Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6039,2,Mod(1,6039)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6039, 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("6039.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6039 = 3^{2} \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6039.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2216577807\) |
Analytic rank: | \(1\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6039.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.62068 | −1.85310 | −0.926550 | − | 0.376171i | \(-0.877241\pi\) | ||||
−0.926550 | + | 0.376171i | \(0.877241\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.86797 | 2.43398 | ||||||||
\(5\) | −4.12800 | −1.84610 | −0.923050 | − | 0.384681i | \(-0.874312\pi\) | ||||
−0.923050 | + | 0.384681i | \(0.874312\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.639358 | −0.241655 | −0.120827 | − | 0.992674i | \(-0.538555\pi\) | ||||
−0.120827 | + | 0.992674i | \(0.538555\pi\) | |||||||
\(8\) | −7.51602 | −2.65731 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.8182 | 3.42101 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.39765 | 0.942340 | 0.471170 | − | 0.882042i | \(-0.343832\pi\) | ||||
0.471170 | + | 0.882042i | \(0.343832\pi\) | |||||||
\(14\) | 1.67555 | 0.447810 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.96116 | 2.49029 | ||||||||
\(17\) | −2.27541 | −0.551868 | −0.275934 | − | 0.961177i | \(-0.588987\pi\) | ||||
−0.275934 | + | 0.961177i | \(0.588987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.83711 | −0.880294 | −0.440147 | − | 0.897926i | \(-0.645074\pi\) | ||||
−0.440147 | + | 0.897926i | \(0.645074\pi\) | |||||||
\(20\) | −20.0950 | −4.49337 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.62068 | 0.558731 | ||||||||
\(23\) | −0.231954 | −0.0483657 | −0.0241829 | − | 0.999708i | \(-0.507698\pi\) | ||||
−0.0241829 | + | 0.999708i | \(0.507698\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.0404 | 2.40808 | ||||||||
\(26\) | −8.90417 | −1.74625 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.11237 | −0.588183 | ||||||||
\(29\) | 5.21505 | 0.968410 | 0.484205 | − | 0.874955i | \(-0.339109\pi\) | ||||
0.484205 | + | 0.874955i | \(0.339109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.79146 | −1.21978 | −0.609891 | − | 0.792485i | \(-0.708787\pi\) | ||||
−0.609891 | + | 0.792485i | \(0.708787\pi\) | |||||||
\(32\) | −11.0730 | −1.95744 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.96313 | 1.02267 | ||||||||
\(35\) | 2.63927 | 0.446118 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.00835933 | 0.00137427 | 0.000687133 | − | 1.00000i | \(-0.499781\pi\) | ||||
0.000687133 | 1.00000i | \(0.499781\pi\) | ||||||||
\(38\) | 10.0558 | 1.63127 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 31.0262 | 4.90567 | ||||||||
\(41\) | 1.25345 | 0.195756 | 0.0978778 | − | 0.995198i | \(-0.468795\pi\) | ||||
0.0978778 | + | 0.995198i | \(0.468795\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.91520 | −0.902059 | −0.451029 | − | 0.892509i | \(-0.648943\pi\) | ||||
−0.451029 | + | 0.892509i | \(0.648943\pi\) | |||||||
\(44\) | −4.86797 | −0.733873 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.607877 | 0.0896266 | ||||||||
\(47\) | 2.04677 | 0.298552 | 0.149276 | − | 0.988796i | \(-0.452306\pi\) | ||||
0.149276 | + | 0.988796i | \(0.452306\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.59122 | −0.941603 | ||||||||
\(50\) | −31.5541 | −4.46242 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 16.5397 | 2.29364 | ||||||||
\(53\) | 5.78491 | 0.794618 | 0.397309 | − | 0.917685i | \(-0.369944\pi\) | ||||
0.397309 | + | 0.917685i | \(0.369944\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.12800 | 0.556620 | ||||||||
\(56\) | 4.80543 | 0.642152 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13.6670 | −1.79456 | ||||||||
\(59\) | 6.98726 | 0.909664 | 0.454832 | − | 0.890577i | \(-0.349699\pi\) | ||||
0.454832 | + | 0.890577i | \(0.349699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | ||||||||
\(62\) | 17.7983 | 2.26038 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.09640 | 1.13705 | ||||||||
\(65\) | −14.0255 | −1.73965 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.12479 | −0.503923 | −0.251962 | − | 0.967737i | \(-0.581076\pi\) | ||||
−0.251962 | + | 0.967737i | \(0.581076\pi\) | |||||||
\(68\) | −11.0766 | −1.34324 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.91669 | −0.826702 | ||||||||
\(71\) | −2.69731 | −0.320111 | −0.160056 | − | 0.987108i | \(-0.551167\pi\) | ||||
−0.160056 | + | 0.987108i | \(0.551167\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.26305 | 0.733035 | 0.366517 | − | 0.930411i | \(-0.380550\pi\) | ||||
0.366517 | + | 0.930411i | \(0.380550\pi\) | |||||||
\(74\) | −0.0219071 | −0.00254665 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.6789 | −2.14262 | ||||||||
\(77\) | 0.639358 | 0.0728616 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.96236 | 0.445800 | 0.222900 | − | 0.974841i | \(-0.428448\pi\) | ||||
0.222900 | + | 0.974841i | \(0.428448\pi\) | |||||||
\(80\) | −41.1197 | −4.59732 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.28489 | −0.362755 | ||||||||
\(83\) | −2.54007 | −0.278809 | −0.139404 | − | 0.990236i | \(-0.544519\pi\) | ||||
−0.139404 | + | 0.990236i | \(0.544519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.39291 | 1.01880 | ||||||||
\(86\) | 15.5018 | 1.67161 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.51602 | 0.801211 | ||||||||
\(89\) | 13.7324 | 1.45564 | 0.727818 | − | 0.685770i | \(-0.240534\pi\) | ||||
0.727818 | + | 0.685770i | \(0.240534\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.17232 | −0.227721 | ||||||||
\(92\) | −1.12914 | −0.117721 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.36393 | −0.553248 | ||||||||
\(95\) | 15.8396 | 1.62511 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.19208 | −0.527175 | −0.263588 | − | 0.964635i | \(-0.584906\pi\) | ||||
−0.263588 | + | 0.964635i | \(0.584906\pi\) | |||||||
\(98\) | 17.2735 | 1.74489 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 58.6123 | 5.86123 | ||||||||
\(101\) | −12.9663 | −1.29019 | −0.645097 | − | 0.764101i | \(-0.723183\pi\) | ||||
−0.645097 | + | 0.764101i | \(0.723183\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.0846 | 1.78193 | 0.890964 | − | 0.454075i | \(-0.150030\pi\) | ||||
0.890964 | + | 0.454075i | \(0.150030\pi\) | |||||||
\(104\) | −25.5368 | −2.50409 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.1604 | −1.47251 | ||||||||
\(107\) | 15.0119 | 1.45126 | 0.725628 | − | 0.688088i | \(-0.241550\pi\) | ||||
0.725628 | + | 0.688088i | \(0.241550\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.845703 | −0.0810037 | −0.0405018 | − | 0.999179i | \(-0.512896\pi\) | ||||
−0.0405018 | + | 0.999179i | \(0.512896\pi\) | |||||||
\(110\) | −10.8182 | −1.03147 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.36875 | −0.601790 | ||||||||
\(113\) | −5.27747 | −0.496462 | −0.248231 | − | 0.968701i | \(-0.579849\pi\) | ||||
−0.248231 | + | 0.968701i | \(0.579849\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.957506 | 0.0892879 | ||||||||
\(116\) | 25.3867 | 2.35709 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −18.3114 | −1.68570 | ||||||||
\(119\) | 1.45480 | 0.133362 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.62068 | 0.237265 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −33.0606 | −2.96893 | ||||||||
\(125\) | −29.0629 | −2.59946 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.53585 | 0.225021 | 0.112510 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112510 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(128\) | −1.69281 | −0.149625 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 36.7564 | 3.22375 | ||||||||
\(131\) | 20.6328 | 1.80270 | 0.901350 | − | 0.433092i | \(-0.142578\pi\) | ||||
0.901350 | + | 0.433092i | \(0.142578\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.45329 | 0.212727 | ||||||||
\(134\) | 10.8098 | 0.933821 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.1020 | 1.46649 | ||||||||
\(137\) | 2.22550 | 0.190137 | 0.0950686 | − | 0.995471i | \(-0.469693\pi\) | ||||
0.0950686 | + | 0.995471i | \(0.469693\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.85310 | 0.241996 | 0.120998 | − | 0.992653i | \(-0.461390\pi\) | ||||
0.120998 | + | 0.992653i | \(0.461390\pi\) | |||||||
\(140\) | 12.8479 | 1.08584 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.06878 | 0.593199 | ||||||||
\(143\) | −3.39765 | −0.284126 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.5277 | −1.78778 | ||||||||
\(146\) | −16.4135 | −1.35839 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0406929 | 0.00334494 | ||||||||
\(149\) | 4.97733 | 0.407759 | 0.203879 | − | 0.978996i | \(-0.434645\pi\) | ||||
0.203879 | + | 0.978996i | \(0.434645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.9900 | 1.95228 | 0.976138 | − | 0.217149i | \(-0.0696759\pi\) | ||||
0.976138 | + | 0.217149i | \(0.0696759\pi\) | |||||||
\(152\) | 28.8398 | 2.33922 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.67555 | −0.135020 | ||||||||
\(155\) | 28.0352 | 2.25184 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6861 | 1.73074 | 0.865371 | − | 0.501131i | \(-0.167083\pi\) | ||||
0.865371 | + | 0.501131i | \(0.167083\pi\) | |||||||
\(158\) | −10.3841 | −0.826112 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 45.7093 | 3.61363 | ||||||||
\(161\) | 0.148302 | 0.0116878 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.46311 | 0.114599 | 0.0572996 | − | 0.998357i | \(-0.481751\pi\) | ||||
0.0572996 | + | 0.998357i | \(0.481751\pi\) | |||||||
\(164\) | 6.10174 | 0.476466 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.65670 | 0.516660 | ||||||||
\(167\) | −1.34205 | −0.103851 | −0.0519253 | − | 0.998651i | \(-0.516536\pi\) | ||||
−0.0519253 | + | 0.998651i | \(0.516536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.45594 | −0.111996 | ||||||||
\(170\) | −24.6158 | −1.88795 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −28.7950 | −2.19560 | ||||||||
\(173\) | −20.7606 | −1.57840 | −0.789199 | − | 0.614137i | \(-0.789504\pi\) | ||||
−0.789199 | + | 0.614137i | \(0.789504\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.69813 | −0.581924 | ||||||||
\(176\) | −9.96116 | −0.750851 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −35.9884 | −2.69744 | ||||||||
\(179\) | −1.18299 | −0.0884206 | −0.0442103 | − | 0.999022i | \(-0.514077\pi\) | ||||
−0.0442103 | + | 0.999022i | \(0.514077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.98508 | −0.667856 | −0.333928 | − | 0.942599i | \(-0.608374\pi\) | ||||
−0.333928 | + | 0.942599i | \(0.608374\pi\) | |||||||
\(182\) | 5.69295 | 0.421990 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.74337 | 0.128523 | ||||||||
\(185\) | −0.0345073 | −0.00253703 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.27541 | 0.166395 | ||||||||
\(188\) | 9.96361 | 0.726671 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −41.5106 | −3.01149 | ||||||||
\(191\) | −25.1907 | −1.82274 | −0.911369 | − | 0.411591i | \(-0.864973\pi\) | ||||
−0.911369 | + | 0.411591i | \(0.864973\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.01947 | 0.433291 | 0.216645 | − | 0.976250i | \(-0.430488\pi\) | ||||
0.216645 | + | 0.976250i | \(0.430488\pi\) | |||||||
\(194\) | 13.6068 | 0.976909 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −32.0858 | −2.29185 | ||||||||
\(197\) | −22.1592 | −1.57878 | −0.789389 | − | 0.613894i | \(-0.789602\pi\) | ||||
−0.789389 | + | 0.613894i | \(0.789602\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.21905 | 0.299081 | 0.149540 | − | 0.988756i | \(-0.452221\pi\) | ||||
0.149540 | + | 0.988756i | \(0.452221\pi\) | |||||||
\(200\) | −90.4960 | −6.39903 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 33.9805 | 2.39086 | ||||||||
\(203\) | −3.33428 | −0.234021 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.17424 | −0.361384 | ||||||||
\(206\) | −47.3939 | −3.30209 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 33.8446 | 2.34670 | ||||||||
\(209\) | 3.83711 | 0.265419 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.98072 | −0.342887 | −0.171443 | − | 0.985194i | \(-0.554843\pi\) | ||||
−0.171443 | + | 0.985194i | \(0.554843\pi\) | |||||||
\(212\) | 28.1607 | 1.93409 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −39.3414 | −2.68932 | ||||||||
\(215\) | 24.4179 | 1.66529 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.34218 | 0.294766 | ||||||||
\(218\) | 2.21632 | 0.150108 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.0950 | 1.35480 | ||||||||
\(221\) | −7.73106 | −0.520048 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.93611 | −0.263581 | −0.131791 | − | 0.991278i | \(-0.542073\pi\) | ||||
−0.131791 | + | 0.991278i | \(0.542073\pi\) | |||||||
\(224\) | 7.07959 | 0.473025 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.8306 | 0.919995 | ||||||||
\(227\) | 19.4854 | 1.29329 | 0.646647 | − | 0.762789i | \(-0.276171\pi\) | ||||
0.646647 | + | 0.762789i | \(0.276171\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.52720 | −0.629575 | −0.314787 | − | 0.949162i | \(-0.601933\pi\) | ||||
−0.314787 | + | 0.949162i | \(0.601933\pi\) | |||||||
\(230\) | −2.50932 | −0.165460 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −39.1964 | −2.57337 | ||||||||
\(233\) | −25.2717 | −1.65561 | −0.827803 | − | 0.561019i | \(-0.810409\pi\) | ||||
−0.827803 | + | 0.561019i | \(0.810409\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.44908 | −0.551157 | ||||||||
\(236\) | 34.0137 | 2.21411 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.81257 | −0.247132 | ||||||||
\(239\) | 1.36331 | 0.0881853 | 0.0440927 | − | 0.999027i | \(-0.485960\pi\) | ||||
0.0440927 | + | 0.999027i | \(0.485960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.47697 | 0.481634 | 0.240817 | − | 0.970571i | \(-0.422585\pi\) | ||||
0.240817 | + | 0.970571i | \(0.422585\pi\) | |||||||
\(242\) | −2.62068 | −0.168464 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.86797 | −0.311640 | ||||||||
\(245\) | 27.2086 | 1.73829 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.0372 | −0.829536 | ||||||||
\(248\) | 51.0448 | 3.24135 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 76.1644 | 4.81706 | ||||||||
\(251\) | −3.90296 | −0.246353 | −0.123176 | − | 0.992385i | \(-0.539308\pi\) | ||||
−0.123176 | + | 0.992385i | \(0.539308\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.231954 | 0.0145828 | ||||||||
\(254\) | −6.64566 | −0.416986 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.7565 | −0.859780 | ||||||||
\(257\) | −8.69767 | −0.542546 | −0.271273 | − | 0.962502i | \(-0.587445\pi\) | ||||
−0.271273 | + | 0.962502i | \(0.587445\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.00534460 | −0.000332098 0 | ||||||||
\(260\) | −68.2758 | −4.23429 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −54.0721 | −3.34058 | ||||||||
\(263\) | 24.6129 | 1.51770 | 0.758849 | − | 0.651266i | \(-0.225762\pi\) | ||||
0.758849 | + | 0.651266i | \(0.225762\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.8801 | −1.46694 | ||||||||
\(266\) | −6.42929 | −0.394205 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −20.0793 | −1.22654 | ||||||||
\(269\) | 9.87079 | 0.601833 | 0.300916 | − | 0.953651i | \(-0.402707\pi\) | ||||
0.300916 | + | 0.953651i | \(0.402707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.8200 | −1.02174 | −0.510871 | − | 0.859658i | \(-0.670677\pi\) | ||||
−0.510871 | + | 0.859658i | \(0.670677\pi\) | |||||||
\(272\) | −22.6657 | −1.37431 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.83232 | −0.352344 | ||||||||
\(275\) | −12.0404 | −0.726064 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.27328 | −0.256757 | −0.128378 | − | 0.991725i | \(-0.540977\pi\) | ||||
−0.128378 | + | 0.991725i | \(0.540977\pi\) | |||||||
\(278\) | −7.47705 | −0.448444 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.8368 | −1.18548 | ||||||||
\(281\) | −8.03268 | −0.479190 | −0.239595 | − | 0.970873i | \(-0.577015\pi\) | ||||
−0.239595 | + | 0.970873i | \(0.577015\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2077 | 0.904006 | 0.452003 | − | 0.892016i | \(-0.350710\pi\) | ||||
0.452003 | + | 0.892016i | \(0.350710\pi\) | |||||||
\(284\) | −13.1304 | −0.779146 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.90417 | 0.526514 | ||||||||
\(287\) | −0.801402 | −0.0473053 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8225 | −0.695441 | ||||||||
\(290\) | 56.4173 | 3.31294 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 30.4883 | 1.78419 | ||||||||
\(293\) | 20.1569 | 1.17758 | 0.588788 | − | 0.808287i | \(-0.299605\pi\) | ||||
0.588788 | + | 0.808287i | \(0.299605\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.8434 | −1.67933 | ||||||||
\(296\) | −0.0628289 | −0.00365186 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.0440 | −0.755618 | ||||||||
\(299\) | −0.788099 | −0.0455770 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.78193 | 0.217987 | ||||||||
\(302\) | −62.8701 | −3.61777 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −38.2221 | −2.19219 | ||||||||
\(305\) | 4.12800 | 0.236369 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.07947 | 0.404047 | 0.202023 | − | 0.979381i | \(-0.435248\pi\) | ||||
0.202023 | + | 0.979381i | \(0.435248\pi\) | |||||||
\(308\) | 3.11237 | 0.177344 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −73.4712 | −4.17289 | ||||||||
\(311\) | 10.2641 | 0.582026 | 0.291013 | − | 0.956719i | \(-0.406008\pi\) | ||||
0.291013 | + | 0.956719i | \(0.406008\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.0568 | 0.738012 | 0.369006 | − | 0.929427i | \(-0.379698\pi\) | ||||
0.369006 | + | 0.929427i | \(0.379698\pi\) | |||||||
\(314\) | −56.8325 | −3.20724 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.2886 | 1.08507 | ||||||||
\(317\) | 16.3206 | 0.916656 | 0.458328 | − | 0.888783i | \(-0.348449\pi\) | ||||
0.458328 | + | 0.888783i | \(0.348449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.21505 | −0.291987 | ||||||||
\(320\) | −37.5500 | −2.09911 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.388651 | −0.0216587 | ||||||||
\(323\) | 8.73101 | 0.485807 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 40.9092 | 2.26923 | ||||||||
\(326\) | −3.83433 | −0.212364 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.42094 | −0.520184 | ||||||||
\(329\) | −1.30862 | −0.0721466 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.8397 | −0.870631 | −0.435315 | − | 0.900278i | \(-0.643363\pi\) | ||||
−0.435315 | + | 0.900278i | \(0.643363\pi\) | |||||||
\(332\) | −12.3650 | −0.678615 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.51707 | 0.192446 | ||||||||
\(335\) | 17.0272 | 0.930293 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.3236 | 1.81525 | 0.907626 | − | 0.419780i | \(-0.137893\pi\) | ||||
0.907626 | + | 0.419780i | \(0.137893\pi\) | |||||||
\(338\) | 3.81556 | 0.207539 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 45.7243 | 2.47975 | ||||||||
\(341\) | 6.79146 | 0.367778 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.68966 | 0.469197 | ||||||||
\(344\) | 44.4587 | 2.39705 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 54.4069 | 2.92493 | ||||||||
\(347\) | 20.0513 | 1.07641 | 0.538206 | − | 0.842814i | \(-0.319102\pi\) | ||||
0.538206 | + | 0.842814i | \(0.319102\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.1440 | −1.61357 | −0.806786 | − | 0.590844i | \(-0.798795\pi\) | ||||
−0.806786 | + | 0.590844i | \(0.798795\pi\) | |||||||
\(350\) | 20.1744 | 1.07836 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 11.0730 | 0.590191 | ||||||||
\(353\) | 6.43535 | 0.342519 | 0.171259 | − | 0.985226i | \(-0.445216\pi\) | ||||
0.171259 | + | 0.985226i | \(0.445216\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.1345 | 0.590958 | ||||||||
\(356\) | 66.8491 | 3.54299 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.10023 | 0.163852 | ||||||||
\(359\) | −19.5047 | −1.02942 | −0.514708 | − | 0.857365i | \(-0.672100\pi\) | ||||
−0.514708 | + | 0.857365i | \(0.672100\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.27656 | −0.225082 | ||||||||
\(362\) | 23.5470 | 1.23760 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.5748 | −0.554268 | ||||||||
\(365\) | −25.8539 | −1.35325 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.5866 | −1.44001 | −0.720004 | − | 0.693969i | \(-0.755860\pi\) | ||||
−0.720004 | + | 0.693969i | \(0.755860\pi\) | |||||||
\(368\) | −2.31053 | −0.120445 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.0904327 | 0.00470137 | ||||||||
\(371\) | −3.69863 | −0.192023 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.80244 | −0.248661 | −0.124331 | − | 0.992241i | \(-0.539678\pi\) | ||||
−0.124331 | + | 0.992241i | \(0.539678\pi\) | |||||||
\(374\) | −5.96313 | −0.308346 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.3836 | −0.793348 | ||||||||
\(377\) | 17.7189 | 0.912571 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.3813 | −1.25239 | −0.626193 | − | 0.779668i | \(-0.715388\pi\) | ||||
−0.626193 | + | 0.779668i | \(0.715388\pi\) | |||||||
\(380\) | 77.1067 | 3.95549 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 66.0169 | 3.37772 | ||||||||
\(383\) | −36.5592 | −1.86809 | −0.934044 | − | 0.357159i | \(-0.883745\pi\) | ||||
−0.934044 | + | 0.357159i | \(0.883745\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.63927 | −0.134510 | ||||||||
\(386\) | −15.7751 | −0.802932 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.2748 | −1.28314 | ||||||||
\(389\) | −18.4912 | −0.937539 | −0.468770 | − | 0.883320i | \(-0.655303\pi\) | ||||
−0.468770 | + | 0.883320i | \(0.655303\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.527791 | 0.0266915 | ||||||||
\(392\) | 49.5398 | 2.50214 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 58.0722 | 2.92563 | ||||||||
\(395\) | −16.3566 | −0.822991 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.3234 | 1.77283 | 0.886414 | − | 0.462893i | \(-0.153189\pi\) | ||||
0.886414 | + | 0.462893i | \(0.153189\pi\) | |||||||
\(398\) | −11.0568 | −0.554226 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 119.936 | 5.99682 | ||||||||
\(401\) | −30.7487 | −1.53552 | −0.767759 | − | 0.640739i | \(-0.778628\pi\) | ||||
−0.767759 | + | 0.640739i | \(0.778628\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.0750 | −1.14945 | ||||||||
\(404\) | −63.1194 | −3.14031 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.73809 | 0.433664 | ||||||||
\(407\) | −0.00835933 | −0.000414357 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.4879 | 1.30974 | 0.654872 | − | 0.755740i | \(-0.272723\pi\) | ||||
0.654872 | + | 0.755740i | \(0.272723\pi\) | |||||||
\(410\) | 13.5600 | 0.669682 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 88.0351 | 4.33718 | ||||||||
\(413\) | −4.46736 | −0.219824 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.4854 | 0.514708 | ||||||||
\(416\) | −37.6221 | −1.84458 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.0558 | −0.491848 | ||||||||
\(419\) | 32.9507 | 1.60975 | 0.804875 | − | 0.593445i | \(-0.202232\pi\) | ||||
0.804875 | + | 0.593445i | \(0.202232\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.537173 | 0.0261802 | 0.0130901 | − | 0.999914i | \(-0.495833\pi\) | ||||
0.0130901 | + | 0.999914i | \(0.495833\pi\) | |||||||
\(422\) | 13.0529 | 0.635404 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −43.4795 | −2.11155 | ||||||||
\(425\) | −27.3969 | −1.32894 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.639358 | 0.0309407 | ||||||||
\(428\) | 73.0774 | 3.53233 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −63.9916 | −3.08595 | ||||||||
\(431\) | −24.2267 | −1.16696 | −0.583480 | − | 0.812127i | \(-0.698309\pi\) | ||||
−0.583480 | + | 0.812127i | \(0.698309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.0674 | 0.772151 | 0.386076 | − | 0.922467i | \(-0.373830\pi\) | ||||
0.386076 | + | 0.922467i | \(0.373830\pi\) | |||||||
\(434\) | −11.3795 | −0.546231 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.11685 | −0.197162 | ||||||||
\(437\) | 0.890034 | 0.0425761 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.3777 | 1.25894 | 0.629468 | − | 0.777026i | \(-0.283273\pi\) | ||||
0.629468 | + | 0.777026i | \(0.283273\pi\) | |||||||
\(440\) | −31.0262 | −1.47911 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.2606 | 0.963700 | ||||||||
\(443\) | 27.7002 | 1.31608 | 0.658039 | − | 0.752984i | \(-0.271386\pi\) | ||||
0.658039 | + | 0.752984i | \(0.271386\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −56.6876 | −2.68725 | ||||||||
\(446\) | 10.3153 | 0.488443 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.81586 | −0.274773 | ||||||||
\(449\) | −28.8938 | −1.36358 | −0.681792 | − | 0.731546i | \(-0.738799\pi\) | ||||
−0.681792 | + | 0.731546i | \(0.738799\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.25345 | −0.0590225 | ||||||||
\(452\) | −25.6905 | −1.20838 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −51.0651 | −2.39660 | ||||||||
\(455\) | 8.96734 | 0.420395 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.17075 | −0.241877 | −0.120939 | − | 0.992660i | \(-0.538590\pi\) | ||||
−0.120939 | + | 0.992660i | \(0.538590\pi\) | |||||||
\(458\) | 24.9677 | 1.16667 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.66111 | 0.217325 | ||||||||
\(461\) | −0.443270 | −0.0206451 | −0.0103226 | − | 0.999947i | \(-0.503286\pi\) | ||||
−0.0103226 | + | 0.999947i | \(0.503286\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.752394 | −0.0349667 | −0.0174834 | − | 0.999847i | \(-0.505565\pi\) | ||||
−0.0174834 | + | 0.999847i | \(0.505565\pi\) | |||||||
\(464\) | 51.9479 | 2.41162 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 66.2291 | 3.06800 | ||||||||
\(467\) | −18.1513 | −0.839942 | −0.419971 | − | 0.907538i | \(-0.637960\pi\) | ||||
−0.419971 | + | 0.907538i | \(0.637960\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.63722 | 0.121775 | ||||||||
\(470\) | 22.1423 | 1.02135 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −52.5164 | −2.41726 | ||||||||
\(473\) | 5.91520 | 0.271981 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −46.2004 | −2.11982 | ||||||||
\(476\) | 7.08193 | 0.324600 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.57281 | −0.163416 | ||||||||
\(479\) | −27.0401 | −1.23549 | −0.617747 | − | 0.786377i | \(-0.711954\pi\) | ||||
−0.617747 | + | 0.786377i | \(0.711954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0284021 | 0.00129502 | ||||||||
\(482\) | −19.5948 | −0.892516 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.86797 | 0.221271 | ||||||||
\(485\) | 21.4329 | 0.973218 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.5533 | 0.568843 | 0.284421 | − | 0.958699i | \(-0.408199\pi\) | ||||
0.284421 | + | 0.958699i | \(0.408199\pi\) | |||||||
\(488\) | 7.51602 | 0.340234 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −71.3050 | −3.22123 | ||||||||
\(491\) | 17.7127 | 0.799361 | 0.399681 | − | 0.916654i | \(-0.369121\pi\) | ||||
0.399681 | + | 0.916654i | \(0.369121\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.8664 | −0.534435 | ||||||||
\(494\) | 34.1663 | 1.53721 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −67.6508 | −3.03761 | ||||||||
\(497\) | 1.72455 | 0.0773564 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.9820 | −1.25265 | −0.626323 | − | 0.779563i | \(-0.715441\pi\) | ||||
−0.626323 | + | 0.779563i | \(0.715441\pi\) | |||||||
\(500\) | −141.477 | −6.32704 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.2284 | 0.456517 | ||||||||
\(503\) | −8.96909 | −0.399912 | −0.199956 | − | 0.979805i | \(-0.564080\pi\) | ||||
−0.199956 | + | 0.979805i | \(0.564080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 53.5249 | 2.38182 | ||||||||
\(506\) | −0.607877 | −0.0270234 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.3444 | 0.547696 | ||||||||
\(509\) | 6.64241 | 0.294420 | 0.147210 | − | 0.989105i | \(-0.452971\pi\) | ||||
0.147210 | + | 0.989105i | \(0.452971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.00433 | −0.177141 | ||||||||
\(512\) | 39.4369 | 1.74288 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.7938 | 1.00539 | ||||||||
\(515\) | −74.6532 | −3.28961 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.04677 | −0.0900169 | ||||||||
\(518\) | 0.0140065 | 0.000615410 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 105.416 | 4.62281 | ||||||||
\(521\) | −0.260058 | −0.0113933 | −0.00569667 | − | 0.999984i | \(-0.501813\pi\) | ||||
−0.00569667 | + | 0.999984i | \(0.501813\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.7386 | 0.906838 | 0.453419 | − | 0.891298i | \(-0.350204\pi\) | ||||
0.453419 | + | 0.891298i | \(0.350204\pi\) | |||||||
\(524\) | 100.440 | 4.38774 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −64.5026 | −2.81245 | ||||||||
\(527\) | 15.4534 | 0.673159 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9462 | −0.997661 | ||||||||
\(530\) | 62.5822 | 2.71840 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.9425 | 0.517774 | ||||||||
\(533\) | 4.25878 | 0.184468 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −61.9692 | −2.67916 | ||||||||
\(536\) | 31.0020 | 1.33908 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −25.8682 | −1.11526 | ||||||||
\(539\) | 6.59122 | 0.283904 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.3924 | −0.876738 | −0.438369 | − | 0.898795i | \(-0.644444\pi\) | ||||
−0.438369 | + | 0.898795i | \(0.644444\pi\) | |||||||
\(542\) | 44.0798 | 1.89339 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 25.1956 | 1.08025 | ||||||||
\(545\) | 3.49107 | 0.149541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7406 | 0.673019 | 0.336509 | − | 0.941680i | \(-0.390754\pi\) | ||||
0.336509 | + | 0.941680i | \(0.390754\pi\) | |||||||
\(548\) | 10.8337 | 0.462791 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 31.5541 | 1.34547 | ||||||||
\(551\) | −20.0107 | −0.852486 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.53337 | −0.107730 | ||||||||
\(554\) | 11.1989 | 0.475796 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.8888 | 0.589015 | ||||||||
\(557\) | −31.8995 | −1.35162 | −0.675812 | − | 0.737074i | \(-0.736207\pi\) | ||||
−0.675812 | + | 0.737074i | \(0.736207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.0978 | −0.850046 | ||||||||
\(560\) | 26.2902 | 1.11096 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.0511 | 0.887987 | ||||||||
\(563\) | 22.4287 | 0.945258 | 0.472629 | − | 0.881261i | \(-0.343305\pi\) | ||||
0.472629 | + | 0.881261i | \(0.343305\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.7854 | 0.916519 | ||||||||
\(566\) | −39.8546 | −1.67522 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.2730 | 0.850637 | ||||||||
\(569\) | −1.24170 | −0.0520547 | −0.0260274 | − | 0.999661i | \(-0.508286\pi\) | ||||
−0.0260274 | + | 0.999661i | \(0.508286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.51920 | −0.0635766 | −0.0317883 | − | 0.999495i | \(-0.510120\pi\) | ||||
−0.0317883 | + | 0.999495i | \(0.510120\pi\) | |||||||
\(572\) | −16.5397 | −0.691558 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.10022 | 0.0876614 | ||||||||
\(575\) | −2.79282 | −0.116469 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.7053 | −1.19502 | −0.597509 | − | 0.801862i | \(-0.703843\pi\) | ||||
−0.597509 | + | 0.801862i | \(0.703843\pi\) | |||||||
\(578\) | 30.9830 | 1.28872 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −104.796 | −4.35143 | ||||||||
\(581\) | 1.62401 | 0.0673754 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.78491 | −0.239586 | ||||||||
\(584\) | −47.0732 | −1.94790 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −52.8247 | −2.18217 | ||||||||
\(587\) | −40.9540 | −1.69035 | −0.845176 | − | 0.534488i | \(-0.820504\pi\) | ||||
−0.845176 | + | 0.534488i | \(0.820504\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.0596 | 1.07377 | ||||||||
\(590\) | 75.5894 | 3.11197 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.0832686 | 0.00342232 | ||||||||
\(593\) | −47.1502 | −1.93623 | −0.968113 | − | 0.250515i | \(-0.919400\pi\) | ||||
−0.968113 | + | 0.250515i | \(0.919400\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00543 | −0.246199 | ||||||||
\(596\) | 24.2295 | 0.992478 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.06536 | 0.0844587 | ||||||||
\(599\) | 17.6382 | 0.720676 | 0.360338 | − | 0.932822i | \(-0.382661\pi\) | ||||
0.360338 | + | 0.932822i | \(0.382661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2149 | −0.906163 | −0.453082 | − | 0.891469i | \(-0.649675\pi\) | ||||
−0.453082 | + | 0.891469i | \(0.649675\pi\) | |||||||
\(602\) | −9.91122 | −0.403951 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 116.782 | 4.75181 | ||||||||
\(605\) | −4.12800 | −0.167827 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.1450 | 1.22355 | 0.611775 | − | 0.791032i | \(-0.290456\pi\) | ||||
0.611775 | + | 0.791032i | \(0.290456\pi\) | |||||||
\(608\) | 42.4883 | 1.72313 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.8182 | −0.438015 | ||||||||
\(611\) | 6.95422 | 0.281338 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.8524 | −0.842219 | −0.421110 | − | 0.907010i | \(-0.638359\pi\) | ||||
−0.421110 | + | 0.907010i | \(0.638359\pi\) | |||||||
\(614\) | −18.5530 | −0.748739 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.80543 | −0.193616 | ||||||||
\(617\) | −15.5474 | −0.625913 | −0.312956 | − | 0.949768i | \(-0.601319\pi\) | ||||
−0.312956 | + | 0.949768i | \(0.601319\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.1684 | 1.29296 | 0.646479 | − | 0.762932i | \(-0.276241\pi\) | ||||
0.646479 | + | 0.762932i | \(0.276241\pi\) | |||||||
\(620\) | 136.474 | 5.48094 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.8990 | −1.07855 | ||||||||
\(623\) | −8.77995 | −0.351761 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 59.7695 | 2.39078 | ||||||||
\(626\) | −34.2176 | −1.36761 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 105.567 | 4.21260 | ||||||||
\(629\) | −0.0190209 | −0.000758413 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.52156 | −0.379047 | −0.189524 | − | 0.981876i | \(-0.560694\pi\) | ||||
−0.189524 | + | 0.981876i | \(0.560694\pi\) | |||||||
\(632\) | −29.7812 | −1.18463 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −42.7710 | −1.69866 | ||||||||
\(635\) | −10.4680 | −0.415410 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.3947 | −0.887310 | ||||||||
\(638\) | 13.6670 | 0.541080 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.98794 | 0.276223 | ||||||||
\(641\) | −32.6251 | −1.28861 | −0.644306 | − | 0.764767i | \(-0.722854\pi\) | ||||
−0.644306 | + | 0.764767i | \(0.722854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −48.8116 | −1.92494 | −0.962472 | − | 0.271382i | \(-0.912519\pi\) | ||||
−0.962472 | + | 0.271382i | \(0.912519\pi\) | |||||||
\(644\) | 0.721927 | 0.0284479 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −22.8812 | −0.900249 | ||||||||
\(647\) | 3.82743 | 0.150472 | 0.0752359 | − | 0.997166i | \(-0.476029\pi\) | ||||
0.0752359 | + | 0.997166i | \(0.476029\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.98726 | −0.274274 | ||||||||
\(650\) | −107.210 | −4.20512 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.12235 | 0.278933 | ||||||||
\(653\) | 11.7107 | 0.458275 | 0.229138 | − | 0.973394i | \(-0.426409\pi\) | ||||
0.229138 | + | 0.973394i | \(0.426409\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −85.1724 | −3.32796 | ||||||||
\(656\) | 12.4858 | 0.487488 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.42947 | 0.133695 | ||||||||
\(659\) | −48.5716 | −1.89208 | −0.946040 | − | 0.324050i | \(-0.894956\pi\) | ||||
−0.946040 | + | 0.324050i | \(0.894956\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.4239 | −1.45562 | −0.727811 | − | 0.685778i | \(-0.759462\pi\) | ||||
−0.727811 | + | 0.685778i | \(0.759462\pi\) | |||||||
\(662\) | 41.5109 | 1.61337 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.0912 | 0.740882 | ||||||||
\(665\) | −10.1272 | −0.392716 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.20965 | −0.0468378 | ||||||||
\(668\) | −6.53303 | −0.252771 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −44.6227 | −1.72393 | ||||||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.73519 | 0.375264 | 0.187632 | − | 0.982239i | \(-0.439919\pi\) | ||||
0.187632 | + | 0.982239i | \(0.439919\pi\) | |||||||
\(674\) | −87.3305 | −3.36384 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.08748 | −0.272596 | ||||||||
\(677\) | −1.47674 | −0.0567556 | −0.0283778 | − | 0.999597i | \(-0.509034\pi\) | ||||
−0.0283778 | + | 0.999597i | \(0.509034\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.31960 | 0.127394 | ||||||||
\(680\) | −70.5973 | −2.70728 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −17.7983 | −0.681530 | ||||||||
\(683\) | −31.8263 | −1.21780 | −0.608900 | − | 0.793247i | \(-0.708389\pi\) | ||||
−0.608900 | + | 0.793247i | \(0.708389\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.18687 | −0.351012 | ||||||||
\(686\) | −22.7728 | −0.869470 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −58.9222 | −2.24639 | ||||||||
\(689\) | 19.6551 | 0.748800 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.9701 | −1.59662 | −0.798308 | − | 0.602249i | \(-0.794271\pi\) | ||||
−0.798308 | + | 0.602249i | \(0.794271\pi\) | |||||||
\(692\) | −101.062 | −3.84179 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −52.5481 | −1.99470 | ||||||||
\(695\) | −11.7776 | −0.446750 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.85211 | −0.108031 | ||||||||
\(698\) | 78.9978 | 2.99011 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −37.4743 | −1.41639 | ||||||||
\(701\) | −11.3844 | −0.429984 | −0.214992 | − | 0.976616i | \(-0.568973\pi\) | ||||
−0.214992 | + | 0.976616i | \(0.568973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0320757 | −0.00120976 | ||||||||
\(704\) | −9.09640 | −0.342833 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.8650 | −0.634722 | ||||||||
\(707\) | 8.29010 | 0.311781 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.6077 | −1.33727 | −0.668637 | − | 0.743589i | \(-0.733122\pi\) | ||||
−0.668637 | + | 0.743589i | \(0.733122\pi\) | |||||||
\(710\) | −29.1800 | −1.09510 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −103.213 | −3.86808 | ||||||||
\(713\) | 1.57531 | 0.0589957 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.0255 | 0.524525 | ||||||||
\(716\) | −5.75874 | −0.215214 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 51.1155 | 1.90761 | ||||||||
\(719\) | 21.7668 | 0.811764 | 0.405882 | − | 0.913925i | \(-0.366964\pi\) | ||||
0.405882 | + | 0.913925i | \(0.366964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5625 | −0.430611 | ||||||||
\(722\) | 11.2075 | 0.417099 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −43.7391 | −1.62555 | ||||||||
\(725\) | 62.7913 | 2.33201 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.0400 | −0.891594 | −0.445797 | − | 0.895134i | \(-0.647080\pi\) | ||||
−0.445797 | + | 0.895134i | \(0.647080\pi\) | |||||||
\(728\) | 16.3272 | 0.605126 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 67.7548 | 2.50772 | ||||||||
\(731\) | 13.4595 | 0.497818 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.5940 | 0.908398 | 0.454199 | − | 0.890900i | \(-0.349925\pi\) | ||||
0.454199 | + | 0.890900i | \(0.349925\pi\) | |||||||
\(734\) | 72.2957 | 2.66848 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.56842 | 0.0946732 | ||||||||
\(737\) | 4.12479 | 0.151939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.40759 | 0.346064 | 0.173032 | − | 0.984916i | \(-0.444644\pi\) | ||||
0.173032 | + | 0.984916i | \(0.444644\pi\) | |||||||
\(740\) | −0.167981 | −0.00617509 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.69292 | 0.355838 | ||||||||
\(743\) | 25.2236 | 0.925364 | 0.462682 | − | 0.886524i | \(-0.346887\pi\) | ||||
0.462682 | + | 0.886524i | \(0.346887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.5464 | −0.752763 | ||||||||
\(746\) | 12.5857 | 0.460794 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.0766 | 0.405002 | ||||||||
\(749\) | −9.59798 | −0.350703 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.5585 | −1.40702 | −0.703509 | − | 0.710686i | \(-0.748385\pi\) | ||||
−0.703509 | + | 0.710686i | \(0.748385\pi\) | |||||||
\(752\) | 20.3882 | 0.743482 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −46.4356 | −1.69109 | ||||||||
\(755\) | −99.0307 | −3.60410 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −45.4064 | −1.65032 | −0.825162 | − | 0.564896i | \(-0.808916\pi\) | ||||
−0.825162 | + | 0.564896i | \(0.808916\pi\) | |||||||
\(758\) | 63.8957 | 2.32080 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −119.051 | −4.31843 | ||||||||
\(761\) | 2.88067 | 0.104424 | 0.0522121 | − | 0.998636i | \(-0.483373\pi\) | ||||
0.0522121 | + | 0.998636i | \(0.483373\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.540707 | 0.0195749 | ||||||||
\(764\) | −122.628 | −4.43651 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 95.8099 | 3.46175 | ||||||||
\(767\) | 23.7403 | 0.857212 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.4764 | −1.82023 | −0.910113 | − | 0.414361i | \(-0.864005\pi\) | ||||
−0.910113 | + | 0.414361i | \(0.864005\pi\) | |||||||
\(770\) | 6.91669 | 0.249260 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 29.3026 | 1.05462 | ||||||||
\(773\) | −46.6675 | −1.67851 | −0.839257 | − | 0.543735i | \(-0.817010\pi\) | ||||
−0.839257 | + | 0.543735i | \(0.817010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −81.7720 | −2.93734 | ||||||||
\(776\) | 39.0238 | 1.40087 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48.4594 | 1.73735 | ||||||||
\(779\) | −4.80962 | −0.172323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.69731 | 0.0965172 | ||||||||
\(782\) | −1.38317 | −0.0494621 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −65.6562 | −2.34486 | ||||||||
\(785\) | −89.5205 | −3.19512 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.1302 | −0.539332 | −0.269666 | − | 0.962954i | \(-0.586913\pi\) | ||||
−0.269666 | + | 0.962954i | \(0.586913\pi\) | |||||||
\(788\) | −107.870 | −3.84272 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 42.8655 | 1.52509 | ||||||||
\(791\) | 3.37419 | 0.119972 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.39765 | −0.120654 | ||||||||
\(794\) | −92.5712 | −3.28523 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.5382 | 0.727957 | ||||||||
\(797\) | 0.575451 | 0.0203835 | 0.0101918 | − | 0.999948i | \(-0.496756\pi\) | ||||
0.0101918 | + | 0.999948i | \(0.496756\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.65725 | −0.164762 | ||||||||
\(800\) | −133.323 | −4.71368 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 80.5826 | 2.84547 | ||||||||
\(803\) | −6.26305 | −0.221018 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.612189 | −0.0215768 | ||||||||
\(806\) | 60.4723 | 2.13005 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 97.4549 | 3.42845 | ||||||||
\(809\) | 17.2764 | 0.607406 | 0.303703 | − | 0.952767i | \(-0.401777\pi\) | ||||
0.303703 | + | 0.952767i | \(0.401777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.50916 | 0.193453 | 0.0967264 | − | 0.995311i | \(-0.469163\pi\) | ||||
0.0967264 | + | 0.995311i | \(0.469163\pi\) | |||||||
\(812\) | −16.2312 | −0.569602 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.0219071 | 0.000767845 0 | ||||||||
\(815\) | −6.03971 | −0.211562 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.6973 | 0.794077 | ||||||||
\(818\) | −69.4164 | −2.42709 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −25.1880 | −0.879603 | ||||||||
\(821\) | 20.9755 | 0.732049 | 0.366025 | − | 0.930605i | \(-0.380719\pi\) | ||||
0.366025 | + | 0.930605i | \(0.380719\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.3390 | 0.883263 | 0.441631 | − | 0.897197i | \(-0.354400\pi\) | ||||
0.441631 | + | 0.897197i | \(0.354400\pi\) | |||||||
\(824\) | −135.924 | −4.73514 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.7075 | 0.407357 | ||||||||
\(827\) | 44.1075 | 1.53377 | 0.766884 | − | 0.641786i | \(-0.221806\pi\) | ||||
0.766884 | + | 0.641786i | \(0.221806\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.3771 | 0.742456 | 0.371228 | − | 0.928542i | \(-0.378937\pi\) | ||||
0.371228 | + | 0.928542i | \(0.378937\pi\) | |||||||
\(830\) | −27.4789 | −0.953806 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 30.9064 | 1.07149 | ||||||||
\(833\) | 14.9977 | 0.519641 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.53997 | 0.191719 | ||||||||
\(836\) | 18.6789 | 0.646025 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −86.3534 | −2.98303 | ||||||||
\(839\) | −14.8834 | −0.513833 | −0.256917 | − | 0.966434i | \(-0.582707\pi\) | ||||
−0.256917 | + | 0.966434i | \(0.582707\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.80329 | −0.0621826 | ||||||||
\(842\) | −1.40776 | −0.0485146 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −24.2460 | −0.834580 | ||||||||
\(845\) | 6.01014 | 0.206755 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.639358 | −0.0219686 | ||||||||
\(848\) | 57.6244 | 1.97883 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 71.7985 | 2.46267 | ||||||||
\(851\) | −0.00193898 | −6.64673e−5 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.8057 | −1.43140 | −0.715700 | − | 0.698408i | \(-0.753892\pi\) | ||||
−0.715700 | + | 0.698408i | \(0.753892\pi\) | |||||||
\(854\) | −1.67555 | −0.0573362 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −112.830 | −3.85644 | ||||||||
\(857\) | 21.9535 | 0.749918 | 0.374959 | − | 0.927041i | \(-0.377657\pi\) | ||||
0.374959 | + | 0.927041i | \(0.377657\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.9211 | 0.440863 | 0.220432 | − | 0.975402i | \(-0.429253\pi\) | ||||
0.220432 | + | 0.975402i | \(0.429253\pi\) | |||||||
\(860\) | 118.866 | 4.05329 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 63.4905 | 2.16250 | ||||||||
\(863\) | −20.4337 | −0.695573 | −0.347786 | − | 0.937574i | \(-0.613067\pi\) | ||||
−0.347786 | + | 0.937574i | \(0.613067\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 85.6998 | 2.91388 | ||||||||
\(866\) | −42.1076 | −1.43087 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 21.1376 | 0.717456 | ||||||||
\(869\) | −3.96236 | −0.134414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.0146 | −0.474867 | ||||||||
\(872\) | 6.35632 | 0.215252 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.33249 | −0.0788978 | ||||||||
\(875\) | 18.5816 | 0.628172 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 41.8719 | 1.41391 | 0.706957 | − | 0.707257i | \(-0.250068\pi\) | ||||
0.706957 | + | 0.707257i | \(0.250068\pi\) | |||||||
\(878\) | −69.1274 | −2.33294 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 41.1197 | 1.38614 | ||||||||
\(881\) | 4.45061 | 0.149945 | 0.0749724 | − | 0.997186i | \(-0.476113\pi\) | ||||
0.0749724 | + | 0.997186i | \(0.476113\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8793 | 0.668990 | 0.334495 | − | 0.942398i | \(-0.391434\pi\) | ||||
0.334495 | + | 0.942398i | \(0.391434\pi\) | |||||||
\(884\) | −37.6345 | −1.26579 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −72.5935 | −2.43883 | ||||||||
\(887\) | 29.2454 | 0.981966 | 0.490983 | − | 0.871169i | \(-0.336638\pi\) | ||||
0.490983 | + | 0.871169i | \(0.336638\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.62132 | −0.0543773 | ||||||||
\(890\) | 148.560 | 4.97974 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.1608 | −0.641552 | ||||||||
\(893\) | −7.85370 | −0.262814 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.88338 | 0.163233 | ||||||||
\(896\) | 1.08231 | 0.0361576 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 75.7215 | 2.52686 | ||||||||
\(899\) | −35.4178 | −1.18125 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.1630 | −0.438525 | ||||||||
\(902\) | 3.28489 | 0.109375 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 39.6656 | 1.31926 | ||||||||
\(905\) | 37.0904 | 1.23293 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.0733 | −1.03177 | −0.515886 | − | 0.856657i | \(-0.672537\pi\) | ||||
−0.515886 | + | 0.856657i | \(0.672537\pi\) | |||||||
\(908\) | 94.8544 | 3.14786 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −23.5005 | −0.779035 | ||||||||
\(911\) | 42.3077 | 1.40172 | 0.700859 | − | 0.713300i | \(-0.252800\pi\) | ||||
0.700859 | + | 0.713300i | \(0.252800\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.54007 | 0.0840640 | ||||||||
\(914\) | 13.5509 | 0.448223 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.3781 | −1.53237 | ||||||||
\(917\) | −13.1918 | −0.435631 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.8295 | 1.57775 | 0.788874 | − | 0.614555i | \(-0.210664\pi\) | ||||
0.788874 | + | 0.614555i | \(0.210664\pi\) | |||||||
\(920\) | −7.19664 | −0.237266 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.16167 | 0.0382575 | ||||||||
\(923\) | −9.16452 | −0.301654 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.100650 | 0.00330934 | ||||||||
\(926\) | 1.97178 | 0.0647968 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −57.7461 | −1.89561 | ||||||||
\(929\) | 45.8569 | 1.50452 | 0.752258 | − | 0.658869i | \(-0.228965\pi\) | ||||
0.752258 | + | 0.658869i | \(0.228965\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.2913 | 0.828888 | ||||||||
\(932\) | −123.022 | −4.02972 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 47.5687 | 1.55650 | ||||||||
\(935\) | −9.39291 | −0.307181 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.1627 | −1.83475 | −0.917377 | − | 0.398019i | \(-0.869698\pi\) | ||||
−0.917377 | + | 0.398019i | \(0.869698\pi\) | |||||||
\(938\) | −6.91131 | −0.225662 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −41.1298 | −1.34151 | ||||||||
\(941\) | 60.4814 | 1.97164 | 0.985819 | − | 0.167814i | \(-0.0536709\pi\) | ||||
0.985819 | + | 0.167814i | \(0.0536709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.290742 | −0.00946786 | ||||||||
\(944\) | 69.6012 | 2.26533 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.5018 | −0.504008 | ||||||||
\(947\) | −50.3674 | −1.63672 | −0.818360 | − | 0.574706i | \(-0.805116\pi\) | ||||
−0.818360 | + | 0.574706i | \(0.805116\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.2797 | 0.690768 | ||||||||
\(950\) | 121.077 | 3.92824 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.9343 | −0.354384 | ||||||||
\(953\) | −37.2162 | −1.20555 | −0.602775 | − | 0.797911i | \(-0.705938\pi\) | ||||
−0.602775 | + | 0.797911i | \(0.705938\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 103.987 | 3.36495 | ||||||||
\(956\) | 6.63656 | 0.214642 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 70.8635 | 2.28950 | ||||||||
\(959\) | −1.42289 | −0.0459475 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1240 | 0.487869 | ||||||||
\(962\) | −0.0744329 | −0.00239981 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 36.3976 | 1.17229 | ||||||||
\(965\) | −24.8484 | −0.799898 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.27617 | −0.169670 | −0.0848352 | − | 0.996395i | \(-0.527036\pi\) | ||||
−0.0848352 | + | 0.996395i | \(0.527036\pi\) | |||||||
\(968\) | −7.51602 | −0.241574 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −56.1688 | −1.80347 | ||||||||
\(971\) | 29.9077 | 0.959785 | 0.479892 | − | 0.877327i | \(-0.340676\pi\) | ||||
0.479892 | + | 0.877327i | \(0.340676\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.82415 | −0.0584796 | ||||||||
\(974\) | −32.8981 | −1.05412 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.96116 | −0.318849 | ||||||||
\(977\) | −33.7657 | −1.08026 | −0.540130 | − | 0.841581i | \(-0.681625\pi\) | ||||
−0.540130 | + | 0.841581i | \(0.681625\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.7324 | −0.438891 | ||||||||
\(980\) | 132.450 | 4.23097 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −46.4192 | −1.48130 | ||||||||
\(983\) | 20.0762 | 0.640331 | 0.320165 | − | 0.947362i | \(-0.396261\pi\) | ||||
0.320165 | + | 0.947362i | \(0.396261\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 91.4732 | 2.91458 | ||||||||
\(986\) | 31.0980 | 0.990361 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −63.4646 | −2.01908 | ||||||||
\(989\) | 1.37205 | 0.0436287 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.9157 | 0.505579 | 0.252790 | − | 0.967521i | \(-0.418652\pi\) | ||||
0.252790 | + | 0.967521i | \(0.418652\pi\) | |||||||
\(992\) | 75.2017 | 2.38765 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.51948 | −0.143349 | ||||||||
\(995\) | −17.4163 | −0.552132 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.6749 | 1.22485 | 0.612424 | − | 0.790530i | \(-0.290195\pi\) | ||||
0.612424 | + | 0.790530i | \(0.290195\pi\) | |||||||
\(998\) | 73.3319 | 2.32128 | ||||||||
\(999\) | 0 | 0 |
(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 | 6039.2.a.n.1.2 | ✓ | 25 | |
3.2 | odd | 2 | 6039.2.a.o.1.24 | yes | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6039.2.a.n.1.2 | ✓ | 25 | 1.1 | even | 1 | trivial | |
6039.2.a.o.1.24 | yes | 25 | 3.2 | odd | 2 |