Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1518129839\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.561553 | −0.212247 | −0.106124 | − | 0.994353i | \(-0.533844\pi\) | ||||
−0.106124 | + | 0.994353i | \(0.533844\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | −2.56155 | −0.772337 | −0.386169 | − | 0.922428i | \(-0.626202\pi\) | ||||
−0.386169 | + | 0.922428i | \(0.626202\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.561553 | 0.150081 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.43845 | 0.833946 | 0.416973 | − | 0.908919i | \(-0.363091\pi\) | ||||
0.416973 | + | 0.908919i | \(0.363091\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0.561553 | 0.122541 | ||||||||
\(22\) | 2.56155 | 0.546125 | ||||||||
\(23\) | 3.12311 | 0.651213 | 0.325606 | − | 0.945505i | \(-0.394432\pi\) | ||||
0.325606 | + | 0.945505i | \(0.394432\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.561553 | −0.106124 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | −2.00000 | −0.365148 | ||||||||
\(31\) | 1.12311 | 0.201716 | 0.100858 | − | 0.994901i | \(-0.467841\pi\) | ||||
0.100858 | + | 0.994901i | \(0.467841\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.56155 | 0.445909 | ||||||||
\(34\) | −3.43845 | −0.589689 | ||||||||
\(35\) | 1.12311 | 0.189839 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.12311 | −1.49983 | −0.749915 | − | 0.661535i | \(-0.769905\pi\) | ||||
−0.749915 | + | 0.661535i | \(0.769905\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 2.00000 | 0.316228 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | −0.561553 | −0.0866495 | ||||||||
\(43\) | 1.12311 | 0.171272 | 0.0856360 | − | 0.996326i | \(-0.472708\pi\) | ||||
0.0856360 | + | 0.996326i | \(0.472708\pi\) | |||||||
\(44\) | −2.56155 | −0.386169 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | −3.12311 | −0.460477 | ||||||||
\(47\) | −10.2462 | −1.49456 | −0.747282 | − | 0.664507i | \(-0.768641\pi\) | ||||
−0.747282 | + | 0.664507i | \(0.768641\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.68466 | −0.954951 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −3.43845 | −0.481479 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | 6.56155 | 0.901299 | 0.450649 | − | 0.892701i | \(-0.351193\pi\) | ||||
0.450649 | + | 0.892701i | \(0.351193\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 5.12311 | 0.690799 | ||||||||
\(56\) | 0.561553 | 0.0750407 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 2.00000 | 0.258199 | ||||||||
\(61\) | 11.1231 | 1.42417 | 0.712084 | − | 0.702094i | \(-0.247752\pi\) | ||||
0.712084 | + | 0.702094i | \(0.247752\pi\) | |||||||
\(62\) | −1.12311 | −0.142635 | ||||||||
\(63\) | −0.561553 | −0.0707490 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | −2.56155 | −0.315305 | ||||||||
\(67\) | 11.6847 | 1.42751 | 0.713754 | − | 0.700396i | \(-0.246993\pi\) | ||||
0.713754 | + | 0.700396i | \(0.246993\pi\) | |||||||
\(68\) | 3.43845 | 0.416973 | ||||||||
\(69\) | −3.12311 | −0.375978 | ||||||||
\(70\) | −1.12311 | −0.134237 | ||||||||
\(71\) | 2.24621 | 0.266576 | 0.133288 | − | 0.991077i | \(-0.457446\pi\) | ||||
0.133288 | + | 0.991077i | \(0.457446\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 3.68466 | 0.431257 | 0.215628 | − | 0.976476i | \(-0.430820\pi\) | ||||
0.215628 | + | 0.976476i | \(0.430820\pi\) | |||||||
\(74\) | 9.12311 | 1.06054 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 1.43845 | 0.163926 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | 7.36932 | 0.829113 | 0.414556 | − | 0.910024i | \(-0.363937\pi\) | ||||
0.414556 | + | 0.910024i | \(0.363937\pi\) | |||||||
\(80\) | −2.00000 | −0.223607 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.00000 | −0.220863 | ||||||||
\(83\) | 11.3693 | 1.24794 | 0.623972 | − | 0.781446i | \(-0.285518\pi\) | ||||
0.623972 | + | 0.781446i | \(0.285518\pi\) | |||||||
\(84\) | 0.561553 | 0.0612704 | ||||||||
\(85\) | −6.87689 | −0.745904 | ||||||||
\(86\) | −1.12311 | −0.121108 | ||||||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 2.56155 | 0.273062 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 0.561553 | 0.0588667 | ||||||||
\(92\) | 3.12311 | 0.325606 | ||||||||
\(93\) | −1.12311 | −0.116461 | ||||||||
\(94\) | 10.2462 | 1.05682 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 4.24621 | 0.431137 | 0.215569 | − | 0.976489i | \(-0.430839\pi\) | ||||
0.215569 | + | 0.976489i | \(0.430839\pi\) | |||||||
\(98\) | 6.68466 | 0.675252 | ||||||||
\(99\) | −2.56155 | −0.257446 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −3.68466 | −0.366637 | −0.183319 | − | 0.983054i | \(-0.558684\pi\) | ||||
−0.183319 | + | 0.983054i | \(0.558684\pi\) | |||||||
\(102\) | 3.43845 | 0.340457 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | −1.12311 | −0.109604 | ||||||||
\(106\) | −6.56155 | −0.637314 | ||||||||
\(107\) | 8.56155 | 0.827677 | 0.413838 | − | 0.910350i | \(-0.364188\pi\) | ||||
0.413838 | + | 0.910350i | \(0.364188\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −6.24621 | −0.598279 | −0.299139 | − | 0.954209i | \(-0.596700\pi\) | ||||
−0.299139 | + | 0.954209i | \(0.596700\pi\) | |||||||
\(110\) | −5.12311 | −0.488469 | ||||||||
\(111\) | 9.12311 | 0.865927 | ||||||||
\(112\) | −0.561553 | −0.0530618 | ||||||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | −2.00000 | −0.187317 | ||||||||
\(115\) | −6.24621 | −0.582462 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 8.00000 | 0.736460 | ||||||||
\(119\) | −1.93087 | −0.177003 | ||||||||
\(120\) | −2.00000 | −0.182574 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | −11.1231 | −1.00704 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 1.12311 | 0.100858 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0.561553 | 0.0500271 | ||||||||
\(127\) | −11.6847 | −1.03685 | −0.518423 | − | 0.855124i | \(-0.673481\pi\) | ||||
−0.518423 | + | 0.855124i | \(0.673481\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.12311 | −0.0988839 | ||||||||
\(130\) | −2.00000 | −0.175412 | ||||||||
\(131\) | 21.3693 | 1.86705 | 0.933523 | − | 0.358518i | \(-0.116718\pi\) | ||||
0.933523 | + | 0.358518i | \(0.116718\pi\) | |||||||
\(132\) | 2.56155 | 0.222955 | ||||||||
\(133\) | 1.12311 | 0.0973856 | ||||||||
\(134\) | −11.6847 | −1.00940 | ||||||||
\(135\) | 2.00000 | 0.172133 | ||||||||
\(136\) | −3.43845 | −0.294844 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 3.12311 | 0.265856 | ||||||||
\(139\) | −12.8078 | −1.08634 | −0.543170 | − | 0.839623i | \(-0.682776\pi\) | ||||
−0.543170 | + | 0.839623i | \(0.682776\pi\) | |||||||
\(140\) | 1.12311 | 0.0949197 | ||||||||
\(141\) | 10.2462 | 0.862887 | ||||||||
\(142\) | −2.24621 | −0.188498 | ||||||||
\(143\) | 2.56155 | 0.214208 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −12.0000 | −0.996546 | ||||||||
\(146\) | −3.68466 | −0.304945 | ||||||||
\(147\) | 6.68466 | 0.551341 | ||||||||
\(148\) | −9.12311 | −0.749915 | ||||||||
\(149\) | 6.31534 | 0.517373 | 0.258686 | − | 0.965961i | \(-0.416710\pi\) | ||||
0.258686 | + | 0.965961i | \(0.416710\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | −7.36932 | −0.599707 | −0.299853 | − | 0.953985i | \(-0.596938\pi\) | ||||
−0.299853 | + | 0.953985i | \(0.596938\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | 3.43845 | 0.277982 | ||||||||
\(154\) | −1.43845 | −0.115913 | ||||||||
\(155\) | −2.24621 | −0.180420 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −6.80776 | −0.543319 | −0.271659 | − | 0.962393i | \(-0.587572\pi\) | ||||
−0.271659 | + | 0.962393i | \(0.587572\pi\) | |||||||
\(158\) | −7.36932 | −0.586271 | ||||||||
\(159\) | −6.56155 | −0.520365 | ||||||||
\(160\) | 2.00000 | 0.158114 | ||||||||
\(161\) | −1.75379 | −0.138218 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −22.4924 | −1.76174 | −0.880871 | − | 0.473356i | \(-0.843042\pi\) | ||||
−0.880871 | + | 0.473356i | \(0.843042\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | −5.12311 | −0.398833 | ||||||||
\(166\) | −11.3693 | −0.882430 | ||||||||
\(167\) | −3.19224 | −0.247023 | −0.123511 | − | 0.992343i | \(-0.539416\pi\) | ||||
−0.123511 | + | 0.992343i | \(0.539416\pi\) | |||||||
\(168\) | −0.561553 | −0.0433247 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 6.87689 | 0.527434 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 1.12311 | 0.0856360 | ||||||||
\(173\) | 20.8078 | 1.58199 | 0.790993 | − | 0.611826i | \(-0.209565\pi\) | ||||
0.790993 | + | 0.611826i | \(0.209565\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | 0.561553 | 0.0424494 | ||||||||
\(176\) | −2.56155 | −0.193084 | ||||||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | −2.00000 | −0.149906 | ||||||||
\(179\) | −10.8078 | −0.807810 | −0.403905 | − | 0.914801i | \(-0.632347\pi\) | ||||
−0.403905 | + | 0.914801i | \(0.632347\pi\) | |||||||
\(180\) | −2.00000 | −0.149071 | ||||||||
\(181\) | 15.9309 | 1.18413 | 0.592066 | − | 0.805889i | \(-0.298312\pi\) | ||||
0.592066 | + | 0.805889i | \(0.298312\pi\) | |||||||
\(182\) | −0.561553 | −0.0416251 | ||||||||
\(183\) | −11.1231 | −0.822244 | ||||||||
\(184\) | −3.12311 | −0.230238 | ||||||||
\(185\) | 18.2462 | 1.34149 | ||||||||
\(186\) | 1.12311 | 0.0823501 | ||||||||
\(187\) | −8.80776 | −0.644087 | ||||||||
\(188\) | −10.2462 | −0.747282 | ||||||||
\(189\) | 0.561553 | 0.0408470 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | −3.68466 | −0.266613 | −0.133306 | − | 0.991075i | \(-0.542559\pi\) | ||||
−0.133306 | + | 0.991075i | \(0.542559\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −0.630683 | −0.0453976 | −0.0226988 | − | 0.999742i | \(-0.507226\pi\) | ||||
−0.0226988 | + | 0.999742i | \(0.507226\pi\) | |||||||
\(194\) | −4.24621 | −0.304860 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | −6.68466 | −0.477476 | ||||||||
\(197\) | 18.4924 | 1.31753 | 0.658765 | − | 0.752349i | \(-0.271079\pi\) | ||||
0.658765 | + | 0.752349i | \(0.271079\pi\) | |||||||
\(198\) | 2.56155 | 0.182042 | ||||||||
\(199\) | −19.6847 | −1.39541 | −0.697704 | − | 0.716386i | \(-0.745795\pi\) | ||||
−0.697704 | + | 0.716386i | \(0.745795\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −11.6847 | −0.824172 | ||||||||
\(202\) | 3.68466 | 0.259252 | ||||||||
\(203\) | −3.36932 | −0.236480 | ||||||||
\(204\) | −3.43845 | −0.240739 | ||||||||
\(205\) | −4.00000 | −0.279372 | ||||||||
\(206\) | 1.00000 | 0.0696733 | ||||||||
\(207\) | 3.12311 | 0.217071 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 5.12311 | 0.354373 | ||||||||
\(210\) | 1.12311 | 0.0775017 | ||||||||
\(211\) | 8.49242 | 0.584642 | 0.292321 | − | 0.956320i | \(-0.405572\pi\) | ||||
0.292321 | + | 0.956320i | \(0.405572\pi\) | |||||||
\(212\) | 6.56155 | 0.450649 | ||||||||
\(213\) | −2.24621 | −0.153908 | ||||||||
\(214\) | −8.56155 | −0.585256 | ||||||||
\(215\) | −2.24621 | −0.153190 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −0.630683 | −0.0428136 | ||||||||
\(218\) | 6.24621 | 0.423047 | ||||||||
\(219\) | −3.68466 | −0.248986 | ||||||||
\(220\) | 5.12311 | 0.345400 | ||||||||
\(221\) | −3.43845 | −0.231295 | ||||||||
\(222\) | −9.12311 | −0.612303 | ||||||||
\(223\) | −5.68466 | −0.380673 | −0.190336 | − | 0.981719i | \(-0.560958\pi\) | ||||
−0.190336 | + | 0.981719i | \(0.560958\pi\) | |||||||
\(224\) | 0.561553 | 0.0375203 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | −4.00000 | −0.266076 | ||||||||
\(227\) | −4.80776 | −0.319103 | −0.159551 | − | 0.987190i | \(-0.551005\pi\) | ||||
−0.159551 | + | 0.987190i | \(0.551005\pi\) | |||||||
\(228\) | 2.00000 | 0.132453 | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | 6.24621 | 0.411863 | ||||||||
\(231\) | −1.43845 | −0.0946429 | ||||||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | 24.4924 | 1.60455 | 0.802276 | − | 0.596953i | \(-0.203622\pi\) | ||||
0.802276 | + | 0.596953i | \(0.203622\pi\) | |||||||
\(234\) | 1.00000 | 0.0653720 | ||||||||
\(235\) | 20.4924 | 1.33678 | ||||||||
\(236\) | −8.00000 | −0.520756 | ||||||||
\(237\) | −7.36932 | −0.478689 | ||||||||
\(238\) | 1.93087 | 0.125160 | ||||||||
\(239\) | −2.56155 | −0.165693 | −0.0828465 | − | 0.996562i | \(-0.526401\pi\) | ||||
−0.0828465 | + | 0.996562i | \(0.526401\pi\) | |||||||
\(240\) | 2.00000 | 0.129099 | ||||||||
\(241\) | −8.31534 | −0.535638 | −0.267819 | − | 0.963469i | \(-0.586303\pi\) | ||||
−0.267819 | + | 0.963469i | \(0.586303\pi\) | |||||||
\(242\) | 4.43845 | 0.285314 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.1231 | 0.712084 | ||||||||
\(245\) | 13.3693 | 0.854134 | ||||||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 2.00000 | 0.127257 | ||||||||
\(248\) | −1.12311 | −0.0713173 | ||||||||
\(249\) | −11.3693 | −0.720501 | ||||||||
\(250\) | −12.0000 | −0.758947 | ||||||||
\(251\) | 5.75379 | 0.363176 | 0.181588 | − | 0.983375i | \(-0.441876\pi\) | ||||
0.181588 | + | 0.983375i | \(0.441876\pi\) | |||||||
\(252\) | −0.561553 | −0.0353745 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 11.6847 | 0.733161 | ||||||||
\(255\) | 6.87689 | 0.430648 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.1231 | 1.31762 | 0.658812 | − | 0.752308i | \(-0.271059\pi\) | ||||
0.658812 | + | 0.752308i | \(0.271059\pi\) | |||||||
\(258\) | 1.12311 | 0.0699215 | ||||||||
\(259\) | 5.12311 | 0.318334 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | −21.3693 | −1.32020 | ||||||||
\(263\) | 0.315342 | 0.0194448 | 0.00972240 | − | 0.999953i | \(-0.496905\pi\) | ||||
0.00972240 | + | 0.999953i | \(0.496905\pi\) | |||||||
\(264\) | −2.56155 | −0.157653 | ||||||||
\(265\) | −13.1231 | −0.806146 | ||||||||
\(266\) | −1.12311 | −0.0688620 | ||||||||
\(267\) | −2.00000 | −0.122398 | ||||||||
\(268\) | 11.6847 | 0.713754 | ||||||||
\(269\) | −11.7538 | −0.716641 | −0.358321 | − | 0.933599i | \(-0.616651\pi\) | ||||
−0.358321 | + | 0.933599i | \(0.616651\pi\) | |||||||
\(270\) | −2.00000 | −0.121716 | ||||||||
\(271\) | −11.3693 | −0.690637 | −0.345318 | − | 0.938486i | \(-0.612229\pi\) | ||||
−0.345318 | + | 0.938486i | \(0.612229\pi\) | |||||||
\(272\) | 3.43845 | 0.208486 | ||||||||
\(273\) | −0.561553 | −0.0339867 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 2.56155 | 0.154467 | ||||||||
\(276\) | −3.12311 | −0.187989 | ||||||||
\(277\) | 6.00000 | 0.360505 | 0.180253 | − | 0.983620i | \(-0.442309\pi\) | ||||
0.180253 | + | 0.983620i | \(0.442309\pi\) | |||||||
\(278\) | 12.8078 | 0.768159 | ||||||||
\(279\) | 1.12311 | 0.0672386 | ||||||||
\(280\) | −1.12311 | −0.0671184 | ||||||||
\(281\) | −22.4924 | −1.34179 | −0.670893 | − | 0.741554i | \(-0.734089\pi\) | ||||
−0.670893 | + | 0.741554i | \(0.734089\pi\) | |||||||
\(282\) | −10.2462 | −0.610153 | ||||||||
\(283\) | 21.6155 | 1.28491 | 0.642455 | − | 0.766324i | \(-0.277916\pi\) | ||||
0.642455 | + | 0.766324i | \(0.277916\pi\) | |||||||
\(284\) | 2.24621 | 0.133288 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | −2.56155 | −0.151468 | ||||||||
\(287\) | −1.12311 | −0.0662948 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −5.17708 | −0.304534 | ||||||||
\(290\) | 12.0000 | 0.704664 | ||||||||
\(291\) | −4.24621 | −0.248917 | ||||||||
\(292\) | 3.68466 | 0.215628 | ||||||||
\(293\) | −7.61553 | −0.444904 | −0.222452 | − | 0.974944i | \(-0.571406\pi\) | ||||
−0.222452 | + | 0.974944i | \(0.571406\pi\) | |||||||
\(294\) | −6.68466 | −0.389857 | ||||||||
\(295\) | 16.0000 | 0.931556 | ||||||||
\(296\) | 9.12311 | 0.530270 | ||||||||
\(297\) | 2.56155 | 0.148636 | ||||||||
\(298\) | −6.31534 | −0.365838 | ||||||||
\(299\) | −3.12311 | −0.180614 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −0.630683 | −0.0363520 | ||||||||
\(302\) | 7.36932 | 0.424057 | ||||||||
\(303\) | 3.68466 | 0.211678 | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | −22.2462 | −1.27381 | ||||||||
\(306\) | −3.43845 | −0.196563 | ||||||||
\(307\) | 21.4384 | 1.22356 | 0.611778 | − | 0.791029i | \(-0.290454\pi\) | ||||
0.611778 | + | 0.791029i | \(0.290454\pi\) | |||||||
\(308\) | 1.43845 | 0.0819631 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 2.24621 | 0.127576 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −16.2462 | −0.918290 | −0.459145 | − | 0.888361i | \(-0.651844\pi\) | ||||
−0.459145 | + | 0.888361i | \(0.651844\pi\) | |||||||
\(314\) | 6.80776 | 0.384184 | ||||||||
\(315\) | 1.12311 | 0.0632798 | ||||||||
\(316\) | 7.36932 | 0.414556 | ||||||||
\(317\) | −13.0540 | −0.733184 | −0.366592 | − | 0.930382i | \(-0.619476\pi\) | ||||
−0.366592 | + | 0.930382i | \(0.619476\pi\) | |||||||
\(318\) | 6.56155 | 0.367954 | ||||||||
\(319\) | −15.3693 | −0.860517 | ||||||||
\(320\) | −2.00000 | −0.111803 | ||||||||
\(321\) | −8.56155 | −0.477859 | ||||||||
\(322\) | 1.75379 | 0.0977348 | ||||||||
\(323\) | −6.87689 | −0.382641 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 22.4924 | 1.24574 | ||||||||
\(327\) | 6.24621 | 0.345416 | ||||||||
\(328\) | −2.00000 | −0.110432 | ||||||||
\(329\) | 5.75379 | 0.317217 | ||||||||
\(330\) | 5.12311 | 0.282018 | ||||||||
\(331\) | 21.9309 | 1.20543 | 0.602715 | − | 0.797957i | \(-0.294086\pi\) | ||||
0.602715 | + | 0.797957i | \(0.294086\pi\) | |||||||
\(332\) | 11.3693 | 0.623972 | ||||||||
\(333\) | −9.12311 | −0.499943 | ||||||||
\(334\) | 3.19224 | 0.174671 | ||||||||
\(335\) | −23.3693 | −1.27680 | ||||||||
\(336\) | 0.561553 | 0.0306352 | ||||||||
\(337\) | −27.9309 | −1.52149 | −0.760746 | − | 0.649050i | \(-0.775167\pi\) | ||||
−0.760746 | + | 0.649050i | \(0.775167\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −4.00000 | −0.217250 | ||||||||
\(340\) | −6.87689 | −0.372952 | ||||||||
\(341\) | −2.87689 | −0.155793 | ||||||||
\(342\) | 2.00000 | 0.108148 | ||||||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | −1.12311 | −0.0605538 | ||||||||
\(345\) | 6.24621 | 0.336285 | ||||||||
\(346\) | −20.8078 | −1.11863 | ||||||||
\(347\) | −16.8769 | −0.905999 | −0.453000 | − | 0.891511i | \(-0.649646\pi\) | ||||
−0.453000 | + | 0.891511i | \(0.649646\pi\) | |||||||
\(348\) | −6.00000 | −0.321634 | ||||||||
\(349\) | 1.75379 | 0.0938782 | 0.0469391 | − | 0.998898i | \(-0.485053\pi\) | ||||
0.0469391 | + | 0.998898i | \(0.485053\pi\) | |||||||
\(350\) | −0.561553 | −0.0300163 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 2.56155 | 0.136531 | ||||||||
\(353\) | −14.3153 | −0.761929 | −0.380964 | − | 0.924590i | \(-0.624408\pi\) | ||||
−0.380964 | + | 0.924590i | \(0.624408\pi\) | |||||||
\(354\) | −8.00000 | −0.425195 | ||||||||
\(355\) | −4.49242 | −0.238433 | ||||||||
\(356\) | 2.00000 | 0.106000 | ||||||||
\(357\) | 1.93087 | 0.102192 | ||||||||
\(358\) | 10.8078 | 0.571208 | ||||||||
\(359\) | 19.0540 | 1.00563 | 0.502815 | − | 0.864394i | \(-0.332298\pi\) | ||||
0.502815 | + | 0.864394i | \(0.332298\pi\) | |||||||
\(360\) | 2.00000 | 0.105409 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | −15.9309 | −0.837308 | ||||||||
\(363\) | 4.43845 | 0.232958 | ||||||||
\(364\) | 0.561553 | 0.0294334 | ||||||||
\(365\) | −7.36932 | −0.385728 | ||||||||
\(366\) | 11.1231 | 0.581414 | ||||||||
\(367\) | −13.7538 | −0.717942 | −0.358971 | − | 0.933349i | \(-0.616872\pi\) | ||||
−0.358971 | + | 0.933349i | \(0.616872\pi\) | |||||||
\(368\) | 3.12311 | 0.162803 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | −18.2462 | −0.948575 | ||||||||
\(371\) | −3.68466 | −0.191298 | ||||||||
\(372\) | −1.12311 | −0.0582303 | ||||||||
\(373\) | −29.3693 | −1.52069 | −0.760343 | − | 0.649522i | \(-0.774969\pi\) | ||||
−0.760343 | + | 0.649522i | \(0.774969\pi\) | |||||||
\(374\) | 8.80776 | 0.455439 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | 10.2462 | 0.528408 | ||||||||
\(377\) | −6.00000 | −0.309016 | ||||||||
\(378\) | −0.561553 | −0.0288832 | ||||||||
\(379\) | −12.8078 | −0.657891 | −0.328945 | − | 0.944349i | \(-0.606693\pi\) | ||||
−0.328945 | + | 0.944349i | \(0.606693\pi\) | |||||||
\(380\) | 4.00000 | 0.205196 | ||||||||
\(381\) | 11.6847 | 0.598623 | ||||||||
\(382\) | 3.68466 | 0.188524 | ||||||||
\(383\) | 4.49242 | 0.229552 | 0.114776 | − | 0.993391i | \(-0.463385\pi\) | ||||
0.114776 | + | 0.993391i | \(0.463385\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −2.87689 | −0.146620 | ||||||||
\(386\) | 0.630683 | 0.0321009 | ||||||||
\(387\) | 1.12311 | 0.0570907 | ||||||||
\(388\) | 4.24621 | 0.215569 | ||||||||
\(389\) | 2.56155 | 0.129876 | 0.0649379 | − | 0.997889i | \(-0.479315\pi\) | ||||
0.0649379 | + | 0.997889i | \(0.479315\pi\) | |||||||
\(390\) | 2.00000 | 0.101274 | ||||||||
\(391\) | 10.7386 | 0.543076 | ||||||||
\(392\) | 6.68466 | 0.337626 | ||||||||
\(393\) | −21.3693 | −1.07794 | ||||||||
\(394\) | −18.4924 | −0.931635 | ||||||||
\(395\) | −14.7386 | −0.741581 | ||||||||
\(396\) | −2.56155 | −0.128723 | ||||||||
\(397\) | 17.6155 | 0.884098 | 0.442049 | − | 0.896991i | \(-0.354252\pi\) | ||||
0.442049 | + | 0.896991i | \(0.354252\pi\) | |||||||
\(398\) | 19.6847 | 0.986703 | ||||||||
\(399\) | −1.12311 | −0.0562256 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 5.36932 | 0.268131 | 0.134065 | − | 0.990972i | \(-0.457197\pi\) | ||||
0.134065 | + | 0.990972i | \(0.457197\pi\) | |||||||
\(402\) | 11.6847 | 0.582778 | ||||||||
\(403\) | −1.12311 | −0.0559459 | ||||||||
\(404\) | −3.68466 | −0.183319 | ||||||||
\(405\) | −2.00000 | −0.0993808 | ||||||||
\(406\) | 3.36932 | 0.167216 | ||||||||
\(407\) | 23.3693 | 1.15837 | ||||||||
\(408\) | 3.43845 | 0.170229 | ||||||||
\(409\) | 21.3693 | 1.05664 | 0.528322 | − | 0.849044i | \(-0.322821\pi\) | ||||
0.528322 | + | 0.849044i | \(0.322821\pi\) | |||||||
\(410\) | 4.00000 | 0.197546 | ||||||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | −1.00000 | −0.0492665 | ||||||||
\(413\) | 4.49242 | 0.221058 | ||||||||
\(414\) | −3.12311 | −0.153492 | ||||||||
\(415\) | −22.7386 | −1.11620 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 12.8078 | 0.627199 | ||||||||
\(418\) | −5.12311 | −0.250579 | ||||||||
\(419\) | −19.9309 | −0.973687 | −0.486843 | − | 0.873489i | \(-0.661852\pi\) | ||||
−0.486843 | + | 0.873489i | \(0.661852\pi\) | |||||||
\(420\) | −1.12311 | −0.0548019 | ||||||||
\(421\) | 17.0540 | 0.831160 | 0.415580 | − | 0.909557i | \(-0.363579\pi\) | ||||
0.415580 | + | 0.909557i | \(0.363579\pi\) | |||||||
\(422\) | −8.49242 | −0.413405 | ||||||||
\(423\) | −10.2462 | −0.498188 | ||||||||
\(424\) | −6.56155 | −0.318657 | ||||||||
\(425\) | −3.43845 | −0.166789 | ||||||||
\(426\) | 2.24621 | 0.108829 | ||||||||
\(427\) | −6.24621 | −0.302275 | ||||||||
\(428\) | 8.56155 | 0.413838 | ||||||||
\(429\) | −2.56155 | −0.123673 | ||||||||
\(430\) | 2.24621 | 0.108322 | ||||||||
\(431\) | −32.0000 | −1.54139 | −0.770693 | − | 0.637207i | \(-0.780090\pi\) | ||||
−0.770693 | + | 0.637207i | \(0.780090\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −22.4924 | −1.08092 | −0.540458 | − | 0.841371i | \(-0.681749\pi\) | ||||
−0.540458 | + | 0.841371i | \(0.681749\pi\) | |||||||
\(434\) | 0.630683 | 0.0302738 | ||||||||
\(435\) | 12.0000 | 0.575356 | ||||||||
\(436\) | −6.24621 | −0.299139 | ||||||||
\(437\) | −6.24621 | −0.298797 | ||||||||
\(438\) | 3.68466 | 0.176060 | ||||||||
\(439\) | −11.0540 | −0.527577 | −0.263789 | − | 0.964580i | \(-0.584972\pi\) | ||||
−0.263789 | + | 0.964580i | \(0.584972\pi\) | |||||||
\(440\) | −5.12311 | −0.244234 | ||||||||
\(441\) | −6.68466 | −0.318317 | ||||||||
\(442\) | 3.43845 | 0.163550 | ||||||||
\(443\) | −12.4924 | −0.593533 | −0.296766 | − | 0.954950i | \(-0.595908\pi\) | ||||
−0.296766 | + | 0.954950i | \(0.595908\pi\) | |||||||
\(444\) | 9.12311 | 0.432963 | ||||||||
\(445\) | −4.00000 | −0.189618 | ||||||||
\(446\) | 5.68466 | 0.269176 | ||||||||
\(447\) | −6.31534 | −0.298705 | ||||||||
\(448\) | −0.561553 | −0.0265309 | ||||||||
\(449\) | −26.3153 | −1.24190 | −0.620949 | − | 0.783851i | \(-0.713253\pi\) | ||||
−0.620949 | + | 0.783851i | \(0.713253\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −5.12311 | −0.241238 | ||||||||
\(452\) | 4.00000 | 0.188144 | ||||||||
\(453\) | 7.36932 | 0.346241 | ||||||||
\(454\) | 4.80776 | 0.225640 | ||||||||
\(455\) | −1.12311 | −0.0526520 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 8.63068 | 0.403726 | 0.201863 | − | 0.979414i | \(-0.435300\pi\) | ||||
0.201863 | + | 0.979414i | \(0.435300\pi\) | |||||||
\(458\) | 6.00000 | 0.280362 | ||||||||
\(459\) | −3.43845 | −0.160493 | ||||||||
\(460\) | −6.24621 | −0.291231 | ||||||||
\(461\) | 8.24621 | 0.384064 | 0.192032 | − | 0.981389i | \(-0.438492\pi\) | ||||
0.192032 | + | 0.981389i | \(0.438492\pi\) | |||||||
\(462\) | 1.43845 | 0.0669226 | ||||||||
\(463\) | 13.1231 | 0.609882 | 0.304941 | − | 0.952371i | \(-0.401363\pi\) | ||||
0.304941 | + | 0.952371i | \(0.401363\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 2.24621 | 0.104166 | ||||||||
\(466\) | −24.4924 | −1.13459 | ||||||||
\(467\) | −38.1771 | −1.76662 | −0.883312 | − | 0.468785i | \(-0.844692\pi\) | ||||
−0.883312 | + | 0.468785i | \(0.844692\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | −6.56155 | −0.302984 | ||||||||
\(470\) | −20.4924 | −0.945245 | ||||||||
\(471\) | 6.80776 | 0.313685 | ||||||||
\(472\) | 8.00000 | 0.368230 | ||||||||
\(473\) | −2.87689 | −0.132280 | ||||||||
\(474\) | 7.36932 | 0.338484 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | −1.93087 | −0.0885013 | ||||||||
\(477\) | 6.56155 | 0.300433 | ||||||||
\(478\) | 2.56155 | 0.117163 | ||||||||
\(479\) | −5.12311 | −0.234081 | −0.117040 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117040 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(480\) | −2.00000 | −0.0912871 | ||||||||
\(481\) | 9.12311 | 0.415978 | ||||||||
\(482\) | 8.31534 | 0.378753 | ||||||||
\(483\) | 1.75379 | 0.0798002 | ||||||||
\(484\) | −4.43845 | −0.201748 | ||||||||
\(485\) | −8.49242 | −0.385621 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 5.61553 | 0.254464 | 0.127232 | − | 0.991873i | \(-0.459391\pi\) | ||||
0.127232 | + | 0.991873i | \(0.459391\pi\) | |||||||
\(488\) | −11.1231 | −0.503519 | ||||||||
\(489\) | 22.4924 | 1.01714 | ||||||||
\(490\) | −13.3693 | −0.603964 | ||||||||
\(491\) | 15.4384 | 0.696727 | 0.348364 | − | 0.937359i | \(-0.386737\pi\) | ||||
0.348364 | + | 0.937359i | \(0.386737\pi\) | |||||||
\(492\) | −2.00000 | −0.0901670 | ||||||||
\(493\) | 20.6307 | 0.929159 | ||||||||
\(494\) | −2.00000 | −0.0899843 | ||||||||
\(495\) | 5.12311 | 0.230266 | ||||||||
\(496\) | 1.12311 | 0.0504289 | ||||||||
\(497\) | −1.26137 | −0.0565800 | ||||||||
\(498\) | 11.3693 | 0.509471 | ||||||||
\(499\) | 22.7386 | 1.01792 | 0.508961 | − | 0.860790i | \(-0.330030\pi\) | ||||
0.508961 | + | 0.860790i | \(0.330030\pi\) | |||||||
\(500\) | 12.0000 | 0.536656 | ||||||||
\(501\) | 3.19224 | 0.142619 | ||||||||
\(502\) | −5.75379 | −0.256804 | ||||||||
\(503\) | −10.6307 | −0.473999 | −0.236999 | − | 0.971510i | \(-0.576164\pi\) | ||||
−0.236999 | + | 0.971510i | \(0.576164\pi\) | |||||||
\(504\) | 0.561553 | 0.0250136 | ||||||||
\(505\) | 7.36932 | 0.327930 | ||||||||
\(506\) | 8.00000 | 0.355643 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −11.6847 | −0.518423 | ||||||||
\(509\) | 7.93087 | 0.351530 | 0.175765 | − | 0.984432i | \(-0.443760\pi\) | ||||
0.175765 | + | 0.984432i | \(0.443760\pi\) | |||||||
\(510\) | −6.87689 | −0.304514 | ||||||||
\(511\) | −2.06913 | −0.0915329 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.00000 | 0.0883022 | ||||||||
\(514\) | −21.1231 | −0.931700 | ||||||||
\(515\) | 2.00000 | 0.0881305 | ||||||||
\(516\) | −1.12311 | −0.0494420 | ||||||||
\(517\) | 26.2462 | 1.15431 | ||||||||
\(518\) | −5.12311 | −0.225096 | ||||||||
\(519\) | −20.8078 | −0.913359 | ||||||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | 6.87689 | 0.301282 | 0.150641 | − | 0.988589i | \(-0.451866\pi\) | ||||
0.150641 | + | 0.988589i | \(0.451866\pi\) | |||||||
\(522\) | −6.00000 | −0.262613 | ||||||||
\(523\) | −26.5616 | −1.16146 | −0.580728 | − | 0.814098i | \(-0.697232\pi\) | ||||
−0.580728 | + | 0.814098i | \(0.697232\pi\) | |||||||
\(524\) | 21.3693 | 0.933523 | ||||||||
\(525\) | −0.561553 | −0.0245082 | ||||||||
\(526\) | −0.315342 | −0.0137495 | ||||||||
\(527\) | 3.86174 | 0.168220 | ||||||||
\(528\) | 2.56155 | 0.111477 | ||||||||
\(529\) | −13.2462 | −0.575922 | ||||||||
\(530\) | 13.1231 | 0.570031 | ||||||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 1.12311 | 0.0486928 | ||||||||
\(533\) | −2.00000 | −0.0866296 | ||||||||
\(534\) | 2.00000 | 0.0865485 | ||||||||
\(535\) | −17.1231 | −0.740296 | ||||||||
\(536\) | −11.6847 | −0.504700 | ||||||||
\(537\) | 10.8078 | 0.466389 | ||||||||
\(538\) | 11.7538 | 0.506742 | ||||||||
\(539\) | 17.1231 | 0.737544 | ||||||||
\(540\) | 2.00000 | 0.0860663 | ||||||||
\(541\) | −16.5616 | −0.712037 | −0.356018 | − | 0.934479i | \(-0.615866\pi\) | ||||
−0.356018 | + | 0.934479i | \(0.615866\pi\) | |||||||
\(542\) | 11.3693 | 0.488354 | ||||||||
\(543\) | −15.9309 | −0.683659 | ||||||||
\(544\) | −3.43845 | −0.147422 | ||||||||
\(545\) | 12.4924 | 0.535117 | ||||||||
\(546\) | 0.561553 | 0.0240322 | ||||||||
\(547\) | 8.00000 | 0.342055 | 0.171028 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171028 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(548\) | −6.00000 | −0.256307 | ||||||||
\(549\) | 11.1231 | 0.474723 | ||||||||
\(550\) | −2.56155 | −0.109225 | ||||||||
\(551\) | −12.0000 | −0.511217 | ||||||||
\(552\) | 3.12311 | 0.132928 | ||||||||
\(553\) | −4.13826 | −0.175977 | ||||||||
\(554\) | −6.00000 | −0.254916 | ||||||||
\(555\) | −18.2462 | −0.774509 | ||||||||
\(556\) | −12.8078 | −0.543170 | ||||||||
\(557\) | 4.87689 | 0.206641 | 0.103320 | − | 0.994648i | \(-0.467053\pi\) | ||||
0.103320 | + | 0.994648i | \(0.467053\pi\) | |||||||
\(558\) | −1.12311 | −0.0475449 | ||||||||
\(559\) | −1.12311 | −0.0475023 | ||||||||
\(560\) | 1.12311 | 0.0474599 | ||||||||
\(561\) | 8.80776 | 0.371864 | ||||||||
\(562\) | 22.4924 | 0.948786 | ||||||||
\(563\) | 33.6155 | 1.41673 | 0.708363 | − | 0.705849i | \(-0.249434\pi\) | ||||
0.708363 | + | 0.705849i | \(0.249434\pi\) | |||||||
\(564\) | 10.2462 | 0.431443 | ||||||||
\(565\) | −8.00000 | −0.336563 | ||||||||
\(566\) | −21.6155 | −0.908568 | ||||||||
\(567\) | −0.561553 | −0.0235830 | ||||||||
\(568\) | −2.24621 | −0.0942489 | ||||||||
\(569\) | 0.630683 | 0.0264396 | 0.0132198 | − | 0.999913i | \(-0.495792\pi\) | ||||
0.0132198 | + | 0.999913i | \(0.495792\pi\) | |||||||
\(570\) | 4.00000 | 0.167542 | ||||||||
\(571\) | −26.2462 | −1.09837 | −0.549185 | − | 0.835701i | \(-0.685062\pi\) | ||||
−0.549185 | + | 0.835701i | \(0.685062\pi\) | |||||||
\(572\) | 2.56155 | 0.107104 | ||||||||
\(573\) | 3.68466 | 0.153929 | ||||||||
\(574\) | 1.12311 | 0.0468775 | ||||||||
\(575\) | −3.12311 | −0.130243 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −20.8078 | −0.866239 | −0.433119 | − | 0.901337i | \(-0.642587\pi\) | ||||
−0.433119 | + | 0.901337i | \(0.642587\pi\) | |||||||
\(578\) | 5.17708 | 0.215338 | ||||||||
\(579\) | 0.630683 | 0.0262103 | ||||||||
\(580\) | −12.0000 | −0.498273 | ||||||||
\(581\) | −6.38447 | −0.264873 | ||||||||
\(582\) | 4.24621 | 0.176011 | ||||||||
\(583\) | −16.8078 | −0.696106 | ||||||||
\(584\) | −3.68466 | −0.152472 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 7.61553 | 0.314595 | ||||||||
\(587\) | −36.4924 | −1.50620 | −0.753102 | − | 0.657904i | \(-0.771443\pi\) | ||||
−0.753102 | + | 0.657904i | \(0.771443\pi\) | |||||||
\(588\) | 6.68466 | 0.275671 | ||||||||
\(589\) | −2.24621 | −0.0925535 | ||||||||
\(590\) | −16.0000 | −0.658710 | ||||||||
\(591\) | −18.4924 | −0.760677 | ||||||||
\(592\) | −9.12311 | −0.374957 | ||||||||
\(593\) | 13.6847 | 0.561962 | 0.280981 | − | 0.959713i | \(-0.409340\pi\) | ||||
0.280981 | + | 0.959713i | \(0.409340\pi\) | |||||||
\(594\) | −2.56155 | −0.105102 | ||||||||
\(595\) | 3.86174 | 0.158316 | ||||||||
\(596\) | 6.31534 | 0.258686 | ||||||||
\(597\) | 19.6847 | 0.805639 | ||||||||
\(598\) | 3.12311 | 0.127713 | ||||||||
\(599\) | 9.93087 | 0.405764 | 0.202882 | − | 0.979203i | \(-0.434969\pi\) | ||||
0.202882 | + | 0.979203i | \(0.434969\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 3.75379 | 0.153120 | 0.0765601 | − | 0.997065i | \(-0.475606\pi\) | ||||
0.0765601 | + | 0.997065i | \(0.475606\pi\) | |||||||
\(602\) | 0.630683 | 0.0257047 | ||||||||
\(603\) | 11.6847 | 0.475836 | ||||||||
\(604\) | −7.36932 | −0.299853 | ||||||||
\(605\) | 8.87689 | 0.360897 | ||||||||
\(606\) | −3.68466 | −0.149679 | ||||||||
\(607\) | −14.8769 | −0.603835 | −0.301917 | − | 0.953334i | \(-0.597627\pi\) | ||||
−0.301917 | + | 0.953334i | \(0.597627\pi\) | |||||||
\(608\) | 2.00000 | 0.0811107 | ||||||||
\(609\) | 3.36932 | 0.136532 | ||||||||
\(610\) | 22.2462 | 0.900723 | ||||||||
\(611\) | 10.2462 | 0.414517 | ||||||||
\(612\) | 3.43845 | 0.138991 | ||||||||
\(613\) | −43.7926 | −1.76877 | −0.884383 | − | 0.466761i | \(-0.845421\pi\) | ||||
−0.884383 | + | 0.466761i | \(0.845421\pi\) | |||||||
\(614\) | −21.4384 | −0.865185 | ||||||||
\(615\) | 4.00000 | 0.161296 | ||||||||
\(616\) | −1.43845 | −0.0579567 | ||||||||
\(617\) | −12.2462 | −0.493014 | −0.246507 | − | 0.969141i | \(-0.579283\pi\) | ||||
−0.246507 | + | 0.969141i | \(0.579283\pi\) | |||||||
\(618\) | −1.00000 | −0.0402259 | ||||||||
\(619\) | −6.49242 | −0.260952 | −0.130476 | − | 0.991451i | \(-0.541651\pi\) | ||||
−0.130476 | + | 0.991451i | \(0.541651\pi\) | |||||||
\(620\) | −2.24621 | −0.0902100 | ||||||||
\(621\) | −3.12311 | −0.125326 | ||||||||
\(622\) | 18.0000 | 0.721734 | ||||||||
\(623\) | −1.12311 | −0.0449963 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 16.2462 | 0.649329 | ||||||||
\(627\) | −5.12311 | −0.204597 | ||||||||
\(628\) | −6.80776 | −0.271659 | ||||||||
\(629\) | −31.3693 | −1.25078 | ||||||||
\(630\) | −1.12311 | −0.0447456 | ||||||||
\(631\) | −37.0540 | −1.47510 | −0.737548 | − | 0.675295i | \(-0.764016\pi\) | ||||
−0.737548 | + | 0.675295i | \(0.764016\pi\) | |||||||
\(632\) | −7.36932 | −0.293136 | ||||||||
\(633\) | −8.49242 | −0.337543 | ||||||||
\(634\) | 13.0540 | 0.518440 | ||||||||
\(635\) | 23.3693 | 0.927383 | ||||||||
\(636\) | −6.56155 | −0.260182 | ||||||||
\(637\) | 6.68466 | 0.264856 | ||||||||
\(638\) | 15.3693 | 0.608477 | ||||||||
\(639\) | 2.24621 | 0.0888587 | ||||||||
\(640\) | 2.00000 | 0.0790569 | ||||||||
\(641\) | −38.8078 | −1.53281 | −0.766407 | − | 0.642355i | \(-0.777958\pi\) | ||||
−0.766407 | + | 0.642355i | \(0.777958\pi\) | |||||||
\(642\) | 8.56155 | 0.337898 | ||||||||
\(643\) | −24.7386 | −0.975596 | −0.487798 | − | 0.872956i | \(-0.662200\pi\) | ||||
−0.487798 | + | 0.872956i | \(0.662200\pi\) | |||||||
\(644\) | −1.75379 | −0.0691090 | ||||||||
\(645\) | 2.24621 | 0.0884445 | ||||||||
\(646\) | 6.87689 | 0.270568 | ||||||||
\(647\) | −8.24621 | −0.324192 | −0.162096 | − | 0.986775i | \(-0.551825\pi\) | ||||
−0.162096 | + | 0.986775i | \(0.551825\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 20.4924 | 0.804398 | ||||||||
\(650\) | −1.00000 | −0.0392232 | ||||||||
\(651\) | 0.630683 | 0.0247184 | ||||||||
\(652\) | −22.4924 | −0.880871 | ||||||||
\(653\) | 18.8769 | 0.738710 | 0.369355 | − | 0.929288i | \(-0.379579\pi\) | ||||
0.369355 | + | 0.929288i | \(0.379579\pi\) | |||||||
\(654\) | −6.24621 | −0.244246 | ||||||||
\(655\) | −42.7386 | −1.66994 | ||||||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | 3.68466 | 0.143752 | ||||||||
\(658\) | −5.75379 | −0.224306 | ||||||||
\(659\) | 21.5464 | 0.839328 | 0.419664 | − | 0.907679i | \(-0.362148\pi\) | ||||
0.419664 | + | 0.907679i | \(0.362148\pi\) | |||||||
\(660\) | −5.12311 | −0.199417 | ||||||||
\(661\) | −18.2462 | −0.709695 | −0.354848 | − | 0.934924i | \(-0.615467\pi\) | ||||
−0.354848 | + | 0.934924i | \(0.615467\pi\) | |||||||
\(662\) | −21.9309 | −0.852367 | ||||||||
\(663\) | 3.43845 | 0.133538 | ||||||||
\(664\) | −11.3693 | −0.441215 | ||||||||
\(665\) | −2.24621 | −0.0871043 | ||||||||
\(666\) | 9.12311 | 0.353513 | ||||||||
\(667\) | 18.7386 | 0.725563 | ||||||||
\(668\) | −3.19224 | −0.123511 | ||||||||
\(669\) | 5.68466 | 0.219782 | ||||||||
\(670\) | 23.3693 | 0.902835 | ||||||||
\(671\) | −28.4924 | −1.09994 | ||||||||
\(672\) | −0.561553 | −0.0216624 | ||||||||
\(673\) | −1.68466 | −0.0649388 | −0.0324694 | − | 0.999473i | \(-0.510337\pi\) | ||||
−0.0324694 | + | 0.999473i | \(0.510337\pi\) | |||||||
\(674\) | 27.9309 | 1.07586 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −24.2462 | −0.931858 | −0.465929 | − | 0.884822i | \(-0.654280\pi\) | ||||
−0.465929 | + | 0.884822i | \(0.654280\pi\) | |||||||
\(678\) | 4.00000 | 0.153619 | ||||||||
\(679\) | −2.38447 | −0.0915076 | ||||||||
\(680\) | 6.87689 | 0.263717 | ||||||||
\(681\) | 4.80776 | 0.184234 | ||||||||
\(682\) | 2.87689 | 0.110162 | ||||||||
\(683\) | 5.43845 | 0.208096 | 0.104048 | − | 0.994572i | \(-0.466820\pi\) | ||||
0.104048 | + | 0.994572i | \(0.466820\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | −7.68466 | −0.293402 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | 1.12311 | 0.0428180 | ||||||||
\(689\) | −6.56155 | −0.249975 | ||||||||
\(690\) | −6.24621 | −0.237789 | ||||||||
\(691\) | −21.7538 | −0.827553 | −0.413777 | − | 0.910378i | \(-0.635791\pi\) | ||||
−0.413777 | + | 0.910378i | \(0.635791\pi\) | |||||||
\(692\) | 20.8078 | 0.790993 | ||||||||
\(693\) | 1.43845 | 0.0546421 | ||||||||
\(694\) | 16.8769 | 0.640638 | ||||||||
\(695\) | 25.6155 | 0.971652 | ||||||||
\(696\) | 6.00000 | 0.227429 | ||||||||
\(697\) | 6.87689 | 0.260481 | ||||||||
\(698\) | −1.75379 | −0.0663819 | ||||||||
\(699\) | −24.4924 | −0.926388 | ||||||||
\(700\) | 0.561553 | 0.0212247 | ||||||||
\(701\) | −17.3693 | −0.656030 | −0.328015 | − | 0.944673i | \(-0.606380\pi\) | ||||
−0.328015 | + | 0.944673i | \(0.606380\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 18.2462 | 0.688169 | ||||||||
\(704\) | −2.56155 | −0.0965422 | ||||||||
\(705\) | −20.4924 | −0.771789 | ||||||||
\(706\) | 14.3153 | 0.538765 | ||||||||
\(707\) | 2.06913 | 0.0778177 | ||||||||
\(708\) | 8.00000 | 0.300658 | ||||||||
\(709\) | 8.73863 | 0.328186 | 0.164093 | − | 0.986445i | \(-0.447530\pi\) | ||||
0.164093 | + | 0.986445i | \(0.447530\pi\) | |||||||
\(710\) | 4.49242 | 0.168598 | ||||||||
\(711\) | 7.36932 | 0.276371 | ||||||||
\(712\) | −2.00000 | −0.0749532 | ||||||||
\(713\) | 3.50758 | 0.131360 | ||||||||
\(714\) | −1.93087 | −0.0722610 | ||||||||
\(715\) | −5.12311 | −0.191593 | ||||||||
\(716\) | −10.8078 | −0.403905 | ||||||||
\(717\) | 2.56155 | 0.0956629 | ||||||||
\(718\) | −19.0540 | −0.711088 | ||||||||
\(719\) | 11.1922 | 0.417400 | 0.208700 | − | 0.977980i | \(-0.433077\pi\) | ||||
0.208700 | + | 0.977980i | \(0.433077\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | 0.561553 | 0.0209133 | ||||||||
\(722\) | 15.0000 | 0.558242 | ||||||||
\(723\) | 8.31534 | 0.309251 | ||||||||
\(724\) | 15.9309 | 0.592066 | ||||||||
\(725\) | −6.00000 | −0.222834 | ||||||||
\(726\) | −4.43845 | −0.164726 | ||||||||
\(727\) | −21.9309 | −0.813371 | −0.406685 | − | 0.913568i | \(-0.633316\pi\) | ||||
−0.406685 | + | 0.913568i | \(0.633316\pi\) | |||||||
\(728\) | −0.561553 | −0.0208125 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.36932 | 0.272751 | ||||||||
\(731\) | 3.86174 | 0.142832 | ||||||||
\(732\) | −11.1231 | −0.411122 | ||||||||
\(733\) | 46.1080 | 1.70304 | 0.851518 | − | 0.524325i | \(-0.175682\pi\) | ||||
0.851518 | + | 0.524325i | \(0.175682\pi\) | |||||||
\(734\) | 13.7538 | 0.507662 | ||||||||
\(735\) | −13.3693 | −0.493135 | ||||||||
\(736\) | −3.12311 | −0.115119 | ||||||||
\(737\) | −29.9309 | −1.10252 | ||||||||
\(738\) | −2.00000 | −0.0736210 | ||||||||
\(739\) | −25.3693 | −0.933225 | −0.466613 | − | 0.884462i | \(-0.654526\pi\) | ||||
−0.466613 | + | 0.884462i | \(0.654526\pi\) | |||||||
\(740\) | 18.2462 | 0.670744 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 3.68466 | 0.135268 | ||||||||
\(743\) | 6.73863 | 0.247216 | 0.123608 | − | 0.992331i | \(-0.460553\pi\) | ||||
0.123608 | + | 0.992331i | \(0.460553\pi\) | |||||||
\(744\) | 1.12311 | 0.0411750 | ||||||||
\(745\) | −12.6307 | −0.462752 | ||||||||
\(746\) | 29.3693 | 1.07529 | ||||||||
\(747\) | 11.3693 | 0.415982 | ||||||||
\(748\) | −8.80776 | −0.322044 | ||||||||
\(749\) | −4.80776 | −0.175672 | ||||||||
\(750\) | 12.0000 | 0.438178 | ||||||||
\(751\) | −18.7386 | −0.683782 | −0.341891 | − | 0.939740i | \(-0.611067\pi\) | ||||
−0.341891 | + | 0.939740i | \(0.611067\pi\) | |||||||
\(752\) | −10.2462 | −0.373641 | ||||||||
\(753\) | −5.75379 | −0.209680 | ||||||||
\(754\) | 6.00000 | 0.218507 | ||||||||
\(755\) | 14.7386 | 0.536394 | ||||||||
\(756\) | 0.561553 | 0.0204235 | ||||||||
\(757\) | −1.50758 | −0.0547938 | −0.0273969 | − | 0.999625i | \(-0.508722\pi\) | ||||
−0.0273969 | + | 0.999625i | \(0.508722\pi\) | |||||||
\(758\) | 12.8078 | 0.465199 | ||||||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | −4.00000 | −0.145095 | ||||||||
\(761\) | −20.2462 | −0.733925 | −0.366962 | − | 0.930236i | \(-0.619602\pi\) | ||||
−0.366962 | + | 0.930236i | \(0.619602\pi\) | |||||||
\(762\) | −11.6847 | −0.423291 | ||||||||
\(763\) | 3.50758 | 0.126983 | ||||||||
\(764\) | −3.68466 | −0.133306 | ||||||||
\(765\) | −6.87689 | −0.248635 | ||||||||
\(766\) | −4.49242 | −0.162318 | ||||||||
\(767\) | 8.00000 | 0.288863 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 5.93087 | 0.213873 | 0.106936 | − | 0.994266i | \(-0.465896\pi\) | ||||
0.106936 | + | 0.994266i | \(0.465896\pi\) | |||||||
\(770\) | 2.87689 | 0.103676 | ||||||||
\(771\) | −21.1231 | −0.760730 | ||||||||
\(772\) | −0.630683 | −0.0226988 | ||||||||
\(773\) | −45.0540 | −1.62048 | −0.810239 | − | 0.586099i | \(-0.800663\pi\) | ||||
−0.810239 | + | 0.586099i | \(0.800663\pi\) | |||||||
\(774\) | −1.12311 | −0.0403692 | ||||||||
\(775\) | −1.12311 | −0.0403431 | ||||||||
\(776\) | −4.24621 | −0.152430 | ||||||||
\(777\) | −5.12311 | −0.183790 | ||||||||
\(778\) | −2.56155 | −0.0918361 | ||||||||
\(779\) | −4.00000 | −0.143315 | ||||||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | −5.75379 | −0.205887 | ||||||||
\(782\) | −10.7386 | −0.384013 | ||||||||
\(783\) | −6.00000 | −0.214423 | ||||||||
\(784\) | −6.68466 | −0.238738 | ||||||||
\(785\) | 13.6155 | 0.485959 | ||||||||
\(786\) | 21.3693 | 0.762218 | ||||||||
\(787\) | 45.8617 | 1.63479 | 0.817397 | − | 0.576074i | \(-0.195416\pi\) | ||||
0.817397 | + | 0.576074i | \(0.195416\pi\) | |||||||
\(788\) | 18.4924 | 0.658765 | ||||||||
\(789\) | −0.315342 | −0.0112265 | ||||||||
\(790\) | 14.7386 | 0.524377 | ||||||||
\(791\) | −2.24621 | −0.0798661 | ||||||||
\(792\) | 2.56155 | 0.0910208 | ||||||||
\(793\) | −11.1231 | −0.394993 | ||||||||
\(794\) | −17.6155 | −0.625152 | ||||||||
\(795\) | 13.1231 | 0.465429 | ||||||||
\(796\) | −19.6847 | −0.697704 | ||||||||
\(797\) | 32.7386 | 1.15966 | 0.579831 | − | 0.814737i | \(-0.303119\pi\) | ||||
0.579831 | + | 0.814737i | \(0.303119\pi\) | |||||||
\(798\) | 1.12311 | 0.0397575 | ||||||||
\(799\) | −35.2311 | −1.24639 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 2.00000 | 0.0706665 | ||||||||
\(802\) | −5.36932 | −0.189597 | ||||||||
\(803\) | −9.43845 | −0.333076 | ||||||||
\(804\) | −11.6847 | −0.412086 | ||||||||
\(805\) | 3.50758 | 0.123626 | ||||||||
\(806\) | 1.12311 | 0.0395597 | ||||||||
\(807\) | 11.7538 | 0.413753 | ||||||||
\(808\) | 3.68466 | 0.129626 | ||||||||
\(809\) | −23.3693 | −0.821621 | −0.410811 | − | 0.911721i | \(-0.634754\pi\) | ||||
−0.410811 | + | 0.911721i | \(0.634754\pi\) | |||||||
\(810\) | 2.00000 | 0.0702728 | ||||||||
\(811\) | −39.2311 | −1.37759 | −0.688794 | − | 0.724957i | \(-0.741860\pi\) | ||||
−0.688794 | + | 0.724957i | \(0.741860\pi\) | |||||||
\(812\) | −3.36932 | −0.118240 | ||||||||
\(813\) | 11.3693 | 0.398739 | ||||||||
\(814\) | −23.3693 | −0.819094 | ||||||||
\(815\) | 44.9848 | 1.57575 | ||||||||
\(816\) | −3.43845 | −0.120370 | ||||||||
\(817\) | −2.24621 | −0.0785850 | ||||||||
\(818\) | −21.3693 | −0.747161 | ||||||||
\(819\) | 0.561553 | 0.0196222 | ||||||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | 2.17708 | 0.0759806 | 0.0379903 | − | 0.999278i | \(-0.487904\pi\) | ||||
0.0379903 | + | 0.999278i | \(0.487904\pi\) | |||||||
\(822\) | −6.00000 | −0.209274 | ||||||||
\(823\) | 8.00000 | 0.278862 | 0.139431 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139431 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(824\) | 1.00000 | 0.0348367 | ||||||||
\(825\) | −2.56155 | −0.0891818 | ||||||||
\(826\) | −4.49242 | −0.156311 | ||||||||
\(827\) | 1.75379 | 0.0609852 | 0.0304926 | − | 0.999535i | \(-0.490292\pi\) | ||||
0.0304926 | + | 0.999535i | \(0.490292\pi\) | |||||||
\(828\) | 3.12311 | 0.108535 | ||||||||
\(829\) | 49.2311 | 1.70987 | 0.854933 | − | 0.518739i | \(-0.173598\pi\) | ||||
0.854933 | + | 0.518739i | \(0.173598\pi\) | |||||||
\(830\) | 22.7386 | 0.789269 | ||||||||
\(831\) | −6.00000 | −0.208138 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −22.9848 | −0.796378 | ||||||||
\(834\) | −12.8078 | −0.443497 | ||||||||
\(835\) | 6.38447 | 0.220944 | ||||||||
\(836\) | 5.12311 | 0.177186 | ||||||||
\(837\) | −1.12311 | −0.0388202 | ||||||||
\(838\) | 19.9309 | 0.688500 | ||||||||
\(839\) | −46.2462 | −1.59660 | −0.798298 | − | 0.602262i | \(-0.794266\pi\) | ||||
−0.798298 | + | 0.602262i | \(0.794266\pi\) | |||||||
\(840\) | 1.12311 | 0.0387508 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −17.0540 | −0.587719 | ||||||||
\(843\) | 22.4924 | 0.774680 | ||||||||
\(844\) | 8.49242 | 0.292321 | ||||||||
\(845\) | −2.00000 | −0.0688021 | ||||||||
\(846\) | 10.2462 | 0.352272 | ||||||||
\(847\) | 2.49242 | 0.0856407 | ||||||||
\(848\) | 6.56155 | 0.225325 | ||||||||
\(849\) | −21.6155 | −0.741843 | ||||||||
\(850\) | 3.43845 | 0.117938 | ||||||||
\(851\) | −28.4924 | −0.976708 | ||||||||
\(852\) | −2.24621 | −0.0769539 | ||||||||
\(853\) | 23.3002 | 0.797783 | 0.398892 | − | 0.916998i | \(-0.369395\pi\) | ||||
0.398892 | + | 0.916998i | \(0.369395\pi\) | |||||||
\(854\) | 6.24621 | 0.213741 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | −8.56155 | −0.292628 | ||||||||
\(857\) | 35.9309 | 1.22738 | 0.613688 | − | 0.789549i | \(-0.289685\pi\) | ||||
0.613688 | + | 0.789549i | \(0.289685\pi\) | |||||||
\(858\) | 2.56155 | 0.0874500 | ||||||||
\(859\) | 5.61553 | 0.191599 | 0.0957997 | − | 0.995401i | \(-0.469459\pi\) | ||||
0.0957997 | + | 0.995401i | \(0.469459\pi\) | |||||||
\(860\) | −2.24621 | −0.0765952 | ||||||||
\(861\) | 1.12311 | 0.0382753 | ||||||||
\(862\) | 32.0000 | 1.08992 | ||||||||
\(863\) | −29.7538 | −1.01283 | −0.506415 | − | 0.862290i | \(-0.669030\pi\) | ||||
−0.506415 | + | 0.862290i | \(0.669030\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −41.6155 | −1.41497 | ||||||||
\(866\) | 22.4924 | 0.764324 | ||||||||
\(867\) | 5.17708 | 0.175823 | ||||||||
\(868\) | −0.630683 | −0.0214068 | ||||||||
\(869\) | −18.8769 | −0.640355 | ||||||||
\(870\) | −12.0000 | −0.406838 | ||||||||
\(871\) | −11.6847 | −0.395920 | ||||||||
\(872\) | 6.24621 | 0.211523 | ||||||||
\(873\) | 4.24621 | 0.143712 | ||||||||
\(874\) | 6.24621 | 0.211281 | ||||||||
\(875\) | −6.73863 | −0.227807 | ||||||||
\(876\) | −3.68466 | −0.124493 | ||||||||
\(877\) | −36.9848 | −1.24889 | −0.624445 | − | 0.781069i | \(-0.714675\pi\) | ||||
−0.624445 | + | 0.781069i | \(0.714675\pi\) | |||||||
\(878\) | 11.0540 | 0.373054 | ||||||||
\(879\) | 7.61553 | 0.256865 | ||||||||
\(880\) | 5.12311 | 0.172700 | ||||||||
\(881\) | 2.73863 | 0.0922669 | 0.0461335 | − | 0.998935i | \(-0.485310\pi\) | ||||
0.0461335 | + | 0.998935i | \(0.485310\pi\) | |||||||
\(882\) | 6.68466 | 0.225084 | ||||||||
\(883\) | −38.9157 | −1.30962 | −0.654809 | − | 0.755794i | \(-0.727251\pi\) | ||||
−0.654809 | + | 0.755794i | \(0.727251\pi\) | |||||||
\(884\) | −3.43845 | −0.115647 | ||||||||
\(885\) | −16.0000 | −0.537834 | ||||||||
\(886\) | 12.4924 | 0.419691 | ||||||||
\(887\) | 31.1231 | 1.04501 | 0.522506 | − | 0.852636i | \(-0.324997\pi\) | ||||
0.522506 | + | 0.852636i | \(0.324997\pi\) | |||||||
\(888\) | −9.12311 | −0.306151 | ||||||||
\(889\) | 6.56155 | 0.220067 | ||||||||
\(890\) | 4.00000 | 0.134080 | ||||||||
\(891\) | −2.56155 | −0.0858152 | ||||||||
\(892\) | −5.68466 | −0.190336 | ||||||||
\(893\) | 20.4924 | 0.685753 | ||||||||
\(894\) | 6.31534 | 0.211217 | ||||||||
\(895\) | 21.6155 | 0.722527 | ||||||||
\(896\) | 0.561553 | 0.0187602 | ||||||||
\(897\) | 3.12311 | 0.104277 | ||||||||
\(898\) | 26.3153 | 0.878154 | ||||||||
\(899\) | 6.73863 | 0.224746 | ||||||||
\(900\) | −1.00000 | −0.0333333 | ||||||||
\(901\) | 22.5616 | 0.751634 | ||||||||
\(902\) | 5.12311 | 0.170581 | ||||||||
\(903\) | 0.630683 | 0.0209878 | ||||||||
\(904\) | −4.00000 | −0.133038 | ||||||||
\(905\) | −31.8617 | −1.05912 | ||||||||
\(906\) | −7.36932 | −0.244829 | ||||||||
\(907\) | −55.5464 | −1.84439 | −0.922194 | − | 0.386728i | \(-0.873605\pi\) | ||||
−0.922194 | + | 0.386728i | \(0.873605\pi\) | |||||||
\(908\) | −4.80776 | −0.159551 | ||||||||
\(909\) | −3.68466 | −0.122212 | ||||||||
\(910\) | 1.12311 | 0.0372306 | ||||||||
\(911\) | 10.7386 | 0.355787 | 0.177893 | − | 0.984050i | \(-0.443072\pi\) | ||||
0.177893 | + | 0.984050i | \(0.443072\pi\) | |||||||
\(912\) | 2.00000 | 0.0662266 | ||||||||
\(913\) | −29.1231 | −0.963834 | ||||||||
\(914\) | −8.63068 | −0.285478 | ||||||||
\(915\) | 22.2462 | 0.735437 | ||||||||
\(916\) | −6.00000 | −0.198246 | ||||||||
\(917\) | −12.0000 | −0.396275 | ||||||||
\(918\) | 3.43845 | 0.113486 | ||||||||
\(919\) | −32.8078 | −1.08223 | −0.541114 | − | 0.840949i | \(-0.681997\pi\) | ||||
−0.541114 | + | 0.840949i | \(0.681997\pi\) | |||||||
\(920\) | 6.24621 | 0.205931 | ||||||||
\(921\) | −21.4384 | −0.706421 | ||||||||
\(922\) | −8.24621 | −0.271575 | ||||||||
\(923\) | −2.24621 | −0.0739349 | ||||||||
\(924\) | −1.43845 | −0.0473214 | ||||||||
\(925\) | 9.12311 | 0.299966 | ||||||||
\(926\) | −13.1231 | −0.431252 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | 0.384472 | 0.0126141 | 0.00630706 | − | 0.999980i | \(-0.497992\pi\) | ||||
0.00630706 | + | 0.999980i | \(0.497992\pi\) | |||||||
\(930\) | −2.24621 | −0.0736562 | ||||||||
\(931\) | 13.3693 | 0.438162 | ||||||||
\(932\) | 24.4924 | 0.802276 | ||||||||
\(933\) | 18.0000 | 0.589294 | ||||||||
\(934\) | 38.1771 | 1.24919 | ||||||||
\(935\) | 17.6155 | 0.576089 | ||||||||
\(936\) | 1.00000 | 0.0326860 | ||||||||
\(937\) | 48.7386 | 1.59222 | 0.796111 | − | 0.605151i | \(-0.206887\pi\) | ||||
0.796111 | + | 0.605151i | \(0.206887\pi\) | |||||||
\(938\) | 6.56155 | 0.214242 | ||||||||
\(939\) | 16.2462 | 0.530175 | ||||||||
\(940\) | 20.4924 | 0.668389 | ||||||||
\(941\) | −19.4384 | −0.633675 | −0.316838 | − | 0.948480i | \(-0.602621\pi\) | ||||
−0.316838 | + | 0.948480i | \(0.602621\pi\) | |||||||
\(942\) | −6.80776 | −0.221809 | ||||||||
\(943\) | 6.24621 | 0.203405 | ||||||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | −1.12311 | −0.0365346 | ||||||||
\(946\) | 2.87689 | 0.0935359 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | −7.36932 | −0.239344 | ||||||||
\(949\) | −3.68466 | −0.119609 | ||||||||
\(950\) | −2.00000 | −0.0648886 | ||||||||
\(951\) | 13.0540 | 0.423304 | ||||||||
\(952\) | 1.93087 | 0.0625798 | ||||||||
\(953\) | 13.1922 | 0.427338 | 0.213669 | − | 0.976906i | \(-0.431459\pi\) | ||||
0.213669 | + | 0.976906i | \(0.431459\pi\) | |||||||
\(954\) | −6.56155 | −0.212438 | ||||||||
\(955\) | 7.36932 | 0.238465 | ||||||||
\(956\) | −2.56155 | −0.0828465 | ||||||||
\(957\) | 15.3693 | 0.496819 | ||||||||
\(958\) | 5.12311 | 0.165520 | ||||||||
\(959\) | 3.36932 | 0.108801 | ||||||||
\(960\) | 2.00000 | 0.0645497 | ||||||||
\(961\) | −29.7386 | −0.959311 | ||||||||
\(962\) | −9.12311 | −0.294141 | ||||||||
\(963\) | 8.56155 | 0.275892 | ||||||||
\(964\) | −8.31534 | −0.267819 | ||||||||
\(965\) | 1.26137 | 0.0406048 | ||||||||
\(966\) | −1.75379 | −0.0564272 | ||||||||
\(967\) | 17.1231 | 0.550642 | 0.275321 | − | 0.961352i | \(-0.411216\pi\) | ||||
0.275321 | + | 0.961352i | \(0.411216\pi\) | |||||||
\(968\) | 4.43845 | 0.142657 | ||||||||
\(969\) | 6.87689 | 0.220918 | ||||||||
\(970\) | 8.49242 | 0.272675 | ||||||||
\(971\) | 13.6155 | 0.436943 | 0.218472 | − | 0.975843i | \(-0.429893\pi\) | ||||
0.218472 | + | 0.975843i | \(0.429893\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 7.19224 | 0.230572 | ||||||||
\(974\) | −5.61553 | −0.179933 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 11.1231 | 0.356042 | ||||||||
\(977\) | −15.1231 | −0.483831 | −0.241916 | − | 0.970297i | \(-0.577776\pi\) | ||||
−0.241916 | + | 0.970297i | \(0.577776\pi\) | |||||||
\(978\) | −22.4924 | −0.719228 | ||||||||
\(979\) | −5.12311 | −0.163735 | ||||||||
\(980\) | 13.3693 | 0.427067 | ||||||||
\(981\) | −6.24621 | −0.199426 | ||||||||
\(982\) | −15.4384 | −0.492661 | ||||||||
\(983\) | 20.8078 | 0.663665 | 0.331832 | − | 0.943338i | \(-0.392333\pi\) | ||||
0.331832 | + | 0.943338i | \(0.392333\pi\) | |||||||
\(984\) | 2.00000 | 0.0637577 | ||||||||
\(985\) | −36.9848 | −1.17844 | ||||||||
\(986\) | −20.6307 | −0.657015 | ||||||||
\(987\) | −5.75379 | −0.183145 | ||||||||
\(988\) | 2.00000 | 0.0636285 | ||||||||
\(989\) | 3.50758 | 0.111534 | ||||||||
\(990\) | −5.12311 | −0.162823 | ||||||||
\(991\) | −55.8617 | −1.77451 | −0.887253 | − | 0.461283i | \(-0.847389\pi\) | ||||
−0.887253 | + | 0.461283i | \(0.847389\pi\) | |||||||
\(992\) | −1.12311 | −0.0356586 | ||||||||
\(993\) | −21.9309 | −0.695955 | ||||||||
\(994\) | 1.26137 | 0.0400081 | ||||||||
\(995\) | 39.3693 | 1.24809 | ||||||||
\(996\) | −11.3693 | −0.360251 | ||||||||
\(997\) | 50.4924 | 1.59911 | 0.799556 | − | 0.600592i | \(-0.205068\pi\) | ||||
0.799556 | + | 0.600592i | \(0.205068\pi\) | |||||||
\(998\) | −22.7386 | −0.719779 | ||||||||
\(999\) | 9.12311 | 0.288642 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8034.2.a.l.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.l.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |