Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4003,2,Mod(1,4003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4003, 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("4003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4003.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: | \(31.9641159291\) |
Analytic rank: | \(0\) |
Dimension: | \(179\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.40245 | −1.69879 | −0.849393 | − | 0.527761i | \(-0.823032\pi\) | ||||
−0.849393 | + | 0.527761i | \(0.823032\pi\) | |||||||
\(3\) | 0.531316 | 0.306755 | 0.153378 | − | 0.988168i | \(-0.450985\pi\) | ||||
0.153378 | + | 0.988168i | \(0.450985\pi\) | |||||||
\(4\) | 3.77174 | 1.88587 | ||||||||
\(5\) | 3.68505 | 1.64801 | 0.824003 | − | 0.566586i | \(-0.191736\pi\) | ||||
0.824003 | + | 0.566586i | \(0.191736\pi\) | |||||||
\(6\) | −1.27646 | −0.521112 | ||||||||
\(7\) | −3.72446 | −1.40771 | −0.703857 | − | 0.710341i | \(-0.748541\pi\) | ||||
−0.703857 | + | 0.710341i | \(0.748541\pi\) | |||||||
\(8\) | −4.25652 | −1.50491 | ||||||||
\(9\) | −2.71770 | −0.905901 | ||||||||
\(10\) | −8.85314 | −2.79961 | ||||||||
\(11\) | −4.55164 | −1.37237 | −0.686186 | − | 0.727426i | \(-0.740716\pi\) | ||||
−0.686186 | + | 0.727426i | \(0.740716\pi\) | |||||||
\(12\) | 2.00399 | 0.578501 | ||||||||
\(13\) | −0.961640 | −0.266711 | −0.133355 | − | 0.991068i | \(-0.542575\pi\) | ||||
−0.133355 | + | 0.991068i | \(0.542575\pi\) | |||||||
\(14\) | 8.94782 | 2.39140 | ||||||||
\(15\) | 1.95793 | 0.505535 | ||||||||
\(16\) | 2.68256 | 0.670640 | ||||||||
\(17\) | −4.53477 | −1.09984 | −0.549922 | − | 0.835216i | \(-0.685342\pi\) | ||||
−0.549922 | + | 0.835216i | \(0.685342\pi\) | |||||||
\(18\) | 6.52913 | 1.53893 | ||||||||
\(19\) | −1.62642 | −0.373125 | −0.186563 | − | 0.982443i | \(-0.559735\pi\) | ||||
−0.186563 | + | 0.982443i | \(0.559735\pi\) | |||||||
\(20\) | 13.8991 | 3.10793 | ||||||||
\(21\) | −1.97887 | −0.431824 | ||||||||
\(22\) | 10.9351 | 2.33137 | ||||||||
\(23\) | 0.930366 | 0.193995 | 0.0969974 | − | 0.995285i | \(-0.469076\pi\) | ||||
0.0969974 | + | 0.995285i | \(0.469076\pi\) | |||||||
\(24\) | −2.26156 | −0.461638 | ||||||||
\(25\) | 8.57962 | 1.71592 | ||||||||
\(26\) | 2.31029 | 0.453085 | ||||||||
\(27\) | −3.03791 | −0.584645 | ||||||||
\(28\) | −14.0477 | −2.65477 | ||||||||
\(29\) | 6.79752 | 1.26227 | 0.631134 | − | 0.775674i | \(-0.282590\pi\) | ||||
0.631134 | + | 0.775674i | \(0.282590\pi\) | |||||||
\(30\) | −4.70381 | −0.858795 | ||||||||
\(31\) | −5.57489 | −1.00128 | −0.500640 | − | 0.865656i | \(-0.666902\pi\) | ||||
−0.500640 | + | 0.865656i | \(0.666902\pi\) | |||||||
\(32\) | 2.06833 | 0.365632 | ||||||||
\(33\) | −2.41836 | −0.420982 | ||||||||
\(34\) | 10.8945 | 1.86840 | ||||||||
\(35\) | −13.7248 | −2.31992 | ||||||||
\(36\) | −10.2505 | −1.70841 | ||||||||
\(37\) | 2.73533 | 0.449686 | 0.224843 | − | 0.974395i | \(-0.427813\pi\) | ||||
0.224843 | + | 0.974395i | \(0.427813\pi\) | |||||||
\(38\) | 3.90738 | 0.633860 | ||||||||
\(39\) | −0.510935 | −0.0818150 | ||||||||
\(40\) | −15.6855 | −2.48009 | ||||||||
\(41\) | −9.14250 | −1.42782 | −0.713909 | − | 0.700238i | \(-0.753077\pi\) | ||||
−0.713909 | + | 0.700238i | \(0.753077\pi\) | |||||||
\(42\) | 4.75412 | 0.733576 | ||||||||
\(43\) | 1.82354 | 0.278087 | 0.139044 | − | 0.990286i | \(-0.455597\pi\) | ||||
0.139044 | + | 0.990286i | \(0.455597\pi\) | |||||||
\(44\) | −17.1676 | −2.58812 | ||||||||
\(45\) | −10.0149 | −1.49293 | ||||||||
\(46\) | −2.23515 | −0.329556 | ||||||||
\(47\) | 0.00696210 | 0.00101553 | 0.000507764 | − | 1.00000i | \(-0.499838\pi\) | ||||
0.000507764 | 1.00000i | \(0.499838\pi\) | ||||||||
\(48\) | 1.42529 | 0.205723 | ||||||||
\(49\) | 6.87162 | 0.981660 | ||||||||
\(50\) | −20.6121 | −2.91499 | ||||||||
\(51\) | −2.40940 | −0.337383 | ||||||||
\(52\) | −3.62706 | −0.502983 | ||||||||
\(53\) | −8.51154 | −1.16915 | −0.584575 | − | 0.811340i | \(-0.698739\pi\) | ||||
−0.584575 | + | 0.811340i | \(0.698739\pi\) | |||||||
\(54\) | 7.29841 | 0.993187 | ||||||||
\(55\) | −16.7730 | −2.26168 | ||||||||
\(56\) | 15.8532 | 2.11848 | ||||||||
\(57\) | −0.864141 | −0.114458 | ||||||||
\(58\) | −16.3307 | −2.14432 | ||||||||
\(59\) | 5.88485 | 0.766142 | 0.383071 | − | 0.923719i | \(-0.374866\pi\) | ||||
0.383071 | + | 0.923719i | \(0.374866\pi\) | |||||||
\(60\) | 7.38480 | 0.953374 | ||||||||
\(61\) | 13.4394 | 1.72074 | 0.860372 | − | 0.509666i | \(-0.170231\pi\) | ||||
0.860372 | + | 0.509666i | \(0.170231\pi\) | |||||||
\(62\) | 13.3934 | 1.70096 | ||||||||
\(63\) | 10.1220 | 1.27525 | ||||||||
\(64\) | −10.3342 | −1.29177 | ||||||||
\(65\) | −3.54369 | −0.439541 | ||||||||
\(66\) | 5.80998 | 0.715159 | ||||||||
\(67\) | 12.6636 | 1.54710 | 0.773550 | − | 0.633735i | \(-0.218479\pi\) | ||||
0.773550 | + | 0.633735i | \(0.218479\pi\) | |||||||
\(68\) | −17.1040 | −2.07416 | ||||||||
\(69\) | 0.494318 | 0.0595090 | ||||||||
\(70\) | 32.9732 | 3.94105 | ||||||||
\(71\) | 13.4749 | 1.59917 | 0.799586 | − | 0.600552i | \(-0.205052\pi\) | ||||
0.799586 | + | 0.600552i | \(0.205052\pi\) | |||||||
\(72\) | 11.5679 | 1.36330 | ||||||||
\(73\) | 5.62058 | 0.657839 | 0.328919 | − | 0.944358i | \(-0.393316\pi\) | ||||
0.328919 | + | 0.944358i | \(0.393316\pi\) | |||||||
\(74\) | −6.57149 | −0.763920 | ||||||||
\(75\) | 4.55849 | 0.526369 | ||||||||
\(76\) | −6.13442 | −0.703667 | ||||||||
\(77\) | 16.9524 | 1.93191 | ||||||||
\(78\) | 1.22749 | 0.138986 | ||||||||
\(79\) | −8.28466 | −0.932097 | −0.466048 | − | 0.884759i | \(-0.654323\pi\) | ||||
−0.466048 | + | 0.884759i | \(0.654323\pi\) | |||||||
\(80\) | 9.88538 | 1.10522 | ||||||||
\(81\) | 6.53902 | 0.726558 | ||||||||
\(82\) | 21.9644 | 2.42556 | ||||||||
\(83\) | −7.24734 | −0.795499 | −0.397750 | − | 0.917494i | \(-0.630209\pi\) | ||||
−0.397750 | + | 0.917494i | \(0.630209\pi\) | |||||||
\(84\) | −7.46378 | −0.814365 | ||||||||
\(85\) | −16.7109 | −1.81255 | ||||||||
\(86\) | −4.38096 | −0.472411 | ||||||||
\(87\) | 3.61163 | 0.387208 | ||||||||
\(88\) | 19.3741 | 2.06529 | ||||||||
\(89\) | −4.63487 | −0.491295 | −0.245648 | − | 0.969359i | \(-0.579001\pi\) | ||||
−0.245648 | + | 0.969359i | \(0.579001\pi\) | |||||||
\(90\) | 24.0602 | 2.53617 | ||||||||
\(91\) | 3.58159 | 0.375453 | ||||||||
\(92\) | 3.50910 | 0.365849 | ||||||||
\(93\) | −2.96203 | −0.307148 | ||||||||
\(94\) | −0.0167261 | −0.00172516 | ||||||||
\(95\) | −5.99343 | −0.614913 | ||||||||
\(96\) | 1.09893 | 0.112160 | ||||||||
\(97\) | 16.1394 | 1.63871 | 0.819354 | − | 0.573288i | \(-0.194332\pi\) | ||||
0.819354 | + | 0.573288i | \(0.194332\pi\) | |||||||
\(98\) | −16.5087 | −1.66763 | ||||||||
\(99\) | 12.3700 | 1.24323 | ||||||||
\(100\) | 32.3601 | 3.23601 | ||||||||
\(101\) | 14.9590 | 1.48848 | 0.744240 | − | 0.667913i | \(-0.232812\pi\) | ||||
0.744240 | + | 0.667913i | \(0.232812\pi\) | |||||||
\(102\) | 5.78844 | 0.573141 | ||||||||
\(103\) | 4.30526 | 0.424210 | 0.212105 | − | 0.977247i | \(-0.431968\pi\) | ||||
0.212105 | + | 0.977247i | \(0.431968\pi\) | |||||||
\(104\) | 4.09324 | 0.401375 | ||||||||
\(105\) | −7.29223 | −0.711649 | ||||||||
\(106\) | 20.4485 | 1.98614 | ||||||||
\(107\) | 4.05218 | 0.391739 | 0.195869 | − | 0.980630i | \(-0.437247\pi\) | ||||
0.195869 | + | 0.980630i | \(0.437247\pi\) | |||||||
\(108\) | −11.4582 | −1.10257 | ||||||||
\(109\) | −5.95759 | −0.570633 | −0.285317 | − | 0.958433i | \(-0.592099\pi\) | ||||
−0.285317 | + | 0.958433i | \(0.592099\pi\) | |||||||
\(110\) | 40.2963 | 3.84210 | ||||||||
\(111\) | 1.45333 | 0.137944 | ||||||||
\(112\) | −9.99110 | −0.944070 | ||||||||
\(113\) | 8.51615 | 0.801132 | 0.400566 | − | 0.916268i | \(-0.368814\pi\) | ||||
0.400566 | + | 0.916268i | \(0.368814\pi\) | |||||||
\(114\) | 2.07605 | 0.194440 | ||||||||
\(115\) | 3.42845 | 0.319705 | ||||||||
\(116\) | 25.6385 | 2.38048 | ||||||||
\(117\) | 2.61345 | 0.241614 | ||||||||
\(118\) | −14.1380 | −1.30151 | ||||||||
\(119\) | 16.8896 | 1.54827 | ||||||||
\(120\) | −8.33395 | −0.760782 | ||||||||
\(121\) | 9.71745 | 0.883404 | ||||||||
\(122\) | −32.2875 | −2.92318 | ||||||||
\(123\) | −4.85756 | −0.437991 | ||||||||
\(124\) | −21.0270 | −1.88828 | ||||||||
\(125\) | 13.1911 | 1.17985 | ||||||||
\(126\) | −24.3175 | −2.16638 | ||||||||
\(127\) | 1.59636 | 0.141654 | 0.0708271 | − | 0.997489i | \(-0.477436\pi\) | ||||
0.0708271 | + | 0.997489i | \(0.477436\pi\) | |||||||
\(128\) | 20.6906 | 1.82881 | ||||||||
\(129\) | 0.968876 | 0.0853048 | ||||||||
\(130\) | 8.51353 | 0.746686 | ||||||||
\(131\) | 9.27761 | 0.810588 | 0.405294 | − | 0.914186i | \(-0.367169\pi\) | ||||
0.405294 | + | 0.914186i | \(0.367169\pi\) | |||||||
\(132\) | −9.12143 | −0.793919 | ||||||||
\(133\) | 6.05752 | 0.525254 | ||||||||
\(134\) | −30.4235 | −2.62819 | ||||||||
\(135\) | −11.1948 | −0.963499 | ||||||||
\(136\) | 19.3023 | 1.65516 | ||||||||
\(137\) | −0.567671 | −0.0484994 | −0.0242497 | − | 0.999706i | \(-0.507720\pi\) | ||||
−0.0242497 | + | 0.999706i | \(0.507720\pi\) | |||||||
\(138\) | −1.18757 | −0.101093 | ||||||||
\(139\) | −14.5660 | −1.23547 | −0.617735 | − | 0.786386i | \(-0.711950\pi\) | ||||
−0.617735 | + | 0.786386i | \(0.711950\pi\) | |||||||
\(140\) | −51.7666 | −4.37507 | ||||||||
\(141\) | 0.00369908 | 0.000311518 0 | ||||||||
\(142\) | −32.3726 | −2.71665 | ||||||||
\(143\) | 4.37704 | 0.366027 | ||||||||
\(144\) | −7.29041 | −0.607534 | ||||||||
\(145\) | 25.0492 | 2.08023 | ||||||||
\(146\) | −13.5031 | −1.11753 | ||||||||
\(147\) | 3.65100 | 0.301130 | ||||||||
\(148\) | 10.3170 | 0.848050 | ||||||||
\(149\) | 15.0172 | 1.23026 | 0.615130 | − | 0.788426i | \(-0.289104\pi\) | ||||
0.615130 | + | 0.788426i | \(0.289104\pi\) | |||||||
\(150\) | −10.9515 | −0.894188 | ||||||||
\(151\) | −5.15372 | −0.419404 | −0.209702 | − | 0.977765i | \(-0.567249\pi\) | ||||
−0.209702 | + | 0.977765i | \(0.567249\pi\) | |||||||
\(152\) | 6.92287 | 0.561519 | ||||||||
\(153\) | 12.3242 | 0.996349 | ||||||||
\(154\) | −40.7273 | −3.28190 | ||||||||
\(155\) | −20.5438 | −1.65011 | ||||||||
\(156\) | −1.92711 | −0.154293 | ||||||||
\(157\) | 0.592735 | 0.0473054 | 0.0236527 | − | 0.999720i | \(-0.492470\pi\) | ||||
0.0236527 | + | 0.999720i | \(0.492470\pi\) | |||||||
\(158\) | 19.9034 | 1.58343 | ||||||||
\(159\) | −4.52232 | −0.358643 | ||||||||
\(160\) | 7.62189 | 0.602563 | ||||||||
\(161\) | −3.46511 | −0.273089 | ||||||||
\(162\) | −15.7096 | −1.23427 | ||||||||
\(163\) | 8.45251 | 0.662052 | 0.331026 | − | 0.943622i | \(-0.392605\pi\) | ||||
0.331026 | + | 0.943622i | \(0.392605\pi\) | |||||||
\(164\) | −34.4832 | −2.69268 | ||||||||
\(165\) | −8.91179 | −0.693782 | ||||||||
\(166\) | 17.4113 | 1.35138 | ||||||||
\(167\) | 4.67789 | 0.361986 | 0.180993 | − | 0.983484i | \(-0.442069\pi\) | ||||
0.180993 | + | 0.983484i | \(0.442069\pi\) | |||||||
\(168\) | 8.42308 | 0.649855 | ||||||||
\(169\) | −12.0752 | −0.928865 | ||||||||
\(170\) | 40.1469 | 3.07913 | ||||||||
\(171\) | 4.42012 | 0.338015 | ||||||||
\(172\) | 6.87793 | 0.524437 | ||||||||
\(173\) | 14.3882 | 1.09391 | 0.546957 | − | 0.837161i | \(-0.315786\pi\) | ||||
0.546957 | + | 0.837161i | \(0.315786\pi\) | |||||||
\(174\) | −8.67675 | −0.657783 | ||||||||
\(175\) | −31.9545 | −2.41553 | ||||||||
\(176\) | −12.2101 | −0.920368 | ||||||||
\(177\) | 3.12671 | 0.235018 | ||||||||
\(178\) | 11.1350 | 0.834605 | ||||||||
\(179\) | −5.02893 | −0.375880 | −0.187940 | − | 0.982181i | \(-0.560181\pi\) | ||||
−0.187940 | + | 0.982181i | \(0.560181\pi\) | |||||||
\(180\) | −37.7736 | −2.81548 | ||||||||
\(181\) | 13.9492 | 1.03684 | 0.518419 | − | 0.855127i | \(-0.326521\pi\) | ||||
0.518419 | + | 0.855127i | \(0.326521\pi\) | |||||||
\(182\) | −8.60458 | −0.637814 | ||||||||
\(183\) | 7.14059 | 0.527848 | ||||||||
\(184\) | −3.96012 | −0.291944 | ||||||||
\(185\) | 10.0799 | 0.741085 | ||||||||
\(186\) | 7.11611 | 0.521778 | ||||||||
\(187\) | 20.6406 | 1.50939 | ||||||||
\(188\) | 0.0262593 | 0.00191515 | ||||||||
\(189\) | 11.3146 | 0.823014 | ||||||||
\(190\) | 14.3989 | 1.04460 | ||||||||
\(191\) | 2.30215 | 0.166578 | 0.0832888 | − | 0.996525i | \(-0.473458\pi\) | ||||
0.0832888 | + | 0.996525i | \(0.473458\pi\) | |||||||
\(192\) | −5.49071 | −0.396258 | ||||||||
\(193\) | 5.40944 | 0.389380 | 0.194690 | − | 0.980865i | \(-0.437630\pi\) | ||||
0.194690 | + | 0.980865i | \(0.437630\pi\) | |||||||
\(194\) | −38.7740 | −2.78381 | ||||||||
\(195\) | −1.88282 | −0.134832 | ||||||||
\(196\) | 25.9180 | 1.85128 | ||||||||
\(197\) | −5.41283 | −0.385648 | −0.192824 | − | 0.981233i | \(-0.561765\pi\) | ||||
−0.192824 | + | 0.981233i | \(0.561765\pi\) | |||||||
\(198\) | −29.7183 | −2.11199 | ||||||||
\(199\) | −0.666988 | −0.0472816 | −0.0236408 | − | 0.999721i | \(-0.507526\pi\) | ||||
−0.0236408 | + | 0.999721i | \(0.507526\pi\) | |||||||
\(200\) | −36.5193 | −2.58230 | ||||||||
\(201\) | 6.72835 | 0.474582 | ||||||||
\(202\) | −35.9383 | −2.52861 | ||||||||
\(203\) | −25.3171 | −1.77691 | ||||||||
\(204\) | −9.08762 | −0.636261 | ||||||||
\(205\) | −33.6906 | −2.35305 | ||||||||
\(206\) | −10.3431 | −0.720641 | ||||||||
\(207\) | −2.52846 | −0.175740 | ||||||||
\(208\) | −2.57966 | −0.178867 | ||||||||
\(209\) | 7.40286 | 0.512067 | ||||||||
\(210\) | 17.5192 | 1.20894 | ||||||||
\(211\) | 6.99575 | 0.481607 | 0.240804 | − | 0.970574i | \(-0.422589\pi\) | ||||
0.240804 | + | 0.970574i | \(0.422589\pi\) | |||||||
\(212\) | −32.1033 | −2.20487 | ||||||||
\(213\) | 7.15941 | 0.490555 | ||||||||
\(214\) | −9.73514 | −0.665480 | ||||||||
\(215\) | 6.71984 | 0.458289 | ||||||||
\(216\) | 12.9309 | 0.879836 | ||||||||
\(217\) | 20.7635 | 1.40952 | ||||||||
\(218\) | 14.3128 | 0.969384 | ||||||||
\(219\) | 2.98630 | 0.201796 | ||||||||
\(220\) | −63.2636 | −4.26523 | ||||||||
\(221\) | 4.36082 | 0.293340 | ||||||||
\(222\) | −3.49154 | −0.234337 | ||||||||
\(223\) | −2.58693 | −0.173234 | −0.0866168 | − | 0.996242i | \(-0.527606\pi\) | ||||
−0.0866168 | + | 0.996242i | \(0.527606\pi\) | |||||||
\(224\) | −7.70340 | −0.514705 | ||||||||
\(225\) | −23.3169 | −1.55446 | ||||||||
\(226\) | −20.4596 | −1.36095 | ||||||||
\(227\) | −20.2380 | −1.34324 | −0.671620 | − | 0.740896i | \(-0.734401\pi\) | ||||
−0.671620 | + | 0.740896i | \(0.734401\pi\) | |||||||
\(228\) | −3.25932 | −0.215854 | ||||||||
\(229\) | −11.7467 | −0.776241 | −0.388120 | − | 0.921609i | \(-0.626876\pi\) | ||||
−0.388120 | + | 0.921609i | \(0.626876\pi\) | |||||||
\(230\) | −8.23666 | −0.543109 | ||||||||
\(231\) | 9.00709 | 0.592623 | ||||||||
\(232\) | −28.9338 | −1.89959 | ||||||||
\(233\) | 10.7120 | 0.701764 | 0.350882 | − | 0.936420i | \(-0.385882\pi\) | ||||
0.350882 | + | 0.936420i | \(0.385882\pi\) | |||||||
\(234\) | −6.27868 | −0.410450 | ||||||||
\(235\) | 0.0256557 | 0.00167359 | ||||||||
\(236\) | 22.1961 | 1.44485 | ||||||||
\(237\) | −4.40177 | −0.285926 | ||||||||
\(238\) | −40.5763 | −2.63017 | ||||||||
\(239\) | −6.62790 | −0.428723 | −0.214362 | − | 0.976754i | \(-0.568767\pi\) | ||||
−0.214362 | + | 0.976754i | \(0.568767\pi\) | |||||||
\(240\) | 5.25226 | 0.339032 | ||||||||
\(241\) | −12.4011 | −0.798827 | −0.399414 | − | 0.916771i | \(-0.630786\pi\) | ||||
−0.399414 | + | 0.916771i | \(0.630786\pi\) | |||||||
\(242\) | −23.3456 | −1.50071 | ||||||||
\(243\) | 12.5880 | 0.807521 | ||||||||
\(244\) | 50.6901 | 3.24510 | ||||||||
\(245\) | 25.3223 | 1.61778 | ||||||||
\(246\) | 11.6700 | 0.744053 | ||||||||
\(247\) | 1.56403 | 0.0995166 | ||||||||
\(248\) | 23.7296 | 1.50683 | ||||||||
\(249\) | −3.85063 | −0.244024 | ||||||||
\(250\) | −31.6908 | −2.00430 | ||||||||
\(251\) | −3.81667 | −0.240906 | −0.120453 | − | 0.992719i | \(-0.538435\pi\) | ||||
−0.120453 | + | 0.992719i | \(0.538435\pi\) | |||||||
\(252\) | 38.1775 | 2.40496 | ||||||||
\(253\) | −4.23469 | −0.266233 | ||||||||
\(254\) | −3.83517 | −0.240640 | ||||||||
\(255\) | −8.87875 | −0.556009 | ||||||||
\(256\) | −29.0397 | −1.81498 | ||||||||
\(257\) | −13.1308 | −0.819078 | −0.409539 | − | 0.912293i | \(-0.634310\pi\) | ||||
−0.409539 | + | 0.912293i | \(0.634310\pi\) | |||||||
\(258\) | −2.32767 | −0.144914 | ||||||||
\(259\) | −10.1876 | −0.633030 | ||||||||
\(260\) | −13.3659 | −0.828918 | ||||||||
\(261\) | −18.4736 | −1.14349 | ||||||||
\(262\) | −22.2889 | −1.37702 | ||||||||
\(263\) | 0.683836 | 0.0421671 | 0.0210836 | − | 0.999778i | \(-0.493288\pi\) | ||||
0.0210836 | + | 0.999778i | \(0.493288\pi\) | |||||||
\(264\) | 10.2938 | 0.633539 | ||||||||
\(265\) | −31.3655 | −1.92677 | ||||||||
\(266\) | −14.5529 | −0.892294 | ||||||||
\(267\) | −2.46258 | −0.150707 | ||||||||
\(268\) | 47.7637 | 2.91763 | ||||||||
\(269\) | 8.79990 | 0.536539 | 0.268270 | − | 0.963344i | \(-0.413548\pi\) | ||||
0.268270 | + | 0.963344i | \(0.413548\pi\) | |||||||
\(270\) | 26.8950 | 1.63678 | ||||||||
\(271\) | −18.8359 | −1.14420 | −0.572098 | − | 0.820185i | \(-0.693870\pi\) | ||||
−0.572098 | + | 0.820185i | \(0.693870\pi\) | |||||||
\(272\) | −12.1648 | −0.737599 | ||||||||
\(273\) | 1.90296 | 0.115172 | ||||||||
\(274\) | 1.36380 | 0.0823901 | ||||||||
\(275\) | −39.0513 | −2.35488 | ||||||||
\(276\) | 1.86444 | 0.112226 | ||||||||
\(277\) | 14.6318 | 0.879138 | 0.439569 | − | 0.898209i | \(-0.355131\pi\) | ||||
0.439569 | + | 0.898209i | \(0.355131\pi\) | |||||||
\(278\) | 34.9940 | 2.09880 | ||||||||
\(279\) | 15.1509 | 0.907060 | ||||||||
\(280\) | 58.4200 | 3.49126 | ||||||||
\(281\) | 31.4621 | 1.87687 | 0.938435 | − | 0.345456i | \(-0.112276\pi\) | ||||
0.938435 | + | 0.345456i | \(0.112276\pi\) | |||||||
\(282\) | −0.00888683 | −0.000529203 0 | ||||||||
\(283\) | −28.2365 | −1.67849 | −0.839244 | − | 0.543755i | \(-0.817002\pi\) | ||||
−0.839244 | + | 0.543755i | \(0.817002\pi\) | |||||||
\(284\) | 50.8237 | 3.01583 | ||||||||
\(285\) | −3.18440 | −0.188628 | ||||||||
\(286\) | −10.5156 | −0.621801 | ||||||||
\(287\) | 34.0509 | 2.00996 | ||||||||
\(288\) | −5.62110 | −0.331226 | ||||||||
\(289\) | 3.56413 | 0.209655 | ||||||||
\(290\) | −60.1794 | −3.53386 | ||||||||
\(291\) | 8.57512 | 0.502683 | ||||||||
\(292\) | 21.1994 | 1.24060 | ||||||||
\(293\) | −16.1451 | −0.943206 | −0.471603 | − | 0.881811i | \(-0.656324\pi\) | ||||
−0.471603 | + | 0.881811i | \(0.656324\pi\) | |||||||
\(294\) | −8.77133 | −0.511554 | ||||||||
\(295\) | 21.6860 | 1.26261 | ||||||||
\(296\) | −11.6430 | −0.676735 | ||||||||
\(297\) | 13.8275 | 0.802351 | ||||||||
\(298\) | −36.0781 | −2.08995 | ||||||||
\(299\) | −0.894678 | −0.0517405 | ||||||||
\(300\) | 17.1934 | 0.992664 | ||||||||
\(301\) | −6.79171 | −0.391467 | ||||||||
\(302\) | 12.3815 | 0.712477 | ||||||||
\(303\) | 7.94797 | 0.456599 | ||||||||
\(304\) | −4.36296 | −0.250233 | ||||||||
\(305\) | 49.5251 | 2.83580 | ||||||||
\(306\) | −29.6081 | −1.69258 | ||||||||
\(307\) | −21.6345 | −1.23475 | −0.617373 | − | 0.786671i | \(-0.711803\pi\) | ||||
−0.617373 | + | 0.786671i | \(0.711803\pi\) | |||||||
\(308\) | 63.9402 | 3.64333 | ||||||||
\(309\) | 2.28745 | 0.130129 | ||||||||
\(310\) | 49.3553 | 2.80319 | ||||||||
\(311\) | −33.0908 | −1.87641 | −0.938205 | − | 0.346081i | \(-0.887512\pi\) | ||||
−0.938205 | + | 0.346081i | \(0.887512\pi\) | |||||||
\(312\) | 2.17480 | 0.123124 | ||||||||
\(313\) | 17.5740 | 0.993339 | 0.496670 | − | 0.867940i | \(-0.334556\pi\) | ||||
0.496670 | + | 0.867940i | \(0.334556\pi\) | |||||||
\(314\) | −1.42401 | −0.0803617 | ||||||||
\(315\) | 37.3000 | 2.10162 | ||||||||
\(316\) | −31.2476 | −1.75782 | ||||||||
\(317\) | 26.9746 | 1.51504 | 0.757521 | − | 0.652811i | \(-0.226410\pi\) | ||||
0.757521 | + | 0.652811i | \(0.226410\pi\) | |||||||
\(318\) | 10.8646 | 0.609258 | ||||||||
\(319\) | −30.9399 | −1.73230 | ||||||||
\(320\) | −38.0819 | −2.12885 | ||||||||
\(321\) | 2.15299 | 0.120168 | ||||||||
\(322\) | 8.32475 | 0.463920 | ||||||||
\(323\) | 7.37542 | 0.410379 | ||||||||
\(324\) | 24.6635 | 1.37020 | ||||||||
\(325\) | −8.25050 | −0.457656 | ||||||||
\(326\) | −20.3067 | −1.12468 | ||||||||
\(327\) | −3.16536 | −0.175045 | ||||||||
\(328\) | 38.9152 | 2.14873 | ||||||||
\(329\) | −0.0259301 | −0.00142957 | ||||||||
\(330\) | 21.4101 | 1.17859 | ||||||||
\(331\) | 15.0177 | 0.825450 | 0.412725 | − | 0.910856i | \(-0.364577\pi\) | ||||
0.412725 | + | 0.910856i | \(0.364577\pi\) | |||||||
\(332\) | −27.3351 | −1.50021 | ||||||||
\(333\) | −7.43383 | −0.407371 | ||||||||
\(334\) | −11.2384 | −0.614936 | ||||||||
\(335\) | 46.6659 | 2.54963 | ||||||||
\(336\) | −5.30843 | −0.289599 | ||||||||
\(337\) | −17.8446 | −0.972057 | −0.486028 | − | 0.873943i | \(-0.661555\pi\) | ||||
−0.486028 | + | 0.873943i | \(0.661555\pi\) | |||||||
\(338\) | 29.0101 | 1.57794 | ||||||||
\(339\) | 4.52477 | 0.245752 | ||||||||
\(340\) | −63.0291 | −3.41823 | ||||||||
\(341\) | 25.3749 | 1.37413 | ||||||||
\(342\) | −10.6191 | −0.574214 | ||||||||
\(343\) | 0.478148 | 0.0258176 | ||||||||
\(344\) | −7.76193 | −0.418495 | ||||||||
\(345\) | 1.82159 | 0.0980711 | ||||||||
\(346\) | −34.5669 | −1.85833 | ||||||||
\(347\) | 21.1764 | 1.13681 | 0.568404 | − | 0.822750i | \(-0.307561\pi\) | ||||
0.568404 | + | 0.822750i | \(0.307561\pi\) | |||||||
\(348\) | 13.6221 | 0.730224 | ||||||||
\(349\) | −28.2073 | −1.50990 | −0.754951 | − | 0.655781i | \(-0.772339\pi\) | ||||
−0.754951 | + | 0.655781i | \(0.772339\pi\) | |||||||
\(350\) | 76.7688 | 4.10347 | ||||||||
\(351\) | 2.92137 | 0.155931 | ||||||||
\(352\) | −9.41428 | −0.501783 | ||||||||
\(353\) | 14.4580 | 0.769524 | 0.384762 | − | 0.923016i | \(-0.374284\pi\) | ||||
0.384762 | + | 0.923016i | \(0.374284\pi\) | |||||||
\(354\) | −7.51176 | −0.399246 | ||||||||
\(355\) | 49.6556 | 2.63545 | ||||||||
\(356\) | −17.4815 | −0.926520 | ||||||||
\(357\) | 8.97370 | 0.474939 | ||||||||
\(358\) | 12.0817 | 0.638539 | ||||||||
\(359\) | −30.3420 | −1.60139 | −0.800694 | − | 0.599073i | \(-0.795536\pi\) | ||||
−0.800694 | + | 0.599073i | \(0.795536\pi\) | |||||||
\(360\) | 42.6285 | 2.24672 | ||||||||
\(361\) | −16.3548 | −0.860777 | ||||||||
\(362\) | −33.5123 | −1.76137 | ||||||||
\(363\) | 5.16304 | 0.270989 | ||||||||
\(364\) | 13.5088 | 0.708056 | ||||||||
\(365\) | 20.7121 | 1.08412 | ||||||||
\(366\) | −17.1549 | −0.896700 | ||||||||
\(367\) | 26.8768 | 1.40296 | 0.701480 | − | 0.712689i | \(-0.252523\pi\) | ||||
0.701480 | + | 0.712689i | \(0.252523\pi\) | |||||||
\(368\) | 2.49576 | 0.130101 | ||||||||
\(369\) | 24.8466 | 1.29346 | ||||||||
\(370\) | −24.2163 | −1.25895 | ||||||||
\(371\) | 31.7009 | 1.64583 | ||||||||
\(372\) | −11.1720 | −0.579242 | ||||||||
\(373\) | −10.9308 | −0.565975 | −0.282988 | − | 0.959124i | \(-0.591326\pi\) | ||||
−0.282988 | + | 0.959124i | \(0.591326\pi\) | |||||||
\(374\) | −49.5880 | −2.56414 | ||||||||
\(375\) | 7.00863 | 0.361924 | ||||||||
\(376\) | −0.0296343 | −0.00152827 | ||||||||
\(377\) | −6.53677 | −0.336661 | ||||||||
\(378\) | −27.1826 | −1.39812 | ||||||||
\(379\) | 23.9213 | 1.22875 | 0.614377 | − | 0.789013i | \(-0.289408\pi\) | ||||
0.614377 | + | 0.789013i | \(0.289408\pi\) | |||||||
\(380\) | −22.6057 | −1.15965 | ||||||||
\(381\) | 0.848172 | 0.0434532 | ||||||||
\(382\) | −5.53078 | −0.282980 | ||||||||
\(383\) | 34.5908 | 1.76751 | 0.883754 | − | 0.467952i | \(-0.155008\pi\) | ||||
0.883754 | + | 0.467952i | \(0.155008\pi\) | |||||||
\(384\) | 10.9933 | 0.560997 | ||||||||
\(385\) | 62.4706 | 3.18380 | ||||||||
\(386\) | −12.9959 | −0.661473 | ||||||||
\(387\) | −4.95584 | −0.251920 | ||||||||
\(388\) | 60.8737 | 3.09039 | ||||||||
\(389\) | 14.7327 | 0.746980 | 0.373490 | − | 0.927634i | \(-0.378161\pi\) | ||||
0.373490 | + | 0.927634i | \(0.378161\pi\) | |||||||
\(390\) | 4.52338 | 0.229050 | ||||||||
\(391\) | −4.21900 | −0.213364 | ||||||||
\(392\) | −29.2492 | −1.47731 | ||||||||
\(393\) | 4.92934 | 0.248652 | ||||||||
\(394\) | 13.0040 | 0.655134 | ||||||||
\(395\) | −30.5294 | −1.53610 | ||||||||
\(396\) | 46.6565 | 2.34458 | ||||||||
\(397\) | 9.26071 | 0.464782 | 0.232391 | − | 0.972622i | \(-0.425345\pi\) | ||||
0.232391 | + | 0.972622i | \(0.425345\pi\) | |||||||
\(398\) | 1.60240 | 0.0803212 | ||||||||
\(399\) | 3.21846 | 0.161125 | ||||||||
\(400\) | 23.0153 | 1.15077 | ||||||||
\(401\) | −8.29084 | −0.414025 | −0.207012 | − | 0.978338i | \(-0.566374\pi\) | ||||
−0.207012 | + | 0.978338i | \(0.566374\pi\) | |||||||
\(402\) | −16.1645 | −0.806212 | ||||||||
\(403\) | 5.36104 | 0.267052 | ||||||||
\(404\) | 56.4216 | 2.80708 | ||||||||
\(405\) | 24.0966 | 1.19737 | ||||||||
\(406\) | 60.8230 | 3.01859 | ||||||||
\(407\) | −12.4503 | −0.617137 | ||||||||
\(408\) | 10.2556 | 0.507729 | ||||||||
\(409\) | −31.7640 | −1.57063 | −0.785314 | − | 0.619098i | \(-0.787498\pi\) | ||||
−0.785314 | + | 0.619098i | \(0.787498\pi\) | |||||||
\(410\) | 80.9398 | 3.99733 | ||||||||
\(411\) | −0.301613 | −0.0148775 | ||||||||
\(412\) | 16.2383 | 0.800005 | ||||||||
\(413\) | −21.9179 | −1.07851 | ||||||||
\(414\) | 6.07449 | 0.298545 | ||||||||
\(415\) | −26.7068 | −1.31099 | ||||||||
\(416\) | −1.98899 | −0.0975180 | ||||||||
\(417\) | −7.73914 | −0.378987 | ||||||||
\(418\) | −17.7850 | −0.869892 | ||||||||
\(419\) | 25.6892 | 1.25500 | 0.627499 | − | 0.778617i | \(-0.284079\pi\) | ||||
0.627499 | + | 0.778617i | \(0.284079\pi\) | |||||||
\(420\) | −27.5044 | −1.34208 | ||||||||
\(421\) | −2.80135 | −0.136529 | −0.0682647 | − | 0.997667i | \(-0.521746\pi\) | ||||
−0.0682647 | + | 0.997667i | \(0.521746\pi\) | |||||||
\(422\) | −16.8069 | −0.818147 | ||||||||
\(423\) | −0.0189209 | −0.000919967 0 | ||||||||
\(424\) | 36.2295 | 1.75946 | ||||||||
\(425\) | −38.9066 | −1.88725 | ||||||||
\(426\) | −17.2001 | −0.833347 | ||||||||
\(427\) | −50.0547 | −2.42232 | ||||||||
\(428\) | 15.2838 | 0.738769 | ||||||||
\(429\) | 2.32559 | 0.112281 | ||||||||
\(430\) | −16.1441 | −0.778535 | ||||||||
\(431\) | 9.53568 | 0.459317 | 0.229659 | − | 0.973271i | \(-0.426239\pi\) | ||||
0.229659 | + | 0.973271i | \(0.426239\pi\) | |||||||
\(432\) | −8.14937 | −0.392087 | ||||||||
\(433\) | 35.6273 | 1.71214 | 0.856068 | − | 0.516862i | \(-0.172900\pi\) | ||||
0.856068 | + | 0.516862i | \(0.172900\pi\) | |||||||
\(434\) | −49.8831 | −2.39446 | ||||||||
\(435\) | 13.3091 | 0.638120 | ||||||||
\(436\) | −22.4705 | −1.07614 | ||||||||
\(437\) | −1.51316 | −0.0723844 | ||||||||
\(438\) | −7.17443 | −0.342807 | ||||||||
\(439\) | −14.0985 | −0.672885 | −0.336443 | − | 0.941704i | \(-0.609224\pi\) | ||||
−0.336443 | + | 0.941704i | \(0.609224\pi\) | |||||||
\(440\) | 71.3947 | 3.40361 | ||||||||
\(441\) | −18.6750 | −0.889287 | ||||||||
\(442\) | −10.4766 | −0.498322 | ||||||||
\(443\) | 20.7098 | 0.983953 | 0.491977 | − | 0.870608i | \(-0.336275\pi\) | ||||
0.491977 | + | 0.870608i | \(0.336275\pi\) | |||||||
\(444\) | 5.48158 | 0.260144 | ||||||||
\(445\) | −17.0797 | −0.809657 | ||||||||
\(446\) | 6.21495 | 0.294287 | ||||||||
\(447\) | 7.97890 | 0.377389 | ||||||||
\(448\) | 38.4892 | 1.81844 | ||||||||
\(449\) | 31.4922 | 1.48621 | 0.743105 | − | 0.669175i | \(-0.233352\pi\) | ||||
0.743105 | + | 0.669175i | \(0.233352\pi\) | |||||||
\(450\) | 56.0175 | 2.64069 | ||||||||
\(451\) | 41.6134 | 1.95950 | ||||||||
\(452\) | 32.1207 | 1.51083 | ||||||||
\(453\) | −2.73826 | −0.128654 | ||||||||
\(454\) | 48.6206 | 2.28188 | ||||||||
\(455\) | 13.1984 | 0.618749 | ||||||||
\(456\) | 3.67823 | 0.172249 | ||||||||
\(457\) | −5.33720 | −0.249664 | −0.124832 | − | 0.992178i | \(-0.539839\pi\) | ||||
−0.124832 | + | 0.992178i | \(0.539839\pi\) | |||||||
\(458\) | 28.2207 | 1.31867 | ||||||||
\(459\) | 13.7762 | 0.643018 | ||||||||
\(460\) | 12.9312 | 0.602922 | ||||||||
\(461\) | 4.49903 | 0.209541 | 0.104770 | − | 0.994496i | \(-0.466589\pi\) | ||||
0.104770 | + | 0.994496i | \(0.466589\pi\) | |||||||
\(462\) | −21.6390 | −1.00674 | ||||||||
\(463\) | −26.9593 | −1.25291 | −0.626453 | − | 0.779460i | \(-0.715494\pi\) | ||||
−0.626453 | + | 0.779460i | \(0.715494\pi\) | |||||||
\(464\) | 18.2348 | 0.846528 | ||||||||
\(465\) | −10.9152 | −0.506182 | ||||||||
\(466\) | −25.7349 | −1.19215 | ||||||||
\(467\) | 14.1420 | 0.654413 | 0.327207 | − | 0.944953i | \(-0.393893\pi\) | ||||
0.327207 | + | 0.944953i | \(0.393893\pi\) | |||||||
\(468\) | 9.85727 | 0.455653 | ||||||||
\(469\) | −47.1650 | −2.17788 | ||||||||
\(470\) | −0.0616365 | −0.00284308 | ||||||||
\(471\) | 0.314930 | 0.0145112 | ||||||||
\(472\) | −25.0490 | −1.15297 | ||||||||
\(473\) | −8.30010 | −0.381639 | ||||||||
\(474\) | 10.5750 | 0.485727 | ||||||||
\(475\) | −13.9540 | −0.640255 | ||||||||
\(476\) | 63.7032 | 2.91983 | ||||||||
\(477\) | 23.1318 | 1.05913 | ||||||||
\(478\) | 15.9232 | 0.728309 | ||||||||
\(479\) | −40.2979 | −1.84126 | −0.920630 | − | 0.390436i | \(-0.872324\pi\) | ||||
−0.920630 | + | 0.390436i | \(0.872324\pi\) | |||||||
\(480\) | 4.04963 | 0.184840 | ||||||||
\(481\) | −2.63041 | −0.119936 | ||||||||
\(482\) | 29.7930 | 1.35704 | ||||||||
\(483\) | −1.84107 | −0.0837716 | ||||||||
\(484\) | 36.6517 | 1.66599 | ||||||||
\(485\) | 59.4746 | 2.70060 | ||||||||
\(486\) | −30.2420 | −1.37180 | ||||||||
\(487\) | 23.9537 | 1.08544 | 0.542722 | − | 0.839912i | \(-0.317394\pi\) | ||||
0.542722 | + | 0.839912i | \(0.317394\pi\) | |||||||
\(488\) | −57.2052 | −2.58956 | ||||||||
\(489\) | 4.49095 | 0.203088 | ||||||||
\(490\) | −60.8354 | −2.74826 | ||||||||
\(491\) | 10.1271 | 0.457029 | 0.228515 | − | 0.973541i | \(-0.426613\pi\) | ||||
0.228515 | + | 0.973541i | \(0.426613\pi\) | |||||||
\(492\) | −18.3215 | −0.825995 | ||||||||
\(493\) | −30.8252 | −1.38830 | ||||||||
\(494\) | −3.75749 | −0.169057 | ||||||||
\(495\) | 45.5842 | 2.04886 | ||||||||
\(496\) | −14.9550 | −0.671498 | ||||||||
\(497\) | −50.1866 | −2.25118 | ||||||||
\(498\) | 9.25093 | 0.414544 | ||||||||
\(499\) | −16.4721 | −0.737391 | −0.368695 | − | 0.929550i | \(-0.620195\pi\) | ||||
−0.368695 | + | 0.929550i | \(0.620195\pi\) | |||||||
\(500\) | 49.7534 | 2.22504 | ||||||||
\(501\) | 2.48544 | 0.111041 | ||||||||
\(502\) | 9.16933 | 0.409247 | ||||||||
\(503\) | −42.7945 | −1.90811 | −0.954057 | − | 0.299625i | \(-0.903138\pi\) | ||||
−0.954057 | + | 0.299625i | \(0.903138\pi\) | |||||||
\(504\) | −43.0844 | −1.91913 | ||||||||
\(505\) | 55.1248 | 2.45302 | ||||||||
\(506\) | 10.1736 | 0.452273 | ||||||||
\(507\) | −6.41577 | −0.284934 | ||||||||
\(508\) | 6.02106 | 0.267142 | ||||||||
\(509\) | −10.4592 | −0.463594 | −0.231797 | − | 0.972764i | \(-0.574461\pi\) | ||||
−0.231797 | + | 0.972764i | \(0.574461\pi\) | |||||||
\(510\) | 21.3307 | 0.944540 | ||||||||
\(511\) | −20.9336 | −0.926049 | ||||||||
\(512\) | 28.3851 | 1.25446 | ||||||||
\(513\) | 4.94090 | 0.218146 | ||||||||
\(514\) | 31.5461 | 1.39144 | ||||||||
\(515\) | 15.8651 | 0.699100 | ||||||||
\(516\) | 3.65435 | 0.160874 | ||||||||
\(517\) | −0.0316890 | −0.00139368 | ||||||||
\(518\) | 24.4753 | 1.07538 | ||||||||
\(519\) | 7.64468 | 0.335564 | ||||||||
\(520\) | 15.0838 | 0.661468 | ||||||||
\(521\) | 22.9617 | 1.00597 | 0.502985 | − | 0.864295i | \(-0.332235\pi\) | ||||
0.502985 | + | 0.864295i | \(0.332235\pi\) | |||||||
\(522\) | 44.3819 | 1.94254 | ||||||||
\(523\) | −13.0327 | −0.569880 | −0.284940 | − | 0.958545i | \(-0.591974\pi\) | ||||
−0.284940 | + | 0.958545i | \(0.591974\pi\) | |||||||
\(524\) | 34.9928 | 1.52867 | ||||||||
\(525\) | −16.9779 | −0.740977 | ||||||||
\(526\) | −1.64288 | −0.0716329 | ||||||||
\(527\) | 25.2808 | 1.10125 | ||||||||
\(528\) | −6.48740 | −0.282328 | ||||||||
\(529\) | −22.1344 | −0.962366 | ||||||||
\(530\) | 75.3539 | 3.27316 | ||||||||
\(531\) | −15.9933 | −0.694049 | ||||||||
\(532\) | 22.8474 | 0.990562 | ||||||||
\(533\) | 8.79179 | 0.380815 | ||||||||
\(534\) | 5.91621 | 0.256020 | ||||||||
\(535\) | 14.9325 | 0.645588 | ||||||||
\(536\) | −53.9027 | −2.32824 | ||||||||
\(537\) | −2.67195 | −0.115303 | ||||||||
\(538\) | −21.1413 | −0.911465 | ||||||||
\(539\) | −31.2772 | −1.34720 | ||||||||
\(540\) | −42.2241 | −1.81704 | ||||||||
\(541\) | 0.553213 | 0.0237845 | 0.0118922 | − | 0.999929i | \(-0.496214\pi\) | ||||
0.0118922 | + | 0.999929i | \(0.496214\pi\) | |||||||
\(542\) | 45.2521 | 1.94374 | ||||||||
\(543\) | 7.41145 | 0.318056 | ||||||||
\(544\) | −9.37938 | −0.402138 | ||||||||
\(545\) | −21.9540 | −0.940407 | ||||||||
\(546\) | −4.57175 | −0.195653 | ||||||||
\(547\) | 29.4848 | 1.26068 | 0.630339 | − | 0.776320i | \(-0.282916\pi\) | ||||
0.630339 | + | 0.776320i | \(0.282916\pi\) | |||||||
\(548\) | −2.14111 | −0.0914637 | ||||||||
\(549\) | −36.5244 | −1.55882 | ||||||||
\(550\) | 93.8187 | 4.00044 | ||||||||
\(551\) | −11.0556 | −0.470984 | ||||||||
\(552\) | −2.10407 | −0.0895554 | ||||||||
\(553\) | 30.8559 | 1.31213 | ||||||||
\(554\) | −35.1520 | −1.49347 | ||||||||
\(555\) | 5.35559 | 0.227332 | ||||||||
\(556\) | −54.9392 | −2.32994 | ||||||||
\(557\) | 28.1256 | 1.19172 | 0.595859 | − | 0.803089i | \(-0.296812\pi\) | ||||
0.595859 | + | 0.803089i | \(0.296812\pi\) | |||||||
\(558\) | −36.3992 | −1.54090 | ||||||||
\(559\) | −1.75359 | −0.0741689 | ||||||||
\(560\) | −36.8177 | −1.55583 | ||||||||
\(561\) | 10.9667 | 0.463015 | ||||||||
\(562\) | −75.5859 | −3.18840 | ||||||||
\(563\) | −24.1593 | −1.01819 | −0.509097 | − | 0.860709i | \(-0.670021\pi\) | ||||
−0.509097 | + | 0.860709i | \(0.670021\pi\) | |||||||
\(564\) | 0.0139520 | 0.000587484 0 | ||||||||
\(565\) | 31.3825 | 1.32027 | ||||||||
\(566\) | 67.8367 | 2.85139 | ||||||||
\(567\) | −24.3543 | −1.02279 | ||||||||
\(568\) | −57.3560 | −2.40660 | ||||||||
\(569\) | −0.973316 | −0.0408035 | −0.0204018 | − | 0.999792i | \(-0.506495\pi\) | ||||
−0.0204018 | + | 0.999792i | \(0.506495\pi\) | |||||||
\(570\) | 7.65036 | 0.320438 | ||||||||
\(571\) | 4.56550 | 0.191060 | 0.0955302 | − | 0.995427i | \(-0.469545\pi\) | ||||
0.0955302 | + | 0.995427i | \(0.469545\pi\) | |||||||
\(572\) | 16.5091 | 0.690279 | ||||||||
\(573\) | 1.22317 | 0.0510986 | ||||||||
\(574\) | −81.8054 | −3.41449 | ||||||||
\(575\) | 7.98219 | 0.332880 | ||||||||
\(576\) | 28.0852 | 1.17022 | ||||||||
\(577\) | 6.52578 | 0.271672 | 0.135836 | − | 0.990731i | \(-0.456628\pi\) | ||||
0.135836 | + | 0.990731i | \(0.456628\pi\) | |||||||
\(578\) | −8.56264 | −0.356159 | ||||||||
\(579\) | 2.87412 | 0.119444 | ||||||||
\(580\) | 94.4793 | 3.92304 | ||||||||
\(581\) | 26.9925 | 1.11984 | ||||||||
\(582\) | −20.6013 | −0.853950 | ||||||||
\(583\) | 38.7415 | 1.60451 | ||||||||
\(584\) | −23.9241 | −0.989985 | ||||||||
\(585\) | 9.63071 | 0.398181 | ||||||||
\(586\) | 38.7877 | 1.60230 | ||||||||
\(587\) | −9.16410 | −0.378243 | −0.189122 | − | 0.981954i | \(-0.560564\pi\) | ||||
−0.189122 | + | 0.981954i | \(0.560564\pi\) | |||||||
\(588\) | 13.7706 | 0.567892 | ||||||||
\(589\) | 9.06709 | 0.373603 | ||||||||
\(590\) | −52.0994 | −2.14490 | ||||||||
\(591\) | −2.87592 | −0.118300 | ||||||||
\(592\) | 7.33770 | 0.301578 | ||||||||
\(593\) | 39.4750 | 1.62104 | 0.810522 | − | 0.585709i | \(-0.199184\pi\) | ||||
0.810522 | + | 0.585709i | \(0.199184\pi\) | |||||||
\(594\) | −33.2197 | −1.36302 | ||||||||
\(595\) | 62.2390 | 2.55155 | ||||||||
\(596\) | 56.6412 | 2.32011 | ||||||||
\(597\) | −0.354382 | −0.0145039 | ||||||||
\(598\) | 2.14941 | 0.0878961 | ||||||||
\(599\) | 1.12553 | 0.0459878 | 0.0229939 | − | 0.999736i | \(-0.492680\pi\) | ||||
0.0229939 | + | 0.999736i | \(0.492680\pi\) | |||||||
\(600\) | −19.4033 | −0.792135 | ||||||||
\(601\) | −27.8163 | −1.13465 | −0.567324 | − | 0.823494i | \(-0.692021\pi\) | ||||
−0.567324 | + | 0.823494i | \(0.692021\pi\) | |||||||
\(602\) | 16.3167 | 0.665019 | ||||||||
\(603\) | −34.4158 | −1.40152 | ||||||||
\(604\) | −19.4385 | −0.790942 | ||||||||
\(605\) | 35.8093 | 1.45586 | ||||||||
\(606\) | −19.0946 | −0.775664 | ||||||||
\(607\) | −39.2607 | −1.59354 | −0.796772 | − | 0.604280i | \(-0.793461\pi\) | ||||
−0.796772 | + | 0.604280i | \(0.793461\pi\) | |||||||
\(608\) | −3.36396 | −0.136427 | ||||||||
\(609\) | −13.4514 | −0.545078 | ||||||||
\(610\) | −118.981 | −4.81741 | ||||||||
\(611\) | −0.00669504 | −0.000270852 0 | ||||||||
\(612\) | 46.4836 | 1.87899 | ||||||||
\(613\) | −33.3735 | −1.34794 | −0.673972 | − | 0.738757i | \(-0.735413\pi\) | ||||
−0.673972 | + | 0.738757i | \(0.735413\pi\) | |||||||
\(614\) | 51.9757 | 2.09757 | ||||||||
\(615\) | −17.9003 | −0.721812 | ||||||||
\(616\) | −72.1583 | −2.90734 | ||||||||
\(617\) | 32.9871 | 1.32801 | 0.664006 | − | 0.747728i | \(-0.268855\pi\) | ||||
0.664006 | + | 0.747728i | \(0.268855\pi\) | |||||||
\(618\) | −5.49548 | −0.221061 | ||||||||
\(619\) | −25.1461 | −1.01071 | −0.505354 | − | 0.862912i | \(-0.668638\pi\) | ||||
−0.505354 | + | 0.862912i | \(0.668638\pi\) | |||||||
\(620\) | −77.4858 | −3.11190 | ||||||||
\(621\) | −2.82637 | −0.113418 | ||||||||
\(622\) | 79.4989 | 3.18762 | ||||||||
\(623\) | 17.2624 | 0.691603 | ||||||||
\(624\) | −1.37061 | −0.0548685 | ||||||||
\(625\) | 5.71173 | 0.228469 | ||||||||
\(626\) | −42.2205 | −1.68747 | ||||||||
\(627\) | 3.93326 | 0.157079 | ||||||||
\(628\) | 2.23564 | 0.0892119 | ||||||||
\(629\) | −12.4041 | −0.494584 | ||||||||
\(630\) | −89.6113 | −3.57020 | ||||||||
\(631\) | −12.5900 | −0.501199 | −0.250600 | − | 0.968091i | \(-0.580628\pi\) | ||||
−0.250600 | + | 0.968091i | \(0.580628\pi\) | |||||||
\(632\) | 35.2638 | 1.40272 | ||||||||
\(633\) | 3.71695 | 0.147736 | ||||||||
\(634\) | −64.8049 | −2.57373 | ||||||||
\(635\) | 5.88268 | 0.233447 | ||||||||
\(636\) | −17.0570 | −0.676355 | ||||||||
\(637\) | −6.60803 | −0.261819 | ||||||||
\(638\) | 74.3314 | 2.94281 | ||||||||
\(639\) | −36.6207 | −1.44869 | ||||||||
\(640\) | 76.2460 | 3.01389 | ||||||||
\(641\) | 9.64446 | 0.380933 | 0.190467 | − | 0.981694i | \(-0.439000\pi\) | ||||
0.190467 | + | 0.981694i | \(0.439000\pi\) | |||||||
\(642\) | −5.17243 | −0.204140 | ||||||||
\(643\) | −30.6630 | −1.20923 | −0.604615 | − | 0.796518i | \(-0.706673\pi\) | ||||
−0.604615 | + | 0.796518i | \(0.706673\pi\) | |||||||
\(644\) | −13.0695 | −0.515011 | ||||||||
\(645\) | 3.57036 | 0.140583 | ||||||||
\(646\) | −17.7190 | −0.697147 | ||||||||
\(647\) | 4.70041 | 0.184792 | 0.0923961 | − | 0.995722i | \(-0.470547\pi\) | ||||
0.0923961 | + | 0.995722i | \(0.470547\pi\) | |||||||
\(648\) | −27.8335 | −1.09340 | ||||||||
\(649\) | −26.7857 | −1.05143 | ||||||||
\(650\) | 19.8214 | 0.777459 | ||||||||
\(651\) | 11.0320 | 0.432377 | ||||||||
\(652\) | 31.8807 | 1.24854 | ||||||||
\(653\) | 1.28980 | 0.0504737 | 0.0252368 | − | 0.999682i | \(-0.491966\pi\) | ||||
0.0252368 | + | 0.999682i | \(0.491966\pi\) | |||||||
\(654\) | 7.60461 | 0.297364 | ||||||||
\(655\) | 34.1885 | 1.33585 | ||||||||
\(656\) | −24.5253 | −0.957553 | ||||||||
\(657\) | −15.2751 | −0.595937 | ||||||||
\(658\) | 0.0622956 | 0.00242854 | ||||||||
\(659\) | 2.27456 | 0.0886044 | 0.0443022 | − | 0.999018i | \(-0.485894\pi\) | ||||
0.0443022 | + | 0.999018i | \(0.485894\pi\) | |||||||
\(660\) | −33.6130 | −1.30838 | ||||||||
\(661\) | −34.9853 | −1.36077 | −0.680384 | − | 0.732855i | \(-0.738187\pi\) | ||||
−0.680384 | + | 0.732855i | \(0.738187\pi\) | |||||||
\(662\) | −36.0793 | −1.40226 | ||||||||
\(663\) | 2.31697 | 0.0899837 | ||||||||
\(664\) | 30.8484 | 1.19715 | ||||||||
\(665\) | 22.3223 | 0.865622 | ||||||||
\(666\) | 17.8594 | 0.692036 | ||||||||
\(667\) | 6.32419 | 0.244873 | ||||||||
\(668\) | 17.6438 | 0.682659 | ||||||||
\(669\) | −1.37448 | −0.0531403 | ||||||||
\(670\) | −112.112 | −4.33128 | ||||||||
\(671\) | −61.1715 | −2.36150 | ||||||||
\(672\) | −4.09294 | −0.157889 | ||||||||
\(673\) | 19.3350 | 0.745310 | 0.372655 | − | 0.927970i | \(-0.378447\pi\) | ||||
0.372655 | + | 0.927970i | \(0.378447\pi\) | |||||||
\(674\) | 42.8706 | 1.65132 | ||||||||
\(675\) | −26.0641 | −1.00321 | ||||||||
\(676\) | −45.5447 | −1.75172 | ||||||||
\(677\) | 2.44623 | 0.0940161 | 0.0470081 | − | 0.998895i | \(-0.485031\pi\) | ||||
0.0470081 | + | 0.998895i | \(0.485031\pi\) | |||||||
\(678\) | −10.8705 | −0.417479 | ||||||||
\(679\) | −60.1106 | −2.30683 | ||||||||
\(680\) | 71.1301 | 2.72771 | ||||||||
\(681\) | −10.7528 | −0.412046 | ||||||||
\(682\) | −60.9618 | −2.33435 | ||||||||
\(683\) | 43.6124 | 1.66878 | 0.834391 | − | 0.551173i | \(-0.185820\pi\) | ||||
0.834391 | + | 0.551173i | \(0.185820\pi\) | |||||||
\(684\) | 16.6715 | 0.637452 | ||||||||
\(685\) | −2.09190 | −0.0799273 | ||||||||
\(686\) | −1.14872 | −0.0438585 | ||||||||
\(687\) | −6.24118 | −0.238116 | ||||||||
\(688\) | 4.89176 | 0.186497 | ||||||||
\(689\) | 8.18504 | 0.311825 | ||||||||
\(690\) | −4.37627 | −0.166602 | ||||||||
\(691\) | 7.34138 | 0.279279 | 0.139640 | − | 0.990202i | \(-0.455406\pi\) | ||||
0.139640 | + | 0.990202i | \(0.455406\pi\) | |||||||
\(692\) | 54.2686 | 2.06298 | ||||||||
\(693\) | −46.0717 | −1.75012 | ||||||||
\(694\) | −50.8751 | −1.93119 | ||||||||
\(695\) | −53.6764 | −2.03606 | ||||||||
\(696\) | −15.3730 | −0.582711 | ||||||||
\(697\) | 41.4591 | 1.57038 | ||||||||
\(698\) | 67.7665 | 2.56500 | ||||||||
\(699\) | 5.69144 | 0.215270 | ||||||||
\(700\) | −120.524 | −4.55538 | ||||||||
\(701\) | −23.0622 | −0.871047 | −0.435523 | − | 0.900177i | \(-0.643437\pi\) | ||||
−0.435523 | + | 0.900177i | \(0.643437\pi\) | |||||||
\(702\) | −7.01844 | −0.264894 | ||||||||
\(703\) | −4.44879 | −0.167789 | ||||||||
\(704\) | 47.0374 | 1.77279 | ||||||||
\(705\) | 0.0136313 | 0.000513384 0 | ||||||||
\(706\) | −34.7346 | −1.30726 | ||||||||
\(707\) | −55.7144 | −2.09535 | ||||||||
\(708\) | 11.7932 | 0.443214 | ||||||||
\(709\) | 24.0778 | 0.904262 | 0.452131 | − | 0.891952i | \(-0.350664\pi\) | ||||
0.452131 | + | 0.891952i | \(0.350664\pi\) | |||||||
\(710\) | −119.295 | −4.47706 | ||||||||
\(711\) | 22.5152 | 0.844388 | ||||||||
\(712\) | 19.7284 | 0.739353 | ||||||||
\(713\) | −5.18669 | −0.194243 | ||||||||
\(714\) | −21.5588 | −0.806819 | ||||||||
\(715\) | 16.1296 | 0.603214 | ||||||||
\(716\) | −18.9678 | −0.708861 | ||||||||
\(717\) | −3.52151 | −0.131513 | ||||||||
\(718\) | 72.8950 | 2.72042 | ||||||||
\(719\) | −12.9172 | −0.481732 | −0.240866 | − | 0.970558i | \(-0.577431\pi\) | ||||
−0.240866 | + | 0.970558i | \(0.577431\pi\) | |||||||
\(720\) | −26.8655 | −1.00122 | ||||||||
\(721\) | −16.0348 | −0.597166 | ||||||||
\(722\) | 39.2914 | 1.46228 | ||||||||
\(723\) | −6.58892 | −0.245045 | ||||||||
\(724\) | 52.6129 | 1.95534 | ||||||||
\(725\) | 58.3201 | 2.16596 | ||||||||
\(726\) | −12.4039 | −0.460352 | ||||||||
\(727\) | −23.3028 | −0.864254 | −0.432127 | − | 0.901813i | \(-0.642237\pi\) | ||||
−0.432127 | + | 0.901813i | \(0.642237\pi\) | |||||||
\(728\) | −15.2451 | −0.565021 | ||||||||
\(729\) | −12.9289 | −0.478846 | ||||||||
\(730\) | −49.7597 | −1.84169 | ||||||||
\(731\) | −8.26933 | −0.305852 | ||||||||
\(732\) | 26.9325 | 0.995453 | ||||||||
\(733\) | −5.86554 | −0.216649 | −0.108324 | − | 0.994116i | \(-0.534549\pi\) | ||||
−0.108324 | + | 0.994116i | \(0.534549\pi\) | |||||||
\(734\) | −64.5701 | −2.38333 | ||||||||
\(735\) | 13.4541 | 0.496263 | ||||||||
\(736\) | 1.92430 | 0.0709307 | ||||||||
\(737\) | −57.6400 | −2.12320 | ||||||||
\(738\) | −59.6926 | −2.19731 | ||||||||
\(739\) | −14.6011 | −0.537110 | −0.268555 | − | 0.963264i | \(-0.586546\pi\) | ||||
−0.268555 | + | 0.963264i | \(0.586546\pi\) | |||||||
\(740\) | 38.0186 | 1.39759 | ||||||||
\(741\) | 0.830992 | 0.0305273 | ||||||||
\(742\) | −76.1597 | −2.79591 | ||||||||
\(743\) | −0.784316 | −0.0287738 | −0.0143869 | − | 0.999897i | \(-0.504580\pi\) | ||||
−0.0143869 | + | 0.999897i | \(0.504580\pi\) | |||||||
\(744\) | 12.6079 | 0.462229 | ||||||||
\(745\) | 55.3393 | 2.02748 | ||||||||
\(746\) | 26.2606 | 0.961471 | ||||||||
\(747\) | 19.6961 | 0.720644 | ||||||||
\(748\) | 77.8512 | 2.84652 | ||||||||
\(749\) | −15.0922 | −0.551456 | ||||||||
\(750\) | −16.8378 | −0.614831 | ||||||||
\(751\) | 47.0600 | 1.71724 | 0.858622 | − | 0.512610i | \(-0.171321\pi\) | ||||
0.858622 | + | 0.512610i | \(0.171321\pi\) | |||||||
\(752\) | 0.0186763 | 0.000681054 0 | ||||||||
\(753\) | −2.02786 | −0.0738992 | ||||||||
\(754\) | 15.7042 | 0.571914 | ||||||||
\(755\) | −18.9917 | −0.691180 | ||||||||
\(756\) | 42.6757 | 1.55210 | ||||||||
\(757\) | 31.3356 | 1.13891 | 0.569457 | − | 0.822021i | \(-0.307154\pi\) | ||||
0.569457 | + | 0.822021i | \(0.307154\pi\) | |||||||
\(758\) | −57.4695 | −2.08739 | ||||||||
\(759\) | −2.24996 | −0.0816684 | ||||||||
\(760\) | 25.5111 | 0.925386 | ||||||||
\(761\) | 30.2889 | 1.09797 | 0.548986 | − | 0.835832i | \(-0.315014\pi\) | ||||
0.548986 | + | 0.835832i | \(0.315014\pi\) | |||||||
\(762\) | −2.03769 | −0.0738176 | ||||||||
\(763\) | 22.1888 | 0.803289 | ||||||||
\(764\) | 8.68311 | 0.314144 | ||||||||
\(765\) | 45.4152 | 1.64199 | ||||||||
\(766\) | −83.1025 | −3.00262 | ||||||||
\(767\) | −5.65911 | −0.204339 | ||||||||
\(768\) | −15.4293 | −0.556756 | ||||||||
\(769\) | 32.8298 | 1.18387 | 0.591936 | − | 0.805985i | \(-0.298364\pi\) | ||||
0.591936 | + | 0.805985i | \(0.298364\pi\) | |||||||
\(770\) | −150.082 | −5.40858 | ||||||||
\(771\) | −6.97662 | −0.251257 | ||||||||
\(772\) | 20.4030 | 0.734321 | ||||||||
\(773\) | −19.8103 | −0.712529 | −0.356264 | − | 0.934385i | \(-0.615950\pi\) | ||||
−0.356264 | + | 0.934385i | \(0.615950\pi\) | |||||||
\(774\) | 11.9061 | 0.427957 | ||||||||
\(775\) | −47.8304 | −1.71812 | ||||||||
\(776\) | −68.6976 | −2.46610 | ||||||||
\(777\) | −5.41286 | −0.194185 | ||||||||
\(778\) | −35.3946 | −1.26896 | ||||||||
\(779\) | 14.8695 | 0.532755 | ||||||||
\(780\) | −7.10152 | −0.254275 | ||||||||
\(781\) | −61.3328 | −2.19466 | ||||||||
\(782\) | 10.1359 | 0.362459 | ||||||||
\(783\) | −20.6502 | −0.737979 | ||||||||
\(784\) | 18.4335 | 0.658341 | ||||||||
\(785\) | 2.18426 | 0.0779596 | ||||||||
\(786\) | −11.8425 | −0.422407 | ||||||||
\(787\) | 27.1225 | 0.966814 | 0.483407 | − | 0.875396i | \(-0.339399\pi\) | ||||
0.483407 | + | 0.875396i | \(0.339399\pi\) | |||||||
\(788\) | −20.4158 | −0.727283 | ||||||||
\(789\) | 0.363333 | 0.0129350 | ||||||||
\(790\) | 73.3452 | 2.60951 | ||||||||
\(791\) | −31.7181 | −1.12777 | ||||||||
\(792\) | −52.6532 | −1.87095 | ||||||||
\(793\) | −12.9239 | −0.458941 | ||||||||
\(794\) | −22.2484 | −0.789565 | ||||||||
\(795\) | −16.6650 | −0.591046 | ||||||||
\(796\) | −2.51571 | −0.0891669 | ||||||||
\(797\) | 33.4659 | 1.18542 | 0.592711 | − | 0.805415i | \(-0.298058\pi\) | ||||
0.592711 | + | 0.805415i | \(0.298058\pi\) | |||||||
\(798\) | −7.73217 | −0.273716 | ||||||||
\(799\) | −0.0315715 | −0.00111692 | ||||||||
\(800\) | 17.7454 | 0.627396 | ||||||||
\(801\) | 12.5962 | 0.445065 | ||||||||
\(802\) | 19.9183 | 0.703339 | ||||||||
\(803\) | −25.5829 | −0.902799 | ||||||||
\(804\) | 25.3776 | 0.895000 | ||||||||
\(805\) | −12.7691 | −0.450053 | ||||||||
\(806\) | −12.8796 | −0.453664 | ||||||||
\(807\) | 4.67553 | 0.164586 | ||||||||
\(808\) | −63.6734 | −2.24002 | ||||||||
\(809\) | 50.1002 | 1.76143 | 0.880715 | − | 0.473647i | \(-0.157063\pi\) | ||||
0.880715 | + | 0.473647i | \(0.157063\pi\) | |||||||
\(810\) | −57.8909 | −2.03408 | ||||||||
\(811\) | 45.4847 | 1.59718 | 0.798591 | − | 0.601874i | \(-0.205579\pi\) | ||||
0.798591 | + | 0.601874i | \(0.205579\pi\) | |||||||
\(812\) | −95.4897 | −3.35103 | ||||||||
\(813\) | −10.0078 | −0.350989 | ||||||||
\(814\) | 29.9111 | 1.04838 | ||||||||
\(815\) | 31.1480 | 1.09107 | ||||||||
\(816\) | −6.46335 | −0.226263 | ||||||||
\(817\) | −2.96583 | −0.103761 | ||||||||
\(818\) | 76.3112 | 2.66816 | ||||||||
\(819\) | −9.73371 | −0.340123 | ||||||||
\(820\) | −127.072 | −4.43756 | ||||||||
\(821\) | −8.80201 | −0.307192 | −0.153596 | − | 0.988134i | \(-0.549085\pi\) | ||||
−0.153596 | + | 0.988134i | \(0.549085\pi\) | |||||||
\(822\) | 0.724608 | 0.0252736 | ||||||||
\(823\) | 39.6846 | 1.38332 | 0.691660 | − | 0.722224i | \(-0.256880\pi\) | ||||
0.691660 | + | 0.722224i | \(0.256880\pi\) | |||||||
\(824\) | −18.3254 | −0.638396 | ||||||||
\(825\) | −20.7486 | −0.722374 | ||||||||
\(826\) | 52.6566 | 1.83216 | ||||||||
\(827\) | −5.61691 | −0.195319 | −0.0976595 | − | 0.995220i | \(-0.531136\pi\) | ||||
−0.0976595 | + | 0.995220i | \(0.531136\pi\) | |||||||
\(828\) | −9.53670 | −0.331423 | ||||||||
\(829\) | −49.5241 | −1.72004 | −0.860022 | − | 0.510257i | \(-0.829550\pi\) | ||||
−0.860022 | + | 0.510257i | \(0.829550\pi\) | |||||||
\(830\) | 64.1617 | 2.22709 | ||||||||
\(831\) | 7.77409 | 0.269680 | ||||||||
\(832\) | 9.93775 | 0.344529 | ||||||||
\(833\) | −31.1612 | −1.07967 | ||||||||
\(834\) | 18.5929 | 0.643818 | ||||||||
\(835\) | 17.2383 | 0.596555 | ||||||||
\(836\) | 27.9217 | 0.965692 | ||||||||
\(837\) | 16.9360 | 0.585394 | ||||||||
\(838\) | −61.7168 | −2.13197 | ||||||||
\(839\) | 17.9937 | 0.621210 | 0.310605 | − | 0.950539i | \(-0.399468\pi\) | ||||
0.310605 | + | 0.950539i | \(0.399468\pi\) | |||||||
\(840\) | 31.0395 | 1.07096 | ||||||||
\(841\) | 17.2063 | 0.593321 | ||||||||
\(842\) | 6.73009 | 0.231934 | ||||||||
\(843\) | 16.7163 | 0.575740 | ||||||||
\(844\) | 26.3862 | 0.908249 | ||||||||
\(845\) | −44.4979 | −1.53078 | ||||||||
\(846\) | 0.0454565 | 0.00156283 | ||||||||
\(847\) | −36.1923 | −1.24358 | ||||||||
\(848\) | −22.8327 | −0.784079 | ||||||||
\(849\) | −15.0025 | −0.514885 | ||||||||
\(850\) | 93.4709 | 3.20603 | ||||||||
\(851\) | 2.54486 | 0.0872368 | ||||||||
\(852\) | 27.0035 | 0.925123 | ||||||||
\(853\) | 1.68063 | 0.0575437 | 0.0287718 | − | 0.999586i | \(-0.490840\pi\) | ||||
0.0287718 | + | 0.999586i | \(0.490840\pi\) | |||||||
\(854\) | 120.254 | 4.11500 | ||||||||
\(855\) | 16.2884 | 0.557050 | ||||||||
\(856\) | −17.2482 | −0.589530 | ||||||||
\(857\) | 54.6431 | 1.86657 | 0.933287 | − | 0.359132i | \(-0.116927\pi\) | ||||
0.933287 | + | 0.359132i | \(0.116927\pi\) | |||||||
\(858\) | −5.58711 | −0.190741 | ||||||||
\(859\) | 49.5204 | 1.68961 | 0.844807 | − | 0.535070i | \(-0.179715\pi\) | ||||
0.844807 | + | 0.535070i | \(0.179715\pi\) | |||||||
\(860\) | 25.3455 | 0.864275 | ||||||||
\(861\) | 18.0918 | 0.616566 | ||||||||
\(862\) | −22.9089 | −0.780282 | ||||||||
\(863\) | 11.8646 | 0.403876 | 0.201938 | − | 0.979398i | \(-0.435276\pi\) | ||||
0.201938 | + | 0.979398i | \(0.435276\pi\) | |||||||
\(864\) | −6.28338 | −0.213765 | ||||||||
\(865\) | 53.0213 | 1.80278 | ||||||||
\(866\) | −85.5926 | −2.90855 | ||||||||
\(867\) | 1.89368 | 0.0643128 | ||||||||
\(868\) | 78.3144 | 2.65817 | ||||||||
\(869\) | 37.7088 | 1.27918 | ||||||||
\(870\) | −31.9743 | −1.08403 | ||||||||
\(871\) | −12.1778 | −0.412629 | ||||||||
\(872\) | 25.3586 | 0.858750 | ||||||||
\(873\) | −43.8621 | −1.48451 | ||||||||
\(874\) | 3.63529 | 0.122966 | ||||||||
\(875\) | −49.1297 | −1.66089 | ||||||||
\(876\) | 11.2636 | 0.380561 | ||||||||
\(877\) | −0.524102 | −0.0176977 | −0.00884884 | − | 0.999961i | \(-0.502817\pi\) | ||||
−0.00884884 | + | 0.999961i | \(0.502817\pi\) | |||||||
\(878\) | 33.8709 | 1.14309 | ||||||||
\(879\) | −8.57814 | −0.289333 | ||||||||
\(880\) | −44.9947 | −1.51677 | ||||||||
\(881\) | −29.9250 | −1.00820 | −0.504100 | − | 0.863646i | \(-0.668176\pi\) | ||||
−0.504100 | + | 0.863646i | \(0.668176\pi\) | |||||||
\(882\) | 44.8657 | 1.51071 | ||||||||
\(883\) | 13.9165 | 0.468327 | 0.234164 | − | 0.972197i | \(-0.424765\pi\) | ||||
0.234164 | + | 0.972197i | \(0.424765\pi\) | |||||||
\(884\) | 16.4479 | 0.553202 | ||||||||
\(885\) | 11.5221 | 0.387311 | ||||||||
\(886\) | −49.7542 | −1.67153 | ||||||||
\(887\) | 6.80436 | 0.228468 | 0.114234 | − | 0.993454i | \(-0.463559\pi\) | ||||
0.114234 | + | 0.993454i | \(0.463559\pi\) | |||||||
\(888\) | −6.18611 | −0.207592 | ||||||||
\(889\) | −5.94559 | −0.199409 | ||||||||
\(890\) | 41.0331 | 1.37543 | ||||||||
\(891\) | −29.7633 | −0.997108 | ||||||||
\(892\) | −9.75723 | −0.326696 | ||||||||
\(893\) | −0.0113233 | −0.000378919 0 | ||||||||
\(894\) | −19.1689 | −0.641103 | ||||||||
\(895\) | −18.5319 | −0.619452 | ||||||||
\(896\) | −77.0614 | −2.57444 | ||||||||
\(897\) | −0.475356 | −0.0158717 | ||||||||
\(898\) | −75.6583 | −2.52475 | ||||||||
\(899\) | −37.8954 | −1.26388 | ||||||||
\(900\) | −87.9452 | −2.93151 | ||||||||
\(901\) | 38.5979 | 1.28588 | ||||||||
\(902\) | −99.9739 | −3.32877 | ||||||||
\(903\) | −3.60854 | −0.120085 | ||||||||
\(904\) | −36.2491 | −1.20563 | ||||||||
\(905\) | 51.4037 | 1.70872 | ||||||||
\(906\) | 6.57851 | 0.218556 | ||||||||
\(907\) | −31.3774 | −1.04187 | −0.520935 | − | 0.853596i | \(-0.674417\pi\) | ||||
−0.520935 | + | 0.853596i | \(0.674417\pi\) | |||||||
\(908\) | −76.3324 | −2.53318 | ||||||||
\(909\) | −40.6542 | −1.34842 | ||||||||
\(910\) | −31.7083 | −1.05112 | ||||||||
\(911\) | 38.0252 | 1.25983 | 0.629916 | − | 0.776664i | \(-0.283089\pi\) | ||||
0.629916 | + | 0.776664i | \(0.283089\pi\) | |||||||
\(912\) | −2.31811 | −0.0767603 | ||||||||
\(913\) | 32.9873 | 1.09172 | ||||||||
\(914\) | 12.8223 | 0.424125 | ||||||||
\(915\) | 26.3135 | 0.869896 | ||||||||
\(916\) | −44.3054 | −1.46389 | ||||||||
\(917\) | −34.5541 | −1.14108 | ||||||||
\(918\) | −33.0966 | −1.09235 | ||||||||
\(919\) | 25.1917 | 0.830996 | 0.415498 | − | 0.909594i | \(-0.363607\pi\) | ||||
0.415498 | + | 0.909594i | \(0.363607\pi\) | |||||||
\(920\) | −14.5933 | −0.481125 | ||||||||
\(921\) | −11.4948 | −0.378765 | ||||||||
\(922\) | −10.8087 | −0.355965 | ||||||||
\(923\) | −12.9580 | −0.426517 | ||||||||
\(924\) | 33.9724 | 1.11761 | ||||||||
\(925\) | 23.4681 | 0.771627 | ||||||||
\(926\) | 64.7683 | 2.12842 | ||||||||
\(927\) | −11.7004 | −0.384292 | ||||||||
\(928\) | 14.0595 | 0.461525 | ||||||||
\(929\) | −10.1468 | −0.332905 | −0.166452 | − | 0.986049i | \(-0.553231\pi\) | ||||
−0.166452 | + | 0.986049i | \(0.553231\pi\) | |||||||
\(930\) | 26.2232 | 0.859894 | ||||||||
\(931\) | −11.1761 | −0.366282 | ||||||||
\(932\) | 40.4028 | 1.32344 | ||||||||
\(933\) | −17.5817 | −0.575599 | ||||||||
\(934\) | −33.9754 | −1.11171 | ||||||||
\(935\) | 76.0619 | 2.48749 | ||||||||
\(936\) | −11.1242 | −0.363606 | ||||||||
\(937\) | 9.16785 | 0.299501 | 0.149750 | − | 0.988724i | \(-0.452153\pi\) | ||||
0.149750 | + | 0.988724i | \(0.452153\pi\) | |||||||
\(938\) | 113.311 | 3.69974 | ||||||||
\(939\) | 9.33733 | 0.304712 | ||||||||
\(940\) | 0.0967668 | 0.00315619 | ||||||||
\(941\) | 42.8846 | 1.39800 | 0.698998 | − | 0.715123i | \(-0.253629\pi\) | ||||
0.698998 | + | 0.715123i | \(0.253629\pi\) | |||||||
\(942\) | −0.756601 | −0.0246514 | ||||||||
\(943\) | −8.50587 | −0.276989 | ||||||||
\(944\) | 15.7865 | 0.513806 | ||||||||
\(945\) | 41.6948 | 1.35633 | ||||||||
\(946\) | 19.9405 | 0.648323 | ||||||||
\(947\) | −27.5142 | −0.894093 | −0.447046 | − | 0.894511i | \(-0.647524\pi\) | ||||
−0.447046 | + | 0.894511i | \(0.647524\pi\) | |||||||
\(948\) | −16.6024 | −0.539219 | ||||||||
\(949\) | −5.40497 | −0.175453 | ||||||||
\(950\) | 33.5238 | 1.08766 | ||||||||
\(951\) | 14.3320 | 0.464747 | ||||||||
\(952\) | −71.8908 | −2.32999 | ||||||||
\(953\) | 56.2198 | 1.82114 | 0.910568 | − | 0.413358i | \(-0.135644\pi\) | ||||
0.910568 | + | 0.413358i | \(0.135644\pi\) | |||||||
\(954\) | −55.5730 | −1.79924 | ||||||||
\(955\) | 8.48354 | 0.274521 | ||||||||
\(956\) | −24.9987 | −0.808517 | ||||||||
\(957\) | −16.4389 | −0.531393 | ||||||||
\(958\) | 96.8136 | 3.12791 | ||||||||
\(959\) | 2.11427 | 0.0682733 | ||||||||
\(960\) | −20.2335 | −0.653035 | ||||||||
\(961\) | 0.0793760 | 0.00256052 | ||||||||
\(962\) | 6.31941 | 0.203746 | ||||||||
\(963\) | −11.0126 | −0.354877 | ||||||||
\(964\) | −46.7739 | −1.50649 | ||||||||
\(965\) | 19.9341 | 0.641700 | ||||||||
\(966\) | 4.42307 | 0.142310 | ||||||||
\(967\) | 34.3461 | 1.10450 | 0.552249 | − | 0.833679i | \(-0.313770\pi\) | ||||
0.552249 | + | 0.833679i | \(0.313770\pi\) | |||||||
\(968\) | −41.3625 | −1.32944 | ||||||||
\(969\) | 3.91868 | 0.125886 | ||||||||
\(970\) | −142.884 | −4.58774 | ||||||||
\(971\) | −40.9303 | −1.31352 | −0.656758 | − | 0.754101i | \(-0.728073\pi\) | ||||
−0.656758 | + | 0.754101i | \(0.728073\pi\) | |||||||
\(972\) | 47.4787 | 1.52288 | ||||||||
\(973\) | 54.2505 | 1.73919 | ||||||||
\(974\) | −57.5474 | −1.84394 | ||||||||
\(975\) | −4.38362 | −0.140388 | ||||||||
\(976\) | 36.0521 | 1.15400 | ||||||||
\(977\) | −12.6748 | −0.405502 | −0.202751 | − | 0.979230i | \(-0.564988\pi\) | ||||
−0.202751 | + | 0.979230i | \(0.564988\pi\) | |||||||
\(978\) | −10.7893 | −0.345003 | ||||||||
\(979\) | 21.0963 | 0.674240 | ||||||||
\(980\) | 95.5092 | 3.05093 | ||||||||
\(981\) | 16.1910 | 0.516937 | ||||||||
\(982\) | −24.3298 | −0.776394 | ||||||||
\(983\) | −32.7916 | −1.04589 | −0.522945 | − | 0.852366i | \(-0.675167\pi\) | ||||
−0.522945 | + | 0.852366i | \(0.675167\pi\) | |||||||
\(984\) | 20.6763 | 0.659135 | ||||||||
\(985\) | −19.9466 | −0.635551 | ||||||||
\(986\) | 74.0558 | 2.35842 | ||||||||
\(987\) | −0.0137771 | −0.000438529 0 | ||||||||
\(988\) | 5.89911 | 0.187676 | ||||||||
\(989\) | 1.69656 | 0.0539475 | ||||||||
\(990\) | −109.513 | −3.48057 | ||||||||
\(991\) | 4.19767 | 0.133343 | 0.0666717 | − | 0.997775i | \(-0.478762\pi\) | ||||
0.0666717 | + | 0.997775i | \(0.478762\pi\) | |||||||
\(992\) | −11.5307 | −0.366100 | ||||||||
\(993\) | 7.97917 | 0.253211 | ||||||||
\(994\) | 120.571 | 3.82427 | ||||||||
\(995\) | −2.45789 | −0.0779203 | ||||||||
\(996\) | −14.5236 | −0.460197 | ||||||||
\(997\) | 6.60567 | 0.209204 | 0.104602 | − | 0.994514i | \(-0.466643\pi\) | ||||
0.104602 | + | 0.994514i | \(0.466643\pi\) | |||||||
\(998\) | 39.5732 | 1.25267 | ||||||||
\(999\) | −8.30969 | −0.262907 |
(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 | 4003.2.a.c.1.14 | ✓ | 179 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4003.2.a.c.1.14 | ✓ | 179 | 1.1 | even | 1 | trivial |