1 | 3 | 5.4 | even | 2 | |||
9163.2.a.j.1.3 | 3 | 7.6 | odd | 2 |