Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.62615 | −1.14986 | −0.574931 | − | 0.818202i | \(-0.694971\pi\) | ||||
−0.574931 | + | 0.818202i | \(0.694971\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.644366 | 0.322183 | ||||||||
\(5\) | 0.536374 | 0.239874 | 0.119937 | − | 0.992782i | \(-0.461731\pi\) | ||||
0.119937 | + | 0.992782i | \(0.461731\pi\) | |||||||
\(6\) | 1.62615 | 0.663873 | ||||||||
\(7\) | 4.53678 | 1.71474 | 0.857370 | − | 0.514701i | \(-0.172097\pi\) | ||||
0.857370 | + | 0.514701i | \(0.172097\pi\) | |||||||
\(8\) | 2.20447 | 0.779396 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.872225 | −0.275822 | ||||||||
\(11\) | 2.87790 | 0.867719 | 0.433860 | − | 0.900981i | \(-0.357151\pi\) | ||||
0.433860 | + | 0.900981i | \(0.357151\pi\) | |||||||
\(12\) | −0.644366 | −0.186012 | ||||||||
\(13\) | 1.05243 | 0.291890 | 0.145945 | − | 0.989293i | \(-0.453378\pi\) | ||||
0.145945 | + | 0.989293i | \(0.453378\pi\) | |||||||
\(14\) | −7.37748 | −1.97171 | ||||||||
\(15\) | −0.536374 | −0.138491 | ||||||||
\(16\) | −4.87352 | −1.21838 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −1.62615 | −0.383287 | ||||||||
\(19\) | 6.13593 | 1.40768 | 0.703839 | − | 0.710359i | \(-0.251467\pi\) | ||||
0.703839 | + | 0.710359i | \(0.251467\pi\) | |||||||
\(20\) | 0.345621 | 0.0772832 | ||||||||
\(21\) | −4.53678 | −0.990006 | ||||||||
\(22\) | −4.67990 | −0.997757 | ||||||||
\(23\) | 2.66713 | 0.556134 | 0.278067 | − | 0.960562i | \(-0.410306\pi\) | ||||
0.278067 | + | 0.960562i | \(0.410306\pi\) | |||||||
\(24\) | −2.20447 | −0.449985 | ||||||||
\(25\) | −4.71230 | −0.942461 | ||||||||
\(26\) | −1.71140 | −0.335634 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.92334 | 0.552460 | ||||||||
\(29\) | 4.14006 | 0.768789 | 0.384395 | − | 0.923169i | \(-0.374410\pi\) | ||||
0.384395 | + | 0.923169i | \(0.374410\pi\) | |||||||
\(30\) | 0.872225 | 0.159246 | ||||||||
\(31\) | −2.93407 | −0.526974 | −0.263487 | − | 0.964663i | \(-0.584873\pi\) | ||||
−0.263487 | + | 0.964663i | \(0.584873\pi\) | |||||||
\(32\) | 3.51615 | 0.621574 | ||||||||
\(33\) | −2.87790 | −0.500978 | ||||||||
\(34\) | −1.62615 | −0.278883 | ||||||||
\(35\) | 2.43341 | 0.411321 | ||||||||
\(36\) | 0.644366 | 0.107394 | ||||||||
\(37\) | −5.20943 | −0.856425 | −0.428212 | − | 0.903678i | \(-0.640857\pi\) | ||||
−0.428212 | + | 0.903678i | \(0.640857\pi\) | |||||||
\(38\) | −9.97794 | −1.61864 | ||||||||
\(39\) | −1.05243 | −0.168523 | ||||||||
\(40\) | 1.18242 | 0.186957 | ||||||||
\(41\) | 0.258454 | 0.0403638 | 0.0201819 | − | 0.999796i | \(-0.493575\pi\) | ||||
0.0201819 | + | 0.999796i | \(0.493575\pi\) | |||||||
\(42\) | 7.37748 | 1.13837 | ||||||||
\(43\) | 0.594529 | 0.0906649 | 0.0453324 | − | 0.998972i | \(-0.485565\pi\) | ||||
0.0453324 | + | 0.998972i | \(0.485565\pi\) | |||||||
\(44\) | 1.85442 | 0.279564 | ||||||||
\(45\) | 0.536374 | 0.0799579 | ||||||||
\(46\) | −4.33715 | −0.639477 | ||||||||
\(47\) | 4.62488 | 0.674609 | 0.337304 | − | 0.941396i | \(-0.390485\pi\) | ||||
0.337304 | + | 0.941396i | \(0.390485\pi\) | |||||||
\(48\) | 4.87352 | 0.703433 | ||||||||
\(49\) | 13.5823 | 1.94033 | ||||||||
\(50\) | 7.66291 | 1.08370 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0.678147 | 0.0940421 | ||||||||
\(53\) | −4.78052 | −0.656654 | −0.328327 | − | 0.944564i | \(-0.606485\pi\) | ||||
−0.328327 | + | 0.944564i | \(0.606485\pi\) | |||||||
\(54\) | 1.62615 | 0.221291 | ||||||||
\(55\) | 1.54363 | 0.208143 | ||||||||
\(56\) | 10.0012 | 1.33646 | ||||||||
\(57\) | −6.13593 | −0.812724 | ||||||||
\(58\) | −6.73235 | −0.884001 | ||||||||
\(59\) | −2.88225 | −0.375237 | −0.187618 | − | 0.982242i | \(-0.560077\pi\) | ||||
−0.187618 | + | 0.982242i | \(0.560077\pi\) | |||||||
\(60\) | −0.345621 | −0.0446195 | ||||||||
\(61\) | 10.4506 | 1.33806 | 0.669029 | − | 0.743237i | \(-0.266710\pi\) | ||||
0.669029 | + | 0.743237i | \(0.266710\pi\) | |||||||
\(62\) | 4.77124 | 0.605948 | ||||||||
\(63\) | 4.53678 | 0.571580 | ||||||||
\(64\) | 4.02926 | 0.503657 | ||||||||
\(65\) | 0.564494 | 0.0700168 | ||||||||
\(66\) | 4.67990 | 0.576055 | ||||||||
\(67\) | 16.2149 | 1.98096 | 0.990481 | − | 0.137648i | \(-0.0439542\pi\) | ||||
0.990481 | + | 0.137648i | \(0.0439542\pi\) | |||||||
\(68\) | 0.644366 | 0.0781408 | ||||||||
\(69\) | −2.66713 | −0.321084 | ||||||||
\(70\) | −3.95709 | −0.472962 | ||||||||
\(71\) | 9.88860 | 1.17356 | 0.586780 | − | 0.809746i | \(-0.300395\pi\) | ||||
0.586780 | + | 0.809746i | \(0.300395\pi\) | |||||||
\(72\) | 2.20447 | 0.259799 | ||||||||
\(73\) | 2.83517 | 0.331831 | 0.165916 | − | 0.986140i | \(-0.446942\pi\) | ||||
0.165916 | + | 0.986140i | \(0.446942\pi\) | |||||||
\(74\) | 8.47132 | 0.984770 | ||||||||
\(75\) | 4.71230 | 0.544130 | ||||||||
\(76\) | 3.95378 | 0.453530 | ||||||||
\(77\) | 13.0564 | 1.48791 | ||||||||
\(78\) | 1.71140 | 0.193778 | ||||||||
\(79\) | −4.89662 | −0.550913 | −0.275456 | − | 0.961314i | \(-0.588829\pi\) | ||||
−0.275456 | + | 0.961314i | \(0.588829\pi\) | |||||||
\(80\) | −2.61403 | −0.292258 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.420286 | −0.0464128 | ||||||||
\(83\) | 2.12890 | 0.233678 | 0.116839 | − | 0.993151i | \(-0.462724\pi\) | ||||
0.116839 | + | 0.993151i | \(0.462724\pi\) | |||||||
\(84\) | −2.92334 | −0.318963 | ||||||||
\(85\) | 0.536374 | 0.0581779 | ||||||||
\(86\) | −0.966794 | −0.104252 | ||||||||
\(87\) | −4.14006 | −0.443861 | ||||||||
\(88\) | 6.34423 | 0.676297 | ||||||||
\(89\) | −10.2701 | −1.08863 | −0.544313 | − | 0.838882i | \(-0.683210\pi\) | ||||
−0.544313 | + | 0.838882i | \(0.683210\pi\) | |||||||
\(90\) | −0.872225 | −0.0919406 | ||||||||
\(91\) | 4.77462 | 0.500516 | ||||||||
\(92\) | 1.71860 | 0.179177 | ||||||||
\(93\) | 2.93407 | 0.304249 | ||||||||
\(94\) | −7.52076 | −0.775707 | ||||||||
\(95\) | 3.29115 | 0.337665 | ||||||||
\(96\) | −3.51615 | −0.358866 | ||||||||
\(97\) | 11.9098 | 1.20925 | 0.604627 | − | 0.796508i | \(-0.293322\pi\) | ||||
0.604627 | + | 0.796508i | \(0.293322\pi\) | |||||||
\(98\) | −22.0869 | −2.23112 | ||||||||
\(99\) | 2.87790 | 0.289240 | ||||||||
\(100\) | −3.03645 | −0.303645 | ||||||||
\(101\) | −13.8417 | −1.37730 | −0.688651 | − | 0.725093i | \(-0.741797\pi\) | ||||
−0.688651 | + | 0.725093i | \(0.741797\pi\) | |||||||
\(102\) | 1.62615 | 0.161013 | ||||||||
\(103\) | 15.2504 | 1.50267 | 0.751333 | − | 0.659923i | \(-0.229411\pi\) | ||||
0.751333 | + | 0.659923i | \(0.229411\pi\) | |||||||
\(104\) | 2.32004 | 0.227498 | ||||||||
\(105\) | −2.43341 | −0.237476 | ||||||||
\(106\) | 7.77384 | 0.755062 | ||||||||
\(107\) | −13.9722 | −1.35074 | −0.675372 | − | 0.737477i | \(-0.736017\pi\) | ||||
−0.675372 | + | 0.737477i | \(0.736017\pi\) | |||||||
\(108\) | −0.644366 | −0.0620041 | ||||||||
\(109\) | −6.26962 | −0.600520 | −0.300260 | − | 0.953857i | \(-0.597074\pi\) | ||||
−0.300260 | + | 0.953857i | \(0.597074\pi\) | |||||||
\(110\) | −2.51017 | −0.239336 | ||||||||
\(111\) | 5.20943 | 0.494457 | ||||||||
\(112\) | −22.1101 | −2.08921 | ||||||||
\(113\) | −3.82481 | −0.359808 | −0.179904 | − | 0.983684i | \(-0.557579\pi\) | ||||
−0.179904 | + | 0.983684i | \(0.557579\pi\) | |||||||
\(114\) | 9.97794 | 0.934520 | ||||||||
\(115\) | 1.43058 | 0.133402 | ||||||||
\(116\) | 2.66771 | 0.247691 | ||||||||
\(117\) | 1.05243 | 0.0972968 | ||||||||
\(118\) | 4.68697 | 0.431470 | ||||||||
\(119\) | 4.53678 | 0.415886 | ||||||||
\(120\) | −1.18242 | −0.107939 | ||||||||
\(121\) | −2.71770 | −0.247064 | ||||||||
\(122\) | −16.9942 | −1.53858 | ||||||||
\(123\) | −0.258454 | −0.0233040 | ||||||||
\(124\) | −1.89061 | −0.169782 | ||||||||
\(125\) | −5.20943 | −0.465945 | ||||||||
\(126\) | −7.37748 | −0.657238 | ||||||||
\(127\) | 11.5276 | 1.02291 | 0.511455 | − | 0.859310i | \(-0.329107\pi\) | ||||
0.511455 | + | 0.859310i | \(0.329107\pi\) | |||||||
\(128\) | −13.5845 | −1.20071 | ||||||||
\(129\) | −0.594529 | −0.0523454 | ||||||||
\(130\) | −0.917952 | −0.0805097 | ||||||||
\(131\) | 8.80112 | 0.768958 | 0.384479 | − | 0.923134i | \(-0.374381\pi\) | ||||
0.384479 | + | 0.923134i | \(0.374381\pi\) | |||||||
\(132\) | −1.85442 | −0.161406 | ||||||||
\(133\) | 27.8373 | 2.41380 | ||||||||
\(134\) | −26.3678 | −2.27783 | ||||||||
\(135\) | −0.536374 | −0.0461637 | ||||||||
\(136\) | 2.20447 | 0.189031 | ||||||||
\(137\) | −15.2872 | −1.30607 | −0.653037 | − | 0.757326i | \(-0.726505\pi\) | ||||
−0.653037 | + | 0.757326i | \(0.726505\pi\) | |||||||
\(138\) | 4.33715 | 0.369203 | ||||||||
\(139\) | 13.7436 | 1.16572 | 0.582858 | − | 0.812574i | \(-0.301934\pi\) | ||||
0.582858 | + | 0.812574i | \(0.301934\pi\) | |||||||
\(140\) | 1.56800 | 0.132521 | ||||||||
\(141\) | −4.62488 | −0.389486 | ||||||||
\(142\) | −16.0803 | −1.34943 | ||||||||
\(143\) | 3.02878 | 0.253279 | ||||||||
\(144\) | −4.87352 | −0.406127 | ||||||||
\(145\) | 2.22062 | 0.184412 | ||||||||
\(146\) | −4.61041 | −0.381560 | ||||||||
\(147\) | −13.5823 | −1.12025 | ||||||||
\(148\) | −3.35678 | −0.275925 | ||||||||
\(149\) | 2.98768 | 0.244761 | 0.122380 | − | 0.992483i | \(-0.460947\pi\) | ||||
0.122380 | + | 0.992483i | \(0.460947\pi\) | |||||||
\(150\) | −7.66291 | −0.625674 | ||||||||
\(151\) | 23.0024 | 1.87191 | 0.935955 | − | 0.352118i | \(-0.114539\pi\) | ||||
0.935955 | + | 0.352118i | \(0.114539\pi\) | |||||||
\(152\) | 13.5264 | 1.09714 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −21.2316 | −1.71089 | ||||||||
\(155\) | −1.57376 | −0.126407 | ||||||||
\(156\) | −0.678147 | −0.0542952 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | 7.96264 | 0.633474 | ||||||||
\(159\) | 4.78052 | 0.379120 | ||||||||
\(160\) | 1.88597 | 0.149099 | ||||||||
\(161\) | 12.1001 | 0.953625 | ||||||||
\(162\) | −1.62615 | −0.127762 | ||||||||
\(163\) | 14.6184 | 1.14500 | 0.572502 | − | 0.819903i | \(-0.305973\pi\) | ||||
0.572502 | + | 0.819903i | \(0.305973\pi\) | |||||||
\(164\) | 0.166539 | 0.0130045 | ||||||||
\(165\) | −1.54363 | −0.120171 | ||||||||
\(166\) | −3.46192 | −0.268697 | ||||||||
\(167\) | −0.252002 | −0.0195005 | −0.00975025 | − | 0.999952i | \(-0.503104\pi\) | ||||
−0.00975025 | + | 0.999952i | \(0.503104\pi\) | |||||||
\(168\) | −10.0012 | −0.771607 | ||||||||
\(169\) | −11.8924 | −0.914800 | ||||||||
\(170\) | −0.872225 | −0.0668966 | ||||||||
\(171\) | 6.13593 | 0.469226 | ||||||||
\(172\) | 0.383094 | 0.0292107 | ||||||||
\(173\) | 15.8601 | 1.20582 | 0.602909 | − | 0.797810i | \(-0.294008\pi\) | ||||
0.602909 | + | 0.797810i | \(0.294008\pi\) | |||||||
\(174\) | 6.73235 | 0.510378 | ||||||||
\(175\) | −21.3787 | −1.61607 | ||||||||
\(176\) | −14.0255 | −1.05721 | ||||||||
\(177\) | 2.88225 | 0.216643 | ||||||||
\(178\) | 16.7007 | 1.25177 | ||||||||
\(179\) | 20.2145 | 1.51091 | 0.755453 | − | 0.655203i | \(-0.227417\pi\) | ||||
0.755453 | + | 0.655203i | \(0.227417\pi\) | |||||||
\(180\) | 0.345621 | 0.0257611 | ||||||||
\(181\) | 0.965690 | 0.0717791 | 0.0358896 | − | 0.999356i | \(-0.488574\pi\) | ||||
0.0358896 | + | 0.999356i | \(0.488574\pi\) | |||||||
\(182\) | −7.76425 | −0.575525 | ||||||||
\(183\) | −10.4506 | −0.772528 | ||||||||
\(184\) | 5.87959 | 0.433449 | ||||||||
\(185\) | −2.79420 | −0.205434 | ||||||||
\(186\) | −4.77124 | −0.349844 | ||||||||
\(187\) | 2.87790 | 0.210453 | ||||||||
\(188\) | 2.98012 | 0.217347 | ||||||||
\(189\) | −4.53678 | −0.330002 | ||||||||
\(190\) | −5.35191 | −0.388268 | ||||||||
\(191\) | −17.6222 | −1.27510 | −0.637550 | − | 0.770409i | \(-0.720052\pi\) | ||||
−0.637550 | + | 0.770409i | \(0.720052\pi\) | |||||||
\(192\) | −4.02926 | −0.290786 | ||||||||
\(193\) | −14.3544 | −1.03325 | −0.516625 | − | 0.856212i | \(-0.672812\pi\) | ||||
−0.516625 | + | 0.856212i | \(0.672812\pi\) | |||||||
\(194\) | −19.3671 | −1.39048 | ||||||||
\(195\) | −0.564494 | −0.0404242 | ||||||||
\(196\) | 8.75199 | 0.625142 | ||||||||
\(197\) | 6.30328 | 0.449090 | 0.224545 | − | 0.974464i | \(-0.427910\pi\) | ||||
0.224545 | + | 0.974464i | \(0.427910\pi\) | |||||||
\(198\) | −4.67990 | −0.332586 | ||||||||
\(199\) | −22.9260 | −1.62518 | −0.812592 | − | 0.582833i | \(-0.801944\pi\) | ||||
−0.812592 | + | 0.582833i | \(0.801944\pi\) | |||||||
\(200\) | −10.3881 | −0.734550 | ||||||||
\(201\) | −16.2149 | −1.14371 | ||||||||
\(202\) | 22.5087 | 1.58371 | ||||||||
\(203\) | 18.7825 | 1.31827 | ||||||||
\(204\) | −0.644366 | −0.0451146 | ||||||||
\(205\) | 0.138628 | 0.00968221 | ||||||||
\(206\) | −24.7994 | −1.72786 | ||||||||
\(207\) | 2.66713 | 0.185378 | ||||||||
\(208\) | −5.12902 | −0.355634 | ||||||||
\(209\) | 17.6586 | 1.22147 | ||||||||
\(210\) | 3.95709 | 0.273065 | ||||||||
\(211\) | −28.1637 | −1.93887 | −0.969433 | − | 0.245357i | \(-0.921095\pi\) | ||||
−0.969433 | + | 0.245357i | \(0.921095\pi\) | |||||||
\(212\) | −3.08040 | −0.211563 | ||||||||
\(213\) | −9.88860 | −0.677556 | ||||||||
\(214\) | 22.7209 | 1.55317 | ||||||||
\(215\) | 0.318890 | 0.0217481 | ||||||||
\(216\) | −2.20447 | −0.149995 | ||||||||
\(217\) | −13.3112 | −0.903624 | ||||||||
\(218\) | 10.1953 | 0.690516 | ||||||||
\(219\) | −2.83517 | −0.191583 | ||||||||
\(220\) | 0.994662 | 0.0670601 | ||||||||
\(221\) | 1.05243 | 0.0707938 | ||||||||
\(222\) | −8.47132 | −0.568558 | ||||||||
\(223\) | −12.3845 | −0.829328 | −0.414664 | − | 0.909975i | \(-0.636101\pi\) | ||||
−0.414664 | + | 0.909975i | \(0.636101\pi\) | |||||||
\(224\) | 15.9520 | 1.06584 | ||||||||
\(225\) | −4.71230 | −0.314154 | ||||||||
\(226\) | 6.21971 | 0.413729 | ||||||||
\(227\) | −11.2981 | −0.749878 | −0.374939 | − | 0.927049i | \(-0.622336\pi\) | ||||
−0.374939 | + | 0.927049i | \(0.622336\pi\) | |||||||
\(228\) | −3.95378 | −0.261846 | ||||||||
\(229\) | 7.65246 | 0.505689 | 0.252844 | − | 0.967507i | \(-0.418634\pi\) | ||||
0.252844 | + | 0.967507i | \(0.418634\pi\) | |||||||
\(230\) | −2.32633 | −0.153394 | ||||||||
\(231\) | −13.0564 | −0.859047 | ||||||||
\(232\) | 9.12661 | 0.599191 | ||||||||
\(233\) | −3.81049 | −0.249634 | −0.124817 | − | 0.992180i | \(-0.539834\pi\) | ||||
−0.124817 | + | 0.992180i | \(0.539834\pi\) | |||||||
\(234\) | −1.71140 | −0.111878 | ||||||||
\(235\) | 2.48067 | 0.161821 | ||||||||
\(236\) | −1.85722 | −0.120895 | ||||||||
\(237\) | 4.89662 | 0.318070 | ||||||||
\(238\) | −7.37748 | −0.478211 | ||||||||
\(239\) | −12.0878 | −0.781897 | −0.390948 | − | 0.920413i | \(-0.627853\pi\) | ||||
−0.390948 | + | 0.920413i | \(0.627853\pi\) | |||||||
\(240\) | 2.61403 | 0.168735 | ||||||||
\(241\) | −6.32255 | −0.407271 | −0.203636 | − | 0.979047i | \(-0.565276\pi\) | ||||
−0.203636 | + | 0.979047i | \(0.565276\pi\) | |||||||
\(242\) | 4.41939 | 0.284089 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.73398 | 0.431099 | ||||||||
\(245\) | 7.28521 | 0.465435 | ||||||||
\(246\) | 0.420286 | 0.0267964 | ||||||||
\(247\) | 6.45761 | 0.410888 | ||||||||
\(248\) | −6.46805 | −0.410722 | ||||||||
\(249\) | −2.12890 | −0.134914 | ||||||||
\(250\) | 8.47131 | 0.535773 | ||||||||
\(251\) | 0.350954 | 0.0221520 | 0.0110760 | − | 0.999939i | \(-0.496474\pi\) | ||||
0.0110760 | + | 0.999939i | \(0.496474\pi\) | |||||||
\(252\) | 2.92334 | 0.184153 | ||||||||
\(253\) | 7.67572 | 0.482568 | ||||||||
\(254\) | −18.7456 | −1.17620 | ||||||||
\(255\) | −0.536374 | −0.0335890 | ||||||||
\(256\) | 14.0319 | 0.876994 | ||||||||
\(257\) | −20.1141 | −1.25469 | −0.627343 | − | 0.778743i | \(-0.715858\pi\) | ||||
−0.627343 | + | 0.778743i | \(0.715858\pi\) | |||||||
\(258\) | 0.966794 | 0.0601900 | ||||||||
\(259\) | −23.6340 | −1.46855 | ||||||||
\(260\) | 0.363740 | 0.0225582 | ||||||||
\(261\) | 4.14006 | 0.256263 | ||||||||
\(262\) | −14.3119 | −0.884195 | ||||||||
\(263\) | −15.3035 | −0.943653 | −0.471826 | − | 0.881691i | \(-0.656405\pi\) | ||||
−0.471826 | + | 0.881691i | \(0.656405\pi\) | |||||||
\(264\) | −6.34423 | −0.390460 | ||||||||
\(265\) | −2.56414 | −0.157514 | ||||||||
\(266\) | −45.2677 | −2.77554 | ||||||||
\(267\) | 10.2701 | 0.628519 | ||||||||
\(268\) | 10.4483 | 0.638232 | ||||||||
\(269\) | 20.3913 | 1.24328 | 0.621641 | − | 0.783302i | \(-0.286466\pi\) | ||||
0.621641 | + | 0.783302i | \(0.286466\pi\) | |||||||
\(270\) | 0.872225 | 0.0530819 | ||||||||
\(271\) | 25.8269 | 1.56887 | 0.784435 | − | 0.620211i | \(-0.212953\pi\) | ||||
0.784435 | + | 0.620211i | \(0.212953\pi\) | |||||||
\(272\) | −4.87352 | −0.295501 | ||||||||
\(273\) | −4.77462 | −0.288973 | ||||||||
\(274\) | 24.8593 | 1.50180 | ||||||||
\(275\) | −13.5615 | −0.817791 | ||||||||
\(276\) | −1.71860 | −0.103448 | ||||||||
\(277\) | −20.2293 | −1.21546 | −0.607731 | − | 0.794143i | \(-0.707920\pi\) | ||||
−0.607731 | + | 0.794143i | \(0.707920\pi\) | |||||||
\(278\) | −22.3491 | −1.34041 | ||||||||
\(279\) | −2.93407 | −0.175658 | ||||||||
\(280\) | 5.36436 | 0.320582 | ||||||||
\(281\) | 5.07183 | 0.302560 | 0.151280 | − | 0.988491i | \(-0.451661\pi\) | ||||
0.151280 | + | 0.988491i | \(0.451661\pi\) | |||||||
\(282\) | 7.52076 | 0.447855 | ||||||||
\(283\) | 11.7889 | 0.700778 | 0.350389 | − | 0.936604i | \(-0.386049\pi\) | ||||
0.350389 | + | 0.936604i | \(0.386049\pi\) | |||||||
\(284\) | 6.37187 | 0.378101 | ||||||||
\(285\) | −3.29115 | −0.194951 | ||||||||
\(286\) | −4.92524 | −0.291236 | ||||||||
\(287\) | 1.17255 | 0.0692134 | ||||||||
\(288\) | 3.51615 | 0.207191 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −3.61106 | −0.212049 | ||||||||
\(291\) | −11.9098 | −0.698164 | ||||||||
\(292\) | 1.82688 | 0.106910 | ||||||||
\(293\) | −13.3955 | −0.782574 | −0.391287 | − | 0.920269i | \(-0.627970\pi\) | ||||
−0.391287 | + | 0.920269i | \(0.627970\pi\) | |||||||
\(294\) | 22.0869 | 1.28814 | ||||||||
\(295\) | −1.54596 | −0.0900094 | ||||||||
\(296\) | −11.4840 | −0.667494 | ||||||||
\(297\) | −2.87790 | −0.166993 | ||||||||
\(298\) | −4.85843 | −0.281441 | ||||||||
\(299\) | 2.80695 | 0.162330 | ||||||||
\(300\) | 3.03645 | 0.175309 | ||||||||
\(301\) | 2.69725 | 0.155467 | ||||||||
\(302\) | −37.4054 | −2.15244 | ||||||||
\(303\) | 13.8417 | 0.795186 | ||||||||
\(304\) | −29.9036 | −1.71509 | ||||||||
\(305\) | 5.60541 | 0.320965 | ||||||||
\(306\) | −1.62615 | −0.0929608 | ||||||||
\(307\) | −5.92232 | −0.338005 | −0.169002 | − | 0.985616i | \(-0.554055\pi\) | ||||
−0.169002 | + | 0.985616i | \(0.554055\pi\) | |||||||
\(308\) | 8.41308 | 0.479380 | ||||||||
\(309\) | −15.2504 | −0.867565 | ||||||||
\(310\) | 2.55917 | 0.145351 | ||||||||
\(311\) | 13.1833 | 0.747554 | 0.373777 | − | 0.927519i | \(-0.378063\pi\) | ||||
0.373777 | + | 0.927519i | \(0.378063\pi\) | |||||||
\(312\) | −2.32004 | −0.131346 | ||||||||
\(313\) | 15.1808 | 0.858069 | 0.429035 | − | 0.903288i | \(-0.358854\pi\) | ||||
0.429035 | + | 0.903288i | \(0.358854\pi\) | |||||||
\(314\) | 1.62615 | 0.0917690 | ||||||||
\(315\) | 2.43341 | 0.137107 | ||||||||
\(316\) | −3.15521 | −0.177495 | ||||||||
\(317\) | −18.2857 | −1.02702 | −0.513512 | − | 0.858082i | \(-0.671656\pi\) | ||||
−0.513512 | + | 0.858082i | \(0.671656\pi\) | |||||||
\(318\) | −7.77384 | −0.435935 | ||||||||
\(319\) | 11.9147 | 0.667093 | ||||||||
\(320\) | 2.16119 | 0.120814 | ||||||||
\(321\) | 13.9722 | 0.779852 | ||||||||
\(322\) | −19.6767 | −1.09654 | ||||||||
\(323\) | 6.13593 | 0.341412 | ||||||||
\(324\) | 0.644366 | 0.0357981 | ||||||||
\(325\) | −4.95935 | −0.275095 | ||||||||
\(326\) | −23.7718 | −1.31660 | ||||||||
\(327\) | 6.26962 | 0.346711 | ||||||||
\(328\) | 0.569754 | 0.0314594 | ||||||||
\(329\) | 20.9821 | 1.15678 | ||||||||
\(330\) | 2.51017 | 0.138181 | ||||||||
\(331\) | 5.35412 | 0.294289 | 0.147145 | − | 0.989115i | \(-0.452992\pi\) | ||||
0.147145 | + | 0.989115i | \(0.452992\pi\) | |||||||
\(332\) | 1.37179 | 0.0752869 | ||||||||
\(333\) | −5.20943 | −0.285475 | ||||||||
\(334\) | 0.409793 | 0.0224229 | ||||||||
\(335\) | 8.69724 | 0.475181 | ||||||||
\(336\) | 22.1101 | 1.20620 | ||||||||
\(337\) | 28.5799 | 1.55685 | 0.778423 | − | 0.627740i | \(-0.216020\pi\) | ||||
0.778423 | + | 0.627740i | \(0.216020\pi\) | |||||||
\(338\) | 19.3388 | 1.05189 | ||||||||
\(339\) | 3.82481 | 0.207735 | ||||||||
\(340\) | 0.345621 | 0.0187439 | ||||||||
\(341\) | −8.44395 | −0.457266 | ||||||||
\(342\) | −9.97794 | −0.539545 | ||||||||
\(343\) | 29.8626 | 1.61243 | ||||||||
\(344\) | 1.31062 | 0.0706639 | ||||||||
\(345\) | −1.43058 | −0.0770197 | ||||||||
\(346\) | −25.7909 | −1.38652 | ||||||||
\(347\) | −31.9705 | −1.71627 | −0.858134 | − | 0.513425i | \(-0.828376\pi\) | ||||
−0.858134 | + | 0.513425i | \(0.828376\pi\) | |||||||
\(348\) | −2.66771 | −0.143004 | ||||||||
\(349\) | −1.57124 | −0.0841065 | −0.0420533 | − | 0.999115i | \(-0.513390\pi\) | ||||
−0.0420533 | + | 0.999115i | \(0.513390\pi\) | |||||||
\(350\) | 34.7649 | 1.85826 | ||||||||
\(351\) | −1.05243 | −0.0561743 | ||||||||
\(352\) | 10.1191 | 0.539351 | ||||||||
\(353\) | −10.1771 | −0.541674 | −0.270837 | − | 0.962625i | \(-0.587300\pi\) | ||||
−0.270837 | + | 0.962625i | \(0.587300\pi\) | |||||||
\(354\) | −4.68697 | −0.249110 | ||||||||
\(355\) | 5.30399 | 0.281506 | ||||||||
\(356\) | −6.61769 | −0.350737 | ||||||||
\(357\) | −4.53678 | −0.240112 | ||||||||
\(358\) | −32.8719 | −1.73733 | ||||||||
\(359\) | 23.4680 | 1.23859 | 0.619297 | − | 0.785157i | \(-0.287418\pi\) | ||||
0.619297 | + | 0.785157i | \(0.287418\pi\) | |||||||
\(360\) | 1.18242 | 0.0623189 | ||||||||
\(361\) | 18.6496 | 0.981559 | ||||||||
\(362\) | −1.57036 | −0.0825361 | ||||||||
\(363\) | 2.71770 | 0.142642 | ||||||||
\(364\) | 3.07660 | 0.161258 | ||||||||
\(365\) | 1.52071 | 0.0795976 | ||||||||
\(366\) | 16.9942 | 0.888300 | ||||||||
\(367\) | −24.7603 | −1.29248 | −0.646239 | − | 0.763135i | \(-0.723659\pi\) | ||||
−0.646239 | + | 0.763135i | \(0.723659\pi\) | |||||||
\(368\) | −12.9983 | −0.677583 | ||||||||
\(369\) | 0.258454 | 0.0134546 | ||||||||
\(370\) | 4.54379 | 0.236221 | ||||||||
\(371\) | −21.6881 | −1.12599 | ||||||||
\(372\) | 1.89061 | 0.0980237 | ||||||||
\(373\) | 2.41072 | 0.124822 | 0.0624111 | − | 0.998051i | \(-0.480121\pi\) | ||||
0.0624111 | + | 0.998051i | \(0.480121\pi\) | |||||||
\(374\) | −4.67990 | −0.241992 | ||||||||
\(375\) | 5.20943 | 0.269014 | ||||||||
\(376\) | 10.1954 | 0.525788 | ||||||||
\(377\) | 4.35710 | 0.224402 | ||||||||
\(378\) | 7.37748 | 0.379457 | ||||||||
\(379\) | 6.38995 | 0.328230 | 0.164115 | − | 0.986441i | \(-0.447523\pi\) | ||||
0.164115 | + | 0.986441i | \(0.447523\pi\) | |||||||
\(380\) | 2.12071 | 0.108790 | ||||||||
\(381\) | −11.5276 | −0.590577 | ||||||||
\(382\) | 28.6564 | 1.46619 | ||||||||
\(383\) | −14.6608 | −0.749132 | −0.374566 | − | 0.927200i | \(-0.622208\pi\) | ||||
−0.374566 | + | 0.927200i | \(0.622208\pi\) | |||||||
\(384\) | 13.5845 | 0.693230 | ||||||||
\(385\) | 7.00310 | 0.356911 | ||||||||
\(386\) | 23.3423 | 1.18809 | ||||||||
\(387\) | 0.594529 | 0.0302216 | ||||||||
\(388\) | 7.67425 | 0.389601 | ||||||||
\(389\) | 20.7383 | 1.05147 | 0.525736 | − | 0.850648i | \(-0.323790\pi\) | ||||
0.525736 | + | 0.850648i | \(0.323790\pi\) | |||||||
\(390\) | 0.917952 | 0.0464823 | ||||||||
\(391\) | 2.66713 | 0.134882 | ||||||||
\(392\) | 29.9418 | 1.51229 | ||||||||
\(393\) | −8.80112 | −0.443958 | ||||||||
\(394\) | −10.2501 | −0.516392 | ||||||||
\(395\) | −2.62642 | −0.132149 | ||||||||
\(396\) | 1.85442 | 0.0931881 | ||||||||
\(397\) | −31.1806 | −1.56491 | −0.782455 | − | 0.622707i | \(-0.786033\pi\) | ||||
−0.782455 | + | 0.622707i | \(0.786033\pi\) | |||||||
\(398\) | 37.2812 | 1.86874 | ||||||||
\(399\) | −27.8373 | −1.39361 | ||||||||
\(400\) | 22.9655 | 1.14828 | ||||||||
\(401\) | −39.3277 | −1.96393 | −0.981965 | − | 0.189064i | \(-0.939455\pi\) | ||||
−0.981965 | + | 0.189064i | \(0.939455\pi\) | |||||||
\(402\) | 26.3678 | 1.31511 | ||||||||
\(403\) | −3.08789 | −0.153819 | ||||||||
\(404\) | −8.91912 | −0.443743 | ||||||||
\(405\) | 0.536374 | 0.0266526 | ||||||||
\(406\) | −30.5432 | −1.51583 | ||||||||
\(407\) | −14.9922 | −0.743136 | ||||||||
\(408\) | −2.20447 | −0.109137 | ||||||||
\(409\) | 10.1598 | 0.502368 | 0.251184 | − | 0.967939i | \(-0.419180\pi\) | ||||
0.251184 | + | 0.967939i | \(0.419180\pi\) | |||||||
\(410\) | −0.225430 | −0.0111332 | ||||||||
\(411\) | 15.2872 | 0.754062 | ||||||||
\(412\) | 9.82683 | 0.484133 | ||||||||
\(413\) | −13.0761 | −0.643433 | ||||||||
\(414\) | −4.33715 | −0.213159 | ||||||||
\(415\) | 1.14189 | 0.0560531 | ||||||||
\(416\) | 3.70049 | 0.181431 | ||||||||
\(417\) | −13.7436 | −0.673026 | ||||||||
\(418\) | −28.7155 | −1.40452 | ||||||||
\(419\) | 3.04043 | 0.148535 | 0.0742674 | − | 0.997238i | \(-0.476338\pi\) | ||||
0.0742674 | + | 0.997238i | \(0.476338\pi\) | |||||||
\(420\) | −1.56800 | −0.0765108 | ||||||||
\(421\) | −27.7553 | −1.35271 | −0.676355 | − | 0.736575i | \(-0.736442\pi\) | ||||
−0.676355 | + | 0.736575i | \(0.736442\pi\) | |||||||
\(422\) | 45.7983 | 2.22943 | ||||||||
\(423\) | 4.62488 | 0.224870 | ||||||||
\(424\) | −10.5385 | −0.511794 | ||||||||
\(425\) | −4.71230 | −0.228580 | ||||||||
\(426\) | 16.0803 | 0.779095 | ||||||||
\(427\) | 47.4118 | 2.29442 | ||||||||
\(428\) | −9.00320 | −0.435186 | ||||||||
\(429\) | −3.02878 | −0.146231 | ||||||||
\(430\) | −0.518563 | −0.0250073 | ||||||||
\(431\) | −27.5938 | −1.32915 | −0.664573 | − | 0.747223i | \(-0.731387\pi\) | ||||
−0.664573 | + | 0.747223i | \(0.731387\pi\) | |||||||
\(432\) | 4.87352 | 0.234478 | ||||||||
\(433\) | −13.3618 | −0.642126 | −0.321063 | − | 0.947058i | \(-0.604040\pi\) | ||||
−0.321063 | + | 0.947058i | \(0.604040\pi\) | |||||||
\(434\) | 21.6460 | 1.03904 | ||||||||
\(435\) | −2.22062 | −0.106470 | ||||||||
\(436\) | −4.03993 | −0.193477 | ||||||||
\(437\) | 16.3653 | 0.782858 | ||||||||
\(438\) | 4.61041 | 0.220294 | ||||||||
\(439\) | −4.65570 | −0.222205 | −0.111102 | − | 0.993809i | \(-0.535438\pi\) | ||||
−0.111102 | + | 0.993809i | \(0.535438\pi\) | |||||||
\(440\) | 3.40288 | 0.162226 | ||||||||
\(441\) | 13.5823 | 0.646778 | ||||||||
\(442\) | −1.71140 | −0.0814031 | ||||||||
\(443\) | −16.4031 | −0.779337 | −0.389668 | − | 0.920955i | \(-0.627410\pi\) | ||||
−0.389668 | + | 0.920955i | \(0.627410\pi\) | |||||||
\(444\) | 3.35678 | 0.159306 | ||||||||
\(445\) | −5.50860 | −0.261133 | ||||||||
\(446\) | 20.1391 | 0.953613 | ||||||||
\(447\) | −2.98768 | −0.141313 | ||||||||
\(448\) | 18.2798 | 0.863641 | ||||||||
\(449\) | −2.98737 | −0.140983 | −0.0704915 | − | 0.997512i | \(-0.522457\pi\) | ||||
−0.0704915 | + | 0.997512i | \(0.522457\pi\) | |||||||
\(450\) | 7.66291 | 0.361233 | ||||||||
\(451\) | 0.743805 | 0.0350244 | ||||||||
\(452\) | −2.46458 | −0.115924 | ||||||||
\(453\) | −23.0024 | −1.08075 | ||||||||
\(454\) | 18.3723 | 0.862256 | ||||||||
\(455\) | 2.56098 | 0.120061 | ||||||||
\(456\) | −13.5264 | −0.633434 | ||||||||
\(457\) | 37.8455 | 1.77034 | 0.885168 | − | 0.465272i | \(-0.154043\pi\) | ||||
0.885168 | + | 0.465272i | \(0.154043\pi\) | |||||||
\(458\) | −12.4441 | −0.581472 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0.921814 | 0.0429798 | ||||||||
\(461\) | −5.61583 | −0.261556 | −0.130778 | − | 0.991412i | \(-0.541747\pi\) | ||||
−0.130778 | + | 0.991412i | \(0.541747\pi\) | |||||||
\(462\) | 21.2316 | 0.987785 | ||||||||
\(463\) | 16.2899 | 0.757056 | 0.378528 | − | 0.925590i | \(-0.376430\pi\) | ||||
0.378528 | + | 0.925590i | \(0.376430\pi\) | |||||||
\(464\) | −20.1767 | −0.936678 | ||||||||
\(465\) | 1.57376 | 0.0729813 | ||||||||
\(466\) | 6.19643 | 0.287044 | ||||||||
\(467\) | 25.0009 | 1.15691 | 0.578453 | − | 0.815716i | \(-0.303657\pi\) | ||||
0.578453 | + | 0.815716i | \(0.303657\pi\) | |||||||
\(468\) | 0.678147 | 0.0313474 | ||||||||
\(469\) | 73.5633 | 3.39684 | ||||||||
\(470\) | −4.03394 | −0.186072 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | −6.35382 | −0.292458 | ||||||||
\(473\) | 1.71100 | 0.0786716 | ||||||||
\(474\) | −7.96264 | −0.365736 | ||||||||
\(475\) | −28.9144 | −1.32668 | ||||||||
\(476\) | 2.92334 | 0.133991 | ||||||||
\(477\) | −4.78052 | −0.218885 | ||||||||
\(478\) | 19.6566 | 0.899073 | ||||||||
\(479\) | 18.2803 | 0.835247 | 0.417624 | − | 0.908620i | \(-0.362863\pi\) | ||||
0.417624 | + | 0.908620i | \(0.362863\pi\) | |||||||
\(480\) | −1.88597 | −0.0860825 | ||||||||
\(481\) | −5.48254 | −0.249982 | ||||||||
\(482\) | 10.2814 | 0.468306 | ||||||||
\(483\) | −12.1001 | −0.550576 | ||||||||
\(484\) | −1.75119 | −0.0795996 | ||||||||
\(485\) | 6.38809 | 0.290068 | ||||||||
\(486\) | 1.62615 | 0.0737637 | ||||||||
\(487\) | 11.9082 | 0.539611 | 0.269805 | − | 0.962915i | \(-0.413041\pi\) | ||||
0.269805 | + | 0.962915i | \(0.413041\pi\) | |||||||
\(488\) | 23.0379 | 1.04288 | ||||||||
\(489\) | −14.6184 | −0.661068 | ||||||||
\(490\) | −11.8468 | −0.535186 | ||||||||
\(491\) | 10.9479 | 0.494070 | 0.247035 | − | 0.969007i | \(-0.420544\pi\) | ||||
0.247035 | + | 0.969007i | \(0.420544\pi\) | |||||||
\(492\) | −0.166539 | −0.00750816 | ||||||||
\(493\) | 4.14006 | 0.186459 | ||||||||
\(494\) | −10.5010 | −0.472464 | ||||||||
\(495\) | 1.54363 | 0.0693810 | ||||||||
\(496\) | 14.2993 | 0.642056 | ||||||||
\(497\) | 44.8623 | 2.01235 | ||||||||
\(498\) | 3.46192 | 0.155132 | ||||||||
\(499\) | 1.98410 | 0.0888206 | 0.0444103 | − | 0.999013i | \(-0.485859\pi\) | ||||
0.0444103 | + | 0.999013i | \(0.485859\pi\) | |||||||
\(500\) | −3.35677 | −0.150120 | ||||||||
\(501\) | 0.252002 | 0.0112586 | ||||||||
\(502\) | −0.570703 | −0.0254717 | ||||||||
\(503\) | 38.8310 | 1.73139 | 0.865695 | − | 0.500571i | \(-0.166877\pi\) | ||||
0.865695 | + | 0.500571i | \(0.166877\pi\) | |||||||
\(504\) | 10.0012 | 0.445487 | ||||||||
\(505\) | −7.42433 | −0.330379 | ||||||||
\(506\) | −12.4819 | −0.554887 | ||||||||
\(507\) | 11.8924 | 0.528160 | ||||||||
\(508\) | 7.42799 | 0.329564 | ||||||||
\(509\) | 1.53769 | 0.0681567 | 0.0340784 | − | 0.999419i | \(-0.489150\pi\) | ||||
0.0340784 | + | 0.999419i | \(0.489150\pi\) | |||||||
\(510\) | 0.872225 | 0.0386228 | ||||||||
\(511\) | 12.8625 | 0.569004 | ||||||||
\(512\) | 4.35098 | 0.192288 | ||||||||
\(513\) | −6.13593 | −0.270908 | ||||||||
\(514\) | 32.7086 | 1.44272 | ||||||||
\(515\) | 8.17992 | 0.360450 | ||||||||
\(516\) | −0.383094 | −0.0168648 | ||||||||
\(517\) | 13.3099 | 0.585371 | ||||||||
\(518\) | 38.4325 | 1.68863 | ||||||||
\(519\) | −15.8601 | −0.696180 | ||||||||
\(520\) | 1.24441 | 0.0545709 | ||||||||
\(521\) | 0.0367612 | 0.00161054 | 0.000805269 | − | 1.00000i | \(-0.499744\pi\) | ||||
0.000805269 | 1.00000i | \(0.499744\pi\) | ||||||||
\(522\) | −6.73235 | −0.294667 | ||||||||
\(523\) | −17.1989 | −0.752054 | −0.376027 | − | 0.926609i | \(-0.622710\pi\) | ||||
−0.376027 | + | 0.926609i | \(0.622710\pi\) | |||||||
\(524\) | 5.67114 | 0.247745 | ||||||||
\(525\) | 21.3787 | 0.933041 | ||||||||
\(526\) | 24.8858 | 1.08507 | ||||||||
\(527\) | −2.93407 | −0.127810 | ||||||||
\(528\) | 14.0255 | 0.610382 | ||||||||
\(529\) | −15.8864 | −0.690715 | ||||||||
\(530\) | 4.16968 | 0.181119 | ||||||||
\(531\) | −2.88225 | −0.125079 | ||||||||
\(532\) | 17.9374 | 0.777686 | ||||||||
\(533\) | 0.272004 | 0.0117818 | ||||||||
\(534\) | −16.7007 | −0.722710 | ||||||||
\(535\) | −7.49432 | −0.324008 | ||||||||
\(536\) | 35.7451 | 1.54395 | ||||||||
\(537\) | −20.2145 | −0.872322 | ||||||||
\(538\) | −33.1594 | −1.42960 | ||||||||
\(539\) | 39.0886 | 1.68366 | ||||||||
\(540\) | −0.345621 | −0.0148732 | ||||||||
\(541\) | 25.0584 | 1.07734 | 0.538672 | − | 0.842515i | \(-0.318926\pi\) | ||||
0.538672 | + | 0.842515i | \(0.318926\pi\) | |||||||
\(542\) | −41.9984 | −1.80398 | ||||||||
\(543\) | −0.965690 | −0.0414417 | ||||||||
\(544\) | 3.51615 | 0.150754 | ||||||||
\(545\) | −3.36286 | −0.144049 | ||||||||
\(546\) | 7.76425 | 0.332279 | ||||||||
\(547\) | 43.4640 | 1.85839 | 0.929193 | − | 0.369595i | \(-0.120504\pi\) | ||||
0.929193 | + | 0.369595i | \(0.120504\pi\) | |||||||
\(548\) | −9.85055 | −0.420794 | ||||||||
\(549\) | 10.4506 | 0.446019 | ||||||||
\(550\) | 22.0531 | 0.940347 | ||||||||
\(551\) | 25.4031 | 1.08221 | ||||||||
\(552\) | −5.87959 | −0.250252 | ||||||||
\(553\) | −22.2149 | −0.944672 | ||||||||
\(554\) | 32.8959 | 1.39761 | ||||||||
\(555\) | 2.79420 | 0.118607 | ||||||||
\(556\) | 8.85590 | 0.375574 | ||||||||
\(557\) | −42.2867 | −1.79174 | −0.895872 | − | 0.444312i | \(-0.853448\pi\) | ||||
−0.895872 | + | 0.444312i | \(0.853448\pi\) | |||||||
\(558\) | 4.77124 | 0.201983 | ||||||||
\(559\) | 0.625698 | 0.0264642 | ||||||||
\(560\) | −11.8593 | −0.501146 | ||||||||
\(561\) | −2.87790 | −0.121505 | ||||||||
\(562\) | −8.24756 | −0.347902 | ||||||||
\(563\) | 7.91695 | 0.333660 | 0.166830 | − | 0.985986i | \(-0.446647\pi\) | ||||
0.166830 | + | 0.985986i | \(0.446647\pi\) | |||||||
\(564\) | −2.98012 | −0.125486 | ||||||||
\(565\) | −2.05153 | −0.0863084 | ||||||||
\(566\) | −19.1705 | −0.805798 | ||||||||
\(567\) | 4.53678 | 0.190527 | ||||||||
\(568\) | 21.7991 | 0.914669 | ||||||||
\(569\) | −29.0022 | −1.21584 | −0.607918 | − | 0.794000i | \(-0.707995\pi\) | ||||
−0.607918 | + | 0.794000i | \(0.707995\pi\) | |||||||
\(570\) | 5.35191 | 0.224167 | ||||||||
\(571\) | 35.6894 | 1.49356 | 0.746778 | − | 0.665073i | \(-0.231600\pi\) | ||||
0.746778 | + | 0.665073i | \(0.231600\pi\) | |||||||
\(572\) | 1.95164 | 0.0816021 | ||||||||
\(573\) | 17.6222 | 0.736180 | ||||||||
\(574\) | −1.90674 | −0.0795858 | ||||||||
\(575\) | −12.5683 | −0.524134 | ||||||||
\(576\) | 4.02926 | 0.167886 | ||||||||
\(577\) | 23.5907 | 0.982093 | 0.491046 | − | 0.871133i | \(-0.336615\pi\) | ||||
0.491046 | + | 0.871133i | \(0.336615\pi\) | |||||||
\(578\) | −1.62615 | −0.0676389 | ||||||||
\(579\) | 14.3544 | 0.596547 | ||||||||
\(580\) | 1.43089 | 0.0594145 | ||||||||
\(581\) | 9.65836 | 0.400696 | ||||||||
\(582\) | 19.3671 | 0.802792 | ||||||||
\(583\) | −13.7578 | −0.569791 | ||||||||
\(584\) | 6.25003 | 0.258628 | ||||||||
\(585\) | 0.564494 | 0.0233389 | ||||||||
\(586\) | 21.7831 | 0.899852 | ||||||||
\(587\) | −34.7455 | −1.43410 | −0.717049 | − | 0.697022i | \(-0.754508\pi\) | ||||
−0.717049 | + | 0.697022i | \(0.754508\pi\) | |||||||
\(588\) | −8.75199 | −0.360926 | ||||||||
\(589\) | −18.0032 | −0.741811 | ||||||||
\(590\) | 2.51397 | 0.103498 | ||||||||
\(591\) | −6.30328 | −0.259282 | ||||||||
\(592\) | 25.3883 | 1.04345 | ||||||||
\(593\) | −25.9954 | −1.06751 | −0.533753 | − | 0.845641i | \(-0.679219\pi\) | ||||
−0.533753 | + | 0.845641i | \(0.679219\pi\) | |||||||
\(594\) | 4.67990 | 0.192018 | ||||||||
\(595\) | 2.43341 | 0.0997600 | ||||||||
\(596\) | 1.92516 | 0.0788577 | ||||||||
\(597\) | 22.9260 | 0.938300 | ||||||||
\(598\) | −4.56453 | −0.186657 | ||||||||
\(599\) | 36.7339 | 1.50091 | 0.750453 | − | 0.660924i | \(-0.229836\pi\) | ||||
0.750453 | + | 0.660924i | \(0.229836\pi\) | |||||||
\(600\) | 10.3881 | 0.424093 | ||||||||
\(601\) | 1.49323 | 0.0609103 | 0.0304552 | − | 0.999536i | \(-0.490304\pi\) | ||||
0.0304552 | + | 0.999536i | \(0.490304\pi\) | |||||||
\(602\) | −4.38613 | −0.178765 | ||||||||
\(603\) | 16.2149 | 0.660321 | ||||||||
\(604\) | 14.8220 | 0.603097 | ||||||||
\(605\) | −1.45770 | −0.0592640 | ||||||||
\(606\) | −22.5087 | −0.914354 | ||||||||
\(607\) | −12.0497 | −0.489082 | −0.244541 | − | 0.969639i | \(-0.578637\pi\) | ||||
−0.244541 | + | 0.969639i | \(0.578637\pi\) | |||||||
\(608\) | 21.5749 | 0.874976 | ||||||||
\(609\) | −18.7825 | −0.761106 | ||||||||
\(610\) | −9.11524 | −0.369065 | ||||||||
\(611\) | 4.86735 | 0.196912 | ||||||||
\(612\) | 0.644366 | 0.0260469 | ||||||||
\(613\) | −28.2428 | −1.14072 | −0.570359 | − | 0.821396i | \(-0.693196\pi\) | ||||
−0.570359 | + | 0.821396i | \(0.693196\pi\) | |||||||
\(614\) | 9.63058 | 0.388659 | ||||||||
\(615\) | −0.138628 | −0.00559003 | ||||||||
\(616\) | 28.7823 | 1.15967 | ||||||||
\(617\) | −42.3589 | −1.70530 | −0.852652 | − | 0.522479i | \(-0.825007\pi\) | ||||
−0.852652 | + | 0.522479i | \(0.825007\pi\) | |||||||
\(618\) | 24.7994 | 0.997580 | ||||||||
\(619\) | −32.6557 | −1.31254 | −0.656271 | − | 0.754525i | \(-0.727867\pi\) | ||||
−0.656271 | + | 0.754525i | \(0.727867\pi\) | |||||||
\(620\) | −1.01408 | −0.0407263 | ||||||||
\(621\) | −2.66713 | −0.107028 | ||||||||
\(622\) | −21.4380 | −0.859584 | ||||||||
\(623\) | −46.5930 | −1.86671 | ||||||||
\(624\) | 5.12902 | 0.205325 | ||||||||
\(625\) | 20.7673 | 0.830693 | ||||||||
\(626\) | −24.6863 | −0.986662 | ||||||||
\(627\) | −17.6586 | −0.705216 | ||||||||
\(628\) | −0.644366 | −0.0257130 | ||||||||
\(629\) | −5.20943 | −0.207714 | ||||||||
\(630\) | −3.95709 | −0.157654 | ||||||||
\(631\) | 36.0897 | 1.43671 | 0.718355 | − | 0.695677i | \(-0.244896\pi\) | ||||
0.718355 | + | 0.695677i | \(0.244896\pi\) | |||||||
\(632\) | −10.7944 | −0.429379 | ||||||||
\(633\) | 28.1637 | 1.11940 | ||||||||
\(634\) | 29.7352 | 1.18094 | ||||||||
\(635\) | 6.18311 | 0.245369 | ||||||||
\(636\) | 3.08040 | 0.122146 | ||||||||
\(637\) | 14.2944 | 0.566365 | ||||||||
\(638\) | −19.3750 | −0.767065 | ||||||||
\(639\) | 9.88860 | 0.391187 | ||||||||
\(640\) | −7.28636 | −0.288019 | ||||||||
\(641\) | 45.2127 | 1.78579 | 0.892897 | − | 0.450262i | \(-0.148669\pi\) | ||||
0.892897 | + | 0.450262i | \(0.148669\pi\) | |||||||
\(642\) | −22.7209 | −0.896722 | ||||||||
\(643\) | 18.8719 | 0.744234 | 0.372117 | − | 0.928186i | \(-0.378632\pi\) | ||||
0.372117 | + | 0.928186i | \(0.378632\pi\) | |||||||
\(644\) | 7.79692 | 0.307242 | ||||||||
\(645\) | −0.318890 | −0.0125563 | ||||||||
\(646\) | −9.97794 | −0.392577 | ||||||||
\(647\) | 47.7355 | 1.87668 | 0.938338 | − | 0.345718i | \(-0.112365\pi\) | ||||
0.938338 | + | 0.345718i | \(0.112365\pi\) | |||||||
\(648\) | 2.20447 | 0.0865996 | ||||||||
\(649\) | −8.29482 | −0.325600 | ||||||||
\(650\) | 8.06465 | 0.316322 | ||||||||
\(651\) | 13.3112 | 0.521708 | ||||||||
\(652\) | 9.41961 | 0.368901 | ||||||||
\(653\) | 45.2808 | 1.77198 | 0.885988 | − | 0.463708i | \(-0.153481\pi\) | ||||
0.885988 | + | 0.463708i | \(0.153481\pi\) | |||||||
\(654\) | −10.1953 | −0.398669 | ||||||||
\(655\) | 4.72069 | 0.184453 | ||||||||
\(656\) | −1.25958 | −0.0491785 | ||||||||
\(657\) | 2.83517 | 0.110610 | ||||||||
\(658\) | −34.1200 | −1.33014 | ||||||||
\(659\) | −1.61714 | −0.0629950 | −0.0314975 | − | 0.999504i | \(-0.510028\pi\) | ||||
−0.0314975 | + | 0.999504i | \(0.510028\pi\) | |||||||
\(660\) | −0.994662 | −0.0387172 | ||||||||
\(661\) | −50.1186 | −1.94939 | −0.974695 | − | 0.223540i | \(-0.928239\pi\) | ||||
−0.974695 | + | 0.223540i | \(0.928239\pi\) | |||||||
\(662\) | −8.70661 | −0.338392 | ||||||||
\(663\) | −1.05243 | −0.0408728 | ||||||||
\(664\) | 4.69310 | 0.182128 | ||||||||
\(665\) | 14.9312 | 0.579008 | ||||||||
\(666\) | 8.47132 | 0.328257 | ||||||||
\(667\) | 11.0420 | 0.427550 | ||||||||
\(668\) | −0.162381 | −0.00628272 | ||||||||
\(669\) | 12.3845 | 0.478813 | ||||||||
\(670\) | −14.1430 | −0.546392 | ||||||||
\(671\) | 30.0757 | 1.16106 | ||||||||
\(672\) | −15.9520 | −0.615362 | ||||||||
\(673\) | 33.3422 | 1.28525 | 0.642623 | − | 0.766182i | \(-0.277846\pi\) | ||||
0.642623 | + | 0.766182i | \(0.277846\pi\) | |||||||
\(674\) | −46.4752 | −1.79016 | ||||||||
\(675\) | 4.71230 | 0.181377 | ||||||||
\(676\) | −7.66305 | −0.294733 | ||||||||
\(677\) | −33.5004 | −1.28753 | −0.643763 | − | 0.765225i | \(-0.722628\pi\) | ||||
−0.643763 | + | 0.765225i | \(0.722628\pi\) | |||||||
\(678\) | −6.21971 | −0.238867 | ||||||||
\(679\) | 54.0320 | 2.07356 | ||||||||
\(680\) | 1.18242 | 0.0453437 | ||||||||
\(681\) | 11.2981 | 0.432942 | ||||||||
\(682\) | 13.7311 | 0.525793 | ||||||||
\(683\) | −29.2586 | −1.11955 | −0.559775 | − | 0.828644i | \(-0.689113\pi\) | ||||
−0.559775 | + | 0.828644i | \(0.689113\pi\) | |||||||
\(684\) | 3.95378 | 0.151177 | ||||||||
\(685\) | −8.19966 | −0.313293 | ||||||||
\(686\) | −48.5610 | −1.85407 | ||||||||
\(687\) | −7.65246 | −0.291960 | ||||||||
\(688\) | −2.89745 | −0.110464 | ||||||||
\(689\) | −5.03114 | −0.191671 | ||||||||
\(690\) | 2.32633 | 0.0885620 | ||||||||
\(691\) | 25.4297 | 0.967392 | 0.483696 | − | 0.875236i | \(-0.339294\pi\) | ||||
0.483696 | + | 0.875236i | \(0.339294\pi\) | |||||||
\(692\) | 10.2197 | 0.388494 | ||||||||
\(693\) | 13.0564 | 0.495971 | ||||||||
\(694\) | 51.9889 | 1.97347 | ||||||||
\(695\) | 7.37170 | 0.279625 | ||||||||
\(696\) | −9.12661 | −0.345943 | ||||||||
\(697\) | 0.258454 | 0.00978965 | ||||||||
\(698\) | 2.55507 | 0.0967109 | ||||||||
\(699\) | 3.81049 | 0.144126 | ||||||||
\(700\) | −13.7757 | −0.520671 | ||||||||
\(701\) | −28.3858 | −1.07212 | −0.536058 | − | 0.844181i | \(-0.680087\pi\) | ||||
−0.536058 | + | 0.844181i | \(0.680087\pi\) | |||||||
\(702\) | 1.71140 | 0.0645927 | ||||||||
\(703\) | −31.9647 | −1.20557 | ||||||||
\(704\) | 11.5958 | 0.437033 | ||||||||
\(705\) | −2.48067 | −0.0934273 | ||||||||
\(706\) | 16.5495 | 0.622850 | ||||||||
\(707\) | −62.7967 | −2.36171 | ||||||||
\(708\) | 1.85722 | 0.0697986 | ||||||||
\(709\) | −9.70194 | −0.364364 | −0.182182 | − | 0.983265i | \(-0.558316\pi\) | ||||
−0.182182 | + | 0.983265i | \(0.558316\pi\) | |||||||
\(710\) | −8.62508 | −0.323693 | ||||||||
\(711\) | −4.89662 | −0.183638 | ||||||||
\(712\) | −22.6400 | −0.848471 | ||||||||
\(713\) | −7.82553 | −0.293068 | ||||||||
\(714\) | 7.37748 | 0.276095 | ||||||||
\(715\) | 1.62456 | 0.0607550 | ||||||||
\(716\) | 13.0256 | 0.486788 | ||||||||
\(717\) | 12.0878 | 0.451428 | ||||||||
\(718\) | −38.1625 | −1.42421 | ||||||||
\(719\) | 9.74472 | 0.363417 | 0.181708 | − | 0.983352i | \(-0.441837\pi\) | ||||
0.181708 | + | 0.983352i | \(0.441837\pi\) | |||||||
\(720\) | −2.61403 | −0.0974192 | ||||||||
\(721\) | 69.1876 | 2.57668 | ||||||||
\(722\) | −30.3271 | −1.12866 | ||||||||
\(723\) | 6.32255 | 0.235138 | ||||||||
\(724\) | 0.622257 | 0.0231260 | ||||||||
\(725\) | −19.5092 | −0.724553 | ||||||||
\(726\) | −4.41939 | −0.164019 | ||||||||
\(727\) | 15.3997 | 0.571144 | 0.285572 | − | 0.958357i | \(-0.407816\pi\) | ||||
0.285572 | + | 0.958357i | \(0.407816\pi\) | |||||||
\(728\) | 10.5255 | 0.390101 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.47290 | −0.0915263 | ||||||||
\(731\) | 0.594529 | 0.0219895 | ||||||||
\(732\) | −6.73398 | −0.248895 | ||||||||
\(733\) | 27.3353 | 1.00965 | 0.504827 | − | 0.863221i | \(-0.331556\pi\) | ||||
0.504827 | + | 0.863221i | \(0.331556\pi\) | |||||||
\(734\) | 40.2640 | 1.48617 | ||||||||
\(735\) | −7.28521 | −0.268719 | ||||||||
\(736\) | 9.37802 | 0.345678 | ||||||||
\(737\) | 46.6648 | 1.71892 | ||||||||
\(738\) | −0.420286 | −0.0154709 | ||||||||
\(739\) | −45.5885 | −1.67700 | −0.838499 | − | 0.544903i | \(-0.816567\pi\) | ||||
−0.838499 | + | 0.544903i | \(0.816567\pi\) | |||||||
\(740\) | −1.80049 | −0.0661872 | ||||||||
\(741\) | −6.45761 | −0.237226 | ||||||||
\(742\) | 35.2682 | 1.29473 | ||||||||
\(743\) | 40.5650 | 1.48819 | 0.744093 | − | 0.668076i | \(-0.232882\pi\) | ||||
0.744093 | + | 0.668076i | \(0.232882\pi\) | |||||||
\(744\) | 6.46805 | 0.237130 | ||||||||
\(745\) | 1.60252 | 0.0587117 | ||||||||
\(746\) | −3.92019 | −0.143528 | ||||||||
\(747\) | 2.12890 | 0.0778926 | ||||||||
\(748\) | 1.85442 | 0.0678043 | ||||||||
\(749\) | −63.3887 | −2.31617 | ||||||||
\(750\) | −8.47131 | −0.309329 | ||||||||
\(751\) | −20.1819 | −0.736450 | −0.368225 | − | 0.929737i | \(-0.620034\pi\) | ||||
−0.368225 | + | 0.929737i | \(0.620034\pi\) | |||||||
\(752\) | −22.5395 | −0.821931 | ||||||||
\(753\) | −0.350954 | −0.0127895 | ||||||||
\(754\) | −7.08531 | −0.258032 | ||||||||
\(755\) | 12.3379 | 0.449022 | ||||||||
\(756\) | −2.92334 | −0.106321 | ||||||||
\(757\) | 14.4041 | 0.523526 | 0.261763 | − | 0.965132i | \(-0.415696\pi\) | ||||
0.261763 | + | 0.965132i | \(0.415696\pi\) | |||||||
\(758\) | −10.3910 | −0.377419 | ||||||||
\(759\) | −7.67572 | −0.278611 | ||||||||
\(760\) | 7.25523 | 0.263175 | ||||||||
\(761\) | 0.929157 | 0.0336819 | 0.0168410 | − | 0.999858i | \(-0.494639\pi\) | ||||
0.0168410 | + | 0.999858i | \(0.494639\pi\) | |||||||
\(762\) | 18.7456 | 0.679082 | ||||||||
\(763\) | −28.4438 | −1.02974 | ||||||||
\(764\) | −11.3552 | −0.410815 | ||||||||
\(765\) | 0.536374 | 0.0193926 | ||||||||
\(766\) | 23.8407 | 0.861398 | ||||||||
\(767\) | −3.03335 | −0.109528 | ||||||||
\(768\) | −14.0319 | −0.506333 | ||||||||
\(769\) | 14.8258 | 0.534631 | 0.267316 | − | 0.963609i | \(-0.413863\pi\) | ||||
0.267316 | + | 0.963609i | \(0.413863\pi\) | |||||||
\(770\) | −11.3881 | −0.410399 | ||||||||
\(771\) | 20.1141 | 0.724393 | ||||||||
\(772\) | −9.24945 | −0.332895 | ||||||||
\(773\) | −10.7624 | −0.387097 | −0.193549 | − | 0.981091i | \(-0.562000\pi\) | ||||
−0.193549 | + | 0.981091i | \(0.562000\pi\) | |||||||
\(774\) | −0.966794 | −0.0347507 | ||||||||
\(775\) | 13.8262 | 0.496653 | ||||||||
\(776\) | 26.2547 | 0.942489 | ||||||||
\(777\) | 23.6340 | 0.847865 | ||||||||
\(778\) | −33.7236 | −1.20905 | ||||||||
\(779\) | 1.58586 | 0.0568192 | ||||||||
\(780\) | −0.363740 | −0.0130240 | ||||||||
\(781\) | 28.4584 | 1.01832 | ||||||||
\(782\) | −4.33715 | −0.155096 | ||||||||
\(783\) | −4.14006 | −0.147954 | ||||||||
\(784\) | −66.1938 | −2.36407 | ||||||||
\(785\) | −0.536374 | −0.0191440 | ||||||||
\(786\) | 14.3119 | 0.510490 | ||||||||
\(787\) | 21.4583 | 0.764904 | 0.382452 | − | 0.923975i | \(-0.375080\pi\) | ||||
0.382452 | + | 0.923975i | \(0.375080\pi\) | |||||||
\(788\) | 4.06162 | 0.144689 | ||||||||
\(789\) | 15.3035 | 0.544818 | ||||||||
\(790\) | 4.27095 | 0.151954 | ||||||||
\(791\) | −17.3523 | −0.616977 | ||||||||
\(792\) | 6.34423 | 0.225432 | ||||||||
\(793\) | 10.9984 | 0.390566 | ||||||||
\(794\) | 50.7044 | 1.79943 | ||||||||
\(795\) | 2.56414 | 0.0909408 | ||||||||
\(796\) | −14.7727 | −0.523606 | ||||||||
\(797\) | 1.32287 | 0.0468583 | 0.0234292 | − | 0.999725i | \(-0.492542\pi\) | ||||
0.0234292 | + | 0.999725i | \(0.492542\pi\) | |||||||
\(798\) | 45.2677 | 1.60246 | ||||||||
\(799\) | 4.62488 | 0.163617 | ||||||||
\(800\) | −16.5692 | −0.585809 | ||||||||
\(801\) | −10.2701 | −0.362875 | ||||||||
\(802\) | 63.9527 | 2.25825 | ||||||||
\(803\) | 8.15933 | 0.287936 | ||||||||
\(804\) | −10.4483 | −0.368483 | ||||||||
\(805\) | 6.49020 | 0.228750 | ||||||||
\(806\) | 5.02138 | 0.176870 | ||||||||
\(807\) | −20.3913 | −0.717809 | ||||||||
\(808\) | −30.5136 | −1.07346 | ||||||||
\(809\) | 32.0313 | 1.12616 | 0.563080 | − | 0.826402i | \(-0.309616\pi\) | ||||
0.563080 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(810\) | −0.872225 | −0.0306469 | ||||||||
\(811\) | 45.0726 | 1.58271 | 0.791357 | − | 0.611354i | \(-0.209375\pi\) | ||||
0.791357 | + | 0.611354i | \(0.209375\pi\) | |||||||
\(812\) | 12.1028 | 0.424725 | ||||||||
\(813\) | −25.8269 | −0.905788 | ||||||||
\(814\) | 24.3796 | 0.854504 | ||||||||
\(815\) | 7.84095 | 0.274656 | ||||||||
\(816\) | 4.87352 | 0.170607 | ||||||||
\(817\) | 3.64799 | 0.127627 | ||||||||
\(818\) | −16.5213 | −0.577654 | ||||||||
\(819\) | 4.77462 | 0.166839 | ||||||||
\(820\) | 0.0893272 | 0.00311944 | ||||||||
\(821\) | −3.23973 | −0.113067 | −0.0565337 | − | 0.998401i | \(-0.518005\pi\) | ||||
−0.0565337 | + | 0.998401i | \(0.518005\pi\) | |||||||
\(822\) | −24.8593 | −0.867067 | ||||||||
\(823\) | −29.2894 | −1.02097 | −0.510483 | − | 0.859888i | \(-0.670533\pi\) | ||||
−0.510483 | + | 0.859888i | \(0.670533\pi\) | |||||||
\(824\) | 33.6190 | 1.17117 | ||||||||
\(825\) | 13.5615 | 0.472152 | ||||||||
\(826\) | 21.2637 | 0.739860 | ||||||||
\(827\) | 35.2182 | 1.22466 | 0.612328 | − | 0.790604i | \(-0.290233\pi\) | ||||
0.612328 | + | 0.790604i | \(0.290233\pi\) | |||||||
\(828\) | 1.71860 | 0.0597256 | ||||||||
\(829\) | −0.0569368 | −0.00197750 | −0.000988748 | − | 1.00000i | \(-0.500315\pi\) | ||||
−0.000988748 | 1.00000i | \(0.500315\pi\) | ||||||||
\(830\) | −1.85688 | −0.0644534 | ||||||||
\(831\) | 20.2293 | 0.701748 | ||||||||
\(832\) | 4.24049 | 0.147013 | ||||||||
\(833\) | 13.5823 | 0.470600 | ||||||||
\(834\) | 22.3491 | 0.773888 | ||||||||
\(835\) | −0.135167 | −0.00467766 | ||||||||
\(836\) | 11.3786 | 0.393537 | ||||||||
\(837\) | 2.93407 | 0.101416 | ||||||||
\(838\) | −4.94420 | −0.170795 | ||||||||
\(839\) | −43.2435 | −1.49293 | −0.746466 | − | 0.665423i | \(-0.768251\pi\) | ||||
−0.746466 | + | 0.665423i | \(0.768251\pi\) | |||||||
\(840\) | −5.36436 | −0.185088 | ||||||||
\(841\) | −11.8599 | −0.408963 | ||||||||
\(842\) | 45.1343 | 1.55543 | ||||||||
\(843\) | −5.07183 | −0.174683 | ||||||||
\(844\) | −18.1477 | −0.624669 | ||||||||
\(845\) | −6.37877 | −0.219436 | ||||||||
\(846\) | −7.52076 | −0.258569 | ||||||||
\(847\) | −12.3296 | −0.423650 | ||||||||
\(848\) | 23.2980 | 0.800055 | ||||||||
\(849\) | −11.7889 | −0.404594 | ||||||||
\(850\) | 7.66291 | 0.262836 | ||||||||
\(851\) | −13.8942 | −0.476287 | ||||||||
\(852\) | −6.37187 | −0.218297 | ||||||||
\(853\) | 32.4019 | 1.10942 | 0.554711 | − | 0.832043i | \(-0.312829\pi\) | ||||
0.554711 | + | 0.832043i | \(0.312829\pi\) | |||||||
\(854\) | −77.0988 | −2.63827 | ||||||||
\(855\) | 3.29115 | 0.112555 | ||||||||
\(856\) | −30.8012 | −1.05276 | ||||||||
\(857\) | 38.6500 | 1.32026 | 0.660130 | − | 0.751152i | \(-0.270501\pi\) | ||||
0.660130 | + | 0.751152i | \(0.270501\pi\) | |||||||
\(858\) | 4.92524 | 0.168145 | ||||||||
\(859\) | −52.1116 | −1.77802 | −0.889012 | − | 0.457883i | \(-0.848608\pi\) | ||||
−0.889012 | + | 0.457883i | \(0.848608\pi\) | |||||||
\(860\) | 0.205482 | 0.00700687 | ||||||||
\(861\) | −1.17255 | −0.0399604 | ||||||||
\(862\) | 44.8717 | 1.52833 | ||||||||
\(863\) | −29.6109 | −1.00797 | −0.503983 | − | 0.863714i | \(-0.668133\pi\) | ||||
−0.503983 | + | 0.863714i | \(0.668133\pi\) | |||||||
\(864\) | −3.51615 | −0.119622 | ||||||||
\(865\) | 8.50693 | 0.289244 | ||||||||
\(866\) | 21.7282 | 0.738356 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −8.57729 | −0.291132 | ||||||||
\(869\) | −14.0920 | −0.478037 | ||||||||
\(870\) | 3.61106 | 0.122426 | ||||||||
\(871\) | 17.0650 | 0.578224 | ||||||||
\(872\) | −13.8212 | −0.468043 | ||||||||
\(873\) | 11.9098 | 0.403085 | ||||||||
\(874\) | −26.6124 | −0.900179 | ||||||||
\(875\) | −23.6340 | −0.798975 | ||||||||
\(876\) | −1.82688 | −0.0617247 | ||||||||
\(877\) | −15.6832 | −0.529583 | −0.264792 | − | 0.964306i | \(-0.585303\pi\) | ||||
−0.264792 | + | 0.964306i | \(0.585303\pi\) | |||||||
\(878\) | 7.57088 | 0.255505 | ||||||||
\(879\) | 13.3955 | 0.451819 | ||||||||
\(880\) | −7.52292 | −0.253598 | ||||||||
\(881\) | −49.5529 | −1.66948 | −0.834740 | − | 0.550644i | \(-0.814382\pi\) | ||||
−0.834740 | + | 0.550644i | \(0.814382\pi\) | |||||||
\(882\) | −22.0869 | −0.743705 | ||||||||
\(883\) | 13.7529 | 0.462821 | 0.231410 | − | 0.972856i | \(-0.425666\pi\) | ||||
0.231410 | + | 0.972856i | \(0.425666\pi\) | |||||||
\(884\) | 0.678147 | 0.0228086 | ||||||||
\(885\) | 1.54596 | 0.0519670 | ||||||||
\(886\) | 26.6740 | 0.896130 | ||||||||
\(887\) | 20.0163 | 0.672082 | 0.336041 | − | 0.941847i | \(-0.390912\pi\) | ||||
0.336041 | + | 0.941847i | \(0.390912\pi\) | |||||||
\(888\) | 11.4840 | 0.385378 | ||||||||
\(889\) | 52.2982 | 1.75402 | ||||||||
\(890\) | 8.95782 | 0.300267 | ||||||||
\(891\) | 2.87790 | 0.0964132 | ||||||||
\(892\) | −7.98015 | −0.267195 | ||||||||
\(893\) | 28.3780 | 0.949632 | ||||||||
\(894\) | 4.85843 | 0.162490 | ||||||||
\(895\) | 10.8426 | 0.362426 | ||||||||
\(896\) | −61.6297 | −2.05891 | ||||||||
\(897\) | −2.80695 | −0.0937214 | ||||||||
\(898\) | 4.85792 | 0.162111 | ||||||||
\(899\) | −12.1472 | −0.405132 | ||||||||
\(900\) | −3.03645 | −0.101215 | ||||||||
\(901\) | −4.78052 | −0.159262 | ||||||||
\(902\) | −1.20954 | −0.0402733 | ||||||||
\(903\) | −2.69725 | −0.0897587 | ||||||||
\(904\) | −8.43166 | −0.280433 | ||||||||
\(905\) | 0.517971 | 0.0172179 | ||||||||
\(906\) | 37.4054 | 1.24271 | ||||||||
\(907\) | −45.4528 | −1.50924 | −0.754618 | − | 0.656164i | \(-0.772178\pi\) | ||||
−0.754618 | + | 0.656164i | \(0.772178\pi\) | |||||||
\(908\) | −7.28007 | −0.241598 | ||||||||
\(909\) | −13.8417 | −0.459101 | ||||||||
\(910\) | −4.16454 | −0.138053 | ||||||||
\(911\) | −35.1316 | −1.16396 | −0.581980 | − | 0.813203i | \(-0.697722\pi\) | ||||
−0.581980 | + | 0.813203i | \(0.697722\pi\) | |||||||
\(912\) | 29.9036 | 0.990207 | ||||||||
\(913\) | 6.12677 | 0.202767 | ||||||||
\(914\) | −61.5424 | −2.03564 | ||||||||
\(915\) | −5.60541 | −0.185309 | ||||||||
\(916\) | 4.93098 | 0.162924 | ||||||||
\(917\) | 39.9287 | 1.31856 | ||||||||
\(918\) | 1.62615 | 0.0536710 | ||||||||
\(919\) | −3.92819 | −0.129579 | −0.0647896 | − | 0.997899i | \(-0.520638\pi\) | ||||
−0.0647896 | + | 0.997899i | \(0.520638\pi\) | |||||||
\(920\) | 3.15366 | 0.103973 | ||||||||
\(921\) | 5.92232 | 0.195147 | ||||||||
\(922\) | 9.13219 | 0.300753 | ||||||||
\(923\) | 10.4070 | 0.342551 | ||||||||
\(924\) | −8.41308 | −0.276770 | ||||||||
\(925\) | 24.5484 | 0.807147 | ||||||||
\(926\) | −26.4898 | −0.870510 | ||||||||
\(927\) | 15.2504 | 0.500889 | ||||||||
\(928\) | 14.5571 | 0.477859 | ||||||||
\(929\) | 4.22701 | 0.138684 | 0.0693419 | − | 0.997593i | \(-0.477910\pi\) | ||||
0.0693419 | + | 0.997593i | \(0.477910\pi\) | |||||||
\(930\) | −2.55917 | −0.0839184 | ||||||||
\(931\) | 83.3402 | 2.73137 | ||||||||
\(932\) | −2.45535 | −0.0804276 | ||||||||
\(933\) | −13.1833 | −0.431600 | ||||||||
\(934\) | −40.6553 | −1.33028 | ||||||||
\(935\) | 1.54363 | 0.0504821 | ||||||||
\(936\) | 2.32004 | 0.0758328 | ||||||||
\(937\) | 50.7125 | 1.65671 | 0.828353 | − | 0.560206i | \(-0.189278\pi\) | ||||
0.828353 | + | 0.560206i | \(0.189278\pi\) | |||||||
\(938\) | −119.625 | −3.90589 | ||||||||
\(939\) | −15.1808 | −0.495407 | ||||||||
\(940\) | 1.59846 | 0.0521359 | ||||||||
\(941\) | 30.3991 | 0.990984 | 0.495492 | − | 0.868613i | \(-0.334988\pi\) | ||||
0.495492 | + | 0.868613i | \(0.334988\pi\) | |||||||
\(942\) | −1.62615 | −0.0529828 | ||||||||
\(943\) | 0.689330 | 0.0224477 | ||||||||
\(944\) | 14.0467 | 0.457181 | ||||||||
\(945\) | −2.43341 | −0.0791588 | ||||||||
\(946\) | −2.78234 | −0.0904615 | ||||||||
\(947\) | 16.9509 | 0.550830 | 0.275415 | − | 0.961325i | \(-0.411185\pi\) | ||||
0.275415 | + | 0.961325i | \(0.411185\pi\) | |||||||
\(948\) | 3.15521 | 0.102477 | ||||||||
\(949\) | 2.98380 | 0.0968584 | ||||||||
\(950\) | 47.0191 | 1.52550 | ||||||||
\(951\) | 18.2857 | 0.592953 | ||||||||
\(952\) | 10.0012 | 0.324140 | ||||||||
\(953\) | −4.80852 | −0.155763 | −0.0778815 | − | 0.996963i | \(-0.524816\pi\) | ||||
−0.0778815 | + | 0.996963i | \(0.524816\pi\) | |||||||
\(954\) | 7.77384 | 0.251687 | ||||||||
\(955\) | −9.45211 | −0.305863 | ||||||||
\(956\) | −7.78898 | −0.251914 | ||||||||
\(957\) | −11.9147 | −0.385146 | ||||||||
\(958\) | −29.7265 | −0.960419 | ||||||||
\(959\) | −69.3546 | −2.23958 | ||||||||
\(960\) | −2.16119 | −0.0697520 | ||||||||
\(961\) | −22.3912 | −0.722298 | ||||||||
\(962\) | 8.91543 | 0.287445 | ||||||||
\(963\) | −13.9722 | −0.450248 | ||||||||
\(964\) | −4.07404 | −0.131216 | ||||||||
\(965\) | −7.69930 | −0.247849 | ||||||||
\(966\) | 19.6767 | 0.633086 | ||||||||
\(967\) | −8.11932 | −0.261100 | −0.130550 | − | 0.991442i | \(-0.541674\pi\) | ||||
−0.130550 | + | 0.991442i | \(0.541674\pi\) | |||||||
\(968\) | −5.99107 | −0.192560 | ||||||||
\(969\) | −6.13593 | −0.197114 | ||||||||
\(970\) | −10.3880 | −0.333539 | ||||||||
\(971\) | 7.69890 | 0.247069 | 0.123535 | − | 0.992340i | \(-0.460577\pi\) | ||||
0.123535 | + | 0.992340i | \(0.460577\pi\) | |||||||
\(972\) | −0.644366 | −0.0206680 | ||||||||
\(973\) | 62.3516 | 1.99890 | ||||||||
\(974\) | −19.3645 | −0.620478 | ||||||||
\(975\) | 4.95935 | 0.158826 | ||||||||
\(976\) | −50.9311 | −1.63026 | ||||||||
\(977\) | −47.4683 | −1.51865 | −0.759323 | − | 0.650713i | \(-0.774470\pi\) | ||||
−0.759323 | + | 0.650713i | \(0.774470\pi\) | |||||||
\(978\) | 23.7718 | 0.760137 | ||||||||
\(979\) | −29.5563 | −0.944622 | ||||||||
\(980\) | 4.69434 | 0.149955 | ||||||||
\(981\) | −6.26962 | −0.200173 | ||||||||
\(982\) | −17.8029 | −0.568112 | ||||||||
\(983\) | −17.1451 | −0.546845 | −0.273423 | − | 0.961894i | \(-0.588156\pi\) | ||||
−0.273423 | + | 0.961894i | \(0.588156\pi\) | |||||||
\(984\) | −0.569754 | −0.0181631 | ||||||||
\(985\) | 3.38092 | 0.107725 | ||||||||
\(986\) | −6.73235 | −0.214402 | ||||||||
\(987\) | −20.9821 | −0.667866 | ||||||||
\(988\) | 4.16106 | 0.132381 | ||||||||
\(989\) | 1.58568 | 0.0504218 | ||||||||
\(990\) | −2.51017 | −0.0797786 | ||||||||
\(991\) | 54.3776 | 1.72736 | 0.863681 | − | 0.504039i | \(-0.168153\pi\) | ||||
0.863681 | + | 0.504039i | \(0.168153\pi\) | |||||||
\(992\) | −10.3166 | −0.327553 | ||||||||
\(993\) | −5.35412 | −0.169908 | ||||||||
\(994\) | −72.9529 | −2.31393 | ||||||||
\(995\) | −12.2969 | −0.389839 | ||||||||
\(996\) | −1.37179 | −0.0434669 | ||||||||
\(997\) | −30.7869 | −0.975031 | −0.487516 | − | 0.873114i | \(-0.662097\pi\) | ||||
−0.487516 | + | 0.873114i | \(0.662097\pi\) | |||||||
\(998\) | −3.22645 | −0.102131 | ||||||||
\(999\) | 5.20943 | 0.164819 |
(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 | 8007.2.a.j.1.16 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.j.1.16 | ✓ | 64 | 1.1 | even | 1 | trivial |