Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(106\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42329 | −1.71352 | −0.856762 | − | 0.515712i | \(-0.827527\pi\) | ||||
−0.856762 | + | 0.515712i | \(0.827527\pi\) | |||||||
\(3\) | −0.918445 | −0.530264 | −0.265132 | − | 0.964212i | \(-0.585416\pi\) | ||||
−0.265132 | + | 0.964212i | \(0.585416\pi\) | |||||||
\(4\) | 3.87233 | 1.93616 | ||||||||
\(5\) | −2.10804 | −0.942744 | −0.471372 | − | 0.881934i | \(-0.656241\pi\) | ||||
−0.471372 | + | 0.881934i | \(0.656241\pi\) | |||||||
\(6\) | 2.22566 | 0.908621 | ||||||||
\(7\) | −2.69568 | −1.01887 | −0.509436 | − | 0.860509i | \(-0.670146\pi\) | ||||
−0.509436 | + | 0.860509i | \(0.670146\pi\) | |||||||
\(8\) | −4.53719 | −1.60414 | ||||||||
\(9\) | −2.15646 | −0.718820 | ||||||||
\(10\) | 5.10839 | 1.61541 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −3.55652 | −1.02668 | ||||||||
\(13\) | −1.31790 | −0.365519 | −0.182759 | − | 0.983158i | \(-0.558503\pi\) | ||||
−0.182759 | + | 0.983158i | \(0.558503\pi\) | |||||||
\(14\) | 6.53241 | 1.74586 | ||||||||
\(15\) | 1.93612 | 0.499904 | ||||||||
\(16\) | 3.25026 | 0.812566 | ||||||||
\(17\) | −1.02624 | −0.248900 | −0.124450 | − | 0.992226i | \(-0.539717\pi\) | ||||
−0.124450 | + | 0.992226i | \(0.539717\pi\) | |||||||
\(18\) | 5.22572 | 1.23171 | ||||||||
\(19\) | 1.40367 | 0.322023 | 0.161012 | − | 0.986953i | \(-0.448524\pi\) | ||||
0.161012 | + | 0.986953i | \(0.448524\pi\) | |||||||
\(20\) | −8.16302 | −1.82531 | ||||||||
\(21\) | 2.47583 | 0.540271 | ||||||||
\(22\) | −2.42329 | −0.516647 | ||||||||
\(23\) | −7.47517 | −1.55868 | −0.779340 | − | 0.626601i | \(-0.784445\pi\) | ||||
−0.779340 | + | 0.626601i | \(0.784445\pi\) | |||||||
\(24\) | 4.16716 | 0.850618 | ||||||||
\(25\) | −0.556169 | −0.111234 | ||||||||
\(26\) | 3.19364 | 0.626325 | ||||||||
\(27\) | 4.73592 | 0.911429 | ||||||||
\(28\) | −10.4386 | −1.97270 | ||||||||
\(29\) | 4.75007 | 0.882066 | 0.441033 | − | 0.897491i | \(-0.354612\pi\) | ||||
0.441033 | + | 0.897491i | \(0.354612\pi\) | |||||||
\(30\) | −4.69177 | −0.856597 | ||||||||
\(31\) | 4.78215 | 0.858899 | 0.429450 | − | 0.903091i | \(-0.358708\pi\) | ||||
0.429450 | + | 0.903091i | \(0.358708\pi\) | |||||||
\(32\) | 1.19805 | 0.211788 | ||||||||
\(33\) | −0.918445 | −0.159881 | ||||||||
\(34\) | 2.48687 | 0.426495 | ||||||||
\(35\) | 5.68260 | 0.960535 | ||||||||
\(36\) | −8.35052 | −1.39175 | ||||||||
\(37\) | −7.86278 | −1.29263 | −0.646317 | − | 0.763069i | \(-0.723691\pi\) | ||||
−0.646317 | + | 0.763069i | \(0.723691\pi\) | |||||||
\(38\) | −3.40149 | −0.551795 | ||||||||
\(39\) | 1.21042 | 0.193822 | ||||||||
\(40\) | 9.56457 | 1.51229 | ||||||||
\(41\) | 8.85425 | 1.38280 | 0.691401 | − | 0.722471i | \(-0.256994\pi\) | ||||
0.691401 | + | 0.722471i | \(0.256994\pi\) | |||||||
\(42\) | −5.99966 | −0.925768 | ||||||||
\(43\) | −3.78885 | −0.577794 | −0.288897 | − | 0.957360i | \(-0.593289\pi\) | ||||
−0.288897 | + | 0.957360i | \(0.593289\pi\) | |||||||
\(44\) | 3.87233 | 0.583775 | ||||||||
\(45\) | 4.54590 | 0.677663 | ||||||||
\(46\) | 18.1145 | 2.67083 | ||||||||
\(47\) | −12.0893 | −1.76340 | −0.881702 | − | 0.471807i | \(-0.843602\pi\) | ||||
−0.881702 | + | 0.471807i | \(0.843602\pi\) | |||||||
\(48\) | −2.98519 | −0.430875 | ||||||||
\(49\) | 0.266696 | 0.0380995 | ||||||||
\(50\) | 1.34776 | 0.190602 | ||||||||
\(51\) | 0.942544 | 0.131983 | ||||||||
\(52\) | −5.10333 | −0.707704 | ||||||||
\(53\) | 3.68886 | 0.506704 | 0.253352 | − | 0.967374i | \(-0.418467\pi\) | ||||
0.253352 | + | 0.967374i | \(0.418467\pi\) | |||||||
\(54\) | −11.4765 | −1.56175 | ||||||||
\(55\) | −2.10804 | −0.284248 | ||||||||
\(56\) | 12.2308 | 1.63441 | ||||||||
\(57\) | −1.28919 | −0.170758 | ||||||||
\(58\) | −11.5108 | −1.51144 | ||||||||
\(59\) | 7.33831 | 0.955366 | 0.477683 | − | 0.878532i | \(-0.341477\pi\) | ||||
0.477683 | + | 0.878532i | \(0.341477\pi\) | |||||||
\(60\) | 7.49728 | 0.967895 | ||||||||
\(61\) | 3.68949 | 0.472391 | 0.236195 | − | 0.971706i | \(-0.424100\pi\) | ||||
0.236195 | + | 0.971706i | \(0.424100\pi\) | |||||||
\(62\) | −11.5885 | −1.47174 | ||||||||
\(63\) | 5.81313 | 0.732385 | ||||||||
\(64\) | −9.40375 | −1.17547 | ||||||||
\(65\) | 2.77818 | 0.344591 | ||||||||
\(66\) | 2.22566 | 0.273959 | ||||||||
\(67\) | −3.00896 | −0.367603 | −0.183801 | − | 0.982963i | \(-0.558840\pi\) | ||||
−0.183801 | + | 0.982963i | \(0.558840\pi\) | |||||||
\(68\) | −3.97393 | −0.481910 | ||||||||
\(69\) | 6.86553 | 0.826512 | ||||||||
\(70\) | −13.7706 | −1.64590 | ||||||||
\(71\) | 4.85676 | 0.576391 | 0.288196 | − | 0.957572i | \(-0.406945\pi\) | ||||
0.288196 | + | 0.957572i | \(0.406945\pi\) | |||||||
\(72\) | 9.78426 | 1.15309 | ||||||||
\(73\) | 13.9945 | 1.63794 | 0.818968 | − | 0.573839i | \(-0.194546\pi\) | ||||
0.818968 | + | 0.573839i | \(0.194546\pi\) | |||||||
\(74\) | 19.0538 | 2.21496 | ||||||||
\(75\) | 0.510810 | 0.0589833 | ||||||||
\(76\) | 5.43546 | 0.623490 | ||||||||
\(77\) | −2.69568 | −0.307201 | ||||||||
\(78\) | −2.93319 | −0.332118 | ||||||||
\(79\) | −11.2438 | −1.26503 | −0.632516 | − | 0.774548i | \(-0.717978\pi\) | ||||
−0.632516 | + | 0.774548i | \(0.717978\pi\) | |||||||
\(80\) | −6.85168 | −0.766042 | ||||||||
\(81\) | 2.11969 | 0.235521 | ||||||||
\(82\) | −21.4564 | −2.36946 | ||||||||
\(83\) | 15.9306 | 1.74862 | 0.874308 | − | 0.485372i | \(-0.161316\pi\) | ||||
0.874308 | + | 0.485372i | \(0.161316\pi\) | |||||||
\(84\) | 9.58724 | 1.04605 | ||||||||
\(85\) | 2.16335 | 0.234649 | ||||||||
\(86\) | 9.18148 | 0.990064 | ||||||||
\(87\) | −4.36268 | −0.467728 | ||||||||
\(88\) | −4.53719 | −0.483666 | ||||||||
\(89\) | 8.85401 | 0.938524 | 0.469262 | − | 0.883059i | \(-0.344520\pi\) | ||||
0.469262 | + | 0.883059i | \(0.344520\pi\) | |||||||
\(90\) | −11.0160 | −1.16119 | ||||||||
\(91\) | 3.55263 | 0.372417 | ||||||||
\(92\) | −28.9463 | −3.01786 | ||||||||
\(93\) | −4.39214 | −0.455444 | ||||||||
\(94\) | 29.2958 | 3.02163 | ||||||||
\(95\) | −2.95899 | −0.303586 | ||||||||
\(96\) | −1.10034 | −0.112303 | ||||||||
\(97\) | 6.42119 | 0.651973 | 0.325987 | − | 0.945374i | \(-0.394304\pi\) | ||||
0.325987 | + | 0.945374i | \(0.394304\pi\) | |||||||
\(98\) | −0.646282 | −0.0652843 | ||||||||
\(99\) | −2.15646 | −0.216732 | ||||||||
\(100\) | −2.15367 | −0.215367 | ||||||||
\(101\) | −15.5113 | −1.54343 | −0.771716 | − | 0.635968i | \(-0.780601\pi\) | ||||
−0.771716 | + | 0.635968i | \(0.780601\pi\) | |||||||
\(102\) | −2.28406 | −0.226155 | ||||||||
\(103\) | 11.6308 | 1.14602 | 0.573008 | − | 0.819549i | \(-0.305776\pi\) | ||||
0.573008 | + | 0.819549i | \(0.305776\pi\) | |||||||
\(104\) | 5.97955 | 0.586343 | ||||||||
\(105\) | −5.21916 | −0.509338 | ||||||||
\(106\) | −8.93917 | −0.868249 | ||||||||
\(107\) | −15.2861 | −1.47776 | −0.738881 | − | 0.673836i | \(-0.764646\pi\) | ||||
−0.738881 | + | 0.673836i | \(0.764646\pi\) | |||||||
\(108\) | 18.3390 | 1.76468 | ||||||||
\(109\) | −1.18087 | −0.113107 | −0.0565533 | − | 0.998400i | \(-0.518011\pi\) | ||||
−0.0565533 | + | 0.998400i | \(0.518011\pi\) | |||||||
\(110\) | 5.10839 | 0.487066 | ||||||||
\(111\) | 7.22153 | 0.685437 | ||||||||
\(112\) | −8.76167 | −0.827900 | ||||||||
\(113\) | 10.0801 | 0.948254 | 0.474127 | − | 0.880456i | \(-0.342764\pi\) | ||||
0.474127 | + | 0.880456i | \(0.342764\pi\) | |||||||
\(114\) | 3.12408 | 0.292597 | ||||||||
\(115\) | 15.7579 | 1.46944 | ||||||||
\(116\) | 18.3938 | 1.70782 | ||||||||
\(117\) | 2.84199 | 0.262742 | ||||||||
\(118\) | −17.7828 | −1.63704 | ||||||||
\(119\) | 2.76641 | 0.253597 | ||||||||
\(120\) | −8.78453 | −0.801915 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −8.94069 | −0.809452 | ||||||||
\(123\) | −8.13214 | −0.733251 | ||||||||
\(124\) | 18.5180 | 1.66297 | ||||||||
\(125\) | 11.7126 | 1.04761 | ||||||||
\(126\) | −14.0869 | −1.25496 | ||||||||
\(127\) | 1.53610 | 0.136307 | 0.0681533 | − | 0.997675i | \(-0.478289\pi\) | ||||
0.0681533 | + | 0.997675i | \(0.478289\pi\) | |||||||
\(128\) | 20.3919 | 1.80241 | ||||||||
\(129\) | 3.47985 | 0.306384 | ||||||||
\(130\) | −6.73233 | −0.590464 | ||||||||
\(131\) | 1.09698 | 0.0958435 | 0.0479218 | − | 0.998851i | \(-0.484740\pi\) | ||||
0.0479218 | + | 0.998851i | \(0.484740\pi\) | |||||||
\(132\) | −3.55652 | −0.309555 | ||||||||
\(133\) | −3.78384 | −0.328100 | ||||||||
\(134\) | 7.29157 | 0.629896 | ||||||||
\(135\) | −9.98351 | −0.859244 | ||||||||
\(136\) | 4.65624 | 0.399269 | ||||||||
\(137\) | 8.42685 | 0.719954 | 0.359977 | − | 0.932961i | \(-0.382784\pi\) | ||||
0.359977 | + | 0.932961i | \(0.382784\pi\) | |||||||
\(138\) | −16.6372 | −1.41625 | ||||||||
\(139\) | −6.46863 | −0.548662 | −0.274331 | − | 0.961635i | \(-0.588456\pi\) | ||||
−0.274331 | + | 0.961635i | \(0.588456\pi\) | |||||||
\(140\) | 22.0049 | 1.85975 | ||||||||
\(141\) | 11.1033 | 0.935070 | ||||||||
\(142\) | −11.7693 | −0.987660 | ||||||||
\(143\) | −1.31790 | −0.110208 | ||||||||
\(144\) | −7.00906 | −0.584088 | ||||||||
\(145\) | −10.0133 | −0.831562 | ||||||||
\(146\) | −33.9128 | −2.80664 | ||||||||
\(147\) | −0.244946 | −0.0202028 | ||||||||
\(148\) | −30.4473 | −2.50275 | ||||||||
\(149\) | 7.03937 | 0.576688 | 0.288344 | − | 0.957527i | \(-0.406895\pi\) | ||||
0.288344 | + | 0.957527i | \(0.406895\pi\) | |||||||
\(150\) | −1.23784 | −0.101069 | ||||||||
\(151\) | 4.48252 | 0.364782 | 0.182391 | − | 0.983226i | \(-0.441616\pi\) | ||||
0.182391 | + | 0.983226i | \(0.441616\pi\) | |||||||
\(152\) | −6.36870 | −0.516570 | ||||||||
\(153\) | 2.21304 | 0.178914 | ||||||||
\(154\) | 6.53241 | 0.526397 | ||||||||
\(155\) | −10.0810 | −0.809722 | ||||||||
\(156\) | 4.68712 | 0.375270 | ||||||||
\(157\) | −3.92980 | −0.313632 | −0.156816 | − | 0.987628i | \(-0.550123\pi\) | ||||
−0.156816 | + | 0.987628i | \(0.550123\pi\) | |||||||
\(158\) | 27.2471 | 2.16766 | ||||||||
\(159\) | −3.38802 | −0.268687 | ||||||||
\(160\) | −2.52554 | −0.199661 | ||||||||
\(161\) | 20.1507 | 1.58809 | ||||||||
\(162\) | −5.13663 | −0.403572 | ||||||||
\(163\) | 13.9010 | 1.08881 | 0.544406 | − | 0.838822i | \(-0.316755\pi\) | ||||
0.544406 | + | 0.838822i | \(0.316755\pi\) | |||||||
\(164\) | 34.2866 | 2.67733 | ||||||||
\(165\) | 1.93612 | 0.150727 | ||||||||
\(166\) | −38.6046 | −2.99629 | ||||||||
\(167\) | 1.96335 | 0.151929 | 0.0759645 | − | 0.997111i | \(-0.475796\pi\) | ||||
0.0759645 | + | 0.997111i | \(0.475796\pi\) | |||||||
\(168\) | −11.2333 | −0.866670 | ||||||||
\(169\) | −11.2631 | −0.866396 | ||||||||
\(170\) | −5.24243 | −0.402076 | ||||||||
\(171\) | −3.02695 | −0.231477 | ||||||||
\(172\) | −14.6717 | −1.11870 | ||||||||
\(173\) | −8.60803 | −0.654457 | −0.327228 | − | 0.944945i | \(-0.606115\pi\) | ||||
−0.327228 | + | 0.944945i | \(0.606115\pi\) | |||||||
\(174\) | 10.5720 | 0.801463 | ||||||||
\(175\) | 1.49925 | 0.113333 | ||||||||
\(176\) | 3.25026 | 0.244998 | ||||||||
\(177\) | −6.73983 | −0.506597 | ||||||||
\(178\) | −21.4558 | −1.60818 | ||||||||
\(179\) | 15.5556 | 1.16268 | 0.581340 | − | 0.813660i | \(-0.302528\pi\) | ||||
0.581340 | + | 0.813660i | \(0.302528\pi\) | |||||||
\(180\) | 17.6032 | 1.31207 | ||||||||
\(181\) | −8.95677 | −0.665752 | −0.332876 | − | 0.942971i | \(-0.608019\pi\) | ||||
−0.332876 | + | 0.942971i | \(0.608019\pi\) | |||||||
\(182\) | −8.60904 | −0.638145 | ||||||||
\(183\) | −3.38859 | −0.250492 | ||||||||
\(184\) | 33.9162 | 2.50034 | ||||||||
\(185\) | 16.5751 | 1.21862 | ||||||||
\(186\) | 10.6434 | 0.780414 | ||||||||
\(187\) | −1.02624 | −0.0750461 | ||||||||
\(188\) | −46.8137 | −3.41424 | ||||||||
\(189\) | −12.7665 | −0.928629 | ||||||||
\(190\) | 7.17048 | 0.520201 | ||||||||
\(191\) | 23.1298 | 1.67361 | 0.836806 | − | 0.547499i | \(-0.184420\pi\) | ||||
0.836806 | + | 0.547499i | \(0.184420\pi\) | |||||||
\(192\) | 8.63683 | 0.623309 | ||||||||
\(193\) | −26.7959 | −1.92881 | −0.964405 | − | 0.264431i | \(-0.914816\pi\) | ||||
−0.964405 | + | 0.264431i | \(0.914816\pi\) | |||||||
\(194\) | −15.5604 | −1.11717 | ||||||||
\(195\) | −2.55160 | −0.182724 | ||||||||
\(196\) | 1.03273 | 0.0737668 | ||||||||
\(197\) | −1.59916 | −0.113935 | −0.0569676 | − | 0.998376i | \(-0.518143\pi\) | ||||
−0.0569676 | + | 0.998376i | \(0.518143\pi\) | |||||||
\(198\) | 5.22572 | 0.371376 | ||||||||
\(199\) | 12.0933 | 0.857271 | 0.428636 | − | 0.903477i | \(-0.358994\pi\) | ||||
0.428636 | + | 0.903477i | \(0.358994\pi\) | |||||||
\(200\) | 2.52344 | 0.178434 | ||||||||
\(201\) | 2.76356 | 0.194927 | ||||||||
\(202\) | 37.5883 | 2.64471 | ||||||||
\(203\) | −12.8047 | −0.898712 | ||||||||
\(204\) | 3.64984 | 0.255540 | ||||||||
\(205\) | −18.6651 | −1.30363 | ||||||||
\(206\) | −28.1848 | −1.96373 | ||||||||
\(207\) | 16.1199 | 1.12041 | ||||||||
\(208\) | −4.28351 | −0.297008 | ||||||||
\(209\) | 1.40367 | 0.0970937 | ||||||||
\(210\) | 12.6475 | 0.872762 | ||||||||
\(211\) | −8.61138 | −0.592832 | −0.296416 | − | 0.955059i | \(-0.595791\pi\) | ||||
−0.296416 | + | 0.955059i | \(0.595791\pi\) | |||||||
\(212\) | 14.2845 | 0.981062 | ||||||||
\(213\) | −4.46066 | −0.305640 | ||||||||
\(214\) | 37.0426 | 2.53218 | ||||||||
\(215\) | 7.98705 | 0.544712 | ||||||||
\(216\) | −21.4878 | −1.46206 | ||||||||
\(217\) | −12.8911 | −0.875108 | ||||||||
\(218\) | 2.86158 | 0.193811 | ||||||||
\(219\) | −12.8532 | −0.868539 | ||||||||
\(220\) | −8.16302 | −0.550351 | ||||||||
\(221\) | 1.35248 | 0.0909775 | ||||||||
\(222\) | −17.4999 | −1.17451 | ||||||||
\(223\) | −5.52585 | −0.370038 | −0.185019 | − | 0.982735i | \(-0.559235\pi\) | ||||
−0.185019 | + | 0.982735i | \(0.559235\pi\) | |||||||
\(224\) | −3.22956 | −0.215784 | ||||||||
\(225\) | 1.19936 | 0.0799570 | ||||||||
\(226\) | −24.4269 | −1.62486 | ||||||||
\(227\) | −7.32329 | −0.486064 | −0.243032 | − | 0.970018i | \(-0.578142\pi\) | ||||
−0.243032 | + | 0.970018i | \(0.578142\pi\) | |||||||
\(228\) | −4.99217 | −0.330614 | ||||||||
\(229\) | −1.07543 | −0.0710664 | −0.0355332 | − | 0.999368i | \(-0.511313\pi\) | ||||
−0.0355332 | + | 0.999368i | \(0.511313\pi\) | |||||||
\(230\) | −38.1860 | −2.51791 | ||||||||
\(231\) | 2.47583 | 0.162898 | ||||||||
\(232\) | −21.5520 | −1.41496 | ||||||||
\(233\) | −1.67722 | −0.109879 | −0.0549393 | − | 0.998490i | \(-0.517497\pi\) | ||||
−0.0549393 | + | 0.998490i | \(0.517497\pi\) | |||||||
\(234\) | −6.88696 | −0.450215 | ||||||||
\(235\) | 25.4847 | 1.66244 | ||||||||
\(236\) | 28.4163 | 1.84975 | ||||||||
\(237\) | 10.3268 | 0.670801 | ||||||||
\(238\) | −6.70382 | −0.434544 | ||||||||
\(239\) | −10.8477 | −0.701682 | −0.350841 | − | 0.936435i | \(-0.614104\pi\) | ||||
−0.350841 | + | 0.936435i | \(0.614104\pi\) | |||||||
\(240\) | 6.29289 | 0.406205 | ||||||||
\(241\) | −7.48950 | −0.482441 | −0.241221 | − | 0.970470i | \(-0.577548\pi\) | ||||
−0.241221 | + | 0.970470i | \(0.577548\pi\) | |||||||
\(242\) | −2.42329 | −0.155775 | ||||||||
\(243\) | −16.1546 | −1.03632 | ||||||||
\(244\) | 14.2869 | 0.914625 | ||||||||
\(245\) | −0.562206 | −0.0359180 | ||||||||
\(246\) | 19.7065 | 1.25644 | ||||||||
\(247\) | −1.84989 | −0.117706 | ||||||||
\(248\) | −21.6975 | −1.37779 | ||||||||
\(249\) | −14.6314 | −0.927229 | ||||||||
\(250\) | −28.3831 | −1.79510 | ||||||||
\(251\) | 27.7115 | 1.74914 | 0.874568 | − | 0.484903i | \(-0.161145\pi\) | ||||
0.874568 | + | 0.484903i | \(0.161145\pi\) | |||||||
\(252\) | 22.5103 | 1.41802 | ||||||||
\(253\) | −7.47517 | −0.469960 | ||||||||
\(254\) | −3.72241 | −0.233565 | ||||||||
\(255\) | −1.98692 | −0.124426 | ||||||||
\(256\) | −30.6080 | −1.91300 | ||||||||
\(257\) | 9.95515 | 0.620985 | 0.310492 | − | 0.950576i | \(-0.399506\pi\) | ||||
0.310492 | + | 0.950576i | \(0.399506\pi\) | |||||||
\(258\) | −8.43268 | −0.524996 | ||||||||
\(259\) | 21.1956 | 1.31703 | ||||||||
\(260\) | 10.7580 | 0.667184 | ||||||||
\(261\) | −10.2433 | −0.634046 | ||||||||
\(262\) | −2.65830 | −0.164230 | ||||||||
\(263\) | −17.1976 | −1.06045 | −0.530225 | − | 0.847857i | \(-0.677892\pi\) | ||||
−0.530225 | + | 0.847857i | \(0.677892\pi\) | |||||||
\(264\) | 4.16716 | 0.256471 | ||||||||
\(265\) | −7.77627 | −0.477692 | ||||||||
\(266\) | 9.16933 | 0.562208 | ||||||||
\(267\) | −8.13192 | −0.497666 | ||||||||
\(268\) | −11.6517 | −0.711739 | ||||||||
\(269\) | −2.54516 | −0.155181 | −0.0775904 | − | 0.996985i | \(-0.524723\pi\) | ||||
−0.0775904 | + | 0.996985i | \(0.524723\pi\) | |||||||
\(270\) | 24.1929 | 1.47234 | ||||||||
\(271\) | −2.92557 | −0.177716 | −0.0888580 | − | 0.996044i | \(-0.528322\pi\) | ||||
−0.0888580 | + | 0.996044i | \(0.528322\pi\) | |||||||
\(272\) | −3.33555 | −0.202247 | ||||||||
\(273\) | −3.26289 | −0.197479 | ||||||||
\(274\) | −20.4207 | −1.23366 | ||||||||
\(275\) | −0.556169 | −0.0335382 | ||||||||
\(276\) | 26.5856 | 1.60026 | ||||||||
\(277\) | 8.69420 | 0.522384 | 0.261192 | − | 0.965287i | \(-0.415884\pi\) | ||||
0.261192 | + | 0.965287i | \(0.415884\pi\) | |||||||
\(278\) | 15.6753 | 0.940145 | ||||||||
\(279\) | −10.3125 | −0.617394 | ||||||||
\(280\) | −25.7830 | −1.54083 | ||||||||
\(281\) | 23.3912 | 1.39540 | 0.697701 | − | 0.716389i | \(-0.254207\pi\) | ||||
0.697701 | + | 0.716389i | \(0.254207\pi\) | |||||||
\(282\) | −26.9066 | −1.60227 | ||||||||
\(283\) | 24.8099 | 1.47479 | 0.737397 | − | 0.675459i | \(-0.236055\pi\) | ||||
0.737397 | + | 0.675459i | \(0.236055\pi\) | |||||||
\(284\) | 18.8070 | 1.11599 | ||||||||
\(285\) | 2.71767 | 0.160981 | ||||||||
\(286\) | 3.19364 | 0.188844 | ||||||||
\(287\) | −23.8682 | −1.40890 | ||||||||
\(288\) | −2.58355 | −0.152237 | ||||||||
\(289\) | −15.9468 | −0.938049 | ||||||||
\(290\) | 24.2652 | 1.42490 | ||||||||
\(291\) | −5.89751 | −0.345718 | ||||||||
\(292\) | 54.1914 | 3.17131 | ||||||||
\(293\) | 9.94455 | 0.580967 | 0.290483 | − | 0.956880i | \(-0.406184\pi\) | ||||
0.290483 | + | 0.956880i | \(0.406184\pi\) | |||||||
\(294\) | 0.593574 | 0.0346180 | ||||||||
\(295\) | −15.4694 | −0.900666 | ||||||||
\(296\) | 35.6749 | 2.07356 | ||||||||
\(297\) | 4.73592 | 0.274806 | ||||||||
\(298\) | −17.0584 | −0.988168 | ||||||||
\(299\) | 9.85149 | 0.569727 | ||||||||
\(300\) | 1.97803 | 0.114201 | ||||||||
\(301\) | 10.2135 | 0.588698 | ||||||||
\(302\) | −10.8624 | −0.625063 | ||||||||
\(303\) | 14.2463 | 0.818427 | ||||||||
\(304\) | 4.56229 | 0.261665 | ||||||||
\(305\) | −7.77759 | −0.445343 | ||||||||
\(306\) | −5.36284 | −0.306573 | ||||||||
\(307\) | 11.2560 | 0.642414 | 0.321207 | − | 0.947009i | \(-0.395912\pi\) | ||||
0.321207 | + | 0.947009i | \(0.395912\pi\) | |||||||
\(308\) | −10.4386 | −0.594792 | ||||||||
\(309\) | −10.6823 | −0.607692 | ||||||||
\(310\) | 24.4291 | 1.38748 | ||||||||
\(311\) | 12.4455 | 0.705721 | 0.352861 | − | 0.935676i | \(-0.385209\pi\) | ||||
0.352861 | + | 0.935676i | \(0.385209\pi\) | |||||||
\(312\) | −5.49188 | −0.310917 | ||||||||
\(313\) | −3.16794 | −0.179062 | −0.0895312 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895312 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(314\) | 9.52305 | 0.537417 | ||||||||
\(315\) | −12.2543 | −0.690452 | ||||||||
\(316\) | −43.5398 | −2.44931 | ||||||||
\(317\) | −2.69488 | −0.151360 | −0.0756798 | − | 0.997132i | \(-0.524113\pi\) | ||||
−0.0756798 | + | 0.997132i | \(0.524113\pi\) | |||||||
\(318\) | 8.21014 | 0.460402 | ||||||||
\(319\) | 4.75007 | 0.265953 | ||||||||
\(320\) | 19.8235 | 1.10817 | ||||||||
\(321\) | 14.0394 | 0.783605 | ||||||||
\(322\) | −48.8309 | −2.72124 | ||||||||
\(323\) | −1.44050 | −0.0801515 | ||||||||
\(324\) | 8.20814 | 0.456008 | ||||||||
\(325\) | 0.732973 | 0.0406580 | ||||||||
\(326\) | −33.6862 | −1.86571 | ||||||||
\(327\) | 1.08456 | 0.0599764 | ||||||||
\(328\) | −40.1734 | −2.21821 | ||||||||
\(329\) | 32.5889 | 1.79668 | ||||||||
\(330\) | −4.69177 | −0.258274 | ||||||||
\(331\) | 14.0372 | 0.771553 | 0.385777 | − | 0.922592i | \(-0.373934\pi\) | ||||
0.385777 | + | 0.922592i | \(0.373934\pi\) | |||||||
\(332\) | 61.6887 | 3.38561 | ||||||||
\(333\) | 16.9558 | 0.929170 | ||||||||
\(334\) | −4.75777 | −0.260334 | ||||||||
\(335\) | 6.34300 | 0.346555 | ||||||||
\(336\) | 8.04711 | 0.439006 | ||||||||
\(337\) | 21.0536 | 1.14686 | 0.573430 | − | 0.819255i | \(-0.305612\pi\) | ||||
0.573430 | + | 0.819255i | \(0.305612\pi\) | |||||||
\(338\) | 27.2939 | 1.48459 | ||||||||
\(339\) | −9.25800 | −0.502825 | ||||||||
\(340\) | 8.37721 | 0.454318 | ||||||||
\(341\) | 4.78215 | 0.258968 | ||||||||
\(342\) | 7.33518 | 0.396641 | ||||||||
\(343\) | 18.1508 | 0.980053 | ||||||||
\(344\) | 17.1907 | 0.926862 | ||||||||
\(345\) | −14.4728 | −0.779190 | ||||||||
\(346\) | 20.8597 | 1.12143 | ||||||||
\(347\) | 35.7373 | 1.91848 | 0.959239 | − | 0.282595i | \(-0.0911954\pi\) | ||||
0.959239 | + | 0.282595i | \(0.0911954\pi\) | |||||||
\(348\) | −16.8937 | −0.905598 | ||||||||
\(349\) | −15.1078 | −0.808701 | −0.404351 | − | 0.914604i | \(-0.632502\pi\) | ||||
−0.404351 | + | 0.914604i | \(0.632502\pi\) | |||||||
\(350\) | −3.63312 | −0.194199 | ||||||||
\(351\) | −6.24146 | −0.333144 | ||||||||
\(352\) | 1.19805 | 0.0638564 | ||||||||
\(353\) | −2.53152 | −0.134739 | −0.0673696 | − | 0.997728i | \(-0.521461\pi\) | ||||
−0.0673696 | + | 0.997728i | \(0.521461\pi\) | |||||||
\(354\) | 16.3326 | 0.868065 | ||||||||
\(355\) | −10.2382 | −0.543389 | ||||||||
\(356\) | 34.2856 | 1.81714 | ||||||||
\(357\) | −2.54080 | −0.134473 | ||||||||
\(358\) | −37.6957 | −1.99228 | ||||||||
\(359\) | −5.30166 | −0.279811 | −0.139905 | − | 0.990165i | \(-0.544680\pi\) | ||||
−0.139905 | + | 0.990165i | \(0.544680\pi\) | |||||||
\(360\) | −20.6256 | −1.08707 | ||||||||
\(361\) | −17.0297 | −0.896301 | ||||||||
\(362\) | 21.7048 | 1.14078 | ||||||||
\(363\) | −0.918445 | −0.0482059 | ||||||||
\(364\) | 13.7569 | 0.721060 | ||||||||
\(365\) | −29.5010 | −1.54415 | ||||||||
\(366\) | 8.21153 | 0.429224 | ||||||||
\(367\) | 9.13428 | 0.476806 | 0.238403 | − | 0.971166i | \(-0.423376\pi\) | ||||
0.238403 | + | 0.971166i | \(0.423376\pi\) | |||||||
\(368\) | −24.2963 | −1.26653 | ||||||||
\(369\) | −19.0938 | −0.993985 | ||||||||
\(370\) | −40.1661 | −2.08814 | ||||||||
\(371\) | −9.94399 | −0.516266 | ||||||||
\(372\) | −17.0078 | −0.881813 | ||||||||
\(373\) | 6.53079 | 0.338151 | 0.169076 | − | 0.985603i | \(-0.445922\pi\) | ||||
0.169076 | + | 0.985603i | \(0.445922\pi\) | |||||||
\(374\) | 2.48687 | 0.128593 | ||||||||
\(375\) | −10.7574 | −0.555510 | ||||||||
\(376\) | 54.8514 | 2.82874 | ||||||||
\(377\) | −6.26010 | −0.322411 | ||||||||
\(378\) | 30.9370 | 1.59123 | ||||||||
\(379\) | −19.6425 | −1.00897 | −0.504485 | − | 0.863421i | \(-0.668318\pi\) | ||||
−0.504485 | + | 0.863421i | \(0.668318\pi\) | |||||||
\(380\) | −11.4582 | −0.587791 | ||||||||
\(381\) | −1.41082 | −0.0722785 | ||||||||
\(382\) | −56.0502 | −2.86778 | ||||||||
\(383\) | −28.0869 | −1.43517 | −0.717586 | − | 0.696470i | \(-0.754753\pi\) | ||||
−0.717586 | + | 0.696470i | \(0.754753\pi\) | |||||||
\(384\) | −18.7288 | −0.955752 | ||||||||
\(385\) | 5.68260 | 0.289612 | ||||||||
\(386\) | 64.9341 | 3.30506 | ||||||||
\(387\) | 8.17050 | 0.415330 | ||||||||
\(388\) | 24.8650 | 1.26233 | ||||||||
\(389\) | 14.8286 | 0.751841 | 0.375921 | − | 0.926652i | \(-0.377327\pi\) | ||||
0.375921 | + | 0.926652i | \(0.377327\pi\) | |||||||
\(390\) | 6.18327 | 0.313102 | ||||||||
\(391\) | 7.67131 | 0.387955 | ||||||||
\(392\) | −1.21005 | −0.0611168 | ||||||||
\(393\) | −1.00752 | −0.0508224 | ||||||||
\(394\) | 3.87522 | 0.195231 | ||||||||
\(395\) | 23.7025 | 1.19260 | ||||||||
\(396\) | −8.35052 | −0.419629 | ||||||||
\(397\) | 0.513142 | 0.0257539 | 0.0128769 | − | 0.999917i | \(-0.495901\pi\) | ||||
0.0128769 | + | 0.999917i | \(0.495901\pi\) | |||||||
\(398\) | −29.3056 | −1.46895 | ||||||||
\(399\) | 3.47525 | 0.173980 | ||||||||
\(400\) | −1.80770 | −0.0903848 | ||||||||
\(401\) | 33.4550 | 1.67066 | 0.835332 | − | 0.549746i | \(-0.185276\pi\) | ||||
0.835332 | + | 0.549746i | \(0.185276\pi\) | |||||||
\(402\) | −6.69690 | −0.334011 | ||||||||
\(403\) | −6.30238 | −0.313944 | ||||||||
\(404\) | −60.0648 | −2.98834 | ||||||||
\(405\) | −4.46840 | −0.222036 | ||||||||
\(406\) | 31.0294 | 1.53996 | ||||||||
\(407\) | −7.86278 | −0.389744 | ||||||||
\(408\) | −4.27650 | −0.211718 | ||||||||
\(409\) | −2.57499 | −0.127325 | −0.0636625 | − | 0.997971i | \(-0.520278\pi\) | ||||
−0.0636625 | + | 0.997971i | \(0.520278\pi\) | |||||||
\(410\) | 45.2310 | 2.23380 | ||||||||
\(411\) | −7.73960 | −0.381766 | ||||||||
\(412\) | 45.0383 | 2.21888 | ||||||||
\(413\) | −19.7817 | −0.973395 | ||||||||
\(414\) | −39.0631 | −1.91985 | ||||||||
\(415\) | −33.5824 | −1.64850 | ||||||||
\(416\) | −1.57891 | −0.0774123 | ||||||||
\(417\) | 5.94108 | 0.290936 | ||||||||
\(418\) | −3.40149 | −0.166372 | ||||||||
\(419\) | 24.7432 | 1.20879 | 0.604393 | − | 0.796687i | \(-0.293416\pi\) | ||||
0.604393 | + | 0.796687i | \(0.293416\pi\) | |||||||
\(420\) | −20.2103 | −0.986161 | ||||||||
\(421\) | −22.4123 | −1.09231 | −0.546154 | − | 0.837685i | \(-0.683909\pi\) | ||||
−0.546154 | + | 0.837685i | \(0.683909\pi\) | |||||||
\(422\) | 20.8678 | 1.01583 | ||||||||
\(423\) | 26.0701 | 1.26757 | ||||||||
\(424\) | −16.7371 | −0.812823 | ||||||||
\(425\) | 0.570762 | 0.0276860 | ||||||||
\(426\) | 10.8095 | 0.523721 | ||||||||
\(427\) | −9.94568 | −0.481305 | ||||||||
\(428\) | −59.1928 | −2.86119 | ||||||||
\(429\) | 1.21042 | 0.0584394 | ||||||||
\(430\) | −19.3549 | −0.933377 | ||||||||
\(431\) | −3.30159 | −0.159032 | −0.0795161 | − | 0.996834i | \(-0.525338\pi\) | ||||
−0.0795161 | + | 0.996834i | \(0.525338\pi\) | |||||||
\(432\) | 15.3930 | 0.740596 | ||||||||
\(433\) | 6.45790 | 0.310347 | 0.155174 | − | 0.987887i | \(-0.450406\pi\) | ||||
0.155174 | + | 0.987887i | \(0.450406\pi\) | |||||||
\(434\) | 31.2390 | 1.49952 | ||||||||
\(435\) | 9.19669 | 0.440948 | ||||||||
\(436\) | −4.57270 | −0.218993 | ||||||||
\(437\) | −10.4926 | −0.501931 | ||||||||
\(438\) | 31.1470 | 1.48826 | ||||||||
\(439\) | −16.7949 | −0.801577 | −0.400788 | − | 0.916171i | \(-0.631264\pi\) | ||||
−0.400788 | + | 0.916171i | \(0.631264\pi\) | |||||||
\(440\) | 9.56457 | 0.455973 | ||||||||
\(441\) | −0.575119 | −0.0273866 | ||||||||
\(442\) | −3.27744 | −0.155892 | ||||||||
\(443\) | −30.6915 | −1.45820 | −0.729098 | − | 0.684409i | \(-0.760060\pi\) | ||||
−0.729098 | + | 0.684409i | \(0.760060\pi\) | |||||||
\(444\) | 27.9641 | 1.32712 | ||||||||
\(445\) | −18.6646 | −0.884788 | ||||||||
\(446\) | 13.3907 | 0.634069 | ||||||||
\(447\) | −6.46528 | −0.305797 | ||||||||
\(448\) | 25.3495 | 1.19765 | ||||||||
\(449\) | −1.56946 | −0.0740674 | −0.0370337 | − | 0.999314i | \(-0.511791\pi\) | ||||
−0.0370337 | + | 0.999314i | \(0.511791\pi\) | |||||||
\(450\) | −2.90638 | −0.137008 | ||||||||
\(451\) | 8.85425 | 0.416930 | ||||||||
\(452\) | 39.0334 | 1.83598 | ||||||||
\(453\) | −4.11695 | −0.193431 | ||||||||
\(454\) | 17.7464 | 0.832882 | ||||||||
\(455\) | −7.48908 | −0.351094 | ||||||||
\(456\) | 5.84930 | 0.273919 | ||||||||
\(457\) | −34.5254 | −1.61503 | −0.807516 | − | 0.589845i | \(-0.799189\pi\) | ||||
−0.807516 | + | 0.589845i | \(0.799189\pi\) | |||||||
\(458\) | 2.60608 | 0.121774 | ||||||||
\(459\) | −4.86019 | −0.226854 | ||||||||
\(460\) | 61.0199 | 2.84507 | ||||||||
\(461\) | 27.4203 | 1.27709 | 0.638544 | − | 0.769585i | \(-0.279537\pi\) | ||||
0.638544 | + | 0.769585i | \(0.279537\pi\) | |||||||
\(462\) | −5.99966 | −0.279129 | ||||||||
\(463\) | −3.61913 | −0.168195 | −0.0840976 | − | 0.996458i | \(-0.526801\pi\) | ||||
−0.0840976 | + | 0.996458i | \(0.526801\pi\) | |||||||
\(464\) | 15.4390 | 0.716736 | ||||||||
\(465\) | 9.25880 | 0.429367 | ||||||||
\(466\) | 4.06440 | 0.188280 | ||||||||
\(467\) | 2.56468 | 0.118679 | 0.0593397 | − | 0.998238i | \(-0.481100\pi\) | ||||
0.0593397 | + | 0.998238i | \(0.481100\pi\) | |||||||
\(468\) | 11.0051 | 0.508712 | ||||||||
\(469\) | 8.11119 | 0.374540 | ||||||||
\(470\) | −61.7568 | −2.84863 | ||||||||
\(471\) | 3.60931 | 0.166308 | ||||||||
\(472\) | −33.2953 | −1.53254 | ||||||||
\(473\) | −3.78885 | −0.174212 | ||||||||
\(474\) | −25.0249 | −1.14943 | ||||||||
\(475\) | −0.780676 | −0.0358199 | ||||||||
\(476\) | 10.7125 | 0.491005 | ||||||||
\(477\) | −7.95488 | −0.364229 | ||||||||
\(478\) | 26.2872 | 1.20235 | ||||||||
\(479\) | −2.93213 | −0.133973 | −0.0669863 | − | 0.997754i | \(-0.521338\pi\) | ||||
−0.0669863 | + | 0.997754i | \(0.521338\pi\) | |||||||
\(480\) | 2.31957 | 0.105873 | ||||||||
\(481\) | 10.3623 | 0.472482 | ||||||||
\(482\) | 18.1492 | 0.826674 | ||||||||
\(483\) | −18.5073 | −0.842110 | ||||||||
\(484\) | 3.87233 | 0.176015 | ||||||||
\(485\) | −13.5361 | −0.614644 | ||||||||
\(486\) | 39.1472 | 1.77575 | ||||||||
\(487\) | −10.3197 | −0.467628 | −0.233814 | − | 0.972281i | \(-0.575121\pi\) | ||||
−0.233814 | + | 0.972281i | \(0.575121\pi\) | |||||||
\(488\) | −16.7399 | −0.757780 | ||||||||
\(489\) | −12.7673 | −0.577358 | ||||||||
\(490\) | 1.36239 | 0.0615464 | ||||||||
\(491\) | −17.6388 | −0.796027 | −0.398014 | − | 0.917380i | \(-0.630300\pi\) | ||||
−0.398014 | + | 0.917380i | \(0.630300\pi\) | |||||||
\(492\) | −31.4903 | −1.41969 | ||||||||
\(493\) | −4.87471 | −0.219546 | ||||||||
\(494\) | 4.48281 | 0.201691 | ||||||||
\(495\) | 4.54590 | 0.204323 | ||||||||
\(496\) | 15.5432 | 0.697912 | ||||||||
\(497\) | −13.0923 | −0.587269 | ||||||||
\(498\) | 35.4562 | 1.58883 | ||||||||
\(499\) | −26.2776 | −1.17635 | −0.588175 | − | 0.808734i | \(-0.700153\pi\) | ||||
−0.588175 | + | 0.808734i | \(0.700153\pi\) | |||||||
\(500\) | 45.3551 | 2.02834 | ||||||||
\(501\) | −1.80323 | −0.0805625 | ||||||||
\(502\) | −67.1530 | −2.99719 | ||||||||
\(503\) | −36.6836 | −1.63564 | −0.817819 | − | 0.575475i | \(-0.804817\pi\) | ||||
−0.817819 | + | 0.575475i | \(0.804817\pi\) | |||||||
\(504\) | −26.3753 | −1.17485 | ||||||||
\(505\) | 32.6984 | 1.45506 | ||||||||
\(506\) | 18.1145 | 0.805287 | ||||||||
\(507\) | 10.3446 | 0.459419 | ||||||||
\(508\) | 5.94827 | 0.263912 | ||||||||
\(509\) | −22.0754 | −0.978473 | −0.489236 | − | 0.872151i | \(-0.662724\pi\) | ||||
−0.489236 | + | 0.872151i | \(0.662724\pi\) | |||||||
\(510\) | 4.81488 | 0.213207 | ||||||||
\(511\) | −37.7248 | −1.66885 | ||||||||
\(512\) | 33.3881 | 1.47556 | ||||||||
\(513\) | 6.64766 | 0.293501 | ||||||||
\(514\) | −24.1242 | −1.06407 | ||||||||
\(515\) | −24.5182 | −1.08040 | ||||||||
\(516\) | 13.4751 | 0.593209 | ||||||||
\(517\) | −12.0893 | −0.531686 | ||||||||
\(518\) | −51.3629 | −2.25676 | ||||||||
\(519\) | 7.90600 | 0.347035 | ||||||||
\(520\) | −12.6051 | −0.552771 | ||||||||
\(521\) | −26.7323 | −1.17116 | −0.585581 | − | 0.810614i | \(-0.699133\pi\) | ||||
−0.585581 | + | 0.810614i | \(0.699133\pi\) | |||||||
\(522\) | 24.8225 | 1.08645 | ||||||||
\(523\) | 2.28156 | 0.0997655 | 0.0498827 | − | 0.998755i | \(-0.484115\pi\) | ||||
0.0498827 | + | 0.998755i | \(0.484115\pi\) | |||||||
\(524\) | 4.24786 | 0.185569 | ||||||||
\(525\) | −1.37698 | −0.0600964 | ||||||||
\(526\) | 41.6747 | 1.81711 | ||||||||
\(527\) | −4.90763 | −0.213780 | ||||||||
\(528\) | −2.98519 | −0.129914 | ||||||||
\(529\) | 32.8781 | 1.42948 | ||||||||
\(530\) | 18.8441 | 0.818537 | ||||||||
\(531\) | −15.8248 | −0.686736 | ||||||||
\(532\) | −14.6523 | −0.635256 | ||||||||
\(533\) | −11.6690 | −0.505440 | ||||||||
\(534\) | 19.7060 | 0.852762 | ||||||||
\(535\) | 32.2237 | 1.39315 | ||||||||
\(536\) | 13.6522 | 0.589685 | ||||||||
\(537\) | −14.2870 | −0.616528 | ||||||||
\(538\) | 6.16765 | 0.265906 | ||||||||
\(539\) | 0.266696 | 0.0114874 | ||||||||
\(540\) | −38.6594 | −1.66364 | ||||||||
\(541\) | −27.4207 | −1.17891 | −0.589455 | − | 0.807801i | \(-0.700657\pi\) | ||||
−0.589455 | + | 0.807801i | \(0.700657\pi\) | |||||||
\(542\) | 7.08951 | 0.304520 | ||||||||
\(543\) | 8.22630 | 0.353024 | ||||||||
\(544\) | −1.22949 | −0.0527138 | ||||||||
\(545\) | 2.48931 | 0.106631 | ||||||||
\(546\) | 7.90693 | 0.338385 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 32.6315 | 1.39395 | ||||||||
\(549\) | −7.95623 | −0.339564 | ||||||||
\(550\) | 1.34776 | 0.0574686 | ||||||||
\(551\) | 6.66752 | 0.284046 | ||||||||
\(552\) | −31.1502 | −1.32584 | ||||||||
\(553\) | 30.3098 | 1.28890 | ||||||||
\(554\) | −21.0686 | −0.895118 | ||||||||
\(555\) | −15.2233 | −0.646192 | ||||||||
\(556\) | −25.0486 | −1.06230 | ||||||||
\(557\) | −41.1637 | −1.74416 | −0.872081 | − | 0.489362i | \(-0.837230\pi\) | ||||
−0.872081 | + | 0.489362i | \(0.837230\pi\) | |||||||
\(558\) | 24.9902 | 1.05792 | ||||||||
\(559\) | 4.99331 | 0.211195 | ||||||||
\(560\) | 18.4700 | 0.780498 | ||||||||
\(561\) | 0.942544 | 0.0397942 | ||||||||
\(562\) | −56.6836 | −2.39105 | ||||||||
\(563\) | −41.9675 | −1.76872 | −0.884360 | − | 0.466806i | \(-0.845405\pi\) | ||||
−0.884360 | + | 0.466806i | \(0.845405\pi\) | |||||||
\(564\) | 42.9958 | 1.81045 | ||||||||
\(565\) | −21.2492 | −0.893961 | ||||||||
\(566\) | −60.1215 | −2.52710 | ||||||||
\(567\) | −5.71402 | −0.239966 | ||||||||
\(568\) | −22.0360 | −0.924611 | ||||||||
\(569\) | −15.5916 | −0.653636 | −0.326818 | − | 0.945087i | \(-0.605976\pi\) | ||||
−0.326818 | + | 0.945087i | \(0.605976\pi\) | |||||||
\(570\) | −6.58569 | −0.275844 | ||||||||
\(571\) | −30.3166 | −1.26871 | −0.634355 | − | 0.773042i | \(-0.718734\pi\) | ||||
−0.634355 | + | 0.773042i | \(0.718734\pi\) | |||||||
\(572\) | −5.10333 | −0.213381 | ||||||||
\(573\) | −21.2434 | −0.887457 | ||||||||
\(574\) | 57.8396 | 2.41418 | ||||||||
\(575\) | 4.15745 | 0.173378 | ||||||||
\(576\) | 20.2788 | 0.844950 | ||||||||
\(577\) | 35.9008 | 1.49457 | 0.747285 | − | 0.664504i | \(-0.231357\pi\) | ||||
0.747285 | + | 0.664504i | \(0.231357\pi\) | |||||||
\(578\) | 38.6438 | 1.60737 | ||||||||
\(579\) | 24.6105 | 1.02278 | ||||||||
\(580\) | −38.7749 | −1.61004 | ||||||||
\(581\) | −42.9439 | −1.78162 | ||||||||
\(582\) | 14.2914 | 0.592396 | ||||||||
\(583\) | 3.68886 | 0.152777 | ||||||||
\(584\) | −63.4958 | −2.62748 | ||||||||
\(585\) | −5.99103 | −0.247698 | ||||||||
\(586\) | −24.0985 | −0.995501 | ||||||||
\(587\) | 8.33164 | 0.343884 | 0.171942 | − | 0.985107i | \(-0.444996\pi\) | ||||
0.171942 | + | 0.985107i | \(0.444996\pi\) | |||||||
\(588\) | −0.948510 | −0.0391159 | ||||||||
\(589\) | 6.71254 | 0.276586 | ||||||||
\(590\) | 37.4869 | 1.54331 | ||||||||
\(591\) | 1.46874 | 0.0604158 | ||||||||
\(592\) | −25.5561 | −1.05035 | ||||||||
\(593\) | −10.7932 | −0.443225 | −0.221613 | − | 0.975135i | \(-0.571132\pi\) | ||||
−0.221613 | + | 0.975135i | \(0.571132\pi\) | |||||||
\(594\) | −11.4765 | −0.470887 | ||||||||
\(595\) | −5.83171 | −0.239077 | ||||||||
\(596\) | 27.2588 | 1.11656 | ||||||||
\(597\) | −11.1070 | −0.454580 | ||||||||
\(598\) | −23.8730 | −0.976240 | ||||||||
\(599\) | −18.5253 | −0.756924 | −0.378462 | − | 0.925617i | \(-0.623547\pi\) | ||||
−0.378462 | + | 0.925617i | \(0.623547\pi\) | |||||||
\(600\) | −2.31764 | −0.0946174 | ||||||||
\(601\) | 44.5411 | 1.81687 | 0.908435 | − | 0.418027i | \(-0.137278\pi\) | ||||
0.908435 | + | 0.418027i | \(0.137278\pi\) | |||||||
\(602\) | −24.7503 | −1.00875 | ||||||||
\(603\) | 6.48869 | 0.264240 | ||||||||
\(604\) | 17.3578 | 0.706278 | ||||||||
\(605\) | −2.10804 | −0.0857040 | ||||||||
\(606\) | −34.5228 | −1.40239 | ||||||||
\(607\) | −22.1435 | −0.898775 | −0.449388 | − | 0.893337i | \(-0.648358\pi\) | ||||
−0.449388 | + | 0.893337i | \(0.648358\pi\) | |||||||
\(608\) | 1.68167 | 0.0682005 | ||||||||
\(609\) | 11.7604 | 0.476555 | ||||||||
\(610\) | 18.8473 | 0.763106 | ||||||||
\(611\) | 15.9324 | 0.644557 | ||||||||
\(612\) | 8.56963 | 0.346407 | ||||||||
\(613\) | −22.7573 | −0.919157 | −0.459578 | − | 0.888137i | \(-0.651999\pi\) | ||||
−0.459578 | + | 0.888137i | \(0.651999\pi\) | |||||||
\(614\) | −27.2765 | −1.10079 | ||||||||
\(615\) | 17.1429 | 0.691268 | ||||||||
\(616\) | 12.2308 | 0.492794 | ||||||||
\(617\) | −5.65514 | −0.227667 | −0.113834 | − | 0.993500i | \(-0.536313\pi\) | ||||
−0.113834 | + | 0.993500i | \(0.536313\pi\) | |||||||
\(618\) | 25.8862 | 1.04129 | ||||||||
\(619\) | −8.76926 | −0.352466 | −0.176233 | − | 0.984348i | \(-0.556391\pi\) | ||||
−0.176233 | + | 0.984348i | \(0.556391\pi\) | |||||||
\(620\) | −39.0368 | −1.56775 | ||||||||
\(621\) | −35.4018 | −1.42063 | ||||||||
\(622\) | −30.1591 | −1.20927 | ||||||||
\(623\) | −23.8676 | −0.956235 | ||||||||
\(624\) | 3.93417 | 0.157493 | ||||||||
\(625\) | −21.9098 | −0.876393 | ||||||||
\(626\) | 7.67682 | 0.306828 | ||||||||
\(627\) | −1.28919 | −0.0514853 | ||||||||
\(628\) | −15.2175 | −0.607244 | ||||||||
\(629\) | 8.06910 | 0.321736 | ||||||||
\(630\) | 29.6957 | 1.18311 | ||||||||
\(631\) | −0.148030 | −0.00589297 | −0.00294649 | − | 0.999996i | \(-0.500938\pi\) | ||||
−0.00294649 | + | 0.999996i | \(0.500938\pi\) | |||||||
\(632\) | 51.0154 | 2.02929 | ||||||||
\(633\) | 7.90907 | 0.314357 | ||||||||
\(634\) | 6.53048 | 0.259358 | ||||||||
\(635\) | −3.23815 | −0.128502 | ||||||||
\(636\) | −13.1195 | −0.520222 | ||||||||
\(637\) | −0.351478 | −0.0139261 | ||||||||
\(638\) | −11.5108 | −0.455716 | ||||||||
\(639\) | −10.4734 | −0.414321 | ||||||||
\(640\) | −42.9869 | −1.69921 | ||||||||
\(641\) | −11.8264 | −0.467115 | −0.233557 | − | 0.972343i | \(-0.575037\pi\) | ||||
−0.233557 | + | 0.972343i | \(0.575037\pi\) | |||||||
\(642\) | −34.0216 | −1.34273 | ||||||||
\(643\) | −14.1666 | −0.558676 | −0.279338 | − | 0.960193i | \(-0.590115\pi\) | ||||
−0.279338 | + | 0.960193i | \(0.590115\pi\) | |||||||
\(644\) | 78.0300 | 3.07481 | ||||||||
\(645\) | −7.33566 | −0.288841 | ||||||||
\(646\) | 3.49074 | 0.137341 | ||||||||
\(647\) | 19.0243 | 0.747923 | 0.373962 | − | 0.927444i | \(-0.377999\pi\) | ||||
0.373962 | + | 0.927444i | \(0.377999\pi\) | |||||||
\(648\) | −9.61745 | −0.377809 | ||||||||
\(649\) | 7.33831 | 0.288054 | ||||||||
\(650\) | −1.77621 | −0.0696685 | ||||||||
\(651\) | 11.8398 | 0.464039 | ||||||||
\(652\) | 53.8293 | 2.10812 | ||||||||
\(653\) | 8.26613 | 0.323479 | 0.161739 | − | 0.986834i | \(-0.448290\pi\) | ||||
0.161739 | + | 0.986834i | \(0.448290\pi\) | |||||||
\(654\) | −2.62820 | −0.102771 | ||||||||
\(655\) | −2.31248 | −0.0903559 | ||||||||
\(656\) | 28.7787 | 1.12362 | ||||||||
\(657\) | −30.1786 | −1.17738 | ||||||||
\(658\) | −78.9722 | −3.07866 | ||||||||
\(659\) | −35.7654 | −1.39322 | −0.696612 | − | 0.717448i | \(-0.745310\pi\) | ||||
−0.696612 | + | 0.717448i | \(0.745310\pi\) | |||||||
\(660\) | 7.49728 | 0.291831 | ||||||||
\(661\) | 1.30544 | 0.0507757 | 0.0253879 | − | 0.999678i | \(-0.491918\pi\) | ||||
0.0253879 | + | 0.999678i | \(0.491918\pi\) | |||||||
\(662\) | −34.0161 | −1.32207 | ||||||||
\(663\) | −1.24218 | −0.0482421 | ||||||||
\(664\) | −72.2804 | −2.80502 | ||||||||
\(665\) | 7.97648 | 0.309315 | ||||||||
\(666\) | −41.0887 | −1.59216 | ||||||||
\(667\) | −35.5075 | −1.37486 | ||||||||
\(668\) | 7.60275 | 0.294159 | ||||||||
\(669\) | 5.07518 | 0.196218 | ||||||||
\(670\) | −15.3709 | −0.593830 | ||||||||
\(671\) | 3.68949 | 0.142431 | ||||||||
\(672\) | 2.96618 | 0.114423 | ||||||||
\(673\) | 14.6344 | 0.564115 | 0.282057 | − | 0.959398i | \(-0.408983\pi\) | ||||
0.282057 | + | 0.959398i | \(0.408983\pi\) | |||||||
\(674\) | −51.0188 | −1.96517 | ||||||||
\(675\) | −2.63397 | −0.101382 | ||||||||
\(676\) | −43.6146 | −1.67748 | ||||||||
\(677\) | −8.61393 | −0.331060 | −0.165530 | − | 0.986205i | \(-0.552934\pi\) | ||||
−0.165530 | + | 0.986205i | \(0.552934\pi\) | |||||||
\(678\) | 22.4348 | 0.861603 | ||||||||
\(679\) | −17.3095 | −0.664277 | ||||||||
\(680\) | −9.81554 | −0.376409 | ||||||||
\(681\) | 6.72604 | 0.257742 | ||||||||
\(682\) | −11.5885 | −0.443748 | ||||||||
\(683\) | 6.50361 | 0.248854 | 0.124427 | − | 0.992229i | \(-0.460291\pi\) | ||||
0.124427 | + | 0.992229i | \(0.460291\pi\) | |||||||
\(684\) | −11.7213 | −0.448177 | ||||||||
\(685\) | −17.7641 | −0.678733 | ||||||||
\(686\) | −43.9847 | −1.67934 | ||||||||
\(687\) | 0.987723 | 0.0376840 | ||||||||
\(688\) | −12.3148 | −0.469496 | ||||||||
\(689\) | −4.86154 | −0.185210 | ||||||||
\(690\) | 35.0718 | 1.33516 | ||||||||
\(691\) | −33.1087 | −1.25952 | −0.629758 | − | 0.776791i | \(-0.716846\pi\) | ||||
−0.629758 | + | 0.776791i | \(0.716846\pi\) | |||||||
\(692\) | −33.3331 | −1.26714 | ||||||||
\(693\) | 5.81313 | 0.220822 | ||||||||
\(694\) | −86.6018 | −3.28736 | ||||||||
\(695\) | 13.6361 | 0.517248 | ||||||||
\(696\) | 19.7943 | 0.750300 | ||||||||
\(697\) | −9.08658 | −0.344179 | ||||||||
\(698\) | 36.6105 | 1.38573 | ||||||||
\(699\) | 1.54044 | 0.0582647 | ||||||||
\(700\) | 5.80560 | 0.219431 | ||||||||
\(701\) | 33.0709 | 1.24907 | 0.624535 | − | 0.780997i | \(-0.285288\pi\) | ||||
0.624535 | + | 0.780997i | \(0.285288\pi\) | |||||||
\(702\) | 15.1248 | 0.570851 | ||||||||
\(703\) | −11.0367 | −0.416258 | ||||||||
\(704\) | −9.40375 | −0.354417 | ||||||||
\(705\) | −23.4063 | −0.881532 | ||||||||
\(706\) | 6.13460 | 0.230879 | ||||||||
\(707\) | 41.8135 | 1.57256 | ||||||||
\(708\) | −26.0988 | −0.980854 | ||||||||
\(709\) | −34.6498 | −1.30130 | −0.650650 | − | 0.759378i | \(-0.725503\pi\) | ||||
−0.650650 | + | 0.759378i | \(0.725503\pi\) | |||||||
\(710\) | 24.8102 | 0.931110 | ||||||||
\(711\) | 24.2469 | 0.909329 | ||||||||
\(712\) | −40.1723 | −1.50552 | ||||||||
\(713\) | −35.7474 | −1.33875 | ||||||||
\(714\) | 6.15709 | 0.230423 | ||||||||
\(715\) | 2.77818 | 0.103898 | ||||||||
\(716\) | 60.2364 | 2.25114 | ||||||||
\(717\) | 9.96306 | 0.372077 | ||||||||
\(718\) | 12.8475 | 0.479463 | ||||||||
\(719\) | 3.76103 | 0.140263 | 0.0701315 | − | 0.997538i | \(-0.477658\pi\) | ||||
0.0701315 | + | 0.997538i | \(0.477658\pi\) | |||||||
\(720\) | 14.7754 | 0.550646 | ||||||||
\(721\) | −31.3529 | −1.16764 | ||||||||
\(722\) | 41.2679 | 1.53583 | ||||||||
\(723\) | 6.87869 | 0.255821 | ||||||||
\(724\) | −34.6836 | −1.28900 | ||||||||
\(725\) | −2.64184 | −0.0981155 | ||||||||
\(726\) | 2.22566 | 0.0826019 | ||||||||
\(727\) | 42.9574 | 1.59320 | 0.796602 | − | 0.604505i | \(-0.206629\pi\) | ||||
0.796602 | + | 0.604505i | \(0.206629\pi\) | |||||||
\(728\) | −16.1189 | −0.597408 | ||||||||
\(729\) | 8.47802 | 0.314001 | ||||||||
\(730\) | 71.4895 | 2.64595 | ||||||||
\(731\) | 3.88827 | 0.143813 | ||||||||
\(732\) | −13.1217 | −0.484993 | ||||||||
\(733\) | 32.5724 | 1.20309 | 0.601545 | − | 0.798839i | \(-0.294552\pi\) | ||||
0.601545 | + | 0.798839i | \(0.294552\pi\) | |||||||
\(734\) | −22.1350 | −0.817018 | ||||||||
\(735\) | 0.516355 | 0.0190461 | ||||||||
\(736\) | −8.95563 | −0.330109 | ||||||||
\(737\) | −3.00896 | −0.110836 | ||||||||
\(738\) | 46.2699 | 1.70322 | ||||||||
\(739\) | −30.1478 | −1.10900 | −0.554502 | − | 0.832183i | \(-0.687091\pi\) | ||||
−0.554502 | + | 0.832183i | \(0.687091\pi\) | |||||||
\(740\) | 64.1840 | 2.35945 | ||||||||
\(741\) | 1.69902 | 0.0624151 | ||||||||
\(742\) | 24.0972 | 0.884635 | ||||||||
\(743\) | 27.1034 | 0.994328 | 0.497164 | − | 0.867657i | \(-0.334375\pi\) | ||||
0.497164 | + | 0.867657i | \(0.334375\pi\) | |||||||
\(744\) | 19.9280 | 0.730595 | ||||||||
\(745\) | −14.8393 | −0.543669 | ||||||||
\(746\) | −15.8260 | −0.579431 | ||||||||
\(747\) | −34.3538 | −1.25694 | ||||||||
\(748\) | −3.97393 | −0.145301 | ||||||||
\(749\) | 41.2064 | 1.50565 | ||||||||
\(750\) | 26.0683 | 0.951879 | ||||||||
\(751\) | −23.9887 | −0.875359 | −0.437680 | − | 0.899131i | \(-0.644200\pi\) | ||||
−0.437680 | + | 0.899131i | \(0.644200\pi\) | |||||||
\(752\) | −39.2934 | −1.43288 | ||||||||
\(753\) | −25.4515 | −0.927505 | ||||||||
\(754\) | 15.1700 | 0.552460 | ||||||||
\(755\) | −9.44933 | −0.343896 | ||||||||
\(756\) | −49.4362 | −1.79798 | ||||||||
\(757\) | −20.4233 | −0.742297 | −0.371149 | − | 0.928573i | \(-0.621036\pi\) | ||||
−0.371149 | + | 0.928573i | \(0.621036\pi\) | |||||||
\(758\) | 47.5996 | 1.72889 | ||||||||
\(759\) | 6.86553 | 0.249203 | ||||||||
\(760\) | 13.4255 | 0.486993 | ||||||||
\(761\) | 26.0309 | 0.943619 | 0.471810 | − | 0.881701i | \(-0.343601\pi\) | ||||
0.471810 | + | 0.881701i | \(0.343601\pi\) | |||||||
\(762\) | 3.41882 | 0.123851 | ||||||||
\(763\) | 3.18324 | 0.115241 | ||||||||
\(764\) | 89.5661 | 3.24039 | ||||||||
\(765\) | −4.66518 | −0.168670 | ||||||||
\(766\) | 68.0626 | 2.45920 | ||||||||
\(767\) | −9.67113 | −0.349204 | ||||||||
\(768\) | 28.1117 | 1.01439 | ||||||||
\(769\) | 32.7648 | 1.18153 | 0.590765 | − | 0.806844i | \(-0.298826\pi\) | ||||
0.590765 | + | 0.806844i | \(0.298826\pi\) | |||||||
\(770\) | −13.7706 | −0.496257 | ||||||||
\(771\) | −9.14325 | −0.329286 | ||||||||
\(772\) | −103.762 | −3.73449 | ||||||||
\(773\) | −14.4067 | −0.518175 | −0.259087 | − | 0.965854i | \(-0.583422\pi\) | ||||
−0.259087 | + | 0.965854i | \(0.583422\pi\) | |||||||
\(774\) | −19.7995 | −0.711678 | ||||||||
\(775\) | −2.65968 | −0.0955386 | ||||||||
\(776\) | −29.1342 | −1.04586 | ||||||||
\(777\) | −19.4669 | −0.698373 | ||||||||
\(778\) | −35.9340 | −1.28830 | ||||||||
\(779\) | 12.4284 | 0.445295 | ||||||||
\(780\) | −9.88064 | −0.353784 | ||||||||
\(781\) | 4.85676 | 0.173788 | ||||||||
\(782\) | −18.5898 | −0.664770 | ||||||||
\(783\) | 22.4960 | 0.803940 | ||||||||
\(784\) | 0.866833 | 0.0309583 | ||||||||
\(785\) | 8.28418 | 0.295675 | ||||||||
\(786\) | 2.44150 | 0.0870854 | ||||||||
\(787\) | −45.9728 | −1.63875 | −0.819377 | − | 0.573254i | \(-0.805681\pi\) | ||||
−0.819377 | + | 0.573254i | \(0.805681\pi\) | |||||||
\(788\) | −6.19246 | −0.220597 | ||||||||
\(789\) | 15.7950 | 0.562319 | ||||||||
\(790\) | −57.4379 | −2.04355 | ||||||||
\(791\) | −27.1727 | −0.966149 | ||||||||
\(792\) | 9.78426 | 0.347669 | ||||||||
\(793\) | −4.86236 | −0.172668 | ||||||||
\(794\) | −1.24349 | −0.0441298 | ||||||||
\(795\) | 7.14207 | 0.253303 | ||||||||
\(796\) | 46.8292 | 1.65982 | ||||||||
\(797\) | −24.0229 | −0.850935 | −0.425467 | − | 0.904974i | \(-0.639890\pi\) | ||||
−0.425467 | + | 0.904974i | \(0.639890\pi\) | |||||||
\(798\) | −8.42153 | −0.298119 | ||||||||
\(799\) | 12.4065 | 0.438911 | ||||||||
\(800\) | −0.666319 | −0.0235579 | ||||||||
\(801\) | −19.0933 | −0.674629 | ||||||||
\(802\) | −81.0711 | −2.86272 | ||||||||
\(803\) | 13.9945 | 0.493856 | ||||||||
\(804\) | 10.7014 | 0.377410 | ||||||||
\(805\) | −42.4784 | −1.49717 | ||||||||
\(806\) | 15.2725 | 0.537950 | ||||||||
\(807\) | 2.33758 | 0.0822869 | ||||||||
\(808\) | 70.3777 | 2.47588 | ||||||||
\(809\) | 40.7641 | 1.43319 | 0.716595 | − | 0.697490i | \(-0.245700\pi\) | ||||
0.716595 | + | 0.697490i | \(0.245700\pi\) | |||||||
\(810\) | 10.8282 | 0.380465 | ||||||||
\(811\) | −54.1288 | −1.90072 | −0.950360 | − | 0.311151i | \(-0.899285\pi\) | ||||
−0.950360 | + | 0.311151i | \(0.899285\pi\) | |||||||
\(812\) | −49.5839 | −1.74005 | ||||||||
\(813\) | 2.68698 | 0.0942364 | ||||||||
\(814\) | 19.0538 | 0.667835 | ||||||||
\(815\) | −29.3039 | −1.02647 | ||||||||
\(816\) | 3.06352 | 0.107245 | ||||||||
\(817\) | −5.31829 | −0.186063 | ||||||||
\(818\) | 6.23994 | 0.218174 | ||||||||
\(819\) | −7.66110 | −0.267700 | ||||||||
\(820\) | −72.2774 | −2.52404 | ||||||||
\(821\) | −52.1354 | −1.81954 | −0.909768 | − | 0.415116i | \(-0.863741\pi\) | ||||
−0.909768 | + | 0.415116i | \(0.863741\pi\) | |||||||
\(822\) | 18.7553 | 0.654165 | ||||||||
\(823\) | 47.7734 | 1.66528 | 0.832638 | − | 0.553817i | \(-0.186829\pi\) | ||||
0.832638 | + | 0.553817i | \(0.186829\pi\) | |||||||
\(824\) | −52.7711 | −1.83837 | ||||||||
\(825\) | 0.510810 | 0.0177841 | ||||||||
\(826\) | 47.9368 | 1.66794 | ||||||||
\(827\) | −14.3208 | −0.497984 | −0.248992 | − | 0.968505i | \(-0.580099\pi\) | ||||
−0.248992 | + | 0.968505i | \(0.580099\pi\) | |||||||
\(828\) | 62.4215 | 2.16930 | ||||||||
\(829\) | 33.8554 | 1.17585 | 0.587924 | − | 0.808916i | \(-0.299945\pi\) | ||||
0.587924 | + | 0.808916i | \(0.299945\pi\) | |||||||
\(830\) | 81.3799 | 2.82474 | ||||||||
\(831\) | −7.98515 | −0.277002 | ||||||||
\(832\) | 12.3932 | 0.429656 | ||||||||
\(833\) | −0.273694 | −0.00948294 | ||||||||
\(834\) | −14.3969 | −0.498525 | ||||||||
\(835\) | −4.13883 | −0.143230 | ||||||||
\(836\) | 5.43546 | 0.187989 | ||||||||
\(837\) | 22.6479 | 0.782826 | ||||||||
\(838\) | −59.9600 | −2.07128 | ||||||||
\(839\) | 8.09662 | 0.279526 | 0.139763 | − | 0.990185i | \(-0.455366\pi\) | ||||
0.139763 | + | 0.990185i | \(0.455366\pi\) | |||||||
\(840\) | 23.6803 | 0.817048 | ||||||||
\(841\) | −6.43685 | −0.221960 | ||||||||
\(842\) | 54.3114 | 1.87170 | ||||||||
\(843\) | −21.4835 | −0.739932 | ||||||||
\(844\) | −33.3461 | −1.14782 | ||||||||
\(845\) | 23.7432 | 0.816790 | ||||||||
\(846\) | −63.1753 | −2.17201 | ||||||||
\(847\) | −2.69568 | −0.0926247 | ||||||||
\(848\) | 11.9898 | 0.411730 | ||||||||
\(849\) | −22.7865 | −0.782031 | ||||||||
\(850\) | −1.38312 | −0.0474407 | ||||||||
\(851\) | 58.7756 | 2.01480 | ||||||||
\(852\) | −17.2732 | −0.591768 | ||||||||
\(853\) | 20.7415 | 0.710176 | 0.355088 | − | 0.934833i | \(-0.384451\pi\) | ||||
0.355088 | + | 0.934833i | \(0.384451\pi\) | |||||||
\(854\) | 24.1013 | 0.824728 | ||||||||
\(855\) | 6.38093 | 0.218223 | ||||||||
\(856\) | 69.3559 | 2.37054 | ||||||||
\(857\) | 6.04129 | 0.206367 | 0.103183 | − | 0.994662i | \(-0.467097\pi\) | ||||
0.103183 | + | 0.994662i | \(0.467097\pi\) | |||||||
\(858\) | −2.93319 | −0.100137 | ||||||||
\(859\) | −5.01431 | −0.171086 | −0.0855431 | − | 0.996334i | \(-0.527263\pi\) | ||||
−0.0855431 | + | 0.996334i | \(0.527263\pi\) | |||||||
\(860\) | 30.9285 | 1.05465 | ||||||||
\(861\) | 21.9217 | 0.747088 | ||||||||
\(862\) | 8.00072 | 0.272506 | ||||||||
\(863\) | 7.10321 | 0.241796 | 0.120898 | − | 0.992665i | \(-0.461423\pi\) | ||||
0.120898 | + | 0.992665i | \(0.461423\pi\) | |||||||
\(864\) | 5.67388 | 0.193029 | ||||||||
\(865\) | 18.1461 | 0.616985 | ||||||||
\(866\) | −15.6494 | −0.531787 | ||||||||
\(867\) | 14.6463 | 0.497414 | ||||||||
\(868\) | −49.9187 | −1.69435 | ||||||||
\(869\) | −11.2438 | −0.381421 | ||||||||
\(870\) | −22.2862 | −0.755574 | ||||||||
\(871\) | 3.96549 | 0.134366 | ||||||||
\(872\) | 5.35782 | 0.181439 | ||||||||
\(873\) | −13.8470 | −0.468651 | ||||||||
\(874\) | 25.4267 | 0.860071 | ||||||||
\(875\) | −31.5735 | −1.06738 | ||||||||
\(876\) | −49.7718 | −1.68163 | ||||||||
\(877\) | −8.19348 | −0.276674 | −0.138337 | − | 0.990385i | \(-0.544176\pi\) | ||||
−0.138337 | + | 0.990385i | \(0.544176\pi\) | |||||||
\(878\) | 40.6989 | 1.37352 | ||||||||
\(879\) | −9.13352 | −0.308066 | ||||||||
\(880\) | −6.85168 | −0.230970 | ||||||||
\(881\) | 21.0986 | 0.710831 | 0.355416 | − | 0.934708i | \(-0.384339\pi\) | ||||
0.355416 | + | 0.934708i | \(0.384339\pi\) | |||||||
\(882\) | 1.39368 | 0.0469277 | ||||||||
\(883\) | 41.3137 | 1.39032 | 0.695159 | − | 0.718856i | \(-0.255334\pi\) | ||||
0.695159 | + | 0.718856i | \(0.255334\pi\) | |||||||
\(884\) | 5.23723 | 0.176147 | ||||||||
\(885\) | 14.2078 | 0.477591 | ||||||||
\(886\) | 74.3743 | 2.49865 | ||||||||
\(887\) | 10.9280 | 0.366925 | 0.183462 | − | 0.983027i | \(-0.441269\pi\) | ||||
0.183462 | + | 0.983027i | \(0.441269\pi\) | |||||||
\(888\) | −32.7655 | −1.09954 | ||||||||
\(889\) | −4.14083 | −0.138879 | ||||||||
\(890\) | 45.2297 | 1.51610 | ||||||||
\(891\) | 2.11969 | 0.0710124 | ||||||||
\(892\) | −21.3979 | −0.716454 | ||||||||
\(893\) | −16.9693 | −0.567857 | ||||||||
\(894\) | 15.6672 | 0.523990 | ||||||||
\(895\) | −32.7918 | −1.09611 | ||||||||
\(896\) | −54.9701 | −1.83642 | ||||||||
\(897\) | −9.04805 | −0.302106 | ||||||||
\(898\) | 3.80326 | 0.126916 | ||||||||
\(899\) | 22.7155 | 0.757605 | ||||||||
\(900\) | 4.64430 | 0.154810 | ||||||||
\(901\) | −3.78565 | −0.126118 | ||||||||
\(902\) | −21.4564 | −0.714420 | ||||||||
\(903\) | −9.38057 | −0.312166 | ||||||||
\(904\) | −45.7352 | −1.52113 | ||||||||
\(905\) | 18.8812 | 0.627633 | ||||||||
\(906\) | 9.97655 | 0.331449 | ||||||||
\(907\) | −7.61973 | −0.253009 | −0.126504 | − | 0.991966i | \(-0.540376\pi\) | ||||
−0.126504 | + | 0.991966i | \(0.540376\pi\) | |||||||
\(908\) | −28.3582 | −0.941099 | ||||||||
\(909\) | 33.4495 | 1.10945 | ||||||||
\(910\) | 18.1482 | 0.601607 | ||||||||
\(911\) | 11.0538 | 0.366228 | 0.183114 | − | 0.983092i | \(-0.441382\pi\) | ||||
0.183114 | + | 0.983092i | \(0.441382\pi\) | |||||||
\(912\) | −4.19021 | −0.138752 | ||||||||
\(913\) | 15.9306 | 0.527228 | ||||||||
\(914\) | 83.6651 | 2.76740 | ||||||||
\(915\) | 7.14328 | 0.236150 | ||||||||
\(916\) | −4.16441 | −0.137596 | ||||||||
\(917\) | −2.95711 | −0.0976523 | ||||||||
\(918\) | 11.7776 | 0.388720 | ||||||||
\(919\) | 25.4030 | 0.837968 | 0.418984 | − | 0.907994i | \(-0.362386\pi\) | ||||
0.418984 | + | 0.907994i | \(0.362386\pi\) | |||||||
\(920\) | −71.4968 | −2.35718 | ||||||||
\(921\) | −10.3380 | −0.340649 | ||||||||
\(922\) | −66.4472 | −2.18832 | ||||||||
\(923\) | −6.40070 | −0.210682 | ||||||||
\(924\) | 9.58724 | 0.315397 | ||||||||
\(925\) | 4.37303 | 0.143784 | ||||||||
\(926\) | 8.77019 | 0.288206 | ||||||||
\(927\) | −25.0813 | −0.823780 | ||||||||
\(928\) | 5.69083 | 0.186811 | ||||||||
\(929\) | 0.877180 | 0.0287793 | 0.0143897 | − | 0.999896i | \(-0.495419\pi\) | ||||
0.0143897 | + | 0.999896i | \(0.495419\pi\) | |||||||
\(930\) | −22.4368 | −0.735730 | ||||||||
\(931\) | 0.374353 | 0.0122689 | ||||||||
\(932\) | −6.49476 | −0.212743 | ||||||||
\(933\) | −11.4305 | −0.374219 | ||||||||
\(934\) | −6.21497 | −0.203360 | ||||||||
\(935\) | 2.16335 | 0.0707492 | ||||||||
\(936\) | −12.8946 | −0.421475 | ||||||||
\(937\) | 13.5802 | 0.443646 | 0.221823 | − | 0.975087i | \(-0.428799\pi\) | ||||
0.221823 | + | 0.975087i | \(0.428799\pi\) | |||||||
\(938\) | −19.6557 | −0.641783 | ||||||||
\(939\) | 2.90958 | 0.0949504 | ||||||||
\(940\) | 98.6851 | 3.21875 | ||||||||
\(941\) | −6.10609 | −0.199053 | −0.0995265 | − | 0.995035i | \(-0.531733\pi\) | ||||
−0.0995265 | + | 0.995035i | \(0.531733\pi\) | |||||||
\(942\) | −8.74639 | −0.284973 | ||||||||
\(943\) | −66.1870 | −2.15535 | ||||||||
\(944\) | 23.8514 | 0.776298 | ||||||||
\(945\) | 26.9124 | 0.875459 | ||||||||
\(946\) | 9.18148 | 0.298516 | ||||||||
\(947\) | 42.2325 | 1.37237 | 0.686187 | − | 0.727425i | \(-0.259283\pi\) | ||||
0.686187 | + | 0.727425i | \(0.259283\pi\) | |||||||
\(948\) | 39.9889 | 1.29878 | ||||||||
\(949\) | −18.4433 | −0.598696 | ||||||||
\(950\) | 1.89180 | 0.0613782 | ||||||||
\(951\) | 2.47510 | 0.0802607 | ||||||||
\(952\) | −12.5517 | −0.406804 | ||||||||
\(953\) | 18.7654 | 0.607870 | 0.303935 | − | 0.952693i | \(-0.401699\pi\) | ||||
0.303935 | + | 0.952693i | \(0.401699\pi\) | |||||||
\(954\) | 19.2770 | 0.624115 | ||||||||
\(955\) | −48.7585 | −1.57779 | ||||||||
\(956\) | −42.0060 | −1.35857 | ||||||||
\(957\) | −4.36268 | −0.141025 | ||||||||
\(958\) | 7.10541 | 0.229565 | ||||||||
\(959\) | −22.7161 | −0.733541 | ||||||||
\(960\) | −18.2068 | −0.587621 | ||||||||
\(961\) | −8.13106 | −0.262292 | ||||||||
\(962\) | −25.1109 | −0.809609 | ||||||||
\(963\) | 32.9638 | 1.06224 | ||||||||
\(964\) | −29.0018 | −0.934085 | ||||||||
\(965\) | 56.4868 | 1.81837 | ||||||||
\(966\) | 44.8485 | 1.44298 | ||||||||
\(967\) | −39.6513 | −1.27510 | −0.637550 | − | 0.770409i | \(-0.720052\pi\) | ||||
−0.637550 | + | 0.770409i | \(0.720052\pi\) | |||||||
\(968\) | −4.53719 | −0.145831 | ||||||||
\(969\) | 1.32302 | 0.0425015 | ||||||||
\(970\) | 32.8019 | 1.05321 | ||||||||
\(971\) | −38.9569 | −1.25019 | −0.625093 | − | 0.780550i | \(-0.714939\pi\) | ||||
−0.625093 | + | 0.780550i | \(0.714939\pi\) | |||||||
\(972\) | −62.5559 | −2.00648 | ||||||||
\(973\) | 17.4374 | 0.559016 | ||||||||
\(974\) | 25.0075 | 0.801292 | ||||||||
\(975\) | −0.673195 | −0.0215595 | ||||||||
\(976\) | 11.9918 | 0.383848 | ||||||||
\(977\) | 27.6929 | 0.885973 | 0.442986 | − | 0.896528i | \(-0.353919\pi\) | ||||
0.442986 | + | 0.896528i | \(0.353919\pi\) | |||||||
\(978\) | 30.9389 | 0.989317 | ||||||||
\(979\) | 8.85401 | 0.282976 | ||||||||
\(980\) | −2.17705 | −0.0695432 | ||||||||
\(981\) | 2.54649 | 0.0813032 | ||||||||
\(982\) | 42.7439 | 1.36401 | ||||||||
\(983\) | −39.7200 | −1.26687 | −0.633436 | − | 0.773795i | \(-0.718356\pi\) | ||||
−0.633436 | + | 0.773795i | \(0.718356\pi\) | |||||||
\(984\) | 36.8971 | 1.17624 | ||||||||
\(985\) | 3.37108 | 0.107412 | ||||||||
\(986\) | 11.8128 | 0.376197 | ||||||||
\(987\) | −29.9311 | −0.952717 | ||||||||
\(988\) | −7.16337 | −0.227897 | ||||||||
\(989\) | 28.3223 | 0.900596 | ||||||||
\(990\) | −11.0160 | −0.350112 | ||||||||
\(991\) | 14.2432 | 0.452452 | 0.226226 | − | 0.974075i | \(-0.427361\pi\) | ||||
0.226226 | + | 0.974075i | \(0.427361\pi\) | |||||||
\(992\) | 5.72926 | 0.181904 | ||||||||
\(993\) | −12.8924 | −0.409127 | ||||||||
\(994\) | 31.7263 | 1.00630 | ||||||||
\(995\) | −25.4932 | −0.808187 | ||||||||
\(996\) | −56.6577 | −1.79527 | ||||||||
\(997\) | 15.4930 | 0.490667 | 0.245334 | − | 0.969439i | \(-0.421103\pi\) | ||||
0.245334 | + | 0.969439i | \(0.421103\pi\) | |||||||
\(998\) | 63.6783 | 2.01570 | ||||||||
\(999\) | −37.2375 | −1.17814 |
(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 | 6017.2.a.c.1.11 | ✓ | 106 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.c.1.11 | ✓ | 106 | 1.1 | even | 1 | trivial |