Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1155.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(9.22272143346\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
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 | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56155 | 1.10418 | 0.552092 | − | 0.833783i | \(-0.313830\pi\) | ||||
0.552092 | + | 0.833783i | \(0.313830\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.56155 | −0.637501 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.43845 | −0.862121 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.56155 | 0.493806 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.438447 | −0.126569 | ||||||||
\(13\) | −7.12311 | −1.97559 | −0.987797 | − | 0.155747i | \(-0.950222\pi\) | ||||
−0.987797 | + | 0.155747i | \(0.950222\pi\) | |||||||
\(14\) | −1.56155 | −0.417343 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 0.561553 | 0.136197 | 0.0680983 | − | 0.997679i | \(-0.478307\pi\) | ||||
0.0680983 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(18\) | 1.56155 | 0.368062 | ||||||||
\(19\) | −2.56155 | −0.587661 | −0.293830 | − | 0.955858i | \(-0.594930\pi\) | ||||
−0.293830 | + | 0.955858i | \(0.594930\pi\) | |||||||
\(20\) | 0.438447 | 0.0980398 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 1.56155 | 0.332924 | ||||||||
\(23\) | −1.43845 | −0.299937 | −0.149968 | − | 0.988691i | \(-0.547917\pi\) | ||||
−0.149968 | + | 0.988691i | \(0.547917\pi\) | |||||||
\(24\) | 2.43845 | 0.497746 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −11.1231 | −2.18142 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.438447 | −0.0828587 | ||||||||
\(29\) | 1.68466 | 0.312833 | 0.156417 | − | 0.987691i | \(-0.450006\pi\) | ||||
0.156417 | + | 0.987691i | \(0.450006\pi\) | |||||||
\(30\) | −1.56155 | −0.285099 | ||||||||
\(31\) | −5.12311 | −0.920137 | −0.460068 | − | 0.887883i | \(-0.652175\pi\) | ||||
−0.460068 | + | 0.887883i | \(0.652175\pi\) | |||||||
\(32\) | −2.43845 | −0.431061 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.876894 | 0.150386 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0.438447 | 0.0730745 | ||||||||
\(37\) | −7.12311 | −1.17103 | −0.585516 | − | 0.810661i | \(-0.699108\pi\) | ||||
−0.585516 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | 7.12311 | 1.14061 | ||||||||
\(40\) | −2.43845 | −0.385552 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 1.56155 | 0.240953 | ||||||||
\(43\) | 2.56155 | 0.390633 | 0.195317 | − | 0.980740i | \(-0.437427\pi\) | ||||
0.195317 | + | 0.980740i | \(0.437427\pi\) | |||||||
\(44\) | 0.438447 | 0.0660984 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −2.24621 | −0.331186 | ||||||||
\(47\) | −5.12311 | −0.747282 | −0.373641 | − | 0.927573i | \(-0.621891\pi\) | ||||
−0.373641 | + | 0.927573i | \(0.621891\pi\) | |||||||
\(48\) | 4.68466 | 0.676172 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.56155 | 0.220837 | ||||||||
\(51\) | −0.561553 | −0.0786331 | ||||||||
\(52\) | −3.12311 | −0.433097 | ||||||||
\(53\) | −13.6847 | −1.87973 | −0.939866 | − | 0.341543i | \(-0.889051\pi\) | ||||
−0.939866 | + | 0.341543i | \(0.889051\pi\) | |||||||
\(54\) | −1.56155 | −0.212500 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 2.43845 | 0.325851 | ||||||||
\(57\) | 2.56155 | 0.339286 | ||||||||
\(58\) | 2.63068 | 0.345426 | ||||||||
\(59\) | 10.5616 | 1.37500 | 0.687499 | − | 0.726186i | \(-0.258709\pi\) | ||||
0.687499 | + | 0.726186i | \(0.258709\pi\) | |||||||
\(60\) | −0.438447 | −0.0566033 | ||||||||
\(61\) | −3.43845 | −0.440248 | −0.220124 | − | 0.975472i | \(-0.570646\pi\) | ||||
−0.220124 | + | 0.975472i | \(0.570646\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | −7.12311 | −0.883513 | ||||||||
\(66\) | −1.56155 | −0.192214 | ||||||||
\(67\) | 6.87689 | 0.840146 | 0.420073 | − | 0.907490i | \(-0.362004\pi\) | ||||
0.420073 | + | 0.907490i | \(0.362004\pi\) | |||||||
\(68\) | 0.246211 | 0.0298575 | ||||||||
\(69\) | 1.43845 | 0.173169 | ||||||||
\(70\) | −1.56155 | −0.186641 | ||||||||
\(71\) | 5.12311 | 0.608001 | 0.304000 | − | 0.952672i | \(-0.401678\pi\) | ||||
0.304000 | + | 0.952672i | \(0.401678\pi\) | |||||||
\(72\) | −2.43845 | −0.287374 | ||||||||
\(73\) | −11.1231 | −1.30186 | −0.650931 | − | 0.759137i | \(-0.725621\pi\) | ||||
−0.650931 | + | 0.759137i | \(0.725621\pi\) | |||||||
\(74\) | −11.1231 | −1.29303 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −1.12311 | −0.128829 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 11.1231 | 1.25944 | ||||||||
\(79\) | −10.2462 | −1.15279 | −0.576394 | − | 0.817172i | \(-0.695541\pi\) | ||||
−0.576394 | + | 0.817172i | \(0.695541\pi\) | |||||||
\(80\) | −4.68466 | −0.523761 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.12311 | 0.344889 | ||||||||
\(83\) | −5.43845 | −0.596947 | −0.298474 | − | 0.954418i | \(-0.596477\pi\) | ||||
−0.298474 | + | 0.954418i | \(0.596477\pi\) | |||||||
\(84\) | 0.438447 | 0.0478385 | ||||||||
\(85\) | 0.561553 | 0.0609090 | ||||||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | −1.68466 | −0.180614 | ||||||||
\(88\) | −2.43845 | −0.259939 | ||||||||
\(89\) | −2.31534 | −0.245426 | −0.122713 | − | 0.992442i | \(-0.539159\pi\) | ||||
−0.122713 | + | 0.992442i | \(0.539159\pi\) | |||||||
\(90\) | 1.56155 | 0.164602 | ||||||||
\(91\) | 7.12311 | 0.746704 | ||||||||
\(92\) | −0.630683 | −0.0657533 | ||||||||
\(93\) | 5.12311 | 0.531241 | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | −2.56155 | −0.262810 | ||||||||
\(96\) | 2.43845 | 0.248873 | ||||||||
\(97\) | 2.80776 | 0.285085 | 0.142543 | − | 0.989789i | \(-0.454472\pi\) | ||||
0.142543 | + | 0.989789i | \(0.454472\pi\) | |||||||
\(98\) | 1.56155 | 0.157741 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0.438447 | 0.0438447 | ||||||||
\(101\) | −12.2462 | −1.21854 | −0.609272 | − | 0.792961i | \(-0.708538\pi\) | ||||
−0.609272 | + | 0.792961i | \(0.708538\pi\) | |||||||
\(102\) | −0.876894 | −0.0868255 | ||||||||
\(103\) | 3.68466 | 0.363060 | 0.181530 | − | 0.983385i | \(-0.441895\pi\) | ||||
0.181530 | + | 0.983385i | \(0.441895\pi\) | |||||||
\(104\) | 17.3693 | 1.70320 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | −21.3693 | −2.07557 | ||||||||
\(107\) | 19.3693 | 1.87250 | 0.936251 | − | 0.351331i | \(-0.114271\pi\) | ||||
0.936251 | + | 0.351331i | \(0.114271\pi\) | |||||||
\(108\) | −0.438447 | −0.0421896 | ||||||||
\(109\) | 18.4924 | 1.77125 | 0.885626 | − | 0.464398i | \(-0.153729\pi\) | ||||
0.885626 | + | 0.464398i | \(0.153729\pi\) | |||||||
\(110\) | 1.56155 | 0.148888 | ||||||||
\(111\) | 7.12311 | 0.676095 | ||||||||
\(112\) | 4.68466 | 0.442659 | ||||||||
\(113\) | 8.56155 | 0.805403 | 0.402702 | − | 0.915331i | \(-0.368071\pi\) | ||||
0.402702 | + | 0.915331i | \(0.368071\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | −1.43845 | −0.134136 | ||||||||
\(116\) | 0.738634 | 0.0685804 | ||||||||
\(117\) | −7.12311 | −0.658531 | ||||||||
\(118\) | 16.4924 | 1.51825 | ||||||||
\(119\) | −0.561553 | −0.0514775 | ||||||||
\(120\) | 2.43845 | 0.222599 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −5.36932 | −0.486115 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | −2.24621 | −0.201716 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.56155 | −0.139114 | ||||||||
\(127\) | 0.807764 | 0.0716775 | 0.0358387 | − | 0.999358i | \(-0.488590\pi\) | ||||
0.0358387 | + | 0.999358i | \(0.488590\pi\) | |||||||
\(128\) | 13.5616 | 1.19868 | ||||||||
\(129\) | −2.56155 | −0.225532 | ||||||||
\(130\) | −11.1231 | −0.975561 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | −0.438447 | −0.0381619 | ||||||||
\(133\) | 2.56155 | 0.222115 | ||||||||
\(134\) | 10.7386 | 0.927677 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −1.36932 | −0.117418 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | 2.24621 | 0.191210 | ||||||||
\(139\) | −20.0000 | −1.69638 | −0.848189 | − | 0.529694i | \(-0.822307\pi\) | ||||
−0.848189 | + | 0.529694i | \(0.822307\pi\) | |||||||
\(140\) | −0.438447 | −0.0370556 | ||||||||
\(141\) | 5.12311 | 0.431443 | ||||||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | −7.12311 | −0.595664 | ||||||||
\(144\) | −4.68466 | −0.390388 | ||||||||
\(145\) | 1.68466 | 0.139903 | ||||||||
\(146\) | −17.3693 | −1.43749 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −3.12311 | −0.256718 | ||||||||
\(149\) | 0.246211 | 0.0201704 | 0.0100852 | − | 0.999949i | \(-0.496790\pi\) | ||||
0.0100852 | + | 0.999949i | \(0.496790\pi\) | |||||||
\(150\) | −1.56155 | −0.127500 | ||||||||
\(151\) | 5.12311 | 0.416912 | 0.208456 | − | 0.978032i | \(-0.433156\pi\) | ||||
0.208456 | + | 0.978032i | \(0.433156\pi\) | |||||||
\(152\) | 6.24621 | 0.506635 | ||||||||
\(153\) | 0.561553 | 0.0453989 | ||||||||
\(154\) | −1.56155 | −0.125834 | ||||||||
\(155\) | −5.12311 | −0.411498 | ||||||||
\(156\) | 3.12311 | 0.250049 | ||||||||
\(157\) | −11.4384 | −0.912887 | −0.456444 | − | 0.889752i | \(-0.650877\pi\) | ||||
−0.456444 | + | 0.889752i | \(0.650877\pi\) | |||||||
\(158\) | −16.0000 | −1.27289 | ||||||||
\(159\) | 13.6847 | 1.08526 | ||||||||
\(160\) | −2.43845 | −0.192776 | ||||||||
\(161\) | 1.43845 | 0.113366 | ||||||||
\(162\) | 1.56155 | 0.122687 | ||||||||
\(163\) | 20.0000 | 1.56652 | 0.783260 | − | 0.621694i | \(-0.213555\pi\) | ||||
0.783260 | + | 0.621694i | \(0.213555\pi\) | |||||||
\(164\) | 0.876894 | 0.0684739 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | −8.49242 | −0.659140 | ||||||||
\(167\) | 2.24621 | 0.173817 | 0.0869085 | − | 0.996216i | \(-0.472301\pi\) | ||||
0.0869085 | + | 0.996216i | \(0.472301\pi\) | |||||||
\(168\) | −2.43845 | −0.188130 | ||||||||
\(169\) | 37.7386 | 2.90297 | ||||||||
\(170\) | 0.876894 | 0.0672547 | ||||||||
\(171\) | −2.56155 | −0.195887 | ||||||||
\(172\) | 1.12311 | 0.0856360 | ||||||||
\(173\) | −4.24621 | −0.322833 | −0.161417 | − | 0.986886i | \(-0.551606\pi\) | ||||
−0.161417 | + | 0.986886i | \(0.551606\pi\) | |||||||
\(174\) | −2.63068 | −0.199432 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −4.68466 | −0.353119 | ||||||||
\(177\) | −10.5616 | −0.793855 | ||||||||
\(178\) | −3.61553 | −0.270995 | ||||||||
\(179\) | −19.3693 | −1.44773 | −0.723865 | − | 0.689941i | \(-0.757636\pi\) | ||||
−0.723865 | + | 0.689941i | \(0.757636\pi\) | |||||||
\(180\) | 0.438447 | 0.0326799 | ||||||||
\(181\) | −20.2462 | −1.50489 | −0.752445 | − | 0.658656i | \(-0.771125\pi\) | ||||
−0.752445 | + | 0.658656i | \(0.771125\pi\) | |||||||
\(182\) | 11.1231 | 0.824499 | ||||||||
\(183\) | 3.43845 | 0.254177 | ||||||||
\(184\) | 3.50758 | 0.258582 | ||||||||
\(185\) | −7.12311 | −0.523701 | ||||||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | 0.561553 | 0.0410648 | ||||||||
\(188\) | −2.24621 | −0.163822 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −5.56155 | −0.401371 | ||||||||
\(193\) | 22.4924 | 1.61904 | 0.809520 | − | 0.587092i | \(-0.199727\pi\) | ||||
0.809520 | + | 0.587092i | \(0.199727\pi\) | |||||||
\(194\) | 4.38447 | 0.314787 | ||||||||
\(195\) | 7.12311 | 0.510096 | ||||||||
\(196\) | 0.438447 | 0.0313177 | ||||||||
\(197\) | −23.1231 | −1.64745 | −0.823727 | − | 0.566987i | \(-0.808109\pi\) | ||||
−0.823727 | + | 0.566987i | \(0.808109\pi\) | |||||||
\(198\) | 1.56155 | 0.110975 | ||||||||
\(199\) | 20.4924 | 1.45267 | 0.726335 | − | 0.687341i | \(-0.241222\pi\) | ||||
0.726335 | + | 0.687341i | \(0.241222\pi\) | |||||||
\(200\) | −2.43845 | −0.172424 | ||||||||
\(201\) | −6.87689 | −0.485059 | ||||||||
\(202\) | −19.1231 | −1.34550 | ||||||||
\(203\) | −1.68466 | −0.118240 | ||||||||
\(204\) | −0.246211 | −0.0172382 | ||||||||
\(205\) | 2.00000 | 0.139686 | ||||||||
\(206\) | 5.75379 | 0.400885 | ||||||||
\(207\) | −1.43845 | −0.0999790 | ||||||||
\(208\) | 33.3693 | 2.31375 | ||||||||
\(209\) | −2.56155 | −0.177186 | ||||||||
\(210\) | 1.56155 | 0.107757 | ||||||||
\(211\) | −3.36932 | −0.231953 | −0.115977 | − | 0.993252i | \(-0.537000\pi\) | ||||
−0.115977 | + | 0.993252i | \(0.537000\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | −5.12311 | −0.351029 | ||||||||
\(214\) | 30.2462 | 2.06759 | ||||||||
\(215\) | 2.56155 | 0.174696 | ||||||||
\(216\) | 2.43845 | 0.165915 | ||||||||
\(217\) | 5.12311 | 0.347779 | ||||||||
\(218\) | 28.8769 | 1.95579 | ||||||||
\(219\) | 11.1231 | 0.751630 | ||||||||
\(220\) | 0.438447 | 0.0295601 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 11.1231 | 0.746534 | ||||||||
\(223\) | 14.5616 | 0.975114 | 0.487557 | − | 0.873091i | \(-0.337888\pi\) | ||||
0.487557 | + | 0.873091i | \(0.337888\pi\) | |||||||
\(224\) | 2.43845 | 0.162926 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 13.3693 | 0.889314 | ||||||||
\(227\) | −25.9309 | −1.72109 | −0.860546 | − | 0.509373i | \(-0.829878\pi\) | ||||
−0.860546 | + | 0.509373i | \(0.829878\pi\) | |||||||
\(228\) | 1.12311 | 0.0743795 | ||||||||
\(229\) | 10.4924 | 0.693359 | 0.346679 | − | 0.937984i | \(-0.387309\pi\) | ||||
0.346679 | + | 0.937984i | \(0.387309\pi\) | |||||||
\(230\) | −2.24621 | −0.148111 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | −4.10795 | −0.269700 | ||||||||
\(233\) | −23.6155 | −1.54710 | −0.773552 | − | 0.633732i | \(-0.781522\pi\) | ||||
−0.773552 | + | 0.633732i | \(0.781522\pi\) | |||||||
\(234\) | −11.1231 | −0.727140 | ||||||||
\(235\) | −5.12311 | −0.334195 | ||||||||
\(236\) | 4.63068 | 0.301432 | ||||||||
\(237\) | 10.2462 | 0.665563 | ||||||||
\(238\) | −0.876894 | −0.0568406 | ||||||||
\(239\) | 19.6847 | 1.27329 | 0.636647 | − | 0.771155i | \(-0.280321\pi\) | ||||
0.636647 | + | 0.771155i | \(0.280321\pi\) | |||||||
\(240\) | 4.68466 | 0.302393 | ||||||||
\(241\) | −0.246211 | −0.0158599 | −0.00792993 | − | 0.999969i | \(-0.502524\pi\) | ||||
−0.00792993 | + | 0.999969i | \(0.502524\pi\) | |||||||
\(242\) | 1.56155 | 0.100380 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.50758 | −0.0965128 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −3.12311 | −0.199122 | ||||||||
\(247\) | 18.2462 | 1.16098 | ||||||||
\(248\) | 12.4924 | 0.793270 | ||||||||
\(249\) | 5.43845 | 0.344648 | ||||||||
\(250\) | 1.56155 | 0.0987613 | ||||||||
\(251\) | 24.4924 | 1.54595 | 0.772974 | − | 0.634438i | \(-0.218768\pi\) | ||||
0.772974 | + | 0.634438i | \(0.218768\pi\) | |||||||
\(252\) | −0.438447 | −0.0276196 | ||||||||
\(253\) | −1.43845 | −0.0904344 | ||||||||
\(254\) | 1.26137 | 0.0791452 | ||||||||
\(255\) | −0.561553 | −0.0351658 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | 9.36932 | 0.584442 | 0.292221 | − | 0.956351i | \(-0.405606\pi\) | ||||
0.292221 | + | 0.956351i | \(0.405606\pi\) | |||||||
\(258\) | −4.00000 | −0.249029 | ||||||||
\(259\) | 7.12311 | 0.442608 | ||||||||
\(260\) | −3.12311 | −0.193687 | ||||||||
\(261\) | 1.68466 | 0.104278 | ||||||||
\(262\) | 6.24621 | 0.385892 | ||||||||
\(263\) | −18.2462 | −1.12511 | −0.562555 | − | 0.826760i | \(-0.690181\pi\) | ||||
−0.562555 | + | 0.826760i | \(0.690181\pi\) | |||||||
\(264\) | 2.43845 | 0.150076 | ||||||||
\(265\) | −13.6847 | −0.840642 | ||||||||
\(266\) | 4.00000 | 0.245256 | ||||||||
\(267\) | 2.31534 | 0.141697 | ||||||||
\(268\) | 3.01515 | 0.184180 | ||||||||
\(269\) | 1.68466 | 0.102715 | 0.0513577 | − | 0.998680i | \(-0.483645\pi\) | ||||
0.0513577 | + | 0.998680i | \(0.483645\pi\) | |||||||
\(270\) | −1.56155 | −0.0950331 | ||||||||
\(271\) | −13.9309 | −0.846240 | −0.423120 | − | 0.906074i | \(-0.639065\pi\) | ||||
−0.423120 | + | 0.906074i | \(0.639065\pi\) | |||||||
\(272\) | −2.63068 | −0.159509 | ||||||||
\(273\) | −7.12311 | −0.431110 | ||||||||
\(274\) | 15.6155 | 0.943369 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0.630683 | 0.0379627 | ||||||||
\(277\) | −24.7386 | −1.48640 | −0.743200 | − | 0.669069i | \(-0.766693\pi\) | ||||
−0.743200 | + | 0.669069i | \(0.766693\pi\) | |||||||
\(278\) | −31.2311 | −1.87311 | ||||||||
\(279\) | −5.12311 | −0.306712 | ||||||||
\(280\) | 2.43845 | 0.145725 | ||||||||
\(281\) | 14.4924 | 0.864545 | 0.432273 | − | 0.901743i | \(-0.357712\pi\) | ||||
0.432273 | + | 0.901743i | \(0.357712\pi\) | |||||||
\(282\) | 8.00000 | 0.476393 | ||||||||
\(283\) | 6.24621 | 0.371299 | 0.185649 | − | 0.982616i | \(-0.440561\pi\) | ||||
0.185649 | + | 0.982616i | \(0.440561\pi\) | |||||||
\(284\) | 2.24621 | 0.133288 | ||||||||
\(285\) | 2.56155 | 0.151733 | ||||||||
\(286\) | −11.1231 | −0.657723 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | −2.43845 | −0.143687 | ||||||||
\(289\) | −16.6847 | −0.981450 | ||||||||
\(290\) | 2.63068 | 0.154479 | ||||||||
\(291\) | −2.80776 | −0.164594 | ||||||||
\(292\) | −4.87689 | −0.285399 | ||||||||
\(293\) | −26.1771 | −1.52928 | −0.764641 | − | 0.644457i | \(-0.777084\pi\) | ||||
−0.764641 | + | 0.644457i | \(0.777084\pi\) | |||||||
\(294\) | −1.56155 | −0.0910716 | ||||||||
\(295\) | 10.5616 | 0.614917 | ||||||||
\(296\) | 17.3693 | 1.00957 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | 0.384472 | 0.0222719 | ||||||||
\(299\) | 10.2462 | 0.592554 | ||||||||
\(300\) | −0.438447 | −0.0253138 | ||||||||
\(301\) | −2.56155 | −0.147645 | ||||||||
\(302\) | 8.00000 | 0.460348 | ||||||||
\(303\) | 12.2462 | 0.703526 | ||||||||
\(304\) | 12.0000 | 0.688247 | ||||||||
\(305\) | −3.43845 | −0.196885 | ||||||||
\(306\) | 0.876894 | 0.0501287 | ||||||||
\(307\) | 11.3693 | 0.648881 | 0.324441 | − | 0.945906i | \(-0.394824\pi\) | ||||
0.324441 | + | 0.945906i | \(0.394824\pi\) | |||||||
\(308\) | −0.438447 | −0.0249828 | ||||||||
\(309\) | −3.68466 | −0.209613 | ||||||||
\(310\) | −8.00000 | −0.454369 | ||||||||
\(311\) | −16.0000 | −0.907277 | −0.453638 | − | 0.891186i | \(-0.649874\pi\) | ||||
−0.453638 | + | 0.891186i | \(0.649874\pi\) | |||||||
\(312\) | −17.3693 | −0.983344 | ||||||||
\(313\) | −2.31534 | −0.130871 | −0.0654354 | − | 0.997857i | \(-0.520844\pi\) | ||||
−0.0654354 | + | 0.997857i | \(0.520844\pi\) | |||||||
\(314\) | −17.8617 | −1.00800 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | −4.49242 | −0.252719 | ||||||||
\(317\) | −22.4924 | −1.26330 | −0.631650 | − | 0.775254i | \(-0.717622\pi\) | ||||
−0.631650 | + | 0.775254i | \(0.717622\pi\) | |||||||
\(318\) | 21.3693 | 1.19833 | ||||||||
\(319\) | 1.68466 | 0.0943228 | ||||||||
\(320\) | 5.56155 | 0.310900 | ||||||||
\(321\) | −19.3693 | −1.08109 | ||||||||
\(322\) | 2.24621 | 0.125176 | ||||||||
\(323\) | −1.43845 | −0.0800373 | ||||||||
\(324\) | 0.438447 | 0.0243582 | ||||||||
\(325\) | −7.12311 | −0.395119 | ||||||||
\(326\) | 31.2311 | 1.72973 | ||||||||
\(327\) | −18.4924 | −1.02263 | ||||||||
\(328\) | −4.87689 | −0.269281 | ||||||||
\(329\) | 5.12311 | 0.282446 | ||||||||
\(330\) | −1.56155 | −0.0859607 | ||||||||
\(331\) | −23.6847 | −1.30183 | −0.650913 | − | 0.759152i | \(-0.725614\pi\) | ||||
−0.650913 | + | 0.759152i | \(0.725614\pi\) | |||||||
\(332\) | −2.38447 | −0.130865 | ||||||||
\(333\) | −7.12311 | −0.390344 | ||||||||
\(334\) | 3.50758 | 0.191926 | ||||||||
\(335\) | 6.87689 | 0.375725 | ||||||||
\(336\) | −4.68466 | −0.255569 | ||||||||
\(337\) | −9.05398 | −0.493201 | −0.246601 | − | 0.969117i | \(-0.579314\pi\) | ||||
−0.246601 | + | 0.969117i | \(0.579314\pi\) | |||||||
\(338\) | 58.9309 | 3.20542 | ||||||||
\(339\) | −8.56155 | −0.465000 | ||||||||
\(340\) | 0.246211 | 0.0133527 | ||||||||
\(341\) | −5.12311 | −0.277432 | ||||||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −6.24621 | −0.336773 | ||||||||
\(345\) | 1.43845 | 0.0774434 | ||||||||
\(346\) | −6.63068 | −0.356468 | ||||||||
\(347\) | −14.2462 | −0.764777 | −0.382388 | − | 0.924002i | \(-0.624898\pi\) | ||||
−0.382388 | + | 0.924002i | \(0.624898\pi\) | |||||||
\(348\) | −0.738634 | −0.0395949 | ||||||||
\(349\) | −9.19224 | −0.492049 | −0.246025 | − | 0.969264i | \(-0.579124\pi\) | ||||
−0.246025 | + | 0.969264i | \(0.579124\pi\) | |||||||
\(350\) | −1.56155 | −0.0834685 | ||||||||
\(351\) | 7.12311 | 0.380203 | ||||||||
\(352\) | −2.43845 | −0.129970 | ||||||||
\(353\) | −30.0000 | −1.59674 | −0.798369 | − | 0.602168i | \(-0.794304\pi\) | ||||
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | −16.4924 | −0.876562 | ||||||||
\(355\) | 5.12311 | 0.271906 | ||||||||
\(356\) | −1.01515 | −0.0538031 | ||||||||
\(357\) | 0.561553 | 0.0297205 | ||||||||
\(358\) | −30.2462 | −1.59856 | ||||||||
\(359\) | −4.31534 | −0.227755 | −0.113878 | − | 0.993495i | \(-0.536327\pi\) | ||||
−0.113878 | + | 0.993495i | \(0.536327\pi\) | |||||||
\(360\) | −2.43845 | −0.128517 | ||||||||
\(361\) | −12.4384 | −0.654655 | ||||||||
\(362\) | −31.6155 | −1.66168 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 3.12311 | 0.163695 | ||||||||
\(365\) | −11.1231 | −0.582210 | ||||||||
\(366\) | 5.36932 | 0.280659 | ||||||||
\(367\) | 17.4384 | 0.910280 | 0.455140 | − | 0.890420i | \(-0.349589\pi\) | ||||
0.455140 | + | 0.890420i | \(0.349589\pi\) | |||||||
\(368\) | 6.73863 | 0.351276 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | −11.1231 | −0.578263 | ||||||||
\(371\) | 13.6847 | 0.710472 | ||||||||
\(372\) | 2.24621 | 0.116461 | ||||||||
\(373\) | −0.561553 | −0.0290761 | −0.0145381 | − | 0.999894i | \(-0.504628\pi\) | ||||
−0.0145381 | + | 0.999894i | \(0.504628\pi\) | |||||||
\(374\) | 0.876894 | 0.0453431 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 12.4924 | 0.644247 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 1.56155 | 0.0803176 | ||||||||
\(379\) | 23.0540 | 1.18420 | 0.592102 | − | 0.805863i | \(-0.298298\pi\) | ||||
0.592102 | + | 0.805863i | \(0.298298\pi\) | |||||||
\(380\) | −1.12311 | −0.0576141 | ||||||||
\(381\) | −0.807764 | −0.0413830 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.4924 | −0.638333 | −0.319166 | − | 0.947699i | \(-0.603403\pi\) | ||||
−0.319166 | + | 0.947699i | \(0.603403\pi\) | |||||||
\(384\) | −13.5616 | −0.692060 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | 35.1231 | 1.78772 | ||||||||
\(387\) | 2.56155 | 0.130211 | ||||||||
\(388\) | 1.23106 | 0.0624974 | ||||||||
\(389\) | −21.8617 | −1.10843 | −0.554217 | − | 0.832372i | \(-0.686982\pi\) | ||||
−0.554217 | + | 0.832372i | \(0.686982\pi\) | |||||||
\(390\) | 11.1231 | 0.563240 | ||||||||
\(391\) | −0.807764 | −0.0408504 | ||||||||
\(392\) | −2.43845 | −0.123160 | ||||||||
\(393\) | −4.00000 | −0.201773 | ||||||||
\(394\) | −36.1080 | −1.81909 | ||||||||
\(395\) | −10.2462 | −0.515543 | ||||||||
\(396\) | 0.438447 | 0.0220328 | ||||||||
\(397\) | 14.0000 | 0.702640 | 0.351320 | − | 0.936255i | \(-0.385733\pi\) | ||||
0.351320 | + | 0.936255i | \(0.385733\pi\) | |||||||
\(398\) | 32.0000 | 1.60402 | ||||||||
\(399\) | −2.56155 | −0.128238 | ||||||||
\(400\) | −4.68466 | −0.234233 | ||||||||
\(401\) | −34.4924 | −1.72247 | −0.861235 | − | 0.508207i | \(-0.830308\pi\) | ||||
−0.861235 | + | 0.508207i | \(0.830308\pi\) | |||||||
\(402\) | −10.7386 | −0.535594 | ||||||||
\(403\) | 36.4924 | 1.81782 | ||||||||
\(404\) | −5.36932 | −0.267133 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −2.63068 | −0.130559 | ||||||||
\(407\) | −7.12311 | −0.353079 | ||||||||
\(408\) | 1.36932 | 0.0677913 | ||||||||
\(409\) | −8.24621 | −0.407749 | −0.203874 | − | 0.978997i | \(-0.565353\pi\) | ||||
−0.203874 | + | 0.978997i | \(0.565353\pi\) | |||||||
\(410\) | 3.12311 | 0.154239 | ||||||||
\(411\) | −10.0000 | −0.493264 | ||||||||
\(412\) | 1.61553 | 0.0795914 | ||||||||
\(413\) | −10.5616 | −0.519700 | ||||||||
\(414\) | −2.24621 | −0.110395 | ||||||||
\(415\) | −5.43845 | −0.266963 | ||||||||
\(416\) | 17.3693 | 0.851601 | ||||||||
\(417\) | 20.0000 | 0.979404 | ||||||||
\(418\) | −4.00000 | −0.195646 | ||||||||
\(419\) | 11.1922 | 0.546777 | 0.273388 | − | 0.961904i | \(-0.411856\pi\) | ||||
0.273388 | + | 0.961904i | \(0.411856\pi\) | |||||||
\(420\) | 0.438447 | 0.0213940 | ||||||||
\(421\) | 30.1771 | 1.47074 | 0.735370 | − | 0.677665i | \(-0.237008\pi\) | ||||
0.735370 | + | 0.677665i | \(0.237008\pi\) | |||||||
\(422\) | −5.26137 | −0.256119 | ||||||||
\(423\) | −5.12311 | −0.249094 | ||||||||
\(424\) | 33.3693 | 1.62056 | ||||||||
\(425\) | 0.561553 | 0.0272393 | ||||||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | 3.43845 | 0.166398 | ||||||||
\(428\) | 8.49242 | 0.410497 | ||||||||
\(429\) | 7.12311 | 0.343907 | ||||||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | −14.7386 | −0.709935 | −0.354968 | − | 0.934879i | \(-0.615508\pi\) | ||||
−0.354968 | + | 0.934879i | \(0.615508\pi\) | |||||||
\(432\) | 4.68466 | 0.225391 | ||||||||
\(433\) | −12.7386 | −0.612180 | −0.306090 | − | 0.952003i | \(-0.599021\pi\) | ||||
−0.306090 | + | 0.952003i | \(0.599021\pi\) | |||||||
\(434\) | 8.00000 | 0.384012 | ||||||||
\(435\) | −1.68466 | −0.0807732 | ||||||||
\(436\) | 8.10795 | 0.388300 | ||||||||
\(437\) | 3.68466 | 0.176261 | ||||||||
\(438\) | 17.3693 | 0.829938 | ||||||||
\(439\) | 21.9309 | 1.04670 | 0.523352 | − | 0.852117i | \(-0.324681\pi\) | ||||
0.523352 | + | 0.852117i | \(0.324681\pi\) | |||||||
\(440\) | −2.43845 | −0.116248 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −6.24621 | −0.297102 | ||||||||
\(443\) | −18.7386 | −0.890299 | −0.445150 | − | 0.895456i | \(-0.646850\pi\) | ||||
−0.445150 | + | 0.895456i | \(0.646850\pi\) | |||||||
\(444\) | 3.12311 | 0.148216 | ||||||||
\(445\) | −2.31534 | −0.109758 | ||||||||
\(446\) | 22.7386 | 1.07671 | ||||||||
\(447\) | −0.246211 | −0.0116454 | ||||||||
\(448\) | −5.56155 | −0.262759 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 1.56155 | 0.0736123 | ||||||||
\(451\) | 2.00000 | 0.0941763 | ||||||||
\(452\) | 3.75379 | 0.176563 | ||||||||
\(453\) | −5.12311 | −0.240704 | ||||||||
\(454\) | −40.4924 | −1.90040 | ||||||||
\(455\) | 7.12311 | 0.333936 | ||||||||
\(456\) | −6.24621 | −0.292506 | ||||||||
\(457\) | −18.3153 | −0.856756 | −0.428378 | − | 0.903600i | \(-0.640915\pi\) | ||||
−0.428378 | + | 0.903600i | \(0.640915\pi\) | |||||||
\(458\) | 16.3845 | 0.765596 | ||||||||
\(459\) | −0.561553 | −0.0262110 | ||||||||
\(460\) | −0.630683 | −0.0294058 | ||||||||
\(461\) | 32.2462 | 1.50186 | 0.750928 | − | 0.660384i | \(-0.229607\pi\) | ||||
0.750928 | + | 0.660384i | \(0.229607\pi\) | |||||||
\(462\) | 1.56155 | 0.0726500 | ||||||||
\(463\) | 27.8617 | 1.29484 | 0.647422 | − | 0.762131i | \(-0.275847\pi\) | ||||
0.647422 | + | 0.762131i | \(0.275847\pi\) | |||||||
\(464\) | −7.89205 | −0.366379 | ||||||||
\(465\) | 5.12311 | 0.237578 | ||||||||
\(466\) | −36.8769 | −1.70829 | ||||||||
\(467\) | 16.4924 | 0.763178 | 0.381589 | − | 0.924332i | \(-0.375377\pi\) | ||||
0.381589 | + | 0.924332i | \(0.375377\pi\) | |||||||
\(468\) | −3.12311 | −0.144366 | ||||||||
\(469\) | −6.87689 | −0.317545 | ||||||||
\(470\) | −8.00000 | −0.369012 | ||||||||
\(471\) | 11.4384 | 0.527056 | ||||||||
\(472\) | −25.7538 | −1.18541 | ||||||||
\(473\) | 2.56155 | 0.117780 | ||||||||
\(474\) | 16.0000 | 0.734904 | ||||||||
\(475\) | −2.56155 | −0.117532 | ||||||||
\(476\) | −0.246211 | −0.0112851 | ||||||||
\(477\) | −13.6847 | −0.626577 | ||||||||
\(478\) | 30.7386 | 1.40595 | ||||||||
\(479\) | −36.4924 | −1.66738 | −0.833691 | − | 0.552232i | \(-0.813776\pi\) | ||||
−0.833691 | + | 0.552232i | \(0.813776\pi\) | |||||||
\(480\) | 2.43845 | 0.111299 | ||||||||
\(481\) | 50.7386 | 2.31348 | ||||||||
\(482\) | −0.384472 | −0.0175122 | ||||||||
\(483\) | −1.43845 | −0.0654516 | ||||||||
\(484\) | 0.438447 | 0.0199294 | ||||||||
\(485\) | 2.80776 | 0.127494 | ||||||||
\(486\) | −1.56155 | −0.0708335 | ||||||||
\(487\) | −9.61553 | −0.435721 | −0.217861 | − | 0.975980i | \(-0.569908\pi\) | ||||
−0.217861 | + | 0.975980i | \(0.569908\pi\) | |||||||
\(488\) | 8.38447 | 0.379547 | ||||||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | 1.56155 | 0.0705438 | ||||||||
\(491\) | 33.3002 | 1.50282 | 0.751408 | − | 0.659838i | \(-0.229375\pi\) | ||||
0.751408 | + | 0.659838i | \(0.229375\pi\) | |||||||
\(492\) | −0.876894 | −0.0395335 | ||||||||
\(493\) | 0.946025 | 0.0426068 | ||||||||
\(494\) | 28.4924 | 1.28193 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 24.0000 | 1.07763 | ||||||||
\(497\) | −5.12311 | −0.229803 | ||||||||
\(498\) | 8.49242 | 0.380555 | ||||||||
\(499\) | −7.05398 | −0.315779 | −0.157890 | − | 0.987457i | \(-0.550469\pi\) | ||||
−0.157890 | + | 0.987457i | \(0.550469\pi\) | |||||||
\(500\) | 0.438447 | 0.0196080 | ||||||||
\(501\) | −2.24621 | −0.100353 | ||||||||
\(502\) | 38.2462 | 1.70701 | ||||||||
\(503\) | −40.8078 | −1.81953 | −0.909764 | − | 0.415126i | \(-0.863738\pi\) | ||||
−0.909764 | + | 0.415126i | \(0.863738\pi\) | |||||||
\(504\) | 2.43845 | 0.108617 | ||||||||
\(505\) | −12.2462 | −0.544949 | ||||||||
\(506\) | −2.24621 | −0.0998563 | ||||||||
\(507\) | −37.7386 | −1.67603 | ||||||||
\(508\) | 0.354162 | 0.0157134 | ||||||||
\(509\) | −1.19224 | −0.0528449 | −0.0264225 | − | 0.999651i | \(-0.508412\pi\) | ||||
−0.0264225 | + | 0.999651i | \(0.508412\pi\) | |||||||
\(510\) | −0.876894 | −0.0388295 | ||||||||
\(511\) | 11.1231 | 0.492057 | ||||||||
\(512\) | −11.4233 | −0.504843 | ||||||||
\(513\) | 2.56155 | 0.113095 | ||||||||
\(514\) | 14.6307 | 0.645332 | ||||||||
\(515\) | 3.68466 | 0.162365 | ||||||||
\(516\) | −1.12311 | −0.0494420 | ||||||||
\(517\) | −5.12311 | −0.225314 | ||||||||
\(518\) | 11.1231 | 0.488721 | ||||||||
\(519\) | 4.24621 | 0.186388 | ||||||||
\(520\) | 17.3693 | 0.761695 | ||||||||
\(521\) | −3.93087 | −0.172215 | −0.0861073 | − | 0.996286i | \(-0.527443\pi\) | ||||
−0.0861073 | + | 0.996286i | \(0.527443\pi\) | |||||||
\(522\) | 2.63068 | 0.115142 | ||||||||
\(523\) | −30.2462 | −1.32257 | −0.661287 | − | 0.750133i | \(-0.729990\pi\) | ||||
−0.661287 | + | 0.750133i | \(0.729990\pi\) | |||||||
\(524\) | 1.75379 | 0.0766146 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | −28.4924 | −1.24233 | ||||||||
\(527\) | −2.87689 | −0.125319 | ||||||||
\(528\) | 4.68466 | 0.203874 | ||||||||
\(529\) | −20.9309 | −0.910038 | ||||||||
\(530\) | −21.3693 | −0.928224 | ||||||||
\(531\) | 10.5616 | 0.458332 | ||||||||
\(532\) | 1.12311 | 0.0486928 | ||||||||
\(533\) | −14.2462 | −0.617072 | ||||||||
\(534\) | 3.61553 | 0.156459 | ||||||||
\(535\) | 19.3693 | 0.837409 | ||||||||
\(536\) | −16.7689 | −0.724308 | ||||||||
\(537\) | 19.3693 | 0.835848 | ||||||||
\(538\) | 2.63068 | 0.113417 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −0.438447 | −0.0188678 | ||||||||
\(541\) | −22.4924 | −0.967025 | −0.483512 | − | 0.875338i | \(-0.660639\pi\) | ||||
−0.483512 | + | 0.875338i | \(0.660639\pi\) | |||||||
\(542\) | −21.7538 | −0.934405 | ||||||||
\(543\) | 20.2462 | 0.868848 | ||||||||
\(544\) | −1.36932 | −0.0587090 | ||||||||
\(545\) | 18.4924 | 0.792128 | ||||||||
\(546\) | −11.1231 | −0.476025 | ||||||||
\(547\) | −23.0540 | −0.985717 | −0.492858 | − | 0.870110i | \(-0.664048\pi\) | ||||
−0.492858 | + | 0.870110i | \(0.664048\pi\) | |||||||
\(548\) | 4.38447 | 0.187295 | ||||||||
\(549\) | −3.43845 | −0.146749 | ||||||||
\(550\) | 1.56155 | 0.0665848 | ||||||||
\(551\) | −4.31534 | −0.183840 | ||||||||
\(552\) | −3.50758 | −0.149292 | ||||||||
\(553\) | 10.2462 | 0.435713 | ||||||||
\(554\) | −38.6307 | −1.64126 | ||||||||
\(555\) | 7.12311 | 0.302359 | ||||||||
\(556\) | −8.76894 | −0.371886 | ||||||||
\(557\) | 18.4924 | 0.783549 | 0.391775 | − | 0.920061i | \(-0.371861\pi\) | ||||
0.391775 | + | 0.920061i | \(0.371861\pi\) | |||||||
\(558\) | −8.00000 | −0.338667 | ||||||||
\(559\) | −18.2462 | −0.771733 | ||||||||
\(560\) | 4.68466 | 0.197963 | ||||||||
\(561\) | −0.561553 | −0.0237088 | ||||||||
\(562\) | 22.6307 | 0.954618 | ||||||||
\(563\) | 24.4924 | 1.03223 | 0.516116 | − | 0.856519i | \(-0.327377\pi\) | ||||
0.516116 | + | 0.856519i | \(0.327377\pi\) | |||||||
\(564\) | 2.24621 | 0.0945826 | ||||||||
\(565\) | 8.56155 | 0.360187 | ||||||||
\(566\) | 9.75379 | 0.409982 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −12.4924 | −0.524170 | ||||||||
\(569\) | −22.8078 | −0.956151 | −0.478076 | − | 0.878319i | \(-0.658666\pi\) | ||||
−0.478076 | + | 0.878319i | \(0.658666\pi\) | |||||||
\(570\) | 4.00000 | 0.167542 | ||||||||
\(571\) | −14.2462 | −0.596185 | −0.298093 | − | 0.954537i | \(-0.596350\pi\) | ||||
−0.298093 | + | 0.954537i | \(0.596350\pi\) | |||||||
\(572\) | −3.12311 | −0.130584 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.12311 | −0.130356 | ||||||||
\(575\) | −1.43845 | −0.0599874 | ||||||||
\(576\) | 5.56155 | 0.231731 | ||||||||
\(577\) | 26.9848 | 1.12339 | 0.561697 | − | 0.827343i | \(-0.310149\pi\) | ||||
0.561697 | + | 0.827343i | \(0.310149\pi\) | |||||||
\(578\) | −26.0540 | −1.08370 | ||||||||
\(579\) | −22.4924 | −0.934753 | ||||||||
\(580\) | 0.738634 | 0.0306701 | ||||||||
\(581\) | 5.43845 | 0.225625 | ||||||||
\(582\) | −4.38447 | −0.181742 | ||||||||
\(583\) | −13.6847 | −0.566761 | ||||||||
\(584\) | 27.1231 | 1.12236 | ||||||||
\(585\) | −7.12311 | −0.294504 | ||||||||
\(586\) | −40.8769 | −1.68861 | ||||||||
\(587\) | 28.9848 | 1.19633 | 0.598166 | − | 0.801372i | \(-0.295896\pi\) | ||||
0.598166 | + | 0.801372i | \(0.295896\pi\) | |||||||
\(588\) | −0.438447 | −0.0180813 | ||||||||
\(589\) | 13.1231 | 0.540728 | ||||||||
\(590\) | 16.4924 | 0.678982 | ||||||||
\(591\) | 23.1231 | 0.951157 | ||||||||
\(592\) | 33.3693 | 1.37147 | ||||||||
\(593\) | −0.246211 | −0.0101107 | −0.00505534 | − | 0.999987i | \(-0.501609\pi\) | ||||
−0.00505534 | + | 0.999987i | \(0.501609\pi\) | |||||||
\(594\) | −1.56155 | −0.0640713 | ||||||||
\(595\) | −0.561553 | −0.0230214 | ||||||||
\(596\) | 0.107951 | 0.00442183 | ||||||||
\(597\) | −20.4924 | −0.838699 | ||||||||
\(598\) | 16.0000 | 0.654289 | ||||||||
\(599\) | 0.630683 | 0.0257690 | 0.0128845 | − | 0.999917i | \(-0.495899\pi\) | ||||
0.0128845 | + | 0.999917i | \(0.495899\pi\) | |||||||
\(600\) | 2.43845 | 0.0995492 | ||||||||
\(601\) | −9.05398 | −0.369319 | −0.184660 | − | 0.982803i | \(-0.559118\pi\) | ||||
−0.184660 | + | 0.982803i | \(0.559118\pi\) | |||||||
\(602\) | −4.00000 | −0.163028 | ||||||||
\(603\) | 6.87689 | 0.280049 | ||||||||
\(604\) | 2.24621 | 0.0913970 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 19.1231 | 0.776823 | ||||||||
\(607\) | 23.3693 | 0.948531 | 0.474266 | − | 0.880382i | \(-0.342714\pi\) | ||||
0.474266 | + | 0.880382i | \(0.342714\pi\) | |||||||
\(608\) | 6.24621 | 0.253317 | ||||||||
\(609\) | 1.68466 | 0.0682658 | ||||||||
\(610\) | −5.36932 | −0.217397 | ||||||||
\(611\) | 36.4924 | 1.47633 | ||||||||
\(612\) | 0.246211 | 0.00995250 | ||||||||
\(613\) | −10.0000 | −0.403896 | −0.201948 | − | 0.979396i | \(-0.564727\pi\) | ||||
−0.201948 | + | 0.979396i | \(0.564727\pi\) | |||||||
\(614\) | 17.7538 | 0.716485 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 2.43845 | 0.0982478 | ||||||||
\(617\) | 4.24621 | 0.170946 | 0.0854730 | − | 0.996340i | \(-0.472760\pi\) | ||||
0.0854730 | + | 0.996340i | \(0.472760\pi\) | |||||||
\(618\) | −5.75379 | −0.231451 | ||||||||
\(619\) | 1.12311 | 0.0451414 | 0.0225707 | − | 0.999745i | \(-0.492815\pi\) | ||||
0.0225707 | + | 0.999745i | \(0.492815\pi\) | |||||||
\(620\) | −2.24621 | −0.0902100 | ||||||||
\(621\) | 1.43845 | 0.0577229 | ||||||||
\(622\) | −24.9848 | −1.00180 | ||||||||
\(623\) | 2.31534 | 0.0927622 | ||||||||
\(624\) | −33.3693 | −1.33584 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −3.61553 | −0.144506 | ||||||||
\(627\) | 2.56155 | 0.102299 | ||||||||
\(628\) | −5.01515 | −0.200126 | ||||||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | −1.56155 | −0.0622138 | ||||||||
\(631\) | 29.3002 | 1.16642 | 0.583211 | − | 0.812321i | \(-0.301796\pi\) | ||||
0.583211 | + | 0.812321i | \(0.301796\pi\) | |||||||
\(632\) | 24.9848 | 0.993844 | ||||||||
\(633\) | 3.36932 | 0.133918 | ||||||||
\(634\) | −35.1231 | −1.39492 | ||||||||
\(635\) | 0.807764 | 0.0320551 | ||||||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | −7.12311 | −0.282228 | ||||||||
\(638\) | 2.63068 | 0.104150 | ||||||||
\(639\) | 5.12311 | 0.202667 | ||||||||
\(640\) | 13.5616 | 0.536067 | ||||||||
\(641\) | −12.7386 | −0.503146 | −0.251573 | − | 0.967838i | \(-0.580948\pi\) | ||||
−0.251573 | + | 0.967838i | \(0.580948\pi\) | |||||||
\(642\) | −30.2462 | −1.19372 | ||||||||
\(643\) | −25.3002 | −0.997742 | −0.498871 | − | 0.866676i | \(-0.666252\pi\) | ||||
−0.498871 | + | 0.866676i | \(0.666252\pi\) | |||||||
\(644\) | 0.630683 | 0.0248524 | ||||||||
\(645\) | −2.56155 | −0.100861 | ||||||||
\(646\) | −2.24621 | −0.0883760 | ||||||||
\(647\) | −10.2462 | −0.402820 | −0.201410 | − | 0.979507i | \(-0.564552\pi\) | ||||
−0.201410 | + | 0.979507i | \(0.564552\pi\) | |||||||
\(648\) | −2.43845 | −0.0957913 | ||||||||
\(649\) | 10.5616 | 0.414577 | ||||||||
\(650\) | −11.1231 | −0.436284 | ||||||||
\(651\) | −5.12311 | −0.200790 | ||||||||
\(652\) | 8.76894 | 0.343418 | ||||||||
\(653\) | 6.17708 | 0.241728 | 0.120864 | − | 0.992669i | \(-0.461434\pi\) | ||||
0.120864 | + | 0.992669i | \(0.461434\pi\) | |||||||
\(654\) | −28.8769 | −1.12918 | ||||||||
\(655\) | 4.00000 | 0.156293 | ||||||||
\(656\) | −9.36932 | −0.365810 | ||||||||
\(657\) | −11.1231 | −0.433954 | ||||||||
\(658\) | 8.00000 | 0.311872 | ||||||||
\(659\) | 0.315342 | 0.0122840 | 0.00614198 | − | 0.999981i | \(-0.498045\pi\) | ||||
0.00614198 | + | 0.999981i | \(0.498045\pi\) | |||||||
\(660\) | −0.438447 | −0.0170665 | ||||||||
\(661\) | 10.4924 | 0.408108 | 0.204054 | − | 0.978960i | \(-0.434588\pi\) | ||||
0.204054 | + | 0.978960i | \(0.434588\pi\) | |||||||
\(662\) | −36.9848 | −1.43746 | ||||||||
\(663\) | 4.00000 | 0.155347 | ||||||||
\(664\) | 13.2614 | 0.514641 | ||||||||
\(665\) | 2.56155 | 0.0993328 | ||||||||
\(666\) | −11.1231 | −0.431012 | ||||||||
\(667\) | −2.42329 | −0.0938302 | ||||||||
\(668\) | 0.984845 | 0.0381048 | ||||||||
\(669\) | −14.5616 | −0.562982 | ||||||||
\(670\) | 10.7386 | 0.414870 | ||||||||
\(671\) | −3.43845 | −0.132740 | ||||||||
\(672\) | −2.43845 | −0.0940651 | ||||||||
\(673\) | 8.56155 | 0.330024 | 0.165012 | − | 0.986292i | \(-0.447234\pi\) | ||||
0.165012 | + | 0.986292i | \(0.447234\pi\) | |||||||
\(674\) | −14.1383 | −0.544585 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 16.5464 | 0.636400 | ||||||||
\(677\) | 16.0691 | 0.617587 | 0.308793 | − | 0.951129i | \(-0.400075\pi\) | ||||
0.308793 | + | 0.951129i | \(0.400075\pi\) | |||||||
\(678\) | −13.3693 | −0.513446 | ||||||||
\(679\) | −2.80776 | −0.107752 | ||||||||
\(680\) | −1.36932 | −0.0525109 | ||||||||
\(681\) | 25.9309 | 0.993673 | ||||||||
\(682\) | −8.00000 | −0.306336 | ||||||||
\(683\) | −40.4924 | −1.54940 | −0.774700 | − | 0.632329i | \(-0.782099\pi\) | ||||
−0.774700 | + | 0.632329i | \(0.782099\pi\) | |||||||
\(684\) | −1.12311 | −0.0429430 | ||||||||
\(685\) | 10.0000 | 0.382080 | ||||||||
\(686\) | −1.56155 | −0.0596204 | ||||||||
\(687\) | −10.4924 | −0.400311 | ||||||||
\(688\) | −12.0000 | −0.457496 | ||||||||
\(689\) | 97.4773 | 3.71359 | ||||||||
\(690\) | 2.24621 | 0.0855118 | ||||||||
\(691\) | 30.8769 | 1.17461 | 0.587306 | − | 0.809365i | \(-0.300188\pi\) | ||||
0.587306 | + | 0.809365i | \(0.300188\pi\) | |||||||
\(692\) | −1.86174 | −0.0707727 | ||||||||
\(693\) | −1.00000 | −0.0379869 | ||||||||
\(694\) | −22.2462 | −0.844455 | ||||||||
\(695\) | −20.0000 | −0.758643 | ||||||||
\(696\) | 4.10795 | 0.155711 | ||||||||
\(697\) | 1.12311 | 0.0425407 | ||||||||
\(698\) | −14.3542 | −0.543313 | ||||||||
\(699\) | 23.6155 | 0.893221 | ||||||||
\(700\) | −0.438447 | −0.0165717 | ||||||||
\(701\) | 26.3153 | 0.993917 | 0.496958 | − | 0.867774i | \(-0.334450\pi\) | ||||
0.496958 | + | 0.867774i | \(0.334450\pi\) | |||||||
\(702\) | 11.1231 | 0.419815 | ||||||||
\(703\) | 18.2462 | 0.688169 | ||||||||
\(704\) | 5.56155 | 0.209609 | ||||||||
\(705\) | 5.12311 | 0.192947 | ||||||||
\(706\) | −46.8466 | −1.76309 | ||||||||
\(707\) | 12.2462 | 0.460566 | ||||||||
\(708\) | −4.63068 | −0.174032 | ||||||||
\(709\) | −42.8078 | −1.60768 | −0.803840 | − | 0.594846i | \(-0.797213\pi\) | ||||
−0.803840 | + | 0.594846i | \(0.797213\pi\) | |||||||
\(710\) | 8.00000 | 0.300235 | ||||||||
\(711\) | −10.2462 | −0.384263 | ||||||||
\(712\) | 5.64584 | 0.211587 | ||||||||
\(713\) | 7.36932 | 0.275983 | ||||||||
\(714\) | 0.876894 | 0.0328169 | ||||||||
\(715\) | −7.12311 | −0.266389 | ||||||||
\(716\) | −8.49242 | −0.317377 | ||||||||
\(717\) | −19.6847 | −0.735137 | ||||||||
\(718\) | −6.73863 | −0.251484 | ||||||||
\(719\) | 23.5464 | 0.878132 | 0.439066 | − | 0.898455i | \(-0.355309\pi\) | ||||
0.439066 | + | 0.898455i | \(0.355309\pi\) | |||||||
\(720\) | −4.68466 | −0.174587 | ||||||||
\(721\) | −3.68466 | −0.137224 | ||||||||
\(722\) | −19.4233 | −0.722860 | ||||||||
\(723\) | 0.246211 | 0.00915669 | ||||||||
\(724\) | −8.87689 | −0.329907 | ||||||||
\(725\) | 1.68466 | 0.0625666 | ||||||||
\(726\) | −1.56155 | −0.0579547 | ||||||||
\(727\) | 22.5616 | 0.836762 | 0.418381 | − | 0.908272i | \(-0.362598\pi\) | ||||
0.418381 | + | 0.908272i | \(0.362598\pi\) | |||||||
\(728\) | −17.3693 | −0.643750 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −17.3693 | −0.642867 | ||||||||
\(731\) | 1.43845 | 0.0532029 | ||||||||
\(732\) | 1.50758 | 0.0557217 | ||||||||
\(733\) | −52.2462 | −1.92976 | −0.964879 | − | 0.262695i | \(-0.915389\pi\) | ||||
−0.964879 | + | 0.262695i | \(0.915389\pi\) | |||||||
\(734\) | 27.2311 | 1.00512 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 3.50758 | 0.129291 | ||||||||
\(737\) | 6.87689 | 0.253314 | ||||||||
\(738\) | 3.12311 | 0.114963 | ||||||||
\(739\) | −4.63068 | −0.170342 | −0.0851712 | − | 0.996366i | \(-0.527144\pi\) | ||||
−0.0851712 | + | 0.996366i | \(0.527144\pi\) | |||||||
\(740\) | −3.12311 | −0.114808 | ||||||||
\(741\) | −18.2462 | −0.670291 | ||||||||
\(742\) | 21.3693 | 0.784492 | ||||||||
\(743\) | 6.38447 | 0.234224 | 0.117112 | − | 0.993119i | \(-0.462636\pi\) | ||||
0.117112 | + | 0.993119i | \(0.462636\pi\) | |||||||
\(744\) | −12.4924 | −0.457994 | ||||||||
\(745\) | 0.246211 | 0.00902048 | ||||||||
\(746\) | −0.876894 | −0.0321054 | ||||||||
\(747\) | −5.43845 | −0.198982 | ||||||||
\(748\) | 0.246211 | 0.00900237 | ||||||||
\(749\) | −19.3693 | −0.707739 | ||||||||
\(750\) | −1.56155 | −0.0570198 | ||||||||
\(751\) | −3.68466 | −0.134455 | −0.0672275 | − | 0.997738i | \(-0.521415\pi\) | ||||
−0.0672275 | + | 0.997738i | \(0.521415\pi\) | |||||||
\(752\) | 24.0000 | 0.875190 | ||||||||
\(753\) | −24.4924 | −0.892553 | ||||||||
\(754\) | −18.7386 | −0.682421 | ||||||||
\(755\) | 5.12311 | 0.186449 | ||||||||
\(756\) | 0.438447 | 0.0159462 | ||||||||
\(757\) | 1.50758 | 0.0547938 | 0.0273969 | − | 0.999625i | \(-0.491278\pi\) | ||||
0.0273969 | + | 0.999625i | \(0.491278\pi\) | |||||||
\(758\) | 36.0000 | 1.30758 | ||||||||
\(759\) | 1.43845 | 0.0522123 | ||||||||
\(760\) | 6.24621 | 0.226574 | ||||||||
\(761\) | −3.75379 | −0.136075 | −0.0680374 | − | 0.997683i | \(-0.521674\pi\) | ||||
−0.0680374 | + | 0.997683i | \(0.521674\pi\) | |||||||
\(762\) | −1.26137 | −0.0456945 | ||||||||
\(763\) | −18.4924 | −0.669471 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.561553 | 0.0203030 | ||||||||
\(766\) | −19.5076 | −0.704837 | ||||||||
\(767\) | −75.2311 | −2.71644 | ||||||||
\(768\) | −10.0540 | −0.362792 | ||||||||
\(769\) | 1.82292 | 0.0657361 | 0.0328681 | − | 0.999460i | \(-0.489536\pi\) | ||||
0.0328681 | + | 0.999460i | \(0.489536\pi\) | |||||||
\(770\) | −1.56155 | −0.0562745 | ||||||||
\(771\) | −9.36932 | −0.337428 | ||||||||
\(772\) | 9.86174 | 0.354932 | ||||||||
\(773\) | −24.7386 | −0.889787 | −0.444893 | − | 0.895584i | \(-0.646758\pi\) | ||||
−0.444893 | + | 0.895584i | \(0.646758\pi\) | |||||||
\(774\) | 4.00000 | 0.143777 | ||||||||
\(775\) | −5.12311 | −0.184027 | ||||||||
\(776\) | −6.84658 | −0.245778 | ||||||||
\(777\) | −7.12311 | −0.255540 | ||||||||
\(778\) | −34.1383 | −1.22392 | ||||||||
\(779\) | −5.12311 | −0.183554 | ||||||||
\(780\) | 3.12311 | 0.111825 | ||||||||
\(781\) | 5.12311 | 0.183319 | ||||||||
\(782\) | −1.26137 | −0.0451064 | ||||||||
\(783\) | −1.68466 | −0.0602048 | ||||||||
\(784\) | −4.68466 | −0.167309 | ||||||||
\(785\) | −11.4384 | −0.408256 | ||||||||
\(786\) | −6.24621 | −0.222795 | ||||||||
\(787\) | −32.4924 | −1.15823 | −0.579115 | − | 0.815246i | \(-0.696602\pi\) | ||||
−0.579115 | + | 0.815246i | \(0.696602\pi\) | |||||||
\(788\) | −10.1383 | −0.361161 | ||||||||
\(789\) | 18.2462 | 0.649582 | ||||||||
\(790\) | −16.0000 | −0.569254 | ||||||||
\(791\) | −8.56155 | −0.304414 | ||||||||
\(792\) | −2.43845 | −0.0866464 | ||||||||
\(793\) | 24.4924 | 0.869751 | ||||||||
\(794\) | 21.8617 | 0.775844 | ||||||||
\(795\) | 13.6847 | 0.485345 | ||||||||
\(796\) | 8.98485 | 0.318459 | ||||||||
\(797\) | 12.7386 | 0.451226 | 0.225613 | − | 0.974217i | \(-0.427562\pi\) | ||||
0.225613 | + | 0.974217i | \(0.427562\pi\) | |||||||
\(798\) | −4.00000 | −0.141598 | ||||||||
\(799\) | −2.87689 | −0.101777 | ||||||||
\(800\) | −2.43845 | −0.0862121 | ||||||||
\(801\) | −2.31534 | −0.0818086 | ||||||||
\(802\) | −53.8617 | −1.90192 | ||||||||
\(803\) | −11.1231 | −0.392526 | ||||||||
\(804\) | −3.01515 | −0.106336 | ||||||||
\(805\) | 1.43845 | 0.0506986 | ||||||||
\(806\) | 56.9848 | 2.00721 | ||||||||
\(807\) | −1.68466 | −0.0593028 | ||||||||
\(808\) | 29.8617 | 1.05053 | ||||||||
\(809\) | 26.0000 | 0.914111 | 0.457056 | − | 0.889438i | \(-0.348904\pi\) | ||||
0.457056 | + | 0.889438i | \(0.348904\pi\) | |||||||
\(810\) | 1.56155 | 0.0548674 | ||||||||
\(811\) | −4.00000 | −0.140459 | −0.0702295 | − | 0.997531i | \(-0.522373\pi\) | ||||
−0.0702295 | + | 0.997531i | \(0.522373\pi\) | |||||||
\(812\) | −0.738634 | −0.0259210 | ||||||||
\(813\) | 13.9309 | 0.488577 | ||||||||
\(814\) | −11.1231 | −0.389865 | ||||||||
\(815\) | 20.0000 | 0.700569 | ||||||||
\(816\) | 2.63068 | 0.0920923 | ||||||||
\(817\) | −6.56155 | −0.229560 | ||||||||
\(818\) | −12.8769 | −0.450230 | ||||||||
\(819\) | 7.12311 | 0.248901 | ||||||||
\(820\) | 0.876894 | 0.0306225 | ||||||||
\(821\) | 37.5464 | 1.31038 | 0.655189 | − | 0.755465i | \(-0.272589\pi\) | ||||
0.655189 | + | 0.755465i | \(0.272589\pi\) | |||||||
\(822\) | −15.6155 | −0.544654 | ||||||||
\(823\) | −22.7386 | −0.792619 | −0.396309 | − | 0.918117i | \(-0.629709\pi\) | ||||
−0.396309 | + | 0.918117i | \(0.629709\pi\) | |||||||
\(824\) | −8.98485 | −0.313002 | ||||||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | −16.4924 | −0.573845 | ||||||||
\(827\) | −2.73863 | −0.0952316 | −0.0476158 | − | 0.998866i | \(-0.515162\pi\) | ||||
−0.0476158 | + | 0.998866i | \(0.515162\pi\) | |||||||
\(828\) | −0.630683 | −0.0219178 | ||||||||
\(829\) | 33.2311 | 1.15416 | 0.577081 | − | 0.816687i | \(-0.304192\pi\) | ||||
0.577081 | + | 0.816687i | \(0.304192\pi\) | |||||||
\(830\) | −8.49242 | −0.294776 | ||||||||
\(831\) | 24.7386 | 0.858174 | ||||||||
\(832\) | −39.6155 | −1.37342 | ||||||||
\(833\) | 0.561553 | 0.0194567 | ||||||||
\(834\) | 31.2311 | 1.08144 | ||||||||
\(835\) | 2.24621 | 0.0777333 | ||||||||
\(836\) | −1.12311 | −0.0388434 | ||||||||
\(837\) | 5.12311 | 0.177080 | ||||||||
\(838\) | 17.4773 | 0.603742 | ||||||||
\(839\) | −34.4233 | −1.18842 | −0.594212 | − | 0.804308i | \(-0.702536\pi\) | ||||
−0.594212 | + | 0.804308i | \(0.702536\pi\) | |||||||
\(840\) | −2.43845 | −0.0841344 | ||||||||
\(841\) | −26.1619 | −0.902135 | ||||||||
\(842\) | 47.1231 | 1.62397 | ||||||||
\(843\) | −14.4924 | −0.499146 | ||||||||
\(844\) | −1.47727 | −0.0508496 | ||||||||
\(845\) | 37.7386 | 1.29825 | ||||||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 64.1080 | 2.20148 | ||||||||
\(849\) | −6.24621 | −0.214369 | ||||||||
\(850\) | 0.876894 | 0.0300772 | ||||||||
\(851\) | 10.2462 | 0.351236 | ||||||||
\(852\) | −2.24621 | −0.0769539 | ||||||||
\(853\) | 2.49242 | 0.0853389 | 0.0426695 | − | 0.999089i | \(-0.486414\pi\) | ||||
0.0426695 | + | 0.999089i | \(0.486414\pi\) | |||||||
\(854\) | 5.36932 | 0.183734 | ||||||||
\(855\) | −2.56155 | −0.0876033 | ||||||||
\(856\) | −47.2311 | −1.61432 | ||||||||
\(857\) | 13.5076 | 0.461410 | 0.230705 | − | 0.973024i | \(-0.425897\pi\) | ||||
0.230705 | + | 0.973024i | \(0.425897\pi\) | |||||||
\(858\) | 11.1231 | 0.379737 | ||||||||
\(859\) | −41.1231 | −1.40310 | −0.701551 | − | 0.712619i | \(-0.747509\pi\) | ||||
−0.701551 | + | 0.712619i | \(0.747509\pi\) | |||||||
\(860\) | 1.12311 | 0.0382976 | ||||||||
\(861\) | 2.00000 | 0.0681598 | ||||||||
\(862\) | −23.0152 | −0.783899 | ||||||||
\(863\) | 31.5464 | 1.07385 | 0.536926 | − | 0.843629i | \(-0.319585\pi\) | ||||
0.536926 | + | 0.843629i | \(0.319585\pi\) | |||||||
\(864\) | 2.43845 | 0.0829577 | ||||||||
\(865\) | −4.24621 | −0.144376 | ||||||||
\(866\) | −19.8920 | −0.675959 | ||||||||
\(867\) | 16.6847 | 0.566641 | ||||||||
\(868\) | 2.24621 | 0.0762414 | ||||||||
\(869\) | −10.2462 | −0.347579 | ||||||||
\(870\) | −2.63068 | −0.0891885 | ||||||||
\(871\) | −48.9848 | −1.65979 | ||||||||
\(872\) | −45.0928 | −1.52703 | ||||||||
\(873\) | 2.80776 | 0.0950284 | ||||||||
\(874\) | 5.75379 | 0.194625 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 4.87689 | 0.164775 | ||||||||
\(877\) | −46.6695 | −1.57592 | −0.787959 | − | 0.615728i | \(-0.788862\pi\) | ||||
−0.787959 | + | 0.615728i | \(0.788862\pi\) | |||||||
\(878\) | 34.2462 | 1.15575 | ||||||||
\(879\) | 26.1771 | 0.882931 | ||||||||
\(880\) | −4.68466 | −0.157920 | ||||||||
\(881\) | 31.9309 | 1.07578 | 0.537889 | − | 0.843016i | \(-0.319222\pi\) | ||||
0.537889 | + | 0.843016i | \(0.319222\pi\) | |||||||
\(882\) | 1.56155 | 0.0525802 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | −1.75379 | −0.0589863 | ||||||||
\(885\) | −10.5616 | −0.355023 | ||||||||
\(886\) | −29.2614 | −0.983055 | ||||||||
\(887\) | −33.4384 | −1.12275 | −0.561377 | − | 0.827560i | \(-0.689728\pi\) | ||||
−0.561377 | + | 0.827560i | \(0.689728\pi\) | |||||||
\(888\) | −17.3693 | −0.582876 | ||||||||
\(889\) | −0.807764 | −0.0270915 | ||||||||
\(890\) | −3.61553 | −0.121193 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 6.38447 | 0.213768 | ||||||||
\(893\) | 13.1231 | 0.439148 | ||||||||
\(894\) | −0.384472 | −0.0128587 | ||||||||
\(895\) | −19.3693 | −0.647445 | ||||||||
\(896\) | −13.5616 | −0.453060 | ||||||||
\(897\) | −10.2462 | −0.342111 | ||||||||
\(898\) | 3.12311 | 0.104219 | ||||||||
\(899\) | −8.63068 | −0.287849 | ||||||||
\(900\) | 0.438447 | 0.0146149 | ||||||||
\(901\) | −7.68466 | −0.256013 | ||||||||
\(902\) | 3.12311 | 0.103988 | ||||||||
\(903\) | 2.56155 | 0.0852431 | ||||||||
\(904\) | −20.8769 | −0.694355 | ||||||||
\(905\) | −20.2462 | −0.673007 | ||||||||
\(906\) | −8.00000 | −0.265782 | ||||||||
\(907\) | 57.4773 | 1.90850 | 0.954251 | − | 0.299008i | \(-0.0966557\pi\) | ||||
0.954251 | + | 0.299008i | \(0.0966557\pi\) | |||||||
\(908\) | −11.3693 | −0.377304 | ||||||||
\(909\) | −12.2462 | −0.406181 | ||||||||
\(910\) | 11.1231 | 0.368727 | ||||||||
\(911\) | 20.4924 | 0.678944 | 0.339472 | − | 0.940616i | \(-0.389752\pi\) | ||||
0.339472 | + | 0.940616i | \(0.389752\pi\) | |||||||
\(912\) | −12.0000 | −0.397360 | ||||||||
\(913\) | −5.43845 | −0.179986 | ||||||||
\(914\) | −28.6004 | −0.946016 | ||||||||
\(915\) | 3.43845 | 0.113672 | ||||||||
\(916\) | 4.60037 | 0.152001 | ||||||||
\(917\) | −4.00000 | −0.132092 | ||||||||
\(918\) | −0.876894 | −0.0289418 | ||||||||
\(919\) | −19.8617 | −0.655178 | −0.327589 | − | 0.944820i | \(-0.606236\pi\) | ||||
−0.327589 | + | 0.944820i | \(0.606236\pi\) | |||||||
\(920\) | 3.50758 | 0.115641 | ||||||||
\(921\) | −11.3693 | −0.374632 | ||||||||
\(922\) | 50.3542 | 1.65833 | ||||||||
\(923\) | −36.4924 | −1.20116 | ||||||||
\(924\) | 0.438447 | 0.0144239 | ||||||||
\(925\) | −7.12311 | −0.234206 | ||||||||
\(926\) | 43.5076 | 1.42975 | ||||||||
\(927\) | 3.68466 | 0.121020 | ||||||||
\(928\) | −4.10795 | −0.134850 | ||||||||
\(929\) | −22.9848 | −0.754108 | −0.377054 | − | 0.926191i | \(-0.623063\pi\) | ||||
−0.377054 | + | 0.926191i | \(0.623063\pi\) | |||||||
\(930\) | 8.00000 | 0.262330 | ||||||||
\(931\) | −2.56155 | −0.0839515 | ||||||||
\(932\) | −10.3542 | −0.339162 | ||||||||
\(933\) | 16.0000 | 0.523816 | ||||||||
\(934\) | 25.7538 | 0.842690 | ||||||||
\(935\) | 0.561553 | 0.0183647 | ||||||||
\(936\) | 17.3693 | 0.567734 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | −10.7386 | −0.350629 | ||||||||
\(939\) | 2.31534 | 0.0755583 | ||||||||
\(940\) | −2.24621 | −0.0732633 | ||||||||
\(941\) | 7.61553 | 0.248259 | 0.124130 | − | 0.992266i | \(-0.460386\pi\) | ||||
0.124130 | + | 0.992266i | \(0.460386\pi\) | |||||||
\(942\) | 17.8617 | 0.581967 | ||||||||
\(943\) | −2.87689 | −0.0936846 | ||||||||
\(944\) | −49.4773 | −1.61035 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 31.0540 | 1.00912 | 0.504559 | − | 0.863377i | \(-0.331655\pi\) | ||||
0.504559 | + | 0.863377i | \(0.331655\pi\) | |||||||
\(948\) | 4.49242 | 0.145907 | ||||||||
\(949\) | 79.2311 | 2.57195 | ||||||||
\(950\) | −4.00000 | −0.129777 | ||||||||
\(951\) | 22.4924 | 0.729367 | ||||||||
\(952\) | 1.36932 | 0.0443798 | ||||||||
\(953\) | 15.7538 | 0.510315 | 0.255158 | − | 0.966899i | \(-0.417873\pi\) | ||||
0.255158 | + | 0.966899i | \(0.417873\pi\) | |||||||
\(954\) | −21.3693 | −0.691857 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.63068 | 0.279136 | ||||||||
\(957\) | −1.68466 | −0.0544573 | ||||||||
\(958\) | −56.9848 | −1.84110 | ||||||||
\(959\) | −10.0000 | −0.322917 | ||||||||
\(960\) | −5.56155 | −0.179498 | ||||||||
\(961\) | −4.75379 | −0.153348 | ||||||||
\(962\) | 79.2311 | 2.55451 | ||||||||
\(963\) | 19.3693 | 0.624168 | ||||||||
\(964\) | −0.107951 | −0.00347686 | ||||||||
\(965\) | 22.4924 | 0.724057 | ||||||||
\(966\) | −2.24621 | −0.0722707 | ||||||||
\(967\) | 30.5616 | 0.982793 | 0.491397 | − | 0.870936i | \(-0.336487\pi\) | ||||
0.491397 | + | 0.870936i | \(0.336487\pi\) | |||||||
\(968\) | −2.43845 | −0.0783747 | ||||||||
\(969\) | 1.43845 | 0.0462096 | ||||||||
\(970\) | 4.38447 | 0.140777 | ||||||||
\(971\) | 4.80776 | 0.154288 | 0.0771442 | − | 0.997020i | \(-0.475420\pi\) | ||||
0.0771442 | + | 0.997020i | \(0.475420\pi\) | |||||||
\(972\) | −0.438447 | −0.0140632 | ||||||||
\(973\) | 20.0000 | 0.641171 | ||||||||
\(974\) | −15.0152 | −0.481117 | ||||||||
\(975\) | 7.12311 | 0.228122 | ||||||||
\(976\) | 16.1080 | 0.515603 | ||||||||
\(977\) | −6.17708 | −0.197622 | −0.0988112 | − | 0.995106i | \(-0.531504\pi\) | ||||
−0.0988112 | + | 0.995106i | \(0.531504\pi\) | |||||||
\(978\) | −31.2311 | −0.998659 | ||||||||
\(979\) | −2.31534 | −0.0739986 | ||||||||
\(980\) | 0.438447 | 0.0140057 | ||||||||
\(981\) | 18.4924 | 0.590418 | ||||||||
\(982\) | 52.0000 | 1.65939 | ||||||||
\(983\) | 49.6155 | 1.58249 | 0.791245 | − | 0.611500i | \(-0.209433\pi\) | ||||
0.791245 | + | 0.611500i | \(0.209433\pi\) | |||||||
\(984\) | 4.87689 | 0.155470 | ||||||||
\(985\) | −23.1231 | −0.736763 | ||||||||
\(986\) | 1.47727 | 0.0470458 | ||||||||
\(987\) | −5.12311 | −0.163070 | ||||||||
\(988\) | 8.00000 | 0.254514 | ||||||||
\(989\) | −3.68466 | −0.117165 | ||||||||
\(990\) | 1.56155 | 0.0496294 | ||||||||
\(991\) | 57.4384 | 1.82459 | 0.912296 | − | 0.409531i | \(-0.134308\pi\) | ||||
0.912296 | + | 0.409531i | \(0.134308\pi\) | |||||||
\(992\) | 12.4924 | 0.396635 | ||||||||
\(993\) | 23.6847 | 0.751610 | ||||||||
\(994\) | −8.00000 | −0.253745 | ||||||||
\(995\) | 20.4924 | 0.649653 | ||||||||
\(996\) | 2.38447 | 0.0755549 | ||||||||
\(997\) | −2.00000 | −0.0633406 | −0.0316703 | − | 0.999498i | \(-0.510083\pi\) | ||||
−0.0316703 | + | 0.999498i | \(0.510083\pi\) | |||||||
\(998\) | −11.0152 | −0.348679 | ||||||||
\(999\) | 7.12311 | 0.225365 |
(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 | 1155.2.a.o.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 3465.2.a.z.1.1 | 2 | |||
5.4 | even | 2 | 5775.2.a.bm.1.1 | 2 | |||
7.6 | odd | 2 | 8085.2.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.o.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3465.2.a.z.1.1 | 2 | 3.2 | odd | 2 | |||
5775.2.a.bm.1.1 | 2 | 5.4 | even | 2 | |||
8085.2.a.bb.1.2 | 2 | 7.6 | odd | 2 |