Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.45267 | −1.02720 | −0.513598 | − | 0.858031i | \(-0.671688\pi\) | ||||
−0.513598 | + | 0.858031i | \(0.671688\pi\) | |||||||
\(3\) | 2.41257 | 1.39290 | 0.696449 | − | 0.717607i | \(-0.254762\pi\) | ||||
0.696449 | + | 0.717607i | \(0.254762\pi\) | |||||||
\(4\) | 0.110263 | 0.0551313 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.50468 | −1.43078 | ||||||||
\(7\) | −1.25057 | −0.472671 | −0.236336 | − | 0.971671i | \(-0.575946\pi\) | ||||
−0.236336 | + | 0.971671i | \(0.575946\pi\) | |||||||
\(8\) | 2.74517 | 0.970565 | ||||||||
\(9\) | 2.82049 | 0.940164 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.46616 | 0.743576 | 0.371788 | − | 0.928318i | \(-0.378745\pi\) | ||||
0.371788 | + | 0.928318i | \(0.378745\pi\) | |||||||
\(12\) | 0.266016 | 0.0767922 | ||||||||
\(13\) | 2.06969 | 0.574029 | 0.287015 | − | 0.957926i | \(-0.407337\pi\) | ||||
0.287015 | + | 0.957926i | \(0.407337\pi\) | |||||||
\(14\) | 1.81667 | 0.485526 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.20837 | −1.05209 | ||||||||
\(17\) | −1.42467 | −0.345532 | −0.172766 | − | 0.984963i | \(-0.555271\pi\) | ||||
−0.172766 | + | 0.984963i | \(0.555271\pi\) | |||||||
\(18\) | −4.09725 | −0.965732 | ||||||||
\(19\) | −0.479813 | −0.110077 | −0.0550384 | − | 0.998484i | \(-0.517528\pi\) | ||||
−0.0550384 | + | 0.998484i | \(0.517528\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.01709 | −0.658383 | ||||||||
\(22\) | −3.58253 | −0.763798 | ||||||||
\(23\) | −2.87475 | −0.599426 | −0.299713 | − | 0.954029i | \(-0.596891\pi\) | ||||
−0.299713 | + | 0.954029i | \(0.596891\pi\) | |||||||
\(24\) | 6.62292 | 1.35190 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00659 | −0.589640 | ||||||||
\(27\) | −0.433079 | −0.0833461 | ||||||||
\(28\) | −0.137891 | −0.0260590 | ||||||||
\(29\) | −9.26441 | −1.72036 | −0.860179 | − | 0.509992i | \(-0.829648\pi\) | ||||
−0.860179 | + | 0.509992i | \(0.829648\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.180654 | 0.0324465 | 0.0162232 | − | 0.999868i | \(-0.494836\pi\) | ||||
0.0162232 | + | 0.999868i | \(0.494836\pi\) | |||||||
\(32\) | 0.623041 | 0.110139 | ||||||||
\(33\) | 5.94979 | 1.03573 | ||||||||
\(34\) | 2.06958 | 0.354929 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.310994 | 0.0518324 | ||||||||
\(37\) | 0.824807 | 0.135597 | 0.0677987 | − | 0.997699i | \(-0.478402\pi\) | ||||
0.0677987 | + | 0.997699i | \(0.478402\pi\) | |||||||
\(38\) | 0.697012 | 0.113070 | ||||||||
\(39\) | 4.99327 | 0.799564 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.12498 | 0.175693 | 0.0878464 | − | 0.996134i | \(-0.472002\pi\) | ||||
0.0878464 | + | 0.996134i | \(0.472002\pi\) | |||||||
\(42\) | 4.38285 | 0.676288 | ||||||||
\(43\) | −3.43795 | −0.524282 | −0.262141 | − | 0.965030i | \(-0.584429\pi\) | ||||
−0.262141 | + | 0.965030i | \(0.584429\pi\) | |||||||
\(44\) | 0.271925 | 0.0409943 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.17607 | 0.615728 | ||||||||
\(47\) | −3.00871 | −0.438866 | −0.219433 | − | 0.975628i | \(-0.570421\pi\) | ||||
−0.219433 | + | 0.975628i | \(0.570421\pi\) | |||||||
\(48\) | −10.1530 | −1.46546 | ||||||||
\(49\) | −5.43607 | −0.776582 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.43711 | −0.481291 | ||||||||
\(52\) | 0.228209 | 0.0316470 | ||||||||
\(53\) | −12.3733 | −1.69961 | −0.849804 | − | 0.527099i | \(-0.823280\pi\) | ||||
−0.849804 | + | 0.527099i | \(0.823280\pi\) | |||||||
\(54\) | 0.629123 | 0.0856128 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.43303 | −0.458758 | ||||||||
\(57\) | −1.15758 | −0.153326 | ||||||||
\(58\) | 13.4582 | 1.76714 | ||||||||
\(59\) | 0.433111 | 0.0563863 | 0.0281931 | − | 0.999602i | \(-0.491025\pi\) | ||||
0.0281931 | + | 0.999602i | \(0.491025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.88745 | −0.497737 | −0.248868 | − | 0.968537i | \(-0.580059\pi\) | ||||
−0.248868 | + | 0.968537i | \(0.580059\pi\) | |||||||
\(62\) | −0.262432 | −0.0333289 | ||||||||
\(63\) | −3.52722 | −0.444388 | ||||||||
\(64\) | 7.51166 | 0.938957 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.64311 | −1.06389 | ||||||||
\(67\) | 5.24447 | 0.640714 | 0.320357 | − | 0.947297i | \(-0.396197\pi\) | ||||
0.320357 | + | 0.947297i | \(0.396197\pi\) | |||||||
\(68\) | −0.157087 | −0.0190496 | ||||||||
\(69\) | −6.93552 | −0.834939 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.3247 | 1.70003 | 0.850013 | − | 0.526762i | \(-0.176594\pi\) | ||||
0.850013 | + | 0.526762i | \(0.176594\pi\) | |||||||
\(72\) | 7.74273 | 0.912490 | ||||||||
\(73\) | −4.35588 | −0.509818 | −0.254909 | − | 0.966965i | \(-0.582045\pi\) | ||||
−0.254909 | + | 0.966965i | \(0.582045\pi\) | |||||||
\(74\) | −1.19818 | −0.139285 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0529054 | −0.00606867 | ||||||||
\(77\) | −3.08411 | −0.351467 | ||||||||
\(78\) | −7.25360 | −0.821309 | ||||||||
\(79\) | −7.28837 | −0.820005 | −0.410003 | − | 0.912084i | \(-0.634472\pi\) | ||||
−0.410003 | + | 0.912084i | \(0.634472\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.50630 | −1.05626 | ||||||||
\(82\) | −1.63423 | −0.180471 | ||||||||
\(83\) | −1.09208 | −0.119871 | −0.0599357 | − | 0.998202i | \(-0.519090\pi\) | ||||
−0.0599357 | + | 0.998202i | \(0.519090\pi\) | |||||||
\(84\) | −0.332672 | −0.0362975 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.99422 | 0.538541 | ||||||||
\(87\) | −22.3510 | −2.39628 | ||||||||
\(88\) | 6.77004 | 0.721689 | ||||||||
\(89\) | −12.2161 | −1.29490 | −0.647452 | − | 0.762106i | \(-0.724166\pi\) | ||||
−0.647452 | + | 0.762106i | \(0.724166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.58830 | −0.271327 | ||||||||
\(92\) | −0.316977 | −0.0330471 | ||||||||
\(93\) | 0.435841 | 0.0451946 | ||||||||
\(94\) | 4.37068 | 0.450801 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50313 | 0.153412 | ||||||||
\(97\) | −9.80240 | −0.995283 | −0.497642 | − | 0.867383i | \(-0.665801\pi\) | ||||
−0.497642 | + | 0.867383i | \(0.665801\pi\) | |||||||
\(98\) | 7.89684 | 0.797702 | ||||||||
\(99\) | 6.95579 | 0.699083 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.5462 | −1.04939 | −0.524695 | − | 0.851291i | \(-0.675820\pi\) | ||||
−0.524695 | + | 0.851291i | \(0.675820\pi\) | |||||||
\(102\) | 4.99300 | 0.494380 | ||||||||
\(103\) | 7.56058 | 0.744966 | 0.372483 | − | 0.928039i | \(-0.378506\pi\) | ||||
0.372483 | + | 0.928039i | \(0.378506\pi\) | |||||||
\(104\) | 5.68166 | 0.557133 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.9744 | 1.74583 | ||||||||
\(107\) | 4.30799 | 0.416469 | 0.208234 | − | 0.978079i | \(-0.433228\pi\) | ||||
0.208234 | + | 0.978079i | \(0.433228\pi\) | |||||||
\(108\) | −0.0477524 | −0.00459498 | ||||||||
\(109\) | −3.03421 | −0.290625 | −0.145313 | − | 0.989386i | \(-0.546419\pi\) | ||||
−0.145313 | + | 0.989386i | \(0.546419\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.98990 | 0.188873 | ||||||||
\(112\) | 5.26286 | 0.497294 | ||||||||
\(113\) | 5.48438 | 0.515927 | 0.257964 | − | 0.966155i | \(-0.416949\pi\) | ||||
0.257964 | + | 0.966155i | \(0.416949\pi\) | |||||||
\(114\) | 1.68159 | 0.157495 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.02152 | −0.0948455 | ||||||||
\(117\) | 5.83755 | 0.539681 | ||||||||
\(118\) | −0.629169 | −0.0579197 | ||||||||
\(119\) | 1.78165 | 0.163323 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.91804 | −0.447095 | ||||||||
\(122\) | 5.64720 | 0.511273 | ||||||||
\(123\) | 2.71410 | 0.244722 | ||||||||
\(124\) | 0.0199194 | 0.00178882 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.12390 | 0.456474 | ||||||||
\(127\) | 1.82445 | 0.161894 | 0.0809471 | − | 0.996718i | \(-0.474206\pi\) | ||||
0.0809471 | + | 0.996718i | \(0.474206\pi\) | |||||||
\(128\) | −12.1581 | −1.07463 | ||||||||
\(129\) | −8.29429 | −0.730271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7564 | 0.939789 | 0.469895 | − | 0.882722i | \(-0.344292\pi\) | ||||
0.469895 | + | 0.882722i | \(0.344292\pi\) | |||||||
\(132\) | 0.656039 | 0.0571009 | ||||||||
\(133\) | 0.600040 | 0.0520301 | ||||||||
\(134\) | −7.61851 | −0.658139 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.91096 | −0.335362 | ||||||||
\(137\) | 18.0907 | 1.54560 | 0.772798 | − | 0.634653i | \(-0.218857\pi\) | ||||
0.772798 | + | 0.634653i | \(0.218857\pi\) | |||||||
\(138\) | 10.0751 | 0.857646 | ||||||||
\(139\) | 9.24847 | 0.784445 | 0.392222 | − | 0.919870i | \(-0.371706\pi\) | ||||
0.392222 | + | 0.919870i | \(0.371706\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.25873 | −0.611296 | ||||||||
\(142\) | −20.8091 | −1.74626 | ||||||||
\(143\) | 5.10420 | 0.426834 | ||||||||
\(144\) | −11.8697 | −0.989138 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.32768 | 0.523683 | ||||||||
\(147\) | −13.1149 | −1.08170 | ||||||||
\(148\) | 0.0909453 | 0.00747566 | ||||||||
\(149\) | 17.0170 | 1.39408 | 0.697042 | − | 0.717030i | \(-0.254499\pi\) | ||||
0.697042 | + | 0.717030i | \(0.254499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.18436 | −0.747413 | −0.373706 | − | 0.927547i | \(-0.621913\pi\) | ||||
−0.373706 | + | 0.927547i | \(0.621913\pi\) | |||||||
\(152\) | −1.31717 | −0.106837 | ||||||||
\(153\) | −4.01826 | −0.324857 | ||||||||
\(154\) | 4.48021 | 0.361025 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.550571 | 0.0440810 | ||||||||
\(157\) | 0.176439 | 0.0140814 | 0.00704069 | − | 0.999975i | \(-0.497759\pi\) | ||||
0.00704069 | + | 0.999975i | \(0.497759\pi\) | |||||||
\(158\) | 10.5876 | 0.842306 | ||||||||
\(159\) | −29.8515 | −2.36738 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.59507 | 0.283331 | ||||||||
\(162\) | 13.8096 | 1.08498 | ||||||||
\(163\) | 9.16744 | 0.718050 | 0.359025 | − | 0.933328i | \(-0.383109\pi\) | ||||
0.359025 | + | 0.933328i | \(0.383109\pi\) | |||||||
\(164\) | 0.124043 | 0.00968616 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.58644 | 0.123131 | ||||||||
\(167\) | 22.5003 | 1.74112 | 0.870562 | − | 0.492058i | \(-0.163755\pi\) | ||||
0.870562 | + | 0.492058i | \(0.163755\pi\) | |||||||
\(168\) | −8.28243 | −0.639003 | ||||||||
\(169\) | −8.71638 | −0.670491 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.35331 | −0.103490 | ||||||||
\(172\) | −0.379077 | −0.0289043 | ||||||||
\(173\) | −5.08571 | −0.386659 | −0.193330 | − | 0.981134i | \(-0.561929\pi\) | ||||
−0.193330 | + | 0.981134i | \(0.561929\pi\) | |||||||
\(174\) | 32.4688 | 2.46145 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.3785 | −0.782310 | ||||||||
\(177\) | 1.04491 | 0.0785403 | ||||||||
\(178\) | 17.7460 | 1.33012 | ||||||||
\(179\) | −15.3122 | −1.14449 | −0.572244 | − | 0.820084i | \(-0.693927\pi\) | ||||
−0.572244 | + | 0.820084i | \(0.693927\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4259 | −1.36958 | −0.684792 | − | 0.728738i | \(-0.740107\pi\) | ||||
−0.684792 | + | 0.728738i | \(0.740107\pi\) | |||||||
\(182\) | 3.75995 | 0.278706 | ||||||||
\(183\) | −9.37874 | −0.693297 | ||||||||
\(184\) | −7.89167 | −0.581782 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.633135 | −0.0464237 | ||||||||
\(187\) | −3.51346 | −0.256930 | ||||||||
\(188\) | −0.331749 | −0.0241952 | ||||||||
\(189\) | 0.541596 | 0.0393953 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7148 | −0.992368 | −0.496184 | − | 0.868217i | \(-0.665266\pi\) | ||||
−0.496184 | + | 0.868217i | \(0.665266\pi\) | |||||||
\(192\) | 18.1224 | 1.30787 | ||||||||
\(193\) | 12.4066 | 0.893047 | 0.446524 | − | 0.894772i | \(-0.352662\pi\) | ||||
0.446524 | + | 0.894772i | \(0.352662\pi\) | |||||||
\(194\) | 14.2397 | 1.02235 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.599395 | −0.0428139 | ||||||||
\(197\) | −7.72970 | −0.550718 | −0.275359 | − | 0.961341i | \(-0.588797\pi\) | ||||
−0.275359 | + | 0.961341i | \(0.588797\pi\) | |||||||
\(198\) | −10.1045 | −0.718095 | ||||||||
\(199\) | −5.15173 | −0.365196 | −0.182598 | − | 0.983188i | \(-0.558451\pi\) | ||||
−0.182598 | + | 0.983188i | \(0.558451\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.6526 | 0.892449 | ||||||||
\(202\) | 15.3202 | 1.07793 | ||||||||
\(203\) | 11.5858 | 0.813164 | ||||||||
\(204\) | −0.378984 | −0.0265342 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.9831 | −0.765226 | ||||||||
\(207\) | −8.10819 | −0.563558 | ||||||||
\(208\) | −8.71002 | −0.603931 | ||||||||
\(209\) | −1.18330 | −0.0818504 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.6216 | −1.41965 | −0.709823 | − | 0.704380i | \(-0.751225\pi\) | ||||
−0.709823 | + | 0.704380i | \(0.751225\pi\) | |||||||
\(212\) | −1.36431 | −0.0937015 | ||||||||
\(213\) | 34.5593 | 2.36796 | ||||||||
\(214\) | −6.25810 | −0.427795 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.18888 | −0.0808928 | ||||||||
\(217\) | −0.225921 | −0.0153365 | ||||||||
\(218\) | 4.40772 | 0.298529 | ||||||||
\(219\) | −10.5089 | −0.710124 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.94862 | −0.198346 | ||||||||
\(222\) | −2.89068 | −0.194010 | ||||||||
\(223\) | 0.789803 | 0.0528891 | 0.0264446 | − | 0.999650i | \(-0.491581\pi\) | ||||
0.0264446 | + | 0.999650i | \(0.491581\pi\) | |||||||
\(224\) | −0.779156 | −0.0520596 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.96702 | −0.529958 | ||||||||
\(227\) | 1.06248 | 0.0705190 | 0.0352595 | − | 0.999378i | \(-0.488774\pi\) | ||||
0.0352595 | + | 0.999378i | \(0.488774\pi\) | |||||||
\(228\) | −0.127638 | −0.00845303 | ||||||||
\(229\) | 18.7377 | 1.23822 | 0.619110 | − | 0.785304i | \(-0.287493\pi\) | ||||
0.619110 | + | 0.785304i | \(0.287493\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.44063 | −0.489558 | ||||||||
\(232\) | −25.4324 | −1.66972 | ||||||||
\(233\) | 20.6141 | 1.35047 | 0.675237 | − | 0.737601i | \(-0.264041\pi\) | ||||
0.675237 | + | 0.737601i | \(0.264041\pi\) | |||||||
\(234\) | −8.48005 | −0.554358 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.0477559 | 0.00310865 | ||||||||
\(237\) | −17.5837 | −1.14218 | ||||||||
\(238\) | −2.58815 | −0.167765 | ||||||||
\(239\) | −17.2630 | −1.11665 | −0.558324 | − | 0.829623i | \(-0.688555\pi\) | ||||
−0.558324 | + | 0.829623i | \(0.688555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 7.14431 | 0.459254 | ||||||||
\(243\) | −21.6354 | −1.38791 | ||||||||
\(244\) | −0.428640 | −0.0274409 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.94270 | −0.251377 | ||||||||
\(247\) | −0.993065 | −0.0631872 | ||||||||
\(248\) | 0.495927 | 0.0314914 | ||||||||
\(249\) | −2.63472 | −0.166969 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.5943 | −1.36302 | −0.681510 | − | 0.731809i | \(-0.738677\pi\) | ||||
−0.681510 | + | 0.731809i | \(0.738677\pi\) | |||||||
\(252\) | −0.388920 | −0.0244997 | ||||||||
\(253\) | −7.08959 | −0.445719 | ||||||||
\(254\) | −2.65034 | −0.166297 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.63841 | 0.164900 | ||||||||
\(257\) | −22.2276 | −1.38652 | −0.693261 | − | 0.720687i | \(-0.743827\pi\) | ||||
−0.693261 | + | 0.720687i | \(0.743827\pi\) | |||||||
\(258\) | 12.0489 | 0.750132 | ||||||||
\(259\) | −1.03148 | −0.0640930 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −26.1302 | −1.61742 | ||||||||
\(262\) | −15.6255 | −0.965348 | ||||||||
\(263\) | −3.89765 | −0.240339 | −0.120170 | − | 0.992753i | \(-0.538344\pi\) | ||||
−0.120170 | + | 0.992753i | \(0.538344\pi\) | |||||||
\(264\) | 16.3332 | 1.00524 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.871663 | −0.0534451 | ||||||||
\(267\) | −29.4722 | −1.80367 | ||||||||
\(268\) | 0.578268 | 0.0353234 | ||||||||
\(269\) | 6.60591 | 0.402769 | 0.201385 | − | 0.979512i | \(-0.435456\pi\) | ||||
0.201385 | + | 0.979512i | \(0.435456\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.8832 | −1.02558 | −0.512791 | − | 0.858513i | \(-0.671388\pi\) | ||||
−0.512791 | + | 0.858513i | \(0.671388\pi\) | |||||||
\(272\) | 5.99552 | 0.363532 | ||||||||
\(273\) | −6.24444 | −0.377931 | ||||||||
\(274\) | −26.2799 | −1.58763 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.764728 | −0.0460312 | ||||||||
\(277\) | −27.0001 | −1.62228 | −0.811140 | − | 0.584852i | \(-0.801153\pi\) | ||||
−0.811140 | + | 0.584852i | \(0.801153\pi\) | |||||||
\(278\) | −13.4350 | −0.805778 | ||||||||
\(279\) | 0.509534 | 0.0305050 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.48720 | −0.565959 | −0.282979 | − | 0.959126i | \(-0.591323\pi\) | ||||
−0.282979 | + | 0.959126i | \(0.591323\pi\) | |||||||
\(282\) | 10.5446 | 0.627920 | ||||||||
\(283\) | 13.7557 | 0.817690 | 0.408845 | − | 0.912604i | \(-0.365932\pi\) | ||||
0.408845 | + | 0.912604i | \(0.365932\pi\) | |||||||
\(284\) | 1.57947 | 0.0937246 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.41474 | −0.438442 | ||||||||
\(287\) | −1.40687 | −0.0830449 | ||||||||
\(288\) | 1.75728 | 0.103549 | ||||||||
\(289\) | −14.9703 | −0.880607 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.6490 | −1.38633 | ||||||||
\(292\) | −0.480291 | −0.0281069 | ||||||||
\(293\) | −11.4782 | −0.670561 | −0.335280 | − | 0.942118i | \(-0.608831\pi\) | ||||
−0.335280 | + | 0.942118i | \(0.608831\pi\) | |||||||
\(294\) | 19.0517 | 1.11112 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.26424 | 0.131606 | ||||||||
\(297\) | −1.06804 | −0.0619742 | ||||||||
\(298\) | −24.7201 | −1.43200 | ||||||||
\(299\) | −5.94984 | −0.344088 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.29940 | 0.247813 | ||||||||
\(302\) | 13.3419 | 0.767739 | ||||||||
\(303\) | −25.4435 | −1.46169 | ||||||||
\(304\) | 2.01923 | 0.115811 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.83722 | 0.333692 | ||||||||
\(307\) | 11.8355 | 0.675485 | 0.337743 | − | 0.941238i | \(-0.390337\pi\) | ||||
0.337743 | + | 0.941238i | \(0.390337\pi\) | |||||||
\(308\) | −0.340062 | −0.0193768 | ||||||||
\(309\) | 18.2404 | 1.03766 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.53844 | −0.314056 | −0.157028 | − | 0.987594i | \(-0.550191\pi\) | ||||
−0.157028 | + | 0.987594i | \(0.550191\pi\) | |||||||
\(312\) | 13.7074 | 0.776029 | ||||||||
\(313\) | 24.8522 | 1.40473 | 0.702365 | − | 0.711817i | \(-0.252127\pi\) | ||||
0.702365 | + | 0.711817i | \(0.252127\pi\) | |||||||
\(314\) | −0.256309 | −0.0144643 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.803634 | −0.0452079 | ||||||||
\(317\) | −15.8127 | −0.888130 | −0.444065 | − | 0.895994i | \(-0.646464\pi\) | ||||
−0.444065 | + | 0.895994i | \(0.646464\pi\) | |||||||
\(318\) | 43.3645 | 2.43176 | ||||||||
\(319\) | −22.8475 | −1.27922 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.3933 | 0.580098 | ||||||||
\(322\) | −5.22247 | −0.291037 | ||||||||
\(323\) | 0.683574 | 0.0380351 | ||||||||
\(324\) | −1.04819 | −0.0582327 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.3173 | −0.737578 | ||||||||
\(327\) | −7.32025 | −0.404811 | ||||||||
\(328\) | 3.08827 | 0.170521 | ||||||||
\(329\) | 3.76261 | 0.207439 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.4865 | 1.29093 | 0.645467 | − | 0.763789i | \(-0.276663\pi\) | ||||
0.645467 | + | 0.763789i | \(0.276663\pi\) | |||||||
\(332\) | −0.120416 | −0.00660866 | ||||||||
\(333\) | 2.32636 | 0.127484 | ||||||||
\(334\) | −32.6856 | −1.78848 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.6970 | 0.692679 | ||||||||
\(337\) | 11.1318 | 0.606385 | 0.303193 | − | 0.952929i | \(-0.401947\pi\) | ||||
0.303193 | + | 0.952929i | \(0.401947\pi\) | |||||||
\(338\) | 12.6621 | 0.688725 | ||||||||
\(339\) | 13.2315 | 0.718634 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.445523 | 0.0241264 | ||||||||
\(342\) | 1.96592 | 0.106305 | ||||||||
\(343\) | 15.5522 | 0.839739 | ||||||||
\(344\) | −9.43776 | −0.508850 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.38788 | 0.397175 | ||||||||
\(347\) | 4.44891 | 0.238830 | 0.119415 | − | 0.992844i | \(-0.461898\pi\) | ||||
0.119415 | + | 0.992844i | \(0.461898\pi\) | |||||||
\(348\) | −2.46448 | −0.132110 | ||||||||
\(349\) | 0.902138 | 0.0482903 | 0.0241452 | − | 0.999708i | \(-0.492314\pi\) | ||||
0.0241452 | + | 0.999708i | \(0.492314\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.896340 | −0.0478431 | ||||||||
\(352\) | 1.53652 | 0.0818968 | ||||||||
\(353\) | −0.455388 | −0.0242379 | −0.0121189 | − | 0.999927i | \(-0.503858\pi\) | ||||
−0.0121189 | + | 0.999927i | \(0.503858\pi\) | |||||||
\(354\) | −1.51791 | −0.0806763 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.34698 | −0.0713897 | ||||||||
\(357\) | 4.29834 | 0.227493 | ||||||||
\(358\) | 22.2436 | 1.17561 | ||||||||
\(359\) | −8.65154 | −0.456611 | −0.228305 | − | 0.973590i | \(-0.573318\pi\) | ||||
−0.228305 | + | 0.973590i | \(0.573318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7698 | −0.987883 | ||||||||
\(362\) | 26.7668 | 1.40683 | ||||||||
\(363\) | −11.8651 | −0.622757 | ||||||||
\(364\) | −0.285392 | −0.0149586 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.6243 | 0.712151 | ||||||||
\(367\) | 23.7645 | 1.24050 | 0.620249 | − | 0.784405i | \(-0.287031\pi\) | ||||
0.620249 | + | 0.784405i | \(0.287031\pi\) | |||||||
\(368\) | 12.0980 | 0.630651 | ||||||||
\(369\) | 3.17300 | 0.165180 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.4737 | 0.803355 | ||||||||
\(372\) | 0.0480570 | 0.00249164 | ||||||||
\(373\) | −7.72073 | −0.399764 | −0.199882 | − | 0.979820i | \(-0.564056\pi\) | ||||
−0.199882 | + | 0.979820i | \(0.564056\pi\) | |||||||
\(374\) | 5.10391 | 0.263917 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.25944 | −0.425948 | ||||||||
\(377\) | −19.1745 | −0.987536 | ||||||||
\(378\) | −0.786762 | −0.0404667 | ||||||||
\(379\) | 27.7660 | 1.42624 | 0.713122 | − | 0.701040i | \(-0.247281\pi\) | ||||
0.713122 | + | 0.701040i | \(0.247281\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.40162 | 0.225502 | ||||||||
\(382\) | 19.9231 | 1.01936 | ||||||||
\(383\) | −2.17131 | −0.110949 | −0.0554744 | − | 0.998460i | \(-0.517667\pi\) | ||||
−0.0554744 | + | 0.998460i | \(0.517667\pi\) | |||||||
\(384\) | −29.3322 | −1.49685 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.0228 | −0.917334 | ||||||||
\(387\) | −9.69670 | −0.492911 | ||||||||
\(388\) | −1.08084 | −0.0548712 | ||||||||
\(389\) | −16.3022 | −0.826556 | −0.413278 | − | 0.910605i | \(-0.635616\pi\) | ||||
−0.413278 | + | 0.910605i | \(0.635616\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.09555 | 0.207121 | ||||||||
\(392\) | −14.9230 | −0.753723 | ||||||||
\(393\) | 25.9505 | 1.30903 | ||||||||
\(394\) | 11.2287 | 0.565696 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.766963 | 0.0385413 | ||||||||
\(397\) | 4.91814 | 0.246835 | 0.123417 | − | 0.992355i | \(-0.460615\pi\) | ||||
0.123417 | + | 0.992355i | \(0.460615\pi\) | |||||||
\(398\) | 7.48378 | 0.375128 | ||||||||
\(399\) | 1.44764 | 0.0724726 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.97380 | 0.148504 | 0.0742522 | − | 0.997239i | \(-0.476343\pi\) | ||||
0.0742522 | + | 0.997239i | \(0.476343\pi\) | |||||||
\(402\) | −18.3802 | −0.916720 | ||||||||
\(403\) | 0.373899 | 0.0186252 | ||||||||
\(404\) | −1.16285 | −0.0578542 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.8304 | −0.835278 | ||||||||
\(407\) | 2.03411 | 0.100827 | ||||||||
\(408\) | −9.43545 | −0.467125 | ||||||||
\(409\) | −24.3914 | −1.20608 | −0.603039 | − | 0.797712i | \(-0.706044\pi\) | ||||
−0.603039 | + | 0.797712i | \(0.706044\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 43.6451 | 2.15286 | ||||||||
\(412\) | 0.833649 | 0.0410709 | ||||||||
\(413\) | −0.541636 | −0.0266522 | ||||||||
\(414\) | 11.7786 | 0.578885 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.28950 | 0.0632231 | ||||||||
\(417\) | 22.3126 | 1.09265 | ||||||||
\(418\) | 1.71895 | 0.0840764 | ||||||||
\(419\) | −29.8864 | −1.46005 | −0.730023 | − | 0.683422i | \(-0.760491\pi\) | ||||
−0.730023 | + | 0.683422i | \(0.760491\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.05042 | −0.246142 | −0.123071 | − | 0.992398i | \(-0.539274\pi\) | ||||
−0.123071 | + | 0.992398i | \(0.539274\pi\) | |||||||
\(422\) | 29.9564 | 1.45825 | ||||||||
\(423\) | −8.48605 | −0.412606 | ||||||||
\(424\) | −33.9669 | −1.64958 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −50.2034 | −2.43236 | ||||||||
\(427\) | 4.86153 | 0.235266 | ||||||||
\(428\) | 0.475010 | 0.0229605 | ||||||||
\(429\) | 12.3142 | 0.594537 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.0234 | 0.482808 | 0.241404 | − | 0.970425i | \(-0.422392\pi\) | ||||
0.241404 | + | 0.970425i | \(0.422392\pi\) | |||||||
\(432\) | 1.82256 | 0.0876878 | ||||||||
\(433\) | −26.9755 | −1.29636 | −0.648179 | − | 0.761488i | \(-0.724469\pi\) | ||||
−0.648179 | + | 0.761488i | \(0.724469\pi\) | |||||||
\(434\) | 0.328190 | 0.0157536 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.334560 | −0.0160225 | ||||||||
\(437\) | 1.37934 | 0.0659828 | ||||||||
\(438\) | 15.2660 | 0.729436 | ||||||||
\(439\) | 24.6330 | 1.17567 | 0.587835 | − | 0.808981i | \(-0.299980\pi\) | ||||
0.587835 | + | 0.808981i | \(0.299980\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.3324 | −0.730114 | ||||||||
\(442\) | 4.28339 | 0.203740 | ||||||||
\(443\) | −10.5621 | −0.501819 | −0.250910 | − | 0.968010i | \(-0.580730\pi\) | ||||
−0.250910 | + | 0.968010i | \(0.580730\pi\) | |||||||
\(444\) | 0.219412 | 0.0104128 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.14733 | −0.0543275 | ||||||||
\(447\) | 41.0546 | 1.94182 | ||||||||
\(448\) | −9.39386 | −0.443818 | ||||||||
\(449\) | −5.95137 | −0.280863 | −0.140431 | − | 0.990090i | \(-0.544849\pi\) | ||||
−0.140431 | + | 0.990090i | \(0.544849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.77439 | 0.130641 | ||||||||
\(452\) | 0.604722 | 0.0284437 | ||||||||
\(453\) | −22.1579 | −1.04107 | ||||||||
\(454\) | −1.54343 | −0.0724369 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.17776 | −0.148812 | ||||||||
\(457\) | 8.98781 | 0.420432 | 0.210216 | − | 0.977655i | \(-0.432583\pi\) | ||||
0.210216 | + | 0.977655i | \(0.432583\pi\) | |||||||
\(458\) | −27.2197 | −1.27190 | ||||||||
\(459\) | 0.616993 | 0.0287988 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.2131 | 0.801693 | 0.400846 | − | 0.916145i | \(-0.368716\pi\) | ||||
0.400846 | + | 0.916145i | \(0.368716\pi\) | |||||||
\(462\) | 10.8088 | 0.502871 | ||||||||
\(463\) | −17.5090 | −0.813711 | −0.406856 | − | 0.913492i | \(-0.633375\pi\) | ||||
−0.406856 | + | 0.913492i | \(0.633375\pi\) | |||||||
\(464\) | 38.9880 | 1.80997 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.9456 | −1.38720 | ||||||||
\(467\) | −4.34976 | −0.201283 | −0.100641 | − | 0.994923i | \(-0.532089\pi\) | ||||
−0.100641 | + | 0.994923i | \(0.532089\pi\) | |||||||
\(468\) | 0.643663 | 0.0297533 | ||||||||
\(469\) | −6.55858 | −0.302847 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.425672 | 0.0196139 | ||||||||
\(472\) | 1.18897 | 0.0547266 | ||||||||
\(473\) | −8.47854 | −0.389844 | ||||||||
\(474\) | 25.5434 | 1.17325 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.196449 | 0.00900422 | ||||||||
\(477\) | −34.8989 | −1.59791 | ||||||||
\(478\) | 25.0775 | 1.14702 | ||||||||
\(479\) | −28.5754 | −1.30565 | −0.652823 | − | 0.757511i | \(-0.726415\pi\) | ||||
−0.652823 | + | 0.757511i | \(0.726415\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.70710 | 0.0778369 | ||||||||
\(482\) | −1.45267 | −0.0661675 | ||||||||
\(483\) | 8.67336 | 0.394652 | ||||||||
\(484\) | −0.542276 | −0.0246489 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 31.4292 | 1.42566 | ||||||||
\(487\) | 15.6356 | 0.708516 | 0.354258 | − | 0.935148i | \(-0.384734\pi\) | ||||
0.354258 | + | 0.935148i | \(0.384734\pi\) | |||||||
\(488\) | −10.6717 | −0.483086 | ||||||||
\(489\) | 22.1171 | 1.00017 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.4298 | −0.696338 | −0.348169 | − | 0.937432i | \(-0.613196\pi\) | ||||
−0.348169 | + | 0.937432i | \(0.613196\pi\) | |||||||
\(492\) | 0.299263 | 0.0134918 | ||||||||
\(493\) | 13.1987 | 0.594439 | ||||||||
\(494\) | 1.44260 | 0.0649057 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.760260 | −0.0341367 | ||||||||
\(497\) | −17.9140 | −0.803553 | ||||||||
\(498\) | 3.82739 | 0.171509 | ||||||||
\(499\) | 1.64702 | 0.0737308 | 0.0368654 | − | 0.999320i | \(-0.488263\pi\) | ||||
0.0368654 | + | 0.999320i | \(0.488263\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 54.2835 | 2.42521 | ||||||||
\(502\) | 31.3695 | 1.40009 | ||||||||
\(503\) | −39.2147 | −1.74850 | −0.874249 | − | 0.485477i | \(-0.838646\pi\) | ||||
−0.874249 | + | 0.485477i | \(0.838646\pi\) | |||||||
\(504\) | −9.68283 | −0.431308 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.2989 | 0.457840 | ||||||||
\(507\) | −21.0289 | −0.933925 | ||||||||
\(508\) | 0.201169 | 0.00892543 | ||||||||
\(509\) | −1.68682 | −0.0747669 | −0.0373835 | − | 0.999301i | \(-0.511902\pi\) | ||||
−0.0373835 | + | 0.999301i | \(0.511902\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.44734 | 0.240976 | ||||||||
\(512\) | 20.4834 | 0.905247 | ||||||||
\(513\) | 0.207797 | 0.00917447 | ||||||||
\(514\) | 32.2895 | 1.42423 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.914549 | −0.0402608 | ||||||||
\(517\) | −7.41998 | −0.326330 | ||||||||
\(518\) | 1.49840 | 0.0658360 | ||||||||
\(519\) | −12.2696 | −0.538577 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3399 | 0.715862 | 0.357931 | − | 0.933748i | \(-0.383482\pi\) | ||||
0.357931 | + | 0.933748i | \(0.383482\pi\) | |||||||
\(522\) | 37.9586 | 1.66140 | ||||||||
\(523\) | 15.6795 | 0.685617 | 0.342808 | − | 0.939405i | \(-0.388622\pi\) | ||||
0.342808 | + | 0.939405i | \(0.388622\pi\) | |||||||
\(524\) | 1.18603 | 0.0518118 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.66201 | 0.246875 | ||||||||
\(527\) | −0.257372 | −0.0112113 | ||||||||
\(528\) | −25.0389 | −1.08968 | ||||||||
\(529\) | −14.7358 | −0.640689 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.22159 | 0.0530123 | ||||||||
\(532\) | 0.0661620 | 0.00286848 | ||||||||
\(533\) | 2.32837 | 0.100853 | ||||||||
\(534\) | 42.8135 | 1.85272 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 14.3970 | 0.621855 | ||||||||
\(537\) | −36.9417 | −1.59415 | ||||||||
\(538\) | −9.59623 | −0.413723 | ||||||||
\(539\) | −13.4062 | −0.577448 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.92084 | −0.168570 | −0.0842851 | − | 0.996442i | \(-0.526861\pi\) | ||||
−0.0842851 | + | 0.996442i | \(0.526861\pi\) | |||||||
\(542\) | 24.5258 | 1.05347 | ||||||||
\(543\) | −44.4537 | −1.90769 | ||||||||
\(544\) | −0.887626 | −0.0380566 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.07114 | 0.388209 | ||||||||
\(547\) | 36.8903 | 1.57732 | 0.788658 | − | 0.614832i | \(-0.210776\pi\) | ||||
0.788658 | + | 0.614832i | \(0.210776\pi\) | |||||||
\(548\) | 1.99473 | 0.0852106 | ||||||||
\(549\) | −10.9645 | −0.467954 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.44519 | 0.189371 | ||||||||
\(552\) | −19.0392 | −0.810363 | ||||||||
\(553\) | 9.11462 | 0.387593 | ||||||||
\(554\) | 39.2224 | 1.66640 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.01976 | 0.0432474 | ||||||||
\(557\) | 0.602249 | 0.0255181 | 0.0127591 | − | 0.999919i | \(-0.495939\pi\) | ||||
0.0127591 | + | 0.999919i | \(0.495939\pi\) | |||||||
\(558\) | −0.740187 | −0.0313346 | ||||||||
\(559\) | −7.11549 | −0.300953 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.47647 | −0.357877 | ||||||||
\(562\) | 13.7818 | 0.581350 | ||||||||
\(563\) | −7.05189 | −0.297202 | −0.148601 | − | 0.988897i | \(-0.547477\pi\) | ||||
−0.148601 | + | 0.988897i | \(0.547477\pi\) | |||||||
\(564\) | −0.800366 | −0.0337015 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19.9825 | −0.839928 | ||||||||
\(567\) | 11.8883 | 0.499262 | ||||||||
\(568\) | 39.3237 | 1.64999 | ||||||||
\(569\) | 32.0383 | 1.34311 | 0.671557 | − | 0.740953i | \(-0.265626\pi\) | ||||
0.671557 | + | 0.740953i | \(0.265626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.2459 | 1.14020 | 0.570102 | − | 0.821574i | \(-0.306904\pi\) | ||||
0.570102 | + | 0.821574i | \(0.306904\pi\) | |||||||
\(572\) | 0.562802 | 0.0235319 | ||||||||
\(573\) | −33.0879 | −1.38227 | ||||||||
\(574\) | 2.04372 | 0.0853034 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 21.1866 | 0.882773 | ||||||||
\(577\) | 2.31753 | 0.0964802 | 0.0482401 | − | 0.998836i | \(-0.484639\pi\) | ||||
0.0482401 | + | 0.998836i | \(0.484639\pi\) | |||||||
\(578\) | 21.7470 | 0.904556 | ||||||||
\(579\) | 29.9318 | 1.24392 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.36572 | 0.0566598 | ||||||||
\(582\) | 34.3543 | 1.42403 | ||||||||
\(583\) | −30.5146 | −1.26379 | ||||||||
\(584\) | −11.9577 | −0.494811 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.6740 | 0.688797 | ||||||||
\(587\) | 3.75229 | 0.154874 | 0.0774369 | − | 0.996997i | \(-0.475326\pi\) | ||||
0.0774369 | + | 0.996997i | \(0.475326\pi\) | |||||||
\(588\) | −1.44608 | −0.0596354 | ||||||||
\(589\) | −0.0866804 | −0.00357160 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.6484 | −0.767094 | ||||||||
\(592\) | −3.47109 | −0.142661 | ||||||||
\(593\) | 34.1569 | 1.40266 | 0.701328 | − | 0.712839i | \(-0.252591\pi\) | ||||
0.701328 | + | 0.712839i | \(0.252591\pi\) | |||||||
\(594\) | 1.55152 | 0.0636596 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.87633 | 0.0768577 | ||||||||
\(597\) | −12.4289 | −0.508681 | ||||||||
\(598\) | 8.64317 | 0.353446 | ||||||||
\(599\) | −19.0779 | −0.779503 | −0.389752 | − | 0.920920i | \(-0.627439\pi\) | ||||
−0.389752 | + | 0.920920i | \(0.627439\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.3859 | 0.913140 | 0.456570 | − | 0.889687i | \(-0.349078\pi\) | ||||
0.456570 | + | 0.889687i | \(0.349078\pi\) | |||||||
\(602\) | −6.24562 | −0.254553 | ||||||||
\(603\) | 14.7920 | 0.602376 | ||||||||
\(604\) | −1.01269 | −0.0412058 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 36.9611 | 1.50144 | ||||||||
\(607\) | −39.6985 | −1.61131 | −0.805656 | − | 0.592384i | \(-0.798187\pi\) | ||||
−0.805656 | + | 0.592384i | \(0.798187\pi\) | |||||||
\(608\) | −0.298943 | −0.0121237 | ||||||||
\(609\) | 27.9515 | 1.13265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.22711 | −0.251922 | ||||||||
\(612\) | −0.443063 | −0.0179098 | ||||||||
\(613\) | −22.1222 | −0.893505 | −0.446753 | − | 0.894658i | \(-0.647420\pi\) | ||||
−0.446753 | + | 0.894658i | \(0.647420\pi\) | |||||||
\(614\) | −17.1931 | −0.693856 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.46642 | −0.341122 | ||||||||
\(617\) | 4.59367 | 0.184934 | 0.0924670 | − | 0.995716i | \(-0.470525\pi\) | ||||
0.0924670 | + | 0.995716i | \(0.470525\pi\) | |||||||
\(618\) | −26.4974 | −1.06588 | ||||||||
\(619\) | −11.6527 | −0.468364 | −0.234182 | − | 0.972193i | \(-0.575241\pi\) | ||||
−0.234182 | + | 0.972193i | \(0.575241\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.24499 | 0.0499598 | ||||||||
\(622\) | 8.04555 | 0.322597 | ||||||||
\(623\) | 15.2771 | 0.612064 | ||||||||
\(624\) | −21.0135 | −0.841215 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −36.1022 | −1.44293 | ||||||||
\(627\) | −2.85479 | −0.114009 | ||||||||
\(628\) | 0.0194546 | 0.000776324 0 | ||||||||
\(629\) | −1.17507 | −0.0468533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.75293 | −0.149402 | −0.0747010 | − | 0.997206i | \(-0.523800\pi\) | ||||
−0.0747010 | + | 0.997206i | \(0.523800\pi\) | |||||||
\(632\) | −20.0078 | −0.795869 | ||||||||
\(633\) | −49.7509 | −1.97742 | ||||||||
\(634\) | 22.9707 | 0.912284 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.29150 | −0.130517 | ||||||||
\(637\) | −11.2510 | −0.445781 | ||||||||
\(638\) | 33.1900 | 1.31401 | ||||||||
\(639\) | 40.4026 | 1.59830 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.9147 | 1.22106 | 0.610529 | − | 0.791994i | \(-0.290957\pi\) | ||||
0.610529 | + | 0.791994i | \(0.290957\pi\) | |||||||
\(642\) | −15.0981 | −0.595875 | ||||||||
\(643\) | −22.1044 | −0.871712 | −0.435856 | − | 0.900017i | \(-0.643554\pi\) | ||||
−0.435856 | + | 0.900017i | \(0.643554\pi\) | |||||||
\(644\) | 0.396402 | 0.0156204 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.993010 | −0.0390695 | ||||||||
\(647\) | 32.9443 | 1.29517 | 0.647586 | − | 0.761992i | \(-0.275778\pi\) | ||||
0.647586 | + | 0.761992i | \(0.275778\pi\) | |||||||
\(648\) | −26.0965 | −1.02517 | ||||||||
\(649\) | 1.06812 | 0.0419275 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.545050 | −0.0213622 | ||||||||
\(652\) | 1.01083 | 0.0395870 | ||||||||
\(653\) | 40.1758 | 1.57220 | 0.786100 | − | 0.618100i | \(-0.212097\pi\) | ||||
0.786100 | + | 0.618100i | \(0.212097\pi\) | |||||||
\(654\) | 10.6339 | 0.415820 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.73434 | −0.184845 | ||||||||
\(657\) | −12.2857 | −0.479312 | ||||||||
\(658\) | −5.46585 | −0.213081 | ||||||||
\(659\) | −24.7128 | −0.962672 | −0.481336 | − | 0.876536i | \(-0.659848\pi\) | ||||
−0.481336 | + | 0.876536i | \(0.659848\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.9928 | 0.505361 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(662\) | −34.1182 | −1.32604 | ||||||||
\(663\) | −7.11375 | −0.276275 | ||||||||
\(664\) | −2.99795 | −0.116343 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.37944 | −0.130951 | ||||||||
\(667\) | 26.6328 | 1.03123 | ||||||||
\(668\) | 2.48094 | 0.0959904 | ||||||||
\(669\) | 1.90545 | 0.0736691 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.58708 | −0.370105 | ||||||||
\(672\) | −1.87977 | −0.0725137 | ||||||||
\(673\) | −6.53422 | −0.251876 | −0.125938 | − | 0.992038i | \(-0.540194\pi\) | ||||
−0.125938 | + | 0.992038i | \(0.540194\pi\) | |||||||
\(674\) | −16.1708 | −0.622876 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.961090 | −0.0369650 | ||||||||
\(677\) | −3.97121 | −0.152626 | −0.0763130 | − | 0.997084i | \(-0.524315\pi\) | ||||
−0.0763130 | + | 0.997084i | \(0.524315\pi\) | |||||||
\(678\) | −19.2210 | −0.738178 | ||||||||
\(679\) | 12.2586 | 0.470442 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.56330 | 0.0982258 | ||||||||
\(682\) | −0.647200 | −0.0247826 | ||||||||
\(683\) | −28.9357 | −1.10719 | −0.553596 | − | 0.832785i | \(-0.686745\pi\) | ||||
−0.553596 | + | 0.832785i | \(0.686745\pi\) | |||||||
\(684\) | −0.149219 | −0.00570554 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −22.5923 | −0.862577 | ||||||||
\(687\) | 45.2060 | 1.72471 | ||||||||
\(688\) | 14.4682 | 0.551593 | ||||||||
\(689\) | −25.6090 | −0.975624 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.7038 | 1.66257 | 0.831285 | − | 0.555847i | \(-0.187606\pi\) | ||||
0.831285 | + | 0.555847i | \(0.187606\pi\) | |||||||
\(692\) | −0.560763 | −0.0213170 | ||||||||
\(693\) | −8.69870 | −0.330436 | ||||||||
\(694\) | −6.46282 | −0.245325 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −61.3574 | −2.32575 | ||||||||
\(697\) | −1.60272 | −0.0607075 | ||||||||
\(698\) | −1.31051 | −0.0496036 | ||||||||
\(699\) | 49.7329 | 1.88107 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.3881 | −0.958894 | −0.479447 | − | 0.877571i | \(-0.659163\pi\) | ||||
−0.479447 | + | 0.877571i | \(0.659163\pi\) | |||||||
\(702\) | 1.30209 | 0.0491442 | ||||||||
\(703\) | −0.395753 | −0.0149261 | ||||||||
\(704\) | 18.5250 | 0.698186 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.661531 | 0.0248970 | ||||||||
\(707\) | 13.1888 | 0.496016 | ||||||||
\(708\) | 0.115215 | 0.00433003 | ||||||||
\(709\) | 47.6484 | 1.78947 | 0.894737 | − | 0.446594i | \(-0.147363\pi\) | ||||
0.894737 | + | 0.446594i | \(0.147363\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.5568 | −0.770939 | ||||||||
\(712\) | −33.5353 | −1.25679 | ||||||||
\(713\) | −0.519335 | −0.0194493 | ||||||||
\(714\) | −6.24409 | −0.233679 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.68836 | −0.0630970 | ||||||||
\(717\) | −41.6481 | −1.55538 | ||||||||
\(718\) | 12.5679 | 0.469028 | ||||||||
\(719\) | −22.1579 | −0.826351 | −0.413175 | − | 0.910651i | \(-0.635580\pi\) | ||||
−0.413175 | + | 0.910651i | \(0.635580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.45504 | −0.352124 | ||||||||
\(722\) | 27.2664 | 1.01475 | ||||||||
\(723\) | 2.41257 | 0.0897244 | ||||||||
\(724\) | −2.03168 | −0.0755069 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.2361 | 0.639693 | ||||||||
\(727\) | −11.4060 | −0.423026 | −0.211513 | − | 0.977375i | \(-0.567839\pi\) | ||||
−0.211513 | + | 0.977375i | \(0.567839\pi\) | |||||||
\(728\) | −7.10532 | −0.263341 | ||||||||
\(729\) | −23.6779 | −0.876961 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.89793 | 0.181157 | ||||||||
\(732\) | −1.03412 | −0.0382223 | ||||||||
\(733\) | 32.1861 | 1.18882 | 0.594411 | − | 0.804162i | \(-0.297385\pi\) | ||||
0.594411 | + | 0.804162i | \(0.297385\pi\) | |||||||
\(734\) | −34.5221 | −1.27423 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.79108 | −0.0660202 | ||||||||
\(737\) | 12.9337 | 0.476420 | ||||||||
\(738\) | −4.60934 | −0.169672 | ||||||||
\(739\) | 6.90721 | 0.254086 | 0.127043 | − | 0.991897i | \(-0.459451\pi\) | ||||
0.127043 | + | 0.991897i | \(0.459451\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.39584 | −0.0880133 | ||||||||
\(742\) | −22.4783 | −0.825203 | ||||||||
\(743\) | −31.6170 | −1.15991 | −0.579957 | − | 0.814647i | \(-0.696931\pi\) | ||||
−0.579957 | + | 0.814647i | \(0.696931\pi\) | |||||||
\(744\) | 1.19646 | 0.0438643 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 11.2157 | 0.410636 | ||||||||
\(747\) | −3.08020 | −0.112699 | ||||||||
\(748\) | −0.387403 | −0.0141649 | ||||||||
\(749\) | −5.38744 | −0.196853 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.3963 | −0.525327 | −0.262664 | − | 0.964887i | \(-0.584601\pi\) | ||||
−0.262664 | + | 0.964887i | \(0.584601\pi\) | |||||||
\(752\) | 12.6618 | 0.461727 | ||||||||
\(753\) | −52.0978 | −1.89855 | ||||||||
\(754\) | 27.8543 | 1.01439 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.0597177 | 0.00217191 | ||||||||
\(757\) | 31.1923 | 1.13370 | 0.566852 | − | 0.823820i | \(-0.308161\pi\) | ||||
0.566852 | + | 0.823820i | \(0.308161\pi\) | |||||||
\(758\) | −40.3350 | −1.46503 | ||||||||
\(759\) | −17.1041 | −0.620841 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.10282 | 0.148727 | 0.0743636 | − | 0.997231i | \(-0.476307\pi\) | ||||
0.0743636 | + | 0.997231i | \(0.476307\pi\) | |||||||
\(762\) | −6.39412 | −0.231635 | ||||||||
\(763\) | 3.79450 | 0.137370 | ||||||||
\(764\) | −1.51223 | −0.0547105 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.15421 | 0.113966 | ||||||||
\(767\) | 0.896407 | 0.0323674 | ||||||||
\(768\) | 6.36534 | 0.229689 | ||||||||
\(769\) | −13.7105 | −0.494413 | −0.247206 | − | 0.968963i | \(-0.579513\pi\) | ||||
−0.247206 | + | 0.968963i | \(0.579513\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −53.6257 | −1.93128 | ||||||||
\(772\) | 1.36798 | 0.0492348 | ||||||||
\(773\) | −34.2990 | −1.23365 | −0.616825 | − | 0.787100i | \(-0.711582\pi\) | ||||
−0.616825 | + | 0.787100i | \(0.711582\pi\) | |||||||
\(774\) | 14.0861 | 0.506316 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −26.9093 | −0.965987 | ||||||||
\(777\) | −2.48851 | −0.0892750 | ||||||||
\(778\) | 23.6818 | 0.849035 | ||||||||
\(779\) | −0.539781 | −0.0193397 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.3270 | 1.26410 | ||||||||
\(782\) | −5.94951 | −0.212754 | ||||||||
\(783\) | 4.01222 | 0.143385 | ||||||||
\(784\) | 22.8770 | 0.817035 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −37.6976 | −1.34463 | ||||||||
\(787\) | 1.05124 | 0.0374728 | 0.0187364 | − | 0.999824i | \(-0.494036\pi\) | ||||
0.0187364 | + | 0.999824i | \(0.494036\pi\) | |||||||
\(788\) | −0.852296 | −0.0303618 | ||||||||
\(789\) | −9.40335 | −0.334768 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.85861 | −0.243864 | ||||||||
\(792\) | 19.0948 | 0.678506 | ||||||||
\(793\) | −8.04582 | −0.285716 | ||||||||
\(794\) | −7.14446 | −0.253547 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.568042 | −0.0201337 | ||||||||
\(797\) | −46.9746 | −1.66393 | −0.831963 | − | 0.554832i | \(-0.812783\pi\) | ||||
−0.831963 | + | 0.554832i | \(0.812783\pi\) | |||||||
\(798\) | −2.10295 | −0.0744435 | ||||||||
\(799\) | 4.28642 | 0.151642 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −34.4554 | −1.21742 | ||||||||
\(802\) | −4.31996 | −0.152543 | ||||||||
\(803\) | −10.7423 | −0.379088 | ||||||||
\(804\) | 1.39511 | 0.0492018 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.543153 | −0.0191318 | ||||||||
\(807\) | 15.9372 | 0.561016 | ||||||||
\(808\) | −28.9512 | −1.01850 | ||||||||
\(809\) | −40.7051 | −1.43111 | −0.715557 | − | 0.698554i | \(-0.753827\pi\) | ||||
−0.715557 | + | 0.698554i | \(0.753827\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.80946 | −0.344457 | −0.172228 | − | 0.985057i | \(-0.555097\pi\) | ||||
−0.172228 | + | 0.985057i | \(0.555097\pi\) | |||||||
\(812\) | 1.27748 | 0.0448307 | ||||||||
\(813\) | −40.7319 | −1.42853 | ||||||||
\(814\) | −2.95490 | −0.103569 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 14.4646 | 0.506363 | ||||||||
\(817\) | 1.64957 | 0.0577113 | ||||||||
\(818\) | 35.4328 | 1.23888 | ||||||||
\(819\) | −7.30026 | −0.255092 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.27965 | −0.254061 | −0.127031 | − | 0.991899i | \(-0.540545\pi\) | ||||
−0.127031 | + | 0.991899i | \(0.540545\pi\) | |||||||
\(822\) | −63.4022 | −2.21140 | ||||||||
\(823\) | −10.9222 | −0.380725 | −0.190362 | − | 0.981714i | \(-0.560966\pi\) | ||||
−0.190362 | + | 0.981714i | \(0.560966\pi\) | |||||||
\(824\) | 20.7551 | 0.723039 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.786821 | 0.0273770 | ||||||||
\(827\) | −19.4083 | −0.674894 | −0.337447 | − | 0.941344i | \(-0.609563\pi\) | ||||
−0.337447 | + | 0.941344i | \(0.609563\pi\) | |||||||
\(828\) | −0.894030 | −0.0310697 | ||||||||
\(829\) | 28.4668 | 0.988692 | 0.494346 | − | 0.869265i | \(-0.335408\pi\) | ||||
0.494346 | + | 0.869265i | \(0.335408\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −65.1397 | −2.25967 | ||||||||
\(832\) | 15.5468 | 0.538989 | ||||||||
\(833\) | 7.74459 | 0.268334 | ||||||||
\(834\) | −32.4129 | −1.12237 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.130473 | −0.00451252 | ||||||||
\(837\) | −0.0782376 | −0.00270429 | ||||||||
\(838\) | 43.4152 | 1.49975 | ||||||||
\(839\) | −19.8074 | −0.683826 | −0.341913 | − | 0.939732i | \(-0.611075\pi\) | ||||
−0.341913 | + | 0.939732i | \(0.611075\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 56.8293 | 1.95963 | ||||||||
\(842\) | 7.33662 | 0.252836 | ||||||||
\(843\) | −22.8885 | −0.788322 | ||||||||
\(844\) | −2.27378 | −0.0782669 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.3275 | 0.423827 | ||||||||
\(847\) | 6.15036 | 0.211329 | ||||||||
\(848\) | 52.0715 | 1.78814 | ||||||||
\(849\) | 33.1865 | 1.13896 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.37111 | −0.0812806 | ||||||||
\(852\) | 3.81059 | 0.130549 | ||||||||
\(853\) | −8.54067 | −0.292427 | −0.146214 | − | 0.989253i | \(-0.546709\pi\) | ||||
−0.146214 | + | 0.989253i | \(0.546709\pi\) | |||||||
\(854\) | −7.06222 | −0.241664 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.8262 | 0.404210 | ||||||||
\(857\) | −9.52177 | −0.325257 | −0.162629 | − | 0.986687i | \(-0.551997\pi\) | ||||
−0.162629 | + | 0.986687i | \(0.551997\pi\) | |||||||
\(858\) | −17.8886 | −0.610705 | ||||||||
\(859\) | −32.9092 | −1.12285 | −0.561423 | − | 0.827529i | \(-0.689746\pi\) | ||||
−0.561423 | + | 0.827529i | \(0.689746\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.39417 | −0.115673 | ||||||||
\(862\) | −14.5607 | −0.495939 | ||||||||
\(863\) | 2.93045 | 0.0997538 | 0.0498769 | − | 0.998755i | \(-0.484117\pi\) | ||||
0.0498769 | + | 0.998755i | \(0.484117\pi\) | |||||||
\(864\) | −0.269826 | −0.00917967 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 39.1866 | 1.33161 | ||||||||
\(867\) | −36.1169 | −1.22660 | ||||||||
\(868\) | −0.0249106 | −0.000845522 0 | ||||||||
\(869\) | −17.9743 | −0.609736 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.8544 | 0.367788 | ||||||||
\(872\) | −8.32944 | −0.282071 | ||||||||
\(873\) | −27.6476 | −0.935729 | ||||||||
\(874\) | −2.00373 | −0.0677773 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.15873 | −0.0391500 | ||||||||
\(877\) | 47.5268 | 1.60487 | 0.802434 | − | 0.596741i | \(-0.203538\pi\) | ||||
0.802434 | + | 0.596741i | \(0.203538\pi\) | |||||||
\(878\) | −35.7838 | −1.20764 | ||||||||
\(879\) | −27.6918 | −0.934022 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.8772 | −0.501227 | −0.250614 | − | 0.968087i | \(-0.580632\pi\) | ||||
−0.250614 | + | 0.968087i | \(0.580632\pi\) | |||||||
\(882\) | 22.2730 | 0.749970 | ||||||||
\(883\) | −18.1229 | −0.609884 | −0.304942 | − | 0.952371i | \(-0.598637\pi\) | ||||
−0.304942 | + | 0.952371i | \(0.598637\pi\) | |||||||
\(884\) | −0.325122 | −0.0109351 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.3433 | 0.515467 | ||||||||
\(887\) | 29.7170 | 0.997799 | 0.498899 | − | 0.866660i | \(-0.333738\pi\) | ||||
0.498899 | + | 0.866660i | \(0.333738\pi\) | |||||||
\(888\) | 5.46263 | 0.183314 | ||||||||
\(889\) | −2.28161 | −0.0765227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.4441 | −0.785407 | ||||||||
\(892\) | 0.0870857 | 0.00291584 | ||||||||
\(893\) | 1.44362 | 0.0483089 | ||||||||
\(894\) | −59.6390 | −1.99463 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.2045 | 0.507948 | ||||||||
\(897\) | −14.3544 | −0.479279 | ||||||||
\(898\) | 8.64540 | 0.288501 | ||||||||
\(899\) | −1.67366 | −0.0558196 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.6279 | 0.587269 | ||||||||
\(902\) | −4.03028 | −0.134194 | ||||||||
\(903\) | 10.3726 | 0.345178 | ||||||||
\(904\) | 15.0556 | 0.500741 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 32.1882 | 1.06938 | ||||||||
\(907\) | 42.0265 | 1.39547 | 0.697733 | − | 0.716358i | \(-0.254192\pi\) | ||||
0.697733 | + | 0.716358i | \(0.254192\pi\) | |||||||
\(908\) | 0.117151 | 0.00388780 | ||||||||
\(909\) | −29.7455 | −0.986597 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.7145 | −1.61398 | −0.806992 | − | 0.590562i | \(-0.798906\pi\) | ||||
−0.806992 | + | 0.590562i | \(0.798906\pi\) | |||||||
\(912\) | 4.87153 | 0.161313 | ||||||||
\(913\) | −2.69325 | −0.0891335 | ||||||||
\(914\) | −13.0564 | −0.431866 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.06606 | 0.0682647 | ||||||||
\(917\) | −13.4516 | −0.444211 | ||||||||
\(918\) | −0.896290 | −0.0295820 | ||||||||
\(919\) | 14.6475 | 0.483177 | 0.241589 | − | 0.970379i | \(-0.422332\pi\) | ||||
0.241589 | + | 0.970379i | \(0.422332\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.5539 | 0.940882 | ||||||||
\(922\) | −25.0050 | −0.823495 | ||||||||
\(923\) | 29.6477 | 0.975865 | ||||||||
\(924\) | −0.820423 | −0.0269899 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 25.4349 | 0.835841 | ||||||||
\(927\) | 21.3246 | 0.700390 | ||||||||
\(928\) | −5.77211 | −0.189479 | ||||||||
\(929\) | 45.7110 | 1.49973 | 0.749864 | − | 0.661592i | \(-0.230119\pi\) | ||||
0.749864 | + | 0.661592i | \(0.230119\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.60830 | 0.0854836 | ||||||||
\(932\) | 2.27296 | 0.0744533 | ||||||||
\(933\) | −13.3619 | −0.437448 | ||||||||
\(934\) | 6.31878 | 0.206757 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 16.0251 | 0.523796 | ||||||||
\(937\) | −39.7753 | −1.29940 | −0.649701 | − | 0.760190i | \(-0.725106\pi\) | ||||
−0.649701 | + | 0.760190i | \(0.725106\pi\) | |||||||
\(938\) | 9.52748 | 0.311083 | ||||||||
\(939\) | 59.9577 | 1.95665 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0359 | 0.587953 | 0.293977 | − | 0.955813i | \(-0.405021\pi\) | ||||
0.293977 | + | 0.955813i | \(0.405021\pi\) | |||||||
\(942\) | −0.618362 | −0.0201473 | ||||||||
\(943\) | −3.23404 | −0.105315 | ||||||||
\(944\) | −1.82269 | −0.0593235 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.3166 | 0.400446 | ||||||||
\(947\) | 34.4377 | 1.11908 | 0.559538 | − | 0.828805i | \(-0.310979\pi\) | ||||
0.559538 | + | 0.828805i | \(0.310979\pi\) | |||||||
\(948\) | −1.93882 | −0.0629700 | ||||||||
\(949\) | −9.01534 | −0.292650 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.1493 | −1.23707 | ||||||||
\(952\) | 4.89093 | 0.158516 | ||||||||
\(953\) | 30.0386 | 0.973045 | 0.486522 | − | 0.873668i | \(-0.338265\pi\) | ||||
0.486522 | + | 0.873668i | \(0.338265\pi\) | |||||||
\(954\) | 50.6967 | 1.64137 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.90346 | −0.0615622 | ||||||||
\(957\) | −55.1213 | −1.78182 | ||||||||
\(958\) | 41.5108 | 1.34115 | ||||||||
\(959\) | −22.6237 | −0.730558 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9674 | −0.998947 | ||||||||
\(962\) | −2.47985 | −0.0799537 | ||||||||
\(963\) | 12.1506 | 0.391549 | ||||||||
\(964\) | 0.110263 | 0.00355132 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.5996 | −0.405384 | ||||||||
\(967\) | −47.3839 | −1.52376 | −0.761882 | − | 0.647716i | \(-0.775724\pi\) | ||||
−0.761882 | + | 0.647716i | \(0.775724\pi\) | |||||||
\(968\) | −13.5009 | −0.433934 | ||||||||
\(969\) | 1.64917 | 0.0529790 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.81587 | 0.218732 | 0.109366 | − | 0.994002i | \(-0.465118\pi\) | ||||
0.109366 | + | 0.994002i | \(0.465118\pi\) | |||||||
\(972\) | −2.38557 | −0.0765173 | ||||||||
\(973\) | −11.5659 | −0.370784 | ||||||||
\(974\) | −22.7134 | −0.727784 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.3598 | 0.523665 | ||||||||
\(977\) | −51.4729 | −1.64676 | −0.823382 | − | 0.567488i | \(-0.807915\pi\) | ||||
−0.823382 | + | 0.567488i | \(0.807915\pi\) | |||||||
\(978\) | −32.1289 | −1.02737 | ||||||||
\(979\) | −30.1269 | −0.962860 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.55797 | −0.273235 | ||||||||
\(982\) | 22.4145 | 0.715275 | ||||||||
\(983\) | −17.8746 | −0.570112 | −0.285056 | − | 0.958511i | \(-0.592012\pi\) | ||||
−0.285056 | + | 0.958511i | \(0.592012\pi\) | |||||||
\(984\) | 7.45067 | 0.237519 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −19.1734 | −0.610606 | ||||||||
\(987\) | 9.07756 | 0.288942 | ||||||||
\(988\) | −0.109498 | −0.00348359 | ||||||||
\(989\) | 9.88323 | 0.314268 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.7353 | 0.912805 | 0.456403 | − | 0.889773i | \(-0.349138\pi\) | ||||
0.456403 | + | 0.889773i | \(0.349138\pi\) | |||||||
\(992\) | 0.112555 | 0.00357363 | ||||||||
\(993\) | 56.6627 | 1.79814 | ||||||||
\(994\) | 26.0232 | 0.825407 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.290511 | −0.00920519 | ||||||||
\(997\) | −44.7201 | −1.41630 | −0.708150 | − | 0.706062i | \(-0.750470\pi\) | ||||
−0.708150 | + | 0.706062i | \(0.750470\pi\) | |||||||
\(998\) | −2.39258 | −0.0757359 | ||||||||
\(999\) | −0.357207 | −0.0113015 |
(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 | 6025.2.a.p.1.13 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.13 | ✓ | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.34 | yes | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.34 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.13 | ✓ | 46 | 5.2 | odd | 4 | ||
1205.2.b.c.724.34 | yes | 46 | 5.3 | odd | 4 | ||
6025.2.a.p.1.13 | 46 | 1.1 | even | 1 | trivial | ||
6025.2.a.p.1.34 | 46 | 5.4 | even | 2 | inner |