Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, 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("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.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: | \(64.2156933055\) |
Analytic rank: | \(1\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-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 | ||||||||
\(3\) | −1.55257 | −0.896376 | −0.448188 | − | 0.893939i | \(-0.647930\pi\) | ||||
−0.448188 | + | 0.893939i | \(0.647930\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.63171 | 1.17694 | 0.588468 | − | 0.808521i | \(-0.299731\pi\) | ||||
0.588468 | + | 0.808521i | \(0.299731\pi\) | |||||||
\(6\) | −1.55257 | −0.633833 | ||||||||
\(7\) | −0.882040 | −0.333380 | −0.166690 | − | 0.986009i | \(-0.553308\pi\) | ||||
−0.166690 | + | 0.986009i | \(0.553308\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.589531 | −0.196510 | ||||||||
\(10\) | 2.63171 | 0.832219 | ||||||||
\(11\) | 5.91348 | 1.78298 | 0.891491 | − | 0.453039i | \(-0.149660\pi\) | ||||
0.891491 | + | 0.453039i | \(0.149660\pi\) | |||||||
\(12\) | −1.55257 | −0.448188 | ||||||||
\(13\) | −0.542391 | −0.150432 | −0.0752160 | − | 0.997167i | \(-0.523965\pi\) | ||||
−0.0752160 | + | 0.997167i | \(0.523965\pi\) | |||||||
\(14\) | −0.882040 | −0.235735 | ||||||||
\(15\) | −4.08591 | −1.05498 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.94551 | −1.19946 | −0.599731 | − | 0.800202i | \(-0.704726\pi\) | ||||
−0.599731 | + | 0.800202i | \(0.704726\pi\) | |||||||
\(18\) | −0.589531 | −0.138954 | ||||||||
\(19\) | −6.50514 | −1.49238 | −0.746191 | − | 0.665732i | \(-0.768119\pi\) | ||||
−0.746191 | + | 0.665732i | \(0.768119\pi\) | |||||||
\(20\) | 2.63171 | 0.588468 | ||||||||
\(21\) | 1.36943 | 0.298834 | ||||||||
\(22\) | 5.91348 | 1.26076 | ||||||||
\(23\) | −5.08202 | −1.05968 | −0.529838 | − | 0.848099i | \(-0.677747\pi\) | ||||
−0.529838 | + | 0.848099i | \(0.677747\pi\) | |||||||
\(24\) | −1.55257 | −0.316917 | ||||||||
\(25\) | 1.92589 | 0.385178 | ||||||||
\(26\) | −0.542391 | −0.106372 | ||||||||
\(27\) | 5.57299 | 1.07252 | ||||||||
\(28\) | −0.882040 | −0.166690 | ||||||||
\(29\) | 9.49183 | 1.76259 | 0.881295 | − | 0.472567i | \(-0.156673\pi\) | ||||
0.881295 | + | 0.472567i | \(0.156673\pi\) | |||||||
\(30\) | −4.08591 | −0.745981 | ||||||||
\(31\) | −1.26198 | −0.226658 | −0.113329 | − | 0.993558i | \(-0.536151\pi\) | ||||
−0.113329 | + | 0.993558i | \(0.536151\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −9.18108 | −1.59822 | ||||||||
\(34\) | −4.94551 | −0.848147 | ||||||||
\(35\) | −2.32127 | −0.392367 | ||||||||
\(36\) | −0.589531 | −0.0982552 | ||||||||
\(37\) | −9.40266 | −1.54579 | −0.772894 | − | 0.634535i | \(-0.781191\pi\) | ||||
−0.772894 | + | 0.634535i | \(0.781191\pi\) | |||||||
\(38\) | −6.50514 | −1.05527 | ||||||||
\(39\) | 0.842099 | 0.134844 | ||||||||
\(40\) | 2.63171 | 0.416110 | ||||||||
\(41\) | −1.75849 | −0.274630 | −0.137315 | − | 0.990527i | \(-0.543847\pi\) | ||||
−0.137315 | + | 0.990527i | \(0.543847\pi\) | |||||||
\(42\) | 1.36943 | 0.211307 | ||||||||
\(43\) | −7.78177 | −1.18671 | −0.593354 | − | 0.804942i | \(-0.702197\pi\) | ||||
−0.593354 | + | 0.804942i | \(0.702197\pi\) | |||||||
\(44\) | 5.91348 | 0.891491 | ||||||||
\(45\) | −1.55147 | −0.231280 | ||||||||
\(46\) | −5.08202 | −0.749303 | ||||||||
\(47\) | −1.60840 | −0.234609 | −0.117305 | − | 0.993096i | \(-0.537425\pi\) | ||||
−0.117305 | + | 0.993096i | \(0.537425\pi\) | |||||||
\(48\) | −1.55257 | −0.224094 | ||||||||
\(49\) | −6.22201 | −0.888858 | ||||||||
\(50\) | 1.92589 | 0.272362 | ||||||||
\(51\) | 7.67824 | 1.07517 | ||||||||
\(52\) | −0.542391 | −0.0752160 | ||||||||
\(53\) | −6.48916 | −0.891354 | −0.445677 | − | 0.895194i | \(-0.647037\pi\) | ||||
−0.445677 | + | 0.895194i | \(0.647037\pi\) | |||||||
\(54\) | 5.57299 | 0.758388 | ||||||||
\(55\) | 15.5626 | 2.09846 | ||||||||
\(56\) | −0.882040 | −0.117868 | ||||||||
\(57\) | 10.0997 | 1.33773 | ||||||||
\(58\) | 9.49183 | 1.24634 | ||||||||
\(59\) | 3.01774 | 0.392876 | 0.196438 | − | 0.980516i | \(-0.437063\pi\) | ||||
0.196438 | + | 0.980516i | \(0.437063\pi\) | |||||||
\(60\) | −4.08591 | −0.527488 | ||||||||
\(61\) | 6.91687 | 0.885615 | 0.442807 | − | 0.896617i | \(-0.353983\pi\) | ||||
0.442807 | + | 0.896617i | \(0.353983\pi\) | |||||||
\(62\) | −1.26198 | −0.160272 | ||||||||
\(63\) | 0.519990 | 0.0655126 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.42741 | −0.177049 | ||||||||
\(66\) | −9.18108 | −1.13011 | ||||||||
\(67\) | −6.48951 | −0.792820 | −0.396410 | − | 0.918074i | \(-0.629744\pi\) | ||||
−0.396410 | + | 0.918074i | \(0.629744\pi\) | |||||||
\(68\) | −4.94551 | −0.599731 | ||||||||
\(69\) | 7.89019 | 0.949867 | ||||||||
\(70\) | −2.32127 | −0.277445 | ||||||||
\(71\) | −3.38169 | −0.401332 | −0.200666 | − | 0.979660i | \(-0.564311\pi\) | ||||
−0.200666 | + | 0.979660i | \(0.564311\pi\) | |||||||
\(72\) | −0.589531 | −0.0694769 | ||||||||
\(73\) | −11.2083 | −1.31183 | −0.655916 | − | 0.754834i | \(-0.727717\pi\) | ||||
−0.655916 | + | 0.754834i | \(0.727717\pi\) | |||||||
\(74\) | −9.40266 | −1.09304 | ||||||||
\(75\) | −2.99008 | −0.345264 | ||||||||
\(76\) | −6.50514 | −0.746191 | ||||||||
\(77\) | −5.21593 | −0.594410 | ||||||||
\(78\) | 0.842099 | 0.0953489 | ||||||||
\(79\) | 10.2201 | 1.14985 | 0.574927 | − | 0.818205i | \(-0.305030\pi\) | ||||
0.574927 | + | 0.818205i | \(0.305030\pi\) | |||||||
\(80\) | 2.63171 | 0.294234 | ||||||||
\(81\) | −6.88386 | −0.764873 | ||||||||
\(82\) | −1.75849 | −0.194193 | ||||||||
\(83\) | −7.97223 | −0.875066 | −0.437533 | − | 0.899202i | \(-0.644148\pi\) | ||||
−0.437533 | + | 0.899202i | \(0.644148\pi\) | |||||||
\(84\) | 1.36943 | 0.149417 | ||||||||
\(85\) | −13.0151 | −1.41169 | ||||||||
\(86\) | −7.78177 | −0.839129 | ||||||||
\(87\) | −14.7367 | −1.57994 | ||||||||
\(88\) | 5.91348 | 0.630379 | ||||||||
\(89\) | −7.41763 | −0.786267 | −0.393134 | − | 0.919481i | \(-0.628609\pi\) | ||||
−0.393134 | + | 0.919481i | \(0.628609\pi\) | |||||||
\(90\) | −1.55147 | −0.163540 | ||||||||
\(91\) | 0.478410 | 0.0501510 | ||||||||
\(92\) | −5.08202 | −0.529838 | ||||||||
\(93\) | 1.95931 | 0.203171 | ||||||||
\(94\) | −1.60840 | −0.165894 | ||||||||
\(95\) | −17.1196 | −1.75644 | ||||||||
\(96\) | −1.55257 | −0.158458 | ||||||||
\(97\) | 1.29495 | 0.131482 | 0.0657410 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657410 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(98\) | −6.22201 | −0.628517 | ||||||||
\(99\) | −3.48618 | −0.350375 | ||||||||
\(100\) | 1.92589 | 0.192589 | ||||||||
\(101\) | 8.20757 | 0.816684 | 0.408342 | − | 0.912829i | \(-0.366107\pi\) | ||||
0.408342 | + | 0.912829i | \(0.366107\pi\) | |||||||
\(102\) | 7.67824 | 0.760259 | ||||||||
\(103\) | 0.559554 | 0.0551345 | 0.0275673 | − | 0.999620i | \(-0.491224\pi\) | ||||
0.0275673 | + | 0.999620i | \(0.491224\pi\) | |||||||
\(104\) | −0.542391 | −0.0531858 | ||||||||
\(105\) | 3.60393 | 0.351708 | ||||||||
\(106\) | −6.48916 | −0.630283 | ||||||||
\(107\) | 0.00863711 | 0.000834981 0 | 0.000417490 | − | 1.00000i | \(-0.499867\pi\) | ||||
0.000417490 | 1.00000i | \(0.499867\pi\) | ||||||||
\(108\) | 5.57299 | 0.536261 | ||||||||
\(109\) | −7.33424 | −0.702493 | −0.351247 | − | 0.936283i | \(-0.614242\pi\) | ||||
−0.351247 | + | 0.936283i | \(0.614242\pi\) | |||||||
\(110\) | 15.5626 | 1.48383 | ||||||||
\(111\) | 14.5983 | 1.38561 | ||||||||
\(112\) | −0.882040 | −0.0833450 | ||||||||
\(113\) | −13.1405 | −1.23615 | −0.618076 | − | 0.786118i | \(-0.712088\pi\) | ||||
−0.618076 | + | 0.786118i | \(0.712088\pi\) | |||||||
\(114\) | 10.0997 | 0.945921 | ||||||||
\(115\) | −13.3744 | −1.24717 | ||||||||
\(116\) | 9.49183 | 0.881295 | ||||||||
\(117\) | 0.319756 | 0.0295615 | ||||||||
\(118\) | 3.01774 | 0.277805 | ||||||||
\(119\) | 4.36214 | 0.399876 | ||||||||
\(120\) | −4.08591 | −0.372991 | ||||||||
\(121\) | 23.9693 | 2.17902 | ||||||||
\(122\) | 6.91687 | 0.626224 | ||||||||
\(123\) | 2.73018 | 0.246172 | ||||||||
\(124\) | −1.26198 | −0.113329 | ||||||||
\(125\) | −8.09016 | −0.723606 | ||||||||
\(126\) | 0.519990 | 0.0463244 | ||||||||
\(127\) | −5.95706 | −0.528604 | −0.264302 | − | 0.964440i | \(-0.585141\pi\) | ||||
−0.264302 | + | 0.964440i | \(0.585141\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 12.0817 | 1.06374 | ||||||||
\(130\) | −1.42741 | −0.125193 | ||||||||
\(131\) | −2.48326 | −0.216963 | −0.108482 | − | 0.994098i | \(-0.534599\pi\) | ||||
−0.108482 | + | 0.994098i | \(0.534599\pi\) | |||||||
\(132\) | −9.18108 | −0.799111 | ||||||||
\(133\) | 5.73779 | 0.497530 | ||||||||
\(134\) | −6.48951 | −0.560608 | ||||||||
\(135\) | 14.6665 | 1.26229 | ||||||||
\(136\) | −4.94551 | −0.424074 | ||||||||
\(137\) | −6.15230 | −0.525627 | −0.262813 | − | 0.964847i | \(-0.584650\pi\) | ||||
−0.262813 | + | 0.964847i | \(0.584650\pi\) | |||||||
\(138\) | 7.89019 | 0.671657 | ||||||||
\(139\) | −0.266066 | −0.0225674 | −0.0112837 | − | 0.999936i | \(-0.503592\pi\) | ||||
−0.0112837 | + | 0.999936i | \(0.503592\pi\) | |||||||
\(140\) | −2.32127 | −0.196183 | ||||||||
\(141\) | 2.49715 | 0.210298 | ||||||||
\(142\) | −3.38169 | −0.283785 | ||||||||
\(143\) | −3.20742 | −0.268218 | ||||||||
\(144\) | −0.589531 | −0.0491276 | ||||||||
\(145\) | 24.9797 | 2.07445 | ||||||||
\(146\) | −11.2083 | −0.927605 | ||||||||
\(147\) | 9.66009 | 0.796751 | ||||||||
\(148\) | −9.40266 | −0.772894 | ||||||||
\(149\) | 21.3333 | 1.74769 | 0.873846 | − | 0.486203i | \(-0.161618\pi\) | ||||
0.873846 | + | 0.486203i | \(0.161618\pi\) | |||||||
\(150\) | −2.99008 | −0.244139 | ||||||||
\(151\) | 15.0180 | 1.22215 | 0.611075 | − | 0.791573i | \(-0.290737\pi\) | ||||
0.611075 | + | 0.791573i | \(0.290737\pi\) | |||||||
\(152\) | −6.50514 | −0.527636 | ||||||||
\(153\) | 2.91553 | 0.235707 | ||||||||
\(154\) | −5.21593 | −0.420311 | ||||||||
\(155\) | −3.32116 | −0.266762 | ||||||||
\(156\) | 0.842099 | 0.0674218 | ||||||||
\(157\) | 10.0160 | 0.799361 | 0.399681 | − | 0.916655i | \(-0.369121\pi\) | ||||
0.399681 | + | 0.916655i | \(0.369121\pi\) | |||||||
\(158\) | 10.2201 | 0.813070 | ||||||||
\(159\) | 10.0749 | 0.798988 | ||||||||
\(160\) | 2.63171 | 0.208055 | ||||||||
\(161\) | 4.48255 | 0.353274 | ||||||||
\(162\) | −6.88386 | −0.540847 | ||||||||
\(163\) | 10.0724 | 0.788929 | 0.394464 | − | 0.918911i | \(-0.370930\pi\) | ||||
0.394464 | + | 0.918911i | \(0.370930\pi\) | |||||||
\(164\) | −1.75849 | −0.137315 | ||||||||
\(165\) | −24.1619 | −1.88100 | ||||||||
\(166\) | −7.97223 | −0.618765 | ||||||||
\(167\) | 19.4175 | 1.50257 | 0.751284 | − | 0.659979i | \(-0.229435\pi\) | ||||
0.751284 | + | 0.659979i | \(0.229435\pi\) | |||||||
\(168\) | 1.36943 | 0.105654 | ||||||||
\(169\) | −12.7058 | −0.977370 | ||||||||
\(170\) | −13.0151 | −0.998215 | ||||||||
\(171\) | 3.83498 | 0.293268 | ||||||||
\(172\) | −7.78177 | −0.593354 | ||||||||
\(173\) | −0.00547070 | −0.000415929 0 | −0.000207965 | − | 1.00000i | \(-0.500066\pi\) | ||||
−0.000207965 | 1.00000i | \(0.500066\pi\) | ||||||||
\(174\) | −14.7367 | −1.11719 | ||||||||
\(175\) | −1.69871 | −0.128411 | ||||||||
\(176\) | 5.91348 | 0.445745 | ||||||||
\(177\) | −4.68524 | −0.352165 | ||||||||
\(178\) | −7.41763 | −0.555975 | ||||||||
\(179\) | −21.0505 | −1.57339 | −0.786694 | − | 0.617343i | \(-0.788209\pi\) | ||||
−0.786694 | + | 0.617343i | \(0.788209\pi\) | |||||||
\(180\) | −1.55147 | −0.115640 | ||||||||
\(181\) | 15.3500 | 1.14096 | 0.570478 | − | 0.821313i | \(-0.306758\pi\) | ||||
0.570478 | + | 0.821313i | \(0.306758\pi\) | |||||||
\(182\) | 0.478410 | 0.0354621 | ||||||||
\(183\) | −10.7389 | −0.793844 | ||||||||
\(184\) | −5.08202 | −0.374652 | ||||||||
\(185\) | −24.7451 | −1.81929 | ||||||||
\(186\) | 1.95931 | 0.143664 | ||||||||
\(187\) | −29.2452 | −2.13862 | ||||||||
\(188\) | −1.60840 | −0.117305 | ||||||||
\(189\) | −4.91560 | −0.357558 | ||||||||
\(190\) | −17.1196 | −1.24199 | ||||||||
\(191\) | −0.740802 | −0.0536026 | −0.0268013 | − | 0.999641i | \(-0.508532\pi\) | ||||
−0.0268013 | + | 0.999641i | \(0.508532\pi\) | |||||||
\(192\) | −1.55257 | −0.112047 | ||||||||
\(193\) | −6.69960 | −0.482247 | −0.241124 | − | 0.970494i | \(-0.577516\pi\) | ||||
−0.241124 | + | 0.970494i | \(0.577516\pi\) | |||||||
\(194\) | 1.29495 | 0.0929719 | ||||||||
\(195\) | 2.21616 | 0.158702 | ||||||||
\(196\) | −6.22201 | −0.444429 | ||||||||
\(197\) | −14.5701 | −1.03807 | −0.519037 | − | 0.854752i | \(-0.673709\pi\) | ||||
−0.519037 | + | 0.854752i | \(0.673709\pi\) | |||||||
\(198\) | −3.48618 | −0.247752 | ||||||||
\(199\) | 18.2544 | 1.29402 | 0.647010 | − | 0.762481i | \(-0.276019\pi\) | ||||
0.647010 | + | 0.762481i | \(0.276019\pi\) | |||||||
\(200\) | 1.92589 | 0.136181 | ||||||||
\(201\) | 10.0754 | 0.710664 | ||||||||
\(202\) | 8.20757 | 0.577483 | ||||||||
\(203\) | −8.37218 | −0.587612 | ||||||||
\(204\) | 7.67824 | 0.537584 | ||||||||
\(205\) | −4.62783 | −0.323222 | ||||||||
\(206\) | 0.559554 | 0.0389860 | ||||||||
\(207\) | 2.99601 | 0.208237 | ||||||||
\(208\) | −0.542391 | −0.0376080 | ||||||||
\(209\) | −38.4680 | −2.66089 | ||||||||
\(210\) | 3.60393 | 0.248695 | ||||||||
\(211\) | 2.29284 | 0.157846 | 0.0789229 | − | 0.996881i | \(-0.474852\pi\) | ||||
0.0789229 | + | 0.996881i | \(0.474852\pi\) | |||||||
\(212\) | −6.48916 | −0.445677 | ||||||||
\(213\) | 5.25030 | 0.359745 | ||||||||
\(214\) | 0.00863711 | 0.000590420 0 | ||||||||
\(215\) | −20.4793 | −1.39668 | ||||||||
\(216\) | 5.57299 | 0.379194 | ||||||||
\(217\) | 1.11312 | 0.0755633 | ||||||||
\(218\) | −7.33424 | −0.496738 | ||||||||
\(219\) | 17.4016 | 1.17589 | ||||||||
\(220\) | 15.5626 | 1.04923 | ||||||||
\(221\) | 2.68240 | 0.180438 | ||||||||
\(222\) | 14.5983 | 0.979772 | ||||||||
\(223\) | 2.95621 | 0.197962 | 0.0989812 | − | 0.995089i | \(-0.468442\pi\) | ||||
0.0989812 | + | 0.995089i | \(0.468442\pi\) | |||||||
\(224\) | −0.882040 | −0.0589338 | ||||||||
\(225\) | −1.13537 | −0.0756915 | ||||||||
\(226\) | −13.1405 | −0.874092 | ||||||||
\(227\) | 17.2714 | 1.14634 | 0.573171 | − | 0.819436i | \(-0.305713\pi\) | ||||
0.573171 | + | 0.819436i | \(0.305713\pi\) | |||||||
\(228\) | 10.0997 | 0.668867 | ||||||||
\(229\) | −12.4178 | −0.820593 | −0.410297 | − | 0.911952i | \(-0.634575\pi\) | ||||
−0.410297 | + | 0.911952i | \(0.634575\pi\) | |||||||
\(230\) | −13.3744 | −0.881882 | ||||||||
\(231\) | 8.09808 | 0.532815 | ||||||||
\(232\) | 9.49183 | 0.623169 | ||||||||
\(233\) | −9.05913 | −0.593483 | −0.296742 | − | 0.954958i | \(-0.595900\pi\) | ||||
−0.296742 | + | 0.954958i | \(0.595900\pi\) | |||||||
\(234\) | 0.319756 | 0.0209031 | ||||||||
\(235\) | −4.23284 | −0.276120 | ||||||||
\(236\) | 3.01774 | 0.196438 | ||||||||
\(237\) | −15.8674 | −1.03070 | ||||||||
\(238\) | 4.36214 | 0.282755 | ||||||||
\(239\) | 11.5170 | 0.744973 | 0.372487 | − | 0.928038i | \(-0.378505\pi\) | ||||
0.372487 | + | 0.928038i | \(0.378505\pi\) | |||||||
\(240\) | −4.08591 | −0.263744 | ||||||||
\(241\) | −2.75272 | −0.177319 | −0.0886593 | − | 0.996062i | \(-0.528258\pi\) | ||||
−0.0886593 | + | 0.996062i | \(0.528258\pi\) | |||||||
\(242\) | 23.9693 | 1.54080 | ||||||||
\(243\) | −6.03132 | −0.386909 | ||||||||
\(244\) | 6.91687 | 0.442807 | ||||||||
\(245\) | −16.3745 | −1.04613 | ||||||||
\(246\) | 2.73018 | 0.174070 | ||||||||
\(247\) | 3.52833 | 0.224502 | ||||||||
\(248\) | −1.26198 | −0.0801358 | ||||||||
\(249\) | 12.3774 | 0.784388 | ||||||||
\(250\) | −8.09016 | −0.511667 | ||||||||
\(251\) | 1.12731 | 0.0711555 | 0.0355777 | − | 0.999367i | \(-0.488673\pi\) | ||||
0.0355777 | + | 0.999367i | \(0.488673\pi\) | |||||||
\(252\) | 0.519990 | 0.0327563 | ||||||||
\(253\) | −30.0524 | −1.88938 | ||||||||
\(254\) | −5.95706 | −0.373779 | ||||||||
\(255\) | 20.2069 | 1.26540 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.288177 | 0.0179760 | 0.00898799 | − | 0.999960i | \(-0.497139\pi\) | ||||
0.00898799 | + | 0.999960i | \(0.497139\pi\) | |||||||
\(258\) | 12.0817 | 0.752175 | ||||||||
\(259\) | 8.29352 | 0.515334 | ||||||||
\(260\) | −1.42741 | −0.0885245 | ||||||||
\(261\) | −5.59573 | −0.346367 | ||||||||
\(262\) | −2.48326 | −0.153416 | ||||||||
\(263\) | −28.6909 | −1.76916 | −0.884579 | − | 0.466391i | \(-0.845554\pi\) | ||||
−0.884579 | + | 0.466391i | \(0.845554\pi\) | |||||||
\(264\) | −9.18108 | −0.565057 | ||||||||
\(265\) | −17.0776 | −1.04907 | ||||||||
\(266\) | 5.73779 | 0.351807 | ||||||||
\(267\) | 11.5164 | 0.704791 | ||||||||
\(268\) | −6.48951 | −0.396410 | ||||||||
\(269\) | 7.36450 | 0.449021 | 0.224511 | − | 0.974472i | \(-0.427922\pi\) | ||||
0.224511 | + | 0.974472i | \(0.427922\pi\) | |||||||
\(270\) | 14.6665 | 0.892574 | ||||||||
\(271\) | −2.69132 | −0.163486 | −0.0817430 | − | 0.996653i | \(-0.526049\pi\) | ||||
−0.0817430 | + | 0.996653i | \(0.526049\pi\) | |||||||
\(272\) | −4.94551 | −0.299865 | ||||||||
\(273\) | −0.742765 | −0.0449542 | ||||||||
\(274\) | −6.15230 | −0.371674 | ||||||||
\(275\) | 11.3887 | 0.686766 | ||||||||
\(276\) | 7.89019 | 0.474934 | ||||||||
\(277\) | 14.8917 | 0.894755 | 0.447377 | − | 0.894345i | \(-0.352358\pi\) | ||||
0.447377 | + | 0.894345i | \(0.352358\pi\) | |||||||
\(278\) | −0.266066 | −0.0159576 | ||||||||
\(279\) | 0.743976 | 0.0445407 | ||||||||
\(280\) | −2.32127 | −0.138723 | ||||||||
\(281\) | −11.3827 | −0.679037 | −0.339518 | − | 0.940599i | \(-0.610264\pi\) | ||||
−0.339518 | + | 0.940599i | \(0.610264\pi\) | |||||||
\(282\) | 2.49715 | 0.148703 | ||||||||
\(283\) | −21.5999 | −1.28398 | −0.641991 | − | 0.766712i | \(-0.721891\pi\) | ||||
−0.641991 | + | 0.766712i | \(0.721891\pi\) | |||||||
\(284\) | −3.38169 | −0.200666 | ||||||||
\(285\) | 26.5794 | 1.57443 | ||||||||
\(286\) | −3.20742 | −0.189659 | ||||||||
\(287\) | 1.55106 | 0.0915561 | ||||||||
\(288\) | −0.589531 | −0.0347385 | ||||||||
\(289\) | 7.45804 | 0.438708 | ||||||||
\(290\) | 24.9797 | 1.46686 | ||||||||
\(291\) | −2.01050 | −0.117857 | ||||||||
\(292\) | −11.2083 | −0.655916 | ||||||||
\(293\) | −5.88354 | −0.343720 | −0.171860 | − | 0.985121i | \(-0.554978\pi\) | ||||
−0.171860 | + | 0.985121i | \(0.554978\pi\) | |||||||
\(294\) | 9.66009 | 0.563388 | ||||||||
\(295\) | 7.94181 | 0.462390 | ||||||||
\(296\) | −9.40266 | −0.546518 | ||||||||
\(297\) | 32.9558 | 1.91229 | ||||||||
\(298\) | 21.3333 | 1.23580 | ||||||||
\(299\) | 2.75644 | 0.159409 | ||||||||
\(300\) | −2.99008 | −0.172632 | ||||||||
\(301\) | 6.86383 | 0.395625 | ||||||||
\(302\) | 15.0180 | 0.864190 | ||||||||
\(303\) | −12.7428 | −0.732056 | ||||||||
\(304\) | −6.50514 | −0.373095 | ||||||||
\(305\) | 18.2032 | 1.04231 | ||||||||
\(306\) | 2.91553 | 0.166670 | ||||||||
\(307\) | 27.9241 | 1.59371 | 0.796857 | − | 0.604168i | \(-0.206495\pi\) | ||||
0.796857 | + | 0.604168i | \(0.206495\pi\) | |||||||
\(308\) | −5.21593 | −0.297205 | ||||||||
\(309\) | −0.868746 | −0.0494212 | ||||||||
\(310\) | −3.32116 | −0.188629 | ||||||||
\(311\) | −0.221177 | −0.0125418 | −0.00627089 | − | 0.999980i | \(-0.501996\pi\) | ||||
−0.00627089 | + | 0.999980i | \(0.501996\pi\) | |||||||
\(312\) | 0.842099 | 0.0476744 | ||||||||
\(313\) | 15.9954 | 0.904115 | 0.452058 | − | 0.891989i | \(-0.350690\pi\) | ||||
0.452058 | + | 0.891989i | \(0.350690\pi\) | |||||||
\(314\) | 10.0160 | 0.565234 | ||||||||
\(315\) | 1.36846 | 0.0771041 | ||||||||
\(316\) | 10.2201 | 0.574927 | ||||||||
\(317\) | −10.4611 | −0.587555 | −0.293778 | − | 0.955874i | \(-0.594912\pi\) | ||||
−0.293778 | + | 0.955874i | \(0.594912\pi\) | |||||||
\(318\) | 10.0749 | 0.564970 | ||||||||
\(319\) | 56.1298 | 3.14266 | ||||||||
\(320\) | 2.63171 | 0.147117 | ||||||||
\(321\) | −0.0134097 | −0.000748456 0 | ||||||||
\(322\) | 4.48255 | 0.249803 | ||||||||
\(323\) | 32.1712 | 1.79005 | ||||||||
\(324\) | −6.88386 | −0.382437 | ||||||||
\(325\) | −1.04459 | −0.0579432 | ||||||||
\(326\) | 10.0724 | 0.557857 | ||||||||
\(327\) | 11.3869 | 0.629698 | ||||||||
\(328\) | −1.75849 | −0.0970963 | ||||||||
\(329\) | 1.41867 | 0.0782140 | ||||||||
\(330\) | −24.1619 | −1.33007 | ||||||||
\(331\) | −3.16315 | −0.173862 | −0.0869311 | − | 0.996214i | \(-0.527706\pi\) | ||||
−0.0869311 | + | 0.996214i | \(0.527706\pi\) | |||||||
\(332\) | −7.97223 | −0.437533 | ||||||||
\(333\) | 5.54316 | 0.303763 | ||||||||
\(334\) | 19.4175 | 1.06248 | ||||||||
\(335\) | −17.0785 | −0.933098 | ||||||||
\(336\) | 1.36943 | 0.0747084 | ||||||||
\(337\) | −29.8037 | −1.62351 | −0.811755 | − | 0.583999i | \(-0.801487\pi\) | ||||
−0.811755 | + | 0.583999i | \(0.801487\pi\) | |||||||
\(338\) | −12.7058 | −0.691105 | ||||||||
\(339\) | 20.4015 | 1.10806 | ||||||||
\(340\) | −13.0151 | −0.705845 | ||||||||
\(341\) | −7.46269 | −0.404127 | ||||||||
\(342\) | 3.83498 | 0.207372 | ||||||||
\(343\) | 11.6623 | 0.629707 | ||||||||
\(344\) | −7.78177 | −0.419565 | ||||||||
\(345\) | 20.7647 | 1.11793 | ||||||||
\(346\) | −0.00547070 | −0.000294107 0 | ||||||||
\(347\) | −5.26729 | −0.282763 | −0.141382 | − | 0.989955i | \(-0.545154\pi\) | ||||
−0.141382 | + | 0.989955i | \(0.545154\pi\) | |||||||
\(348\) | −14.7367 | −0.789971 | ||||||||
\(349\) | −24.9944 | −1.33792 | −0.668960 | − | 0.743298i | \(-0.733260\pi\) | ||||
−0.668960 | + | 0.743298i | \(0.733260\pi\) | |||||||
\(350\) | −1.69871 | −0.0908000 | ||||||||
\(351\) | −3.02274 | −0.161342 | ||||||||
\(352\) | 5.91348 | 0.315190 | ||||||||
\(353\) | −22.8772 | −1.21763 | −0.608814 | − | 0.793313i | \(-0.708355\pi\) | ||||
−0.608814 | + | 0.793313i | \(0.708355\pi\) | |||||||
\(354\) | −4.68524 | −0.249018 | ||||||||
\(355\) | −8.89962 | −0.472343 | ||||||||
\(356\) | −7.41763 | −0.393134 | ||||||||
\(357\) | −6.77251 | −0.358439 | ||||||||
\(358\) | −21.0505 | −1.11255 | ||||||||
\(359\) | 0.243368 | 0.0128445 | 0.00642223 | − | 0.999979i | \(-0.497956\pi\) | ||||
0.00642223 | + | 0.999979i | \(0.497956\pi\) | |||||||
\(360\) | −1.55147 | −0.0817699 | ||||||||
\(361\) | 23.3168 | 1.22720 | ||||||||
\(362\) | 15.3500 | 0.806778 | ||||||||
\(363\) | −37.2139 | −1.95322 | ||||||||
\(364\) | 0.478410 | 0.0250755 | ||||||||
\(365\) | −29.4970 | −1.54394 | ||||||||
\(366\) | −10.7389 | −0.561332 | ||||||||
\(367\) | −10.2883 | −0.537046 | −0.268523 | − | 0.963273i | \(-0.586536\pi\) | ||||
−0.268523 | + | 0.963273i | \(0.586536\pi\) | |||||||
\(368\) | −5.08202 | −0.264919 | ||||||||
\(369\) | 1.03668 | 0.0539676 | ||||||||
\(370\) | −24.7451 | −1.28643 | ||||||||
\(371\) | 5.72370 | 0.297160 | ||||||||
\(372\) | 1.95931 | 0.101585 | ||||||||
\(373\) | −29.5349 | −1.52926 | −0.764629 | − | 0.644471i | \(-0.777078\pi\) | ||||
−0.764629 | + | 0.644471i | \(0.777078\pi\) | |||||||
\(374\) | −29.2452 | −1.51223 | ||||||||
\(375\) | 12.5605 | 0.648623 | ||||||||
\(376\) | −1.60840 | −0.0829469 | ||||||||
\(377\) | −5.14828 | −0.265150 | ||||||||
\(378\) | −4.91560 | −0.252831 | ||||||||
\(379\) | −31.9775 | −1.64257 | −0.821286 | − | 0.570517i | \(-0.806743\pi\) | ||||
−0.821286 | + | 0.570517i | \(0.806743\pi\) | |||||||
\(380\) | −17.1196 | −0.878218 | ||||||||
\(381\) | 9.24874 | 0.473827 | ||||||||
\(382\) | −0.740802 | −0.0379027 | ||||||||
\(383\) | 18.6199 | 0.951432 | 0.475716 | − | 0.879599i | \(-0.342189\pi\) | ||||
0.475716 | + | 0.879599i | \(0.342189\pi\) | |||||||
\(384\) | −1.55257 | −0.0792292 | ||||||||
\(385\) | −13.7268 | −0.699583 | ||||||||
\(386\) | −6.69960 | −0.341000 | ||||||||
\(387\) | 4.58759 | 0.233201 | ||||||||
\(388\) | 1.29495 | 0.0657410 | ||||||||
\(389\) | −23.6433 | −1.19876 | −0.599381 | − | 0.800464i | \(-0.704587\pi\) | ||||
−0.599381 | + | 0.800464i | \(0.704587\pi\) | |||||||
\(390\) | 2.21616 | 0.112220 | ||||||||
\(391\) | 25.1332 | 1.27104 | ||||||||
\(392\) | −6.22201 | −0.314259 | ||||||||
\(393\) | 3.85542 | 0.194480 | ||||||||
\(394\) | −14.5701 | −0.734029 | ||||||||
\(395\) | 26.8964 | 1.35330 | ||||||||
\(396\) | −3.48618 | −0.175187 | ||||||||
\(397\) | 4.67201 | 0.234481 | 0.117241 | − | 0.993104i | \(-0.462595\pi\) | ||||
0.117241 | + | 0.993104i | \(0.462595\pi\) | |||||||
\(398\) | 18.2544 | 0.915010 | ||||||||
\(399\) | −8.90832 | −0.445974 | ||||||||
\(400\) | 1.92589 | 0.0962945 | ||||||||
\(401\) | 14.7675 | 0.737454 | 0.368727 | − | 0.929538i | \(-0.379794\pi\) | ||||
0.368727 | + | 0.929538i | \(0.379794\pi\) | |||||||
\(402\) | 10.0754 | 0.502516 | ||||||||
\(403\) | 0.684486 | 0.0340967 | ||||||||
\(404\) | 8.20757 | 0.408342 | ||||||||
\(405\) | −18.1163 | −0.900207 | ||||||||
\(406\) | −8.37218 | −0.415504 | ||||||||
\(407\) | −55.6024 | −2.75611 | ||||||||
\(408\) | 7.67824 | 0.380129 | ||||||||
\(409\) | −23.0521 | −1.13985 | −0.569927 | − | 0.821695i | \(-0.693029\pi\) | ||||
−0.569927 | + | 0.821695i | \(0.693029\pi\) | |||||||
\(410\) | −4.62783 | −0.228552 | ||||||||
\(411\) | 9.55187 | 0.471159 | ||||||||
\(412\) | 0.559554 | 0.0275673 | ||||||||
\(413\) | −2.66177 | −0.130977 | ||||||||
\(414\) | 2.99601 | 0.147246 | ||||||||
\(415\) | −20.9806 | −1.02990 | ||||||||
\(416\) | −0.542391 | −0.0265929 | ||||||||
\(417\) | 0.413086 | 0.0202289 | ||||||||
\(418\) | −38.4680 | −1.88153 | ||||||||
\(419\) | −39.7993 | −1.94432 | −0.972161 | − | 0.234314i | \(-0.924716\pi\) | ||||
−0.972161 | + | 0.234314i | \(0.924716\pi\) | |||||||
\(420\) | 3.60393 | 0.175854 | ||||||||
\(421\) | −9.88650 | −0.481838 | −0.240919 | − | 0.970545i | \(-0.577449\pi\) | ||||
−0.240919 | + | 0.970545i | \(0.577449\pi\) | |||||||
\(422\) | 2.29284 | 0.111614 | ||||||||
\(423\) | 0.948203 | 0.0461032 | ||||||||
\(424\) | −6.48916 | −0.315141 | ||||||||
\(425\) | −9.52451 | −0.462006 | ||||||||
\(426\) | 5.25030 | 0.254378 | ||||||||
\(427\) | −6.10096 | −0.295246 | ||||||||
\(428\) | 0.00863711 | 0.000417490 0 | ||||||||
\(429\) | 4.97973 | 0.240424 | ||||||||
\(430\) | −20.4793 | −0.987601 | ||||||||
\(431\) | 6.91554 | 0.333110 | 0.166555 | − | 0.986032i | \(-0.446736\pi\) | ||||
0.166555 | + | 0.986032i | \(0.446736\pi\) | |||||||
\(432\) | 5.57299 | 0.268131 | ||||||||
\(433\) | 2.07242 | 0.0995942 | 0.0497971 | − | 0.998759i | \(-0.484143\pi\) | ||||
0.0497971 | + | 0.998759i | \(0.484143\pi\) | |||||||
\(434\) | 1.11312 | 0.0534313 | ||||||||
\(435\) | −38.7828 | −1.85949 | ||||||||
\(436\) | −7.33424 | −0.351247 | ||||||||
\(437\) | 33.0593 | 1.58144 | ||||||||
\(438\) | 17.4016 | 0.831482 | ||||||||
\(439\) | 13.0518 | 0.622930 | 0.311465 | − | 0.950258i | \(-0.399180\pi\) | ||||
0.311465 | + | 0.950258i | \(0.399180\pi\) | |||||||
\(440\) | 15.5626 | 0.741916 | ||||||||
\(441\) | 3.66807 | 0.174670 | ||||||||
\(442\) | 2.68240 | 0.127589 | ||||||||
\(443\) | 23.0493 | 1.09510 | 0.547552 | − | 0.836771i | \(-0.315560\pi\) | ||||
0.547552 | + | 0.836771i | \(0.315560\pi\) | |||||||
\(444\) | 14.5983 | 0.692803 | ||||||||
\(445\) | −19.5210 | −0.925386 | ||||||||
\(446\) | 2.95621 | 0.139981 | ||||||||
\(447\) | −33.1214 | −1.56659 | ||||||||
\(448\) | −0.882040 | −0.0416725 | ||||||||
\(449\) | −1.94533 | −0.0918059 | −0.0459030 | − | 0.998946i | \(-0.514617\pi\) | ||||
−0.0459030 | + | 0.998946i | \(0.514617\pi\) | |||||||
\(450\) | −1.13537 | −0.0535220 | ||||||||
\(451\) | −10.3988 | −0.489660 | ||||||||
\(452\) | −13.1405 | −0.618076 | ||||||||
\(453\) | −23.3165 | −1.09551 | ||||||||
\(454\) | 17.2714 | 0.810586 | ||||||||
\(455\) | 1.25904 | 0.0590245 | ||||||||
\(456\) | 10.0997 | 0.472960 | ||||||||
\(457\) | 36.3128 | 1.69864 | 0.849320 | − | 0.527878i | \(-0.177012\pi\) | ||||
0.849320 | + | 0.527878i | \(0.177012\pi\) | |||||||
\(458\) | −12.4178 | −0.580247 | ||||||||
\(459\) | −27.5613 | −1.28645 | ||||||||
\(460\) | −13.3744 | −0.623585 | ||||||||
\(461\) | 6.56578 | 0.305799 | 0.152899 | − | 0.988242i | \(-0.451139\pi\) | ||||
0.152899 | + | 0.988242i | \(0.451139\pi\) | |||||||
\(462\) | 8.09808 | 0.376757 | ||||||||
\(463\) | −18.5160 | −0.860509 | −0.430255 | − | 0.902708i | \(-0.641576\pi\) | ||||
−0.430255 | + | 0.902708i | \(0.641576\pi\) | |||||||
\(464\) | 9.49183 | 0.440647 | ||||||||
\(465\) | 5.15633 | 0.239119 | ||||||||
\(466\) | −9.05913 | −0.419656 | ||||||||
\(467\) | −29.8689 | −1.38217 | −0.691085 | − | 0.722774i | \(-0.742867\pi\) | ||||
−0.691085 | + | 0.722774i | \(0.742867\pi\) | |||||||
\(468\) | 0.319756 | 0.0147807 | ||||||||
\(469\) | 5.72401 | 0.264310 | ||||||||
\(470\) | −4.23284 | −0.195246 | ||||||||
\(471\) | −15.5505 | −0.716528 | ||||||||
\(472\) | 3.01774 | 0.138903 | ||||||||
\(473\) | −46.0173 | −2.11588 | ||||||||
\(474\) | −15.8674 | −0.728816 | ||||||||
\(475\) | −12.5282 | −0.574833 | ||||||||
\(476\) | 4.36214 | 0.199938 | ||||||||
\(477\) | 3.82556 | 0.175160 | ||||||||
\(478\) | 11.5170 | 0.526776 | ||||||||
\(479\) | 31.0213 | 1.41740 | 0.708699 | − | 0.705511i | \(-0.249282\pi\) | ||||
0.708699 | + | 0.705511i | \(0.249282\pi\) | |||||||
\(480\) | −4.08591 | −0.186495 | ||||||||
\(481\) | 5.09991 | 0.232536 | ||||||||
\(482\) | −2.75272 | −0.125383 | ||||||||
\(483\) | −6.95946 | −0.316666 | ||||||||
\(484\) | 23.9693 | 1.08951 | ||||||||
\(485\) | 3.40793 | 0.154746 | ||||||||
\(486\) | −6.03132 | −0.273586 | ||||||||
\(487\) | 19.7355 | 0.894299 | 0.447150 | − | 0.894459i | \(-0.352439\pi\) | ||||
0.447150 | + | 0.894459i | \(0.352439\pi\) | |||||||
\(488\) | 6.91687 | 0.313112 | ||||||||
\(489\) | −15.6380 | −0.707177 | ||||||||
\(490\) | −16.3745 | −0.739725 | ||||||||
\(491\) | −20.3203 | −0.917040 | −0.458520 | − | 0.888684i | \(-0.651620\pi\) | ||||
−0.458520 | + | 0.888684i | \(0.651620\pi\) | |||||||
\(492\) | 2.73018 | 0.123086 | ||||||||
\(493\) | −46.9419 | −2.11416 | ||||||||
\(494\) | 3.52833 | 0.158747 | ||||||||
\(495\) | −9.17462 | −0.412368 | ||||||||
\(496\) | −1.26198 | −0.0566646 | ||||||||
\(497\) | 2.98278 | 0.133796 | ||||||||
\(498\) | 12.3774 | 0.554646 | ||||||||
\(499\) | −7.99526 | −0.357917 | −0.178958 | − | 0.983857i | \(-0.557273\pi\) | ||||
−0.178958 | + | 0.983857i | \(0.557273\pi\) | |||||||
\(500\) | −8.09016 | −0.361803 | ||||||||
\(501\) | −30.1469 | −1.34687 | ||||||||
\(502\) | 1.12731 | 0.0503145 | ||||||||
\(503\) | 42.6353 | 1.90101 | 0.950507 | − | 0.310704i | \(-0.100565\pi\) | ||||
0.950507 | + | 0.310704i | \(0.100565\pi\) | |||||||
\(504\) | 0.519990 | 0.0231622 | ||||||||
\(505\) | 21.5999 | 0.961185 | ||||||||
\(506\) | −30.0524 | −1.33599 | ||||||||
\(507\) | 19.7266 | 0.876091 | ||||||||
\(508\) | −5.95706 | −0.264302 | ||||||||
\(509\) | 22.6908 | 1.00575 | 0.502876 | − | 0.864359i | \(-0.332275\pi\) | ||||
0.502876 | + | 0.864359i | \(0.332275\pi\) | |||||||
\(510\) | 20.2069 | 0.894776 | ||||||||
\(511\) | 9.88616 | 0.437338 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −36.2531 | −1.60061 | ||||||||
\(514\) | 0.288177 | 0.0127109 | ||||||||
\(515\) | 1.47258 | 0.0648898 | ||||||||
\(516\) | 12.0817 | 0.531868 | ||||||||
\(517\) | −9.51125 | −0.418304 | ||||||||
\(518\) | 8.29352 | 0.364396 | ||||||||
\(519\) | 0.00849363 | 0.000372829 0 | ||||||||
\(520\) | −1.42741 | −0.0625963 | ||||||||
\(521\) | −3.94159 | −0.172684 | −0.0863420 | − | 0.996266i | \(-0.527518\pi\) | ||||
−0.0863420 | + | 0.996266i | \(0.527518\pi\) | |||||||
\(522\) | −5.59573 | −0.244919 | ||||||||
\(523\) | 15.8239 | 0.691932 | 0.345966 | − | 0.938247i | \(-0.387551\pi\) | ||||
0.345966 | + | 0.938247i | \(0.387551\pi\) | |||||||
\(524\) | −2.48326 | −0.108482 | ||||||||
\(525\) | 2.63737 | 0.115104 | ||||||||
\(526\) | −28.6909 | −1.25098 | ||||||||
\(527\) | 6.24113 | 0.271868 | ||||||||
\(528\) | −9.18108 | −0.399555 | ||||||||
\(529\) | 2.82696 | 0.122911 | ||||||||
\(530\) | −17.0776 | −0.741802 | ||||||||
\(531\) | −1.77905 | −0.0772042 | ||||||||
\(532\) | 5.73779 | 0.248765 | ||||||||
\(533\) | 0.953788 | 0.0413132 | ||||||||
\(534\) | 11.5164 | 0.498362 | ||||||||
\(535\) | 0.0227303 | 0.000982719 0 | ||||||||
\(536\) | −6.48951 | −0.280304 | ||||||||
\(537\) | 32.6823 | 1.41035 | ||||||||
\(538\) | 7.36450 | 0.317506 | ||||||||
\(539\) | −36.7937 | −1.58482 | ||||||||
\(540\) | 14.6665 | 0.631145 | ||||||||
\(541\) | 6.35580 | 0.273257 | 0.136629 | − | 0.990622i | \(-0.456373\pi\) | ||||
0.136629 | + | 0.990622i | \(0.456373\pi\) | |||||||
\(542\) | −2.69132 | −0.115602 | ||||||||
\(543\) | −23.8319 | −1.02273 | ||||||||
\(544\) | −4.94551 | −0.212037 | ||||||||
\(545\) | −19.3016 | −0.826789 | ||||||||
\(546\) | −0.742765 | −0.0317874 | ||||||||
\(547\) | −8.82179 | −0.377193 | −0.188596 | − | 0.982055i | \(-0.560394\pi\) | ||||
−0.188596 | + | 0.982055i | \(0.560394\pi\) | |||||||
\(548\) | −6.15230 | −0.262813 | ||||||||
\(549\) | −4.07771 | −0.174033 | ||||||||
\(550\) | 11.3887 | 0.485617 | ||||||||
\(551\) | −61.7457 | −2.63045 | ||||||||
\(552\) | 7.89019 | 0.335829 | ||||||||
\(553\) | −9.01456 | −0.383338 | ||||||||
\(554\) | 14.8917 | 0.632687 | ||||||||
\(555\) | 38.4184 | 1.63077 | ||||||||
\(556\) | −0.266066 | −0.0112837 | ||||||||
\(557\) | −14.5363 | −0.615922 | −0.307961 | − | 0.951399i | \(-0.599647\pi\) | ||||
−0.307961 | + | 0.951399i | \(0.599647\pi\) | |||||||
\(558\) | 0.743976 | 0.0314950 | ||||||||
\(559\) | 4.22076 | 0.178519 | ||||||||
\(560\) | −2.32127 | −0.0980917 | ||||||||
\(561\) | 45.4051 | 1.91701 | ||||||||
\(562\) | −11.3827 | −0.480152 | ||||||||
\(563\) | 34.8655 | 1.46941 | 0.734704 | − | 0.678388i | \(-0.237321\pi\) | ||||
0.734704 | + | 0.678388i | \(0.237321\pi\) | |||||||
\(564\) | 2.49715 | 0.105149 | ||||||||
\(565\) | −34.5819 | −1.45487 | ||||||||
\(566\) | −21.5999 | −0.907912 | ||||||||
\(567\) | 6.07184 | 0.254993 | ||||||||
\(568\) | −3.38169 | −0.141892 | ||||||||
\(569\) | 26.8211 | 1.12440 | 0.562200 | − | 0.827001i | \(-0.309955\pi\) | ||||
0.562200 | + | 0.827001i | \(0.309955\pi\) | |||||||
\(570\) | 26.5794 | 1.11329 | ||||||||
\(571\) | −12.0883 | −0.505878 | −0.252939 | − | 0.967482i | \(-0.581397\pi\) | ||||
−0.252939 | + | 0.967482i | \(0.581397\pi\) | |||||||
\(572\) | −3.20742 | −0.134109 | ||||||||
\(573\) | 1.15015 | 0.0480480 | ||||||||
\(574\) | 1.55106 | 0.0647399 | ||||||||
\(575\) | −9.78742 | −0.408164 | ||||||||
\(576\) | −0.589531 | −0.0245638 | ||||||||
\(577\) | 33.8792 | 1.41041 | 0.705205 | − | 0.709003i | \(-0.250855\pi\) | ||||
0.705205 | + | 0.709003i | \(0.250855\pi\) | |||||||
\(578\) | 7.45804 | 0.310214 | ||||||||
\(579\) | 10.4016 | 0.432275 | ||||||||
\(580\) | 24.9797 | 1.03723 | ||||||||
\(581\) | 7.03183 | 0.291729 | ||||||||
\(582\) | −2.01050 | −0.0833377 | ||||||||
\(583\) | −38.3735 | −1.58927 | ||||||||
\(584\) | −11.2083 | −0.463802 | ||||||||
\(585\) | 0.841505 | 0.0347920 | ||||||||
\(586\) | −5.88354 | −0.243047 | ||||||||
\(587\) | −44.5269 | −1.83782 | −0.918911 | − | 0.394465i | \(-0.870930\pi\) | ||||
−0.918911 | + | 0.394465i | \(0.870930\pi\) | |||||||
\(588\) | 9.66009 | 0.398375 | ||||||||
\(589\) | 8.20935 | 0.338260 | ||||||||
\(590\) | 7.94181 | 0.326959 | ||||||||
\(591\) | 22.6210 | 0.930504 | ||||||||
\(592\) | −9.40266 | −0.386447 | ||||||||
\(593\) | 3.97893 | 0.163395 | 0.0816976 | − | 0.996657i | \(-0.473966\pi\) | ||||
0.0816976 | + | 0.996657i | \(0.473966\pi\) | |||||||
\(594\) | 32.9558 | 1.35219 | ||||||||
\(595\) | 11.4799 | 0.470629 | ||||||||
\(596\) | 21.3333 | 0.873846 | ||||||||
\(597\) | −28.3412 | −1.15993 | ||||||||
\(598\) | 2.75644 | 0.112719 | ||||||||
\(599\) | 12.5086 | 0.511090 | 0.255545 | − | 0.966797i | \(-0.417745\pi\) | ||||
0.255545 | + | 0.966797i | \(0.417745\pi\) | |||||||
\(600\) | −2.99008 | −0.122069 | ||||||||
\(601\) | −32.0039 | −1.30546 | −0.652732 | − | 0.757589i | \(-0.726377\pi\) | ||||
−0.652732 | + | 0.757589i | \(0.726377\pi\) | |||||||
\(602\) | 6.86383 | 0.279749 | ||||||||
\(603\) | 3.82577 | 0.155797 | ||||||||
\(604\) | 15.0180 | 0.611075 | ||||||||
\(605\) | 63.0801 | 2.56457 | ||||||||
\(606\) | −12.7428 | −0.517642 | ||||||||
\(607\) | 27.9887 | 1.13603 | 0.568013 | − | 0.823020i | \(-0.307712\pi\) | ||||
0.568013 | + | 0.823020i | \(0.307712\pi\) | |||||||
\(608\) | −6.50514 | −0.263818 | ||||||||
\(609\) | 12.9984 | 0.526721 | ||||||||
\(610\) | 18.2032 | 0.737026 | ||||||||
\(611\) | 0.872382 | 0.0352928 | ||||||||
\(612\) | 2.91553 | 0.117853 | ||||||||
\(613\) | −33.7759 | −1.36420 | −0.682098 | − | 0.731261i | \(-0.738932\pi\) | ||||
−0.682098 | + | 0.731261i | \(0.738932\pi\) | |||||||
\(614\) | 27.9241 | 1.12693 | ||||||||
\(615\) | 7.18503 | 0.289728 | ||||||||
\(616\) | −5.21593 | −0.210156 | ||||||||
\(617\) | −18.2996 | −0.736714 | −0.368357 | − | 0.929684i | \(-0.620080\pi\) | ||||
−0.368357 | + | 0.929684i | \(0.620080\pi\) | |||||||
\(618\) | −0.868746 | −0.0349461 | ||||||||
\(619\) | 5.98223 | 0.240446 | 0.120223 | − | 0.992747i | \(-0.461639\pi\) | ||||
0.120223 | + | 0.992747i | \(0.461639\pi\) | |||||||
\(620\) | −3.32116 | −0.133381 | ||||||||
\(621\) | −28.3221 | −1.13653 | ||||||||
\(622\) | −0.221177 | −0.00886838 | ||||||||
\(623\) | 6.54265 | 0.262126 | ||||||||
\(624\) | 0.842099 | 0.0337109 | ||||||||
\(625\) | −30.9204 | −1.23682 | ||||||||
\(626\) | 15.9954 | 0.639306 | ||||||||
\(627\) | 59.7242 | 2.38516 | ||||||||
\(628\) | 10.0160 | 0.399681 | ||||||||
\(629\) | 46.5009 | 1.85411 | ||||||||
\(630\) | 1.36846 | 0.0545209 | ||||||||
\(631\) | 27.0906 | 1.07846 | 0.539229 | − | 0.842159i | \(-0.318716\pi\) | ||||
0.539229 | + | 0.842159i | \(0.318716\pi\) | |||||||
\(632\) | 10.2201 | 0.406535 | ||||||||
\(633\) | −3.55979 | −0.141489 | ||||||||
\(634\) | −10.4611 | −0.415464 | ||||||||
\(635\) | −15.6772 | −0.622132 | ||||||||
\(636\) | 10.0749 | 0.399494 | ||||||||
\(637\) | 3.37476 | 0.133713 | ||||||||
\(638\) | 56.1298 | 2.22220 | ||||||||
\(639\) | 1.99361 | 0.0788660 | ||||||||
\(640\) | 2.63171 | 0.104027 | ||||||||
\(641\) | −19.7405 | −0.779701 | −0.389851 | − | 0.920878i | \(-0.627473\pi\) | ||||
−0.389851 | + | 0.920878i | \(0.627473\pi\) | |||||||
\(642\) | −0.0134097 | −0.000529239 0 | ||||||||
\(643\) | −7.04426 | −0.277798 | −0.138899 | − | 0.990307i | \(-0.544356\pi\) | ||||
−0.138899 | + | 0.990307i | \(0.544356\pi\) | |||||||
\(644\) | 4.48255 | 0.176637 | ||||||||
\(645\) | 31.7956 | 1.25195 | ||||||||
\(646\) | 32.1712 | 1.26576 | ||||||||
\(647\) | −2.08754 | −0.0820696 | −0.0410348 | − | 0.999158i | \(-0.513065\pi\) | ||||
−0.0410348 | + | 0.999158i | \(0.513065\pi\) | |||||||
\(648\) | −6.88386 | −0.270424 | ||||||||
\(649\) | 17.8453 | 0.700491 | ||||||||
\(650\) | −1.04459 | −0.0409720 | ||||||||
\(651\) | −1.72819 | −0.0677331 | ||||||||
\(652\) | 10.0724 | 0.394464 | ||||||||
\(653\) | 4.67434 | 0.182921 | 0.0914606 | − | 0.995809i | \(-0.470846\pi\) | ||||
0.0914606 | + | 0.995809i | \(0.470846\pi\) | |||||||
\(654\) | 11.3869 | 0.445264 | ||||||||
\(655\) | −6.53520 | −0.255352 | ||||||||
\(656\) | −1.75849 | −0.0686575 | ||||||||
\(657\) | 6.60764 | 0.257789 | ||||||||
\(658\) | 1.41867 | 0.0553057 | ||||||||
\(659\) | −21.7121 | −0.845784 | −0.422892 | − | 0.906180i | \(-0.638985\pi\) | ||||
−0.422892 | + | 0.906180i | \(0.638985\pi\) | |||||||
\(660\) | −24.1619 | −0.940502 | ||||||||
\(661\) | 9.91003 | 0.385455 | 0.192728 | − | 0.981252i | \(-0.438267\pi\) | ||||
0.192728 | + | 0.981252i | \(0.438267\pi\) | |||||||
\(662\) | −3.16315 | −0.122939 | ||||||||
\(663\) | −4.16460 | −0.161740 | ||||||||
\(664\) | −7.97223 | −0.309383 | ||||||||
\(665\) | 15.1002 | 0.585561 | ||||||||
\(666\) | 5.54316 | 0.214793 | ||||||||
\(667\) | −48.2377 | −1.86777 | ||||||||
\(668\) | 19.4175 | 0.751284 | ||||||||
\(669\) | −4.58972 | −0.177449 | ||||||||
\(670\) | −17.0785 | −0.659800 | ||||||||
\(671\) | 40.9028 | 1.57903 | ||||||||
\(672\) | 1.36943 | 0.0528268 | ||||||||
\(673\) | 26.9480 | 1.03877 | 0.519384 | − | 0.854541i | \(-0.326161\pi\) | ||||
0.519384 | + | 0.854541i | \(0.326161\pi\) | |||||||
\(674\) | −29.8037 | −1.14799 | ||||||||
\(675\) | 10.7330 | 0.413112 | ||||||||
\(676\) | −12.7058 | −0.488685 | ||||||||
\(677\) | −27.5716 | −1.05966 | −0.529831 | − | 0.848103i | \(-0.677744\pi\) | ||||
−0.529831 | + | 0.848103i | \(0.677744\pi\) | |||||||
\(678\) | 20.4015 | 0.783515 | ||||||||
\(679\) | −1.14220 | −0.0438335 | ||||||||
\(680\) | −13.0151 | −0.499108 | ||||||||
\(681\) | −26.8150 | −1.02755 | ||||||||
\(682\) | −7.46269 | −0.285761 | ||||||||
\(683\) | −43.6122 | −1.66878 | −0.834388 | − | 0.551178i | \(-0.814178\pi\) | ||||
−0.834388 | + | 0.551178i | \(0.814178\pi\) | |||||||
\(684\) | 3.83498 | 0.146634 | ||||||||
\(685\) | −16.1911 | −0.618629 | ||||||||
\(686\) | 11.6623 | 0.445270 | ||||||||
\(687\) | 19.2795 | 0.735560 | ||||||||
\(688\) | −7.78177 | −0.296677 | ||||||||
\(689\) | 3.51966 | 0.134088 | ||||||||
\(690\) | 20.7647 | 0.790498 | ||||||||
\(691\) | 9.32740 | 0.354831 | 0.177416 | − | 0.984136i | \(-0.443226\pi\) | ||||
0.177416 | + | 0.984136i | \(0.443226\pi\) | |||||||
\(692\) | −0.00547070 | −0.000207965 0 | ||||||||
\(693\) | 3.07495 | 0.116808 | ||||||||
\(694\) | −5.26729 | −0.199944 | ||||||||
\(695\) | −0.700208 | −0.0265604 | ||||||||
\(696\) | −14.7367 | −0.558594 | ||||||||
\(697\) | 8.69662 | 0.329408 | ||||||||
\(698\) | −24.9944 | −0.946052 | ||||||||
\(699\) | 14.0649 | 0.531984 | ||||||||
\(700\) | −1.69871 | −0.0642053 | ||||||||
\(701\) | −8.74867 | −0.330433 | −0.165216 | − | 0.986257i | \(-0.552832\pi\) | ||||
−0.165216 | + | 0.986257i | \(0.552832\pi\) | |||||||
\(702\) | −3.02274 | −0.114086 | ||||||||
\(703\) | 61.1656 | 2.30690 | ||||||||
\(704\) | 5.91348 | 0.222873 | ||||||||
\(705\) | 6.57178 | 0.247507 | ||||||||
\(706\) | −22.8772 | −0.860993 | ||||||||
\(707\) | −7.23941 | −0.272266 | ||||||||
\(708\) | −4.68524 | −0.176082 | ||||||||
\(709\) | −41.2119 | −1.54775 | −0.773873 | − | 0.633341i | \(-0.781683\pi\) | ||||
−0.773873 | + | 0.633341i | \(0.781683\pi\) | |||||||
\(710\) | −8.89962 | −0.333997 | ||||||||
\(711\) | −6.02509 | −0.225958 | ||||||||
\(712\) | −7.41763 | −0.277987 | ||||||||
\(713\) | 6.41341 | 0.240184 | ||||||||
\(714\) | −6.77251 | −0.253455 | ||||||||
\(715\) | −8.44099 | −0.315675 | ||||||||
\(716\) | −21.0505 | −0.786694 | ||||||||
\(717\) | −17.8809 | −0.667776 | ||||||||
\(718\) | 0.243368 | 0.00908240 | ||||||||
\(719\) | 37.0291 | 1.38095 | 0.690475 | − | 0.723356i | \(-0.257401\pi\) | ||||
0.690475 | + | 0.723356i | \(0.257401\pi\) | |||||||
\(720\) | −1.55147 | −0.0578200 | ||||||||
\(721\) | −0.493549 | −0.0183807 | ||||||||
\(722\) | 23.3168 | 0.867762 | ||||||||
\(723\) | 4.27379 | 0.158944 | ||||||||
\(724\) | 15.3500 | 0.570478 | ||||||||
\(725\) | 18.2802 | 0.678911 | ||||||||
\(726\) | −37.2139 | −1.38114 | ||||||||
\(727\) | 47.1436 | 1.74846 | 0.874230 | − | 0.485512i | \(-0.161367\pi\) | ||||
0.874230 | + | 0.485512i | \(0.161367\pi\) | |||||||
\(728\) | 0.478410 | 0.0177311 | ||||||||
\(729\) | 30.0156 | 1.11169 | ||||||||
\(730\) | −29.4970 | −1.09173 | ||||||||
\(731\) | 38.4848 | 1.42341 | ||||||||
\(732\) | −10.7389 | −0.396922 | ||||||||
\(733\) | 27.9809 | 1.03350 | 0.516748 | − | 0.856137i | \(-0.327142\pi\) | ||||
0.516748 | + | 0.856137i | \(0.327142\pi\) | |||||||
\(734\) | −10.2883 | −0.379749 | ||||||||
\(735\) | 25.4225 | 0.937725 | ||||||||
\(736\) | −5.08202 | −0.187326 | ||||||||
\(737\) | −38.3756 | −1.41358 | ||||||||
\(738\) | 1.03668 | 0.0381609 | ||||||||
\(739\) | 20.7881 | 0.764703 | 0.382351 | − | 0.924017i | \(-0.375114\pi\) | ||||
0.382351 | + | 0.924017i | \(0.375114\pi\) | |||||||
\(740\) | −24.7451 | −0.909646 | ||||||||
\(741\) | −5.47797 | −0.201238 | ||||||||
\(742\) | 5.72370 | 0.210124 | ||||||||
\(743\) | −48.8925 | −1.79369 | −0.896845 | − | 0.442344i | \(-0.854147\pi\) | ||||
−0.896845 | + | 0.442344i | \(0.854147\pi\) | |||||||
\(744\) | 1.95931 | 0.0718318 | ||||||||
\(745\) | 56.1430 | 2.05692 | ||||||||
\(746\) | −29.5349 | −1.08135 | ||||||||
\(747\) | 4.69988 | 0.171960 | ||||||||
\(748\) | −29.2452 | −1.06931 | ||||||||
\(749\) | −0.00761827 | −0.000278366 0 | ||||||||
\(750\) | 12.5605 | 0.458646 | ||||||||
\(751\) | −37.6155 | −1.37261 | −0.686304 | − | 0.727315i | \(-0.740768\pi\) | ||||
−0.686304 | + | 0.727315i | \(0.740768\pi\) | |||||||
\(752\) | −1.60840 | −0.0586523 | ||||||||
\(753\) | −1.75023 | −0.0637820 | ||||||||
\(754\) | −5.14828 | −0.187489 | ||||||||
\(755\) | 39.5231 | 1.43839 | ||||||||
\(756\) | −4.91560 | −0.178779 | ||||||||
\(757\) | 20.9612 | 0.761847 | 0.380923 | − | 0.924607i | \(-0.375606\pi\) | ||||
0.380923 | + | 0.924607i | \(0.375606\pi\) | |||||||
\(758\) | −31.9775 | −1.16147 | ||||||||
\(759\) | 46.6585 | 1.69360 | ||||||||
\(760\) | −17.1196 | −0.620994 | ||||||||
\(761\) | −44.1859 | −1.60174 | −0.800869 | − | 0.598840i | \(-0.795628\pi\) | ||||
−0.800869 | + | 0.598840i | \(0.795628\pi\) | |||||||
\(762\) | 9.24874 | 0.335047 | ||||||||
\(763\) | 6.46910 | 0.234197 | ||||||||
\(764\) | −0.740802 | −0.0268013 | ||||||||
\(765\) | 7.67283 | 0.277412 | ||||||||
\(766\) | 18.6199 | 0.672764 | ||||||||
\(767\) | −1.63679 | −0.0591012 | ||||||||
\(768\) | −1.55257 | −0.0560235 | ||||||||
\(769\) | −28.5036 | −1.02787 | −0.513934 | − | 0.857830i | \(-0.671812\pi\) | ||||
−0.513934 | + | 0.857830i | \(0.671812\pi\) | |||||||
\(770\) | −13.7268 | −0.494680 | ||||||||
\(771\) | −0.447414 | −0.0161132 | ||||||||
\(772\) | −6.69960 | −0.241124 | ||||||||
\(773\) | 32.6834 | 1.17554 | 0.587769 | − | 0.809028i | \(-0.300006\pi\) | ||||
0.587769 | + | 0.809028i | \(0.300006\pi\) | |||||||
\(774\) | 4.58759 | 0.164898 | ||||||||
\(775\) | −2.43043 | −0.0873038 | ||||||||
\(776\) | 1.29495 | 0.0464859 | ||||||||
\(777\) | −12.8763 | −0.461933 | ||||||||
\(778\) | −23.6433 | −0.847653 | ||||||||
\(779\) | 11.4392 | 0.409853 | ||||||||
\(780\) | 2.21616 | 0.0793512 | ||||||||
\(781\) | −19.9975 | −0.715568 | ||||||||
\(782\) | 25.1332 | 0.898761 | ||||||||
\(783\) | 52.8979 | 1.89042 | ||||||||
\(784\) | −6.22201 | −0.222214 | ||||||||
\(785\) | 26.3591 | 0.940797 | ||||||||
\(786\) | 3.85542 | 0.137518 | ||||||||
\(787\) | −5.16397 | −0.184076 | −0.0920378 | − | 0.995756i | \(-0.529338\pi\) | ||||
−0.0920378 | + | 0.995756i | \(0.529338\pi\) | |||||||
\(788\) | −14.5701 | −0.519037 | ||||||||
\(789\) | 44.5446 | 1.58583 | ||||||||
\(790\) | 26.8964 | 0.956931 | ||||||||
\(791\) | 11.5904 | 0.412108 | ||||||||
\(792\) | −3.48618 | −0.123876 | ||||||||
\(793\) | −3.75165 | −0.133225 | ||||||||
\(794\) | 4.67201 | 0.165803 | ||||||||
\(795\) | 26.5141 | 0.940358 | ||||||||
\(796\) | 18.2544 | 0.647010 | ||||||||
\(797\) | −16.2077 | −0.574105 | −0.287052 | − | 0.957915i | \(-0.592675\pi\) | ||||
−0.287052 | + | 0.957915i | \(0.592675\pi\) | |||||||
\(798\) | −8.90832 | −0.315351 | ||||||||
\(799\) | 7.95436 | 0.281405 | ||||||||
\(800\) | 1.92589 | 0.0680905 | ||||||||
\(801\) | 4.37292 | 0.154510 | ||||||||
\(802\) | 14.7675 | 0.521459 | ||||||||
\(803\) | −66.2800 | −2.33897 | ||||||||
\(804\) | 10.0754 | 0.355332 | ||||||||
\(805\) | 11.7968 | 0.415781 | ||||||||
\(806\) | 0.684486 | 0.0241100 | ||||||||
\(807\) | −11.4339 | −0.402492 | ||||||||
\(808\) | 8.20757 | 0.288741 | ||||||||
\(809\) | 26.0475 | 0.915783 | 0.457891 | − | 0.889008i | \(-0.348605\pi\) | ||||
0.457891 | + | 0.889008i | \(0.348605\pi\) | |||||||
\(810\) | −18.1163 | −0.636542 | ||||||||
\(811\) | −42.0203 | −1.47553 | −0.737766 | − | 0.675056i | \(-0.764119\pi\) | ||||
−0.737766 | + | 0.675056i | \(0.764119\pi\) | |||||||
\(812\) | −8.37218 | −0.293806 | ||||||||
\(813\) | 4.17846 | 0.146545 | ||||||||
\(814\) | −55.6024 | −1.94886 | ||||||||
\(815\) | 26.5075 | 0.928518 | ||||||||
\(816\) | 7.67824 | 0.268792 | ||||||||
\(817\) | 50.6215 | 1.77102 | ||||||||
\(818\) | −23.0521 | −0.805999 | ||||||||
\(819\) | −0.282038 | −0.00985520 | ||||||||
\(820\) | −4.62783 | −0.161611 | ||||||||
\(821\) | −53.1911 | −1.85638 | −0.928191 | − | 0.372104i | \(-0.878636\pi\) | ||||
−0.928191 | + | 0.372104i | \(0.878636\pi\) | |||||||
\(822\) | 9.55187 | 0.333160 | ||||||||
\(823\) | 21.7285 | 0.757407 | 0.378703 | − | 0.925518i | \(-0.376370\pi\) | ||||
0.378703 | + | 0.925518i | \(0.376370\pi\) | |||||||
\(824\) | 0.559554 | 0.0194930 | ||||||||
\(825\) | −17.6818 | −0.615600 | ||||||||
\(826\) | −2.66177 | −0.0926147 | ||||||||
\(827\) | 4.42385 | 0.153832 | 0.0769162 | − | 0.997038i | \(-0.475493\pi\) | ||||
0.0769162 | + | 0.997038i | \(0.475493\pi\) | |||||||
\(828\) | 2.99601 | 0.104119 | ||||||||
\(829\) | 30.9185 | 1.07384 | 0.536922 | − | 0.843632i | \(-0.319587\pi\) | ||||
0.536922 | + | 0.843632i | \(0.319587\pi\) | |||||||
\(830\) | −20.9806 | −0.728247 | ||||||||
\(831\) | −23.1204 | −0.802036 | ||||||||
\(832\) | −0.542391 | −0.0188040 | ||||||||
\(833\) | 30.7710 | 1.06615 | ||||||||
\(834\) | 0.413086 | 0.0143040 | ||||||||
\(835\) | 51.1011 | 1.76843 | ||||||||
\(836\) | −38.4680 | −1.33044 | ||||||||
\(837\) | −7.03300 | −0.243096 | ||||||||
\(838\) | −39.7993 | −1.37484 | ||||||||
\(839\) | −10.8624 | −0.375010 | −0.187505 | − | 0.982264i | \(-0.560040\pi\) | ||||
−0.187505 | + | 0.982264i | \(0.560040\pi\) | |||||||
\(840\) | 3.60393 | 0.124348 | ||||||||
\(841\) | 61.0949 | 2.10672 | ||||||||
\(842\) | −9.88650 | −0.340711 | ||||||||
\(843\) | 17.6725 | 0.608672 | ||||||||
\(844\) | 2.29284 | 0.0789229 | ||||||||
\(845\) | −33.4380 | −1.15030 | ||||||||
\(846\) | 0.948203 | 0.0325999 | ||||||||
\(847\) | −21.1419 | −0.726443 | ||||||||
\(848\) | −6.48916 | −0.222839 | ||||||||
\(849\) | 33.5354 | 1.15093 | ||||||||
\(850\) | −9.52451 | −0.326688 | ||||||||
\(851\) | 47.7845 | 1.63803 | ||||||||
\(852\) | 5.25030 | 0.179872 | ||||||||
\(853\) | 37.7761 | 1.29343 | 0.646714 | − | 0.762733i | \(-0.276143\pi\) | ||||
0.646714 | + | 0.762733i | \(0.276143\pi\) | |||||||
\(854\) | −6.10096 | −0.208770 | ||||||||
\(855\) | 10.0926 | 0.345158 | ||||||||
\(856\) | 0.00863711 | 0.000295210 0 | ||||||||
\(857\) | −45.5128 | −1.55469 | −0.777343 | − | 0.629077i | \(-0.783433\pi\) | ||||
−0.777343 | + | 0.629077i | \(0.783433\pi\) | |||||||
\(858\) | 4.97973 | 0.170005 | ||||||||
\(859\) | 27.2305 | 0.929094 | 0.464547 | − | 0.885549i | \(-0.346217\pi\) | ||||
0.464547 | + | 0.885549i | \(0.346217\pi\) | |||||||
\(860\) | −20.4793 | −0.698340 | ||||||||
\(861\) | −2.40812 | −0.0820687 | ||||||||
\(862\) | 6.91554 | 0.235544 | ||||||||
\(863\) | 1.49875 | 0.0510181 | 0.0255091 | − | 0.999675i | \(-0.491879\pi\) | ||||
0.0255091 | + | 0.999675i | \(0.491879\pi\) | |||||||
\(864\) | 5.57299 | 0.189597 | ||||||||
\(865\) | −0.0143973 | −0.000489522 0 | ||||||||
\(866\) | 2.07242 | 0.0704237 | ||||||||
\(867\) | −11.5791 | −0.393248 | ||||||||
\(868\) | 1.11312 | 0.0377816 | ||||||||
\(869\) | 60.4365 | 2.05017 | ||||||||
\(870\) | −38.7828 | −1.31486 | ||||||||
\(871\) | 3.51985 | 0.119266 | ||||||||
\(872\) | −7.33424 | −0.248369 | ||||||||
\(873\) | −0.763412 | −0.0258376 | ||||||||
\(874\) | 33.0593 | 1.11825 | ||||||||
\(875\) | 7.13585 | 0.241236 | ||||||||
\(876\) | 17.4016 | 0.587947 | ||||||||
\(877\) | −13.4100 | −0.452823 | −0.226412 | − | 0.974032i | \(-0.572699\pi\) | ||||
−0.226412 | + | 0.974032i | \(0.572699\pi\) | |||||||
\(878\) | 13.0518 | 0.440478 | ||||||||
\(879\) | 9.13460 | 0.308102 | ||||||||
\(880\) | 15.5626 | 0.524614 | ||||||||
\(881\) | −46.6340 | −1.57114 | −0.785570 | − | 0.618773i | \(-0.787630\pi\) | ||||
−0.785570 | + | 0.618773i | \(0.787630\pi\) | |||||||
\(882\) | 3.66807 | 0.123510 | ||||||||
\(883\) | 37.6874 | 1.26828 | 0.634141 | − | 0.773218i | \(-0.281354\pi\) | ||||
0.634141 | + | 0.773218i | \(0.281354\pi\) | |||||||
\(884\) | 2.68240 | 0.0902188 | ||||||||
\(885\) | −12.3302 | −0.414475 | ||||||||
\(886\) | 23.0493 | 0.774356 | ||||||||
\(887\) | −5.27908 | −0.177254 | −0.0886271 | − | 0.996065i | \(-0.528248\pi\) | ||||
−0.0886271 | + | 0.996065i | \(0.528248\pi\) | |||||||
\(888\) | 14.5983 | 0.489886 | ||||||||
\(889\) | 5.25436 | 0.176226 | ||||||||
\(890\) | −19.5210 | −0.654347 | ||||||||
\(891\) | −40.7076 | −1.36376 | ||||||||
\(892\) | 2.95621 | 0.0989812 | ||||||||
\(893\) | 10.4629 | 0.350127 | ||||||||
\(894\) | −33.1214 | −1.10775 | ||||||||
\(895\) | −55.3988 | −1.85178 | ||||||||
\(896\) | −0.882040 | −0.0294669 | ||||||||
\(897\) | −4.27956 | −0.142890 | ||||||||
\(898\) | −1.94533 | −0.0649166 | ||||||||
\(899\) | −11.9785 | −0.399505 | ||||||||
\(900\) | −1.13537 | −0.0378458 | ||||||||
\(901\) | 32.0922 | 1.06915 | ||||||||
\(902\) | −10.3988 | −0.346242 | ||||||||
\(903\) | −10.6566 | −0.354628 | ||||||||
\(904\) | −13.1405 | −0.437046 | ||||||||
\(905\) | 40.3967 | 1.34283 | ||||||||
\(906\) | −23.3165 | −0.774639 | ||||||||
\(907\) | 49.7010 | 1.65030 | 0.825148 | − | 0.564917i | \(-0.191092\pi\) | ||||
0.825148 | + | 0.564917i | \(0.191092\pi\) | |||||||
\(908\) | 17.2714 | 0.573171 | ||||||||
\(909\) | −4.83862 | −0.160487 | ||||||||
\(910\) | 1.25904 | 0.0417367 | ||||||||
\(911\) | 58.0575 | 1.92353 | 0.961766 | − | 0.273872i | \(-0.0883044\pi\) | ||||
0.961766 | + | 0.273872i | \(0.0883044\pi\) | |||||||
\(912\) | 10.0997 | 0.334434 | ||||||||
\(913\) | −47.1436 | −1.56023 | ||||||||
\(914\) | 36.3128 | 1.20112 | ||||||||
\(915\) | −28.2617 | −0.934303 | ||||||||
\(916\) | −12.4178 | −0.410297 | ||||||||
\(917\) | 2.19033 | 0.0723311 | ||||||||
\(918\) | −27.5613 | −0.909658 | ||||||||
\(919\) | −23.3875 | −0.771482 | −0.385741 | − | 0.922607i | \(-0.626054\pi\) | ||||
−0.385741 | + | 0.922607i | \(0.626054\pi\) | |||||||
\(920\) | −13.3744 | −0.440941 | ||||||||
\(921\) | −43.3541 | −1.42857 | ||||||||
\(922\) | 6.56578 | 0.216232 | ||||||||
\(923\) | 1.83420 | 0.0603733 | ||||||||
\(924\) | 8.09808 | 0.266407 | ||||||||
\(925\) | −18.1085 | −0.595404 | ||||||||
\(926\) | −18.5160 | −0.608472 | ||||||||
\(927\) | −0.329875 | −0.0108345 | ||||||||
\(928\) | 9.49183 | 0.311585 | ||||||||
\(929\) | 36.0194 | 1.18176 | 0.590879 | − | 0.806760i | \(-0.298781\pi\) | ||||
0.590879 | + | 0.806760i | \(0.298781\pi\) | |||||||
\(930\) | 5.15633 | 0.169083 | ||||||||
\(931\) | 40.4750 | 1.32651 | ||||||||
\(932\) | −9.05913 | −0.296742 | ||||||||
\(933\) | 0.343392 | 0.0112422 | ||||||||
\(934\) | −29.8689 | −0.977342 | ||||||||
\(935\) | −76.9648 | −2.51702 | ||||||||
\(936\) | 0.319756 | 0.0104516 | ||||||||
\(937\) | 53.8068 | 1.75779 | 0.878897 | − | 0.477012i | \(-0.158280\pi\) | ||||
0.878897 | + | 0.477012i | \(0.158280\pi\) | |||||||
\(938\) | 5.72401 | 0.186895 | ||||||||
\(939\) | −24.8340 | −0.810427 | ||||||||
\(940\) | −4.23284 | −0.138060 | ||||||||
\(941\) | −7.32756 | −0.238872 | −0.119436 | − | 0.992842i | \(-0.538109\pi\) | ||||
−0.119436 | + | 0.992842i | \(0.538109\pi\) | |||||||
\(942\) | −15.5505 | −0.506662 | ||||||||
\(943\) | 8.93668 | 0.291018 | ||||||||
\(944\) | 3.01774 | 0.0982190 | ||||||||
\(945\) | −12.9364 | −0.420822 | ||||||||
\(946\) | −46.0173 | −1.49615 | ||||||||
\(947\) | −35.9251 | −1.16741 | −0.583705 | − | 0.811966i | \(-0.698397\pi\) | ||||
−0.583705 | + | 0.811966i | \(0.698397\pi\) | |||||||
\(948\) | −15.8674 | −0.515351 | ||||||||
\(949\) | 6.07927 | 0.197342 | ||||||||
\(950\) | −12.5282 | −0.406468 | ||||||||
\(951\) | 16.2416 | 0.526670 | ||||||||
\(952\) | 4.36214 | 0.141378 | ||||||||
\(953\) | 47.8518 | 1.55007 | 0.775036 | − | 0.631917i | \(-0.217732\pi\) | ||||
0.775036 | + | 0.631917i | \(0.217732\pi\) | |||||||
\(954\) | 3.82556 | 0.123857 | ||||||||
\(955\) | −1.94958 | −0.0630868 | ||||||||
\(956\) | 11.5170 | 0.372487 | ||||||||
\(957\) | −87.1453 | −2.81701 | ||||||||
\(958\) | 31.0213 | 1.00225 | ||||||||
\(959\) | 5.42658 | 0.175233 | ||||||||
\(960\) | −4.08591 | −0.131872 | ||||||||
\(961\) | −29.4074 | −0.948626 | ||||||||
\(962\) | 5.09991 | 0.164428 | ||||||||
\(963\) | −0.00509184 | −0.000164082 0 | ||||||||
\(964\) | −2.75272 | −0.0886593 | ||||||||
\(965\) | −17.6314 | −0.567574 | ||||||||
\(966\) | −6.95946 | −0.223917 | ||||||||
\(967\) | 35.0205 | 1.12618 | 0.563092 | − | 0.826394i | \(-0.309612\pi\) | ||||
0.563092 | + | 0.826394i | \(0.309612\pi\) | |||||||
\(968\) | 23.9693 | 0.770401 | ||||||||
\(969\) | −49.9480 | −1.60456 | ||||||||
\(970\) | 3.40793 | 0.109422 | ||||||||
\(971\) | 12.7728 | 0.409897 | 0.204949 | − | 0.978773i | \(-0.434297\pi\) | ||||
0.204949 | + | 0.978773i | \(0.434297\pi\) | |||||||
\(972\) | −6.03132 | −0.193455 | ||||||||
\(973\) | 0.234681 | 0.00752352 | ||||||||
\(974\) | 19.7355 | 0.632365 | ||||||||
\(975\) | 1.62179 | 0.0519388 | ||||||||
\(976\) | 6.91687 | 0.221404 | ||||||||
\(977\) | −11.3687 | −0.363716 | −0.181858 | − | 0.983325i | \(-0.558211\pi\) | ||||
−0.181858 | + | 0.983325i | \(0.558211\pi\) | |||||||
\(978\) | −15.6380 | −0.500049 | ||||||||
\(979\) | −43.8640 | −1.40190 | ||||||||
\(980\) | −16.3745 | −0.523064 | ||||||||
\(981\) | 4.32377 | 0.138047 | ||||||||
\(982\) | −20.3203 | −0.648445 | ||||||||
\(983\) | −43.0587 | −1.37336 | −0.686679 | − | 0.726961i | \(-0.740932\pi\) | ||||
−0.686679 | + | 0.726961i | \(0.740932\pi\) | |||||||
\(984\) | 2.73018 | 0.0870348 | ||||||||
\(985\) | −38.3442 | −1.22175 | ||||||||
\(986\) | −46.9419 | −1.49494 | ||||||||
\(987\) | −2.20259 | −0.0701092 | ||||||||
\(988\) | 3.52833 | 0.112251 | ||||||||
\(989\) | 39.5471 | 1.25752 | ||||||||
\(990\) | −9.17462 | −0.291588 | ||||||||
\(991\) | 56.8558 | 1.80608 | 0.903042 | − | 0.429551i | \(-0.141328\pi\) | ||||
0.903042 | + | 0.429551i | \(0.141328\pi\) | |||||||
\(992\) | −1.26198 | −0.0400679 | ||||||||
\(993\) | 4.91100 | 0.155846 | ||||||||
\(994\) | 2.98278 | 0.0946082 | ||||||||
\(995\) | 48.0403 | 1.52298 | ||||||||
\(996\) | 12.3774 | 0.392194 | ||||||||
\(997\) | 14.4490 | 0.457604 | 0.228802 | − | 0.973473i | \(-0.426519\pi\) | ||||
0.228802 | + | 0.973473i | \(0.426519\pi\) | |||||||
\(998\) | −7.99526 | −0.253085 | ||||||||
\(999\) | −52.4009 | −1.65789 |
(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 | 8042.2.a.a.1.19 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.a.1.19 | ✓ | 67 | 1.1 | even | 1 | trivial |