Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5225,2,Mod(1,5225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5225, 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("5225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5225 = 5^{2} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5225.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: | \(41.7218350561\) |
Analytic rank: | \(0\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 5 x^{14} - 11 x^{13} + 87 x^{12} - 4 x^{11} - 545 x^{10} + 431 x^{9} + 1480 x^{8} - 1763 x^{7} + \cdots + 15 \) |
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 | 1.14 | ||
Root | \(2.61792\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.61792 | 1.85115 | 0.925575 | − | 0.378563i | \(-0.123582\pi\) | ||||
0.925575 | + | 0.378563i | \(0.123582\pi\) | |||||||
\(3\) | 2.17802 | 1.25748 | 0.628739 | − | 0.777616i | \(-0.283571\pi\) | ||||
0.628739 | + | 0.777616i | \(0.283571\pi\) | |||||||
\(4\) | 4.85352 | 2.42676 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.70188 | 2.32778 | ||||||||
\(7\) | 4.94832 | 1.87029 | 0.935144 | − | 0.354268i | \(-0.115270\pi\) | ||||
0.935144 | + | 0.354268i | \(0.115270\pi\) | |||||||
\(8\) | 7.47030 | 2.64115 | ||||||||
\(9\) | 1.74376 | 0.581253 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 10.5710 | 3.05160 | ||||||||
\(13\) | −4.20557 | −1.16642 | −0.583208 | − | 0.812323i | \(-0.698203\pi\) | ||||
−0.583208 | + | 0.812323i | \(0.698203\pi\) | |||||||
\(14\) | 12.9543 | 3.46218 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.84962 | 2.46240 | ||||||||
\(17\) | −6.38851 | −1.54944 | −0.774720 | − | 0.632304i | \(-0.782109\pi\) | ||||
−0.774720 | + | 0.632304i | \(0.782109\pi\) | |||||||
\(18\) | 4.56502 | 1.07599 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.7775 | 2.35185 | ||||||||
\(22\) | 2.61792 | 0.558143 | ||||||||
\(23\) | 6.66227 | 1.38918 | 0.694590 | − | 0.719406i | \(-0.255586\pi\) | ||||
0.694590 | + | 0.719406i | \(0.255586\pi\) | |||||||
\(24\) | 16.2704 | 3.32119 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −11.0099 | −2.15921 | ||||||||
\(27\) | −2.73612 | −0.526566 | ||||||||
\(28\) | 24.0168 | 4.53874 | ||||||||
\(29\) | −6.65643 | −1.23607 | −0.618034 | − | 0.786151i | \(-0.712071\pi\) | ||||
−0.618034 | + | 0.786151i | \(0.712071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.53855 | −1.71317 | −0.856587 | − | 0.516002i | \(-0.827420\pi\) | ||||
−0.856587 | + | 0.516002i | \(0.827420\pi\) | |||||||
\(32\) | 10.8449 | 1.91713 | ||||||||
\(33\) | 2.17802 | 0.379144 | ||||||||
\(34\) | −16.7246 | −2.86825 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.46336 | 1.41056 | ||||||||
\(37\) | −3.69327 | −0.607170 | −0.303585 | − | 0.952804i | \(-0.598184\pi\) | ||||
−0.303585 | + | 0.952804i | \(0.598184\pi\) | |||||||
\(38\) | 2.61792 | 0.424683 | ||||||||
\(39\) | −9.15980 | −1.46674 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.08046 | −0.168740 | −0.0843701 | − | 0.996434i | \(-0.526888\pi\) | ||||
−0.0843701 | + | 0.996434i | \(0.526888\pi\) | |||||||
\(42\) | 28.2147 | 4.35362 | ||||||||
\(43\) | 9.58018 | 1.46096 | 0.730482 | − | 0.682932i | \(-0.239296\pi\) | ||||
0.730482 | + | 0.682932i | \(0.239296\pi\) | |||||||
\(44\) | 4.85352 | 0.731696 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17.4413 | 2.57158 | ||||||||
\(47\) | 2.90169 | 0.423256 | 0.211628 | − | 0.977350i | \(-0.432124\pi\) | ||||
0.211628 | + | 0.977350i | \(0.432124\pi\) | |||||||
\(48\) | 21.4526 | 3.09642 | ||||||||
\(49\) | 17.4858 | 2.49798 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.9143 | −1.94839 | ||||||||
\(52\) | −20.4118 | −2.83061 | ||||||||
\(53\) | −6.75151 | −0.927391 | −0.463695 | − | 0.885995i | \(-0.653477\pi\) | ||||
−0.463695 | + | 0.885995i | \(0.653477\pi\) | |||||||
\(54\) | −7.16294 | −0.974753 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 36.9654 | 4.93971 | ||||||||
\(57\) | 2.17802 | 0.288485 | ||||||||
\(58\) | −17.4260 | −2.28815 | ||||||||
\(59\) | −0.613007 | −0.0798067 | −0.0399034 | − | 0.999204i | \(-0.512705\pi\) | ||||
−0.0399034 | + | 0.999204i | \(0.512705\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.33665 | 0.171140 | 0.0855701 | − | 0.996332i | \(-0.472729\pi\) | ||||
0.0855701 | + | 0.996332i | \(0.472729\pi\) | |||||||
\(62\) | −24.9712 | −3.17134 | ||||||||
\(63\) | 8.62866 | 1.08711 | ||||||||
\(64\) | 8.69200 | 1.08650 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.70188 | 0.701853 | ||||||||
\(67\) | 0.386619 | 0.0472330 | 0.0236165 | − | 0.999721i | \(-0.492482\pi\) | ||||
0.0236165 | + | 0.999721i | \(0.492482\pi\) | |||||||
\(68\) | −31.0067 | −3.76012 | ||||||||
\(69\) | 14.5105 | 1.74686 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.38483 | 1.11377 | 0.556887 | − | 0.830588i | \(-0.311996\pi\) | ||||
0.556887 | + | 0.830588i | \(0.311996\pi\) | |||||||
\(72\) | 13.0264 | 1.53517 | ||||||||
\(73\) | −1.97456 | −0.231105 | −0.115552 | − | 0.993301i | \(-0.536864\pi\) | ||||
−0.115552 | + | 0.993301i | \(0.536864\pi\) | |||||||
\(74\) | −9.66869 | −1.12396 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.85352 | 0.556737 | ||||||||
\(77\) | 4.94832 | 0.563913 | ||||||||
\(78\) | −23.9797 | −2.71516 | ||||||||
\(79\) | −6.61494 | −0.744238 | −0.372119 | − | 0.928185i | \(-0.621369\pi\) | ||||
−0.372119 | + | 0.928185i | \(0.621369\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1906 | −1.24340 | ||||||||
\(82\) | −2.82857 | −0.312364 | ||||||||
\(83\) | −0.100761 | −0.0110600 | −0.00553000 | − | 0.999985i | \(-0.501760\pi\) | ||||
−0.00553000 | + | 0.999985i | \(0.501760\pi\) | |||||||
\(84\) | 52.3089 | 5.70737 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 25.0802 | 2.70446 | ||||||||
\(87\) | −14.4978 | −1.55433 | ||||||||
\(88\) | 7.47030 | 0.796336 | ||||||||
\(89\) | 2.48738 | 0.263661 | 0.131831 | − | 0.991272i | \(-0.457914\pi\) | ||||
0.131831 | + | 0.991272i | \(0.457914\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.8105 | −2.18153 | ||||||||
\(92\) | 32.3355 | 3.37121 | ||||||||
\(93\) | −20.7751 | −2.15428 | ||||||||
\(94\) | 7.59641 | 0.783510 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 23.6205 | 2.41075 | ||||||||
\(97\) | −17.3288 | −1.75947 | −0.879737 | − | 0.475461i | \(-0.842281\pi\) | ||||
−0.879737 | + | 0.475461i | \(0.842281\pi\) | |||||||
\(98\) | 45.7766 | 4.62413 | ||||||||
\(99\) | 1.74376 | 0.175254 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.71209 | −0.966389 | −0.483194 | − | 0.875513i | \(-0.660524\pi\) | ||||
−0.483194 | + | 0.875513i | \(0.660524\pi\) | |||||||
\(102\) | −36.4265 | −3.60676 | ||||||||
\(103\) | 15.6212 | 1.53920 | 0.769602 | − | 0.638524i | \(-0.220455\pi\) | ||||
0.769602 | + | 0.638524i | \(0.220455\pi\) | |||||||
\(104\) | −31.4168 | −3.08068 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.6749 | −1.71674 | ||||||||
\(107\) | −5.49210 | −0.530941 | −0.265471 | − | 0.964119i | \(-0.585527\pi\) | ||||
−0.265471 | + | 0.964119i | \(0.585527\pi\) | |||||||
\(108\) | −13.2798 | −1.27785 | ||||||||
\(109\) | 13.5177 | 1.29476 | 0.647378 | − | 0.762169i | \(-0.275865\pi\) | ||||
0.647378 | + | 0.762169i | \(0.275865\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.04400 | −0.763503 | ||||||||
\(112\) | 48.7390 | 4.60540 | ||||||||
\(113\) | −11.1897 | −1.05264 | −0.526318 | − | 0.850288i | \(-0.676428\pi\) | ||||
−0.526318 | + | 0.850288i | \(0.676428\pi\) | |||||||
\(114\) | 5.70188 | 0.534030 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −32.3071 | −2.99964 | ||||||||
\(117\) | −7.33349 | −0.677982 | ||||||||
\(118\) | −1.60481 | −0.147734 | ||||||||
\(119\) | −31.6124 | −2.89790 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 3.49924 | 0.316806 | ||||||||
\(123\) | −2.35327 | −0.212187 | ||||||||
\(124\) | −46.2955 | −4.15746 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 22.5892 | 2.01240 | ||||||||
\(127\) | 6.65255 | 0.590319 | 0.295159 | − | 0.955448i | \(-0.404627\pi\) | ||||
0.295159 | + | 0.955448i | \(0.404627\pi\) | |||||||
\(128\) | 1.06509 | 0.0941412 | ||||||||
\(129\) | 20.8658 | 1.83713 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.4455 | 1.61159 | 0.805797 | − | 0.592192i | \(-0.201737\pi\) | ||||
0.805797 | + | 0.592192i | \(0.201737\pi\) | |||||||
\(132\) | 10.5710 | 0.920092 | ||||||||
\(133\) | 4.94832 | 0.429073 | ||||||||
\(134\) | 1.01214 | 0.0874355 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −47.7240 | −4.09230 | ||||||||
\(137\) | −15.3705 | −1.31319 | −0.656597 | − | 0.754242i | \(-0.728005\pi\) | ||||
−0.656597 | + | 0.754242i | \(0.728005\pi\) | |||||||
\(138\) | 37.9875 | 3.23371 | ||||||||
\(139\) | −2.38661 | −0.202430 | −0.101215 | − | 0.994865i | \(-0.532273\pi\) | ||||
−0.101215 | + | 0.994865i | \(0.532273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.31994 | 0.532235 | ||||||||
\(142\) | 24.5688 | 2.06176 | ||||||||
\(143\) | −4.20557 | −0.351687 | ||||||||
\(144\) | 17.1753 | 1.43128 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.16924 | −0.427809 | ||||||||
\(147\) | 38.0844 | 3.14115 | ||||||||
\(148\) | −17.9254 | −1.47346 | ||||||||
\(149\) | −10.6114 | −0.869317 | −0.434659 | − | 0.900595i | \(-0.643131\pi\) | ||||
−0.434659 | + | 0.900595i | \(0.643131\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.8914 | 1.21185 | 0.605923 | − | 0.795523i | \(-0.292804\pi\) | ||||
0.605923 | + | 0.795523i | \(0.292804\pi\) | |||||||
\(152\) | 7.47030 | 0.605921 | ||||||||
\(153\) | −11.1400 | −0.900616 | ||||||||
\(154\) | 12.9543 | 1.04389 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −44.4573 | −3.55943 | ||||||||
\(157\) | 5.84649 | 0.466601 | 0.233300 | − | 0.972405i | \(-0.425047\pi\) | ||||
0.233300 | + | 0.972405i | \(0.425047\pi\) | |||||||
\(158\) | −17.3174 | −1.37770 | ||||||||
\(159\) | −14.7049 | −1.16617 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.9670 | 2.59817 | ||||||||
\(162\) | −29.2961 | −2.30172 | ||||||||
\(163\) | −3.65131 | −0.285993 | −0.142996 | − | 0.989723i | \(-0.545674\pi\) | ||||
−0.142996 | + | 0.989723i | \(0.545674\pi\) | |||||||
\(164\) | −5.24405 | −0.409492 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.263785 | −0.0204737 | ||||||||
\(167\) | −8.34211 | −0.645532 | −0.322766 | − | 0.946479i | \(-0.604613\pi\) | ||||
−0.322766 | + | 0.946479i | \(0.604613\pi\) | |||||||
\(168\) | 80.5112 | 6.21158 | ||||||||
\(169\) | 4.68682 | 0.360524 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.74376 | 0.133348 | ||||||||
\(172\) | 46.4976 | 3.54541 | ||||||||
\(173\) | 14.4715 | 1.10025 | 0.550124 | − | 0.835083i | \(-0.314580\pi\) | ||||
0.550124 | + | 0.835083i | \(0.314580\pi\) | |||||||
\(174\) | −37.9542 | −2.87730 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.84962 | 0.742443 | ||||||||
\(177\) | −1.33514 | −0.100355 | ||||||||
\(178\) | 6.51176 | 0.488077 | ||||||||
\(179\) | 23.2230 | 1.73577 | 0.867884 | − | 0.496766i | \(-0.165479\pi\) | ||||
0.867884 | + | 0.496766i | \(0.165479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.66090 | 0.272112 | 0.136056 | − | 0.990701i | \(-0.456557\pi\) | ||||
0.136056 | + | 0.990701i | \(0.456557\pi\) | |||||||
\(182\) | −54.4803 | −4.03834 | ||||||||
\(183\) | 2.91124 | 0.215205 | ||||||||
\(184\) | 49.7691 | 3.66903 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −54.3877 | −3.98790 | ||||||||
\(187\) | −6.38851 | −0.467174 | ||||||||
\(188\) | 14.0834 | 1.02714 | ||||||||
\(189\) | −13.5392 | −0.984830 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.3590 | 1.69020 | 0.845099 | − | 0.534610i | \(-0.179541\pi\) | ||||
0.845099 | + | 0.534610i | \(0.179541\pi\) | |||||||
\(192\) | 18.9313 | 1.36625 | ||||||||
\(193\) | 25.1709 | 1.81184 | 0.905922 | − | 0.423445i | \(-0.139179\pi\) | ||||
0.905922 | + | 0.423445i | \(0.139179\pi\) | |||||||
\(194\) | −45.3655 | −3.25705 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 84.8678 | 6.06199 | ||||||||
\(197\) | 6.98835 | 0.497899 | 0.248950 | − | 0.968516i | \(-0.419915\pi\) | ||||
0.248950 | + | 0.968516i | \(0.419915\pi\) | |||||||
\(198\) | 4.56502 | 0.324422 | ||||||||
\(199\) | 11.5381 | 0.817911 | 0.408955 | − | 0.912554i | \(-0.365893\pi\) | ||||
0.408955 | + | 0.912554i | \(0.365893\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.842063 | 0.0593946 | ||||||||
\(202\) | −25.4255 | −1.78893 | ||||||||
\(203\) | −32.9381 | −2.31180 | ||||||||
\(204\) | −67.5332 | −4.72827 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 40.8951 | 2.84930 | ||||||||
\(207\) | 11.6174 | 0.807464 | ||||||||
\(208\) | −41.4232 | −2.87219 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.7660 | 0.947687 | 0.473844 | − | 0.880609i | \(-0.342866\pi\) | ||||
0.473844 | + | 0.880609i | \(0.342866\pi\) | |||||||
\(212\) | −32.7686 | −2.25055 | ||||||||
\(213\) | 20.4403 | 1.40055 | ||||||||
\(214\) | −14.3779 | −0.982853 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −20.4396 | −1.39074 | ||||||||
\(217\) | −47.1998 | −3.20413 | ||||||||
\(218\) | 35.3882 | 2.39679 | ||||||||
\(219\) | −4.30062 | −0.290609 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 26.8673 | 1.80729 | ||||||||
\(222\) | −21.0586 | −1.41336 | ||||||||
\(223\) | −18.7373 | −1.25474 | −0.627371 | − | 0.778720i | \(-0.715869\pi\) | ||||
−0.627371 | + | 0.778720i | \(0.715869\pi\) | |||||||
\(224\) | 53.6642 | 3.58559 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −29.2937 | −1.94859 | ||||||||
\(227\) | −21.7922 | −1.44640 | −0.723199 | − | 0.690640i | \(-0.757329\pi\) | ||||
−0.723199 | + | 0.690640i | \(0.757329\pi\) | |||||||
\(228\) | 10.5710 | 0.700085 | ||||||||
\(229\) | −15.5530 | −1.02777 | −0.513886 | − | 0.857859i | \(-0.671795\pi\) | ||||
−0.513886 | + | 0.857859i | \(0.671795\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.7775 | 0.709109 | ||||||||
\(232\) | −49.7255 | −3.26464 | ||||||||
\(233\) | 27.0173 | 1.76996 | 0.884982 | − | 0.465625i | \(-0.154170\pi\) | ||||
0.884982 | + | 0.465625i | \(0.154170\pi\) | |||||||
\(234\) | −19.1985 | −1.25505 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.97524 | −0.193672 | ||||||||
\(237\) | −14.4074 | −0.935864 | ||||||||
\(238\) | −82.7587 | −5.36445 | ||||||||
\(239\) | −26.5139 | −1.71504 | −0.857521 | − | 0.514449i | \(-0.827997\pi\) | ||||
−0.857521 | + | 0.514449i | \(0.827997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.1879 | −1.04275 | −0.521377 | − | 0.853327i | \(-0.674581\pi\) | ||||
−0.521377 | + | 0.853327i | \(0.674581\pi\) | |||||||
\(242\) | 2.61792 | 0.168286 | ||||||||
\(243\) | −16.1649 | −1.03698 | ||||||||
\(244\) | 6.48745 | 0.415316 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.16068 | −0.392790 | ||||||||
\(247\) | −4.20557 | −0.267594 | ||||||||
\(248\) | −71.2558 | −4.52475 | ||||||||
\(249\) | −0.219460 | −0.0139077 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.48202 | 0.156664 | 0.0783319 | − | 0.996927i | \(-0.475041\pi\) | ||||
0.0783319 | + | 0.996927i | \(0.475041\pi\) | |||||||
\(252\) | 41.8794 | 2.63815 | ||||||||
\(253\) | 6.66227 | 0.418853 | ||||||||
\(254\) | 17.4159 | 1.09277 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.5957 | −0.912230 | ||||||||
\(257\) | −1.75270 | −0.109330 | −0.0546651 | − | 0.998505i | \(-0.517409\pi\) | ||||
−0.0546651 | + | 0.998505i | \(0.517409\pi\) | |||||||
\(258\) | 54.6250 | 3.40081 | ||||||||
\(259\) | −18.2755 | −1.13558 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.6072 | −0.718468 | ||||||||
\(262\) | 48.2890 | 2.98330 | ||||||||
\(263\) | −15.9328 | −0.982460 | −0.491230 | − | 0.871030i | \(-0.663452\pi\) | ||||
−0.491230 | + | 0.871030i | \(0.663452\pi\) | |||||||
\(264\) | 16.2704 | 1.00138 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.9543 | 0.794280 | ||||||||
\(267\) | 5.41755 | 0.331549 | ||||||||
\(268\) | 1.87646 | 0.114623 | ||||||||
\(269\) | −5.40061 | −0.329281 | −0.164641 | − | 0.986354i | \(-0.552646\pi\) | ||||
−0.164641 | + | 0.986354i | \(0.552646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.761668 | −0.0462680 | −0.0231340 | − | 0.999732i | \(-0.507364\pi\) | ||||
−0.0231340 | + | 0.999732i | \(0.507364\pi\) | |||||||
\(272\) | −62.9243 | −3.81535 | ||||||||
\(273\) | −45.3256 | −2.74323 | ||||||||
\(274\) | −40.2389 | −2.43092 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 70.4272 | 4.23922 | ||||||||
\(277\) | 26.9579 | 1.61974 | 0.809872 | − | 0.586606i | \(-0.199536\pi\) | ||||
0.809872 | + | 0.586606i | \(0.199536\pi\) | |||||||
\(278\) | −6.24797 | −0.374729 | ||||||||
\(279\) | −16.6329 | −0.995787 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.4983 | 1.10352 | 0.551759 | − | 0.834004i | \(-0.313957\pi\) | ||||
0.551759 | + | 0.834004i | \(0.313957\pi\) | |||||||
\(282\) | 16.5451 | 0.985247 | ||||||||
\(283\) | 18.9028 | 1.12365 | 0.561827 | − | 0.827255i | \(-0.310099\pi\) | ||||
0.561827 | + | 0.827255i | \(0.310099\pi\) | |||||||
\(284\) | 45.5495 | 2.70286 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.0099 | −0.651026 | ||||||||
\(287\) | −5.34648 | −0.315593 | ||||||||
\(288\) | 18.9110 | 1.11434 | ||||||||
\(289\) | 23.8130 | 1.40077 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −37.7424 | −2.21250 | ||||||||
\(292\) | −9.58356 | −0.560835 | ||||||||
\(293\) | 13.8515 | 0.809214 | 0.404607 | − | 0.914491i | \(-0.367408\pi\) | ||||
0.404607 | + | 0.914491i | \(0.367408\pi\) | |||||||
\(294\) | 99.7021 | 5.81475 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −27.5898 | −1.60363 | ||||||||
\(297\) | −2.73612 | −0.158766 | ||||||||
\(298\) | −27.7797 | −1.60924 | ||||||||
\(299\) | −28.0186 | −1.62036 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 47.4057 | 2.73242 | ||||||||
\(302\) | 38.9846 | 2.24331 | ||||||||
\(303\) | −21.1531 | −1.21521 | ||||||||
\(304\) | 9.84962 | 0.564914 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −29.1637 | −1.66718 | ||||||||
\(307\) | 0.233341 | 0.0133175 | 0.00665874 | − | 0.999978i | \(-0.497880\pi\) | ||||
0.00665874 | + | 0.999978i | \(0.497880\pi\) | |||||||
\(308\) | 24.0168 | 1.36848 | ||||||||
\(309\) | 34.0233 | 1.93552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.70278 | 0.436784 | 0.218392 | − | 0.975861i | \(-0.429919\pi\) | ||||
0.218392 | + | 0.975861i | \(0.429919\pi\) | |||||||
\(312\) | −68.4264 | −3.87388 | ||||||||
\(313\) | 14.9273 | 0.843742 | 0.421871 | − | 0.906656i | \(-0.361374\pi\) | ||||
0.421871 | + | 0.906656i | \(0.361374\pi\) | |||||||
\(314\) | 15.3057 | 0.863749 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −32.1057 | −1.80609 | ||||||||
\(317\) | −3.39011 | −0.190408 | −0.0952038 | − | 0.995458i | \(-0.530350\pi\) | ||||
−0.0952038 | + | 0.995458i | \(0.530350\pi\) | |||||||
\(318\) | −38.4963 | −2.15876 | ||||||||
\(319\) | −6.65643 | −0.372689 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.9619 | −0.667648 | ||||||||
\(322\) | 86.3051 | 4.80960 | ||||||||
\(323\) | −6.38851 | −0.355466 | ||||||||
\(324\) | −54.3137 | −3.01743 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.55885 | −0.529416 | ||||||||
\(327\) | 29.4417 | 1.62813 | ||||||||
\(328\) | −8.07139 | −0.445668 | ||||||||
\(329\) | 14.3585 | 0.791610 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.10646 | −0.445571 | −0.222786 | − | 0.974867i | \(-0.571515\pi\) | ||||
−0.222786 | + | 0.974867i | \(0.571515\pi\) | |||||||
\(332\) | −0.489047 | −0.0268399 | ||||||||
\(333\) | −6.44017 | −0.352919 | ||||||||
\(334\) | −21.8390 | −1.19498 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 106.154 | 5.79120 | ||||||||
\(337\) | 13.4558 | 0.732984 | 0.366492 | − | 0.930421i | \(-0.380559\pi\) | ||||
0.366492 | + | 0.930421i | \(0.380559\pi\) | |||||||
\(338\) | 12.2697 | 0.667385 | ||||||||
\(339\) | −24.3713 | −1.32367 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.53855 | −0.516541 | ||||||||
\(342\) | 4.56502 | 0.246848 | ||||||||
\(343\) | 51.8872 | 2.80165 | ||||||||
\(344\) | 71.5667 | 3.85862 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 37.8853 | 2.03673 | ||||||||
\(347\) | −15.8117 | −0.848819 | −0.424409 | − | 0.905470i | \(-0.639518\pi\) | ||||
−0.424409 | + | 0.905470i | \(0.639518\pi\) | |||||||
\(348\) | −70.3654 | −3.77198 | ||||||||
\(349\) | −7.24809 | −0.387981 | −0.193991 | − | 0.981003i | \(-0.562143\pi\) | ||||
−0.193991 | + | 0.981003i | \(0.562143\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.5069 | 0.614194 | ||||||||
\(352\) | 10.8449 | 0.578038 | ||||||||
\(353\) | −11.6864 | −0.622005 | −0.311003 | − | 0.950409i | \(-0.600665\pi\) | ||||
−0.311003 | + | 0.950409i | \(0.600665\pi\) | |||||||
\(354\) | −3.49529 | −0.185773 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.0725 | 0.639843 | ||||||||
\(357\) | −68.8522 | −3.64405 | ||||||||
\(358\) | 60.7960 | 3.21317 | ||||||||
\(359\) | 27.1065 | 1.43063 | 0.715313 | − | 0.698804i | \(-0.246284\pi\) | ||||
0.715313 | + | 0.698804i | \(0.246284\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 9.58395 | 0.503721 | ||||||||
\(363\) | 2.17802 | 0.114316 | ||||||||
\(364\) | −101.004 | −5.29405 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 7.62140 | 0.398377 | ||||||||
\(367\) | −12.9734 | −0.677207 | −0.338604 | − | 0.940929i | \(-0.609955\pi\) | ||||
−0.338604 | + | 0.940929i | \(0.609955\pi\) | |||||||
\(368\) | 65.6208 | 3.42072 | ||||||||
\(369\) | −1.88407 | −0.0980806 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.4086 | −1.73449 | ||||||||
\(372\) | −100.832 | −5.22792 | ||||||||
\(373\) | −25.2889 | −1.30941 | −0.654704 | − | 0.755885i | \(-0.727207\pi\) | ||||
−0.654704 | + | 0.755885i | \(0.727207\pi\) | |||||||
\(374\) | −16.7246 | −0.864809 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.6765 | 1.11788 | ||||||||
\(377\) | 27.9941 | 1.44177 | ||||||||
\(378\) | −35.4445 | −1.82307 | ||||||||
\(379\) | −25.0016 | −1.28425 | −0.642123 | − | 0.766602i | \(-0.721946\pi\) | ||||
−0.642123 | + | 0.766602i | \(0.721946\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.4894 | 0.742313 | ||||||||
\(382\) | 61.1521 | 3.12881 | ||||||||
\(383\) | −2.66127 | −0.135985 | −0.0679923 | − | 0.997686i | \(-0.521659\pi\) | ||||
−0.0679923 | + | 0.997686i | \(0.521659\pi\) | |||||||
\(384\) | 2.31978 | 0.118381 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 65.8956 | 3.35400 | ||||||||
\(387\) | 16.7055 | 0.849189 | ||||||||
\(388\) | −84.1057 | −4.26982 | ||||||||
\(389\) | 6.77412 | 0.343462 | 0.171731 | − | 0.985144i | \(-0.445064\pi\) | ||||
0.171731 | + | 0.985144i | \(0.445064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.5620 | −2.15245 | ||||||||
\(392\) | 130.624 | 6.59753 | ||||||||
\(393\) | 40.1747 | 2.02654 | ||||||||
\(394\) | 18.2949 | 0.921686 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.46336 | 0.425300 | ||||||||
\(397\) | 20.9430 | 1.05110 | 0.525550 | − | 0.850763i | \(-0.323860\pi\) | ||||
0.525550 | + | 0.850763i | \(0.323860\pi\) | |||||||
\(398\) | 30.2057 | 1.51408 | ||||||||
\(399\) | 10.7775 | 0.539551 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.8352 | 0.790774 | 0.395387 | − | 0.918515i | \(-0.370611\pi\) | ||||
0.395387 | + | 0.918515i | \(0.370611\pi\) | |||||||
\(402\) | 2.20446 | 0.109948 | ||||||||
\(403\) | 40.1150 | 1.99827 | ||||||||
\(404\) | −47.1378 | −2.34519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −86.2295 | −4.27950 | ||||||||
\(407\) | −3.69327 | −0.183069 | ||||||||
\(408\) | −103.944 | −5.14598 | ||||||||
\(409\) | −1.16027 | −0.0573715 | −0.0286857 | − | 0.999588i | \(-0.509132\pi\) | ||||
−0.0286857 | + | 0.999588i | \(0.509132\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −33.4773 | −1.65131 | ||||||||
\(412\) | 75.8178 | 3.73528 | ||||||||
\(413\) | −3.03335 | −0.149262 | ||||||||
\(414\) | 30.4134 | 1.49474 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −45.6092 | −2.23617 | ||||||||
\(417\) | −5.19809 | −0.254551 | ||||||||
\(418\) | 2.61792 | 0.128047 | ||||||||
\(419\) | 0.923724 | 0.0451269 | 0.0225634 | − | 0.999745i | \(-0.492817\pi\) | ||||
0.0225634 | + | 0.999745i | \(0.492817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0507 | 0.636054 | 0.318027 | − | 0.948082i | \(-0.396980\pi\) | ||||
0.318027 | + | 0.948082i | \(0.396980\pi\) | |||||||
\(422\) | 36.0382 | 1.75431 | ||||||||
\(423\) | 5.05985 | 0.246018 | ||||||||
\(424\) | −50.4357 | −2.44938 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 53.5112 | 2.59263 | ||||||||
\(427\) | 6.61415 | 0.320081 | ||||||||
\(428\) | −26.6560 | −1.28847 | ||||||||
\(429\) | −9.15980 | −0.442239 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.3251 | 0.979025 | 0.489513 | − | 0.871996i | \(-0.337175\pi\) | ||||
0.489513 | + | 0.871996i | \(0.337175\pi\) | |||||||
\(432\) | −26.9497 | −1.29662 | ||||||||
\(433\) | −20.5451 | −0.987333 | −0.493666 | − | 0.869651i | \(-0.664344\pi\) | ||||
−0.493666 | + | 0.869651i | \(0.664344\pi\) | |||||||
\(434\) | −123.565 | −5.93133 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 65.6082 | 3.14206 | ||||||||
\(437\) | 6.66227 | 0.318700 | ||||||||
\(438\) | −11.2587 | −0.537961 | ||||||||
\(439\) | −7.67668 | −0.366388 | −0.183194 | − | 0.983077i | \(-0.558644\pi\) | ||||
−0.183194 | + | 0.983077i | \(0.558644\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30.4911 | 1.45196 | ||||||||
\(442\) | 70.3365 | 3.34557 | ||||||||
\(443\) | 9.04317 | 0.429654 | 0.214827 | − | 0.976652i | \(-0.431081\pi\) | ||||
0.214827 | + | 0.976652i | \(0.431081\pi\) | |||||||
\(444\) | −39.0417 | −1.85284 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −49.0528 | −2.32272 | ||||||||
\(447\) | −23.1117 | −1.09315 | ||||||||
\(448\) | 43.0107 | 2.03207 | ||||||||
\(449\) | −9.97433 | −0.470718 | −0.235359 | − | 0.971909i | \(-0.575627\pi\) | ||||
−0.235359 | + | 0.971909i | \(0.575627\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.08046 | −0.0508771 | ||||||||
\(452\) | −54.3093 | −2.55449 | ||||||||
\(453\) | 32.4338 | 1.52387 | ||||||||
\(454\) | −57.0502 | −2.67750 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.2704 | 0.761933 | ||||||||
\(457\) | 18.7284 | 0.876077 | 0.438038 | − | 0.898956i | \(-0.355673\pi\) | ||||
0.438038 | + | 0.898956i | \(0.355673\pi\) | |||||||
\(458\) | −40.7166 | −1.90256 | ||||||||
\(459\) | 17.4797 | 0.815883 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.5036 | −1.23440 | −0.617198 | − | 0.786808i | \(-0.711732\pi\) | ||||
−0.617198 | + | 0.786808i | \(0.711732\pi\) | |||||||
\(462\) | 28.2147 | 1.31267 | ||||||||
\(463\) | 18.1944 | 0.845564 | 0.422782 | − | 0.906231i | \(-0.361054\pi\) | ||||
0.422782 | + | 0.906231i | \(0.361054\pi\) | |||||||
\(464\) | −65.5633 | −3.04370 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 70.7293 | 3.27647 | ||||||||
\(467\) | 13.5114 | 0.625234 | 0.312617 | − | 0.949879i | \(-0.398794\pi\) | ||||
0.312617 | + | 0.949879i | \(0.398794\pi\) | |||||||
\(468\) | −35.5933 | −1.64530 | ||||||||
\(469\) | 1.91311 | 0.0883394 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.7338 | 0.586741 | ||||||||
\(472\) | −4.57934 | −0.210781 | ||||||||
\(473\) | 9.58018 | 0.440497 | ||||||||
\(474\) | −37.7176 | −1.73243 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −153.431 | −7.03251 | ||||||||
\(477\) | −11.7730 | −0.539048 | ||||||||
\(478\) | −69.4114 | −3.17480 | ||||||||
\(479\) | −15.0739 | −0.688743 | −0.344371 | − | 0.938833i | \(-0.611908\pi\) | ||||
−0.344371 | + | 0.938833i | \(0.611908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.5323 | 0.708212 | ||||||||
\(482\) | −42.3786 | −1.93029 | ||||||||
\(483\) | 71.8027 | 3.26714 | ||||||||
\(484\) | 4.85352 | 0.220615 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −42.3185 | −1.91961 | ||||||||
\(487\) | −41.3382 | −1.87321 | −0.936607 | − | 0.350381i | \(-0.886052\pi\) | ||||
−0.936607 | + | 0.350381i | \(0.886052\pi\) | |||||||
\(488\) | 9.98515 | 0.452007 | ||||||||
\(489\) | −7.95262 | −0.359630 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.4695 | −1.32994 | −0.664970 | − | 0.746870i | \(-0.731556\pi\) | ||||
−0.664970 | + | 0.746870i | \(0.731556\pi\) | |||||||
\(492\) | −11.4216 | −0.514927 | ||||||||
\(493\) | 42.5246 | 1.91521 | ||||||||
\(494\) | −11.0099 | −0.495357 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −93.9511 | −4.21853 | ||||||||
\(497\) | 46.4391 | 2.08308 | ||||||||
\(498\) | −0.574529 | −0.0257453 | ||||||||
\(499\) | 0.211110 | 0.00945058 | 0.00472529 | − | 0.999989i | \(-0.498496\pi\) | ||||
0.00472529 | + | 0.999989i | \(0.498496\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.1693 | −0.811743 | ||||||||
\(502\) | 6.49774 | 0.290008 | ||||||||
\(503\) | −7.94133 | −0.354086 | −0.177043 | − | 0.984203i | \(-0.556653\pi\) | ||||
−0.177043 | + | 0.984203i | \(0.556653\pi\) | |||||||
\(504\) | 64.4587 | 2.87122 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.4413 | 0.775361 | ||||||||
\(507\) | 10.2080 | 0.453352 | ||||||||
\(508\) | 32.2883 | 1.43256 | ||||||||
\(509\) | 7.40748 | 0.328331 | 0.164165 | − | 0.986433i | \(-0.447507\pi\) | ||||
0.164165 | + | 0.986433i | \(0.447507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.77074 | −0.432232 | ||||||||
\(512\) | −40.3405 | −1.78282 | ||||||||
\(513\) | −2.73612 | −0.120803 | ||||||||
\(514\) | −4.58842 | −0.202387 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 101.273 | 4.45827 | ||||||||
\(517\) | 2.90169 | 0.127616 | ||||||||
\(518\) | −47.8438 | −2.10213 | ||||||||
\(519\) | 31.5192 | 1.38354 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.9680 | 0.655760 | 0.327880 | − | 0.944719i | \(-0.393666\pi\) | ||||
0.327880 | + | 0.944719i | \(0.393666\pi\) | |||||||
\(522\) | −30.3868 | −1.32999 | ||||||||
\(523\) | 6.78937 | 0.296878 | 0.148439 | − | 0.988922i | \(-0.452575\pi\) | ||||
0.148439 | + | 0.988922i | \(0.452575\pi\) | |||||||
\(524\) | 89.5257 | 3.91095 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −41.7109 | −1.81868 | ||||||||
\(527\) | 60.9371 | 2.65446 | ||||||||
\(528\) | 21.4526 | 0.933606 | ||||||||
\(529\) | 21.3859 | 0.929820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.06894 | −0.0463879 | ||||||||
\(532\) | 24.0168 | 1.04126 | ||||||||
\(533\) | 4.54397 | 0.196821 | ||||||||
\(534\) | 14.1827 | 0.613746 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.88816 | 0.124749 | ||||||||
\(537\) | 50.5801 | 2.18269 | ||||||||
\(538\) | −14.1384 | −0.609549 | ||||||||
\(539\) | 17.4858 | 0.753168 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.8957 | −0.941368 | −0.470684 | − | 0.882302i | \(-0.655993\pi\) | ||||
−0.470684 | + | 0.882302i | \(0.655993\pi\) | |||||||
\(542\) | −1.99399 | −0.0856491 | ||||||||
\(543\) | 7.97350 | 0.342176 | ||||||||
\(544\) | −69.2830 | −2.97048 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −118.659 | −5.07813 | ||||||||
\(547\) | −16.7053 | −0.714266 | −0.357133 | − | 0.934054i | \(-0.616246\pi\) | ||||
−0.357133 | + | 0.934054i | \(0.616246\pi\) | |||||||
\(548\) | −74.6012 | −3.18681 | ||||||||
\(549\) | 2.33079 | 0.0994757 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.65643 | −0.283573 | ||||||||
\(552\) | 108.398 | 4.61373 | ||||||||
\(553\) | −32.7328 | −1.39194 | ||||||||
\(554\) | 70.5738 | 2.99839 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.5835 | −0.491249 | ||||||||
\(557\) | −23.8953 | −1.01248 | −0.506238 | − | 0.862394i | \(-0.668964\pi\) | ||||
−0.506238 | + | 0.862394i | \(0.668964\pi\) | |||||||
\(558\) | −43.5437 | −1.84335 | ||||||||
\(559\) | −40.2901 | −1.70409 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.9143 | −0.587461 | ||||||||
\(562\) | 48.4272 | 2.04278 | ||||||||
\(563\) | −17.6090 | −0.742129 | −0.371065 | − | 0.928607i | \(-0.621007\pi\) | ||||
−0.371065 | + | 0.928607i | \(0.621007\pi\) | |||||||
\(564\) | 30.6739 | 1.29161 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 49.4860 | 2.08005 | ||||||||
\(567\) | −55.3745 | −2.32551 | ||||||||
\(568\) | 70.1075 | 2.94164 | ||||||||
\(569\) | 38.1265 | 1.59835 | 0.799174 | − | 0.601100i | \(-0.205271\pi\) | ||||
0.799174 | + | 0.601100i | \(0.205271\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.37976 | −0.266985 | −0.133492 | − | 0.991050i | \(-0.542619\pi\) | ||||
−0.133492 | + | 0.991050i | \(0.542619\pi\) | |||||||
\(572\) | −20.4118 | −0.853461 | ||||||||
\(573\) | 50.8763 | 2.12539 | ||||||||
\(574\) | −13.9967 | −0.584210 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 15.1567 | 0.631531 | ||||||||
\(577\) | −19.3120 | −0.803969 | −0.401985 | − | 0.915646i | \(-0.631679\pi\) | ||||
−0.401985 | + | 0.915646i | \(0.631679\pi\) | |||||||
\(578\) | 62.3406 | 2.59303 | ||||||||
\(579\) | 54.8227 | 2.27835 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.498599 | −0.0206854 | ||||||||
\(582\) | −98.8068 | −4.09567 | ||||||||
\(583\) | −6.75151 | −0.279619 | ||||||||
\(584\) | −14.7505 | −0.610381 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.2622 | 1.49798 | ||||||||
\(587\) | −10.2671 | −0.423769 | −0.211884 | − | 0.977295i | \(-0.567960\pi\) | ||||
−0.211884 | + | 0.977295i | \(0.567960\pi\) | |||||||
\(588\) | 184.844 | 7.62282 | ||||||||
\(589\) | −9.53855 | −0.393029 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.2207 | 0.626097 | ||||||||
\(592\) | −36.3773 | −1.49510 | ||||||||
\(593\) | 28.6849 | 1.17795 | 0.588975 | − | 0.808151i | \(-0.299532\pi\) | ||||
0.588975 | + | 0.808151i | \(0.299532\pi\) | |||||||
\(594\) | −7.16294 | −0.293899 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −51.5025 | −2.10962 | ||||||||
\(597\) | 25.1301 | 1.02851 | ||||||||
\(598\) | −73.3507 | −2.99953 | ||||||||
\(599\) | −21.3984 | −0.874315 | −0.437158 | − | 0.899385i | \(-0.644015\pi\) | ||||
−0.437158 | + | 0.899385i | \(0.644015\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.6616 | −1.49546 | −0.747729 | − | 0.664004i | \(-0.768856\pi\) | ||||
−0.747729 | + | 0.664004i | \(0.768856\pi\) | |||||||
\(602\) | 124.105 | 5.05812 | ||||||||
\(603\) | 0.674170 | 0.0274543 | ||||||||
\(604\) | 72.2758 | 2.94086 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −55.3772 | −2.24954 | ||||||||
\(607\) | 47.9867 | 1.94772 | 0.973860 | − | 0.227150i | \(-0.0729408\pi\) | ||||
0.973860 | + | 0.227150i | \(0.0729408\pi\) | |||||||
\(608\) | 10.8449 | 0.439821 | ||||||||
\(609\) | −71.7398 | −2.90704 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.2033 | −0.493692 | ||||||||
\(612\) | −54.0682 | −2.18558 | ||||||||
\(613\) | 25.0991 | 1.01374 | 0.506872 | − | 0.862021i | \(-0.330802\pi\) | ||||
0.506872 | + | 0.862021i | \(0.330802\pi\) | |||||||
\(614\) | 0.610869 | 0.0246527 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.9654 | 1.48938 | ||||||||
\(617\) | −7.05585 | −0.284058 | −0.142029 | − | 0.989863i | \(-0.545363\pi\) | ||||
−0.142029 | + | 0.989863i | \(0.545363\pi\) | |||||||
\(618\) | 89.0703 | 3.58293 | ||||||||
\(619\) | 15.8586 | 0.637410 | 0.318705 | − | 0.947854i | \(-0.396752\pi\) | ||||
0.318705 | + | 0.947854i | \(0.396752\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.2288 | −0.731495 | ||||||||
\(622\) | 20.1653 | 0.808554 | ||||||||
\(623\) | 12.3083 | 0.493123 | ||||||||
\(624\) | −90.2205 | −3.61171 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 39.0786 | 1.56189 | ||||||||
\(627\) | 2.17802 | 0.0869816 | ||||||||
\(628\) | 28.3761 | 1.13233 | ||||||||
\(629\) | 23.5945 | 0.940773 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.11637 | 0.124061 | 0.0620303 | − | 0.998074i | \(-0.480242\pi\) | ||||
0.0620303 | + | 0.998074i | \(0.480242\pi\) | |||||||
\(632\) | −49.4155 | −1.96564 | ||||||||
\(633\) | 29.9825 | 1.19170 | ||||||||
\(634\) | −8.87505 | −0.352473 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −71.3705 | −2.83002 | ||||||||
\(637\) | −73.5379 | −2.91368 | ||||||||
\(638\) | −17.4260 | −0.689903 | ||||||||
\(639\) | 16.3649 | 0.647384 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.2203 | −0.917147 | −0.458573 | − | 0.888657i | \(-0.651639\pi\) | ||||
−0.458573 | + | 0.888657i | \(0.651639\pi\) | |||||||
\(642\) | −31.3153 | −1.23592 | ||||||||
\(643\) | 17.3300 | 0.683428 | 0.341714 | − | 0.939804i | \(-0.388993\pi\) | ||||
0.341714 | + | 0.939804i | \(0.388993\pi\) | |||||||
\(644\) | 160.006 | 6.30512 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.7246 | −0.658021 | ||||||||
\(647\) | −33.8000 | −1.32881 | −0.664407 | − | 0.747371i | \(-0.731316\pi\) | ||||
−0.664407 | + | 0.747371i | \(0.731316\pi\) | |||||||
\(648\) | −83.5970 | −3.28400 | ||||||||
\(649\) | −0.613007 | −0.0240626 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −102.802 | −4.02912 | ||||||||
\(652\) | −17.7217 | −0.694036 | ||||||||
\(653\) | 23.8491 | 0.933289 | 0.466644 | − | 0.884445i | \(-0.345463\pi\) | ||||
0.466644 | + | 0.884445i | \(0.345463\pi\) | |||||||
\(654\) | 77.0761 | 3.01391 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −10.6422 | −0.415506 | ||||||||
\(657\) | −3.44315 | −0.134330 | ||||||||
\(658\) | 37.5894 | 1.46539 | ||||||||
\(659\) | −34.8028 | −1.35572 | −0.677862 | − | 0.735189i | \(-0.737093\pi\) | ||||
−0.677862 | + | 0.735189i | \(0.737093\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.3984 | −1.61021 | −0.805105 | − | 0.593132i | \(-0.797891\pi\) | ||||
−0.805105 | + | 0.593132i | \(0.797891\pi\) | |||||||
\(662\) | −21.2221 | −0.824820 | ||||||||
\(663\) | 58.5175 | 2.27263 | ||||||||
\(664\) | −0.752717 | −0.0292111 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.8599 | −0.653306 | ||||||||
\(667\) | −44.3469 | −1.71712 | ||||||||
\(668\) | −40.4886 | −1.56655 | ||||||||
\(669\) | −40.8102 | −1.57781 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.33665 | 0.0516007 | ||||||||
\(672\) | 116.882 | 4.50880 | ||||||||
\(673\) | 49.3984 | 1.90417 | 0.952085 | − | 0.305835i | \(-0.0989354\pi\) | ||||
0.952085 | + | 0.305835i | \(0.0989354\pi\) | |||||||
\(674\) | 35.2262 | 1.35686 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.7476 | 0.874906 | ||||||||
\(677\) | 36.6932 | 1.41023 | 0.705117 | − | 0.709091i | \(-0.250895\pi\) | ||||
0.705117 | + | 0.709091i | \(0.250895\pi\) | |||||||
\(678\) | −63.8022 | −2.45031 | ||||||||
\(679\) | −85.7484 | −3.29072 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −47.4637 | −1.81881 | ||||||||
\(682\) | −24.9712 | −0.956196 | ||||||||
\(683\) | −26.3703 | −1.00903 | −0.504516 | − | 0.863403i | \(-0.668329\pi\) | ||||
−0.504516 | + | 0.863403i | \(0.668329\pi\) | |||||||
\(684\) | 8.46336 | 0.323605 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 135.837 | 5.18627 | ||||||||
\(687\) | −33.8747 | −1.29240 | ||||||||
\(688\) | 94.3611 | 3.59748 | ||||||||
\(689\) | 28.3939 | 1.08172 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.3427 | 0.507581 | 0.253791 | − | 0.967259i | \(-0.418323\pi\) | ||||
0.253791 | + | 0.967259i | \(0.418323\pi\) | |||||||
\(692\) | 70.2378 | 2.67004 | ||||||||
\(693\) | 8.62866 | 0.327776 | ||||||||
\(694\) | −41.3939 | −1.57129 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −108.303 | −4.10521 | ||||||||
\(697\) | 6.90255 | 0.261453 | ||||||||
\(698\) | −18.9749 | −0.718212 | ||||||||
\(699\) | 58.8442 | 2.22569 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.00399 | −0.264537 | −0.132268 | − | 0.991214i | \(-0.542226\pi\) | ||||
−0.132268 | + | 0.991214i | \(0.542226\pi\) | |||||||
\(702\) | 30.1243 | 1.13697 | ||||||||
\(703\) | −3.69327 | −0.139294 | ||||||||
\(704\) | 8.69200 | 0.327592 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.5941 | −1.15143 | ||||||||
\(707\) | −48.0585 | −1.80743 | ||||||||
\(708\) | −6.48013 | −0.243538 | ||||||||
\(709\) | −30.5543 | −1.14749 | −0.573745 | − | 0.819034i | \(-0.694510\pi\) | ||||
−0.573745 | + | 0.819034i | \(0.694510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.5348 | −0.432591 | ||||||||
\(712\) | 18.5814 | 0.696369 | ||||||||
\(713\) | −63.5484 | −2.37991 | ||||||||
\(714\) | −180.250 | −6.74568 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 112.713 | 4.21229 | ||||||||
\(717\) | −57.7478 | −2.15663 | ||||||||
\(718\) | 70.9627 | 2.64831 | ||||||||
\(719\) | −29.1224 | −1.08608 | −0.543042 | − | 0.839706i | \(-0.682727\pi\) | ||||
−0.543042 | + | 0.839706i | \(0.682727\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 77.2987 | 2.87875 | ||||||||
\(722\) | 2.61792 | 0.0974290 | ||||||||
\(723\) | −35.2575 | −1.31124 | ||||||||
\(724\) | 17.7682 | 0.660351 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.70188 | 0.211617 | ||||||||
\(727\) | 20.4576 | 0.758731 | 0.379366 | − | 0.925247i | \(-0.376142\pi\) | ||||
0.379366 | + | 0.925247i | \(0.376142\pi\) | |||||||
\(728\) | −155.460 | −5.76175 | ||||||||
\(729\) | −1.63574 | −0.0605829 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −61.2030 | −2.26368 | ||||||||
\(732\) | 14.1298 | 0.522251 | ||||||||
\(733\) | −43.2636 | −1.59798 | −0.798989 | − | 0.601346i | \(-0.794631\pi\) | ||||
−0.798989 | + | 0.601346i | \(0.794631\pi\) | |||||||
\(734\) | −33.9634 | −1.25361 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 72.2520 | 2.66324 | ||||||||
\(737\) | 0.386619 | 0.0142413 | ||||||||
\(738\) | −4.93234 | −0.181562 | ||||||||
\(739\) | −31.1858 | −1.14719 | −0.573595 | − | 0.819139i | \(-0.694452\pi\) | ||||
−0.573595 | + | 0.819139i | \(0.694452\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.15980 | −0.336494 | ||||||||
\(742\) | −87.4611 | −3.21080 | ||||||||
\(743\) | −45.0080 | −1.65118 | −0.825592 | − | 0.564268i | \(-0.809158\pi\) | ||||
−0.825592 | + | 0.564268i | \(0.809158\pi\) | |||||||
\(744\) | −155.196 | −5.68977 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −66.2043 | −2.42391 | ||||||||
\(747\) | −0.175703 | −0.00642865 | ||||||||
\(748\) | −31.0067 | −1.13372 | ||||||||
\(749\) | −27.1767 | −0.993013 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.7716 | −1.08638 | −0.543191 | − | 0.839609i | \(-0.682784\pi\) | ||||
−0.543191 | + | 0.839609i | \(0.682784\pi\) | |||||||
\(752\) | 28.5806 | 1.04223 | ||||||||
\(753\) | 5.40588 | 0.197001 | ||||||||
\(754\) | 73.2863 | 2.66893 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −65.7126 | −2.38995 | ||||||||
\(757\) | −32.1474 | −1.16842 | −0.584209 | − | 0.811603i | \(-0.698595\pi\) | ||||
−0.584209 | + | 0.811603i | \(0.698595\pi\) | |||||||
\(758\) | −65.4522 | −2.37733 | ||||||||
\(759\) | 14.5105 | 0.526699 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.83297 | −0.102695 | −0.0513475 | − | 0.998681i | \(-0.516352\pi\) | ||||
−0.0513475 | + | 0.998681i | \(0.516352\pi\) | |||||||
\(762\) | 37.9321 | 1.37413 | ||||||||
\(763\) | 66.8896 | 2.42157 | ||||||||
\(764\) | 113.373 | 4.10170 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.96700 | −0.251728 | ||||||||
\(767\) | 2.57804 | 0.0930878 | ||||||||
\(768\) | −31.7896 | −1.14711 | ||||||||
\(769\) | −0.197238 | −0.00711259 | −0.00355630 | − | 0.999994i | \(-0.501132\pi\) | ||||
−0.00355630 | + | 0.999994i | \(0.501132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.81740 | −0.137480 | ||||||||
\(772\) | 122.168 | 4.39691 | ||||||||
\(773\) | 39.5489 | 1.42247 | 0.711237 | − | 0.702952i | \(-0.248135\pi\) | ||||
0.711237 | + | 0.702952i | \(0.248135\pi\) | |||||||
\(774\) | 43.7337 | 1.57198 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −129.451 | −4.64703 | ||||||||
\(777\) | −39.8043 | −1.42797 | ||||||||
\(778\) | 17.7341 | 0.635799 | ||||||||
\(779\) | −1.08046 | −0.0387116 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.38483 | 0.335816 | ||||||||
\(782\) | −111.424 | −3.98451 | ||||||||
\(783\) | 18.2128 | 0.650871 | ||||||||
\(784\) | 172.229 | 6.15103 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 105.174 | 3.75144 | ||||||||
\(787\) | 20.2522 | 0.721912 | 0.360956 | − | 0.932583i | \(-0.382450\pi\) | ||||
0.360956 | + | 0.932583i | \(0.382450\pi\) | |||||||
\(788\) | 33.9181 | 1.20828 | ||||||||
\(789\) | −34.7019 | −1.23542 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −55.3700 | −1.96873 | ||||||||
\(792\) | 13.0264 | 0.462872 | ||||||||
\(793\) | −5.62136 | −0.199620 | ||||||||
\(794\) | 54.8272 | 1.94574 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 56.0002 | 1.98487 | ||||||||
\(797\) | 24.5195 | 0.868524 | 0.434262 | − | 0.900787i | \(-0.357009\pi\) | ||||
0.434262 | + | 0.900787i | \(0.357009\pi\) | |||||||
\(798\) | 28.2147 | 0.998790 | ||||||||
\(799\) | −18.5375 | −0.655809 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.33738 | 0.153254 | ||||||||
\(802\) | 41.4554 | 1.46384 | ||||||||
\(803\) | −1.97456 | −0.0696806 | ||||||||
\(804\) | 4.08697 | 0.144136 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 105.018 | 3.69910 | ||||||||
\(807\) | −11.7626 | −0.414064 | ||||||||
\(808\) | −72.5522 | −2.55238 | ||||||||
\(809\) | 18.8544 | 0.662885 | 0.331442 | − | 0.943475i | \(-0.392465\pi\) | ||||
0.331442 | + | 0.943475i | \(0.392465\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.8152 | 1.08207 | 0.541034 | − | 0.841001i | \(-0.318033\pi\) | ||||
0.541034 | + | 0.841001i | \(0.318033\pi\) | |||||||
\(812\) | −159.866 | −5.61019 | ||||||||
\(813\) | −1.65893 | −0.0581811 | ||||||||
\(814\) | −9.66869 | −0.338888 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −137.050 | −4.79772 | ||||||||
\(817\) | 9.58018 | 0.335168 | ||||||||
\(818\) | −3.03749 | −0.106203 | ||||||||
\(819\) | −36.2884 | −1.26802 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.91462 | −0.136621 | −0.0683106 | − | 0.997664i | \(-0.521761\pi\) | ||||
−0.0683106 | + | 0.997664i | \(0.521761\pi\) | |||||||
\(822\) | −87.6410 | −3.05683 | ||||||||
\(823\) | 30.0384 | 1.04707 | 0.523537 | − | 0.852003i | \(-0.324612\pi\) | ||||
0.523537 | + | 0.852003i | \(0.324612\pi\) | |||||||
\(824\) | 116.695 | 4.06526 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.94108 | −0.276306 | ||||||||
\(827\) | −19.0520 | −0.662504 | −0.331252 | − | 0.943542i | \(-0.607471\pi\) | ||||
−0.331252 | + | 0.943542i | \(0.607471\pi\) | |||||||
\(828\) | 56.3852 | 1.95952 | ||||||||
\(829\) | −2.78078 | −0.0965806 | −0.0482903 | − | 0.998833i | \(-0.515377\pi\) | ||||
−0.0482903 | + | 0.998833i | \(0.515377\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 58.7148 | 2.03679 | ||||||||
\(832\) | −36.5548 | −1.26731 | ||||||||
\(833\) | −111.708 | −3.87047 | ||||||||
\(834\) | −13.6082 | −0.471213 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.85352 | 0.167862 | ||||||||
\(837\) | 26.0986 | 0.902099 | ||||||||
\(838\) | 2.41824 | 0.0835367 | ||||||||
\(839\) | −12.1680 | −0.420087 | −0.210044 | − | 0.977692i | \(-0.567361\pi\) | ||||
−0.210044 | + | 0.977692i | \(0.567361\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3081 | 0.527864 | ||||||||
\(842\) | 34.1658 | 1.17743 | ||||||||
\(843\) | 40.2897 | 1.38765 | ||||||||
\(844\) | 66.8133 | 2.29981 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.2463 | 0.455417 | ||||||||
\(847\) | 4.94832 | 0.170026 | ||||||||
\(848\) | −66.4997 | −2.28361 | ||||||||
\(849\) | 41.1706 | 1.41297 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.6056 | −0.843468 | ||||||||
\(852\) | 99.2075 | 3.39879 | ||||||||
\(853\) | 30.8061 | 1.05478 | 0.527390 | − | 0.849623i | \(-0.323171\pi\) | ||||
0.527390 | + | 0.849623i | \(0.323171\pi\) | |||||||
\(854\) | 17.3153 | 0.592519 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41.0276 | −1.40229 | ||||||||
\(857\) | −5.90481 | −0.201705 | −0.100852 | − | 0.994901i | \(-0.532157\pi\) | ||||
−0.100852 | + | 0.994901i | \(0.532157\pi\) | |||||||
\(858\) | −23.9797 | −0.818652 | ||||||||
\(859\) | 28.0485 | 0.957003 | 0.478502 | − | 0.878087i | \(-0.341180\pi\) | ||||
0.478502 | + | 0.878087i | \(0.341180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.6447 | −0.396851 | ||||||||
\(862\) | 53.2095 | 1.81232 | ||||||||
\(863\) | −24.0412 | −0.818374 | −0.409187 | − | 0.912451i | \(-0.634188\pi\) | ||||
−0.409187 | + | 0.912451i | \(0.634188\pi\) | |||||||
\(864\) | −29.6730 | −1.00950 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −53.7854 | −1.82770 | ||||||||
\(867\) | 51.8652 | 1.76143 | ||||||||
\(868\) | −229.085 | −7.77565 | ||||||||
\(869\) | −6.61494 | −0.224396 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.62595 | −0.0550933 | ||||||||
\(872\) | 100.981 | 3.41964 | ||||||||
\(873\) | −30.2172 | −1.02270 | ||||||||
\(874\) | 17.4413 | 0.589961 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −20.8731 | −0.705238 | ||||||||
\(877\) | −46.1837 | −1.55951 | −0.779757 | − | 0.626083i | \(-0.784657\pi\) | ||||
−0.779757 | + | 0.626083i | \(0.784657\pi\) | |||||||
\(878\) | −20.0970 | −0.678240 | ||||||||
\(879\) | 30.1688 | 1.01757 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.5583 | −0.557863 | −0.278931 | − | 0.960311i | \(-0.589980\pi\) | ||||
−0.278931 | + | 0.960311i | \(0.589980\pi\) | |||||||
\(882\) | 79.8232 | 2.68779 | ||||||||
\(883\) | 39.6210 | 1.33335 | 0.666676 | − | 0.745347i | \(-0.267716\pi\) | ||||
0.666676 | + | 0.745347i | \(0.267716\pi\) | |||||||
\(884\) | 130.401 | 4.38586 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.6743 | 0.795354 | ||||||||
\(887\) | 2.31838 | 0.0778436 | 0.0389218 | − | 0.999242i | \(-0.487608\pi\) | ||||
0.0389218 | + | 0.999242i | \(0.487608\pi\) | |||||||
\(888\) | −60.0911 | −2.01652 | ||||||||
\(889\) | 32.9189 | 1.10407 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.1906 | −0.374899 | ||||||||
\(892\) | −90.9419 | −3.04496 | ||||||||
\(893\) | 2.90169 | 0.0971015 | ||||||||
\(894\) | −60.5048 | −2.02358 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.27038 | 0.176071 | ||||||||
\(897\) | −61.0251 | −2.03757 | ||||||||
\(898\) | −26.1120 | −0.871370 | ||||||||
\(899\) | 63.4927 | 2.11760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.1320 | 1.43694 | ||||||||
\(902\) | −2.82857 | −0.0941811 | ||||||||
\(903\) | 103.251 | 3.43596 | ||||||||
\(904\) | −83.5901 | −2.78017 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 84.9091 | 2.82092 | ||||||||
\(907\) | 3.05923 | 0.101580 | 0.0507900 | − | 0.998709i | \(-0.483826\pi\) | ||||
0.0507900 | + | 0.998709i | \(0.483826\pi\) | |||||||
\(908\) | −105.769 | −3.51006 | ||||||||
\(909\) | −16.9355 | −0.561716 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.4953 | −1.70611 | −0.853057 | − | 0.521817i | \(-0.825254\pi\) | ||||
−0.853057 | + | 0.521817i | \(0.825254\pi\) | |||||||
\(912\) | 21.4526 | 0.710368 | ||||||||
\(913\) | −0.100761 | −0.00333471 | ||||||||
\(914\) | 49.0295 | 1.62175 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −75.4868 | −2.49416 | ||||||||
\(917\) | 91.2743 | 3.01414 | ||||||||
\(918\) | 45.7605 | 1.51032 | ||||||||
\(919\) | 47.9995 | 1.58336 | 0.791678 | − | 0.610938i | \(-0.209208\pi\) | ||||
0.791678 | + | 0.610938i | \(0.209208\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.508221 | 0.0167464 | ||||||||
\(922\) | −69.3844 | −2.28505 | ||||||||
\(923\) | −39.4686 | −1.29912 | ||||||||
\(924\) | 52.3089 | 1.72084 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 47.6315 | 1.56527 | ||||||||
\(927\) | 27.2396 | 0.894666 | ||||||||
\(928\) | −72.1886 | −2.36971 | ||||||||
\(929\) | 27.5397 | 0.903548 | 0.451774 | − | 0.892132i | \(-0.350791\pi\) | ||||
0.451774 | + | 0.892132i | \(0.350791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.4858 | 0.573075 | ||||||||
\(932\) | 131.129 | 4.29528 | ||||||||
\(933\) | 16.7768 | 0.549247 | ||||||||
\(934\) | 35.3719 | 1.15740 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −54.7834 | −1.79065 | ||||||||
\(937\) | 7.50039 | 0.245027 | 0.122513 | − | 0.992467i | \(-0.460905\pi\) | ||||
0.122513 | + | 0.992467i | \(0.460905\pi\) | |||||||
\(938\) | 5.00838 | 0.163530 | ||||||||
\(939\) | 32.5119 | 1.06099 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.0396 | −1.37045 | −0.685226 | − | 0.728330i | \(-0.740297\pi\) | ||||
−0.685226 | + | 0.728330i | \(0.740297\pi\) | |||||||
\(942\) | 33.3360 | 1.08615 | ||||||||
\(943\) | −7.19835 | −0.234410 | ||||||||
\(944\) | −6.03789 | −0.196516 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.0802 | 0.815426 | ||||||||
\(947\) | 20.1743 | 0.655576 | 0.327788 | − | 0.944751i | \(-0.393697\pi\) | ||||
0.327788 | + | 0.944751i | \(0.393697\pi\) | |||||||
\(948\) | −69.9268 | −2.27112 | ||||||||
\(949\) | 8.30414 | 0.269564 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.38372 | −0.239434 | ||||||||
\(952\) | −236.154 | −7.65378 | ||||||||
\(953\) | −1.49342 | −0.0483766 | −0.0241883 | − | 0.999707i | \(-0.507700\pi\) | ||||
−0.0241883 | + | 0.999707i | \(0.507700\pi\) | |||||||
\(954\) | −30.8208 | −0.997860 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −128.686 | −4.16200 | ||||||||
\(957\) | −14.4978 | −0.468648 | ||||||||
\(958\) | −39.4622 | −1.27497 | ||||||||
\(959\) | −76.0583 | −2.45605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.9839 | 1.93497 | ||||||||
\(962\) | 40.6624 | 1.31101 | ||||||||
\(963\) | −9.57689 | −0.308611 | ||||||||
\(964\) | −78.5682 | −2.53051 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 187.974 | 6.04797 | ||||||||
\(967\) | 37.4587 | 1.20459 | 0.602295 | − | 0.798274i | \(-0.294253\pi\) | ||||
0.602295 | + | 0.798274i | \(0.294253\pi\) | |||||||
\(968\) | 7.47030 | 0.240104 | ||||||||
\(969\) | −13.9143 | −0.446991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.24513 | −0.264599 | −0.132299 | − | 0.991210i | \(-0.542236\pi\) | ||||
−0.132299 | + | 0.991210i | \(0.542236\pi\) | |||||||
\(972\) | −78.4568 | −2.51650 | ||||||||
\(973\) | −11.8097 | −0.378602 | ||||||||
\(974\) | −108.220 | −3.46760 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.1655 | 0.421416 | ||||||||
\(977\) | 29.8558 | 0.955171 | 0.477586 | − | 0.878585i | \(-0.341512\pi\) | ||||
0.477586 | + | 0.878585i | \(0.341512\pi\) | |||||||
\(978\) | −20.8193 | −0.665729 | ||||||||
\(979\) | 2.48738 | 0.0794969 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.5715 | 0.752581 | ||||||||
\(982\) | −77.1489 | −2.46192 | ||||||||
\(983\) | 25.9753 | 0.828484 | 0.414242 | − | 0.910167i | \(-0.364047\pi\) | ||||
0.414242 | + | 0.910167i | \(0.364047\pi\) | |||||||
\(984\) | −17.5796 | −0.560418 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 111.326 | 3.54535 | ||||||||
\(987\) | 31.2731 | 0.995432 | ||||||||
\(988\) | −20.4118 | −0.649386 | ||||||||
\(989\) | 63.8257 | 2.02954 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.3837 | −1.06047 | −0.530235 | − | 0.847851i | \(-0.677896\pi\) | ||||
−0.530235 | + | 0.847851i | \(0.677896\pi\) | |||||||
\(992\) | −103.445 | −3.28438 | ||||||||
\(993\) | −17.6560 | −0.560297 | ||||||||
\(994\) | 121.574 | 3.85609 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.06515 | −0.0337507 | ||||||||
\(997\) | 11.8321 | 0.374725 | 0.187363 | − | 0.982291i | \(-0.440006\pi\) | ||||
0.187363 | + | 0.982291i | \(0.440006\pi\) | |||||||
\(998\) | 0.552670 | 0.0174945 | ||||||||
\(999\) | 10.1052 | 0.319715 |
(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 | 5225.2.a.y.1.14 | yes | 15 | |
5.4 | even | 2 | 5225.2.a.r.1.2 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5225.2.a.r.1.2 | ✓ | 15 | 5.4 | even | 2 | ||
5225.2.a.y.1.14 | yes | 15 | 1.1 | even | 1 | trivial |