Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75248 | −1.94630 | −0.973150 | − | 0.230170i | \(-0.926072\pi\) | ||||
−0.973150 | + | 0.230170i | \(0.926072\pi\) | |||||||
\(3\) | 1.04725 | 0.604633 | 0.302316 | − | 0.953208i | \(-0.402240\pi\) | ||||
0.302316 | + | 0.953208i | \(0.402240\pi\) | |||||||
\(4\) | 5.57617 | 2.78809 | ||||||||
\(5\) | −2.70262 | −1.20865 | −0.604324 | − | 0.796739i | \(-0.706557\pi\) | ||||
−0.604324 | + | 0.796739i | \(0.706557\pi\) | |||||||
\(6\) | −2.88255 | −1.17680 | ||||||||
\(7\) | 3.33593 | 1.26086 | 0.630432 | − | 0.776245i | \(-0.282878\pi\) | ||||
0.630432 | + | 0.776245i | \(0.282878\pi\) | |||||||
\(8\) | −9.84336 | −3.48015 | ||||||||
\(9\) | −1.90326 | −0.634420 | ||||||||
\(10\) | 7.43892 | 2.35239 | ||||||||
\(11\) | −0.447139 | −0.134818 | −0.0674088 | − | 0.997725i | \(-0.521473\pi\) | ||||
−0.0674088 | + | 0.997725i | \(0.521473\pi\) | |||||||
\(12\) | 5.83967 | 1.68577 | ||||||||
\(13\) | 4.89893 | 1.35872 | 0.679359 | − | 0.733806i | \(-0.262258\pi\) | ||||
0.679359 | + | 0.733806i | \(0.262258\pi\) | |||||||
\(14\) | −9.18210 | −2.45402 | ||||||||
\(15\) | −2.83033 | −0.730788 | ||||||||
\(16\) | 15.9414 | 3.98534 | ||||||||
\(17\) | 3.35196 | 0.812971 | 0.406485 | − | 0.913657i | \(-0.366754\pi\) | ||||
0.406485 | + | 0.913657i | \(0.366754\pi\) | |||||||
\(18\) | 5.23869 | 1.23477 | ||||||||
\(19\) | 1.23881 | 0.284203 | 0.142102 | − | 0.989852i | \(-0.454614\pi\) | ||||
0.142102 | + | 0.989852i | \(0.454614\pi\) | |||||||
\(20\) | −15.0703 | −3.36982 | ||||||||
\(21\) | 3.49357 | 0.762359 | ||||||||
\(22\) | 1.23074 | 0.262396 | ||||||||
\(23\) | 0.723127 | 0.150782 | 0.0753912 | − | 0.997154i | \(-0.475979\pi\) | ||||
0.0753912 | + | 0.997154i | \(0.475979\pi\) | |||||||
\(24\) | −10.3085 | −2.10421 | ||||||||
\(25\) | 2.30415 | 0.460830 | ||||||||
\(26\) | −13.4842 | −2.64447 | ||||||||
\(27\) | −5.13496 | −0.988223 | ||||||||
\(28\) | 18.6017 | 3.51540 | ||||||||
\(29\) | −9.97154 | −1.85167 | −0.925834 | − | 0.377931i | \(-0.876636\pi\) | ||||
−0.925834 | + | 0.377931i | \(0.876636\pi\) | |||||||
\(30\) | 7.79044 | 1.42233 | ||||||||
\(31\) | −7.53893 | −1.35403 | −0.677016 | − | 0.735968i | \(-0.736727\pi\) | ||||
−0.677016 | + | 0.735968i | \(0.736727\pi\) | |||||||
\(32\) | −24.1916 | −4.27652 | ||||||||
\(33\) | −0.468269 | −0.0815151 | ||||||||
\(34\) | −9.22623 | −1.58229 | ||||||||
\(35\) | −9.01575 | −1.52394 | ||||||||
\(36\) | −10.6129 | −1.76882 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −3.40981 | −0.553145 | ||||||||
\(39\) | 5.13042 | 0.821525 | ||||||||
\(40\) | 26.6029 | 4.20628 | ||||||||
\(41\) | −2.21063 | −0.345242 | −0.172621 | − | 0.984988i | \(-0.555224\pi\) | ||||
−0.172621 | + | 0.984988i | \(0.555224\pi\) | |||||||
\(42\) | −9.61599 | −1.48378 | ||||||||
\(43\) | −3.86519 | −0.589437 | −0.294718 | − | 0.955584i | \(-0.595226\pi\) | ||||
−0.294718 | + | 0.955584i | \(0.595226\pi\) | |||||||
\(44\) | −2.49333 | −0.375883 | ||||||||
\(45\) | 5.14378 | 0.766790 | ||||||||
\(46\) | −1.99040 | −0.293468 | ||||||||
\(47\) | 3.74690 | 0.546541 | 0.273270 | − | 0.961937i | \(-0.411895\pi\) | ||||
0.273270 | + | 0.961937i | \(0.411895\pi\) | |||||||
\(48\) | 16.6947 | 2.40967 | ||||||||
\(49\) | 4.12843 | 0.589776 | ||||||||
\(50\) | −6.34214 | −0.896915 | ||||||||
\(51\) | 3.51036 | 0.491549 | ||||||||
\(52\) | 27.3173 | 3.78822 | ||||||||
\(53\) | 2.44279 | 0.335544 | 0.167772 | − | 0.985826i | \(-0.446343\pi\) | ||||
0.167772 | + | 0.985826i | \(0.446343\pi\) | |||||||
\(54\) | 14.1339 | 1.92338 | ||||||||
\(55\) | 1.20845 | 0.162947 | ||||||||
\(56\) | −32.8368 | −4.38800 | ||||||||
\(57\) | 1.29735 | 0.171838 | ||||||||
\(58\) | 27.4465 | 3.60390 | ||||||||
\(59\) | 0.178316 | 0.0232147 | 0.0116074 | − | 0.999933i | \(-0.496305\pi\) | ||||
0.0116074 | + | 0.999933i | \(0.496305\pi\) | |||||||
\(60\) | −15.7824 | −2.03750 | ||||||||
\(61\) | −8.99074 | −1.15115 | −0.575573 | − | 0.817750i | \(-0.695221\pi\) | ||||
−0.575573 | + | 0.817750i | \(0.695221\pi\) | |||||||
\(62\) | 20.7508 | 2.63535 | ||||||||
\(63\) | −6.34914 | −0.799916 | ||||||||
\(64\) | 34.7044 | 4.33805 | ||||||||
\(65\) | −13.2399 | −1.64221 | ||||||||
\(66\) | 1.28890 | 0.158653 | ||||||||
\(67\) | −3.84687 | −0.469970 | −0.234985 | − | 0.971999i | \(-0.575504\pi\) | ||||
−0.234985 | + | 0.971999i | \(0.575504\pi\) | |||||||
\(68\) | 18.6911 | 2.26663 | ||||||||
\(69\) | 0.757298 | 0.0911680 | ||||||||
\(70\) | 24.8157 | 2.96605 | ||||||||
\(71\) | −3.69396 | −0.438392 | −0.219196 | − | 0.975681i | \(-0.570343\pi\) | ||||
−0.219196 | + | 0.975681i | \(0.570343\pi\) | |||||||
\(72\) | 18.7345 | 2.20788 | ||||||||
\(73\) | 10.8238 | 1.26683 | 0.633413 | − | 0.773814i | \(-0.281653\pi\) | ||||
0.633413 | + | 0.773814i | \(0.281653\pi\) | |||||||
\(74\) | 2.75248 | 0.319970 | ||||||||
\(75\) | 2.41303 | 0.278633 | ||||||||
\(76\) | 6.90783 | 0.792383 | ||||||||
\(77\) | −1.49163 | −0.169986 | ||||||||
\(78\) | −14.1214 | −1.59893 | ||||||||
\(79\) | −10.2525 | −1.15349 | −0.576747 | − | 0.816923i | \(-0.695678\pi\) | ||||
−0.576747 | + | 0.816923i | \(0.695678\pi\) | |||||||
\(80\) | −43.0834 | −4.81687 | ||||||||
\(81\) | 0.332168 | 0.0369076 | ||||||||
\(82\) | 6.08472 | 0.671945 | ||||||||
\(83\) | −9.10878 | −0.999819 | −0.499909 | − | 0.866078i | \(-0.666633\pi\) | ||||
−0.499909 | + | 0.866078i | \(0.666633\pi\) | |||||||
\(84\) | 19.4807 | 2.12552 | ||||||||
\(85\) | −9.05908 | −0.982596 | ||||||||
\(86\) | 10.6389 | 1.14722 | ||||||||
\(87\) | −10.4427 | −1.11958 | ||||||||
\(88\) | 4.40135 | 0.469186 | ||||||||
\(89\) | 14.8130 | 1.57017 | 0.785086 | − | 0.619387i | \(-0.212619\pi\) | ||||
0.785086 | + | 0.619387i | \(0.212619\pi\) | |||||||
\(90\) | −14.1582 | −1.49240 | ||||||||
\(91\) | 16.3425 | 1.71316 | ||||||||
\(92\) | 4.03228 | 0.420395 | ||||||||
\(93\) | −7.89518 | −0.818692 | ||||||||
\(94\) | −10.3133 | −1.06373 | ||||||||
\(95\) | −3.34804 | −0.343502 | ||||||||
\(96\) | −25.3348 | −2.58572 | ||||||||
\(97\) | −0.00498767 | −0.000506421 0 | −0.000253210 | − | 1.00000i | \(-0.500081\pi\) | ||||
−0.000253210 | 1.00000i | \(0.500081\pi\) | ||||||||
\(98\) | −11.3634 | −1.14788 | ||||||||
\(99\) | 0.851022 | 0.0855309 | ||||||||
\(100\) | 12.8484 | 1.28484 | ||||||||
\(101\) | 15.0443 | 1.49697 | 0.748483 | − | 0.663154i | \(-0.230783\pi\) | ||||
0.748483 | + | 0.663154i | \(0.230783\pi\) | |||||||
\(102\) | −9.66221 | −0.956701 | ||||||||
\(103\) | −2.86587 | −0.282382 | −0.141191 | − | 0.989982i | \(-0.545093\pi\) | ||||
−0.141191 | + | 0.989982i | \(0.545093\pi\) | |||||||
\(104\) | −48.2219 | −4.72855 | ||||||||
\(105\) | −9.44178 | −0.921424 | ||||||||
\(106\) | −6.72375 | −0.653069 | ||||||||
\(107\) | 18.1977 | 1.75924 | 0.879618 | − | 0.475681i | \(-0.157798\pi\) | ||||
0.879618 | + | 0.475681i | \(0.157798\pi\) | |||||||
\(108\) | −28.6334 | −2.75525 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | −3.32623 | −0.317144 | ||||||||
\(111\) | −1.04725 | −0.0994010 | ||||||||
\(112\) | 53.1793 | 5.02497 | ||||||||
\(113\) | −13.0088 | −1.22376 | −0.611881 | − | 0.790950i | \(-0.709587\pi\) | ||||
−0.611881 | + | 0.790950i | \(0.709587\pi\) | |||||||
\(114\) | −3.57094 | −0.334449 | ||||||||
\(115\) | −1.95434 | −0.182243 | ||||||||
\(116\) | −55.6030 | −5.16261 | ||||||||
\(117\) | −9.32393 | −0.861997 | ||||||||
\(118\) | −0.490811 | −0.0451828 | ||||||||
\(119\) | 11.1819 | 1.02504 | ||||||||
\(120\) | 27.8600 | 2.54325 | ||||||||
\(121\) | −10.8001 | −0.981824 | ||||||||
\(122\) | 24.7469 | 2.24048 | ||||||||
\(123\) | −2.31509 | −0.208745 | ||||||||
\(124\) | −42.0384 | −3.77516 | ||||||||
\(125\) | 7.28585 | 0.651666 | ||||||||
\(126\) | 17.4759 | 1.55688 | ||||||||
\(127\) | −4.46844 | −0.396510 | −0.198255 | − | 0.980151i | \(-0.563527\pi\) | ||||
−0.198255 | + | 0.980151i | \(0.563527\pi\) | |||||||
\(128\) | −47.1400 | −4.16663 | ||||||||
\(129\) | −4.04784 | −0.356393 | ||||||||
\(130\) | 36.4427 | 3.19624 | ||||||||
\(131\) | 9.17000 | 0.801186 | 0.400593 | − | 0.916256i | \(-0.368804\pi\) | ||||
0.400593 | + | 0.916256i | \(0.368804\pi\) | |||||||
\(132\) | −2.61115 | −0.227271 | ||||||||
\(133\) | 4.13259 | 0.358341 | ||||||||
\(134\) | 10.5884 | 0.914702 | ||||||||
\(135\) | 13.8778 | 1.19441 | ||||||||
\(136\) | −32.9946 | −2.82926 | ||||||||
\(137\) | 8.12235 | 0.693939 | 0.346969 | − | 0.937876i | \(-0.387211\pi\) | ||||
0.346969 | + | 0.937876i | \(0.387211\pi\) | |||||||
\(138\) | −2.08445 | −0.177440 | ||||||||
\(139\) | −18.6683 | −1.58343 | −0.791714 | − | 0.610892i | \(-0.790811\pi\) | ||||
−0.791714 | + | 0.610892i | \(0.790811\pi\) | |||||||
\(140\) | −50.2734 | −4.24888 | ||||||||
\(141\) | 3.92395 | 0.330456 | ||||||||
\(142\) | 10.1676 | 0.853243 | ||||||||
\(143\) | −2.19050 | −0.183179 | ||||||||
\(144\) | −30.3405 | −2.52838 | ||||||||
\(145\) | 26.9493 | 2.23801 | ||||||||
\(146\) | −29.7923 | −2.46563 | ||||||||
\(147\) | 4.32351 | 0.356597 | ||||||||
\(148\) | −5.57617 | −0.458359 | ||||||||
\(149\) | 0.899330 | 0.0736760 | 0.0368380 | − | 0.999321i | \(-0.488271\pi\) | ||||
0.0368380 | + | 0.999321i | \(0.488271\pi\) | |||||||
\(150\) | −6.64184 | −0.542304 | ||||||||
\(151\) | −20.2811 | −1.65045 | −0.825226 | − | 0.564803i | \(-0.808952\pi\) | ||||
−0.825226 | + | 0.564803i | \(0.808952\pi\) | |||||||
\(152\) | −12.1941 | −0.989070 | ||||||||
\(153\) | −6.37965 | −0.515764 | ||||||||
\(154\) | 4.10568 | 0.330845 | ||||||||
\(155\) | 20.3749 | 1.63655 | ||||||||
\(156\) | 28.6081 | 2.29048 | ||||||||
\(157\) | −6.52191 | −0.520505 | −0.260252 | − | 0.965541i | \(-0.583806\pi\) | ||||
−0.260252 | + | 0.965541i | \(0.583806\pi\) | |||||||
\(158\) | 28.2198 | 2.24504 | ||||||||
\(159\) | 2.55823 | 0.202881 | ||||||||
\(160\) | 65.3808 | 5.16880 | ||||||||
\(161\) | 2.41230 | 0.190116 | ||||||||
\(162\) | −0.914289 | −0.0718333 | ||||||||
\(163\) | −12.9035 | −1.01068 | −0.505340 | − | 0.862921i | \(-0.668633\pi\) | ||||
−0.505340 | + | 0.862921i | \(0.668633\pi\) | |||||||
\(164\) | −12.3268 | −0.962565 | ||||||||
\(165\) | 1.26555 | 0.0985231 | ||||||||
\(166\) | 25.0718 | 1.94595 | ||||||||
\(167\) | −21.0968 | −1.63252 | −0.816261 | − | 0.577683i | \(-0.803957\pi\) | ||||
−0.816261 | + | 0.577683i | \(0.803957\pi\) | |||||||
\(168\) | −34.3884 | −2.65313 | ||||||||
\(169\) | 10.9995 | 0.846115 | ||||||||
\(170\) | 24.9350 | 1.91243 | ||||||||
\(171\) | −2.35778 | −0.180304 | ||||||||
\(172\) | −21.5530 | −1.64340 | ||||||||
\(173\) | −7.50058 | −0.570259 | −0.285129 | − | 0.958489i | \(-0.592037\pi\) | ||||
−0.285129 | + | 0.958489i | \(0.592037\pi\) | |||||||
\(174\) | 28.7435 | 2.17904 | ||||||||
\(175\) | 7.68649 | 0.581044 | ||||||||
\(176\) | −7.12801 | −0.537294 | ||||||||
\(177\) | 0.186742 | 0.0140364 | ||||||||
\(178\) | −40.7725 | −3.05603 | ||||||||
\(179\) | −5.53584 | −0.413768 | −0.206884 | − | 0.978365i | \(-0.566332\pi\) | ||||
−0.206884 | + | 0.978365i | \(0.566332\pi\) | |||||||
\(180\) | 28.6826 | 2.13788 | ||||||||
\(181\) | 2.33748 | 0.173744 | 0.0868718 | − | 0.996219i | \(-0.472313\pi\) | ||||
0.0868718 | + | 0.996219i | \(0.472313\pi\) | |||||||
\(182\) | −44.9824 | −3.33432 | ||||||||
\(183\) | −9.41560 | −0.696021 | ||||||||
\(184\) | −7.11801 | −0.524746 | ||||||||
\(185\) | 2.70262 | 0.198701 | ||||||||
\(186\) | 21.7314 | 1.59342 | ||||||||
\(187\) | −1.49879 | −0.109603 | ||||||||
\(188\) | 20.8933 | 1.52380 | ||||||||
\(189\) | −17.1299 | −1.24601 | ||||||||
\(190\) | 9.21543 | 0.668557 | ||||||||
\(191\) | 5.22039 | 0.377734 | 0.188867 | − | 0.982003i | \(-0.439518\pi\) | ||||
0.188867 | + | 0.982003i | \(0.439518\pi\) | |||||||
\(192\) | 36.3443 | 2.62292 | ||||||||
\(193\) | −0.253889 | −0.0182753 | −0.00913766 | − | 0.999958i | \(-0.502909\pi\) | ||||
−0.00913766 | + | 0.999958i | \(0.502909\pi\) | |||||||
\(194\) | 0.0137285 | 0.000985647 0 | ||||||||
\(195\) | −13.8656 | −0.992935 | ||||||||
\(196\) | 23.0208 | 1.64435 | ||||||||
\(197\) | 16.4830 | 1.17437 | 0.587184 | − | 0.809454i | \(-0.300237\pi\) | ||||
0.587184 | + | 0.809454i | \(0.300237\pi\) | |||||||
\(198\) | −2.34242 | −0.166469 | ||||||||
\(199\) | 7.17168 | 0.508387 | 0.254193 | − | 0.967153i | \(-0.418190\pi\) | ||||
0.254193 | + | 0.967153i | \(0.418190\pi\) | |||||||
\(200\) | −22.6806 | −1.60376 | ||||||||
\(201\) | −4.02865 | −0.284159 | ||||||||
\(202\) | −41.4093 | −2.91354 | ||||||||
\(203\) | −33.2643 | −2.33470 | ||||||||
\(204\) | 19.5744 | 1.37048 | ||||||||
\(205\) | 5.97449 | 0.417276 | ||||||||
\(206\) | 7.88825 | 0.549601 | ||||||||
\(207\) | −1.37630 | −0.0956594 | ||||||||
\(208\) | 78.0956 | 5.41495 | ||||||||
\(209\) | −0.553922 | −0.0383156 | ||||||||
\(210\) | 25.9884 | 1.79337 | ||||||||
\(211\) | 14.5563 | 1.00209 | 0.501047 | − | 0.865420i | \(-0.332948\pi\) | ||||
0.501047 | + | 0.865420i | \(0.332948\pi\) | |||||||
\(212\) | 13.6214 | 0.935525 | ||||||||
\(213\) | −3.86851 | −0.265066 | ||||||||
\(214\) | −50.0888 | −3.42400 | ||||||||
\(215\) | 10.4461 | 0.712421 | ||||||||
\(216\) | 50.5453 | 3.43917 | ||||||||
\(217\) | −25.1493 | −1.70725 | ||||||||
\(218\) | 2.75248 | 0.186422 | ||||||||
\(219\) | 11.3352 | 0.765965 | ||||||||
\(220\) | 6.73851 | 0.454310 | ||||||||
\(221\) | 16.4210 | 1.10460 | ||||||||
\(222\) | 2.88255 | 0.193464 | ||||||||
\(223\) | 21.1098 | 1.41362 | 0.706810 | − | 0.707404i | \(-0.250134\pi\) | ||||
0.706810 | + | 0.707404i | \(0.250134\pi\) | |||||||
\(224\) | −80.7016 | −5.39210 | ||||||||
\(225\) | −4.38540 | −0.292360 | ||||||||
\(226\) | 35.8064 | 2.38181 | ||||||||
\(227\) | 13.3012 | 0.882834 | 0.441417 | − | 0.897302i | \(-0.354476\pi\) | ||||
0.441417 | + | 0.897302i | \(0.354476\pi\) | |||||||
\(228\) | 7.23426 | 0.479100 | ||||||||
\(229\) | 2.14342 | 0.141641 | 0.0708206 | − | 0.997489i | \(-0.477438\pi\) | ||||
0.0708206 | + | 0.997489i | \(0.477438\pi\) | |||||||
\(230\) | 5.37929 | 0.354700 | ||||||||
\(231\) | −1.56211 | −0.102779 | ||||||||
\(232\) | 98.1534 | 6.44409 | ||||||||
\(233\) | 4.39981 | 0.288241 | 0.144121 | − | 0.989560i | \(-0.453965\pi\) | ||||
0.144121 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(234\) | 25.6640 | 1.67771 | ||||||||
\(235\) | −10.1264 | −0.660576 | ||||||||
\(236\) | 0.994319 | 0.0647247 | ||||||||
\(237\) | −10.7369 | −0.697440 | ||||||||
\(238\) | −30.7781 | −1.99505 | ||||||||
\(239\) | −26.7078 | −1.72758 | −0.863791 | − | 0.503850i | \(-0.831916\pi\) | ||||
−0.863791 | + | 0.503850i | \(0.831916\pi\) | |||||||
\(240\) | −45.1193 | −2.91244 | ||||||||
\(241\) | −9.83072 | −0.633252 | −0.316626 | − | 0.948550i | \(-0.602550\pi\) | ||||
−0.316626 | + | 0.948550i | \(0.602550\pi\) | |||||||
\(242\) | 29.7270 | 1.91093 | ||||||||
\(243\) | 15.7527 | 1.01054 | ||||||||
\(244\) | −50.1339 | −3.20950 | ||||||||
\(245\) | −11.1576 | −0.712831 | ||||||||
\(246\) | 6.37225 | 0.406280 | ||||||||
\(247\) | 6.06885 | 0.386152 | ||||||||
\(248\) | 74.2084 | 4.71224 | ||||||||
\(249\) | −9.53921 | −0.604523 | ||||||||
\(250\) | −20.0542 | −1.26834 | ||||||||
\(251\) | −18.3964 | −1.16117 | −0.580585 | − | 0.814199i | \(-0.697176\pi\) | ||||
−0.580585 | + | 0.814199i | \(0.697176\pi\) | |||||||
\(252\) | −35.4039 | −2.23024 | ||||||||
\(253\) | −0.323339 | −0.0203281 | ||||||||
\(254\) | 12.2993 | 0.771727 | ||||||||
\(255\) | −9.48716 | −0.594109 | ||||||||
\(256\) | 60.3434 | 3.77146 | ||||||||
\(257\) | −24.9057 | −1.55358 | −0.776789 | − | 0.629761i | \(-0.783153\pi\) | ||||
−0.776789 | + | 0.629761i | \(0.783153\pi\) | |||||||
\(258\) | 11.1416 | 0.693647 | ||||||||
\(259\) | −3.33593 | −0.207285 | ||||||||
\(260\) | −73.8282 | −4.57863 | ||||||||
\(261\) | 18.9784 | 1.17473 | ||||||||
\(262\) | −25.2403 | −1.55935 | ||||||||
\(263\) | −24.2552 | −1.49564 | −0.747819 | − | 0.663903i | \(-0.768899\pi\) | ||||
−0.747819 | + | 0.663903i | \(0.768899\pi\) | |||||||
\(264\) | 4.60934 | 0.283685 | ||||||||
\(265\) | −6.60194 | −0.405554 | ||||||||
\(266\) | −11.3749 | −0.697440 | ||||||||
\(267\) | 15.5129 | 0.949377 | ||||||||
\(268\) | −21.4508 | −1.31032 | ||||||||
\(269\) | −3.54338 | −0.216044 | −0.108022 | − | 0.994149i | \(-0.534452\pi\) | ||||
−0.108022 | + | 0.994149i | \(0.534452\pi\) | |||||||
\(270\) | −38.1985 | −2.32469 | ||||||||
\(271\) | 15.2758 | 0.927937 | 0.463969 | − | 0.885852i | \(-0.346425\pi\) | ||||
0.463969 | + | 0.885852i | \(0.346425\pi\) | |||||||
\(272\) | 53.4349 | 3.23996 | ||||||||
\(273\) | 17.1147 | 1.03583 | ||||||||
\(274\) | −22.3566 | −1.35061 | ||||||||
\(275\) | −1.03028 | −0.0621280 | ||||||||
\(276\) | 4.22283 | 0.254184 | ||||||||
\(277\) | −21.9736 | −1.32027 | −0.660133 | − | 0.751149i | \(-0.729500\pi\) | ||||
−0.660133 | + | 0.751149i | \(0.729500\pi\) | |||||||
\(278\) | 51.3843 | 3.08183 | ||||||||
\(279\) | 14.3485 | 0.859024 | ||||||||
\(280\) | 88.7453 | 5.30355 | ||||||||
\(281\) | −23.8190 | −1.42092 | −0.710461 | − | 0.703736i | \(-0.751514\pi\) | ||||
−0.710461 | + | 0.703736i | \(0.751514\pi\) | |||||||
\(282\) | −10.8006 | −0.643168 | ||||||||
\(283\) | 1.30054 | 0.0773089 | 0.0386545 | − | 0.999253i | \(-0.487693\pi\) | ||||
0.0386545 | + | 0.999253i | \(0.487693\pi\) | |||||||
\(284\) | −20.5981 | −1.22227 | ||||||||
\(285\) | −3.50625 | −0.207692 | ||||||||
\(286\) | 6.02933 | 0.356522 | ||||||||
\(287\) | −7.37450 | −0.435303 | ||||||||
\(288\) | 46.0429 | 2.71310 | ||||||||
\(289\) | −5.76434 | −0.339079 | ||||||||
\(290\) | −74.1775 | −4.35585 | ||||||||
\(291\) | −0.00522335 | −0.000306198 0 | ||||||||
\(292\) | 60.3552 | 3.53202 | ||||||||
\(293\) | 2.98604 | 0.174446 | 0.0872232 | − | 0.996189i | \(-0.472201\pi\) | ||||
0.0872232 | + | 0.996189i | \(0.472201\pi\) | |||||||
\(294\) | −11.9004 | −0.694046 | ||||||||
\(295\) | −0.481919 | −0.0280584 | ||||||||
\(296\) | 9.84336 | 0.572134 | ||||||||
\(297\) | 2.29604 | 0.133230 | ||||||||
\(298\) | −2.47539 | −0.143396 | ||||||||
\(299\) | 3.54255 | 0.204871 | ||||||||
\(300\) | 13.4555 | 0.776853 | ||||||||
\(301\) | −12.8940 | −0.743199 | ||||||||
\(302\) | 55.8234 | 3.21227 | ||||||||
\(303\) | 15.7552 | 0.905114 | ||||||||
\(304\) | 19.7484 | 1.13265 | ||||||||
\(305\) | 24.2986 | 1.39133 | ||||||||
\(306\) | 17.5599 | 1.00383 | ||||||||
\(307\) | −0.413311 | −0.0235889 | −0.0117945 | − | 0.999930i | \(-0.503754\pi\) | ||||
−0.0117945 | + | 0.999930i | \(0.503754\pi\) | |||||||
\(308\) | −8.31756 | −0.473937 | ||||||||
\(309\) | −3.00129 | −0.170737 | ||||||||
\(310\) | −56.0815 | −3.18522 | ||||||||
\(311\) | 4.85348 | 0.275216 | 0.137608 | − | 0.990487i | \(-0.456059\pi\) | ||||
0.137608 | + | 0.990487i | \(0.456059\pi\) | |||||||
\(312\) | −50.5006 | −2.85903 | ||||||||
\(313\) | 3.56845 | 0.201701 | 0.100850 | − | 0.994902i | \(-0.467844\pi\) | ||||
0.100850 | + | 0.994902i | \(0.467844\pi\) | |||||||
\(314\) | 17.9514 | 1.01306 | ||||||||
\(315\) | 17.1593 | 0.966817 | ||||||||
\(316\) | −57.1696 | −3.21604 | ||||||||
\(317\) | −0.620200 | −0.0348339 | −0.0174170 | − | 0.999848i | \(-0.505544\pi\) | ||||
−0.0174170 | + | 0.999848i | \(0.505544\pi\) | |||||||
\(318\) | −7.04148 | −0.394867 | ||||||||
\(319\) | 4.45867 | 0.249637 | ||||||||
\(320\) | −93.7927 | −5.24317 | ||||||||
\(321\) | 19.0576 | 1.06369 | ||||||||
\(322\) | −6.63983 | −0.370023 | ||||||||
\(323\) | 4.15245 | 0.231049 | ||||||||
\(324\) | 1.85223 | 0.102902 | ||||||||
\(325\) | 11.2879 | 0.626139 | ||||||||
\(326\) | 35.5167 | 1.96709 | ||||||||
\(327\) | −1.04725 | −0.0579133 | ||||||||
\(328\) | 21.7600 | 1.20150 | ||||||||
\(329\) | 12.4994 | 0.689113 | ||||||||
\(330\) | −3.48341 | −0.191756 | ||||||||
\(331\) | 16.0189 | 0.880481 | 0.440240 | − | 0.897880i | \(-0.354893\pi\) | ||||
0.440240 | + | 0.897880i | \(0.354893\pi\) | |||||||
\(332\) | −50.7921 | −2.78758 | ||||||||
\(333\) | 1.90326 | 0.104298 | ||||||||
\(334\) | 58.0687 | 3.17738 | ||||||||
\(335\) | 10.3966 | 0.568028 | ||||||||
\(336\) | 55.6922 | 3.03826 | ||||||||
\(337\) | −8.77114 | −0.477794 | −0.238897 | − | 0.971045i | \(-0.576786\pi\) | ||||
−0.238897 | + | 0.971045i | \(0.576786\pi\) | |||||||
\(338\) | −30.2759 | −1.64679 | ||||||||
\(339\) | −13.6235 | −0.739926 | ||||||||
\(340\) | −50.5150 | −2.73956 | ||||||||
\(341\) | 3.37095 | 0.182547 | ||||||||
\(342\) | 6.48975 | 0.350926 | ||||||||
\(343\) | −9.57936 | −0.517237 | ||||||||
\(344\) | 38.0465 | 2.05133 | ||||||||
\(345\) | −2.04669 | −0.110190 | ||||||||
\(346\) | 20.6452 | 1.10989 | ||||||||
\(347\) | −1.92975 | −0.103594 | −0.0517971 | − | 0.998658i | \(-0.516495\pi\) | ||||
−0.0517971 | + | 0.998658i | \(0.516495\pi\) | |||||||
\(348\) | −58.2305 | −3.12148 | ||||||||
\(349\) | 26.2258 | 1.40384 | 0.701918 | − | 0.712258i | \(-0.252327\pi\) | ||||
0.701918 | + | 0.712258i | \(0.252327\pi\) | |||||||
\(350\) | −21.1569 | −1.13089 | ||||||||
\(351\) | −25.1558 | −1.34272 | ||||||||
\(352\) | 10.8170 | 0.576549 | ||||||||
\(353\) | 2.23569 | 0.118994 | 0.0594969 | − | 0.998228i | \(-0.481050\pi\) | ||||
0.0594969 | + | 0.998228i | \(0.481050\pi\) | |||||||
\(354\) | −0.514004 | −0.0273190 | ||||||||
\(355\) | 9.98336 | 0.529862 | ||||||||
\(356\) | 82.5997 | 4.37777 | ||||||||
\(357\) | 11.7103 | 0.619775 | ||||||||
\(358\) | 15.2373 | 0.805318 | ||||||||
\(359\) | −19.5995 | −1.03442 | −0.517210 | − | 0.855858i | \(-0.673029\pi\) | ||||
−0.517210 | + | 0.855858i | \(0.673029\pi\) | |||||||
\(360\) | −50.6321 | −2.66855 | ||||||||
\(361\) | −17.4653 | −0.919229 | ||||||||
\(362\) | −6.43388 | −0.338157 | ||||||||
\(363\) | −11.3104 | −0.593643 | ||||||||
\(364\) | 91.1285 | 4.77643 | ||||||||
\(365\) | −29.2525 | −1.53115 | ||||||||
\(366\) | 25.9163 | 1.35467 | ||||||||
\(367\) | 31.0498 | 1.62079 | 0.810393 | − | 0.585887i | \(-0.199254\pi\) | ||||
0.810393 | + | 0.585887i | \(0.199254\pi\) | |||||||
\(368\) | 11.5276 | 0.600919 | ||||||||
\(369\) | 4.20740 | 0.219028 | ||||||||
\(370\) | −7.43892 | −0.386731 | ||||||||
\(371\) | 8.14899 | 0.423074 | ||||||||
\(372\) | −44.0249 | −2.28258 | ||||||||
\(373\) | −31.7553 | −1.64423 | −0.822114 | − | 0.569323i | \(-0.807206\pi\) | ||||
−0.822114 | + | 0.569323i | \(0.807206\pi\) | |||||||
\(374\) | 4.12541 | 0.213320 | ||||||||
\(375\) | 7.63014 | 0.394019 | ||||||||
\(376\) | −36.8821 | −1.90205 | ||||||||
\(377\) | −48.8498 | −2.51589 | ||||||||
\(378\) | 47.1497 | 2.42512 | ||||||||
\(379\) | 18.8937 | 0.970506 | 0.485253 | − | 0.874374i | \(-0.338728\pi\) | ||||
0.485253 | + | 0.874374i | \(0.338728\pi\) | |||||||
\(380\) | −18.6692 | −0.957712 | ||||||||
\(381\) | −4.67959 | −0.239743 | ||||||||
\(382\) | −14.3690 | −0.735184 | ||||||||
\(383\) | −8.58405 | −0.438625 | −0.219312 | − | 0.975655i | \(-0.570381\pi\) | ||||
−0.219312 | + | 0.975655i | \(0.570381\pi\) | |||||||
\(384\) | −49.3676 | −2.51928 | ||||||||
\(385\) | 4.03130 | 0.205454 | ||||||||
\(386\) | 0.698825 | 0.0355693 | ||||||||
\(387\) | 7.35646 | 0.373950 | ||||||||
\(388\) | −0.0278121 | −0.00141194 | ||||||||
\(389\) | 30.8780 | 1.56558 | 0.782789 | − | 0.622287i | \(-0.213796\pi\) | ||||
0.782789 | + | 0.622287i | \(0.213796\pi\) | |||||||
\(390\) | 38.1648 | 1.93255 | ||||||||
\(391\) | 2.42390 | 0.122582 | ||||||||
\(392\) | −40.6376 | −2.05251 | ||||||||
\(393\) | 9.60332 | 0.484423 | ||||||||
\(394\) | −45.3693 | −2.28567 | ||||||||
\(395\) | 27.7085 | 1.39417 | ||||||||
\(396\) | 4.74544 | 0.238468 | ||||||||
\(397\) | −35.1300 | −1.76313 | −0.881563 | − | 0.472066i | \(-0.843508\pi\) | ||||
−0.881563 | + | 0.472066i | \(0.843508\pi\) | |||||||
\(398\) | −19.7399 | −0.989473 | ||||||||
\(399\) | 4.32787 | 0.216665 | ||||||||
\(400\) | 36.7313 | 1.83657 | ||||||||
\(401\) | 5.18820 | 0.259086 | 0.129543 | − | 0.991574i | \(-0.458649\pi\) | ||||
0.129543 | + | 0.991574i | \(0.458649\pi\) | |||||||
\(402\) | 11.0888 | 0.553059 | ||||||||
\(403\) | −36.9327 | −1.83975 | ||||||||
\(404\) | 83.8897 | 4.17367 | ||||||||
\(405\) | −0.897725 | −0.0446083 | ||||||||
\(406\) | 91.5596 | 4.54403 | ||||||||
\(407\) | 0.447139 | 0.0221639 | ||||||||
\(408\) | −34.5537 | −1.71066 | ||||||||
\(409\) | −22.0305 | −1.08934 | −0.544669 | − | 0.838651i | \(-0.683345\pi\) | ||||
−0.544669 | + | 0.838651i | \(0.683345\pi\) | |||||||
\(410\) | −16.4447 | −0.812145 | ||||||||
\(411\) | 8.50616 | 0.419578 | ||||||||
\(412\) | −15.9806 | −0.787306 | ||||||||
\(413\) | 0.594849 | 0.0292706 | ||||||||
\(414\) | 3.78824 | 0.186182 | ||||||||
\(415\) | 24.6176 | 1.20843 | ||||||||
\(416\) | −118.513 | −5.81058 | ||||||||
\(417\) | −19.5505 | −0.957392 | ||||||||
\(418\) | 1.52466 | 0.0745736 | ||||||||
\(419\) | 20.5617 | 1.00450 | 0.502251 | − | 0.864722i | \(-0.332505\pi\) | ||||
0.502251 | + | 0.864722i | \(0.332505\pi\) | |||||||
\(420\) | −52.6490 | −2.56901 | ||||||||
\(421\) | −13.5982 | −0.662735 | −0.331367 | − | 0.943502i | \(-0.607510\pi\) | ||||
−0.331367 | + | 0.943502i | \(0.607510\pi\) | |||||||
\(422\) | −40.0659 | −1.95038 | ||||||||
\(423\) | −7.13131 | −0.346736 | ||||||||
\(424\) | −24.0453 | −1.16774 | ||||||||
\(425\) | 7.72343 | 0.374642 | ||||||||
\(426\) | 10.6480 | 0.515898 | ||||||||
\(427\) | −29.9925 | −1.45144 | ||||||||
\(428\) | 101.473 | 4.90490 | ||||||||
\(429\) | −2.29401 | −0.110756 | ||||||||
\(430\) | −28.7529 | −1.38659 | ||||||||
\(431\) | −29.4436 | −1.41825 | −0.709123 | − | 0.705084i | \(-0.750909\pi\) | ||||
−0.709123 | + | 0.705084i | \(0.750909\pi\) | |||||||
\(432\) | −81.8582 | −3.93841 | ||||||||
\(433\) | −10.7005 | −0.514234 | −0.257117 | − | 0.966380i | \(-0.582773\pi\) | ||||
−0.257117 | + | 0.966380i | \(0.582773\pi\) | |||||||
\(434\) | 69.2232 | 3.32282 | ||||||||
\(435\) | 28.2227 | 1.35318 | ||||||||
\(436\) | −5.57617 | −0.267050 | ||||||||
\(437\) | 0.895819 | 0.0428528 | ||||||||
\(438\) | −31.2001 | −1.49080 | ||||||||
\(439\) | 5.86555 | 0.279948 | 0.139974 | − | 0.990155i | \(-0.455298\pi\) | ||||
0.139974 | + | 0.990155i | \(0.455298\pi\) | |||||||
\(440\) | −11.8952 | −0.567081 | ||||||||
\(441\) | −7.85747 | −0.374165 | ||||||||
\(442\) | −45.1986 | −2.14988 | ||||||||
\(443\) | −38.2169 | −1.81574 | −0.907869 | − | 0.419254i | \(-0.862292\pi\) | ||||
−0.907869 | + | 0.419254i | \(0.862292\pi\) | |||||||
\(444\) | −5.83967 | −0.277139 | ||||||||
\(445\) | −40.0338 | −1.89779 | ||||||||
\(446\) | −58.1045 | −2.75133 | ||||||||
\(447\) | 0.941827 | 0.0445469 | ||||||||
\(448\) | 115.771 | 5.46968 | ||||||||
\(449\) | −17.5524 | −0.828349 | −0.414174 | − | 0.910198i | \(-0.635930\pi\) | ||||
−0.414174 | + | 0.910198i | \(0.635930\pi\) | |||||||
\(450\) | 12.0707 | 0.569020 | ||||||||
\(451\) | 0.988459 | 0.0465447 | ||||||||
\(452\) | −72.5391 | −3.41195 | ||||||||
\(453\) | −21.2395 | −0.997917 | ||||||||
\(454\) | −36.6114 | −1.71826 | ||||||||
\(455\) | −44.1675 | −2.07060 | ||||||||
\(456\) | −12.7703 | −0.598024 | ||||||||
\(457\) | −3.41998 | −0.159980 | −0.0799899 | − | 0.996796i | \(-0.525489\pi\) | ||||
−0.0799899 | + | 0.996796i | \(0.525489\pi\) | |||||||
\(458\) | −5.89974 | −0.275677 | ||||||||
\(459\) | −17.2122 | −0.803397 | ||||||||
\(460\) | −10.8977 | −0.508109 | ||||||||
\(461\) | 12.7712 | 0.594814 | 0.297407 | − | 0.954751i | \(-0.403878\pi\) | ||||
0.297407 | + | 0.954751i | \(0.403878\pi\) | |||||||
\(462\) | 4.29969 | 0.200040 | ||||||||
\(463\) | 7.98062 | 0.370891 | 0.185445 | − | 0.982655i | \(-0.440627\pi\) | ||||
0.185445 | + | 0.982655i | \(0.440627\pi\) | |||||||
\(464\) | −158.960 | −7.37953 | ||||||||
\(465\) | 21.3377 | 0.989510 | ||||||||
\(466\) | −12.1104 | −0.561004 | ||||||||
\(467\) | −31.0775 | −1.43809 | −0.719047 | − | 0.694961i | \(-0.755421\pi\) | ||||
−0.719047 | + | 0.694961i | \(0.755421\pi\) | |||||||
\(468\) | −51.9918 | −2.40332 | ||||||||
\(469\) | −12.8329 | −0.592567 | ||||||||
\(470\) | 27.8729 | 1.28568 | ||||||||
\(471\) | −6.83009 | −0.314714 | ||||||||
\(472\) | −1.75523 | −0.0807908 | ||||||||
\(473\) | 1.72828 | 0.0794664 | ||||||||
\(474\) | 29.5533 | 1.35743 | ||||||||
\(475\) | 2.85441 | 0.130969 | ||||||||
\(476\) | 62.3523 | 2.85791 | ||||||||
\(477\) | −4.64927 | −0.212875 | ||||||||
\(478\) | 73.5127 | 3.36239 | ||||||||
\(479\) | 17.6207 | 0.805110 | 0.402555 | − | 0.915396i | \(-0.368122\pi\) | ||||
0.402555 | + | 0.915396i | \(0.368122\pi\) | |||||||
\(480\) | 68.4703 | 3.12523 | ||||||||
\(481\) | −4.89893 | −0.223372 | ||||||||
\(482\) | 27.0589 | 1.23250 | ||||||||
\(483\) | 2.52629 | 0.114950 | ||||||||
\(484\) | −60.2230 | −2.73741 | ||||||||
\(485\) | 0.0134798 | 0.000612085 0 | ||||||||
\(486\) | −43.3592 | −1.96681 | ||||||||
\(487\) | −38.3287 | −1.73684 | −0.868420 | − | 0.495829i | \(-0.834864\pi\) | ||||
−0.868420 | + | 0.495829i | \(0.834864\pi\) | |||||||
\(488\) | 88.4992 | 4.00617 | ||||||||
\(489\) | −13.5132 | −0.611089 | ||||||||
\(490\) | 30.7110 | 1.38738 | ||||||||
\(491\) | 4.93566 | 0.222743 | 0.111372 | − | 0.993779i | \(-0.464476\pi\) | ||||
0.111372 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(492\) | −12.9093 | −0.581998 | ||||||||
\(493\) | −33.4242 | −1.50535 | ||||||||
\(494\) | −16.7044 | −0.751568 | ||||||||
\(495\) | −2.29999 | −0.103377 | ||||||||
\(496\) | −120.181 | −5.39628 | ||||||||
\(497\) | −12.3228 | −0.552752 | ||||||||
\(498\) | 26.2565 | 1.17658 | ||||||||
\(499\) | 36.8248 | 1.64850 | 0.824252 | − | 0.566223i | \(-0.191596\pi\) | ||||
0.824252 | + | 0.566223i | \(0.191596\pi\) | |||||||
\(500\) | 40.6272 | 1.81690 | ||||||||
\(501\) | −22.0938 | −0.987076 | ||||||||
\(502\) | 50.6358 | 2.25999 | ||||||||
\(503\) | −12.4470 | −0.554983 | −0.277491 | − | 0.960728i | \(-0.589503\pi\) | ||||
−0.277491 | + | 0.960728i | \(0.589503\pi\) | |||||||
\(504\) | 62.4969 | 2.78383 | ||||||||
\(505\) | −40.6591 | −1.80930 | ||||||||
\(506\) | 0.889985 | 0.0395647 | ||||||||
\(507\) | 11.5193 | 0.511588 | ||||||||
\(508\) | −24.9168 | −1.10550 | ||||||||
\(509\) | 29.5028 | 1.30769 | 0.653845 | − | 0.756629i | \(-0.273155\pi\) | ||||
0.653845 | + | 0.756629i | \(0.273155\pi\) | |||||||
\(510\) | 26.1133 | 1.15632 | ||||||||
\(511\) | 36.1073 | 1.59729 | ||||||||
\(512\) | −71.8143 | −3.17377 | ||||||||
\(513\) | −6.36125 | −0.280856 | ||||||||
\(514\) | 68.5527 | 3.02373 | ||||||||
\(515\) | 7.74535 | 0.341301 | ||||||||
\(516\) | −22.5715 | −0.993653 | ||||||||
\(517\) | −1.67538 | −0.0736833 | ||||||||
\(518\) | 9.18210 | 0.403438 | ||||||||
\(519\) | −7.85501 | −0.344797 | ||||||||
\(520\) | 130.325 | 5.71515 | ||||||||
\(521\) | −32.5553 | −1.42627 | −0.713136 | − | 0.701026i | \(-0.752726\pi\) | ||||
−0.713136 | + | 0.701026i | \(0.752726\pi\) | |||||||
\(522\) | −52.2378 | −2.28639 | ||||||||
\(523\) | −0.443058 | −0.0193736 | −0.00968680 | − | 0.999953i | \(-0.503083\pi\) | ||||
−0.00968680 | + | 0.999953i | \(0.503083\pi\) | |||||||
\(524\) | 51.1335 | 2.23378 | ||||||||
\(525\) | 8.04971 | 0.351318 | ||||||||
\(526\) | 66.7620 | 2.91096 | ||||||||
\(527\) | −25.2702 | −1.10079 | ||||||||
\(528\) | −7.46484 | −0.324865 | ||||||||
\(529\) | −22.4771 | −0.977265 | ||||||||
\(530\) | 18.1717 | 0.789330 | ||||||||
\(531\) | −0.339381 | −0.0147279 | ||||||||
\(532\) | 23.0440 | 0.999086 | ||||||||
\(533\) | −10.8297 | −0.469087 | ||||||||
\(534\) | −42.6992 | −1.84777 | ||||||||
\(535\) | −49.1814 | −2.12630 | ||||||||
\(536\) | 37.8661 | 1.63557 | ||||||||
\(537\) | −5.79744 | −0.250178 | ||||||||
\(538\) | 9.75310 | 0.420486 | ||||||||
\(539\) | −1.84598 | −0.0795121 | ||||||||
\(540\) | 77.3852 | 3.33013 | ||||||||
\(541\) | 18.4273 | 0.792252 | 0.396126 | − | 0.918196i | \(-0.370354\pi\) | ||||
0.396126 | + | 0.918196i | \(0.370354\pi\) | |||||||
\(542\) | −42.0463 | −1.80604 | ||||||||
\(543\) | 2.44794 | 0.105051 | ||||||||
\(544\) | −81.0895 | −3.47668 | ||||||||
\(545\) | 2.70262 | 0.115767 | ||||||||
\(546\) | −47.1080 | −2.01604 | ||||||||
\(547\) | −41.4134 | −1.77071 | −0.885355 | − | 0.464917i | \(-0.846084\pi\) | ||||
−0.885355 | + | 0.464917i | \(0.846084\pi\) | |||||||
\(548\) | 45.2916 | 1.93476 | ||||||||
\(549\) | 17.1117 | 0.730310 | ||||||||
\(550\) | 2.83582 | 0.120920 | ||||||||
\(551\) | −12.3529 | −0.526250 | ||||||||
\(552\) | −7.45436 | −0.317279 | ||||||||
\(553\) | −34.2015 | −1.45440 | ||||||||
\(554\) | 60.4820 | 2.56963 | ||||||||
\(555\) | 2.83033 | 0.120141 | ||||||||
\(556\) | −104.098 | −4.41473 | ||||||||
\(557\) | 39.0199 | 1.65333 | 0.826663 | − | 0.562697i | \(-0.190236\pi\) | ||||
0.826663 | + | 0.562697i | \(0.190236\pi\) | |||||||
\(558\) | −39.4941 | −1.67192 | ||||||||
\(559\) | −18.9353 | −0.800878 | ||||||||
\(560\) | −143.723 | −6.07342 | ||||||||
\(561\) | −1.56962 | −0.0662694 | ||||||||
\(562\) | 65.5614 | 2.76554 | ||||||||
\(563\) | −4.12232 | −0.173735 | −0.0868676 | − | 0.996220i | \(-0.527686\pi\) | ||||
−0.0868676 | + | 0.996220i | \(0.527686\pi\) | |||||||
\(564\) | 21.8806 | 0.921341 | ||||||||
\(565\) | 35.1578 | 1.47910 | ||||||||
\(566\) | −3.57971 | −0.150466 | ||||||||
\(567\) | 1.10809 | 0.0465354 | ||||||||
\(568\) | 36.3610 | 1.52567 | ||||||||
\(569\) | 7.97922 | 0.334506 | 0.167253 | − | 0.985914i | \(-0.446510\pi\) | ||||
0.167253 | + | 0.985914i | \(0.446510\pi\) | |||||||
\(570\) | 9.65089 | 0.404231 | ||||||||
\(571\) | −29.9634 | −1.25393 | −0.626965 | − | 0.779047i | \(-0.715703\pi\) | ||||
−0.626965 | + | 0.779047i | \(0.715703\pi\) | |||||||
\(572\) | −12.2146 | −0.510719 | ||||||||
\(573\) | 5.46707 | 0.228390 | ||||||||
\(574\) | 20.2982 | 0.847231 | ||||||||
\(575\) | 1.66620 | 0.0694852 | ||||||||
\(576\) | −66.0514 | −2.75214 | ||||||||
\(577\) | −7.09252 | −0.295265 | −0.147633 | − | 0.989042i | \(-0.547165\pi\) | ||||
−0.147633 | + | 0.989042i | \(0.547165\pi\) | |||||||
\(578\) | 15.8662 | 0.659949 | ||||||||
\(579\) | −0.265886 | −0.0110499 | ||||||||
\(580\) | 150.274 | 6.23978 | ||||||||
\(581\) | −30.3863 | −1.26063 | ||||||||
\(582\) | 0.0143772 | 0.000595954 0 | ||||||||
\(583\) | −1.09227 | −0.0452372 | ||||||||
\(584\) | −106.542 | −4.40875 | ||||||||
\(585\) | 25.1990 | 1.04185 | ||||||||
\(586\) | −8.21903 | −0.339525 | ||||||||
\(587\) | −19.0066 | −0.784486 | −0.392243 | − | 0.919862i | \(-0.628301\pi\) | ||||
−0.392243 | + | 0.919862i | \(0.628301\pi\) | |||||||
\(588\) | 24.1087 | 0.994225 | ||||||||
\(589\) | −9.33932 | −0.384820 | ||||||||
\(590\) | 1.32648 | 0.0546101 | ||||||||
\(591\) | 17.2619 | 0.710061 | ||||||||
\(592\) | −15.9414 | −0.655186 | ||||||||
\(593\) | 7.50231 | 0.308083 | 0.154041 | − | 0.988064i | \(-0.450771\pi\) | ||||
0.154041 | + | 0.988064i | \(0.450771\pi\) | |||||||
\(594\) | −6.31982 | −0.259305 | ||||||||
\(595\) | −30.2205 | −1.23892 | ||||||||
\(596\) | 5.01482 | 0.205415 | ||||||||
\(597\) | 7.51057 | 0.307387 | ||||||||
\(598\) | −9.75081 | −0.398740 | ||||||||
\(599\) | −42.1320 | −1.72147 | −0.860734 | − | 0.509054i | \(-0.829995\pi\) | ||||
−0.860734 | + | 0.509054i | \(0.829995\pi\) | |||||||
\(600\) | −23.7524 | −0.969686 | ||||||||
\(601\) | 0.300303 | 0.0122496 | 0.00612480 | − | 0.999981i | \(-0.498050\pi\) | ||||
0.00612480 | + | 0.999981i | \(0.498050\pi\) | |||||||
\(602\) | 35.4906 | 1.44649 | ||||||||
\(603\) | 7.32158 | 0.298158 | ||||||||
\(604\) | −113.091 | −4.60160 | ||||||||
\(605\) | 29.1885 | 1.18668 | ||||||||
\(606\) | −43.3660 | −1.76162 | ||||||||
\(607\) | 23.3212 | 0.946578 | 0.473289 | − | 0.880907i | \(-0.343067\pi\) | ||||
0.473289 | + | 0.880907i | \(0.343067\pi\) | |||||||
\(608\) | −29.9689 | −1.21540 | ||||||||
\(609\) | −34.8362 | −1.41164 | ||||||||
\(610\) | −66.8814 | −2.70795 | ||||||||
\(611\) | 18.3558 | 0.742595 | ||||||||
\(612\) | −35.5741 | −1.43800 | ||||||||
\(613\) | −2.00742 | −0.0810787 | −0.0405394 | − | 0.999178i | \(-0.512908\pi\) | ||||
−0.0405394 | + | 0.999178i | \(0.512908\pi\) | |||||||
\(614\) | 1.13763 | 0.0459111 | ||||||||
\(615\) | 6.25681 | 0.252299 | ||||||||
\(616\) | 14.6826 | 0.591579 | ||||||||
\(617\) | −15.4738 | −0.622951 | −0.311476 | − | 0.950254i | \(-0.600823\pi\) | ||||
−0.311476 | + | 0.950254i | \(0.600823\pi\) | |||||||
\(618\) | 8.26101 | 0.332306 | ||||||||
\(619\) | −45.3020 | −1.82084 | −0.910420 | − | 0.413686i | \(-0.864241\pi\) | ||||
−0.910420 | + | 0.413686i | \(0.864241\pi\) | |||||||
\(620\) | 113.614 | 4.56284 | ||||||||
\(621\) | −3.71323 | −0.149007 | ||||||||
\(622\) | −13.3591 | −0.535652 | ||||||||
\(623\) | 49.4150 | 1.97977 | ||||||||
\(624\) | 81.7859 | 3.27406 | ||||||||
\(625\) | −31.2116 | −1.24847 | ||||||||
\(626\) | −9.82212 | −0.392571 | ||||||||
\(627\) | −0.580097 | −0.0231668 | ||||||||
\(628\) | −36.3673 | −1.45121 | ||||||||
\(629\) | −3.35196 | −0.133652 | ||||||||
\(630\) | −47.2307 | −1.88172 | ||||||||
\(631\) | 34.3793 | 1.36862 | 0.684309 | − | 0.729192i | \(-0.260104\pi\) | ||||
0.684309 | + | 0.729192i | \(0.260104\pi\) | |||||||
\(632\) | 100.919 | 4.01433 | ||||||||
\(633\) | 15.2441 | 0.605899 | ||||||||
\(634\) | 1.70709 | 0.0677972 | ||||||||
\(635\) | 12.0765 | 0.479241 | ||||||||
\(636\) | 14.2651 | 0.565649 | ||||||||
\(637\) | 20.2249 | 0.801339 | ||||||||
\(638\) | −12.2724 | −0.485869 | ||||||||
\(639\) | 7.03055 | 0.278124 | ||||||||
\(640\) | 127.401 | 5.03598 | ||||||||
\(641\) | −37.8024 | −1.49311 | −0.746553 | − | 0.665326i | \(-0.768293\pi\) | ||||
−0.746553 | + | 0.665326i | \(0.768293\pi\) | |||||||
\(642\) | −52.4557 | −2.07026 | ||||||||
\(643\) | 10.7348 | 0.423338 | 0.211669 | − | 0.977341i | \(-0.432110\pi\) | ||||
0.211669 | + | 0.977341i | \(0.432110\pi\) | |||||||
\(644\) | 13.4514 | 0.530060 | ||||||||
\(645\) | 10.9398 | 0.430753 | ||||||||
\(646\) | −11.4296 | −0.449690 | ||||||||
\(647\) | 42.5228 | 1.67174 | 0.835872 | − | 0.548925i | \(-0.184963\pi\) | ||||
0.835872 | + | 0.548925i | \(0.184963\pi\) | |||||||
\(648\) | −3.26965 | −0.128444 | ||||||||
\(649\) | −0.0797319 | −0.00312975 | ||||||||
\(650\) | −31.0697 | −1.21865 | ||||||||
\(651\) | −26.3378 | −1.03226 | ||||||||
\(652\) | −71.9521 | −2.81786 | ||||||||
\(653\) | 5.20122 | 0.203539 | 0.101770 | − | 0.994808i | \(-0.467550\pi\) | ||||
0.101770 | + | 0.994808i | \(0.467550\pi\) | |||||||
\(654\) | 2.88255 | 0.112717 | ||||||||
\(655\) | −24.7830 | −0.968353 | ||||||||
\(656\) | −35.2404 | −1.37591 | ||||||||
\(657\) | −20.6004 | −0.803700 | ||||||||
\(658\) | −34.4044 | −1.34122 | ||||||||
\(659\) | −23.3092 | −0.907998 | −0.453999 | − | 0.891002i | \(-0.650003\pi\) | ||||
−0.453999 | + | 0.891002i | \(0.650003\pi\) | |||||||
\(660\) | 7.05693 | 0.274691 | ||||||||
\(661\) | 17.1593 | 0.667421 | 0.333711 | − | 0.942676i | \(-0.391699\pi\) | ||||
0.333711 | + | 0.942676i | \(0.391699\pi\) | |||||||
\(662\) | −44.0919 | −1.71368 | ||||||||
\(663\) | 17.1970 | 0.667876 | ||||||||
\(664\) | 89.6610 | 3.47952 | ||||||||
\(665\) | −11.1688 | −0.433108 | ||||||||
\(666\) | −5.23869 | −0.202995 | ||||||||
\(667\) | −7.21069 | −0.279199 | ||||||||
\(668\) | −117.640 | −4.55161 | ||||||||
\(669\) | 22.1074 | 0.854721 | ||||||||
\(670\) | −28.6165 | −1.10555 | ||||||||
\(671\) | 4.02012 | 0.155195 | ||||||||
\(672\) | −84.5151 | −3.26024 | ||||||||
\(673\) | 21.4583 | 0.827158 | 0.413579 | − | 0.910468i | \(-0.364279\pi\) | ||||
0.413579 | + | 0.910468i | \(0.364279\pi\) | |||||||
\(674\) | 24.1424 | 0.929931 | ||||||||
\(675\) | −11.8317 | −0.455403 | ||||||||
\(676\) | 61.3351 | 2.35904 | ||||||||
\(677\) | −33.1920 | −1.27567 | −0.637836 | − | 0.770172i | \(-0.720170\pi\) | ||||
−0.637836 | + | 0.770172i | \(0.720170\pi\) | |||||||
\(678\) | 37.4984 | 1.44012 | ||||||||
\(679\) | −0.0166385 | −0.000638527 0 | ||||||||
\(680\) | 89.1718 | 3.41958 | ||||||||
\(681\) | 13.9298 | 0.533790 | ||||||||
\(682\) | −9.27850 | −0.355292 | ||||||||
\(683\) | 32.8804 | 1.25813 | 0.629066 | − | 0.777352i | \(-0.283438\pi\) | ||||
0.629066 | + | 0.777352i | \(0.283438\pi\) | |||||||
\(684\) | −13.1474 | −0.502703 | ||||||||
\(685\) | −21.9516 | −0.838728 | ||||||||
\(686\) | 26.3670 | 1.00670 | ||||||||
\(687\) | 2.24471 | 0.0856409 | ||||||||
\(688\) | −61.6164 | −2.34910 | ||||||||
\(689\) | 11.9671 | 0.455909 | ||||||||
\(690\) | 5.63348 | 0.214463 | ||||||||
\(691\) | 28.6210 | 1.08879 | 0.544396 | − | 0.838828i | \(-0.316759\pi\) | ||||
0.544396 | + | 0.838828i | \(0.316759\pi\) | |||||||
\(692\) | −41.8245 | −1.58993 | ||||||||
\(693\) | 2.83895 | 0.107843 | ||||||||
\(694\) | 5.31160 | 0.201625 | ||||||||
\(695\) | 50.4534 | 1.91381 | ||||||||
\(696\) | 102.792 | 3.89631 | ||||||||
\(697\) | −7.40995 | −0.280672 | ||||||||
\(698\) | −72.1862 | −2.73229 | ||||||||
\(699\) | 4.60772 | 0.174280 | ||||||||
\(700\) | 42.8612 | 1.62000 | ||||||||
\(701\) | 2.29515 | 0.0866868 | 0.0433434 | − | 0.999060i | \(-0.486199\pi\) | ||||
0.0433434 | + | 0.999060i | \(0.486199\pi\) | |||||||
\(702\) | 69.2409 | 2.61333 | ||||||||
\(703\) | −1.23881 | −0.0467227 | ||||||||
\(704\) | −15.5177 | −0.584845 | ||||||||
\(705\) | −10.6050 | −0.399406 | ||||||||
\(706\) | −6.15370 | −0.231598 | ||||||||
\(707\) | 50.1868 | 1.88747 | ||||||||
\(708\) | 1.04130 | 0.0391346 | ||||||||
\(709\) | −4.33283 | −0.162723 | −0.0813614 | − | 0.996685i | \(-0.525927\pi\) | ||||
−0.0813614 | + | 0.996685i | \(0.525927\pi\) | |||||||
\(710\) | −27.4790 | −1.03127 | ||||||||
\(711\) | 19.5131 | 0.731799 | ||||||||
\(712\) | −145.809 | −5.46444 | ||||||||
\(713\) | −5.45161 | −0.204164 | ||||||||
\(714\) | −32.2325 | −1.20627 | ||||||||
\(715\) | 5.92010 | 0.221399 | ||||||||
\(716\) | −30.8688 | −1.15362 | ||||||||
\(717\) | −27.9698 | −1.04455 | ||||||||
\(718\) | 53.9472 | 2.01329 | ||||||||
\(719\) | 29.5785 | 1.10309 | 0.551546 | − | 0.834145i | \(-0.314038\pi\) | ||||
0.551546 | + | 0.834145i | \(0.314038\pi\) | |||||||
\(720\) | 81.9989 | 3.05592 | ||||||||
\(721\) | −9.56033 | −0.356045 | ||||||||
\(722\) | 48.0731 | 1.78910 | ||||||||
\(723\) | −10.2953 | −0.382885 | ||||||||
\(724\) | 13.0342 | 0.484412 | ||||||||
\(725\) | −22.9759 | −0.853305 | ||||||||
\(726\) | 31.1317 | 1.15541 | ||||||||
\(727\) | 30.4695 | 1.13005 | 0.565026 | − | 0.825073i | \(-0.308866\pi\) | ||||
0.565026 | + | 0.825073i | \(0.308866\pi\) | |||||||
\(728\) | −160.865 | −5.96205 | ||||||||
\(729\) | 15.5006 | 0.574097 | ||||||||
\(730\) | 80.5172 | 2.98007 | ||||||||
\(731\) | −12.9560 | −0.479195 | ||||||||
\(732\) | −52.5030 | −1.94057 | ||||||||
\(733\) | 10.9215 | 0.403395 | 0.201698 | − | 0.979448i | \(-0.435354\pi\) | ||||
0.201698 | + | 0.979448i | \(0.435354\pi\) | |||||||
\(734\) | −85.4641 | −3.15454 | ||||||||
\(735\) | −11.6848 | −0.431001 | ||||||||
\(736\) | −17.4936 | −0.644824 | ||||||||
\(737\) | 1.72009 | 0.0633601 | ||||||||
\(738\) | −11.5808 | −0.426295 | ||||||||
\(739\) | −20.1716 | −0.742023 | −0.371011 | − | 0.928628i | \(-0.620989\pi\) | ||||
−0.371011 | + | 0.928628i | \(0.620989\pi\) | |||||||
\(740\) | 15.0703 | 0.553994 | ||||||||
\(741\) | 6.35563 | 0.233480 | ||||||||
\(742\) | −22.4300 | −0.823430 | ||||||||
\(743\) | 23.3945 | 0.858262 | 0.429131 | − | 0.903242i | \(-0.358820\pi\) | ||||
0.429131 | + | 0.903242i | \(0.358820\pi\) | |||||||
\(744\) | 77.7151 | 2.84917 | ||||||||
\(745\) | −2.43055 | −0.0890483 | ||||||||
\(746\) | 87.4060 | 3.20016 | ||||||||
\(747\) | 17.3364 | 0.634304 | ||||||||
\(748\) | −8.35754 | −0.305582 | ||||||||
\(749\) | 60.7062 | 2.21815 | ||||||||
\(750\) | −21.0018 | −0.766879 | ||||||||
\(751\) | −5.63299 | −0.205551 | −0.102775 | − | 0.994705i | \(-0.532772\pi\) | ||||
−0.102775 | + | 0.994705i | \(0.532772\pi\) | |||||||
\(752\) | 59.7306 | 2.17815 | ||||||||
\(753\) | −19.2657 | −0.702081 | ||||||||
\(754\) | 134.458 | 4.89669 | ||||||||
\(755\) | 54.8121 | 1.99482 | ||||||||
\(756\) | −95.5191 | −3.47400 | ||||||||
\(757\) | −10.4411 | −0.379487 | −0.189743 | − | 0.981834i | \(-0.560766\pi\) | ||||
−0.189743 | + | 0.981834i | \(0.560766\pi\) | |||||||
\(758\) | −52.0047 | −1.88890 | ||||||||
\(759\) | −0.338618 | −0.0122910 | ||||||||
\(760\) | 32.9560 | 1.19544 | ||||||||
\(761\) | −5.59752 | −0.202910 | −0.101455 | − | 0.994840i | \(-0.532350\pi\) | ||||
−0.101455 | + | 0.994840i | \(0.532350\pi\) | |||||||
\(762\) | 12.8805 | 0.466611 | ||||||||
\(763\) | −3.33593 | −0.120769 | ||||||||
\(764\) | 29.1098 | 1.05316 | ||||||||
\(765\) | 17.2418 | 0.623378 | ||||||||
\(766\) | 23.6275 | 0.853695 | ||||||||
\(767\) | 0.873556 | 0.0315423 | ||||||||
\(768\) | 63.1949 | 2.28035 | ||||||||
\(769\) | 50.1109 | 1.80704 | 0.903522 | − | 0.428542i | \(-0.140973\pi\) | ||||
0.903522 | + | 0.428542i | \(0.140973\pi\) | |||||||
\(770\) | −11.0961 | −0.399875 | ||||||||
\(771\) | −26.0826 | −0.939344 | ||||||||
\(772\) | −1.41573 | −0.0509532 | ||||||||
\(773\) | −38.8668 | −1.39794 | −0.698970 | − | 0.715151i | \(-0.746358\pi\) | ||||
−0.698970 | + | 0.715151i | \(0.746358\pi\) | |||||||
\(774\) | −20.2486 | −0.727819 | ||||||||
\(775\) | −17.3708 | −0.623979 | ||||||||
\(776\) | 0.0490954 | 0.00176242 | ||||||||
\(777\) | −3.49357 | −0.125331 | ||||||||
\(778\) | −84.9913 | −3.04709 | ||||||||
\(779\) | −2.73855 | −0.0981189 | ||||||||
\(780\) | −77.3169 | −2.76839 | ||||||||
\(781\) | 1.65171 | 0.0591029 | ||||||||
\(782\) | −6.67174 | −0.238581 | ||||||||
\(783\) | 51.2034 | 1.82986 | ||||||||
\(784\) | 65.8128 | 2.35046 | ||||||||
\(785\) | 17.6262 | 0.629107 | ||||||||
\(786\) | −26.4330 | −0.942834 | ||||||||
\(787\) | 52.5476 | 1.87312 | 0.936559 | − | 0.350510i | \(-0.113992\pi\) | ||||
0.936559 | + | 0.350510i | \(0.113992\pi\) | |||||||
\(788\) | 91.9122 | 3.27424 | ||||||||
\(789\) | −25.4013 | −0.904311 | ||||||||
\(790\) | −76.2673 | −2.71347 | ||||||||
\(791\) | −43.3963 | −1.54300 | ||||||||
\(792\) | −8.37691 | −0.297661 | ||||||||
\(793\) | −44.0450 | −1.56408 | ||||||||
\(794\) | 96.6949 | 3.43157 | ||||||||
\(795\) | −6.91391 | −0.245211 | ||||||||
\(796\) | 39.9905 | 1.41743 | ||||||||
\(797\) | −23.5460 | −0.834043 | −0.417021 | − | 0.908897i | \(-0.636926\pi\) | ||||
−0.417021 | + | 0.908897i | \(0.636926\pi\) | |||||||
\(798\) | −11.9124 | −0.421695 | ||||||||
\(799\) | 12.5595 | 0.444322 | ||||||||
\(800\) | −55.7412 | −1.97075 | ||||||||
\(801\) | −28.1929 | −0.996148 | ||||||||
\(802\) | −14.2804 | −0.504260 | ||||||||
\(803\) | −4.83973 | −0.170790 | ||||||||
\(804\) | −22.4644 | −0.792259 | ||||||||
\(805\) | −6.51954 | −0.229783 | ||||||||
\(806\) | 101.657 | 3.58070 | ||||||||
\(807\) | −3.71082 | −0.130627 | ||||||||
\(808\) | −148.087 | −5.20967 | ||||||||
\(809\) | −24.4445 | −0.859425 | −0.429712 | − | 0.902966i | \(-0.641385\pi\) | ||||
−0.429712 | + | 0.902966i | \(0.641385\pi\) | |||||||
\(810\) | 2.47097 | 0.0868212 | ||||||||
\(811\) | 47.6556 | 1.67341 | 0.836707 | − | 0.547652i | \(-0.184478\pi\) | ||||
0.836707 | + | 0.547652i | \(0.184478\pi\) | |||||||
\(812\) | −185.488 | −6.50934 | ||||||||
\(813\) | 15.9976 | 0.561061 | ||||||||
\(814\) | −1.23074 | −0.0431376 | ||||||||
\(815\) | 34.8732 | 1.22156 | ||||||||
\(816\) | 55.9599 | 1.95899 | ||||||||
\(817\) | −4.78825 | −0.167520 | ||||||||
\(818\) | 60.6386 | 2.12018 | ||||||||
\(819\) | −31.1040 | −1.08686 | ||||||||
\(820\) | 33.3148 | 1.16340 | ||||||||
\(821\) | −52.3103 | −1.82564 | −0.912821 | − | 0.408360i | \(-0.866101\pi\) | ||||
−0.912821 | + | 0.408360i | \(0.866101\pi\) | |||||||
\(822\) | −23.4131 | −0.816625 | ||||||||
\(823\) | −12.4650 | −0.434504 | −0.217252 | − | 0.976116i | \(-0.569709\pi\) | ||||
−0.217252 | + | 0.976116i | \(0.569709\pi\) | |||||||
\(824\) | 28.2098 | 0.982734 | ||||||||
\(825\) | −1.07896 | −0.0375646 | ||||||||
\(826\) | −1.63731 | −0.0569694 | ||||||||
\(827\) | −22.9820 | −0.799161 | −0.399580 | − | 0.916698i | \(-0.630844\pi\) | ||||
−0.399580 | + | 0.916698i | \(0.630844\pi\) | |||||||
\(828\) | −7.67448 | −0.266707 | ||||||||
\(829\) | 1.90556 | 0.0661829 | 0.0330915 | − | 0.999452i | \(-0.489465\pi\) | ||||
0.0330915 | + | 0.999452i | \(0.489465\pi\) | |||||||
\(830\) | −67.7595 | −2.35197 | ||||||||
\(831\) | −23.0119 | −0.798275 | ||||||||
\(832\) | 170.014 | 5.89418 | ||||||||
\(833\) | 13.8383 | 0.479470 | ||||||||
\(834\) | 53.8125 | 1.86337 | ||||||||
\(835\) | 57.0167 | 1.97315 | ||||||||
\(836\) | −3.08876 | −0.106827 | ||||||||
\(837\) | 38.7121 | 1.33809 | ||||||||
\(838\) | −56.5956 | −1.95506 | ||||||||
\(839\) | −14.4469 | −0.498762 | −0.249381 | − | 0.968405i | \(-0.580227\pi\) | ||||
−0.249381 | + | 0.968405i | \(0.580227\pi\) | |||||||
\(840\) | 92.9389 | 3.20670 | ||||||||
\(841\) | 70.4315 | 2.42867 | ||||||||
\(842\) | 37.4288 | 1.28988 | ||||||||
\(843\) | −24.9445 | −0.859136 | ||||||||
\(844\) | 81.1682 | 2.79393 | ||||||||
\(845\) | −29.7274 | −1.02265 | ||||||||
\(846\) | 19.6288 | 0.674853 | ||||||||
\(847\) | −36.0283 | −1.23795 | ||||||||
\(848\) | 38.9415 | 1.33726 | ||||||||
\(849\) | 1.36199 | 0.0467435 | ||||||||
\(850\) | −21.2586 | −0.729165 | ||||||||
\(851\) | −0.723127 | −0.0247885 | ||||||||
\(852\) | −21.5715 | −0.739027 | ||||||||
\(853\) | 8.07892 | 0.276617 | 0.138308 | − | 0.990389i | \(-0.455833\pi\) | ||||
0.138308 | + | 0.990389i | \(0.455833\pi\) | |||||||
\(854\) | 82.5539 | 2.82494 | ||||||||
\(855\) | 6.37218 | 0.217924 | ||||||||
\(856\) | −179.126 | −6.12241 | ||||||||
\(857\) | 9.09217 | 0.310583 | 0.155291 | − | 0.987869i | \(-0.450368\pi\) | ||||
0.155291 | + | 0.987869i | \(0.450368\pi\) | |||||||
\(858\) | 6.31424 | 0.215565 | ||||||||
\(859\) | 26.4213 | 0.901484 | 0.450742 | − | 0.892654i | \(-0.351159\pi\) | ||||
0.450742 | + | 0.892654i | \(0.351159\pi\) | |||||||
\(860\) | 58.2495 | 1.98629 | ||||||||
\(861\) | −7.72298 | −0.263198 | ||||||||
\(862\) | 81.0430 | 2.76034 | ||||||||
\(863\) | −10.3828 | −0.353434 | −0.176717 | − | 0.984262i | \(-0.556548\pi\) | ||||
−0.176717 | + | 0.984262i | \(0.556548\pi\) | |||||||
\(864\) | 124.223 | 4.22615 | ||||||||
\(865\) | 20.2712 | 0.689242 | ||||||||
\(866\) | 29.4530 | 1.00085 | ||||||||
\(867\) | −6.03673 | −0.205018 | ||||||||
\(868\) | −140.237 | −4.75996 | ||||||||
\(869\) | 4.58428 | 0.155511 | ||||||||
\(870\) | −77.6827 | −2.63369 | ||||||||
\(871\) | −18.8455 | −0.638556 | ||||||||
\(872\) | 9.84336 | 0.333338 | ||||||||
\(873\) | 0.00949282 | 0.000321283 0 | ||||||||
\(874\) | −2.46573 | −0.0834045 | ||||||||
\(875\) | 24.3051 | 0.821662 | ||||||||
\(876\) | 63.2073 | 2.13558 | ||||||||
\(877\) | 0.126829 | 0.00428271 | 0.00214136 | − | 0.999998i | \(-0.499318\pi\) | ||||
0.00214136 | + | 0.999998i | \(0.499318\pi\) | |||||||
\(878\) | −16.1448 | −0.544862 | ||||||||
\(879\) | 3.12714 | 0.105476 | ||||||||
\(880\) | 19.2643 | 0.649399 | ||||||||
\(881\) | −31.3266 | −1.05542 | −0.527710 | − | 0.849425i | \(-0.676949\pi\) | ||||
−0.527710 | + | 0.849425i | \(0.676949\pi\) | |||||||
\(882\) | 21.6276 | 0.728238 | ||||||||
\(883\) | 50.9822 | 1.71569 | 0.857843 | − | 0.513912i | \(-0.171804\pi\) | ||||
0.857843 | + | 0.513912i | \(0.171804\pi\) | |||||||
\(884\) | 91.5665 | 3.07971 | ||||||||
\(885\) | −0.504692 | −0.0169650 | ||||||||
\(886\) | 105.191 | 3.53397 | ||||||||
\(887\) | −0.347598 | −0.0116712 | −0.00583560 | − | 0.999983i | \(-0.501858\pi\) | ||||
−0.00583560 | + | 0.999983i | \(0.501858\pi\) | |||||||
\(888\) | 10.3085 | 0.345931 | ||||||||
\(889\) | −14.9064 | −0.499944 | ||||||||
\(890\) | 110.192 | 3.69366 | ||||||||
\(891\) | −0.148526 | −0.00497579 | ||||||||
\(892\) | 117.712 | 3.94129 | ||||||||
\(893\) | 4.64170 | 0.155329 | ||||||||
\(894\) | −2.59236 | −0.0867016 | ||||||||
\(895\) | 14.9613 | 0.500100 | ||||||||
\(896\) | −157.256 | −5.25354 | ||||||||
\(897\) | 3.70995 | 0.123872 | ||||||||
\(898\) | 48.3127 | 1.61222 | ||||||||
\(899\) | 75.1747 | 2.50722 | ||||||||
\(900\) | −24.4537 | −0.815124 | ||||||||
\(901\) | 8.18816 | 0.272787 | ||||||||
\(902\) | −2.72072 | −0.0905900 | ||||||||
\(903\) | −13.5033 | −0.449362 | ||||||||
\(904\) | 128.050 | 4.25888 | ||||||||
\(905\) | −6.31732 | −0.209995 | ||||||||
\(906\) | 58.4613 | 1.94225 | ||||||||
\(907\) | 44.2098 | 1.46796 | 0.733982 | − | 0.679169i | \(-0.237660\pi\) | ||||
0.733982 | + | 0.679169i | \(0.237660\pi\) | |||||||
\(908\) | 74.1700 | 2.46142 | ||||||||
\(909\) | −28.6332 | −0.949704 | ||||||||
\(910\) | 121.570 | 4.03002 | ||||||||
\(911\) | 18.2971 | 0.606210 | 0.303105 | − | 0.952957i | \(-0.401977\pi\) | ||||
0.303105 | + | 0.952957i | \(0.401977\pi\) | |||||||
\(912\) | 20.6815 | 0.684834 | ||||||||
\(913\) | 4.07289 | 0.134793 | ||||||||
\(914\) | 9.41344 | 0.311369 | ||||||||
\(915\) | 25.4468 | 0.841244 | ||||||||
\(916\) | 11.9521 | 0.394908 | ||||||||
\(917\) | 30.5905 | 1.01019 | ||||||||
\(918\) | 47.3763 | 1.56365 | ||||||||
\(919\) | 22.8623 | 0.754156 | 0.377078 | − | 0.926181i | \(-0.376929\pi\) | ||||
0.377078 | + | 0.926181i | \(0.376929\pi\) | |||||||
\(920\) | 19.2373 | 0.634234 | ||||||||
\(921\) | −0.432842 | −0.0142626 | ||||||||
\(922\) | −35.1525 | −1.15769 | ||||||||
\(923\) | −18.0964 | −0.595651 | ||||||||
\(924\) | −8.71060 | −0.286558 | ||||||||
\(925\) | −2.30415 | −0.0757601 | ||||||||
\(926\) | −21.9665 | −0.721865 | ||||||||
\(927\) | 5.45448 | 0.179149 | ||||||||
\(928\) | 241.228 | 7.91869 | ||||||||
\(929\) | 17.8539 | 0.585767 | 0.292884 | − | 0.956148i | \(-0.405385\pi\) | ||||
0.292884 | + | 0.956148i | \(0.405385\pi\) | |||||||
\(930\) | −58.7316 | −1.92588 | ||||||||
\(931\) | 5.11435 | 0.167616 | ||||||||
\(932\) | 24.5341 | 0.803641 | ||||||||
\(933\) | 5.08283 | 0.166404 | ||||||||
\(934\) | 85.5403 | 2.79896 | ||||||||
\(935\) | 4.05067 | 0.132471 | ||||||||
\(936\) | 91.7788 | 2.99988 | ||||||||
\(937\) | −1.84611 | −0.0603099 | −0.0301549 | − | 0.999545i | \(-0.509600\pi\) | ||||
−0.0301549 | + | 0.999545i | \(0.509600\pi\) | |||||||
\(938\) | 35.3223 | 1.15331 | ||||||||
\(939\) | 3.73708 | 0.121955 | ||||||||
\(940\) | −56.4667 | −1.84174 | ||||||||
\(941\) | 3.09992 | 0.101055 | 0.0505273 | − | 0.998723i | \(-0.483910\pi\) | ||||
0.0505273 | + | 0.998723i | \(0.483910\pi\) | |||||||
\(942\) | 18.7997 | 0.612528 | ||||||||
\(943\) | −1.59857 | −0.0520565 | ||||||||
\(944\) | 2.84259 | 0.0925186 | ||||||||
\(945\) | 46.2955 | 1.50599 | ||||||||
\(946\) | −4.75706 | −0.154666 | ||||||||
\(947\) | 2.27193 | 0.0738278 | 0.0369139 | − | 0.999318i | \(-0.488247\pi\) | ||||
0.0369139 | + | 0.999318i | \(0.488247\pi\) | |||||||
\(948\) | −59.8711 | −1.94452 | ||||||||
\(949\) | 53.0249 | 1.72126 | ||||||||
\(950\) | −7.85673 | −0.254906 | ||||||||
\(951\) | −0.649507 | −0.0210617 | ||||||||
\(952\) | −110.068 | −3.56731 | ||||||||
\(953\) | −42.9917 | −1.39264 | −0.696319 | − | 0.717732i | \(-0.745180\pi\) | ||||
−0.696319 | + | 0.717732i | \(0.745180\pi\) | |||||||
\(954\) | 12.7970 | 0.414320 | ||||||||
\(955\) | −14.1087 | −0.456548 | ||||||||
\(956\) | −148.927 | −4.81665 | ||||||||
\(957\) | 4.66936 | 0.150939 | ||||||||
\(958\) | −48.5007 | −1.56699 | ||||||||
\(959\) | 27.0956 | 0.874962 | ||||||||
\(960\) | −98.2248 | −3.17019 | ||||||||
\(961\) | 25.8355 | 0.833403 | ||||||||
\(962\) | 13.4842 | 0.434749 | ||||||||
\(963\) | −34.6349 | −1.11609 | ||||||||
\(964\) | −54.8178 | −1.76556 | ||||||||
\(965\) | 0.686165 | 0.0220884 | ||||||||
\(966\) | −6.95359 | −0.223728 | ||||||||
\(967\) | −47.2081 | −1.51811 | −0.759055 | − | 0.651027i | \(-0.774339\pi\) | ||||
−0.759055 | + | 0.651027i | \(0.774339\pi\) | |||||||
\(968\) | 106.309 | 3.41690 | ||||||||
\(969\) | 4.34868 | 0.139700 | ||||||||
\(970\) | −0.0371028 | −0.00119130 | ||||||||
\(971\) | −3.38992 | −0.108788 | −0.0543939 | − | 0.998520i | \(-0.517323\pi\) | ||||
−0.0543939 | + | 0.998520i | \(0.517323\pi\) | |||||||
\(972\) | 87.8400 | 2.81747 | ||||||||
\(973\) | −62.2763 | −1.99649 | ||||||||
\(974\) | 105.499 | 3.38041 | ||||||||
\(975\) | 11.8213 | 0.378584 | ||||||||
\(976\) | −143.325 | −4.58771 | ||||||||
\(977\) | 51.0116 | 1.63200 | 0.816002 | − | 0.578049i | \(-0.196186\pi\) | ||||
0.816002 | + | 0.578049i | \(0.196186\pi\) | |||||||
\(978\) | 37.1950 | 1.18936 | ||||||||
\(979\) | −6.62346 | −0.211687 | ||||||||
\(980\) | −62.2166 | −1.98743 | ||||||||
\(981\) | 1.90326 | 0.0607664 | ||||||||
\(982\) | −13.5853 | −0.433525 | ||||||||
\(983\) | −41.2820 | −1.31669 | −0.658346 | − | 0.752716i | \(-0.728744\pi\) | ||||
−0.658346 | + | 0.752716i | \(0.728744\pi\) | |||||||
\(984\) | 22.7883 | 0.726464 | ||||||||
\(985\) | −44.5474 | −1.41940 | ||||||||
\(986\) | 91.9997 | 2.92987 | ||||||||
\(987\) | 13.0900 | 0.416660 | ||||||||
\(988\) | 33.8410 | 1.07662 | ||||||||
\(989\) | −2.79503 | −0.0888767 | ||||||||
\(990\) | 6.33068 | 0.201202 | ||||||||
\(991\) | 15.7928 | 0.501676 | 0.250838 | − | 0.968029i | \(-0.419294\pi\) | ||||
0.250838 | + | 0.968029i | \(0.419294\pi\) | |||||||
\(992\) | 182.379 | 5.79054 | ||||||||
\(993\) | 16.7759 | 0.532367 | ||||||||
\(994\) | 33.9183 | 1.07582 | ||||||||
\(995\) | −19.3823 | −0.614461 | ||||||||
\(996\) | −53.1923 | −1.68546 | ||||||||
\(997\) | −2.21630 | −0.0701908 | −0.0350954 | − | 0.999384i | \(-0.511174\pi\) | ||||
−0.0350954 | + | 0.999384i | \(0.511174\pi\) | |||||||
\(998\) | −101.360 | −3.20849 | ||||||||
\(999\) | 5.13496 | 0.162463 |
(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 | 4033.2.a.d.1.4 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.4 | ✓ | 79 | 1.1 | even | 1 | trivial |