Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.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: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0772262 | −0.0546072 | −0.0273036 | − | 0.999627i | \(-0.508692\pi\) | ||||
−0.0273036 | + | 0.999627i | \(0.508692\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.99404 | −0.997018 | ||||||||
\(5\) | 3.97384 | 1.77715 | 0.888577 | − | 0.458727i | \(-0.151695\pi\) | ||||
0.888577 | + | 0.458727i | \(0.151695\pi\) | |||||||
\(6\) | 0.0772262 | 0.0315275 | ||||||||
\(7\) | 0.969209 | 0.366327 | 0.183163 | − | 0.983083i | \(-0.441366\pi\) | ||||
0.183163 | + | 0.983083i | \(0.441366\pi\) | |||||||
\(8\) | 0.308444 | 0.109052 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.306884 | −0.0970454 | ||||||||
\(11\) | 2.24354 | 0.676452 | 0.338226 | − | 0.941065i | \(-0.390173\pi\) | ||||
0.338226 | + | 0.941065i | \(0.390173\pi\) | |||||||
\(12\) | 1.99404 | 0.575629 | ||||||||
\(13\) | 4.20360 | 1.16587 | 0.582934 | − | 0.812520i | \(-0.301905\pi\) | ||||
0.582934 | + | 0.812520i | \(0.301905\pi\) | |||||||
\(14\) | −0.0748483 | −0.0200041 | ||||||||
\(15\) | −3.97384 | −1.02604 | ||||||||
\(16\) | 3.96425 | 0.991063 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.0772262 | −0.0182024 | ||||||||
\(19\) | 5.15523 | 1.18269 | 0.591346 | − | 0.806418i | \(-0.298597\pi\) | ||||
0.591346 | + | 0.806418i | \(0.298597\pi\) | |||||||
\(20\) | −7.92398 | −1.77185 | ||||||||
\(21\) | −0.969209 | −0.211499 | ||||||||
\(22\) | −0.173260 | −0.0369391 | ||||||||
\(23\) | 0.911156 | 0.189989 | 0.0949946 | − | 0.995478i | \(-0.469717\pi\) | ||||
0.0949946 | + | 0.995478i | \(0.469717\pi\) | |||||||
\(24\) | −0.308444 | −0.0629609 | ||||||||
\(25\) | 10.7914 | 2.15828 | ||||||||
\(26\) | −0.324628 | −0.0636647 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.93264 | −0.365234 | ||||||||
\(29\) | 8.81167 | 1.63629 | 0.818143 | − | 0.575014i | \(-0.195003\pi\) | ||||
0.818143 | + | 0.575014i | \(0.195003\pi\) | |||||||
\(30\) | 0.306884 | 0.0560292 | ||||||||
\(31\) | −5.98124 | −1.07426 | −0.537131 | − | 0.843499i | \(-0.680492\pi\) | ||||
−0.537131 | + | 0.843499i | \(0.680492\pi\) | |||||||
\(32\) | −0.923033 | −0.163171 | ||||||||
\(33\) | −2.24354 | −0.390550 | ||||||||
\(34\) | 0.0772262 | 0.0132442 | ||||||||
\(35\) | 3.85148 | 0.651019 | ||||||||
\(36\) | −1.99404 | −0.332339 | ||||||||
\(37\) | 4.64710 | 0.763979 | 0.381989 | − | 0.924167i | \(-0.375239\pi\) | ||||
0.381989 | + | 0.924167i | \(0.375239\pi\) | |||||||
\(38\) | −0.398119 | −0.0645835 | ||||||||
\(39\) | −4.20360 | −0.673114 | ||||||||
\(40\) | 1.22571 | 0.193801 | ||||||||
\(41\) | −10.0598 | −1.57108 | −0.785541 | − | 0.618810i | \(-0.787615\pi\) | ||||
−0.785541 | + | 0.618810i | \(0.787615\pi\) | |||||||
\(42\) | 0.0748483 | 0.0115493 | ||||||||
\(43\) | 9.32461 | 1.42199 | 0.710995 | − | 0.703198i | \(-0.248245\pi\) | ||||
0.710995 | + | 0.703198i | \(0.248245\pi\) | |||||||
\(44\) | −4.47370 | −0.674435 | ||||||||
\(45\) | 3.97384 | 0.592385 | ||||||||
\(46\) | −0.0703651 | −0.0103748 | ||||||||
\(47\) | 6.28523 | 0.916796 | 0.458398 | − | 0.888747i | \(-0.348423\pi\) | ||||
0.458398 | + | 0.888747i | \(0.348423\pi\) | |||||||
\(48\) | −3.96425 | −0.572191 | ||||||||
\(49\) | −6.06063 | −0.865805 | ||||||||
\(50\) | −0.833378 | −0.117857 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −8.38212 | −1.16239 | ||||||||
\(53\) | −4.67370 | −0.641981 | −0.320991 | − | 0.947082i | \(-0.604016\pi\) | ||||
−0.320991 | + | 0.947082i | \(0.604016\pi\) | |||||||
\(54\) | 0.0772262 | 0.0105092 | ||||||||
\(55\) | 8.91546 | 1.20216 | ||||||||
\(56\) | 0.298947 | 0.0399485 | ||||||||
\(57\) | −5.15523 | −0.682827 | ||||||||
\(58\) | −0.680492 | −0.0893530 | ||||||||
\(59\) | −7.12284 | −0.927315 | −0.463658 | − | 0.886014i | \(-0.653463\pi\) | ||||
−0.463658 | + | 0.886014i | \(0.653463\pi\) | |||||||
\(60\) | 7.92398 | 1.02298 | ||||||||
\(61\) | −7.64526 | −0.978875 | −0.489437 | − | 0.872038i | \(-0.662798\pi\) | ||||
−0.489437 | + | 0.872038i | \(0.662798\pi\) | |||||||
\(62\) | 0.461908 | 0.0586624 | ||||||||
\(63\) | 0.969209 | 0.122109 | ||||||||
\(64\) | −7.85722 | −0.982153 | ||||||||
\(65\) | 16.7044 | 2.07193 | ||||||||
\(66\) | 0.173260 | 0.0213268 | ||||||||
\(67\) | 10.6038 | 1.29546 | 0.647728 | − | 0.761871i | \(-0.275719\pi\) | ||||
0.647728 | + | 0.761871i | \(0.275719\pi\) | |||||||
\(68\) | 1.99404 | 0.241812 | ||||||||
\(69\) | −0.911156 | −0.109690 | ||||||||
\(70\) | −0.297435 | −0.0355503 | ||||||||
\(71\) | 0.523273 | 0.0621010 | 0.0310505 | − | 0.999518i | \(-0.490115\pi\) | ||||
0.0310505 | + | 0.999518i | \(0.490115\pi\) | |||||||
\(72\) | 0.308444 | 0.0363505 | ||||||||
\(73\) | −9.82633 | −1.15008 | −0.575042 | − | 0.818124i | \(-0.695014\pi\) | ||||
−0.575042 | + | 0.818124i | \(0.695014\pi\) | |||||||
\(74\) | −0.358878 | −0.0417187 | ||||||||
\(75\) | −10.7914 | −1.24608 | ||||||||
\(76\) | −10.2797 | −1.17917 | ||||||||
\(77\) | 2.17446 | 0.247802 | ||||||||
\(78\) | 0.324628 | 0.0367569 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | 15.7533 | 1.76127 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.776883 | 0.0857923 | ||||||||
\(83\) | 12.4060 | 1.36173 | 0.680865 | − | 0.732409i | \(-0.261604\pi\) | ||||
0.680865 | + | 0.732409i | \(0.261604\pi\) | |||||||
\(84\) | 1.93264 | 0.210868 | ||||||||
\(85\) | −3.97384 | −0.431023 | ||||||||
\(86\) | −0.720104 | −0.0776508 | ||||||||
\(87\) | −8.81167 | −0.944711 | ||||||||
\(88\) | 0.692006 | 0.0737681 | ||||||||
\(89\) | 11.7149 | 1.24178 | 0.620889 | − | 0.783898i | \(-0.286772\pi\) | ||||
0.620889 | + | 0.783898i | \(0.286772\pi\) | |||||||
\(90\) | −0.306884 | −0.0323485 | ||||||||
\(91\) | 4.07416 | 0.427088 | ||||||||
\(92\) | −1.81688 | −0.189423 | ||||||||
\(93\) | 5.98124 | 0.620225 | ||||||||
\(94\) | −0.485385 | −0.0500636 | ||||||||
\(95\) | 20.4861 | 2.10183 | ||||||||
\(96\) | 0.923033 | 0.0942066 | ||||||||
\(97\) | −15.9767 | −1.62219 | −0.811093 | − | 0.584917i | \(-0.801127\pi\) | ||||
−0.811093 | + | 0.584917i | \(0.801127\pi\) | |||||||
\(98\) | 0.468040 | 0.0472792 | ||||||||
\(99\) | 2.24354 | 0.225484 | ||||||||
\(100\) | −21.5184 | −2.15184 | ||||||||
\(101\) | −3.75524 | −0.373660 | −0.186830 | − | 0.982392i | \(-0.559821\pi\) | ||||
−0.186830 | + | 0.982392i | \(0.559821\pi\) | |||||||
\(102\) | −0.0772262 | −0.00764653 | ||||||||
\(103\) | 9.38168 | 0.924404 | 0.462202 | − | 0.886775i | \(-0.347059\pi\) | ||||
0.462202 | + | 0.886775i | \(0.347059\pi\) | |||||||
\(104\) | 1.29657 | 0.127140 | ||||||||
\(105\) | −3.85148 | −0.375866 | ||||||||
\(106\) | 0.360932 | 0.0350568 | ||||||||
\(107\) | −17.8136 | −1.72211 | −0.861055 | − | 0.508513i | \(-0.830195\pi\) | ||||
−0.861055 | + | 0.508513i | \(0.830195\pi\) | |||||||
\(108\) | 1.99404 | 0.191876 | ||||||||
\(109\) | −17.9566 | −1.71993 | −0.859964 | − | 0.510355i | \(-0.829514\pi\) | ||||
−0.859964 | + | 0.510355i | \(0.829514\pi\) | |||||||
\(110\) | −0.688507 | −0.0656466 | ||||||||
\(111\) | −4.64710 | −0.441083 | ||||||||
\(112\) | 3.84219 | 0.363053 | ||||||||
\(113\) | −15.5944 | −1.46700 | −0.733499 | − | 0.679691i | \(-0.762114\pi\) | ||||
−0.733499 | + | 0.679691i | \(0.762114\pi\) | |||||||
\(114\) | 0.398119 | 0.0372873 | ||||||||
\(115\) | 3.62079 | 0.337640 | ||||||||
\(116\) | −17.5708 | −1.63141 | ||||||||
\(117\) | 4.20360 | 0.388623 | ||||||||
\(118\) | 0.550070 | 0.0506381 | ||||||||
\(119\) | −0.969209 | −0.0888472 | ||||||||
\(120\) | −1.22571 | −0.111891 | ||||||||
\(121\) | −5.96654 | −0.542412 | ||||||||
\(122\) | 0.590414 | 0.0534536 | ||||||||
\(123\) | 10.0598 | 0.907064 | ||||||||
\(124\) | 11.9268 | 1.07106 | ||||||||
\(125\) | 23.0140 | 2.05844 | ||||||||
\(126\) | −0.0748483 | −0.00666802 | ||||||||
\(127\) | 6.24289 | 0.553967 | 0.276984 | − | 0.960875i | \(-0.410665\pi\) | ||||
0.276984 | + | 0.960875i | \(0.410665\pi\) | |||||||
\(128\) | 2.45285 | 0.216803 | ||||||||
\(129\) | −9.32461 | −0.820986 | ||||||||
\(130\) | −1.29002 | −0.113142 | ||||||||
\(131\) | 2.03547 | 0.177840 | 0.0889198 | − | 0.996039i | \(-0.471659\pi\) | ||||
0.0889198 | + | 0.996039i | \(0.471659\pi\) | |||||||
\(132\) | 4.47370 | 0.389385 | ||||||||
\(133\) | 4.99650 | 0.433251 | ||||||||
\(134\) | −0.818889 | −0.0707412 | ||||||||
\(135\) | −3.97384 | −0.342013 | ||||||||
\(136\) | −0.308444 | −0.0264489 | ||||||||
\(137\) | 9.67979 | 0.827000 | 0.413500 | − | 0.910504i | \(-0.364306\pi\) | ||||
0.413500 | + | 0.910504i | \(0.364306\pi\) | |||||||
\(138\) | 0.0703651 | 0.00598987 | ||||||||
\(139\) | −11.1227 | −0.943416 | −0.471708 | − | 0.881755i | \(-0.656362\pi\) | ||||
−0.471708 | + | 0.881755i | \(0.656362\pi\) | |||||||
\(140\) | −7.67999 | −0.649077 | ||||||||
\(141\) | −6.28523 | −0.529312 | ||||||||
\(142\) | −0.0404104 | −0.00339116 | ||||||||
\(143\) | 9.43093 | 0.788654 | ||||||||
\(144\) | 3.96425 | 0.330354 | ||||||||
\(145\) | 35.0162 | 2.90793 | ||||||||
\(146\) | 0.758850 | 0.0628029 | ||||||||
\(147\) | 6.06063 | 0.499873 | ||||||||
\(148\) | −9.26649 | −0.761700 | ||||||||
\(149\) | −14.8967 | −1.22038 | −0.610192 | − | 0.792254i | \(-0.708908\pi\) | ||||
−0.610192 | + | 0.792254i | \(0.708908\pi\) | |||||||
\(150\) | 0.833378 | 0.0680450 | ||||||||
\(151\) | 11.1404 | 0.906593 | 0.453297 | − | 0.891360i | \(-0.350248\pi\) | ||||
0.453297 | + | 0.891360i | \(0.350248\pi\) | |||||||
\(152\) | 1.59010 | 0.128974 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −0.167925 | −0.0135318 | ||||||||
\(155\) | −23.7685 | −1.90913 | ||||||||
\(156\) | 8.38212 | 0.671107 | ||||||||
\(157\) | −5.48902 | −0.438072 | −0.219036 | − | 0.975717i | \(-0.570291\pi\) | ||||
−0.219036 | + | 0.975717i | \(0.570291\pi\) | |||||||
\(158\) | −0.0772262 | −0.00614379 | ||||||||
\(159\) | 4.67370 | 0.370648 | ||||||||
\(160\) | −3.66798 | −0.289979 | ||||||||
\(161\) | 0.883100 | 0.0695981 | ||||||||
\(162\) | −0.0772262 | −0.00606746 | ||||||||
\(163\) | −7.76532 | −0.608227 | −0.304113 | − | 0.952636i | \(-0.598360\pi\) | ||||
−0.304113 | + | 0.952636i | \(0.598360\pi\) | |||||||
\(164\) | 20.0597 | 1.56640 | ||||||||
\(165\) | −8.91546 | −0.694067 | ||||||||
\(166\) | −0.958065 | −0.0743603 | ||||||||
\(167\) | 11.4568 | 0.886550 | 0.443275 | − | 0.896386i | \(-0.353817\pi\) | ||||
0.443275 | + | 0.896386i | \(0.353817\pi\) | |||||||
\(168\) | −0.298947 | −0.0230643 | ||||||||
\(169\) | 4.67022 | 0.359247 | ||||||||
\(170\) | 0.306884 | 0.0235370 | ||||||||
\(171\) | 5.15523 | 0.394231 | ||||||||
\(172\) | −18.5936 | −1.41775 | ||||||||
\(173\) | 6.32459 | 0.480850 | 0.240425 | − | 0.970668i | \(-0.422713\pi\) | ||||
0.240425 | + | 0.970668i | \(0.422713\pi\) | |||||||
\(174\) | 0.680492 | 0.0515880 | ||||||||
\(175\) | 10.4591 | 0.790634 | ||||||||
\(176\) | 8.89395 | 0.670407 | ||||||||
\(177\) | 7.12284 | 0.535386 | ||||||||
\(178\) | −0.904699 | −0.0678100 | ||||||||
\(179\) | −0.513577 | −0.0383865 | −0.0191933 | − | 0.999816i | \(-0.506110\pi\) | ||||
−0.0191933 | + | 0.999816i | \(0.506110\pi\) | |||||||
\(180\) | −7.92398 | −0.590618 | ||||||||
\(181\) | 5.46475 | 0.406192 | 0.203096 | − | 0.979159i | \(-0.434900\pi\) | ||||
0.203096 | + | 0.979159i | \(0.434900\pi\) | |||||||
\(182\) | −0.314632 | −0.0233221 | ||||||||
\(183\) | 7.64526 | 0.565154 | ||||||||
\(184\) | 0.281041 | 0.0207186 | ||||||||
\(185\) | 18.4668 | 1.35771 | ||||||||
\(186\) | −0.461908 | −0.0338687 | ||||||||
\(187\) | −2.24354 | −0.164064 | ||||||||
\(188\) | −12.5330 | −0.914062 | ||||||||
\(189\) | −0.969209 | −0.0704996 | ||||||||
\(190\) | −1.58206 | −0.114775 | ||||||||
\(191\) | 11.9704 | 0.866147 | 0.433073 | − | 0.901359i | \(-0.357429\pi\) | ||||
0.433073 | + | 0.901359i | \(0.357429\pi\) | |||||||
\(192\) | 7.85722 | 0.567046 | ||||||||
\(193\) | −19.2282 | −1.38408 | −0.692038 | − | 0.721861i | \(-0.743287\pi\) | ||||
−0.692038 | + | 0.721861i | \(0.743287\pi\) | |||||||
\(194\) | 1.23382 | 0.0885830 | ||||||||
\(195\) | −16.7044 | −1.19623 | ||||||||
\(196\) | 12.0851 | 0.863223 | ||||||||
\(197\) | −2.72447 | −0.194111 | −0.0970553 | − | 0.995279i | \(-0.530942\pi\) | ||||
−0.0970553 | + | 0.995279i | \(0.530942\pi\) | |||||||
\(198\) | −0.173260 | −0.0123130 | ||||||||
\(199\) | 7.25954 | 0.514615 | 0.257308 | − | 0.966330i | \(-0.417165\pi\) | ||||
0.257308 | + | 0.966330i | \(0.417165\pi\) | |||||||
\(200\) | 3.32854 | 0.235363 | ||||||||
\(201\) | −10.6038 | −0.747932 | ||||||||
\(202\) | 0.290003 | 0.0204045 | ||||||||
\(203\) | 8.54035 | 0.599415 | ||||||||
\(204\) | −1.99404 | −0.139610 | ||||||||
\(205\) | −39.9761 | −2.79205 | ||||||||
\(206\) | −0.724511 | −0.0504791 | ||||||||
\(207\) | 0.911156 | 0.0633297 | ||||||||
\(208\) | 16.6641 | 1.15545 | ||||||||
\(209\) | 11.5660 | 0.800035 | ||||||||
\(210\) | 0.297435 | 0.0205250 | ||||||||
\(211\) | 12.2282 | 0.841827 | 0.420913 | − | 0.907101i | \(-0.361710\pi\) | ||||
0.420913 | + | 0.907101i | \(0.361710\pi\) | |||||||
\(212\) | 9.31952 | 0.640067 | ||||||||
\(213\) | −0.523273 | −0.0358540 | ||||||||
\(214\) | 1.37568 | 0.0940395 | ||||||||
\(215\) | 37.0545 | 2.52709 | ||||||||
\(216\) | −0.308444 | −0.0209870 | ||||||||
\(217\) | −5.79707 | −0.393531 | ||||||||
\(218\) | 1.38672 | 0.0939204 | ||||||||
\(219\) | 9.82633 | 0.664002 | ||||||||
\(220\) | −17.7777 | −1.19858 | ||||||||
\(221\) | −4.20360 | −0.282764 | ||||||||
\(222\) | 0.358878 | 0.0240863 | ||||||||
\(223\) | −5.02084 | −0.336221 | −0.168110 | − | 0.985768i | \(-0.553766\pi\) | ||||
−0.168110 | + | 0.985768i | \(0.553766\pi\) | |||||||
\(224\) | −0.894611 | −0.0597737 | ||||||||
\(225\) | 10.7914 | 0.719426 | ||||||||
\(226\) | 1.20430 | 0.0801086 | ||||||||
\(227\) | 26.4815 | 1.75764 | 0.878821 | − | 0.477152i | \(-0.158331\pi\) | ||||
0.878821 | + | 0.477152i | \(0.158331\pi\) | |||||||
\(228\) | 10.2797 | 0.680791 | ||||||||
\(229\) | 17.7040 | 1.16991 | 0.584956 | − | 0.811065i | \(-0.301112\pi\) | ||||
0.584956 | + | 0.811065i | \(0.301112\pi\) | |||||||
\(230\) | −0.279619 | −0.0184376 | ||||||||
\(231\) | −2.17446 | −0.143069 | ||||||||
\(232\) | 2.71791 | 0.178440 | ||||||||
\(233\) | −10.5370 | −0.690303 | −0.345152 | − | 0.938547i | \(-0.612173\pi\) | ||||
−0.345152 | + | 0.938547i | \(0.612173\pi\) | |||||||
\(234\) | −0.324628 | −0.0212216 | ||||||||
\(235\) | 24.9765 | 1.62929 | ||||||||
\(236\) | 14.2032 | 0.924550 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 0.0748483 | 0.00485170 | ||||||||
\(239\) | 2.98042 | 0.192788 | 0.0963938 | − | 0.995343i | \(-0.469269\pi\) | ||||
0.0963938 | + | 0.995343i | \(0.469269\pi\) | |||||||
\(240\) | −15.7533 | −1.01687 | ||||||||
\(241\) | 30.6112 | 1.97184 | 0.985922 | − | 0.167207i | \(-0.0534750\pi\) | ||||
0.985922 | + | 0.167207i | \(0.0534750\pi\) | |||||||
\(242\) | 0.460773 | 0.0296196 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 15.2449 | 0.975956 | ||||||||
\(245\) | −24.0840 | −1.53867 | ||||||||
\(246\) | −0.776883 | −0.0495322 | ||||||||
\(247\) | 21.6705 | 1.37886 | ||||||||
\(248\) | −1.84488 | −0.117150 | ||||||||
\(249\) | −12.4060 | −0.786196 | ||||||||
\(250\) | −1.77729 | −0.112405 | ||||||||
\(251\) | 7.16445 | 0.452216 | 0.226108 | − | 0.974102i | \(-0.427400\pi\) | ||||
0.226108 | + | 0.974102i | \(0.427400\pi\) | |||||||
\(252\) | −1.93264 | −0.121745 | ||||||||
\(253\) | 2.04421 | 0.128519 | ||||||||
\(254\) | −0.482115 | −0.0302506 | ||||||||
\(255\) | 3.97384 | 0.248851 | ||||||||
\(256\) | 15.5250 | 0.970314 | ||||||||
\(257\) | −21.1190 | −1.31737 | −0.658684 | − | 0.752419i | \(-0.728887\pi\) | ||||
−0.658684 | + | 0.752419i | \(0.728887\pi\) | |||||||
\(258\) | 0.720104 | 0.0448317 | ||||||||
\(259\) | 4.50401 | 0.279866 | ||||||||
\(260\) | −33.3092 | −2.06575 | ||||||||
\(261\) | 8.81167 | 0.545429 | ||||||||
\(262\) | −0.157191 | −0.00971132 | ||||||||
\(263\) | 7.71210 | 0.475548 | 0.237774 | − | 0.971320i | \(-0.423582\pi\) | ||||
0.237774 | + | 0.971320i | \(0.423582\pi\) | |||||||
\(264\) | −0.692006 | −0.0425901 | ||||||||
\(265\) | −18.5725 | −1.14090 | ||||||||
\(266\) | −0.385861 | −0.0236586 | ||||||||
\(267\) | −11.7149 | −0.716941 | ||||||||
\(268\) | −21.1443 | −1.29159 | ||||||||
\(269\) | −14.4083 | −0.878488 | −0.439244 | − | 0.898368i | \(-0.644754\pi\) | ||||
−0.439244 | + | 0.898368i | \(0.644754\pi\) | |||||||
\(270\) | 0.306884 | 0.0186764 | ||||||||
\(271\) | 17.8076 | 1.08174 | 0.540868 | − | 0.841107i | \(-0.318096\pi\) | ||||
0.540868 | + | 0.841107i | \(0.318096\pi\) | |||||||
\(272\) | −3.96425 | −0.240368 | ||||||||
\(273\) | −4.07416 | −0.246580 | ||||||||
\(274\) | −0.747533 | −0.0451601 | ||||||||
\(275\) | 24.2109 | 1.45997 | ||||||||
\(276\) | 1.81688 | 0.109363 | ||||||||
\(277\) | −8.79316 | −0.528330 | −0.264165 | − | 0.964478i | \(-0.585096\pi\) | ||||
−0.264165 | + | 0.964478i | \(0.585096\pi\) | |||||||
\(278\) | 0.858965 | 0.0515173 | ||||||||
\(279\) | −5.98124 | −0.358087 | ||||||||
\(280\) | 1.18797 | 0.0709946 | ||||||||
\(281\) | 13.1633 | 0.785256 | 0.392628 | − | 0.919697i | \(-0.371566\pi\) | ||||
0.392628 | + | 0.919697i | \(0.371566\pi\) | |||||||
\(282\) | 0.485385 | 0.0289042 | ||||||||
\(283\) | −6.40170 | −0.380542 | −0.190271 | − | 0.981732i | \(-0.560937\pi\) | ||||
−0.190271 | + | 0.981732i | \(0.560937\pi\) | |||||||
\(284\) | −1.04342 | −0.0619158 | ||||||||
\(285\) | −20.4861 | −1.21349 | ||||||||
\(286\) | −0.728315 | −0.0430662 | ||||||||
\(287\) | −9.75008 | −0.575529 | ||||||||
\(288\) | −0.923033 | −0.0543902 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −2.70417 | −0.158794 | ||||||||
\(291\) | 15.9767 | 0.936570 | ||||||||
\(292\) | 19.5941 | 1.14666 | ||||||||
\(293\) | 13.6630 | 0.798200 | 0.399100 | − | 0.916907i | \(-0.369323\pi\) | ||||
0.399100 | + | 0.916907i | \(0.369323\pi\) | |||||||
\(294\) | −0.468040 | −0.0272966 | ||||||||
\(295\) | −28.3050 | −1.64798 | ||||||||
\(296\) | 1.43337 | 0.0833130 | ||||||||
\(297\) | −2.24354 | −0.130183 | ||||||||
\(298\) | 1.15041 | 0.0666417 | ||||||||
\(299\) | 3.83013 | 0.221502 | ||||||||
\(300\) | 21.5184 | 1.24237 | ||||||||
\(301\) | 9.03749 | 0.520912 | ||||||||
\(302\) | −0.860331 | −0.0495065 | ||||||||
\(303\) | 3.75524 | 0.215733 | ||||||||
\(304\) | 20.4366 | 1.17212 | ||||||||
\(305\) | −30.3810 | −1.73961 | ||||||||
\(306\) | 0.0772262 | 0.00441473 | ||||||||
\(307\) | −10.0727 | −0.574877 | −0.287438 | − | 0.957799i | \(-0.592804\pi\) | ||||
−0.287438 | + | 0.957799i | \(0.592804\pi\) | |||||||
\(308\) | −4.33595 | −0.247063 | ||||||||
\(309\) | −9.38168 | −0.533705 | ||||||||
\(310\) | 1.83555 | 0.104252 | ||||||||
\(311\) | −12.2887 | −0.696830 | −0.348415 | − | 0.937340i | \(-0.613280\pi\) | ||||
−0.348415 | + | 0.937340i | \(0.613280\pi\) | |||||||
\(312\) | −1.29657 | −0.0734041 | ||||||||
\(313\) | 23.9963 | 1.35635 | 0.678176 | − | 0.734900i | \(-0.262771\pi\) | ||||
0.678176 | + | 0.734900i | \(0.262771\pi\) | |||||||
\(314\) | 0.423896 | 0.0239219 | ||||||||
\(315\) | 3.85148 | 0.217006 | ||||||||
\(316\) | −1.99404 | −0.112173 | ||||||||
\(317\) | 11.6608 | 0.654933 | 0.327467 | − | 0.944863i | \(-0.393805\pi\) | ||||
0.327467 | + | 0.944863i | \(0.393805\pi\) | |||||||
\(318\) | −0.360932 | −0.0202400 | ||||||||
\(319\) | 19.7693 | 1.10687 | ||||||||
\(320\) | −31.2233 | −1.74544 | ||||||||
\(321\) | 17.8136 | 0.994260 | ||||||||
\(322\) | −0.0681985 | −0.00380055 | ||||||||
\(323\) | −5.15523 | −0.286845 | ||||||||
\(324\) | −1.99404 | −0.110780 | ||||||||
\(325\) | 45.3626 | 2.51627 | ||||||||
\(326\) | 0.599686 | 0.0332135 | ||||||||
\(327\) | 17.9566 | 0.993001 | ||||||||
\(328\) | −3.10290 | −0.171329 | ||||||||
\(329\) | 6.09171 | 0.335847 | ||||||||
\(330\) | 0.688507 | 0.0379011 | ||||||||
\(331\) | 8.21275 | 0.451413 | 0.225707 | − | 0.974195i | \(-0.427531\pi\) | ||||
0.225707 | + | 0.974195i | \(0.427531\pi\) | |||||||
\(332\) | −24.7379 | −1.35767 | ||||||||
\(333\) | 4.64710 | 0.254660 | ||||||||
\(334\) | −0.884761 | −0.0484120 | ||||||||
\(335\) | 42.1377 | 2.30223 | ||||||||
\(336\) | −3.84219 | −0.209609 | ||||||||
\(337\) | 28.2986 | 1.54152 | 0.770761 | − | 0.637124i | \(-0.219876\pi\) | ||||
0.770761 | + | 0.637124i | \(0.219876\pi\) | |||||||
\(338\) | −0.360663 | −0.0196175 | ||||||||
\(339\) | 15.5944 | 0.846971 | ||||||||
\(340\) | 7.92398 | 0.429738 | ||||||||
\(341\) | −13.4191 | −0.726687 | ||||||||
\(342\) | −0.398119 | −0.0215278 | ||||||||
\(343\) | −12.6585 | −0.683494 | ||||||||
\(344\) | 2.87612 | 0.155070 | ||||||||
\(345\) | −3.62079 | −0.194937 | ||||||||
\(346\) | −0.488424 | −0.0262578 | ||||||||
\(347\) | −36.4996 | −1.95940 | −0.979702 | − | 0.200462i | \(-0.935756\pi\) | ||||
−0.979702 | + | 0.200462i | \(0.935756\pi\) | |||||||
\(348\) | 17.5708 | 0.941894 | ||||||||
\(349\) | −19.4833 | −1.04291 | −0.521457 | − | 0.853277i | \(-0.674611\pi\) | ||||
−0.521457 | + | 0.853277i | \(0.674611\pi\) | |||||||
\(350\) | −0.807717 | −0.0431743 | ||||||||
\(351\) | −4.20360 | −0.224371 | ||||||||
\(352\) | −2.07086 | −0.110377 | ||||||||
\(353\) | −7.15305 | −0.380719 | −0.190359 | − | 0.981714i | \(-0.560965\pi\) | ||||
−0.190359 | + | 0.981714i | \(0.560965\pi\) | |||||||
\(354\) | −0.550070 | −0.0292359 | ||||||||
\(355\) | 2.07940 | 0.110363 | ||||||||
\(356\) | −23.3600 | −1.23808 | ||||||||
\(357\) | 0.969209 | 0.0512960 | ||||||||
\(358\) | 0.0396616 | 0.00209618 | ||||||||
\(359\) | −21.6440 | −1.14233 | −0.571164 | − | 0.820836i | \(-0.693508\pi\) | ||||
−0.571164 | + | 0.820836i | \(0.693508\pi\) | |||||||
\(360\) | 1.22571 | 0.0646004 | ||||||||
\(361\) | 7.57644 | 0.398760 | ||||||||
\(362\) | −0.422022 | −0.0221810 | ||||||||
\(363\) | 5.96654 | 0.313162 | ||||||||
\(364\) | −8.12403 | −0.425815 | ||||||||
\(365\) | −39.0482 | −2.04388 | ||||||||
\(366\) | −0.590414 | −0.0308614 | ||||||||
\(367\) | 8.73558 | 0.455994 | 0.227997 | − | 0.973662i | \(-0.426782\pi\) | ||||
0.227997 | + | 0.973662i | \(0.426782\pi\) | |||||||
\(368\) | 3.61205 | 0.188291 | ||||||||
\(369\) | −10.0598 | −0.523694 | ||||||||
\(370\) | −1.42612 | −0.0741406 | ||||||||
\(371\) | −4.52979 | −0.235175 | ||||||||
\(372\) | −11.9268 | −0.618376 | ||||||||
\(373\) | 17.9776 | 0.930847 | 0.465423 | − | 0.885088i | \(-0.345902\pi\) | ||||
0.465423 | + | 0.885088i | \(0.345902\pi\) | |||||||
\(374\) | 0.173260 | 0.00895906 | ||||||||
\(375\) | −23.0140 | −1.18844 | ||||||||
\(376\) | 1.93864 | 0.0999779 | ||||||||
\(377\) | 37.0407 | 1.90769 | ||||||||
\(378\) | 0.0748483 | 0.00384978 | ||||||||
\(379\) | 9.12246 | 0.468589 | 0.234295 | − | 0.972166i | \(-0.424722\pi\) | ||||
0.234295 | + | 0.972166i | \(0.424722\pi\) | |||||||
\(380\) | −40.8500 | −2.09556 | ||||||||
\(381\) | −6.24289 | −0.319833 | ||||||||
\(382\) | −0.924427 | −0.0472978 | ||||||||
\(383\) | −7.15889 | −0.365802 | −0.182901 | − | 0.983131i | \(-0.558549\pi\) | ||||
−0.182901 | + | 0.983131i | \(0.558549\pi\) | |||||||
\(384\) | −2.45285 | −0.125171 | ||||||||
\(385\) | 8.64094 | 0.440383 | ||||||||
\(386\) | 1.48492 | 0.0755805 | ||||||||
\(387\) | 9.32461 | 0.473996 | ||||||||
\(388\) | 31.8581 | 1.61735 | ||||||||
\(389\) | −6.40124 | −0.324556 | −0.162278 | − | 0.986745i | \(-0.551884\pi\) | ||||
−0.162278 | + | 0.986745i | \(0.551884\pi\) | |||||||
\(390\) | 1.29002 | 0.0653226 | ||||||||
\(391\) | −0.911156 | −0.0460791 | ||||||||
\(392\) | −1.86937 | −0.0944173 | ||||||||
\(393\) | −2.03547 | −0.102676 | ||||||||
\(394\) | 0.210401 | 0.0105998 | ||||||||
\(395\) | 3.97384 | 0.199945 | ||||||||
\(396\) | −4.47370 | −0.224812 | ||||||||
\(397\) | −12.8193 | −0.643382 | −0.321691 | − | 0.946845i | \(-0.604251\pi\) | ||||
−0.321691 | + | 0.946845i | \(0.604251\pi\) | |||||||
\(398\) | −0.560627 | −0.0281017 | ||||||||
\(399\) | −4.99650 | −0.250138 | ||||||||
\(400\) | 42.7798 | 2.13899 | ||||||||
\(401\) | −13.7344 | −0.685865 | −0.342932 | − | 0.939360i | \(-0.611420\pi\) | ||||
−0.342932 | + | 0.939360i | \(0.611420\pi\) | |||||||
\(402\) | 0.818889 | 0.0408425 | ||||||||
\(403\) | −25.1427 | −1.25245 | ||||||||
\(404\) | 7.48808 | 0.372546 | ||||||||
\(405\) | 3.97384 | 0.197462 | ||||||||
\(406\) | −0.659539 | −0.0327324 | ||||||||
\(407\) | 10.4259 | 0.516795 | ||||||||
\(408\) | 0.308444 | 0.0152703 | ||||||||
\(409\) | 35.9545 | 1.77783 | 0.888917 | − | 0.458068i | \(-0.151458\pi\) | ||||
0.888917 | + | 0.458068i | \(0.151458\pi\) | |||||||
\(410\) | 3.08720 | 0.152466 | ||||||||
\(411\) | −9.67979 | −0.477469 | ||||||||
\(412\) | −18.7074 | −0.921648 | ||||||||
\(413\) | −6.90352 | −0.339700 | ||||||||
\(414\) | −0.0703651 | −0.00345826 | ||||||||
\(415\) | 49.2993 | 2.42001 | ||||||||
\(416\) | −3.88006 | −0.190235 | ||||||||
\(417\) | 11.1227 | 0.544682 | ||||||||
\(418\) | −0.893196 | −0.0436876 | ||||||||
\(419\) | −19.5474 | −0.954954 | −0.477477 | − | 0.878644i | \(-0.658449\pi\) | ||||
−0.477477 | + | 0.878644i | \(0.658449\pi\) | |||||||
\(420\) | 7.67999 | 0.374745 | ||||||||
\(421\) | −33.1930 | −1.61773 | −0.808865 | − | 0.587994i | \(-0.799918\pi\) | ||||
−0.808865 | + | 0.587994i | \(0.799918\pi\) | |||||||
\(422\) | −0.944340 | −0.0459698 | ||||||||
\(423\) | 6.28523 | 0.305599 | ||||||||
\(424\) | −1.44157 | −0.0700090 | ||||||||
\(425\) | −10.7914 | −0.523459 | ||||||||
\(426\) | 0.0404104 | 0.00195789 | ||||||||
\(427\) | −7.40985 | −0.358588 | ||||||||
\(428\) | 35.5210 | 1.71697 | ||||||||
\(429\) | −9.43093 | −0.455329 | ||||||||
\(430\) | −2.86158 | −0.137997 | ||||||||
\(431\) | 28.5281 | 1.37415 | 0.687075 | − | 0.726587i | \(-0.258894\pi\) | ||||
0.687075 | + | 0.726587i | \(0.258894\pi\) | |||||||
\(432\) | −3.96425 | −0.190730 | ||||||||
\(433\) | −1.31607 | −0.0632463 | −0.0316232 | − | 0.999500i | \(-0.510068\pi\) | ||||
−0.0316232 | + | 0.999500i | \(0.510068\pi\) | |||||||
\(434\) | 0.447685 | 0.0214896 | ||||||||
\(435\) | −35.0162 | −1.67890 | ||||||||
\(436\) | 35.8060 | 1.71480 | ||||||||
\(437\) | 4.69722 | 0.224699 | ||||||||
\(438\) | −0.758850 | −0.0362593 | ||||||||
\(439\) | −14.3459 | −0.684691 | −0.342345 | − | 0.939574i | \(-0.611221\pi\) | ||||
−0.342345 | + | 0.939574i | \(0.611221\pi\) | |||||||
\(440\) | 2.74992 | 0.131097 | ||||||||
\(441\) | −6.06063 | −0.288602 | ||||||||
\(442\) | 0.324628 | 0.0154410 | ||||||||
\(443\) | −33.3972 | −1.58675 | −0.793373 | − | 0.608735i | \(-0.791677\pi\) | ||||
−0.793373 | + | 0.608735i | \(0.791677\pi\) | |||||||
\(444\) | 9.26649 | 0.439768 | ||||||||
\(445\) | 46.5532 | 2.20683 | ||||||||
\(446\) | 0.387741 | 0.0183601 | ||||||||
\(447\) | 14.8967 | 0.704589 | ||||||||
\(448\) | −7.61529 | −0.359789 | ||||||||
\(449\) | 17.5037 | 0.826049 | 0.413025 | − | 0.910720i | \(-0.364472\pi\) | ||||
0.413025 | + | 0.910720i | \(0.364472\pi\) | |||||||
\(450\) | −0.833378 | −0.0392858 | ||||||||
\(451\) | −22.5696 | −1.06276 | ||||||||
\(452\) | 31.0958 | 1.46262 | ||||||||
\(453\) | −11.1404 | −0.523422 | ||||||||
\(454\) | −2.04507 | −0.0959798 | ||||||||
\(455\) | 16.1901 | 0.759002 | ||||||||
\(456\) | −1.59010 | −0.0744634 | ||||||||
\(457\) | 37.9848 | 1.77686 | 0.888428 | − | 0.459017i | \(-0.151798\pi\) | ||||
0.888428 | + | 0.459017i | \(0.151798\pi\) | |||||||
\(458\) | −1.36721 | −0.0638856 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −7.21998 | −0.336633 | ||||||||
\(461\) | −8.34655 | −0.388737 | −0.194369 | − | 0.980929i | \(-0.562266\pi\) | ||||
−0.194369 | + | 0.980929i | \(0.562266\pi\) | |||||||
\(462\) | 0.167925 | 0.00781258 | ||||||||
\(463\) | −18.2607 | −0.848646 | −0.424323 | − | 0.905511i | \(-0.639488\pi\) | ||||
−0.424323 | + | 0.905511i | \(0.639488\pi\) | |||||||
\(464\) | 34.9317 | 1.62166 | ||||||||
\(465\) | 23.7685 | 1.10224 | ||||||||
\(466\) | 0.813734 | 0.0376955 | ||||||||
\(467\) | 32.1981 | 1.48995 | 0.744974 | − | 0.667093i | \(-0.232462\pi\) | ||||
0.744974 | + | 0.667093i | \(0.232462\pi\) | |||||||
\(468\) | −8.38212 | −0.387464 | ||||||||
\(469\) | 10.2773 | 0.474560 | ||||||||
\(470\) | −1.92884 | −0.0889708 | ||||||||
\(471\) | 5.48902 | 0.252921 | ||||||||
\(472\) | −2.19700 | −0.101125 | ||||||||
\(473\) | 20.9201 | 0.961908 | ||||||||
\(474\) | 0.0772262 | 0.00354712 | ||||||||
\(475\) | 55.6321 | 2.55258 | ||||||||
\(476\) | 1.93264 | 0.0885823 | ||||||||
\(477\) | −4.67370 | −0.213994 | ||||||||
\(478\) | −0.230167 | −0.0105276 | ||||||||
\(479\) | −21.3171 | −0.974005 | −0.487002 | − | 0.873401i | \(-0.661910\pi\) | ||||
−0.487002 | + | 0.873401i | \(0.661910\pi\) | |||||||
\(480\) | 3.66798 | 0.167420 | ||||||||
\(481\) | 19.5345 | 0.890698 | ||||||||
\(482\) | −2.36399 | −0.107677 | ||||||||
\(483\) | −0.883100 | −0.0401825 | ||||||||
\(484\) | 11.8975 | 0.540795 | ||||||||
\(485\) | −63.4887 | −2.88288 | ||||||||
\(486\) | 0.0772262 | 0.00350305 | ||||||||
\(487\) | 16.2627 | 0.736933 | 0.368467 | − | 0.929641i | \(-0.379883\pi\) | ||||
0.368467 | + | 0.929641i | \(0.379883\pi\) | |||||||
\(488\) | −2.35814 | −0.106748 | ||||||||
\(489\) | 7.76532 | 0.351160 | ||||||||
\(490\) | 1.85991 | 0.0840223 | ||||||||
\(491\) | −30.6258 | −1.38212 | −0.691061 | − | 0.722796i | \(-0.742857\pi\) | ||||
−0.691061 | + | 0.722796i | \(0.742857\pi\) | |||||||
\(492\) | −20.0597 | −0.904360 | ||||||||
\(493\) | −8.81167 | −0.396858 | ||||||||
\(494\) | −1.67353 | −0.0752958 | ||||||||
\(495\) | 8.91546 | 0.400720 | ||||||||
\(496\) | −23.7111 | −1.06466 | ||||||||
\(497\) | 0.507160 | 0.0227493 | ||||||||
\(498\) | 0.958065 | 0.0429319 | ||||||||
\(499\) | 22.8563 | 1.02319 | 0.511593 | − | 0.859228i | \(-0.329055\pi\) | ||||
0.511593 | + | 0.859228i | \(0.329055\pi\) | |||||||
\(500\) | −45.8908 | −2.05230 | ||||||||
\(501\) | −11.4568 | −0.511850 | ||||||||
\(502\) | −0.553283 | −0.0246942 | ||||||||
\(503\) | −18.8295 | −0.839567 | −0.419784 | − | 0.907624i | \(-0.637894\pi\) | ||||
−0.419784 | + | 0.907624i | \(0.637894\pi\) | |||||||
\(504\) | 0.298947 | 0.0133162 | ||||||||
\(505\) | −14.9227 | −0.664052 | ||||||||
\(506\) | −0.157867 | −0.00701803 | ||||||||
\(507\) | −4.67022 | −0.207412 | ||||||||
\(508\) | −12.4486 | −0.552315 | ||||||||
\(509\) | 40.6522 | 1.80188 | 0.900939 | − | 0.433946i | \(-0.142879\pi\) | ||||
0.900939 | + | 0.433946i | \(0.142879\pi\) | |||||||
\(510\) | −0.306884 | −0.0135891 | ||||||||
\(511\) | −9.52377 | −0.421307 | ||||||||
\(512\) | −6.10464 | −0.269789 | ||||||||
\(513\) | −5.15523 | −0.227609 | ||||||||
\(514\) | 1.63094 | 0.0719378 | ||||||||
\(515\) | 37.2813 | 1.64281 | ||||||||
\(516\) | 18.5936 | 0.818538 | ||||||||
\(517\) | 14.1012 | 0.620169 | ||||||||
\(518\) | −0.347828 | −0.0152827 | ||||||||
\(519\) | −6.32459 | −0.277619 | ||||||||
\(520\) | 5.15238 | 0.225947 | ||||||||
\(521\) | 0.364352 | 0.0159625 | 0.00798127 | − | 0.999968i | \(-0.497459\pi\) | ||||
0.00798127 | + | 0.999968i | \(0.497459\pi\) | |||||||
\(522\) | −0.680492 | −0.0297843 | ||||||||
\(523\) | 26.3168 | 1.15075 | 0.575376 | − | 0.817889i | \(-0.304856\pi\) | ||||
0.575376 | + | 0.817889i | \(0.304856\pi\) | |||||||
\(524\) | −4.05880 | −0.177309 | ||||||||
\(525\) | −10.4591 | −0.456473 | ||||||||
\(526\) | −0.595576 | −0.0259684 | ||||||||
\(527\) | 5.98124 | 0.260547 | ||||||||
\(528\) | −8.89395 | −0.387060 | ||||||||
\(529\) | −22.1698 | −0.963904 | ||||||||
\(530\) | 1.43428 | 0.0623013 | ||||||||
\(531\) | −7.12284 | −0.309105 | ||||||||
\(532\) | −9.96320 | −0.431959 | ||||||||
\(533\) | −42.2875 | −1.83167 | ||||||||
\(534\) | 0.904699 | 0.0391501 | ||||||||
\(535\) | −70.7885 | −3.06045 | ||||||||
\(536\) | 3.27067 | 0.141271 | ||||||||
\(537\) | 0.513577 | 0.0221625 | ||||||||
\(538\) | 1.11270 | 0.0479717 | ||||||||
\(539\) | −13.5973 | −0.585676 | ||||||||
\(540\) | 7.92398 | 0.340994 | ||||||||
\(541\) | 43.4504 | 1.86808 | 0.934038 | − | 0.357173i | \(-0.116259\pi\) | ||||
0.934038 | + | 0.357173i | \(0.116259\pi\) | |||||||
\(542\) | −1.37522 | −0.0590706 | ||||||||
\(543\) | −5.46475 | −0.234515 | ||||||||
\(544\) | 0.923033 | 0.0395747 | ||||||||
\(545\) | −71.3565 | −3.05658 | ||||||||
\(546\) | 0.314632 | 0.0134650 | ||||||||
\(547\) | −26.3597 | −1.12706 | −0.563530 | − | 0.826095i | \(-0.690557\pi\) | ||||
−0.563530 | + | 0.826095i | \(0.690557\pi\) | |||||||
\(548\) | −19.3019 | −0.824534 | ||||||||
\(549\) | −7.64526 | −0.326292 | ||||||||
\(550\) | −1.86971 | −0.0797249 | ||||||||
\(551\) | 45.4262 | 1.93522 | ||||||||
\(552\) | −0.281041 | −0.0119619 | ||||||||
\(553\) | 0.969209 | 0.0412150 | ||||||||
\(554\) | 0.679062 | 0.0288506 | ||||||||
\(555\) | −18.4668 | −0.783873 | ||||||||
\(556\) | 22.1791 | 0.940603 | ||||||||
\(557\) | 16.2713 | 0.689435 | 0.344718 | − | 0.938706i | \(-0.387975\pi\) | ||||
0.344718 | + | 0.938706i | \(0.387975\pi\) | |||||||
\(558\) | 0.461908 | 0.0195541 | ||||||||
\(559\) | 39.1969 | 1.65785 | ||||||||
\(560\) | 15.2682 | 0.645201 | ||||||||
\(561\) | 2.24354 | 0.0947223 | ||||||||
\(562\) | −1.01655 | −0.0428806 | ||||||||
\(563\) | −30.6509 | −1.29178 | −0.645891 | − | 0.763429i | \(-0.723514\pi\) | ||||
−0.645891 | + | 0.763429i | \(0.723514\pi\) | |||||||
\(564\) | 12.5330 | 0.527734 | ||||||||
\(565\) | −61.9696 | −2.60708 | ||||||||
\(566\) | 0.494379 | 0.0207803 | ||||||||
\(567\) | 0.969209 | 0.0407029 | ||||||||
\(568\) | 0.161400 | 0.00677221 | ||||||||
\(569\) | −25.2340 | −1.05786 | −0.528932 | − | 0.848664i | \(-0.677407\pi\) | ||||
−0.528932 | + | 0.848664i | \(0.677407\pi\) | |||||||
\(570\) | 1.58206 | 0.0662652 | ||||||||
\(571\) | −10.5534 | −0.441647 | −0.220824 | − | 0.975314i | \(-0.570874\pi\) | ||||
−0.220824 | + | 0.975314i | \(0.570874\pi\) | |||||||
\(572\) | −18.8056 | −0.786302 | ||||||||
\(573\) | −11.9704 | −0.500070 | ||||||||
\(574\) | 0.752961 | 0.0314280 | ||||||||
\(575\) | 9.83263 | 0.410049 | ||||||||
\(576\) | −7.85722 | −0.327384 | ||||||||
\(577\) | 36.2607 | 1.50955 | 0.754777 | − | 0.655981i | \(-0.227745\pi\) | ||||
0.754777 | + | 0.655981i | \(0.227745\pi\) | |||||||
\(578\) | −0.0772262 | −0.00321219 | ||||||||
\(579\) | 19.2282 | 0.799097 | ||||||||
\(580\) | −69.8235 | −2.89926 | ||||||||
\(581\) | 12.0240 | 0.498838 | ||||||||
\(582\) | −1.23382 | −0.0511434 | ||||||||
\(583\) | −10.4856 | −0.434270 | ||||||||
\(584\) | −3.03087 | −0.125418 | ||||||||
\(585\) | 16.7044 | 0.690642 | ||||||||
\(586\) | −1.05514 | −0.0435874 | ||||||||
\(587\) | −36.3668 | −1.50102 | −0.750509 | − | 0.660860i | \(-0.770192\pi\) | ||||
−0.750509 | + | 0.660860i | \(0.770192\pi\) | |||||||
\(588\) | −12.0851 | −0.498382 | ||||||||
\(589\) | −30.8347 | −1.27052 | ||||||||
\(590\) | 2.18589 | 0.0899916 | ||||||||
\(591\) | 2.72447 | 0.112070 | ||||||||
\(592\) | 18.4223 | 0.757151 | ||||||||
\(593\) | −1.21333 | −0.0498256 | −0.0249128 | − | 0.999690i | \(-0.507931\pi\) | ||||
−0.0249128 | + | 0.999690i | \(0.507931\pi\) | |||||||
\(594\) | 0.173260 | 0.00710894 | ||||||||
\(595\) | −3.85148 | −0.157895 | ||||||||
\(596\) | 29.7045 | 1.21674 | ||||||||
\(597\) | −7.25954 | −0.297113 | ||||||||
\(598\) | −0.295786 | −0.0120956 | ||||||||
\(599\) | 1.45725 | 0.0595416 | 0.0297708 | − | 0.999557i | \(-0.490522\pi\) | ||||
0.0297708 | + | 0.999557i | \(0.490522\pi\) | |||||||
\(600\) | −3.32854 | −0.135887 | ||||||||
\(601\) | −11.7909 | −0.480962 | −0.240481 | − | 0.970654i | \(-0.577305\pi\) | ||||
−0.240481 | + | 0.970654i | \(0.577305\pi\) | |||||||
\(602\) | −0.697931 | −0.0284455 | ||||||||
\(603\) | 10.6038 | 0.431819 | ||||||||
\(604\) | −22.2144 | −0.903890 | ||||||||
\(605\) | −23.7100 | −0.963950 | ||||||||
\(606\) | −0.290003 | −0.0117806 | ||||||||
\(607\) | −4.32566 | −0.175573 | −0.0877865 | − | 0.996139i | \(-0.527979\pi\) | ||||
−0.0877865 | + | 0.996139i | \(0.527979\pi\) | |||||||
\(608\) | −4.75845 | −0.192981 | ||||||||
\(609\) | −8.54035 | −0.346073 | ||||||||
\(610\) | 2.34621 | 0.0949953 | ||||||||
\(611\) | 26.4206 | 1.06886 | ||||||||
\(612\) | 1.99404 | 0.0806041 | ||||||||
\(613\) | −41.7279 | −1.68537 | −0.842687 | − | 0.538404i | \(-0.819028\pi\) | ||||
−0.842687 | + | 0.538404i | \(0.819028\pi\) | |||||||
\(614\) | 0.777873 | 0.0313924 | ||||||||
\(615\) | 39.9761 | 1.61199 | ||||||||
\(616\) | 0.670699 | 0.0270232 | ||||||||
\(617\) | −8.35316 | −0.336285 | −0.168143 | − | 0.985763i | \(-0.553777\pi\) | ||||
−0.168143 | + | 0.985763i | \(0.553777\pi\) | |||||||
\(618\) | 0.724511 | 0.0291441 | ||||||||
\(619\) | −26.2401 | −1.05468 | −0.527339 | − | 0.849655i | \(-0.676810\pi\) | ||||
−0.527339 | + | 0.849655i | \(0.676810\pi\) | |||||||
\(620\) | 47.3952 | 1.90344 | ||||||||
\(621\) | −0.911156 | −0.0365634 | ||||||||
\(622\) | 0.949012 | 0.0380519 | ||||||||
\(623\) | 11.3542 | 0.454897 | ||||||||
\(624\) | −16.6641 | −0.667098 | ||||||||
\(625\) | 37.4971 | 1.49988 | ||||||||
\(626\) | −1.85314 | −0.0740665 | ||||||||
\(627\) | −11.5660 | −0.461900 | ||||||||
\(628\) | 10.9453 | 0.436765 | ||||||||
\(629\) | −4.64710 | −0.185292 | ||||||||
\(630\) | −0.297435 | −0.0118501 | ||||||||
\(631\) | −20.9242 | −0.832977 | −0.416489 | − | 0.909141i | \(-0.636739\pi\) | ||||
−0.416489 | + | 0.909141i | \(0.636739\pi\) | |||||||
\(632\) | 0.308444 | 0.0122693 | ||||||||
\(633\) | −12.2282 | −0.486029 | ||||||||
\(634\) | −0.900516 | −0.0357641 | ||||||||
\(635\) | 24.8082 | 0.984485 | ||||||||
\(636\) | −9.31952 | −0.369543 | ||||||||
\(637\) | −25.4765 | −1.00941 | ||||||||
\(638\) | −1.52671 | −0.0604430 | ||||||||
\(639\) | 0.523273 | 0.0207003 | ||||||||
\(640\) | 9.74722 | 0.385293 | ||||||||
\(641\) | −9.44361 | −0.373000 | −0.186500 | − | 0.982455i | \(-0.559714\pi\) | ||||
−0.186500 | + | 0.982455i | \(0.559714\pi\) | |||||||
\(642\) | −1.37568 | −0.0542937 | ||||||||
\(643\) | −16.6916 | −0.658254 | −0.329127 | − | 0.944286i | \(-0.606754\pi\) | ||||
−0.329127 | + | 0.944286i | \(0.606754\pi\) | |||||||
\(644\) | −1.76093 | −0.0693905 | ||||||||
\(645\) | −37.0545 | −1.45902 | ||||||||
\(646\) | 0.398119 | 0.0156638 | ||||||||
\(647\) | −18.6044 | −0.731414 | −0.365707 | − | 0.930730i | \(-0.619173\pi\) | ||||
−0.365707 | + | 0.930730i | \(0.619173\pi\) | |||||||
\(648\) | 0.308444 | 0.0121168 | ||||||||
\(649\) | −15.9804 | −0.627284 | ||||||||
\(650\) | −3.50318 | −0.137406 | ||||||||
\(651\) | 5.79707 | 0.227205 | ||||||||
\(652\) | 15.4843 | 0.606413 | ||||||||
\(653\) | 19.3276 | 0.756349 | 0.378174 | − | 0.925734i | \(-0.376552\pi\) | ||||
0.378174 | + | 0.925734i | \(0.376552\pi\) | |||||||
\(654\) | −1.38672 | −0.0542249 | ||||||||
\(655\) | 8.08862 | 0.316049 | ||||||||
\(656\) | −39.8797 | −1.55704 | ||||||||
\(657\) | −9.82633 | −0.383362 | ||||||||
\(658\) | −0.470439 | −0.0183396 | ||||||||
\(659\) | −1.21646 | −0.0473866 | −0.0236933 | − | 0.999719i | \(-0.507543\pi\) | ||||
−0.0236933 | + | 0.999719i | \(0.507543\pi\) | |||||||
\(660\) | 17.7777 | 0.691998 | ||||||||
\(661\) | 25.0595 | 0.974702 | 0.487351 | − | 0.873206i | \(-0.337963\pi\) | ||||
0.487351 | + | 0.873206i | \(0.337963\pi\) | |||||||
\(662\) | −0.634239 | −0.0246504 | ||||||||
\(663\) | 4.20360 | 0.163254 | ||||||||
\(664\) | 3.82655 | 0.148499 | ||||||||
\(665\) | 19.8553 | 0.769955 | ||||||||
\(666\) | −0.358878 | −0.0139062 | ||||||||
\(667\) | 8.02881 | 0.310877 | ||||||||
\(668\) | −22.8452 | −0.883906 | ||||||||
\(669\) | 5.02084 | 0.194117 | ||||||||
\(670\) | −3.25413 | −0.125718 | ||||||||
\(671\) | −17.1524 | −0.662162 | ||||||||
\(672\) | 0.894611 | 0.0345104 | ||||||||
\(673\) | −24.9616 | −0.962200 | −0.481100 | − | 0.876666i | \(-0.659763\pi\) | ||||
−0.481100 | + | 0.876666i | \(0.659763\pi\) | |||||||
\(674\) | −2.18539 | −0.0841782 | ||||||||
\(675\) | −10.7914 | −0.415361 | ||||||||
\(676\) | −9.31258 | −0.358176 | ||||||||
\(677\) | −1.69418 | −0.0651126 | −0.0325563 | − | 0.999470i | \(-0.510365\pi\) | ||||
−0.0325563 | + | 0.999470i | \(0.510365\pi\) | |||||||
\(678\) | −1.20430 | −0.0462507 | ||||||||
\(679\) | −15.4847 | −0.594250 | ||||||||
\(680\) | −1.22571 | −0.0470037 | ||||||||
\(681\) | −26.4815 | −1.01477 | ||||||||
\(682\) | 1.03631 | 0.0396823 | ||||||||
\(683\) | −35.5865 | −1.36168 | −0.680839 | − | 0.732433i | \(-0.738385\pi\) | ||||
−0.680839 | + | 0.732433i | \(0.738385\pi\) | |||||||
\(684\) | −10.2797 | −0.393055 | ||||||||
\(685\) | 38.4659 | 1.46971 | ||||||||
\(686\) | 0.977567 | 0.0373237 | ||||||||
\(687\) | −17.7040 | −0.675449 | ||||||||
\(688\) | 36.9651 | 1.40928 | ||||||||
\(689\) | −19.6463 | −0.748465 | ||||||||
\(690\) | 0.279619 | 0.0106449 | ||||||||
\(691\) | −20.8279 | −0.792329 | −0.396165 | − | 0.918180i | \(-0.629659\pi\) | ||||
−0.396165 | + | 0.918180i | \(0.629659\pi\) | |||||||
\(692\) | −12.6115 | −0.479416 | ||||||||
\(693\) | 2.17446 | 0.0826008 | ||||||||
\(694\) | 2.81873 | 0.106997 | ||||||||
\(695\) | −44.1999 | −1.67660 | ||||||||
\(696\) | −2.71791 | −0.103022 | ||||||||
\(697\) | 10.0598 | 0.381043 | ||||||||
\(698\) | 1.50462 | 0.0569506 | ||||||||
\(699\) | 10.5370 | 0.398547 | ||||||||
\(700\) | −20.8558 | −0.788277 | ||||||||
\(701\) | −6.18028 | −0.233426 | −0.116713 | − | 0.993166i | \(-0.537236\pi\) | ||||
−0.116713 | + | 0.993166i | \(0.537236\pi\) | |||||||
\(702\) | 0.324628 | 0.0122523 | ||||||||
\(703\) | 23.9569 | 0.903551 | ||||||||
\(704\) | −17.6280 | −0.664379 | ||||||||
\(705\) | −24.9765 | −0.940669 | ||||||||
\(706\) | 0.552403 | 0.0207900 | ||||||||
\(707\) | −3.63961 | −0.136882 | ||||||||
\(708\) | −14.2032 | −0.533789 | ||||||||
\(709\) | −30.4078 | −1.14199 | −0.570994 | − | 0.820954i | \(-0.693442\pi\) | ||||
−0.570994 | + | 0.820954i | \(0.693442\pi\) | |||||||
\(710\) | −0.160584 | −0.00602662 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 3.61340 | 0.135418 | ||||||||
\(713\) | −5.44984 | −0.204098 | ||||||||
\(714\) | −0.0748483 | −0.00280113 | ||||||||
\(715\) | 37.4770 | 1.40156 | ||||||||
\(716\) | 1.02409 | 0.0382721 | ||||||||
\(717\) | −2.98042 | −0.111306 | ||||||||
\(718\) | 1.67148 | 0.0623793 | ||||||||
\(719\) | 12.5377 | 0.467578 | 0.233789 | − | 0.972287i | \(-0.424887\pi\) | ||||
0.233789 | + | 0.972287i | \(0.424887\pi\) | |||||||
\(720\) | 15.7533 | 0.587091 | ||||||||
\(721\) | 9.09280 | 0.338634 | ||||||||
\(722\) | −0.585100 | −0.0217752 | ||||||||
\(723\) | −30.6112 | −1.13844 | ||||||||
\(724\) | −10.8969 | −0.404981 | ||||||||
\(725\) | 95.0902 | 3.53156 | ||||||||
\(726\) | −0.460773 | −0.0171009 | ||||||||
\(727\) | −38.4249 | −1.42510 | −0.712550 | − | 0.701621i | \(-0.752460\pi\) | ||||
−0.712550 | + | 0.701621i | \(0.752460\pi\) | |||||||
\(728\) | 1.25665 | 0.0465746 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.01555 | 0.111610 | ||||||||
\(731\) | −9.32461 | −0.344883 | ||||||||
\(732\) | −15.2449 | −0.563468 | ||||||||
\(733\) | −17.5766 | −0.649205 | −0.324602 | − | 0.945851i | \(-0.605231\pi\) | ||||
−0.324602 | + | 0.945851i | \(0.605231\pi\) | |||||||
\(734\) | −0.674616 | −0.0249005 | ||||||||
\(735\) | 24.0840 | 0.888351 | ||||||||
\(736\) | −0.841026 | −0.0310006 | ||||||||
\(737\) | 23.7900 | 0.876315 | ||||||||
\(738\) | 0.776883 | 0.0285974 | ||||||||
\(739\) | 28.7956 | 1.05926 | 0.529631 | − | 0.848228i | \(-0.322330\pi\) | ||||
0.529631 | + | 0.848228i | \(0.322330\pi\) | |||||||
\(740\) | −36.8235 | −1.35366 | ||||||||
\(741\) | −21.6705 | −0.796086 | ||||||||
\(742\) | 0.349818 | 0.0128422 | ||||||||
\(743\) | 51.0891 | 1.87428 | 0.937139 | − | 0.348958i | \(-0.113464\pi\) | ||||
0.937139 | + | 0.348958i | \(0.113464\pi\) | |||||||
\(744\) | 1.84488 | 0.0676365 | ||||||||
\(745\) | −59.1970 | −2.16881 | ||||||||
\(746\) | −1.38834 | −0.0508309 | ||||||||
\(747\) | 12.4060 | 0.453910 | ||||||||
\(748\) | 4.47370 | 0.163575 | ||||||||
\(749\) | −17.2651 | −0.630854 | ||||||||
\(750\) | 1.77729 | 0.0648973 | ||||||||
\(751\) | 6.85072 | 0.249986 | 0.124993 | − | 0.992158i | \(-0.460109\pi\) | ||||
0.124993 | + | 0.992158i | \(0.460109\pi\) | |||||||
\(752\) | 24.9163 | 0.908602 | ||||||||
\(753\) | −7.16445 | −0.261087 | ||||||||
\(754\) | −2.86051 | −0.104174 | ||||||||
\(755\) | 44.2702 | 1.61116 | ||||||||
\(756\) | 1.93264 | 0.0702893 | ||||||||
\(757\) | 12.8676 | 0.467681 | 0.233841 | − | 0.972275i | \(-0.424871\pi\) | ||||
0.233841 | + | 0.972275i | \(0.424871\pi\) | |||||||
\(758\) | −0.704493 | −0.0255883 | ||||||||
\(759\) | −2.04421 | −0.0742002 | ||||||||
\(760\) | 6.31881 | 0.229207 | ||||||||
\(761\) | −34.4489 | −1.24877 | −0.624385 | − | 0.781116i | \(-0.714651\pi\) | ||||
−0.624385 | + | 0.781116i | \(0.714651\pi\) | |||||||
\(762\) | 0.482115 | 0.0174652 | ||||||||
\(763\) | −17.4037 | −0.630055 | ||||||||
\(764\) | −23.8694 | −0.863564 | ||||||||
\(765\) | −3.97384 | −0.143674 | ||||||||
\(766\) | 0.552854 | 0.0199754 | ||||||||
\(767\) | −29.9416 | −1.08113 | ||||||||
\(768\) | −15.5250 | −0.560211 | ||||||||
\(769\) | 13.7035 | 0.494160 | 0.247080 | − | 0.968995i | \(-0.420529\pi\) | ||||
0.247080 | + | 0.968995i | \(0.420529\pi\) | |||||||
\(770\) | −0.667307 | −0.0240481 | ||||||||
\(771\) | 21.1190 | 0.760583 | ||||||||
\(772\) | 38.3417 | 1.37995 | ||||||||
\(773\) | −33.9039 | −1.21944 | −0.609719 | − | 0.792618i | \(-0.708718\pi\) | ||||
−0.609719 | + | 0.792618i | \(0.708718\pi\) | |||||||
\(774\) | −0.720104 | −0.0258836 | ||||||||
\(775\) | −64.5458 | −2.31855 | ||||||||
\(776\) | −4.92792 | −0.176902 | ||||||||
\(777\) | −4.50401 | −0.161581 | ||||||||
\(778\) | 0.494344 | 0.0177231 | ||||||||
\(779\) | −51.8608 | −1.85811 | ||||||||
\(780\) | 33.3092 | 1.19266 | ||||||||
\(781\) | 1.17398 | 0.0420084 | ||||||||
\(782\) | 0.0703651 | 0.00251625 | ||||||||
\(783\) | −8.81167 | −0.314904 | ||||||||
\(784\) | −24.0259 | −0.858067 | ||||||||
\(785\) | −21.8125 | −0.778521 | ||||||||
\(786\) | 0.157191 | 0.00560683 | ||||||||
\(787\) | −26.2076 | −0.934199 | −0.467099 | − | 0.884205i | \(-0.654701\pi\) | ||||
−0.467099 | + | 0.884205i | \(0.654701\pi\) | |||||||
\(788\) | 5.43269 | 0.193532 | ||||||||
\(789\) | −7.71210 | −0.274558 | ||||||||
\(790\) | −0.306884 | −0.0109185 | ||||||||
\(791\) | −15.1142 | −0.537400 | ||||||||
\(792\) | 0.692006 | 0.0245894 | ||||||||
\(793\) | −32.1376 | −1.14124 | ||||||||
\(794\) | 0.989985 | 0.0351332 | ||||||||
\(795\) | 18.5725 | 0.658699 | ||||||||
\(796\) | −14.4758 | −0.513081 | ||||||||
\(797\) | 21.2731 | 0.753533 | 0.376766 | − | 0.926308i | \(-0.377036\pi\) | ||||
0.376766 | + | 0.926308i | \(0.377036\pi\) | |||||||
\(798\) | 0.385861 | 0.0136593 | ||||||||
\(799\) | −6.28523 | −0.222356 | ||||||||
\(800\) | −9.96080 | −0.352167 | ||||||||
\(801\) | 11.7149 | 0.413926 | ||||||||
\(802\) | 1.06066 | 0.0374531 | ||||||||
\(803\) | −22.0457 | −0.777978 | ||||||||
\(804\) | 21.1443 | 0.745702 | ||||||||
\(805\) | 3.50930 | 0.123686 | ||||||||
\(806\) | 1.94168 | 0.0683926 | ||||||||
\(807\) | 14.4083 | 0.507195 | ||||||||
\(808\) | −1.15828 | −0.0407482 | ||||||||
\(809\) | −24.8521 | −0.873754 | −0.436877 | − | 0.899521i | \(-0.643915\pi\) | ||||
−0.436877 | + | 0.899521i | \(0.643915\pi\) | |||||||
\(810\) | −0.306884 | −0.0107828 | ||||||||
\(811\) | 22.7050 | 0.797280 | 0.398640 | − | 0.917108i | \(-0.369482\pi\) | ||||
0.398640 | + | 0.917108i | \(0.369482\pi\) | |||||||
\(812\) | −17.0298 | −0.597628 | ||||||||
\(813\) | −17.8076 | −0.624541 | ||||||||
\(814\) | −0.805156 | −0.0282207 | ||||||||
\(815\) | −30.8581 | −1.08091 | ||||||||
\(816\) | 3.96425 | 0.138777 | ||||||||
\(817\) | 48.0705 | 1.68177 | ||||||||
\(818\) | −2.77663 | −0.0970825 | ||||||||
\(819\) | 4.07416 | 0.142363 | ||||||||
\(820\) | 79.7139 | 2.78373 | ||||||||
\(821\) | −9.70595 | −0.338740 | −0.169370 | − | 0.985553i | \(-0.554173\pi\) | ||||
−0.169370 | + | 0.985553i | \(0.554173\pi\) | |||||||
\(822\) | 0.747533 | 0.0260732 | ||||||||
\(823\) | 40.9355 | 1.42692 | 0.713461 | − | 0.700695i | \(-0.247127\pi\) | ||||
0.713461 | + | 0.700695i | \(0.247127\pi\) | |||||||
\(824\) | 2.89372 | 0.100808 | ||||||||
\(825\) | −24.2109 | −0.842915 | ||||||||
\(826\) | 0.533133 | 0.0185501 | ||||||||
\(827\) | −1.97906 | −0.0688186 | −0.0344093 | − | 0.999408i | \(-0.510955\pi\) | ||||
−0.0344093 | + | 0.999408i | \(0.510955\pi\) | |||||||
\(828\) | −1.81688 | −0.0631409 | ||||||||
\(829\) | 22.1285 | 0.768554 | 0.384277 | − | 0.923218i | \(-0.374451\pi\) | ||||
0.384277 | + | 0.923218i | \(0.374451\pi\) | |||||||
\(830\) | −3.80719 | −0.132150 | ||||||||
\(831\) | 8.79316 | 0.305031 | ||||||||
\(832\) | −33.0286 | −1.14506 | ||||||||
\(833\) | 6.06063 | 0.209989 | ||||||||
\(834\) | −0.858965 | −0.0297435 | ||||||||
\(835\) | 45.5273 | 1.57554 | ||||||||
\(836\) | −23.0630 | −0.797649 | ||||||||
\(837\) | 5.98124 | 0.206742 | ||||||||
\(838\) | 1.50957 | 0.0521473 | ||||||||
\(839\) | −54.0788 | −1.86701 | −0.933504 | − | 0.358567i | \(-0.883265\pi\) | ||||
−0.933504 | + | 0.358567i | \(0.883265\pi\) | |||||||
\(840\) | −1.18797 | −0.0409887 | ||||||||
\(841\) | 48.6456 | 1.67743 | ||||||||
\(842\) | 2.56337 | 0.0883397 | ||||||||
\(843\) | −13.1633 | −0.453368 | ||||||||
\(844\) | −24.3835 | −0.839316 | ||||||||
\(845\) | 18.5587 | 0.638438 | ||||||||
\(846\) | −0.485385 | −0.0166879 | ||||||||
\(847\) | −5.78282 | −0.198700 | ||||||||
\(848\) | −18.5277 | −0.636244 | ||||||||
\(849\) | 6.40170 | 0.219706 | ||||||||
\(850\) | 0.833378 | 0.0285846 | ||||||||
\(851\) | 4.23423 | 0.145148 | ||||||||
\(852\) | 1.04342 | 0.0357471 | ||||||||
\(853\) | −11.0610 | −0.378722 | −0.189361 | − | 0.981908i | \(-0.560642\pi\) | ||||
−0.189361 | + | 0.981908i | \(0.560642\pi\) | |||||||
\(854\) | 0.572235 | 0.0195815 | ||||||||
\(855\) | 20.4861 | 0.700609 | ||||||||
\(856\) | −5.49451 | −0.187799 | ||||||||
\(857\) | −3.19086 | −0.108998 | −0.0544989 | − | 0.998514i | \(-0.517356\pi\) | ||||
−0.0544989 | + | 0.998514i | \(0.517356\pi\) | |||||||
\(858\) | 0.728315 | 0.0248643 | ||||||||
\(859\) | −23.6911 | −0.808331 | −0.404166 | − | 0.914686i | \(-0.632438\pi\) | ||||
−0.404166 | + | 0.914686i | \(0.632438\pi\) | |||||||
\(860\) | −73.8880 | −2.51956 | ||||||||
\(861\) | 9.75008 | 0.332282 | ||||||||
\(862\) | −2.20312 | −0.0750384 | ||||||||
\(863\) | −17.0542 | −0.580532 | −0.290266 | − | 0.956946i | \(-0.593744\pi\) | ||||
−0.290266 | + | 0.956946i | \(0.593744\pi\) | |||||||
\(864\) | 0.923033 | 0.0314022 | ||||||||
\(865\) | 25.1329 | 0.854544 | ||||||||
\(866\) | 0.101635 | 0.00345370 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 11.5596 | 0.392357 | ||||||||
\(869\) | 2.24354 | 0.0761068 | ||||||||
\(870\) | 2.70417 | 0.0916798 | ||||||||
\(871\) | 44.5740 | 1.51033 | ||||||||
\(872\) | −5.53860 | −0.187561 | ||||||||
\(873\) | −15.9767 | −0.540729 | ||||||||
\(874\) | −0.362749 | −0.0122702 | ||||||||
\(875\) | 22.3054 | 0.754060 | ||||||||
\(876\) | −19.5941 | −0.662022 | ||||||||
\(877\) | 18.9616 | 0.640286 | 0.320143 | − | 0.947369i | \(-0.396269\pi\) | ||||
0.320143 | + | 0.947369i | \(0.396269\pi\) | |||||||
\(878\) | 1.10788 | 0.0373890 | ||||||||
\(879\) | −13.6630 | −0.460841 | ||||||||
\(880\) | 35.3431 | 1.19142 | ||||||||
\(881\) | 35.1250 | 1.18339 | 0.591696 | − | 0.806161i | \(-0.298459\pi\) | ||||
0.591696 | + | 0.806161i | \(0.298459\pi\) | |||||||
\(882\) | 0.468040 | 0.0157597 | ||||||||
\(883\) | −17.3198 | −0.582859 | −0.291430 | − | 0.956592i | \(-0.594131\pi\) | ||||
−0.291430 | + | 0.956592i | \(0.594131\pi\) | |||||||
\(884\) | 8.38212 | 0.281921 | ||||||||
\(885\) | 28.3050 | 0.951463 | ||||||||
\(886\) | 2.57914 | 0.0866477 | ||||||||
\(887\) | 11.3192 | 0.380061 | 0.190030 | − | 0.981778i | \(-0.439141\pi\) | ||||
0.190030 | + | 0.981778i | \(0.439141\pi\) | |||||||
\(888\) | −1.43337 | −0.0481008 | ||||||||
\(889\) | 6.05067 | 0.202933 | ||||||||
\(890\) | −3.59513 | −0.120509 | ||||||||
\(891\) | 2.24354 | 0.0751614 | ||||||||
\(892\) | 10.0117 | 0.335218 | ||||||||
\(893\) | 32.4019 | 1.08429 | ||||||||
\(894\) | −1.15041 | −0.0384756 | ||||||||
\(895\) | −2.04087 | −0.0682188 | ||||||||
\(896\) | 2.37732 | 0.0794208 | ||||||||
\(897\) | −3.83013 | −0.127884 | ||||||||
\(898\) | −1.35174 | −0.0451082 | ||||||||
\(899\) | −52.7047 | −1.75780 | ||||||||
\(900\) | −21.5184 | −0.717280 | ||||||||
\(901\) | 4.67370 | 0.155703 | ||||||||
\(902\) | 1.74297 | 0.0580344 | ||||||||
\(903\) | −9.03749 | −0.300749 | ||||||||
\(904\) | −4.81000 | −0.159978 | ||||||||
\(905\) | 21.7160 | 0.721865 | ||||||||
\(906\) | 0.860331 | 0.0285826 | ||||||||
\(907\) | 50.8849 | 1.68960 | 0.844802 | − | 0.535079i | \(-0.179718\pi\) | ||||
0.844802 | + | 0.535079i | \(0.179718\pi\) | |||||||
\(908\) | −52.8051 | −1.75240 | ||||||||
\(909\) | −3.75524 | −0.124553 | ||||||||
\(910\) | −1.25030 | −0.0414469 | ||||||||
\(911\) | 14.5824 | 0.483137 | 0.241568 | − | 0.970384i | \(-0.422338\pi\) | ||||
0.241568 | + | 0.970384i | \(0.422338\pi\) | |||||||
\(912\) | −20.4366 | −0.676725 | ||||||||
\(913\) | 27.8332 | 0.921146 | ||||||||
\(914\) | −2.93342 | −0.0970290 | ||||||||
\(915\) | 30.3810 | 1.00437 | ||||||||
\(916\) | −35.3024 | −1.16642 | ||||||||
\(917\) | 1.97279 | 0.0651474 | ||||||||
\(918\) | −0.0772262 | −0.00254884 | ||||||||
\(919\) | −5.88730 | −0.194204 | −0.0971021 | − | 0.995274i | \(-0.530957\pi\) | ||||
−0.0971021 | + | 0.995274i | \(0.530957\pi\) | |||||||
\(920\) | 1.11681 | 0.0368201 | ||||||||
\(921\) | 10.0727 | 0.331905 | ||||||||
\(922\) | 0.644572 | 0.0212279 | ||||||||
\(923\) | 2.19963 | 0.0724016 | ||||||||
\(924\) | 4.33595 | 0.142642 | ||||||||
\(925\) | 50.1487 | 1.64888 | ||||||||
\(926\) | 1.41020 | 0.0463422 | ||||||||
\(927\) | 9.38168 | 0.308135 | ||||||||
\(928\) | −8.13346 | −0.266994 | ||||||||
\(929\) | 50.7581 | 1.66532 | 0.832659 | − | 0.553786i | \(-0.186818\pi\) | ||||
0.832659 | + | 0.553786i | \(0.186818\pi\) | |||||||
\(930\) | −1.83555 | −0.0601900 | ||||||||
\(931\) | −31.2440 | −1.02398 | ||||||||
\(932\) | 21.0112 | 0.688245 | ||||||||
\(933\) | 12.2887 | 0.402315 | ||||||||
\(934\) | −2.48653 | −0.0813619 | ||||||||
\(935\) | −8.91546 | −0.291567 | ||||||||
\(936\) | 1.29657 | 0.0423799 | ||||||||
\(937\) | −52.1072 | −1.70227 | −0.851135 | − | 0.524947i | \(-0.824085\pi\) | ||||
−0.851135 | + | 0.524947i | \(0.824085\pi\) | |||||||
\(938\) | −0.793674 | −0.0259144 | ||||||||
\(939\) | −23.9963 | −0.783090 | ||||||||
\(940\) | −49.8040 | −1.62443 | ||||||||
\(941\) | −25.2428 | −0.822892 | −0.411446 | − | 0.911434i | \(-0.634976\pi\) | ||||
−0.411446 | + | 0.911434i | \(0.634976\pi\) | |||||||
\(942\) | −0.423896 | −0.0138113 | ||||||||
\(943\) | −9.16607 | −0.298488 | ||||||||
\(944\) | −28.2367 | −0.919028 | ||||||||
\(945\) | −3.85148 | −0.125289 | ||||||||
\(946\) | −1.61558 | −0.0525271 | ||||||||
\(947\) | 23.3555 | 0.758951 | 0.379475 | − | 0.925202i | \(-0.376104\pi\) | ||||
0.379475 | + | 0.925202i | \(0.376104\pi\) | |||||||
\(948\) | 1.99404 | 0.0647633 | ||||||||
\(949\) | −41.3059 | −1.34085 | ||||||||
\(950\) | −4.29626 | −0.139389 | ||||||||
\(951\) | −11.6608 | −0.378126 | ||||||||
\(952\) | −0.298947 | −0.00968892 | ||||||||
\(953\) | −46.3239 | −1.50058 | −0.750290 | − | 0.661109i | \(-0.770086\pi\) | ||||
−0.750290 | + | 0.661109i | \(0.770086\pi\) | |||||||
\(954\) | 0.360932 | 0.0116856 | ||||||||
\(955\) | 47.5684 | 1.53928 | ||||||||
\(956\) | −5.94307 | −0.192213 | ||||||||
\(957\) | −19.7693 | −0.639052 | ||||||||
\(958\) | 1.64624 | 0.0531877 | ||||||||
\(959\) | 9.38174 | 0.302952 | ||||||||
\(960\) | 31.2233 | 1.00773 | ||||||||
\(961\) | 4.77518 | 0.154038 | ||||||||
\(962\) | −1.50858 | −0.0486385 | ||||||||
\(963\) | −17.8136 | −0.574036 | ||||||||
\(964\) | −61.0399 | −1.96596 | ||||||||
\(965\) | −76.4098 | −2.45972 | ||||||||
\(966\) | 0.0681985 | 0.00219425 | ||||||||
\(967\) | 0.0804894 | 0.00258836 | 0.00129418 | − | 0.999999i | \(-0.499588\pi\) | ||||
0.00129418 | + | 0.999999i | \(0.499588\pi\) | |||||||
\(968\) | −1.84034 | −0.0591509 | ||||||||
\(969\) | 5.15523 | 0.165610 | ||||||||
\(970\) | 4.90299 | 0.157426 | ||||||||
\(971\) | 49.7075 | 1.59519 | 0.797594 | − | 0.603194i | \(-0.206106\pi\) | ||||
0.797594 | + | 0.603194i | \(0.206106\pi\) | |||||||
\(972\) | 1.99404 | 0.0639587 | ||||||||
\(973\) | −10.7802 | −0.345598 | ||||||||
\(974\) | −1.25591 | −0.0402418 | ||||||||
\(975\) | −45.3626 | −1.45277 | ||||||||
\(976\) | −30.3077 | −0.970127 | ||||||||
\(977\) | 24.2420 | 0.775570 | 0.387785 | − | 0.921750i | \(-0.373240\pi\) | ||||
0.387785 | + | 0.921750i | \(0.373240\pi\) | |||||||
\(978\) | −0.599686 | −0.0191758 | ||||||||
\(979\) | 26.2829 | 0.840004 | ||||||||
\(980\) | 48.0243 | 1.53408 | ||||||||
\(981\) | −17.9566 | −0.573309 | ||||||||
\(982\) | 2.36511 | 0.0754738 | ||||||||
\(983\) | 37.3517 | 1.19133 | 0.595667 | − | 0.803232i | \(-0.296888\pi\) | ||||
0.595667 | + | 0.803232i | \(0.296888\pi\) | |||||||
\(984\) | 3.10290 | 0.0989167 | ||||||||
\(985\) | −10.8266 | −0.344964 | ||||||||
\(986\) | 0.680492 | 0.0216713 | ||||||||
\(987\) | −6.09171 | −0.193901 | ||||||||
\(988\) | −43.2118 | −1.37475 | ||||||||
\(989\) | 8.49617 | 0.270162 | ||||||||
\(990\) | −0.688507 | −0.0218822 | ||||||||
\(991\) | 40.4445 | 1.28476 | 0.642380 | − | 0.766386i | \(-0.277947\pi\) | ||||
0.642380 | + | 0.766386i | \(0.277947\pi\) | |||||||
\(992\) | 5.52088 | 0.175288 | ||||||||
\(993\) | −8.21275 | −0.260624 | ||||||||
\(994\) | −0.0391661 | −0.00124227 | ||||||||
\(995\) | 28.8482 | 0.914551 | ||||||||
\(996\) | 24.7379 | 0.783851 | ||||||||
\(997\) | 22.2361 | 0.704225 | 0.352113 | − | 0.935958i | \(-0.385463\pi\) | ||||
0.352113 | + | 0.935958i | \(0.385463\pi\) | |||||||
\(998\) | −1.76510 | −0.0558733 | ||||||||
\(999\) | −4.64710 | −0.147028 |
(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 | 4029.2.a.l.1.16 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.16 | ✓ | 32 | 1.1 | even | 1 | trivial |