Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, 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("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.254687 | −0.180091 | −0.0900455 | − | 0.995938i | \(-0.528701\pi\) | ||||
−0.0900455 | + | 0.995938i | \(0.528701\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.93513 | −0.967567 | ||||||||
\(5\) | −0.644426 | −0.288196 | −0.144098 | − | 0.989563i | \(-0.546028\pi\) | ||||
−0.144098 | + | 0.989563i | \(0.546028\pi\) | |||||||
\(6\) | 0.254687 | 0.103976 | ||||||||
\(7\) | 3.73934 | 1.41334 | 0.706669 | − | 0.707544i | \(-0.250197\pi\) | ||||
0.706669 | + | 0.707544i | \(0.250197\pi\) | |||||||
\(8\) | 1.00223 | 0.354341 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.164127 | 0.0519015 | ||||||||
\(11\) | −2.16169 | −0.651775 | −0.325887 | − | 0.945409i | \(-0.605663\pi\) | ||||
−0.325887 | + | 0.945409i | \(0.605663\pi\) | |||||||
\(12\) | 1.93513 | 0.558625 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −0.952363 | −0.254530 | ||||||||
\(15\) | 0.644426 | 0.166390 | ||||||||
\(16\) | 3.61501 | 0.903754 | ||||||||
\(17\) | 6.60210 | 1.60124 | 0.800622 | − | 0.599170i | \(-0.204503\pi\) | ||||
0.800622 | + | 0.599170i | \(0.204503\pi\) | |||||||
\(18\) | −0.254687 | −0.0600303 | ||||||||
\(19\) | 5.07149 | 1.16348 | 0.581740 | − | 0.813375i | \(-0.302372\pi\) | ||||
0.581740 | + | 0.813375i | \(0.302372\pi\) | |||||||
\(20\) | 1.24705 | 0.278849 | ||||||||
\(21\) | −3.73934 | −0.815991 | ||||||||
\(22\) | 0.550555 | 0.117379 | ||||||||
\(23\) | −1.31455 | −0.274103 | −0.137052 | − | 0.990564i | \(-0.543763\pi\) | ||||
−0.137052 | + | 0.990564i | \(0.543763\pi\) | |||||||
\(24\) | −1.00223 | −0.204579 | ||||||||
\(25\) | −4.58471 | −0.916943 | ||||||||
\(26\) | −0.254687 | −0.0499483 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −7.23613 | −1.36750 | ||||||||
\(29\) | 6.79091 | 1.26104 | 0.630520 | − | 0.776173i | \(-0.282842\pi\) | ||||
0.630520 | + | 0.776173i | \(0.282842\pi\) | |||||||
\(30\) | −0.164127 | −0.0299654 | ||||||||
\(31\) | −2.74661 | −0.493306 | −0.246653 | − | 0.969104i | \(-0.579331\pi\) | ||||
−0.246653 | + | 0.969104i | \(0.579331\pi\) | |||||||
\(32\) | −2.92515 | −0.517099 | ||||||||
\(33\) | 2.16169 | 0.376302 | ||||||||
\(34\) | −1.68147 | −0.288370 | ||||||||
\(35\) | −2.40973 | −0.407319 | ||||||||
\(36\) | −1.93513 | −0.322522 | ||||||||
\(37\) | −2.15149 | −0.353702 | −0.176851 | − | 0.984238i | \(-0.556591\pi\) | ||||
−0.176851 | + | 0.984238i | \(0.556591\pi\) | |||||||
\(38\) | −1.29164 | −0.209532 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −0.645862 | −0.102120 | ||||||||
\(41\) | 1.71235 | 0.267424 | 0.133712 | − | 0.991020i | \(-0.457310\pi\) | ||||
0.133712 | + | 0.991020i | \(0.457310\pi\) | |||||||
\(42\) | 0.952363 | 0.146953 | ||||||||
\(43\) | 6.80465 | 1.03770 | 0.518850 | − | 0.854866i | \(-0.326360\pi\) | ||||
0.518850 | + | 0.854866i | \(0.326360\pi\) | |||||||
\(44\) | 4.18316 | 0.630636 | ||||||||
\(45\) | −0.644426 | −0.0960654 | ||||||||
\(46\) | 0.334800 | 0.0493635 | ||||||||
\(47\) | 4.86401 | 0.709488 | 0.354744 | − | 0.934963i | \(-0.384568\pi\) | ||||
0.354744 | + | 0.934963i | \(0.384568\pi\) | |||||||
\(48\) | −3.61501 | −0.521782 | ||||||||
\(49\) | 6.98268 | 0.997526 | ||||||||
\(50\) | 1.16767 | 0.165133 | ||||||||
\(51\) | −6.60210 | −0.924478 | ||||||||
\(52\) | −1.93513 | −0.268355 | ||||||||
\(53\) | 1.28229 | 0.176136 | 0.0880681 | − | 0.996114i | \(-0.471931\pi\) | ||||
0.0880681 | + | 0.996114i | \(0.471931\pi\) | |||||||
\(54\) | 0.254687 | 0.0346585 | ||||||||
\(55\) | 1.39305 | 0.187839 | ||||||||
\(56\) | 3.74767 | 0.500804 | ||||||||
\(57\) | −5.07149 | −0.671735 | ||||||||
\(58\) | −1.72956 | −0.227102 | ||||||||
\(59\) | 4.33667 | 0.564587 | 0.282293 | − | 0.959328i | \(-0.408905\pi\) | ||||
0.282293 | + | 0.959328i | \(0.408905\pi\) | |||||||
\(60\) | −1.24705 | −0.160994 | ||||||||
\(61\) | −9.11013 | −1.16643 | −0.583217 | − | 0.812317i | \(-0.698206\pi\) | ||||
−0.583217 | + | 0.812317i | \(0.698206\pi\) | |||||||
\(62\) | 0.699527 | 0.0888400 | ||||||||
\(63\) | 3.73934 | 0.471113 | ||||||||
\(64\) | −6.48503 | −0.810629 | ||||||||
\(65\) | −0.644426 | −0.0799312 | ||||||||
\(66\) | −0.550555 | −0.0677687 | ||||||||
\(67\) | −10.0994 | −1.23384 | −0.616920 | − | 0.787026i | \(-0.711620\pi\) | ||||
−0.616920 | + | 0.787026i | \(0.711620\pi\) | |||||||
\(68\) | −12.7759 | −1.54931 | ||||||||
\(69\) | 1.31455 | 0.158254 | ||||||||
\(70\) | 0.613727 | 0.0733544 | ||||||||
\(71\) | 1.97915 | 0.234882 | 0.117441 | − | 0.993080i | \(-0.462531\pi\) | ||||
0.117441 | + | 0.993080i | \(0.462531\pi\) | |||||||
\(72\) | 1.00223 | 0.118114 | ||||||||
\(73\) | −10.0930 | −1.18129 | −0.590647 | − | 0.806930i | \(-0.701127\pi\) | ||||
−0.590647 | + | 0.806930i | \(0.701127\pi\) | |||||||
\(74\) | 0.547956 | 0.0636986 | ||||||||
\(75\) | 4.58471 | 0.529397 | ||||||||
\(76\) | −9.81401 | −1.12574 | ||||||||
\(77\) | −8.08331 | −0.921178 | ||||||||
\(78\) | 0.254687 | 0.0288376 | ||||||||
\(79\) | −11.7940 | −1.32693 | −0.663463 | − | 0.748209i | \(-0.730914\pi\) | ||||
−0.663463 | + | 0.748209i | \(0.730914\pi\) | |||||||
\(80\) | −2.32961 | −0.260458 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.436113 | −0.0481606 | ||||||||
\(83\) | 11.9265 | 1.30910 | 0.654552 | − | 0.756017i | \(-0.272857\pi\) | ||||
0.654552 | + | 0.756017i | \(0.272857\pi\) | |||||||
\(84\) | 7.23613 | 0.789527 | ||||||||
\(85\) | −4.25456 | −0.461472 | ||||||||
\(86\) | −1.73306 | −0.186880 | ||||||||
\(87\) | −6.79091 | −0.728062 | ||||||||
\(88\) | −2.16651 | −0.230951 | ||||||||
\(89\) | −7.92637 | −0.840193 | −0.420097 | − | 0.907479i | \(-0.638004\pi\) | ||||
−0.420097 | + | 0.907479i | \(0.638004\pi\) | |||||||
\(90\) | 0.164127 | 0.0173005 | ||||||||
\(91\) | 3.73934 | 0.391990 | ||||||||
\(92\) | 2.54384 | 0.265213 | ||||||||
\(93\) | 2.74661 | 0.284811 | ||||||||
\(94\) | −1.23880 | −0.127772 | ||||||||
\(95\) | −3.26820 | −0.335310 | ||||||||
\(96\) | 2.92515 | 0.298547 | ||||||||
\(97\) | 13.9493 | 1.41634 | 0.708170 | − | 0.706042i | \(-0.249521\pi\) | ||||
0.708170 | + | 0.706042i | \(0.249521\pi\) | |||||||
\(98\) | −1.77840 | −0.179645 | ||||||||
\(99\) | −2.16169 | −0.217258 | ||||||||
\(100\) | 8.87204 | 0.887204 | ||||||||
\(101\) | −4.53003 | −0.450754 | −0.225377 | − | 0.974272i | \(-0.572361\pi\) | ||||
−0.225377 | + | 0.974272i | \(0.572361\pi\) | |||||||
\(102\) | 1.68147 | 0.166490 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 1.00223 | 0.0982766 | ||||||||
\(105\) | 2.40973 | 0.235166 | ||||||||
\(106\) | −0.326583 | −0.0317205 | ||||||||
\(107\) | −9.63958 | −0.931893 | −0.465946 | − | 0.884813i | \(-0.654286\pi\) | ||||
−0.465946 | + | 0.884813i | \(0.654286\pi\) | |||||||
\(108\) | 1.93513 | 0.186208 | ||||||||
\(109\) | 6.50575 | 0.623138 | 0.311569 | − | 0.950223i | \(-0.399145\pi\) | ||||
0.311569 | + | 0.950223i | \(0.399145\pi\) | |||||||
\(110\) | −0.354792 | −0.0338281 | ||||||||
\(111\) | 2.15149 | 0.204210 | ||||||||
\(112\) | 13.5178 | 1.27731 | ||||||||
\(113\) | 14.2418 | 1.33976 | 0.669878 | − | 0.742472i | \(-0.266347\pi\) | ||||
0.669878 | + | 0.742472i | \(0.266347\pi\) | |||||||
\(114\) | 1.29164 | 0.120973 | ||||||||
\(115\) | 0.847132 | 0.0789955 | ||||||||
\(116\) | −13.1413 | −1.22014 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −1.10450 | −0.101677 | ||||||||
\(119\) | 24.6875 | 2.26310 | ||||||||
\(120\) | 0.645862 | 0.0589589 | ||||||||
\(121\) | −6.32709 | −0.575190 | ||||||||
\(122\) | 2.32023 | 0.210064 | ||||||||
\(123\) | −1.71235 | −0.154397 | ||||||||
\(124\) | 5.31507 | 0.477307 | ||||||||
\(125\) | 6.17664 | 0.552456 | ||||||||
\(126\) | −0.952363 | −0.0848432 | ||||||||
\(127\) | −5.59992 | −0.496913 | −0.248456 | − | 0.968643i | \(-0.579923\pi\) | ||||
−0.248456 | + | 0.968643i | \(0.579923\pi\) | |||||||
\(128\) | 7.50196 | 0.663086 | ||||||||
\(129\) | −6.80465 | −0.599116 | ||||||||
\(130\) | 0.164127 | 0.0143949 | ||||||||
\(131\) | 10.0378 | 0.877003 | 0.438501 | − | 0.898731i | \(-0.355509\pi\) | ||||
0.438501 | + | 0.898731i | \(0.355509\pi\) | |||||||
\(132\) | −4.18316 | −0.364098 | ||||||||
\(133\) | 18.9640 | 1.64439 | ||||||||
\(134\) | 2.57219 | 0.222204 | ||||||||
\(135\) | 0.644426 | 0.0554634 | ||||||||
\(136\) | 6.61681 | 0.567387 | ||||||||
\(137\) | 5.55075 | 0.474233 | 0.237116 | − | 0.971481i | \(-0.423798\pi\) | ||||
0.237116 | + | 0.971481i | \(0.423798\pi\) | |||||||
\(138\) | −0.334800 | −0.0285001 | ||||||||
\(139\) | 8.74256 | 0.741534 | 0.370767 | − | 0.928726i | \(-0.379095\pi\) | ||||
0.370767 | + | 0.928726i | \(0.379095\pi\) | |||||||
\(140\) | 4.66315 | 0.394108 | ||||||||
\(141\) | −4.86401 | −0.409623 | ||||||||
\(142\) | −0.504064 | −0.0423001 | ||||||||
\(143\) | −2.16169 | −0.180770 | ||||||||
\(144\) | 3.61501 | 0.301251 | ||||||||
\(145\) | −4.37624 | −0.363427 | ||||||||
\(146\) | 2.57055 | 0.212740 | ||||||||
\(147\) | −6.98268 | −0.575922 | ||||||||
\(148\) | 4.16342 | 0.342231 | ||||||||
\(149\) | 10.0949 | 0.827003 | 0.413501 | − | 0.910504i | \(-0.364306\pi\) | ||||
0.413501 | + | 0.910504i | \(0.364306\pi\) | |||||||
\(150\) | −1.16767 | −0.0953397 | ||||||||
\(151\) | 0.629840 | 0.0512557 | 0.0256278 | − | 0.999672i | \(-0.491842\pi\) | ||||
0.0256278 | + | 0.999672i | \(0.491842\pi\) | |||||||
\(152\) | 5.08279 | 0.412269 | ||||||||
\(153\) | 6.60210 | 0.533748 | ||||||||
\(154\) | 2.05871 | 0.165896 | ||||||||
\(155\) | 1.76999 | 0.142169 | ||||||||
\(156\) | 1.93513 | 0.154935 | ||||||||
\(157\) | 2.57454 | 0.205471 | 0.102735 | − | 0.994709i | \(-0.467241\pi\) | ||||
0.102735 | + | 0.994709i | \(0.467241\pi\) | |||||||
\(158\) | 3.00377 | 0.238967 | ||||||||
\(159\) | −1.28229 | −0.101692 | ||||||||
\(160\) | 1.88505 | 0.149026 | ||||||||
\(161\) | −4.91556 | −0.387401 | ||||||||
\(162\) | −0.254687 | −0.0200101 | ||||||||
\(163\) | −8.11253 | −0.635422 | −0.317711 | − | 0.948188i | \(-0.602914\pi\) | ||||
−0.317711 | + | 0.948188i | \(0.602914\pi\) | |||||||
\(164\) | −3.31362 | −0.258751 | ||||||||
\(165\) | −1.39305 | −0.108449 | ||||||||
\(166\) | −3.03753 | −0.235758 | ||||||||
\(167\) | 14.8223 | 1.14698 | 0.573490 | − | 0.819212i | \(-0.305589\pi\) | ||||
0.573490 | + | 0.819212i | \(0.305589\pi\) | |||||||
\(168\) | −3.74767 | −0.289139 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 1.08358 | 0.0831070 | ||||||||
\(171\) | 5.07149 | 0.387827 | ||||||||
\(172\) | −13.1679 | −1.00404 | ||||||||
\(173\) | −5.58518 | −0.424634 | −0.212317 | − | 0.977201i | \(-0.568101\pi\) | ||||
−0.212317 | + | 0.977201i | \(0.568101\pi\) | |||||||
\(174\) | 1.72956 | 0.131117 | ||||||||
\(175\) | −17.1438 | −1.29595 | ||||||||
\(176\) | −7.81455 | −0.589044 | ||||||||
\(177\) | −4.33667 | −0.325964 | ||||||||
\(178\) | 2.01874 | 0.151311 | ||||||||
\(179\) | −6.51826 | −0.487197 | −0.243599 | − | 0.969876i | \(-0.578328\pi\) | ||||
−0.243599 | + | 0.969876i | \(0.578328\pi\) | |||||||
\(180\) | 1.24705 | 0.0929497 | ||||||||
\(181\) | 5.43008 | 0.403615 | 0.201807 | − | 0.979425i | \(-0.435319\pi\) | ||||
0.201807 | + | 0.979425i | \(0.435319\pi\) | |||||||
\(182\) | −0.952363 | −0.0705938 | ||||||||
\(183\) | 9.11013 | 0.673440 | ||||||||
\(184\) | −1.31748 | −0.0971261 | ||||||||
\(185\) | 1.38647 | 0.101936 | ||||||||
\(186\) | −0.699527 | −0.0512918 | ||||||||
\(187\) | −14.2717 | −1.04365 | ||||||||
\(188\) | −9.41251 | −0.686478 | ||||||||
\(189\) | −3.73934 | −0.271997 | ||||||||
\(190\) | 0.832369 | 0.0603864 | ||||||||
\(191\) | 18.9436 | 1.37071 | 0.685354 | − | 0.728210i | \(-0.259647\pi\) | ||||
0.685354 | + | 0.728210i | \(0.259647\pi\) | |||||||
\(192\) | 6.48503 | 0.468017 | ||||||||
\(193\) | 3.56540 | 0.256643 | 0.128322 | − | 0.991733i | \(-0.459041\pi\) | ||||
0.128322 | + | 0.991733i | \(0.459041\pi\) | |||||||
\(194\) | −3.55271 | −0.255070 | ||||||||
\(195\) | 0.644426 | 0.0461483 | ||||||||
\(196\) | −13.5124 | −0.965173 | ||||||||
\(197\) | −10.2323 | −0.729024 | −0.364512 | − | 0.931199i | \(-0.618764\pi\) | ||||
−0.364512 | + | 0.931199i | \(0.618764\pi\) | |||||||
\(198\) | 0.550555 | 0.0391263 | ||||||||
\(199\) | 24.0522 | 1.70502 | 0.852509 | − | 0.522713i | \(-0.175080\pi\) | ||||
0.852509 | + | 0.522713i | \(0.175080\pi\) | |||||||
\(200\) | −4.59493 | −0.324911 | ||||||||
\(201\) | 10.0994 | 0.712358 | ||||||||
\(202\) | 1.15374 | 0.0811768 | ||||||||
\(203\) | 25.3935 | 1.78228 | ||||||||
\(204\) | 12.7759 | 0.894495 | ||||||||
\(205\) | −1.10348 | −0.0770705 | ||||||||
\(206\) | 0.254687 | 0.0177449 | ||||||||
\(207\) | −1.31455 | −0.0913678 | ||||||||
\(208\) | 3.61501 | 0.250656 | ||||||||
\(209\) | −10.9630 | −0.758326 | ||||||||
\(210\) | −0.613727 | −0.0423512 | ||||||||
\(211\) | 11.5341 | 0.794041 | 0.397020 | − | 0.917810i | \(-0.370044\pi\) | ||||
0.397020 | + | 0.917810i | \(0.370044\pi\) | |||||||
\(212\) | −2.48140 | −0.170424 | ||||||||
\(213\) | −1.97915 | −0.135609 | ||||||||
\(214\) | 2.45508 | 0.167826 | ||||||||
\(215\) | −4.38509 | −0.299061 | ||||||||
\(216\) | −1.00223 | −0.0681930 | ||||||||
\(217\) | −10.2705 | −0.697209 | ||||||||
\(218\) | −1.65693 | −0.112222 | ||||||||
\(219\) | 10.0930 | 0.682020 | ||||||||
\(220\) | −2.69574 | −0.181747 | ||||||||
\(221\) | 6.60210 | 0.444105 | ||||||||
\(222\) | −0.547956 | −0.0367764 | ||||||||
\(223\) | 24.6702 | 1.65204 | 0.826018 | − | 0.563644i | \(-0.190601\pi\) | ||||
0.826018 | + | 0.563644i | \(0.190601\pi\) | |||||||
\(224\) | −10.9382 | −0.730836 | ||||||||
\(225\) | −4.58471 | −0.305648 | ||||||||
\(226\) | −3.62720 | −0.241278 | ||||||||
\(227\) | −20.4670 | −1.35845 | −0.679223 | − | 0.733932i | \(-0.737683\pi\) | ||||
−0.679223 | + | 0.733932i | \(0.737683\pi\) | |||||||
\(228\) | 9.81401 | 0.649949 | ||||||||
\(229\) | 2.02798 | 0.134013 | 0.0670063 | − | 0.997753i | \(-0.478655\pi\) | ||||
0.0670063 | + | 0.997753i | \(0.478655\pi\) | |||||||
\(230\) | −0.215754 | −0.0142264 | ||||||||
\(231\) | 8.08331 | 0.531842 | ||||||||
\(232\) | 6.80604 | 0.446839 | ||||||||
\(233\) | −4.31964 | −0.282989 | −0.141494 | − | 0.989939i | \(-0.545191\pi\) | ||||
−0.141494 | + | 0.989939i | \(0.545191\pi\) | |||||||
\(234\) | −0.254687 | −0.0166494 | ||||||||
\(235\) | −3.13449 | −0.204472 | ||||||||
\(236\) | −8.39205 | −0.546276 | ||||||||
\(237\) | 11.7940 | 0.766101 | ||||||||
\(238\) | −6.28759 | −0.407564 | ||||||||
\(239\) | −4.38877 | −0.283886 | −0.141943 | − | 0.989875i | \(-0.545335\pi\) | ||||
−0.141943 | + | 0.989875i | \(0.545335\pi\) | |||||||
\(240\) | 2.32961 | 0.150376 | ||||||||
\(241\) | 18.4681 | 1.18963 | 0.594817 | − | 0.803861i | \(-0.297225\pi\) | ||||
0.594817 | + | 0.803861i | \(0.297225\pi\) | |||||||
\(242\) | 1.61143 | 0.103587 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 17.6293 | 1.12860 | ||||||||
\(245\) | −4.49982 | −0.287483 | ||||||||
\(246\) | 0.436113 | 0.0278056 | ||||||||
\(247\) | 5.07149 | 0.322691 | ||||||||
\(248\) | −2.75273 | −0.174799 | ||||||||
\(249\) | −11.9265 | −0.755811 | ||||||||
\(250\) | −1.57311 | −0.0994923 | ||||||||
\(251\) | −11.2714 | −0.711446 | −0.355723 | − | 0.934592i | \(-0.615765\pi\) | ||||
−0.355723 | + | 0.934592i | \(0.615765\pi\) | |||||||
\(252\) | −7.23613 | −0.455833 | ||||||||
\(253\) | 2.84166 | 0.178654 | ||||||||
\(254\) | 1.42623 | 0.0894896 | ||||||||
\(255\) | 4.25456 | 0.266431 | ||||||||
\(256\) | 11.0594 | 0.691213 | ||||||||
\(257\) | 14.3567 | 0.895547 | 0.447774 | − | 0.894147i | \(-0.352217\pi\) | ||||
0.447774 | + | 0.894147i | \(0.352217\pi\) | |||||||
\(258\) | 1.73306 | 0.107895 | ||||||||
\(259\) | −8.04515 | −0.499901 | ||||||||
\(260\) | 1.24705 | 0.0773388 | ||||||||
\(261\) | 6.79091 | 0.420347 | ||||||||
\(262\) | −2.55649 | −0.157940 | ||||||||
\(263\) | 18.9401 | 1.16789 | 0.583947 | − | 0.811792i | \(-0.301508\pi\) | ||||
0.583947 | + | 0.811792i | \(0.301508\pi\) | |||||||
\(264\) | 2.16651 | 0.133339 | ||||||||
\(265\) | −0.826342 | −0.0507618 | ||||||||
\(266\) | −4.82990 | −0.296140 | ||||||||
\(267\) | 7.92637 | 0.485086 | ||||||||
\(268\) | 19.5437 | 1.19382 | ||||||||
\(269\) | 26.4369 | 1.61189 | 0.805945 | − | 0.591991i | \(-0.201658\pi\) | ||||
0.805945 | + | 0.591991i | \(0.201658\pi\) | |||||||
\(270\) | −0.164127 | −0.00998846 | ||||||||
\(271\) | −15.6578 | −0.951142 | −0.475571 | − | 0.879677i | \(-0.657759\pi\) | ||||
−0.475571 | + | 0.879677i | \(0.657759\pi\) | |||||||
\(272\) | 23.8667 | 1.44713 | ||||||||
\(273\) | −3.73934 | −0.226315 | ||||||||
\(274\) | −1.41370 | −0.0854050 | ||||||||
\(275\) | 9.91074 | 0.597640 | ||||||||
\(276\) | −2.54384 | −0.153121 | ||||||||
\(277\) | 0.0438679 | 0.00263577 | 0.00131788 | − | 0.999999i | \(-0.499581\pi\) | ||||
0.00131788 | + | 0.999999i | \(0.499581\pi\) | |||||||
\(278\) | −2.22662 | −0.133544 | ||||||||
\(279\) | −2.74661 | −0.164435 | ||||||||
\(280\) | −2.41510 | −0.144330 | ||||||||
\(281\) | −8.85075 | −0.527991 | −0.263996 | − | 0.964524i | \(-0.585040\pi\) | ||||
−0.263996 | + | 0.964524i | \(0.585040\pi\) | |||||||
\(282\) | 1.23880 | 0.0737695 | ||||||||
\(283\) | −0.731884 | −0.0435060 | −0.0217530 | − | 0.999763i | \(-0.506925\pi\) | ||||
−0.0217530 | + | 0.999763i | \(0.506925\pi\) | |||||||
\(284\) | −3.82992 | −0.227264 | ||||||||
\(285\) | 3.26820 | 0.193592 | ||||||||
\(286\) | 0.550555 | 0.0325550 | ||||||||
\(287\) | 6.40306 | 0.377961 | ||||||||
\(288\) | −2.92515 | −0.172366 | ||||||||
\(289\) | 26.5877 | 1.56398 | ||||||||
\(290\) | 1.11457 | 0.0654499 | ||||||||
\(291\) | −13.9493 | −0.817724 | ||||||||
\(292\) | 19.5313 | 1.14298 | ||||||||
\(293\) | −17.4078 | −1.01698 | −0.508488 | − | 0.861069i | \(-0.669795\pi\) | ||||
−0.508488 | + | 0.861069i | \(0.669795\pi\) | |||||||
\(294\) | 1.77840 | 0.103718 | ||||||||
\(295\) | −2.79467 | −0.162712 | ||||||||
\(296\) | −2.15628 | −0.125331 | ||||||||
\(297\) | 2.16169 | 0.125434 | ||||||||
\(298\) | −2.57103 | −0.148936 | ||||||||
\(299\) | −1.31455 | −0.0760226 | ||||||||
\(300\) | −8.87204 | −0.512227 | ||||||||
\(301\) | 25.4449 | 1.46662 | ||||||||
\(302\) | −0.160412 | −0.00923069 | ||||||||
\(303\) | 4.53003 | 0.260243 | ||||||||
\(304\) | 18.3335 | 1.05150 | ||||||||
\(305\) | 5.87081 | 0.336161 | ||||||||
\(306\) | −1.68147 | −0.0961232 | ||||||||
\(307\) | 6.42085 | 0.366457 | 0.183229 | − | 0.983070i | \(-0.441345\pi\) | ||||
0.183229 | + | 0.983070i | \(0.441345\pi\) | |||||||
\(308\) | 15.6423 | 0.891302 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −0.450794 | −0.0256034 | ||||||||
\(311\) | 21.8263 | 1.23766 | 0.618828 | − | 0.785527i | \(-0.287608\pi\) | ||||
0.618828 | + | 0.785527i | \(0.287608\pi\) | |||||||
\(312\) | −1.00223 | −0.0567400 | ||||||||
\(313\) | −26.9981 | −1.52602 | −0.763012 | − | 0.646384i | \(-0.776280\pi\) | ||||
−0.763012 | + | 0.646384i | \(0.776280\pi\) | |||||||
\(314\) | −0.655702 | −0.0370034 | ||||||||
\(315\) | −2.40973 | −0.135773 | ||||||||
\(316\) | 22.8229 | 1.28389 | ||||||||
\(317\) | −29.5618 | −1.66036 | −0.830178 | − | 0.557498i | \(-0.811761\pi\) | ||||
−0.830178 | + | 0.557498i | \(0.811761\pi\) | |||||||
\(318\) | 0.326583 | 0.0183139 | ||||||||
\(319\) | −14.6799 | −0.821914 | ||||||||
\(320\) | 4.17912 | 0.233620 | ||||||||
\(321\) | 9.63958 | 0.538029 | ||||||||
\(322\) | 1.25193 | 0.0697674 | ||||||||
\(323\) | 33.4825 | 1.86301 | ||||||||
\(324\) | −1.93513 | −0.107507 | ||||||||
\(325\) | −4.58471 | −0.254314 | ||||||||
\(326\) | 2.06616 | 0.114434 | ||||||||
\(327\) | −6.50575 | −0.359769 | ||||||||
\(328\) | 1.71616 | 0.0947593 | ||||||||
\(329\) | 18.1882 | 1.00275 | ||||||||
\(330\) | 0.354792 | 0.0195307 | ||||||||
\(331\) | 3.54256 | 0.194716 | 0.0973582 | − | 0.995249i | \(-0.468961\pi\) | ||||
0.0973582 | + | 0.995249i | \(0.468961\pi\) | |||||||
\(332\) | −23.0794 | −1.26665 | ||||||||
\(333\) | −2.15149 | −0.117901 | ||||||||
\(334\) | −3.77504 | −0.206561 | ||||||||
\(335\) | 6.50833 | 0.355588 | ||||||||
\(336\) | −13.5178 | −0.737455 | ||||||||
\(337\) | −17.6455 | −0.961214 | −0.480607 | − | 0.876936i | \(-0.659584\pi\) | ||||
−0.480607 | + | 0.876936i | \(0.659584\pi\) | |||||||
\(338\) | −0.254687 | −0.0138532 | ||||||||
\(339\) | −14.2418 | −0.773508 | ||||||||
\(340\) | 8.23315 | 0.446505 | ||||||||
\(341\) | 5.93733 | 0.321525 | ||||||||
\(342\) | −1.29164 | −0.0698441 | ||||||||
\(343\) | −0.0647594 | −0.00349668 | ||||||||
\(344\) | 6.81981 | 0.367700 | ||||||||
\(345\) | −0.847132 | −0.0456081 | ||||||||
\(346\) | 1.42247 | 0.0764727 | ||||||||
\(347\) | 21.9422 | 1.17792 | 0.588959 | − | 0.808163i | \(-0.299538\pi\) | ||||
0.588959 | + | 0.808163i | \(0.299538\pi\) | |||||||
\(348\) | 13.1413 | 0.704449 | ||||||||
\(349\) | 15.6683 | 0.838703 | 0.419351 | − | 0.907824i | \(-0.362258\pi\) | ||||
0.419351 | + | 0.907824i | \(0.362258\pi\) | |||||||
\(350\) | 4.36631 | 0.233389 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 6.32328 | 0.337032 | ||||||||
\(353\) | 23.1715 | 1.23330 | 0.616648 | − | 0.787239i | \(-0.288490\pi\) | ||||
0.616648 | + | 0.787239i | \(0.288490\pi\) | |||||||
\(354\) | 1.10450 | 0.0587033 | ||||||||
\(355\) | −1.27542 | −0.0676920 | ||||||||
\(356\) | 15.3386 | 0.812943 | ||||||||
\(357\) | −24.6875 | −1.30660 | ||||||||
\(358\) | 1.66012 | 0.0877399 | ||||||||
\(359\) | 26.0955 | 1.37727 | 0.688635 | − | 0.725109i | \(-0.258210\pi\) | ||||
0.688635 | + | 0.725109i | \(0.258210\pi\) | |||||||
\(360\) | −0.645862 | −0.0340399 | ||||||||
\(361\) | 6.72001 | 0.353685 | ||||||||
\(362\) | −1.38297 | −0.0726874 | ||||||||
\(363\) | 6.32709 | 0.332086 | ||||||||
\(364\) | −7.23613 | −0.379276 | ||||||||
\(365\) | 6.50418 | 0.340444 | ||||||||
\(366\) | −2.32023 | −0.121281 | ||||||||
\(367\) | 15.3892 | 0.803310 | 0.401655 | − | 0.915791i | \(-0.368435\pi\) | ||||
0.401655 | + | 0.915791i | \(0.368435\pi\) | |||||||
\(368\) | −4.75213 | −0.247722 | ||||||||
\(369\) | 1.71235 | 0.0891413 | ||||||||
\(370\) | −0.353117 | −0.0183577 | ||||||||
\(371\) | 4.79492 | 0.248940 | ||||||||
\(372\) | −5.31507 | −0.275573 | ||||||||
\(373\) | −15.1942 | −0.786724 | −0.393362 | − | 0.919384i | \(-0.628688\pi\) | ||||
−0.393362 | + | 0.919384i | \(0.628688\pi\) | |||||||
\(374\) | 3.63482 | 0.187952 | ||||||||
\(375\) | −6.17664 | −0.318960 | ||||||||
\(376\) | 4.87485 | 0.251401 | ||||||||
\(377\) | 6.79091 | 0.349750 | ||||||||
\(378\) | 0.952363 | 0.0489842 | ||||||||
\(379\) | −10.8656 | −0.558126 | −0.279063 | − | 0.960273i | \(-0.590024\pi\) | ||||
−0.279063 | + | 0.960273i | \(0.590024\pi\) | |||||||
\(380\) | 6.32441 | 0.324435 | ||||||||
\(381\) | 5.59992 | 0.286893 | ||||||||
\(382\) | −4.82468 | −0.246852 | ||||||||
\(383\) | 7.53663 | 0.385104 | 0.192552 | − | 0.981287i | \(-0.438324\pi\) | ||||
0.192552 | + | 0.981287i | \(0.438324\pi\) | |||||||
\(384\) | −7.50196 | −0.382833 | ||||||||
\(385\) | 5.20909 | 0.265480 | ||||||||
\(386\) | −0.908062 | −0.0462192 | ||||||||
\(387\) | 6.80465 | 0.345900 | ||||||||
\(388\) | −26.9938 | −1.37040 | ||||||||
\(389\) | 4.82746 | 0.244762 | 0.122381 | − | 0.992483i | \(-0.460947\pi\) | ||||
0.122381 | + | 0.992483i | \(0.460947\pi\) | |||||||
\(390\) | −0.164127 | −0.00831090 | ||||||||
\(391\) | −8.67881 | −0.438906 | ||||||||
\(392\) | 6.99824 | 0.353465 | ||||||||
\(393\) | −10.0378 | −0.506338 | ||||||||
\(394\) | 2.60604 | 0.131291 | ||||||||
\(395\) | 7.60035 | 0.382415 | ||||||||
\(396\) | 4.18316 | 0.210212 | ||||||||
\(397\) | −13.3155 | −0.668285 | −0.334142 | − | 0.942523i | \(-0.608447\pi\) | ||||
−0.334142 | + | 0.942523i | \(0.608447\pi\) | |||||||
\(398\) | −6.12580 | −0.307058 | ||||||||
\(399\) | −18.9640 | −0.949389 | ||||||||
\(400\) | −16.5738 | −0.828690 | ||||||||
\(401\) | −16.9664 | −0.847261 | −0.423630 | − | 0.905835i | \(-0.639244\pi\) | ||||
−0.423630 | + | 0.905835i | \(0.639244\pi\) | |||||||
\(402\) | −2.57219 | −0.128289 | ||||||||
\(403\) | −2.74661 | −0.136819 | ||||||||
\(404\) | 8.76621 | 0.436135 | ||||||||
\(405\) | −0.644426 | −0.0320218 | ||||||||
\(406\) | −6.46741 | −0.320972 | ||||||||
\(407\) | 4.65085 | 0.230534 | ||||||||
\(408\) | −6.61681 | −0.327581 | ||||||||
\(409\) | 7.28698 | 0.360318 | 0.180159 | − | 0.983638i | \(-0.442339\pi\) | ||||
0.180159 | + | 0.983638i | \(0.442339\pi\) | |||||||
\(410\) | 0.281043 | 0.0138797 | ||||||||
\(411\) | −5.55075 | −0.273798 | ||||||||
\(412\) | 1.93513 | 0.0953372 | ||||||||
\(413\) | 16.2163 | 0.797953 | ||||||||
\(414\) | 0.334800 | 0.0164545 | ||||||||
\(415\) | −7.68575 | −0.377279 | ||||||||
\(416\) | −2.92515 | −0.143417 | ||||||||
\(417\) | −8.74256 | −0.428125 | ||||||||
\(418\) | 2.79214 | 0.136568 | ||||||||
\(419\) | 31.9297 | 1.55987 | 0.779935 | − | 0.625861i | \(-0.215252\pi\) | ||||
0.779935 | + | 0.625861i | \(0.215252\pi\) | |||||||
\(420\) | −4.66315 | −0.227538 | ||||||||
\(421\) | 25.2163 | 1.22897 | 0.614484 | − | 0.788929i | \(-0.289364\pi\) | ||||
0.614484 | + | 0.788929i | \(0.289364\pi\) | |||||||
\(422\) | −2.93759 | −0.143000 | ||||||||
\(423\) | 4.86401 | 0.236496 | ||||||||
\(424\) | 1.28515 | 0.0624123 | ||||||||
\(425\) | −30.2687 | −1.46825 | ||||||||
\(426\) | 0.504064 | 0.0244220 | ||||||||
\(427\) | −34.0659 | −1.64856 | ||||||||
\(428\) | 18.6539 | 0.901669 | ||||||||
\(429\) | 2.16169 | 0.104367 | ||||||||
\(430\) | 1.11683 | 0.0538582 | ||||||||
\(431\) | 28.1693 | 1.35687 | 0.678434 | − | 0.734661i | \(-0.262659\pi\) | ||||
0.678434 | + | 0.734661i | \(0.262659\pi\) | |||||||
\(432\) | −3.61501 | −0.173927 | ||||||||
\(433\) | 14.6452 | 0.703805 | 0.351903 | − | 0.936037i | \(-0.385535\pi\) | ||||
0.351903 | + | 0.936037i | \(0.385535\pi\) | |||||||
\(434\) | 2.61577 | 0.125561 | ||||||||
\(435\) | 4.37624 | 0.209825 | ||||||||
\(436\) | −12.5895 | −0.602928 | ||||||||
\(437\) | −6.66674 | −0.318914 | ||||||||
\(438\) | −2.57055 | −0.122826 | ||||||||
\(439\) | −27.9316 | −1.33310 | −0.666550 | − | 0.745460i | \(-0.732230\pi\) | ||||
−0.666550 | + | 0.745460i | \(0.732230\pi\) | |||||||
\(440\) | 1.39615 | 0.0665591 | ||||||||
\(441\) | 6.98268 | 0.332509 | ||||||||
\(442\) | −1.68147 | −0.0799793 | ||||||||
\(443\) | −8.49135 | −0.403436 | −0.201718 | − | 0.979444i | \(-0.564653\pi\) | ||||
−0.201718 | + | 0.979444i | \(0.564653\pi\) | |||||||
\(444\) | −4.16342 | −0.197587 | ||||||||
\(445\) | 5.10796 | 0.242140 | ||||||||
\(446\) | −6.28317 | −0.297517 | ||||||||
\(447\) | −10.0949 | −0.477470 | ||||||||
\(448\) | −24.2497 | −1.14569 | ||||||||
\(449\) | −7.50853 | −0.354350 | −0.177175 | − | 0.984179i | \(-0.556696\pi\) | ||||
−0.177175 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(450\) | 1.16767 | 0.0550444 | ||||||||
\(451\) | −3.70157 | −0.174300 | ||||||||
\(452\) | −27.5598 | −1.29630 | ||||||||
\(453\) | −0.629840 | −0.0295925 | ||||||||
\(454\) | 5.21269 | 0.244644 | ||||||||
\(455\) | −2.40973 | −0.112970 | ||||||||
\(456\) | −5.08279 | −0.238023 | ||||||||
\(457\) | 38.7505 | 1.81267 | 0.906335 | − | 0.422560i | \(-0.138868\pi\) | ||||
0.906335 | + | 0.422560i | \(0.138868\pi\) | |||||||
\(458\) | −0.516500 | −0.0241345 | ||||||||
\(459\) | −6.60210 | −0.308159 | ||||||||
\(460\) | −1.63932 | −0.0764335 | ||||||||
\(461\) | 13.1493 | 0.612425 | 0.306213 | − | 0.951963i | \(-0.400938\pi\) | ||||
0.306213 | + | 0.951963i | \(0.400938\pi\) | |||||||
\(462\) | −2.05871 | −0.0957801 | ||||||||
\(463\) | 8.91855 | 0.414480 | 0.207240 | − | 0.978290i | \(-0.433552\pi\) | ||||
0.207240 | + | 0.978290i | \(0.433552\pi\) | |||||||
\(464\) | 24.5492 | 1.13967 | ||||||||
\(465\) | −1.76999 | −0.0820813 | ||||||||
\(466\) | 1.10016 | 0.0509637 | ||||||||
\(467\) | −29.5599 | −1.36787 | −0.683935 | − | 0.729543i | \(-0.739733\pi\) | ||||
−0.683935 | + | 0.729543i | \(0.739733\pi\) | |||||||
\(468\) | −1.93513 | −0.0894516 | ||||||||
\(469\) | −37.7652 | −1.74383 | ||||||||
\(470\) | 0.798315 | 0.0368235 | ||||||||
\(471\) | −2.57454 | −0.118628 | ||||||||
\(472\) | 4.34634 | 0.200056 | ||||||||
\(473\) | −14.7096 | −0.676346 | ||||||||
\(474\) | −3.00377 | −0.137968 | ||||||||
\(475\) | −23.2513 | −1.06684 | ||||||||
\(476\) | −47.7736 | −2.18970 | ||||||||
\(477\) | 1.28229 | 0.0587120 | ||||||||
\(478\) | 1.11776 | 0.0511254 | ||||||||
\(479\) | 20.6892 | 0.945316 | 0.472658 | − | 0.881246i | \(-0.343295\pi\) | ||||
0.472658 | + | 0.881246i | \(0.343295\pi\) | |||||||
\(480\) | −1.88505 | −0.0860402 | ||||||||
\(481\) | −2.15149 | −0.0980994 | ||||||||
\(482\) | −4.70358 | −0.214242 | ||||||||
\(483\) | 4.91556 | 0.223666 | ||||||||
\(484\) | 12.2438 | 0.556535 | ||||||||
\(485\) | −8.98931 | −0.408184 | ||||||||
\(486\) | 0.254687 | 0.0115528 | ||||||||
\(487\) | −30.5248 | −1.38321 | −0.691605 | − | 0.722276i | \(-0.743096\pi\) | ||||
−0.691605 | + | 0.722276i | \(0.743096\pi\) | |||||||
\(488\) | −9.13043 | −0.413315 | ||||||||
\(489\) | 8.11253 | 0.366861 | ||||||||
\(490\) | 1.14605 | 0.0517731 | ||||||||
\(491\) | −40.7131 | −1.83735 | −0.918677 | − | 0.395009i | \(-0.870742\pi\) | ||||
−0.918677 | + | 0.395009i | \(0.870742\pi\) | |||||||
\(492\) | 3.31362 | 0.149390 | ||||||||
\(493\) | 44.8343 | 2.01923 | ||||||||
\(494\) | −1.29164 | −0.0581138 | ||||||||
\(495\) | 1.39305 | 0.0626130 | ||||||||
\(496\) | −9.92905 | −0.445827 | ||||||||
\(497\) | 7.40072 | 0.331968 | ||||||||
\(498\) | 3.03753 | 0.136115 | ||||||||
\(499\) | −17.9990 | −0.805746 | −0.402873 | − | 0.915256i | \(-0.631988\pi\) | ||||
−0.402873 | + | 0.915256i | \(0.631988\pi\) | |||||||
\(500\) | −11.9526 | −0.534538 | ||||||||
\(501\) | −14.8223 | −0.662209 | ||||||||
\(502\) | 2.87069 | 0.128125 | ||||||||
\(503\) | −8.49851 | −0.378930 | −0.189465 | − | 0.981887i | \(-0.560675\pi\) | ||||
−0.189465 | + | 0.981887i | \(0.560675\pi\) | |||||||
\(504\) | 3.74767 | 0.166935 | ||||||||
\(505\) | 2.91927 | 0.129906 | ||||||||
\(506\) | −0.723734 | −0.0321739 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 10.8366 | 0.480797 | ||||||||
\(509\) | −19.6135 | −0.869351 | −0.434676 | − | 0.900587i | \(-0.643137\pi\) | ||||
−0.434676 | + | 0.900587i | \(0.643137\pi\) | |||||||
\(510\) | −1.08358 | −0.0479819 | ||||||||
\(511\) | −37.7411 | −1.66957 | ||||||||
\(512\) | −17.8206 | −0.787567 | ||||||||
\(513\) | −5.07149 | −0.223912 | ||||||||
\(514\) | −3.65647 | −0.161280 | ||||||||
\(515\) | 0.644426 | 0.0283968 | ||||||||
\(516\) | 13.1679 | 0.579685 | ||||||||
\(517\) | −10.5145 | −0.462427 | ||||||||
\(518\) | 2.04900 | 0.0900277 | ||||||||
\(519\) | 5.58518 | 0.245162 | ||||||||
\(520\) | −0.645862 | −0.0283229 | ||||||||
\(521\) | 39.6357 | 1.73647 | 0.868237 | − | 0.496150i | \(-0.165253\pi\) | ||||
0.868237 | + | 0.496150i | \(0.165253\pi\) | |||||||
\(522\) | −1.72956 | −0.0757007 | ||||||||
\(523\) | −26.5714 | −1.16189 | −0.580943 | − | 0.813945i | \(-0.697316\pi\) | ||||
−0.580943 | + | 0.813945i | \(0.697316\pi\) | |||||||
\(524\) | −19.4244 | −0.848559 | ||||||||
\(525\) | 17.1438 | 0.748218 | ||||||||
\(526\) | −4.82379 | −0.210327 | ||||||||
\(527\) | −18.1334 | −0.789904 | ||||||||
\(528\) | 7.81455 | 0.340084 | ||||||||
\(529\) | −21.2719 | −0.924867 | ||||||||
\(530\) | 0.210459 | 0.00914174 | ||||||||
\(531\) | 4.33667 | 0.188196 | ||||||||
\(532\) | −36.6980 | −1.59106 | ||||||||
\(533\) | 1.71235 | 0.0741700 | ||||||||
\(534\) | −2.01874 | −0.0873596 | ||||||||
\(535\) | 6.21199 | 0.268568 | ||||||||
\(536\) | −10.1219 | −0.437200 | ||||||||
\(537\) | 6.51826 | 0.281284 | ||||||||
\(538\) | −6.73315 | −0.290287 | ||||||||
\(539\) | −15.0944 | −0.650162 | ||||||||
\(540\) | −1.24705 | −0.0536645 | ||||||||
\(541\) | 0.912594 | 0.0392355 | 0.0196177 | − | 0.999808i | \(-0.493755\pi\) | ||||
0.0196177 | + | 0.999808i | \(0.493755\pi\) | |||||||
\(542\) | 3.98783 | 0.171292 | ||||||||
\(543\) | −5.43008 | −0.233027 | ||||||||
\(544\) | −19.3122 | −0.828002 | ||||||||
\(545\) | −4.19248 | −0.179586 | ||||||||
\(546\) | 0.952363 | 0.0407574 | ||||||||
\(547\) | −12.8909 | −0.551173 | −0.275586 | − | 0.961276i | \(-0.588872\pi\) | ||||
−0.275586 | + | 0.961276i | \(0.588872\pi\) | |||||||
\(548\) | −10.7414 | −0.458852 | ||||||||
\(549\) | −9.11013 | −0.388811 | ||||||||
\(550\) | −2.52414 | −0.107630 | ||||||||
\(551\) | 34.4400 | 1.46719 | ||||||||
\(552\) | 1.31748 | 0.0560758 | ||||||||
\(553\) | −44.1017 | −1.87540 | ||||||||
\(554\) | −0.0111726 | −0.000474678 0 | ||||||||
\(555\) | −1.38647 | −0.0588526 | ||||||||
\(556\) | −16.9180 | −0.717484 | ||||||||
\(557\) | −34.7494 | −1.47238 | −0.736189 | − | 0.676776i | \(-0.763377\pi\) | ||||
−0.736189 | + | 0.676776i | \(0.763377\pi\) | |||||||
\(558\) | 0.699527 | 0.0296133 | ||||||||
\(559\) | 6.80465 | 0.287806 | ||||||||
\(560\) | −8.71121 | −0.368116 | ||||||||
\(561\) | 14.2717 | 0.602552 | ||||||||
\(562\) | 2.25417 | 0.0950865 | ||||||||
\(563\) | 1.06371 | 0.0448300 | 0.0224150 | − | 0.999749i | \(-0.492864\pi\) | ||||
0.0224150 | + | 0.999749i | \(0.492864\pi\) | |||||||
\(564\) | 9.41251 | 0.396338 | ||||||||
\(565\) | −9.17778 | −0.386112 | ||||||||
\(566\) | 0.186402 | 0.00783504 | ||||||||
\(567\) | 3.73934 | 0.157038 | ||||||||
\(568\) | 1.98356 | 0.0832283 | ||||||||
\(569\) | −2.43593 | −0.102119 | −0.0510597 | − | 0.998696i | \(-0.516260\pi\) | ||||
−0.0510597 | + | 0.998696i | \(0.516260\pi\) | |||||||
\(570\) | −0.832369 | −0.0348641 | ||||||||
\(571\) | −6.01254 | −0.251617 | −0.125809 | − | 0.992055i | \(-0.540152\pi\) | ||||
−0.125809 | + | 0.992055i | \(0.540152\pi\) | |||||||
\(572\) | 4.18316 | 0.174907 | ||||||||
\(573\) | −18.9436 | −0.791379 | ||||||||
\(574\) | −1.63078 | −0.0680673 | ||||||||
\(575\) | 6.02685 | 0.251337 | ||||||||
\(576\) | −6.48503 | −0.270210 | ||||||||
\(577\) | −9.32838 | −0.388345 | −0.194173 | − | 0.980967i | \(-0.562202\pi\) | ||||
−0.194173 | + | 0.980967i | \(0.562202\pi\) | |||||||
\(578\) | −6.77154 | −0.281659 | ||||||||
\(579\) | −3.56540 | −0.148173 | ||||||||
\(580\) | 8.46861 | 0.351640 | ||||||||
\(581\) | 44.5973 | 1.85021 | ||||||||
\(582\) | 3.55271 | 0.147265 | ||||||||
\(583\) | −2.77192 | −0.114801 | ||||||||
\(584\) | −10.1155 | −0.418581 | ||||||||
\(585\) | −0.644426 | −0.0266437 | ||||||||
\(586\) | 4.43355 | 0.183148 | ||||||||
\(587\) | 8.00992 | 0.330605 | 0.165302 | − | 0.986243i | \(-0.447140\pi\) | ||||
0.165302 | + | 0.986243i | \(0.447140\pi\) | |||||||
\(588\) | 13.5124 | 0.557243 | ||||||||
\(589\) | −13.9294 | −0.573952 | ||||||||
\(590\) | 0.711766 | 0.0293029 | ||||||||
\(591\) | 10.2323 | 0.420902 | ||||||||
\(592\) | −7.77766 | −0.319660 | ||||||||
\(593\) | 30.2498 | 1.24221 | 0.621106 | − | 0.783727i | \(-0.286684\pi\) | ||||
0.621106 | + | 0.783727i | \(0.286684\pi\) | |||||||
\(594\) | −0.550555 | −0.0225896 | ||||||||
\(595\) | −15.9093 | −0.652217 | ||||||||
\(596\) | −19.5349 | −0.800181 | ||||||||
\(597\) | −24.0522 | −0.984392 | ||||||||
\(598\) | 0.334800 | 0.0136910 | ||||||||
\(599\) | 19.8497 | 0.811037 | 0.405519 | − | 0.914087i | \(-0.367091\pi\) | ||||
0.405519 | + | 0.914087i | \(0.367091\pi\) | |||||||
\(600\) | 4.59493 | 0.187587 | ||||||||
\(601\) | 41.7106 | 1.70141 | 0.850705 | − | 0.525643i | \(-0.176175\pi\) | ||||
0.850705 | + | 0.525643i | \(0.176175\pi\) | |||||||
\(602\) | −6.48049 | −0.264125 | ||||||||
\(603\) | −10.0994 | −0.411280 | ||||||||
\(604\) | −1.21883 | −0.0495933 | ||||||||
\(605\) | 4.07734 | 0.165767 | ||||||||
\(606\) | −1.15374 | −0.0468675 | ||||||||
\(607\) | −43.3222 | −1.75839 | −0.879196 | − | 0.476460i | \(-0.841920\pi\) | ||||
−0.879196 | + | 0.476460i | \(0.841920\pi\) | |||||||
\(608\) | −14.8349 | −0.601634 | ||||||||
\(609\) | −25.3935 | −1.02900 | ||||||||
\(610\) | −1.49522 | −0.0605397 | ||||||||
\(611\) | 4.86401 | 0.196777 | ||||||||
\(612\) | −12.7759 | −0.516437 | ||||||||
\(613\) | 0.808238 | 0.0326444 | 0.0163222 | − | 0.999867i | \(-0.494804\pi\) | ||||
0.0163222 | + | 0.999867i | \(0.494804\pi\) | |||||||
\(614\) | −1.63531 | −0.0659957 | ||||||||
\(615\) | 1.10348 | 0.0444967 | ||||||||
\(616\) | −8.10132 | −0.326411 | ||||||||
\(617\) | −41.6766 | −1.67784 | −0.838918 | − | 0.544257i | \(-0.816812\pi\) | ||||
−0.838918 | + | 0.544257i | \(0.816812\pi\) | |||||||
\(618\) | −0.254687 | −0.0102450 | ||||||||
\(619\) | 43.6835 | 1.75579 | 0.877894 | − | 0.478855i | \(-0.158948\pi\) | ||||
0.877894 | + | 0.478855i | \(0.158948\pi\) | |||||||
\(620\) | −3.42517 | −0.137558 | ||||||||
\(621\) | 1.31455 | 0.0527512 | ||||||||
\(622\) | −5.55888 | −0.222891 | ||||||||
\(623\) | −29.6394 | −1.18748 | ||||||||
\(624\) | −3.61501 | −0.144716 | ||||||||
\(625\) | 18.9432 | 0.757727 | ||||||||
\(626\) | 6.87607 | 0.274823 | ||||||||
\(627\) | 10.9630 | 0.437820 | ||||||||
\(628\) | −4.98208 | −0.198807 | ||||||||
\(629\) | −14.2043 | −0.566364 | ||||||||
\(630\) | 0.613727 | 0.0244515 | ||||||||
\(631\) | 4.26254 | 0.169689 | 0.0848446 | − | 0.996394i | \(-0.472961\pi\) | ||||
0.0848446 | + | 0.996394i | \(0.472961\pi\) | |||||||
\(632\) | −11.8203 | −0.470185 | ||||||||
\(633\) | −11.5341 | −0.458440 | ||||||||
\(634\) | 7.52901 | 0.299015 | ||||||||
\(635\) | 3.60874 | 0.143208 | ||||||||
\(636\) | 2.48140 | 0.0983941 | ||||||||
\(637\) | 6.98268 | 0.276664 | ||||||||
\(638\) | 3.73877 | 0.148019 | ||||||||
\(639\) | 1.97915 | 0.0782939 | ||||||||
\(640\) | −4.83446 | −0.191099 | ||||||||
\(641\) | 30.2657 | 1.19542 | 0.597712 | − | 0.801711i | \(-0.296077\pi\) | ||||
0.597712 | + | 0.801711i | \(0.296077\pi\) | |||||||
\(642\) | −2.45508 | −0.0968941 | ||||||||
\(643\) | 19.5187 | 0.769741 | 0.384871 | − | 0.922970i | \(-0.374246\pi\) | ||||
0.384871 | + | 0.922970i | \(0.374246\pi\) | |||||||
\(644\) | 9.51228 | 0.374836 | ||||||||
\(645\) | 4.38509 | 0.172663 | ||||||||
\(646\) | −8.52755 | −0.335512 | ||||||||
\(647\) | 13.9595 | 0.548803 | 0.274402 | − | 0.961615i | \(-0.411520\pi\) | ||||
0.274402 | + | 0.961615i | \(0.411520\pi\) | |||||||
\(648\) | 1.00223 | 0.0393712 | ||||||||
\(649\) | −9.37455 | −0.367983 | ||||||||
\(650\) | 1.16767 | 0.0457997 | ||||||||
\(651\) | 10.2705 | 0.402534 | ||||||||
\(652\) | 15.6988 | 0.614814 | ||||||||
\(653\) | 28.5723 | 1.11812 | 0.559060 | − | 0.829127i | \(-0.311162\pi\) | ||||
0.559060 | + | 0.829127i | \(0.311162\pi\) | |||||||
\(654\) | 1.65693 | 0.0647912 | ||||||||
\(655\) | −6.46859 | −0.252749 | ||||||||
\(656\) | 6.19016 | 0.241685 | ||||||||
\(657\) | −10.0930 | −0.393764 | ||||||||
\(658\) | −4.63230 | −0.180586 | ||||||||
\(659\) | 37.5112 | 1.46123 | 0.730615 | − | 0.682790i | \(-0.239234\pi\) | ||||
0.730615 | + | 0.682790i | \(0.239234\pi\) | |||||||
\(660\) | 2.69574 | 0.104932 | ||||||||
\(661\) | −33.2455 | −1.29310 | −0.646549 | − | 0.762872i | \(-0.723789\pi\) | ||||
−0.646549 | + | 0.762872i | \(0.723789\pi\) | |||||||
\(662\) | −0.902244 | −0.0350667 | ||||||||
\(663\) | −6.60210 | −0.256404 | ||||||||
\(664\) | 11.9531 | 0.463869 | ||||||||
\(665\) | −12.2209 | −0.473907 | ||||||||
\(666\) | 0.547956 | 0.0212329 | ||||||||
\(667\) | −8.92701 | −0.345655 | ||||||||
\(668\) | −28.6831 | −1.10978 | ||||||||
\(669\) | −24.6702 | −0.953803 | ||||||||
\(670\) | −1.65759 | −0.0640382 | ||||||||
\(671\) | 19.6933 | 0.760251 | ||||||||
\(672\) | 10.9382 | 0.421948 | ||||||||
\(673\) | 28.0118 | 1.07978 | 0.539888 | − | 0.841737i | \(-0.318467\pi\) | ||||
0.539888 | + | 0.841737i | \(0.318467\pi\) | |||||||
\(674\) | 4.49409 | 0.173106 | ||||||||
\(675\) | 4.58471 | 0.176466 | ||||||||
\(676\) | −1.93513 | −0.0744282 | ||||||||
\(677\) | 35.7561 | 1.37422 | 0.687109 | − | 0.726555i | \(-0.258880\pi\) | ||||
0.687109 | + | 0.726555i | \(0.258880\pi\) | |||||||
\(678\) | 3.62720 | 0.139302 | ||||||||
\(679\) | 52.1613 | 2.00177 | ||||||||
\(680\) | −4.26404 | −0.163519 | ||||||||
\(681\) | 20.4670 | 0.784299 | ||||||||
\(682\) | −1.51216 | −0.0579037 | ||||||||
\(683\) | −7.99852 | −0.306055 | −0.153027 | − | 0.988222i | \(-0.548902\pi\) | ||||
−0.153027 | + | 0.988222i | \(0.548902\pi\) | |||||||
\(684\) | −9.81401 | −0.375248 | ||||||||
\(685\) | −3.57705 | −0.136672 | ||||||||
\(686\) | 0.0164934 | 0.000629720 0 | ||||||||
\(687\) | −2.02798 | −0.0773722 | ||||||||
\(688\) | 24.5989 | 0.937824 | ||||||||
\(689\) | 1.28229 | 0.0488514 | ||||||||
\(690\) | 0.215754 | 0.00821361 | ||||||||
\(691\) | −9.17935 | −0.349199 | −0.174599 | − | 0.984640i | \(-0.555863\pi\) | ||||
−0.174599 | + | 0.984640i | \(0.555863\pi\) | |||||||
\(692\) | 10.8081 | 0.410862 | ||||||||
\(693\) | −8.08331 | −0.307059 | ||||||||
\(694\) | −5.58839 | −0.212132 | ||||||||
\(695\) | −5.63393 | −0.213707 | ||||||||
\(696\) | −6.80604 | −0.257982 | ||||||||
\(697\) | 11.3051 | 0.428211 | ||||||||
\(698\) | −3.99051 | −0.151043 | ||||||||
\(699\) | 4.31964 | 0.163384 | ||||||||
\(700\) | 33.1756 | 1.25392 | ||||||||
\(701\) | 6.22959 | 0.235288 | 0.117644 | − | 0.993056i | \(-0.462466\pi\) | ||||
0.117644 | + | 0.993056i | \(0.462466\pi\) | |||||||
\(702\) | 0.254687 | 0.00961255 | ||||||||
\(703\) | −10.9112 | −0.411525 | ||||||||
\(704\) | 14.0186 | 0.528347 | ||||||||
\(705\) | 3.13449 | 0.118052 | ||||||||
\(706\) | −5.90149 | −0.222105 | ||||||||
\(707\) | −16.9393 | −0.637069 | ||||||||
\(708\) | 8.39205 | 0.315392 | ||||||||
\(709\) | −46.8130 | −1.75810 | −0.879049 | − | 0.476731i | \(-0.841822\pi\) | ||||
−0.879049 | + | 0.476731i | \(0.841822\pi\) | |||||||
\(710\) | 0.324832 | 0.0121907 | ||||||||
\(711\) | −11.7940 | −0.442309 | ||||||||
\(712\) | −7.94403 | −0.297715 | ||||||||
\(713\) | 3.61057 | 0.135217 | ||||||||
\(714\) | 6.28759 | 0.235307 | ||||||||
\(715\) | 1.39305 | 0.0520971 | ||||||||
\(716\) | 12.6137 | 0.471396 | ||||||||
\(717\) | 4.38877 | 0.163902 | ||||||||
\(718\) | −6.64620 | −0.248034 | ||||||||
\(719\) | −22.9077 | −0.854314 | −0.427157 | − | 0.904177i | \(-0.640485\pi\) | ||||
−0.427157 | + | 0.904177i | \(0.640485\pi\) | |||||||
\(720\) | −2.32961 | −0.0868194 | ||||||||
\(721\) | −3.73934 | −0.139260 | ||||||||
\(722\) | −1.71150 | −0.0636954 | ||||||||
\(723\) | −18.4681 | −0.686835 | ||||||||
\(724\) | −10.5079 | −0.390524 | ||||||||
\(725\) | −31.1344 | −1.15630 | ||||||||
\(726\) | −1.61143 | −0.0598057 | ||||||||
\(727\) | 32.6195 | 1.20979 | 0.604895 | − | 0.796305i | \(-0.293215\pi\) | ||||
0.604895 | + | 0.796305i | \(0.293215\pi\) | |||||||
\(728\) | 3.74767 | 0.138898 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.65653 | −0.0613109 | ||||||||
\(731\) | 44.9249 | 1.66161 | ||||||||
\(732\) | −17.6293 | −0.651599 | ||||||||
\(733\) | 3.46368 | 0.127934 | 0.0639670 | − | 0.997952i | \(-0.479625\pi\) | ||||
0.0639670 | + | 0.997952i | \(0.479625\pi\) | |||||||
\(734\) | −3.91943 | −0.144669 | ||||||||
\(735\) | 4.49982 | 0.165978 | ||||||||
\(736\) | 3.84527 | 0.141739 | ||||||||
\(737\) | 21.8318 | 0.804186 | ||||||||
\(738\) | −0.436113 | −0.0160535 | ||||||||
\(739\) | −23.0306 | −0.847194 | −0.423597 | − | 0.905851i | \(-0.639233\pi\) | ||||
−0.423597 | + | 0.905851i | \(0.639233\pi\) | |||||||
\(740\) | −2.68301 | −0.0986296 | ||||||||
\(741\) | −5.07149 | −0.186306 | ||||||||
\(742\) | −1.22121 | −0.0448319 | ||||||||
\(743\) | 41.3720 | 1.51779 | 0.758896 | − | 0.651211i | \(-0.225739\pi\) | ||||
0.758896 | + | 0.651211i | \(0.225739\pi\) | |||||||
\(744\) | 2.75273 | 0.100920 | ||||||||
\(745\) | −6.50539 | −0.238339 | ||||||||
\(746\) | 3.86976 | 0.141682 | ||||||||
\(747\) | 11.9265 | 0.436368 | ||||||||
\(748\) | 27.6177 | 1.00980 | ||||||||
\(749\) | −36.0457 | −1.31708 | ||||||||
\(750\) | 1.57311 | 0.0574419 | ||||||||
\(751\) | −2.76373 | −0.100850 | −0.0504250 | − | 0.998728i | \(-0.516058\pi\) | ||||
−0.0504250 | + | 0.998728i | \(0.516058\pi\) | |||||||
\(752\) | 17.5835 | 0.641203 | ||||||||
\(753\) | 11.2714 | 0.410753 | ||||||||
\(754\) | −1.72956 | −0.0629868 | ||||||||
\(755\) | −0.405886 | −0.0147717 | ||||||||
\(756\) | 7.23613 | 0.263176 | ||||||||
\(757\) | −25.7833 | −0.937111 | −0.468556 | − | 0.883434i | \(-0.655225\pi\) | ||||
−0.468556 | + | 0.883434i | \(0.655225\pi\) | |||||||
\(758\) | 2.76732 | 0.100514 | ||||||||
\(759\) | −2.84166 | −0.103146 | ||||||||
\(760\) | −3.27548 | −0.118814 | ||||||||
\(761\) | −22.3274 | −0.809367 | −0.404683 | − | 0.914457i | \(-0.632618\pi\) | ||||
−0.404683 | + | 0.914457i | \(0.632618\pi\) | |||||||
\(762\) | −1.42623 | −0.0516668 | ||||||||
\(763\) | 24.3272 | 0.880705 | ||||||||
\(764\) | −36.6584 | −1.32625 | ||||||||
\(765\) | −4.25456 | −0.153824 | ||||||||
\(766\) | −1.91948 | −0.0693538 | ||||||||
\(767\) | 4.33667 | 0.156588 | ||||||||
\(768\) | −11.0594 | −0.399072 | ||||||||
\(769\) | −11.3354 | −0.408764 | −0.204382 | − | 0.978891i | \(-0.565518\pi\) | ||||
−0.204382 | + | 0.978891i | \(0.565518\pi\) | |||||||
\(770\) | −1.32669 | −0.0478106 | ||||||||
\(771\) | −14.3567 | −0.517044 | ||||||||
\(772\) | −6.89953 | −0.248320 | ||||||||
\(773\) | −31.8718 | −1.14635 | −0.573174 | − | 0.819433i | \(-0.694288\pi\) | ||||
−0.573174 | + | 0.819433i | \(0.694288\pi\) | |||||||
\(774\) | −1.73306 | −0.0622934 | ||||||||
\(775\) | 12.5924 | 0.452334 | ||||||||
\(776\) | 13.9804 | 0.501867 | ||||||||
\(777\) | 8.04515 | 0.288618 | ||||||||
\(778\) | −1.22949 | −0.0440794 | ||||||||
\(779\) | 8.68416 | 0.311142 | ||||||||
\(780\) | −1.24705 | −0.0446516 | ||||||||
\(781\) | −4.27831 | −0.153090 | ||||||||
\(782\) | 2.21038 | 0.0790431 | ||||||||
\(783\) | −6.79091 | −0.242687 | ||||||||
\(784\) | 25.2425 | 0.901518 | ||||||||
\(785\) | −1.65910 | −0.0592158 | ||||||||
\(786\) | 2.55649 | 0.0911869 | ||||||||
\(787\) | 18.3423 | 0.653833 | 0.326917 | − | 0.945053i | \(-0.393990\pi\) | ||||
0.326917 | + | 0.945053i | \(0.393990\pi\) | |||||||
\(788\) | 19.8009 | 0.705379 | ||||||||
\(789\) | −18.9401 | −0.674284 | ||||||||
\(790\) | −1.93571 | −0.0688695 | ||||||||
\(791\) | 53.2549 | 1.89353 | ||||||||
\(792\) | −2.16651 | −0.0769835 | ||||||||
\(793\) | −9.11013 | −0.323510 | ||||||||
\(794\) | 3.39128 | 0.120352 | ||||||||
\(795\) | 0.826342 | 0.0293073 | ||||||||
\(796\) | −46.5443 | −1.64972 | ||||||||
\(797\) | 0.714027 | 0.0252921 | 0.0126461 | − | 0.999920i | \(-0.495975\pi\) | ||||
0.0126461 | + | 0.999920i | \(0.495975\pi\) | |||||||
\(798\) | 4.82990 | 0.170977 | ||||||||
\(799\) | 32.1126 | 1.13606 | ||||||||
\(800\) | 13.4110 | 0.474150 | ||||||||
\(801\) | −7.92637 | −0.280064 | ||||||||
\(802\) | 4.32112 | 0.152584 | ||||||||
\(803\) | 21.8179 | 0.769937 | ||||||||
\(804\) | −19.5437 | −0.689254 | ||||||||
\(805\) | 3.16772 | 0.111647 | ||||||||
\(806\) | 0.699527 | 0.0246398 | ||||||||
\(807\) | −26.4369 | −0.930625 | ||||||||
\(808\) | −4.54012 | −0.159721 | ||||||||
\(809\) | −11.6088 | −0.408145 | −0.204072 | − | 0.978956i | \(-0.565418\pi\) | ||||
−0.204072 | + | 0.978956i | \(0.565418\pi\) | |||||||
\(810\) | 0.164127 | 0.00576684 | ||||||||
\(811\) | 36.2146 | 1.27167 | 0.635834 | − | 0.771826i | \(-0.280656\pi\) | ||||
0.635834 | + | 0.771826i | \(0.280656\pi\) | |||||||
\(812\) | −49.1399 | −1.72447 | ||||||||
\(813\) | 15.6578 | 0.549142 | ||||||||
\(814\) | −1.18451 | −0.0415171 | ||||||||
\(815\) | 5.22792 | 0.183126 | ||||||||
\(816\) | −23.8667 | −0.835501 | ||||||||
\(817\) | 34.5097 | 1.20734 | ||||||||
\(818\) | −1.85590 | −0.0648900 | ||||||||
\(819\) | 3.73934 | 0.130663 | ||||||||
\(820\) | 2.13539 | 0.0745709 | ||||||||
\(821\) | −12.7163 | −0.443802 | −0.221901 | − | 0.975069i | \(-0.571226\pi\) | ||||
−0.221901 | + | 0.975069i | \(0.571226\pi\) | |||||||
\(822\) | 1.41370 | 0.0493086 | ||||||||
\(823\) | −57.3548 | −1.99926 | −0.999632 | − | 0.0271267i | \(-0.991364\pi\) | ||||
−0.999632 | + | 0.0271267i | \(0.991364\pi\) | |||||||
\(824\) | −1.00223 | −0.0349143 | ||||||||
\(825\) | −9.91074 | −0.345048 | ||||||||
\(826\) | −4.13009 | −0.143704 | ||||||||
\(827\) | −30.0051 | −1.04338 | −0.521690 | − | 0.853135i | \(-0.674698\pi\) | ||||
−0.521690 | + | 0.853135i | \(0.674698\pi\) | |||||||
\(828\) | 2.54384 | 0.0884045 | ||||||||
\(829\) | −55.1564 | −1.91566 | −0.957831 | − | 0.287332i | \(-0.907232\pi\) | ||||
−0.957831 | + | 0.287332i | \(0.907232\pi\) | |||||||
\(830\) | 1.95746 | 0.0679445 | ||||||||
\(831\) | −0.0438679 | −0.00152176 | ||||||||
\(832\) | −6.48503 | −0.224828 | ||||||||
\(833\) | 46.1003 | 1.59728 | ||||||||
\(834\) | 2.22662 | 0.0771015 | ||||||||
\(835\) | −9.55185 | −0.330555 | ||||||||
\(836\) | 21.2149 | 0.733732 | ||||||||
\(837\) | 2.74661 | 0.0949368 | ||||||||
\(838\) | −8.13210 | −0.280919 | ||||||||
\(839\) | −44.0453 | −1.52061 | −0.760307 | − | 0.649564i | \(-0.774951\pi\) | ||||
−0.760307 | + | 0.649564i | \(0.774951\pi\) | |||||||
\(840\) | 2.41510 | 0.0833289 | ||||||||
\(841\) | 17.1165 | 0.590223 | ||||||||
\(842\) | −6.42227 | −0.221326 | ||||||||
\(843\) | 8.85075 | 0.304836 | ||||||||
\(844\) | −22.3201 | −0.768288 | ||||||||
\(845\) | −0.644426 | −0.0221689 | ||||||||
\(846\) | −1.23880 | −0.0425908 | ||||||||
\(847\) | −23.6591 | −0.812938 | ||||||||
\(848\) | 4.63550 | 0.159184 | ||||||||
\(849\) | 0.731884 | 0.0251182 | ||||||||
\(850\) | 7.70906 | 0.264419 | ||||||||
\(851\) | 2.82824 | 0.0969510 | ||||||||
\(852\) | 3.82992 | 0.131211 | ||||||||
\(853\) | 9.63675 | 0.329956 | 0.164978 | − | 0.986297i | \(-0.447245\pi\) | ||||
0.164978 | + | 0.986297i | \(0.447245\pi\) | |||||||
\(854\) | 8.67615 | 0.296892 | ||||||||
\(855\) | −3.26820 | −0.111770 | ||||||||
\(856\) | −9.66106 | −0.330208 | ||||||||
\(857\) | 5.95689 | 0.203484 | 0.101742 | − | 0.994811i | \(-0.467558\pi\) | ||||
0.101742 | + | 0.994811i | \(0.467558\pi\) | |||||||
\(858\) | −0.550555 | −0.0187956 | ||||||||
\(859\) | −52.8737 | −1.80403 | −0.902014 | − | 0.431707i | \(-0.857911\pi\) | ||||
−0.902014 | + | 0.431707i | \(0.857911\pi\) | |||||||
\(860\) | 8.48575 | 0.289362 | ||||||||
\(861\) | −6.40306 | −0.218216 | ||||||||
\(862\) | −7.17437 | −0.244360 | ||||||||
\(863\) | −18.4493 | −0.628022 | −0.314011 | − | 0.949419i | \(-0.601673\pi\) | ||||
−0.314011 | + | 0.949419i | \(0.601673\pi\) | |||||||
\(864\) | 2.92515 | 0.0995158 | ||||||||
\(865\) | 3.59924 | 0.122378 | ||||||||
\(866\) | −3.72995 | −0.126749 | ||||||||
\(867\) | −26.5877 | −0.902965 | ||||||||
\(868\) | 19.8749 | 0.674596 | ||||||||
\(869\) | 25.4949 | 0.864857 | ||||||||
\(870\) | −1.11457 | −0.0377875 | ||||||||
\(871\) | −10.0994 | −0.342206 | ||||||||
\(872\) | 6.52025 | 0.220804 | ||||||||
\(873\) | 13.9493 | 0.472113 | ||||||||
\(874\) | 1.69793 | 0.0574335 | ||||||||
\(875\) | 23.0966 | 0.780807 | ||||||||
\(876\) | −19.5313 | −0.659900 | ||||||||
\(877\) | 6.40935 | 0.216428 | 0.108214 | − | 0.994128i | \(-0.465487\pi\) | ||||
0.108214 | + | 0.994128i | \(0.465487\pi\) | |||||||
\(878\) | 7.11381 | 0.240080 | ||||||||
\(879\) | 17.4078 | 0.587151 | ||||||||
\(880\) | 5.03590 | 0.169760 | ||||||||
\(881\) | 27.7176 | 0.933828 | 0.466914 | − | 0.884303i | \(-0.345366\pi\) | ||||
0.466914 | + | 0.884303i | \(0.345366\pi\) | |||||||
\(882\) | −1.77840 | −0.0598818 | ||||||||
\(883\) | −21.2500 | −0.715120 | −0.357560 | − | 0.933890i | \(-0.616391\pi\) | ||||
−0.357560 | + | 0.933890i | \(0.616391\pi\) | |||||||
\(884\) | −12.7759 | −0.429702 | ||||||||
\(885\) | 2.79467 | 0.0939417 | ||||||||
\(886\) | 2.16264 | 0.0726553 | ||||||||
\(887\) | 39.7947 | 1.33617 | 0.668087 | − | 0.744083i | \(-0.267113\pi\) | ||||
0.668087 | + | 0.744083i | \(0.267113\pi\) | |||||||
\(888\) | 2.15628 | 0.0723601 | ||||||||
\(889\) | −20.9400 | −0.702306 | ||||||||
\(890\) | −1.30093 | −0.0436073 | ||||||||
\(891\) | −2.16169 | −0.0724194 | ||||||||
\(892\) | −47.7401 | −1.59846 | ||||||||
\(893\) | 24.6678 | 0.825475 | ||||||||
\(894\) | 2.57103 | 0.0859881 | ||||||||
\(895\) | 4.20054 | 0.140408 | ||||||||
\(896\) | 28.0524 | 0.937165 | ||||||||
\(897\) | 1.31455 | 0.0438917 | ||||||||
\(898\) | 1.91233 | 0.0638152 | ||||||||
\(899\) | −18.6520 | −0.622079 | ||||||||
\(900\) | 8.87204 | 0.295735 | ||||||||
\(901\) | 8.46581 | 0.282037 | ||||||||
\(902\) | 0.942742 | 0.0313899 | ||||||||
\(903\) | −25.4449 | −0.846754 | ||||||||
\(904\) | 14.2735 | 0.474730 | ||||||||
\(905\) | −3.49929 | −0.116320 | ||||||||
\(906\) | 0.160412 | 0.00532934 | ||||||||
\(907\) | 17.2661 | 0.573312 | 0.286656 | − | 0.958034i | \(-0.407456\pi\) | ||||
0.286656 | + | 0.958034i | \(0.407456\pi\) | |||||||
\(908\) | 39.6065 | 1.31439 | ||||||||
\(909\) | −4.53003 | −0.150251 | ||||||||
\(910\) | 0.613727 | 0.0203449 | ||||||||
\(911\) | −29.8074 | −0.987564 | −0.493782 | − | 0.869586i | \(-0.664386\pi\) | ||||
−0.493782 | + | 0.869586i | \(0.664386\pi\) | |||||||
\(912\) | −18.3335 | −0.607083 | ||||||||
\(913\) | −25.7814 | −0.853240 | ||||||||
\(914\) | −9.86925 | −0.326446 | ||||||||
\(915\) | −5.87081 | −0.194083 | ||||||||
\(916\) | −3.92441 | −0.129666 | ||||||||
\(917\) | 37.5346 | 1.23950 | ||||||||
\(918\) | 1.68147 | 0.0554968 | ||||||||
\(919\) | −46.2600 | −1.52598 | −0.762988 | − | 0.646413i | \(-0.776268\pi\) | ||||
−0.762988 | + | 0.646413i | \(0.776268\pi\) | |||||||
\(920\) | 0.849020 | 0.0279914 | ||||||||
\(921\) | −6.42085 | −0.211574 | ||||||||
\(922\) | −3.34897 | −0.110292 | ||||||||
\(923\) | 1.97915 | 0.0651445 | ||||||||
\(924\) | −15.6423 | −0.514593 | ||||||||
\(925\) | 9.86396 | 0.324325 | ||||||||
\(926\) | −2.27144 | −0.0746442 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −19.8645 | −0.652083 | ||||||||
\(929\) | 1.34876 | 0.0442512 | 0.0221256 | − | 0.999755i | \(-0.492957\pi\) | ||||
0.0221256 | + | 0.999755i | \(0.492957\pi\) | |||||||
\(930\) | 0.450794 | 0.0147821 | ||||||||
\(931\) | 35.4126 | 1.16060 | ||||||||
\(932\) | 8.35908 | 0.273811 | ||||||||
\(933\) | −21.8263 | −0.714561 | ||||||||
\(934\) | 7.52854 | 0.246341 | ||||||||
\(935\) | 9.19706 | 0.300776 | ||||||||
\(936\) | 1.00223 | 0.0327589 | ||||||||
\(937\) | −13.3982 | −0.437702 | −0.218851 | − | 0.975758i | \(-0.570231\pi\) | ||||
−0.218851 | + | 0.975758i | \(0.570231\pi\) | |||||||
\(938\) | 9.61831 | 0.314049 | ||||||||
\(939\) | 26.9981 | 0.881050 | ||||||||
\(940\) | 6.06567 | 0.197840 | ||||||||
\(941\) | 15.0246 | 0.489788 | 0.244894 | − | 0.969550i | \(-0.421247\pi\) | ||||
0.244894 | + | 0.969550i | \(0.421247\pi\) | |||||||
\(942\) | 0.655702 | 0.0213639 | ||||||||
\(943\) | −2.25097 | −0.0733018 | ||||||||
\(944\) | 15.6771 | 0.510247 | ||||||||
\(945\) | 2.40973 | 0.0783885 | ||||||||
\(946\) | 3.74633 | 0.121804 | ||||||||
\(947\) | 32.1115 | 1.04348 | 0.521741 | − | 0.853104i | \(-0.325283\pi\) | ||||
0.521741 | + | 0.853104i | \(0.325283\pi\) | |||||||
\(948\) | −22.8229 | −0.741254 | ||||||||
\(949\) | −10.0930 | −0.327632 | ||||||||
\(950\) | 5.92182 | 0.192129 | ||||||||
\(951\) | 29.5618 | 0.958607 | ||||||||
\(952\) | 24.7425 | 0.801909 | ||||||||
\(953\) | −16.7620 | −0.542973 | −0.271487 | − | 0.962442i | \(-0.587515\pi\) | ||||
−0.271487 | + | 0.962442i | \(0.587515\pi\) | |||||||
\(954\) | −0.326583 | −0.0105735 | ||||||||
\(955\) | −12.2077 | −0.395033 | ||||||||
\(956\) | 8.49287 | 0.274679 | ||||||||
\(957\) | 14.6799 | 0.474532 | ||||||||
\(958\) | −5.26929 | −0.170243 | ||||||||
\(959\) | 20.7562 | 0.670251 | ||||||||
\(960\) | −4.17912 | −0.134881 | ||||||||
\(961\) | −23.4561 | −0.756649 | ||||||||
\(962\) | 0.547956 | 0.0176668 | ||||||||
\(963\) | −9.63958 | −0.310631 | ||||||||
\(964\) | −35.7382 | −1.15105 | ||||||||
\(965\) | −2.29764 | −0.0739636 | ||||||||
\(966\) | −1.25193 | −0.0402802 | ||||||||
\(967\) | 49.6640 | 1.59709 | 0.798544 | − | 0.601937i | \(-0.205604\pi\) | ||||
0.798544 | + | 0.601937i | \(0.205604\pi\) | |||||||
\(968\) | −6.34119 | −0.203813 | ||||||||
\(969\) | −33.4825 | −1.07561 | ||||||||
\(970\) | 2.28946 | 0.0735102 | ||||||||
\(971\) | −49.0060 | −1.57268 | −0.786339 | − | 0.617795i | \(-0.788026\pi\) | ||||
−0.786339 | + | 0.617795i | \(0.788026\pi\) | |||||||
\(972\) | 1.93513 | 0.0620695 | ||||||||
\(973\) | 32.6914 | 1.04804 | ||||||||
\(974\) | 7.77427 | 0.249104 | ||||||||
\(975\) | 4.58471 | 0.146828 | ||||||||
\(976\) | −32.9333 | −1.05417 | ||||||||
\(977\) | −53.9425 | −1.72577 | −0.862886 | − | 0.505398i | \(-0.831346\pi\) | ||||
−0.862886 | + | 0.505398i | \(0.831346\pi\) | |||||||
\(978\) | −2.06616 | −0.0660684 | ||||||||
\(979\) | 17.1344 | 0.547617 | ||||||||
\(980\) | 8.70776 | 0.278159 | ||||||||
\(981\) | 6.50575 | 0.207713 | ||||||||
\(982\) | 10.3691 | 0.330891 | ||||||||
\(983\) | 21.3824 | 0.681992 | 0.340996 | − | 0.940065i | \(-0.389236\pi\) | ||||
0.340996 | + | 0.940065i | \(0.389236\pi\) | |||||||
\(984\) | −1.71616 | −0.0547093 | ||||||||
\(985\) | 6.59398 | 0.210102 | ||||||||
\(986\) | −11.4187 | −0.363646 | ||||||||
\(987\) | −18.1882 | −0.578936 | ||||||||
\(988\) | −9.81401 | −0.312225 | ||||||||
\(989\) | −8.94507 | −0.284437 | ||||||||
\(990\) | −0.354792 | −0.0112760 | ||||||||
\(991\) | 50.0625 | 1.59029 | 0.795143 | − | 0.606421i | \(-0.207396\pi\) | ||||
0.795143 | + | 0.606421i | \(0.207396\pi\) | |||||||
\(992\) | 8.03427 | 0.255088 | ||||||||
\(993\) | −3.54256 | −0.112420 | ||||||||
\(994\) | −1.88487 | −0.0597844 | ||||||||
\(995\) | −15.4999 | −0.491380 | ||||||||
\(996\) | 23.0794 | 0.731298 | ||||||||
\(997\) | 36.5990 | 1.15910 | 0.579552 | − | 0.814935i | \(-0.303228\pi\) | ||||
0.579552 | + | 0.814935i | \(0.303228\pi\) | |||||||
\(998\) | 4.58411 | 0.145108 | ||||||||
\(999\) | 2.15149 | 0.0680700 |
(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 | 4017.2.a.j.1.11 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.11 | ✓ | 25 | 1.1 | even | 1 | trivial |