Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.940078 | 0.664735 | 0.332368 | − | 0.943150i | \(-0.392152\pi\) | ||||
0.332368 | + | 0.943150i | \(0.392152\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.11625 | −0.558127 | ||||||||
\(5\) | −1.95082 | −0.872434 | −0.436217 | − | 0.899841i | \(-0.643682\pi\) | ||||
−0.436217 | + | 0.899841i | \(0.643682\pi\) | |||||||
\(6\) | −0.940078 | −0.383785 | ||||||||
\(7\) | −0.363346 | −0.137332 | −0.0686659 | − | 0.997640i | \(-0.521874\pi\) | ||||
−0.0686659 | + | 0.997640i | \(0.521874\pi\) | |||||||
\(8\) | −2.92952 | −1.03574 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.83392 | −0.579938 | ||||||||
\(11\) | 1.99973 | 0.602940 | 0.301470 | − | 0.953476i | \(-0.402523\pi\) | ||||
0.301470 | + | 0.953476i | \(0.402523\pi\) | |||||||
\(12\) | 1.11625 | 0.322235 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −0.341574 | −0.0912894 | ||||||||
\(15\) | 1.95082 | 0.503700 | ||||||||
\(16\) | −0.521471 | −0.130368 | ||||||||
\(17\) | −2.22976 | −0.540795 | −0.270398 | − | 0.962749i | \(-0.587155\pi\) | ||||
−0.270398 | + | 0.962749i | \(0.587155\pi\) | |||||||
\(18\) | 0.940078 | 0.221578 | ||||||||
\(19\) | −5.96553 | −1.36859 | −0.684294 | − | 0.729206i | \(-0.739889\pi\) | ||||
−0.684294 | + | 0.729206i | \(0.739889\pi\) | |||||||
\(20\) | 2.17761 | 0.486929 | ||||||||
\(21\) | 0.363346 | 0.0792886 | ||||||||
\(22\) | 1.87990 | 0.400796 | ||||||||
\(23\) | −1.97893 | −0.412635 | −0.206317 | − | 0.978485i | \(-0.566148\pi\) | ||||
−0.206317 | + | 0.978485i | \(0.566148\pi\) | |||||||
\(24\) | 2.92952 | 0.597986 | ||||||||
\(25\) | −1.19429 | −0.238859 | ||||||||
\(26\) | 0.940078 | 0.184364 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.405586 | 0.0766486 | ||||||||
\(29\) | −1.52189 | −0.282607 | −0.141304 | − | 0.989966i | \(-0.545129\pi\) | ||||
−0.141304 | + | 0.989966i | \(0.545129\pi\) | |||||||
\(30\) | 1.83392 | 0.334827 | ||||||||
\(31\) | −6.18222 | −1.11036 | −0.555180 | − | 0.831730i | \(-0.687351\pi\) | ||||
−0.555180 | + | 0.831730i | \(0.687351\pi\) | |||||||
\(32\) | 5.36882 | 0.949082 | ||||||||
\(33\) | −1.99973 | −0.348108 | ||||||||
\(34\) | −2.09614 | −0.359486 | ||||||||
\(35\) | 0.708823 | 0.119813 | ||||||||
\(36\) | −1.11625 | −0.186042 | ||||||||
\(37\) | 2.13653 | 0.351244 | 0.175622 | − | 0.984458i | \(-0.443806\pi\) | ||||
0.175622 | + | 0.984458i | \(0.443806\pi\) | |||||||
\(38\) | −5.60807 | −0.909749 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 5.71497 | 0.903617 | ||||||||
\(41\) | −0.409818 | −0.0640028 | −0.0320014 | − | 0.999488i | \(-0.510188\pi\) | ||||
−0.0320014 | + | 0.999488i | \(0.510188\pi\) | |||||||
\(42\) | 0.341574 | 0.0527059 | ||||||||
\(43\) | 10.8205 | 1.65011 | 0.825057 | − | 0.565049i | \(-0.191143\pi\) | ||||
0.825057 | + | 0.565049i | \(0.191143\pi\) | |||||||
\(44\) | −2.23220 | −0.336517 | ||||||||
\(45\) | −1.95082 | −0.290811 | ||||||||
\(46\) | −1.86035 | −0.274293 | ||||||||
\(47\) | −11.1414 | −1.62514 | −0.812568 | − | 0.582866i | \(-0.801931\pi\) | ||||
−0.812568 | + | 0.582866i | \(0.801931\pi\) | |||||||
\(48\) | 0.521471 | 0.0752679 | ||||||||
\(49\) | −6.86798 | −0.981140 | ||||||||
\(50\) | −1.12273 | −0.158778 | ||||||||
\(51\) | 2.22976 | 0.312228 | ||||||||
\(52\) | −1.11625 | −0.154797 | ||||||||
\(53\) | 1.45789 | 0.200256 | 0.100128 | − | 0.994975i | \(-0.468075\pi\) | ||||
0.100128 | + | 0.994975i | \(0.468075\pi\) | |||||||
\(54\) | −0.940078 | −0.127928 | ||||||||
\(55\) | −3.90111 | −0.526025 | ||||||||
\(56\) | 1.06443 | 0.142240 | ||||||||
\(57\) | 5.96553 | 0.790154 | ||||||||
\(58\) | −1.43069 | −0.187859 | ||||||||
\(59\) | −2.75815 | −0.359081 | −0.179540 | − | 0.983751i | \(-0.557461\pi\) | ||||
−0.179540 | + | 0.983751i | \(0.557461\pi\) | |||||||
\(60\) | −2.17761 | −0.281128 | ||||||||
\(61\) | −2.43812 | −0.312170 | −0.156085 | − | 0.987744i | \(-0.549887\pi\) | ||||
−0.156085 | + | 0.987744i | \(0.549887\pi\) | |||||||
\(62\) | −5.81177 | −0.738096 | ||||||||
\(63\) | −0.363346 | −0.0457773 | ||||||||
\(64\) | 6.09005 | 0.761256 | ||||||||
\(65\) | −1.95082 | −0.241970 | ||||||||
\(66\) | −1.87990 | −0.231399 | ||||||||
\(67\) | 0.0721191 | 0.00881075 | 0.00440538 | − | 0.999990i | \(-0.498598\pi\) | ||||
0.00440538 | + | 0.999990i | \(0.498598\pi\) | |||||||
\(68\) | 2.48897 | 0.301832 | ||||||||
\(69\) | 1.97893 | 0.238235 | ||||||||
\(70\) | 0.666349 | 0.0796440 | ||||||||
\(71\) | 11.4933 | 1.36400 | 0.682001 | − | 0.731351i | \(-0.261110\pi\) | ||||
0.682001 | + | 0.731351i | \(0.261110\pi\) | |||||||
\(72\) | −2.92952 | −0.345247 | ||||||||
\(73\) | 10.7686 | 1.26036 | 0.630182 | − | 0.776448i | \(-0.282980\pi\) | ||||
0.630182 | + | 0.776448i | \(0.282980\pi\) | |||||||
\(74\) | 2.00851 | 0.233484 | ||||||||
\(75\) | 1.19429 | 0.137905 | ||||||||
\(76\) | 6.65905 | 0.763845 | ||||||||
\(77\) | −0.726592 | −0.0828029 | ||||||||
\(78\) | −0.940078 | −0.106443 | ||||||||
\(79\) | 8.03620 | 0.904143 | 0.452072 | − | 0.891982i | \(-0.350685\pi\) | ||||
0.452072 | + | 0.891982i | \(0.350685\pi\) | |||||||
\(80\) | 1.01730 | 0.113737 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.385261 | −0.0425449 | ||||||||
\(83\) | 10.8876 | 1.19507 | 0.597535 | − | 0.801843i | \(-0.296147\pi\) | ||||
0.597535 | + | 0.801843i | \(0.296147\pi\) | |||||||
\(84\) | −0.405586 | −0.0442531 | ||||||||
\(85\) | 4.34986 | 0.471808 | ||||||||
\(86\) | 10.1721 | 1.09689 | ||||||||
\(87\) | 1.52189 | 0.163163 | ||||||||
\(88\) | −5.85824 | −0.624490 | ||||||||
\(89\) | 8.54917 | 0.906211 | 0.453105 | − | 0.891457i | \(-0.350316\pi\) | ||||
0.453105 | + | 0.891457i | \(0.350316\pi\) | |||||||
\(90\) | −1.83392 | −0.193313 | ||||||||
\(91\) | −0.363346 | −0.0380890 | ||||||||
\(92\) | 2.20898 | 0.230302 | ||||||||
\(93\) | 6.18222 | 0.641067 | ||||||||
\(94\) | −10.4738 | −1.08029 | ||||||||
\(95\) | 11.6377 | 1.19400 | ||||||||
\(96\) | −5.36882 | −0.547953 | ||||||||
\(97\) | −13.4153 | −1.36211 | −0.681057 | − | 0.732230i | \(-0.738480\pi\) | ||||
−0.681057 | + | 0.732230i | \(0.738480\pi\) | |||||||
\(98\) | −6.45644 | −0.652199 | ||||||||
\(99\) | 1.99973 | 0.200980 | ||||||||
\(100\) | 1.33313 | 0.133313 | ||||||||
\(101\) | −6.35586 | −0.632431 | −0.316216 | − | 0.948687i | \(-0.602412\pi\) | ||||
−0.316216 | + | 0.948687i | \(0.602412\pi\) | |||||||
\(102\) | 2.09614 | 0.207549 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | −2.92952 | −0.287263 | ||||||||
\(105\) | −0.708823 | −0.0691741 | ||||||||
\(106\) | 1.37053 | 0.133117 | ||||||||
\(107\) | 3.80533 | 0.367875 | 0.183938 | − | 0.982938i | \(-0.441116\pi\) | ||||
0.183938 | + | 0.982938i | \(0.441116\pi\) | |||||||
\(108\) | 1.11625 | 0.107412 | ||||||||
\(109\) | 3.96810 | 0.380075 | 0.190038 | − | 0.981777i | \(-0.439139\pi\) | ||||
0.190038 | + | 0.981777i | \(0.439139\pi\) | |||||||
\(110\) | −3.66735 | −0.349668 | ||||||||
\(111\) | −2.13653 | −0.202791 | ||||||||
\(112\) | 0.189474 | 0.0179037 | ||||||||
\(113\) | −1.14996 | −0.108179 | −0.0540893 | − | 0.998536i | \(-0.517226\pi\) | ||||
−0.0540893 | + | 0.998536i | \(0.517226\pi\) | |||||||
\(114\) | 5.60807 | 0.525244 | ||||||||
\(115\) | 3.86053 | 0.359997 | ||||||||
\(116\) | 1.69881 | 0.157731 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −2.59288 | −0.238694 | ||||||||
\(119\) | 0.810173 | 0.0742684 | ||||||||
\(120\) | −5.71497 | −0.521703 | ||||||||
\(121\) | −7.00110 | −0.636463 | ||||||||
\(122\) | −2.29203 | −0.207510 | ||||||||
\(123\) | 0.409818 | 0.0369520 | ||||||||
\(124\) | 6.90093 | 0.619722 | ||||||||
\(125\) | 12.0840 | 1.08082 | ||||||||
\(126\) | −0.341574 | −0.0304298 | ||||||||
\(127\) | −4.69610 | −0.416711 | −0.208356 | − | 0.978053i | \(-0.566811\pi\) | ||||
−0.208356 | + | 0.978053i | \(0.566811\pi\) | |||||||
\(128\) | −5.01252 | −0.443048 | ||||||||
\(129\) | −10.8205 | −0.952694 | ||||||||
\(130\) | −1.83392 | −0.160846 | ||||||||
\(131\) | 4.34589 | 0.379702 | 0.189851 | − | 0.981813i | \(-0.439199\pi\) | ||||
0.189851 | + | 0.981813i | \(0.439199\pi\) | |||||||
\(132\) | 2.23220 | 0.194288 | ||||||||
\(133\) | 2.16755 | 0.187951 | ||||||||
\(134\) | 0.0677976 | 0.00585682 | ||||||||
\(135\) | 1.95082 | 0.167900 | ||||||||
\(136\) | 6.53212 | 0.560124 | ||||||||
\(137\) | 20.9667 | 1.79131 | 0.895655 | − | 0.444750i | \(-0.146708\pi\) | ||||
0.895655 | + | 0.444750i | \(0.146708\pi\) | |||||||
\(138\) | 1.86035 | 0.158363 | ||||||||
\(139\) | 21.8389 | 1.85235 | 0.926174 | − | 0.377096i | \(-0.123077\pi\) | ||||
0.926174 | + | 0.377096i | \(0.123077\pi\) | |||||||
\(140\) | −0.791227 | −0.0668708 | ||||||||
\(141\) | 11.1414 | 0.938273 | ||||||||
\(142\) | 10.8046 | 0.906700 | ||||||||
\(143\) | 1.99973 | 0.167225 | ||||||||
\(144\) | −0.521471 | −0.0434559 | ||||||||
\(145\) | 2.96893 | 0.246556 | ||||||||
\(146\) | 10.1233 | 0.837808 | ||||||||
\(147\) | 6.86798 | 0.566461 | ||||||||
\(148\) | −2.38491 | −0.196039 | ||||||||
\(149\) | 18.1511 | 1.48700 | 0.743498 | − | 0.668738i | \(-0.233165\pi\) | ||||
0.743498 | + | 0.668738i | \(0.233165\pi\) | |||||||
\(150\) | 1.12273 | 0.0916704 | ||||||||
\(151\) | 8.10513 | 0.659586 | 0.329793 | − | 0.944053i | \(-0.393021\pi\) | ||||
0.329793 | + | 0.944053i | \(0.393021\pi\) | |||||||
\(152\) | 17.4762 | 1.41750 | ||||||||
\(153\) | −2.22976 | −0.180265 | ||||||||
\(154\) | −0.683053 | −0.0550420 | ||||||||
\(155\) | 12.0604 | 0.968716 | ||||||||
\(156\) | 1.11625 | 0.0893718 | ||||||||
\(157\) | −4.49931 | −0.359084 | −0.179542 | − | 0.983750i | \(-0.557462\pi\) | ||||
−0.179542 | + | 0.983750i | \(0.557462\pi\) | |||||||
\(158\) | 7.55465 | 0.601016 | ||||||||
\(159\) | −1.45789 | −0.115618 | ||||||||
\(160\) | −10.4736 | −0.828012 | ||||||||
\(161\) | 0.719035 | 0.0566679 | ||||||||
\(162\) | 0.940078 | 0.0738595 | ||||||||
\(163\) | −13.5433 | −1.06080 | −0.530398 | − | 0.847749i | \(-0.677958\pi\) | ||||
−0.530398 | + | 0.847749i | \(0.677958\pi\) | |||||||
\(164\) | 0.457461 | 0.0357217 | ||||||||
\(165\) | 3.90111 | 0.303701 | ||||||||
\(166\) | 10.2352 | 0.794406 | ||||||||
\(167\) | −5.80573 | −0.449261 | −0.224630 | − | 0.974444i | \(-0.572117\pi\) | ||||
−0.224630 | + | 0.974444i | \(0.572117\pi\) | |||||||
\(168\) | −1.06443 | −0.0821225 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 4.08920 | 0.313628 | ||||||||
\(171\) | −5.96553 | −0.456196 | ||||||||
\(172\) | −12.0784 | −0.920973 | ||||||||
\(173\) | −9.85387 | −0.749176 | −0.374588 | − | 0.927191i | \(-0.622216\pi\) | ||||
−0.374588 | + | 0.927191i | \(0.622216\pi\) | |||||||
\(174\) | 1.43069 | 0.108460 | ||||||||
\(175\) | 0.433942 | 0.0328029 | ||||||||
\(176\) | −1.04280 | −0.0786040 | ||||||||
\(177\) | 2.75815 | 0.207315 | ||||||||
\(178\) | 8.03689 | 0.602390 | ||||||||
\(179\) | −3.97070 | −0.296784 | −0.148392 | − | 0.988929i | \(-0.547410\pi\) | ||||
−0.148392 | + | 0.988929i | \(0.547410\pi\) | |||||||
\(180\) | 2.17761 | 0.162310 | ||||||||
\(181\) | 11.3750 | 0.845497 | 0.422749 | − | 0.906247i | \(-0.361065\pi\) | ||||
0.422749 | + | 0.906247i | \(0.361065\pi\) | |||||||
\(182\) | −0.341574 | −0.0253191 | ||||||||
\(183\) | 2.43812 | 0.180231 | ||||||||
\(184\) | 5.79731 | 0.427383 | ||||||||
\(185\) | −4.16799 | −0.306437 | ||||||||
\(186\) | 5.81177 | 0.426140 | ||||||||
\(187\) | −4.45890 | −0.326067 | ||||||||
\(188\) | 12.4366 | 0.907032 | ||||||||
\(189\) | 0.363346 | 0.0264295 | ||||||||
\(190\) | 10.9403 | 0.793696 | ||||||||
\(191\) | 15.8544 | 1.14719 | 0.573593 | − | 0.819140i | \(-0.305549\pi\) | ||||
0.573593 | + | 0.819140i | \(0.305549\pi\) | |||||||
\(192\) | −6.09005 | −0.439512 | ||||||||
\(193\) | −14.6916 | −1.05753 | −0.528763 | − | 0.848770i | \(-0.677344\pi\) | ||||
−0.528763 | + | 0.848770i | \(0.677344\pi\) | |||||||
\(194\) | −12.6114 | −0.905446 | ||||||||
\(195\) | 1.95082 | 0.139701 | ||||||||
\(196\) | 7.66641 | 0.547600 | ||||||||
\(197\) | 9.75438 | 0.694971 | 0.347485 | − | 0.937685i | \(-0.387036\pi\) | ||||
0.347485 | + | 0.937685i | \(0.387036\pi\) | |||||||
\(198\) | 1.87990 | 0.133599 | ||||||||
\(199\) | 22.2546 | 1.57758 | 0.788792 | − | 0.614660i | \(-0.210707\pi\) | ||||
0.788792 | + | 0.614660i | \(0.210707\pi\) | |||||||
\(200\) | 3.49871 | 0.247396 | ||||||||
\(201\) | −0.0721191 | −0.00508689 | ||||||||
\(202\) | −5.97500 | −0.420400 | ||||||||
\(203\) | 0.552971 | 0.0388110 | ||||||||
\(204\) | −2.48897 | −0.174263 | ||||||||
\(205\) | 0.799482 | 0.0558382 | ||||||||
\(206\) | −0.940078 | −0.0654983 | ||||||||
\(207\) | −1.97893 | −0.137545 | ||||||||
\(208\) | −0.521471 | −0.0361575 | ||||||||
\(209\) | −11.9294 | −0.825176 | ||||||||
\(210\) | −0.666349 | −0.0459825 | ||||||||
\(211\) | 15.3333 | 1.05559 | 0.527793 | − | 0.849373i | \(-0.323020\pi\) | ||||
0.527793 | + | 0.849373i | \(0.323020\pi\) | |||||||
\(212\) | −1.62737 | −0.111768 | ||||||||
\(213\) | −11.4933 | −0.787507 | ||||||||
\(214\) | 3.57731 | 0.244540 | ||||||||
\(215\) | −21.1089 | −1.43962 | ||||||||
\(216\) | 2.92952 | 0.199329 | ||||||||
\(217\) | 2.24629 | 0.152488 | ||||||||
\(218\) | 3.73033 | 0.252650 | ||||||||
\(219\) | −10.7686 | −0.727671 | ||||||||
\(220\) | 4.35463 | 0.293589 | ||||||||
\(221\) | −2.22976 | −0.149990 | ||||||||
\(222\) | −2.00851 | −0.134802 | ||||||||
\(223\) | 11.1131 | 0.744191 | 0.372095 | − | 0.928194i | \(-0.378639\pi\) | ||||
0.372095 | + | 0.928194i | \(0.378639\pi\) | |||||||
\(224\) | −1.95074 | −0.130339 | ||||||||
\(225\) | −1.19429 | −0.0796195 | ||||||||
\(226\) | −1.08105 | −0.0719102 | ||||||||
\(227\) | 1.68257 | 0.111676 | 0.0558380 | − | 0.998440i | \(-0.482217\pi\) | ||||
0.0558380 | + | 0.998440i | \(0.482217\pi\) | |||||||
\(228\) | −6.65905 | −0.441006 | ||||||||
\(229\) | 21.7690 | 1.43853 | 0.719267 | − | 0.694734i | \(-0.244478\pi\) | ||||
0.719267 | + | 0.694734i | \(0.244478\pi\) | |||||||
\(230\) | 3.62920 | 0.239303 | ||||||||
\(231\) | 0.726592 | 0.0478063 | ||||||||
\(232\) | 4.45840 | 0.292708 | ||||||||
\(233\) | 27.7588 | 1.81854 | 0.909270 | − | 0.416206i | \(-0.136641\pi\) | ||||
0.909270 | + | 0.416206i | \(0.136641\pi\) | |||||||
\(234\) | 0.940078 | 0.0614548 | ||||||||
\(235\) | 21.7348 | 1.41782 | ||||||||
\(236\) | 3.07880 | 0.200413 | ||||||||
\(237\) | −8.03620 | −0.522007 | ||||||||
\(238\) | 0.761625 | 0.0493688 | ||||||||
\(239\) | −16.5132 | −1.06815 | −0.534076 | − | 0.845436i | \(-0.679340\pi\) | ||||
−0.534076 | + | 0.845436i | \(0.679340\pi\) | |||||||
\(240\) | −1.01730 | −0.0656663 | ||||||||
\(241\) | −16.5745 | −1.06766 | −0.533828 | − | 0.845593i | \(-0.679247\pi\) | ||||
−0.533828 | + | 0.845593i | \(0.679247\pi\) | |||||||
\(242\) | −6.58158 | −0.423080 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 2.72156 | 0.174230 | ||||||||
\(245\) | 13.3982 | 0.855980 | ||||||||
\(246\) | 0.385261 | 0.0245633 | ||||||||
\(247\) | −5.96553 | −0.379578 | ||||||||
\(248\) | 18.1110 | 1.15005 | ||||||||
\(249\) | −10.8876 | −0.689974 | ||||||||
\(250\) | 11.3599 | 0.718461 | ||||||||
\(251\) | −17.0792 | −1.07803 | −0.539014 | − | 0.842297i | \(-0.681203\pi\) | ||||
−0.539014 | + | 0.842297i | \(0.681203\pi\) | |||||||
\(252\) | 0.405586 | 0.0255495 | ||||||||
\(253\) | −3.95731 | −0.248794 | ||||||||
\(254\) | −4.41470 | −0.277003 | ||||||||
\(255\) | −4.34986 | −0.272399 | ||||||||
\(256\) | −16.8923 | −1.05577 | ||||||||
\(257\) | −14.9303 | −0.931324 | −0.465662 | − | 0.884963i | \(-0.654184\pi\) | ||||
−0.465662 | + | 0.884963i | \(0.654184\pi\) | |||||||
\(258\) | −10.1721 | −0.633290 | ||||||||
\(259\) | −0.776300 | −0.0482370 | ||||||||
\(260\) | 2.17761 | 0.135050 | ||||||||
\(261\) | −1.52189 | −0.0942024 | ||||||||
\(262\) | 4.08548 | 0.252402 | ||||||||
\(263\) | 24.9300 | 1.53725 | 0.768626 | − | 0.639699i | \(-0.220941\pi\) | ||||
0.768626 | + | 0.639699i | \(0.220941\pi\) | |||||||
\(264\) | 5.85824 | 0.360550 | ||||||||
\(265\) | −2.84408 | −0.174710 | ||||||||
\(266\) | 2.03767 | 0.124937 | ||||||||
\(267\) | −8.54917 | −0.523201 | ||||||||
\(268\) | −0.0805032 | −0.00491752 | ||||||||
\(269\) | −5.86892 | −0.357834 | −0.178917 | − | 0.983864i | \(-0.557259\pi\) | ||||
−0.178917 | + | 0.983864i | \(0.557259\pi\) | |||||||
\(270\) | 1.83392 | 0.111609 | ||||||||
\(271\) | 17.2185 | 1.04595 | 0.522975 | − | 0.852348i | \(-0.324822\pi\) | ||||
0.522975 | + | 0.852348i | \(0.324822\pi\) | |||||||
\(272\) | 1.16275 | 0.0705023 | ||||||||
\(273\) | 0.363346 | 0.0219907 | ||||||||
\(274\) | 19.7104 | 1.19075 | ||||||||
\(275\) | −2.38826 | −0.144017 | ||||||||
\(276\) | −2.20898 | −0.132965 | ||||||||
\(277\) | −10.4297 | −0.626662 | −0.313331 | − | 0.949644i | \(-0.601445\pi\) | ||||
−0.313331 | + | 0.949644i | \(0.601445\pi\) | |||||||
\(278\) | 20.5302 | 1.23132 | ||||||||
\(279\) | −6.18222 | −0.370120 | ||||||||
\(280\) | −2.07651 | −0.124095 | ||||||||
\(281\) | 19.2605 | 1.14898 | 0.574492 | − | 0.818510i | \(-0.305200\pi\) | ||||
0.574492 | + | 0.818510i | \(0.305200\pi\) | |||||||
\(282\) | 10.4738 | 0.623703 | ||||||||
\(283\) | −14.3040 | −0.850287 | −0.425143 | − | 0.905126i | \(-0.639776\pi\) | ||||
−0.425143 | + | 0.905126i | \(0.639776\pi\) | |||||||
\(284\) | −12.8294 | −0.761286 | ||||||||
\(285\) | −11.6377 | −0.689358 | ||||||||
\(286\) | 1.87990 | 0.111161 | ||||||||
\(287\) | 0.148906 | 0.00878962 | ||||||||
\(288\) | 5.36882 | 0.316361 | ||||||||
\(289\) | −12.0282 | −0.707541 | ||||||||
\(290\) | 2.79102 | 0.163895 | ||||||||
\(291\) | 13.4153 | 0.786417 | ||||||||
\(292\) | −12.0204 | −0.703443 | ||||||||
\(293\) | 12.3450 | 0.721203 | 0.360601 | − | 0.932720i | \(-0.382571\pi\) | ||||
0.360601 | + | 0.932720i | \(0.382571\pi\) | |||||||
\(294\) | 6.45644 | 0.376547 | ||||||||
\(295\) | 5.38066 | 0.313274 | ||||||||
\(296\) | −6.25902 | −0.363798 | ||||||||
\(297\) | −1.99973 | −0.116036 | ||||||||
\(298\) | 17.0635 | 0.988459 | ||||||||
\(299\) | −1.97893 | −0.114444 | ||||||||
\(300\) | −1.33313 | −0.0769685 | ||||||||
\(301\) | −3.93159 | −0.226613 | ||||||||
\(302\) | 7.61946 | 0.438451 | ||||||||
\(303\) | 6.35586 | 0.365134 | ||||||||
\(304\) | 3.11085 | 0.178420 | ||||||||
\(305\) | 4.75634 | 0.272347 | ||||||||
\(306\) | −2.09614 | −0.119829 | ||||||||
\(307\) | −27.0107 | −1.54158 | −0.770792 | − | 0.637087i | \(-0.780139\pi\) | ||||
−0.770792 | + | 0.637087i | \(0.780139\pi\) | |||||||
\(308\) | 0.811061 | 0.0462145 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 11.3377 | 0.643940 | ||||||||
\(311\) | −30.3100 | −1.71872 | −0.859361 | − | 0.511369i | \(-0.829139\pi\) | ||||
−0.859361 | + | 0.511369i | \(0.829139\pi\) | |||||||
\(312\) | 2.92952 | 0.165851 | ||||||||
\(313\) | 0.581827 | 0.0328868 | 0.0164434 | − | 0.999865i | \(-0.494766\pi\) | ||||
0.0164434 | + | 0.999865i | \(0.494766\pi\) | |||||||
\(314\) | −4.22970 | −0.238696 | ||||||||
\(315\) | 0.708823 | 0.0399377 | ||||||||
\(316\) | −8.97044 | −0.504626 | ||||||||
\(317\) | −10.0796 | −0.566128 | −0.283064 | − | 0.959101i | \(-0.591351\pi\) | ||||
−0.283064 | + | 0.959101i | \(0.591351\pi\) | |||||||
\(318\) | −1.37053 | −0.0768553 | ||||||||
\(319\) | −3.04335 | −0.170395 | ||||||||
\(320\) | −11.8806 | −0.664146 | ||||||||
\(321\) | −3.80533 | −0.212393 | ||||||||
\(322\) | 0.675949 | 0.0376692 | ||||||||
\(323\) | 13.3017 | 0.740125 | ||||||||
\(324\) | −1.11625 | −0.0620141 | ||||||||
\(325\) | −1.19429 | −0.0662475 | ||||||||
\(326\) | −12.7318 | −0.705149 | ||||||||
\(327\) | −3.96810 | −0.219437 | ||||||||
\(328\) | 1.20057 | 0.0662904 | ||||||||
\(329\) | 4.04817 | 0.223183 | ||||||||
\(330\) | 3.66735 | 0.201881 | ||||||||
\(331\) | −18.8863 | −1.03808 | −0.519042 | − | 0.854749i | \(-0.673711\pi\) | ||||
−0.519042 | + | 0.854749i | \(0.673711\pi\) | |||||||
\(332\) | −12.1533 | −0.667001 | ||||||||
\(333\) | 2.13653 | 0.117081 | ||||||||
\(334\) | −5.45783 | −0.298639 | ||||||||
\(335\) | −0.140692 | −0.00768680 | ||||||||
\(336\) | −0.189474 | −0.0103367 | ||||||||
\(337\) | −6.62308 | −0.360782 | −0.180391 | − | 0.983595i | \(-0.557736\pi\) | ||||
−0.180391 | + | 0.983595i | \(0.557736\pi\) | |||||||
\(338\) | 0.940078 | 0.0511335 | ||||||||
\(339\) | 1.14996 | 0.0624570 | ||||||||
\(340\) | −4.85554 | −0.263329 | ||||||||
\(341\) | −12.3628 | −0.669481 | ||||||||
\(342\) | −5.60807 | −0.303250 | ||||||||
\(343\) | 5.03887 | 0.272074 | ||||||||
\(344\) | −31.6990 | −1.70909 | ||||||||
\(345\) | −3.86053 | −0.207844 | ||||||||
\(346\) | −9.26340 | −0.498004 | ||||||||
\(347\) | −12.9059 | −0.692824 | −0.346412 | − | 0.938083i | \(-0.612600\pi\) | ||||
−0.346412 | + | 0.938083i | \(0.612600\pi\) | |||||||
\(348\) | −1.69881 | −0.0910658 | ||||||||
\(349\) | −7.35854 | −0.393894 | −0.196947 | − | 0.980414i | \(-0.563103\pi\) | ||||
−0.196947 | + | 0.980414i | \(0.563103\pi\) | |||||||
\(350\) | 0.407939 | 0.0218053 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 10.7362 | 0.572240 | ||||||||
\(353\) | 22.9517 | 1.22160 | 0.610799 | − | 0.791786i | \(-0.290848\pi\) | ||||
0.610799 | + | 0.791786i | \(0.290848\pi\) | |||||||
\(354\) | 2.59288 | 0.137810 | ||||||||
\(355\) | −22.4213 | −1.19000 | ||||||||
\(356\) | −9.54304 | −0.505780 | ||||||||
\(357\) | −0.810173 | −0.0428789 | ||||||||
\(358\) | −3.73276 | −0.197283 | ||||||||
\(359\) | 35.4244 | 1.86963 | 0.934814 | − | 0.355138i | \(-0.115566\pi\) | ||||
0.934814 | + | 0.355138i | \(0.115566\pi\) | |||||||
\(360\) | 5.71497 | 0.301206 | ||||||||
\(361\) | 16.5876 | 0.873032 | ||||||||
\(362\) | 10.6934 | 0.562032 | ||||||||
\(363\) | 7.00110 | 0.367462 | ||||||||
\(364\) | 0.405586 | 0.0212585 | ||||||||
\(365\) | −21.0075 | −1.09958 | ||||||||
\(366\) | 2.29203 | 0.119806 | ||||||||
\(367\) | −32.6938 | −1.70660 | −0.853301 | − | 0.521418i | \(-0.825403\pi\) | ||||
−0.853301 | + | 0.521418i | \(0.825403\pi\) | |||||||
\(368\) | 1.03195 | 0.0537943 | ||||||||
\(369\) | −0.409818 | −0.0213343 | ||||||||
\(370\) | −3.91824 | −0.203700 | ||||||||
\(371\) | −0.529717 | −0.0275015 | ||||||||
\(372\) | −6.90093 | −0.357797 | ||||||||
\(373\) | 2.27042 | 0.117558 | 0.0587789 | − | 0.998271i | \(-0.481279\pi\) | ||||
0.0587789 | + | 0.998271i | \(0.481279\pi\) | |||||||
\(374\) | −4.19171 | −0.216748 | ||||||||
\(375\) | −12.0840 | −0.624013 | ||||||||
\(376\) | 32.6389 | 1.68322 | ||||||||
\(377\) | −1.52189 | −0.0783811 | ||||||||
\(378\) | 0.341574 | 0.0175686 | ||||||||
\(379\) | 16.7685 | 0.861340 | 0.430670 | − | 0.902509i | \(-0.358277\pi\) | ||||
0.430670 | + | 0.902509i | \(0.358277\pi\) | |||||||
\(380\) | −12.9906 | −0.666405 | ||||||||
\(381\) | 4.69610 | 0.240588 | ||||||||
\(382\) | 14.9044 | 0.762576 | ||||||||
\(383\) | −6.32751 | −0.323321 | −0.161660 | − | 0.986846i | \(-0.551685\pi\) | ||||
−0.161660 | + | 0.986846i | \(0.551685\pi\) | |||||||
\(384\) | 5.01252 | 0.255794 | ||||||||
\(385\) | 1.41745 | 0.0722401 | ||||||||
\(386\) | −13.8113 | −0.702975 | ||||||||
\(387\) | 10.8205 | 0.550038 | ||||||||
\(388\) | 14.9748 | 0.760233 | ||||||||
\(389\) | 17.5492 | 0.889782 | 0.444891 | − | 0.895585i | \(-0.353242\pi\) | ||||
0.444891 | + | 0.895585i | \(0.353242\pi\) | |||||||
\(390\) | 1.83392 | 0.0928644 | ||||||||
\(391\) | 4.41252 | 0.223151 | ||||||||
\(392\) | 20.1199 | 1.01621 | ||||||||
\(393\) | −4.34589 | −0.219221 | ||||||||
\(394\) | 9.16988 | 0.461972 | ||||||||
\(395\) | −15.6772 | −0.788805 | ||||||||
\(396\) | −2.23220 | −0.112172 | ||||||||
\(397\) | 12.9479 | 0.649836 | 0.324918 | − | 0.945742i | \(-0.394663\pi\) | ||||
0.324918 | + | 0.945742i | \(0.394663\pi\) | |||||||
\(398\) | 20.9210 | 1.04868 | ||||||||
\(399\) | −2.16755 | −0.108513 | ||||||||
\(400\) | 0.622789 | 0.0311395 | ||||||||
\(401\) | −25.5064 | −1.27373 | −0.636864 | − | 0.770976i | \(-0.719769\pi\) | ||||
−0.636864 | + | 0.770976i | \(0.719769\pi\) | |||||||
\(402\) | −0.0677976 | −0.00338144 | ||||||||
\(403\) | −6.18222 | −0.307959 | ||||||||
\(404\) | 7.09475 | 0.352977 | ||||||||
\(405\) | −1.95082 | −0.0969371 | ||||||||
\(406\) | 0.519836 | 0.0257990 | ||||||||
\(407\) | 4.27248 | 0.211779 | ||||||||
\(408\) | −6.53212 | −0.323388 | ||||||||
\(409\) | −16.8621 | −0.833776 | −0.416888 | − | 0.908958i | \(-0.636879\pi\) | ||||
−0.416888 | + | 0.908958i | \(0.636879\pi\) | |||||||
\(410\) | 0.751575 | 0.0371176 | ||||||||
\(411\) | −20.9667 | −1.03421 | ||||||||
\(412\) | 1.11625 | 0.0549939 | ||||||||
\(413\) | 1.00216 | 0.0493132 | ||||||||
\(414\) | −1.86035 | −0.0914310 | ||||||||
\(415\) | −21.2398 | −1.04262 | ||||||||
\(416\) | 5.36882 | 0.263228 | ||||||||
\(417\) | −21.8389 | −1.06945 | ||||||||
\(418\) | −11.2146 | −0.548524 | ||||||||
\(419\) | 4.01833 | 0.196308 | 0.0981542 | − | 0.995171i | \(-0.468706\pi\) | ||||
0.0981542 | + | 0.995171i | \(0.468706\pi\) | |||||||
\(420\) | 0.791227 | 0.0386079 | ||||||||
\(421\) | −15.3640 | −0.748794 | −0.374397 | − | 0.927268i | \(-0.622150\pi\) | ||||
−0.374397 | + | 0.927268i | \(0.622150\pi\) | |||||||
\(422\) | 14.4145 | 0.701686 | ||||||||
\(423\) | −11.1414 | −0.541712 | ||||||||
\(424\) | −4.27091 | −0.207414 | ||||||||
\(425\) | 2.66298 | 0.129174 | ||||||||
\(426\) | −10.8046 | −0.523484 | ||||||||
\(427\) | 0.885882 | 0.0428708 | ||||||||
\(428\) | −4.24771 | −0.205321 | ||||||||
\(429\) | −1.99973 | −0.0965477 | ||||||||
\(430\) | −19.8440 | −0.956964 | ||||||||
\(431\) | −21.3395 | −1.02789 | −0.513945 | − | 0.857823i | \(-0.671816\pi\) | ||||
−0.513945 | + | 0.857823i | \(0.671816\pi\) | |||||||
\(432\) | 0.521471 | 0.0250893 | ||||||||
\(433\) | −4.61830 | −0.221941 | −0.110971 | − | 0.993824i | \(-0.535396\pi\) | ||||
−0.110971 | + | 0.993824i | \(0.535396\pi\) | |||||||
\(434\) | 2.11168 | 0.101364 | ||||||||
\(435\) | −2.96893 | −0.142349 | ||||||||
\(436\) | −4.42941 | −0.212130 | ||||||||
\(437\) | 11.8054 | 0.564727 | ||||||||
\(438\) | −10.1233 | −0.483709 | ||||||||
\(439\) | 11.8407 | 0.565125 | 0.282562 | − | 0.959249i | \(-0.408816\pi\) | ||||
0.282562 | + | 0.959249i | \(0.408816\pi\) | |||||||
\(440\) | 11.4284 | 0.544827 | ||||||||
\(441\) | −6.86798 | −0.327047 | ||||||||
\(442\) | −2.09614 | −0.0997034 | ||||||||
\(443\) | −11.7872 | −0.560028 | −0.280014 | − | 0.959996i | \(-0.590339\pi\) | ||||
−0.280014 | + | 0.959996i | \(0.590339\pi\) | |||||||
\(444\) | 2.38491 | 0.113183 | ||||||||
\(445\) | −16.6779 | −0.790609 | ||||||||
\(446\) | 10.4472 | 0.494690 | ||||||||
\(447\) | −18.1511 | −0.858518 | ||||||||
\(448\) | −2.21280 | −0.104545 | ||||||||
\(449\) | 1.56138 | 0.0736862 | 0.0368431 | − | 0.999321i | \(-0.488270\pi\) | ||||
0.0368431 | + | 0.999321i | \(0.488270\pi\) | |||||||
\(450\) | −1.12273 | −0.0529259 | ||||||||
\(451\) | −0.819523 | −0.0385898 | ||||||||
\(452\) | 1.28364 | 0.0603774 | ||||||||
\(453\) | −8.10513 | −0.380812 | ||||||||
\(454\) | 1.58175 | 0.0742350 | ||||||||
\(455\) | 0.708823 | 0.0332302 | ||||||||
\(456\) | −17.4762 | −0.818396 | ||||||||
\(457\) | 8.20490 | 0.383809 | 0.191905 | − | 0.981414i | \(-0.438534\pi\) | ||||
0.191905 | + | 0.981414i | \(0.438534\pi\) | |||||||
\(458\) | 20.4645 | 0.956244 | ||||||||
\(459\) | 2.22976 | 0.104076 | ||||||||
\(460\) | −4.30933 | −0.200924 | ||||||||
\(461\) | 11.6349 | 0.541890 | 0.270945 | − | 0.962595i | \(-0.412664\pi\) | ||||
0.270945 | + | 0.962595i | \(0.412664\pi\) | |||||||
\(462\) | 0.683053 | 0.0317785 | ||||||||
\(463\) | 30.4947 | 1.41721 | 0.708605 | − | 0.705605i | \(-0.249325\pi\) | ||||
0.708605 | + | 0.705605i | \(0.249325\pi\) | |||||||
\(464\) | 0.793619 | 0.0368429 | ||||||||
\(465\) | −12.0604 | −0.559289 | ||||||||
\(466\) | 26.0955 | 1.20885 | ||||||||
\(467\) | −24.8221 | −1.14863 | −0.574315 | − | 0.818634i | \(-0.694732\pi\) | ||||
−0.574315 | + | 0.818634i | \(0.694732\pi\) | |||||||
\(468\) | −1.11625 | −0.0515988 | ||||||||
\(469\) | −0.0262042 | −0.00121000 | ||||||||
\(470\) | 20.4324 | 0.942478 | ||||||||
\(471\) | 4.49931 | 0.207317 | ||||||||
\(472\) | 8.08007 | 0.371915 | ||||||||
\(473\) | 21.6381 | 0.994920 | ||||||||
\(474\) | −7.55465 | −0.346997 | ||||||||
\(475\) | 7.12460 | 0.326899 | ||||||||
\(476\) | −0.904358 | −0.0414512 | ||||||||
\(477\) | 1.45789 | 0.0667520 | ||||||||
\(478\) | −15.5237 | −0.710039 | ||||||||
\(479\) | 33.8138 | 1.54499 | 0.772496 | − | 0.635019i | \(-0.219008\pi\) | ||||
0.772496 | + | 0.635019i | \(0.219008\pi\) | |||||||
\(480\) | 10.4736 | 0.478053 | ||||||||
\(481\) | 2.13653 | 0.0974175 | ||||||||
\(482\) | −15.5813 | −0.709709 | ||||||||
\(483\) | −0.719035 | −0.0327172 | ||||||||
\(484\) | 7.81500 | 0.355227 | ||||||||
\(485\) | 26.1708 | 1.18836 | ||||||||
\(486\) | −0.940078 | −0.0426428 | ||||||||
\(487\) | −14.2467 | −0.645580 | −0.322790 | − | 0.946471i | \(-0.604621\pi\) | ||||
−0.322790 | + | 0.946471i | \(0.604621\pi\) | |||||||
\(488\) | 7.14253 | 0.323327 | ||||||||
\(489\) | 13.5433 | 0.612451 | ||||||||
\(490\) | 12.5954 | 0.569000 | ||||||||
\(491\) | 14.4413 | 0.651727 | 0.325864 | − | 0.945417i | \(-0.394345\pi\) | ||||
0.325864 | + | 0.945417i | \(0.394345\pi\) | |||||||
\(492\) | −0.457461 | −0.0206239 | ||||||||
\(493\) | 3.39343 | 0.152833 | ||||||||
\(494\) | −5.60807 | −0.252319 | ||||||||
\(495\) | −3.90111 | −0.175342 | ||||||||
\(496\) | 3.22385 | 0.144755 | ||||||||
\(497\) | −4.17604 | −0.187321 | ||||||||
\(498\) | −10.2352 | −0.458650 | ||||||||
\(499\) | −8.54587 | −0.382565 | −0.191283 | − | 0.981535i | \(-0.561265\pi\) | ||||
−0.191283 | + | 0.981535i | \(0.561265\pi\) | |||||||
\(500\) | −13.4888 | −0.603236 | ||||||||
\(501\) | 5.80573 | 0.259381 | ||||||||
\(502\) | −16.0557 | −0.716603 | ||||||||
\(503\) | 39.4044 | 1.75696 | 0.878478 | − | 0.477783i | \(-0.158559\pi\) | ||||
0.878478 | + | 0.477783i | \(0.158559\pi\) | |||||||
\(504\) | 1.06443 | 0.0474135 | ||||||||
\(505\) | 12.3991 | 0.551755 | ||||||||
\(506\) | −3.72018 | −0.165382 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 5.24204 | 0.232578 | ||||||||
\(509\) | −37.1959 | −1.64868 | −0.824340 | − | 0.566096i | \(-0.808453\pi\) | ||||
−0.824340 | + | 0.566096i | \(0.808453\pi\) | |||||||
\(510\) | −4.08920 | −0.181073 | ||||||||
\(511\) | −3.91271 | −0.173088 | ||||||||
\(512\) | −5.85501 | −0.258757 | ||||||||
\(513\) | 5.96553 | 0.263385 | ||||||||
\(514\) | −14.0356 | −0.619084 | ||||||||
\(515\) | 1.95082 | 0.0859635 | ||||||||
\(516\) | 12.0784 | 0.531724 | ||||||||
\(517\) | −22.2797 | −0.979860 | ||||||||
\(518\) | −0.729783 | −0.0320648 | ||||||||
\(519\) | 9.85387 | 0.432537 | ||||||||
\(520\) | 5.71497 | 0.250618 | ||||||||
\(521\) | 13.2940 | 0.582420 | 0.291210 | − | 0.956659i | \(-0.405942\pi\) | ||||
0.291210 | + | 0.956659i | \(0.405942\pi\) | |||||||
\(522\) | −1.43069 | −0.0626196 | ||||||||
\(523\) | 9.08576 | 0.397292 | 0.198646 | − | 0.980071i | \(-0.436346\pi\) | ||||
0.198646 | + | 0.980071i | \(0.436346\pi\) | |||||||
\(524\) | −4.85112 | −0.211922 | ||||||||
\(525\) | −0.433942 | −0.0189388 | ||||||||
\(526\) | 23.4362 | 1.02187 | ||||||||
\(527\) | 13.7848 | 0.600477 | ||||||||
\(528\) | 1.04280 | 0.0453820 | ||||||||
\(529\) | −19.0838 | −0.829733 | ||||||||
\(530\) | −2.67365 | −0.116136 | ||||||||
\(531\) | −2.75815 | −0.119694 | ||||||||
\(532\) | −2.41954 | −0.104900 | ||||||||
\(533\) | −0.409818 | −0.0177512 | ||||||||
\(534\) | −8.03689 | −0.347790 | ||||||||
\(535\) | −7.42352 | −0.320947 | ||||||||
\(536\) | −0.211274 | −0.00912567 | ||||||||
\(537\) | 3.97070 | 0.171348 | ||||||||
\(538\) | −5.51724 | −0.237865 | ||||||||
\(539\) | −13.7341 | −0.591569 | ||||||||
\(540\) | −2.17761 | −0.0937095 | ||||||||
\(541\) | −1.58666 | −0.0682157 | −0.0341078 | − | 0.999418i | \(-0.510859\pi\) | ||||
−0.0341078 | + | 0.999418i | \(0.510859\pi\) | |||||||
\(542\) | 16.1867 | 0.695280 | ||||||||
\(543\) | −11.3750 | −0.488148 | ||||||||
\(544\) | −11.9712 | −0.513259 | ||||||||
\(545\) | −7.74106 | −0.331591 | ||||||||
\(546\) | 0.341574 | 0.0146180 | ||||||||
\(547\) | −3.55748 | −0.152107 | −0.0760534 | − | 0.997104i | \(-0.524232\pi\) | ||||
−0.0760534 | + | 0.997104i | \(0.524232\pi\) | |||||||
\(548\) | −23.4042 | −0.999778 | ||||||||
\(549\) | −2.43812 | −0.104057 | ||||||||
\(550\) | −2.24515 | −0.0957335 | ||||||||
\(551\) | 9.07886 | 0.386772 | ||||||||
\(552\) | −5.79731 | −0.246750 | ||||||||
\(553\) | −2.91992 | −0.124168 | ||||||||
\(554\) | −9.80477 | −0.416565 | ||||||||
\(555\) | 4.16799 | 0.176922 | ||||||||
\(556\) | −24.3777 | −1.03385 | ||||||||
\(557\) | 29.0416 | 1.23053 | 0.615265 | − | 0.788320i | \(-0.289049\pi\) | ||||
0.615265 | + | 0.788320i | \(0.289049\pi\) | |||||||
\(558\) | −5.81177 | −0.246032 | ||||||||
\(559\) | 10.8205 | 0.457659 | ||||||||
\(560\) | −0.369631 | −0.0156198 | ||||||||
\(561\) | 4.45890 | 0.188255 | ||||||||
\(562\) | 18.1064 | 0.763771 | ||||||||
\(563\) | −4.84002 | −0.203983 | −0.101991 | − | 0.994785i | \(-0.532521\pi\) | ||||
−0.101991 | + | 0.994785i | \(0.532521\pi\) | |||||||
\(564\) | −12.4366 | −0.523675 | ||||||||
\(565\) | 2.24336 | 0.0943788 | ||||||||
\(566\) | −13.4469 | −0.565216 | ||||||||
\(567\) | −0.363346 | −0.0152591 | ||||||||
\(568\) | −33.6698 | −1.41275 | ||||||||
\(569\) | 2.20459 | 0.0924213 | 0.0462106 | − | 0.998932i | \(-0.485285\pi\) | ||||
0.0462106 | + | 0.998932i | \(0.485285\pi\) | |||||||
\(570\) | −10.9403 | −0.458240 | ||||||||
\(571\) | −15.0088 | −0.628100 | −0.314050 | − | 0.949407i | \(-0.601686\pi\) | ||||
−0.314050 | + | 0.949407i | \(0.601686\pi\) | |||||||
\(572\) | −2.23220 | −0.0933330 | ||||||||
\(573\) | −15.8544 | −0.662329 | ||||||||
\(574\) | 0.139983 | 0.00584277 | ||||||||
\(575\) | 2.36342 | 0.0985614 | ||||||||
\(576\) | 6.09005 | 0.253752 | ||||||||
\(577\) | 26.0752 | 1.08553 | 0.542763 | − | 0.839886i | \(-0.317378\pi\) | ||||
0.542763 | + | 0.839886i | \(0.317378\pi\) | |||||||
\(578\) | −11.3074 | −0.470327 | ||||||||
\(579\) | 14.6916 | 0.610563 | ||||||||
\(580\) | −3.31408 | −0.137610 | ||||||||
\(581\) | −3.95597 | −0.164121 | ||||||||
\(582\) | 12.6114 | 0.522759 | ||||||||
\(583\) | 2.91537 | 0.120742 | ||||||||
\(584\) | −31.5467 | −1.30541 | ||||||||
\(585\) | −1.95082 | −0.0806566 | ||||||||
\(586\) | 11.6053 | 0.479409 | ||||||||
\(587\) | 24.5676 | 1.01401 | 0.507006 | − | 0.861943i | \(-0.330752\pi\) | ||||
0.507006 | + | 0.861943i | \(0.330752\pi\) | |||||||
\(588\) | −7.66641 | −0.316157 | ||||||||
\(589\) | 36.8803 | 1.51963 | ||||||||
\(590\) | 5.05824 | 0.208245 | ||||||||
\(591\) | −9.75438 | −0.401242 | ||||||||
\(592\) | −1.11414 | −0.0457909 | ||||||||
\(593\) | 24.1549 | 0.991921 | 0.495961 | − | 0.868345i | \(-0.334816\pi\) | ||||
0.495961 | + | 0.868345i | \(0.334816\pi\) | |||||||
\(594\) | −1.87990 | −0.0771332 | ||||||||
\(595\) | −1.58050 | −0.0647943 | ||||||||
\(596\) | −20.2612 | −0.829932 | ||||||||
\(597\) | −22.2546 | −0.910819 | ||||||||
\(598\) | −1.86035 | −0.0760752 | ||||||||
\(599\) | −19.7524 | −0.807061 | −0.403530 | − | 0.914966i | \(-0.632217\pi\) | ||||
−0.403530 | + | 0.914966i | \(0.632217\pi\) | |||||||
\(600\) | −3.49871 | −0.142834 | ||||||||
\(601\) | −36.9777 | −1.50835 | −0.754175 | − | 0.656673i | \(-0.771963\pi\) | ||||
−0.754175 | + | 0.656673i | \(0.771963\pi\) | |||||||
\(602\) | −3.69601 | −0.150638 | ||||||||
\(603\) | 0.0721191 | 0.00293692 | ||||||||
\(604\) | −9.04738 | −0.368133 | ||||||||
\(605\) | 13.6579 | 0.555272 | ||||||||
\(606\) | 5.97500 | 0.242718 | ||||||||
\(607\) | 25.8702 | 1.05004 | 0.525020 | − | 0.851090i | \(-0.324058\pi\) | ||||
0.525020 | + | 0.851090i | \(0.324058\pi\) | |||||||
\(608\) | −32.0279 | −1.29890 | ||||||||
\(609\) | −0.552971 | −0.0224075 | ||||||||
\(610\) | 4.47133 | 0.181039 | ||||||||
\(611\) | −11.1414 | −0.450732 | ||||||||
\(612\) | 2.48897 | 0.100611 | ||||||||
\(613\) | 4.23254 | 0.170951 | 0.0854754 | − | 0.996340i | \(-0.472759\pi\) | ||||
0.0854754 | + | 0.996340i | \(0.472759\pi\) | |||||||
\(614\) | −25.3922 | −1.02475 | ||||||||
\(615\) | −0.799482 | −0.0322382 | ||||||||
\(616\) | 2.12857 | 0.0857624 | ||||||||
\(617\) | −27.6785 | −1.11429 | −0.557147 | − | 0.830414i | \(-0.688104\pi\) | ||||
−0.557147 | + | 0.830414i | \(0.688104\pi\) | |||||||
\(618\) | 0.940078 | 0.0378155 | ||||||||
\(619\) | 14.3567 | 0.577044 | 0.288522 | − | 0.957473i | \(-0.406836\pi\) | ||||
0.288522 | + | 0.957473i | \(0.406836\pi\) | |||||||
\(620\) | −13.4625 | −0.540666 | ||||||||
\(621\) | 1.97893 | 0.0794116 | ||||||||
\(622\) | −28.4938 | −1.14250 | ||||||||
\(623\) | −3.10631 | −0.124452 | ||||||||
\(624\) | 0.521471 | 0.0208756 | ||||||||
\(625\) | −17.6022 | −0.704088 | ||||||||
\(626\) | 0.546963 | 0.0218610 | ||||||||
\(627\) | 11.9294 | 0.476416 | ||||||||
\(628\) | 5.02237 | 0.200414 | ||||||||
\(629\) | −4.76394 | −0.189951 | ||||||||
\(630\) | 0.666349 | 0.0265480 | ||||||||
\(631\) | −3.90054 | −0.155278 | −0.0776391 | − | 0.996982i | \(-0.524738\pi\) | ||||
−0.0776391 | + | 0.996982i | \(0.524738\pi\) | |||||||
\(632\) | −23.5422 | −0.936459 | ||||||||
\(633\) | −15.3333 | −0.609443 | ||||||||
\(634\) | −9.47563 | −0.376325 | ||||||||
\(635\) | 9.16126 | 0.363553 | ||||||||
\(636\) | 1.62737 | 0.0645295 | ||||||||
\(637\) | −6.86798 | −0.272119 | ||||||||
\(638\) | −2.86099 | −0.113268 | ||||||||
\(639\) | 11.4933 | 0.454667 | ||||||||
\(640\) | 9.77853 | 0.386530 | ||||||||
\(641\) | 7.88596 | 0.311477 | 0.155738 | − | 0.987798i | \(-0.450224\pi\) | ||||
0.155738 | + | 0.987798i | \(0.450224\pi\) | |||||||
\(642\) | −3.57731 | −0.141185 | ||||||||
\(643\) | 18.0104 | 0.710261 | 0.355131 | − | 0.934817i | \(-0.384436\pi\) | ||||
0.355131 | + | 0.934817i | \(0.384436\pi\) | |||||||
\(644\) | −0.802625 | −0.0316279 | ||||||||
\(645\) | 21.1089 | 0.831163 | ||||||||
\(646\) | 12.5046 | 0.491988 | ||||||||
\(647\) | −1.54626 | −0.0607899 | −0.0303950 | − | 0.999538i | \(-0.509677\pi\) | ||||
−0.0303950 | + | 0.999538i | \(0.509677\pi\) | |||||||
\(648\) | −2.92952 | −0.115082 | ||||||||
\(649\) | −5.51555 | −0.216504 | ||||||||
\(650\) | −1.12273 | −0.0440370 | ||||||||
\(651\) | −2.24629 | −0.0880389 | ||||||||
\(652\) | 15.1178 | 0.592059 | ||||||||
\(653\) | −30.6869 | −1.20087 | −0.600435 | − | 0.799674i | \(-0.705006\pi\) | ||||
−0.600435 | + | 0.799674i | \(0.705006\pi\) | |||||||
\(654\) | −3.73033 | −0.145867 | ||||||||
\(655\) | −8.47807 | −0.331265 | ||||||||
\(656\) | 0.213708 | 0.00834390 | ||||||||
\(657\) | 10.7686 | 0.420121 | ||||||||
\(658\) | 3.80560 | 0.148358 | ||||||||
\(659\) | 6.68165 | 0.260280 | 0.130140 | − | 0.991496i | \(-0.458457\pi\) | ||||
0.130140 | + | 0.991496i | \(0.458457\pi\) | |||||||
\(660\) | −4.35463 | −0.169504 | ||||||||
\(661\) | −19.1587 | −0.745185 | −0.372593 | − | 0.927995i | \(-0.621531\pi\) | ||||
−0.372593 | + | 0.927995i | \(0.621531\pi\) | |||||||
\(662\) | −17.7546 | −0.690051 | ||||||||
\(663\) | 2.22976 | 0.0865965 | ||||||||
\(664\) | −31.8955 | −1.23778 | ||||||||
\(665\) | −4.22851 | −0.163975 | ||||||||
\(666\) | 2.00851 | 0.0778281 | ||||||||
\(667\) | 3.01170 | 0.116613 | ||||||||
\(668\) | 6.48066 | 0.250744 | ||||||||
\(669\) | −11.1131 | −0.429659 | ||||||||
\(670\) | −0.132261 | −0.00510969 | ||||||||
\(671\) | −4.87558 | −0.188220 | ||||||||
\(672\) | 1.95074 | 0.0752514 | ||||||||
\(673\) | 17.6735 | 0.681263 | 0.340632 | − | 0.940197i | \(-0.389359\pi\) | ||||
0.340632 | + | 0.940197i | \(0.389359\pi\) | |||||||
\(674\) | −6.22621 | −0.239825 | ||||||||
\(675\) | 1.19429 | 0.0459684 | ||||||||
\(676\) | −1.11625 | −0.0429328 | ||||||||
\(677\) | 37.0818 | 1.42517 | 0.712584 | − | 0.701587i | \(-0.247525\pi\) | ||||
0.712584 | + | 0.701587i | \(0.247525\pi\) | |||||||
\(678\) | 1.08105 | 0.0415174 | ||||||||
\(679\) | 4.87439 | 0.187062 | ||||||||
\(680\) | −12.7430 | −0.488672 | ||||||||
\(681\) | −1.68257 | −0.0644762 | ||||||||
\(682\) | −11.6220 | −0.445028 | ||||||||
\(683\) | 24.9633 | 0.955193 | 0.477597 | − | 0.878579i | \(-0.341508\pi\) | ||||
0.477597 | + | 0.878579i | \(0.341508\pi\) | |||||||
\(684\) | 6.65905 | 0.254615 | ||||||||
\(685\) | −40.9024 | −1.56280 | ||||||||
\(686\) | 4.73693 | 0.180857 | ||||||||
\(687\) | −21.7690 | −0.830538 | ||||||||
\(688\) | −5.64259 | −0.215122 | ||||||||
\(689\) | 1.45789 | 0.0555411 | ||||||||
\(690\) | −3.62920 | −0.138161 | ||||||||
\(691\) | 37.2090 | 1.41550 | 0.707748 | − | 0.706465i | \(-0.249711\pi\) | ||||
0.707748 | + | 0.706465i | \(0.249711\pi\) | |||||||
\(692\) | 10.9994 | 0.418135 | ||||||||
\(693\) | −0.726592 | −0.0276010 | ||||||||
\(694\) | −12.1325 | −0.460544 | ||||||||
\(695\) | −42.6037 | −1.61605 | ||||||||
\(696\) | −4.45840 | −0.168995 | ||||||||
\(697\) | 0.913793 | 0.0346124 | ||||||||
\(698\) | −6.91760 | −0.261835 | ||||||||
\(699\) | −27.7588 | −1.04993 | ||||||||
\(700\) | −0.484389 | −0.0183082 | ||||||||
\(701\) | 5.78338 | 0.218435 | 0.109218 | − | 0.994018i | \(-0.465165\pi\) | ||||
0.109218 | + | 0.994018i | \(0.465165\pi\) | |||||||
\(702\) | −0.940078 | −0.0354810 | ||||||||
\(703\) | −12.7456 | −0.480708 | ||||||||
\(704\) | 12.1784 | 0.458992 | ||||||||
\(705\) | −21.7348 | −0.818581 | ||||||||
\(706\) | 21.5764 | 0.812039 | ||||||||
\(707\) | 2.30938 | 0.0868530 | ||||||||
\(708\) | −3.07880 | −0.115708 | ||||||||
\(709\) | −35.2990 | −1.32568 | −0.662841 | − | 0.748760i | \(-0.730649\pi\) | ||||
−0.662841 | + | 0.748760i | \(0.730649\pi\) | |||||||
\(710\) | −21.0778 | −0.791036 | ||||||||
\(711\) | 8.03620 | 0.301381 | ||||||||
\(712\) | −25.0450 | −0.938600 | ||||||||
\(713\) | 12.2342 | 0.458173 | ||||||||
\(714\) | −0.761625 | −0.0285031 | ||||||||
\(715\) | −3.90111 | −0.145893 | ||||||||
\(716\) | 4.43230 | 0.165643 | ||||||||
\(717\) | 16.5132 | 0.616698 | ||||||||
\(718\) | 33.3017 | 1.24281 | ||||||||
\(719\) | 28.8586 | 1.07624 | 0.538121 | − | 0.842867i | \(-0.319134\pi\) | ||||
0.538121 | + | 0.842867i | \(0.319134\pi\) | |||||||
\(720\) | 1.01730 | 0.0379124 | ||||||||
\(721\) | 0.363346 | 0.0135317 | ||||||||
\(722\) | 15.5936 | 0.580335 | ||||||||
\(723\) | 16.5745 | 0.616412 | ||||||||
\(724\) | −12.6974 | −0.471895 | ||||||||
\(725\) | 1.81758 | 0.0675031 | ||||||||
\(726\) | 6.58158 | 0.244265 | ||||||||
\(727\) | 22.4518 | 0.832693 | 0.416346 | − | 0.909206i | \(-0.363310\pi\) | ||||
0.416346 | + | 0.909206i | \(0.363310\pi\) | |||||||
\(728\) | 1.06443 | 0.0394504 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −19.7487 | −0.730933 | ||||||||
\(731\) | −24.1271 | −0.892374 | ||||||||
\(732\) | −2.72156 | −0.100592 | ||||||||
\(733\) | 0.202654 | 0.00748521 | 0.00374261 | − | 0.999993i | \(-0.498809\pi\) | ||||
0.00374261 | + | 0.999993i | \(0.498809\pi\) | |||||||
\(734\) | −30.7347 | −1.13444 | ||||||||
\(735\) | −13.3982 | −0.494200 | ||||||||
\(736\) | −10.6245 | −0.391624 | ||||||||
\(737\) | 0.144218 | 0.00531235 | ||||||||
\(738\) | −0.385261 | −0.0141816 | ||||||||
\(739\) | −11.7675 | −0.432873 | −0.216437 | − | 0.976297i | \(-0.569444\pi\) | ||||
−0.216437 | + | 0.976297i | \(0.569444\pi\) | |||||||
\(740\) | 4.65254 | 0.171031 | ||||||||
\(741\) | 5.96553 | 0.219149 | ||||||||
\(742\) | −0.497975 | −0.0182813 | ||||||||
\(743\) | 6.90155 | 0.253193 | 0.126597 | − | 0.991954i | \(-0.459595\pi\) | ||||
0.126597 | + | 0.991954i | \(0.459595\pi\) | |||||||
\(744\) | −18.1110 | −0.663980 | ||||||||
\(745\) | −35.4096 | −1.29731 | ||||||||
\(746\) | 2.13437 | 0.0781448 | ||||||||
\(747\) | 10.8876 | 0.398357 | ||||||||
\(748\) | 4.97726 | 0.181987 | ||||||||
\(749\) | −1.38265 | −0.0505210 | ||||||||
\(750\) | −11.3599 | −0.414804 | ||||||||
\(751\) | −43.7926 | −1.59802 | −0.799008 | − | 0.601320i | \(-0.794642\pi\) | ||||
−0.799008 | + | 0.601320i | \(0.794642\pi\) | |||||||
\(752\) | 5.80990 | 0.211865 | ||||||||
\(753\) | 17.0792 | 0.622399 | ||||||||
\(754\) | −1.43069 | −0.0521027 | ||||||||
\(755\) | −15.8117 | −0.575446 | ||||||||
\(756\) | −0.405586 | −0.0147510 | ||||||||
\(757\) | 0.472591 | 0.0171766 | 0.00858830 | − | 0.999963i | \(-0.497266\pi\) | ||||
0.00858830 | + | 0.999963i | \(0.497266\pi\) | |||||||
\(758\) | 15.7637 | 0.572563 | ||||||||
\(759\) | 3.95731 | 0.143641 | ||||||||
\(760\) | −34.0929 | −1.23668 | ||||||||
\(761\) | 31.2067 | 1.13124 | 0.565621 | − | 0.824665i | \(-0.308636\pi\) | ||||
0.565621 | + | 0.824665i | \(0.308636\pi\) | |||||||
\(762\) | 4.41470 | 0.159928 | ||||||||
\(763\) | −1.44179 | −0.0521965 | ||||||||
\(764\) | −17.6976 | −0.640276 | ||||||||
\(765\) | 4.34986 | 0.157269 | ||||||||
\(766\) | −5.94836 | −0.214923 | ||||||||
\(767\) | −2.75815 | −0.0995911 | ||||||||
\(768\) | 16.8923 | 0.609547 | ||||||||
\(769\) | 44.7549 | 1.61390 | 0.806951 | − | 0.590618i | \(-0.201116\pi\) | ||||
0.806951 | + | 0.590618i | \(0.201116\pi\) | |||||||
\(770\) | 1.33252 | 0.0480205 | ||||||||
\(771\) | 14.9303 | 0.537700 | ||||||||
\(772\) | 16.3996 | 0.590233 | ||||||||
\(773\) | 41.2095 | 1.48220 | 0.741101 | − | 0.671394i | \(-0.234304\pi\) | ||||
0.741101 | + | 0.671394i | \(0.234304\pi\) | |||||||
\(774\) | 10.1721 | 0.365630 | ||||||||
\(775\) | 7.38339 | 0.265219 | ||||||||
\(776\) | 39.3003 | 1.41080 | ||||||||
\(777\) | 0.776300 | 0.0278496 | ||||||||
\(778\) | 16.4977 | 0.591470 | ||||||||
\(779\) | 2.44478 | 0.0875934 | ||||||||
\(780\) | −2.17761 | −0.0779710 | ||||||||
\(781\) | 22.9834 | 0.822411 | ||||||||
\(782\) | 4.14811 | 0.148336 | ||||||||
\(783\) | 1.52189 | 0.0543878 | ||||||||
\(784\) | 3.58145 | 0.127909 | ||||||||
\(785\) | 8.77735 | 0.313277 | ||||||||
\(786\) | −4.08548 | −0.145724 | ||||||||
\(787\) | 24.8745 | 0.886680 | 0.443340 | − | 0.896354i | \(-0.353794\pi\) | ||||
0.443340 | + | 0.896354i | \(0.353794\pi\) | |||||||
\(788\) | −10.8884 | −0.387882 | ||||||||
\(789\) | −24.9300 | −0.887533 | ||||||||
\(790\) | −14.7378 | −0.524347 | ||||||||
\(791\) | 0.417832 | 0.0148564 | ||||||||
\(792\) | −5.85824 | −0.208163 | ||||||||
\(793\) | −2.43812 | −0.0865803 | ||||||||
\(794\) | 12.1720 | 0.431969 | ||||||||
\(795\) | 2.84408 | 0.100869 | ||||||||
\(796\) | −24.8417 | −0.880492 | ||||||||
\(797\) | −9.33618 | −0.330704 | −0.165352 | − | 0.986235i | \(-0.552876\pi\) | ||||
−0.165352 | + | 0.986235i | \(0.552876\pi\) | |||||||
\(798\) | −2.03767 | −0.0721327 | ||||||||
\(799\) | 24.8425 | 0.878866 | ||||||||
\(800\) | −6.41194 | −0.226696 | ||||||||
\(801\) | 8.54917 | 0.302070 | ||||||||
\(802\) | −23.9780 | −0.846693 | ||||||||
\(803\) | 21.5341 | 0.759924 | ||||||||
\(804\) | 0.0805032 | 0.00283913 | ||||||||
\(805\) | −1.40271 | −0.0494390 | ||||||||
\(806\) | −5.81177 | −0.204711 | ||||||||
\(807\) | 5.86892 | 0.206596 | ||||||||
\(808\) | 18.6196 | 0.655036 | ||||||||
\(809\) | 37.5827 | 1.32134 | 0.660668 | − | 0.750678i | \(-0.270273\pi\) | ||||
0.660668 | + | 0.750678i | \(0.270273\pi\) | |||||||
\(810\) | −1.83392 | −0.0644375 | ||||||||
\(811\) | −46.0354 | −1.61652 | −0.808260 | − | 0.588826i | \(-0.799590\pi\) | ||||
−0.808260 | + | 0.588826i | \(0.799590\pi\) | |||||||
\(812\) | −0.617256 | −0.0216614 | ||||||||
\(813\) | −17.2185 | −0.603880 | ||||||||
\(814\) | 4.01646 | 0.140777 | ||||||||
\(815\) | 26.4207 | 0.925475 | ||||||||
\(816\) | −1.16275 | −0.0407045 | ||||||||
\(817\) | −64.5502 | −2.25833 | ||||||||
\(818\) | −15.8517 | −0.554241 | ||||||||
\(819\) | −0.363346 | −0.0126963 | ||||||||
\(820\) | −0.892424 | −0.0311648 | ||||||||
\(821\) | −3.55570 | −0.124095 | −0.0620473 | − | 0.998073i | \(-0.519763\pi\) | ||||
−0.0620473 | + | 0.998073i | \(0.519763\pi\) | |||||||
\(822\) | −19.7104 | −0.687478 | ||||||||
\(823\) | 4.62255 | 0.161132 | 0.0805660 | − | 0.996749i | \(-0.474327\pi\) | ||||
0.0805660 | + | 0.996749i | \(0.474327\pi\) | |||||||
\(824\) | 2.92952 | 0.102055 | ||||||||
\(825\) | 2.38826 | 0.0831485 | ||||||||
\(826\) | 0.942112 | 0.0327803 | ||||||||
\(827\) | 24.9504 | 0.867612 | 0.433806 | − | 0.901006i | \(-0.357170\pi\) | ||||
0.433806 | + | 0.901006i | \(0.357170\pi\) | |||||||
\(828\) | 2.20898 | 0.0767675 | ||||||||
\(829\) | −18.3119 | −0.636000 | −0.318000 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.318000 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(830\) | −19.9671 | −0.693067 | ||||||||
\(831\) | 10.4297 | 0.361804 | ||||||||
\(832\) | 6.09005 | 0.211135 | ||||||||
\(833\) | 15.3139 | 0.530596 | ||||||||
\(834\) | −20.5302 | −0.710904 | ||||||||
\(835\) | 11.3259 | 0.391950 | ||||||||
\(836\) | 13.3163 | 0.460553 | ||||||||
\(837\) | 6.18222 | 0.213689 | ||||||||
\(838\) | 3.77755 | 0.130493 | ||||||||
\(839\) | 19.2523 | 0.664663 | 0.332332 | − | 0.943163i | \(-0.392165\pi\) | ||||
0.332332 | + | 0.943163i | \(0.392165\pi\) | |||||||
\(840\) | 2.07651 | 0.0716465 | ||||||||
\(841\) | −26.6839 | −0.920133 | ||||||||
\(842\) | −14.4433 | −0.497750 | ||||||||
\(843\) | −19.2605 | −0.663366 | ||||||||
\(844\) | −17.1158 | −0.589151 | ||||||||
\(845\) | −1.95082 | −0.0671103 | ||||||||
\(846\) | −10.4738 | −0.360095 | ||||||||
\(847\) | 2.54382 | 0.0874067 | ||||||||
\(848\) | −0.760246 | −0.0261069 | ||||||||
\(849\) | 14.3040 | 0.490913 | ||||||||
\(850\) | 2.50341 | 0.0858663 | ||||||||
\(851\) | −4.22804 | −0.144935 | ||||||||
\(852\) | 12.8294 | 0.439529 | ||||||||
\(853\) | −52.3913 | −1.79384 | −0.896922 | − | 0.442189i | \(-0.854202\pi\) | ||||
−0.896922 | + | 0.442189i | \(0.854202\pi\) | |||||||
\(854\) | 0.832798 | 0.0284978 | ||||||||
\(855\) | 11.6377 | 0.398001 | ||||||||
\(856\) | −11.1478 | −0.381024 | ||||||||
\(857\) | 45.9744 | 1.57046 | 0.785228 | − | 0.619207i | \(-0.212546\pi\) | ||||
0.785228 | + | 0.619207i | \(0.212546\pi\) | |||||||
\(858\) | −1.87990 | −0.0641787 | ||||||||
\(859\) | −13.0709 | −0.445974 | −0.222987 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222987 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(860\) | 23.5629 | 0.803488 | ||||||||
\(861\) | −0.148906 | −0.00507469 | ||||||||
\(862\) | −20.0608 | −0.683274 | ||||||||
\(863\) | −41.9159 | −1.42683 | −0.713417 | − | 0.700740i | \(-0.752853\pi\) | ||||
−0.713417 | + | 0.700740i | \(0.752853\pi\) | |||||||
\(864\) | −5.36882 | −0.182651 | ||||||||
\(865\) | 19.2231 | 0.653606 | ||||||||
\(866\) | −4.34156 | −0.147532 | ||||||||
\(867\) | 12.0282 | 0.408499 | ||||||||
\(868\) | −2.50743 | −0.0851076 | ||||||||
\(869\) | 16.0702 | 0.545144 | ||||||||
\(870\) | −2.79102 | −0.0946246 | ||||||||
\(871\) | 0.0721191 | 0.00244366 | ||||||||
\(872\) | −11.6246 | −0.393660 | ||||||||
\(873\) | −13.4153 | −0.454038 | ||||||||
\(874\) | 11.0980 | 0.375394 | ||||||||
\(875\) | −4.39066 | −0.148431 | ||||||||
\(876\) | 12.0204 | 0.406133 | ||||||||
\(877\) | −24.9212 | −0.841531 | −0.420765 | − | 0.907170i | \(-0.638238\pi\) | ||||
−0.420765 | + | 0.907170i | \(0.638238\pi\) | |||||||
\(878\) | 11.1312 | 0.375659 | ||||||||
\(879\) | −12.3450 | −0.416387 | ||||||||
\(880\) | 2.03432 | 0.0685768 | ||||||||
\(881\) | −16.9630 | −0.571497 | −0.285749 | − | 0.958305i | \(-0.592242\pi\) | ||||
−0.285749 | + | 0.958305i | \(0.592242\pi\) | |||||||
\(882\) | −6.45644 | −0.217400 | ||||||||
\(883\) | −9.83390 | −0.330937 | −0.165469 | − | 0.986215i | \(-0.552914\pi\) | ||||
−0.165469 | + | 0.986215i | \(0.552914\pi\) | |||||||
\(884\) | 2.48897 | 0.0837132 | ||||||||
\(885\) | −5.38066 | −0.180869 | ||||||||
\(886\) | −11.0809 | −0.372270 | ||||||||
\(887\) | 25.0602 | 0.841438 | 0.420719 | − | 0.907191i | \(-0.361778\pi\) | ||||
0.420719 | + | 0.907191i | \(0.361778\pi\) | |||||||
\(888\) | 6.25902 | 0.210039 | ||||||||
\(889\) | 1.70631 | 0.0572278 | ||||||||
\(890\) | −15.6785 | −0.525546 | ||||||||
\(891\) | 1.99973 | 0.0669933 | ||||||||
\(892\) | −12.4051 | −0.415353 | ||||||||
\(893\) | 66.4642 | 2.22414 | ||||||||
\(894\) | −17.0635 | −0.570687 | ||||||||
\(895\) | 7.74612 | 0.258924 | ||||||||
\(896\) | 1.82128 | 0.0608446 | ||||||||
\(897\) | 1.97893 | 0.0660744 | ||||||||
\(898\) | 1.46782 | 0.0489818 | ||||||||
\(899\) | 9.40864 | 0.313796 | ||||||||
\(900\) | 1.33313 | 0.0444378 | ||||||||
\(901\) | −3.25073 | −0.108298 | ||||||||
\(902\) | −0.770416 | −0.0256520 | ||||||||
\(903\) | 3.93159 | 0.130835 | ||||||||
\(904\) | 3.36882 | 0.112045 | ||||||||
\(905\) | −22.1906 | −0.737641 | ||||||||
\(906\) | −7.61946 | −0.253140 | ||||||||
\(907\) | 25.1854 | 0.836268 | 0.418134 | − | 0.908385i | \(-0.362684\pi\) | ||||
0.418134 | + | 0.908385i | \(0.362684\pi\) | |||||||
\(908\) | −1.87817 | −0.0623294 | ||||||||
\(909\) | −6.35586 | −0.210810 | ||||||||
\(910\) | 0.666349 | 0.0220893 | ||||||||
\(911\) | 16.1748 | 0.535896 | 0.267948 | − | 0.963433i | \(-0.413655\pi\) | ||||
0.267948 | + | 0.963433i | \(0.413655\pi\) | |||||||
\(912\) | −3.11085 | −0.103011 | ||||||||
\(913\) | 21.7722 | 0.720556 | ||||||||
\(914\) | 7.71325 | 0.255132 | ||||||||
\(915\) | −4.75634 | −0.157240 | ||||||||
\(916\) | −24.2997 | −0.802884 | ||||||||
\(917\) | −1.57906 | −0.0521453 | ||||||||
\(918\) | 2.09614 | 0.0691831 | ||||||||
\(919\) | −46.6478 | −1.53877 | −0.769385 | − | 0.638786i | \(-0.779437\pi\) | ||||
−0.769385 | + | 0.638786i | \(0.779437\pi\) | |||||||
\(920\) | −11.3095 | −0.372864 | ||||||||
\(921\) | 27.0107 | 0.890033 | ||||||||
\(922\) | 10.9377 | 0.360214 | ||||||||
\(923\) | 11.4933 | 0.378306 | ||||||||
\(924\) | −0.811061 | −0.0266820 | ||||||||
\(925\) | −2.55165 | −0.0838976 | ||||||||
\(926\) | 28.6674 | 0.942070 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −8.17073 | −0.268217 | ||||||||
\(929\) | −41.9061 | −1.37489 | −0.687447 | − | 0.726235i | \(-0.741269\pi\) | ||||
−0.687447 | + | 0.726235i | \(0.741269\pi\) | |||||||
\(930\) | −11.3377 | −0.371779 | ||||||||
\(931\) | 40.9712 | 1.34278 | ||||||||
\(932\) | −30.9859 | −1.01498 | ||||||||
\(933\) | 30.3100 | 0.992305 | ||||||||
\(934\) | −23.3347 | −0.763535 | ||||||||
\(935\) | 8.69852 | 0.284472 | ||||||||
\(936\) | −2.92952 | −0.0957544 | ||||||||
\(937\) | −19.0891 | −0.623615 | −0.311807 | − | 0.950145i | \(-0.600934\pi\) | ||||
−0.311807 | + | 0.950145i | \(0.600934\pi\) | |||||||
\(938\) | −0.0246340 | −0.000804328 0 | ||||||||
\(939\) | −0.581827 | −0.0189872 | ||||||||
\(940\) | −24.2616 | −0.791326 | ||||||||
\(941\) | −48.5957 | −1.58417 | −0.792087 | − | 0.610408i | \(-0.791006\pi\) | ||||
−0.792087 | + | 0.610408i | \(0.791006\pi\) | |||||||
\(942\) | 4.22970 | 0.137811 | ||||||||
\(943\) | 0.810999 | 0.0264098 | ||||||||
\(944\) | 1.43830 | 0.0468126 | ||||||||
\(945\) | −0.708823 | −0.0230580 | ||||||||
\(946\) | 20.3415 | 0.661359 | ||||||||
\(947\) | −24.1898 | −0.786063 | −0.393031 | − | 0.919525i | \(-0.628574\pi\) | ||||
−0.393031 | + | 0.919525i | \(0.628574\pi\) | |||||||
\(948\) | 8.97044 | 0.291346 | ||||||||
\(949\) | 10.7686 | 0.349562 | ||||||||
\(950\) | 6.69768 | 0.217301 | ||||||||
\(951\) | 10.0796 | 0.326854 | ||||||||
\(952\) | −2.37342 | −0.0769229 | ||||||||
\(953\) | 22.1662 | 0.718033 | 0.359017 | − | 0.933331i | \(-0.383112\pi\) | ||||
0.359017 | + | 0.933331i | \(0.383112\pi\) | |||||||
\(954\) | 1.37053 | 0.0443724 | ||||||||
\(955\) | −30.9292 | −1.00084 | ||||||||
\(956\) | 18.4330 | 0.596164 | ||||||||
\(957\) | 3.04335 | 0.0983777 | ||||||||
\(958\) | 31.7876 | 1.02701 | ||||||||
\(959\) | −7.61818 | −0.246004 | ||||||||
\(960\) | 11.8806 | 0.383445 | ||||||||
\(961\) | 7.21990 | 0.232900 | ||||||||
\(962\) | 2.00851 | 0.0647569 | ||||||||
\(963\) | 3.80533 | 0.122625 | ||||||||
\(964\) | 18.5013 | 0.595888 | ||||||||
\(965\) | 28.6607 | 0.922622 | ||||||||
\(966\) | −0.675949 | −0.0217483 | ||||||||
\(967\) | 10.2777 | 0.330510 | 0.165255 | − | 0.986251i | \(-0.447155\pi\) | ||||
0.165255 | + | 0.986251i | \(0.447155\pi\) | |||||||
\(968\) | 20.5099 | 0.659212 | ||||||||
\(969\) | −13.3017 | −0.427312 | ||||||||
\(970\) | 24.6026 | 0.789942 | ||||||||
\(971\) | 22.4892 | 0.721713 | 0.360856 | − | 0.932621i | \(-0.382484\pi\) | ||||
0.360856 | + | 0.932621i | \(0.382484\pi\) | |||||||
\(972\) | 1.11625 | 0.0358038 | ||||||||
\(973\) | −7.93506 | −0.254386 | ||||||||
\(974\) | −13.3930 | −0.429140 | ||||||||
\(975\) | 1.19429 | 0.0382480 | ||||||||
\(976\) | 1.27141 | 0.0406969 | ||||||||
\(977\) | 46.0872 | 1.47446 | 0.737231 | − | 0.675641i | \(-0.236133\pi\) | ||||
0.737231 | + | 0.675641i | \(0.236133\pi\) | |||||||
\(978\) | 12.7318 | 0.407118 | ||||||||
\(979\) | 17.0960 | 0.546391 | ||||||||
\(980\) | −14.9558 | −0.477745 | ||||||||
\(981\) | 3.96810 | 0.126692 | ||||||||
\(982\) | 13.5760 | 0.433226 | ||||||||
\(983\) | −0.0339864 | −0.00108400 | −0.000541999 | − | 1.00000i | \(-0.500173\pi\) | ||||
−0.000541999 | 1.00000i | \(0.500173\pi\) | ||||||||
\(984\) | −1.20057 | −0.0382728 | ||||||||
\(985\) | −19.0291 | −0.606316 | ||||||||
\(986\) | 3.19009 | 0.101593 | ||||||||
\(987\) | −4.04817 | −0.128855 | ||||||||
\(988\) | 6.65905 | 0.211853 | ||||||||
\(989\) | −21.4130 | −0.680895 | ||||||||
\(990\) | −3.66735 | −0.116556 | ||||||||
\(991\) | −23.4112 | −0.743681 | −0.371841 | − | 0.928297i | \(-0.621273\pi\) | ||||
−0.371841 | + | 0.928297i | \(0.621273\pi\) | |||||||
\(992\) | −33.1912 | −1.05382 | ||||||||
\(993\) | 18.8863 | 0.599338 | ||||||||
\(994\) | −3.92580 | −0.124519 | ||||||||
\(995\) | −43.4147 | −1.37634 | ||||||||
\(996\) | 12.1533 | 0.385093 | ||||||||
\(997\) | 16.0225 | 0.507437 | 0.253718 | − | 0.967278i | \(-0.418346\pi\) | ||||
0.253718 | + | 0.967278i | \(0.418346\pi\) | |||||||
\(998\) | −8.03378 | −0.254305 | ||||||||
\(999\) | −2.13653 | −0.0675969 |
(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 | 4017.2.a.j.1.15 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.15 | ✓ | 25 | 1.1 | even | 1 | trivial |