Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
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: | \( x^{10} - 3x^{9} - 10x^{8} + 32x^{7} + 32x^{6} - 118x^{5} - 29x^{4} + 182x^{3} - 28x^{2} - 101x + 43 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.31926\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.31926 | −0.932855 | −0.466428 | − | 0.884559i | \(-0.654459\pi\) | ||||
−0.466428 | + | 0.884559i | \(0.654459\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.259562 | −0.129781 | ||||||||
\(5\) | 4.11119 | 1.83858 | 0.919289 | − | 0.393582i | \(-0.128764\pi\) | ||||
0.919289 | + | 0.393582i | \(0.128764\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.74867 | −1.03890 | −0.519450 | − | 0.854501i | \(-0.673863\pi\) | ||||
−0.519450 | + | 0.854501i | \(0.673863\pi\) | |||||||
\(8\) | 2.98094 | 1.05392 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.42371 | −1.71513 | ||||||||
\(11\) | −4.56858 | −1.37748 | −0.688740 | − | 0.725009i | \(-0.741836\pi\) | ||||
−0.688740 | + | 0.725009i | \(0.741836\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.36237 | −1.76460 | −0.882302 | − | 0.470683i | \(-0.844007\pi\) | ||||
−0.882302 | + | 0.470683i | \(0.844007\pi\) | |||||||
\(14\) | 3.62620 | 0.969143 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.41350 | −0.853376 | ||||||||
\(17\) | 3.25232 | 0.788803 | 0.394402 | − | 0.918938i | \(-0.370952\pi\) | ||||
0.394402 | + | 0.918938i | \(0.370952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.59861 | 1.51383 | 0.756913 | − | 0.653516i | \(-0.226707\pi\) | ||||
0.756913 | + | 0.653516i | \(0.226707\pi\) | |||||||
\(20\) | −1.06711 | −0.238613 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.02713 | 1.28499 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.9019 | 2.38037 | ||||||||
\(26\) | 8.39360 | 1.64612 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.713450 | 0.134829 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.08138 | −1.63106 | −0.815532 | − | 0.578712i | \(-0.803556\pi\) | ||||
−0.815532 | + | 0.578712i | \(0.803556\pi\) | |||||||
\(32\) | −1.45860 | −0.257846 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.29064 | −0.735839 | ||||||||
\(35\) | −11.3003 | −1.91010 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.61278 | 1.08714 | 0.543568 | − | 0.839365i | \(-0.317073\pi\) | ||||
0.543568 | + | 0.839365i | \(0.317073\pi\) | |||||||
\(38\) | −8.70526 | −1.41218 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.2552 | 1.93772 | ||||||||
\(41\) | 2.61975 | 0.409137 | 0.204568 | − | 0.978852i | \(-0.434421\pi\) | ||||
0.204568 | + | 0.978852i | \(0.434421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.65344 | −1.31964 | −0.659819 | − | 0.751425i | \(-0.729367\pi\) | ||||
−0.659819 | + | 0.751425i | \(0.729367\pi\) | |||||||
\(44\) | 1.18583 | 0.178771 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.31926 | 0.194514 | ||||||||
\(47\) | 5.78296 | 0.843531 | 0.421766 | − | 0.906705i | \(-0.361410\pi\) | ||||
0.421766 | + | 0.906705i | \(0.361410\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.555185 | 0.0793122 | ||||||||
\(50\) | −15.7016 | −2.22054 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.65143 | 0.229012 | ||||||||
\(53\) | −1.33533 | −0.183422 | −0.0917111 | − | 0.995786i | \(-0.529234\pi\) | ||||
−0.0917111 | + | 0.995786i | \(0.529234\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.7823 | −2.53260 | ||||||||
\(56\) | −8.19363 | −1.09492 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.31926 | 0.173227 | ||||||||
\(59\) | −7.66955 | −0.998491 | −0.499245 | − | 0.866461i | \(-0.666389\pi\) | ||||
−0.499245 | + | 0.866461i | \(0.666389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.22375 | 0.668833 | 0.334416 | − | 0.942425i | \(-0.391461\pi\) | ||||
0.334416 | + | 0.942425i | \(0.391461\pi\) | |||||||
\(62\) | 11.9807 | 1.52155 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.75127 | 1.09391 | ||||||||
\(65\) | −26.1569 | −3.24436 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.97447 | 0.241219 | 0.120610 | − | 0.992700i | \(-0.461515\pi\) | ||||
0.120610 | + | 0.992700i | \(0.461515\pi\) | |||||||
\(68\) | −0.844178 | −0.102372 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 14.9080 | 1.78185 | ||||||||
\(71\) | 4.65159 | 0.552042 | 0.276021 | − | 0.961152i | \(-0.410984\pi\) | ||||
0.276021 | + | 0.961152i | \(0.410984\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.95340 | −0.813834 | −0.406917 | − | 0.913465i | \(-0.633396\pi\) | ||||
−0.406917 | + | 0.913465i | \(0.633396\pi\) | |||||||
\(74\) | −8.72396 | −1.01414 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.71275 | −0.196466 | ||||||||
\(77\) | 12.5575 | 1.43106 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.90285 | 1.11416 | 0.557079 | − | 0.830460i | \(-0.311922\pi\) | ||||
0.557079 | + | 0.830460i | \(0.311922\pi\) | |||||||
\(80\) | −14.0336 | −1.56900 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.45613 | −0.381665 | ||||||||
\(83\) | 11.5122 | 1.26363 | 0.631816 | − | 0.775119i | \(-0.282310\pi\) | ||||
0.631816 | + | 0.775119i | \(0.282310\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.3709 | 1.45028 | ||||||||
\(86\) | 11.4161 | 1.23103 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.6187 | −1.45176 | ||||||||
\(89\) | 2.94778 | 0.312464 | 0.156232 | − | 0.987720i | \(-0.450065\pi\) | ||||
0.156232 | + | 0.987720i | \(0.450065\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.4881 | 1.83325 | ||||||||
\(92\) | 0.259562 | 0.0270612 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.62921 | −0.786893 | ||||||||
\(95\) | 27.1281 | 2.78329 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.26492 | 0.229968 | 0.114984 | − | 0.993367i | \(-0.463318\pi\) | ||||
0.114984 | + | 0.993367i | \(0.463318\pi\) | |||||||
\(98\) | −0.732432 | −0.0739868 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.08927 | −0.308927 | ||||||||
\(101\) | 0.171130 | 0.0170281 | 0.00851403 | − | 0.999964i | \(-0.497290\pi\) | ||||
0.00851403 | + | 0.999964i | \(0.497290\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.1919 | −1.39837 | −0.699187 | − | 0.714939i | \(-0.746454\pi\) | ||||
−0.699187 | + | 0.714939i | \(0.746454\pi\) | |||||||
\(104\) | −18.9659 | −1.85976 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.76165 | 0.171106 | ||||||||
\(107\) | 4.01155 | 0.387811 | 0.193906 | − | 0.981020i | \(-0.437884\pi\) | ||||
0.193906 | + | 0.981020i | \(0.437884\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.73215 | −0.165910 | −0.0829551 | − | 0.996553i | \(-0.526436\pi\) | ||||
−0.0829551 | + | 0.996553i | \(0.526436\pi\) | |||||||
\(110\) | 24.7787 | 2.36255 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.38259 | 0.886572 | ||||||||
\(113\) | 3.63931 | 0.342358 | 0.171179 | − | 0.985240i | \(-0.445242\pi\) | ||||
0.171179 | + | 0.985240i | \(0.445242\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.11119 | −0.383370 | ||||||||
\(116\) | 0.259562 | 0.0240997 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.1181 | 0.931447 | ||||||||
\(119\) | −8.93955 | −0.819487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.87194 | 0.897449 | ||||||||
\(122\) | −6.89147 | −0.623924 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.35718 | 0.211681 | ||||||||
\(125\) | 28.3749 | 2.53792 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.40280 | 0.213214 | 0.106607 | − | 0.994301i | \(-0.466001\pi\) | ||||
0.106607 | + | 0.994301i | \(0.466001\pi\) | |||||||
\(128\) | −8.62798 | −0.762613 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 34.5077 | 3.02652 | ||||||||
\(131\) | 15.6553 | 1.36781 | 0.683907 | − | 0.729569i | \(-0.260279\pi\) | ||||
0.683907 | + | 0.729569i | \(0.260279\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.1374 | −1.57271 | ||||||||
\(134\) | −2.60483 | −0.225023 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.69497 | 0.831337 | ||||||||
\(137\) | 20.2050 | 1.72623 | 0.863113 | − | 0.505010i | \(-0.168511\pi\) | ||||
0.863113 | + | 0.505010i | \(0.168511\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.94680 | 0.758857 | 0.379429 | − | 0.925221i | \(-0.376121\pi\) | ||||
0.379429 | + | 0.925221i | \(0.376121\pi\) | |||||||
\(140\) | 2.93313 | 0.247894 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.13664 | −0.514976 | ||||||||
\(143\) | 29.0670 | 2.43071 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.11119 | −0.341416 | ||||||||
\(146\) | 9.17332 | 0.759189 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.71643 | −0.141089 | ||||||||
\(149\) | −8.40338 | −0.688432 | −0.344216 | − | 0.938890i | \(-0.611855\pi\) | ||||
−0.344216 | + | 0.938890i | \(0.611855\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.901268 | 0.0733442 | 0.0366721 | − | 0.999327i | \(-0.488324\pi\) | ||||
0.0366721 | + | 0.999327i | \(0.488324\pi\) | |||||||
\(152\) | 19.6701 | 1.59545 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.5666 | −1.33497 | ||||||||
\(155\) | −37.3353 | −2.99884 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.4829 | 1.79433 | 0.897164 | − | 0.441697i | \(-0.145623\pi\) | ||||
0.897164 | + | 0.441697i | \(0.145623\pi\) | |||||||
\(158\) | −13.0644 | −1.03935 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.99656 | −0.474070 | ||||||||
\(161\) | 2.74867 | 0.216626 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.39140 | −0.578939 | −0.289470 | − | 0.957187i | \(-0.593479\pi\) | ||||
−0.289470 | + | 0.957187i | \(0.593479\pi\) | |||||||
\(164\) | −0.679988 | −0.0530981 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.1876 | −1.17878 | ||||||||
\(167\) | 1.89972 | 0.147004 | 0.0735022 | − | 0.997295i | \(-0.476582\pi\) | ||||
0.0735022 | + | 0.997295i | \(0.476582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.4798 | 2.11383 | ||||||||
\(170\) | −17.6396 | −1.35290 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.24610 | 0.171264 | ||||||||
\(173\) | 0.795280 | 0.0604641 | 0.0302320 | − | 0.999543i | \(-0.490375\pi\) | ||||
0.0302320 | + | 0.999543i | \(0.490375\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −32.7143 | −2.47297 | ||||||||
\(176\) | 15.5949 | 1.17551 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.88888 | −0.291484 | ||||||||
\(179\) | 6.16453 | 0.460759 | 0.230379 | − | 0.973101i | \(-0.426003\pi\) | ||||
0.230379 | + | 0.973101i | \(0.426003\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.0943 | −1.27061 | −0.635304 | − | 0.772262i | \(-0.719125\pi\) | ||||
−0.635304 | + | 0.772262i | \(0.719125\pi\) | |||||||
\(182\) | −23.0712 | −1.71015 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.98094 | −0.219758 | ||||||||
\(185\) | 27.1864 | 1.99878 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.8585 | −1.08656 | ||||||||
\(188\) | −1.50104 | −0.109474 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −35.7890 | −2.59640 | ||||||||
\(191\) | −4.58496 | −0.331756 | −0.165878 | − | 0.986146i | \(-0.553046\pi\) | ||||
−0.165878 | + | 0.986146i | \(0.553046\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8598 | 1.06963 | 0.534817 | − | 0.844968i | \(-0.320381\pi\) | ||||
0.534817 | + | 0.844968i | \(0.320381\pi\) | |||||||
\(194\) | −2.98801 | −0.214527 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.144105 | −0.0102932 | ||||||||
\(197\) | 16.8176 | 1.19820 | 0.599101 | − | 0.800674i | \(-0.295525\pi\) | ||||
0.599101 | + | 0.800674i | \(0.295525\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.6701 | 0.756386 | 0.378193 | − | 0.925727i | \(-0.376546\pi\) | ||||
0.378193 | + | 0.925727i | \(0.376546\pi\) | |||||||
\(200\) | 35.4788 | 2.50873 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.225764 | −0.0158847 | ||||||||
\(203\) | 2.74867 | 0.192919 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.7703 | 0.752230 | ||||||||
\(206\) | 18.7228 | 1.30448 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 21.7180 | 1.50587 | ||||||||
\(209\) | −30.1463 | −2.08526 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.1044 | −1.65942 | −0.829709 | − | 0.558197i | \(-0.811493\pi\) | ||||
−0.829709 | + | 0.558197i | \(0.811493\pi\) | |||||||
\(212\) | 0.346602 | 0.0238047 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.29226 | −0.361772 | ||||||||
\(215\) | −35.5759 | −2.42626 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 24.9617 | 1.69451 | ||||||||
\(218\) | 2.28516 | 0.154770 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.87517 | 0.328684 | ||||||||
\(221\) | −20.6925 | −1.39193 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.944548 | 0.0632516 | 0.0316258 | − | 0.999500i | \(-0.489932\pi\) | ||||
0.0316258 | + | 0.999500i | \(0.489932\pi\) | |||||||
\(224\) | 4.00920 | 0.267876 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.80119 | −0.319370 | ||||||||
\(227\) | −20.3135 | −1.34825 | −0.674126 | − | 0.738617i | \(-0.735479\pi\) | ||||
−0.674126 | + | 0.738617i | \(0.735479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.86545 | 0.453682 | 0.226841 | − | 0.973932i | \(-0.427160\pi\) | ||||
0.226841 | + | 0.973932i | \(0.427160\pi\) | |||||||
\(230\) | 5.42371 | 0.357629 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.98094 | −0.195708 | ||||||||
\(233\) | 9.87907 | 0.647199 | 0.323600 | − | 0.946194i | \(-0.395107\pi\) | ||||
0.323600 | + | 0.946194i | \(0.395107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 23.7748 | 1.55090 | ||||||||
\(236\) | 1.99072 | 0.129585 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.7936 | 0.764463 | ||||||||
\(239\) | −9.96016 | −0.644269 | −0.322134 | − | 0.946694i | \(-0.604400\pi\) | ||||
−0.322134 | + | 0.946694i | \(0.604400\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.96142 | 0.448425 | 0.224212 | − | 0.974540i | \(-0.428019\pi\) | ||||
0.224212 | + | 0.974540i | \(0.428019\pi\) | |||||||
\(242\) | −13.0236 | −0.837190 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.35589 | −0.0868018 | ||||||||
\(245\) | 2.28247 | 0.145822 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −41.9828 | −2.67130 | ||||||||
\(248\) | −27.0711 | −1.71901 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −37.4337 | −2.36752 | ||||||||
\(251\) | −10.0183 | −0.632352 | −0.316176 | − | 0.948701i | \(-0.602399\pi\) | ||||
−0.316176 | + | 0.948701i | \(0.602399\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.56858 | 0.287224 | ||||||||
\(254\) | −3.16991 | −0.198898 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.12002 | −0.382501 | ||||||||
\(257\) | 4.87303 | 0.303971 | 0.151986 | − | 0.988383i | \(-0.451433\pi\) | ||||
0.151986 | + | 0.988383i | \(0.451433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.1764 | −1.12942 | ||||||||
\(260\) | 6.78934 | 0.421057 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −20.6534 | −1.27597 | ||||||||
\(263\) | −5.63631 | −0.347549 | −0.173775 | − | 0.984785i | \(-0.555596\pi\) | ||||
−0.173775 | + | 0.984785i | \(0.555596\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.48981 | −0.337236 | ||||||||
\(266\) | 23.9279 | 1.46711 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.512496 | −0.0313057 | ||||||||
\(269\) | 20.0520 | 1.22259 | 0.611296 | − | 0.791402i | \(-0.290648\pi\) | ||||
0.611296 | + | 0.791402i | \(0.290648\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.8081 | 0.778039 | 0.389020 | − | 0.921229i | \(-0.372814\pi\) | ||||
0.389020 | + | 0.921229i | \(0.372814\pi\) | |||||||
\(272\) | −11.1018 | −0.673146 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −26.6555 | −1.61032 | ||||||||
\(275\) | −54.3746 | −3.27891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.1150 | 0.788002 | 0.394001 | − | 0.919110i | \(-0.371091\pi\) | ||||
0.394001 | + | 0.919110i | \(0.371091\pi\) | |||||||
\(278\) | −11.8031 | −0.707904 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −33.6855 | −2.01310 | ||||||||
\(281\) | −3.97492 | −0.237124 | −0.118562 | − | 0.992947i | \(-0.537828\pi\) | ||||
−0.118562 | + | 0.992947i | \(0.537828\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.04216 | −0.240281 | −0.120141 | − | 0.992757i | \(-0.538335\pi\) | ||||
−0.120141 | + | 0.992757i | \(0.538335\pi\) | |||||||
\(284\) | −1.20738 | −0.0716446 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −38.3469 | −2.26750 | ||||||||
\(287\) | −7.20083 | −0.425052 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.42243 | −0.377790 | ||||||||
\(290\) | 5.42371 | 0.318491 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.80484 | 0.105620 | ||||||||
\(293\) | −8.95096 | −0.522921 | −0.261460 | − | 0.965214i | \(-0.584204\pi\) | ||||
−0.261460 | + | 0.965214i | \(0.584204\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.5310 | −1.83580 | ||||||||
\(296\) | 19.7123 | 1.14576 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.0862 | 0.642207 | ||||||||
\(299\) | 6.36237 | 0.367945 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.7855 | 1.37097 | ||||||||
\(302\) | −1.18900 | −0.0684195 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22.5244 | −1.29186 | ||||||||
\(305\) | 21.4758 | 1.22970 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.10039 | 0.176949 | 0.0884743 | − | 0.996078i | \(-0.471801\pi\) | ||||
0.0884743 | + | 0.996078i | \(0.471801\pi\) | |||||||
\(308\) | −3.25945 | −0.185725 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 49.2548 | 2.79748 | ||||||||
\(311\) | 4.41722 | 0.250478 | 0.125239 | − | 0.992127i | \(-0.460030\pi\) | ||||
0.125239 | + | 0.992127i | \(0.460030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.0162 | 0.679194 | 0.339597 | − | 0.940571i | \(-0.389709\pi\) | ||||
0.339597 | + | 0.940571i | \(0.389709\pi\) | |||||||
\(314\) | −29.6607 | −1.67385 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.57040 | −0.144596 | ||||||||
\(317\) | −28.1477 | −1.58093 | −0.790466 | − | 0.612506i | \(-0.790161\pi\) | ||||
−0.790466 | + | 0.612506i | \(0.790161\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.56858 | 0.255791 | ||||||||
\(320\) | 35.9781 | 2.01124 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.62620 | −0.202080 | ||||||||
\(323\) | 21.4608 | 1.19411 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −75.7241 | −4.20042 | ||||||||
\(326\) | 9.75115 | 0.540066 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.80933 | 0.431198 | ||||||||
\(329\) | −15.8954 | −0.876344 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.5216 | 1.01804 | 0.509019 | − | 0.860755i | \(-0.330008\pi\) | ||||
0.509019 | + | 0.860755i | \(0.330008\pi\) | |||||||
\(332\) | −2.98814 | −0.163995 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.50621 | −0.137134 | ||||||||
\(335\) | 8.11740 | 0.443501 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.49971 | −0.299588 | −0.149794 | − | 0.988717i | \(-0.547861\pi\) | ||||
−0.149794 | + | 0.988717i | \(0.547861\pi\) | |||||||
\(338\) | −36.2529 | −1.97190 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.47057 | −0.188218 | ||||||||
\(341\) | 41.4890 | 2.24676 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.7147 | 0.956502 | ||||||||
\(344\) | −25.7954 | −1.39080 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.04918 | −0.0564042 | ||||||||
\(347\) | 21.8641 | 1.17373 | 0.586863 | − | 0.809686i | \(-0.300363\pi\) | ||||
0.586863 | + | 0.809686i | \(0.300363\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.1439 | 1.07828 | 0.539138 | − | 0.842217i | \(-0.318750\pi\) | ||||
0.539138 | + | 0.842217i | \(0.318750\pi\) | |||||||
\(350\) | 43.1585 | 2.30692 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.66372 | 0.355177 | ||||||||
\(353\) | 11.2359 | 0.598029 | 0.299014 | − | 0.954249i | \(-0.403342\pi\) | ||||
0.299014 | + | 0.954249i | \(0.403342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.1236 | 1.01497 | ||||||||
\(356\) | −0.765132 | −0.0405519 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.13260 | −0.429821 | ||||||||
\(359\) | 30.9360 | 1.63274 | 0.816369 | − | 0.577531i | \(-0.195984\pi\) | ||||
0.816369 | + | 0.577531i | \(0.195984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24.5417 | 1.29167 | ||||||||
\(362\) | 22.5517 | 1.18529 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.53923 | −0.237921 | ||||||||
\(365\) | −28.5867 | −1.49630 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.8506 | −1.19279 | −0.596396 | − | 0.802691i | \(-0.703401\pi\) | ||||
−0.596396 | + | 0.802691i | \(0.703401\pi\) | |||||||
\(368\) | 3.41350 | 0.177941 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −35.8658 | −1.86458 | ||||||||
\(371\) | 3.67039 | 0.190557 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.59121 | −0.393058 | −0.196529 | − | 0.980498i | \(-0.562967\pi\) | ||||
−0.196529 | + | 0.980498i | \(0.562967\pi\) | |||||||
\(374\) | 19.6021 | 1.01360 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.2387 | 0.889016 | ||||||||
\(377\) | 6.36237 | 0.327679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5273 | −0.746216 | −0.373108 | − | 0.927788i | \(-0.621708\pi\) | ||||
−0.373108 | + | 0.927788i | \(0.621708\pi\) | |||||||
\(380\) | −7.04143 | −0.361218 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.04874 | 0.309481 | ||||||||
\(383\) | 32.5891 | 1.66523 | 0.832614 | − | 0.553854i | \(-0.186843\pi\) | ||||
0.832614 | + | 0.553854i | \(0.186843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 51.6263 | 2.63112 | ||||||||
\(386\) | −19.6039 | −0.997814 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.587887 | −0.0298454 | ||||||||
\(389\) | 29.9827 | 1.52018 | 0.760092 | − | 0.649816i | \(-0.225154\pi\) | ||||
0.760092 | + | 0.649816i | \(0.225154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.25232 | −0.164477 | ||||||||
\(392\) | 1.65498 | 0.0835889 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −22.1867 | −1.11775 | ||||||||
\(395\) | 40.7125 | 2.04847 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.70605 | 0.135813 | 0.0679063 | − | 0.997692i | \(-0.478368\pi\) | ||||
0.0679063 | + | 0.997692i | \(0.478368\pi\) | |||||||
\(398\) | −14.0767 | −0.705599 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −40.6271 | −2.03135 | ||||||||
\(401\) | −20.8363 | −1.04052 | −0.520259 | − | 0.854009i | \(-0.674164\pi\) | ||||
−0.520259 | + | 0.854009i | \(0.674164\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 57.7791 | 2.87818 | ||||||||
\(404\) | −0.0444188 | −0.00220992 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.62620 | −0.179965 | ||||||||
\(407\) | −30.2110 | −1.49751 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.56957 | −0.423738 | −0.211869 | − | 0.977298i | \(-0.567955\pi\) | ||||
−0.211869 | + | 0.977298i | \(0.567955\pi\) | |||||||
\(410\) | −14.2088 | −0.701722 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.68369 | 0.181482 | ||||||||
\(413\) | 21.0811 | 1.03733 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 47.3289 | 2.32329 | ||||||||
\(416\) | 9.28013 | 0.454996 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 39.7707 | 1.94525 | ||||||||
\(419\) | −13.0013 | −0.635157 | −0.317578 | − | 0.948232i | \(-0.602870\pi\) | ||||
−0.317578 | + | 0.948232i | \(0.602870\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6385 | 1.10333 | 0.551667 | − | 0.834064i | \(-0.313992\pi\) | ||||
0.551667 | + | 0.834064i | \(0.313992\pi\) | |||||||
\(422\) | 31.7999 | 1.54800 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.98055 | −0.193313 | ||||||||
\(425\) | 38.7086 | 1.87764 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.3584 | −0.694850 | ||||||||
\(428\) | −1.04125 | −0.0503305 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 46.9338 | 2.26335 | ||||||||
\(431\) | 31.8549 | 1.53439 | 0.767197 | − | 0.641411i | \(-0.221651\pi\) | ||||
0.767197 | + | 0.641411i | \(0.221651\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0708 | −0.676200 | −0.338100 | − | 0.941110i | \(-0.609784\pi\) | ||||
−0.338100 | + | 0.941110i | \(0.609784\pi\) | |||||||
\(434\) | −32.9309 | −1.58073 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.449601 | 0.0215320 | ||||||||
\(437\) | −6.59861 | −0.315654 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.82152 | 0.421028 | 0.210514 | − | 0.977591i | \(-0.432486\pi\) | ||||
0.210514 | + | 0.977591i | \(0.432486\pi\) | |||||||
\(440\) | −55.9889 | −2.66917 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 27.2987 | 1.29847 | ||||||||
\(443\) | 33.8771 | 1.60955 | 0.804776 | − | 0.593579i | \(-0.202285\pi\) | ||||
0.804776 | + | 0.593579i | \(0.202285\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.1189 | 0.574491 | ||||||||
\(446\) | −1.24610 | −0.0590046 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −24.0544 | −1.13646 | ||||||||
\(449\) | −3.91466 | −0.184744 | −0.0923721 | − | 0.995725i | \(-0.529445\pi\) | ||||
−0.0923721 | + | 0.995725i | \(0.529445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.9686 | −0.563577 | ||||||||
\(452\) | −0.944627 | −0.0444315 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 26.7987 | 1.25772 | ||||||||
\(455\) | 71.8967 | 3.37057 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.8594 | −0.928985 | −0.464493 | − | 0.885577i | \(-0.653763\pi\) | ||||
−0.464493 | + | 0.885577i | \(0.653763\pi\) | |||||||
\(458\) | −9.05729 | −0.423219 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.06711 | 0.0497542 | ||||||||
\(461\) | 16.4586 | 0.766553 | 0.383277 | − | 0.923634i | \(-0.374796\pi\) | ||||
0.383277 | + | 0.923634i | \(0.374796\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.4972 | 1.18496 | 0.592478 | − | 0.805587i | \(-0.298150\pi\) | ||||
0.592478 | + | 0.805587i | \(0.298150\pi\) | |||||||
\(464\) | 3.41350 | 0.158468 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.0330 | −0.603743 | ||||||||
\(467\) | 22.8174 | 1.05586 | 0.527931 | − | 0.849287i | \(-0.322968\pi\) | ||||
0.527931 | + | 0.849287i | \(0.322968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.42715 | −0.250603 | ||||||||
\(470\) | −31.3651 | −1.44676 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.8625 | −1.05233 | ||||||||
\(473\) | 39.5340 | 1.81777 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 78.5358 | 3.60347 | ||||||||
\(476\) | 2.32037 | 0.106354 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.1400 | 0.601010 | ||||||||
\(479\) | −43.4778 | −1.98655 | −0.993276 | − | 0.115770i | \(-0.963067\pi\) | ||||
−0.993276 | + | 0.115770i | \(0.963067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.0730 | −1.91836 | ||||||||
\(482\) | −9.18390 | −0.418315 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.56238 | −0.116472 | ||||||||
\(485\) | 9.31151 | 0.422814 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.07464 | −0.0486965 | −0.0243482 | − | 0.999704i | \(-0.507751\pi\) | ||||
−0.0243482 | + | 0.999704i | \(0.507751\pi\) | |||||||
\(488\) | 15.5717 | 0.704898 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.01117 | −0.136031 | ||||||||
\(491\) | −12.4335 | −0.561117 | −0.280558 | − | 0.959837i | \(-0.590520\pi\) | ||||
−0.280558 | + | 0.959837i | \(0.590520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.25232 | −0.146477 | ||||||||
\(494\) | 55.3861 | 2.49194 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.9993 | 1.39191 | ||||||||
\(497\) | −12.7857 | −0.573517 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.45558 | −0.333758 | −0.166879 | − | 0.985977i | \(-0.553369\pi\) | ||||
−0.166879 | + | 0.985977i | \(0.553369\pi\) | |||||||
\(500\) | −7.36503 | −0.329374 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.2168 | 0.589893 | ||||||||
\(503\) | −39.4744 | −1.76008 | −0.880039 | − | 0.474901i | \(-0.842484\pi\) | ||||
−0.880039 | + | 0.474901i | \(0.842484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.703547 | 0.0313074 | ||||||||
\(506\) | −6.02713 | −0.267939 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.623676 | −0.0276711 | ||||||||
\(509\) | 43.4583 | 1.92625 | 0.963127 | − | 0.269047i | \(-0.0867085\pi\) | ||||
0.963127 | + | 0.269047i | \(0.0867085\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.1126 | 0.845491 | ||||||||
\(512\) | 25.3298 | 1.11943 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.42878 | −0.283561 | ||||||||
\(515\) | −58.3457 | −2.57102 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.4199 | −1.16195 | ||||||||
\(518\) | 23.9793 | 1.05359 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −77.9722 | −3.41931 | ||||||||
\(521\) | 34.6729 | 1.51905 | 0.759525 | − | 0.650478i | \(-0.225432\pi\) | ||||
0.759525 | + | 0.650478i | \(0.225432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.0232653 | 0.00101732 | 0.000508660 | − | 1.00000i | \(-0.499838\pi\) | ||||
0.000508660 | 1.00000i | \(0.499838\pi\) | ||||||||
\(524\) | −4.06353 | −0.177516 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.43573 | 0.324213 | ||||||||
\(527\) | −29.5355 | −1.28659 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 7.24247 | 0.314593 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.70778 | 0.204108 | ||||||||
\(533\) | −16.6678 | −0.721964 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.4922 | 0.713022 | ||||||||
\(536\) | 5.88577 | 0.254226 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −26.4537 | −1.14050 | ||||||||
\(539\) | −2.53641 | −0.109251 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.9131 | 1.50103 | 0.750515 | − | 0.660853i | \(-0.229806\pi\) | ||||
0.750515 | + | 0.660853i | \(0.229806\pi\) | |||||||
\(542\) | −16.8972 | −0.725798 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.74382 | −0.203390 | ||||||||
\(545\) | −7.12121 | −0.305039 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.1866 | −0.435547 | −0.217774 | − | 0.975999i | \(-0.569879\pi\) | ||||
−0.217774 | + | 0.975999i | \(0.569879\pi\) | |||||||
\(548\) | −5.24444 | −0.224031 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 71.7341 | 3.05875 | ||||||||
\(551\) | −6.59861 | −0.281110 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.2197 | −1.15750 | ||||||||
\(554\) | −17.3020 | −0.735092 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.32225 | −0.0984852 | ||||||||
\(557\) | −11.2100 | −0.474985 | −0.237492 | − | 0.971389i | \(-0.576326\pi\) | ||||
−0.237492 | + | 0.971389i | \(0.576326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.0564 | 2.32864 | ||||||||
\(560\) | 38.5736 | 1.63003 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.24394 | 0.221202 | ||||||||
\(563\) | 8.18989 | 0.345163 | 0.172581 | − | 0.984995i | \(-0.444789\pi\) | ||||
0.172581 | + | 0.984995i | \(0.444789\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.9619 | 0.629451 | ||||||||
\(566\) | 5.33264 | 0.224148 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 13.8661 | 0.581810 | ||||||||
\(569\) | −40.6958 | −1.70606 | −0.853028 | − | 0.521865i | \(-0.825237\pi\) | ||||
−0.853028 | + | 0.521865i | \(0.825237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.4479 | −1.65084 | −0.825422 | − | 0.564516i | \(-0.809063\pi\) | ||||
−0.825422 | + | 0.564516i | \(0.809063\pi\) | |||||||
\(572\) | −7.54469 | −0.315459 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.49975 | 0.396512 | ||||||||
\(575\) | −11.9019 | −0.496342 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.5420 | 1.52126 | 0.760632 | − | 0.649183i | \(-0.224889\pi\) | ||||
0.760632 | + | 0.649183i | \(0.224889\pi\) | |||||||
\(578\) | 8.47283 | 0.352423 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.06711 | 0.0443092 | ||||||||
\(581\) | −31.6433 | −1.31279 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.10058 | 0.252660 | ||||||||
\(584\) | −20.7277 | −0.857717 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.8086 | 0.487810 | ||||||||
\(587\) | −6.69668 | −0.276402 | −0.138201 | − | 0.990404i | \(-0.544132\pi\) | ||||
−0.138201 | + | 0.990404i | \(0.544132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −59.9245 | −2.46915 | ||||||||
\(590\) | 41.5974 | 1.71254 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22.5728 | −0.927735 | ||||||||
\(593\) | −39.0591 | −1.60397 | −0.801983 | − | 0.597347i | \(-0.796222\pi\) | ||||
−0.801983 | + | 0.597347i | \(0.796222\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.7522 | −1.50669 | ||||||||
\(596\) | 2.18120 | 0.0893454 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.39360 | −0.343240 | ||||||||
\(599\) | 3.20208 | 0.130834 | 0.0654168 | − | 0.997858i | \(-0.479162\pi\) | ||||
0.0654168 | + | 0.997858i | \(0.479162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.6424 | −1.12756 | −0.563778 | − | 0.825927i | \(-0.690653\pi\) | ||||
−0.563778 | + | 0.825927i | \(0.690653\pi\) | |||||||
\(602\) | −31.3791 | −1.27892 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.233935 | −0.00951868 | ||||||||
\(605\) | 40.5854 | 1.65003 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.4334 | 1.35702 | 0.678510 | − | 0.734591i | \(-0.262626\pi\) | ||||
0.678510 | + | 0.734591i | \(0.262626\pi\) | |||||||
\(608\) | −9.62471 | −0.390334 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.3321 | −1.14713 | ||||||||
\(611\) | −36.7933 | −1.48850 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.7380 | −0.595263 | −0.297631 | − | 0.954681i | \(-0.596197\pi\) | ||||
−0.297631 | + | 0.954681i | \(0.596197\pi\) | |||||||
\(614\) | −4.09021 | −0.165067 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 37.4332 | 1.50823 | ||||||||
\(617\) | 21.9315 | 0.882927 | 0.441464 | − | 0.897279i | \(-0.354459\pi\) | ||||
0.441464 | + | 0.897279i | \(0.354459\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.7740 | 1.27710 | 0.638552 | − | 0.769578i | \(-0.279534\pi\) | ||||
0.638552 | + | 0.769578i | \(0.279534\pi\) | |||||||
\(620\) | 9.69081 | 0.389192 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.82745 | −0.233660 | ||||||||
\(623\) | −8.10248 | −0.324619 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 57.1450 | 2.28580 | ||||||||
\(626\) | −15.8524 | −0.633590 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.83570 | −0.232870 | ||||||||
\(629\) | 21.5069 | 0.857535 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8173 | −0.709297 | −0.354649 | − | 0.935000i | \(-0.615400\pi\) | ||||
−0.354649 | + | 0.935000i | \(0.615400\pi\) | |||||||
\(632\) | 29.5198 | 1.17424 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 37.1340 | 1.47478 | ||||||||
\(635\) | 9.87836 | 0.392011 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.53230 | −0.139955 | ||||||||
\(638\) | −6.02713 | −0.238616 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −35.4712 | −1.40212 | ||||||||
\(641\) | 18.3619 | 0.725253 | 0.362627 | − | 0.931935i | \(-0.381880\pi\) | ||||
0.362627 | + | 0.931935i | \(0.381880\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.5879 | 1.32458 | 0.662289 | − | 0.749248i | \(-0.269585\pi\) | ||||
0.662289 | + | 0.749248i | \(0.269585\pi\) | |||||||
\(644\) | −0.713450 | −0.0281139 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −28.3123 | −1.11393 | ||||||||
\(647\) | 32.8327 | 1.29079 | 0.645394 | − | 0.763850i | \(-0.276693\pi\) | ||||
0.645394 | + | 0.763850i | \(0.276693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.0390 | 1.37540 | ||||||||
\(650\) | 99.8995 | 3.91838 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.91853 | 0.0751353 | ||||||||
\(653\) | 11.6542 | 0.456064 | 0.228032 | − | 0.973654i | \(-0.426771\pi\) | ||||
0.228032 | + | 0.973654i | \(0.426771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 64.3621 | 2.51483 | ||||||||
\(656\) | −8.94253 | −0.349147 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 20.9702 | 0.817502 | ||||||||
\(659\) | −15.2217 | −0.592952 | −0.296476 | − | 0.955040i | \(-0.595811\pi\) | ||||
−0.296476 | + | 0.955040i | \(0.595811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6959 | 0.532708 | 0.266354 | − | 0.963875i | \(-0.414181\pi\) | ||||
0.266354 | + | 0.963875i | \(0.414181\pi\) | |||||||
\(662\) | −24.4347 | −0.949682 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 34.3173 | 1.33177 | ||||||||
\(665\) | −74.5663 | −2.89156 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −0.493094 | −0.0190784 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.7089 | −0.413722 | ||||||||
\(671\) | −23.8651 | −0.921303 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.63456 | 0.140102 | 0.0700510 | − | 0.997543i | \(-0.477684\pi\) | ||||
0.0700510 | + | 0.997543i | \(0.477684\pi\) | |||||||
\(674\) | 7.25553 | 0.279472 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.13270 | −0.274335 | ||||||||
\(677\) | 25.3809 | 0.975467 | 0.487734 | − | 0.872993i | \(-0.337824\pi\) | ||||
0.487734 | + | 0.872993i | \(0.337824\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.22552 | −0.238913 | ||||||||
\(680\) | 39.8578 | 1.52848 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −54.7347 | −2.09590 | ||||||||
\(683\) | 3.84356 | 0.147070 | 0.0735349 | − | 0.997293i | \(-0.476572\pi\) | ||||
0.0735349 | + | 0.997293i | \(0.476572\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 83.0664 | 3.17380 | ||||||||
\(686\) | −23.3702 | −0.892278 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 29.5386 | 1.12615 | ||||||||
\(689\) | 8.49589 | 0.323668 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.4972 | −1.54058 | −0.770292 | − | 0.637691i | \(-0.779890\pi\) | ||||
−0.770292 | + | 0.637691i | \(0.779890\pi\) | |||||||
\(692\) | −0.206424 | −0.00784708 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.8444 | −1.09492 | ||||||||
\(695\) | 36.7820 | 1.39522 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.52027 | 0.322728 | ||||||||
\(698\) | −26.5749 | −1.00588 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.49138 | 0.320944 | ||||||||
\(701\) | 16.8344 | 0.635827 | 0.317913 | − | 0.948120i | \(-0.397018\pi\) | ||||
0.317913 | + | 0.948120i | \(0.397018\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.6352 | 1.64573 | ||||||||
\(704\) | −39.9809 | −1.50684 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.8231 | −0.557874 | ||||||||
\(707\) | −0.470380 | −0.0176904 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.94456 | −0.0730294 | −0.0365147 | − | 0.999333i | \(-0.511626\pi\) | ||||
−0.0365147 | + | 0.999333i | \(0.511626\pi\) | |||||||
\(710\) | −25.2289 | −0.946824 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.78717 | 0.329313 | ||||||||
\(713\) | 9.08138 | 0.340100 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 119.500 | 4.46905 | ||||||||
\(716\) | −1.60008 | −0.0597977 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −40.8125 | −1.52311 | ||||||||
\(719\) | −13.5879 | −0.506742 | −0.253371 | − | 0.967369i | \(-0.581539\pi\) | ||||
−0.253371 | + | 0.967369i | \(0.581539\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.0089 | 1.45277 | ||||||||
\(722\) | −32.3768 | −1.20494 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.43702 | 0.164901 | ||||||||
\(725\) | −11.9019 | −0.442024 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.3198 | 1.38412 | 0.692058 | − | 0.721842i | \(-0.256704\pi\) | ||||
0.692058 | + | 0.721842i | \(0.256704\pi\) | |||||||
\(728\) | 52.1309 | 1.93210 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 37.7132 | 1.39583 | ||||||||
\(731\) | −28.1437 | −1.04093 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.8847 | −0.623650 | −0.311825 | − | 0.950139i | \(-0.600940\pi\) | ||||
−0.311825 | + | 0.950139i | \(0.600940\pi\) | |||||||
\(734\) | 30.1458 | 1.11270 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.45860 | 0.0537646 | ||||||||
\(737\) | −9.02051 | −0.332275 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.1714 | −0.815588 | −0.407794 | − | 0.913074i | \(-0.633702\pi\) | ||||
−0.407794 | + | 0.913074i | \(0.633702\pi\) | |||||||
\(740\) | −7.05655 | −0.259404 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.84219 | −0.177762 | ||||||||
\(743\) | 1.45976 | 0.0535535 | 0.0267767 | − | 0.999641i | \(-0.491476\pi\) | ||||
0.0267767 | + | 0.999641i | \(0.491476\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.5479 | −1.26574 | ||||||||
\(746\) | 10.0148 | 0.366666 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.85670 | 0.141015 | ||||||||
\(749\) | −11.0264 | −0.402897 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.9248 | −0.617596 | −0.308798 | − | 0.951128i | \(-0.599927\pi\) | ||||
−0.308798 | + | 0.951128i | \(0.599927\pi\) | |||||||
\(752\) | −19.7402 | −0.719849 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.39360 | −0.305677 | ||||||||
\(755\) | 3.70528 | 0.134849 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.6215 | 0.858539 | 0.429270 | − | 0.903176i | \(-0.358771\pi\) | ||||
0.429270 | + | 0.903176i | \(0.358771\pi\) | |||||||
\(758\) | 19.1652 | 0.696112 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 80.8674 | 2.93337 | ||||||||
\(761\) | 15.3396 | 0.556059 | 0.278029 | − | 0.960573i | \(-0.410319\pi\) | ||||
0.278029 | + | 0.960573i | \(0.410319\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.76112 | 0.172364 | ||||||||
\(764\) | 1.19008 | 0.0430556 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.9935 | −1.55342 | ||||||||
\(767\) | 48.7965 | 1.76194 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.1320 | −1.15871 | −0.579355 | − | 0.815075i | \(-0.696696\pi\) | ||||
−0.579355 | + | 0.815075i | \(0.696696\pi\) | |||||||
\(770\) | −68.1084 | −2.45446 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.85705 | −0.138818 | ||||||||
\(773\) | 0.152416 | 0.00548201 | 0.00274101 | − | 0.999996i | \(-0.499128\pi\) | ||||
0.00274101 | + | 0.999996i | \(0.499128\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −108.085 | −3.88254 | ||||||||
\(776\) | 6.75159 | 0.242368 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −39.5549 | −1.41811 | ||||||||
\(779\) | 17.2867 | 0.619361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.2512 | −0.760427 | ||||||||
\(782\) | 4.29064 | 0.153433 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.89513 | −0.0676831 | ||||||||
\(785\) | 92.4313 | 3.29901 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.3720 | 1.61734 | 0.808669 | − | 0.588264i | \(-0.200189\pi\) | ||||
0.808669 | + | 0.588264i | \(0.200189\pi\) | |||||||
\(788\) | −4.36520 | −0.155504 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −53.7102 | −1.91092 | ||||||||
\(791\) | −10.0033 | −0.355675 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −33.2354 | −1.18023 | ||||||||
\(794\) | −3.56997 | −0.126693 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.76956 | −0.0981645 | ||||||||
\(797\) | 43.4238 | 1.53815 | 0.769076 | − | 0.639158i | \(-0.220717\pi\) | ||||
0.769076 | + | 0.639158i | \(0.220717\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.8080 | 0.665380 | ||||||||
\(800\) | −17.3600 | −0.613769 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 27.4885 | 0.970652 | ||||||||
\(803\) | 31.7672 | 1.12104 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.3003 | 0.398283 | ||||||||
\(806\) | −76.2255 | −2.68493 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.510128 | 0.0179463 | ||||||||
\(809\) | 9.14016 | 0.321351 | 0.160675 | − | 0.987007i | \(-0.448633\pi\) | ||||
0.160675 | + | 0.987007i | \(0.448633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.0277 | −0.913957 | −0.456979 | − | 0.889478i | \(-0.651068\pi\) | ||||
−0.456979 | + | 0.889478i | \(0.651068\pi\) | |||||||
\(812\) | −0.713450 | −0.0250372 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 39.8561 | 1.39696 | ||||||||
\(815\) | −30.3874 | −1.06443 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −57.1007 | −1.99770 | ||||||||
\(818\) | 11.3055 | 0.395286 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.79556 | −0.0976251 | ||||||||
\(821\) | 2.03323 | 0.0709603 | 0.0354802 | − | 0.999370i | \(-0.488704\pi\) | ||||
0.0354802 | + | 0.999370i | \(0.488704\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.62311 | −0.196009 | −0.0980047 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980047 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(824\) | −42.3053 | −1.47378 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.8113 | −0.967680 | ||||||||
\(827\) | −16.9600 | −0.589757 | −0.294878 | − | 0.955535i | \(-0.595279\pi\) | ||||
−0.294878 | + | 0.955535i | \(0.595279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.3835 | −1.02053 | −0.510265 | − | 0.860017i | \(-0.670453\pi\) | ||||
−0.510265 | + | 0.860017i | \(0.670453\pi\) | |||||||
\(830\) | −62.4390 | −2.16729 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −55.6788 | −1.93032 | ||||||||
\(833\) | 1.80564 | 0.0625617 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.81009 | 0.270279 | ||||||||
\(836\) | 7.82483 | 0.270627 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.1521 | 0.592509 | ||||||||
\(839\) | −22.6490 | −0.781931 | −0.390966 | − | 0.920405i | \(-0.627859\pi\) | ||||
−0.390966 | + | 0.920405i | \(0.627859\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −29.8660 | −1.02925 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.25659 | 0.215361 | ||||||||
\(845\) | 112.975 | 3.88644 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.1347 | −0.932359 | ||||||||
\(848\) | 4.55817 | 0.156528 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −51.0666 | −1.75157 | ||||||||
\(851\) | −6.61278 | −0.226683 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.58645 | −0.122798 | −0.0613988 | − | 0.998113i | \(-0.519556\pi\) | ||||
−0.0613988 | + | 0.998113i | \(0.519556\pi\) | |||||||
\(854\) | 18.9424 | 0.648195 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.9582 | 0.408723 | ||||||||
\(857\) | −35.4173 | −1.20983 | −0.604916 | − | 0.796290i | \(-0.706793\pi\) | ||||
−0.604916 | + | 0.796290i | \(0.706793\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.0733 | −1.53788 | −0.768941 | − | 0.639320i | \(-0.779216\pi\) | ||||
−0.768941 | + | 0.639320i | \(0.779216\pi\) | |||||||
\(860\) | 9.23415 | 0.314882 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −42.0247 | −1.43137 | ||||||||
\(863\) | 31.8710 | 1.08490 | 0.542451 | − | 0.840087i | \(-0.317496\pi\) | ||||
0.542451 | + | 0.840087i | \(0.317496\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.26955 | 0.111168 | ||||||||
\(866\) | 18.5630 | 0.630797 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.47911 | −0.219915 | ||||||||
\(869\) | −45.2420 | −1.53473 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.5623 | −0.425657 | ||||||||
\(872\) | −5.16345 | −0.174856 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.70526 | 0.294460 | ||||||||
\(875\) | −77.9931 | −2.63665 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.5013 | 1.57024 | 0.785119 | − | 0.619345i | \(-0.212602\pi\) | ||||
0.785119 | + | 0.619345i | \(0.212602\pi\) | |||||||
\(878\) | −11.6378 | −0.392758 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 64.1134 | 2.16126 | ||||||||
\(881\) | −46.8173 | −1.57731 | −0.788657 | − | 0.614834i | \(-0.789223\pi\) | ||||
−0.788657 | + | 0.614834i | \(0.789223\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.4950 | 0.656059 | 0.328030 | − | 0.944667i | \(-0.393615\pi\) | ||||
0.328030 | + | 0.944667i | \(0.393615\pi\) | |||||||
\(884\) | 5.37097 | 0.180645 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −44.6927 | −1.50148 | ||||||||
\(887\) | −30.4696 | −1.02307 | −0.511534 | − | 0.859263i | \(-0.670923\pi\) | ||||
−0.511534 | + | 0.859263i | \(0.670923\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.60451 | −0.221508 | ||||||||
\(890\) | −15.9879 | −0.535917 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.245169 | −0.00820885 | ||||||||
\(893\) | 38.1595 | 1.27696 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.3435 | 0.847141 | ||||||||
\(896\) | 23.7155 | 0.792278 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.16444 | 0.172340 | ||||||||
\(899\) | 9.08138 | 0.302881 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.34293 | −0.144684 | ||||||||
\(902\) | 15.7896 | 0.525736 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.8486 | 0.360818 | ||||||||
\(905\) | −70.2778 | −2.33611 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.3091 | 1.00640 | 0.503199 | − | 0.864171i | \(-0.332156\pi\) | ||||
0.503199 | + | 0.864171i | \(0.332156\pi\) | |||||||
\(908\) | 5.27260 | 0.174977 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −94.8502 | −3.14425 | ||||||||
\(911\) | 5.21341 | 0.172728 | 0.0863639 | − | 0.996264i | \(-0.472475\pi\) | ||||
0.0863639 | + | 0.996264i | \(0.472475\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.5945 | −1.74063 | ||||||||
\(914\) | 26.1997 | 0.866609 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.78201 | −0.0588792 | ||||||||
\(917\) | −43.0314 | −1.42102 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4577 | 0.839774 | 0.419887 | − | 0.907577i | \(-0.362070\pi\) | ||||
0.419887 | + | 0.907577i | \(0.362070\pi\) | |||||||
\(920\) | −12.2552 | −0.404042 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.7131 | −0.715083 | ||||||||
\(923\) | −29.5952 | −0.974137 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 78.7045 | 2.58779 | ||||||||
\(926\) | −33.6373 | −1.10539 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.45860 | 0.0478808 | ||||||||
\(929\) | 25.6824 | 0.842614 | 0.421307 | − | 0.906918i | \(-0.361572\pi\) | ||||
0.421307 | + | 0.906918i | \(0.361572\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.66345 | 0.120065 | ||||||||
\(932\) | −2.56423 | −0.0839941 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −30.1020 | −0.984967 | ||||||||
\(935\) | −61.0860 | −1.99773 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.5910 | 1.03203 | 0.516017 | − | 0.856579i | \(-0.327414\pi\) | ||||
0.516017 | + | 0.856579i | \(0.327414\pi\) | |||||||
\(938\) | 7.15981 | 0.233776 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.17104 | −0.201277 | ||||||||
\(941\) | 11.2334 | 0.366197 | 0.183099 | − | 0.983095i | \(-0.441387\pi\) | ||||
0.183099 | + | 0.983095i | \(0.441387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.61975 | −0.0853109 | ||||||||
\(944\) | 26.1800 | 0.852088 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −52.1554 | −1.69572 | ||||||||
\(947\) | −3.53968 | −0.115024 | −0.0575120 | − | 0.998345i | \(-0.518317\pi\) | ||||
−0.0575120 | + | 0.998345i | \(0.518317\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.2401 | 1.43609 | ||||||||
\(950\) | −103.609 | −3.36152 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −26.6483 | −0.863676 | ||||||||
\(953\) | 19.3911 | 0.628139 | 0.314070 | − | 0.949400i | \(-0.398307\pi\) | ||||
0.314070 | + | 0.949400i | \(0.398307\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.8496 | −0.609960 | ||||||||
\(956\) | 2.58528 | 0.0836138 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 57.3584 | 1.85317 | ||||||||
\(959\) | −55.5368 | −1.79338 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.4715 | 1.66037 | ||||||||
\(962\) | 55.5051 | 1.78956 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.80692 | −0.0581970 | ||||||||
\(965\) | 61.0916 | 1.96661 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.7607 | −0.828409 | −0.414204 | − | 0.910184i | \(-0.635940\pi\) | ||||
−0.414204 | + | 0.910184i | \(0.635940\pi\) | |||||||
\(968\) | 29.4277 | 0.945841 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.2843 | −0.394424 | ||||||||
\(971\) | 1.98623 | 0.0637411 | 0.0318706 | − | 0.999492i | \(-0.489854\pi\) | ||||
0.0318706 | + | 0.999492i | \(0.489854\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.5918 | −0.788377 | ||||||||
\(974\) | 1.41772 | 0.0454268 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.8313 | −0.570766 | ||||||||
\(977\) | −62.0767 | −1.98601 | −0.993004 | − | 0.118080i | \(-0.962326\pi\) | ||||
−0.993004 | + | 0.118080i | \(0.962326\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.4672 | −0.430413 | ||||||||
\(980\) | −0.592443 | −0.0189249 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.4030 | 0.523441 | ||||||||
\(983\) | −10.1811 | −0.324726 | −0.162363 | − | 0.986731i | \(-0.551912\pi\) | ||||
−0.162363 | + | 0.986731i | \(0.551912\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 69.1401 | 2.20299 | ||||||||
\(986\) | 4.29064 | 0.136642 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.8971 | 0.346684 | ||||||||
\(989\) | 8.65344 | 0.275163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.7804 | 1.20013 | 0.600067 | − | 0.799950i | \(-0.295141\pi\) | ||||
0.600067 | + | 0.799950i | \(0.295141\pi\) | |||||||
\(992\) | 13.2461 | 0.420563 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.8676 | 0.535008 | ||||||||
\(995\) | 43.8670 | 1.39068 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58.3762 | −1.84879 | −0.924396 | − | 0.381435i | \(-0.875430\pi\) | ||||
−0.924396 | + | 0.381435i | \(0.875430\pi\) | |||||||
\(998\) | 9.83583 | 0.311348 | ||||||||
\(999\) | 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 | 6003.2.a.l.1.4 | 10 | ||
3.2 | odd | 2 | 667.2.a.a.1.7 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.a.1.7 | ✓ | 10 | 3.2 | odd | 2 | ||
6003.2.a.l.1.4 | 10 | 1.1 | even | 1 | trivial |