Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52937 | −1.78853 | −0.894267 | − | 0.447534i | \(-0.852302\pi\) | ||||
−0.894267 | + | 0.447534i | \(0.852302\pi\) | |||||||
\(3\) | 0.978887 | 0.565160 | 0.282580 | − | 0.959244i | \(-0.408810\pi\) | ||||
0.282580 | + | 0.959244i | \(0.408810\pi\) | |||||||
\(4\) | 4.39770 | 2.19885 | ||||||||
\(5\) | −0.161932 | −0.0724183 | −0.0362092 | − | 0.999344i | \(-0.511528\pi\) | ||||
−0.0362092 | + | 0.999344i | \(0.511528\pi\) | |||||||
\(6\) | −2.47596 | −1.01081 | ||||||||
\(7\) | −2.77531 | −1.04897 | −0.524485 | − | 0.851420i | \(-0.675742\pi\) | ||||
−0.524485 | + | 0.851420i | \(0.675742\pi\) | |||||||
\(8\) | −6.06468 | −2.14419 | ||||||||
\(9\) | −2.04178 | −0.680594 | ||||||||
\(10\) | 0.409586 | 0.129523 | ||||||||
\(11\) | −5.90921 | −1.78169 | −0.890847 | − | 0.454304i | \(-0.849888\pi\) | ||||
−0.890847 | + | 0.454304i | \(0.849888\pi\) | |||||||
\(12\) | 4.30485 | 1.24270 | ||||||||
\(13\) | −4.84469 | −1.34367 | −0.671837 | − | 0.740699i | \(-0.734494\pi\) | ||||
−0.671837 | + | 0.740699i | \(0.734494\pi\) | |||||||
\(14\) | 7.01979 | 1.87612 | ||||||||
\(15\) | −0.158513 | −0.0409280 | ||||||||
\(16\) | 6.54440 | 1.63610 | ||||||||
\(17\) | −7.33022 | −1.77784 | −0.888920 | − | 0.458062i | \(-0.848544\pi\) | ||||
−0.888920 | + | 0.458062i | \(0.848544\pi\) | |||||||
\(18\) | 5.16442 | 1.21726 | ||||||||
\(19\) | 4.31064 | 0.988928 | 0.494464 | − | 0.869198i | \(-0.335364\pi\) | ||||
0.494464 | + | 0.869198i | \(0.335364\pi\) | |||||||
\(20\) | −0.712130 | −0.159237 | ||||||||
\(21\) | −2.71672 | −0.592836 | ||||||||
\(22\) | 14.9466 | 3.18662 | ||||||||
\(23\) | 0.421572 | 0.0879038 | 0.0439519 | − | 0.999034i | \(-0.486005\pi\) | ||||
0.0439519 | + | 0.999034i | \(0.486005\pi\) | |||||||
\(24\) | −5.93663 | −1.21181 | ||||||||
\(25\) | −4.97378 | −0.994756 | ||||||||
\(26\) | 12.2540 | 2.40321 | ||||||||
\(27\) | −4.93533 | −0.949805 | ||||||||
\(28\) | −12.2050 | −2.30653 | ||||||||
\(29\) | −4.33717 | −0.805392 | −0.402696 | − | 0.915334i | \(-0.631927\pi\) | ||||
−0.402696 | + | 0.915334i | \(0.631927\pi\) | |||||||
\(30\) | 0.400939 | 0.0732010 | ||||||||
\(31\) | 6.27802 | 1.12757 | 0.563783 | − | 0.825923i | \(-0.309346\pi\) | ||||
0.563783 | + | 0.825923i | \(0.309346\pi\) | |||||||
\(32\) | −4.42384 | −0.782031 | ||||||||
\(33\) | −5.78444 | −1.00694 | ||||||||
\(34\) | 18.5408 | 3.17973 | ||||||||
\(35\) | 0.449413 | 0.0759646 | ||||||||
\(36\) | −8.97915 | −1.49653 | ||||||||
\(37\) | −2.79770 | −0.459939 | −0.229970 | − | 0.973198i | \(-0.573863\pi\) | ||||
−0.229970 | + | 0.973198i | \(0.573863\pi\) | |||||||
\(38\) | −10.9032 | −1.76873 | ||||||||
\(39\) | −4.74240 | −0.759391 | ||||||||
\(40\) | 0.982067 | 0.155278 | ||||||||
\(41\) | 0.785168 | 0.122623 | 0.0613113 | − | 0.998119i | \(-0.480472\pi\) | ||||
0.0613113 | + | 0.998119i | \(0.480472\pi\) | |||||||
\(42\) | 6.87158 | 1.06031 | ||||||||
\(43\) | −2.17649 | −0.331911 | −0.165955 | − | 0.986133i | \(-0.553071\pi\) | ||||
−0.165955 | + | 0.986133i | \(0.553071\pi\) | |||||||
\(44\) | −25.9870 | −3.91768 | ||||||||
\(45\) | 0.330630 | 0.0492874 | ||||||||
\(46\) | −1.06631 | −0.157219 | ||||||||
\(47\) | −7.48652 | −1.09202 | −0.546010 | − | 0.837778i | \(-0.683854\pi\) | ||||
−0.546010 | + | 0.837778i | \(0.683854\pi\) | |||||||
\(48\) | 6.40622 | 0.924659 | ||||||||
\(49\) | 0.702360 | 0.100337 | ||||||||
\(50\) | 12.5805 | 1.77915 | ||||||||
\(51\) | −7.17546 | −1.00477 | ||||||||
\(52\) | −21.3055 | −2.95454 | ||||||||
\(53\) | −5.34627 | −0.734367 | −0.367183 | − | 0.930149i | \(-0.619678\pi\) | ||||
−0.367183 | + | 0.930149i | \(0.619678\pi\) | |||||||
\(54\) | 12.4833 | 1.69876 | ||||||||
\(55\) | 0.956891 | 0.129027 | ||||||||
\(56\) | 16.8314 | 2.24919 | ||||||||
\(57\) | 4.21962 | 0.558903 | ||||||||
\(58\) | 10.9703 | 1.44047 | ||||||||
\(59\) | −0.387777 | −0.0504843 | −0.0252421 | − | 0.999681i | \(-0.508036\pi\) | ||||
−0.0252421 | + | 0.999681i | \(0.508036\pi\) | |||||||
\(60\) | −0.697095 | −0.0899945 | ||||||||
\(61\) | 8.26994 | 1.05886 | 0.529429 | − | 0.848354i | \(-0.322406\pi\) | ||||
0.529429 | + | 0.848354i | \(0.322406\pi\) | |||||||
\(62\) | −15.8794 | −2.01669 | ||||||||
\(63\) | 5.66658 | 0.713922 | ||||||||
\(64\) | −1.89929 | −0.237411 | ||||||||
\(65\) | 0.784511 | 0.0973066 | ||||||||
\(66\) | 14.6310 | 1.80095 | ||||||||
\(67\) | −4.85640 | −0.593304 | −0.296652 | − | 0.954986i | \(-0.595870\pi\) | ||||
−0.296652 | + | 0.954986i | \(0.595870\pi\) | |||||||
\(68\) | −32.2362 | −3.90921 | ||||||||
\(69\) | 0.412671 | 0.0496797 | ||||||||
\(70\) | −1.13673 | −0.135865 | ||||||||
\(71\) | −12.5617 | −1.49080 | −0.745399 | − | 0.666618i | \(-0.767741\pi\) | ||||
−0.745399 | + | 0.666618i | \(0.767741\pi\) | |||||||
\(72\) | 12.3827 | 1.45932 | ||||||||
\(73\) | −6.31076 | −0.738618 | −0.369309 | − | 0.929307i | \(-0.620406\pi\) | ||||
−0.369309 | + | 0.929307i | \(0.620406\pi\) | |||||||
\(74\) | 7.07642 | 0.822617 | ||||||||
\(75\) | −4.86876 | −0.562196 | ||||||||
\(76\) | 18.9569 | 2.17451 | ||||||||
\(77\) | 16.3999 | 1.86894 | ||||||||
\(78\) | 11.9953 | 1.35820 | ||||||||
\(79\) | 11.4447 | 1.28763 | 0.643816 | − | 0.765180i | \(-0.277350\pi\) | ||||
0.643816 | + | 0.765180i | \(0.277350\pi\) | |||||||
\(80\) | −1.05975 | −0.118484 | ||||||||
\(81\) | 1.29421 | 0.143802 | ||||||||
\(82\) | −1.98598 | −0.219315 | ||||||||
\(83\) | 2.64018 | 0.289797 | 0.144898 | − | 0.989447i | \(-0.453714\pi\) | ||||
0.144898 | + | 0.989447i | \(0.453714\pi\) | |||||||
\(84\) | −11.9473 | −1.30356 | ||||||||
\(85\) | 1.18700 | 0.128748 | ||||||||
\(86\) | 5.50513 | 0.593634 | ||||||||
\(87\) | −4.24560 | −0.455176 | ||||||||
\(88\) | 35.8374 | 3.82028 | ||||||||
\(89\) | −3.89044 | −0.412385 | −0.206193 | − | 0.978511i | \(-0.566107\pi\) | ||||
−0.206193 | + | 0.978511i | \(0.566107\pi\) | |||||||
\(90\) | −0.836286 | −0.0881522 | ||||||||
\(91\) | 13.4455 | 1.40947 | ||||||||
\(92\) | 1.85395 | 0.193287 | ||||||||
\(93\) | 6.14547 | 0.637255 | ||||||||
\(94\) | 18.9362 | 1.95312 | ||||||||
\(95\) | −0.698031 | −0.0716165 | ||||||||
\(96\) | −4.33043 | −0.441973 | ||||||||
\(97\) | −6.96996 | −0.707692 | −0.353846 | − | 0.935304i | \(-0.615126\pi\) | ||||
−0.353846 | + | 0.935304i | \(0.615126\pi\) | |||||||
\(98\) | −1.77653 | −0.179456 | ||||||||
\(99\) | 12.0653 | 1.21261 | ||||||||
\(100\) | −21.8732 | −2.18732 | ||||||||
\(101\) | 10.6031 | 1.05505 | 0.527523 | − | 0.849541i | \(-0.323121\pi\) | ||||
0.527523 | + | 0.849541i | \(0.323121\pi\) | |||||||
\(102\) | 18.1494 | 1.79706 | ||||||||
\(103\) | −8.56052 | −0.843493 | −0.421746 | − | 0.906714i | \(-0.638583\pi\) | ||||
−0.421746 | + | 0.906714i | \(0.638583\pi\) | |||||||
\(104\) | 29.3815 | 2.88109 | ||||||||
\(105\) | 0.439924 | 0.0429322 | ||||||||
\(106\) | 13.5227 | 1.31344 | ||||||||
\(107\) | 11.3294 | 1.09526 | 0.547628 | − | 0.836722i | \(-0.315531\pi\) | ||||
0.547628 | + | 0.836722i | \(0.315531\pi\) | |||||||
\(108\) | −21.7041 | −2.08848 | ||||||||
\(109\) | −13.8526 | −1.32684 | −0.663421 | − | 0.748247i | \(-0.730896\pi\) | ||||
−0.663421 | + | 0.748247i | \(0.730896\pi\) | |||||||
\(110\) | −2.42033 | −0.230769 | ||||||||
\(111\) | −2.73863 | −0.259939 | ||||||||
\(112\) | −18.1627 | −1.71622 | ||||||||
\(113\) | 5.60689 | 0.527452 | 0.263726 | − | 0.964598i | \(-0.415048\pi\) | ||||
0.263726 | + | 0.964598i | \(0.415048\pi\) | |||||||
\(114\) | −10.6730 | −0.999616 | ||||||||
\(115\) | −0.0682660 | −0.00636584 | ||||||||
\(116\) | −19.0736 | −1.77094 | ||||||||
\(117\) | 9.89179 | 0.914496 | ||||||||
\(118\) | 0.980831 | 0.0902928 | ||||||||
\(119\) | 20.3437 | 1.86490 | ||||||||
\(120\) | 0.961332 | 0.0877572 | ||||||||
\(121\) | 23.9187 | 2.17443 | ||||||||
\(122\) | −20.9177 | −1.89380 | ||||||||
\(123\) | 0.768590 | 0.0693015 | ||||||||
\(124\) | 27.6089 | 2.47935 | ||||||||
\(125\) | 1.61508 | 0.144457 | ||||||||
\(126\) | −14.3329 | −1.27687 | ||||||||
\(127\) | 12.1835 | 1.08111 | 0.540555 | − | 0.841309i | \(-0.318214\pi\) | ||||
0.540555 | + | 0.841309i | \(0.318214\pi\) | |||||||
\(128\) | 13.6517 | 1.20665 | ||||||||
\(129\) | −2.13053 | −0.187583 | ||||||||
\(130\) | −1.98432 | −0.174036 | ||||||||
\(131\) | −3.49359 | −0.305237 | −0.152618 | − | 0.988285i | \(-0.548771\pi\) | ||||
−0.152618 | + | 0.988285i | \(0.548771\pi\) | |||||||
\(132\) | −25.4383 | −2.21412 | ||||||||
\(133\) | −11.9634 | −1.03735 | ||||||||
\(134\) | 12.2836 | 1.06114 | ||||||||
\(135\) | 0.799189 | 0.0687833 | ||||||||
\(136\) | 44.4555 | 3.81202 | ||||||||
\(137\) | 2.76726 | 0.236423 | 0.118212 | − | 0.992988i | \(-0.462284\pi\) | ||||
0.118212 | + | 0.992988i | \(0.462284\pi\) | |||||||
\(138\) | −1.04380 | −0.0888539 | ||||||||
\(139\) | 6.93485 | 0.588206 | 0.294103 | − | 0.955774i | \(-0.404979\pi\) | ||||
0.294103 | + | 0.955774i | \(0.404979\pi\) | |||||||
\(140\) | 1.97638 | 0.167035 | ||||||||
\(141\) | −7.32845 | −0.617167 | ||||||||
\(142\) | 31.7732 | 2.66634 | ||||||||
\(143\) | 28.6283 | 2.39401 | ||||||||
\(144\) | −13.3622 | −1.11352 | ||||||||
\(145\) | 0.702327 | 0.0583251 | ||||||||
\(146\) | 15.9622 | 1.32104 | ||||||||
\(147\) | 0.687531 | 0.0567066 | ||||||||
\(148\) | −12.3035 | −1.01134 | ||||||||
\(149\) | −8.29142 | −0.679259 | −0.339630 | − | 0.940559i | \(-0.610302\pi\) | ||||
−0.339630 | + | 0.940559i | \(0.610302\pi\) | |||||||
\(150\) | 12.3149 | 1.00551 | ||||||||
\(151\) | 1.74227 | 0.141784 | 0.0708919 | − | 0.997484i | \(-0.477415\pi\) | ||||
0.0708919 | + | 0.997484i | \(0.477415\pi\) | |||||||
\(152\) | −26.1426 | −2.12045 | ||||||||
\(153\) | 14.9667 | 1.20999 | ||||||||
\(154\) | −41.4814 | −3.34267 | ||||||||
\(155\) | −1.01661 | −0.0816564 | ||||||||
\(156\) | −20.8557 | −1.66979 | ||||||||
\(157\) | −19.0365 | −1.51928 | −0.759639 | − | 0.650345i | \(-0.774624\pi\) | ||||
−0.759639 | + | 0.650345i | \(0.774624\pi\) | |||||||
\(158\) | −28.9479 | −2.30297 | ||||||||
\(159\) | −5.23339 | −0.415035 | ||||||||
\(160\) | 0.716362 | 0.0566334 | ||||||||
\(161\) | −1.16999 | −0.0922084 | ||||||||
\(162\) | −3.27354 | −0.257194 | ||||||||
\(163\) | 6.52152 | 0.510805 | 0.255402 | − | 0.966835i | \(-0.417792\pi\) | ||||
0.255402 | + | 0.966835i | \(0.417792\pi\) | |||||||
\(164\) | 3.45294 | 0.269629 | ||||||||
\(165\) | 0.936688 | 0.0729211 | ||||||||
\(166\) | −6.67798 | −0.518311 | ||||||||
\(167\) | 1.85396 | 0.143464 | 0.0717320 | − | 0.997424i | \(-0.477147\pi\) | ||||
0.0717320 | + | 0.997424i | \(0.477147\pi\) | |||||||
\(168\) | 16.4760 | 1.27115 | ||||||||
\(169\) | 10.4710 | 0.805460 | ||||||||
\(170\) | −3.00236 | −0.230270 | ||||||||
\(171\) | −8.80137 | −0.673058 | ||||||||
\(172\) | −9.57154 | −0.729823 | ||||||||
\(173\) | 3.33392 | 0.253473 | 0.126737 | − | 0.991936i | \(-0.459550\pi\) | ||||
0.126737 | + | 0.991936i | \(0.459550\pi\) | |||||||
\(174\) | 10.7387 | 0.814097 | ||||||||
\(175\) | 13.8038 | 1.04347 | ||||||||
\(176\) | −38.6722 | −2.91503 | ||||||||
\(177\) | −0.379590 | −0.0285317 | ||||||||
\(178\) | 9.84035 | 0.737565 | ||||||||
\(179\) | −17.8353 | −1.33307 | −0.666535 | − | 0.745473i | \(-0.732223\pi\) | ||||
−0.666535 | + | 0.745473i | \(0.732223\pi\) | |||||||
\(180\) | 1.45401 | 0.108376 | ||||||||
\(181\) | −4.80281 | −0.356990 | −0.178495 | − | 0.983941i | \(-0.557123\pi\) | ||||
−0.178495 | + | 0.983941i | \(0.557123\pi\) | |||||||
\(182\) | −34.0087 | −2.52089 | ||||||||
\(183\) | 8.09533 | 0.598424 | ||||||||
\(184\) | −2.55670 | −0.188482 | ||||||||
\(185\) | 0.453038 | 0.0333080 | ||||||||
\(186\) | −15.5441 | −1.13975 | ||||||||
\(187\) | 43.3158 | 3.16757 | ||||||||
\(188\) | −32.9235 | −2.40119 | ||||||||
\(189\) | 13.6971 | 0.996317 | ||||||||
\(190\) | 1.76558 | 0.128088 | ||||||||
\(191\) | −5.30196 | −0.383637 | −0.191818 | − | 0.981430i | \(-0.561438\pi\) | ||||
−0.191818 | + | 0.981430i | \(0.561438\pi\) | |||||||
\(192\) | −1.85918 | −0.134175 | ||||||||
\(193\) | −7.62107 | −0.548577 | −0.274288 | − | 0.961647i | \(-0.588442\pi\) | ||||
−0.274288 | + | 0.961647i | \(0.588442\pi\) | |||||||
\(194\) | 17.6296 | 1.26573 | ||||||||
\(195\) | 0.767947 | 0.0549938 | ||||||||
\(196\) | 3.08877 | 0.220627 | ||||||||
\(197\) | −9.54886 | −0.680328 | −0.340164 | − | 0.940366i | \(-0.610483\pi\) | ||||
−0.340164 | + | 0.940366i | \(0.610483\pi\) | |||||||
\(198\) | −30.5176 | −2.16879 | ||||||||
\(199\) | −2.40958 | −0.170810 | −0.0854052 | − | 0.996346i | \(-0.527218\pi\) | ||||
−0.0854052 | + | 0.996346i | \(0.527218\pi\) | |||||||
\(200\) | 30.1644 | 2.13294 | ||||||||
\(201\) | −4.75386 | −0.335312 | ||||||||
\(202\) | −26.8191 | −1.88698 | ||||||||
\(203\) | 12.0370 | 0.844832 | ||||||||
\(204\) | −31.5555 | −2.20933 | ||||||||
\(205\) | −0.127144 | −0.00888012 | ||||||||
\(206\) | 21.6527 | 1.50862 | ||||||||
\(207\) | −0.860757 | −0.0598267 | ||||||||
\(208\) | −31.7055 | −2.19838 | ||||||||
\(209\) | −25.4724 | −1.76197 | ||||||||
\(210\) | −1.11273 | −0.0767856 | ||||||||
\(211\) | 19.4546 | 1.33931 | 0.669656 | − | 0.742671i | \(-0.266441\pi\) | ||||
0.669656 | + | 0.742671i | \(0.266441\pi\) | |||||||
\(212\) | −23.5113 | −1.61476 | ||||||||
\(213\) | −12.2965 | −0.842541 | ||||||||
\(214\) | −28.6563 | −1.95890 | ||||||||
\(215\) | 0.352443 | 0.0240364 | ||||||||
\(216\) | 29.9312 | 2.03656 | ||||||||
\(217\) | −17.4235 | −1.18278 | ||||||||
\(218\) | 35.0384 | 2.37310 | ||||||||
\(219\) | −6.17752 | −0.417438 | ||||||||
\(220\) | 4.20813 | 0.283712 | ||||||||
\(221\) | 35.5126 | 2.38884 | ||||||||
\(222\) | 6.92701 | 0.464910 | ||||||||
\(223\) | 22.5652 | 1.51108 | 0.755540 | − | 0.655102i | \(-0.227374\pi\) | ||||
0.755540 | + | 0.655102i | \(0.227374\pi\) | |||||||
\(224\) | 12.2775 | 0.820327 | ||||||||
\(225\) | 10.1554 | 0.677024 | ||||||||
\(226\) | −14.1819 | −0.943366 | ||||||||
\(227\) | 26.5079 | 1.75939 | 0.879697 | − | 0.475535i | \(-0.157746\pi\) | ||||
0.879697 | + | 0.475535i | \(0.157746\pi\) | |||||||
\(228\) | 18.5567 | 1.22894 | ||||||||
\(229\) | −18.6626 | −1.23326 | −0.616630 | − | 0.787253i | \(-0.711503\pi\) | ||||
−0.616630 | + | 0.787253i | \(0.711503\pi\) | |||||||
\(230\) | 0.172670 | 0.0113855 | ||||||||
\(231\) | 16.0536 | 1.05625 | ||||||||
\(232\) | 26.3035 | 1.72691 | ||||||||
\(233\) | −0.0871996 | −0.00571263 | −0.00285632 | − | 0.999996i | \(-0.500909\pi\) | ||||
−0.00285632 | + | 0.999996i | \(0.500909\pi\) | |||||||
\(234\) | −25.0200 | −1.63561 | ||||||||
\(235\) | 1.21231 | 0.0790823 | ||||||||
\(236\) | −1.70533 | −0.111007 | ||||||||
\(237\) | 11.2031 | 0.727719 | ||||||||
\(238\) | −51.4566 | −3.33544 | ||||||||
\(239\) | −19.4038 | −1.25513 | −0.627563 | − | 0.778566i | \(-0.715947\pi\) | ||||
−0.627563 | + | 0.778566i | \(0.715947\pi\) | |||||||
\(240\) | −1.03737 | −0.0669622 | ||||||||
\(241\) | 24.5488 | 1.58133 | 0.790665 | − | 0.612250i | \(-0.209735\pi\) | ||||
0.790665 | + | 0.612250i | \(0.209735\pi\) | |||||||
\(242\) | −60.4993 | −3.88904 | ||||||||
\(243\) | 16.0729 | 1.03108 | ||||||||
\(244\) | 36.3688 | 2.32827 | ||||||||
\(245\) | −0.113735 | −0.00726625 | ||||||||
\(246\) | −1.94405 | −0.123948 | ||||||||
\(247\) | −20.8837 | −1.32880 | ||||||||
\(248\) | −38.0742 | −2.41771 | ||||||||
\(249\) | 2.58443 | 0.163782 | ||||||||
\(250\) | −4.08512 | −0.258366 | ||||||||
\(251\) | −26.3471 | −1.66301 | −0.831507 | − | 0.555515i | \(-0.812521\pi\) | ||||
−0.831507 | + | 0.555515i | \(0.812521\pi\) | |||||||
\(252\) | 24.9200 | 1.56981 | ||||||||
\(253\) | −2.49115 | −0.156618 | ||||||||
\(254\) | −30.8165 | −1.93360 | ||||||||
\(255\) | 1.16194 | 0.0727634 | ||||||||
\(256\) | −30.7315 | −1.92072 | ||||||||
\(257\) | −26.5632 | −1.65697 | −0.828484 | − | 0.560013i | \(-0.810796\pi\) | ||||
−0.828484 | + | 0.560013i | \(0.810796\pi\) | |||||||
\(258\) | 5.38890 | 0.335498 | ||||||||
\(259\) | 7.76449 | 0.482462 | ||||||||
\(260\) | 3.45005 | 0.213963 | ||||||||
\(261\) | 8.85555 | 0.548145 | ||||||||
\(262\) | 8.83658 | 0.545926 | ||||||||
\(263\) | −29.8178 | −1.83864 | −0.919321 | − | 0.393508i | \(-0.871261\pi\) | ||||
−0.919321 | + | 0.393508i | \(0.871261\pi\) | |||||||
\(264\) | 35.0808 | 2.15907 | ||||||||
\(265\) | 0.865734 | 0.0531816 | ||||||||
\(266\) | 30.2597 | 1.85534 | ||||||||
\(267\) | −3.80830 | −0.233064 | ||||||||
\(268\) | −21.3570 | −1.30459 | ||||||||
\(269\) | −21.3456 | −1.30147 | −0.650733 | − | 0.759307i | \(-0.725538\pi\) | ||||
−0.650733 | + | 0.759307i | \(0.725538\pi\) | |||||||
\(270\) | −2.02144 | −0.123021 | ||||||||
\(271\) | −1.41354 | −0.0858666 | −0.0429333 | − | 0.999078i | \(-0.513670\pi\) | ||||
−0.0429333 | + | 0.999078i | \(0.513670\pi\) | |||||||
\(272\) | −47.9719 | −2.90872 | ||||||||
\(273\) | 13.1616 | 0.796578 | ||||||||
\(274\) | −6.99943 | −0.422851 | ||||||||
\(275\) | 29.3911 | 1.77235 | ||||||||
\(276\) | 1.81480 | 0.109238 | ||||||||
\(277\) | −31.9542 | −1.91994 | −0.959972 | − | 0.280097i | \(-0.909633\pi\) | ||||
−0.959972 | + | 0.280097i | \(0.909633\pi\) | |||||||
\(278\) | −17.5408 | −1.05203 | ||||||||
\(279\) | −12.8183 | −0.767414 | ||||||||
\(280\) | −2.72554 | −0.162882 | ||||||||
\(281\) | 8.01829 | 0.478331 | 0.239165 | − | 0.970979i | \(-0.423126\pi\) | ||||
0.239165 | + | 0.970979i | \(0.423126\pi\) | |||||||
\(282\) | 18.5364 | 1.10382 | ||||||||
\(283\) | 11.5504 | 0.686598 | 0.343299 | − | 0.939226i | \(-0.388456\pi\) | ||||
0.343299 | + | 0.939226i | \(0.388456\pi\) | |||||||
\(284\) | −55.2426 | −3.27805 | ||||||||
\(285\) | −0.683293 | −0.0404748 | ||||||||
\(286\) | −72.4114 | −4.28178 | ||||||||
\(287\) | −2.17909 | −0.128627 | ||||||||
\(288\) | 9.03250 | 0.532245 | ||||||||
\(289\) | 36.7322 | 2.16072 | ||||||||
\(290\) | −1.77644 | −0.104316 | ||||||||
\(291\) | −6.82280 | −0.399960 | ||||||||
\(292\) | −27.7529 | −1.62411 | ||||||||
\(293\) | −16.5509 | −0.966916 | −0.483458 | − | 0.875368i | \(-0.660619\pi\) | ||||
−0.483458 | + | 0.875368i | \(0.660619\pi\) | |||||||
\(294\) | −1.73902 | −0.101422 | ||||||||
\(295\) | 0.0627936 | 0.00365598 | ||||||||
\(296\) | 16.9672 | 0.986196 | ||||||||
\(297\) | 29.1639 | 1.69226 | ||||||||
\(298\) | 20.9721 | 1.21488 | ||||||||
\(299\) | −2.04238 | −0.118114 | ||||||||
\(300\) | −21.4114 | −1.23619 | ||||||||
\(301\) | 6.04043 | 0.348164 | ||||||||
\(302\) | −4.40684 | −0.253585 | ||||||||
\(303\) | 10.3792 | 0.596270 | ||||||||
\(304\) | 28.2105 | 1.61798 | ||||||||
\(305\) | −1.33917 | −0.0766807 | ||||||||
\(306\) | −37.8563 | −2.16410 | ||||||||
\(307\) | 7.92647 | 0.452388 | 0.226194 | − | 0.974082i | \(-0.427372\pi\) | ||||
0.226194 | + | 0.974082i | \(0.427372\pi\) | |||||||
\(308\) | 72.1219 | 4.10953 | ||||||||
\(309\) | −8.37977 | −0.476709 | ||||||||
\(310\) | 2.57139 | 0.146045 | ||||||||
\(311\) | −14.3157 | −0.811769 | −0.405884 | − | 0.913924i | \(-0.633036\pi\) | ||||
−0.405884 | + | 0.913924i | \(0.633036\pi\) | |||||||
\(312\) | 28.7611 | 1.62828 | ||||||||
\(313\) | 8.01698 | 0.453147 | 0.226573 | − | 0.973994i | \(-0.427248\pi\) | ||||
0.226573 | + | 0.973994i | \(0.427248\pi\) | |||||||
\(314\) | 48.1503 | 2.71728 | ||||||||
\(315\) | −0.917602 | −0.0517010 | ||||||||
\(316\) | 50.3305 | 2.83131 | ||||||||
\(317\) | −9.23607 | −0.518749 | −0.259375 | − | 0.965777i | \(-0.583516\pi\) | ||||
−0.259375 | + | 0.965777i | \(0.583516\pi\) | |||||||
\(318\) | 13.2372 | 0.742304 | ||||||||
\(319\) | 25.6292 | 1.43496 | ||||||||
\(320\) | 0.307556 | 0.0171929 | ||||||||
\(321\) | 11.0902 | 0.618996 | ||||||||
\(322\) | 2.95934 | 0.164918 | ||||||||
\(323\) | −31.5979 | −1.75816 | ||||||||
\(324\) | 5.69157 | 0.316198 | ||||||||
\(325\) | 24.0964 | 1.33663 | ||||||||
\(326\) | −16.4953 | −0.913591 | ||||||||
\(327\) | −13.5602 | −0.749878 | ||||||||
\(328\) | −4.76179 | −0.262926 | ||||||||
\(329\) | 20.7774 | 1.14550 | ||||||||
\(330\) | −2.36923 | −0.130422 | ||||||||
\(331\) | −10.3689 | −0.569924 | −0.284962 | − | 0.958539i | \(-0.591981\pi\) | ||||
−0.284962 | + | 0.958539i | \(0.591981\pi\) | |||||||
\(332\) | 11.6107 | 0.637221 | ||||||||
\(333\) | 5.71229 | 0.313032 | ||||||||
\(334\) | −4.68935 | −0.256590 | ||||||||
\(335\) | 0.786408 | 0.0429660 | ||||||||
\(336\) | −17.7793 | −0.969939 | ||||||||
\(337\) | −19.9650 | −1.08756 | −0.543781 | − | 0.839227i | \(-0.683008\pi\) | ||||
−0.543781 | + | 0.839227i | \(0.683008\pi\) | |||||||
\(338\) | −26.4850 | −1.44059 | ||||||||
\(339\) | 5.48851 | 0.298095 | ||||||||
\(340\) | 5.22007 | 0.283098 | ||||||||
\(341\) | −37.0981 | −2.00898 | ||||||||
\(342\) | 22.2619 | 1.20379 | ||||||||
\(343\) | 17.4779 | 0.943719 | ||||||||
\(344\) | 13.1997 | 0.711679 | ||||||||
\(345\) | −0.0668247 | −0.00359772 | ||||||||
\(346\) | −8.43271 | −0.453345 | ||||||||
\(347\) | −17.6524 | −0.947630 | −0.473815 | − | 0.880624i | \(-0.657123\pi\) | ||||
−0.473815 | + | 0.880624i | \(0.657123\pi\) | |||||||
\(348\) | −18.6709 | −1.00086 | ||||||||
\(349\) | 26.8928 | 1.43954 | 0.719770 | − | 0.694213i | \(-0.244247\pi\) | ||||
0.719770 | + | 0.694213i | \(0.244247\pi\) | |||||||
\(350\) | −34.9149 | −1.86628 | ||||||||
\(351\) | 23.9101 | 1.27623 | ||||||||
\(352\) | 26.1414 | 1.39334 | ||||||||
\(353\) | 29.0029 | 1.54367 | 0.771834 | − | 0.635824i | \(-0.219339\pi\) | ||||
0.771834 | + | 0.635824i | \(0.219339\pi\) | |||||||
\(354\) | 0.960122 | 0.0510299 | ||||||||
\(355\) | 2.03414 | 0.107961 | ||||||||
\(356\) | −17.1090 | −0.906775 | ||||||||
\(357\) | 19.9141 | 1.05397 | ||||||||
\(358\) | 45.1120 | 2.38424 | ||||||||
\(359\) | 5.16606 | 0.272654 | 0.136327 | − | 0.990664i | \(-0.456470\pi\) | ||||
0.136327 | + | 0.990664i | \(0.456470\pi\) | |||||||
\(360\) | −2.00517 | −0.105682 | ||||||||
\(361\) | −0.418423 | −0.0220223 | ||||||||
\(362\) | 12.1481 | 0.638489 | ||||||||
\(363\) | 23.4137 | 1.22890 | ||||||||
\(364\) | 59.1294 | 3.09922 | ||||||||
\(365\) | 1.02192 | 0.0534895 | ||||||||
\(366\) | −20.4761 | −1.07030 | ||||||||
\(367\) | −13.2289 | −0.690543 | −0.345271 | − | 0.938503i | \(-0.612213\pi\) | ||||
−0.345271 | + | 0.938503i | \(0.612213\pi\) | |||||||
\(368\) | 2.75893 | 0.143819 | ||||||||
\(369\) | −1.60314 | −0.0834562 | ||||||||
\(370\) | −1.14590 | −0.0595725 | ||||||||
\(371\) | 14.8376 | 0.770329 | ||||||||
\(372\) | 27.0259 | 1.40123 | ||||||||
\(373\) | 6.43713 | 0.333302 | 0.166651 | − | 0.986016i | \(-0.446705\pi\) | ||||
0.166651 | + | 0.986016i | \(0.446705\pi\) | |||||||
\(374\) | −109.562 | −5.66530 | ||||||||
\(375\) | 1.58098 | 0.0816413 | ||||||||
\(376\) | 45.4033 | 2.34150 | ||||||||
\(377\) | 21.0122 | 1.08218 | ||||||||
\(378\) | −34.6450 | −1.78195 | ||||||||
\(379\) | 17.0804 | 0.877359 | 0.438679 | − | 0.898644i | \(-0.355446\pi\) | ||||
0.438679 | + | 0.898644i | \(0.355446\pi\) | |||||||
\(380\) | −3.06973 | −0.157474 | ||||||||
\(381\) | 11.9262 | 0.611000 | ||||||||
\(382\) | 13.4106 | 0.686147 | ||||||||
\(383\) | −3.91876 | −0.200239 | −0.100120 | − | 0.994975i | \(-0.531923\pi\) | ||||
−0.100120 | + | 0.994975i | \(0.531923\pi\) | |||||||
\(384\) | 13.3634 | 0.681950 | ||||||||
\(385\) | −2.65567 | −0.135346 | ||||||||
\(386\) | 19.2765 | 0.981148 | ||||||||
\(387\) | 4.44391 | 0.225896 | ||||||||
\(388\) | −30.6518 | −1.55611 | ||||||||
\(389\) | 8.48580 | 0.430247 | 0.215124 | − | 0.976587i | \(-0.430985\pi\) | ||||
0.215124 | + | 0.976587i | \(0.430985\pi\) | |||||||
\(390\) | −1.94242 | −0.0983583 | ||||||||
\(391\) | −3.09021 | −0.156279 | ||||||||
\(392\) | −4.25959 | −0.215142 | ||||||||
\(393\) | −3.41983 | −0.172508 | ||||||||
\(394\) | 24.1526 | 1.21679 | ||||||||
\(395\) | −1.85327 | −0.0932482 | ||||||||
\(396\) | 53.0597 | 2.66635 | ||||||||
\(397\) | −3.63753 | −0.182562 | −0.0912812 | − | 0.995825i | \(-0.529096\pi\) | ||||
−0.0912812 | + | 0.995825i | \(0.529096\pi\) | |||||||
\(398\) | 6.09471 | 0.305500 | ||||||||
\(399\) | −11.7108 | −0.586272 | ||||||||
\(400\) | −32.5504 | −1.62752 | ||||||||
\(401\) | −27.3949 | −1.36803 | −0.684017 | − | 0.729466i | \(-0.739769\pi\) | ||||
−0.684017 | + | 0.729466i | \(0.739769\pi\) | |||||||
\(402\) | 12.0243 | 0.599716 | ||||||||
\(403\) | −30.4150 | −1.51508 | ||||||||
\(404\) | 46.6292 | 2.31989 | ||||||||
\(405\) | −0.209575 | −0.0104139 | ||||||||
\(406\) | −30.4460 | −1.51101 | ||||||||
\(407\) | 16.5322 | 0.819470 | ||||||||
\(408\) | 43.5168 | 2.15440 | ||||||||
\(409\) | 14.7397 | 0.728833 | 0.364417 | − | 0.931236i | \(-0.381268\pi\) | ||||
0.364417 | + | 0.931236i | \(0.381268\pi\) | |||||||
\(410\) | 0.321594 | 0.0158824 | ||||||||
\(411\) | 2.70884 | 0.133617 | ||||||||
\(412\) | −37.6466 | −1.85472 | ||||||||
\(413\) | 1.07620 | 0.0529565 | ||||||||
\(414\) | 2.17717 | 0.107002 | ||||||||
\(415\) | −0.427529 | −0.0209866 | ||||||||
\(416\) | 21.4321 | 1.05079 | ||||||||
\(417\) | 6.78843 | 0.332431 | ||||||||
\(418\) | 64.4292 | 3.15133 | ||||||||
\(419\) | −23.6021 | −1.15304 | −0.576520 | − | 0.817083i | \(-0.695590\pi\) | ||||
−0.576520 | + | 0.817083i | \(0.695590\pi\) | |||||||
\(420\) | 1.93466 | 0.0944015 | ||||||||
\(421\) | 29.6978 | 1.44738 | 0.723691 | − | 0.690124i | \(-0.242444\pi\) | ||||
0.723691 | + | 0.690124i | \(0.242444\pi\) | |||||||
\(422\) | −49.2080 | −2.39541 | ||||||||
\(423\) | 15.2858 | 0.743222 | ||||||||
\(424\) | 32.4234 | 1.57462 | ||||||||
\(425\) | 36.4589 | 1.76852 | ||||||||
\(426\) | 31.1023 | 1.50691 | ||||||||
\(427\) | −22.9517 | −1.11071 | ||||||||
\(428\) | 49.8234 | 2.40831 | ||||||||
\(429\) | 28.0238 | 1.35300 | ||||||||
\(430\) | −0.891458 | −0.0429899 | ||||||||
\(431\) | 39.8240 | 1.91825 | 0.959127 | − | 0.282976i | \(-0.0913215\pi\) | ||||
0.959127 | + | 0.282976i | \(0.0913215\pi\) | |||||||
\(432\) | −32.2988 | −1.55398 | ||||||||
\(433\) | −12.4323 | −0.597457 | −0.298728 | − | 0.954338i | \(-0.596562\pi\) | ||||
−0.298728 | + | 0.954338i | \(0.596562\pi\) | |||||||
\(434\) | 44.0704 | 2.11544 | ||||||||
\(435\) | 0.687499 | 0.0329630 | ||||||||
\(436\) | −60.9198 | −2.91753 | ||||||||
\(437\) | 1.81724 | 0.0869304 | ||||||||
\(438\) | 15.6252 | 0.746602 | ||||||||
\(439\) | −30.3138 | −1.44680 | −0.723399 | − | 0.690430i | \(-0.757421\pi\) | ||||
−0.723399 | + | 0.690430i | \(0.757421\pi\) | |||||||
\(440\) | −5.80324 | −0.276659 | ||||||||
\(441\) | −1.43407 | −0.0682888 | ||||||||
\(442\) | −89.8245 | −4.27252 | ||||||||
\(443\) | 19.5072 | 0.926816 | 0.463408 | − | 0.886145i | \(-0.346627\pi\) | ||||
0.463408 | + | 0.886145i | \(0.346627\pi\) | |||||||
\(444\) | −12.0437 | −0.571568 | ||||||||
\(445\) | 0.629987 | 0.0298643 | ||||||||
\(446\) | −57.0758 | −2.70262 | ||||||||
\(447\) | −8.11636 | −0.383891 | ||||||||
\(448\) | 5.27111 | 0.249037 | ||||||||
\(449\) | −26.0914 | −1.23133 | −0.615666 | − | 0.788007i | \(-0.711113\pi\) | ||||
−0.615666 | + | 0.788007i | \(0.711113\pi\) | |||||||
\(450\) | −25.6867 | −1.21088 | ||||||||
\(451\) | −4.63972 | −0.218476 | ||||||||
\(452\) | 24.6575 | 1.15979 | ||||||||
\(453\) | 1.70548 | 0.0801306 | ||||||||
\(454\) | −67.0483 | −3.14673 | ||||||||
\(455\) | −2.17726 | −0.102072 | ||||||||
\(456\) | −25.5907 | −1.19839 | ||||||||
\(457\) | −21.3783 | −1.00003 | −0.500017 | − | 0.866015i | \(-0.666673\pi\) | ||||
−0.500017 | + | 0.866015i | \(0.666673\pi\) | |||||||
\(458\) | 47.2046 | 2.20573 | ||||||||
\(459\) | 36.1771 | 1.68860 | ||||||||
\(460\) | −0.300214 | −0.0139975 | ||||||||
\(461\) | −3.68909 | −0.171818 | −0.0859090 | − | 0.996303i | \(-0.527379\pi\) | ||||
−0.0859090 | + | 0.996303i | \(0.527379\pi\) | |||||||
\(462\) | −40.6056 | −1.88914 | ||||||||
\(463\) | 14.7447 | 0.685245 | 0.342623 | − | 0.939473i | \(-0.388685\pi\) | ||||
0.342623 | + | 0.939473i | \(0.388685\pi\) | |||||||
\(464\) | −28.3842 | −1.31770 | ||||||||
\(465\) | −0.995149 | −0.0461489 | ||||||||
\(466\) | 0.220560 | 0.0102172 | ||||||||
\(467\) | −23.1439 | −1.07097 | −0.535487 | − | 0.844544i | \(-0.679872\pi\) | ||||
−0.535487 | + | 0.844544i | \(0.679872\pi\) | |||||||
\(468\) | 43.5012 | 2.01084 | ||||||||
\(469\) | 13.4780 | 0.622357 | ||||||||
\(470\) | −3.06637 | −0.141441 | ||||||||
\(471\) | −18.6346 | −0.858636 | ||||||||
\(472\) | 2.35174 | 0.108248 | ||||||||
\(473\) | 12.8613 | 0.591363 | ||||||||
\(474\) | −28.3367 | −1.30155 | ||||||||
\(475\) | −21.4401 | −0.983741 | ||||||||
\(476\) | 89.4654 | 4.10064 | ||||||||
\(477\) | 10.9159 | 0.499806 | ||||||||
\(478\) | 49.0793 | 2.24483 | ||||||||
\(479\) | −16.5718 | −0.757186 | −0.378593 | − | 0.925563i | \(-0.623592\pi\) | ||||
−0.378593 | + | 0.925563i | \(0.623592\pi\) | |||||||
\(480\) | 0.701237 | 0.0320069 | ||||||||
\(481\) | 13.5540 | 0.618008 | ||||||||
\(482\) | −62.0930 | −2.82826 | ||||||||
\(483\) | −1.14529 | −0.0521125 | ||||||||
\(484\) | 105.188 | 4.78125 | ||||||||
\(485\) | 1.12866 | 0.0512499 | ||||||||
\(486\) | −40.6542 | −1.84411 | ||||||||
\(487\) | 35.5317 | 1.61010 | 0.805048 | − | 0.593210i | \(-0.202140\pi\) | ||||
0.805048 | + | 0.593210i | \(0.202140\pi\) | |||||||
\(488\) | −50.1545 | −2.27039 | ||||||||
\(489\) | 6.38383 | 0.288687 | ||||||||
\(490\) | 0.287677 | 0.0129959 | ||||||||
\(491\) | 4.57004 | 0.206243 | 0.103121 | − | 0.994669i | \(-0.467117\pi\) | ||||
0.103121 | + | 0.994669i | \(0.467117\pi\) | |||||||
\(492\) | 3.38003 | 0.152384 | ||||||||
\(493\) | 31.7924 | 1.43186 | ||||||||
\(494\) | 52.8225 | 2.37660 | ||||||||
\(495\) | −1.95376 | −0.0878151 | ||||||||
\(496\) | 41.0858 | 1.84481 | ||||||||
\(497\) | 34.8626 | 1.56380 | ||||||||
\(498\) | −6.53698 | −0.292929 | ||||||||
\(499\) | 7.29942 | 0.326767 | 0.163383 | − | 0.986563i | \(-0.447759\pi\) | ||||
0.163383 | + | 0.986563i | \(0.447759\pi\) | |||||||
\(500\) | 7.10263 | 0.317639 | ||||||||
\(501\) | 1.81482 | 0.0810801 | ||||||||
\(502\) | 66.6415 | 2.97436 | ||||||||
\(503\) | −16.8588 | −0.751699 | −0.375849 | − | 0.926681i | \(-0.622649\pi\) | ||||
−0.375849 | + | 0.926681i | \(0.622649\pi\) | |||||||
\(504\) | −34.3660 | −1.53078 | ||||||||
\(505\) | −1.71698 | −0.0764046 | ||||||||
\(506\) | 6.30105 | 0.280116 | ||||||||
\(507\) | 10.2499 | 0.455214 | ||||||||
\(508\) | 53.5794 | 2.37720 | ||||||||
\(509\) | 28.5617 | 1.26598 | 0.632989 | − | 0.774161i | \(-0.281828\pi\) | ||||
0.632989 | + | 0.774161i | \(0.281828\pi\) | |||||||
\(510\) | −2.93897 | −0.130140 | ||||||||
\(511\) | 17.5143 | 0.774788 | ||||||||
\(512\) | 50.4280 | 2.22862 | ||||||||
\(513\) | −21.2744 | −0.939288 | ||||||||
\(514\) | 67.1882 | 2.96354 | ||||||||
\(515\) | 1.38622 | 0.0610843 | ||||||||
\(516\) | −9.36945 | −0.412467 | ||||||||
\(517\) | 44.2394 | 1.94565 | ||||||||
\(518\) | −19.6393 | −0.862900 | ||||||||
\(519\) | 3.26353 | 0.143253 | ||||||||
\(520\) | −4.75781 | −0.208644 | ||||||||
\(521\) | 3.80707 | 0.166791 | 0.0833954 | − | 0.996517i | \(-0.473424\pi\) | ||||
0.0833954 | + | 0.996517i | \(0.473424\pi\) | |||||||
\(522\) | −22.3989 | −0.980375 | ||||||||
\(523\) | −6.09467 | −0.266501 | −0.133251 | − | 0.991082i | \(-0.542542\pi\) | ||||
−0.133251 | + | 0.991082i | \(0.542542\pi\) | |||||||
\(524\) | −15.3638 | −0.671170 | ||||||||
\(525\) | 13.5123 | 0.589727 | ||||||||
\(526\) | 75.4201 | 3.28847 | ||||||||
\(527\) | −46.0193 | −2.00463 | ||||||||
\(528\) | −37.8557 | −1.64746 | ||||||||
\(529\) | −22.8223 | −0.992273 | ||||||||
\(530\) | −2.18976 | −0.0951171 | ||||||||
\(531\) | 0.791756 | 0.0343593 | ||||||||
\(532\) | −52.6113 | −2.28099 | ||||||||
\(533\) | −3.80389 | −0.164765 | ||||||||
\(534\) | 9.63258 | 0.416843 | ||||||||
\(535\) | −1.83460 | −0.0793166 | ||||||||
\(536\) | 29.4525 | 1.27215 | ||||||||
\(537\) | −17.4587 | −0.753399 | ||||||||
\(538\) | 53.9909 | 2.32772 | ||||||||
\(539\) | −4.15039 | −0.178770 | ||||||||
\(540\) | 3.51460 | 0.151244 | ||||||||
\(541\) | −11.8661 | −0.510163 | −0.255081 | − | 0.966920i | \(-0.582102\pi\) | ||||
−0.255081 | + | 0.966920i | \(0.582102\pi\) | |||||||
\(542\) | 3.57537 | 0.153575 | ||||||||
\(543\) | −4.70141 | −0.201757 | ||||||||
\(544\) | 32.4277 | 1.39033 | ||||||||
\(545\) | 2.24319 | 0.0960876 | ||||||||
\(546\) | −33.2906 | −1.42471 | ||||||||
\(547\) | −30.5823 | −1.30760 | −0.653801 | − | 0.756666i | \(-0.726827\pi\) | ||||
−0.653801 | + | 0.756666i | \(0.726827\pi\) | |||||||
\(548\) | 12.1696 | 0.519860 | ||||||||
\(549\) | −16.8854 | −0.720652 | ||||||||
\(550\) | −74.3409 | −3.16991 | ||||||||
\(551\) | −18.6959 | −0.796474 | ||||||||
\(552\) | −2.50272 | −0.106523 | ||||||||
\(553\) | −31.7627 | −1.35069 | ||||||||
\(554\) | 80.8240 | 3.43388 | ||||||||
\(555\) | 0.443473 | 0.0188244 | ||||||||
\(556\) | 30.4974 | 1.29338 | ||||||||
\(557\) | 37.2546 | 1.57853 | 0.789265 | − | 0.614053i | \(-0.210462\pi\) | ||||
0.789265 | + | 0.614053i | \(0.210462\pi\) | |||||||
\(558\) | 32.4223 | 1.37255 | ||||||||
\(559\) | 10.5444 | 0.445980 | ||||||||
\(560\) | 2.94113 | 0.124286 | ||||||||
\(561\) | 42.4013 | 1.79018 | ||||||||
\(562\) | −20.2812 | −0.855511 | ||||||||
\(563\) | 28.2201 | 1.18933 | 0.594667 | − | 0.803972i | \(-0.297284\pi\) | ||||
0.594667 | + | 0.803972i | \(0.297284\pi\) | |||||||
\(564\) | −32.2284 | −1.35706 | ||||||||
\(565\) | −0.907937 | −0.0381972 | ||||||||
\(566\) | −29.2151 | −1.22800 | ||||||||
\(567\) | −3.59185 | −0.150843 | ||||||||
\(568\) | 76.1826 | 3.19655 | ||||||||
\(569\) | 15.5926 | 0.653677 | 0.326838 | − | 0.945080i | \(-0.394017\pi\) | ||||
0.326838 | + | 0.945080i | \(0.394017\pi\) | |||||||
\(570\) | 1.72830 | 0.0723905 | ||||||||
\(571\) | 31.4602 | 1.31657 | 0.658284 | − | 0.752770i | \(-0.271283\pi\) | ||||
0.658284 | + | 0.752770i | \(0.271283\pi\) | |||||||
\(572\) | 125.899 | 5.26409 | ||||||||
\(573\) | −5.19002 | −0.216816 | ||||||||
\(574\) | 5.51171 | 0.230054 | ||||||||
\(575\) | −2.09680 | −0.0874428 | ||||||||
\(576\) | 3.87793 | 0.161580 | ||||||||
\(577\) | −9.15920 | −0.381302 | −0.190651 | − | 0.981658i | \(-0.561060\pi\) | ||||
−0.190651 | + | 0.981658i | \(0.561060\pi\) | |||||||
\(578\) | −92.9092 | −3.86451 | ||||||||
\(579\) | −7.46017 | −0.310034 | ||||||||
\(580\) | 3.08863 | 0.128248 | ||||||||
\(581\) | −7.32731 | −0.303988 | ||||||||
\(582\) | 17.2574 | 0.715341 | ||||||||
\(583\) | 31.5922 | 1.30842 | ||||||||
\(584\) | 38.2727 | 1.58374 | ||||||||
\(585\) | −1.60180 | −0.0662263 | ||||||||
\(586\) | 41.8634 | 1.72936 | ||||||||
\(587\) | −45.2912 | −1.86937 | −0.934684 | − | 0.355479i | \(-0.884318\pi\) | ||||
−0.934684 | + | 0.355479i | \(0.884318\pi\) | |||||||
\(588\) | 3.02356 | 0.124689 | ||||||||
\(589\) | 27.0622 | 1.11508 | ||||||||
\(590\) | −0.158828 | −0.00653885 | ||||||||
\(591\) | −9.34725 | −0.384495 | ||||||||
\(592\) | −18.3093 | −0.752506 | ||||||||
\(593\) | 2.25231 | 0.0924914 | 0.0462457 | − | 0.998930i | \(-0.485274\pi\) | ||||
0.0462457 | + | 0.998930i | \(0.485274\pi\) | |||||||
\(594\) | −73.7662 | −3.02667 | ||||||||
\(595\) | −3.29430 | −0.135053 | ||||||||
\(596\) | −36.4632 | −1.49359 | ||||||||
\(597\) | −2.35870 | −0.0965352 | ||||||||
\(598\) | 5.16594 | 0.211251 | ||||||||
\(599\) | 43.0609 | 1.75942 | 0.879710 | − | 0.475510i | \(-0.157737\pi\) | ||||
0.879710 | + | 0.475510i | \(0.157737\pi\) | |||||||
\(600\) | 29.5275 | 1.20545 | ||||||||
\(601\) | −5.90362 | −0.240814 | −0.120407 | − | 0.992725i | \(-0.538420\pi\) | ||||
−0.120407 | + | 0.992725i | \(0.538420\pi\) | |||||||
\(602\) | −15.2785 | −0.622704 | ||||||||
\(603\) | 9.91571 | 0.403799 | ||||||||
\(604\) | 7.66198 | 0.311762 | ||||||||
\(605\) | −3.87321 | −0.157469 | ||||||||
\(606\) | −26.2528 | −1.06645 | ||||||||
\(607\) | −37.6439 | −1.52792 | −0.763960 | − | 0.645264i | \(-0.776747\pi\) | ||||
−0.763960 | + | 0.645264i | \(0.776747\pi\) | |||||||
\(608\) | −19.0695 | −0.773372 | ||||||||
\(609\) | 11.7829 | 0.477465 | ||||||||
\(610\) | 3.38726 | 0.137146 | ||||||||
\(611\) | 36.2698 | 1.46732 | ||||||||
\(612\) | 65.8192 | 2.66058 | ||||||||
\(613\) | 1.83469 | 0.0741023 | 0.0370511 | − | 0.999313i | \(-0.488204\pi\) | ||||
0.0370511 | + | 0.999313i | \(0.488204\pi\) | |||||||
\(614\) | −20.0490 | −0.809110 | ||||||||
\(615\) | −0.124460 | −0.00501869 | ||||||||
\(616\) | −99.4601 | −4.00736 | ||||||||
\(617\) | 6.79004 | 0.273357 | 0.136678 | − | 0.990615i | \(-0.456357\pi\) | ||||
0.136678 | + | 0.990615i | \(0.456357\pi\) | |||||||
\(618\) | 21.1955 | 0.852609 | ||||||||
\(619\) | −25.0593 | −1.00722 | −0.503609 | − | 0.863932i | \(-0.667995\pi\) | ||||
−0.503609 | + | 0.863932i | \(0.667995\pi\) | |||||||
\(620\) | −4.47077 | −0.179550 | ||||||||
\(621\) | −2.08060 | −0.0834914 | ||||||||
\(622\) | 36.2097 | 1.45188 | ||||||||
\(623\) | 10.7972 | 0.432580 | ||||||||
\(624\) | −31.0361 | −1.24244 | ||||||||
\(625\) | 24.6074 | 0.984294 | ||||||||
\(626\) | −20.2779 | −0.810468 | ||||||||
\(627\) | −24.9346 | −0.995793 | ||||||||
\(628\) | −83.7169 | −3.34067 | ||||||||
\(629\) | 20.5078 | 0.817698 | ||||||||
\(630\) | 2.32095 | 0.0924690 | ||||||||
\(631\) | −31.0347 | −1.23547 | −0.617736 | − | 0.786385i | \(-0.711950\pi\) | ||||
−0.617736 | + | 0.786385i | \(0.711950\pi\) | |||||||
\(632\) | −69.4086 | −2.76093 | ||||||||
\(633\) | 19.0439 | 0.756927 | ||||||||
\(634\) | 23.3614 | 0.927801 | ||||||||
\(635\) | −1.97290 | −0.0782921 | ||||||||
\(636\) | −23.0149 | −0.912601 | ||||||||
\(637\) | −3.40271 | −0.134820 | ||||||||
\(638\) | −64.8258 | −2.56648 | ||||||||
\(639\) | 25.6482 | 1.01463 | ||||||||
\(640\) | −2.21064 | −0.0873834 | ||||||||
\(641\) | 42.8225 | 1.69139 | 0.845694 | − | 0.533668i | \(-0.179187\pi\) | ||||
0.845694 | + | 0.533668i | \(0.179187\pi\) | |||||||
\(642\) | −28.0512 | −1.10709 | ||||||||
\(643\) | −48.7876 | −1.92399 | −0.961997 | − | 0.273060i | \(-0.911964\pi\) | ||||
−0.961997 | + | 0.273060i | \(0.911964\pi\) | |||||||
\(644\) | −5.14528 | −0.202753 | ||||||||
\(645\) | 0.345002 | 0.0135844 | ||||||||
\(646\) | 79.9228 | 3.14452 | ||||||||
\(647\) | −12.6130 | −0.495869 | −0.247934 | − | 0.968777i | \(-0.579752\pi\) | ||||
−0.247934 | + | 0.968777i | \(0.579752\pi\) | |||||||
\(648\) | −7.84899 | −0.308337 | ||||||||
\(649\) | 2.29145 | 0.0899475 | ||||||||
\(650\) | −60.9486 | −2.39060 | ||||||||
\(651\) | −17.0556 | −0.668461 | ||||||||
\(652\) | 28.6797 | 1.12318 | ||||||||
\(653\) | −18.2472 | −0.714067 | −0.357034 | − | 0.934091i | \(-0.616212\pi\) | ||||
−0.357034 | + | 0.934091i | \(0.616212\pi\) | |||||||
\(654\) | 34.2986 | 1.34118 | ||||||||
\(655\) | 0.565725 | 0.0221047 | ||||||||
\(656\) | 5.13845 | 0.200623 | ||||||||
\(657\) | 12.8852 | 0.502699 | ||||||||
\(658\) | −52.5538 | −2.04876 | ||||||||
\(659\) | −18.6429 | −0.726226 | −0.363113 | − | 0.931745i | \(-0.618286\pi\) | ||||
−0.363113 | + | 0.931745i | \(0.618286\pi\) | |||||||
\(660\) | 4.11928 | 0.160343 | ||||||||
\(661\) | 7.55350 | 0.293797 | 0.146899 | − | 0.989152i | \(-0.453071\pi\) | ||||
0.146899 | + | 0.989152i | \(0.453071\pi\) | |||||||
\(662\) | 26.2267 | 1.01933 | ||||||||
\(663\) | 34.7628 | 1.35008 | ||||||||
\(664\) | −16.0118 | −0.621379 | ||||||||
\(665\) | 1.93725 | 0.0751235 | ||||||||
\(666\) | −14.4485 | −0.559868 | ||||||||
\(667\) | −1.82843 | −0.0707970 | ||||||||
\(668\) | 8.15318 | 0.315456 | ||||||||
\(669\) | 22.0888 | 0.854003 | ||||||||
\(670\) | −1.98911 | −0.0768462 | ||||||||
\(671\) | −48.8688 | −1.88656 | ||||||||
\(672\) | 12.0183 | 0.463616 | ||||||||
\(673\) | −41.9897 | −1.61858 | −0.809292 | − | 0.587406i | \(-0.800149\pi\) | ||||
−0.809292 | + | 0.587406i | \(0.800149\pi\) | |||||||
\(674\) | 50.4988 | 1.94514 | ||||||||
\(675\) | 24.5472 | 0.944824 | ||||||||
\(676\) | 46.0483 | 1.77109 | ||||||||
\(677\) | −8.41749 | −0.323510 | −0.161755 | − | 0.986831i | \(-0.551716\pi\) | ||||
−0.161755 | + | 0.986831i | \(0.551716\pi\) | |||||||
\(678\) | −13.8825 | −0.533153 | ||||||||
\(679\) | 19.3438 | 0.742347 | ||||||||
\(680\) | −7.19877 | −0.276060 | ||||||||
\(681\) | 25.9483 | 0.994339 | ||||||||
\(682\) | 93.8348 | 3.59312 | ||||||||
\(683\) | −15.4750 | −0.592133 | −0.296066 | − | 0.955167i | \(-0.595675\pi\) | ||||
−0.296066 | + | 0.955167i | \(0.595675\pi\) | |||||||
\(684\) | −38.7058 | −1.47995 | ||||||||
\(685\) | −0.448109 | −0.0171214 | ||||||||
\(686\) | −44.2081 | −1.68787 | ||||||||
\(687\) | −18.2686 | −0.696990 | ||||||||
\(688\) | −14.2438 | −0.543039 | ||||||||
\(689\) | 25.9010 | 0.986750 | ||||||||
\(690\) | 0.169024 | 0.00643465 | ||||||||
\(691\) | 25.6059 | 0.974095 | 0.487048 | − | 0.873375i | \(-0.338074\pi\) | ||||
0.487048 | + | 0.873375i | \(0.338074\pi\) | |||||||
\(692\) | 14.6616 | 0.557350 | ||||||||
\(693\) | −33.4850 | −1.27199 | ||||||||
\(694\) | 44.6494 | 1.69487 | ||||||||
\(695\) | −1.12298 | −0.0425969 | ||||||||
\(696\) | 25.7482 | 0.975982 | ||||||||
\(697\) | −5.75546 | −0.218003 | ||||||||
\(698\) | −68.0218 | −2.57466 | ||||||||
\(699\) | −0.0853585 | −0.00322855 | ||||||||
\(700\) | 60.7050 | 2.29443 | ||||||||
\(701\) | −3.13580 | −0.118438 | −0.0592188 | − | 0.998245i | \(-0.518861\pi\) | ||||
−0.0592188 | + | 0.998245i | \(0.518861\pi\) | |||||||
\(702\) | −60.4775 | −2.28258 | ||||||||
\(703\) | −12.0599 | −0.454846 | ||||||||
\(704\) | 11.2233 | 0.422993 | ||||||||
\(705\) | 1.18671 | 0.0446942 | ||||||||
\(706\) | −73.3590 | −2.76090 | ||||||||
\(707\) | −29.4269 | −1.10671 | ||||||||
\(708\) | −1.66932 | −0.0627370 | ||||||||
\(709\) | 31.3755 | 1.17833 | 0.589165 | − | 0.808012i | \(-0.299457\pi\) | ||||
0.589165 | + | 0.808012i | \(0.299457\pi\) | |||||||
\(710\) | −5.14510 | −0.193092 | ||||||||
\(711\) | −23.3676 | −0.876355 | ||||||||
\(712\) | 23.5942 | 0.884232 | ||||||||
\(713\) | 2.64663 | 0.0991172 | ||||||||
\(714\) | −50.3702 | −1.88506 | ||||||||
\(715\) | −4.63584 | −0.173370 | ||||||||
\(716\) | −78.4343 | −2.93123 | ||||||||
\(717\) | −18.9941 | −0.709347 | ||||||||
\(718\) | −13.0669 | −0.487652 | ||||||||
\(719\) | −33.4250 | −1.24654 | −0.623271 | − | 0.782006i | \(-0.714197\pi\) | ||||
−0.623271 | + | 0.782006i | \(0.714197\pi\) | |||||||
\(720\) | 2.16378 | 0.0806392 | ||||||||
\(721\) | 23.7581 | 0.884798 | ||||||||
\(722\) | 1.05835 | 0.0393876 | ||||||||
\(723\) | 24.0305 | 0.893705 | ||||||||
\(724\) | −21.1214 | −0.784969 | ||||||||
\(725\) | 21.5721 | 0.801168 | ||||||||
\(726\) | −59.2219 | −2.19793 | ||||||||
\(727\) | 30.0575 | 1.11477 | 0.557385 | − | 0.830254i | \(-0.311805\pi\) | ||||
0.557385 | + | 0.830254i | \(0.311805\pi\) | |||||||
\(728\) | −81.5427 | −3.02218 | ||||||||
\(729\) | 11.8509 | 0.438922 | ||||||||
\(730\) | −2.58480 | −0.0956678 | ||||||||
\(731\) | 15.9541 | 0.590085 | ||||||||
\(732\) | 35.6009 | 1.31585 | ||||||||
\(733\) | 40.3323 | 1.48971 | 0.744853 | − | 0.667228i | \(-0.232519\pi\) | ||||
0.744853 | + | 0.667228i | \(0.232519\pi\) | |||||||
\(734\) | 33.4608 | 1.23506 | ||||||||
\(735\) | −0.111333 | −0.00410659 | ||||||||
\(736\) | −1.86496 | −0.0687435 | ||||||||
\(737\) | 28.6975 | 1.05709 | ||||||||
\(738\) | 4.05493 | 0.149264 | ||||||||
\(739\) | −21.2826 | −0.782895 | −0.391447 | − | 0.920201i | \(-0.628025\pi\) | ||||
−0.391447 | + | 0.920201i | \(0.628025\pi\) | |||||||
\(740\) | 1.99233 | 0.0732394 | ||||||||
\(741\) | −20.4427 | −0.750983 | ||||||||
\(742\) | −37.5297 | −1.37776 | ||||||||
\(743\) | 23.3360 | 0.856114 | 0.428057 | − | 0.903752i | \(-0.359198\pi\) | ||||
0.428057 | + | 0.903752i | \(0.359198\pi\) | |||||||
\(744\) | −37.2703 | −1.36639 | ||||||||
\(745\) | 1.34265 | 0.0491908 | ||||||||
\(746\) | −16.2819 | −0.596122 | ||||||||
\(747\) | −5.39066 | −0.197234 | ||||||||
\(748\) | 190.490 | 6.96501 | ||||||||
\(749\) | −31.4427 | −1.14889 | ||||||||
\(750\) | −3.99887 | −0.146018 | ||||||||
\(751\) | −29.3268 | −1.07015 | −0.535074 | − | 0.844805i | \(-0.679716\pi\) | ||||
−0.535074 | + | 0.844805i | \(0.679716\pi\) | |||||||
\(752\) | −48.9947 | −1.78665 | ||||||||
\(753\) | −25.7908 | −0.939869 | ||||||||
\(754\) | −53.1476 | −1.93552 | ||||||||
\(755\) | −0.282129 | −0.0102677 | ||||||||
\(756\) | 60.2358 | 2.19075 | ||||||||
\(757\) | 10.7547 | 0.390886 | 0.195443 | − | 0.980715i | \(-0.437386\pi\) | ||||
0.195443 | + | 0.980715i | \(0.437386\pi\) | |||||||
\(758\) | −43.2025 | −1.56919 | ||||||||
\(759\) | −2.43856 | −0.0885140 | ||||||||
\(760\) | 4.23333 | 0.153559 | ||||||||
\(761\) | 9.57577 | 0.347122 | 0.173561 | − | 0.984823i | \(-0.444473\pi\) | ||||
0.173561 | + | 0.984823i | \(0.444473\pi\) | |||||||
\(762\) | −30.1659 | −1.09279 | ||||||||
\(763\) | 38.4454 | 1.39182 | ||||||||
\(764\) | −23.3165 | −0.843560 | ||||||||
\(765\) | −2.42359 | −0.0876252 | ||||||||
\(766\) | 9.91198 | 0.358134 | ||||||||
\(767\) | 1.87866 | 0.0678344 | ||||||||
\(768\) | −30.0827 | −1.08551 | ||||||||
\(769\) | −53.5550 | −1.93124 | −0.965621 | − | 0.259955i | \(-0.916292\pi\) | ||||
−0.965621 | + | 0.259955i | \(0.916292\pi\) | |||||||
\(770\) | 6.71717 | 0.242070 | ||||||||
\(771\) | −26.0024 | −0.936453 | ||||||||
\(772\) | −33.5152 | −1.20624 | ||||||||
\(773\) | 20.2335 | 0.727750 | 0.363875 | − | 0.931448i | \(-0.381454\pi\) | ||||
0.363875 | + | 0.931448i | \(0.381454\pi\) | |||||||
\(774\) | −11.2403 | −0.404023 | ||||||||
\(775\) | −31.2255 | −1.12165 | ||||||||
\(776\) | 42.2706 | 1.51742 | ||||||||
\(777\) | 7.60056 | 0.272669 | ||||||||
\(778\) | −21.4637 | −0.769512 | ||||||||
\(779\) | 3.38457 | 0.121265 | ||||||||
\(780\) | 3.37720 | 0.120923 | ||||||||
\(781\) | 74.2297 | 2.65615 | ||||||||
\(782\) | 7.81629 | 0.279510 | ||||||||
\(783\) | 21.4054 | 0.764965 | ||||||||
\(784\) | 4.59652 | 0.164162 | ||||||||
\(785\) | 3.08262 | 0.110024 | ||||||||
\(786\) | 8.65001 | 0.308536 | ||||||||
\(787\) | −7.56890 | −0.269802 | −0.134901 | − | 0.990859i | \(-0.543072\pi\) | ||||
−0.134901 | + | 0.990859i | \(0.543072\pi\) | |||||||
\(788\) | −41.9931 | −1.49594 | ||||||||
\(789\) | −29.1882 | −1.03913 | ||||||||
\(790\) | 4.68760 | 0.166777 | ||||||||
\(791\) | −15.5609 | −0.553281 | ||||||||
\(792\) | −73.1722 | −2.60006 | ||||||||
\(793\) | −40.0653 | −1.42276 | ||||||||
\(794\) | 9.20065 | 0.326519 | ||||||||
\(795\) | 0.847455 | 0.0300561 | ||||||||
\(796\) | −10.5966 | −0.375587 | ||||||||
\(797\) | −55.9963 | −1.98349 | −0.991745 | − | 0.128229i | \(-0.959071\pi\) | ||||
−0.991745 | + | 0.128229i | \(0.959071\pi\) | |||||||
\(798\) | 29.6209 | 1.04857 | ||||||||
\(799\) | 54.8778 | 1.94144 | ||||||||
\(800\) | 22.0032 | 0.777930 | ||||||||
\(801\) | 7.94342 | 0.280667 | ||||||||
\(802\) | 69.2917 | 2.44678 | ||||||||
\(803\) | 37.2916 | 1.31599 | ||||||||
\(804\) | −20.9061 | −0.737301 | ||||||||
\(805\) | 0.189460 | 0.00667757 | ||||||||
\(806\) | 76.9308 | 2.70977 | ||||||||
\(807\) | −20.8949 | −0.735537 | ||||||||
\(808\) | −64.3043 | −2.26222 | ||||||||
\(809\) | −46.9221 | −1.64969 | −0.824846 | − | 0.565357i | \(-0.808738\pi\) | ||||
−0.824846 | + | 0.565357i | \(0.808738\pi\) | |||||||
\(810\) | 0.530092 | 0.0186255 | ||||||||
\(811\) | 26.6826 | 0.936953 | 0.468476 | − | 0.883476i | \(-0.344803\pi\) | ||||
0.468476 | + | 0.883476i | \(0.344803\pi\) | |||||||
\(812\) | 52.9352 | 1.85766 | ||||||||
\(813\) | −1.38370 | −0.0485284 | ||||||||
\(814\) | −41.8160 | −1.46565 | ||||||||
\(815\) | −1.05604 | −0.0369916 | ||||||||
\(816\) | −46.9590 | −1.64390 | ||||||||
\(817\) | −9.38203 | −0.328236 | ||||||||
\(818\) | −37.2822 | −1.30354 | ||||||||
\(819\) | −27.4528 | −0.959279 | ||||||||
\(820\) | −0.559142 | −0.0195261 | ||||||||
\(821\) | 5.80456 | 0.202581 | 0.101290 | − | 0.994857i | \(-0.467703\pi\) | ||||
0.101290 | + | 0.994857i | \(0.467703\pi\) | |||||||
\(822\) | −6.85165 | −0.238979 | ||||||||
\(823\) | −53.0223 | −1.84824 | −0.924120 | − | 0.382102i | \(-0.875200\pi\) | ||||
−0.924120 | + | 0.382102i | \(0.875200\pi\) | |||||||
\(824\) | 51.9168 | 1.80861 | ||||||||
\(825\) | 28.7705 | 1.00166 | ||||||||
\(826\) | −2.72211 | −0.0947144 | ||||||||
\(827\) | −52.3758 | −1.82129 | −0.910643 | − | 0.413194i | \(-0.864413\pi\) | ||||
−0.910643 | + | 0.413194i | \(0.864413\pi\) | |||||||
\(828\) | −3.78536 | −0.131550 | ||||||||
\(829\) | −12.1802 | −0.423035 | −0.211518 | − | 0.977374i | \(-0.567841\pi\) | ||||
−0.211518 | + | 0.977374i | \(0.567841\pi\) | |||||||
\(830\) | 1.08138 | 0.0375352 | ||||||||
\(831\) | −31.2796 | −1.08508 | ||||||||
\(832\) | 9.20144 | 0.319003 | ||||||||
\(833\) | −5.14846 | −0.178383 | ||||||||
\(834\) | −17.1704 | −0.594564 | ||||||||
\(835\) | −0.300216 | −0.0103894 | ||||||||
\(836\) | −112.020 | −3.87430 | ||||||||
\(837\) | −30.9841 | −1.07097 | ||||||||
\(838\) | 59.6985 | 2.06225 | ||||||||
\(839\) | 29.2163 | 1.00866 | 0.504330 | − | 0.863511i | \(-0.331740\pi\) | ||||
0.504330 | + | 0.863511i | \(0.331740\pi\) | |||||||
\(840\) | −2.66800 | −0.0920547 | ||||||||
\(841\) | −10.1890 | −0.351344 | ||||||||
\(842\) | −75.1167 | −2.58869 | ||||||||
\(843\) | 7.84899 | 0.270334 | ||||||||
\(844\) | 85.5558 | 2.94495 | ||||||||
\(845\) | −1.69559 | −0.0583300 | ||||||||
\(846\) | −38.6635 | −1.32928 | ||||||||
\(847\) | −66.3820 | −2.28091 | ||||||||
\(848\) | −34.9881 | −1.20150 | ||||||||
\(849\) | 11.3065 | 0.388038 | ||||||||
\(850\) | −92.2180 | −3.16305 | ||||||||
\(851\) | −1.17943 | −0.0404304 | ||||||||
\(852\) | −54.0763 | −1.85262 | ||||||||
\(853\) | −5.93669 | −0.203268 | −0.101634 | − | 0.994822i | \(-0.532407\pi\) | ||||
−0.101634 | + | 0.994822i | \(0.532407\pi\) | |||||||
\(854\) | 58.0532 | 1.98654 | ||||||||
\(855\) | 1.42523 | 0.0487417 | ||||||||
\(856\) | −68.7093 | −2.34844 | ||||||||
\(857\) | 29.0652 | 0.992847 | 0.496424 | − | 0.868080i | \(-0.334646\pi\) | ||||
0.496424 | + | 0.868080i | \(0.334646\pi\) | |||||||
\(858\) | −70.8825 | −2.41989 | ||||||||
\(859\) | −35.6817 | −1.21745 | −0.608723 | − | 0.793383i | \(-0.708318\pi\) | ||||
−0.608723 | + | 0.793383i | \(0.708318\pi\) | |||||||
\(860\) | 1.54994 | 0.0528525 | ||||||||
\(861\) | −2.13308 | −0.0726951 | ||||||||
\(862\) | −100.730 | −3.43086 | ||||||||
\(863\) | 22.4626 | 0.764636 | 0.382318 | − | 0.924031i | \(-0.375126\pi\) | ||||
0.382318 | + | 0.924031i | \(0.375126\pi\) | |||||||
\(864\) | 21.8331 | 0.742777 | ||||||||
\(865\) | −0.539869 | −0.0183561 | ||||||||
\(866\) | 31.4458 | 1.06857 | ||||||||
\(867\) | 35.9566 | 1.22115 | ||||||||
\(868\) | −76.6232 | −2.60076 | ||||||||
\(869\) | −67.6293 | −2.29417 | ||||||||
\(870\) | −1.73894 | −0.0589555 | ||||||||
\(871\) | 23.5277 | 0.797207 | ||||||||
\(872\) | 84.0118 | 2.84500 | ||||||||
\(873\) | 14.2311 | 0.481651 | ||||||||
\(874\) | −4.59647 | −0.155478 | ||||||||
\(875\) | −4.48234 | −0.151531 | ||||||||
\(876\) | −27.1669 | −0.917884 | ||||||||
\(877\) | −9.38224 | −0.316816 | −0.158408 | − | 0.987374i | \(-0.550636\pi\) | ||||
−0.158408 | + | 0.987374i | \(0.550636\pi\) | |||||||
\(878\) | 76.6747 | 2.58765 | ||||||||
\(879\) | −16.2015 | −0.546463 | ||||||||
\(880\) | 6.26228 | 0.211101 | ||||||||
\(881\) | −45.3864 | −1.52911 | −0.764554 | − | 0.644560i | \(-0.777041\pi\) | ||||
−0.764554 | + | 0.644560i | \(0.777041\pi\) | |||||||
\(882\) | 3.62728 | 0.122137 | ||||||||
\(883\) | 39.8325 | 1.34047 | 0.670235 | − | 0.742149i | \(-0.266193\pi\) | ||||
0.670235 | + | 0.742149i | \(0.266193\pi\) | |||||||
\(884\) | 156.174 | 5.25270 | ||||||||
\(885\) | 0.0614678 | 0.00206622 | ||||||||
\(886\) | −49.3409 | −1.65764 | ||||||||
\(887\) | −41.7081 | −1.40042 | −0.700211 | − | 0.713936i | \(-0.746911\pi\) | ||||
−0.700211 | + | 0.713936i | \(0.746911\pi\) | |||||||
\(888\) | 16.6089 | 0.557359 | ||||||||
\(889\) | −33.8130 | −1.13405 | ||||||||
\(890\) | −1.59347 | −0.0534132 | ||||||||
\(891\) | −7.64778 | −0.256210 | ||||||||
\(892\) | 99.2353 | 3.32264 | ||||||||
\(893\) | −32.2716 | −1.07993 | ||||||||
\(894\) | 20.5293 | 0.686601 | ||||||||
\(895\) | 2.88811 | 0.0965387 | ||||||||
\(896\) | −37.8876 | −1.26574 | ||||||||
\(897\) | −1.99926 | −0.0667534 | ||||||||
\(898\) | 65.9949 | 2.20228 | ||||||||
\(899\) | −27.2288 | −0.908132 | ||||||||
\(900\) | 44.6603 | 1.48868 | ||||||||
\(901\) | 39.1894 | 1.30559 | ||||||||
\(902\) | 11.7356 | 0.390751 | ||||||||
\(903\) | 5.91289 | 0.196769 | ||||||||
\(904\) | −34.0040 | −1.13096 | ||||||||
\(905\) | 0.777730 | 0.0258526 | ||||||||
\(906\) | −4.31380 | −0.143316 | ||||||||
\(907\) | −52.0669 | −1.72885 | −0.864426 | − | 0.502760i | \(-0.832318\pi\) | ||||
−0.864426 | + | 0.502760i | \(0.832318\pi\) | |||||||
\(908\) | 116.574 | 3.86865 | ||||||||
\(909\) | −21.6492 | −0.718057 | ||||||||
\(910\) | 5.50710 | 0.182559 | ||||||||
\(911\) | 49.2509 | 1.63176 | 0.815878 | − | 0.578224i | \(-0.196254\pi\) | ||||
0.815878 | + | 0.578224i | \(0.196254\pi\) | |||||||
\(912\) | 27.6149 | 0.914420 | ||||||||
\(913\) | −15.6013 | −0.516329 | ||||||||
\(914\) | 54.0736 | 1.78860 | ||||||||
\(915\) | −1.31090 | −0.0433369 | ||||||||
\(916\) | −82.0727 | −2.71176 | ||||||||
\(917\) | 9.69581 | 0.320184 | ||||||||
\(918\) | −91.5052 | −3.02012 | ||||||||
\(919\) | −21.4075 | −0.706169 | −0.353084 | − | 0.935591i | \(-0.614867\pi\) | ||||
−0.353084 | + | 0.935591i | \(0.614867\pi\) | |||||||
\(920\) | 0.414012 | 0.0136496 | ||||||||
\(921\) | 7.75912 | 0.255672 | ||||||||
\(922\) | 9.33106 | 0.307302 | ||||||||
\(923\) | 60.8575 | 2.00315 | ||||||||
\(924\) | 70.5992 | 2.32254 | ||||||||
\(925\) | 13.9151 | 0.457527 | ||||||||
\(926\) | −37.2948 | −1.22558 | ||||||||
\(927\) | 17.4787 | 0.574076 | ||||||||
\(928\) | 19.1869 | 0.629841 | ||||||||
\(929\) | −3.33104 | −0.109288 | −0.0546440 | − | 0.998506i | \(-0.517402\pi\) | ||||
−0.0546440 | + | 0.998506i | \(0.517402\pi\) | |||||||
\(930\) | 2.51710 | 0.0825389 | ||||||||
\(931\) | 3.02762 | 0.0992262 | ||||||||
\(932\) | −0.383478 | −0.0125612 | ||||||||
\(933\) | −14.0134 | −0.458780 | ||||||||
\(934\) | 58.5395 | 1.91547 | ||||||||
\(935\) | −7.01423 | −0.229390 | ||||||||
\(936\) | −59.9905 | −1.96085 | ||||||||
\(937\) | 10.5731 | 0.345407 | 0.172703 | − | 0.984974i | \(-0.444750\pi\) | ||||
0.172703 | + | 0.984974i | \(0.444750\pi\) | |||||||
\(938\) | −34.0909 | −1.11311 | ||||||||
\(939\) | 7.84772 | 0.256101 | ||||||||
\(940\) | 5.33137 | 0.173890 | ||||||||
\(941\) | 19.3227 | 0.629903 | 0.314952 | − | 0.949108i | \(-0.398012\pi\) | ||||
0.314952 | + | 0.949108i | \(0.398012\pi\) | |||||||
\(942\) | 47.1337 | 1.53570 | ||||||||
\(943\) | 0.331005 | 0.0107790 | ||||||||
\(944\) | −2.53777 | −0.0825973 | ||||||||
\(945\) | −2.21800 | −0.0721516 | ||||||||
\(946\) | −32.5310 | −1.05767 | ||||||||
\(947\) | 18.9656 | 0.616300 | 0.308150 | − | 0.951338i | \(-0.400290\pi\) | ||||
0.308150 | + | 0.951338i | \(0.400290\pi\) | |||||||
\(948\) | 49.2679 | 1.60015 | ||||||||
\(949\) | 30.5736 | 0.992462 | ||||||||
\(950\) | 54.2300 | 1.75945 | ||||||||
\(951\) | −9.04106 | −0.293177 | ||||||||
\(952\) | −123.378 | −3.99870 | ||||||||
\(953\) | 21.5103 | 0.696789 | 0.348394 | − | 0.937348i | \(-0.386727\pi\) | ||||
0.348394 | + | 0.937348i | \(0.386727\pi\) | |||||||
\(954\) | −27.6104 | −0.893919 | ||||||||
\(955\) | 0.858559 | 0.0277823 | ||||||||
\(956\) | −85.3320 | −2.75984 | ||||||||
\(957\) | 25.0881 | 0.810983 | ||||||||
\(958\) | 41.9163 | 1.35425 | ||||||||
\(959\) | −7.68002 | −0.248001 | ||||||||
\(960\) | 0.301062 | 0.00971673 | ||||||||
\(961\) | 8.41350 | 0.271403 | ||||||||
\(962\) | −34.2830 | −1.10533 | ||||||||
\(963\) | −23.1322 | −0.745425 | ||||||||
\(964\) | 107.959 | 3.47711 | ||||||||
\(965\) | 1.23410 | 0.0397270 | ||||||||
\(966\) | 2.89686 | 0.0932050 | ||||||||
\(967\) | 14.8608 | 0.477891 | 0.238946 | − | 0.971033i | \(-0.423198\pi\) | ||||
0.238946 | + | 0.971033i | \(0.423198\pi\) | |||||||
\(968\) | −145.059 | −4.66239 | ||||||||
\(969\) | −30.9308 | −0.993640 | ||||||||
\(970\) | −2.85480 | −0.0916621 | ||||||||
\(971\) | −0.00316838 | −0.000101678 0 | −5.08390e−5 | − | 1.00000i | \(-0.500016\pi\) | ||||
−5.08390e−5 | 1.00000i | \(0.500016\pi\) | ||||||||
\(972\) | 70.6838 | 2.26718 | ||||||||
\(973\) | −19.2464 | −0.617010 | ||||||||
\(974\) | −89.8728 | −2.87971 | ||||||||
\(975\) | 23.5876 | 0.755409 | ||||||||
\(976\) | 54.1218 | 1.73240 | ||||||||
\(977\) | 47.5620 | 1.52164 | 0.760822 | − | 0.648960i | \(-0.224796\pi\) | ||||
0.760822 | + | 0.648960i | \(0.224796\pi\) | |||||||
\(978\) | −16.1470 | −0.516326 | ||||||||
\(979\) | 22.9894 | 0.734744 | ||||||||
\(980\) | −0.500172 | −0.0159774 | ||||||||
\(981\) | 28.2840 | 0.903040 | ||||||||
\(982\) | −11.5593 | −0.368872 | ||||||||
\(983\) | 25.1112 | 0.800922 | 0.400461 | − | 0.916314i | \(-0.368850\pi\) | ||||
0.400461 | + | 0.916314i | \(0.368850\pi\) | |||||||
\(984\) | −4.66125 | −0.148595 | ||||||||
\(985\) | 1.54627 | 0.0492682 | ||||||||
\(986\) | −80.4147 | −2.56093 | ||||||||
\(987\) | 20.3387 | 0.647389 | ||||||||
\(988\) | −91.8402 | −2.92183 | ||||||||
\(989\) | −0.917544 | −0.0291762 | ||||||||
\(990\) | 4.94179 | 0.157060 | ||||||||
\(991\) | 7.27648 | 0.231145 | 0.115572 | − | 0.993299i | \(-0.463130\pi\) | ||||
0.115572 | + | 0.993299i | \(0.463130\pi\) | |||||||
\(992\) | −27.7729 | −0.881791 | ||||||||
\(993\) | −10.1499 | −0.322098 | ||||||||
\(994\) | −88.1804 | −2.79691 | ||||||||
\(995\) | 0.390188 | 0.0123698 | ||||||||
\(996\) | 11.3656 | 0.360132 | ||||||||
\(997\) | −26.3317 | −0.833932 | −0.416966 | − | 0.908922i | \(-0.636907\pi\) | ||||
−0.416966 | + | 0.908922i | \(0.636907\pi\) | |||||||
\(998\) | −18.4629 | −0.584434 | ||||||||
\(999\) | 13.8076 | 0.436853 |
(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 | 4019.2.a.b.1.15 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.15 | ✓ | 186 | 1.1 | even | 1 | trivial |