Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0140467354\) |
Analytic rank: | \(0\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.53130 | −1.78990 | −0.894948 | − | 0.446170i | \(-0.852788\pi\) | ||||
−0.894948 | + | 0.446170i | \(0.852788\pi\) | |||||||
\(3\) | 1.72523 | 0.996063 | 0.498032 | − | 0.867159i | \(-0.334056\pi\) | ||||
0.498032 | + | 0.867159i | \(0.334056\pi\) | |||||||
\(4\) | 4.40746 | 2.20373 | ||||||||
\(5\) | −1.30306 | −0.582745 | −0.291373 | − | 0.956610i | \(-0.594112\pi\) | ||||
−0.291373 | + | 0.956610i | \(0.594112\pi\) | |||||||
\(6\) | −4.36707 | −1.78285 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −6.09399 | −2.15455 | ||||||||
\(9\) | −0.0235740 | −0.00785799 | ||||||||
\(10\) | 3.29843 | 1.04305 | ||||||||
\(11\) | −0.721143 | −0.217433 | −0.108716 | − | 0.994073i | \(-0.534674\pi\) | ||||
−0.108716 | + | 0.994073i | \(0.534674\pi\) | |||||||
\(12\) | 7.60389 | 2.19505 | ||||||||
\(13\) | 0.841919 | 0.233506 | 0.116753 | − | 0.993161i | \(-0.462751\pi\) | ||||
0.116753 | + | 0.993161i | \(0.462751\pi\) | |||||||
\(14\) | −2.53130 | −0.676517 | ||||||||
\(15\) | −2.24808 | −0.580451 | ||||||||
\(16\) | 6.61079 | 1.65270 | ||||||||
\(17\) | 7.21849 | 1.75074 | 0.875371 | − | 0.483453i | \(-0.160617\pi\) | ||||
0.875371 | + | 0.483453i | \(0.160617\pi\) | |||||||
\(18\) | 0.0596727 | 0.0140650 | ||||||||
\(19\) | −3.82019 | −0.876412 | −0.438206 | − | 0.898875i | \(-0.644386\pi\) | ||||
−0.438206 | + | 0.898875i | \(0.644386\pi\) | |||||||
\(20\) | −5.74318 | −1.28421 | ||||||||
\(21\) | 1.72523 | 0.376477 | ||||||||
\(22\) | 1.82543 | 0.389182 | ||||||||
\(23\) | 0.353318 | 0.0736720 | 0.0368360 | − | 0.999321i | \(-0.488272\pi\) | ||||
0.0368360 | + | 0.999321i | \(0.488272\pi\) | |||||||
\(24\) | −10.5136 | −2.14607 | ||||||||
\(25\) | −3.30204 | −0.660408 | ||||||||
\(26\) | −2.13115 | −0.417952 | ||||||||
\(27\) | −5.21637 | −1.00389 | ||||||||
\(28\) | 4.40746 | 0.832932 | ||||||||
\(29\) | 3.12979 | 0.581187 | 0.290593 | − | 0.956847i | \(-0.406147\pi\) | ||||
0.290593 | + | 0.956847i | \(0.406147\pi\) | |||||||
\(30\) | 5.69055 | 1.03895 | ||||||||
\(31\) | 5.64160 | 1.01326 | 0.506630 | − | 0.862163i | \(-0.330891\pi\) | ||||
0.506630 | + | 0.862163i | \(0.330891\pi\) | |||||||
\(32\) | −4.54587 | −0.803603 | ||||||||
\(33\) | −1.24414 | −0.216577 | ||||||||
\(34\) | −18.2721 | −3.13365 | ||||||||
\(35\) | −1.30306 | −0.220257 | ||||||||
\(36\) | −0.103901 | −0.0173169 | ||||||||
\(37\) | 0.891975 | 0.146640 | 0.0733199 | − | 0.997308i | \(-0.476641\pi\) | ||||
0.0733199 | + | 0.997308i | \(0.476641\pi\) | |||||||
\(38\) | 9.67003 | 1.56869 | ||||||||
\(39\) | 1.45251 | 0.232587 | ||||||||
\(40\) | 7.94083 | 1.25556 | ||||||||
\(41\) | 5.49875 | 0.858761 | 0.429380 | − | 0.903124i | \(-0.358732\pi\) | ||||
0.429380 | + | 0.903124i | \(0.358732\pi\) | |||||||
\(42\) | −4.36707 | −0.673854 | ||||||||
\(43\) | −8.06585 | −1.23003 | −0.615015 | − | 0.788515i | \(-0.710850\pi\) | ||||
−0.615015 | + | 0.788515i | \(0.710850\pi\) | |||||||
\(44\) | −3.17841 | −0.479163 | ||||||||
\(45\) | 0.0307183 | 0.00457921 | ||||||||
\(46\) | −0.894353 | −0.131865 | ||||||||
\(47\) | −3.08589 | −0.450124 | −0.225062 | − | 0.974344i | \(-0.572258\pi\) | ||||
−0.225062 | + | 0.974344i | \(0.572258\pi\) | |||||||
\(48\) | 11.4051 | 1.64619 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 8.35844 | 1.18206 | ||||||||
\(51\) | 12.4536 | 1.74385 | ||||||||
\(52\) | 3.71072 | 0.514585 | ||||||||
\(53\) | 9.23293 | 1.26824 | 0.634120 | − | 0.773235i | \(-0.281362\pi\) | ||||
0.634120 | + | 0.773235i | \(0.281362\pi\) | |||||||
\(54\) | 13.2042 | 1.79686 | ||||||||
\(55\) | 0.939691 | 0.126708 | ||||||||
\(56\) | −6.09399 | −0.814344 | ||||||||
\(57\) | −6.59071 | −0.872961 | ||||||||
\(58\) | −7.92242 | −1.04026 | ||||||||
\(59\) | 2.08753 | 0.271773 | 0.135887 | − | 0.990724i | \(-0.456612\pi\) | ||||
0.135887 | + | 0.990724i | \(0.456612\pi\) | |||||||
\(60\) | −9.90832 | −1.27916 | ||||||||
\(61\) | −5.39601 | −0.690888 | −0.345444 | − | 0.938439i | \(-0.612272\pi\) | ||||
−0.345444 | + | 0.938439i | \(0.612272\pi\) | |||||||
\(62\) | −14.2806 | −1.81363 | ||||||||
\(63\) | −0.0235740 | −0.00297004 | ||||||||
\(64\) | −1.71464 | −0.214330 | ||||||||
\(65\) | −1.09707 | −0.136075 | ||||||||
\(66\) | 3.14928 | 0.387650 | ||||||||
\(67\) | 4.81531 | 0.588284 | 0.294142 | − | 0.955762i | \(-0.404966\pi\) | ||||
0.294142 | + | 0.955762i | \(0.404966\pi\) | |||||||
\(68\) | 31.8152 | 3.85816 | ||||||||
\(69\) | 0.609556 | 0.0733819 | ||||||||
\(70\) | 3.29843 | 0.394237 | ||||||||
\(71\) | 1.37071 | 0.162674 | 0.0813368 | − | 0.996687i | \(-0.474081\pi\) | ||||
0.0813368 | + | 0.996687i | \(0.474081\pi\) | |||||||
\(72\) | 0.143660 | 0.0169305 | ||||||||
\(73\) | 6.46357 | 0.756503 | 0.378252 | − | 0.925703i | \(-0.376525\pi\) | ||||
0.378252 | + | 0.925703i | \(0.376525\pi\) | |||||||
\(74\) | −2.25785 | −0.262470 | ||||||||
\(75\) | −5.69678 | −0.657808 | ||||||||
\(76\) | −16.8373 | −1.93137 | ||||||||
\(77\) | −0.721143 | −0.0821818 | ||||||||
\(78\) | −3.67672 | −0.416307 | ||||||||
\(79\) | 8.56828 | 0.964007 | 0.482003 | − | 0.876169i | \(-0.339909\pi\) | ||||
0.482003 | + | 0.876169i | \(0.339909\pi\) | |||||||
\(80\) | −8.61424 | −0.963101 | ||||||||
\(81\) | −8.92872 | −0.992080 | ||||||||
\(82\) | −13.9190 | −1.53709 | ||||||||
\(83\) | 2.89335 | 0.317586 | 0.158793 | − | 0.987312i | \(-0.449240\pi\) | ||||
0.158793 | + | 0.987312i | \(0.449240\pi\) | |||||||
\(84\) | 7.60389 | 0.829653 | ||||||||
\(85\) | −9.40611 | −1.02024 | ||||||||
\(86\) | 20.4171 | 2.20163 | ||||||||
\(87\) | 5.39961 | 0.578899 | ||||||||
\(88\) | 4.39464 | 0.468470 | ||||||||
\(89\) | −5.28524 | −0.560235 | −0.280117 | − | 0.959966i | \(-0.590373\pi\) | ||||
−0.280117 | + | 0.959966i | \(0.590373\pi\) | |||||||
\(90\) | −0.0777571 | −0.00819631 | ||||||||
\(91\) | 0.841919 | 0.0882571 | ||||||||
\(92\) | 1.55724 | 0.162353 | ||||||||
\(93\) | 9.73306 | 1.00927 | ||||||||
\(94\) | 7.81131 | 0.805675 | ||||||||
\(95\) | 4.97793 | 0.510725 | ||||||||
\(96\) | −7.84267 | −0.800440 | ||||||||
\(97\) | −13.9376 | −1.41515 | −0.707576 | − | 0.706637i | \(-0.750211\pi\) | ||||
−0.707576 | + | 0.706637i | \(0.750211\pi\) | |||||||
\(98\) | −2.53130 | −0.255700 | ||||||||
\(99\) | 0.0170002 | 0.00170859 | ||||||||
\(100\) | −14.5536 | −1.45536 | ||||||||
\(101\) | 10.3686 | 1.03171 | 0.515855 | − | 0.856676i | \(-0.327474\pi\) | ||||
0.515855 | + | 0.856676i | \(0.327474\pi\) | |||||||
\(102\) | −31.5237 | −3.12131 | ||||||||
\(103\) | −15.6779 | −1.54479 | −0.772397 | − | 0.635140i | \(-0.780942\pi\) | ||||
−0.772397 | + | 0.635140i | \(0.780942\pi\) | |||||||
\(104\) | −5.13065 | −0.503102 | ||||||||
\(105\) | −2.24808 | −0.219390 | ||||||||
\(106\) | −23.3713 | −2.27002 | ||||||||
\(107\) | −17.4175 | −1.68381 | −0.841907 | − | 0.539622i | \(-0.818567\pi\) | ||||
−0.841907 | + | 0.539622i | \(0.818567\pi\) | |||||||
\(108\) | −22.9909 | −2.21230 | ||||||||
\(109\) | 3.01641 | 0.288920 | 0.144460 | − | 0.989511i | \(-0.453856\pi\) | ||||
0.144460 | + | 0.989511i | \(0.453856\pi\) | |||||||
\(110\) | −2.37864 | −0.226794 | ||||||||
\(111\) | 1.53886 | 0.146062 | ||||||||
\(112\) | 6.61079 | 0.624661 | ||||||||
\(113\) | 5.61041 | 0.527783 | 0.263891 | − | 0.964552i | \(-0.414994\pi\) | ||||
0.263891 | + | 0.964552i | \(0.414994\pi\) | |||||||
\(114\) | 16.6830 | 1.56251 | ||||||||
\(115\) | −0.460394 | −0.0429320 | ||||||||
\(116\) | 13.7944 | 1.28078 | ||||||||
\(117\) | −0.0198474 | −0.00183489 | ||||||||
\(118\) | −5.28416 | −0.486446 | ||||||||
\(119\) | 7.21849 | 0.661718 | ||||||||
\(120\) | 13.6998 | 1.25061 | ||||||||
\(121\) | −10.4800 | −0.952723 | ||||||||
\(122\) | 13.6589 | 1.23662 | ||||||||
\(123\) | 9.48662 | 0.855380 | ||||||||
\(124\) | 24.8651 | 2.23295 | ||||||||
\(125\) | 10.8180 | 0.967595 | ||||||||
\(126\) | 0.0596727 | 0.00531607 | ||||||||
\(127\) | 3.02753 | 0.268650 | 0.134325 | − | 0.990937i | \(-0.457113\pi\) | ||||
0.134325 | + | 0.990937i | \(0.457113\pi\) | |||||||
\(128\) | 13.4320 | 1.18723 | ||||||||
\(129\) | −13.9155 | −1.22519 | ||||||||
\(130\) | 2.77701 | 0.243560 | ||||||||
\(131\) | 10.3355 | 0.903016 | 0.451508 | − | 0.892267i | \(-0.350886\pi\) | ||||
0.451508 | + | 0.892267i | \(0.350886\pi\) | |||||||
\(132\) | −5.48349 | −0.477277 | ||||||||
\(133\) | −3.82019 | −0.331252 | ||||||||
\(134\) | −12.1890 | −1.05297 | ||||||||
\(135\) | 6.79723 | 0.585012 | ||||||||
\(136\) | −43.9894 | −3.77206 | ||||||||
\(137\) | 10.6889 | 0.913214 | 0.456607 | − | 0.889668i | \(-0.349064\pi\) | ||||
0.456607 | + | 0.889668i | \(0.349064\pi\) | |||||||
\(138\) | −1.54297 | −0.131346 | ||||||||
\(139\) | 22.0592 | 1.87104 | 0.935519 | − | 0.353277i | \(-0.114933\pi\) | ||||
0.935519 | + | 0.353277i | \(0.114933\pi\) | |||||||
\(140\) | −5.74318 | −0.485387 | ||||||||
\(141\) | −5.32388 | −0.448352 | ||||||||
\(142\) | −3.46968 | −0.291169 | ||||||||
\(143\) | −0.607144 | −0.0507719 | ||||||||
\(144\) | −0.155843 | −0.0129869 | ||||||||
\(145\) | −4.07829 | −0.338684 | ||||||||
\(146\) | −16.3612 | −1.35406 | ||||||||
\(147\) | 1.72523 | 0.142295 | ||||||||
\(148\) | 3.93134 | 0.323154 | ||||||||
\(149\) | −4.94614 | −0.405204 | −0.202602 | − | 0.979261i | \(-0.564940\pi\) | ||||
−0.202602 | + | 0.979261i | \(0.564940\pi\) | |||||||
\(150\) | 14.4202 | 1.17741 | ||||||||
\(151\) | 5.57117 | 0.453375 | 0.226688 | − | 0.973968i | \(-0.427210\pi\) | ||||
0.226688 | + | 0.973968i | \(0.427210\pi\) | |||||||
\(152\) | 23.2802 | 1.88827 | ||||||||
\(153\) | −0.170169 | −0.0137573 | ||||||||
\(154\) | 1.82543 | 0.147097 | ||||||||
\(155\) | −7.35133 | −0.590473 | ||||||||
\(156\) | 6.40186 | 0.512559 | ||||||||
\(157\) | 1.46140 | 0.116633 | 0.0583163 | − | 0.998298i | \(-0.481427\pi\) | ||||
0.0583163 | + | 0.998298i | \(0.481427\pi\) | |||||||
\(158\) | −21.6889 | −1.72547 | ||||||||
\(159\) | 15.9289 | 1.26325 | ||||||||
\(160\) | 5.92353 | 0.468296 | ||||||||
\(161\) | 0.353318 | 0.0278454 | ||||||||
\(162\) | 22.6012 | 1.77572 | ||||||||
\(163\) | 14.8377 | 1.16218 | 0.581091 | − | 0.813839i | \(-0.302626\pi\) | ||||
0.581091 | + | 0.813839i | \(0.302626\pi\) | |||||||
\(164\) | 24.2355 | 1.89248 | ||||||||
\(165\) | 1.62119 | 0.126209 | ||||||||
\(166\) | −7.32392 | −0.568447 | ||||||||
\(167\) | 20.2138 | 1.56419 | 0.782094 | − | 0.623161i | \(-0.214152\pi\) | ||||
0.782094 | + | 0.623161i | \(0.214152\pi\) | |||||||
\(168\) | −10.5136 | −0.811138 | ||||||||
\(169\) | −12.2912 | −0.945475 | ||||||||
\(170\) | 23.8097 | 1.82612 | ||||||||
\(171\) | 0.0900571 | 0.00688684 | ||||||||
\(172\) | −35.5499 | −2.71066 | ||||||||
\(173\) | −19.3943 | −1.47452 | −0.737259 | − | 0.675610i | \(-0.763880\pi\) | ||||
−0.737259 | + | 0.675610i | \(0.763880\pi\) | |||||||
\(174\) | −13.6680 | −1.03617 | ||||||||
\(175\) | −3.30204 | −0.249611 | ||||||||
\(176\) | −4.76732 | −0.359350 | ||||||||
\(177\) | 3.60147 | 0.270703 | ||||||||
\(178\) | 13.3785 | 1.00276 | ||||||||
\(179\) | 16.3504 | 1.22209 | 0.611043 | − | 0.791598i | \(-0.290750\pi\) | ||||
0.611043 | + | 0.791598i | \(0.290750\pi\) | |||||||
\(180\) | 0.135390 | 0.0100913 | ||||||||
\(181\) | 12.6634 | 0.941266 | 0.470633 | − | 0.882329i | \(-0.344026\pi\) | ||||
0.470633 | + | 0.882329i | \(0.344026\pi\) | |||||||
\(182\) | −2.13115 | −0.157971 | ||||||||
\(183\) | −9.30937 | −0.688168 | ||||||||
\(184\) | −2.15312 | −0.158730 | ||||||||
\(185\) | −1.16230 | −0.0854536 | ||||||||
\(186\) | −24.6373 | −1.80649 | ||||||||
\(187\) | −5.20556 | −0.380668 | ||||||||
\(188\) | −13.6009 | −0.991951 | ||||||||
\(189\) | −5.21637 | −0.379435 | ||||||||
\(190\) | −12.6006 | −0.914145 | ||||||||
\(191\) | −10.1547 | −0.734766 | −0.367383 | − | 0.930070i | \(-0.619746\pi\) | ||||
−0.367383 | + | 0.930070i | \(0.619746\pi\) | |||||||
\(192\) | −2.95815 | −0.213486 | ||||||||
\(193\) | 8.35507 | 0.601411 | 0.300706 | − | 0.953717i | \(-0.402778\pi\) | ||||
0.300706 | + | 0.953717i | \(0.402778\pi\) | |||||||
\(194\) | 35.2803 | 2.53298 | ||||||||
\(195\) | −1.89270 | −0.135539 | ||||||||
\(196\) | 4.40746 | 0.314819 | ||||||||
\(197\) | −11.5488 | −0.822816 | −0.411408 | − | 0.911451i | \(-0.634963\pi\) | ||||
−0.411408 | + | 0.911451i | \(0.634963\pi\) | |||||||
\(198\) | −0.0430326 | −0.00305819 | ||||||||
\(199\) | −12.1635 | −0.862250 | −0.431125 | − | 0.902292i | \(-0.641883\pi\) | ||||
−0.431125 | + | 0.902292i | \(0.641883\pi\) | |||||||
\(200\) | 20.1226 | 1.42288 | ||||||||
\(201\) | 8.30753 | 0.585968 | ||||||||
\(202\) | −26.2459 | −1.84665 | ||||||||
\(203\) | 3.12979 | 0.219668 | ||||||||
\(204\) | 54.8886 | 3.84297 | ||||||||
\(205\) | −7.16519 | −0.500439 | ||||||||
\(206\) | 39.6855 | 2.76502 | ||||||||
\(207\) | −0.00832912 | −0.000578914 0 | ||||||||
\(208\) | 5.56575 | 0.385915 | ||||||||
\(209\) | 2.75490 | 0.190561 | ||||||||
\(210\) | 5.69055 | 0.392685 | ||||||||
\(211\) | −4.71501 | −0.324595 | −0.162297 | − | 0.986742i | \(-0.551890\pi\) | ||||
−0.162297 | + | 0.986742i | \(0.551890\pi\) | |||||||
\(212\) | 40.6938 | 2.79486 | ||||||||
\(213\) | 2.36480 | 0.162033 | ||||||||
\(214\) | 44.0889 | 3.01385 | ||||||||
\(215\) | 10.5103 | 0.716795 | ||||||||
\(216\) | 31.7885 | 2.16293 | ||||||||
\(217\) | 5.64160 | 0.382977 | ||||||||
\(218\) | −7.63543 | −0.517136 | ||||||||
\(219\) | 11.1512 | 0.753525 | ||||||||
\(220\) | 4.14165 | 0.279230 | ||||||||
\(221\) | 6.07738 | 0.408809 | ||||||||
\(222\) | −3.89532 | −0.261437 | ||||||||
\(223\) | 10.8126 | 0.724066 | 0.362033 | − | 0.932165i | \(-0.382083\pi\) | ||||
0.362033 | + | 0.932165i | \(0.382083\pi\) | |||||||
\(224\) | −4.54587 | −0.303733 | ||||||||
\(225\) | 0.0778422 | 0.00518948 | ||||||||
\(226\) | −14.2016 | −0.944677 | ||||||||
\(227\) | 14.3050 | 0.949457 | 0.474729 | − | 0.880132i | \(-0.342546\pi\) | ||||
0.474729 | + | 0.880132i | \(0.342546\pi\) | |||||||
\(228\) | −29.0483 | −1.92377 | ||||||||
\(229\) | 21.2236 | 1.40249 | 0.701246 | − | 0.712920i | \(-0.252628\pi\) | ||||
0.701246 | + | 0.712920i | \(0.252628\pi\) | |||||||
\(230\) | 1.16539 | 0.0768438 | ||||||||
\(231\) | −1.24414 | −0.0818583 | ||||||||
\(232\) | −19.0729 | −1.25220 | ||||||||
\(233\) | 22.4807 | 1.47276 | 0.736380 | − | 0.676568i | \(-0.236534\pi\) | ||||
0.736380 | + | 0.676568i | \(0.236534\pi\) | |||||||
\(234\) | 0.0502396 | 0.00328427 | ||||||||
\(235\) | 4.02110 | 0.262307 | ||||||||
\(236\) | 9.20070 | 0.598915 | ||||||||
\(237\) | 14.7823 | 0.960212 | ||||||||
\(238\) | −18.2721 | −1.18441 | ||||||||
\(239\) | 25.7090 | 1.66298 | 0.831489 | − | 0.555541i | \(-0.187489\pi\) | ||||
0.831489 | + | 0.555541i | \(0.187489\pi\) | |||||||
\(240\) | −14.8616 | −0.959310 | ||||||||
\(241\) | −29.5350 | −1.90252 | −0.951259 | − | 0.308392i | \(-0.900209\pi\) | ||||
−0.951259 | + | 0.308392i | \(0.900209\pi\) | |||||||
\(242\) | 26.5279 | 1.70528 | ||||||||
\(243\) | 0.244982 | 0.0157156 | ||||||||
\(244\) | −23.7827 | −1.52253 | ||||||||
\(245\) | −1.30306 | −0.0832493 | ||||||||
\(246\) | −24.0135 | −1.53104 | ||||||||
\(247\) | −3.21629 | −0.204648 | ||||||||
\(248\) | −34.3799 | −2.18312 | ||||||||
\(249\) | 4.99170 | 0.316336 | ||||||||
\(250\) | −27.3837 | −1.73190 | ||||||||
\(251\) | −16.3953 | −1.03486 | −0.517431 | − | 0.855725i | \(-0.673112\pi\) | ||||
−0.517431 | + | 0.855725i | \(0.673112\pi\) | |||||||
\(252\) | −0.103901 | −0.00654517 | ||||||||
\(253\) | −0.254793 | −0.0160187 | ||||||||
\(254\) | −7.66358 | −0.480856 | ||||||||
\(255\) | −16.2277 | −1.01622 | ||||||||
\(256\) | −30.5711 | −1.91069 | ||||||||
\(257\) | 29.9290 | 1.86692 | 0.933459 | − | 0.358683i | \(-0.116774\pi\) | ||||
0.933459 | + | 0.358683i | \(0.116774\pi\) | |||||||
\(258\) | 35.2242 | 2.19296 | ||||||||
\(259\) | 0.891975 | 0.0554246 | ||||||||
\(260\) | −4.83529 | −0.299872 | ||||||||
\(261\) | −0.0737815 | −0.00456696 | ||||||||
\(262\) | −26.1622 | −1.61631 | ||||||||
\(263\) | 24.2003 | 1.49226 | 0.746128 | − | 0.665802i | \(-0.231911\pi\) | ||||
0.746128 | + | 0.665802i | \(0.231911\pi\) | |||||||
\(264\) | 7.58177 | 0.466626 | ||||||||
\(265\) | −12.0310 | −0.739061 | ||||||||
\(266\) | 9.67003 | 0.592908 | ||||||||
\(267\) | −9.11827 | −0.558029 | ||||||||
\(268\) | 21.2233 | 1.29642 | ||||||||
\(269\) | −17.0955 | −1.04233 | −0.521165 | − | 0.853456i | \(-0.674502\pi\) | ||||
−0.521165 | + | 0.853456i | \(0.674502\pi\) | |||||||
\(270\) | −17.2058 | −1.04711 | ||||||||
\(271\) | 29.5525 | 1.79519 | 0.897593 | − | 0.440824i | \(-0.145314\pi\) | ||||
0.897593 | + | 0.440824i | \(0.145314\pi\) | |||||||
\(272\) | 47.7199 | 2.89344 | ||||||||
\(273\) | 1.45251 | 0.0879096 | ||||||||
\(274\) | −27.0568 | −1.63456 | ||||||||
\(275\) | 2.38124 | 0.143594 | ||||||||
\(276\) | 2.68659 | 0.161714 | ||||||||
\(277\) | −4.45754 | −0.267828 | −0.133914 | − | 0.990993i | \(-0.542755\pi\) | ||||
−0.133914 | + | 0.990993i | \(0.542755\pi\) | |||||||
\(278\) | −55.8384 | −3.34896 | ||||||||
\(279\) | −0.132995 | −0.00796220 | ||||||||
\(280\) | 7.94083 | 0.474555 | ||||||||
\(281\) | 16.2924 | 0.971921 | 0.485961 | − | 0.873981i | \(-0.338470\pi\) | ||||
0.485961 | + | 0.873981i | \(0.338470\pi\) | |||||||
\(282\) | 13.4763 | 0.802503 | ||||||||
\(283\) | −7.23941 | −0.430338 | −0.215169 | − | 0.976577i | \(-0.569030\pi\) | ||||
−0.215169 | + | 0.976577i | \(0.569030\pi\) | |||||||
\(284\) | 6.04136 | 0.358489 | ||||||||
\(285\) | 8.58809 | 0.508714 | ||||||||
\(286\) | 1.53686 | 0.0908765 | ||||||||
\(287\) | 5.49875 | 0.324581 | ||||||||
\(288\) | 0.107164 | 0.00631471 | ||||||||
\(289\) | 35.1066 | 2.06509 | ||||||||
\(290\) | 10.3234 | 0.606209 | ||||||||
\(291\) | −24.0457 | −1.40958 | ||||||||
\(292\) | 28.4879 | 1.66713 | ||||||||
\(293\) | −17.3033 | −1.01087 | −0.505435 | − | 0.862865i | \(-0.668668\pi\) | ||||
−0.505435 | + | 0.862865i | \(0.668668\pi\) | |||||||
\(294\) | −4.36707 | −0.254693 | ||||||||
\(295\) | −2.72017 | −0.158375 | ||||||||
\(296\) | −5.43569 | −0.315943 | ||||||||
\(297\) | 3.76175 | 0.218279 | ||||||||
\(298\) | 12.5201 | 0.725272 | ||||||||
\(299\) | 0.297465 | 0.0172029 | ||||||||
\(300\) | −25.1083 | −1.44963 | ||||||||
\(301\) | −8.06585 | −0.464908 | ||||||||
\(302\) | −14.1023 | −0.811495 | ||||||||
\(303\) | 17.8882 | 1.02765 | ||||||||
\(304\) | −25.2545 | −1.44844 | ||||||||
\(305\) | 7.03132 | 0.402612 | ||||||||
\(306\) | 0.430747 | 0.0246242 | ||||||||
\(307\) | −7.64360 | −0.436243 | −0.218122 | − | 0.975922i | \(-0.569993\pi\) | ||||
−0.218122 | + | 0.975922i | \(0.569993\pi\) | |||||||
\(308\) | −3.17841 | −0.181107 | ||||||||
\(309\) | −27.0481 | −1.53871 | ||||||||
\(310\) | 18.6084 | 1.05689 | ||||||||
\(311\) | 21.0490 | 1.19358 | 0.596789 | − | 0.802398i | \(-0.296443\pi\) | ||||
0.596789 | + | 0.802398i | \(0.296443\pi\) | |||||||
\(312\) | −8.85156 | −0.501121 | ||||||||
\(313\) | −25.1947 | −1.42409 | −0.712043 | − | 0.702135i | \(-0.752230\pi\) | ||||
−0.712043 | + | 0.702135i | \(0.752230\pi\) | |||||||
\(314\) | −3.69924 | −0.208760 | ||||||||
\(315\) | 0.0307183 | 0.00173078 | ||||||||
\(316\) | 37.7643 | 2.12441 | ||||||||
\(317\) | 23.8691 | 1.34062 | 0.670312 | − | 0.742080i | \(-0.266160\pi\) | ||||
0.670312 | + | 0.742080i | \(0.266160\pi\) | |||||||
\(318\) | −40.3209 | −2.26108 | ||||||||
\(319\) | −2.25702 | −0.126369 | ||||||||
\(320\) | 2.23427 | 0.124900 | ||||||||
\(321\) | −30.0493 | −1.67719 | ||||||||
\(322\) | −0.894353 | −0.0498404 | ||||||||
\(323\) | −27.5760 | −1.53437 | ||||||||
\(324\) | −39.3530 | −2.18628 | ||||||||
\(325\) | −2.78005 | −0.154209 | ||||||||
\(326\) | −37.5587 | −2.08018 | ||||||||
\(327\) | 5.20401 | 0.287782 | ||||||||
\(328\) | −33.5094 | −1.85024 | ||||||||
\(329\) | −3.08589 | −0.170131 | ||||||||
\(330\) | −4.10370 | −0.225901 | ||||||||
\(331\) | 26.3966 | 1.45089 | 0.725444 | − | 0.688282i | \(-0.241635\pi\) | ||||
0.725444 | + | 0.688282i | \(0.241635\pi\) | |||||||
\(332\) | 12.7523 | 0.699875 | ||||||||
\(333\) | −0.0210274 | −0.00115229 | ||||||||
\(334\) | −51.1670 | −2.79973 | ||||||||
\(335\) | −6.27463 | −0.342820 | ||||||||
\(336\) | 11.4051 | 0.622201 | ||||||||
\(337\) | −17.0247 | −0.927396 | −0.463698 | − | 0.885993i | \(-0.653478\pi\) | ||||
−0.463698 | + | 0.885993i | \(0.653478\pi\) | |||||||
\(338\) | 31.1126 | 1.69230 | ||||||||
\(339\) | 9.67926 | 0.525705 | ||||||||
\(340\) | −41.4571 | −2.24833 | ||||||||
\(341\) | −4.06840 | −0.220316 | ||||||||
\(342\) | −0.227961 | −0.0123267 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 49.1533 | 2.65017 | ||||||||
\(345\) | −0.794287 | −0.0427630 | ||||||||
\(346\) | 49.0926 | 2.63924 | ||||||||
\(347\) | −4.94361 | −0.265387 | −0.132693 | − | 0.991157i | \(-0.542363\pi\) | ||||
−0.132693 | + | 0.991157i | \(0.542363\pi\) | |||||||
\(348\) | 23.7986 | 1.27574 | ||||||||
\(349\) | 17.3781 | 0.930229 | 0.465114 | − | 0.885251i | \(-0.346013\pi\) | ||||
0.465114 | + | 0.885251i | \(0.346013\pi\) | |||||||
\(350\) | 8.35844 | 0.446777 | ||||||||
\(351\) | −4.39176 | −0.234415 | ||||||||
\(352\) | 3.27822 | 0.174730 | ||||||||
\(353\) | −1.25769 | −0.0669400 | −0.0334700 | − | 0.999440i | \(-0.510656\pi\) | ||||
−0.0334700 | + | 0.999440i | \(0.510656\pi\) | |||||||
\(354\) | −9.11640 | −0.484531 | ||||||||
\(355\) | −1.78612 | −0.0947972 | ||||||||
\(356\) | −23.2945 | −1.23461 | ||||||||
\(357\) | 12.4536 | 0.659113 | ||||||||
\(358\) | −41.3877 | −2.18741 | ||||||||
\(359\) | −31.2615 | −1.64992 | −0.824958 | − | 0.565193i | \(-0.808802\pi\) | ||||
−0.824958 | + | 0.565193i | \(0.808802\pi\) | |||||||
\(360\) | −0.187197 | −0.00986615 | ||||||||
\(361\) | −4.40615 | −0.231903 | ||||||||
\(362\) | −32.0549 | −1.68477 | ||||||||
\(363\) | −18.0804 | −0.948972 | ||||||||
\(364\) | 3.71072 | 0.194495 | ||||||||
\(365\) | −8.42241 | −0.440849 | ||||||||
\(366\) | 23.5648 | 1.23175 | ||||||||
\(367\) | −24.2682 | −1.26679 | −0.633395 | − | 0.773828i | \(-0.718339\pi\) | ||||
−0.633395 | + | 0.773828i | \(0.718339\pi\) | |||||||
\(368\) | 2.33571 | 0.121757 | ||||||||
\(369\) | −0.129627 | −0.00674814 | ||||||||
\(370\) | 2.94211 | 0.152953 | ||||||||
\(371\) | 9.23293 | 0.479350 | ||||||||
\(372\) | 42.8981 | 2.22416 | ||||||||
\(373\) | 23.2261 | 1.20260 | 0.601302 | − | 0.799022i | \(-0.294649\pi\) | ||||
0.601302 | + | 0.799022i | \(0.294649\pi\) | |||||||
\(374\) | 13.1768 | 0.681357 | ||||||||
\(375\) | 18.6636 | 0.963786 | ||||||||
\(376\) | 18.8054 | 0.969815 | ||||||||
\(377\) | 2.63503 | 0.135711 | ||||||||
\(378\) | 13.2042 | 0.679149 | ||||||||
\(379\) | 33.1981 | 1.70527 | 0.852635 | − | 0.522507i | \(-0.175003\pi\) | ||||
0.852635 | + | 0.522507i | \(0.175003\pi\) | |||||||
\(380\) | 21.9400 | 1.12550 | ||||||||
\(381\) | 5.22320 | 0.267592 | ||||||||
\(382\) | 25.7045 | 1.31516 | ||||||||
\(383\) | −1.70574 | −0.0871592 | −0.0435796 | − | 0.999050i | \(-0.513876\pi\) | ||||
−0.0435796 | + | 0.999050i | \(0.513876\pi\) | |||||||
\(384\) | 23.1733 | 1.18256 | ||||||||
\(385\) | 0.939691 | 0.0478911 | ||||||||
\(386\) | −21.1492 | −1.07646 | ||||||||
\(387\) | 0.190144 | 0.00966558 | ||||||||
\(388\) | −61.4296 | −3.11861 | ||||||||
\(389\) | −1.99761 | −0.101283 | −0.0506414 | − | 0.998717i | \(-0.516127\pi\) | ||||
−0.0506414 | + | 0.998717i | \(0.516127\pi\) | |||||||
\(390\) | 4.79098 | 0.242601 | ||||||||
\(391\) | 2.55042 | 0.128981 | ||||||||
\(392\) | −6.09399 | −0.307793 | ||||||||
\(393\) | 17.8311 | 0.899461 | ||||||||
\(394\) | 29.2334 | 1.47276 | ||||||||
\(395\) | −11.1650 | −0.561770 | ||||||||
\(396\) | 0.0749277 | 0.00376526 | ||||||||
\(397\) | −20.7005 | −1.03893 | −0.519465 | − | 0.854492i | \(-0.673869\pi\) | ||||
−0.519465 | + | 0.854492i | \(0.673869\pi\) | |||||||
\(398\) | 30.7895 | 1.54334 | ||||||||
\(399\) | −6.59071 | −0.329948 | ||||||||
\(400\) | −21.8291 | −1.09145 | ||||||||
\(401\) | 8.40382 | 0.419667 | 0.209833 | − | 0.977737i | \(-0.432708\pi\) | ||||
0.209833 | + | 0.977737i | \(0.432708\pi\) | |||||||
\(402\) | −21.0288 | −1.04882 | ||||||||
\(403\) | 4.74977 | 0.236603 | ||||||||
\(404\) | 45.6990 | 2.27361 | ||||||||
\(405\) | 11.6346 | 0.578130 | ||||||||
\(406\) | −7.92242 | −0.393183 | ||||||||
\(407\) | −0.643241 | −0.0318843 | ||||||||
\(408\) | −75.8920 | −3.75721 | ||||||||
\(409\) | −37.1213 | −1.83553 | −0.917765 | − | 0.397125i | \(-0.870008\pi\) | ||||
−0.917765 | + | 0.397125i | \(0.870008\pi\) | |||||||
\(410\) | 18.1372 | 0.895734 | ||||||||
\(411\) | 18.4408 | 0.909619 | ||||||||
\(412\) | −69.0999 | −3.40431 | ||||||||
\(413\) | 2.08753 | 0.102721 | ||||||||
\(414\) | 0.0210835 | 0.00103620 | ||||||||
\(415\) | −3.77020 | −0.185072 | ||||||||
\(416\) | −3.82725 | −0.187646 | ||||||||
\(417\) | 38.0572 | 1.86367 | ||||||||
\(418\) | −6.97347 | −0.341084 | ||||||||
\(419\) | 17.3588 | 0.848032 | 0.424016 | − | 0.905655i | \(-0.360620\pi\) | ||||
0.424016 | + | 0.905655i | \(0.360620\pi\) | |||||||
\(420\) | −9.90832 | −0.483476 | ||||||||
\(421\) | 6.83181 | 0.332962 | 0.166481 | − | 0.986045i | \(-0.446760\pi\) | ||||
0.166481 | + | 0.986045i | \(0.446760\pi\) | |||||||
\(422\) | 11.9351 | 0.580991 | ||||||||
\(423\) | 0.0727468 | 0.00353707 | ||||||||
\(424\) | −56.2654 | −2.73249 | ||||||||
\(425\) | −23.8357 | −1.15620 | ||||||||
\(426\) | −5.98600 | −0.290023 | ||||||||
\(427\) | −5.39601 | −0.261131 | ||||||||
\(428\) | −76.7670 | −3.71067 | ||||||||
\(429\) | −1.04746 | −0.0505720 | ||||||||
\(430\) | −26.6046 | −1.28299 | ||||||||
\(431\) | −23.6055 | −1.13704 | −0.568518 | − | 0.822671i | \(-0.692483\pi\) | ||||
−0.568518 | + | 0.822671i | \(0.692483\pi\) | |||||||
\(432\) | −34.4843 | −1.65913 | ||||||||
\(433\) | 18.9735 | 0.911808 | 0.455904 | − | 0.890029i | \(-0.349316\pi\) | ||||
0.455904 | + | 0.890029i | \(0.349316\pi\) | |||||||
\(434\) | −14.2806 | −0.685488 | ||||||||
\(435\) | −7.03600 | −0.337351 | ||||||||
\(436\) | 13.2947 | 0.636701 | ||||||||
\(437\) | −1.34974 | −0.0645670 | ||||||||
\(438\) | −28.2269 | −1.34873 | ||||||||
\(439\) | −10.5105 | −0.501638 | −0.250819 | − | 0.968034i | \(-0.580700\pi\) | ||||
−0.250819 | + | 0.968034i | \(0.580700\pi\) | |||||||
\(440\) | −5.72647 | −0.272999 | ||||||||
\(441\) | −0.0235740 | −0.00112257 | ||||||||
\(442\) | −15.3837 | −0.731726 | ||||||||
\(443\) | 4.48793 | 0.213228 | 0.106614 | − | 0.994300i | \(-0.465999\pi\) | ||||
0.106614 | + | 0.994300i | \(0.465999\pi\) | |||||||
\(444\) | 6.78248 | 0.321882 | ||||||||
\(445\) | 6.88698 | 0.326474 | ||||||||
\(446\) | −27.3699 | −1.29600 | ||||||||
\(447\) | −8.53324 | −0.403608 | ||||||||
\(448\) | −1.71464 | −0.0810090 | ||||||||
\(449\) | −31.2102 | −1.47290 | −0.736449 | − | 0.676493i | \(-0.763499\pi\) | ||||
−0.736449 | + | 0.676493i | \(0.763499\pi\) | |||||||
\(450\) | −0.197042 | −0.00928863 | ||||||||
\(451\) | −3.96538 | −0.186723 | ||||||||
\(452\) | 24.7276 | 1.16309 | ||||||||
\(453\) | 9.61156 | 0.451590 | ||||||||
\(454\) | −36.2102 | −1.69943 | ||||||||
\(455\) | −1.09707 | −0.0514314 | ||||||||
\(456\) | 40.1638 | 1.88084 | ||||||||
\(457\) | −6.27089 | −0.293340 | −0.146670 | − | 0.989185i | \(-0.546856\pi\) | ||||
−0.146670 | + | 0.989185i | \(0.546856\pi\) | |||||||
\(458\) | −53.7231 | −2.51032 | ||||||||
\(459\) | −37.6543 | −1.75755 | ||||||||
\(460\) | −2.02917 | −0.0946105 | ||||||||
\(461\) | 11.6575 | 0.542944 | 0.271472 | − | 0.962446i | \(-0.412490\pi\) | ||||
0.271472 | + | 0.962446i | \(0.412490\pi\) | |||||||
\(462\) | 3.14928 | 0.146518 | ||||||||
\(463\) | 12.6268 | 0.586818 | 0.293409 | − | 0.955987i | \(-0.405210\pi\) | ||||
0.293409 | + | 0.955987i | \(0.405210\pi\) | |||||||
\(464\) | 20.6903 | 0.960525 | ||||||||
\(465\) | −12.6828 | −0.588148 | ||||||||
\(466\) | −56.9053 | −2.63609 | ||||||||
\(467\) | −40.3467 | −1.86702 | −0.933510 | − | 0.358550i | \(-0.883271\pi\) | ||||
−0.933510 | + | 0.358550i | \(0.883271\pi\) | |||||||
\(468\) | −0.0874766 | −0.00404361 | ||||||||
\(469\) | 4.81531 | 0.222350 | ||||||||
\(470\) | −10.1786 | −0.469503 | ||||||||
\(471\) | 2.52126 | 0.116173 | ||||||||
\(472\) | −12.7214 | −0.585550 | ||||||||
\(473\) | 5.81663 | 0.267449 | ||||||||
\(474\) | −37.4183 | −1.71868 | ||||||||
\(475\) | 12.6144 | 0.578789 | ||||||||
\(476\) | 31.8152 | 1.45825 | ||||||||
\(477\) | −0.217657 | −0.00996582 | ||||||||
\(478\) | −65.0771 | −2.97656 | ||||||||
\(479\) | 38.8981 | 1.77730 | 0.888650 | − | 0.458586i | \(-0.151644\pi\) | ||||
0.888650 | + | 0.458586i | \(0.151644\pi\) | |||||||
\(480\) | 10.2195 | 0.466452 | ||||||||
\(481\) | 0.750971 | 0.0342413 | ||||||||
\(482\) | 74.7619 | 3.40531 | ||||||||
\(483\) | 0.609556 | 0.0277358 | ||||||||
\(484\) | −46.1900 | −2.09954 | ||||||||
\(485\) | 18.1615 | 0.824673 | ||||||||
\(486\) | −0.620123 | −0.0281293 | ||||||||
\(487\) | 8.00409 | 0.362700 | 0.181350 | − | 0.983419i | \(-0.441953\pi\) | ||||
0.181350 | + | 0.983419i | \(0.441953\pi\) | |||||||
\(488\) | 32.8833 | 1.48856 | ||||||||
\(489\) | 25.5985 | 1.15761 | ||||||||
\(490\) | 3.29843 | 0.149008 | ||||||||
\(491\) | 8.27877 | 0.373616 | 0.186808 | − | 0.982396i | \(-0.440186\pi\) | ||||
0.186808 | + | 0.982396i | \(0.440186\pi\) | |||||||
\(492\) | 41.8119 | 1.88503 | ||||||||
\(493\) | 22.5923 | 1.01751 | ||||||||
\(494\) | 8.14138 | 0.366298 | ||||||||
\(495\) | −0.0221523 | −0.000995670 0 | ||||||||
\(496\) | 37.2954 | 1.67461 | ||||||||
\(497\) | 1.37071 | 0.0614848 | ||||||||
\(498\) | −12.6355 | −0.566209 | ||||||||
\(499\) | 27.0555 | 1.21117 | 0.605586 | − | 0.795780i | \(-0.292939\pi\) | ||||
0.605586 | + | 0.795780i | \(0.292939\pi\) | |||||||
\(500\) | 47.6801 | 2.13232 | ||||||||
\(501\) | 34.8734 | 1.55803 | ||||||||
\(502\) | 41.5013 | 1.85230 | ||||||||
\(503\) | −0.897705 | −0.0400267 | −0.0200133 | − | 0.999800i | \(-0.506371\pi\) | ||||
−0.0200133 | + | 0.999800i | \(0.506371\pi\) | |||||||
\(504\) | 0.143660 | 0.00639911 | ||||||||
\(505\) | −13.5108 | −0.601224 | ||||||||
\(506\) | 0.644956 | 0.0286718 | ||||||||
\(507\) | −21.2051 | −0.941753 | ||||||||
\(508\) | 13.3437 | 0.592032 | ||||||||
\(509\) | 7.86666 | 0.348684 | 0.174342 | − | 0.984685i | \(-0.444220\pi\) | ||||
0.174342 | + | 0.984685i | \(0.444220\pi\) | |||||||
\(510\) | 41.0772 | 1.81893 | ||||||||
\(511\) | 6.46357 | 0.285931 | ||||||||
\(512\) | 50.5204 | 2.23271 | ||||||||
\(513\) | 19.9275 | 0.879821 | ||||||||
\(514\) | −75.7591 | −3.34159 | ||||||||
\(515\) | 20.4293 | 0.900221 | ||||||||
\(516\) | −61.3319 | −2.69998 | ||||||||
\(517\) | 2.22537 | 0.0978716 | ||||||||
\(518\) | −2.25785 | −0.0992043 | ||||||||
\(519\) | −33.4596 | −1.46871 | ||||||||
\(520\) | 6.68554 | 0.293180 | ||||||||
\(521\) | −17.6662 | −0.773969 | −0.386985 | − | 0.922086i | \(-0.626483\pi\) | ||||
−0.386985 | + | 0.922086i | \(0.626483\pi\) | |||||||
\(522\) | 0.186763 | 0.00817439 | ||||||||
\(523\) | −39.5190 | −1.72805 | −0.864023 | − | 0.503452i | \(-0.832063\pi\) | ||||
−0.864023 | + | 0.503452i | \(0.832063\pi\) | |||||||
\(524\) | 45.5533 | 1.99000 | ||||||||
\(525\) | −5.69678 | −0.248628 | ||||||||
\(526\) | −61.2582 | −2.67099 | ||||||||
\(527\) | 40.7238 | 1.77396 | ||||||||
\(528\) | −8.22473 | −0.357936 | ||||||||
\(529\) | −22.8752 | −0.994572 | ||||||||
\(530\) | 30.4541 | 1.32284 | ||||||||
\(531\) | −0.0492114 | −0.00213559 | ||||||||
\(532\) | −16.8373 | −0.729991 | ||||||||
\(533\) | 4.62950 | 0.200526 | ||||||||
\(534\) | 23.0811 | 0.998815 | ||||||||
\(535\) | 22.6960 | 0.981235 | ||||||||
\(536\) | −29.3445 | −1.26749 | ||||||||
\(537\) | 28.2082 | 1.21727 | ||||||||
\(538\) | 43.2738 | 1.86566 | ||||||||
\(539\) | −0.721143 | −0.0310618 | ||||||||
\(540\) | 29.9585 | 1.28921 | ||||||||
\(541\) | 24.4309 | 1.05037 | 0.525184 | − | 0.850989i | \(-0.323996\pi\) | ||||
0.525184 | + | 0.850989i | \(0.323996\pi\) | |||||||
\(542\) | −74.8061 | −3.21320 | ||||||||
\(543\) | 21.8474 | 0.937561 | ||||||||
\(544\) | −32.8143 | −1.40690 | ||||||||
\(545\) | −3.93056 | −0.168367 | ||||||||
\(546\) | −3.67672 | −0.157349 | ||||||||
\(547\) | 37.7618 | 1.61458 | 0.807289 | − | 0.590156i | \(-0.200934\pi\) | ||||
0.807289 | + | 0.590156i | \(0.200934\pi\) | |||||||
\(548\) | 47.1109 | 2.01248 | ||||||||
\(549\) | 0.127205 | 0.00542900 | ||||||||
\(550\) | −6.02763 | −0.257019 | ||||||||
\(551\) | −11.9564 | −0.509359 | ||||||||
\(552\) | −3.71463 | −0.158105 | ||||||||
\(553\) | 8.56828 | 0.364360 | ||||||||
\(554\) | 11.2834 | 0.479384 | ||||||||
\(555\) | −2.00523 | −0.0851172 | ||||||||
\(556\) | 97.2251 | 4.12326 | ||||||||
\(557\) | 11.4267 | 0.484164 | 0.242082 | − | 0.970256i | \(-0.422170\pi\) | ||||
0.242082 | + | 0.970256i | \(0.422170\pi\) | |||||||
\(558\) | 0.336649 | 0.0142515 | ||||||||
\(559\) | −6.79079 | −0.287220 | ||||||||
\(560\) | −8.61424 | −0.364018 | ||||||||
\(561\) | −8.98080 | −0.379170 | ||||||||
\(562\) | −41.2408 | −1.73964 | ||||||||
\(563\) | 2.97078 | 0.125203 | 0.0626017 | − | 0.998039i | \(-0.480060\pi\) | ||||
0.0626017 | + | 0.998039i | \(0.480060\pi\) | |||||||
\(564\) | −23.4648 | −0.988046 | ||||||||
\(565\) | −7.31069 | −0.307563 | ||||||||
\(566\) | 18.3251 | 0.770261 | ||||||||
\(567\) | −8.92872 | −0.374971 | ||||||||
\(568\) | −8.35311 | −0.350489 | ||||||||
\(569\) | −34.4412 | −1.44385 | −0.721924 | − | 0.691972i | \(-0.756742\pi\) | ||||
−0.721924 | + | 0.691972i | \(0.756742\pi\) | |||||||
\(570\) | −21.7390 | −0.910546 | ||||||||
\(571\) | 13.1595 | 0.550707 | 0.275353 | − | 0.961343i | \(-0.411205\pi\) | ||||
0.275353 | + | 0.961343i | \(0.411205\pi\) | |||||||
\(572\) | −2.67596 | −0.111888 | ||||||||
\(573\) | −17.5192 | −0.731874 | ||||||||
\(574\) | −13.9190 | −0.580966 | ||||||||
\(575\) | −1.16667 | −0.0486535 | ||||||||
\(576\) | 0.0404208 | 0.00168420 | ||||||||
\(577\) | −17.7916 | −0.740673 | −0.370336 | − | 0.928898i | \(-0.620758\pi\) | ||||
−0.370336 | + | 0.928898i | \(0.620758\pi\) | |||||||
\(578\) | −88.8652 | −3.69631 | ||||||||
\(579\) | 14.4144 | 0.599044 | ||||||||
\(580\) | −17.9749 | −0.746368 | ||||||||
\(581\) | 2.89335 | 0.120036 | ||||||||
\(582\) | 60.8667 | 2.52300 | ||||||||
\(583\) | −6.65826 | −0.275757 | ||||||||
\(584\) | −39.3889 | −1.62993 | ||||||||
\(585\) | 0.0258623 | 0.00106927 | ||||||||
\(586\) | 43.7998 | 1.80935 | ||||||||
\(587\) | 31.6925 | 1.30809 | 0.654044 | − | 0.756456i | \(-0.273071\pi\) | ||||
0.654044 | + | 0.756456i | \(0.273071\pi\) | |||||||
\(588\) | 7.60389 | 0.313579 | ||||||||
\(589\) | −21.5520 | −0.888033 | ||||||||
\(590\) | 6.88556 | 0.283474 | ||||||||
\(591\) | −19.9243 | −0.819577 | ||||||||
\(592\) | 5.89665 | 0.242351 | ||||||||
\(593\) | 29.0118 | 1.19137 | 0.595686 | − | 0.803217i | \(-0.296880\pi\) | ||||
0.595686 | + | 0.803217i | \(0.296880\pi\) | |||||||
\(594\) | −9.52209 | −0.390696 | ||||||||
\(595\) | −9.40611 | −0.385613 | ||||||||
\(596\) | −21.7999 | −0.892959 | ||||||||
\(597\) | −20.9849 | −0.858855 | ||||||||
\(598\) | −0.752973 | −0.0307914 | ||||||||
\(599\) | −38.7779 | −1.58442 | −0.792211 | − | 0.610247i | \(-0.791070\pi\) | ||||
−0.792211 | + | 0.610247i | \(0.791070\pi\) | |||||||
\(600\) | 34.7162 | 1.41728 | ||||||||
\(601\) | 10.7421 | 0.438181 | 0.219090 | − | 0.975705i | \(-0.429691\pi\) | ||||
0.219090 | + | 0.975705i | \(0.429691\pi\) | |||||||
\(602\) | 20.4171 | 0.832137 | ||||||||
\(603\) | −0.113516 | −0.00462273 | ||||||||
\(604\) | 24.5547 | 0.999116 | ||||||||
\(605\) | 13.6560 | 0.555195 | ||||||||
\(606\) | −45.2803 | −1.83938 | ||||||||
\(607\) | 40.7250 | 1.65298 | 0.826489 | − | 0.562952i | \(-0.190335\pi\) | ||||
0.826489 | + | 0.562952i | \(0.190335\pi\) | |||||||
\(608\) | 17.3661 | 0.704287 | ||||||||
\(609\) | 5.39961 | 0.218803 | ||||||||
\(610\) | −17.7983 | −0.720634 | ||||||||
\(611\) | −2.59807 | −0.105107 | ||||||||
\(612\) | −0.750011 | −0.0303174 | ||||||||
\(613\) | −30.1012 | −1.21578 | −0.607889 | − | 0.794022i | \(-0.707983\pi\) | ||||
−0.607889 | + | 0.794022i | \(0.707983\pi\) | |||||||
\(614\) | 19.3482 | 0.780831 | ||||||||
\(615\) | −12.3616 | −0.498469 | ||||||||
\(616\) | 4.39464 | 0.177065 | ||||||||
\(617\) | 32.6160 | 1.31307 | 0.656534 | − | 0.754296i | \(-0.272022\pi\) | ||||
0.656534 | + | 0.754296i | \(0.272022\pi\) | |||||||
\(618\) | 68.4667 | 2.75414 | ||||||||
\(619\) | 22.3052 | 0.896521 | 0.448261 | − | 0.893903i | \(-0.352044\pi\) | ||||
0.448261 | + | 0.893903i | \(0.352044\pi\) | |||||||
\(620\) | −32.4007 | −1.30124 | ||||||||
\(621\) | −1.84304 | −0.0739586 | ||||||||
\(622\) | −53.2812 | −2.13638 | ||||||||
\(623\) | −5.28524 | −0.211749 | ||||||||
\(624\) | 9.60220 | 0.384396 | ||||||||
\(625\) | 2.41366 | 0.0965462 | ||||||||
\(626\) | 63.7752 | 2.54897 | ||||||||
\(627\) | 4.75285 | 0.189810 | ||||||||
\(628\) | 6.44107 | 0.257027 | ||||||||
\(629\) | 6.43871 | 0.256728 | ||||||||
\(630\) | −0.0777571 | −0.00309792 | ||||||||
\(631\) | −15.8887 | −0.632517 | −0.316259 | − | 0.948673i | \(-0.602427\pi\) | ||||
−0.316259 | + | 0.948673i | \(0.602427\pi\) | |||||||
\(632\) | −52.2150 | −2.07700 | ||||||||
\(633\) | −8.13448 | −0.323317 | ||||||||
\(634\) | −60.4198 | −2.39958 | ||||||||
\(635\) | −3.94505 | −0.156555 | ||||||||
\(636\) | 70.2062 | 2.78386 | ||||||||
\(637\) | 0.841919 | 0.0333580 | ||||||||
\(638\) | 5.71319 | 0.226187 | ||||||||
\(639\) | −0.0323131 | −0.00127829 | ||||||||
\(640\) | −17.5027 | −0.691854 | ||||||||
\(641\) | 10.7468 | 0.424473 | 0.212237 | − | 0.977218i | \(-0.431925\pi\) | ||||
0.212237 | + | 0.977218i | \(0.431925\pi\) | |||||||
\(642\) | 76.0636 | 3.00199 | ||||||||
\(643\) | 19.4609 | 0.767465 | 0.383732 | − | 0.923444i | \(-0.374638\pi\) | ||||
0.383732 | + | 0.923444i | \(0.374638\pi\) | |||||||
\(644\) | 1.55724 | 0.0613637 | ||||||||
\(645\) | 18.1327 | 0.713973 | ||||||||
\(646\) | 69.8030 | 2.74636 | ||||||||
\(647\) | 50.1856 | 1.97300 | 0.986500 | − | 0.163760i | \(-0.0523622\pi\) | ||||
0.986500 | + | 0.163760i | \(0.0523622\pi\) | |||||||
\(648\) | 54.4116 | 2.13749 | ||||||||
\(649\) | −1.50541 | −0.0590924 | ||||||||
\(650\) | 7.03713 | 0.276019 | ||||||||
\(651\) | 9.73306 | 0.381469 | ||||||||
\(652\) | 65.3967 | 2.56113 | ||||||||
\(653\) | 10.3850 | 0.406395 | 0.203197 | − | 0.979138i | \(-0.434867\pi\) | ||||
0.203197 | + | 0.979138i | \(0.434867\pi\) | |||||||
\(654\) | −13.1729 | −0.515100 | ||||||||
\(655\) | −13.4677 | −0.526229 | ||||||||
\(656\) | 36.3511 | 1.41927 | ||||||||
\(657\) | −0.152372 | −0.00594460 | ||||||||
\(658\) | 7.81131 | 0.304516 | ||||||||
\(659\) | 0.140891 | 0.00548833 | 0.00274416 | − | 0.999996i | \(-0.499127\pi\) | ||||
0.00274416 | + | 0.999996i | \(0.499127\pi\) | |||||||
\(660\) | 7.14531 | 0.278131 | ||||||||
\(661\) | −3.30832 | −0.128679 | −0.0643395 | − | 0.997928i | \(-0.520494\pi\) | ||||
−0.0643395 | + | 0.997928i | \(0.520494\pi\) | |||||||
\(662\) | −66.8176 | −2.59694 | ||||||||
\(663\) | 10.4849 | 0.407200 | ||||||||
\(664\) | −17.6321 | −0.684256 | ||||||||
\(665\) | 4.97793 | 0.193036 | ||||||||
\(666\) | 0.0532266 | 0.00206249 | ||||||||
\(667\) | 1.10581 | 0.0428172 | ||||||||
\(668\) | 89.0913 | 3.44705 | ||||||||
\(669\) | 18.6543 | 0.721216 | ||||||||
\(670\) | 15.8829 | 0.613612 | ||||||||
\(671\) | 3.89129 | 0.150222 | ||||||||
\(672\) | −7.84267 | −0.302538 | ||||||||
\(673\) | 18.0308 | 0.695037 | 0.347519 | − | 0.937673i | \(-0.387024\pi\) | ||||
0.347519 | + | 0.937673i | \(0.387024\pi\) | |||||||
\(674\) | 43.0946 | 1.65994 | ||||||||
\(675\) | 17.2246 | 0.662977 | ||||||||
\(676\) | −54.1729 | −2.08357 | ||||||||
\(677\) | 1.73646 | 0.0667374 | 0.0333687 | − | 0.999443i | \(-0.489376\pi\) | ||||
0.0333687 | + | 0.999443i | \(0.489376\pi\) | |||||||
\(678\) | −24.5011 | −0.940958 | ||||||||
\(679\) | −13.9376 | −0.534877 | ||||||||
\(680\) | 57.3208 | 2.19815 | ||||||||
\(681\) | 24.6795 | 0.945720 | ||||||||
\(682\) | 10.2983 | 0.394343 | ||||||||
\(683\) | 20.6257 | 0.789221 | 0.394610 | − | 0.918849i | \(-0.370880\pi\) | ||||
0.394610 | + | 0.918849i | \(0.370880\pi\) | |||||||
\(684\) | 0.396923 | 0.0151767 | ||||||||
\(685\) | −13.9283 | −0.532172 | ||||||||
\(686\) | −2.53130 | −0.0966453 | ||||||||
\(687\) | 36.6156 | 1.39697 | ||||||||
\(688\) | −53.3216 | −2.03287 | ||||||||
\(689\) | 7.77338 | 0.296142 | ||||||||
\(690\) | 2.01058 | 0.0765413 | ||||||||
\(691\) | 4.11720 | 0.156626 | 0.0783128 | − | 0.996929i | \(-0.475047\pi\) | ||||
0.0783128 | + | 0.996929i | \(0.475047\pi\) | |||||||
\(692\) | −85.4794 | −3.24944 | ||||||||
\(693\) | 0.0170002 | 0.000645784 0 | ||||||||
\(694\) | 12.5137 | 0.475015 | ||||||||
\(695\) | −28.7444 | −1.09034 | ||||||||
\(696\) | −32.9052 | −1.24727 | ||||||||
\(697\) | 39.6927 | 1.50347 | ||||||||
\(698\) | −43.9891 | −1.66501 | ||||||||
\(699\) | 38.7844 | 1.46696 | ||||||||
\(700\) | −14.5536 | −0.550075 | ||||||||
\(701\) | 24.5896 | 0.928735 | 0.464368 | − | 0.885642i | \(-0.346282\pi\) | ||||
0.464368 | + | 0.885642i | \(0.346282\pi\) | |||||||
\(702\) | 11.1168 | 0.419578 | ||||||||
\(703\) | −3.40751 | −0.128517 | ||||||||
\(704\) | 1.23650 | 0.0466023 | ||||||||
\(705\) | 6.93733 | 0.261275 | ||||||||
\(706\) | 3.18358 | 0.119816 | ||||||||
\(707\) | 10.3686 | 0.389950 | ||||||||
\(708\) | 15.8734 | 0.596557 | ||||||||
\(709\) | 22.9289 | 0.861114 | 0.430557 | − | 0.902563i | \(-0.358317\pi\) | ||||
0.430557 | + | 0.902563i | \(0.358317\pi\) | |||||||
\(710\) | 4.52119 | 0.169677 | ||||||||
\(711\) | −0.201988 | −0.00757516 | ||||||||
\(712\) | 32.2083 | 1.20706 | ||||||||
\(713\) | 1.99328 | 0.0746489 | ||||||||
\(714\) | −31.5237 | −1.17974 | ||||||||
\(715\) | 0.791144 | 0.0295871 | ||||||||
\(716\) | 72.0637 | 2.69315 | ||||||||
\(717\) | 44.3540 | 1.65643 | ||||||||
\(718\) | 79.1320 | 2.95318 | ||||||||
\(719\) | 27.3228 | 1.01897 | 0.509485 | − | 0.860480i | \(-0.329836\pi\) | ||||
0.509485 | + | 0.860480i | \(0.329836\pi\) | |||||||
\(720\) | 0.203072 | 0.00756804 | ||||||||
\(721\) | −15.6779 | −0.583877 | ||||||||
\(722\) | 11.1533 | 0.415082 | ||||||||
\(723\) | −50.9548 | −1.89503 | ||||||||
\(724\) | 55.8136 | 2.07430 | ||||||||
\(725\) | −10.3347 | −0.383820 | ||||||||
\(726\) | 45.7667 | 1.69856 | ||||||||
\(727\) | 6.59392 | 0.244555 | 0.122277 | − | 0.992496i | \(-0.460980\pi\) | ||||
0.122277 | + | 0.992496i | \(0.460980\pi\) | |||||||
\(728\) | −5.13065 | −0.190155 | ||||||||
\(729\) | 27.2088 | 1.00773 | ||||||||
\(730\) | 21.3196 | 0.789074 | ||||||||
\(731\) | −58.2233 | −2.15347 | ||||||||
\(732\) | −41.0307 | −1.51654 | ||||||||
\(733\) | −10.6378 | −0.392914 | −0.196457 | − | 0.980512i | \(-0.562944\pi\) | ||||
−0.196457 | + | 0.980512i | \(0.562944\pi\) | |||||||
\(734\) | 61.4300 | 2.26742 | ||||||||
\(735\) | −2.24808 | −0.0829216 | ||||||||
\(736\) | −1.60614 | −0.0592030 | ||||||||
\(737\) | −3.47253 | −0.127912 | ||||||||
\(738\) | 0.328126 | 0.0120785 | ||||||||
\(739\) | 20.2306 | 0.744194 | 0.372097 | − | 0.928194i | \(-0.378639\pi\) | ||||
0.372097 | + | 0.928194i | \(0.378639\pi\) | |||||||
\(740\) | −5.12277 | −0.188317 | ||||||||
\(741\) | −5.54885 | −0.203842 | ||||||||
\(742\) | −23.3713 | −0.857986 | ||||||||
\(743\) | −32.8780 | −1.20618 | −0.603088 | − | 0.797675i | \(-0.706063\pi\) | ||||
−0.603088 | + | 0.797675i | \(0.706063\pi\) | |||||||
\(744\) | −59.3132 | −2.17453 | ||||||||
\(745\) | 6.44511 | 0.236131 | ||||||||
\(746\) | −58.7922 | −2.15254 | ||||||||
\(747\) | −0.0682078 | −0.00249559 | ||||||||
\(748\) | −22.9433 | −0.838890 | ||||||||
\(749\) | −17.4175 | −0.636422 | ||||||||
\(750\) | −47.2432 | −1.72508 | ||||||||
\(751\) | 28.1426 | 1.02694 | 0.513469 | − | 0.858108i | \(-0.328360\pi\) | ||||
0.513469 | + | 0.858108i | \(0.328360\pi\) | |||||||
\(752\) | −20.4002 | −0.743918 | ||||||||
\(753\) | −28.2857 | −1.03079 | ||||||||
\(754\) | −6.67003 | −0.242908 | ||||||||
\(755\) | −7.25956 | −0.264202 | ||||||||
\(756\) | −22.9909 | −0.836172 | ||||||||
\(757\) | 11.7670 | 0.427678 | 0.213839 | − | 0.976869i | \(-0.431403\pi\) | ||||
0.213839 | + | 0.976869i | \(0.431403\pi\) | |||||||
\(758\) | −84.0341 | −3.05226 | ||||||||
\(759\) | −0.439577 | −0.0159556 | ||||||||
\(760\) | −30.3355 | −1.10038 | ||||||||
\(761\) | −25.4656 | −0.923128 | −0.461564 | − | 0.887107i | \(-0.652712\pi\) | ||||
−0.461564 | + | 0.887107i | \(0.652712\pi\) | |||||||
\(762\) | −13.2215 | −0.478963 | ||||||||
\(763\) | 3.01641 | 0.109201 | ||||||||
\(764\) | −44.7563 | −1.61923 | ||||||||
\(765\) | 0.221740 | 0.00801701 | ||||||||
\(766\) | 4.31773 | 0.156006 | ||||||||
\(767\) | 1.75753 | 0.0634608 | ||||||||
\(768\) | −52.7422 | −1.90317 | ||||||||
\(769\) | −26.6857 | −0.962310 | −0.481155 | − | 0.876635i | \(-0.659783\pi\) | ||||
−0.481155 | + | 0.876635i | \(0.659783\pi\) | |||||||
\(770\) | −2.37864 | −0.0857201 | ||||||||
\(771\) | 51.6344 | 1.85957 | ||||||||
\(772\) | 36.8247 | 1.32535 | ||||||||
\(773\) | 51.7495 | 1.86130 | 0.930650 | − | 0.365912i | \(-0.119243\pi\) | ||||
0.930650 | + | 0.365912i | \(0.119243\pi\) | |||||||
\(774\) | −0.481311 | −0.0173004 | ||||||||
\(775\) | −18.6288 | −0.669165 | ||||||||
\(776\) | 84.9359 | 3.04902 | ||||||||
\(777\) | 1.53886 | 0.0552064 | ||||||||
\(778\) | 5.05654 | 0.181286 | ||||||||
\(779\) | −21.0063 | −0.752628 | ||||||||
\(780\) | −8.34200 | −0.298691 | ||||||||
\(781\) | −0.988479 | −0.0353705 | ||||||||
\(782\) | −6.45588 | −0.230862 | ||||||||
\(783\) | −16.3261 | −0.583448 | ||||||||
\(784\) | 6.61079 | 0.236099 | ||||||||
\(785\) | −1.90429 | −0.0679671 | ||||||||
\(786\) | −45.1359 | −1.60994 | ||||||||
\(787\) | 15.2801 | 0.544676 | 0.272338 | − | 0.962202i | \(-0.412203\pi\) | ||||
0.272338 | + | 0.962202i | \(0.412203\pi\) | |||||||
\(788\) | −50.9008 | −1.81327 | ||||||||
\(789\) | 41.7512 | 1.48638 | ||||||||
\(790\) | 28.2618 | 1.00551 | ||||||||
\(791\) | 5.61041 | 0.199483 | ||||||||
\(792\) | −0.103599 | −0.00368124 | ||||||||
\(793\) | −4.54300 | −0.161327 | ||||||||
\(794\) | 52.3992 | 1.85958 | ||||||||
\(795\) | −20.7563 | −0.736152 | ||||||||
\(796\) | −53.6103 | −1.90017 | ||||||||
\(797\) | 12.2004 | 0.432159 | 0.216080 | − | 0.976376i | \(-0.430673\pi\) | ||||
0.216080 | + | 0.976376i | \(0.430673\pi\) | |||||||
\(798\) | 16.6830 | 0.590574 | ||||||||
\(799\) | −22.2755 | −0.788050 | ||||||||
\(800\) | 15.0106 | 0.530706 | ||||||||
\(801\) | 0.124594 | 0.00440232 | ||||||||
\(802\) | −21.2726 | −0.751160 | ||||||||
\(803\) | −4.66115 | −0.164489 | ||||||||
\(804\) | 36.6151 | 1.29131 | ||||||||
\(805\) | −0.460394 | −0.0162268 | ||||||||
\(806\) | −12.0231 | −0.423495 | ||||||||
\(807\) | −29.4937 | −1.03823 | ||||||||
\(808\) | −63.1859 | −2.22287 | ||||||||
\(809\) | 10.9534 | 0.385101 | 0.192550 | − | 0.981287i | \(-0.438324\pi\) | ||||
0.192550 | + | 0.981287i | \(0.438324\pi\) | |||||||
\(810\) | −29.4507 | −1.03479 | ||||||||
\(811\) | 36.0109 | 1.26451 | 0.632257 | − | 0.774759i | \(-0.282129\pi\) | ||||
0.632257 | + | 0.774759i | \(0.282129\pi\) | |||||||
\(812\) | 13.7944 | 0.484089 | ||||||||
\(813\) | 50.9849 | 1.78812 | ||||||||
\(814\) | 1.62823 | 0.0570696 | ||||||||
\(815\) | −19.3344 | −0.677256 | ||||||||
\(816\) | 82.3279 | 2.88205 | ||||||||
\(817\) | 30.8131 | 1.07801 | ||||||||
\(818\) | 93.9649 | 3.28541 | ||||||||
\(819\) | −0.0198474 | −0.000693524 0 | ||||||||
\(820\) | −31.5803 | −1.10283 | ||||||||
\(821\) | 12.3969 | 0.432656 | 0.216328 | − | 0.976321i | \(-0.430592\pi\) | ||||
0.216328 | + | 0.976321i | \(0.430592\pi\) | |||||||
\(822\) | −46.6792 | −1.62812 | ||||||||
\(823\) | −17.9161 | −0.624515 | −0.312258 | − | 0.949997i | \(-0.601085\pi\) | ||||
−0.312258 | + | 0.949997i | \(0.601085\pi\) | |||||||
\(824\) | 95.5413 | 3.32834 | ||||||||
\(825\) | 4.10819 | 0.143029 | ||||||||
\(826\) | −5.28416 | −0.183859 | ||||||||
\(827\) | −31.9229 | −1.11007 | −0.555034 | − | 0.831828i | \(-0.687295\pi\) | ||||
−0.555034 | + | 0.831828i | \(0.687295\pi\) | |||||||
\(828\) | −0.0367103 | −0.00127577 | ||||||||
\(829\) | −18.1689 | −0.631031 | −0.315515 | − | 0.948920i | \(-0.602177\pi\) | ||||
−0.315515 | + | 0.948920i | \(0.602177\pi\) | |||||||
\(830\) | 9.54350 | 0.331260 | ||||||||
\(831\) | −7.69029 | −0.266773 | ||||||||
\(832\) | −1.44359 | −0.0500474 | ||||||||
\(833\) | 7.21849 | 0.250106 | ||||||||
\(834\) | −96.3342 | −3.33578 | ||||||||
\(835\) | −26.3397 | −0.911523 | ||||||||
\(836\) | 12.1421 | 0.419944 | ||||||||
\(837\) | −29.4286 | −1.01720 | ||||||||
\(838\) | −43.9402 | −1.51789 | ||||||||
\(839\) | −39.2360 | −1.35458 | −0.677289 | − | 0.735717i | \(-0.736845\pi\) | ||||
−0.677289 | + | 0.735717i | \(0.736845\pi\) | |||||||
\(840\) | 13.6998 | 0.472687 | ||||||||
\(841\) | −19.2044 | −0.662222 | ||||||||
\(842\) | −17.2933 | −0.595968 | ||||||||
\(843\) | 28.1081 | 0.968095 | ||||||||
\(844\) | −20.7812 | −0.715319 | ||||||||
\(845\) | 16.0161 | 0.550971 | ||||||||
\(846\) | −0.184144 | −0.00633099 | ||||||||
\(847\) | −10.4800 | −0.360095 | ||||||||
\(848\) | 61.0369 | 2.09602 | ||||||||
\(849\) | −12.4897 | −0.428644 | ||||||||
\(850\) | 60.3353 | 2.06948 | ||||||||
\(851\) | 0.315151 | 0.0108032 | ||||||||
\(852\) | 10.4227 | 0.357077 | ||||||||
\(853\) | 3.92968 | 0.134550 | 0.0672748 | − | 0.997734i | \(-0.478570\pi\) | ||||
0.0672748 | + | 0.997734i | \(0.478570\pi\) | |||||||
\(854\) | 13.6589 | 0.467398 | ||||||||
\(855\) | −0.117350 | −0.00401327 | ||||||||
\(856\) | 106.142 | 3.62787 | ||||||||
\(857\) | −4.29732 | −0.146794 | −0.0733968 | − | 0.997303i | \(-0.523384\pi\) | ||||
−0.0733968 | + | 0.997303i | \(0.523384\pi\) | |||||||
\(858\) | 2.65144 | 0.0905187 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | 46.3236 | 1.57962 | ||||||||
\(861\) | 9.48662 | 0.323303 | ||||||||
\(862\) | 59.7525 | 2.03518 | ||||||||
\(863\) | 35.6307 | 1.21288 | 0.606441 | − | 0.795129i | \(-0.292597\pi\) | ||||
0.606441 | + | 0.795129i | \(0.292597\pi\) | |||||||
\(864\) | 23.7129 | 0.806729 | ||||||||
\(865\) | 25.2719 | 0.859269 | ||||||||
\(866\) | −48.0275 | −1.63204 | ||||||||
\(867\) | 60.5670 | 2.05696 | ||||||||
\(868\) | 24.8651 | 0.843977 | ||||||||
\(869\) | −6.17895 | −0.209607 | ||||||||
\(870\) | 17.8102 | 0.603823 | ||||||||
\(871\) | 4.05410 | 0.137368 | ||||||||
\(872\) | −18.3820 | −0.622492 | ||||||||
\(873\) | 0.328566 | 0.0111203 | ||||||||
\(874\) | 3.41660 | 0.115568 | ||||||||
\(875\) | 10.8180 | 0.365717 | ||||||||
\(876\) | 49.1483 | 1.66057 | ||||||||
\(877\) | −10.0328 | −0.338785 | −0.169392 | − | 0.985549i | \(-0.554181\pi\) | ||||
−0.169392 | + | 0.985549i | \(0.554181\pi\) | |||||||
\(878\) | 26.6052 | 0.897881 | ||||||||
\(879\) | −29.8522 | −1.00689 | ||||||||
\(880\) | 6.21210 | 0.209410 | ||||||||
\(881\) | 13.5260 | 0.455703 | 0.227851 | − | 0.973696i | \(-0.426830\pi\) | ||||
0.227851 | + | 0.973696i | \(0.426830\pi\) | |||||||
\(882\) | 0.0596727 | 0.00200929 | ||||||||
\(883\) | 35.9934 | 1.21127 | 0.605637 | − | 0.795741i | \(-0.292919\pi\) | ||||
0.605637 | + | 0.795741i | \(0.292919\pi\) | |||||||
\(884\) | 26.7858 | 0.900905 | ||||||||
\(885\) | −4.69293 | −0.157751 | ||||||||
\(886\) | −11.3603 | −0.381656 | ||||||||
\(887\) | −54.7566 | −1.83855 | −0.919273 | − | 0.393620i | \(-0.871222\pi\) | ||||
−0.919273 | + | 0.393620i | \(0.871222\pi\) | |||||||
\(888\) | −9.37783 | −0.314699 | ||||||||
\(889\) | 3.02753 | 0.101540 | ||||||||
\(890\) | −17.4330 | −0.584355 | ||||||||
\(891\) | 6.43888 | 0.215711 | ||||||||
\(892\) | 47.6562 | 1.59565 | ||||||||
\(893\) | 11.7887 | 0.394494 | ||||||||
\(894\) | 21.6002 | 0.722417 | ||||||||
\(895\) | −21.3055 | −0.712165 | ||||||||
\(896\) | 13.4320 | 0.448731 | ||||||||
\(897\) | 0.513197 | 0.0171351 | ||||||||
\(898\) | 79.0021 | 2.63634 | ||||||||
\(899\) | 17.6570 | 0.588894 | ||||||||
\(900\) | 0.343086 | 0.0114362 | ||||||||
\(901\) | 66.6478 | 2.22036 | ||||||||
\(902\) | 10.0376 | 0.334214 | ||||||||
\(903\) | −13.9155 | −0.463078 | ||||||||
\(904\) | −34.1898 | −1.13714 | ||||||||
\(905\) | −16.5012 | −0.548519 | ||||||||
\(906\) | −24.3297 | −0.808300 | ||||||||
\(907\) | 4.93892 | 0.163994 | 0.0819971 | − | 0.996633i | \(-0.473870\pi\) | ||||
0.0819971 | + | 0.996633i | \(0.473870\pi\) | |||||||
\(908\) | 63.0488 | 2.09235 | ||||||||
\(909\) | −0.244428 | −0.00810717 | ||||||||
\(910\) | 2.77701 | 0.0920569 | ||||||||
\(911\) | −39.7087 | −1.31561 | −0.657803 | − | 0.753190i | \(-0.728514\pi\) | ||||
−0.657803 | + | 0.753190i | \(0.728514\pi\) | |||||||
\(912\) | −43.5698 | −1.44274 | ||||||||
\(913\) | −2.08652 | −0.0690537 | ||||||||
\(914\) | 15.8735 | 0.525048 | ||||||||
\(915\) | 12.1307 | 0.401027 | ||||||||
\(916\) | 93.5420 | 3.09071 | ||||||||
\(917\) | 10.3355 | 0.341308 | ||||||||
\(918\) | 95.3142 | 3.14584 | ||||||||
\(919\) | −34.2537 | −1.12992 | −0.564962 | − | 0.825117i | \(-0.691109\pi\) | ||||
−0.564962 | + | 0.825117i | \(0.691109\pi\) | |||||||
\(920\) | 2.80564 | 0.0924992 | ||||||||
\(921\) | −13.1870 | −0.434526 | ||||||||
\(922\) | −29.5086 | −0.971813 | ||||||||
\(923\) | 1.15403 | 0.0379853 | ||||||||
\(924\) | −5.48349 | −0.180394 | ||||||||
\(925\) | −2.94534 | −0.0968420 | ||||||||
\(926\) | −31.9622 | −1.05034 | ||||||||
\(927\) | 0.369592 | 0.0121390 | ||||||||
\(928\) | −14.2276 | −0.467044 | ||||||||
\(929\) | 35.0451 | 1.14979 | 0.574896 | − | 0.818226i | \(-0.305042\pi\) | ||||
0.574896 | + | 0.818226i | \(0.305042\pi\) | |||||||
\(930\) | 32.1038 | 1.05272 | ||||||||
\(931\) | −3.82019 | −0.125202 | ||||||||
\(932\) | 99.0828 | 3.24557 | ||||||||
\(933\) | 36.3144 | 1.18888 | ||||||||
\(934\) | 102.129 | 3.34177 | ||||||||
\(935\) | 6.78315 | 0.221833 | ||||||||
\(936\) | 0.120950 | 0.00395337 | ||||||||
\(937\) | 61.0833 | 1.99550 | 0.997752 | − | 0.0670201i | \(-0.0213492\pi\) | ||||
0.997752 | + | 0.0670201i | \(0.0213492\pi\) | |||||||
\(938\) | −12.1890 | −0.397984 | ||||||||
\(939\) | −43.4666 | −1.41848 | ||||||||
\(940\) | 17.7228 | 0.578055 | ||||||||
\(941\) | 0.806963 | 0.0263063 | 0.0131531 | − | 0.999913i | \(-0.495813\pi\) | ||||
0.0131531 | + | 0.999913i | \(0.495813\pi\) | |||||||
\(942\) | −6.38205 | −0.207938 | ||||||||
\(943\) | 1.94281 | 0.0632666 | ||||||||
\(944\) | 13.8002 | 0.449159 | ||||||||
\(945\) | 6.79723 | 0.221114 | ||||||||
\(946\) | −14.7236 | −0.478706 | ||||||||
\(947\) | −4.22403 | −0.137263 | −0.0686313 | − | 0.997642i | \(-0.521863\pi\) | ||||
−0.0686313 | + | 0.997642i | \(0.521863\pi\) | |||||||
\(948\) | 65.1523 | 2.11605 | ||||||||
\(949\) | 5.44180 | 0.176648 | ||||||||
\(950\) | −31.9308 | −1.03597 | ||||||||
\(951\) | 41.1798 | 1.33535 | ||||||||
\(952\) | −43.9894 | −1.42571 | ||||||||
\(953\) | 21.7187 | 0.703538 | 0.351769 | − | 0.936087i | \(-0.385580\pi\) | ||||
0.351769 | + | 0.936087i | \(0.385580\pi\) | |||||||
\(954\) | 0.550954 | 0.0178378 | ||||||||
\(955\) | 13.2321 | 0.428182 | ||||||||
\(956\) | 113.311 | 3.66475 | ||||||||
\(957\) | −3.89389 | −0.125872 | ||||||||
\(958\) | −98.4627 | −3.18118 | ||||||||
\(959\) | 10.6889 | 0.345163 | ||||||||
\(960\) | 3.85464 | 0.124408 | ||||||||
\(961\) | 0.827611 | 0.0266971 | ||||||||
\(962\) | −1.90093 | −0.0612884 | ||||||||
\(963\) | 0.410600 | 0.0132314 | ||||||||
\(964\) | −130.174 | −4.19264 | ||||||||
\(965\) | −10.8871 | −0.350470 | ||||||||
\(966\) | −1.54297 | −0.0496441 | ||||||||
\(967\) | 14.4520 | 0.464746 | 0.232373 | − | 0.972627i | \(-0.425351\pi\) | ||||
0.232373 | + | 0.972627i | \(0.425351\pi\) | |||||||
\(968\) | 63.8648 | 2.05269 | ||||||||
\(969\) | −47.5750 | −1.52833 | ||||||||
\(970\) | −45.9723 | −1.47608 | ||||||||
\(971\) | 17.4354 | 0.559528 | 0.279764 | − | 0.960069i | \(-0.409744\pi\) | ||||
0.279764 | + | 0.960069i | \(0.409744\pi\) | |||||||
\(972\) | 1.07975 | 0.0346330 | ||||||||
\(973\) | 22.0592 | 0.707186 | ||||||||
\(974\) | −20.2607 | −0.649196 | ||||||||
\(975\) | −4.79623 | −0.153602 | ||||||||
\(976\) | −35.6719 | −1.14183 | ||||||||
\(977\) | −0.920220 | −0.0294404 | −0.0147202 | − | 0.999892i | \(-0.504686\pi\) | ||||
−0.0147202 | + | 0.999892i | \(0.504686\pi\) | |||||||
\(978\) | −64.7975 | −2.07200 | ||||||||
\(979\) | 3.81142 | 0.121813 | ||||||||
\(980\) | −5.74318 | −0.183459 | ||||||||
\(981\) | −0.0711088 | −0.00227033 | ||||||||
\(982\) | −20.9560 | −0.668733 | ||||||||
\(983\) | −41.2655 | −1.31616 | −0.658082 | − | 0.752946i | \(-0.728632\pi\) | ||||
−0.658082 | + | 0.752946i | \(0.728632\pi\) | |||||||
\(984\) | −57.8114 | −1.84296 | ||||||||
\(985\) | 15.0487 | 0.479493 | ||||||||
\(986\) | −57.1879 | −1.82123 | ||||||||
\(987\) | −5.32388 | −0.169461 | ||||||||
\(988\) | −14.1757 | −0.450988 | ||||||||
\(989\) | −2.84981 | −0.0906188 | ||||||||
\(990\) | 0.0560739 | 0.00178215 | ||||||||
\(991\) | 4.49250 | 0.142709 | 0.0713544 | − | 0.997451i | \(-0.477268\pi\) | ||||
0.0713544 | + | 0.997451i | \(0.477268\pi\) | |||||||
\(992\) | −25.6459 | −0.814259 | ||||||||
\(993\) | 45.5402 | 1.44518 | ||||||||
\(994\) | −3.46968 | −0.110051 | ||||||||
\(995\) | 15.8498 | 0.502472 | ||||||||
\(996\) | 22.0007 | 0.697119 | ||||||||
\(997\) | 29.1720 | 0.923886 | 0.461943 | − | 0.886910i | \(-0.347153\pi\) | ||||
0.461943 | + | 0.886910i | \(0.347153\pi\) | |||||||
\(998\) | −68.4855 | −2.16787 | ||||||||
\(999\) | −4.65287 | −0.147210 |
(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 | 6013.2.a.e.1.5 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.e.1.5 | ✓ | 109 | 1.1 | even | 1 | trivial |