Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.34123 | −1.92906 | −0.964530 | − | 0.263972i | \(-0.914967\pi\) | ||||
−0.964530 | + | 0.263972i | \(0.914967\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.21966 | −0.545449 | −0.272724 | − | 0.962092i | \(-0.587925\pi\) | ||||
−0.272724 | + | 0.962092i | \(0.587925\pi\) | |||||||
\(6\) | −3.34123 | −1.36405 | ||||||||
\(7\) | 1.21220 | 0.458167 | 0.229084 | − | 0.973407i | \(-0.426427\pi\) | ||||
0.229084 | + | 0.973407i | \(0.426427\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.16382 | 2.72127 | ||||||||
\(10\) | −1.21966 | −0.385691 | ||||||||
\(11\) | −1.48208 | −0.446863 | −0.223432 | − | 0.974720i | \(-0.571726\pi\) | ||||
−0.223432 | + | 0.974720i | \(0.571726\pi\) | |||||||
\(12\) | −3.34123 | −0.964530 | ||||||||
\(13\) | −2.69785 | −0.748250 | −0.374125 | − | 0.927378i | \(-0.622057\pi\) | ||||
−0.374125 | + | 0.927378i | \(0.622057\pi\) | |||||||
\(14\) | 1.21220 | 0.323973 | ||||||||
\(15\) | 4.07517 | 1.05220 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.46441 | 0.597706 | 0.298853 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298853 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(18\) | 8.16382 | 1.92423 | ||||||||
\(19\) | 6.34284 | 1.45515 | 0.727574 | − | 0.686030i | \(-0.240648\pi\) | ||||
0.727574 | + | 0.686030i | \(0.240648\pi\) | |||||||
\(20\) | −1.21966 | −0.272724 | ||||||||
\(21\) | −4.05023 | −0.883833 | ||||||||
\(22\) | −1.48208 | −0.315980 | ||||||||
\(23\) | −0.258764 | −0.0539561 | −0.0269780 | − | 0.999636i | \(-0.508588\pi\) | ||||
−0.0269780 | + | 0.999636i | \(0.508588\pi\) | |||||||
\(24\) | −3.34123 | −0.682026 | ||||||||
\(25\) | −3.51243 | −0.702485 | ||||||||
\(26\) | −2.69785 | −0.529093 | ||||||||
\(27\) | −17.2535 | −3.32044 | ||||||||
\(28\) | 1.21220 | 0.229084 | ||||||||
\(29\) | −0.940582 | −0.174662 | −0.0873309 | − | 0.996179i | \(-0.527834\pi\) | ||||
−0.0873309 | + | 0.996179i | \(0.527834\pi\) | |||||||
\(30\) | 4.07517 | 0.744021 | ||||||||
\(31\) | 5.09661 | 0.915378 | 0.457689 | − | 0.889112i | \(-0.348677\pi\) | ||||
0.457689 | + | 0.889112i | \(0.348677\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.95196 | 0.862026 | ||||||||
\(34\) | 2.46441 | 0.422642 | ||||||||
\(35\) | −1.47847 | −0.249907 | ||||||||
\(36\) | 8.16382 | 1.36064 | ||||||||
\(37\) | 0.621932 | 0.102245 | 0.0511225 | − | 0.998692i | \(-0.483720\pi\) | ||||
0.0511225 | + | 0.998692i | \(0.483720\pi\) | |||||||
\(38\) | 6.34284 | 1.02894 | ||||||||
\(39\) | 9.01416 | 1.44342 | ||||||||
\(40\) | −1.21966 | −0.192845 | ||||||||
\(41\) | 2.70955 | 0.423160 | 0.211580 | − | 0.977361i | \(-0.432139\pi\) | ||||
0.211580 | + | 0.977361i | \(0.432139\pi\) | |||||||
\(42\) | −4.05023 | −0.624964 | ||||||||
\(43\) | −0.396684 | −0.0604937 | −0.0302469 | − | 0.999542i | \(-0.509629\pi\) | ||||
−0.0302469 | + | 0.999542i | \(0.509629\pi\) | |||||||
\(44\) | −1.48208 | −0.223432 | ||||||||
\(45\) | −9.95710 | −1.48432 | ||||||||
\(46\) | −0.258764 | −0.0381527 | ||||||||
\(47\) | −6.14729 | −0.896674 | −0.448337 | − | 0.893865i | \(-0.647984\pi\) | ||||
−0.448337 | + | 0.893865i | \(0.647984\pi\) | |||||||
\(48\) | −3.34123 | −0.482265 | ||||||||
\(49\) | −5.53058 | −0.790083 | ||||||||
\(50\) | −3.51243 | −0.496732 | ||||||||
\(51\) | −8.23415 | −1.15301 | ||||||||
\(52\) | −2.69785 | −0.374125 | ||||||||
\(53\) | −10.2505 | −1.40801 | −0.704005 | − | 0.710195i | \(-0.748607\pi\) | ||||
−0.704005 | + | 0.710195i | \(0.748607\pi\) | |||||||
\(54\) | −17.2535 | −2.34791 | ||||||||
\(55\) | 1.80763 | 0.243741 | ||||||||
\(56\) | 1.21220 | 0.161987 | ||||||||
\(57\) | −21.1929 | −2.80707 | ||||||||
\(58\) | −0.940582 | −0.123505 | ||||||||
\(59\) | 2.37335 | 0.308984 | 0.154492 | − | 0.987994i | \(-0.450626\pi\) | ||||
0.154492 | + | 0.987994i | \(0.450626\pi\) | |||||||
\(60\) | 4.07517 | 0.526102 | ||||||||
\(61\) | −0.765657 | −0.0980324 | −0.0490162 | − | 0.998798i | \(-0.515609\pi\) | ||||
−0.0490162 | + | 0.998798i | \(0.515609\pi\) | |||||||
\(62\) | 5.09661 | 0.647270 | ||||||||
\(63\) | 9.89616 | 1.24680 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.29047 | 0.408132 | ||||||||
\(66\) | 4.95196 | 0.609545 | ||||||||
\(67\) | −6.41950 | −0.784267 | −0.392134 | − | 0.919908i | \(-0.628263\pi\) | ||||
−0.392134 | + | 0.919908i | \(0.628263\pi\) | |||||||
\(68\) | 2.46441 | 0.298853 | ||||||||
\(69\) | 0.864591 | 0.104085 | ||||||||
\(70\) | −1.47847 | −0.176711 | ||||||||
\(71\) | 10.3122 | 1.22383 | 0.611915 | − | 0.790924i | \(-0.290400\pi\) | ||||
0.611915 | + | 0.790924i | \(0.290400\pi\) | |||||||
\(72\) | 8.16382 | 0.962116 | ||||||||
\(73\) | 10.5627 | 1.23627 | 0.618137 | − | 0.786070i | \(-0.287888\pi\) | ||||
0.618137 | + | 0.786070i | \(0.287888\pi\) | |||||||
\(74\) | 0.621932 | 0.0722981 | ||||||||
\(75\) | 11.7358 | 1.35514 | ||||||||
\(76\) | 6.34284 | 0.727574 | ||||||||
\(77\) | −1.79657 | −0.204738 | ||||||||
\(78\) | 9.01416 | 1.02065 | ||||||||
\(79\) | −8.44573 | −0.950219 | −0.475110 | − | 0.879927i | \(-0.657592\pi\) | ||||
−0.475110 | + | 0.879927i | \(0.657592\pi\) | |||||||
\(80\) | −1.21966 | −0.136362 | ||||||||
\(81\) | 33.1566 | 3.68406 | ||||||||
\(82\) | 2.70955 | 0.299219 | ||||||||
\(83\) | 10.3832 | 1.13970 | 0.569851 | − | 0.821748i | \(-0.307001\pi\) | ||||
0.569851 | + | 0.821748i | \(0.307001\pi\) | |||||||
\(84\) | −4.05023 | −0.441916 | ||||||||
\(85\) | −3.00574 | −0.326018 | ||||||||
\(86\) | −0.396684 | −0.0427755 | ||||||||
\(87\) | 3.14270 | 0.336933 | ||||||||
\(88\) | −1.48208 | −0.157990 | ||||||||
\(89\) | 17.4152 | 1.84601 | 0.923005 | − | 0.384787i | \(-0.125725\pi\) | ||||
0.923005 | + | 0.384787i | \(0.125725\pi\) | |||||||
\(90\) | −9.95710 | −1.04957 | ||||||||
\(91\) | −3.27033 | −0.342824 | ||||||||
\(92\) | −0.258764 | −0.0269780 | ||||||||
\(93\) | −17.0289 | −1.76582 | ||||||||
\(94\) | −6.14729 | −0.634045 | ||||||||
\(95\) | −7.73611 | −0.793709 | ||||||||
\(96\) | −3.34123 | −0.341013 | ||||||||
\(97\) | 4.34938 | 0.441613 | 0.220806 | − | 0.975318i | \(-0.429131\pi\) | ||||
0.220806 | + | 0.975318i | \(0.429131\pi\) | |||||||
\(98\) | −5.53058 | −0.558673 | ||||||||
\(99\) | −12.0994 | −1.21604 | ||||||||
\(100\) | −3.51243 | −0.351243 | ||||||||
\(101\) | 4.89335 | 0.486906 | 0.243453 | − | 0.969913i | \(-0.421720\pi\) | ||||
0.243453 | + | 0.969913i | \(0.421720\pi\) | |||||||
\(102\) | −8.23415 | −0.815302 | ||||||||
\(103\) | −16.7617 | −1.65158 | −0.825789 | − | 0.563979i | \(-0.809270\pi\) | ||||
−0.825789 | + | 0.563979i | \(0.809270\pi\) | |||||||
\(104\) | −2.69785 | −0.264546 | ||||||||
\(105\) | 4.93991 | 0.482086 | ||||||||
\(106\) | −10.2505 | −0.995613 | ||||||||
\(107\) | 12.3674 | 1.19560 | 0.597800 | − | 0.801646i | \(-0.296042\pi\) | ||||
0.597800 | + | 0.801646i | \(0.296042\pi\) | |||||||
\(108\) | −17.2535 | −1.66022 | ||||||||
\(109\) | −15.2467 | −1.46037 | −0.730183 | − | 0.683251i | \(-0.760565\pi\) | ||||
−0.730183 | + | 0.683251i | \(0.760565\pi\) | |||||||
\(110\) | 1.80763 | 0.172351 | ||||||||
\(111\) | −2.07802 | −0.197237 | ||||||||
\(112\) | 1.21220 | 0.114542 | ||||||||
\(113\) | 4.39295 | 0.413254 | 0.206627 | − | 0.978420i | \(-0.433751\pi\) | ||||
0.206627 | + | 0.978420i | \(0.433751\pi\) | |||||||
\(114\) | −21.1929 | −1.98490 | ||||||||
\(115\) | 0.315605 | 0.0294303 | ||||||||
\(116\) | −0.940582 | −0.0873309 | ||||||||
\(117\) | −22.0248 | −2.03619 | ||||||||
\(118\) | 2.37335 | 0.218484 | ||||||||
\(119\) | 2.98735 | 0.273850 | ||||||||
\(120\) | 4.07517 | 0.372010 | ||||||||
\(121\) | −8.80345 | −0.800313 | ||||||||
\(122\) | −0.765657 | −0.0693194 | ||||||||
\(123\) | −9.05322 | −0.816301 | ||||||||
\(124\) | 5.09661 | 0.457689 | ||||||||
\(125\) | 10.3823 | 0.928619 | ||||||||
\(126\) | 9.89616 | 0.881620 | ||||||||
\(127\) | 9.72778 | 0.863201 | 0.431600 | − | 0.902065i | \(-0.357949\pi\) | ||||
0.431600 | + | 0.902065i | \(0.357949\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.32541 | 0.116696 | ||||||||
\(130\) | 3.29047 | 0.288593 | ||||||||
\(131\) | 12.3774 | 1.08142 | 0.540711 | − | 0.841209i | \(-0.318155\pi\) | ||||
0.540711 | + | 0.841209i | \(0.318155\pi\) | |||||||
\(132\) | 4.95196 | 0.431013 | ||||||||
\(133\) | 7.68877 | 0.666701 | ||||||||
\(134\) | −6.41950 | −0.554561 | ||||||||
\(135\) | 21.0435 | 1.81113 | ||||||||
\(136\) | 2.46441 | 0.211321 | ||||||||
\(137\) | −0.763945 | −0.0652682 | −0.0326341 | − | 0.999467i | \(-0.510390\pi\) | ||||
−0.0326341 | + | 0.999467i | \(0.510390\pi\) | |||||||
\(138\) | 0.864591 | 0.0735989 | ||||||||
\(139\) | 5.36732 | 0.455250 | 0.227625 | − | 0.973749i | \(-0.426904\pi\) | ||||
0.227625 | + | 0.973749i | \(0.426904\pi\) | |||||||
\(140\) | −1.47847 | −0.124953 | ||||||||
\(141\) | 20.5395 | 1.72974 | ||||||||
\(142\) | 10.3122 | 0.865378 | ||||||||
\(143\) | 3.99843 | 0.334366 | ||||||||
\(144\) | 8.16382 | 0.680319 | ||||||||
\(145\) | 1.14719 | 0.0952691 | ||||||||
\(146\) | 10.5627 | 0.874178 | ||||||||
\(147\) | 18.4789 | 1.52412 | ||||||||
\(148\) | 0.621932 | 0.0511225 | ||||||||
\(149\) | −18.6843 | −1.53068 | −0.765339 | − | 0.643628i | \(-0.777429\pi\) | ||||
−0.765339 | + | 0.643628i | \(0.777429\pi\) | |||||||
\(150\) | 11.7358 | 0.958227 | ||||||||
\(151\) | 16.3982 | 1.33447 | 0.667234 | − | 0.744848i | \(-0.267478\pi\) | ||||
0.667234 | + | 0.744848i | \(0.267478\pi\) | |||||||
\(152\) | 6.34284 | 0.514472 | ||||||||
\(153\) | 20.1190 | 1.62652 | ||||||||
\(154\) | −1.79657 | −0.144772 | ||||||||
\(155\) | −6.21613 | −0.499292 | ||||||||
\(156\) | 9.01416 | 0.721710 | ||||||||
\(157\) | 11.5783 | 0.924046 | 0.462023 | − | 0.886868i | \(-0.347124\pi\) | ||||
0.462023 | + | 0.886868i | \(0.347124\pi\) | |||||||
\(158\) | −8.44573 | −0.671907 | ||||||||
\(159\) | 34.2492 | 2.71614 | ||||||||
\(160\) | −1.21966 | −0.0964227 | ||||||||
\(161\) | −0.313673 | −0.0247209 | ||||||||
\(162\) | 33.1566 | 2.60502 | ||||||||
\(163\) | 2.77315 | 0.217210 | 0.108605 | − | 0.994085i | \(-0.465362\pi\) | ||||
0.108605 | + | 0.994085i | \(0.465362\pi\) | |||||||
\(164\) | 2.70955 | 0.211580 | ||||||||
\(165\) | −6.03972 | −0.470191 | ||||||||
\(166\) | 10.3832 | 0.805891 | ||||||||
\(167\) | 13.3818 | 1.03551 | 0.517756 | − | 0.855529i | \(-0.326768\pi\) | ||||
0.517756 | + | 0.855529i | \(0.326768\pi\) | |||||||
\(168\) | −4.05023 | −0.312482 | ||||||||
\(169\) | −5.72158 | −0.440121 | ||||||||
\(170\) | −3.00574 | −0.230530 | ||||||||
\(171\) | 51.7818 | 3.95986 | ||||||||
\(172\) | −0.396684 | −0.0302469 | ||||||||
\(173\) | −11.2336 | −0.854072 | −0.427036 | − | 0.904235i | \(-0.640442\pi\) | ||||
−0.427036 | + | 0.904235i | \(0.640442\pi\) | |||||||
\(174\) | 3.14270 | 0.238248 | ||||||||
\(175\) | −4.25775 | −0.321856 | ||||||||
\(176\) | −1.48208 | −0.111716 | ||||||||
\(177\) | −7.92990 | −0.596048 | ||||||||
\(178\) | 17.4152 | 1.30533 | ||||||||
\(179\) | 4.85748 | 0.363065 | 0.181533 | − | 0.983385i | \(-0.441894\pi\) | ||||
0.181533 | + | 0.983385i | \(0.441894\pi\) | |||||||
\(180\) | −9.95710 | −0.742158 | ||||||||
\(181\) | 11.3297 | 0.842127 | 0.421064 | − | 0.907031i | \(-0.361657\pi\) | ||||
0.421064 | + | 0.907031i | \(0.361657\pi\) | |||||||
\(182\) | −3.27033 | −0.242413 | ||||||||
\(183\) | 2.55824 | 0.189110 | ||||||||
\(184\) | −0.258764 | −0.0190764 | ||||||||
\(185\) | −0.758546 | −0.0557694 | ||||||||
\(186\) | −17.0289 | −1.24862 | ||||||||
\(187\) | −3.65244 | −0.267093 | ||||||||
\(188\) | −6.14729 | −0.448337 | ||||||||
\(189\) | −20.9147 | −1.52132 | ||||||||
\(190\) | −7.73611 | −0.561237 | ||||||||
\(191\) | 18.9452 | 1.37082 | 0.685412 | − | 0.728155i | \(-0.259622\pi\) | ||||
0.685412 | + | 0.728155i | \(0.259622\pi\) | |||||||
\(192\) | −3.34123 | −0.241133 | ||||||||
\(193\) | −8.34283 | −0.600530 | −0.300265 | − | 0.953856i | \(-0.597075\pi\) | ||||
−0.300265 | + | 0.953856i | \(0.597075\pi\) | |||||||
\(194\) | 4.34938 | 0.312267 | ||||||||
\(195\) | −10.9942 | −0.787312 | ||||||||
\(196\) | −5.53058 | −0.395041 | ||||||||
\(197\) | 11.5578 | 0.823456 | 0.411728 | − | 0.911307i | \(-0.364925\pi\) | ||||
0.411728 | + | 0.911307i | \(0.364925\pi\) | |||||||
\(198\) | −12.0994 | −0.859869 | ||||||||
\(199\) | 18.1935 | 1.28970 | 0.644851 | − | 0.764308i | \(-0.276919\pi\) | ||||
0.644851 | + | 0.764308i | \(0.276919\pi\) | |||||||
\(200\) | −3.51243 | −0.248366 | ||||||||
\(201\) | 21.4490 | 1.51290 | ||||||||
\(202\) | 4.89335 | 0.344295 | ||||||||
\(203\) | −1.14017 | −0.0800243 | ||||||||
\(204\) | −8.23415 | −0.576506 | ||||||||
\(205\) | −3.30473 | −0.230812 | ||||||||
\(206\) | −16.7617 | −1.16784 | ||||||||
\(207\) | −2.11251 | −0.146829 | ||||||||
\(208\) | −2.69785 | −0.187063 | ||||||||
\(209\) | −9.40058 | −0.650252 | ||||||||
\(210\) | 4.93991 | 0.340886 | ||||||||
\(211\) | 16.2521 | 1.11884 | 0.559420 | − | 0.828885i | \(-0.311024\pi\) | ||||
0.559420 | + | 0.828885i | \(0.311024\pi\) | |||||||
\(212\) | −10.2505 | −0.704005 | ||||||||
\(213\) | −34.4553 | −2.36084 | ||||||||
\(214\) | 12.3674 | 0.845416 | ||||||||
\(215\) | 0.483820 | 0.0329962 | ||||||||
\(216\) | −17.2535 | −1.17395 | ||||||||
\(217\) | 6.17809 | 0.419396 | ||||||||
\(218\) | −15.2467 | −1.03263 | ||||||||
\(219\) | −35.2925 | −2.38485 | ||||||||
\(220\) | 1.80763 | 0.121871 | ||||||||
\(221\) | −6.64861 | −0.447234 | ||||||||
\(222\) | −2.07802 | −0.139467 | ||||||||
\(223\) | 25.1112 | 1.68157 | 0.840784 | − | 0.541371i | \(-0.182095\pi\) | ||||
0.840784 | + | 0.541371i | \(0.182095\pi\) | |||||||
\(224\) | 1.21220 | 0.0809933 | ||||||||
\(225\) | −28.6748 | −1.91166 | ||||||||
\(226\) | 4.39295 | 0.292215 | ||||||||
\(227\) | −7.01735 | −0.465758 | −0.232879 | − | 0.972506i | \(-0.574815\pi\) | ||||
−0.232879 | + | 0.972506i | \(0.574815\pi\) | |||||||
\(228\) | −21.1929 | −1.40353 | ||||||||
\(229\) | 1.11907 | 0.0739500 | 0.0369750 | − | 0.999316i | \(-0.488228\pi\) | ||||
0.0369750 | + | 0.999316i | \(0.488228\pi\) | |||||||
\(230\) | 0.315605 | 0.0208104 | ||||||||
\(231\) | 6.00276 | 0.394952 | ||||||||
\(232\) | −0.940582 | −0.0617523 | ||||||||
\(233\) | 12.2990 | 0.805737 | 0.402868 | − | 0.915258i | \(-0.368013\pi\) | ||||
0.402868 | + | 0.915258i | \(0.368013\pi\) | |||||||
\(234\) | −22.0248 | −1.43981 | ||||||||
\(235\) | 7.49761 | 0.489090 | ||||||||
\(236\) | 2.37335 | 0.154492 | ||||||||
\(237\) | 28.2191 | 1.83303 | ||||||||
\(238\) | 2.98735 | 0.193641 | ||||||||
\(239\) | 25.8095 | 1.66948 | 0.834739 | − | 0.550646i | \(-0.185619\pi\) | ||||
0.834739 | + | 0.550646i | \(0.185619\pi\) | |||||||
\(240\) | 4.07517 | 0.263051 | ||||||||
\(241\) | 14.9085 | 0.960342 | 0.480171 | − | 0.877175i | \(-0.340575\pi\) | ||||
0.480171 | + | 0.877175i | \(0.340575\pi\) | |||||||
\(242\) | −8.80345 | −0.565907 | ||||||||
\(243\) | −59.0231 | −3.78633 | ||||||||
\(244\) | −0.765657 | −0.0490162 | ||||||||
\(245\) | 6.74543 | 0.430950 | ||||||||
\(246\) | −9.05322 | −0.577212 | ||||||||
\(247\) | −17.1121 | −1.08881 | ||||||||
\(248\) | 5.09661 | 0.323635 | ||||||||
\(249\) | −34.6926 | −2.19856 | ||||||||
\(250\) | 10.3823 | 0.656633 | ||||||||
\(251\) | 19.2015 | 1.21199 | 0.605993 | − | 0.795470i | \(-0.292776\pi\) | ||||
0.605993 | + | 0.795470i | \(0.292776\pi\) | |||||||
\(252\) | 9.89616 | 0.623400 | ||||||||
\(253\) | 0.383509 | 0.0241110 | ||||||||
\(254\) | 9.72778 | 0.610375 | ||||||||
\(255\) | 10.0429 | 0.628909 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.60640 | 0.287340 | 0.143670 | − | 0.989626i | \(-0.454110\pi\) | ||||
0.143670 | + | 0.989626i | \(0.454110\pi\) | |||||||
\(258\) | 1.32541 | 0.0825166 | ||||||||
\(259\) | 0.753903 | 0.0468453 | ||||||||
\(260\) | 3.29047 | 0.204066 | ||||||||
\(261\) | −7.67875 | −0.475303 | ||||||||
\(262\) | 12.3774 | 0.764680 | ||||||||
\(263\) | 9.92093 | 0.611751 | 0.305875 | − | 0.952072i | \(-0.401051\pi\) | ||||
0.305875 | + | 0.952072i | \(0.401051\pi\) | |||||||
\(264\) | 4.95196 | 0.304772 | ||||||||
\(265\) | 12.5021 | 0.767997 | ||||||||
\(266\) | 7.68877 | 0.471429 | ||||||||
\(267\) | −58.1883 | −3.56107 | ||||||||
\(268\) | −6.41950 | −0.392134 | ||||||||
\(269\) | −1.01115 | −0.0616510 | −0.0308255 | − | 0.999525i | \(-0.509814\pi\) | ||||
−0.0308255 | + | 0.999525i | \(0.509814\pi\) | |||||||
\(270\) | 21.0435 | 1.28066 | ||||||||
\(271\) | −4.03444 | −0.245075 | −0.122537 | − | 0.992464i | \(-0.539103\pi\) | ||||
−0.122537 | + | 0.992464i | \(0.539103\pi\) | |||||||
\(272\) | 2.46441 | 0.149427 | ||||||||
\(273\) | 10.9269 | 0.661328 | ||||||||
\(274\) | −0.763945 | −0.0461516 | ||||||||
\(275\) | 5.20569 | 0.313915 | ||||||||
\(276\) | 0.864591 | 0.0520423 | ||||||||
\(277\) | −12.7012 | −0.763144 | −0.381572 | − | 0.924339i | \(-0.624617\pi\) | ||||
−0.381572 | + | 0.924339i | \(0.624617\pi\) | |||||||
\(278\) | 5.36732 | 0.321911 | ||||||||
\(279\) | 41.6078 | 2.49099 | ||||||||
\(280\) | −1.47847 | −0.0883554 | ||||||||
\(281\) | 15.4255 | 0.920206 | 0.460103 | − | 0.887866i | \(-0.347812\pi\) | ||||
0.460103 | + | 0.887866i | \(0.347812\pi\) | |||||||
\(282\) | 20.5395 | 1.22311 | ||||||||
\(283\) | −21.1494 | −1.25720 | −0.628600 | − | 0.777729i | \(-0.716372\pi\) | ||||
−0.628600 | + | 0.777729i | \(0.716372\pi\) | |||||||
\(284\) | 10.3122 | 0.611915 | ||||||||
\(285\) | 25.8481 | 1.53111 | ||||||||
\(286\) | 3.99843 | 0.236432 | ||||||||
\(287\) | 3.28450 | 0.193878 | ||||||||
\(288\) | 8.16382 | 0.481058 | ||||||||
\(289\) | −10.9267 | −0.642747 | ||||||||
\(290\) | 1.14719 | 0.0673654 | ||||||||
\(291\) | −14.5323 | −0.851897 | ||||||||
\(292\) | 10.5627 | 0.618137 | ||||||||
\(293\) | −0.915584 | −0.0534890 | −0.0267445 | − | 0.999642i | \(-0.508514\pi\) | ||||
−0.0267445 | + | 0.999642i | \(0.508514\pi\) | |||||||
\(294\) | 18.4789 | 1.07771 | ||||||||
\(295\) | −2.89468 | −0.168535 | ||||||||
\(296\) | 0.621932 | 0.0361490 | ||||||||
\(297\) | 25.5711 | 1.48378 | ||||||||
\(298\) | −18.6843 | −1.08235 | ||||||||
\(299\) | 0.698109 | 0.0403727 | ||||||||
\(300\) | 11.7358 | 0.677568 | ||||||||
\(301\) | −0.480859 | −0.0277163 | ||||||||
\(302\) | 16.3982 | 0.943611 | ||||||||
\(303\) | −16.3498 | −0.939272 | ||||||||
\(304\) | 6.34284 | 0.363787 | ||||||||
\(305\) | 0.933842 | 0.0534717 | ||||||||
\(306\) | 20.1190 | 1.15013 | ||||||||
\(307\) | −6.21151 | −0.354510 | −0.177255 | − | 0.984165i | \(-0.556722\pi\) | ||||
−0.177255 | + | 0.984165i | \(0.556722\pi\) | |||||||
\(308\) | −1.79657 | −0.102369 | ||||||||
\(309\) | 56.0047 | 3.18599 | ||||||||
\(310\) | −6.21613 | −0.353053 | ||||||||
\(311\) | 0.368999 | 0.0209240 | 0.0104620 | − | 0.999945i | \(-0.496670\pi\) | ||||
0.0104620 | + | 0.999945i | \(0.496670\pi\) | |||||||
\(312\) | 9.01416 | 0.510326 | ||||||||
\(313\) | 2.93116 | 0.165679 | 0.0828394 | − | 0.996563i | \(-0.473601\pi\) | ||||
0.0828394 | + | 0.996563i | \(0.473601\pi\) | |||||||
\(314\) | 11.5783 | 0.653399 | ||||||||
\(315\) | −12.0700 | −0.680065 | ||||||||
\(316\) | −8.44573 | −0.475110 | ||||||||
\(317\) | −1.58766 | −0.0891718 | −0.0445859 | − | 0.999006i | \(-0.514197\pi\) | ||||
−0.0445859 | + | 0.999006i | \(0.514197\pi\) | |||||||
\(318\) | 34.2492 | 1.92060 | ||||||||
\(319\) | 1.39402 | 0.0780499 | ||||||||
\(320\) | −1.21966 | −0.0681811 | ||||||||
\(321\) | −41.3223 | −2.30638 | ||||||||
\(322\) | −0.313673 | −0.0174803 | ||||||||
\(323\) | 15.6313 | 0.869751 | ||||||||
\(324\) | 33.1566 | 1.84203 | ||||||||
\(325\) | 9.47602 | 0.525635 | ||||||||
\(326\) | 2.77315 | 0.153590 | ||||||||
\(327\) | 50.9427 | 2.81714 | ||||||||
\(328\) | 2.70955 | 0.149610 | ||||||||
\(329\) | −7.45173 | −0.410827 | ||||||||
\(330\) | −6.03972 | −0.332476 | ||||||||
\(331\) | 11.4159 | 0.627474 | 0.313737 | − | 0.949510i | \(-0.398419\pi\) | ||||
0.313737 | + | 0.949510i | \(0.398419\pi\) | |||||||
\(332\) | 10.3832 | 0.569851 | ||||||||
\(333\) | 5.07734 | 0.278236 | ||||||||
\(334\) | 13.3818 | 0.732217 | ||||||||
\(335\) | 7.82962 | 0.427778 | ||||||||
\(336\) | −4.05023 | −0.220958 | ||||||||
\(337\) | −16.0047 | −0.871834 | −0.435917 | − | 0.899987i | \(-0.643576\pi\) | ||||
−0.435917 | + | 0.899987i | \(0.643576\pi\) | |||||||
\(338\) | −5.72158 | −0.311213 | ||||||||
\(339\) | −14.6779 | −0.797192 | ||||||||
\(340\) | −3.00574 | −0.163009 | ||||||||
\(341\) | −7.55357 | −0.409049 | ||||||||
\(342\) | 51.7818 | 2.80004 | ||||||||
\(343\) | −15.1895 | −0.820157 | ||||||||
\(344\) | −0.396684 | −0.0213878 | ||||||||
\(345\) | −1.05451 | −0.0567728 | ||||||||
\(346\) | −11.2336 | −0.603920 | ||||||||
\(347\) | 14.1373 | 0.758927 | 0.379464 | − | 0.925207i | \(-0.376109\pi\) | ||||
0.379464 | + | 0.925207i | \(0.376109\pi\) | |||||||
\(348\) | 3.14270 | 0.168467 | ||||||||
\(349\) | −16.1681 | −0.865456 | −0.432728 | − | 0.901524i | \(-0.642449\pi\) | ||||
−0.432728 | + | 0.901524i | \(0.642449\pi\) | |||||||
\(350\) | −4.25775 | −0.227586 | ||||||||
\(351\) | 46.5475 | 2.48452 | ||||||||
\(352\) | −1.48208 | −0.0789950 | ||||||||
\(353\) | −3.51525 | −0.187098 | −0.0935488 | − | 0.995615i | \(-0.529821\pi\) | ||||
−0.0935488 | + | 0.995615i | \(0.529821\pi\) | |||||||
\(354\) | −7.92990 | −0.421470 | ||||||||
\(355\) | −12.5774 | −0.667536 | ||||||||
\(356\) | 17.4152 | 0.923005 | ||||||||
\(357\) | −9.98141 | −0.528272 | ||||||||
\(358\) | 4.85748 | 0.256726 | ||||||||
\(359\) | −21.8168 | −1.15145 | −0.575723 | − | 0.817645i | \(-0.695279\pi\) | ||||
−0.575723 | + | 0.817645i | \(0.695279\pi\) | |||||||
\(360\) | −9.95710 | −0.524785 | ||||||||
\(361\) | 21.2316 | 1.11745 | ||||||||
\(362\) | 11.3297 | 0.595474 | ||||||||
\(363\) | 29.4143 | 1.54385 | ||||||||
\(364\) | −3.27033 | −0.171412 | ||||||||
\(365\) | −12.8829 | −0.674324 | ||||||||
\(366\) | 2.55824 | 0.133721 | ||||||||
\(367\) | 30.4989 | 1.59203 | 0.796015 | − | 0.605277i | \(-0.206938\pi\) | ||||
0.796015 | + | 0.605277i | \(0.206938\pi\) | |||||||
\(368\) | −0.258764 | −0.0134890 | ||||||||
\(369\) | 22.1203 | 1.15153 | ||||||||
\(370\) | −0.758546 | −0.0394349 | ||||||||
\(371\) | −12.4256 | −0.645104 | ||||||||
\(372\) | −17.0289 | −0.882909 | ||||||||
\(373\) | −11.8630 | −0.614242 | −0.307121 | − | 0.951670i | \(-0.599366\pi\) | ||||
−0.307121 | + | 0.951670i | \(0.599366\pi\) | |||||||
\(374\) | −3.65244 | −0.188863 | ||||||||
\(375\) | −34.6896 | −1.79136 | ||||||||
\(376\) | −6.14729 | −0.317022 | ||||||||
\(377\) | 2.53755 | 0.130691 | ||||||||
\(378\) | −20.9147 | −1.07573 | ||||||||
\(379\) | 33.6585 | 1.72892 | 0.864460 | − | 0.502702i | \(-0.167661\pi\) | ||||
0.864460 | + | 0.502702i | \(0.167661\pi\) | |||||||
\(380\) | −7.73611 | −0.396854 | ||||||||
\(381\) | −32.5028 | −1.66517 | ||||||||
\(382\) | 18.9452 | 0.969319 | ||||||||
\(383\) | 0.407761 | 0.0208356 | 0.0104178 | − | 0.999946i | \(-0.496684\pi\) | ||||
0.0104178 | + | 0.999946i | \(0.496684\pi\) | |||||||
\(384\) | −3.34123 | −0.170506 | ||||||||
\(385\) | 2.19121 | 0.111674 | ||||||||
\(386\) | −8.34283 | −0.424639 | ||||||||
\(387\) | −3.23846 | −0.164620 | ||||||||
\(388\) | 4.34938 | 0.220806 | ||||||||
\(389\) | −35.9046 | −1.82043 | −0.910217 | − | 0.414131i | \(-0.864085\pi\) | ||||
−0.910217 | + | 0.414131i | \(0.864085\pi\) | |||||||
\(390\) | −10.9942 | −0.556714 | ||||||||
\(391\) | −0.637700 | −0.0322499 | ||||||||
\(392\) | −5.53058 | −0.279336 | ||||||||
\(393\) | −41.3559 | −2.08613 | ||||||||
\(394\) | 11.5578 | 0.582272 | ||||||||
\(395\) | 10.3009 | 0.518296 | ||||||||
\(396\) | −12.0994 | −0.608019 | ||||||||
\(397\) | −6.57815 | −0.330148 | −0.165074 | − | 0.986281i | \(-0.552786\pi\) | ||||
−0.165074 | + | 0.986281i | \(0.552786\pi\) | |||||||
\(398\) | 18.1935 | 0.911957 | ||||||||
\(399\) | −25.6900 | −1.28611 | ||||||||
\(400\) | −3.51243 | −0.175621 | ||||||||
\(401\) | 5.15226 | 0.257292 | 0.128646 | − | 0.991691i | \(-0.458937\pi\) | ||||
0.128646 | + | 0.991691i | \(0.458937\pi\) | |||||||
\(402\) | 21.4490 | 1.06978 | ||||||||
\(403\) | −13.7499 | −0.684932 | ||||||||
\(404\) | 4.89335 | 0.243453 | ||||||||
\(405\) | −40.4397 | −2.00947 | ||||||||
\(406\) | −1.14017 | −0.0565857 | ||||||||
\(407\) | −0.921751 | −0.0456895 | ||||||||
\(408\) | −8.23415 | −0.407651 | ||||||||
\(409\) | 25.0138 | 1.23685 | 0.618425 | − | 0.785843i | \(-0.287771\pi\) | ||||
0.618425 | + | 0.785843i | \(0.287771\pi\) | |||||||
\(410\) | −3.30473 | −0.163209 | ||||||||
\(411\) | 2.55252 | 0.125906 | ||||||||
\(412\) | −16.7617 | −0.825789 | ||||||||
\(413\) | 2.87696 | 0.141566 | ||||||||
\(414\) | −2.11251 | −0.103824 | ||||||||
\(415\) | −12.6640 | −0.621649 | ||||||||
\(416\) | −2.69785 | −0.132273 | ||||||||
\(417\) | −17.9335 | −0.878206 | ||||||||
\(418\) | −9.40058 | −0.459798 | ||||||||
\(419\) | −2.10910 | −0.103036 | −0.0515181 | − | 0.998672i | \(-0.516406\pi\) | ||||
−0.0515181 | + | 0.998672i | \(0.516406\pi\) | |||||||
\(420\) | 4.93991 | 0.241043 | ||||||||
\(421\) | 28.4560 | 1.38686 | 0.693431 | − | 0.720523i | \(-0.256098\pi\) | ||||
0.693431 | + | 0.720523i | \(0.256098\pi\) | |||||||
\(422\) | 16.2521 | 0.791139 | ||||||||
\(423\) | −50.1854 | −2.44010 | ||||||||
\(424\) | −10.2505 | −0.497807 | ||||||||
\(425\) | −8.65605 | −0.419880 | ||||||||
\(426\) | −34.4553 | −1.66937 | ||||||||
\(427\) | −0.928127 | −0.0449152 | ||||||||
\(428\) | 12.3674 | 0.597800 | ||||||||
\(429\) | −13.3597 | −0.645011 | ||||||||
\(430\) | 0.483820 | 0.0233319 | ||||||||
\(431\) | −19.7425 | −0.950963 | −0.475482 | − | 0.879726i | \(-0.657726\pi\) | ||||
−0.475482 | + | 0.879726i | \(0.657726\pi\) | |||||||
\(432\) | −17.2535 | −0.830111 | ||||||||
\(433\) | 3.51768 | 0.169049 | 0.0845244 | − | 0.996421i | \(-0.473063\pi\) | ||||
0.0845244 | + | 0.996421i | \(0.473063\pi\) | |||||||
\(434\) | 6.17809 | 0.296558 | ||||||||
\(435\) | −3.83303 | −0.183780 | ||||||||
\(436\) | −15.2467 | −0.730183 | ||||||||
\(437\) | −1.64130 | −0.0785141 | ||||||||
\(438\) | −35.2925 | −1.68634 | ||||||||
\(439\) | −10.3595 | −0.494431 | −0.247215 | − | 0.968961i | \(-0.579516\pi\) | ||||
−0.247215 | + | 0.968961i | \(0.579516\pi\) | |||||||
\(440\) | 1.80763 | 0.0861755 | ||||||||
\(441\) | −45.1507 | −2.15003 | ||||||||
\(442\) | −6.64861 | −0.316242 | ||||||||
\(443\) | 21.0921 | 1.00212 | 0.501058 | − | 0.865413i | \(-0.332944\pi\) | ||||
0.501058 | + | 0.865413i | \(0.332944\pi\) | |||||||
\(444\) | −2.07802 | −0.0986183 | ||||||||
\(445\) | −21.2407 | −1.00690 | ||||||||
\(446\) | 25.1112 | 1.18905 | ||||||||
\(447\) | 62.4286 | 2.95277 | ||||||||
\(448\) | 1.21220 | 0.0572709 | ||||||||
\(449\) | 13.1074 | 0.618575 | 0.309288 | − | 0.950969i | \(-0.399909\pi\) | ||||
0.309288 | + | 0.950969i | \(0.399909\pi\) | |||||||
\(450\) | −28.6748 | −1.35174 | ||||||||
\(451\) | −4.01576 | −0.189095 | ||||||||
\(452\) | 4.39295 | 0.206627 | ||||||||
\(453\) | −54.7902 | −2.57427 | ||||||||
\(454\) | −7.01735 | −0.329341 | ||||||||
\(455\) | 3.98870 | 0.186993 | ||||||||
\(456\) | −21.1929 | −0.992448 | ||||||||
\(457\) | 22.4781 | 1.05148 | 0.525742 | − | 0.850644i | \(-0.323788\pi\) | ||||
0.525742 | + | 0.850644i | \(0.323788\pi\) | |||||||
\(458\) | 1.11907 | 0.0522906 | ||||||||
\(459\) | −42.5197 | −1.98465 | ||||||||
\(460\) | 0.315605 | 0.0147151 | ||||||||
\(461\) | 4.57015 | 0.212853 | 0.106427 | − | 0.994321i | \(-0.466059\pi\) | ||||
0.106427 | + | 0.994321i | \(0.466059\pi\) | |||||||
\(462\) | 6.00276 | 0.279273 | ||||||||
\(463\) | −22.5910 | −1.04989 | −0.524945 | − | 0.851136i | \(-0.675914\pi\) | ||||
−0.524945 | + | 0.851136i | \(0.675914\pi\) | |||||||
\(464\) | −0.940582 | −0.0436654 | ||||||||
\(465\) | 20.7695 | 0.963164 | ||||||||
\(466\) | 12.2990 | 0.569742 | ||||||||
\(467\) | 4.44727 | 0.205795 | 0.102898 | − | 0.994692i | \(-0.467189\pi\) | ||||
0.102898 | + | 0.994692i | \(0.467189\pi\) | |||||||
\(468\) | −22.0248 | −1.01810 | ||||||||
\(469\) | −7.78170 | −0.359326 | ||||||||
\(470\) | 7.49761 | 0.345839 | ||||||||
\(471\) | −38.6856 | −1.78254 | ||||||||
\(472\) | 2.37335 | 0.109242 | ||||||||
\(473\) | 0.587917 | 0.0270324 | ||||||||
\(474\) | 28.2191 | 1.29615 | ||||||||
\(475\) | −22.2788 | −1.02222 | ||||||||
\(476\) | 2.98735 | 0.136925 | ||||||||
\(477\) | −83.6830 | −3.83158 | ||||||||
\(478\) | 25.8095 | 1.18050 | ||||||||
\(479\) | 13.7272 | 0.627211 | 0.313606 | − | 0.949553i | \(-0.398463\pi\) | ||||
0.313606 | + | 0.949553i | \(0.398463\pi\) | |||||||
\(480\) | 4.07517 | 0.186005 | ||||||||
\(481\) | −1.67788 | −0.0765048 | ||||||||
\(482\) | 14.9085 | 0.679064 | ||||||||
\(483\) | 1.04805 | 0.0476881 | ||||||||
\(484\) | −8.80345 | −0.400157 | ||||||||
\(485\) | −5.30477 | −0.240877 | ||||||||
\(486\) | −59.0231 | −2.67734 | ||||||||
\(487\) | −33.0006 | −1.49540 | −0.747700 | − | 0.664037i | \(-0.768842\pi\) | ||||
−0.747700 | + | 0.664037i | \(0.768842\pi\) | |||||||
\(488\) | −0.765657 | −0.0346597 | ||||||||
\(489\) | −9.26572 | −0.419010 | ||||||||
\(490\) | 6.74543 | 0.304728 | ||||||||
\(491\) | −9.59044 | −0.432810 | −0.216405 | − | 0.976304i | \(-0.569433\pi\) | ||||
−0.216405 | + | 0.976304i | \(0.569433\pi\) | |||||||
\(492\) | −9.05322 | −0.408151 | ||||||||
\(493\) | −2.31798 | −0.104396 | ||||||||
\(494\) | −17.1121 | −0.769908 | ||||||||
\(495\) | 14.7572 | 0.663287 | ||||||||
\(496\) | 5.09661 | 0.228844 | ||||||||
\(497\) | 12.5004 | 0.560719 | ||||||||
\(498\) | −34.6926 | −1.55461 | ||||||||
\(499\) | −11.2467 | −0.503473 | −0.251736 | − | 0.967796i | \(-0.581002\pi\) | ||||
−0.251736 | + | 0.967796i | \(0.581002\pi\) | |||||||
\(500\) | 10.3823 | 0.464309 | ||||||||
\(501\) | −44.7115 | −1.99756 | ||||||||
\(502\) | 19.2015 | 0.857004 | ||||||||
\(503\) | −14.1676 | −0.631701 | −0.315851 | − | 0.948809i | \(-0.602290\pi\) | ||||
−0.315851 | + | 0.948809i | \(0.602290\pi\) | |||||||
\(504\) | 9.89616 | 0.440810 | ||||||||
\(505\) | −5.96823 | −0.265583 | ||||||||
\(506\) | 0.383509 | 0.0170490 | ||||||||
\(507\) | 19.1171 | 0.849021 | ||||||||
\(508\) | 9.72778 | 0.431600 | ||||||||
\(509\) | −28.3512 | −1.25664 | −0.628322 | − | 0.777954i | \(-0.716258\pi\) | ||||
−0.628322 | + | 0.777954i | \(0.716258\pi\) | |||||||
\(510\) | 10.0429 | 0.444706 | ||||||||
\(511\) | 12.8041 | 0.566420 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −109.436 | −4.83173 | ||||||||
\(514\) | 4.60640 | 0.203180 | ||||||||
\(515\) | 20.4436 | 0.900851 | ||||||||
\(516\) | 1.32541 | 0.0583480 | ||||||||
\(517\) | 9.11076 | 0.400691 | ||||||||
\(518\) | 0.753903 | 0.0331246 | ||||||||
\(519\) | 37.5340 | 1.64756 | ||||||||
\(520\) | 3.29047 | 0.144297 | ||||||||
\(521\) | 43.7602 | 1.91717 | 0.958584 | − | 0.284810i | \(-0.0919306\pi\) | ||||
0.958584 | + | 0.284810i | \(0.0919306\pi\) | |||||||
\(522\) | −7.67875 | −0.336090 | ||||||||
\(523\) | 30.9261 | 1.35231 | 0.676153 | − | 0.736761i | \(-0.263646\pi\) | ||||
0.676153 | + | 0.736761i | \(0.263646\pi\) | |||||||
\(524\) | 12.3774 | 0.540711 | ||||||||
\(525\) | 14.2261 | 0.620880 | ||||||||
\(526\) | 9.92093 | 0.432573 | ||||||||
\(527\) | 12.5601 | 0.547127 | ||||||||
\(528\) | 4.95196 | 0.215507 | ||||||||
\(529\) | −22.9330 | −0.997089 | ||||||||
\(530\) | 12.5021 | 0.543056 | ||||||||
\(531\) | 19.3756 | 0.840829 | ||||||||
\(532\) | 7.68877 | 0.333350 | ||||||||
\(533\) | −7.30996 | −0.316630 | ||||||||
\(534\) | −58.1883 | −2.51805 | ||||||||
\(535\) | −15.0840 | −0.652138 | ||||||||
\(536\) | −6.41950 | −0.277280 | ||||||||
\(537\) | −16.2300 | −0.700374 | ||||||||
\(538\) | −1.01115 | −0.0435938 | ||||||||
\(539\) | 8.19675 | 0.353059 | ||||||||
\(540\) | 21.0435 | 0.905566 | ||||||||
\(541\) | −13.4798 | −0.579544 | −0.289772 | − | 0.957096i | \(-0.593579\pi\) | ||||
−0.289772 | + | 0.957096i | \(0.593579\pi\) | |||||||
\(542\) | −4.03444 | −0.173294 | ||||||||
\(543\) | −37.8550 | −1.62451 | ||||||||
\(544\) | 2.46441 | 0.105661 | ||||||||
\(545\) | 18.5958 | 0.796555 | ||||||||
\(546\) | 10.9269 | 0.467629 | ||||||||
\(547\) | −1.43467 | −0.0613422 | −0.0306711 | − | 0.999530i | \(-0.509764\pi\) | ||||
−0.0306711 | + | 0.999530i | \(0.509764\pi\) | |||||||
\(548\) | −0.763945 | −0.0326341 | ||||||||
\(549\) | −6.25069 | −0.266773 | ||||||||
\(550\) | 5.20569 | 0.221971 | ||||||||
\(551\) | −5.96596 | −0.254159 | ||||||||
\(552\) | 0.864591 | 0.0367995 | ||||||||
\(553\) | −10.2379 | −0.435359 | ||||||||
\(554\) | −12.7012 | −0.539624 | ||||||||
\(555\) | 2.53448 | 0.107583 | ||||||||
\(556\) | 5.36732 | 0.227625 | ||||||||
\(557\) | −33.2740 | −1.40987 | −0.704933 | − | 0.709274i | \(-0.749023\pi\) | ||||
−0.704933 | + | 0.709274i | \(0.749023\pi\) | |||||||
\(558\) | 41.6078 | 1.76140 | ||||||||
\(559\) | 1.07020 | 0.0452645 | ||||||||
\(560\) | −1.47847 | −0.0624767 | ||||||||
\(561\) | 12.2037 | 0.515239 | ||||||||
\(562\) | 15.4255 | 0.650684 | ||||||||
\(563\) | −25.9575 | −1.09398 | −0.546990 | − | 0.837139i | \(-0.684226\pi\) | ||||
−0.546990 | + | 0.837139i | \(0.684226\pi\) | |||||||
\(564\) | 20.5395 | 0.864870 | ||||||||
\(565\) | −5.35791 | −0.225409 | ||||||||
\(566\) | −21.1494 | −0.888975 | ||||||||
\(567\) | 40.1923 | 1.68792 | ||||||||
\(568\) | 10.3122 | 0.432689 | ||||||||
\(569\) | −21.9936 | −0.922019 | −0.461009 | − | 0.887395i | \(-0.652513\pi\) | ||||
−0.461009 | + | 0.887395i | \(0.652513\pi\) | |||||||
\(570\) | 25.8481 | 1.08266 | ||||||||
\(571\) | 28.0715 | 1.17476 | 0.587378 | − | 0.809313i | \(-0.300160\pi\) | ||||
0.587378 | + | 0.809313i | \(0.300160\pi\) | |||||||
\(572\) | 3.99843 | 0.167183 | ||||||||
\(573\) | −63.3002 | −2.64440 | ||||||||
\(574\) | 3.28450 | 0.137093 | ||||||||
\(575\) | 0.908891 | 0.0379034 | ||||||||
\(576\) | 8.16382 | 0.340159 | ||||||||
\(577\) | −0.973000 | −0.0405065 | −0.0202533 | − | 0.999795i | \(-0.506447\pi\) | ||||
−0.0202533 | + | 0.999795i | \(0.506447\pi\) | |||||||
\(578\) | −10.9267 | −0.454491 | ||||||||
\(579\) | 27.8753 | 1.15846 | ||||||||
\(580\) | 1.14719 | 0.0476345 | ||||||||
\(581\) | 12.5865 | 0.522174 | ||||||||
\(582\) | −14.5323 | −0.602382 | ||||||||
\(583\) | 15.1920 | 0.629188 | ||||||||
\(584\) | 10.5627 | 0.437089 | ||||||||
\(585\) | 26.8628 | 1.11064 | ||||||||
\(586\) | −0.915584 | −0.0378224 | ||||||||
\(587\) | −5.07927 | −0.209644 | −0.104822 | − | 0.994491i | \(-0.533427\pi\) | ||||
−0.104822 | + | 0.994491i | \(0.533427\pi\) | |||||||
\(588\) | 18.4789 | 0.762059 | ||||||||
\(589\) | 32.3270 | 1.33201 | ||||||||
\(590\) | −2.89468 | −0.119172 | ||||||||
\(591\) | −38.6172 | −1.58850 | ||||||||
\(592\) | 0.621932 | 0.0255612 | ||||||||
\(593\) | −48.1262 | −1.97631 | −0.988154 | − | 0.153466i | \(-0.950956\pi\) | ||||
−0.988154 | + | 0.153466i | \(0.950956\pi\) | |||||||
\(594\) | 25.5711 | 1.04919 | ||||||||
\(595\) | −3.64355 | −0.149371 | ||||||||
\(596\) | −18.6843 | −0.765339 | ||||||||
\(597\) | −60.7887 | −2.48791 | ||||||||
\(598\) | 0.698109 | 0.0285478 | ||||||||
\(599\) | −1.07872 | −0.0440753 | −0.0220376 | − | 0.999757i | \(-0.507015\pi\) | ||||
−0.0220376 | + | 0.999757i | \(0.507015\pi\) | |||||||
\(600\) | 11.7358 | 0.479113 | ||||||||
\(601\) | −27.7795 | −1.13315 | −0.566575 | − | 0.824010i | \(-0.691732\pi\) | ||||
−0.566575 | + | 0.824010i | \(0.691732\pi\) | |||||||
\(602\) | −0.480859 | −0.0195984 | ||||||||
\(603\) | −52.4077 | −2.13421 | ||||||||
\(604\) | 16.3982 | 0.667234 | ||||||||
\(605\) | 10.7372 | 0.436530 | ||||||||
\(606\) | −16.3498 | −0.664165 | ||||||||
\(607\) | −46.5379 | −1.88891 | −0.944457 | − | 0.328635i | \(-0.893411\pi\) | ||||
−0.944457 | + | 0.328635i | \(0.893411\pi\) | |||||||
\(608\) | 6.34284 | 0.257236 | ||||||||
\(609\) | 3.80957 | 0.154372 | ||||||||
\(610\) | 0.933842 | 0.0378102 | ||||||||
\(611\) | 16.5845 | 0.670937 | ||||||||
\(612\) | 20.1190 | 0.813262 | ||||||||
\(613\) | 13.8563 | 0.559649 | 0.279825 | − | 0.960051i | \(-0.409724\pi\) | ||||
0.279825 | + | 0.960051i | \(0.409724\pi\) | |||||||
\(614\) | −6.21151 | −0.250676 | ||||||||
\(615\) | 11.0419 | 0.445251 | ||||||||
\(616\) | −1.79657 | −0.0723859 | ||||||||
\(617\) | 26.9736 | 1.08592 | 0.542958 | − | 0.839760i | \(-0.317304\pi\) | ||||
0.542958 | + | 0.839760i | \(0.317304\pi\) | |||||||
\(618\) | 56.0047 | 2.25284 | ||||||||
\(619\) | −38.6323 | −1.55276 | −0.776381 | − | 0.630264i | \(-0.782947\pi\) | ||||
−0.776381 | + | 0.630264i | \(0.782947\pi\) | |||||||
\(620\) | −6.21613 | −0.249646 | ||||||||
\(621\) | 4.46460 | 0.179158 | ||||||||
\(622\) | 0.368999 | 0.0147955 | ||||||||
\(623\) | 21.1107 | 0.845782 | ||||||||
\(624\) | 9.01416 | 0.360855 | ||||||||
\(625\) | 4.89928 | 0.195971 | ||||||||
\(626\) | 2.93116 | 0.117153 | ||||||||
\(627\) | 31.4095 | 1.25438 | ||||||||
\(628\) | 11.5783 | 0.462023 | ||||||||
\(629\) | 1.53269 | 0.0611124 | ||||||||
\(630\) | −12.0700 | −0.480879 | ||||||||
\(631\) | −7.43524 | −0.295992 | −0.147996 | − | 0.988988i | \(-0.547282\pi\) | ||||
−0.147996 | + | 0.988988i | \(0.547282\pi\) | |||||||
\(632\) | −8.44573 | −0.335953 | ||||||||
\(633\) | −54.3020 | −2.15831 | ||||||||
\(634\) | −1.58766 | −0.0630540 | ||||||||
\(635\) | −11.8646 | −0.470832 | ||||||||
\(636\) | 34.2492 | 1.35807 | ||||||||
\(637\) | 14.9207 | 0.591180 | ||||||||
\(638\) | 1.39402 | 0.0551896 | ||||||||
\(639\) | 84.1867 | 3.33038 | ||||||||
\(640\) | −1.21966 | −0.0482113 | ||||||||
\(641\) | 2.07523 | 0.0819667 | 0.0409834 | − | 0.999160i | \(-0.486951\pi\) | ||||
0.0409834 | + | 0.999160i | \(0.486951\pi\) | |||||||
\(642\) | −41.3223 | −1.63086 | ||||||||
\(643\) | −16.3846 | −0.646147 | −0.323073 | − | 0.946374i | \(-0.604716\pi\) | ||||
−0.323073 | + | 0.946374i | \(0.604716\pi\) | |||||||
\(644\) | −0.313673 | −0.0123605 | ||||||||
\(645\) | −1.61655 | −0.0636518 | ||||||||
\(646\) | 15.6313 | 0.615007 | ||||||||
\(647\) | −16.2916 | −0.640487 | −0.320244 | − | 0.947335i | \(-0.603765\pi\) | ||||
−0.320244 | + | 0.947335i | \(0.603765\pi\) | |||||||
\(648\) | 33.1566 | 1.30251 | ||||||||
\(649\) | −3.51749 | −0.138073 | ||||||||
\(650\) | 9.47602 | 0.371680 | ||||||||
\(651\) | −20.6424 | −0.809041 | ||||||||
\(652\) | 2.77315 | 0.108605 | ||||||||
\(653\) | 29.6877 | 1.16177 | 0.580885 | − | 0.813986i | \(-0.302707\pi\) | ||||
0.580885 | + | 0.813986i | \(0.302707\pi\) | |||||||
\(654\) | 50.9427 | 1.99202 | ||||||||
\(655\) | −15.0963 | −0.589860 | ||||||||
\(656\) | 2.70955 | 0.105790 | ||||||||
\(657\) | 86.2323 | 3.36424 | ||||||||
\(658\) | −7.45173 | −0.290498 | ||||||||
\(659\) | 34.2012 | 1.33229 | 0.666144 | − | 0.745823i | \(-0.267944\pi\) | ||||
0.666144 | + | 0.745823i | \(0.267944\pi\) | |||||||
\(660\) | −6.03972 | −0.235096 | ||||||||
\(661\) | 5.20043 | 0.202273 | 0.101137 | − | 0.994873i | \(-0.467752\pi\) | ||||
0.101137 | + | 0.994873i | \(0.467752\pi\) | |||||||
\(662\) | 11.4159 | 0.443691 | ||||||||
\(663\) | 22.2145 | 0.862741 | ||||||||
\(664\) | 10.3832 | 0.402946 | ||||||||
\(665\) | −9.37769 | −0.363651 | ||||||||
\(666\) | 5.07734 | 0.196743 | ||||||||
\(667\) | 0.243389 | 0.00942406 | ||||||||
\(668\) | 13.3818 | 0.517756 | ||||||||
\(669\) | −83.9022 | −3.24384 | ||||||||
\(670\) | 7.82962 | 0.302485 | ||||||||
\(671\) | 1.13476 | 0.0438071 | ||||||||
\(672\) | −4.05023 | −0.156241 | ||||||||
\(673\) | 45.3268 | 1.74722 | 0.873609 | − | 0.486628i | \(-0.161773\pi\) | ||||
0.873609 | + | 0.486628i | \(0.161773\pi\) | |||||||
\(674\) | −16.0047 | −0.616480 | ||||||||
\(675\) | 60.6018 | 2.33256 | ||||||||
\(676\) | −5.72158 | −0.220061 | ||||||||
\(677\) | 39.8869 | 1.53298 | 0.766489 | − | 0.642257i | \(-0.222002\pi\) | ||||
0.766489 | + | 0.642257i | \(0.222002\pi\) | |||||||
\(678\) | −14.6779 | −0.563700 | ||||||||
\(679\) | 5.27230 | 0.202332 | ||||||||
\(680\) | −3.00574 | −0.115265 | ||||||||
\(681\) | 23.4466 | 0.898476 | ||||||||
\(682\) | −7.55357 | −0.289241 | ||||||||
\(683\) | 23.1146 | 0.884455 | 0.442227 | − | 0.896903i | \(-0.354188\pi\) | ||||
0.442227 | + | 0.896903i | \(0.354188\pi\) | |||||||
\(684\) | 51.7818 | 1.97993 | ||||||||
\(685\) | 0.931754 | 0.0356005 | ||||||||
\(686\) | −15.1895 | −0.579939 | ||||||||
\(687\) | −3.73906 | −0.142654 | ||||||||
\(688\) | −0.396684 | −0.0151234 | ||||||||
\(689\) | 27.6543 | 1.05354 | ||||||||
\(690\) | −1.05451 | −0.0401444 | ||||||||
\(691\) | −26.1627 | −0.995275 | −0.497638 | − | 0.867385i | \(-0.665799\pi\) | ||||
−0.497638 | + | 0.867385i | \(0.665799\pi\) | |||||||
\(692\) | −11.2336 | −0.427036 | ||||||||
\(693\) | −14.6669 | −0.557149 | ||||||||
\(694\) | 14.1373 | 0.536643 | ||||||||
\(695\) | −6.54631 | −0.248316 | ||||||||
\(696\) | 3.14270 | 0.119124 | ||||||||
\(697\) | 6.67742 | 0.252925 | ||||||||
\(698\) | −16.1681 | −0.611970 | ||||||||
\(699\) | −41.0939 | −1.55431 | ||||||||
\(700\) | −4.25775 | −0.160928 | ||||||||
\(701\) | −9.08855 | −0.343270 | −0.171635 | − | 0.985161i | \(-0.554905\pi\) | ||||
−0.171635 | + | 0.985161i | \(0.554905\pi\) | |||||||
\(702\) | 46.5475 | 1.75682 | ||||||||
\(703\) | 3.94481 | 0.148781 | ||||||||
\(704\) | −1.48208 | −0.0558579 | ||||||||
\(705\) | −25.0512 | −0.943484 | ||||||||
\(706\) | −3.51525 | −0.132298 | ||||||||
\(707\) | 5.93170 | 0.223085 | ||||||||
\(708\) | −7.92990 | −0.298024 | ||||||||
\(709\) | −23.0240 | −0.864685 | −0.432343 | − | 0.901709i | \(-0.642313\pi\) | ||||
−0.432343 | + | 0.901709i | \(0.642313\pi\) | |||||||
\(710\) | −12.5774 | −0.472020 | ||||||||
\(711\) | −68.9495 | −2.58581 | ||||||||
\(712\) | 17.4152 | 0.652663 | ||||||||
\(713\) | −1.31882 | −0.0493902 | ||||||||
\(714\) | −9.98141 | −0.373545 | ||||||||
\(715\) | −4.87673 | −0.182379 | ||||||||
\(716\) | 4.85748 | 0.181533 | ||||||||
\(717\) | −86.2355 | −3.22052 | ||||||||
\(718\) | −21.8168 | −0.814195 | ||||||||
\(719\) | 19.4536 | 0.725497 | 0.362749 | − | 0.931887i | \(-0.381838\pi\) | ||||
0.362749 | + | 0.931887i | \(0.381838\pi\) | |||||||
\(720\) | −9.95710 | −0.371079 | ||||||||
\(721\) | −20.3185 | −0.756699 | ||||||||
\(722\) | 21.2316 | 0.790159 | ||||||||
\(723\) | −49.8128 | −1.85256 | ||||||||
\(724\) | 11.3297 | 0.421064 | ||||||||
\(725\) | 3.30373 | 0.122697 | ||||||||
\(726\) | 29.4143 | 1.09167 | ||||||||
\(727\) | 24.9028 | 0.923595 | 0.461797 | − | 0.886985i | \(-0.347205\pi\) | ||||
0.461797 | + | 0.886985i | \(0.347205\pi\) | |||||||
\(728\) | −3.27033 | −0.121207 | ||||||||
\(729\) | 97.7402 | 3.62001 | ||||||||
\(730\) | −12.8829 | −0.476819 | ||||||||
\(731\) | −0.977591 | −0.0361575 | ||||||||
\(732\) | 2.55824 | 0.0945552 | ||||||||
\(733\) | 31.1851 | 1.15185 | 0.575925 | − | 0.817503i | \(-0.304642\pi\) | ||||
0.575925 | + | 0.817503i | \(0.304642\pi\) | |||||||
\(734\) | 30.4989 | 1.12574 | ||||||||
\(735\) | −22.5380 | −0.831328 | ||||||||
\(736\) | −0.258764 | −0.00953818 | ||||||||
\(737\) | 9.51420 | 0.350460 | ||||||||
\(738\) | 22.1203 | 0.814258 | ||||||||
\(739\) | −44.6533 | −1.64260 | −0.821298 | − | 0.570499i | \(-0.806750\pi\) | ||||
−0.821298 | + | 0.570499i | \(0.806750\pi\) | |||||||
\(740\) | −0.758546 | −0.0278847 | ||||||||
\(741\) | 57.1753 | 2.10039 | ||||||||
\(742\) | −12.4256 | −0.456157 | ||||||||
\(743\) | 37.5848 | 1.37885 | 0.689426 | − | 0.724356i | \(-0.257863\pi\) | ||||
0.689426 | + | 0.724356i | \(0.257863\pi\) | |||||||
\(744\) | −17.0289 | −0.624311 | ||||||||
\(745\) | 22.7885 | 0.834907 | ||||||||
\(746\) | −11.8630 | −0.434335 | ||||||||
\(747\) | 84.7665 | 3.10144 | ||||||||
\(748\) | −3.65244 | −0.133547 | ||||||||
\(749\) | 14.9917 | 0.547785 | ||||||||
\(750\) | −34.6896 | −1.26668 | ||||||||
\(751\) | −19.1470 | −0.698685 | −0.349343 | − | 0.936995i | \(-0.613595\pi\) | ||||
−0.349343 | + | 0.936995i | \(0.613595\pi\) | |||||||
\(752\) | −6.14729 | −0.224169 | ||||||||
\(753\) | −64.1566 | −2.33799 | ||||||||
\(754\) | 2.53755 | 0.0924123 | ||||||||
\(755\) | −20.0003 | −0.727884 | ||||||||
\(756\) | −20.9147 | −0.760659 | ||||||||
\(757\) | −26.0241 | −0.945863 | −0.472932 | − | 0.881099i | \(-0.656804\pi\) | ||||
−0.472932 | + | 0.881099i | \(0.656804\pi\) | |||||||
\(758\) | 33.6585 | 1.22253 | ||||||||
\(759\) | −1.28139 | −0.0465116 | ||||||||
\(760\) | −7.73611 | −0.280618 | ||||||||
\(761\) | −7.89024 | −0.286021 | −0.143010 | − | 0.989721i | \(-0.545678\pi\) | ||||
−0.143010 | + | 0.989721i | \(0.545678\pi\) | |||||||
\(762\) | −32.5028 | −1.17745 | ||||||||
\(763\) | −18.4820 | −0.669092 | ||||||||
\(764\) | 18.9452 | 0.685412 | ||||||||
\(765\) | −24.5383 | −0.887185 | ||||||||
\(766\) | 0.407761 | 0.0147330 | ||||||||
\(767\) | −6.40295 | −0.231197 | ||||||||
\(768\) | −3.34123 | −0.120566 | ||||||||
\(769\) | −35.8978 | −1.29451 | −0.647254 | − | 0.762274i | \(-0.724083\pi\) | ||||
−0.647254 | + | 0.762274i | \(0.724083\pi\) | |||||||
\(770\) | 2.19121 | 0.0789656 | ||||||||
\(771\) | −15.3911 | −0.554296 | ||||||||
\(772\) | −8.34283 | −0.300265 | ||||||||
\(773\) | 24.1793 | 0.869668 | 0.434834 | − | 0.900511i | \(-0.356807\pi\) | ||||
0.434834 | + | 0.900511i | \(0.356807\pi\) | |||||||
\(774\) | −3.23846 | −0.116404 | ||||||||
\(775\) | −17.9015 | −0.643039 | ||||||||
\(776\) | 4.34938 | 0.156134 | ||||||||
\(777\) | −2.51897 | −0.0903674 | ||||||||
\(778\) | −35.9046 | −1.28724 | ||||||||
\(779\) | 17.1862 | 0.615760 | ||||||||
\(780\) | −10.9942 | −0.393656 | ||||||||
\(781\) | −15.2834 | −0.546884 | ||||||||
\(782\) | −0.637700 | −0.0228041 | ||||||||
\(783\) | 16.2284 | 0.579954 | ||||||||
\(784\) | −5.53058 | −0.197521 | ||||||||
\(785\) | −14.1216 | −0.504020 | ||||||||
\(786\) | −41.3559 | −1.47511 | ||||||||
\(787\) | 22.1478 | 0.789482 | 0.394741 | − | 0.918792i | \(-0.370834\pi\) | ||||
0.394741 | + | 0.918792i | \(0.370834\pi\) | |||||||
\(788\) | 11.5578 | 0.411728 | ||||||||
\(789\) | −33.1481 | −1.18010 | ||||||||
\(790\) | 10.3009 | 0.366491 | ||||||||
\(791\) | 5.32512 | 0.189340 | ||||||||
\(792\) | −12.0994 | −0.429934 | ||||||||
\(793\) | 2.06563 | 0.0733528 | ||||||||
\(794\) | −6.57815 | −0.233450 | ||||||||
\(795\) | −41.7724 | −1.48151 | ||||||||
\(796\) | 18.1935 | 0.644851 | ||||||||
\(797\) | −37.7070 | −1.33565 | −0.667824 | − | 0.744319i | \(-0.732774\pi\) | ||||
−0.667824 | + | 0.744319i | \(0.732774\pi\) | |||||||
\(798\) | −25.6900 | −0.909415 | ||||||||
\(799\) | −15.1494 | −0.535948 | ||||||||
\(800\) | −3.51243 | −0.124183 | ||||||||
\(801\) | 142.175 | 5.02350 | ||||||||
\(802\) | 5.15226 | 0.181933 | ||||||||
\(803\) | −15.6548 | −0.552445 | ||||||||
\(804\) | 21.4490 | 0.756449 | ||||||||
\(805\) | 0.382575 | 0.0134840 | ||||||||
\(806\) | −13.7499 | −0.484320 | ||||||||
\(807\) | 3.37849 | 0.118929 | ||||||||
\(808\) | 4.89335 | 0.172147 | ||||||||
\(809\) | 1.60179 | 0.0563161 | 0.0281580 | − | 0.999603i | \(-0.491036\pi\) | ||||
0.0281580 | + | 0.999603i | \(0.491036\pi\) | |||||||
\(810\) | −40.4397 | −1.42091 | ||||||||
\(811\) | 7.08262 | 0.248704 | 0.124352 | − | 0.992238i | \(-0.460315\pi\) | ||||
0.124352 | + | 0.992238i | \(0.460315\pi\) | |||||||
\(812\) | −1.14017 | −0.0400122 | ||||||||
\(813\) | 13.4800 | 0.472764 | ||||||||
\(814\) | −0.921751 | −0.0323074 | ||||||||
\(815\) | −3.38230 | −0.118477 | ||||||||
\(816\) | −8.23415 | −0.288253 | ||||||||
\(817\) | −2.51610 | −0.0880273 | ||||||||
\(818\) | 25.0138 | 0.874586 | ||||||||
\(819\) | −26.6984 | −0.932918 | ||||||||
\(820\) | −3.30473 | −0.115406 | ||||||||
\(821\) | −20.4638 | −0.714191 | −0.357095 | − | 0.934068i | \(-0.616233\pi\) | ||||
−0.357095 | + | 0.934068i | \(0.616233\pi\) | |||||||
\(822\) | 2.55252 | 0.0890292 | ||||||||
\(823\) | 13.8828 | 0.483924 | 0.241962 | − | 0.970286i | \(-0.422209\pi\) | ||||
0.241962 | + | 0.970286i | \(0.422209\pi\) | |||||||
\(824\) | −16.7617 | −0.583921 | ||||||||
\(825\) | −17.3934 | −0.605561 | ||||||||
\(826\) | 2.87696 | 0.100102 | ||||||||
\(827\) | 49.3448 | 1.71589 | 0.857943 | − | 0.513745i | \(-0.171742\pi\) | ||||
0.857943 | + | 0.513745i | \(0.171742\pi\) | |||||||
\(828\) | −2.11251 | −0.0734147 | ||||||||
\(829\) | 29.8677 | 1.03735 | 0.518675 | − | 0.854972i | \(-0.326426\pi\) | ||||
0.518675 | + | 0.854972i | \(0.326426\pi\) | |||||||
\(830\) | −12.6640 | −0.439573 | ||||||||
\(831\) | 42.4378 | 1.47215 | ||||||||
\(832\) | −2.69785 | −0.0935313 | ||||||||
\(833\) | −13.6296 | −0.472237 | ||||||||
\(834\) | −17.9335 | −0.620985 | ||||||||
\(835\) | −16.3212 | −0.564818 | ||||||||
\(836\) | −9.40058 | −0.325126 | ||||||||
\(837\) | −87.9344 | −3.03946 | ||||||||
\(838\) | −2.10910 | −0.0728575 | ||||||||
\(839\) | −36.6082 | −1.26386 | −0.631928 | − | 0.775027i | \(-0.717736\pi\) | ||||
−0.631928 | + | 0.775027i | \(0.717736\pi\) | |||||||
\(840\) | 4.93991 | 0.170443 | ||||||||
\(841\) | −28.1153 | −0.969493 | ||||||||
\(842\) | 28.4560 | 0.980660 | ||||||||
\(843\) | −51.5400 | −1.77513 | ||||||||
\(844\) | 16.2521 | 0.559420 | ||||||||
\(845\) | 6.97839 | 0.240064 | ||||||||
\(846\) | −50.1854 | −1.72541 | ||||||||
\(847\) | −10.6715 | −0.366677 | ||||||||
\(848\) | −10.2505 | −0.352002 | ||||||||
\(849\) | 70.6650 | 2.42522 | ||||||||
\(850\) | −8.65605 | −0.296900 | ||||||||
\(851\) | −0.160934 | −0.00551674 | ||||||||
\(852\) | −34.4553 | −1.18042 | ||||||||
\(853\) | 32.6349 | 1.11740 | 0.558699 | − | 0.829371i | \(-0.311301\pi\) | ||||
0.558699 | + | 0.829371i | \(0.311301\pi\) | |||||||
\(854\) | −0.928127 | −0.0317599 | ||||||||
\(855\) | −63.1563 | −2.15990 | ||||||||
\(856\) | 12.3674 | 0.422708 | ||||||||
\(857\) | 28.9487 | 0.988869 | 0.494435 | − | 0.869215i | \(-0.335375\pi\) | ||||
0.494435 | + | 0.869215i | \(0.335375\pi\) | |||||||
\(858\) | −13.3597 | −0.456092 | ||||||||
\(859\) | 33.4234 | 1.14039 | 0.570195 | − | 0.821509i | \(-0.306868\pi\) | ||||
0.570195 | + | 0.821509i | \(0.306868\pi\) | |||||||
\(860\) | 0.483820 | 0.0164981 | ||||||||
\(861\) | −10.9743 | −0.374003 | ||||||||
\(862\) | −19.7425 | −0.672432 | ||||||||
\(863\) | 2.24065 | 0.0762728 | 0.0381364 | − | 0.999273i | \(-0.487858\pi\) | ||||
0.0381364 | + | 0.999273i | \(0.487858\pi\) | |||||||
\(864\) | −17.2535 | −0.586977 | ||||||||
\(865\) | 13.7011 | 0.465853 | ||||||||
\(866\) | 3.51768 | 0.119536 | ||||||||
\(867\) | 36.5086 | 1.23990 | ||||||||
\(868\) | 6.17809 | 0.209698 | ||||||||
\(869\) | 12.5172 | 0.424618 | ||||||||
\(870\) | −3.83303 | −0.129952 | ||||||||
\(871\) | 17.3189 | 0.586828 | ||||||||
\(872\) | −15.2467 | −0.516317 | ||||||||
\(873\) | 35.5076 | 1.20175 | ||||||||
\(874\) | −1.64130 | −0.0555178 | ||||||||
\(875\) | 12.5854 | 0.425463 | ||||||||
\(876\) | −35.2925 | −1.19242 | ||||||||
\(877\) | 29.8748 | 1.00880 | 0.504400 | − | 0.863470i | \(-0.331714\pi\) | ||||
0.504400 | + | 0.863470i | \(0.331714\pi\) | |||||||
\(878\) | −10.3595 | −0.349615 | ||||||||
\(879\) | 3.05918 | 0.103184 | ||||||||
\(880\) | 1.80763 | 0.0609353 | ||||||||
\(881\) | 20.2016 | 0.680609 | 0.340305 | − | 0.940315i | \(-0.389470\pi\) | ||||
0.340305 | + | 0.940315i | \(0.389470\pi\) | |||||||
\(882\) | −45.1507 | −1.52030 | ||||||||
\(883\) | −46.3372 | −1.55937 | −0.779685 | − | 0.626172i | \(-0.784621\pi\) | ||||
−0.779685 | + | 0.626172i | \(0.784621\pi\) | |||||||
\(884\) | −6.64861 | −0.223617 | ||||||||
\(885\) | 9.67179 | 0.325114 | ||||||||
\(886\) | 21.0921 | 0.708604 | ||||||||
\(887\) | 53.6955 | 1.80292 | 0.901459 | − | 0.432864i | \(-0.142497\pi\) | ||||
0.901459 | + | 0.432864i | \(0.142497\pi\) | |||||||
\(888\) | −2.07802 | −0.0697337 | ||||||||
\(889\) | 11.7920 | 0.395490 | ||||||||
\(890\) | −21.2407 | −0.711989 | ||||||||
\(891\) | −49.1406 | −1.64627 | ||||||||
\(892\) | 25.1112 | 0.840784 | ||||||||
\(893\) | −38.9913 | −1.30479 | ||||||||
\(894\) | 62.4286 | 2.08792 | ||||||||
\(895\) | −5.92448 | −0.198033 | ||||||||
\(896\) | 1.21220 | 0.0404967 | ||||||||
\(897\) | −2.33254 | −0.0778813 | ||||||||
\(898\) | 13.1074 | 0.437399 | ||||||||
\(899\) | −4.79378 | −0.159881 | ||||||||
\(900\) | −28.6748 | −0.955828 | ||||||||
\(901\) | −25.2613 | −0.841576 | ||||||||
\(902\) | −4.01576 | −0.133710 | ||||||||
\(903\) | 1.60666 | 0.0534663 | ||||||||
\(904\) | 4.39295 | 0.146107 | ||||||||
\(905\) | −13.8183 | −0.459337 | ||||||||
\(906\) | −54.7902 | −1.82028 | ||||||||
\(907\) | −9.82273 | −0.326158 | −0.163079 | − | 0.986613i | \(-0.552143\pi\) | ||||
−0.163079 | + | 0.986613i | \(0.552143\pi\) | |||||||
\(908\) | −7.01735 | −0.232879 | ||||||||
\(909\) | 39.9484 | 1.32501 | ||||||||
\(910\) | 3.98870 | 0.132224 | ||||||||
\(911\) | 32.3563 | 1.07201 | 0.536007 | − | 0.844214i | \(-0.319932\pi\) | ||||
0.536007 | + | 0.844214i | \(0.319932\pi\) | |||||||
\(912\) | −21.1929 | −0.701767 | ||||||||
\(913\) | −15.3887 | −0.509291 | ||||||||
\(914\) | 22.4781 | 0.743511 | ||||||||
\(915\) | −3.12018 | −0.103150 | ||||||||
\(916\) | 1.11907 | 0.0369750 | ||||||||
\(917\) | 15.0039 | 0.495472 | ||||||||
\(918\) | −42.5197 | −1.40336 | ||||||||
\(919\) | 19.4731 | 0.642358 | 0.321179 | − | 0.947019i | \(-0.395921\pi\) | ||||
0.321179 | + | 0.947019i | \(0.395921\pi\) | |||||||
\(920\) | 0.315605 | 0.0104052 | ||||||||
\(921\) | 20.7541 | 0.683871 | ||||||||
\(922\) | 4.57015 | 0.150510 | ||||||||
\(923\) | −27.8207 | −0.915731 | ||||||||
\(924\) | 6.00276 | 0.197476 | ||||||||
\(925\) | −2.18449 | −0.0718256 | ||||||||
\(926\) | −22.5910 | −0.742385 | ||||||||
\(927\) | −136.839 | −4.49440 | ||||||||
\(928\) | −0.940582 | −0.0308761 | ||||||||
\(929\) | 34.8186 | 1.14236 | 0.571181 | − | 0.820824i | \(-0.306485\pi\) | ||||
0.571181 | + | 0.820824i | \(0.306485\pi\) | |||||||
\(930\) | 20.7695 | 0.681060 | ||||||||
\(931\) | −35.0796 | −1.14969 | ||||||||
\(932\) | 12.2990 | 0.402868 | ||||||||
\(933\) | −1.23291 | −0.0403637 | ||||||||
\(934\) | 4.44727 | 0.145519 | ||||||||
\(935\) | 4.45474 | 0.145686 | ||||||||
\(936\) | −22.0248 | −0.719903 | ||||||||
\(937\) | 31.6423 | 1.03371 | 0.516854 | − | 0.856073i | \(-0.327103\pi\) | ||||
0.516854 | + | 0.856073i | \(0.327103\pi\) | |||||||
\(938\) | −7.78170 | −0.254082 | ||||||||
\(939\) | −9.79367 | −0.319604 | ||||||||
\(940\) | 7.49761 | 0.244545 | ||||||||
\(941\) | −21.2057 | −0.691287 | −0.345643 | − | 0.938366i | \(-0.612339\pi\) | ||||
−0.345643 | + | 0.938366i | \(0.612339\pi\) | |||||||
\(942\) | −38.6856 | −1.26045 | ||||||||
\(943\) | −0.701134 | −0.0228321 | ||||||||
\(944\) | 2.37335 | 0.0772459 | ||||||||
\(945\) | 25.5088 | 0.829802 | ||||||||
\(946\) | 0.587917 | 0.0191148 | ||||||||
\(947\) | 7.74830 | 0.251786 | 0.125893 | − | 0.992044i | \(-0.459820\pi\) | ||||
0.125893 | + | 0.992044i | \(0.459820\pi\) | |||||||
\(948\) | 28.2191 | 0.916515 | ||||||||
\(949\) | −28.4967 | −0.925042 | ||||||||
\(950\) | −22.2788 | −0.722819 | ||||||||
\(951\) | 5.30474 | 0.172018 | ||||||||
\(952\) | 2.98735 | 0.0968204 | ||||||||
\(953\) | 18.8056 | 0.609174 | 0.304587 | − | 0.952485i | \(-0.401482\pi\) | ||||
0.304587 | + | 0.952485i | \(0.401482\pi\) | |||||||
\(954\) | −83.6830 | −2.70934 | ||||||||
\(955\) | −23.1067 | −0.747715 | ||||||||
\(956\) | 25.8095 | 0.834739 | ||||||||
\(957\) | −4.65773 | −0.150563 | ||||||||
\(958\) | 13.7272 | 0.443505 | ||||||||
\(959\) | −0.926052 | −0.0299038 | ||||||||
\(960\) | 4.07517 | 0.131526 | ||||||||
\(961\) | −5.02460 | −0.162084 | ||||||||
\(962\) | −1.67788 | −0.0540971 | ||||||||
\(963\) | 100.965 | 3.25355 | ||||||||
\(964\) | 14.9085 | 0.480171 | ||||||||
\(965\) | 10.1754 | 0.327559 | ||||||||
\(966\) | 1.04805 | 0.0337206 | ||||||||
\(967\) | 2.39308 | 0.0769561 | 0.0384781 | − | 0.999259i | \(-0.487749\pi\) | ||||
0.0384781 | + | 0.999259i | \(0.487749\pi\) | |||||||
\(968\) | −8.80345 | −0.282953 | ||||||||
\(969\) | −52.2279 | −1.67780 | ||||||||
\(970\) | −5.30477 | −0.170326 | ||||||||
\(971\) | 41.4345 | 1.32970 | 0.664849 | − | 0.746978i | \(-0.268496\pi\) | ||||
0.664849 | + | 0.746978i | \(0.268496\pi\) | |||||||
\(972\) | −59.0231 | −1.89317 | ||||||||
\(973\) | 6.50625 | 0.208581 | ||||||||
\(974\) | −33.0006 | −1.05741 | ||||||||
\(975\) | −31.6616 | −1.01398 | ||||||||
\(976\) | −0.765657 | −0.0245081 | ||||||||
\(977\) | 15.3409 | 0.490799 | 0.245399 | − | 0.969422i | \(-0.421081\pi\) | ||||
0.245399 | + | 0.969422i | \(0.421081\pi\) | |||||||
\(978\) | −9.26572 | −0.296285 | ||||||||
\(979\) | −25.8107 | −0.824915 | ||||||||
\(980\) | 6.74543 | 0.215475 | ||||||||
\(981\) | −124.471 | −3.97406 | ||||||||
\(982\) | −9.59044 | −0.306043 | ||||||||
\(983\) | −42.7699 | −1.36415 | −0.682074 | − | 0.731283i | \(-0.738922\pi\) | ||||
−0.682074 | + | 0.731283i | \(0.738922\pi\) | |||||||
\(984\) | −9.05322 | −0.288606 | ||||||||
\(985\) | −14.0966 | −0.449153 | ||||||||
\(986\) | −2.31798 | −0.0738194 | ||||||||
\(987\) | 24.8979 | 0.792510 | ||||||||
\(988\) | −17.1121 | −0.544407 | ||||||||
\(989\) | 0.102648 | 0.00326401 | ||||||||
\(990\) | 14.7572 | 0.469014 | ||||||||
\(991\) | 34.3522 | 1.09123 | 0.545617 | − | 0.838034i | \(-0.316295\pi\) | ||||
0.545617 | + | 0.838034i | \(0.316295\pi\) | |||||||
\(992\) | 5.09661 | 0.161817 | ||||||||
\(993\) | −38.1431 | −1.21043 | ||||||||
\(994\) | 12.5004 | 0.396488 | ||||||||
\(995\) | −22.1899 | −0.703467 | ||||||||
\(996\) | −34.6926 | −1.09928 | ||||||||
\(997\) | 28.1056 | 0.890112 | 0.445056 | − | 0.895503i | \(-0.353184\pi\) | ||||
0.445056 | + | 0.895503i | \(0.353184\pi\) | |||||||
\(998\) | −11.2467 | −0.356009 | ||||||||
\(999\) | −10.7305 | −0.339498 |
(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 | 4006.2.a.i.1.1 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.i.1.1 | ✓ | 46 | 1.1 | even | 1 | trivial |