Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4235,2,Mod(1,4235)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4235, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4235.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4235 = 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4235.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: | \(33.8166452560\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 14x^{8} + 26x^{7} + 67x^{6} - 110x^{5} - 132x^{4} + 168x^{3} + 94x^{2} - 54x - 11 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.547729\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4235.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.547729 | −0.387303 | −0.193652 | − | 0.981070i | \(-0.562033\pi\) | ||||
−0.193652 | + | 0.981070i | \(0.562033\pi\) | |||||||
\(3\) | −3.41697 | −1.97279 | −0.986395 | − | 0.164393i | \(-0.947433\pi\) | ||||
−0.986395 | + | 0.164393i | \(0.947433\pi\) | |||||||
\(4\) | −1.69999 | −0.849996 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.87158 | 0.764068 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.02659 | 0.716509 | ||||||||
\(9\) | 8.67570 | 2.89190 | ||||||||
\(10\) | −0.547729 | −0.173207 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 5.80883 | 1.67686 | ||||||||
\(13\) | −5.13626 | −1.42454 | −0.712270 | − | 0.701905i | \(-0.752333\pi\) | ||||
−0.712270 | + | 0.701905i | \(0.752333\pi\) | |||||||
\(14\) | −0.547729 | −0.146387 | ||||||||
\(15\) | −3.41697 | −0.882258 | ||||||||
\(16\) | 2.28996 | 0.572490 | ||||||||
\(17\) | 1.89313 | 0.459151 | 0.229575 | − | 0.973291i | \(-0.426266\pi\) | ||||
0.229575 | + | 0.973291i | \(0.426266\pi\) | |||||||
\(18\) | −4.75193 | −1.12004 | ||||||||
\(19\) | −0.995867 | −0.228468 | −0.114234 | − | 0.993454i | \(-0.536441\pi\) | ||||
−0.114234 | + | 0.993454i | \(0.536441\pi\) | |||||||
\(20\) | −1.69999 | −0.380130 | ||||||||
\(21\) | −3.41697 | −0.745644 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.47220 | 1.55806 | 0.779030 | − | 0.626986i | \(-0.215712\pi\) | ||||
0.779030 | + | 0.626986i | \(0.215712\pi\) | |||||||
\(24\) | −6.92482 | −1.41352 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.81328 | 0.551729 | ||||||||
\(27\) | −19.3937 | −3.73232 | ||||||||
\(28\) | −1.69999 | −0.321268 | ||||||||
\(29\) | −6.07749 | −1.12856 | −0.564281 | − | 0.825583i | \(-0.690846\pi\) | ||||
−0.564281 | + | 0.825583i | \(0.690846\pi\) | |||||||
\(30\) | 1.87158 | 0.341701 | ||||||||
\(31\) | −9.66473 | −1.73584 | −0.867919 | − | 0.496707i | \(-0.834543\pi\) | ||||
−0.867919 | + | 0.496707i | \(0.834543\pi\) | |||||||
\(32\) | −5.30747 | −0.938237 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.03692 | −0.177830 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −14.7486 | −2.45810 | ||||||||
\(37\) | −1.05699 | −0.173769 | −0.0868844 | − | 0.996218i | \(-0.527691\pi\) | ||||
−0.0868844 | + | 0.996218i | \(0.527691\pi\) | |||||||
\(38\) | 0.545466 | 0.0884862 | ||||||||
\(39\) | 17.5504 | 2.81032 | ||||||||
\(40\) | 2.02659 | 0.320433 | ||||||||
\(41\) | −6.21238 | −0.970211 | −0.485105 | − | 0.874456i | \(-0.661219\pi\) | ||||
−0.485105 | + | 0.874456i | \(0.661219\pi\) | |||||||
\(42\) | 1.87158 | 0.288790 | ||||||||
\(43\) | 11.8635 | 1.80917 | 0.904586 | − | 0.426292i | \(-0.140180\pi\) | ||||
0.904586 | + | 0.426292i | \(0.140180\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.67570 | 1.29330 | ||||||||
\(46\) | −4.09274 | −0.603442 | ||||||||
\(47\) | 2.37309 | 0.346151 | 0.173075 | − | 0.984909i | \(-0.444630\pi\) | ||||
0.173075 | + | 0.984909i | \(0.444630\pi\) | |||||||
\(48\) | −7.82473 | −1.12940 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.547729 | −0.0774606 | ||||||||
\(51\) | −6.46876 | −0.905808 | ||||||||
\(52\) | 8.73160 | 1.21085 | ||||||||
\(53\) | −1.08367 | −0.148853 | −0.0744265 | − | 0.997227i | \(-0.523713\pi\) | ||||
−0.0744265 | + | 0.997227i | \(0.523713\pi\) | |||||||
\(54\) | 10.6225 | 1.44554 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.02659 | 0.270815 | ||||||||
\(57\) | 3.40285 | 0.450719 | ||||||||
\(58\) | 3.32882 | 0.437096 | ||||||||
\(59\) | −1.01785 | −0.132513 | −0.0662563 | − | 0.997803i | \(-0.521106\pi\) | ||||
−0.0662563 | + | 0.997803i | \(0.521106\pi\) | |||||||
\(60\) | 5.80883 | 0.749916 | ||||||||
\(61\) | −7.26140 | −0.929727 | −0.464864 | − | 0.885382i | \(-0.653897\pi\) | ||||
−0.464864 | + | 0.885382i | \(0.653897\pi\) | |||||||
\(62\) | 5.29366 | 0.672295 | ||||||||
\(63\) | 8.67570 | 1.09304 | ||||||||
\(64\) | −1.67286 | −0.209108 | ||||||||
\(65\) | −5.13626 | −0.637074 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.377827 | −0.0461590 | −0.0230795 | − | 0.999734i | \(-0.507347\pi\) | ||||
−0.0230795 | + | 0.999734i | \(0.507347\pi\) | |||||||
\(68\) | −3.21830 | −0.390276 | ||||||||
\(69\) | −25.5323 | −3.07373 | ||||||||
\(70\) | −0.547729 | −0.0654662 | ||||||||
\(71\) | 6.42093 | 0.762024 | 0.381012 | − | 0.924570i | \(-0.375576\pi\) | ||||
0.381012 | + | 0.924570i | \(0.375576\pi\) | |||||||
\(72\) | 17.5821 | 2.07207 | ||||||||
\(73\) | 15.4877 | 1.81270 | 0.906348 | − | 0.422531i | \(-0.138858\pi\) | ||||
0.906348 | + | 0.422531i | \(0.138858\pi\) | |||||||
\(74\) | 0.578947 | 0.0673012 | ||||||||
\(75\) | −3.41697 | −0.394558 | ||||||||
\(76\) | 1.69297 | 0.194197 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −9.61289 | −1.08845 | ||||||||
\(79\) | 11.9247 | 1.34163 | 0.670815 | − | 0.741624i | \(-0.265944\pi\) | ||||
0.670815 | + | 0.741624i | \(0.265944\pi\) | |||||||
\(80\) | 2.28996 | 0.256025 | ||||||||
\(81\) | 40.2406 | 4.47118 | ||||||||
\(82\) | 3.40270 | 0.375766 | ||||||||
\(83\) | 3.22534 | 0.354027 | 0.177013 | − | 0.984208i | \(-0.443356\pi\) | ||||
0.177013 | + | 0.984208i | \(0.443356\pi\) | |||||||
\(84\) | 5.80883 | 0.633795 | ||||||||
\(85\) | 1.89313 | 0.205338 | ||||||||
\(86\) | −6.49800 | −0.700698 | ||||||||
\(87\) | 20.7666 | 2.22641 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.65995 | −0.599953 | −0.299977 | − | 0.953947i | \(-0.596979\pi\) | ||||
−0.299977 | + | 0.953947i | \(0.596979\pi\) | |||||||
\(90\) | −4.75193 | −0.500898 | ||||||||
\(91\) | −5.13626 | −0.538426 | ||||||||
\(92\) | −12.7027 | −1.32435 | ||||||||
\(93\) | 33.0241 | 3.42444 | ||||||||
\(94\) | −1.29981 | −0.134065 | ||||||||
\(95\) | −0.995867 | −0.102174 | ||||||||
\(96\) | 18.1355 | 1.85094 | ||||||||
\(97\) | 12.2829 | 1.24714 | 0.623569 | − | 0.781768i | \(-0.285682\pi\) | ||||
0.623569 | + | 0.781768i | \(0.285682\pi\) | |||||||
\(98\) | −0.547729 | −0.0553290 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.69999 | −0.169999 | ||||||||
\(101\) | −3.74207 | −0.372350 | −0.186175 | − | 0.982517i | \(-0.559609\pi\) | ||||
−0.186175 | + | 0.982517i | \(0.559609\pi\) | |||||||
\(102\) | 3.54313 | 0.350822 | ||||||||
\(103\) | 6.95088 | 0.684891 | 0.342445 | − | 0.939538i | \(-0.388745\pi\) | ||||
0.342445 | + | 0.939538i | \(0.388745\pi\) | |||||||
\(104\) | −10.4091 | −1.02070 | ||||||||
\(105\) | −3.41697 | −0.333462 | ||||||||
\(106\) | 0.593556 | 0.0576512 | ||||||||
\(107\) | −12.9654 | −1.25341 | −0.626707 | − | 0.779255i | \(-0.715598\pi\) | ||||
−0.626707 | + | 0.779255i | \(0.715598\pi\) | |||||||
\(108\) | 32.9691 | 3.17246 | ||||||||
\(109\) | −2.08725 | −0.199922 | −0.0999611 | − | 0.994991i | \(-0.531872\pi\) | ||||
−0.0999611 | + | 0.994991i | \(0.531872\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.61172 | 0.342809 | ||||||||
\(112\) | 2.28996 | 0.216381 | ||||||||
\(113\) | −9.61055 | −0.904084 | −0.452042 | − | 0.891997i | \(-0.649304\pi\) | ||||
−0.452042 | + | 0.891997i | \(0.649304\pi\) | |||||||
\(114\) | −1.86384 | −0.174565 | ||||||||
\(115\) | 7.47220 | 0.696786 | ||||||||
\(116\) | 10.3317 | 0.959273 | ||||||||
\(117\) | −44.5606 | −4.11963 | ||||||||
\(118\) | 0.557506 | 0.0513226 | ||||||||
\(119\) | 1.89313 | 0.173543 | ||||||||
\(120\) | −6.92482 | −0.632146 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 3.97728 | 0.360086 | ||||||||
\(123\) | 21.2275 | 1.91402 | ||||||||
\(124\) | 16.4300 | 1.47546 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.75193 | −0.423336 | ||||||||
\(127\) | 0.280145 | 0.0248589 | 0.0124294 | − | 0.999923i | \(-0.496043\pi\) | ||||
0.0124294 | + | 0.999923i | \(0.496043\pi\) | |||||||
\(128\) | 11.5312 | 1.01922 | ||||||||
\(129\) | −40.5373 | −3.56911 | ||||||||
\(130\) | 2.81328 | 0.246741 | ||||||||
\(131\) | −1.47708 | −0.129053 | −0.0645267 | − | 0.997916i | \(-0.520554\pi\) | ||||
−0.0645267 | + | 0.997916i | \(0.520554\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.995867 | −0.0863526 | ||||||||
\(134\) | 0.206947 | 0.0178775 | ||||||||
\(135\) | −19.3937 | −1.66914 | ||||||||
\(136\) | 3.83660 | 0.328986 | ||||||||
\(137\) | 0.343777 | 0.0293709 | 0.0146854 | − | 0.999892i | \(-0.495325\pi\) | ||||
0.0146854 | + | 0.999892i | \(0.495325\pi\) | |||||||
\(138\) | 13.9848 | 1.19046 | ||||||||
\(139\) | −6.04284 | −0.512547 | −0.256273 | − | 0.966604i | \(-0.582495\pi\) | ||||
−0.256273 | + | 0.966604i | \(0.582495\pi\) | |||||||
\(140\) | −1.69999 | −0.143676 | ||||||||
\(141\) | −8.10878 | −0.682882 | ||||||||
\(142\) | −3.51693 | −0.295134 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 19.8670 | 1.65558 | ||||||||
\(145\) | −6.07749 | −0.504708 | ||||||||
\(146\) | −8.48306 | −0.702063 | ||||||||
\(147\) | −3.41697 | −0.281827 | ||||||||
\(148\) | 1.79688 | 0.147703 | ||||||||
\(149\) | −10.0211 | −0.820959 | −0.410480 | − | 0.911870i | \(-0.634639\pi\) | ||||
−0.410480 | + | 0.911870i | \(0.634639\pi\) | |||||||
\(150\) | 1.87158 | 0.152814 | ||||||||
\(151\) | −9.02415 | −0.734375 | −0.367187 | − | 0.930147i | \(-0.619679\pi\) | ||||
−0.367187 | + | 0.930147i | \(0.619679\pi\) | |||||||
\(152\) | −2.01822 | −0.163699 | ||||||||
\(153\) | 16.4242 | 1.32782 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.66473 | −0.776290 | ||||||||
\(156\) | −29.8356 | −2.38876 | ||||||||
\(157\) | −17.3777 | −1.38689 | −0.693444 | − | 0.720511i | \(-0.743907\pi\) | ||||
−0.693444 | + | 0.720511i | \(0.743907\pi\) | |||||||
\(158\) | −6.53150 | −0.519618 | ||||||||
\(159\) | 3.70286 | 0.293656 | ||||||||
\(160\) | −5.30747 | −0.419592 | ||||||||
\(161\) | 7.47220 | 0.588892 | ||||||||
\(162\) | −22.0410 | −1.73170 | ||||||||
\(163\) | 5.08955 | 0.398645 | 0.199322 | − | 0.979934i | \(-0.436126\pi\) | ||||
0.199322 | + | 0.979934i | \(0.436126\pi\) | |||||||
\(164\) | 10.5610 | 0.824676 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.76661 | −0.137116 | ||||||||
\(167\) | −9.75278 | −0.754692 | −0.377346 | − | 0.926072i | \(-0.623163\pi\) | ||||
−0.377346 | + | 0.926072i | \(0.623163\pi\) | |||||||
\(168\) | −6.92482 | −0.534261 | ||||||||
\(169\) | 13.3811 | 1.02932 | ||||||||
\(170\) | −1.03692 | −0.0795282 | ||||||||
\(171\) | −8.63984 | −0.660705 | ||||||||
\(172\) | −20.1679 | −1.53779 | ||||||||
\(173\) | 21.3455 | 1.62286 | 0.811432 | − | 0.584446i | \(-0.198688\pi\) | ||||
0.811432 | + | 0.584446i | \(0.198688\pi\) | |||||||
\(174\) | −11.3745 | −0.862298 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.47796 | 0.261420 | ||||||||
\(178\) | 3.10012 | 0.232364 | ||||||||
\(179\) | 14.3713 | 1.07416 | 0.537081 | − | 0.843531i | \(-0.319527\pi\) | ||||
0.537081 | + | 0.843531i | \(0.319527\pi\) | |||||||
\(180\) | −14.7486 | −1.09930 | ||||||||
\(181\) | 9.96954 | 0.741030 | 0.370515 | − | 0.928827i | \(-0.379181\pi\) | ||||
0.370515 | + | 0.928827i | \(0.379181\pi\) | |||||||
\(182\) | 2.81328 | 0.208534 | ||||||||
\(183\) | 24.8120 | 1.83416 | ||||||||
\(184\) | 15.1431 | 1.11637 | ||||||||
\(185\) | −1.05699 | −0.0777118 | ||||||||
\(186\) | −18.0883 | −1.32630 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.03423 | −0.294227 | ||||||||
\(189\) | −19.3937 | −1.41068 | ||||||||
\(190\) | 0.545466 | 0.0395722 | ||||||||
\(191\) | 10.5286 | 0.761824 | 0.380912 | − | 0.924611i | \(-0.375610\pi\) | ||||
0.380912 | + | 0.924611i | \(0.375610\pi\) | |||||||
\(192\) | 5.71612 | 0.412526 | ||||||||
\(193\) | 3.02584 | 0.217805 | 0.108902 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108902 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(194\) | −6.72770 | −0.483020 | ||||||||
\(195\) | 17.5504 | 1.25681 | ||||||||
\(196\) | −1.69999 | −0.121428 | ||||||||
\(197\) | −13.0753 | −0.931580 | −0.465790 | − | 0.884895i | \(-0.654230\pi\) | ||||
−0.465790 | + | 0.884895i | \(0.654230\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.98474 | 0.140694 | 0.0703472 | − | 0.997523i | \(-0.477589\pi\) | ||||
0.0703472 | + | 0.997523i | \(0.477589\pi\) | |||||||
\(200\) | 2.02659 | 0.143302 | ||||||||
\(201\) | 1.29103 | 0.0910619 | ||||||||
\(202\) | 2.04964 | 0.144212 | ||||||||
\(203\) | −6.07749 | −0.426556 | ||||||||
\(204\) | 10.9968 | 0.769933 | ||||||||
\(205\) | −6.21238 | −0.433891 | ||||||||
\(206\) | −3.80720 | −0.265260 | ||||||||
\(207\) | 64.8265 | 4.50576 | ||||||||
\(208\) | −11.7618 | −0.815535 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.87158 | 0.129151 | ||||||||
\(211\) | −8.69252 | −0.598418 | −0.299209 | − | 0.954188i | \(-0.596723\pi\) | ||||
−0.299209 | + | 0.954188i | \(0.596723\pi\) | |||||||
\(212\) | 1.84222 | 0.126524 | ||||||||
\(213\) | −21.9401 | −1.50331 | ||||||||
\(214\) | 7.10154 | 0.485451 | ||||||||
\(215\) | 11.8635 | 0.809086 | ||||||||
\(216\) | −39.3032 | −2.67424 | ||||||||
\(217\) | −9.66473 | −0.656085 | ||||||||
\(218\) | 1.14325 | 0.0774305 | ||||||||
\(219\) | −52.9210 | −3.57607 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.72358 | −0.654079 | ||||||||
\(222\) | −1.97825 | −0.132771 | ||||||||
\(223\) | 4.40008 | 0.294651 | 0.147325 | − | 0.989088i | \(-0.452934\pi\) | ||||
0.147325 | + | 0.989088i | \(0.452934\pi\) | |||||||
\(224\) | −5.30747 | −0.354620 | ||||||||
\(225\) | 8.67570 | 0.578380 | ||||||||
\(226\) | 5.26398 | 0.350155 | ||||||||
\(227\) | 14.5394 | 0.965015 | 0.482508 | − | 0.875892i | \(-0.339726\pi\) | ||||
0.482508 | + | 0.875892i | \(0.339726\pi\) | |||||||
\(228\) | −5.78482 | −0.383109 | ||||||||
\(229\) | −10.1524 | −0.670887 | −0.335444 | − | 0.942060i | \(-0.608886\pi\) | ||||
−0.335444 | + | 0.942060i | \(0.608886\pi\) | |||||||
\(230\) | −4.09274 | −0.269867 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.3166 | −0.808625 | ||||||||
\(233\) | −1.63072 | −0.106832 | −0.0534161 | − | 0.998572i | \(-0.517011\pi\) | ||||
−0.0534161 | + | 0.998572i | \(0.517011\pi\) | |||||||
\(234\) | 24.4072 | 1.59555 | ||||||||
\(235\) | 2.37309 | 0.154803 | ||||||||
\(236\) | 1.73034 | 0.112635 | ||||||||
\(237\) | −40.7463 | −2.64676 | ||||||||
\(238\) | −1.03692 | −0.0672136 | ||||||||
\(239\) | 16.1374 | 1.04384 | 0.521922 | − | 0.852993i | \(-0.325215\pi\) | ||||
0.521922 | + | 0.852993i | \(0.325215\pi\) | |||||||
\(240\) | −7.82473 | −0.505084 | ||||||||
\(241\) | −13.7320 | −0.884554 | −0.442277 | − | 0.896879i | \(-0.645829\pi\) | ||||
−0.442277 | + | 0.896879i | \(0.645829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −79.3200 | −5.08838 | ||||||||
\(244\) | 12.3443 | 0.790265 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −11.6269 | −0.741307 | ||||||||
\(247\) | 5.11503 | 0.325461 | ||||||||
\(248\) | −19.5865 | −1.24374 | ||||||||
\(249\) | −11.0209 | −0.698421 | ||||||||
\(250\) | −0.547729 | −0.0346415 | ||||||||
\(251\) | 8.46025 | 0.534006 | 0.267003 | − | 0.963696i | \(-0.413967\pi\) | ||||
0.267003 | + | 0.963696i | \(0.413967\pi\) | |||||||
\(252\) | −14.7486 | −0.929076 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.153444 | −0.00962791 | ||||||||
\(255\) | −6.46876 | −0.405089 | ||||||||
\(256\) | −2.97026 | −0.185641 | ||||||||
\(257\) | −3.85606 | −0.240534 | −0.120267 | − | 0.992742i | \(-0.538375\pi\) | ||||
−0.120267 | + | 0.992742i | \(0.538375\pi\) | |||||||
\(258\) | 22.2035 | 1.38233 | ||||||||
\(259\) | −1.05699 | −0.0656784 | ||||||||
\(260\) | 8.73160 | 0.541511 | ||||||||
\(261\) | −52.7265 | −3.26369 | ||||||||
\(262\) | 0.809042 | 0.0499828 | ||||||||
\(263\) | −29.8124 | −1.83831 | −0.919157 | − | 0.393892i | \(-0.871128\pi\) | ||||
−0.919157 | + | 0.393892i | \(0.871128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.08367 | −0.0665691 | ||||||||
\(266\) | 0.545466 | 0.0334447 | ||||||||
\(267\) | 19.3399 | 1.18358 | ||||||||
\(268\) | 0.642304 | 0.0392349 | ||||||||
\(269\) | 22.7726 | 1.38847 | 0.694236 | − | 0.719748i | \(-0.255742\pi\) | ||||
0.694236 | + | 0.719748i | \(0.255742\pi\) | |||||||
\(270\) | 10.6225 | 0.646465 | ||||||||
\(271\) | −16.6765 | −1.01303 | −0.506513 | − | 0.862232i | \(-0.669066\pi\) | ||||
−0.506513 | + | 0.862232i | \(0.669066\pi\) | |||||||
\(272\) | 4.33518 | 0.262859 | ||||||||
\(273\) | 17.5504 | 1.06220 | ||||||||
\(274\) | −0.188297 | −0.0113754 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 43.4047 | 2.61266 | ||||||||
\(277\) | −16.9595 | −1.01900 | −0.509498 | − | 0.860472i | \(-0.670169\pi\) | ||||
−0.509498 | + | 0.860472i | \(0.670169\pi\) | |||||||
\(278\) | 3.30984 | 0.198511 | ||||||||
\(279\) | −83.8483 | −5.01987 | ||||||||
\(280\) | 2.02659 | 0.121112 | ||||||||
\(281\) | −29.1550 | −1.73924 | −0.869622 | − | 0.493718i | \(-0.835637\pi\) | ||||
−0.869622 | + | 0.493718i | \(0.835637\pi\) | |||||||
\(282\) | 4.44142 | 0.264482 | ||||||||
\(283\) | 10.6838 | 0.635084 | 0.317542 | − | 0.948244i | \(-0.397143\pi\) | ||||
0.317542 | + | 0.948244i | \(0.397143\pi\) | |||||||
\(284\) | −10.9155 | −0.647717 | ||||||||
\(285\) | 3.40285 | 0.201567 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.21238 | −0.366705 | ||||||||
\(288\) | −46.0460 | −2.71329 | ||||||||
\(289\) | −13.4161 | −0.789181 | ||||||||
\(290\) | 3.32882 | 0.195475 | ||||||||
\(291\) | −41.9703 | −2.46034 | ||||||||
\(292\) | −26.3290 | −1.54079 | ||||||||
\(293\) | 12.7473 | 0.744704 | 0.372352 | − | 0.928092i | \(-0.378551\pi\) | ||||
0.372352 | + | 0.928092i | \(0.378551\pi\) | |||||||
\(294\) | 1.87158 | 0.109153 | ||||||||
\(295\) | −1.01785 | −0.0592615 | ||||||||
\(296\) | −2.14210 | −0.124507 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.48884 | 0.317960 | ||||||||
\(299\) | −38.3791 | −2.21952 | ||||||||
\(300\) | 5.80883 | 0.335373 | ||||||||
\(301\) | 11.8635 | 0.683802 | ||||||||
\(302\) | 4.94279 | 0.284426 | ||||||||
\(303\) | 12.7865 | 0.734568 | ||||||||
\(304\) | −2.28050 | −0.130795 | ||||||||
\(305\) | −7.26140 | −0.415787 | ||||||||
\(306\) | −8.99601 | −0.514268 | ||||||||
\(307\) | 20.4869 | 1.16925 | 0.584625 | − | 0.811304i | \(-0.301242\pi\) | ||||
0.584625 | + | 0.811304i | \(0.301242\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −23.7510 | −1.35115 | ||||||||
\(310\) | 5.29366 | 0.300660 | ||||||||
\(311\) | −11.8951 | −0.674508 | −0.337254 | − | 0.941414i | \(-0.609498\pi\) | ||||
−0.337254 | + | 0.941414i | \(0.609498\pi\) | |||||||
\(312\) | 35.5676 | 2.01362 | ||||||||
\(313\) | −8.19054 | −0.462957 | −0.231478 | − | 0.972840i | \(-0.574356\pi\) | ||||
−0.231478 | + | 0.972840i | \(0.574356\pi\) | |||||||
\(314\) | 9.51825 | 0.537146 | ||||||||
\(315\) | 8.67570 | 0.488820 | ||||||||
\(316\) | −20.2719 | −1.14038 | ||||||||
\(317\) | −14.3342 | −0.805090 | −0.402545 | − | 0.915400i | \(-0.631874\pi\) | ||||
−0.402545 | + | 0.915400i | \(0.631874\pi\) | |||||||
\(318\) | −2.02816 | −0.113734 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.67286 | −0.0935159 | ||||||||
\(321\) | 44.3024 | 2.47272 | ||||||||
\(322\) | −4.09274 | −0.228080 | ||||||||
\(323\) | −1.88530 | −0.104901 | ||||||||
\(324\) | −68.4088 | −3.80049 | ||||||||
\(325\) | −5.13626 | −0.284908 | ||||||||
\(326\) | −2.78770 | −0.154396 | ||||||||
\(327\) | 7.13207 | 0.394405 | ||||||||
\(328\) | −12.5900 | −0.695165 | ||||||||
\(329\) | 2.37309 | 0.130833 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.3490 | 0.678763 | 0.339381 | − | 0.940649i | \(-0.389782\pi\) | ||||
0.339381 | + | 0.940649i | \(0.389782\pi\) | |||||||
\(332\) | −5.48305 | −0.300921 | ||||||||
\(333\) | −9.17017 | −0.502522 | ||||||||
\(334\) | 5.34188 | 0.292295 | ||||||||
\(335\) | −0.377827 | −0.0206429 | ||||||||
\(336\) | −7.82473 | −0.426874 | ||||||||
\(337\) | −8.43982 | −0.459746 | −0.229873 | − | 0.973221i | \(-0.573831\pi\) | ||||
−0.229873 | + | 0.973221i | \(0.573831\pi\) | |||||||
\(338\) | −7.32923 | −0.398658 | ||||||||
\(339\) | 32.8390 | 1.78357 | ||||||||
\(340\) | −3.21830 | −0.174537 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.73230 | 0.255893 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 24.0426 | 1.29629 | ||||||||
\(345\) | −25.5323 | −1.37461 | ||||||||
\(346\) | −11.6915 | −0.628541 | ||||||||
\(347\) | −27.2864 | −1.46481 | −0.732404 | − | 0.680870i | \(-0.761602\pi\) | ||||
−0.732404 | + | 0.680870i | \(0.761602\pi\) | |||||||
\(348\) | −35.3031 | −1.89244 | ||||||||
\(349\) | −30.7820 | −1.64772 | −0.823861 | − | 0.566792i | \(-0.808184\pi\) | ||||
−0.823861 | + | 0.566792i | \(0.808184\pi\) | |||||||
\(350\) | −0.547729 | −0.0292774 | ||||||||
\(351\) | 99.6110 | 5.31684 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.4135 | −1.45907 | −0.729537 | − | 0.683941i | \(-0.760265\pi\) | ||||
−0.729537 | + | 0.683941i | \(0.760265\pi\) | |||||||
\(354\) | −1.90498 | −0.101249 | ||||||||
\(355\) | 6.42093 | 0.340787 | ||||||||
\(356\) | 9.62187 | 0.509958 | ||||||||
\(357\) | −6.46876 | −0.342363 | ||||||||
\(358\) | −7.87158 | −0.416026 | ||||||||
\(359\) | 0.531678 | 0.0280609 | 0.0140305 | − | 0.999902i | \(-0.495534\pi\) | ||||
0.0140305 | + | 0.999902i | \(0.495534\pi\) | |||||||
\(360\) | 17.5821 | 0.926659 | ||||||||
\(361\) | −18.0082 | −0.947803 | ||||||||
\(362\) | −5.46061 | −0.287003 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.73160 | 0.457660 | ||||||||
\(365\) | 15.4877 | 0.810663 | ||||||||
\(366\) | −13.5903 | −0.710375 | ||||||||
\(367\) | 34.5626 | 1.80415 | 0.902075 | − | 0.431579i | \(-0.142043\pi\) | ||||
0.902075 | + | 0.431579i | \(0.142043\pi\) | |||||||
\(368\) | 17.1110 | 0.891974 | ||||||||
\(369\) | −53.8967 | −2.80575 | ||||||||
\(370\) | 0.578947 | 0.0300980 | ||||||||
\(371\) | −1.08367 | −0.0562611 | ||||||||
\(372\) | −56.1408 | −2.91076 | ||||||||
\(373\) | 8.13826 | 0.421383 | 0.210692 | − | 0.977553i | \(-0.432428\pi\) | ||||
0.210692 | + | 0.977553i | \(0.432428\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.41697 | −0.176452 | ||||||||
\(376\) | 4.80929 | 0.248020 | ||||||||
\(377\) | 31.2155 | 1.60768 | ||||||||
\(378\) | 10.6225 | 0.546362 | ||||||||
\(379\) | 15.9131 | 0.817403 | 0.408702 | − | 0.912668i | \(-0.365982\pi\) | ||||
0.408702 | + | 0.912668i | \(0.365982\pi\) | |||||||
\(380\) | 1.69297 | 0.0868474 | ||||||||
\(381\) | −0.957248 | −0.0490413 | ||||||||
\(382\) | −5.76683 | −0.295057 | ||||||||
\(383\) | −5.18634 | −0.265010 | −0.132505 | − | 0.991182i | \(-0.542302\pi\) | ||||
−0.132505 | + | 0.991182i | \(0.542302\pi\) | |||||||
\(384\) | −39.4018 | −2.01072 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.65734 | −0.0843565 | ||||||||
\(387\) | 102.924 | 5.23194 | ||||||||
\(388\) | −20.8808 | −1.06006 | ||||||||
\(389\) | −7.02383 | −0.356122 | −0.178061 | − | 0.984019i | \(-0.556982\pi\) | ||||
−0.178061 | + | 0.984019i | \(0.556982\pi\) | |||||||
\(390\) | −9.61289 | −0.486768 | ||||||||
\(391\) | 14.1458 | 0.715385 | ||||||||
\(392\) | 2.02659 | 0.102358 | ||||||||
\(393\) | 5.04715 | 0.254595 | ||||||||
\(394\) | 7.16175 | 0.360804 | ||||||||
\(395\) | 11.9247 | 0.599995 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.9046 | −1.50087 | −0.750435 | − | 0.660944i | \(-0.770156\pi\) | ||||
−0.750435 | + | 0.660944i | \(0.770156\pi\) | |||||||
\(398\) | −1.08710 | −0.0544914 | ||||||||
\(399\) | 3.40285 | 0.170356 | ||||||||
\(400\) | 2.28996 | 0.114498 | ||||||||
\(401\) | 2.34928 | 0.117317 | 0.0586586 | − | 0.998278i | \(-0.481318\pi\) | ||||
0.0586586 | + | 0.998278i | \(0.481318\pi\) | |||||||
\(402\) | −0.707133 | −0.0352686 | ||||||||
\(403\) | 49.6405 | 2.47277 | ||||||||
\(404\) | 6.36149 | 0.316496 | ||||||||
\(405\) | 40.2406 | 1.99957 | ||||||||
\(406\) | 3.32882 | 0.165207 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −13.1096 | −0.649020 | ||||||||
\(409\) | −17.6020 | −0.870361 | −0.435181 | − | 0.900343i | \(-0.643316\pi\) | ||||
−0.435181 | + | 0.900343i | \(0.643316\pi\) | |||||||
\(410\) | 3.40270 | 0.168048 | ||||||||
\(411\) | −1.17468 | −0.0579426 | ||||||||
\(412\) | −11.8164 | −0.582154 | ||||||||
\(413\) | −1.01785 | −0.0500851 | ||||||||
\(414\) | −35.5074 | −1.74509 | ||||||||
\(415\) | 3.22534 | 0.158326 | ||||||||
\(416\) | 27.2605 | 1.33656 | ||||||||
\(417\) | 20.6482 | 1.01115 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.2263 | −1.57436 | −0.787179 | − | 0.616724i | \(-0.788459\pi\) | ||||
−0.787179 | + | 0.616724i | \(0.788459\pi\) | |||||||
\(420\) | 5.80883 | 0.283442 | ||||||||
\(421\) | 16.3940 | 0.798994 | 0.399497 | − | 0.916734i | \(-0.369185\pi\) | ||||
0.399497 | + | 0.916734i | \(0.369185\pi\) | |||||||
\(422\) | 4.76115 | 0.231769 | ||||||||
\(423\) | 20.5882 | 1.00103 | ||||||||
\(424\) | −2.19615 | −0.106655 | ||||||||
\(425\) | 1.89313 | 0.0918301 | ||||||||
\(426\) | 12.0173 | 0.582238 | ||||||||
\(427\) | −7.26140 | −0.351404 | ||||||||
\(428\) | 22.0411 | 1.06540 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.49800 | −0.313362 | ||||||||
\(431\) | −17.7272 | −0.853888 | −0.426944 | − | 0.904278i | \(-0.640410\pi\) | ||||
−0.426944 | + | 0.904278i | \(0.640410\pi\) | |||||||
\(432\) | −44.4108 | −2.13672 | ||||||||
\(433\) | 2.16444 | 0.104016 | 0.0520081 | − | 0.998647i | \(-0.483438\pi\) | ||||
0.0520081 | + | 0.998647i | \(0.483438\pi\) | |||||||
\(434\) | 5.29366 | 0.254104 | ||||||||
\(435\) | 20.7666 | 0.995683 | ||||||||
\(436\) | 3.54831 | 0.169933 | ||||||||
\(437\) | −7.44132 | −0.355966 | ||||||||
\(438\) | 28.9864 | 1.38502 | ||||||||
\(439\) | 20.6454 | 0.985349 | 0.492675 | − | 0.870214i | \(-0.336019\pi\) | ||||
0.492675 | + | 0.870214i | \(0.336019\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.67570 | 0.413128 | ||||||||
\(442\) | 5.32589 | 0.253327 | ||||||||
\(443\) | 16.1681 | 0.768169 | 0.384084 | − | 0.923298i | \(-0.374517\pi\) | ||||
0.384084 | + | 0.923298i | \(0.374517\pi\) | |||||||
\(444\) | −6.13990 | −0.291387 | ||||||||
\(445\) | −5.65995 | −0.268307 | ||||||||
\(446\) | −2.41005 | −0.114119 | ||||||||
\(447\) | 34.2418 | 1.61958 | ||||||||
\(448\) | −1.67286 | −0.0790353 | ||||||||
\(449\) | −5.14485 | −0.242800 | −0.121400 | − | 0.992604i | \(-0.538738\pi\) | ||||
−0.121400 | + | 0.992604i | \(0.538738\pi\) | |||||||
\(450\) | −4.75193 | −0.224008 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 16.3379 | 0.768468 | ||||||||
\(453\) | 30.8353 | 1.44877 | ||||||||
\(454\) | −7.96367 | −0.373753 | ||||||||
\(455\) | −5.13626 | −0.240791 | ||||||||
\(456\) | 6.89620 | 0.322944 | ||||||||
\(457\) | −16.4899 | −0.771364 | −0.385682 | − | 0.922632i | \(-0.626034\pi\) | ||||
−0.385682 | + | 0.922632i | \(0.626034\pi\) | |||||||
\(458\) | 5.56075 | 0.259837 | ||||||||
\(459\) | −36.7147 | −1.71370 | ||||||||
\(460\) | −12.7027 | −0.592266 | ||||||||
\(461\) | 0.891916 | 0.0415407 | 0.0207703 | − | 0.999784i | \(-0.493388\pi\) | ||||
0.0207703 | + | 0.999784i | \(0.493388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.42535 | −0.252137 | −0.126069 | − | 0.992022i | \(-0.540236\pi\) | ||||
−0.126069 | + | 0.992022i | \(0.540236\pi\) | |||||||
\(464\) | −13.9172 | −0.646090 | ||||||||
\(465\) | 33.0241 | 1.53146 | ||||||||
\(466\) | 0.893195 | 0.0413764 | ||||||||
\(467\) | 20.4043 | 0.944199 | 0.472099 | − | 0.881545i | \(-0.343496\pi\) | ||||
0.472099 | + | 0.881545i | \(0.343496\pi\) | |||||||
\(468\) | 75.7527 | 3.50167 | ||||||||
\(469\) | −0.377827 | −0.0174464 | ||||||||
\(470\) | −1.29981 | −0.0599558 | ||||||||
\(471\) | 59.3790 | 2.73604 | ||||||||
\(472\) | −2.06277 | −0.0949466 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 22.3179 | 1.02510 | ||||||||
\(475\) | −0.995867 | −0.0456935 | ||||||||
\(476\) | −3.21830 | −0.147511 | ||||||||
\(477\) | −9.40156 | −0.430468 | ||||||||
\(478\) | −8.83894 | −0.404284 | ||||||||
\(479\) | 27.8248 | 1.27135 | 0.635674 | − | 0.771958i | \(-0.280722\pi\) | ||||
0.635674 | + | 0.771958i | \(0.280722\pi\) | |||||||
\(480\) | 18.1355 | 0.827767 | ||||||||
\(481\) | 5.42899 | 0.247541 | ||||||||
\(482\) | 7.52140 | 0.342590 | ||||||||
\(483\) | −25.5323 | −1.16176 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.2829 | 0.557737 | ||||||||
\(486\) | 43.4459 | 1.97075 | ||||||||
\(487\) | −24.3238 | −1.10222 | −0.551108 | − | 0.834434i | \(-0.685795\pi\) | ||||
−0.551108 | + | 0.834434i | \(0.685795\pi\) | |||||||
\(488\) | −14.7159 | −0.666158 | ||||||||
\(489\) | −17.3909 | −0.786442 | ||||||||
\(490\) | −0.547729 | −0.0247439 | ||||||||
\(491\) | −34.5287 | −1.55826 | −0.779130 | − | 0.626862i | \(-0.784339\pi\) | ||||
−0.779130 | + | 0.626862i | \(0.784339\pi\) | |||||||
\(492\) | −36.0866 | −1.62691 | ||||||||
\(493\) | −11.5055 | −0.518180 | ||||||||
\(494\) | −2.80165 | −0.126052 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.1318 | −0.993749 | ||||||||
\(497\) | 6.42093 | 0.288018 | ||||||||
\(498\) | 6.03647 | 0.270500 | ||||||||
\(499\) | 24.8913 | 1.11429 | 0.557145 | − | 0.830416i | \(-0.311897\pi\) | ||||
0.557145 | + | 0.830416i | \(0.311897\pi\) | |||||||
\(500\) | −1.69999 | −0.0760260 | ||||||||
\(501\) | 33.3250 | 1.48885 | ||||||||
\(502\) | −4.63393 | −0.206822 | ||||||||
\(503\) | 1.31614 | 0.0586839 | 0.0293420 | − | 0.999569i | \(-0.490659\pi\) | ||||
0.0293420 | + | 0.999569i | \(0.490659\pi\) | |||||||
\(504\) | 17.5821 | 0.783170 | ||||||||
\(505\) | −3.74207 | −0.166520 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −45.7229 | −2.03063 | ||||||||
\(508\) | −0.476245 | −0.0211299 | ||||||||
\(509\) | −39.7323 | −1.76110 | −0.880552 | − | 0.473949i | \(-0.842828\pi\) | ||||
−0.880552 | + | 0.473949i | \(0.842828\pi\) | |||||||
\(510\) | 3.54313 | 0.156892 | ||||||||
\(511\) | 15.4877 | 0.685135 | ||||||||
\(512\) | −21.4355 | −0.947325 | ||||||||
\(513\) | 19.3136 | 0.852714 | ||||||||
\(514\) | 2.11208 | 0.0931596 | ||||||||
\(515\) | 6.95088 | 0.306292 | ||||||||
\(516\) | 68.9132 | 3.03373 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.578947 | 0.0254375 | ||||||||
\(519\) | −72.9368 | −3.20157 | ||||||||
\(520\) | −10.4091 | −0.456470 | ||||||||
\(521\) | 6.85790 | 0.300450 | 0.150225 | − | 0.988652i | \(-0.452000\pi\) | ||||
0.150225 | + | 0.988652i | \(0.452000\pi\) | |||||||
\(522\) | 28.8798 | 1.26404 | ||||||||
\(523\) | −25.1836 | −1.10120 | −0.550601 | − | 0.834769i | \(-0.685601\pi\) | ||||
−0.550601 | + | 0.834769i | \(0.685601\pi\) | |||||||
\(524\) | 2.51103 | 0.109695 | ||||||||
\(525\) | −3.41697 | −0.149129 | ||||||||
\(526\) | 16.3291 | 0.711985 | ||||||||
\(527\) | −18.2966 | −0.797011 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.8337 | 1.42755 | ||||||||
\(530\) | 0.593556 | 0.0257824 | ||||||||
\(531\) | −8.83055 | −0.383213 | ||||||||
\(532\) | 1.69297 | 0.0733994 | ||||||||
\(533\) | 31.9084 | 1.38210 | ||||||||
\(534\) | −10.5930 | −0.458405 | ||||||||
\(535\) | −12.9654 | −0.560544 | ||||||||
\(536\) | −0.765703 | −0.0330733 | ||||||||
\(537\) | −49.1063 | −2.11909 | ||||||||
\(538\) | −12.4732 | −0.537760 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 32.9691 | 1.41877 | ||||||||
\(541\) | 8.11776 | 0.349010 | 0.174505 | − | 0.984656i | \(-0.444167\pi\) | ||||
0.174505 | + | 0.984656i | \(0.444167\pi\) | |||||||
\(542\) | 9.13422 | 0.392348 | ||||||||
\(543\) | −34.0656 | −1.46190 | ||||||||
\(544\) | −10.0477 | −0.430792 | ||||||||
\(545\) | −2.08725 | −0.0894080 | ||||||||
\(546\) | −9.61289 | −0.411394 | ||||||||
\(547\) | −44.6673 | −1.90983 | −0.954917 | − | 0.296872i | \(-0.904056\pi\) | ||||
−0.954917 | + | 0.296872i | \(0.904056\pi\) | |||||||
\(548\) | −0.584419 | −0.0249651 | ||||||||
\(549\) | −62.9977 | −2.68868 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.05237 | 0.257840 | ||||||||
\(552\) | −51.7436 | −2.20235 | ||||||||
\(553\) | 11.9247 | 0.507089 | ||||||||
\(554\) | 9.28920 | 0.394660 | ||||||||
\(555\) | 3.61172 | 0.153309 | ||||||||
\(556\) | 10.2728 | 0.435663 | ||||||||
\(557\) | 28.0404 | 1.18811 | 0.594055 | − | 0.804425i | \(-0.297526\pi\) | ||||
0.594055 | + | 0.804425i | \(0.297526\pi\) | |||||||
\(558\) | 45.9262 | 1.94421 | ||||||||
\(559\) | −60.9341 | −2.57724 | ||||||||
\(560\) | 2.28996 | 0.0967684 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.9691 | 0.673615 | ||||||||
\(563\) | −6.35112 | −0.267668 | −0.133834 | − | 0.991004i | \(-0.542729\pi\) | ||||
−0.133834 | + | 0.991004i | \(0.542729\pi\) | |||||||
\(564\) | 13.7849 | 0.580447 | ||||||||
\(565\) | −9.61055 | −0.404319 | ||||||||
\(566\) | −5.85181 | −0.245970 | ||||||||
\(567\) | 40.2406 | 1.68995 | ||||||||
\(568\) | 13.0126 | 0.545997 | ||||||||
\(569\) | 30.0673 | 1.26049 | 0.630243 | − | 0.776398i | \(-0.282955\pi\) | ||||
0.630243 | + | 0.776398i | \(0.282955\pi\) | |||||||
\(570\) | −1.86384 | −0.0780677 | ||||||||
\(571\) | 32.6408 | 1.36597 | 0.682987 | − | 0.730431i | \(-0.260681\pi\) | ||||
0.682987 | + | 0.730431i | \(0.260681\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.9760 | −1.50292 | ||||||||
\(574\) | 3.40270 | 0.142026 | ||||||||
\(575\) | 7.47220 | 0.311612 | ||||||||
\(576\) | −14.5133 | −0.604719 | ||||||||
\(577\) | −21.6013 | −0.899276 | −0.449638 | − | 0.893211i | \(-0.648447\pi\) | ||||
−0.449638 | + | 0.893211i | \(0.648447\pi\) | |||||||
\(578\) | 7.34838 | 0.305652 | ||||||||
\(579\) | −10.3392 | −0.429683 | ||||||||
\(580\) | 10.3317 | 0.429000 | ||||||||
\(581\) | 3.22534 | 0.133810 | ||||||||
\(582\) | 22.9883 | 0.952898 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 31.3873 | 1.29881 | ||||||||
\(585\) | −44.5606 | −1.84235 | ||||||||
\(586\) | −6.98206 | −0.288426 | ||||||||
\(587\) | 39.7625 | 1.64117 | 0.820586 | − | 0.571523i | \(-0.193647\pi\) | ||||
0.820586 | + | 0.571523i | \(0.193647\pi\) | |||||||
\(588\) | 5.80883 | 0.239552 | ||||||||
\(589\) | 9.62479 | 0.396583 | ||||||||
\(590\) | 0.557506 | 0.0229521 | ||||||||
\(591\) | 44.6781 | 1.83781 | ||||||||
\(592\) | −2.42047 | −0.0994809 | ||||||||
\(593\) | −1.43399 | −0.0588869 | −0.0294435 | − | 0.999566i | \(-0.509373\pi\) | ||||
−0.0294435 | + | 0.999566i | \(0.509373\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.89313 | 0.0776106 | ||||||||
\(596\) | 17.0358 | 0.697812 | ||||||||
\(597\) | −6.78180 | −0.277561 | ||||||||
\(598\) | 21.0214 | 0.859628 | ||||||||
\(599\) | −4.61440 | −0.188539 | −0.0942696 | − | 0.995547i | \(-0.530052\pi\) | ||||
−0.0942696 | + | 0.995547i | \(0.530052\pi\) | |||||||
\(600\) | −6.92482 | −0.282704 | ||||||||
\(601\) | −18.5097 | −0.755026 | −0.377513 | − | 0.926004i | \(-0.623221\pi\) | ||||
−0.377513 | + | 0.926004i | \(0.623221\pi\) | |||||||
\(602\) | −6.49800 | −0.264839 | ||||||||
\(603\) | −3.27792 | −0.133487 | ||||||||
\(604\) | 15.3410 | 0.624216 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.00357 | −0.284501 | ||||||||
\(607\) | 15.2719 | 0.619869 | 0.309935 | − | 0.950758i | \(-0.399693\pi\) | ||||
0.309935 | + | 0.950758i | \(0.399693\pi\) | |||||||
\(608\) | 5.28553 | 0.214357 | ||||||||
\(609\) | 20.7666 | 0.841506 | ||||||||
\(610\) | 3.97728 | 0.161035 | ||||||||
\(611\) | −12.1888 | −0.493106 | ||||||||
\(612\) | −27.9210 | −1.12864 | ||||||||
\(613\) | −43.8947 | −1.77289 | −0.886445 | − | 0.462833i | \(-0.846833\pi\) | ||||
−0.886445 | + | 0.462833i | \(0.846833\pi\) | |||||||
\(614\) | −11.2213 | −0.452854 | ||||||||
\(615\) | 21.2275 | 0.855977 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.4746 | 1.87100 | 0.935498 | − | 0.353332i | \(-0.114951\pi\) | ||||
0.935498 | + | 0.353332i | \(0.114951\pi\) | |||||||
\(618\) | 13.0091 | 0.523303 | ||||||||
\(619\) | −14.6272 | −0.587918 | −0.293959 | − | 0.955818i | \(-0.594973\pi\) | ||||
−0.293959 | + | 0.955818i | \(0.594973\pi\) | |||||||
\(620\) | 16.4300 | 0.659844 | ||||||||
\(621\) | −144.914 | −5.81518 | ||||||||
\(622\) | 6.51528 | 0.261239 | ||||||||
\(623\) | −5.65995 | −0.226761 | ||||||||
\(624\) | 40.1898 | 1.60888 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 4.48620 | 0.179305 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 29.5419 | 1.17885 | ||||||||
\(629\) | −2.00102 | −0.0797861 | ||||||||
\(630\) | −4.75193 | −0.189322 | ||||||||
\(631\) | 1.67446 | 0.0666593 | 0.0333296 | − | 0.999444i | \(-0.489389\pi\) | ||||
0.0333296 | + | 0.999444i | \(0.489389\pi\) | |||||||
\(632\) | 24.1665 | 0.961291 | ||||||||
\(633\) | 29.7021 | 1.18055 | ||||||||
\(634\) | 7.85128 | 0.311814 | ||||||||
\(635\) | 0.280145 | 0.0111172 | ||||||||
\(636\) | −6.29483 | −0.249606 | ||||||||
\(637\) | −5.13626 | −0.203506 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 55.7060 | 2.20370 | ||||||||
\(640\) | 11.5312 | 0.455811 | ||||||||
\(641\) | 2.83172 | 0.111846 | 0.0559232 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559232 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(642\) | −24.2658 | −0.957693 | ||||||||
\(643\) | 23.9097 | 0.942906 | 0.471453 | − | 0.881891i | \(-0.343730\pi\) | ||||
0.471453 | + | 0.881891i | \(0.343730\pi\) | |||||||
\(644\) | −12.7027 | −0.500556 | ||||||||
\(645\) | −40.5373 | −1.59616 | ||||||||
\(646\) | 1.03264 | 0.0406285 | ||||||||
\(647\) | 44.5694 | 1.75220 | 0.876102 | − | 0.482125i | \(-0.160135\pi\) | ||||
0.876102 | + | 0.482125i | \(0.160135\pi\) | |||||||
\(648\) | 81.5515 | 3.20364 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.81328 | 0.110346 | ||||||||
\(651\) | 33.0241 | 1.29432 | ||||||||
\(652\) | −8.65220 | −0.338846 | ||||||||
\(653\) | 31.9181 | 1.24905 | 0.624526 | − | 0.781004i | \(-0.285292\pi\) | ||||
0.624526 | + | 0.781004i | \(0.285292\pi\) | |||||||
\(654\) | −3.90645 | −0.152754 | ||||||||
\(655\) | −1.47708 | −0.0577144 | ||||||||
\(656\) | −14.2261 | −0.555436 | ||||||||
\(657\) | 134.366 | 5.24214 | ||||||||
\(658\) | −1.29981 | −0.0506719 | ||||||||
\(659\) | −24.5460 | −0.956175 | −0.478087 | − | 0.878312i | \(-0.658670\pi\) | ||||
−0.478087 | + | 0.878312i | \(0.658670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.5345 | 0.720907 | 0.360454 | − | 0.932777i | \(-0.382622\pi\) | ||||
0.360454 | + | 0.932777i | \(0.382622\pi\) | |||||||
\(662\) | −6.76391 | −0.262887 | ||||||||
\(663\) | 33.2252 | 1.29036 | ||||||||
\(664\) | 6.53645 | 0.253664 | ||||||||
\(665\) | −0.995867 | −0.0386181 | ||||||||
\(666\) | 5.02277 | 0.194628 | ||||||||
\(667\) | −45.4122 | −1.75837 | ||||||||
\(668\) | 16.5796 | 0.641486 | ||||||||
\(669\) | −15.0349 | −0.581284 | ||||||||
\(670\) | 0.206947 | 0.00799507 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 18.1355 | 0.699591 | ||||||||
\(673\) | 43.2084 | 1.66556 | 0.832781 | − | 0.553603i | \(-0.186747\pi\) | ||||
0.832781 | + | 0.553603i | \(0.186747\pi\) | |||||||
\(674\) | 4.62274 | 0.178061 | ||||||||
\(675\) | −19.3937 | −0.746464 | ||||||||
\(676\) | −22.7478 | −0.874915 | ||||||||
\(677\) | −3.22240 | −0.123847 | −0.0619234 | − | 0.998081i | \(-0.519723\pi\) | ||||
−0.0619234 | + | 0.998081i | \(0.519723\pi\) | |||||||
\(678\) | −17.9869 | −0.690782 | ||||||||
\(679\) | 12.2829 | 0.471374 | ||||||||
\(680\) | 3.83660 | 0.147127 | ||||||||
\(681\) | −49.6808 | −1.90377 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.40205 | −0.359759 | −0.179880 | − | 0.983689i | \(-0.557571\pi\) | ||||
−0.179880 | + | 0.983689i | \(0.557571\pi\) | |||||||
\(684\) | 14.6877 | 0.561597 | ||||||||
\(685\) | 0.343777 | 0.0131351 | ||||||||
\(686\) | −0.547729 | −0.0209124 | ||||||||
\(687\) | 34.6904 | 1.32352 | ||||||||
\(688\) | 27.1670 | 1.03573 | ||||||||
\(689\) | 5.56598 | 0.212047 | ||||||||
\(690\) | 13.9848 | 0.532392 | ||||||||
\(691\) | −30.9052 | −1.17569 | −0.587845 | − | 0.808974i | \(-0.700023\pi\) | ||||
−0.587845 | + | 0.808974i | \(0.700023\pi\) | |||||||
\(692\) | −36.2871 | −1.37943 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.9455 | 0.567325 | ||||||||
\(695\) | −6.04284 | −0.229218 | ||||||||
\(696\) | 42.0855 | 1.59525 | ||||||||
\(697\) | −11.7608 | −0.445473 | ||||||||
\(698\) | 16.8602 | 0.638168 | ||||||||
\(699\) | 5.57213 | 0.210757 | ||||||||
\(700\) | −1.69999 | −0.0642537 | ||||||||
\(701\) | −26.1787 | −0.988754 | −0.494377 | − | 0.869248i | \(-0.664604\pi\) | ||||
−0.494377 | + | 0.869248i | \(0.664604\pi\) | |||||||
\(702\) | −54.5599 | −2.05923 | ||||||||
\(703\) | 1.05263 | 0.0397006 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.10878 | −0.305394 | ||||||||
\(706\) | 15.0152 | 0.565104 | ||||||||
\(707\) | −3.74207 | −0.140735 | ||||||||
\(708\) | −5.91251 | −0.222206 | ||||||||
\(709\) | 26.5618 | 0.997548 | 0.498774 | − | 0.866732i | \(-0.333784\pi\) | ||||
0.498774 | + | 0.866732i | \(0.333784\pi\) | |||||||
\(710\) | −3.51693 | −0.131988 | ||||||||
\(711\) | 103.455 | 3.87986 | ||||||||
\(712\) | −11.4704 | −0.429872 | ||||||||
\(713\) | −72.2168 | −2.70454 | ||||||||
\(714\) | 3.54313 | 0.132598 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.4311 | −0.913033 | ||||||||
\(717\) | −55.1411 | −2.05928 | ||||||||
\(718\) | −0.291216 | −0.0108681 | ||||||||
\(719\) | −13.5527 | −0.505430 | −0.252715 | − | 0.967541i | \(-0.581324\pi\) | ||||
−0.252715 | + | 0.967541i | \(0.581324\pi\) | |||||||
\(720\) | 19.8670 | 0.740399 | ||||||||
\(721\) | 6.95088 | 0.258864 | ||||||||
\(722\) | 9.86365 | 0.367087 | ||||||||
\(723\) | 46.9217 | 1.74504 | ||||||||
\(724\) | −16.9481 | −0.629873 | ||||||||
\(725\) | −6.07749 | −0.225712 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.6076 | −1.32061 | −0.660307 | − | 0.750996i | \(-0.729574\pi\) | ||||
−0.660307 | + | 0.750996i | \(0.729574\pi\) | |||||||
\(728\) | −10.4091 | −0.385787 | ||||||||
\(729\) | 150.312 | 5.56713 | ||||||||
\(730\) | −8.48306 | −0.313972 | ||||||||
\(731\) | 22.4592 | 0.830682 | ||||||||
\(732\) | −42.1802 | −1.55903 | ||||||||
\(733\) | −35.5542 | −1.31322 | −0.656612 | − | 0.754228i | \(-0.728011\pi\) | ||||
−0.656612 | + | 0.754228i | \(0.728011\pi\) | |||||||
\(734\) | −18.9309 | −0.698753 | ||||||||
\(735\) | −3.41697 | −0.126037 | ||||||||
\(736\) | −39.6584 | −1.46183 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 29.5208 | 1.08668 | ||||||||
\(739\) | 10.3900 | 0.382202 | 0.191101 | − | 0.981570i | \(-0.438794\pi\) | ||||
0.191101 | + | 0.981570i | \(0.438794\pi\) | |||||||
\(740\) | 1.79688 | 0.0660547 | ||||||||
\(741\) | −17.4779 | −0.642067 | ||||||||
\(742\) | 0.593556 | 0.0217901 | ||||||||
\(743\) | 4.51799 | 0.165749 | 0.0828744 | − | 0.996560i | \(-0.473590\pi\) | ||||
0.0828744 | + | 0.996560i | \(0.473590\pi\) | |||||||
\(744\) | 66.9265 | 2.45364 | ||||||||
\(745\) | −10.0211 | −0.367144 | ||||||||
\(746\) | −4.45756 | −0.163203 | ||||||||
\(747\) | 27.9821 | 1.02381 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.9654 | −0.473746 | ||||||||
\(750\) | 1.87158 | 0.0683403 | ||||||||
\(751\) | −33.6555 | −1.22811 | −0.614053 | − | 0.789265i | \(-0.710462\pi\) | ||||
−0.614053 | + | 0.789265i | \(0.710462\pi\) | |||||||
\(752\) | 5.43428 | 0.198168 | ||||||||
\(753\) | −28.9084 | −1.05348 | ||||||||
\(754\) | −17.0977 | −0.622660 | ||||||||
\(755\) | −9.02415 | −0.328422 | ||||||||
\(756\) | 32.9691 | 1.19908 | ||||||||
\(757\) | −29.9201 | −1.08747 | −0.543733 | − | 0.839258i | \(-0.682990\pi\) | ||||
−0.543733 | + | 0.839258i | \(0.682990\pi\) | |||||||
\(758\) | −8.71610 | −0.316583 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.01822 | −0.0732085 | ||||||||
\(761\) | −33.6178 | −1.21865 | −0.609323 | − | 0.792922i | \(-0.708559\pi\) | ||||
−0.609323 | + | 0.792922i | \(0.708559\pi\) | |||||||
\(762\) | 0.524313 | 0.0189939 | ||||||||
\(763\) | −2.08725 | −0.0755635 | ||||||||
\(764\) | −17.8986 | −0.647547 | ||||||||
\(765\) | 16.4242 | 0.593818 | ||||||||
\(766\) | 2.84071 | 0.102639 | ||||||||
\(767\) | 5.22793 | 0.188770 | ||||||||
\(768\) | 10.1493 | 0.366231 | ||||||||
\(769\) | −9.14233 | −0.329681 | −0.164840 | − | 0.986320i | \(-0.552711\pi\) | ||||
−0.164840 | + | 0.986320i | \(0.552711\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.1760 | 0.474523 | ||||||||
\(772\) | −5.14390 | −0.185133 | ||||||||
\(773\) | 13.2812 | 0.477692 | 0.238846 | − | 0.971057i | \(-0.423231\pi\) | ||||
0.238846 | + | 0.971057i | \(0.423231\pi\) | |||||||
\(774\) | −56.3747 | −2.02635 | ||||||||
\(775\) | −9.66473 | −0.347167 | ||||||||
\(776\) | 24.8924 | 0.893586 | ||||||||
\(777\) | 3.61172 | 0.129570 | ||||||||
\(778\) | 3.84716 | 0.137927 | ||||||||
\(779\) | 6.18671 | 0.221662 | ||||||||
\(780\) | −29.8356 | −1.06829 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −7.74808 | −0.277071 | ||||||||
\(783\) | 117.865 | 4.21215 | ||||||||
\(784\) | 2.28996 | 0.0817843 | ||||||||
\(785\) | −17.3777 | −0.620235 | ||||||||
\(786\) | −2.76448 | −0.0986056 | ||||||||
\(787\) | −4.06389 | −0.144862 | −0.0724310 | − | 0.997373i | \(-0.523076\pi\) | ||||
−0.0724310 | + | 0.997373i | \(0.523076\pi\) | |||||||
\(788\) | 22.2280 | 0.791839 | ||||||||
\(789\) | 101.868 | 3.62661 | ||||||||
\(790\) | −6.53150 | −0.232380 | ||||||||
\(791\) | −9.61055 | −0.341712 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37.2964 | 1.32443 | ||||||||
\(794\) | 16.3796 | 0.581292 | ||||||||
\(795\) | 3.70286 | 0.131327 | ||||||||
\(796\) | −3.37404 | −0.119590 | ||||||||
\(797\) | −33.4979 | −1.18656 | −0.593278 | − | 0.804998i | \(-0.702166\pi\) | ||||
−0.593278 | + | 0.804998i | \(0.702166\pi\) | |||||||
\(798\) | −1.86384 | −0.0659793 | ||||||||
\(799\) | 4.49256 | 0.158935 | ||||||||
\(800\) | −5.30747 | −0.187647 | ||||||||
\(801\) | −49.1040 | −1.73500 | ||||||||
\(802\) | −1.28677 | −0.0454373 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.19473 | −0.0774023 | ||||||||
\(805\) | 7.47220 | 0.263360 | ||||||||
\(806\) | −27.1896 | −0.957712 | ||||||||
\(807\) | −77.8134 | −2.73916 | ||||||||
\(808\) | −7.58366 | −0.266792 | ||||||||
\(809\) | −35.0399 | −1.23194 | −0.615969 | − | 0.787771i | \(-0.711235\pi\) | ||||
−0.615969 | + | 0.787771i | \(0.711235\pi\) | |||||||
\(810\) | −22.0410 | −0.774441 | ||||||||
\(811\) | −19.7702 | −0.694226 | −0.347113 | − | 0.937823i | \(-0.612838\pi\) | ||||
−0.347113 | + | 0.937823i | \(0.612838\pi\) | |||||||
\(812\) | 10.3317 | 0.362571 | ||||||||
\(813\) | 56.9832 | 1.99849 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.08955 | 0.178279 | ||||||||
\(816\) | −14.8132 | −0.518566 | ||||||||
\(817\) | −11.8145 | −0.413337 | ||||||||
\(818\) | 9.64112 | 0.337094 | ||||||||
\(819\) | −44.5606 | −1.55707 | ||||||||
\(820\) | 10.5610 | 0.368806 | ||||||||
\(821\) | −19.0535 | −0.664973 | −0.332486 | − | 0.943108i | \(-0.607888\pi\) | ||||
−0.332486 | + | 0.943108i | \(0.607888\pi\) | |||||||
\(822\) | 0.643406 | 0.0224414 | ||||||||
\(823\) | −32.7006 | −1.13987 | −0.569936 | − | 0.821689i | \(-0.693032\pi\) | ||||
−0.569936 | + | 0.821689i | \(0.693032\pi\) | |||||||
\(824\) | 14.0866 | 0.490731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.557506 | 0.0193981 | ||||||||
\(827\) | −13.7687 | −0.478786 | −0.239393 | − | 0.970923i | \(-0.576948\pi\) | ||||
−0.239393 | + | 0.970923i | \(0.576948\pi\) | |||||||
\(828\) | −110.205 | −3.82988 | ||||||||
\(829\) | 35.5525 | 1.23479 | 0.617394 | − | 0.786654i | \(-0.288188\pi\) | ||||
0.617394 | + | 0.786654i | \(0.288188\pi\) | |||||||
\(830\) | −1.76661 | −0.0613200 | ||||||||
\(831\) | 57.9501 | 2.01027 | ||||||||
\(832\) | 8.59225 | 0.297883 | ||||||||
\(833\) | 1.89313 | 0.0655929 | ||||||||
\(834\) | −11.3096 | −0.391621 | ||||||||
\(835\) | −9.75278 | −0.337509 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 187.435 | 6.47870 | ||||||||
\(838\) | 17.6513 | 0.609754 | ||||||||
\(839\) | −27.9612 | −0.965328 | −0.482664 | − | 0.875806i | \(-0.660331\pi\) | ||||
−0.482664 | + | 0.875806i | \(0.660331\pi\) | |||||||
\(840\) | −6.92482 | −0.238929 | ||||||||
\(841\) | 7.93589 | 0.273651 | ||||||||
\(842\) | −8.97947 | −0.309453 | ||||||||
\(843\) | 99.6220 | 3.43116 | ||||||||
\(844\) | 14.7772 | 0.508653 | ||||||||
\(845\) | 13.3811 | 0.460324 | ||||||||
\(846\) | −11.2768 | −0.387703 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.48155 | −0.0852168 | ||||||||
\(849\) | −36.5061 | −1.25289 | ||||||||
\(850\) | −1.03692 | −0.0355661 | ||||||||
\(851\) | −7.89807 | −0.270742 | ||||||||
\(852\) | 37.2981 | 1.27781 | ||||||||
\(853\) | −27.6775 | −0.947659 | −0.473829 | − | 0.880617i | \(-0.657129\pi\) | ||||
−0.473829 | + | 0.880617i | \(0.657129\pi\) | |||||||
\(854\) | 3.97728 | 0.136100 | ||||||||
\(855\) | −8.63984 | −0.295476 | ||||||||
\(856\) | −26.2756 | −0.898083 | ||||||||
\(857\) | 9.26699 | 0.316554 | 0.158277 | − | 0.987395i | \(-0.449406\pi\) | ||||
0.158277 | + | 0.987395i | \(0.449406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.7659 | −0.606165 | −0.303083 | − | 0.952964i | \(-0.598016\pi\) | ||||
−0.303083 | + | 0.952964i | \(0.598016\pi\) | |||||||
\(860\) | −20.1679 | −0.687720 | ||||||||
\(861\) | 21.2275 | 0.723432 | ||||||||
\(862\) | 9.70969 | 0.330714 | ||||||||
\(863\) | −56.8973 | −1.93681 | −0.968403 | − | 0.249392i | \(-0.919769\pi\) | ||||
−0.968403 | + | 0.249392i | \(0.919769\pi\) | |||||||
\(864\) | 102.931 | 3.50180 | ||||||||
\(865\) | 21.3455 | 0.725767 | ||||||||
\(866\) | −1.18553 | −0.0402858 | ||||||||
\(867\) | 45.8423 | 1.55689 | ||||||||
\(868\) | 16.4300 | 0.557670 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −11.3745 | −0.385631 | ||||||||
\(871\) | 1.94062 | 0.0657553 | ||||||||
\(872\) | −4.23001 | −0.143246 | ||||||||
\(873\) | 106.563 | 3.60660 | ||||||||
\(874\) | 4.07583 | 0.137867 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 89.9653 | 3.03965 | ||||||||
\(877\) | −8.65101 | −0.292124 | −0.146062 | − | 0.989275i | \(-0.546660\pi\) | ||||
−0.146062 | + | 0.989275i | \(0.546660\pi\) | |||||||
\(878\) | −11.3081 | −0.381629 | ||||||||
\(879\) | −43.5571 | −1.46915 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.7680 | 1.10398 | 0.551990 | − | 0.833851i | \(-0.313869\pi\) | ||||
0.551990 | + | 0.833851i | \(0.313869\pi\) | |||||||
\(882\) | −4.75193 | −0.160006 | ||||||||
\(883\) | 11.6739 | 0.392858 | 0.196429 | − | 0.980518i | \(-0.437065\pi\) | ||||
0.196429 | + | 0.980518i | \(0.437065\pi\) | |||||||
\(884\) | 16.5300 | 0.555965 | ||||||||
\(885\) | 3.47796 | 0.116910 | ||||||||
\(886\) | −8.85573 | −0.297514 | ||||||||
\(887\) | 1.68583 | 0.0566046 | 0.0283023 | − | 0.999599i | \(-0.490990\pi\) | ||||
0.0283023 | + | 0.999599i | \(0.490990\pi\) | |||||||
\(888\) | 7.31949 | 0.245626 | ||||||||
\(889\) | 0.280145 | 0.00939577 | ||||||||
\(890\) | 3.10012 | 0.103916 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.48010 | −0.250452 | ||||||||
\(893\) | −2.36328 | −0.0790842 | ||||||||
\(894\) | −18.7552 | −0.627268 | ||||||||
\(895\) | 14.3713 | 0.480380 | ||||||||
\(896\) | 11.5312 | 0.385231 | ||||||||
\(897\) | 131.140 | 4.37865 | ||||||||
\(898\) | 2.81799 | 0.0940374 | ||||||||
\(899\) | 58.7373 | 1.95900 | ||||||||
\(900\) | −14.7486 | −0.491621 | ||||||||
\(901\) | −2.05152 | −0.0683459 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −40.5373 | −1.34900 | ||||||||
\(904\) | −19.4767 | −0.647785 | ||||||||
\(905\) | 9.96954 | 0.331399 | ||||||||
\(906\) | −16.8894 | −0.561112 | ||||||||
\(907\) | −5.39591 | −0.179168 | −0.0895842 | − | 0.995979i | \(-0.528554\pi\) | ||||
−0.0895842 | + | 0.995979i | \(0.528554\pi\) | |||||||
\(908\) | −24.7169 | −0.820259 | ||||||||
\(909\) | −32.4651 | −1.07680 | ||||||||
\(910\) | 2.81328 | 0.0932593 | ||||||||
\(911\) | −13.2051 | −0.437504 | −0.218752 | − | 0.975781i | \(-0.570199\pi\) | ||||
−0.218752 | + | 0.975781i | \(0.570199\pi\) | |||||||
\(912\) | 7.79239 | 0.258032 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.03200 | 0.298752 | ||||||||
\(915\) | 24.8120 | 0.820260 | ||||||||
\(916\) | 17.2589 | 0.570252 | ||||||||
\(917\) | −1.47708 | −0.0487776 | ||||||||
\(918\) | 20.1097 | 0.663720 | ||||||||
\(919\) | −38.0294 | −1.25448 | −0.627238 | − | 0.778828i | \(-0.715815\pi\) | ||||
−0.627238 | + | 0.778828i | \(0.715815\pi\) | |||||||
\(920\) | 15.1431 | 0.499254 | ||||||||
\(921\) | −70.0032 | −2.30668 | ||||||||
\(922\) | −0.488528 | −0.0160888 | ||||||||
\(923\) | −32.9795 | −1.08553 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05699 | −0.0347538 | ||||||||
\(926\) | 2.97162 | 0.0976535 | ||||||||
\(927\) | 60.3037 | 1.98063 | ||||||||
\(928\) | 32.2561 | 1.05886 | ||||||||
\(929\) | −41.2258 | −1.35257 | −0.676287 | − | 0.736638i | \(-0.736412\pi\) | ||||
−0.676287 | + | 0.736638i | \(0.736412\pi\) | |||||||
\(930\) | −18.0883 | −0.593138 | ||||||||
\(931\) | −0.995867 | −0.0326382 | ||||||||
\(932\) | 2.77222 | 0.0908069 | ||||||||
\(933\) | 40.6451 | 1.33066 | ||||||||
\(934\) | −11.1760 | −0.365691 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −90.3063 | −2.95175 | ||||||||
\(937\) | −37.3182 | −1.21913 | −0.609566 | − | 0.792736i | \(-0.708656\pi\) | ||||
−0.609566 | + | 0.792736i | \(0.708656\pi\) | |||||||
\(938\) | 0.206947 | 0.00675707 | ||||||||
\(939\) | 27.9869 | 0.913317 | ||||||||
\(940\) | −4.03423 | −0.131582 | ||||||||
\(941\) | −39.5979 | −1.29085 | −0.645427 | − | 0.763822i | \(-0.723320\pi\) | ||||
−0.645427 | + | 0.763822i | \(0.723320\pi\) | |||||||
\(942\) | −32.5236 | −1.05968 | ||||||||
\(943\) | −46.4201 | −1.51165 | ||||||||
\(944\) | −2.33083 | −0.0758621 | ||||||||
\(945\) | −19.3937 | −0.630877 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.6182 | −1.28742 | −0.643710 | − | 0.765270i | \(-0.722605\pi\) | ||||
−0.643710 | + | 0.765270i | \(0.722605\pi\) | |||||||
\(948\) | 69.2684 | 2.24973 | ||||||||
\(949\) | −79.5487 | −2.58226 | ||||||||
\(950\) | 0.545466 | 0.0176972 | ||||||||
\(951\) | 48.9797 | 1.58827 | ||||||||
\(952\) | 3.83660 | 0.124345 | ||||||||
\(953\) | −48.2126 | −1.56176 | −0.780879 | − | 0.624682i | \(-0.785228\pi\) | ||||
−0.780879 | + | 0.624682i | \(0.785228\pi\) | |||||||
\(954\) | 5.14951 | 0.166722 | ||||||||
\(955\) | 10.5286 | 0.340698 | ||||||||
\(956\) | −27.4335 | −0.887263 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.2405 | −0.492397 | ||||||||
\(959\) | 0.343777 | 0.0111012 | ||||||||
\(960\) | 5.71612 | 0.184487 | ||||||||
\(961\) | 62.4070 | 2.01313 | ||||||||
\(962\) | −2.97362 | −0.0958734 | ||||||||
\(963\) | −112.484 | −3.62475 | ||||||||
\(964\) | 23.3442 | 0.751867 | ||||||||
\(965\) | 3.02584 | 0.0974052 | ||||||||
\(966\) | 13.9848 | 0.449953 | ||||||||
\(967\) | −26.0410 | −0.837421 | −0.418710 | − | 0.908120i | \(-0.637518\pi\) | ||||
−0.418710 | + | 0.908120i | \(0.637518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.44203 | 0.206948 | ||||||||
\(970\) | −6.72770 | −0.216013 | ||||||||
\(971\) | −12.9452 | −0.415433 | −0.207716 | − | 0.978189i | \(-0.566603\pi\) | ||||
−0.207716 | + | 0.978189i | \(0.566603\pi\) | |||||||
\(972\) | 134.843 | 4.32511 | ||||||||
\(973\) | −6.04284 | −0.193725 | ||||||||
\(974\) | 13.3229 | 0.426892 | ||||||||
\(975\) | 17.5504 | 0.562064 | ||||||||
\(976\) | −16.6283 | −0.532259 | ||||||||
\(977\) | 46.1868 | 1.47765 | 0.738823 | − | 0.673899i | \(-0.235382\pi\) | ||||
0.738823 | + | 0.673899i | \(0.235382\pi\) | |||||||
\(978\) | 9.52549 | 0.304591 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.69999 | −0.0543043 | ||||||||
\(981\) | −18.1083 | −0.578155 | ||||||||
\(982\) | 18.9124 | 0.603519 | ||||||||
\(983\) | 21.5777 | 0.688223 | 0.344111 | − | 0.938929i | \(-0.388180\pi\) | ||||
0.344111 | + | 0.938929i | \(0.388180\pi\) | |||||||
\(984\) | 43.0196 | 1.37141 | ||||||||
\(985\) | −13.0753 | −0.416615 | ||||||||
\(986\) | 6.30188 | 0.200693 | ||||||||
\(987\) | −8.10878 | −0.258105 | ||||||||
\(988\) | −8.69551 | −0.276641 | ||||||||
\(989\) | 88.6466 | 2.81880 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.6240 | −1.32223 | −0.661115 | − | 0.750285i | \(-0.729916\pi\) | ||||
−0.661115 | + | 0.750285i | \(0.729916\pi\) | |||||||
\(992\) | 51.2953 | 1.62863 | ||||||||
\(993\) | −42.1962 | −1.33906 | ||||||||
\(994\) | −3.51693 | −0.111550 | ||||||||
\(995\) | 1.98474 | 0.0629205 | ||||||||
\(996\) | 18.7354 | 0.593655 | ||||||||
\(997\) | −8.11693 | −0.257066 | −0.128533 | − | 0.991705i | \(-0.541027\pi\) | ||||
−0.128533 | + | 0.991705i | \(0.541027\pi\) | |||||||
\(998\) | −13.6337 | −0.431568 | ||||||||
\(999\) | 20.4990 | 0.648561 |
(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 | 4235.2.a.bi.1.5 | ✓ | 10 | |
11.10 | odd | 2 | 4235.2.a.bk.1.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4235.2.a.bi.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
4235.2.a.bk.1.6 | yes | 10 | 11.10 | odd | 2 |