Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8085,2,Mod(1,8085)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8085, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8085.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8085.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: | \(64.5590500342\) |
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: | \( x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 104x^{5} + 40x^{4} + 104x^{3} - 48x^{2} - 32x + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.64021\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8085.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64021 | −1.86691 | −0.933456 | − | 0.358692i | \(-0.883223\pi\) | ||||
−0.933456 | + | 0.358692i | \(0.883223\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.97072 | 2.48536 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 2.64021 | 1.07786 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −7.84333 | −2.77304 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.64021 | 0.834908 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −4.97072 | −1.43492 | ||||||||
\(13\) | 1.46829 | 0.407231 | 0.203616 | − | 0.979051i | \(-0.434731\pi\) | ||||
0.203616 | + | 0.979051i | \(0.434731\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 10.7666 | 2.69165 | ||||||||
\(17\) | −1.32245 | −0.320741 | −0.160371 | − | 0.987057i | \(-0.551269\pi\) | ||||
−0.160371 | + | 0.987057i | \(0.551269\pi\) | |||||||
\(18\) | −2.64021 | −0.622304 | ||||||||
\(19\) | 1.90824 | 0.437779 | 0.218890 | − | 0.975750i | \(-0.429757\pi\) | ||||
0.218890 | + | 0.975750i | \(0.429757\pi\) | |||||||
\(20\) | −4.97072 | −1.11149 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.64021 | 0.562895 | ||||||||
\(23\) | 6.10323 | 1.27261 | 0.636305 | − | 0.771437i | \(-0.280462\pi\) | ||||
0.636305 | + | 0.771437i | \(0.280462\pi\) | |||||||
\(24\) | 7.84333 | 1.60101 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.87661 | −0.760265 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.36654 | −0.996542 | −0.498271 | − | 0.867021i | \(-0.666032\pi\) | ||||
−0.498271 | + | 0.867021i | \(0.666032\pi\) | |||||||
\(30\) | −2.64021 | −0.482035 | ||||||||
\(31\) | 5.25881 | 0.944509 | 0.472255 | − | 0.881462i | \(-0.343440\pi\) | ||||
0.472255 | + | 0.881462i | \(0.343440\pi\) | |||||||
\(32\) | −12.7395 | −2.25204 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 3.49155 | 0.598795 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.97072 | 0.828453 | ||||||||
\(37\) | 0.910067 | 0.149614 | 0.0748070 | − | 0.997198i | \(-0.476166\pi\) | ||||
0.0748070 | + | 0.997198i | \(0.476166\pi\) | |||||||
\(38\) | −5.03815 | −0.817295 | ||||||||
\(39\) | −1.46829 | −0.235115 | ||||||||
\(40\) | 7.84333 | 1.24014 | ||||||||
\(41\) | −7.64988 | −1.19471 | −0.597355 | − | 0.801977i | \(-0.703782\pi\) | ||||
−0.597355 | + | 0.801977i | \(0.703782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1646 | −1.55008 | −0.775042 | − | 0.631909i | \(-0.782272\pi\) | ||||
−0.775042 | + | 0.631909i | \(0.782272\pi\) | |||||||
\(44\) | −4.97072 | −0.749364 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −16.1138 | −2.37585 | ||||||||
\(47\) | −4.31503 | −0.629413 | −0.314706 | − | 0.949189i | \(-0.601906\pi\) | ||||
−0.314706 | + | 0.949189i | \(0.601906\pi\) | |||||||
\(48\) | −10.7666 | −1.55403 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.64021 | −0.373382 | ||||||||
\(51\) | 1.32245 | 0.185180 | ||||||||
\(52\) | 7.29847 | 1.01212 | ||||||||
\(53\) | −3.12495 | −0.429245 | −0.214623 | − | 0.976697i | \(-0.568852\pi\) | ||||
−0.214623 | + | 0.976697i | \(0.568852\pi\) | |||||||
\(54\) | 2.64021 | 0.359287 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.90824 | −0.252752 | ||||||||
\(58\) | 14.1688 | 1.86046 | ||||||||
\(59\) | 3.76158 | 0.489717 | 0.244858 | − | 0.969559i | \(-0.421259\pi\) | ||||
0.244858 | + | 0.969559i | \(0.421259\pi\) | |||||||
\(60\) | 4.97072 | 0.641717 | ||||||||
\(61\) | 13.6215 | 1.74405 | 0.872026 | − | 0.489460i | \(-0.162806\pi\) | ||||
0.872026 | + | 0.489460i | \(0.162806\pi\) | |||||||
\(62\) | −13.8844 | −1.76332 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.1017 | 1.51271 | ||||||||
\(65\) | −1.46829 | −0.182119 | ||||||||
\(66\) | −2.64021 | −0.324988 | ||||||||
\(67\) | −10.7458 | −1.31280 | −0.656401 | − | 0.754412i | \(-0.727922\pi\) | ||||
−0.656401 | + | 0.754412i | \(0.727922\pi\) | |||||||
\(68\) | −6.57353 | −0.797157 | ||||||||
\(69\) | −6.10323 | −0.734742 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.68712 | 0.912294 | 0.456147 | − | 0.889905i | \(-0.349229\pi\) | ||||
0.456147 | + | 0.889905i | \(0.349229\pi\) | |||||||
\(72\) | −7.84333 | −0.924345 | ||||||||
\(73\) | 8.62258 | 1.00920 | 0.504599 | − | 0.863354i | \(-0.331641\pi\) | ||||
0.504599 | + | 0.863354i | \(0.331641\pi\) | |||||||
\(74\) | −2.40277 | −0.279316 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 9.48531 | 1.08804 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.87661 | 0.438939 | ||||||||
\(79\) | 4.43519 | 0.498998 | 0.249499 | − | 0.968375i | \(-0.419734\pi\) | ||||
0.249499 | + | 0.968375i | \(0.419734\pi\) | |||||||
\(80\) | −10.7666 | −1.20374 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.1973 | 2.23042 | ||||||||
\(83\) | −15.3931 | −1.68961 | −0.844804 | − | 0.535076i | \(-0.820283\pi\) | ||||
−0.844804 | + | 0.535076i | \(0.820283\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.32245 | 0.143440 | ||||||||
\(86\) | 26.8367 | 2.89387 | ||||||||
\(87\) | 5.36654 | 0.575354 | ||||||||
\(88\) | 7.84333 | 0.836102 | ||||||||
\(89\) | 14.7962 | 1.56839 | 0.784195 | − | 0.620514i | \(-0.213076\pi\) | ||||
0.784195 | + | 0.620514i | \(0.213076\pi\) | |||||||
\(90\) | 2.64021 | 0.278303 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 30.3374 | 3.16290 | ||||||||
\(93\) | −5.25881 | −0.545313 | ||||||||
\(94\) | 11.3926 | 1.17506 | ||||||||
\(95\) | −1.90824 | −0.195781 | ||||||||
\(96\) | 12.7395 | 1.30022 | ||||||||
\(97\) | −10.5475 | −1.07094 | −0.535468 | − | 0.844555i | \(-0.679865\pi\) | ||||
−0.535468 | + | 0.844555i | \(0.679865\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 4.97072 | 0.497072 | ||||||||
\(101\) | −1.15863 | −0.115288 | −0.0576441 | − | 0.998337i | \(-0.518359\pi\) | ||||
−0.0576441 | + | 0.998337i | \(0.518359\pi\) | |||||||
\(102\) | −3.49155 | −0.345715 | ||||||||
\(103\) | −5.82710 | −0.574161 | −0.287081 | − | 0.957906i | \(-0.592685\pi\) | ||||
−0.287081 | + | 0.957906i | \(0.592685\pi\) | |||||||
\(104\) | −11.5163 | −1.12927 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.25053 | 0.801363 | ||||||||
\(107\) | −8.62135 | −0.833457 | −0.416728 | − | 0.909031i | \(-0.636823\pi\) | ||||
−0.416728 | + | 0.909031i | \(0.636823\pi\) | |||||||
\(108\) | −4.97072 | −0.478308 | ||||||||
\(109\) | −0.496925 | −0.0475968 | −0.0237984 | − | 0.999717i | \(-0.507576\pi\) | ||||
−0.0237984 | + | 0.999717i | \(0.507576\pi\) | |||||||
\(110\) | −2.64021 | −0.251734 | ||||||||
\(111\) | −0.910067 | −0.0863797 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.47631 | −0.327024 | −0.163512 | − | 0.986541i | \(-0.552282\pi\) | ||||
−0.163512 | + | 0.986541i | \(0.552282\pi\) | |||||||
\(114\) | 5.03815 | 0.471866 | ||||||||
\(115\) | −6.10323 | −0.569129 | ||||||||
\(116\) | −26.6756 | −2.47677 | ||||||||
\(117\) | 1.46829 | 0.135744 | ||||||||
\(118\) | −9.93138 | −0.914258 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −7.84333 | −0.715995 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −35.9636 | −3.25599 | ||||||||
\(123\) | 7.64988 | 0.689767 | ||||||||
\(124\) | 26.1400 | 2.34745 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.99984 | 0.443664 | 0.221832 | − | 0.975085i | \(-0.428796\pi\) | ||||
0.221832 | + | 0.975085i | \(0.428796\pi\) | |||||||
\(128\) | −6.47211 | −0.572059 | ||||||||
\(129\) | 10.1646 | 0.894942 | ||||||||
\(130\) | 3.87661 | 0.340001 | ||||||||
\(131\) | 7.58371 | 0.662592 | 0.331296 | − | 0.943527i | \(-0.392514\pi\) | ||||
0.331296 | + | 0.943527i | \(0.392514\pi\) | |||||||
\(132\) | 4.97072 | 0.432646 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 28.3711 | 2.45089 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 10.3724 | 0.889427 | ||||||||
\(137\) | 1.59336 | 0.136130 | 0.0680651 | − | 0.997681i | \(-0.478317\pi\) | ||||
0.0680651 | + | 0.997681i | \(0.478317\pi\) | |||||||
\(138\) | 16.1138 | 1.37170 | ||||||||
\(139\) | −2.57556 | −0.218456 | −0.109228 | − | 0.994017i | \(-0.534838\pi\) | ||||
−0.109228 | + | 0.994017i | \(0.534838\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.31503 | 0.363391 | ||||||||
\(142\) | −20.2956 | −1.70317 | ||||||||
\(143\) | −1.46829 | −0.122785 | ||||||||
\(144\) | 10.7666 | 0.897218 | ||||||||
\(145\) | 5.36654 | 0.445667 | ||||||||
\(146\) | −22.7654 | −1.88408 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.52369 | 0.371845 | ||||||||
\(149\) | −5.68525 | −0.465754 | −0.232877 | − | 0.972506i | \(-0.574814\pi\) | ||||
−0.232877 | + | 0.972506i | \(0.574814\pi\) | |||||||
\(150\) | 2.64021 | 0.215572 | ||||||||
\(151\) | −17.3701 | −1.41356 | −0.706778 | − | 0.707435i | \(-0.749852\pi\) | ||||
−0.706778 | + | 0.707435i | \(0.749852\pi\) | |||||||
\(152\) | −14.9669 | −1.21398 | ||||||||
\(153\) | −1.32245 | −0.106914 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.25881 | −0.422397 | ||||||||
\(156\) | −7.29847 | −0.584346 | ||||||||
\(157\) | −3.29676 | −0.263110 | −0.131555 | − | 0.991309i | \(-0.541997\pi\) | ||||
−0.131555 | + | 0.991309i | \(0.541997\pi\) | |||||||
\(158\) | −11.7098 | −0.931585 | ||||||||
\(159\) | 3.12495 | 0.247825 | ||||||||
\(160\) | 12.7395 | 1.00714 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2.64021 | −0.207435 | ||||||||
\(163\) | 19.2220 | 1.50559 | 0.752793 | − | 0.658257i | \(-0.228706\pi\) | ||||
0.752793 | + | 0.658257i | \(0.228706\pi\) | |||||||
\(164\) | −38.0254 | −2.96929 | ||||||||
\(165\) | −1.00000 | −0.0778499 | ||||||||
\(166\) | 40.6410 | 3.15435 | ||||||||
\(167\) | 6.40905 | 0.495947 | 0.247974 | − | 0.968767i | \(-0.420235\pi\) | ||||
0.247974 | + | 0.968767i | \(0.420235\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8441 | −0.834163 | ||||||||
\(170\) | −3.49155 | −0.267789 | ||||||||
\(171\) | 1.90824 | 0.145926 | ||||||||
\(172\) | −50.5253 | −3.85252 | ||||||||
\(173\) | −7.71736 | −0.586740 | −0.293370 | − | 0.955999i | \(-0.594777\pi\) | ||||
−0.293370 | + | 0.955999i | \(0.594777\pi\) | |||||||
\(174\) | −14.1688 | −1.07414 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.7666 | −0.811564 | ||||||||
\(177\) | −3.76158 | −0.282738 | ||||||||
\(178\) | −39.0650 | −2.92805 | ||||||||
\(179\) | 12.3294 | 0.921545 | 0.460772 | − | 0.887518i | \(-0.347572\pi\) | ||||
0.460772 | + | 0.887518i | \(0.347572\pi\) | |||||||
\(180\) | −4.97072 | −0.370496 | ||||||||
\(181\) | 20.4362 | 1.51901 | 0.759504 | − | 0.650503i | \(-0.225442\pi\) | ||||
0.759504 | + | 0.650503i | \(0.225442\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.6215 | −1.00693 | ||||||||
\(184\) | −47.8696 | −3.52899 | ||||||||
\(185\) | −0.910067 | −0.0669094 | ||||||||
\(186\) | 13.8844 | 1.01805 | ||||||||
\(187\) | 1.32245 | 0.0967071 | ||||||||
\(188\) | −21.4488 | −1.56432 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.03815 | 0.365506 | ||||||||
\(191\) | −17.2996 | −1.25175 | −0.625877 | − | 0.779922i | \(-0.715259\pi\) | ||||
−0.625877 | + | 0.779922i | \(0.715259\pi\) | |||||||
\(192\) | −12.1017 | −0.873365 | ||||||||
\(193\) | 2.99867 | 0.215849 | 0.107924 | − | 0.994159i | \(-0.465580\pi\) | ||||
0.107924 | + | 0.994159i | \(0.465580\pi\) | |||||||
\(194\) | 27.8476 | 1.99934 | ||||||||
\(195\) | 1.46829 | 0.105147 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.31748 | −0.592596 | −0.296298 | − | 0.955096i | \(-0.595752\pi\) | ||||
−0.296298 | + | 0.955096i | \(0.595752\pi\) | |||||||
\(198\) | 2.64021 | 0.187632 | ||||||||
\(199\) | 13.5052 | 0.957356 | 0.478678 | − | 0.877990i | \(-0.341116\pi\) | ||||
0.478678 | + | 0.877990i | \(0.341116\pi\) | |||||||
\(200\) | −7.84333 | −0.554607 | ||||||||
\(201\) | 10.7458 | 0.757947 | ||||||||
\(202\) | 3.05903 | 0.215233 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.57353 | 0.460239 | ||||||||
\(205\) | 7.64988 | 0.534291 | ||||||||
\(206\) | 15.3848 | 1.07191 | ||||||||
\(207\) | 6.10323 | 0.424204 | ||||||||
\(208\) | 15.8085 | 1.09613 | ||||||||
\(209\) | −1.90824 | −0.131995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.00583 | 0.206930 | 0.103465 | − | 0.994633i | \(-0.467007\pi\) | ||||
0.103465 | + | 0.994633i | \(0.467007\pi\) | |||||||
\(212\) | −15.5333 | −1.06683 | ||||||||
\(213\) | −7.68712 | −0.526713 | ||||||||
\(214\) | 22.7622 | 1.55599 | ||||||||
\(215\) | 10.1646 | 0.693219 | ||||||||
\(216\) | 7.84333 | 0.533671 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.31199 | 0.0888591 | ||||||||
\(219\) | −8.62258 | −0.582660 | ||||||||
\(220\) | 4.97072 | 0.335126 | ||||||||
\(221\) | −1.94174 | −0.130616 | ||||||||
\(222\) | 2.40277 | 0.161263 | ||||||||
\(223\) | 2.06434 | 0.138238 | 0.0691192 | − | 0.997608i | \(-0.477981\pi\) | ||||
0.0691192 | + | 0.997608i | \(0.477981\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 9.17820 | 0.610525 | ||||||||
\(227\) | 22.7368 | 1.50909 | 0.754546 | − | 0.656247i | \(-0.227857\pi\) | ||||
0.754546 | + | 0.656247i | \(0.227857\pi\) | |||||||
\(228\) | −9.48531 | −0.628180 | ||||||||
\(229\) | −14.9902 | −0.990584 | −0.495292 | − | 0.868727i | \(-0.664939\pi\) | ||||
−0.495292 | + | 0.868727i | \(0.664939\pi\) | |||||||
\(230\) | 16.1138 | 1.06251 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 42.0916 | 2.76345 | ||||||||
\(233\) | −13.9089 | −0.911202 | −0.455601 | − | 0.890184i | \(-0.650576\pi\) | ||||
−0.455601 | + | 0.890184i | \(0.650576\pi\) | |||||||
\(234\) | −3.87661 | −0.253422 | ||||||||
\(235\) | 4.31503 | 0.281482 | ||||||||
\(236\) | 18.6978 | 1.21712 | ||||||||
\(237\) | −4.43519 | −0.288097 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.09118 | −0.523375 | −0.261687 | − | 0.965153i | \(-0.584279\pi\) | ||||
−0.261687 | + | 0.965153i | \(0.584279\pi\) | |||||||
\(240\) | 10.7666 | 0.694982 | ||||||||
\(241\) | 14.7093 | 0.947509 | 0.473755 | − | 0.880657i | \(-0.342898\pi\) | ||||
0.473755 | + | 0.880657i | \(0.342898\pi\) | |||||||
\(242\) | −2.64021 | −0.169719 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 67.7086 | 4.33460 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.1973 | −1.28773 | ||||||||
\(247\) | 2.80185 | 0.178277 | ||||||||
\(248\) | −41.2465 | −2.61916 | ||||||||
\(249\) | 15.3931 | 0.975496 | ||||||||
\(250\) | 2.64021 | 0.166982 | ||||||||
\(251\) | 22.1292 | 1.39678 | 0.698391 | − | 0.715717i | \(-0.253900\pi\) | ||||
0.698391 | + | 0.715717i | \(0.253900\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.10323 | −0.383707 | ||||||||
\(254\) | −13.2006 | −0.828282 | ||||||||
\(255\) | −1.32245 | −0.0828150 | ||||||||
\(256\) | −7.11568 | −0.444730 | ||||||||
\(257\) | −25.2025 | −1.57209 | −0.786045 | − | 0.618169i | \(-0.787875\pi\) | ||||
−0.786045 | + | 0.618169i | \(0.787875\pi\) | |||||||
\(258\) | −26.8367 | −1.67078 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7.29847 | −0.452632 | ||||||||
\(261\) | −5.36654 | −0.332181 | ||||||||
\(262\) | −20.0226 | −1.23700 | ||||||||
\(263\) | −17.8984 | −1.10366 | −0.551832 | − | 0.833956i | \(-0.686071\pi\) | ||||
−0.551832 | + | 0.833956i | \(0.686071\pi\) | |||||||
\(264\) | −7.84333 | −0.482724 | ||||||||
\(265\) | 3.12495 | 0.191964 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.7962 | −0.905511 | ||||||||
\(268\) | −53.4141 | −3.26279 | ||||||||
\(269\) | −16.2110 | −0.988404 | −0.494202 | − | 0.869347i | \(-0.664540\pi\) | ||||
−0.494202 | + | 0.869347i | \(0.664540\pi\) | |||||||
\(270\) | −2.64021 | −0.160678 | ||||||||
\(271\) | 6.78977 | 0.412449 | 0.206224 | − | 0.978505i | \(-0.433882\pi\) | ||||
0.206224 | + | 0.978505i | \(0.433882\pi\) | |||||||
\(272\) | −14.2383 | −0.863324 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.20681 | −0.254143 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −30.3374 | −1.82610 | ||||||||
\(277\) | −10.9969 | −0.660740 | −0.330370 | − | 0.943851i | \(-0.607174\pi\) | ||||
−0.330370 | + | 0.943851i | \(0.607174\pi\) | |||||||
\(278\) | 6.80002 | 0.407838 | ||||||||
\(279\) | 5.25881 | 0.314836 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.4623 | 0.862746 | 0.431373 | − | 0.902174i | \(-0.358029\pi\) | ||||
0.431373 | + | 0.902174i | \(0.358029\pi\) | |||||||
\(282\) | −11.3926 | −0.678420 | ||||||||
\(283\) | 13.6634 | 0.812203 | 0.406101 | − | 0.913828i | \(-0.366888\pi\) | ||||
0.406101 | + | 0.913828i | \(0.366888\pi\) | |||||||
\(284\) | 38.2105 | 2.26738 | ||||||||
\(285\) | 1.90824 | 0.113034 | ||||||||
\(286\) | 3.87661 | 0.229229 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −12.7395 | −0.750681 | ||||||||
\(289\) | −15.2511 | −0.897125 | ||||||||
\(290\) | −14.1688 | −0.832021 | ||||||||
\(291\) | 10.5475 | 0.618305 | ||||||||
\(292\) | 42.8604 | 2.50822 | ||||||||
\(293\) | −18.7269 | −1.09404 | −0.547020 | − | 0.837120i | \(-0.684238\pi\) | ||||
−0.547020 | + | 0.837120i | \(0.684238\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.76158 | −0.219008 | ||||||||
\(296\) | −7.13795 | −0.414885 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | 15.0103 | 0.869522 | ||||||||
\(299\) | 8.96133 | 0.518247 | ||||||||
\(300\) | −4.97072 | −0.286985 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 45.8607 | 2.63899 | ||||||||
\(303\) | 1.15863 | 0.0665616 | ||||||||
\(304\) | 20.5452 | 1.17835 | ||||||||
\(305\) | −13.6215 | −0.779964 | ||||||||
\(306\) | 3.49155 | 0.199598 | ||||||||
\(307\) | −9.11259 | −0.520083 | −0.260041 | − | 0.965597i | \(-0.583736\pi\) | ||||
−0.260041 | + | 0.965597i | \(0.583736\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.82710 | 0.331492 | ||||||||
\(310\) | 13.8844 | 0.788579 | ||||||||
\(311\) | 13.2795 | 0.753010 | 0.376505 | − | 0.926415i | \(-0.377126\pi\) | ||||
0.376505 | + | 0.926415i | \(0.377126\pi\) | |||||||
\(312\) | 11.5163 | 0.651983 | ||||||||
\(313\) | 2.22034 | 0.125501 | 0.0627504 | − | 0.998029i | \(-0.480013\pi\) | ||||
0.0627504 | + | 0.998029i | \(0.480013\pi\) | |||||||
\(314\) | 8.70414 | 0.491203 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 22.0461 | 1.24019 | ||||||||
\(317\) | 22.2699 | 1.25080 | 0.625402 | − | 0.780302i | \(-0.284935\pi\) | ||||
0.625402 | + | 0.780302i | \(0.284935\pi\) | |||||||
\(318\) | −8.25053 | −0.462667 | ||||||||
\(319\) | 5.36654 | 0.300469 | ||||||||
\(320\) | −12.1017 | −0.676506 | ||||||||
\(321\) | 8.62135 | 0.481197 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.52355 | −0.140414 | ||||||||
\(324\) | 4.97072 | 0.276151 | ||||||||
\(325\) | 1.46829 | 0.0814463 | ||||||||
\(326\) | −50.7503 | −2.81080 | ||||||||
\(327\) | 0.496925 | 0.0274800 | ||||||||
\(328\) | 60.0005 | 3.31298 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.64021 | 0.145339 | ||||||||
\(331\) | −20.0057 | −1.09961 | −0.549807 | − | 0.835292i | \(-0.685299\pi\) | ||||
−0.549807 | + | 0.835292i | \(0.685299\pi\) | |||||||
\(332\) | −76.5146 | −4.19928 | ||||||||
\(333\) | 0.910067 | 0.0498714 | ||||||||
\(334\) | −16.9213 | −0.925890 | ||||||||
\(335\) | 10.7458 | 0.587103 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.4230 | 1.92961 | 0.964807 | − | 0.262958i | \(-0.0846982\pi\) | ||||
0.964807 | + | 0.262958i | \(0.0846982\pi\) | |||||||
\(338\) | 28.6308 | 1.55731 | ||||||||
\(339\) | 3.47631 | 0.188807 | ||||||||
\(340\) | 6.57353 | 0.356499 | ||||||||
\(341\) | −5.25881 | −0.284780 | ||||||||
\(342\) | −5.03815 | −0.272432 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 79.7242 | 4.29844 | ||||||||
\(345\) | 6.10323 | 0.328587 | ||||||||
\(346\) | 20.3755 | 1.09539 | ||||||||
\(347\) | −6.74944 | −0.362329 | −0.181165 | − | 0.983453i | \(-0.557987\pi\) | ||||
−0.181165 | + | 0.983453i | \(0.557987\pi\) | |||||||
\(348\) | 26.6756 | 1.42996 | ||||||||
\(349\) | 2.23091 | 0.119418 | 0.0597090 | − | 0.998216i | \(-0.480983\pi\) | ||||
0.0597090 | + | 0.998216i | \(0.480983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.46829 | −0.0783717 | ||||||||
\(352\) | 12.7395 | 0.679017 | ||||||||
\(353\) | 8.24153 | 0.438652 | 0.219326 | − | 0.975652i | \(-0.429614\pi\) | ||||
0.219326 | + | 0.975652i | \(0.429614\pi\) | |||||||
\(354\) | 9.93138 | 0.527847 | ||||||||
\(355\) | −7.68712 | −0.407990 | ||||||||
\(356\) | 73.5476 | 3.89802 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −32.5523 | −1.72044 | ||||||||
\(359\) | 9.67460 | 0.510606 | 0.255303 | − | 0.966861i | \(-0.417825\pi\) | ||||
0.255303 | + | 0.966861i | \(0.417825\pi\) | |||||||
\(360\) | 7.84333 | 0.413380 | ||||||||
\(361\) | −15.3586 | −0.808349 | ||||||||
\(362\) | −53.9558 | −2.83585 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.62258 | −0.451327 | ||||||||
\(366\) | 35.9636 | 1.87985 | ||||||||
\(367\) | −10.1412 | −0.529364 | −0.264682 | − | 0.964336i | \(-0.585267\pi\) | ||||
−0.264682 | + | 0.964336i | \(0.585267\pi\) | |||||||
\(368\) | 65.7111 | 3.42543 | ||||||||
\(369\) | −7.64988 | −0.398237 | ||||||||
\(370\) | 2.40277 | 0.124914 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −26.1400 | −1.35530 | ||||||||
\(373\) | −24.2646 | −1.25637 | −0.628186 | − | 0.778063i | \(-0.716202\pi\) | ||||
−0.628186 | + | 0.778063i | \(0.716202\pi\) | |||||||
\(374\) | −3.49155 | −0.180544 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 33.8442 | 1.74538 | ||||||||
\(377\) | −7.87966 | −0.405823 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.59132 | −0.235840 | −0.117920 | − | 0.993023i | \(-0.537623\pi\) | ||||
−0.117920 | + | 0.993023i | \(0.537623\pi\) | |||||||
\(380\) | −9.48531 | −0.486586 | ||||||||
\(381\) | −4.99984 | −0.256150 | ||||||||
\(382\) | 45.6746 | 2.33691 | ||||||||
\(383\) | 23.2876 | 1.18994 | 0.594971 | − | 0.803747i | \(-0.297163\pi\) | ||||
0.594971 | + | 0.803747i | \(0.297163\pi\) | |||||||
\(384\) | 6.47211 | 0.330278 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.91712 | −0.402971 | ||||||||
\(387\) | −10.1646 | −0.516695 | ||||||||
\(388\) | −52.4287 | −2.66166 | ||||||||
\(389\) | −32.3443 | −1.63992 | −0.819960 | − | 0.572421i | \(-0.806004\pi\) | ||||
−0.819960 | + | 0.572421i | \(0.806004\pi\) | |||||||
\(390\) | −3.87661 | −0.196300 | ||||||||
\(391\) | −8.07121 | −0.408179 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.58371 | −0.382548 | ||||||||
\(394\) | 21.9599 | 1.10632 | ||||||||
\(395\) | −4.43519 | −0.223159 | ||||||||
\(396\) | −4.97072 | −0.249788 | ||||||||
\(397\) | 12.5036 | 0.627538 | 0.313769 | − | 0.949499i | \(-0.398408\pi\) | ||||
0.313769 | + | 0.949499i | \(0.398408\pi\) | |||||||
\(398\) | −35.6565 | −1.78730 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.7666 | 0.538331 | ||||||||
\(401\) | 32.9395 | 1.64492 | 0.822459 | − | 0.568824i | \(-0.192602\pi\) | ||||
0.822459 | + | 0.568824i | \(0.192602\pi\) | |||||||
\(402\) | −28.3711 | −1.41502 | ||||||||
\(403\) | 7.72147 | 0.384634 | ||||||||
\(404\) | −5.75923 | −0.286532 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.910067 | −0.0451103 | ||||||||
\(408\) | −10.3724 | −0.513511 | ||||||||
\(409\) | 5.48449 | 0.271191 | 0.135595 | − | 0.990764i | \(-0.456705\pi\) | ||||
0.135595 | + | 0.990764i | \(0.456705\pi\) | |||||||
\(410\) | −20.1973 | −0.997474 | ||||||||
\(411\) | −1.59336 | −0.0785948 | ||||||||
\(412\) | −28.9649 | −1.42700 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −16.1138 | −0.791951 | ||||||||
\(415\) | 15.3931 | 0.755616 | ||||||||
\(416\) | −18.7053 | −0.917103 | ||||||||
\(417\) | 2.57556 | 0.126126 | ||||||||
\(418\) | 5.03815 | 0.246424 | ||||||||
\(419\) | −5.22081 | −0.255053 | −0.127527 | − | 0.991835i | \(-0.540704\pi\) | ||||
−0.127527 | + | 0.991835i | \(0.540704\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.1044 | −1.75962 | −0.879810 | − | 0.475326i | \(-0.842330\pi\) | ||||
−0.879810 | + | 0.475326i | \(0.842330\pi\) | |||||||
\(422\) | −7.93603 | −0.386320 | ||||||||
\(423\) | −4.31503 | −0.209804 | ||||||||
\(424\) | 24.5100 | 1.19031 | ||||||||
\(425\) | −1.32245 | −0.0641482 | ||||||||
\(426\) | 20.2956 | 0.983327 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −42.8543 | −2.07144 | ||||||||
\(429\) | 1.46829 | 0.0708899 | ||||||||
\(430\) | −26.8367 | −1.29418 | ||||||||
\(431\) | 31.7237 | 1.52808 | 0.764039 | − | 0.645170i | \(-0.223213\pi\) | ||||
0.764039 | + | 0.645170i | \(0.223213\pi\) | |||||||
\(432\) | −10.7666 | −0.518009 | ||||||||
\(433\) | 25.9251 | 1.24588 | 0.622939 | − | 0.782270i | \(-0.285938\pi\) | ||||
0.622939 | + | 0.782270i | \(0.285938\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.36654 | −0.257306 | ||||||||
\(436\) | −2.47008 | −0.118295 | ||||||||
\(437\) | 11.6464 | 0.557123 | ||||||||
\(438\) | 22.7654 | 1.08778 | ||||||||
\(439\) | −27.6259 | −1.31851 | −0.659256 | − | 0.751919i | \(-0.729129\pi\) | ||||
−0.659256 | + | 0.751919i | \(0.729129\pi\) | |||||||
\(440\) | −7.84333 | −0.373916 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.12662 | 0.243848 | ||||||||
\(443\) | 40.1305 | 1.90666 | 0.953329 | − | 0.301932i | \(-0.0976316\pi\) | ||||
0.953329 | + | 0.301932i | \(0.0976316\pi\) | |||||||
\(444\) | −4.52369 | −0.214685 | ||||||||
\(445\) | −14.7962 | −0.701406 | ||||||||
\(446\) | −5.45030 | −0.258079 | ||||||||
\(447\) | 5.68525 | 0.268903 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.6309 | 1.49275 | 0.746377 | − | 0.665523i | \(-0.231791\pi\) | ||||
0.746377 | + | 0.665523i | \(0.231791\pi\) | |||||||
\(450\) | −2.64021 | −0.124461 | ||||||||
\(451\) | 7.64988 | 0.360219 | ||||||||
\(452\) | −17.2798 | −0.812772 | ||||||||
\(453\) | 17.3701 | 0.816117 | ||||||||
\(454\) | −60.0299 | −2.81734 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.9669 | 0.700890 | ||||||||
\(457\) | 16.9286 | 0.791889 | 0.395944 | − | 0.918274i | \(-0.370417\pi\) | ||||
0.395944 | + | 0.918274i | \(0.370417\pi\) | |||||||
\(458\) | 39.5774 | 1.84933 | ||||||||
\(459\) | 1.32245 | 0.0617267 | ||||||||
\(460\) | −30.3374 | −1.41449 | ||||||||
\(461\) | 24.8508 | 1.15742 | 0.578709 | − | 0.815534i | \(-0.303557\pi\) | ||||
0.578709 | + | 0.815534i | \(0.303557\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1176 | 0.841997 | 0.420999 | − | 0.907061i | \(-0.361680\pi\) | ||||
0.420999 | + | 0.907061i | \(0.361680\pi\) | |||||||
\(464\) | −57.7795 | −2.68235 | ||||||||
\(465\) | 5.25881 | 0.243871 | ||||||||
\(466\) | 36.7224 | 1.70113 | ||||||||
\(467\) | 21.9464 | 1.01556 | 0.507779 | − | 0.861487i | \(-0.330467\pi\) | ||||
0.507779 | + | 0.861487i | \(0.330467\pi\) | |||||||
\(468\) | 7.29847 | 0.337372 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −11.3926 | −0.525502 | ||||||||
\(471\) | 3.29676 | 0.151907 | ||||||||
\(472\) | −29.5033 | −1.35800 | ||||||||
\(473\) | 10.1646 | 0.467368 | ||||||||
\(474\) | 11.7098 | 0.537851 | ||||||||
\(475\) | 1.90824 | 0.0875559 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.12495 | −0.143082 | ||||||||
\(478\) | 21.3624 | 0.977095 | ||||||||
\(479\) | −22.8628 | −1.04463 | −0.522315 | − | 0.852753i | \(-0.674931\pi\) | ||||
−0.522315 | + | 0.852753i | \(0.674931\pi\) | |||||||
\(480\) | −12.7395 | −0.581475 | ||||||||
\(481\) | 1.33625 | 0.0609275 | ||||||||
\(482\) | −38.8357 | −1.76892 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.97072 | 0.225942 | ||||||||
\(485\) | 10.5475 | 0.478937 | ||||||||
\(486\) | 2.64021 | 0.119762 | ||||||||
\(487\) | 12.3707 | 0.560569 | 0.280285 | − | 0.959917i | \(-0.409571\pi\) | ||||
0.280285 | + | 0.959917i | \(0.409571\pi\) | |||||||
\(488\) | −106.838 | −4.83632 | ||||||||
\(489\) | −19.2220 | −0.869251 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.6766 | −1.56493 | −0.782467 | − | 0.622692i | \(-0.786039\pi\) | ||||
−0.782467 | + | 0.622692i | \(0.786039\pi\) | |||||||
\(492\) | 38.0254 | 1.71432 | ||||||||
\(493\) | 7.09698 | 0.319632 | ||||||||
\(494\) | −7.39748 | −0.332828 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 56.6195 | 2.54229 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −40.6410 | −1.82116 | ||||||||
\(499\) | −31.1455 | −1.39426 | −0.697131 | − | 0.716944i | \(-0.745540\pi\) | ||||
−0.697131 | + | 0.716944i | \(0.745540\pi\) | |||||||
\(500\) | −4.97072 | −0.222297 | ||||||||
\(501\) | −6.40905 | −0.286335 | ||||||||
\(502\) | −58.4257 | −2.60767 | ||||||||
\(503\) | −31.5669 | −1.40750 | −0.703749 | − | 0.710448i | \(-0.748492\pi\) | ||||
−0.703749 | + | 0.710448i | \(0.748492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.15863 | 0.0515584 | ||||||||
\(506\) | 16.1138 | 0.716346 | ||||||||
\(507\) | 10.8441 | 0.481604 | ||||||||
\(508\) | 24.8528 | 1.10267 | ||||||||
\(509\) | −10.2180 | −0.452904 | −0.226452 | − | 0.974022i | \(-0.572713\pi\) | ||||
−0.226452 | + | 0.974022i | \(0.572713\pi\) | |||||||
\(510\) | 3.49155 | 0.154608 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.7311 | 1.40233 | ||||||||
\(513\) | −1.90824 | −0.0842507 | ||||||||
\(514\) | 66.5400 | 2.93495 | ||||||||
\(515\) | 5.82710 | 0.256773 | ||||||||
\(516\) | 50.5253 | 2.22425 | ||||||||
\(517\) | 4.31503 | 0.189775 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.71736 | 0.338754 | ||||||||
\(520\) | 11.5163 | 0.505024 | ||||||||
\(521\) | −8.95953 | −0.392524 | −0.196262 | − | 0.980551i | \(-0.562880\pi\) | ||||
−0.196262 | + | 0.980551i | \(0.562880\pi\) | |||||||
\(522\) | 14.1688 | 0.620152 | ||||||||
\(523\) | 38.6053 | 1.68809 | 0.844046 | − | 0.536271i | \(-0.180168\pi\) | ||||
0.844046 | + | 0.536271i | \(0.180168\pi\) | |||||||
\(524\) | 37.6965 | 1.64678 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 47.2556 | 2.06044 | ||||||||
\(527\) | −6.95451 | −0.302943 | ||||||||
\(528\) | 10.7666 | 0.468557 | ||||||||
\(529\) | 14.2494 | 0.619538 | ||||||||
\(530\) | −8.25053 | −0.358380 | ||||||||
\(531\) | 3.76158 | 0.163239 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.2323 | −0.486524 | ||||||||
\(534\) | 39.0650 | 1.69051 | ||||||||
\(535\) | 8.62135 | 0.372733 | ||||||||
\(536\) | 84.2825 | 3.64045 | ||||||||
\(537\) | −12.3294 | −0.532054 | ||||||||
\(538\) | 42.8006 | 1.84526 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.97072 | 0.213906 | ||||||||
\(541\) | 23.3879 | 1.00552 | 0.502762 | − | 0.864425i | \(-0.332317\pi\) | ||||
0.502762 | + | 0.864425i | \(0.332317\pi\) | |||||||
\(542\) | −17.9264 | −0.770006 | ||||||||
\(543\) | −20.4362 | −0.876999 | ||||||||
\(544\) | 16.8473 | 0.722323 | ||||||||
\(545\) | 0.496925 | 0.0212859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2222 | 1.03567 | 0.517833 | − | 0.855481i | \(-0.326739\pi\) | ||||
0.517833 | + | 0.855481i | \(0.326739\pi\) | |||||||
\(548\) | 7.92016 | 0.338332 | ||||||||
\(549\) | 13.6215 | 0.581351 | ||||||||
\(550\) | 2.64021 | 0.112579 | ||||||||
\(551\) | −10.2406 | −0.436266 | ||||||||
\(552\) | 47.8696 | 2.03747 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 29.0342 | 1.23354 | ||||||||
\(555\) | 0.910067 | 0.0386302 | ||||||||
\(556\) | −12.8024 | −0.542942 | ||||||||
\(557\) | −37.4636 | −1.58739 | −0.793693 | − | 0.608319i | \(-0.791844\pi\) | ||||
−0.793693 | + | 0.608319i | \(0.791844\pi\) | |||||||
\(558\) | −13.8844 | −0.587772 | ||||||||
\(559\) | −14.9246 | −0.631243 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.32245 | −0.0558339 | ||||||||
\(562\) | −38.1834 | −1.61067 | ||||||||
\(563\) | 16.1375 | 0.680116 | 0.340058 | − | 0.940405i | \(-0.389553\pi\) | ||||
0.340058 | + | 0.940405i | \(0.389553\pi\) | |||||||
\(564\) | 21.4488 | 0.903159 | ||||||||
\(565\) | 3.47631 | 0.146250 | ||||||||
\(566\) | −36.0742 | −1.51631 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −60.2926 | −2.52982 | ||||||||
\(569\) | 23.4149 | 0.981604 | 0.490802 | − | 0.871271i | \(-0.336704\pi\) | ||||
0.490802 | + | 0.871271i | \(0.336704\pi\) | |||||||
\(570\) | −5.03815 | −0.211025 | ||||||||
\(571\) | −26.3177 | −1.10136 | −0.550680 | − | 0.834716i | \(-0.685632\pi\) | ||||
−0.550680 | + | 0.834716i | \(0.685632\pi\) | |||||||
\(572\) | −7.29847 | −0.305165 | ||||||||
\(573\) | 17.2996 | 0.722701 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.10323 | 0.254522 | ||||||||
\(576\) | 12.1017 | 0.504238 | ||||||||
\(577\) | 45.1935 | 1.88143 | 0.940716 | − | 0.339195i | \(-0.110155\pi\) | ||||
0.940716 | + | 0.339195i | \(0.110155\pi\) | |||||||
\(578\) | 40.2662 | 1.67485 | ||||||||
\(579\) | −2.99867 | −0.124620 | ||||||||
\(580\) | 26.6756 | 1.10764 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −27.8476 | −1.15432 | ||||||||
\(583\) | 3.12495 | 0.129422 | ||||||||
\(584\) | −67.6298 | −2.79854 | ||||||||
\(585\) | −1.46829 | −0.0607065 | ||||||||
\(586\) | 49.4431 | 2.04247 | ||||||||
\(587\) | −17.1124 | −0.706303 | −0.353151 | − | 0.935566i | \(-0.614890\pi\) | ||||
−0.353151 | + | 0.935566i | \(0.614890\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0350 | 0.413487 | ||||||||
\(590\) | 9.93138 | 0.408868 | ||||||||
\(591\) | 8.31748 | 0.342135 | ||||||||
\(592\) | 9.79834 | 0.402709 | ||||||||
\(593\) | 15.4135 | 0.632956 | 0.316478 | − | 0.948600i | \(-0.397500\pi\) | ||||
0.316478 | + | 0.948600i | \(0.397500\pi\) | |||||||
\(594\) | −2.64021 | −0.108329 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.2598 | −1.15757 | ||||||||
\(597\) | −13.5052 | −0.552730 | ||||||||
\(598\) | −23.6598 | −0.967521 | ||||||||
\(599\) | −0.638573 | −0.0260914 | −0.0130457 | − | 0.999915i | \(-0.504153\pi\) | ||||
−0.0130457 | + | 0.999915i | \(0.504153\pi\) | |||||||
\(600\) | 7.84333 | 0.320203 | ||||||||
\(601\) | −47.0074 | −1.91747 | −0.958736 | − | 0.284298i | \(-0.908239\pi\) | ||||
−0.958736 | + | 0.284298i | \(0.908239\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.7458 | −0.437601 | ||||||||
\(604\) | −86.3417 | −3.51320 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −3.05903 | −0.124265 | ||||||||
\(607\) | −34.5649 | −1.40294 | −0.701472 | − | 0.712697i | \(-0.747474\pi\) | ||||
−0.701472 | + | 0.712697i | \(0.747474\pi\) | |||||||
\(608\) | −24.3099 | −0.985898 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 35.9636 | 1.45612 | ||||||||
\(611\) | −6.33574 | −0.256317 | ||||||||
\(612\) | −6.57353 | −0.265719 | ||||||||
\(613\) | −11.4623 | −0.462956 | −0.231478 | − | 0.972840i | \(-0.574356\pi\) | ||||
−0.231478 | + | 0.972840i | \(0.574356\pi\) | |||||||
\(614\) | 24.0592 | 0.970949 | ||||||||
\(615\) | −7.64988 | −0.308473 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.48742 | −0.220915 | −0.110458 | − | 0.993881i | \(-0.535232\pi\) | ||||
−0.110458 | + | 0.993881i | \(0.535232\pi\) | |||||||
\(618\) | −15.3848 | −0.618867 | ||||||||
\(619\) | −24.6364 | −0.990222 | −0.495111 | − | 0.868830i | \(-0.664873\pi\) | ||||
−0.495111 | + | 0.868830i | \(0.664873\pi\) | |||||||
\(620\) | −26.1400 | −1.04981 | ||||||||
\(621\) | −6.10323 | −0.244914 | ||||||||
\(622\) | −35.0606 | −1.40580 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −15.8085 | −0.632848 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.86216 | −0.234299 | ||||||||
\(627\) | 1.90824 | 0.0762076 | ||||||||
\(628\) | −16.3873 | −0.653923 | ||||||||
\(629\) | −1.20352 | −0.0479874 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.7720 | −1.34444 | −0.672222 | − | 0.740350i | \(-0.734660\pi\) | ||||
−0.672222 | + | 0.740350i | \(0.734660\pi\) | |||||||
\(632\) | −34.7867 | −1.38374 | ||||||||
\(633\) | −3.00583 | −0.119471 | ||||||||
\(634\) | −58.7974 | −2.33514 | ||||||||
\(635\) | −4.99984 | −0.198413 | ||||||||
\(636\) | 15.5333 | 0.615934 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −14.1688 | −0.560949 | ||||||||
\(639\) | 7.68712 | 0.304098 | ||||||||
\(640\) | 6.47211 | 0.255832 | ||||||||
\(641\) | 12.1006 | 0.477945 | 0.238972 | − | 0.971026i | \(-0.423189\pi\) | ||||
0.238972 | + | 0.971026i | \(0.423189\pi\) | |||||||
\(642\) | −22.7622 | −0.898352 | ||||||||
\(643\) | 5.76993 | 0.227544 | 0.113772 | − | 0.993507i | \(-0.463707\pi\) | ||||
0.113772 | + | 0.993507i | \(0.463707\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.1646 | −0.400230 | ||||||||
\(646\) | 6.66270 | 0.262140 | ||||||||
\(647\) | 45.5459 | 1.79059 | 0.895296 | − | 0.445471i | \(-0.146964\pi\) | ||||
0.895296 | + | 0.445471i | \(0.146964\pi\) | |||||||
\(648\) | −7.84333 | −0.308115 | ||||||||
\(649\) | −3.76158 | −0.147655 | ||||||||
\(650\) | −3.87661 | −0.152053 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 95.5474 | 3.74192 | ||||||||
\(653\) | −38.1388 | −1.49249 | −0.746244 | − | 0.665673i | \(-0.768145\pi\) | ||||
−0.746244 | + | 0.665673i | \(0.768145\pi\) | |||||||
\(654\) | −1.31199 | −0.0513028 | ||||||||
\(655\) | −7.58371 | −0.296320 | ||||||||
\(656\) | −82.3633 | −3.21575 | ||||||||
\(657\) | 8.62258 | 0.336399 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.1962 | −1.60478 | −0.802388 | − | 0.596803i | \(-0.796437\pi\) | ||||
−0.802388 | + | 0.596803i | \(0.796437\pi\) | |||||||
\(660\) | −4.97072 | −0.193485 | ||||||||
\(661\) | −15.8103 | −0.614949 | −0.307474 | − | 0.951556i | \(-0.599484\pi\) | ||||
−0.307474 | + | 0.951556i | \(0.599484\pi\) | |||||||
\(662\) | 52.8193 | 2.05288 | ||||||||
\(663\) | 1.94174 | 0.0754111 | ||||||||
\(664\) | 120.733 | 4.68534 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.40277 | −0.0931054 | ||||||||
\(667\) | −32.7532 | −1.26821 | ||||||||
\(668\) | 31.8576 | 1.23261 | ||||||||
\(669\) | −2.06434 | −0.0798120 | ||||||||
\(670\) | −28.3711 | −1.09607 | ||||||||
\(671\) | −13.6215 | −0.525851 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.7115 | 0.721275 | 0.360637 | − | 0.932706i | \(-0.382559\pi\) | ||||
0.360637 | + | 0.932706i | \(0.382559\pi\) | |||||||
\(674\) | −93.5243 | −3.60242 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −53.9030 | −2.07319 | ||||||||
\(677\) | −17.4216 | −0.669568 | −0.334784 | − | 0.942295i | \(-0.608663\pi\) | ||||
−0.334784 | + | 0.942295i | \(0.608663\pi\) | |||||||
\(678\) | −9.17820 | −0.352487 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −10.3724 | −0.397764 | ||||||||
\(681\) | −22.7368 | −0.871275 | ||||||||
\(682\) | 13.8844 | 0.531660 | ||||||||
\(683\) | 12.8600 | 0.492074 | 0.246037 | − | 0.969260i | \(-0.420872\pi\) | ||||
0.246037 | + | 0.969260i | \(0.420872\pi\) | |||||||
\(684\) | 9.48531 | 0.362680 | ||||||||
\(685\) | −1.59336 | −0.0608792 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.9902 | 0.571914 | ||||||||
\(688\) | −109.438 | −4.17229 | ||||||||
\(689\) | −4.58835 | −0.174802 | ||||||||
\(690\) | −16.1138 | −0.613442 | ||||||||
\(691\) | −34.8830 | −1.32701 | −0.663505 | − | 0.748171i | \(-0.730932\pi\) | ||||
−0.663505 | + | 0.748171i | \(0.730932\pi\) | |||||||
\(692\) | −38.3608 | −1.45826 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.8200 | 0.676437 | ||||||||
\(695\) | 2.57556 | 0.0976965 | ||||||||
\(696\) | −42.0916 | −1.59548 | ||||||||
\(697\) | 10.1166 | 0.383193 | ||||||||
\(698\) | −5.89008 | −0.222943 | ||||||||
\(699\) | 13.9089 | 0.526083 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.6696 | −1.46053 | −0.730266 | − | 0.683163i | \(-0.760604\pi\) | ||||
−0.730266 | + | 0.683163i | \(0.760604\pi\) | |||||||
\(702\) | 3.87661 | 0.146313 | ||||||||
\(703\) | 1.73662 | 0.0654980 | ||||||||
\(704\) | −12.1017 | −0.456100 | ||||||||
\(705\) | −4.31503 | −0.162514 | ||||||||
\(706\) | −21.7594 | −0.818925 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −18.6978 | −0.702706 | ||||||||
\(709\) | 36.9867 | 1.38906 | 0.694531 | − | 0.719462i | \(-0.255612\pi\) | ||||
0.694531 | + | 0.719462i | \(0.255612\pi\) | |||||||
\(710\) | 20.2956 | 0.761682 | ||||||||
\(711\) | 4.43519 | 0.166333 | ||||||||
\(712\) | −116.051 | −4.34920 | ||||||||
\(713\) | 32.0957 | 1.20199 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.46829 | 0.0549111 | ||||||||
\(716\) | 61.2861 | 2.29037 | ||||||||
\(717\) | 8.09118 | 0.302171 | ||||||||
\(718\) | −25.5430 | −0.953256 | ||||||||
\(719\) | −11.0403 | −0.411734 | −0.205867 | − | 0.978580i | \(-0.566001\pi\) | ||||
−0.205867 | + | 0.978580i | \(0.566001\pi\) | |||||||
\(720\) | −10.7666 | −0.401248 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 40.5501 | 1.50912 | ||||||||
\(723\) | −14.7093 | −0.547045 | ||||||||
\(724\) | 101.582 | 3.77528 | ||||||||
\(725\) | −5.36654 | −0.199308 | ||||||||
\(726\) | 2.64021 | 0.0979875 | ||||||||
\(727\) | −40.2559 | −1.49301 | −0.746504 | − | 0.665381i | \(-0.768269\pi\) | ||||
−0.746504 | + | 0.665381i | \(0.768269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 22.7654 | 0.842587 | ||||||||
\(731\) | 13.4422 | 0.497176 | ||||||||
\(732\) | −67.7086 | −2.50258 | ||||||||
\(733\) | −49.5298 | −1.82943 | −0.914713 | − | 0.404105i | \(-0.867583\pi\) | ||||
−0.914713 | + | 0.404105i | \(0.867583\pi\) | |||||||
\(734\) | 26.7748 | 0.988275 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −77.7519 | −2.86597 | ||||||||
\(737\) | 10.7458 | 0.395825 | ||||||||
\(738\) | 20.1973 | 0.743473 | ||||||||
\(739\) | −50.5362 | −1.85900 | −0.929502 | − | 0.368817i | \(-0.879763\pi\) | ||||
−0.929502 | + | 0.368817i | \(0.879763\pi\) | |||||||
\(740\) | −4.52369 | −0.166294 | ||||||||
\(741\) | −2.80185 | −0.102929 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.3856 | −1.18811 | −0.594057 | − | 0.804423i | \(-0.702475\pi\) | ||||
−0.594057 | + | 0.804423i | \(0.702475\pi\) | |||||||
\(744\) | 41.2465 | 1.51217 | ||||||||
\(745\) | 5.68525 | 0.208292 | ||||||||
\(746\) | 64.0636 | 2.34554 | ||||||||
\(747\) | −15.3931 | −0.563203 | ||||||||
\(748\) | 6.57353 | 0.240352 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.64021 | −0.0964069 | ||||||||
\(751\) | −51.3682 | −1.87445 | −0.937227 | − | 0.348721i | \(-0.886616\pi\) | ||||
−0.937227 | + | 0.348721i | \(0.886616\pi\) | |||||||
\(752\) | −46.4583 | −1.69416 | ||||||||
\(753\) | −22.1292 | −0.806432 | ||||||||
\(754\) | 20.8040 | 0.757636 | ||||||||
\(755\) | 17.3701 | 0.632162 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.8641 | −0.467555 | −0.233778 | − | 0.972290i | \(-0.575109\pi\) | ||||
−0.233778 | + | 0.972290i | \(0.575109\pi\) | |||||||
\(758\) | 12.1221 | 0.440293 | ||||||||
\(759\) | 6.10323 | 0.221533 | ||||||||
\(760\) | 14.9669 | 0.542907 | ||||||||
\(761\) | 2.61077 | 0.0946404 | 0.0473202 | − | 0.998880i | \(-0.484932\pi\) | ||||
0.0473202 | + | 0.998880i | \(0.484932\pi\) | |||||||
\(762\) | 13.2006 | 0.478209 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −85.9914 | −3.11106 | ||||||||
\(765\) | 1.32245 | 0.0478133 | ||||||||
\(766\) | −61.4843 | −2.22152 | ||||||||
\(767\) | 5.52311 | 0.199428 | ||||||||
\(768\) | 7.11568 | 0.256765 | ||||||||
\(769\) | −13.4032 | −0.483331 | −0.241666 | − | 0.970360i | \(-0.577694\pi\) | ||||
−0.241666 | + | 0.970360i | \(0.577694\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.2025 | 0.907647 | ||||||||
\(772\) | 14.9055 | 0.536462 | ||||||||
\(773\) | −0.424626 | −0.0152727 | −0.00763637 | − | 0.999971i | \(-0.502431\pi\) | ||||
−0.00763637 | + | 0.999971i | \(0.502431\pi\) | |||||||
\(774\) | 26.8367 | 0.964624 | ||||||||
\(775\) | 5.25881 | 0.188902 | ||||||||
\(776\) | 82.7275 | 2.96974 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 85.3958 | 3.06159 | ||||||||
\(779\) | −14.5978 | −0.523020 | ||||||||
\(780\) | 7.29847 | 0.261327 | ||||||||
\(781\) | −7.68712 | −0.275067 | ||||||||
\(782\) | 21.3097 | 0.762033 | ||||||||
\(783\) | 5.36654 | 0.191785 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.29676 | 0.117666 | ||||||||
\(786\) | 20.0226 | 0.714183 | ||||||||
\(787\) | −13.0742 | −0.466046 | −0.233023 | − | 0.972471i | \(-0.574862\pi\) | ||||
−0.233023 | + | 0.972471i | \(0.574862\pi\) | |||||||
\(788\) | −41.3439 | −1.47281 | ||||||||
\(789\) | 17.8984 | 0.637200 | ||||||||
\(790\) | 11.7098 | 0.416617 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.84333 | 0.278701 | ||||||||
\(793\) | 20.0003 | 0.710233 | ||||||||
\(794\) | −33.0122 | −1.17156 | ||||||||
\(795\) | −3.12495 | −0.110831 | ||||||||
\(796\) | 67.1304 | 2.37937 | ||||||||
\(797\) | −50.9558 | −1.80495 | −0.902474 | − | 0.430744i | \(-0.858251\pi\) | ||||
−0.902474 | + | 0.430744i | \(0.858251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.70642 | 0.201878 | ||||||||
\(800\) | −12.7395 | −0.450409 | ||||||||
\(801\) | 14.7962 | 0.522797 | ||||||||
\(802\) | −86.9672 | −3.07092 | ||||||||
\(803\) | −8.62258 | −0.304284 | ||||||||
\(804\) | 53.4141 | 1.88377 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.3863 | −0.718077 | ||||||||
\(807\) | 16.2110 | 0.570655 | ||||||||
\(808\) | 9.08753 | 0.319698 | ||||||||
\(809\) | 1.27487 | 0.0448222 | 0.0224111 | − | 0.999749i | \(-0.492866\pi\) | ||||
0.0224111 | + | 0.999749i | \(0.492866\pi\) | |||||||
\(810\) | 2.64021 | 0.0927676 | ||||||||
\(811\) | −28.2548 | −0.992159 | −0.496080 | − | 0.868277i | \(-0.665228\pi\) | ||||
−0.496080 | + | 0.868277i | \(0.665228\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.78977 | −0.238128 | ||||||||
\(814\) | 2.40277 | 0.0842170 | ||||||||
\(815\) | −19.2220 | −0.673319 | ||||||||
\(816\) | 14.2383 | 0.498440 | ||||||||
\(817\) | −19.3964 | −0.678595 | ||||||||
\(818\) | −14.4802 | −0.506289 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 38.0254 | 1.32791 | ||||||||
\(821\) | −2.29991 | −0.0802674 | −0.0401337 | − | 0.999194i | \(-0.512778\pi\) | ||||
−0.0401337 | + | 0.999194i | \(0.512778\pi\) | |||||||
\(822\) | 4.20681 | 0.146729 | ||||||||
\(823\) | 23.2401 | 0.810100 | 0.405050 | − | 0.914295i | \(-0.367254\pi\) | ||||
0.405050 | + | 0.914295i | \(0.367254\pi\) | |||||||
\(824\) | 45.7039 | 1.59217 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.6467 | −1.55252 | −0.776258 | − | 0.630415i | \(-0.782885\pi\) | ||||
−0.776258 | + | 0.630415i | \(0.782885\pi\) | |||||||
\(828\) | 30.3374 | 1.05430 | ||||||||
\(829\) | 25.1551 | 0.873672 | 0.436836 | − | 0.899541i | \(-0.356099\pi\) | ||||
0.436836 | + | 0.899541i | \(0.356099\pi\) | |||||||
\(830\) | −40.6410 | −1.41067 | ||||||||
\(831\) | 10.9969 | 0.381479 | ||||||||
\(832\) | 17.7689 | 0.616024 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6.80002 | −0.235465 | ||||||||
\(835\) | −6.40905 | −0.221794 | ||||||||
\(836\) | −9.48531 | −0.328056 | ||||||||
\(837\) | −5.25881 | −0.181771 | ||||||||
\(838\) | 13.7840 | 0.476162 | ||||||||
\(839\) | −11.4878 | −0.396601 | −0.198301 | − | 0.980141i | \(-0.563542\pi\) | ||||
−0.198301 | + | 0.980141i | \(0.563542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.200202 | −0.00690350 | ||||||||
\(842\) | 95.3232 | 3.28506 | ||||||||
\(843\) | −14.4623 | −0.498107 | ||||||||
\(844\) | 14.9411 | 0.514295 | ||||||||
\(845\) | 10.8441 | 0.373049 | ||||||||
\(846\) | 11.3926 | 0.391686 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −33.6451 | −1.15538 | ||||||||
\(849\) | −13.6634 | −0.468926 | ||||||||
\(850\) | 3.49155 | 0.119759 | ||||||||
\(851\) | 5.55434 | 0.190400 | ||||||||
\(852\) | −38.2105 | −1.30907 | ||||||||
\(853\) | 16.9057 | 0.578839 | 0.289419 | − | 0.957202i | \(-0.406538\pi\) | ||||
0.289419 | + | 0.957202i | \(0.406538\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.90824 | −0.0652603 | ||||||||
\(856\) | 67.6201 | 2.31121 | ||||||||
\(857\) | −36.8371 | −1.25833 | −0.629166 | − | 0.777271i | \(-0.716604\pi\) | ||||
−0.629166 | + | 0.777271i | \(0.716604\pi\) | |||||||
\(858\) | −3.87661 | −0.132345 | ||||||||
\(859\) | −6.66817 | −0.227515 | −0.113757 | − | 0.993509i | \(-0.536289\pi\) | ||||
−0.113757 | + | 0.993509i | \(0.536289\pi\) | |||||||
\(860\) | 50.5253 | 1.72290 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −83.7574 | −2.85279 | ||||||||
\(863\) | −18.7919 | −0.639685 | −0.319842 | − | 0.947471i | \(-0.603630\pi\) | ||||
−0.319842 | + | 0.947471i | \(0.603630\pi\) | |||||||
\(864\) | 12.7395 | 0.433406 | ||||||||
\(865\) | 7.71736 | 0.262398 | ||||||||
\(866\) | −68.4477 | −2.32595 | ||||||||
\(867\) | 15.2511 | 0.517955 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.43519 | −0.150454 | ||||||||
\(870\) | 14.1688 | 0.480368 | ||||||||
\(871\) | −15.7779 | −0.534614 | ||||||||
\(872\) | 3.89755 | 0.131988 | ||||||||
\(873\) | −10.5475 | −0.356979 | ||||||||
\(874\) | −30.7490 | −1.04010 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −42.8604 | −1.44812 | ||||||||
\(877\) | −43.7779 | −1.47827 | −0.739137 | − | 0.673555i | \(-0.764766\pi\) | ||||
−0.739137 | + | 0.673555i | \(0.764766\pi\) | |||||||
\(878\) | 72.9382 | 2.46155 | ||||||||
\(879\) | 18.7269 | 0.631644 | ||||||||
\(880\) | 10.7666 | 0.362942 | ||||||||
\(881\) | 6.06844 | 0.204451 | 0.102226 | − | 0.994761i | \(-0.467404\pi\) | ||||
0.102226 | + | 0.994761i | \(0.467404\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.7996 | 0.632658 | 0.316329 | − | 0.948649i | \(-0.397550\pi\) | ||||
0.316329 | + | 0.948649i | \(0.397550\pi\) | |||||||
\(884\) | −9.65187 | −0.324627 | ||||||||
\(885\) | 3.76158 | 0.126444 | ||||||||
\(886\) | −105.953 | −3.55956 | ||||||||
\(887\) | 1.46141 | 0.0490694 | 0.0245347 | − | 0.999699i | \(-0.492190\pi\) | ||||
0.0245347 | + | 0.999699i | \(0.492190\pi\) | |||||||
\(888\) | 7.13795 | 0.239534 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 39.0650 | 1.30946 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 10.2613 | 0.343572 | ||||||||
\(893\) | −8.23411 | −0.275544 | ||||||||
\(894\) | −15.0103 | −0.502019 | ||||||||
\(895\) | −12.3294 | −0.412127 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.96133 | −0.299210 | ||||||||
\(898\) | −83.5123 | −2.78684 | ||||||||
\(899\) | −28.2216 | −0.941244 | ||||||||
\(900\) | 4.97072 | 0.165691 | ||||||||
\(901\) | 4.13259 | 0.137677 | ||||||||
\(902\) | −20.1973 | −0.672497 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.2659 | 0.906849 | ||||||||
\(905\) | −20.4362 | −0.679321 | ||||||||
\(906\) | −45.8607 | −1.52362 | ||||||||
\(907\) | −56.5762 | −1.87858 | −0.939291 | − | 0.343122i | \(-0.888516\pi\) | ||||
−0.939291 | + | 0.343122i | \(0.888516\pi\) | |||||||
\(908\) | 113.018 | 3.75064 | ||||||||
\(909\) | −1.15863 | −0.0384294 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.6779 | −0.718222 | −0.359111 | − | 0.933295i | \(-0.616920\pi\) | ||||
−0.359111 | + | 0.933295i | \(0.616920\pi\) | |||||||
\(912\) | −20.5452 | −0.680321 | ||||||||
\(913\) | 15.3931 | 0.509436 | ||||||||
\(914\) | −44.6952 | −1.47839 | ||||||||
\(915\) | 13.6215 | 0.450312 | ||||||||
\(916\) | −74.5123 | −2.46196 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.49155 | −0.115238 | ||||||||
\(919\) | −27.0999 | −0.893942 | −0.446971 | − | 0.894549i | \(-0.647497\pi\) | ||||
−0.446971 | + | 0.894549i | \(0.647497\pi\) | |||||||
\(920\) | 47.8696 | 1.57821 | ||||||||
\(921\) | 9.11259 | 0.300270 | ||||||||
\(922\) | −65.6114 | −2.16080 | ||||||||
\(923\) | 11.2870 | 0.371515 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.910067 | 0.0299228 | ||||||||
\(926\) | −47.8344 | −1.57193 | ||||||||
\(927\) | −5.82710 | −0.191387 | ||||||||
\(928\) | 68.3670 | 2.24426 | ||||||||
\(929\) | 31.4252 | 1.03103 | 0.515513 | − | 0.856882i | \(-0.327601\pi\) | ||||
0.515513 | + | 0.856882i | \(0.327601\pi\) | |||||||
\(930\) | −13.8844 | −0.455286 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −69.1372 | −2.26467 | ||||||||
\(933\) | −13.2795 | −0.434750 | ||||||||
\(934\) | −57.9432 | −1.89596 | ||||||||
\(935\) | −1.32245 | −0.0432487 | ||||||||
\(936\) | −11.5163 | −0.376422 | ||||||||
\(937\) | −6.06684 | −0.198195 | −0.0990975 | − | 0.995078i | \(-0.531596\pi\) | ||||
−0.0990975 | + | 0.995078i | \(0.531596\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.22034 | −0.0724580 | ||||||||
\(940\) | 21.4488 | 0.699584 | ||||||||
\(941\) | 8.71299 | 0.284035 | 0.142018 | − | 0.989864i | \(-0.454641\pi\) | ||||
0.142018 | + | 0.989864i | \(0.454641\pi\) | |||||||
\(942\) | −8.70414 | −0.283596 | ||||||||
\(943\) | −46.6890 | −1.52040 | ||||||||
\(944\) | 40.4995 | 1.31815 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −26.8367 | −0.872535 | ||||||||
\(947\) | −18.0921 | −0.587914 | −0.293957 | − | 0.955819i | \(-0.594972\pi\) | ||||
−0.293957 | + | 0.955819i | \(0.594972\pi\) | |||||||
\(948\) | −22.0461 | −0.716024 | ||||||||
\(949\) | 12.6605 | 0.410977 | ||||||||
\(950\) | −5.03815 | −0.163459 | ||||||||
\(951\) | −22.2699 | −0.722152 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.58983 | −0.0838927 | −0.0419463 | − | 0.999120i | \(-0.513356\pi\) | ||||
−0.0419463 | + | 0.999120i | \(0.513356\pi\) | |||||||
\(954\) | 8.25053 | 0.267121 | ||||||||
\(955\) | 17.2996 | 0.559802 | ||||||||
\(956\) | −40.2190 | −1.30077 | ||||||||
\(957\) | −5.36654 | −0.173476 | ||||||||
\(958\) | 60.3627 | 1.95023 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 12.1017 | 0.390581 | ||||||||
\(961\) | −3.34496 | −0.107902 | ||||||||
\(962\) | −3.52797 | −0.113746 | ||||||||
\(963\) | −8.62135 | −0.277819 | ||||||||
\(964\) | 73.1158 | 2.35490 | ||||||||
\(965\) | −2.99867 | −0.0965305 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.1943 | −0.874510 | −0.437255 | − | 0.899337i | \(-0.644049\pi\) | ||||
−0.437255 | + | 0.899337i | \(0.644049\pi\) | |||||||
\(968\) | −7.84333 | −0.252094 | ||||||||
\(969\) | 2.52355 | 0.0810680 | ||||||||
\(970\) | −27.8476 | −0.894134 | ||||||||
\(971\) | 43.3753 | 1.39198 | 0.695990 | − | 0.718052i | \(-0.254966\pi\) | ||||
0.695990 | + | 0.718052i | \(0.254966\pi\) | |||||||
\(972\) | −4.97072 | −0.159436 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −32.6612 | −1.04653 | ||||||||
\(975\) | −1.46829 | −0.0470230 | ||||||||
\(976\) | 146.657 | 4.69438 | ||||||||
\(977\) | −12.0461 | −0.385388 | −0.192694 | − | 0.981259i | \(-0.561722\pi\) | ||||
−0.192694 | + | 0.981259i | \(0.561722\pi\) | |||||||
\(978\) | 50.7503 | 1.62281 | ||||||||
\(979\) | −14.7962 | −0.472888 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.496925 | −0.0158656 | ||||||||
\(982\) | 91.5537 | 2.92160 | ||||||||
\(983\) | 25.7593 | 0.821594 | 0.410797 | − | 0.911727i | \(-0.365250\pi\) | ||||
0.410797 | + | 0.911727i | \(0.365250\pi\) | |||||||
\(984\) | −60.0005 | −1.91275 | ||||||||
\(985\) | 8.31748 | 0.265017 | ||||||||
\(986\) | −18.7375 | −0.596725 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.9272 | 0.443084 | ||||||||
\(989\) | −62.0368 | −1.97265 | ||||||||
\(990\) | −2.64021 | −0.0839114 | ||||||||
\(991\) | −23.3082 | −0.740409 | −0.370205 | − | 0.928950i | \(-0.620712\pi\) | ||||
−0.370205 | + | 0.928950i | \(0.620712\pi\) | |||||||
\(992\) | −66.9945 | −2.12708 | ||||||||
\(993\) | 20.0057 | 0.634862 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.5052 | −0.428143 | ||||||||
\(996\) | 76.5146 | 2.42446 | ||||||||
\(997\) | 12.0798 | 0.382570 | 0.191285 | − | 0.981535i | \(-0.438735\pi\) | ||||
0.191285 | + | 0.981535i | \(0.438735\pi\) | |||||||
\(998\) | 82.2306 | 2.60296 | ||||||||
\(999\) | −0.910067 | −0.0287932 |
(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 | 8085.2.a.ci.1.1 | ✓ | 10 | |
7.6 | odd | 2 | 8085.2.a.cj.1.1 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8085.2.a.ci.1.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
8085.2.a.cj.1.1 | yes | 10 | 7.6 | odd | 2 |