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: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.34292\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.34292 | 1.65670 | 0.828348 | − | 0.560213i | \(-0.189281\pi\) | ||||
0.828348 | + | 0.560213i | \(0.189281\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.48929 | 1.74464 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.34292 | −0.956494 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.48929 | 1.23365 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.34292 | 0.740897 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −3.48929 | −1.00727 | ||||||||
\(13\) | 3.14637 | 0.872645 | 0.436322 | − | 0.899790i | \(-0.356281\pi\) | ||||
0.436322 | + | 0.899790i | \(0.356281\pi\) | |||||||
\(14\) | −2.34292 | −0.626173 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.19656 | 0.299139 | ||||||||
\(17\) | 6.48929 | 1.57388 | 0.786942 | − | 0.617027i | \(-0.211663\pi\) | ||||
0.786942 | + | 0.617027i | \(0.211663\pi\) | |||||||
\(18\) | 2.34292 | 0.552232 | ||||||||
\(19\) | 7.17513 | 1.64609 | 0.823044 | − | 0.567977i | \(-0.192274\pi\) | ||||
0.823044 | + | 0.567977i | \(0.192274\pi\) | |||||||
\(20\) | 3.48929 | 0.780229 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −2.34292 | −0.499513 | ||||||||
\(23\) | 2.19656 | 0.458014 | 0.229007 | − | 0.973425i | \(-0.426452\pi\) | ||||
0.229007 | + | 0.973425i | \(0.426452\pi\) | |||||||
\(24\) | −3.48929 | −0.712248 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 7.37169 | 1.44571 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.48929 | −0.659414 | ||||||||
\(29\) | 0.949808 | 0.176375 | 0.0881874 | − | 0.996104i | \(-0.471893\pi\) | ||||
0.0881874 | + | 0.996104i | \(0.471893\pi\) | |||||||
\(30\) | −2.34292 | −0.427757 | ||||||||
\(31\) | −6.12494 | −1.10007 | −0.550036 | − | 0.835141i | \(-0.685386\pi\) | ||||
−0.550036 | + | 0.835141i | \(0.685386\pi\) | |||||||
\(32\) | −4.17513 | −0.738067 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 15.2039 | 2.60745 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 3.48929 | 0.581548 | ||||||||
\(37\) | 0.853635 | 0.140337 | 0.0701683 | − | 0.997535i | \(-0.477646\pi\) | ||||
0.0701683 | + | 0.997535i | \(0.477646\pi\) | |||||||
\(38\) | 16.8108 | 2.72707 | ||||||||
\(39\) | −3.14637 | −0.503822 | ||||||||
\(40\) | 3.48929 | 0.551705 | ||||||||
\(41\) | 3.53948 | 0.552774 | 0.276387 | − | 0.961046i | \(-0.410863\pi\) | ||||
0.276387 | + | 0.961046i | \(0.410863\pi\) | |||||||
\(42\) | 2.34292 | 0.361521 | ||||||||
\(43\) | −5.63565 | −0.859429 | −0.429715 | − | 0.902965i | \(-0.641386\pi\) | ||||
−0.429715 | + | 0.902965i | \(0.641386\pi\) | |||||||
\(44\) | −3.48929 | −0.526030 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 5.14637 | 0.758790 | ||||||||
\(47\) | −1.53948 | −0.224556 | −0.112278 | − | 0.993677i | \(-0.535815\pi\) | ||||
−0.112278 | + | 0.993677i | \(0.535815\pi\) | |||||||
\(48\) | −1.19656 | −0.172708 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.34292 | 0.331339 | ||||||||
\(51\) | −6.48929 | −0.908682 | ||||||||
\(52\) | 10.9786 | 1.52245 | ||||||||
\(53\) | −6.15371 | −0.845277 | −0.422639 | − | 0.906298i | \(-0.638896\pi\) | ||||
−0.422639 | + | 0.906298i | \(0.638896\pi\) | |||||||
\(54\) | −2.34292 | −0.318831 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −3.48929 | −0.466276 | ||||||||
\(57\) | −7.17513 | −0.950370 | ||||||||
\(58\) | 2.22533 | 0.292200 | ||||||||
\(59\) | −5.63565 | −0.733700 | −0.366850 | − | 0.930280i | \(-0.619564\pi\) | ||||
−0.366850 | + | 0.930280i | \(0.619564\pi\) | |||||||
\(60\) | −3.48929 | −0.450465 | ||||||||
\(61\) | 4.58967 | 0.587647 | 0.293824 | − | 0.955860i | \(-0.405072\pi\) | ||||
0.293824 | + | 0.955860i | \(0.405072\pi\) | |||||||
\(62\) | −14.3503 | −1.82249 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −12.1751 | −1.52189 | ||||||||
\(65\) | 3.14637 | 0.390259 | ||||||||
\(66\) | 2.34292 | 0.288394 | ||||||||
\(67\) | −10.3503 | −1.26449 | −0.632243 | − | 0.774770i | \(-0.717866\pi\) | ||||
−0.632243 | + | 0.774770i | \(0.717866\pi\) | |||||||
\(68\) | 22.6430 | 2.74587 | ||||||||
\(69\) | −2.19656 | −0.264434 | ||||||||
\(70\) | −2.34292 | −0.280033 | ||||||||
\(71\) | −8.22533 | −0.976167 | −0.488083 | − | 0.872797i | \(-0.662304\pi\) | ||||
−0.488083 | + | 0.872797i | \(0.662304\pi\) | |||||||
\(72\) | 3.48929 | 0.411217 | ||||||||
\(73\) | −4.68585 | −0.548437 | −0.274218 | − | 0.961667i | \(-0.588419\pi\) | ||||
−0.274218 | + | 0.961667i | \(0.588419\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 25.0361 | 2.87184 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | −7.37169 | −0.834680 | ||||||||
\(79\) | 2.51806 | 0.283304 | 0.141652 | − | 0.989917i | \(-0.454759\pi\) | ||||
0.141652 | + | 0.989917i | \(0.454759\pi\) | |||||||
\(80\) | 1.19656 | 0.133779 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.29273 | 0.915779 | ||||||||
\(83\) | 13.8610 | 1.52144 | 0.760720 | − | 0.649080i | \(-0.224846\pi\) | ||||
0.760720 | + | 0.649080i | \(0.224846\pi\) | |||||||
\(84\) | 3.48929 | 0.380713 | ||||||||
\(85\) | 6.48929 | 0.703862 | ||||||||
\(86\) | −13.2039 | −1.42381 | ||||||||
\(87\) | −0.949808 | −0.101830 | ||||||||
\(88\) | −3.48929 | −0.371959 | ||||||||
\(89\) | −18.3790 | −1.94817 | −0.974087 | − | 0.226173i | \(-0.927378\pi\) | ||||
−0.974087 | + | 0.226173i | \(0.927378\pi\) | |||||||
\(90\) | 2.34292 | 0.246966 | ||||||||
\(91\) | −3.14637 | −0.329829 | ||||||||
\(92\) | 7.66442 | 0.799071 | ||||||||
\(93\) | 6.12494 | 0.635127 | ||||||||
\(94\) | −3.60688 | −0.372022 | ||||||||
\(95\) | 7.17513 | 0.736153 | ||||||||
\(96\) | 4.17513 | 0.426123 | ||||||||
\(97\) | −5.00735 | −0.508419 | −0.254209 | − | 0.967149i | \(-0.581815\pi\) | ||||
−0.254209 | + | 0.967149i | \(0.581815\pi\) | |||||||
\(98\) | 2.34292 | 0.236671 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 3.48929 | 0.348929 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | −15.2039 | −1.50541 | ||||||||
\(103\) | 11.9284 | 1.17534 | 0.587669 | − | 0.809101i | \(-0.300046\pi\) | ||||
0.587669 | + | 0.809101i | \(0.300046\pi\) | |||||||
\(104\) | 10.9786 | 1.07654 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | −14.4177 | −1.40037 | ||||||||
\(107\) | −5.20390 | −0.503080 | −0.251540 | − | 0.967847i | \(-0.580937\pi\) | ||||
−0.251540 | + | 0.967847i | \(0.580937\pi\) | |||||||
\(108\) | −3.48929 | −0.335757 | ||||||||
\(109\) | −10.2253 | −0.979409 | −0.489704 | − | 0.871889i | \(-0.662895\pi\) | ||||
−0.489704 | + | 0.871889i | \(0.662895\pi\) | |||||||
\(110\) | −2.34292 | −0.223389 | ||||||||
\(111\) | −0.853635 | −0.0810234 | ||||||||
\(112\) | −1.19656 | −0.113064 | ||||||||
\(113\) | 11.0748 | 1.04182 | 0.520912 | − | 0.853610i | \(-0.325592\pi\) | ||||
0.520912 | + | 0.853610i | \(0.325592\pi\) | |||||||
\(114\) | −16.8108 | −1.57447 | ||||||||
\(115\) | 2.19656 | 0.204830 | ||||||||
\(116\) | 3.31415 | 0.307711 | ||||||||
\(117\) | 3.14637 | 0.290882 | ||||||||
\(118\) | −13.2039 | −1.21552 | ||||||||
\(119\) | −6.48929 | −0.594872 | ||||||||
\(120\) | −3.48929 | −0.318527 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 10.7533 | 0.973554 | ||||||||
\(123\) | −3.53948 | −0.319144 | ||||||||
\(124\) | −21.3717 | −1.91923 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −2.34292 | −0.208724 | ||||||||
\(127\) | −8.65708 | −0.768191 | −0.384096 | − | 0.923293i | \(-0.625487\pi\) | ||||
−0.384096 | + | 0.923293i | \(0.625487\pi\) | |||||||
\(128\) | −20.1751 | −1.78325 | ||||||||
\(129\) | 5.63565 | 0.496192 | ||||||||
\(130\) | 7.37169 | 0.646540 | ||||||||
\(131\) | 4.75325 | 0.415293 | 0.207647 | − | 0.978204i | \(-0.433420\pi\) | ||||
0.207647 | + | 0.978204i | \(0.433420\pi\) | |||||||
\(132\) | 3.48929 | 0.303704 | ||||||||
\(133\) | −7.17513 | −0.622163 | ||||||||
\(134\) | −24.2499 | −2.09487 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 22.6430 | 1.94162 | ||||||||
\(137\) | 12.1004 | 1.03381 | 0.516903 | − | 0.856044i | \(-0.327085\pi\) | ||||
0.516903 | + | 0.856044i | \(0.327085\pi\) | |||||||
\(138\) | −5.14637 | −0.438088 | ||||||||
\(139\) | −21.4292 | −1.81760 | −0.908802 | − | 0.417228i | \(-0.863002\pi\) | ||||
−0.908802 | + | 0.417228i | \(0.863002\pi\) | |||||||
\(140\) | −3.48929 | −0.294899 | ||||||||
\(141\) | 1.53948 | 0.129648 | ||||||||
\(142\) | −19.2713 | −1.61721 | ||||||||
\(143\) | −3.14637 | −0.263112 | ||||||||
\(144\) | 1.19656 | 0.0997131 | ||||||||
\(145\) | 0.949808 | 0.0788773 | ||||||||
\(146\) | −10.9786 | −0.908594 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 2.97858 | 0.244838 | ||||||||
\(149\) | −8.87819 | −0.727330 | −0.363665 | − | 0.931530i | \(-0.618475\pi\) | ||||
−0.363665 | + | 0.931530i | \(0.618475\pi\) | |||||||
\(150\) | −2.34292 | −0.191299 | ||||||||
\(151\) | 18.9357 | 1.54097 | 0.770484 | − | 0.637459i | \(-0.220015\pi\) | ||||
0.770484 | + | 0.637459i | \(0.220015\pi\) | |||||||
\(152\) | 25.0361 | 2.03070 | ||||||||
\(153\) | 6.48929 | 0.524628 | ||||||||
\(154\) | 2.34292 | 0.188798 | ||||||||
\(155\) | −6.12494 | −0.491967 | ||||||||
\(156\) | −10.9786 | −0.878990 | ||||||||
\(157\) | 10.7146 | 0.855119 | 0.427560 | − | 0.903987i | \(-0.359373\pi\) | ||||
0.427560 | + | 0.903987i | \(0.359373\pi\) | |||||||
\(158\) | 5.89962 | 0.469348 | ||||||||
\(159\) | 6.15371 | 0.488021 | ||||||||
\(160\) | −4.17513 | −0.330073 | ||||||||
\(161\) | −2.19656 | −0.173113 | ||||||||
\(162\) | 2.34292 | 0.184077 | ||||||||
\(163\) | 12.0821 | 0.946343 | 0.473171 | − | 0.880970i | \(-0.343109\pi\) | ||||
0.473171 | + | 0.880970i | \(0.343109\pi\) | |||||||
\(164\) | 12.3503 | 0.964394 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | 32.4752 | 2.52057 | ||||||||
\(167\) | −17.4292 | −1.34871 | −0.674357 | − | 0.738405i | \(-0.735579\pi\) | ||||
−0.674357 | + | 0.738405i | \(0.735579\pi\) | |||||||
\(168\) | 3.48929 | 0.269204 | ||||||||
\(169\) | −3.10038 | −0.238491 | ||||||||
\(170\) | 15.2039 | 1.16609 | ||||||||
\(171\) | 7.17513 | 0.548696 | ||||||||
\(172\) | −19.6644 | −1.49940 | ||||||||
\(173\) | 13.4721 | 1.02426 | 0.512132 | − | 0.858907i | \(-0.328856\pi\) | ||||
0.512132 | + | 0.858907i | \(0.328856\pi\) | |||||||
\(174\) | −2.22533 | −0.168702 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −1.19656 | −0.0901939 | ||||||||
\(177\) | 5.63565 | 0.423602 | ||||||||
\(178\) | −43.0607 | −3.22753 | ||||||||
\(179\) | −12.2253 | −0.913764 | −0.456882 | − | 0.889527i | \(-0.651034\pi\) | ||||
−0.456882 | + | 0.889527i | \(0.651034\pi\) | |||||||
\(180\) | 3.48929 | 0.260076 | ||||||||
\(181\) | −11.9572 | −0.888768 | −0.444384 | − | 0.895836i | \(-0.646577\pi\) | ||||
−0.444384 | + | 0.895836i | \(0.646577\pi\) | |||||||
\(182\) | −7.37169 | −0.546426 | ||||||||
\(183\) | −4.58967 | −0.339278 | ||||||||
\(184\) | 7.66442 | 0.565029 | ||||||||
\(185\) | 0.853635 | 0.0627605 | ||||||||
\(186\) | 14.3503 | 1.05221 | ||||||||
\(187\) | −6.48929 | −0.474544 | ||||||||
\(188\) | −5.37169 | −0.391771 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 16.8108 | 1.21958 | ||||||||
\(191\) | 5.37169 | 0.388682 | 0.194341 | − | 0.980934i | \(-0.437743\pi\) | ||||
0.194341 | + | 0.980934i | \(0.437743\pi\) | |||||||
\(192\) | 12.1751 | 0.878665 | ||||||||
\(193\) | −2.92104 | −0.210261 | −0.105130 | − | 0.994458i | \(-0.533526\pi\) | ||||
−0.105130 | + | 0.994458i | \(0.533526\pi\) | |||||||
\(194\) | −11.7318 | −0.842296 | ||||||||
\(195\) | −3.14637 | −0.225316 | ||||||||
\(196\) | 3.48929 | 0.249235 | ||||||||
\(197\) | 9.27131 | 0.660553 | 0.330277 | − | 0.943884i | \(-0.392858\pi\) | ||||
0.330277 | + | 0.943884i | \(0.392858\pi\) | |||||||
\(198\) | −2.34292 | −0.166504 | ||||||||
\(199\) | −8.78623 | −0.622839 | −0.311420 | − | 0.950272i | \(-0.600804\pi\) | ||||
−0.311420 | + | 0.950272i | \(0.600804\pi\) | |||||||
\(200\) | 3.48929 | 0.246730 | ||||||||
\(201\) | 10.3503 | 0.730052 | ||||||||
\(202\) | 14.0575 | 0.989085 | ||||||||
\(203\) | −0.949808 | −0.0666634 | ||||||||
\(204\) | −22.6430 | −1.58533 | ||||||||
\(205\) | 3.53948 | 0.247208 | ||||||||
\(206\) | 27.9473 | 1.94718 | ||||||||
\(207\) | 2.19656 | 0.152671 | ||||||||
\(208\) | 3.76481 | 0.261042 | ||||||||
\(209\) | −7.17513 | −0.496314 | ||||||||
\(210\) | 2.34292 | 0.161677 | ||||||||
\(211\) | −24.0575 | −1.65619 | −0.828095 | − | 0.560588i | \(-0.810575\pi\) | ||||
−0.828095 | + | 0.560588i | \(0.810575\pi\) | |||||||
\(212\) | −21.4721 | −1.47471 | ||||||||
\(213\) | 8.22533 | 0.563590 | ||||||||
\(214\) | −12.1923 | −0.833452 | ||||||||
\(215\) | −5.63565 | −0.384348 | ||||||||
\(216\) | −3.48929 | −0.237416 | ||||||||
\(217\) | 6.12494 | 0.415788 | ||||||||
\(218\) | −23.9572 | −1.62258 | ||||||||
\(219\) | 4.68585 | 0.316640 | ||||||||
\(220\) | −3.48929 | −0.235248 | ||||||||
\(221\) | 20.4177 | 1.37344 | ||||||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | 8.32150 | 0.557249 | 0.278624 | − | 0.960400i | \(-0.410122\pi\) | ||||
0.278624 | + | 0.960400i | \(0.410122\pi\) | |||||||
\(224\) | 4.17513 | 0.278963 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 25.9473 | 1.72599 | ||||||||
\(227\) | 7.51071 | 0.498503 | 0.249252 | − | 0.968439i | \(-0.419815\pi\) | ||||
0.249252 | + | 0.968439i | \(0.419815\pi\) | |||||||
\(228\) | −25.0361 | −1.65806 | ||||||||
\(229\) | 17.6890 | 1.16892 | 0.584460 | − | 0.811422i | \(-0.301306\pi\) | ||||
0.584460 | + | 0.811422i | \(0.301306\pi\) | |||||||
\(230\) | 5.14637 | 0.339341 | ||||||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 3.31415 | 0.217585 | ||||||||
\(233\) | −6.75325 | −0.442420 | −0.221210 | − | 0.975226i | \(-0.571001\pi\) | ||||
−0.221210 | + | 0.975226i | \(0.571001\pi\) | |||||||
\(234\) | 7.37169 | 0.481903 | ||||||||
\(235\) | −1.53948 | −0.100425 | ||||||||
\(236\) | −19.6644 | −1.28004 | ||||||||
\(237\) | −2.51806 | −0.163565 | ||||||||
\(238\) | −15.2039 | −0.985523 | ||||||||
\(239\) | −12.5223 | −0.809998 | −0.404999 | − | 0.914317i | \(-0.632728\pi\) | ||||
−0.404999 | + | 0.914317i | \(0.632728\pi\) | |||||||
\(240\) | −1.19656 | −0.0772375 | ||||||||
\(241\) | −8.93573 | −0.575601 | −0.287801 | − | 0.957690i | \(-0.592924\pi\) | ||||
−0.287801 | + | 0.957690i | \(0.592924\pi\) | |||||||
\(242\) | 2.34292 | 0.150609 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 16.0147 | 1.02524 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −8.29273 | −0.528725 | ||||||||
\(247\) | 22.5756 | 1.43645 | ||||||||
\(248\) | −21.3717 | −1.35710 | ||||||||
\(249\) | −13.8610 | −0.878404 | ||||||||
\(250\) | 2.34292 | 0.148179 | ||||||||
\(251\) | −28.4998 | −1.79889 | −0.899445 | − | 0.437034i | \(-0.856029\pi\) | ||||
−0.899445 | + | 0.437034i | \(0.856029\pi\) | |||||||
\(252\) | −3.48929 | −0.219805 | ||||||||
\(253\) | −2.19656 | −0.138096 | ||||||||
\(254\) | −20.2829 | −1.27266 | ||||||||
\(255\) | −6.48929 | −0.406375 | ||||||||
\(256\) | −22.9185 | −1.43241 | ||||||||
\(257\) | −19.7894 | −1.23443 | −0.617213 | − | 0.786796i | \(-0.711738\pi\) | ||||
−0.617213 | + | 0.786796i | \(0.711738\pi\) | |||||||
\(258\) | 13.2039 | 0.822039 | ||||||||
\(259\) | −0.853635 | −0.0530423 | ||||||||
\(260\) | 10.9786 | 0.680862 | ||||||||
\(261\) | 0.949808 | 0.0587916 | ||||||||
\(262\) | 11.1365 | 0.688015 | ||||||||
\(263\) | 24.4507 | 1.50769 | 0.753846 | − | 0.657051i | \(-0.228196\pi\) | ||||
0.753846 | + | 0.657051i | \(0.228196\pi\) | |||||||
\(264\) | 3.48929 | 0.214751 | ||||||||
\(265\) | −6.15371 | −0.378020 | ||||||||
\(266\) | −16.8108 | −1.03074 | ||||||||
\(267\) | 18.3790 | 1.12478 | ||||||||
\(268\) | −36.1151 | −2.20608 | ||||||||
\(269\) | 16.0863 | 0.980799 | 0.490400 | − | 0.871498i | \(-0.336851\pi\) | ||||
0.490400 | + | 0.871498i | \(0.336851\pi\) | |||||||
\(270\) | −2.34292 | −0.142586 | ||||||||
\(271\) | −31.2327 | −1.89725 | −0.948625 | − | 0.316403i | \(-0.897525\pi\) | ||||
−0.948625 | + | 0.316403i | \(0.897525\pi\) | |||||||
\(272\) | 7.76481 | 0.470811 | ||||||||
\(273\) | 3.14637 | 0.190427 | ||||||||
\(274\) | 28.3503 | 1.71270 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −7.66442 | −0.461344 | ||||||||
\(277\) | −19.7648 | −1.18755 | −0.593776 | − | 0.804630i | \(-0.702364\pi\) | ||||
−0.593776 | + | 0.804630i | \(0.702364\pi\) | |||||||
\(278\) | −50.2070 | −3.01122 | ||||||||
\(279\) | −6.12494 | −0.366691 | ||||||||
\(280\) | −3.48929 | −0.208525 | ||||||||
\(281\) | 0.350269 | 0.0208953 | 0.0104477 | − | 0.999945i | \(-0.496674\pi\) | ||||
0.0104477 | + | 0.999945i | \(0.496674\pi\) | |||||||
\(282\) | 3.60688 | 0.214787 | ||||||||
\(283\) | −14.3748 | −0.854495 | −0.427247 | − | 0.904135i | \(-0.640517\pi\) | ||||
−0.427247 | + | 0.904135i | \(0.640517\pi\) | |||||||
\(284\) | −28.7005 | −1.70306 | ||||||||
\(285\) | −7.17513 | −0.425018 | ||||||||
\(286\) | −7.37169 | −0.435897 | ||||||||
\(287\) | −3.53948 | −0.208929 | ||||||||
\(288\) | −4.17513 | −0.246022 | ||||||||
\(289\) | 25.1109 | 1.47711 | ||||||||
\(290\) | 2.22533 | 0.130676 | ||||||||
\(291\) | 5.00735 | 0.293536 | ||||||||
\(292\) | −16.3503 | −0.956827 | ||||||||
\(293\) | 22.5468 | 1.31720 | 0.658600 | − | 0.752493i | \(-0.271149\pi\) | ||||
0.658600 | + | 0.752493i | \(0.271149\pi\) | |||||||
\(294\) | −2.34292 | −0.136642 | ||||||||
\(295\) | −5.63565 | −0.328120 | ||||||||
\(296\) | 2.97858 | 0.173126 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −20.8009 | −1.20497 | ||||||||
\(299\) | 6.91117 | 0.399683 | ||||||||
\(300\) | −3.48929 | −0.201454 | ||||||||
\(301\) | 5.63565 | 0.324834 | ||||||||
\(302\) | 44.3650 | 2.55292 | ||||||||
\(303\) | −6.00000 | −0.344691 | ||||||||
\(304\) | 8.58546 | 0.492410 | ||||||||
\(305\) | 4.58967 | 0.262804 | ||||||||
\(306\) | 15.2039 | 0.869149 | ||||||||
\(307\) | 9.89962 | 0.565001 | 0.282500 | − | 0.959267i | \(-0.408836\pi\) | ||||
0.282500 | + | 0.959267i | \(0.408836\pi\) | |||||||
\(308\) | 3.48929 | 0.198821 | ||||||||
\(309\) | −11.9284 | −0.678582 | ||||||||
\(310\) | −14.3503 | −0.815041 | ||||||||
\(311\) | 13.0361 | 0.739210 | 0.369605 | − | 0.929189i | \(-0.379493\pi\) | ||||
0.369605 | + | 0.929189i | \(0.379493\pi\) | |||||||
\(312\) | −10.9786 | −0.621540 | ||||||||
\(313\) | −23.7507 | −1.34247 | −0.671235 | − | 0.741244i | \(-0.734236\pi\) | ||||
−0.671235 | + | 0.741244i | \(0.734236\pi\) | |||||||
\(314\) | 25.1035 | 1.41667 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 8.78623 | 0.494264 | ||||||||
\(317\) | 13.0214 | 0.731356 | 0.365678 | − | 0.930741i | \(-0.380837\pi\) | ||||
0.365678 | + | 0.930741i | \(0.380837\pi\) | |||||||
\(318\) | 14.4177 | 0.808503 | ||||||||
\(319\) | −0.949808 | −0.0531790 | ||||||||
\(320\) | −12.1751 | −0.680611 | ||||||||
\(321\) | 5.20390 | 0.290454 | ||||||||
\(322\) | −5.14637 | −0.286796 | ||||||||
\(323\) | 46.5615 | 2.59075 | ||||||||
\(324\) | 3.48929 | 0.193849 | ||||||||
\(325\) | 3.14637 | 0.174529 | ||||||||
\(326\) | 28.3074 | 1.56780 | ||||||||
\(327\) | 10.2253 | 0.565462 | ||||||||
\(328\) | 12.3503 | 0.681930 | ||||||||
\(329\) | 1.53948 | 0.0848743 | ||||||||
\(330\) | 2.34292 | 0.128974 | ||||||||
\(331\) | 19.2327 | 1.05712 | 0.528562 | − | 0.848895i | \(-0.322732\pi\) | ||||
0.528562 | + | 0.848895i | \(0.322732\pi\) | |||||||
\(332\) | 48.3650 | 2.65437 | ||||||||
\(333\) | 0.853635 | 0.0467789 | ||||||||
\(334\) | −40.8353 | −2.23441 | ||||||||
\(335\) | −10.3503 | −0.565496 | ||||||||
\(336\) | 1.19656 | 0.0652776 | ||||||||
\(337\) | −24.2787 | −1.32254 | −0.661271 | − | 0.750147i | \(-0.729983\pi\) | ||||
−0.661271 | + | 0.750147i | \(0.729983\pi\) | |||||||
\(338\) | −7.26396 | −0.395107 | ||||||||
\(339\) | −11.0748 | −0.601498 | ||||||||
\(340\) | 22.6430 | 1.22799 | ||||||||
\(341\) | 6.12494 | 0.331684 | ||||||||
\(342\) | 16.8108 | 0.909023 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −19.6644 | −1.06023 | ||||||||
\(345\) | −2.19656 | −0.118259 | ||||||||
\(346\) | 31.5640 | 1.69689 | ||||||||
\(347\) | 10.4935 | 0.563321 | 0.281660 | − | 0.959514i | \(-0.409115\pi\) | ||||
0.281660 | + | 0.959514i | \(0.409115\pi\) | |||||||
\(348\) | −3.31415 | −0.177657 | ||||||||
\(349\) | 3.94667 | 0.211261 | 0.105630 | − | 0.994405i | \(-0.466314\pi\) | ||||
0.105630 | + | 0.994405i | \(0.466314\pi\) | |||||||
\(350\) | −2.34292 | −0.125235 | ||||||||
\(351\) | −3.14637 | −0.167941 | ||||||||
\(352\) | 4.17513 | 0.222535 | ||||||||
\(353\) | 18.4507 | 0.982029 | 0.491015 | − | 0.871151i | \(-0.336626\pi\) | ||||
0.491015 | + | 0.871151i | \(0.336626\pi\) | |||||||
\(354\) | 13.2039 | 0.701780 | ||||||||
\(355\) | −8.22533 | −0.436555 | ||||||||
\(356\) | −64.1298 | −3.39887 | ||||||||
\(357\) | 6.48929 | 0.343450 | ||||||||
\(358\) | −28.6430 | −1.51383 | ||||||||
\(359\) | 35.4005 | 1.86836 | 0.934182 | − | 0.356796i | \(-0.116131\pi\) | ||||
0.934182 | + | 0.356796i | \(0.116131\pi\) | |||||||
\(360\) | 3.48929 | 0.183902 | ||||||||
\(361\) | 32.4826 | 1.70961 | ||||||||
\(362\) | −28.0147 | −1.47242 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −10.9786 | −0.575434 | ||||||||
\(365\) | −4.68585 | −0.245268 | ||||||||
\(366\) | −10.7533 | −0.562081 | ||||||||
\(367\) | 10.9498 | 0.571575 | 0.285788 | − | 0.958293i | \(-0.407745\pi\) | ||||
0.285788 | + | 0.958293i | \(0.407745\pi\) | |||||||
\(368\) | 2.62831 | 0.137010 | ||||||||
\(369\) | 3.53948 | 0.184258 | ||||||||
\(370\) | 2.00000 | 0.103975 | ||||||||
\(371\) | 6.15371 | 0.319485 | ||||||||
\(372\) | 21.3717 | 1.10807 | ||||||||
\(373\) | −2.51385 | −0.130162 | −0.0650810 | − | 0.997880i | \(-0.520731\pi\) | ||||
−0.0650810 | + | 0.997880i | \(0.520731\pi\) | |||||||
\(374\) | −15.2039 | −0.786175 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −5.37169 | −0.277024 | ||||||||
\(377\) | 2.98844 | 0.153913 | ||||||||
\(378\) | 2.34292 | 0.120507 | ||||||||
\(379\) | −34.8971 | −1.79254 | −0.896272 | − | 0.443505i | \(-0.853735\pi\) | ||||
−0.896272 | + | 0.443505i | \(0.853735\pi\) | |||||||
\(380\) | 25.0361 | 1.28433 | ||||||||
\(381\) | 8.65708 | 0.443515 | ||||||||
\(382\) | 12.5855 | 0.643928 | ||||||||
\(383\) | 24.5609 | 1.25500 | 0.627502 | − | 0.778615i | \(-0.284078\pi\) | ||||
0.627502 | + | 0.778615i | \(0.284078\pi\) | |||||||
\(384\) | 20.1751 | 1.02956 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | −6.84377 | −0.348339 | ||||||||
\(387\) | −5.63565 | −0.286476 | ||||||||
\(388\) | −17.4721 | −0.887010 | ||||||||
\(389\) | 14.2253 | 0.721253 | 0.360626 | − | 0.932710i | \(-0.382563\pi\) | ||||
0.360626 | + | 0.932710i | \(0.382563\pi\) | |||||||
\(390\) | −7.37169 | −0.373280 | ||||||||
\(391\) | 14.2541 | 0.720861 | ||||||||
\(392\) | 3.48929 | 0.176236 | ||||||||
\(393\) | −4.75325 | −0.239770 | ||||||||
\(394\) | 21.7220 | 1.09434 | ||||||||
\(395\) | 2.51806 | 0.126697 | ||||||||
\(396\) | −3.48929 | −0.175343 | ||||||||
\(397\) | −18.9786 | −0.952507 | −0.476254 | − | 0.879308i | \(-0.658006\pi\) | ||||
−0.476254 | + | 0.879308i | \(0.658006\pi\) | |||||||
\(398\) | −20.5855 | −1.03186 | ||||||||
\(399\) | 7.17513 | 0.359206 | ||||||||
\(400\) | 1.19656 | 0.0598279 | ||||||||
\(401\) | 4.71040 | 0.235226 | 0.117613 | − | 0.993059i | \(-0.462476\pi\) | ||||
0.117613 | + | 0.993059i | \(0.462476\pi\) | |||||||
\(402\) | 24.2499 | 1.20947 | ||||||||
\(403\) | −19.2713 | −0.959972 | ||||||||
\(404\) | 20.9357 | 1.04159 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −2.22533 | −0.110441 | ||||||||
\(407\) | −0.853635 | −0.0423131 | ||||||||
\(408\) | −22.6430 | −1.12100 | ||||||||
\(409\) | 30.1067 | 1.48868 | 0.744339 | − | 0.667802i | \(-0.232765\pi\) | ||||
0.744339 | + | 0.667802i | \(0.232765\pi\) | |||||||
\(410\) | 8.29273 | 0.409549 | ||||||||
\(411\) | −12.1004 | −0.596868 | ||||||||
\(412\) | 41.6216 | 2.05055 | ||||||||
\(413\) | 5.63565 | 0.277312 | ||||||||
\(414\) | 5.14637 | 0.252930 | ||||||||
\(415\) | 13.8610 | 0.680409 | ||||||||
\(416\) | −13.1365 | −0.644070 | ||||||||
\(417\) | 21.4292 | 1.04939 | ||||||||
\(418\) | −16.8108 | −0.822243 | ||||||||
\(419\) | 35.6503 | 1.74163 | 0.870817 | − | 0.491608i | \(-0.163591\pi\) | ||||
0.870817 | + | 0.491608i | \(0.163591\pi\) | |||||||
\(420\) | 3.48929 | 0.170260 | ||||||||
\(421\) | −23.3246 | −1.13677 | −0.568387 | − | 0.822762i | \(-0.692432\pi\) | ||||
−0.568387 | + | 0.822762i | \(0.692432\pi\) | |||||||
\(422\) | −56.3650 | −2.74380 | ||||||||
\(423\) | −1.53948 | −0.0748521 | ||||||||
\(424\) | −21.4721 | −1.04278 | ||||||||
\(425\) | 6.48929 | 0.314777 | ||||||||
\(426\) | 19.2713 | 0.933698 | ||||||||
\(427\) | −4.58967 | −0.222110 | ||||||||
\(428\) | −18.1579 | −0.877696 | ||||||||
\(429\) | 3.14637 | 0.151908 | ||||||||
\(430\) | −13.2039 | −0.636749 | ||||||||
\(431\) | 4.24989 | 0.204710 | 0.102355 | − | 0.994748i | \(-0.467362\pi\) | ||||
0.102355 | + | 0.994748i | \(0.467362\pi\) | |||||||
\(432\) | −1.19656 | −0.0575694 | ||||||||
\(433\) | 31.0361 | 1.49150 | 0.745750 | − | 0.666226i | \(-0.232091\pi\) | ||||
0.745750 | + | 0.666226i | \(0.232091\pi\) | |||||||
\(434\) | 14.3503 | 0.688835 | ||||||||
\(435\) | −0.949808 | −0.0455398 | ||||||||
\(436\) | −35.6791 | −1.70872 | ||||||||
\(437\) | 15.7606 | 0.753932 | ||||||||
\(438\) | 10.9786 | 0.524577 | ||||||||
\(439\) | −19.0319 | −0.908343 | −0.454172 | − | 0.890914i | \(-0.650065\pi\) | ||||
−0.454172 | + | 0.890914i | \(0.650065\pi\) | |||||||
\(440\) | −3.48929 | −0.166345 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 47.8370 | 2.27538 | ||||||||
\(443\) | 34.3994 | 1.63436 | 0.817182 | − | 0.576380i | \(-0.195535\pi\) | ||||
0.817182 | + | 0.576380i | \(0.195535\pi\) | |||||||
\(444\) | −2.97858 | −0.141357 | ||||||||
\(445\) | −18.3790 | −0.871250 | ||||||||
\(446\) | 19.4966 | 0.923192 | ||||||||
\(447\) | 8.87819 | 0.419924 | ||||||||
\(448\) | 12.1751 | 0.575221 | ||||||||
\(449\) | 25.7465 | 1.21505 | 0.607527 | − | 0.794299i | \(-0.292162\pi\) | ||||
0.607527 | + | 0.794299i | \(0.292162\pi\) | |||||||
\(450\) | 2.34292 | 0.110446 | ||||||||
\(451\) | −3.53948 | −0.166668 | ||||||||
\(452\) | 38.6430 | 1.81761 | ||||||||
\(453\) | −18.9357 | −0.889678 | ||||||||
\(454\) | 17.5970 | 0.825869 | ||||||||
\(455\) | −3.14637 | −0.147504 | ||||||||
\(456\) | −25.0361 | −1.17242 | ||||||||
\(457\) | 3.63565 | 0.170069 | 0.0850344 | − | 0.996378i | \(-0.472900\pi\) | ||||
0.0850344 | + | 0.996378i | \(0.472900\pi\) | |||||||
\(458\) | 41.4439 | 1.93655 | ||||||||
\(459\) | −6.48929 | −0.302894 | ||||||||
\(460\) | 7.66442 | 0.357356 | ||||||||
\(461\) | 30.8353 | 1.43615 | 0.718073 | − | 0.695968i | \(-0.245025\pi\) | ||||
0.718073 | + | 0.695968i | \(0.245025\pi\) | |||||||
\(462\) | −2.34292 | −0.109003 | ||||||||
\(463\) | −22.0147 | −1.02311 | −0.511555 | − | 0.859251i | \(-0.670930\pi\) | ||||
−0.511555 | + | 0.859251i | \(0.670930\pi\) | |||||||
\(464\) | 1.13650 | 0.0527607 | ||||||||
\(465\) | 6.12494 | 0.284037 | ||||||||
\(466\) | −15.8223 | −0.732956 | ||||||||
\(467\) | 8.92104 | 0.412816 | 0.206408 | − | 0.978466i | \(-0.433823\pi\) | ||||
0.206408 | + | 0.978466i | \(0.433823\pi\) | |||||||
\(468\) | 10.9786 | 0.507485 | ||||||||
\(469\) | 10.3503 | 0.477931 | ||||||||
\(470\) | −3.60688 | −0.166373 | ||||||||
\(471\) | −10.7146 | −0.493703 | ||||||||
\(472\) | −19.6644 | −0.905128 | ||||||||
\(473\) | 5.63565 | 0.259128 | ||||||||
\(474\) | −5.89962 | −0.270978 | ||||||||
\(475\) | 7.17513 | 0.329218 | ||||||||
\(476\) | −22.6430 | −1.03784 | ||||||||
\(477\) | −6.15371 | −0.281759 | ||||||||
\(478\) | −29.3387 | −1.34192 | ||||||||
\(479\) | 26.8255 | 1.22569 | 0.612844 | − | 0.790204i | \(-0.290025\pi\) | ||||
0.612844 | + | 0.790204i | \(0.290025\pi\) | |||||||
\(480\) | 4.17513 | 0.190568 | ||||||||
\(481\) | 2.68585 | 0.122464 | ||||||||
\(482\) | −20.9357 | −0.953596 | ||||||||
\(483\) | 2.19656 | 0.0999468 | ||||||||
\(484\) | 3.48929 | 0.158604 | ||||||||
\(485\) | −5.00735 | −0.227372 | ||||||||
\(486\) | −2.34292 | −0.106277 | ||||||||
\(487\) | −19.2713 | −0.873266 | −0.436633 | − | 0.899640i | \(-0.643829\pi\) | ||||
−0.436633 | + | 0.899640i | \(0.643829\pi\) | |||||||
\(488\) | 16.0147 | 0.724951 | ||||||||
\(489\) | −12.0821 | −0.546371 | ||||||||
\(490\) | 2.34292 | 0.105842 | ||||||||
\(491\) | −34.6718 | −1.56472 | −0.782358 | − | 0.622830i | \(-0.785983\pi\) | ||||
−0.782358 | + | 0.622830i | \(0.785983\pi\) | |||||||
\(492\) | −12.3503 | −0.556793 | ||||||||
\(493\) | 6.16358 | 0.277594 | ||||||||
\(494\) | 52.8929 | 2.37976 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | −7.32885 | −0.329075 | ||||||||
\(497\) | 8.22533 | 0.368956 | ||||||||
\(498\) | −32.4752 | −1.45525 | ||||||||
\(499\) | 9.94667 | 0.445274 | 0.222637 | − | 0.974901i | \(-0.428533\pi\) | ||||
0.222637 | + | 0.974901i | \(0.428533\pi\) | |||||||
\(500\) | 3.48929 | 0.156046 | ||||||||
\(501\) | 17.4292 | 0.778681 | ||||||||
\(502\) | −66.7728 | −2.98021 | ||||||||
\(503\) | −12.3461 | −0.550484 | −0.275242 | − | 0.961375i | \(-0.588758\pi\) | ||||
−0.275242 | + | 0.961375i | \(0.588758\pi\) | |||||||
\(504\) | −3.48929 | −0.155425 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | −5.14637 | −0.228784 | ||||||||
\(507\) | 3.10038 | 0.137693 | ||||||||
\(508\) | −30.2070 | −1.34022 | ||||||||
\(509\) | −39.3576 | −1.74450 | −0.872248 | − | 0.489064i | \(-0.837338\pi\) | ||||
−0.872248 | + | 0.489064i | \(0.837338\pi\) | |||||||
\(510\) | −15.2039 | −0.673240 | ||||||||
\(511\) | 4.68585 | 0.207290 | ||||||||
\(512\) | −13.3461 | −0.589818 | ||||||||
\(513\) | −7.17513 | −0.316790 | ||||||||
\(514\) | −46.3650 | −2.04507 | ||||||||
\(515\) | 11.9284 | 0.525627 | ||||||||
\(516\) | 19.6644 | 0.865678 | ||||||||
\(517\) | 1.53948 | 0.0677063 | ||||||||
\(518\) | −2.00000 | −0.0878750 | ||||||||
\(519\) | −13.4721 | −0.591359 | ||||||||
\(520\) | 10.9786 | 0.481442 | ||||||||
\(521\) | −38.2933 | −1.67766 | −0.838831 | − | 0.544392i | \(-0.816760\pi\) | ||||
−0.838831 | + | 0.544392i | \(0.816760\pi\) | |||||||
\(522\) | 2.22533 | 0.0973999 | ||||||||
\(523\) | 28.1642 | 1.23153 | 0.615767 | − | 0.787928i | \(-0.288846\pi\) | ||||
0.615767 | + | 0.787928i | \(0.288846\pi\) | |||||||
\(524\) | 16.5855 | 0.724539 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 57.2860 | 2.49779 | ||||||||
\(527\) | −39.7465 | −1.73139 | ||||||||
\(528\) | 1.19656 | 0.0520735 | ||||||||
\(529\) | −18.1751 | −0.790223 | ||||||||
\(530\) | −14.4177 | −0.626264 | ||||||||
\(531\) | −5.63565 | −0.244567 | ||||||||
\(532\) | −25.0361 | −1.08545 | ||||||||
\(533\) | 11.1365 | 0.482375 | ||||||||
\(534\) | 43.0607 | 1.86342 | ||||||||
\(535\) | −5.20390 | −0.224984 | ||||||||
\(536\) | −36.1151 | −1.55993 | ||||||||
\(537\) | 12.2253 | 0.527562 | ||||||||
\(538\) | 37.6890 | 1.62489 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | −3.48929 | −0.150155 | ||||||||
\(541\) | −32.3832 | −1.39226 | −0.696132 | − | 0.717913i | \(-0.745097\pi\) | ||||
−0.696132 | + | 0.717913i | \(0.745097\pi\) | |||||||
\(542\) | −73.1758 | −3.14317 | ||||||||
\(543\) | 11.9572 | 0.513131 | ||||||||
\(544\) | −27.0937 | −1.16163 | ||||||||
\(545\) | −10.2253 | −0.438005 | ||||||||
\(546\) | 7.37169 | 0.315479 | ||||||||
\(547\) | 3.65035 | 0.156078 | 0.0780388 | − | 0.996950i | \(-0.475134\pi\) | ||||
0.0780388 | + | 0.996950i | \(0.475134\pi\) | |||||||
\(548\) | 42.2217 | 1.80362 | ||||||||
\(549\) | 4.58967 | 0.195882 | ||||||||
\(550\) | −2.34292 | −0.0999026 | ||||||||
\(551\) | 6.81500 | 0.290329 | ||||||||
\(552\) | −7.66442 | −0.326220 | ||||||||
\(553\) | −2.51806 | −0.107079 | ||||||||
\(554\) | −46.3074 | −1.96741 | ||||||||
\(555\) | −0.853635 | −0.0362348 | ||||||||
\(556\) | −74.7728 | −3.17107 | ||||||||
\(557\) | 17.0790 | 0.723659 | 0.361829 | − | 0.932244i | \(-0.382152\pi\) | ||||
0.361829 | + | 0.932244i | \(0.382152\pi\) | |||||||
\(558\) | −14.3503 | −0.607495 | ||||||||
\(559\) | −17.7318 | −0.749976 | ||||||||
\(560\) | −1.19656 | −0.0505638 | ||||||||
\(561\) | 6.48929 | 0.273978 | ||||||||
\(562\) | 0.820654 | 0.0346172 | ||||||||
\(563\) | 17.5640 | 0.740236 | 0.370118 | − | 0.928985i | \(-0.379317\pi\) | ||||
0.370118 | + | 0.928985i | \(0.379317\pi\) | |||||||
\(564\) | 5.37169 | 0.226189 | ||||||||
\(565\) | 11.0748 | 0.465918 | ||||||||
\(566\) | −33.6791 | −1.41564 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −28.7005 | −1.20425 | ||||||||
\(569\) | −23.6075 | −0.989678 | −0.494839 | − | 0.868985i | \(-0.664773\pi\) | ||||
−0.494839 | + | 0.868985i | \(0.664773\pi\) | |||||||
\(570\) | −16.8108 | −0.704126 | ||||||||
\(571\) | 35.5542 | 1.48790 | 0.743948 | − | 0.668238i | \(-0.232951\pi\) | ||||
0.743948 | + | 0.668238i | \(0.232951\pi\) | |||||||
\(572\) | −10.9786 | −0.459037 | ||||||||
\(573\) | −5.37169 | −0.224406 | ||||||||
\(574\) | −8.29273 | −0.346132 | ||||||||
\(575\) | 2.19656 | 0.0916028 | ||||||||
\(576\) | −12.1751 | −0.507297 | ||||||||
\(577\) | 45.5296 | 1.89542 | 0.947711 | − | 0.319129i | \(-0.103390\pi\) | ||||
0.947711 | + | 0.319129i | \(0.103390\pi\) | |||||||
\(578\) | 58.8328 | 2.44712 | ||||||||
\(579\) | 2.92104 | 0.121394 | ||||||||
\(580\) | 3.31415 | 0.137613 | ||||||||
\(581\) | −13.8610 | −0.575050 | ||||||||
\(582\) | 11.7318 | 0.486300 | ||||||||
\(583\) | 6.15371 | 0.254861 | ||||||||
\(584\) | −16.3503 | −0.676579 | ||||||||
\(585\) | 3.14637 | 0.130086 | ||||||||
\(586\) | 52.8255 | 2.18220 | ||||||||
\(587\) | 29.5113 | 1.21806 | 0.609031 | − | 0.793146i | \(-0.291558\pi\) | ||||
0.609031 | + | 0.793146i | \(0.291558\pi\) | |||||||
\(588\) | −3.48929 | −0.143896 | ||||||||
\(589\) | −43.9473 | −1.81082 | ||||||||
\(590\) | −13.2039 | −0.543596 | ||||||||
\(591\) | −9.27131 | −0.381371 | ||||||||
\(592\) | 1.02142 | 0.0419802 | ||||||||
\(593\) | −16.9357 | −0.695467 | −0.347734 | − | 0.937593i | \(-0.613049\pi\) | ||||
−0.347734 | + | 0.937593i | \(0.613049\pi\) | |||||||
\(594\) | 2.34292 | 0.0961313 | ||||||||
\(595\) | −6.48929 | −0.266035 | ||||||||
\(596\) | −30.9786 | −1.26893 | ||||||||
\(597\) | 8.78623 | 0.359596 | ||||||||
\(598\) | 16.1923 | 0.662154 | ||||||||
\(599\) | 1.31415 | 0.0536949 | 0.0268474 | − | 0.999640i | \(-0.491453\pi\) | ||||
0.0268474 | + | 0.999640i | \(0.491453\pi\) | |||||||
\(600\) | −3.48929 | −0.142450 | ||||||||
\(601\) | −16.0533 | −0.654829 | −0.327414 | − | 0.944881i | \(-0.606177\pi\) | ||||
−0.327414 | + | 0.944881i | \(0.606177\pi\) | |||||||
\(602\) | 13.2039 | 0.538151 | ||||||||
\(603\) | −10.3503 | −0.421496 | ||||||||
\(604\) | 66.0722 | 2.68844 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −14.0575 | −0.571048 | ||||||||
\(607\) | −39.8568 | −1.61774 | −0.808868 | − | 0.587990i | \(-0.799919\pi\) | ||||
−0.808868 | + | 0.587990i | \(0.799919\pi\) | |||||||
\(608\) | −29.9572 | −1.21492 | ||||||||
\(609\) | 0.949808 | 0.0384882 | ||||||||
\(610\) | 10.7533 | 0.435386 | ||||||||
\(611\) | −4.84377 | −0.195958 | ||||||||
\(612\) | 22.6430 | 0.915289 | ||||||||
\(613\) | −39.4868 | −1.59486 | −0.797428 | − | 0.603414i | \(-0.793807\pi\) | ||||
−0.797428 | + | 0.603414i | \(0.793807\pi\) | |||||||
\(614\) | 23.1940 | 0.936035 | ||||||||
\(615\) | −3.53948 | −0.142726 | ||||||||
\(616\) | 3.48929 | 0.140587 | ||||||||
\(617\) | −2.77781 | −0.111830 | −0.0559152 | − | 0.998436i | \(-0.517808\pi\) | ||||
−0.0559152 | + | 0.998436i | \(0.517808\pi\) | |||||||
\(618\) | −27.9473 | −1.12420 | ||||||||
\(619\) | −31.7220 | −1.27501 | −0.637507 | − | 0.770445i | \(-0.720034\pi\) | ||||
−0.637507 | + | 0.770445i | \(0.720034\pi\) | |||||||
\(620\) | −21.3717 | −0.858308 | ||||||||
\(621\) | −2.19656 | −0.0881448 | ||||||||
\(622\) | 30.5426 | 1.22465 | ||||||||
\(623\) | 18.3790 | 0.736341 | ||||||||
\(624\) | −3.76481 | −0.150713 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −55.6461 | −2.22407 | ||||||||
\(627\) | 7.17513 | 0.286547 | ||||||||
\(628\) | 37.3864 | 1.49188 | ||||||||
\(629\) | 5.53948 | 0.220874 | ||||||||
\(630\) | −2.34292 | −0.0933443 | ||||||||
\(631\) | −5.99579 | −0.238689 | −0.119344 | − | 0.992853i | \(-0.538079\pi\) | ||||
−0.119344 | + | 0.992853i | \(0.538079\pi\) | |||||||
\(632\) | 8.78623 | 0.349497 | ||||||||
\(633\) | 24.0575 | 0.956201 | ||||||||
\(634\) | 30.5082 | 1.21164 | ||||||||
\(635\) | −8.65708 | −0.343546 | ||||||||
\(636\) | 21.4721 | 0.851423 | ||||||||
\(637\) | 3.14637 | 0.124664 | ||||||||
\(638\) | −2.22533 | −0.0881015 | ||||||||
\(639\) | −8.22533 | −0.325389 | ||||||||
\(640\) | −20.1751 | −0.797492 | ||||||||
\(641\) | −20.5426 | −0.811385 | −0.405692 | − | 0.914010i | \(-0.632970\pi\) | ||||
−0.405692 | + | 0.914010i | \(0.632970\pi\) | |||||||
\(642\) | 12.1923 | 0.481194 | ||||||||
\(643\) | −4.51385 | −0.178009 | −0.0890044 | − | 0.996031i | \(-0.528369\pi\) | ||||
−0.0890044 | + | 0.996031i | \(0.528369\pi\) | |||||||
\(644\) | −7.66442 | −0.302021 | ||||||||
\(645\) | 5.63565 | 0.221904 | ||||||||
\(646\) | 109.090 | 4.29209 | ||||||||
\(647\) | −19.0790 | −0.750071 | −0.375036 | − | 0.927010i | \(-0.622370\pi\) | ||||
−0.375036 | + | 0.927010i | \(0.622370\pi\) | |||||||
\(648\) | 3.48929 | 0.137072 | ||||||||
\(649\) | 5.63565 | 0.221219 | ||||||||
\(650\) | 7.37169 | 0.289142 | ||||||||
\(651\) | −6.12494 | −0.240055 | ||||||||
\(652\) | 42.1579 | 1.65103 | ||||||||
\(653\) | 30.7392 | 1.20292 | 0.601458 | − | 0.798904i | \(-0.294587\pi\) | ||||
0.601458 | + | 0.798904i | \(0.294587\pi\) | |||||||
\(654\) | 23.9572 | 0.936799 | ||||||||
\(655\) | 4.75325 | 0.185725 | ||||||||
\(656\) | 4.23519 | 0.165356 | ||||||||
\(657\) | −4.68585 | −0.182812 | ||||||||
\(658\) | 3.60688 | 0.140611 | ||||||||
\(659\) | −31.7079 | −1.23516 | −0.617582 | − | 0.786507i | \(-0.711888\pi\) | ||||
−0.617582 | + | 0.786507i | \(0.711888\pi\) | |||||||
\(660\) | 3.48929 | 0.135820 | ||||||||
\(661\) | 33.6890 | 1.31035 | 0.655175 | − | 0.755477i | \(-0.272595\pi\) | ||||
0.655175 | + | 0.755477i | \(0.272595\pi\) | |||||||
\(662\) | 45.0607 | 1.75133 | ||||||||
\(663\) | −20.4177 | −0.792957 | ||||||||
\(664\) | 48.3650 | 1.87692 | ||||||||
\(665\) | −7.17513 | −0.278240 | ||||||||
\(666\) | 2.00000 | 0.0774984 | ||||||||
\(667\) | 2.08631 | 0.0807822 | ||||||||
\(668\) | −60.8156 | −2.35303 | ||||||||
\(669\) | −8.32150 | −0.321728 | ||||||||
\(670\) | −24.2499 | −0.936855 | ||||||||
\(671\) | −4.58967 | −0.177182 | ||||||||
\(672\) | −4.17513 | −0.161059 | ||||||||
\(673\) | 6.37904 | 0.245894 | 0.122947 | − | 0.992413i | \(-0.460766\pi\) | ||||
0.122947 | + | 0.992413i | \(0.460766\pi\) | |||||||
\(674\) | −56.8830 | −2.19105 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −10.8181 | −0.416082 | ||||||||
\(677\) | −13.6258 | −0.523682 | −0.261841 | − | 0.965111i | \(-0.584330\pi\) | ||||
−0.261841 | + | 0.965111i | \(0.584330\pi\) | |||||||
\(678\) | −25.9473 | −0.996500 | ||||||||
\(679\) | 5.00735 | 0.192164 | ||||||||
\(680\) | 22.6430 | 0.868319 | ||||||||
\(681\) | −7.51071 | −0.287811 | ||||||||
\(682\) | 14.3503 | 0.549500 | ||||||||
\(683\) | −26.6577 | −1.02003 | −0.510014 | − | 0.860166i | \(-0.670360\pi\) | ||||
−0.510014 | + | 0.860166i | \(0.670360\pi\) | |||||||
\(684\) | 25.0361 | 0.957280 | ||||||||
\(685\) | 12.1004 | 0.462332 | ||||||||
\(686\) | −2.34292 | −0.0894532 | ||||||||
\(687\) | −17.6890 | −0.674877 | ||||||||
\(688\) | −6.74338 | −0.257089 | ||||||||
\(689\) | −19.3618 | −0.737627 | ||||||||
\(690\) | −5.14637 | −0.195919 | ||||||||
\(691\) | −41.0080 | −1.56002 | −0.780008 | − | 0.625769i | \(-0.784785\pi\) | ||||
−0.780008 | + | 0.625769i | \(0.784785\pi\) | |||||||
\(692\) | 47.0080 | 1.78697 | ||||||||
\(693\) | 1.00000 | 0.0379869 | ||||||||
\(694\) | 24.5855 | 0.933251 | ||||||||
\(695\) | −21.4292 | −0.812857 | ||||||||
\(696\) | −3.31415 | −0.125623 | ||||||||
\(697\) | 22.9687 | 0.870002 | ||||||||
\(698\) | 9.24675 | 0.349995 | ||||||||
\(699\) | 6.75325 | 0.255431 | ||||||||
\(700\) | −3.48929 | −0.131883 | ||||||||
\(701\) | −1.03550 | −0.0391103 | −0.0195551 | − | 0.999809i | \(-0.506225\pi\) | ||||
−0.0195551 | + | 0.999809i | \(0.506225\pi\) | |||||||
\(702\) | −7.37169 | −0.278227 | ||||||||
\(703\) | 6.12494 | 0.231007 | ||||||||
\(704\) | 12.1751 | 0.458868 | ||||||||
\(705\) | 1.53948 | 0.0579802 | ||||||||
\(706\) | 43.2285 | 1.62692 | ||||||||
\(707\) | −6.00000 | −0.225653 | ||||||||
\(708\) | 19.6644 | 0.739034 | ||||||||
\(709\) | 38.6901 | 1.45304 | 0.726518 | − | 0.687148i | \(-0.241137\pi\) | ||||
0.726518 | + | 0.687148i | \(0.241137\pi\) | |||||||
\(710\) | −19.2713 | −0.723239 | ||||||||
\(711\) | 2.51806 | 0.0944345 | ||||||||
\(712\) | −64.1298 | −2.40336 | ||||||||
\(713\) | −13.4538 | −0.503848 | ||||||||
\(714\) | 15.2039 | 0.568992 | ||||||||
\(715\) | −3.14637 | −0.117667 | ||||||||
\(716\) | −42.6577 | −1.59419 | ||||||||
\(717\) | 12.5223 | 0.467653 | ||||||||
\(718\) | 82.9406 | 3.09531 | ||||||||
\(719\) | 27.7360 | 1.03438 | 0.517190 | − | 0.855871i | \(-0.326978\pi\) | ||||
0.517190 | + | 0.855871i | \(0.326978\pi\) | |||||||
\(720\) | 1.19656 | 0.0445931 | ||||||||
\(721\) | −11.9284 | −0.444236 | ||||||||
\(722\) | 76.1041 | 2.83230 | ||||||||
\(723\) | 8.93573 | 0.332323 | ||||||||
\(724\) | −41.7220 | −1.55058 | ||||||||
\(725\) | 0.949808 | 0.0352750 | ||||||||
\(726\) | −2.34292 | −0.0869540 | ||||||||
\(727\) | 26.8066 | 0.994201 | 0.497100 | − | 0.867693i | \(-0.334398\pi\) | ||||
0.497100 | + | 0.867693i | \(0.334398\pi\) | |||||||
\(728\) | −10.9786 | −0.406893 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.9786 | −0.406335 | ||||||||
\(731\) | −36.5714 | −1.35264 | ||||||||
\(732\) | −16.0147 | −0.591920 | ||||||||
\(733\) | 32.7925 | 1.21122 | 0.605609 | − | 0.795762i | \(-0.292929\pi\) | ||||
0.605609 | + | 0.795762i | \(0.292929\pi\) | |||||||
\(734\) | 25.6546 | 0.946927 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | −9.17092 | −0.338045 | ||||||||
\(737\) | 10.3503 | 0.381257 | ||||||||
\(738\) | 8.29273 | 0.305260 | ||||||||
\(739\) | −29.3142 | −1.07834 | −0.539169 | − | 0.842197i | \(-0.681262\pi\) | ||||
−0.539169 | + | 0.842197i | \(0.681262\pi\) | |||||||
\(740\) | 2.97858 | 0.109495 | ||||||||
\(741\) | −22.5756 | −0.829335 | ||||||||
\(742\) | 14.4177 | 0.529289 | ||||||||
\(743\) | 2.10038 | 0.0770556 | 0.0385278 | − | 0.999258i | \(-0.487733\pi\) | ||||
0.0385278 | + | 0.999258i | \(0.487733\pi\) | |||||||
\(744\) | 21.3717 | 0.783524 | ||||||||
\(745\) | −8.87819 | −0.325272 | ||||||||
\(746\) | −5.88975 | −0.215639 | ||||||||
\(747\) | 13.8610 | 0.507147 | ||||||||
\(748\) | −22.6430 | −0.827910 | ||||||||
\(749\) | 5.20390 | 0.190147 | ||||||||
\(750\) | −2.34292 | −0.0855515 | ||||||||
\(751\) | −26.0533 | −0.950699 | −0.475350 | − | 0.879797i | \(-0.657678\pi\) | ||||
−0.475350 | + | 0.879797i | \(0.657678\pi\) | |||||||
\(752\) | −1.84208 | −0.0671736 | ||||||||
\(753\) | 28.4998 | 1.03859 | ||||||||
\(754\) | 7.00169 | 0.254987 | ||||||||
\(755\) | 18.9357 | 0.689142 | ||||||||
\(756\) | 3.48929 | 0.126904 | ||||||||
\(757\) | 30.9504 | 1.12491 | 0.562456 | − | 0.826827i | \(-0.309857\pi\) | ||||
0.562456 | + | 0.826827i | \(0.309857\pi\) | |||||||
\(758\) | −81.7612 | −2.96970 | ||||||||
\(759\) | 2.19656 | 0.0797300 | ||||||||
\(760\) | 25.0361 | 0.908155 | ||||||||
\(761\) | 0.542616 | 0.0196698 | 0.00983491 | − | 0.999952i | \(-0.496869\pi\) | ||||
0.00983491 | + | 0.999952i | \(0.496869\pi\) | |||||||
\(762\) | 20.2829 | 0.734771 | ||||||||
\(763\) | 10.2253 | 0.370182 | ||||||||
\(764\) | 18.7434 | 0.678112 | ||||||||
\(765\) | 6.48929 | 0.234621 | ||||||||
\(766\) | 57.5443 | 2.07916 | ||||||||
\(767\) | −17.7318 | −0.640259 | ||||||||
\(768\) | 22.9185 | 0.827001 | ||||||||
\(769\) | 21.3184 | 0.768760 | 0.384380 | − | 0.923175i | \(-0.374415\pi\) | ||||
0.384380 | + | 0.923175i | \(0.374415\pi\) | |||||||
\(770\) | 2.34292 | 0.0844331 | ||||||||
\(771\) | 19.7894 | 0.712697 | ||||||||
\(772\) | −10.1923 | −0.366831 | ||||||||
\(773\) | 17.5787 | 0.632263 | 0.316132 | − | 0.948715i | \(-0.397616\pi\) | ||||
0.316132 | + | 0.948715i | \(0.397616\pi\) | |||||||
\(774\) | −13.2039 | −0.474605 | ||||||||
\(775\) | −6.12494 | −0.220014 | ||||||||
\(776\) | −17.4721 | −0.627211 | ||||||||
\(777\) | 0.853635 | 0.0306240 | ||||||||
\(778\) | 33.3288 | 1.19490 | ||||||||
\(779\) | 25.3963 | 0.909915 | ||||||||
\(780\) | −10.9786 | −0.393096 | ||||||||
\(781\) | 8.22533 | 0.294325 | ||||||||
\(782\) | 33.3963 | 1.19425 | ||||||||
\(783\) | −0.949808 | −0.0339434 | ||||||||
\(784\) | 1.19656 | 0.0427342 | ||||||||
\(785\) | 10.7146 | 0.382421 | ||||||||
\(786\) | −11.1365 | −0.397226 | ||||||||
\(787\) | 41.2003 | 1.46863 | 0.734316 | − | 0.678808i | \(-0.237503\pi\) | ||||
0.734316 | + | 0.678808i | \(0.237503\pi\) | |||||||
\(788\) | 32.3503 | 1.15243 | ||||||||
\(789\) | −24.4507 | −0.870466 | ||||||||
\(790\) | 5.89962 | 0.209899 | ||||||||
\(791\) | −11.0748 | −0.393773 | ||||||||
\(792\) | −3.48929 | −0.123986 | ||||||||
\(793\) | 14.4408 | 0.512807 | ||||||||
\(794\) | −44.4653 | −1.57802 | ||||||||
\(795\) | 6.15371 | 0.218250 | ||||||||
\(796\) | −30.6577 | −1.08663 | ||||||||
\(797\) | −40.9933 | −1.45206 | −0.726028 | − | 0.687665i | \(-0.758636\pi\) | ||||
−0.726028 | + | 0.687665i | \(0.758636\pi\) | |||||||
\(798\) | 16.8108 | 0.595095 | ||||||||
\(799\) | −9.99013 | −0.353426 | ||||||||
\(800\) | −4.17513 | −0.147613 | ||||||||
\(801\) | −18.3790 | −0.649391 | ||||||||
\(802\) | 11.0361 | 0.389699 | ||||||||
\(803\) | 4.68585 | 0.165360 | ||||||||
\(804\) | 36.1151 | 1.27368 | ||||||||
\(805\) | −2.19656 | −0.0774185 | ||||||||
\(806\) | −45.1512 | −1.59038 | ||||||||
\(807\) | −16.0863 | −0.566265 | ||||||||
\(808\) | 20.9357 | 0.736516 | ||||||||
\(809\) | 25.7795 | 0.906359 | 0.453179 | − | 0.891419i | \(-0.350290\pi\) | ||||
0.453179 | + | 0.891419i | \(0.350290\pi\) | |||||||
\(810\) | 2.34292 | 0.0823219 | ||||||||
\(811\) | −31.9143 | −1.12066 | −0.560331 | − | 0.828268i | \(-0.689326\pi\) | ||||
−0.560331 | + | 0.828268i | \(0.689326\pi\) | |||||||
\(812\) | −3.31415 | −0.116304 | ||||||||
\(813\) | 31.2327 | 1.09538 | ||||||||
\(814\) | −2.00000 | −0.0701000 | ||||||||
\(815\) | 12.0821 | 0.423217 | ||||||||
\(816\) | −7.76481 | −0.271823 | ||||||||
\(817\) | −40.4366 | −1.41470 | ||||||||
\(818\) | 70.5376 | 2.46629 | ||||||||
\(819\) | −3.14637 | −0.109943 | ||||||||
\(820\) | 12.3503 | 0.431290 | ||||||||
\(821\) | 52.5945 | 1.83556 | 0.917780 | − | 0.397088i | \(-0.129979\pi\) | ||||
0.917780 | + | 0.397088i | \(0.129979\pi\) | |||||||
\(822\) | −28.3503 | −0.988829 | ||||||||
\(823\) | 1.87506 | 0.0653604 | 0.0326802 | − | 0.999466i | \(-0.489596\pi\) | ||||
0.0326802 | + | 0.999466i | \(0.489596\pi\) | |||||||
\(824\) | 41.6216 | 1.44996 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 13.2039 | 0.459423 | ||||||||
\(827\) | 25.1512 | 0.874593 | 0.437296 | − | 0.899317i | \(-0.355936\pi\) | ||||
0.437296 | + | 0.899317i | \(0.355936\pi\) | |||||||
\(828\) | 7.66442 | 0.266357 | ||||||||
\(829\) | −11.6216 | −0.403634 | −0.201817 | − | 0.979423i | \(-0.564685\pi\) | ||||
−0.201817 | + | 0.979423i | \(0.564685\pi\) | |||||||
\(830\) | 32.4752 | 1.12723 | ||||||||
\(831\) | 19.7648 | 0.685634 | ||||||||
\(832\) | −38.3074 | −1.32807 | ||||||||
\(833\) | 6.48929 | 0.224841 | ||||||||
\(834\) | 50.2070 | 1.73853 | ||||||||
\(835\) | −17.4292 | −0.603163 | ||||||||
\(836\) | −25.0361 | −0.865892 | ||||||||
\(837\) | 6.12494 | 0.211709 | ||||||||
\(838\) | 83.5260 | 2.88536 | ||||||||
\(839\) | −46.8641 | −1.61793 | −0.808964 | − | 0.587858i | \(-0.799972\pi\) | ||||
−0.808964 | + | 0.587858i | \(0.799972\pi\) | |||||||
\(840\) | 3.48929 | 0.120392 | ||||||||
\(841\) | −28.0979 | −0.968892 | ||||||||
\(842\) | −54.6478 | −1.88329 | ||||||||
\(843\) | −0.350269 | −0.0120639 | ||||||||
\(844\) | −83.9437 | −2.88946 | ||||||||
\(845\) | −3.10038 | −0.106656 | ||||||||
\(846\) | −3.60688 | −0.124007 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | −7.36327 | −0.252856 | ||||||||
\(849\) | 14.3748 | 0.493343 | ||||||||
\(850\) | 15.2039 | 0.521490 | ||||||||
\(851\) | 1.87506 | 0.0642761 | ||||||||
\(852\) | 28.7005 | 0.983264 | ||||||||
\(853\) | 48.1543 | 1.64877 | 0.824386 | − | 0.566027i | \(-0.191520\pi\) | ||||
0.824386 | + | 0.566027i | \(0.191520\pi\) | |||||||
\(854\) | −10.7533 | −0.367969 | ||||||||
\(855\) | 7.17513 | 0.245384 | ||||||||
\(856\) | −18.1579 | −0.620625 | ||||||||
\(857\) | −44.2730 | −1.51234 | −0.756168 | − | 0.654377i | \(-0.772931\pi\) | ||||
−0.756168 | + | 0.654377i | \(0.772931\pi\) | |||||||
\(858\) | 7.37169 | 0.251665 | ||||||||
\(859\) | 12.8683 | 0.439062 | 0.219531 | − | 0.975606i | \(-0.429547\pi\) | ||||
0.219531 | + | 0.975606i | \(0.429547\pi\) | |||||||
\(860\) | −19.6644 | −0.670551 | ||||||||
\(861\) | 3.53948 | 0.120625 | ||||||||
\(862\) | 9.95715 | 0.339142 | ||||||||
\(863\) | −10.1966 | −0.347095 | −0.173547 | − | 0.984826i | \(-0.555523\pi\) | ||||
−0.173547 | + | 0.984826i | \(0.555523\pi\) | |||||||
\(864\) | 4.17513 | 0.142041 | ||||||||
\(865\) | 13.4721 | 0.458064 | ||||||||
\(866\) | 72.7152 | 2.47096 | ||||||||
\(867\) | −25.1109 | −0.852810 | ||||||||
\(868\) | 21.3717 | 0.725403 | ||||||||
\(869\) | −2.51806 | −0.0854193 | ||||||||
\(870\) | −2.22533 | −0.0754456 | ||||||||
\(871\) | −32.5657 | −1.10345 | ||||||||
\(872\) | −35.6791 | −1.20825 | ||||||||
\(873\) | −5.00735 | −0.169473 | ||||||||
\(874\) | 36.9259 | 1.24904 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 16.3503 | 0.552424 | ||||||||
\(877\) | 32.3937 | 1.09386 | 0.546929 | − | 0.837179i | \(-0.315797\pi\) | ||||
0.546929 | + | 0.837179i | \(0.315797\pi\) | |||||||
\(878\) | −44.5903 | −1.50485 | ||||||||
\(879\) | −22.5468 | −0.760486 | ||||||||
\(880\) | −1.19656 | −0.0403359 | ||||||||
\(881\) | −53.3429 | −1.79717 | −0.898584 | − | 0.438801i | \(-0.855403\pi\) | ||||
−0.898584 | + | 0.438801i | \(0.855403\pi\) | |||||||
\(882\) | 2.34292 | 0.0788903 | ||||||||
\(883\) | 8.92104 | 0.300217 | 0.150108 | − | 0.988670i | \(-0.452038\pi\) | ||||
0.150108 | + | 0.988670i | \(0.452038\pi\) | |||||||
\(884\) | 71.2432 | 2.39617 | ||||||||
\(885\) | 5.63565 | 0.189440 | ||||||||
\(886\) | 80.5951 | 2.70765 | ||||||||
\(887\) | −44.6044 | −1.49767 | −0.748834 | − | 0.662758i | \(-0.769386\pi\) | ||||
−0.748834 | + | 0.662758i | \(0.769386\pi\) | |||||||
\(888\) | −2.97858 | −0.0999545 | ||||||||
\(889\) | 8.65708 | 0.290349 | ||||||||
\(890\) | −43.0607 | −1.44340 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 29.0361 | 0.972201 | ||||||||
\(893\) | −11.0460 | −0.369640 | ||||||||
\(894\) | 20.8009 | 0.695687 | ||||||||
\(895\) | −12.2253 | −0.408648 | ||||||||
\(896\) | 20.1751 | 0.674004 | ||||||||
\(897\) | −6.91117 | −0.230757 | ||||||||
\(898\) | 60.3221 | 2.01298 | ||||||||
\(899\) | −5.81752 | −0.194025 | ||||||||
\(900\) | 3.48929 | 0.116310 | ||||||||
\(901\) | −39.9332 | −1.33037 | ||||||||
\(902\) | −8.29273 | −0.276118 | ||||||||
\(903\) | −5.63565 | −0.187543 | ||||||||
\(904\) | 38.6430 | 1.28525 | ||||||||
\(905\) | −11.9572 | −0.397469 | ||||||||
\(906\) | −44.3650 | −1.47393 | ||||||||
\(907\) | −18.1741 | −0.603460 | −0.301730 | − | 0.953393i | \(-0.597564\pi\) | ||||
−0.301730 | + | 0.953393i | \(0.597564\pi\) | |||||||
\(908\) | 26.2070 | 0.869711 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | −7.37169 | −0.244369 | ||||||||
\(911\) | 11.4637 | 0.379808 | 0.189904 | − | 0.981803i | \(-0.439182\pi\) | ||||
0.189904 | + | 0.981803i | \(0.439182\pi\) | |||||||
\(912\) | −8.58546 | −0.284293 | ||||||||
\(913\) | −13.8610 | −0.458732 | ||||||||
\(914\) | 8.51806 | 0.281752 | ||||||||
\(915\) | −4.58967 | −0.151730 | ||||||||
\(916\) | 61.7220 | 2.03935 | ||||||||
\(917\) | −4.75325 | −0.156966 | ||||||||
\(918\) | −15.2039 | −0.501804 | ||||||||
\(919\) | −57.4783 | −1.89604 | −0.948018 | − | 0.318217i | \(-0.896916\pi\) | ||||
−0.948018 | + | 0.318217i | \(0.896916\pi\) | |||||||
\(920\) | 7.66442 | 0.252689 | ||||||||
\(921\) | −9.89962 | −0.326203 | ||||||||
\(922\) | 72.2448 | 2.37926 | ||||||||
\(923\) | −25.8799 | −0.851847 | ||||||||
\(924\) | −3.48929 | −0.114789 | ||||||||
\(925\) | 0.853635 | 0.0280673 | ||||||||
\(926\) | −51.5787 | −1.69498 | ||||||||
\(927\) | 11.9284 | 0.391780 | ||||||||
\(928\) | −3.96558 | −0.130176 | ||||||||
\(929\) | 37.4355 | 1.22822 | 0.614109 | − | 0.789221i | \(-0.289515\pi\) | ||||
0.614109 | + | 0.789221i | \(0.289515\pi\) | |||||||
\(930\) | 14.3503 | 0.470564 | ||||||||
\(931\) | 7.17513 | 0.235156 | ||||||||
\(932\) | −23.5640 | −0.771866 | ||||||||
\(933\) | −13.0361 | −0.426783 | ||||||||
\(934\) | 20.9013 | 0.683912 | ||||||||
\(935\) | −6.48929 | −0.212222 | ||||||||
\(936\) | 10.9786 | 0.358846 | ||||||||
\(937\) | 33.0754 | 1.08053 | 0.540263 | − | 0.841496i | \(-0.318325\pi\) | ||||
0.540263 | + | 0.841496i | \(0.318325\pi\) | |||||||
\(938\) | 24.2499 | 0.791787 | ||||||||
\(939\) | 23.7507 | 0.775076 | ||||||||
\(940\) | −5.37169 | −0.175205 | ||||||||
\(941\) | 19.1464 | 0.624154 | 0.312077 | − | 0.950057i | \(-0.398975\pi\) | ||||
0.312077 | + | 0.950057i | \(0.398975\pi\) | |||||||
\(942\) | −25.1035 | −0.817917 | ||||||||
\(943\) | 7.77467 | 0.253178 | ||||||||
\(944\) | −6.74338 | −0.219478 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 13.2039 | 0.429296 | ||||||||
\(947\) | 11.1176 | 0.361273 | 0.180637 | − | 0.983550i | \(-0.442184\pi\) | ||||
0.180637 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(948\) | −8.78623 | −0.285363 | ||||||||
\(949\) | −14.7434 | −0.478591 | ||||||||
\(950\) | 16.8108 | 0.545414 | ||||||||
\(951\) | −13.0214 | −0.422249 | ||||||||
\(952\) | −22.6430 | −0.733864 | ||||||||
\(953\) | −10.2008 | −0.330435 | −0.165218 | − | 0.986257i | \(-0.552833\pi\) | ||||
−0.165218 | + | 0.986257i | \(0.552833\pi\) | |||||||
\(954\) | −14.4177 | −0.466789 | ||||||||
\(955\) | 5.37169 | 0.173824 | ||||||||
\(956\) | −43.6938 | −1.41316 | ||||||||
\(957\) | 0.949808 | 0.0307029 | ||||||||
\(958\) | 62.8500 | 2.03059 | ||||||||
\(959\) | −12.1004 | −0.390742 | ||||||||
\(960\) | 12.1751 | 0.392951 | ||||||||
\(961\) | 6.51492 | 0.210159 | ||||||||
\(962\) | 6.29273 | 0.202886 | ||||||||
\(963\) | −5.20390 | −0.167693 | ||||||||
\(964\) | −31.1793 | −1.00422 | ||||||||
\(965\) | −2.92104 | −0.0940316 | ||||||||
\(966\) | 5.14637 | 0.165582 | ||||||||
\(967\) | 0.436577 | 0.0140394 | 0.00701969 | − | 0.999975i | \(-0.497766\pi\) | ||||
0.00701969 | + | 0.999975i | \(0.497766\pi\) | |||||||
\(968\) | 3.48929 | 0.112150 | ||||||||
\(969\) | −46.5615 | −1.49577 | ||||||||
\(970\) | −11.7318 | −0.376686 | ||||||||
\(971\) | 18.6718 | 0.599206 | 0.299603 | − | 0.954064i | \(-0.403146\pi\) | ||||
0.299603 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(972\) | −3.48929 | −0.111919 | ||||||||
\(973\) | 21.4292 | 0.686990 | ||||||||
\(974\) | −45.1512 | −1.44674 | ||||||||
\(975\) | −3.14637 | −0.100764 | ||||||||
\(976\) | 5.49181 | 0.175788 | ||||||||
\(977\) | −19.3246 | −0.618250 | −0.309125 | − | 0.951021i | \(-0.600036\pi\) | ||||
−0.309125 | + | 0.951021i | \(0.600036\pi\) | |||||||
\(978\) | −28.3074 | −0.905172 | ||||||||
\(979\) | 18.3790 | 0.587397 | ||||||||
\(980\) | 3.48929 | 0.111461 | ||||||||
\(981\) | −10.2253 | −0.326470 | ||||||||
\(982\) | −81.2333 | −2.59226 | ||||||||
\(983\) | 48.2583 | 1.53920 | 0.769600 | − | 0.638526i | \(-0.220455\pi\) | ||||
0.769600 | + | 0.638526i | \(0.220455\pi\) | |||||||
\(984\) | −12.3503 | −0.393712 | ||||||||
\(985\) | 9.27131 | 0.295408 | ||||||||
\(986\) | 14.4408 | 0.459888 | ||||||||
\(987\) | −1.53948 | −0.0490022 | ||||||||
\(988\) | 78.7728 | 2.50610 | ||||||||
\(989\) | −12.3790 | −0.393631 | ||||||||
\(990\) | −2.34292 | −0.0744630 | ||||||||
\(991\) | 33.7178 | 1.07108 | 0.535540 | − | 0.844510i | \(-0.320108\pi\) | ||||
0.535540 | + | 0.844510i | \(0.320108\pi\) | |||||||
\(992\) | 25.5725 | 0.811926 | ||||||||
\(993\) | −19.2327 | −0.610330 | ||||||||
\(994\) | 19.2713 | 0.611249 | ||||||||
\(995\) | −8.78623 | −0.278542 | ||||||||
\(996\) | −48.3650 | −1.53250 | ||||||||
\(997\) | −33.8286 | −1.07136 | −0.535682 | − | 0.844420i | \(-0.679945\pi\) | ||||
−0.535682 | + | 0.844420i | \(0.679945\pi\) | |||||||
\(998\) | 23.3043 | 0.737684 | ||||||||
\(999\) | −0.853635 | −0.0270078 |
(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.s.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 3465.2.a.bc.1.1 | 3 | |||
5.4 | even | 2 | 5775.2.a.br.1.1 | 3 | |||
7.6 | odd | 2 | 8085.2.a.bm.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.a.s.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3465.2.a.bc.1.1 | 3 | 3.2 | odd | 2 | |||
5775.2.a.br.1.1 | 3 | 5.4 | even | 2 | |||
8085.2.a.bm.1.3 | 3 | 7.6 | odd | 2 |