Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2738,2,Mod(1,2738)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2738, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2738.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2738.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: | \(21.8630400734\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 8 x^{17} - 8 x^{16} + 209 x^{15} - 253 x^{14} - 1996 x^{13} + 4196 x^{12} + 8667 x^{11} + \cdots + 113 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.26200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2738.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.771034 | −0.445156 | −0.222578 | − | 0.974915i | \(-0.571447\pi\) | ||||
−0.222578 | + | 0.974915i | \(0.571447\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.437041 | −0.195451 | −0.0977253 | − | 0.995213i | \(-0.531157\pi\) | ||||
−0.0977253 | + | 0.995213i | \(0.531157\pi\) | |||||||
\(6\) | −0.771034 | −0.314773 | ||||||||
\(7\) | −4.61128 | −1.74290 | −0.871451 | − | 0.490483i | \(-0.836820\pi\) | ||||
−0.871451 | + | 0.490483i | \(0.836820\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.40551 | −0.801836 | ||||||||
\(10\) | −0.437041 | −0.138204 | ||||||||
\(11\) | −1.80283 | −0.543574 | −0.271787 | − | 0.962357i | \(-0.587615\pi\) | ||||
−0.271787 | + | 0.962357i | \(0.587615\pi\) | |||||||
\(12\) | −0.771034 | −0.222578 | ||||||||
\(13\) | 6.12279 | 1.69816 | 0.849078 | − | 0.528268i | \(-0.177158\pi\) | ||||
0.849078 | + | 0.528268i | \(0.177158\pi\) | |||||||
\(14\) | −4.61128 | −1.23242 | ||||||||
\(15\) | 0.336973 | 0.0870061 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.20519 | −0.534837 | −0.267418 | − | 0.963581i | \(-0.586171\pi\) | ||||
−0.267418 | + | 0.963581i | \(0.586171\pi\) | |||||||
\(18\) | −2.40551 | −0.566983 | ||||||||
\(19\) | 1.36293 | 0.312678 | 0.156339 | − | 0.987703i | \(-0.450031\pi\) | ||||
0.156339 | + | 0.987703i | \(0.450031\pi\) | |||||||
\(20\) | −0.437041 | −0.0977253 | ||||||||
\(21\) | 3.55545 | 0.775864 | ||||||||
\(22\) | −1.80283 | −0.384365 | ||||||||
\(23\) | −0.264734 | −0.0552009 | −0.0276004 | − | 0.999619i | \(-0.508787\pi\) | ||||
−0.0276004 | + | 0.999619i | \(0.508787\pi\) | |||||||
\(24\) | −0.771034 | −0.157387 | ||||||||
\(25\) | −4.80900 | −0.961799 | ||||||||
\(26\) | 6.12279 | 1.20078 | ||||||||
\(27\) | 4.16783 | 0.802099 | ||||||||
\(28\) | −4.61128 | −0.871451 | ||||||||
\(29\) | 5.46031 | 1.01395 | 0.506977 | − | 0.861959i | \(-0.330763\pi\) | ||||
0.506977 | + | 0.861959i | \(0.330763\pi\) | |||||||
\(30\) | 0.336973 | 0.0615226 | ||||||||
\(31\) | 6.80007 | 1.22133 | 0.610665 | − | 0.791889i | \(-0.290902\pi\) | ||||
0.610665 | + | 0.791889i | \(0.290902\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.39004 | 0.241975 | ||||||||
\(34\) | −2.20519 | −0.378187 | ||||||||
\(35\) | 2.01532 | 0.340651 | ||||||||
\(36\) | −2.40551 | −0.400918 | ||||||||
\(37\) | 0 | 0 | ||||||||
\(38\) | 1.36293 | 0.221097 | ||||||||
\(39\) | −4.72088 | −0.755945 | ||||||||
\(40\) | −0.437041 | −0.0691022 | ||||||||
\(41\) | −9.16526 | −1.43137 | −0.715687 | − | 0.698421i | \(-0.753886\pi\) | ||||
−0.715687 | + | 0.698421i | \(0.753886\pi\) | |||||||
\(42\) | 3.55545 | 0.548618 | ||||||||
\(43\) | 4.47531 | 0.682478 | 0.341239 | − | 0.939977i | \(-0.389153\pi\) | ||||
0.341239 | + | 0.939977i | \(0.389153\pi\) | |||||||
\(44\) | −1.80283 | −0.271787 | ||||||||
\(45\) | 1.05130 | 0.156719 | ||||||||
\(46\) | −0.264734 | −0.0390329 | ||||||||
\(47\) | 6.57080 | 0.958449 | 0.479225 | − | 0.877692i | \(-0.340918\pi\) | ||||
0.479225 | + | 0.877692i | \(0.340918\pi\) | |||||||
\(48\) | −0.771034 | −0.111289 | ||||||||
\(49\) | 14.2639 | 2.03770 | ||||||||
\(50\) | −4.80900 | −0.680095 | ||||||||
\(51\) | 1.70027 | 0.238086 | ||||||||
\(52\) | 6.12279 | 0.849078 | ||||||||
\(53\) | 8.81762 | 1.21119 | 0.605597 | − | 0.795772i | \(-0.292934\pi\) | ||||
0.605597 | + | 0.795772i | \(0.292934\pi\) | |||||||
\(54\) | 4.16783 | 0.567170 | ||||||||
\(55\) | 0.787910 | 0.106242 | ||||||||
\(56\) | −4.61128 | −0.616209 | ||||||||
\(57\) | −1.05087 | −0.139191 | ||||||||
\(58\) | 5.46031 | 0.716974 | ||||||||
\(59\) | −14.1979 | −1.84841 | −0.924204 | − | 0.381898i | \(-0.875270\pi\) | ||||
−0.924204 | + | 0.381898i | \(0.875270\pi\) | |||||||
\(60\) | 0.336973 | 0.0435030 | ||||||||
\(61\) | 3.60210 | 0.461201 | 0.230601 | − | 0.973049i | \(-0.425931\pi\) | ||||
0.230601 | + | 0.973049i | \(0.425931\pi\) | |||||||
\(62\) | 6.80007 | 0.863610 | ||||||||
\(63\) | 11.0925 | 1.39752 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.67591 | −0.331906 | ||||||||
\(66\) | 1.39004 | 0.171102 | ||||||||
\(67\) | 2.02599 | 0.247514 | 0.123757 | − | 0.992313i | \(-0.460506\pi\) | ||||
0.123757 | + | 0.992313i | \(0.460506\pi\) | |||||||
\(68\) | −2.20519 | −0.267418 | ||||||||
\(69\) | 0.204119 | 0.0245730 | ||||||||
\(70\) | 2.01532 | 0.240877 | ||||||||
\(71\) | 10.9636 | 1.30114 | 0.650568 | − | 0.759448i | \(-0.274531\pi\) | ||||
0.650568 | + | 0.759448i | \(0.274531\pi\) | |||||||
\(72\) | −2.40551 | −0.283492 | ||||||||
\(73\) | 7.17402 | 0.839656 | 0.419828 | − | 0.907604i | \(-0.362090\pi\) | ||||
0.419828 | + | 0.907604i | \(0.362090\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.70790 | 0.428151 | ||||||||
\(76\) | 1.36293 | 0.156339 | ||||||||
\(77\) | 8.31336 | 0.947395 | ||||||||
\(78\) | −4.72088 | −0.534534 | ||||||||
\(79\) | 12.0992 | 1.36127 | 0.680634 | − | 0.732624i | \(-0.261705\pi\) | ||||
0.680634 | + | 0.732624i | \(0.261705\pi\) | |||||||
\(80\) | −0.437041 | −0.0488626 | ||||||||
\(81\) | 4.00299 | 0.444776 | ||||||||
\(82\) | −9.16526 | −1.01213 | ||||||||
\(83\) | −8.24969 | −0.905521 | −0.452761 | − | 0.891632i | \(-0.649561\pi\) | ||||
−0.452761 | + | 0.891632i | \(0.649561\pi\) | |||||||
\(84\) | 3.55545 | 0.387932 | ||||||||
\(85\) | 0.963757 | 0.104534 | ||||||||
\(86\) | 4.47531 | 0.482585 | ||||||||
\(87\) | −4.21009 | −0.451369 | ||||||||
\(88\) | −1.80283 | −0.192182 | ||||||||
\(89\) | 17.7715 | 1.88377 | 0.941887 | − | 0.335930i | \(-0.109051\pi\) | ||||
0.941887 | + | 0.335930i | \(0.109051\pi\) | |||||||
\(90\) | 1.05130 | 0.110817 | ||||||||
\(91\) | −28.2339 | −2.95972 | ||||||||
\(92\) | −0.264734 | −0.0276004 | ||||||||
\(93\) | −5.24309 | −0.543683 | ||||||||
\(94\) | 6.57080 | 0.677726 | ||||||||
\(95\) | −0.595658 | −0.0611132 | ||||||||
\(96\) | −0.771034 | −0.0786933 | ||||||||
\(97\) | 4.11851 | 0.418171 | 0.209086 | − | 0.977897i | \(-0.432951\pi\) | ||||
0.209086 | + | 0.977897i | \(0.432951\pi\) | |||||||
\(98\) | 14.2639 | 1.44087 | ||||||||
\(99\) | 4.33672 | 0.435857 | ||||||||
\(100\) | −4.80900 | −0.480900 | ||||||||
\(101\) | 2.18445 | 0.217361 | 0.108680 | − | 0.994077i | \(-0.465338\pi\) | ||||
0.108680 | + | 0.994077i | \(0.465338\pi\) | |||||||
\(102\) | 1.70027 | 0.168352 | ||||||||
\(103\) | −6.49235 | −0.639710 | −0.319855 | − | 0.947466i | \(-0.603634\pi\) | ||||
−0.319855 | + | 0.947466i | \(0.603634\pi\) | |||||||
\(104\) | 6.12279 | 0.600389 | ||||||||
\(105\) | −1.55388 | −0.151643 | ||||||||
\(106\) | 8.81762 | 0.856443 | ||||||||
\(107\) | −13.5439 | −1.30934 | −0.654668 | − | 0.755917i | \(-0.727191\pi\) | ||||
−0.654668 | + | 0.755917i | \(0.727191\pi\) | |||||||
\(108\) | 4.16783 | 0.401049 | ||||||||
\(109\) | 14.7429 | 1.41211 | 0.706056 | − | 0.708156i | \(-0.250473\pi\) | ||||
0.706056 | + | 0.708156i | \(0.250473\pi\) | |||||||
\(110\) | 0.787910 | 0.0751243 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.61128 | −0.435725 | ||||||||
\(113\) | 4.86809 | 0.457951 | 0.228976 | − | 0.973432i | \(-0.426462\pi\) | ||||
0.228976 | + | 0.973432i | \(0.426462\pi\) | |||||||
\(114\) | −1.05087 | −0.0984228 | ||||||||
\(115\) | 0.115700 | 0.0107890 | ||||||||
\(116\) | 5.46031 | 0.506977 | ||||||||
\(117\) | −14.7284 | −1.36164 | ||||||||
\(118\) | −14.1979 | −1.30702 | ||||||||
\(119\) | 10.1687 | 0.932168 | ||||||||
\(120\) | 0.336973 | 0.0307613 | ||||||||
\(121\) | −7.74980 | −0.704528 | ||||||||
\(122\) | 3.60210 | 0.326118 | ||||||||
\(123\) | 7.06673 | 0.637185 | ||||||||
\(124\) | 6.80007 | 0.610665 | ||||||||
\(125\) | 4.28693 | 0.383435 | ||||||||
\(126\) | 11.0925 | 0.988196 | ||||||||
\(127\) | 15.2205 | 1.35060 | 0.675299 | − | 0.737544i | \(-0.264014\pi\) | ||||
0.675299 | + | 0.737544i | \(0.264014\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.45061 | −0.303810 | ||||||||
\(130\) | −2.67591 | −0.234693 | ||||||||
\(131\) | −2.37982 | −0.207926 | −0.103963 | − | 0.994581i | \(-0.533152\pi\) | ||||
−0.103963 | + | 0.994581i | \(0.533152\pi\) | |||||||
\(132\) | 1.39004 | 0.120988 | ||||||||
\(133\) | −6.28487 | −0.544968 | ||||||||
\(134\) | 2.02599 | 0.175019 | ||||||||
\(135\) | −1.82151 | −0.156771 | ||||||||
\(136\) | −2.20519 | −0.189093 | ||||||||
\(137\) | 6.29894 | 0.538155 | 0.269077 | − | 0.963119i | \(-0.413281\pi\) | ||||
0.269077 | + | 0.963119i | \(0.413281\pi\) | |||||||
\(138\) | 0.204119 | 0.0173758 | ||||||||
\(139\) | −6.29845 | −0.534228 | −0.267114 | − | 0.963665i | \(-0.586070\pi\) | ||||
−0.267114 | + | 0.963665i | \(0.586070\pi\) | |||||||
\(140\) | 2.01532 | 0.170326 | ||||||||
\(141\) | −5.06630 | −0.426660 | ||||||||
\(142\) | 10.9636 | 0.920042 | ||||||||
\(143\) | −11.0383 | −0.923073 | ||||||||
\(144\) | −2.40551 | −0.200459 | ||||||||
\(145\) | −2.38638 | −0.198178 | ||||||||
\(146\) | 7.17402 | 0.593726 | ||||||||
\(147\) | −10.9980 | −0.907097 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.4374 | 1.75622 | 0.878109 | − | 0.478461i | \(-0.158805\pi\) | ||||
0.878109 | + | 0.478461i | \(0.158805\pi\) | |||||||
\(150\) | 3.70790 | 0.302749 | ||||||||
\(151\) | −14.8068 | −1.20496 | −0.602480 | − | 0.798134i | \(-0.705821\pi\) | ||||
−0.602480 | + | 0.798134i | \(0.705821\pi\) | |||||||
\(152\) | 1.36293 | 0.110549 | ||||||||
\(153\) | 5.30460 | 0.428851 | ||||||||
\(154\) | 8.31336 | 0.669910 | ||||||||
\(155\) | −2.97191 | −0.238710 | ||||||||
\(156\) | −4.72088 | −0.377973 | ||||||||
\(157\) | 13.8800 | 1.10774 | 0.553871 | − | 0.832602i | \(-0.313150\pi\) | ||||
0.553871 | + | 0.832602i | \(0.313150\pi\) | |||||||
\(158\) | 12.0992 | 0.962561 | ||||||||
\(159\) | −6.79868 | −0.539171 | ||||||||
\(160\) | −0.437041 | −0.0345511 | ||||||||
\(161\) | 1.22076 | 0.0962097 | ||||||||
\(162\) | 4.00299 | 0.314504 | ||||||||
\(163\) | −18.8499 | −1.47644 | −0.738218 | − | 0.674562i | \(-0.764332\pi\) | ||||
−0.738218 | + | 0.674562i | \(0.764332\pi\) | |||||||
\(164\) | −9.16526 | −0.715687 | ||||||||
\(165\) | −0.607505 | −0.0472942 | ||||||||
\(166\) | −8.24969 | −0.640300 | ||||||||
\(167\) | −8.01091 | −0.619903 | −0.309952 | − | 0.950752i | \(-0.600313\pi\) | ||||
−0.309952 | + | 0.950752i | \(0.600313\pi\) | |||||||
\(168\) | 3.55545 | 0.274309 | ||||||||
\(169\) | 24.4885 | 1.88373 | ||||||||
\(170\) | 0.963757 | 0.0739168 | ||||||||
\(171\) | −3.27855 | −0.250717 | ||||||||
\(172\) | 4.47531 | 0.341239 | ||||||||
\(173\) | −23.7768 | −1.80772 | −0.903860 | − | 0.427829i | \(-0.859279\pi\) | ||||
−0.903860 | + | 0.427829i | \(0.859279\pi\) | |||||||
\(174\) | −4.21009 | −0.319166 | ||||||||
\(175\) | 22.1756 | 1.67632 | ||||||||
\(176\) | −1.80283 | −0.135893 | ||||||||
\(177\) | 10.9471 | 0.822831 | ||||||||
\(178\) | 17.7715 | 1.33203 | ||||||||
\(179\) | 3.46205 | 0.258766 | 0.129383 | − | 0.991595i | \(-0.458700\pi\) | ||||
0.129383 | + | 0.991595i | \(0.458700\pi\) | |||||||
\(180\) | 1.05130 | 0.0783596 | ||||||||
\(181\) | −4.92424 | −0.366016 | −0.183008 | − | 0.983111i | \(-0.558583\pi\) | ||||
−0.183008 | + | 0.983111i | \(0.558583\pi\) | |||||||
\(182\) | −28.2339 | −2.09284 | ||||||||
\(183\) | −2.77734 | −0.205307 | ||||||||
\(184\) | −0.264734 | −0.0195165 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.24309 | −0.384442 | ||||||||
\(187\) | 3.97558 | 0.290723 | ||||||||
\(188\) | 6.57080 | 0.479225 | ||||||||
\(189\) | −19.2190 | −1.39798 | ||||||||
\(190\) | −0.595658 | −0.0432135 | ||||||||
\(191\) | −19.2951 | −1.39615 | −0.698074 | − | 0.716026i | \(-0.745959\pi\) | ||||
−0.698074 | + | 0.716026i | \(0.745959\pi\) | |||||||
\(192\) | −0.771034 | −0.0556446 | ||||||||
\(193\) | 2.85313 | 0.205373 | 0.102686 | − | 0.994714i | \(-0.467256\pi\) | ||||
0.102686 | + | 0.994714i | \(0.467256\pi\) | |||||||
\(194\) | 4.11851 | 0.295692 | ||||||||
\(195\) | 2.06322 | 0.147750 | ||||||||
\(196\) | 14.2639 | 1.01885 | ||||||||
\(197\) | −4.47251 | −0.318653 | −0.159326 | − | 0.987226i | \(-0.550932\pi\) | ||||
−0.159326 | + | 0.987226i | \(0.550932\pi\) | |||||||
\(198\) | 4.33672 | 0.308197 | ||||||||
\(199\) | −8.01075 | −0.567867 | −0.283933 | − | 0.958844i | \(-0.591639\pi\) | ||||
−0.283933 | + | 0.958844i | \(0.591639\pi\) | |||||||
\(200\) | −4.80900 | −0.340047 | ||||||||
\(201\) | −1.56210 | −0.110182 | ||||||||
\(202\) | 2.18445 | 0.153697 | ||||||||
\(203\) | −25.1791 | −1.76722 | ||||||||
\(204\) | 1.70027 | 0.119043 | ||||||||
\(205\) | 4.00559 | 0.279763 | ||||||||
\(206\) | −6.49235 | −0.452343 | ||||||||
\(207\) | 0.636820 | 0.0442620 | ||||||||
\(208\) | 6.12279 | 0.424539 | ||||||||
\(209\) | −2.45714 | −0.169964 | ||||||||
\(210\) | −1.55388 | −0.107228 | ||||||||
\(211\) | −8.39000 | −0.577591 | −0.288796 | − | 0.957391i | \(-0.593255\pi\) | ||||
−0.288796 | + | 0.957391i | \(0.593255\pi\) | |||||||
\(212\) | 8.81762 | 0.605597 | ||||||||
\(213\) | −8.45328 | −0.579209 | ||||||||
\(214\) | −13.5439 | −0.925840 | ||||||||
\(215\) | −1.95589 | −0.133391 | ||||||||
\(216\) | 4.16783 | 0.283585 | ||||||||
\(217\) | −31.3571 | −2.12866 | ||||||||
\(218\) | 14.7429 | 0.998514 | ||||||||
\(219\) | −5.53141 | −0.373778 | ||||||||
\(220\) | 0.787910 | 0.0531209 | ||||||||
\(221\) | −13.5019 | −0.908236 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.8715 | 0.995869 | 0.497935 | − | 0.867215i | \(-0.334092\pi\) | ||||
0.497935 | + | 0.867215i | \(0.334092\pi\) | |||||||
\(224\) | −4.61128 | −0.308104 | ||||||||
\(225\) | 11.5681 | 0.771205 | ||||||||
\(226\) | 4.86809 | 0.323821 | ||||||||
\(227\) | −10.0974 | −0.670187 | −0.335093 | − | 0.942185i | \(-0.608768\pi\) | ||||
−0.335093 | + | 0.942185i | \(0.608768\pi\) | |||||||
\(228\) | −1.05087 | −0.0695954 | ||||||||
\(229\) | 1.50284 | 0.0993102 | 0.0496551 | − | 0.998766i | \(-0.484188\pi\) | ||||
0.0496551 | + | 0.998766i | \(0.484188\pi\) | |||||||
\(230\) | 0.115700 | 0.00762901 | ||||||||
\(231\) | −6.40988 | −0.421739 | ||||||||
\(232\) | 5.46031 | 0.358487 | ||||||||
\(233\) | −3.35874 | −0.220038 | −0.110019 | − | 0.993929i | \(-0.535091\pi\) | ||||
−0.110019 | + | 0.993929i | \(0.535091\pi\) | |||||||
\(234\) | −14.7284 | −0.962826 | ||||||||
\(235\) | −2.87171 | −0.187329 | ||||||||
\(236\) | −14.1979 | −0.924204 | ||||||||
\(237\) | −9.32890 | −0.605977 | ||||||||
\(238\) | 10.1687 | 0.659142 | ||||||||
\(239\) | −5.36999 | −0.347356 | −0.173678 | − | 0.984803i | \(-0.555565\pi\) | ||||
−0.173678 | + | 0.984803i | \(0.555565\pi\) | |||||||
\(240\) | 0.336973 | 0.0217515 | ||||||||
\(241\) | 6.94226 | 0.447190 | 0.223595 | − | 0.974682i | \(-0.428221\pi\) | ||||
0.223595 | + | 0.974682i | \(0.428221\pi\) | |||||||
\(242\) | −7.74980 | −0.498176 | ||||||||
\(243\) | −15.5899 | −1.00009 | ||||||||
\(244\) | 3.60210 | 0.230601 | ||||||||
\(245\) | −6.23392 | −0.398270 | ||||||||
\(246\) | 7.06673 | 0.450558 | ||||||||
\(247\) | 8.34495 | 0.530977 | ||||||||
\(248\) | 6.80007 | 0.431805 | ||||||||
\(249\) | 6.36079 | 0.403099 | ||||||||
\(250\) | 4.28693 | 0.271129 | ||||||||
\(251\) | 15.7593 | 0.994715 | 0.497358 | − | 0.867546i | \(-0.334304\pi\) | ||||
0.497358 | + | 0.867546i | \(0.334304\pi\) | |||||||
\(252\) | 11.0925 | 0.698760 | ||||||||
\(253\) | 0.477271 | 0.0300057 | ||||||||
\(254\) | 15.2205 | 0.955018 | ||||||||
\(255\) | −0.743089 | −0.0465341 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.4828 | 1.15292 | 0.576461 | − | 0.817124i | \(-0.304433\pi\) | ||||
0.576461 | + | 0.817124i | \(0.304433\pi\) | |||||||
\(258\) | −3.45061 | −0.214826 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2.67591 | −0.165953 | ||||||||
\(261\) | −13.1348 | −0.813025 | ||||||||
\(262\) | −2.37982 | −0.147026 | ||||||||
\(263\) | 14.0173 | 0.864341 | 0.432171 | − | 0.901792i | \(-0.357748\pi\) | ||||
0.432171 | + | 0.901792i | \(0.357748\pi\) | |||||||
\(264\) | 1.39004 | 0.0855512 | ||||||||
\(265\) | −3.85366 | −0.236728 | ||||||||
\(266\) | −6.28487 | −0.385350 | ||||||||
\(267\) | −13.7024 | −0.838574 | ||||||||
\(268\) | 2.02599 | 0.123757 | ||||||||
\(269\) | 5.92245 | 0.361098 | 0.180549 | − | 0.983566i | \(-0.442213\pi\) | ||||
0.180549 | + | 0.983566i | \(0.442213\pi\) | |||||||
\(270\) | −1.82151 | −0.110854 | ||||||||
\(271\) | 0.657318 | 0.0399292 | 0.0199646 | − | 0.999801i | \(-0.493645\pi\) | ||||
0.0199646 | + | 0.999801i | \(0.493645\pi\) | |||||||
\(272\) | −2.20519 | −0.133709 | ||||||||
\(273\) | 21.7693 | 1.31754 | ||||||||
\(274\) | 6.29894 | 0.380533 | ||||||||
\(275\) | 8.66980 | 0.522809 | ||||||||
\(276\) | 0.204119 | 0.0122865 | ||||||||
\(277\) | 13.7460 | 0.825915 | 0.412958 | − | 0.910750i | \(-0.364496\pi\) | ||||
0.412958 | + | 0.910750i | \(0.364496\pi\) | |||||||
\(278\) | −6.29845 | −0.377756 | ||||||||
\(279\) | −16.3576 | −0.979305 | ||||||||
\(280\) | 2.01532 | 0.120438 | ||||||||
\(281\) | 18.0634 | 1.07757 | 0.538787 | − | 0.842442i | \(-0.318883\pi\) | ||||
0.538787 | + | 0.842442i | \(0.318883\pi\) | |||||||
\(282\) | −5.06630 | −0.301694 | ||||||||
\(283\) | 2.66354 | 0.158331 | 0.0791656 | − | 0.996861i | \(-0.474774\pi\) | ||||
0.0791656 | + | 0.996861i | \(0.474774\pi\) | |||||||
\(284\) | 10.9636 | 0.650568 | ||||||||
\(285\) | 0.459272 | 0.0272049 | ||||||||
\(286\) | −11.0383 | −0.652711 | ||||||||
\(287\) | 42.2636 | 2.49474 | ||||||||
\(288\) | −2.40551 | −0.141746 | ||||||||
\(289\) | −12.1371 | −0.713950 | ||||||||
\(290\) | −2.38638 | −0.140133 | ||||||||
\(291\) | −3.17551 | −0.186152 | ||||||||
\(292\) | 7.17402 | 0.419828 | ||||||||
\(293\) | 18.2161 | 1.06420 | 0.532098 | − | 0.846683i | \(-0.321404\pi\) | ||||
0.532098 | + | 0.846683i | \(0.321404\pi\) | |||||||
\(294\) | −10.9980 | −0.641415 | ||||||||
\(295\) | 6.20506 | 0.361273 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.51389 | −0.436000 | ||||||||
\(298\) | 21.4374 | 1.24183 | ||||||||
\(299\) | −1.62091 | −0.0937397 | ||||||||
\(300\) | 3.70790 | 0.214076 | ||||||||
\(301\) | −20.6369 | −1.18949 | ||||||||
\(302\) | −14.8068 | −0.852036 | ||||||||
\(303\) | −1.68428 | −0.0967595 | ||||||||
\(304\) | 1.36293 | 0.0781696 | ||||||||
\(305\) | −1.57426 | −0.0901420 | ||||||||
\(306\) | 5.30460 | 0.303244 | ||||||||
\(307\) | 9.72722 | 0.555162 | 0.277581 | − | 0.960702i | \(-0.410467\pi\) | ||||
0.277581 | + | 0.960702i | \(0.410467\pi\) | |||||||
\(308\) | 8.31336 | 0.473698 | ||||||||
\(309\) | 5.00582 | 0.284771 | ||||||||
\(310\) | −2.97191 | −0.168793 | ||||||||
\(311\) | 15.8511 | 0.898832 | 0.449416 | − | 0.893323i | \(-0.351632\pi\) | ||||
0.449416 | + | 0.893323i | \(0.351632\pi\) | |||||||
\(312\) | −4.72088 | −0.267267 | ||||||||
\(313\) | 0.512343 | 0.0289594 | 0.0144797 | − | 0.999895i | \(-0.495391\pi\) | ||||
0.0144797 | + | 0.999895i | \(0.495391\pi\) | |||||||
\(314\) | 13.8800 | 0.783293 | ||||||||
\(315\) | −4.84786 | −0.273146 | ||||||||
\(316\) | 12.0992 | 0.680634 | ||||||||
\(317\) | −27.6762 | −1.55445 | −0.777225 | − | 0.629223i | \(-0.783373\pi\) | ||||
−0.777225 | + | 0.629223i | \(0.783373\pi\) | |||||||
\(318\) | −6.79868 | −0.381251 | ||||||||
\(319\) | −9.84402 | −0.551159 | ||||||||
\(320\) | −0.437041 | −0.0244313 | ||||||||
\(321\) | 10.4428 | 0.582859 | ||||||||
\(322\) | 1.22076 | 0.0680305 | ||||||||
\(323\) | −3.00553 | −0.167232 | ||||||||
\(324\) | 4.00299 | 0.222388 | ||||||||
\(325\) | −29.4445 | −1.63328 | ||||||||
\(326\) | −18.8499 | −1.04400 | ||||||||
\(327\) | −11.3673 | −0.628611 | ||||||||
\(328\) | −9.16526 | −0.506067 | ||||||||
\(329\) | −30.2998 | −1.67048 | ||||||||
\(330\) | −0.607505 | −0.0334421 | ||||||||
\(331\) | −14.1583 | −0.778212 | −0.389106 | − | 0.921193i | \(-0.627216\pi\) | ||||
−0.389106 | + | 0.921193i | \(0.627216\pi\) | |||||||
\(332\) | −8.24969 | −0.452761 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.01091 | −0.438338 | ||||||||
\(335\) | −0.885439 | −0.0483767 | ||||||||
\(336\) | 3.55545 | 0.193966 | ||||||||
\(337\) | 16.6632 | 0.907700 | 0.453850 | − | 0.891078i | \(-0.350050\pi\) | ||||
0.453850 | + | 0.891078i | \(0.350050\pi\) | |||||||
\(338\) | 24.4885 | 1.33200 | ||||||||
\(339\) | −3.75346 | −0.203860 | ||||||||
\(340\) | 0.963757 | 0.0522671 | ||||||||
\(341\) | −12.2594 | −0.663883 | ||||||||
\(342\) | −3.27855 | −0.177283 | ||||||||
\(343\) | −33.4960 | −1.80862 | ||||||||
\(344\) | 4.47531 | 0.241292 | ||||||||
\(345\) | −0.0892083 | −0.00480281 | ||||||||
\(346\) | −23.7768 | −1.27825 | ||||||||
\(347\) | 18.7895 | 1.00867 | 0.504336 | − | 0.863508i | \(-0.331737\pi\) | ||||
0.504336 | + | 0.863508i | \(0.331737\pi\) | |||||||
\(348\) | −4.21009 | −0.225684 | ||||||||
\(349\) | 14.2446 | 0.762497 | 0.381248 | − | 0.924473i | \(-0.375494\pi\) | ||||
0.381248 | + | 0.924473i | \(0.375494\pi\) | |||||||
\(350\) | 22.1756 | 1.18534 | ||||||||
\(351\) | 25.5187 | 1.36209 | ||||||||
\(352\) | −1.80283 | −0.0960912 | ||||||||
\(353\) | −2.57698 | −0.137159 | −0.0685793 | − | 0.997646i | \(-0.521847\pi\) | ||||
−0.0685793 | + | 0.997646i | \(0.521847\pi\) | |||||||
\(354\) | 10.9471 | 0.581829 | ||||||||
\(355\) | −4.79153 | −0.254308 | ||||||||
\(356\) | 17.7715 | 0.941887 | ||||||||
\(357\) | −7.84045 | −0.414960 | ||||||||
\(358\) | 3.46205 | 0.182975 | ||||||||
\(359\) | −18.3888 | −0.970525 | −0.485263 | − | 0.874368i | \(-0.661276\pi\) | ||||
−0.485263 | + | 0.874368i | \(0.661276\pi\) | |||||||
\(360\) | 1.05130 | 0.0554086 | ||||||||
\(361\) | −17.1424 | −0.902232 | ||||||||
\(362\) | −4.92424 | −0.258812 | ||||||||
\(363\) | 5.97536 | 0.313625 | ||||||||
\(364\) | −28.2339 | −1.47986 | ||||||||
\(365\) | −3.13534 | −0.164111 | ||||||||
\(366\) | −2.77734 | −0.145174 | ||||||||
\(367\) | 22.0762 | 1.15237 | 0.576184 | − | 0.817320i | \(-0.304541\pi\) | ||||
0.576184 | + | 0.817320i | \(0.304541\pi\) | |||||||
\(368\) | −0.264734 | −0.0138002 | ||||||||
\(369\) | 22.0471 | 1.14773 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −40.6605 | −2.11099 | ||||||||
\(372\) | −5.24309 | −0.271841 | ||||||||
\(373\) | 28.7986 | 1.49114 | 0.745568 | − | 0.666429i | \(-0.232178\pi\) | ||||
0.745568 | + | 0.666429i | \(0.232178\pi\) | |||||||
\(374\) | 3.97558 | 0.205572 | ||||||||
\(375\) | −3.30537 | −0.170688 | ||||||||
\(376\) | 6.57080 | 0.338863 | ||||||||
\(377\) | 33.4324 | 1.72185 | ||||||||
\(378\) | −19.2190 | −0.988520 | ||||||||
\(379\) | 8.26297 | 0.424440 | 0.212220 | − | 0.977222i | \(-0.431931\pi\) | ||||
0.212220 | + | 0.977222i | \(0.431931\pi\) | |||||||
\(380\) | −0.595658 | −0.0305566 | ||||||||
\(381\) | −11.7355 | −0.601228 | ||||||||
\(382\) | −19.2951 | −0.987226 | ||||||||
\(383\) | 1.97274 | 0.100802 | 0.0504012 | − | 0.998729i | \(-0.483950\pi\) | ||||
0.0504012 | + | 0.998729i | \(0.483950\pi\) | |||||||
\(384\) | −0.771034 | −0.0393466 | ||||||||
\(385\) | −3.63328 | −0.185169 | ||||||||
\(386\) | 2.85313 | 0.145221 | ||||||||
\(387\) | −10.7654 | −0.547235 | ||||||||
\(388\) | 4.11851 | 0.209086 | ||||||||
\(389\) | −4.87551 | −0.247198 | −0.123599 | − | 0.992332i | \(-0.539444\pi\) | ||||
−0.123599 | + | 0.992332i | \(0.539444\pi\) | |||||||
\(390\) | 2.06322 | 0.104475 | ||||||||
\(391\) | 0.583789 | 0.0295235 | ||||||||
\(392\) | 14.2639 | 0.720437 | ||||||||
\(393\) | 1.83492 | 0.0925595 | ||||||||
\(394\) | −4.47251 | −0.225322 | ||||||||
\(395\) | −5.28785 | −0.266060 | ||||||||
\(396\) | 4.33672 | 0.217928 | ||||||||
\(397\) | −5.51844 | −0.276963 | −0.138481 | − | 0.990365i | \(-0.544222\pi\) | ||||
−0.138481 | + | 0.990365i | \(0.544222\pi\) | |||||||
\(398\) | −8.01075 | −0.401543 | ||||||||
\(399\) | 4.84585 | 0.242596 | ||||||||
\(400\) | −4.80900 | −0.240450 | ||||||||
\(401\) | 37.9560 | 1.89543 | 0.947716 | − | 0.319115i | \(-0.103386\pi\) | ||||
0.947716 | + | 0.319115i | \(0.103386\pi\) | |||||||
\(402\) | −1.56210 | −0.0779107 | ||||||||
\(403\) | 41.6354 | 2.07401 | ||||||||
\(404\) | 2.18445 | 0.108680 | ||||||||
\(405\) | −1.74947 | −0.0869318 | ||||||||
\(406\) | −25.1791 | −1.24962 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.70027 | 0.0841761 | ||||||||
\(409\) | −6.62852 | −0.327759 | −0.163880 | − | 0.986480i | \(-0.552401\pi\) | ||||
−0.163880 | + | 0.986480i | \(0.552401\pi\) | |||||||
\(410\) | 4.00559 | 0.197822 | ||||||||
\(411\) | −4.85669 | −0.239563 | ||||||||
\(412\) | −6.49235 | −0.319855 | ||||||||
\(413\) | 65.4705 | 3.22159 | ||||||||
\(414\) | 0.636820 | 0.0312980 | ||||||||
\(415\) | 3.60545 | 0.176985 | ||||||||
\(416\) | 6.12279 | 0.300194 | ||||||||
\(417\) | 4.85632 | 0.237815 | ||||||||
\(418\) | −2.45714 | −0.120183 | ||||||||
\(419\) | 10.5288 | 0.514365 | 0.257183 | − | 0.966363i | \(-0.417206\pi\) | ||||
0.257183 | + | 0.966363i | \(0.417206\pi\) | |||||||
\(420\) | −1.55388 | −0.0758215 | ||||||||
\(421\) | −17.2148 | −0.838999 | −0.419499 | − | 0.907756i | \(-0.637794\pi\) | ||||
−0.419499 | + | 0.907756i | \(0.637794\pi\) | |||||||
\(422\) | −8.39000 | −0.408419 | ||||||||
\(423\) | −15.8061 | −0.768519 | ||||||||
\(424\) | 8.81762 | 0.428222 | ||||||||
\(425\) | 10.6047 | 0.514406 | ||||||||
\(426\) | −8.45328 | −0.409563 | ||||||||
\(427\) | −16.6103 | −0.803828 | ||||||||
\(428\) | −13.5439 | −0.654668 | ||||||||
\(429\) | 8.51094 | 0.410912 | ||||||||
\(430\) | −1.95589 | −0.0943215 | ||||||||
\(431\) | −38.3116 | −1.84541 | −0.922703 | − | 0.385511i | \(-0.874025\pi\) | ||||
−0.922703 | + | 0.385511i | \(0.874025\pi\) | |||||||
\(432\) | 4.16783 | 0.200525 | ||||||||
\(433\) | −18.6148 | −0.894571 | −0.447285 | − | 0.894391i | \(-0.647609\pi\) | ||||
−0.447285 | + | 0.894391i | \(0.647609\pi\) | |||||||
\(434\) | −31.3571 | −1.50519 | ||||||||
\(435\) | 1.83998 | 0.0882203 | ||||||||
\(436\) | 14.7429 | 0.706056 | ||||||||
\(437\) | −0.360815 | −0.0172601 | ||||||||
\(438\) | −5.53141 | −0.264301 | ||||||||
\(439\) | 10.0078 | 0.477645 | 0.238822 | − | 0.971063i | \(-0.423239\pi\) | ||||
0.238822 | + | 0.971063i | \(0.423239\pi\) | |||||||
\(440\) | 0.787910 | 0.0375621 | ||||||||
\(441\) | −34.3120 | −1.63390 | ||||||||
\(442\) | −13.5019 | −0.642220 | ||||||||
\(443\) | 28.9727 | 1.37654 | 0.688268 | − | 0.725457i | \(-0.258371\pi\) | ||||
0.688268 | + | 0.725457i | \(0.258371\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.76687 | −0.368185 | ||||||||
\(446\) | 14.8715 | 0.704186 | ||||||||
\(447\) | −16.5289 | −0.781792 | ||||||||
\(448\) | −4.61128 | −0.217863 | ||||||||
\(449\) | −9.39644 | −0.443445 | −0.221723 | − | 0.975110i | \(-0.571168\pi\) | ||||
−0.221723 | + | 0.975110i | \(0.571168\pi\) | |||||||
\(450\) | 11.5681 | 0.545324 | ||||||||
\(451\) | 16.5234 | 0.778057 | ||||||||
\(452\) | 4.86809 | 0.228976 | ||||||||
\(453\) | 11.4165 | 0.536396 | ||||||||
\(454\) | −10.0974 | −0.473893 | ||||||||
\(455\) | 12.3394 | 0.578479 | ||||||||
\(456\) | −1.05087 | −0.0492114 | ||||||||
\(457\) | −27.0123 | −1.26358 | −0.631791 | − | 0.775139i | \(-0.717680\pi\) | ||||
−0.631791 | + | 0.775139i | \(0.717680\pi\) | |||||||
\(458\) | 1.50284 | 0.0702229 | ||||||||
\(459\) | −9.19085 | −0.428992 | ||||||||
\(460\) | 0.115700 | 0.00539452 | ||||||||
\(461\) | 27.6922 | 1.28976 | 0.644878 | − | 0.764286i | \(-0.276908\pi\) | ||||
0.644878 | + | 0.764286i | \(0.276908\pi\) | |||||||
\(462\) | −6.40988 | −0.298215 | ||||||||
\(463\) | 27.7284 | 1.28865 | 0.644323 | − | 0.764753i | \(-0.277139\pi\) | ||||
0.644323 | + | 0.764753i | \(0.277139\pi\) | |||||||
\(464\) | 5.46031 | 0.253489 | ||||||||
\(465\) | 2.29144 | 0.106263 | ||||||||
\(466\) | −3.35874 | −0.155590 | ||||||||
\(467\) | 5.72621 | 0.264978 | 0.132489 | − | 0.991185i | \(-0.457703\pi\) | ||||
0.132489 | + | 0.991185i | \(0.457703\pi\) | |||||||
\(468\) | −14.7284 | −0.680821 | ||||||||
\(469\) | −9.34240 | −0.431392 | ||||||||
\(470\) | −2.87171 | −0.132462 | ||||||||
\(471\) | −10.7019 | −0.493119 | ||||||||
\(472\) | −14.1979 | −0.653511 | ||||||||
\(473\) | −8.06822 | −0.370977 | ||||||||
\(474\) | −9.32890 | −0.428490 | ||||||||
\(475\) | −6.55434 | −0.300734 | ||||||||
\(476\) | 10.1687 | 0.466084 | ||||||||
\(477\) | −21.2109 | −0.971178 | ||||||||
\(478\) | −5.36999 | −0.245618 | ||||||||
\(479\) | 16.3598 | 0.747497 | 0.373748 | − | 0.927530i | \(-0.378072\pi\) | ||||
0.373748 | + | 0.927530i | \(0.378072\pi\) | |||||||
\(480\) | 0.336973 | 0.0153806 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.94226 | 0.316211 | ||||||||
\(483\) | −0.941250 | −0.0428284 | ||||||||
\(484\) | −7.74980 | −0.352264 | ||||||||
\(485\) | −1.79996 | −0.0817318 | ||||||||
\(486\) | −15.5899 | −0.707173 | ||||||||
\(487\) | −17.8331 | −0.808096 | −0.404048 | − | 0.914738i | \(-0.632397\pi\) | ||||
−0.404048 | + | 0.914738i | \(0.632397\pi\) | |||||||
\(488\) | 3.60210 | 0.163059 | ||||||||
\(489\) | 14.5339 | 0.657245 | ||||||||
\(490\) | −6.23392 | −0.281620 | ||||||||
\(491\) | −6.51454 | −0.293997 | −0.146999 | − | 0.989137i | \(-0.546961\pi\) | ||||
−0.146999 | + | 0.989137i | \(0.546961\pi\) | |||||||
\(492\) | 7.06673 | 0.318593 | ||||||||
\(493\) | −12.0410 | −0.542300 | ||||||||
\(494\) | 8.34495 | 0.375457 | ||||||||
\(495\) | −1.89532 | −0.0851885 | ||||||||
\(496\) | 6.80007 | 0.305332 | ||||||||
\(497\) | −50.5561 | −2.26775 | ||||||||
\(498\) | 6.36079 | 0.285034 | ||||||||
\(499\) | −2.43802 | −0.109141 | −0.0545705 | − | 0.998510i | \(-0.517379\pi\) | ||||
−0.0545705 | + | 0.998510i | \(0.517379\pi\) | |||||||
\(500\) | 4.28693 | 0.191717 | ||||||||
\(501\) | 6.17668 | 0.275954 | ||||||||
\(502\) | 15.7593 | 0.703370 | ||||||||
\(503\) | −2.80021 | −0.124855 | −0.0624275 | − | 0.998050i | \(-0.519884\pi\) | ||||
−0.0624275 | + | 0.998050i | \(0.519884\pi\) | |||||||
\(504\) | 11.0925 | 0.494098 | ||||||||
\(505\) | −0.954692 | −0.0424833 | ||||||||
\(506\) | 0.477271 | 0.0212173 | ||||||||
\(507\) | −18.8815 | −0.838556 | ||||||||
\(508\) | 15.2205 | 0.675299 | ||||||||
\(509\) | 16.7670 | 0.743184 | 0.371592 | − | 0.928396i | \(-0.378812\pi\) | ||||
0.371592 | + | 0.928396i | \(0.378812\pi\) | |||||||
\(510\) | −0.743089 | −0.0329045 | ||||||||
\(511\) | −33.0815 | −1.46344 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.68047 | 0.250799 | ||||||||
\(514\) | 18.4828 | 0.815239 | ||||||||
\(515\) | 2.83742 | 0.125032 | ||||||||
\(516\) | −3.45061 | −0.151905 | ||||||||
\(517\) | −11.8460 | −0.520988 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.3327 | 0.804718 | ||||||||
\(520\) | −2.67591 | −0.117346 | ||||||||
\(521\) | −28.4899 | −1.24816 | −0.624082 | − | 0.781359i | \(-0.714527\pi\) | ||||
−0.624082 | + | 0.781359i | \(0.714527\pi\) | |||||||
\(522\) | −13.1348 | −0.574896 | ||||||||
\(523\) | −29.5378 | −1.29160 | −0.645798 | − | 0.763508i | \(-0.723475\pi\) | ||||
−0.645798 | + | 0.763508i | \(0.723475\pi\) | |||||||
\(524\) | −2.37982 | −0.103963 | ||||||||
\(525\) | −17.0982 | −0.746225 | ||||||||
\(526\) | 14.0173 | 0.611181 | ||||||||
\(527\) | −14.9954 | −0.653212 | ||||||||
\(528\) | 1.39004 | 0.0604938 | ||||||||
\(529\) | −22.9299 | −0.996953 | ||||||||
\(530\) | −3.85366 | −0.167392 | ||||||||
\(531\) | 34.1531 | 1.48212 | ||||||||
\(532\) | −6.28487 | −0.272484 | ||||||||
\(533\) | −56.1170 | −2.43070 | ||||||||
\(534\) | −13.7024 | −0.592962 | ||||||||
\(535\) | 5.91922 | 0.255910 | ||||||||
\(536\) | 2.02599 | 0.0875093 | ||||||||
\(537\) | −2.66936 | −0.115191 | ||||||||
\(538\) | 5.92245 | 0.255335 | ||||||||
\(539\) | −25.7154 | −1.10764 | ||||||||
\(540\) | −1.82151 | −0.0783853 | ||||||||
\(541\) | −24.4083 | −1.04939 | −0.524697 | − | 0.851289i | \(-0.675822\pi\) | ||||
−0.524697 | + | 0.851289i | \(0.675822\pi\) | |||||||
\(542\) | 0.657318 | 0.0282342 | ||||||||
\(543\) | 3.79675 | 0.162934 | ||||||||
\(544\) | −2.20519 | −0.0945467 | ||||||||
\(545\) | −6.44324 | −0.275998 | ||||||||
\(546\) | 21.7693 | 0.931640 | ||||||||
\(547\) | 15.4314 | 0.659798 | 0.329899 | − | 0.944016i | \(-0.392985\pi\) | ||||
0.329899 | + | 0.944016i | \(0.392985\pi\) | |||||||
\(548\) | 6.29894 | 0.269077 | ||||||||
\(549\) | −8.66487 | −0.369807 | ||||||||
\(550\) | 8.66980 | 0.369682 | ||||||||
\(551\) | 7.44205 | 0.317042 | ||||||||
\(552\) | 0.204119 | 0.00868788 | ||||||||
\(553\) | −55.7929 | −2.37255 | ||||||||
\(554\) | 13.7460 | 0.584010 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.29845 | −0.267114 | ||||||||
\(557\) | −7.37862 | −0.312642 | −0.156321 | − | 0.987706i | \(-0.549963\pi\) | ||||
−0.156321 | + | 0.987706i | \(0.549963\pi\) | |||||||
\(558\) | −16.3576 | −0.692474 | ||||||||
\(559\) | 27.4014 | 1.15895 | ||||||||
\(560\) | 2.01532 | 0.0851628 | ||||||||
\(561\) | −3.06531 | −0.129417 | ||||||||
\(562\) | 18.0634 | 0.761959 | ||||||||
\(563\) | −12.6815 | −0.534462 | −0.267231 | − | 0.963632i | \(-0.586109\pi\) | ||||
−0.267231 | + | 0.963632i | \(0.586109\pi\) | |||||||
\(564\) | −5.06630 | −0.213330 | ||||||||
\(565\) | −2.12755 | −0.0895069 | ||||||||
\(566\) | 2.66354 | 0.111957 | ||||||||
\(567\) | −18.4589 | −0.775201 | ||||||||
\(568\) | 10.9636 | 0.460021 | ||||||||
\(569\) | −10.2519 | −0.429782 | −0.214891 | − | 0.976638i | \(-0.568940\pi\) | ||||
−0.214891 | + | 0.976638i | \(0.568940\pi\) | |||||||
\(570\) | 0.459272 | 0.0192368 | ||||||||
\(571\) | −40.6996 | −1.70322 | −0.851612 | − | 0.524172i | \(-0.824375\pi\) | ||||
−0.851612 | + | 0.524172i | \(0.824375\pi\) | |||||||
\(572\) | −11.0383 | −0.461536 | ||||||||
\(573\) | 14.8772 | 0.621504 | ||||||||
\(574\) | 42.2636 | 1.76405 | ||||||||
\(575\) | 1.27311 | 0.0530922 | ||||||||
\(576\) | −2.40551 | −0.100229 | ||||||||
\(577\) | 31.9538 | 1.33026 | 0.665128 | − | 0.746729i | \(-0.268377\pi\) | ||||
0.665128 | + | 0.746729i | \(0.268377\pi\) | |||||||
\(578\) | −12.1371 | −0.504839 | ||||||||
\(579\) | −2.19986 | −0.0914231 | ||||||||
\(580\) | −2.38638 | −0.0990890 | ||||||||
\(581\) | 38.0416 | 1.57823 | ||||||||
\(582\) | −3.17551 | −0.131629 | ||||||||
\(583\) | −15.8967 | −0.658373 | ||||||||
\(584\) | 7.17402 | 0.296863 | ||||||||
\(585\) | 6.43692 | 0.266134 | ||||||||
\(586\) | 18.2161 | 0.752501 | ||||||||
\(587\) | 25.5344 | 1.05392 | 0.526960 | − | 0.849890i | \(-0.323332\pi\) | ||||
0.526960 | + | 0.849890i | \(0.323332\pi\) | |||||||
\(588\) | −10.9980 | −0.453549 | ||||||||
\(589\) | 9.26805 | 0.381883 | ||||||||
\(590\) | 6.20506 | 0.255458 | ||||||||
\(591\) | 3.44845 | 0.141850 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.36087 | 0.343340 | 0.171670 | − | 0.985155i | \(-0.445084\pi\) | ||||
0.171670 | + | 0.985155i | \(0.445084\pi\) | |||||||
\(594\) | −7.51389 | −0.308298 | ||||||||
\(595\) | −4.44416 | −0.182193 | ||||||||
\(596\) | 21.4374 | 0.878109 | ||||||||
\(597\) | 6.17656 | 0.252790 | ||||||||
\(598\) | −1.62091 | −0.0662840 | ||||||||
\(599\) | −33.0454 | −1.35020 | −0.675098 | − | 0.737728i | \(-0.735899\pi\) | ||||
−0.675098 | + | 0.737728i | \(0.735899\pi\) | |||||||
\(600\) | 3.70790 | 0.151374 | ||||||||
\(601\) | −24.7407 | −1.00919 | −0.504597 | − | 0.863355i | \(-0.668359\pi\) | ||||
−0.504597 | + | 0.863355i | \(0.668359\pi\) | |||||||
\(602\) | −20.6369 | −0.841098 | ||||||||
\(603\) | −4.87353 | −0.198465 | ||||||||
\(604\) | −14.8068 | −0.602480 | ||||||||
\(605\) | 3.38698 | 0.137700 | ||||||||
\(606\) | −1.68428 | −0.0684193 | ||||||||
\(607\) | 4.91360 | 0.199437 | 0.0997184 | − | 0.995016i | \(-0.468206\pi\) | ||||
0.0997184 | + | 0.995016i | \(0.468206\pi\) | |||||||
\(608\) | 1.36293 | 0.0552743 | ||||||||
\(609\) | 19.4139 | 0.786691 | ||||||||
\(610\) | −1.57426 | −0.0637400 | ||||||||
\(611\) | 40.2316 | 1.62760 | ||||||||
\(612\) | 5.30460 | 0.214426 | ||||||||
\(613\) | 7.85791 | 0.317378 | 0.158689 | − | 0.987329i | \(-0.449273\pi\) | ||||
0.158689 | + | 0.987329i | \(0.449273\pi\) | |||||||
\(614\) | 9.72722 | 0.392559 | ||||||||
\(615\) | −3.08845 | −0.124538 | ||||||||
\(616\) | 8.31336 | 0.334955 | ||||||||
\(617\) | −15.2033 | −0.612062 | −0.306031 | − | 0.952022i | \(-0.599001\pi\) | ||||
−0.306031 | + | 0.952022i | \(0.599001\pi\) | |||||||
\(618\) | 5.00582 | 0.201364 | ||||||||
\(619\) | −12.0193 | −0.483097 | −0.241548 | − | 0.970389i | \(-0.577655\pi\) | ||||
−0.241548 | + | 0.970389i | \(0.577655\pi\) | |||||||
\(620\) | −2.97191 | −0.119355 | ||||||||
\(621\) | −1.10337 | −0.0442766 | ||||||||
\(622\) | 15.8511 | 0.635570 | ||||||||
\(623\) | −81.9494 | −3.28323 | ||||||||
\(624\) | −4.72088 | −0.188986 | ||||||||
\(625\) | 22.1714 | 0.886857 | ||||||||
\(626\) | 0.512343 | 0.0204774 | ||||||||
\(627\) | 1.89454 | 0.0756605 | ||||||||
\(628\) | 13.8800 | 0.553871 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −4.84786 | −0.193143 | ||||||||
\(631\) | 10.6060 | 0.422220 | 0.211110 | − | 0.977462i | \(-0.432292\pi\) | ||||
0.211110 | + | 0.977462i | \(0.432292\pi\) | |||||||
\(632\) | 12.0992 | 0.481281 | ||||||||
\(633\) | 6.46897 | 0.257119 | ||||||||
\(634\) | −27.6762 | −1.09916 | ||||||||
\(635\) | −6.65197 | −0.263975 | ||||||||
\(636\) | −6.79868 | −0.269585 | ||||||||
\(637\) | 87.3350 | 3.46034 | ||||||||
\(638\) | −9.84402 | −0.389728 | ||||||||
\(639\) | −26.3729 | −1.04330 | ||||||||
\(640\) | −0.437041 | −0.0172756 | ||||||||
\(641\) | −15.3996 | −0.608248 | −0.304124 | − | 0.952632i | \(-0.598364\pi\) | ||||
−0.304124 | + | 0.952632i | \(0.598364\pi\) | |||||||
\(642\) | 10.4428 | 0.412144 | ||||||||
\(643\) | 9.29202 | 0.366441 | 0.183221 | − | 0.983072i | \(-0.441348\pi\) | ||||
0.183221 | + | 0.983072i | \(0.441348\pi\) | |||||||
\(644\) | 1.22076 | 0.0481048 | ||||||||
\(645\) | 1.50806 | 0.0593797 | ||||||||
\(646\) | −3.00553 | −0.118251 | ||||||||
\(647\) | −47.9199 | −1.88393 | −0.941964 | − | 0.335715i | \(-0.891022\pi\) | ||||
−0.941964 | + | 0.335715i | \(0.891022\pi\) | |||||||
\(648\) | 4.00299 | 0.157252 | ||||||||
\(649\) | 25.5964 | 1.00475 | ||||||||
\(650\) | −29.4445 | −1.15491 | ||||||||
\(651\) | 24.1773 | 0.947585 | ||||||||
\(652\) | −18.8499 | −0.738218 | ||||||||
\(653\) | 11.9266 | 0.466723 | 0.233361 | − | 0.972390i | \(-0.425027\pi\) | ||||
0.233361 | + | 0.972390i | \(0.425027\pi\) | |||||||
\(654\) | −11.3673 | −0.444495 | ||||||||
\(655\) | 1.04008 | 0.0406392 | ||||||||
\(656\) | −9.16526 | −0.357843 | ||||||||
\(657\) | −17.2572 | −0.673266 | ||||||||
\(658\) | −30.2998 | −1.18121 | ||||||||
\(659\) | −18.0042 | −0.701343 | −0.350672 | − | 0.936499i | \(-0.614047\pi\) | ||||
−0.350672 | + | 0.936499i | \(0.614047\pi\) | |||||||
\(660\) | −0.607505 | −0.0236471 | ||||||||
\(661\) | 36.9012 | 1.43529 | 0.717646 | − | 0.696408i | \(-0.245220\pi\) | ||||
0.717646 | + | 0.696408i | \(0.245220\pi\) | |||||||
\(662\) | −14.1583 | −0.550279 | ||||||||
\(663\) | 10.4104 | 0.404307 | ||||||||
\(664\) | −8.24969 | −0.320150 | ||||||||
\(665\) | 2.74675 | 0.106514 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.44553 | −0.0559712 | ||||||||
\(668\) | −8.01091 | −0.309952 | ||||||||
\(669\) | −11.4664 | −0.443318 | ||||||||
\(670\) | −0.885439 | −0.0342075 | ||||||||
\(671\) | −6.49397 | −0.250697 | ||||||||
\(672\) | 3.55545 | 0.137155 | ||||||||
\(673\) | 33.8175 | 1.30357 | 0.651784 | − | 0.758405i | \(-0.274021\pi\) | ||||
0.651784 | + | 0.758405i | \(0.274021\pi\) | |||||||
\(674\) | 16.6632 | 0.641841 | ||||||||
\(675\) | −20.0431 | −0.771458 | ||||||||
\(676\) | 24.4885 | 0.941867 | ||||||||
\(677\) | −43.1009 | −1.65650 | −0.828252 | − | 0.560356i | \(-0.810664\pi\) | ||||
−0.828252 | + | 0.560356i | \(0.810664\pi\) | |||||||
\(678\) | −3.75346 | −0.144151 | ||||||||
\(679\) | −18.9916 | −0.728831 | ||||||||
\(680\) | 0.963757 | 0.0369584 | ||||||||
\(681\) | 7.78542 | 0.298338 | ||||||||
\(682\) | −12.2594 | −0.469436 | ||||||||
\(683\) | 29.4821 | 1.12810 | 0.564050 | − | 0.825740i | \(-0.309242\pi\) | ||||
0.564050 | + | 0.825740i | \(0.309242\pi\) | |||||||
\(684\) | −3.27855 | −0.125358 | ||||||||
\(685\) | −2.75289 | −0.105183 | ||||||||
\(686\) | −33.4960 | −1.27888 | ||||||||
\(687\) | −1.15874 | −0.0442086 | ||||||||
\(688\) | 4.47531 | 0.170620 | ||||||||
\(689\) | 53.9884 | 2.05680 | ||||||||
\(690\) | −0.0892083 | −0.00339610 | ||||||||
\(691\) | 21.3199 | 0.811048 | 0.405524 | − | 0.914084i | \(-0.367089\pi\) | ||||
0.405524 | + | 0.914084i | \(0.367089\pi\) | |||||||
\(692\) | −23.7768 | −0.903860 | ||||||||
\(693\) | −19.9978 | −0.759655 | ||||||||
\(694\) | 18.7895 | 0.713238 | ||||||||
\(695\) | 2.75268 | 0.104415 | ||||||||
\(696\) | −4.21009 | −0.159583 | ||||||||
\(697\) | 20.2111 | 0.765551 | ||||||||
\(698\) | 14.2446 | 0.539167 | ||||||||
\(699\) | 2.58970 | 0.0979514 | ||||||||
\(700\) | 22.1756 | 0.838160 | ||||||||
\(701\) | −23.2915 | −0.879709 | −0.439854 | − | 0.898069i | \(-0.644970\pi\) | ||||
−0.439854 | + | 0.898069i | \(0.644970\pi\) | |||||||
\(702\) | 25.5187 | 0.963142 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.80283 | −0.0679467 | ||||||||
\(705\) | 2.21418 | 0.0833909 | ||||||||
\(706\) | −2.57698 | −0.0969857 | ||||||||
\(707\) | −10.0731 | −0.378838 | ||||||||
\(708\) | 10.9471 | 0.411416 | ||||||||
\(709\) | 2.25990 | 0.0848725 | 0.0424362 | − | 0.999099i | \(-0.486488\pi\) | ||||
0.0424362 | + | 0.999099i | \(0.486488\pi\) | |||||||
\(710\) | −4.79153 | −0.179823 | ||||||||
\(711\) | −29.1047 | −1.09151 | ||||||||
\(712\) | 17.7715 | 0.666015 | ||||||||
\(713\) | −1.80021 | −0.0674184 | ||||||||
\(714\) | −7.84045 | −0.293421 | ||||||||
\(715\) | 4.82421 | 0.180415 | ||||||||
\(716\) | 3.46205 | 0.129383 | ||||||||
\(717\) | 4.14044 | 0.154628 | ||||||||
\(718\) | −18.3888 | −0.686265 | ||||||||
\(719\) | −6.96984 | −0.259931 | −0.129966 | − | 0.991518i | \(-0.541487\pi\) | ||||
−0.129966 | + | 0.991518i | \(0.541487\pi\) | |||||||
\(720\) | 1.05130 | 0.0391798 | ||||||||
\(721\) | 29.9381 | 1.11495 | ||||||||
\(722\) | −17.1424 | −0.637975 | ||||||||
\(723\) | −5.35271 | −0.199070 | ||||||||
\(724\) | −4.92424 | −0.183008 | ||||||||
\(725\) | −26.2586 | −0.975221 | ||||||||
\(726\) | 5.97536 | 0.221766 | ||||||||
\(727\) | 29.8920 | 1.10863 | 0.554316 | − | 0.832306i | \(-0.312980\pi\) | ||||
0.554316 | + | 0.832306i | \(0.312980\pi\) | |||||||
\(728\) | −28.2339 | −1.04642 | ||||||||
\(729\) | 0.0113948 | 0.000422030 0 | ||||||||
\(730\) | −3.13534 | −0.116044 | ||||||||
\(731\) | −9.86890 | −0.365014 | ||||||||
\(732\) | −2.77734 | −0.102653 | ||||||||
\(733\) | 27.8795 | 1.02975 | 0.514876 | − | 0.857265i | \(-0.327838\pi\) | ||||
0.514876 | + | 0.857265i | \(0.327838\pi\) | |||||||
\(734\) | 22.0762 | 0.814847 | ||||||||
\(735\) | 4.80656 | 0.177293 | ||||||||
\(736\) | −0.264734 | −0.00975823 | ||||||||
\(737\) | −3.65251 | −0.134542 | ||||||||
\(738\) | 22.0471 | 0.811565 | ||||||||
\(739\) | −13.3934 | −0.492684 | −0.246342 | − | 0.969183i | \(-0.579229\pi\) | ||||
−0.246342 | + | 0.969183i | \(0.579229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.43424 | −0.236368 | ||||||||
\(742\) | −40.6605 | −1.49270 | ||||||||
\(743\) | 0.0648738 | 0.00237999 | 0.00118999 | − | 0.999999i | \(-0.499621\pi\) | ||||
0.00118999 | + | 0.999999i | \(0.499621\pi\) | |||||||
\(744\) | −5.24309 | −0.192221 | ||||||||
\(745\) | −9.36900 | −0.343254 | ||||||||
\(746\) | 28.7986 | 1.05439 | ||||||||
\(747\) | 19.8447 | 0.726079 | ||||||||
\(748\) | 3.97558 | 0.145362 | ||||||||
\(749\) | 62.4546 | 2.28204 | ||||||||
\(750\) | −3.30537 | −0.120695 | ||||||||
\(751\) | 44.0394 | 1.60702 | 0.803510 | − | 0.595292i | \(-0.202964\pi\) | ||||
0.803510 | + | 0.595292i | \(0.202964\pi\) | |||||||
\(752\) | 6.57080 | 0.239612 | ||||||||
\(753\) | −12.1509 | −0.442804 | ||||||||
\(754\) | 33.4324 | 1.21753 | ||||||||
\(755\) | 6.47118 | 0.235510 | ||||||||
\(756\) | −19.2190 | −0.698989 | ||||||||
\(757\) | 26.9804 | 0.980619 | 0.490309 | − | 0.871548i | \(-0.336884\pi\) | ||||
0.490309 | + | 0.871548i | \(0.336884\pi\) | |||||||
\(758\) | 8.26297 | 0.300125 | ||||||||
\(759\) | −0.367992 | −0.0133573 | ||||||||
\(760\) | −0.595658 | −0.0216068 | ||||||||
\(761\) | 26.3086 | 0.953687 | 0.476844 | − | 0.878988i | \(-0.341781\pi\) | ||||
0.476844 | + | 0.878988i | \(0.341781\pi\) | |||||||
\(762\) | −11.7355 | −0.425132 | ||||||||
\(763\) | −67.9836 | −2.46117 | ||||||||
\(764\) | −19.2951 | −0.698074 | ||||||||
\(765\) | −2.31833 | −0.0838192 | ||||||||
\(766\) | 1.97274 | 0.0712781 | ||||||||
\(767\) | −86.9307 | −3.13889 | ||||||||
\(768\) | −0.771034 | −0.0278223 | ||||||||
\(769\) | −11.5497 | −0.416493 | −0.208247 | − | 0.978076i | \(-0.566776\pi\) | ||||
−0.208247 | + | 0.978076i | \(0.566776\pi\) | |||||||
\(770\) | −3.63328 | −0.130934 | ||||||||
\(771\) | −14.2508 | −0.513231 | ||||||||
\(772\) | 2.85313 | 0.102686 | ||||||||
\(773\) | −10.3121 | −0.370899 | −0.185449 | − | 0.982654i | \(-0.559374\pi\) | ||||
−0.185449 | + | 0.982654i | \(0.559374\pi\) | |||||||
\(774\) | −10.7654 | −0.386954 | ||||||||
\(775\) | −32.7015 | −1.17467 | ||||||||
\(776\) | 4.11851 | 0.147846 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.87551 | −0.174796 | ||||||||
\(779\) | −12.4916 | −0.447560 | ||||||||
\(780\) | 2.06322 | 0.0738750 | ||||||||
\(781\) | −19.7655 | −0.707263 | ||||||||
\(782\) | 0.583789 | 0.0208762 | ||||||||
\(783\) | 22.7577 | 0.813292 | ||||||||
\(784\) | 14.2639 | 0.509426 | ||||||||
\(785\) | −6.06612 | −0.216509 | ||||||||
\(786\) | 1.83492 | 0.0654495 | ||||||||
\(787\) | 42.1958 | 1.50412 | 0.752059 | − | 0.659095i | \(-0.229061\pi\) | ||||
0.752059 | + | 0.659095i | \(0.229061\pi\) | |||||||
\(788\) | −4.47251 | −0.159326 | ||||||||
\(789\) | −10.8078 | −0.384767 | ||||||||
\(790\) | −5.28785 | −0.188133 | ||||||||
\(791\) | −22.4481 | −0.798164 | ||||||||
\(792\) | 4.33672 | 0.154099 | ||||||||
\(793\) | 22.0549 | 0.783191 | ||||||||
\(794\) | −5.51844 | −0.195842 | ||||||||
\(795\) | 2.97130 | 0.105381 | ||||||||
\(796\) | −8.01075 | −0.283933 | ||||||||
\(797\) | 12.5500 | 0.444543 | 0.222272 | − | 0.974985i | \(-0.428653\pi\) | ||||
0.222272 | + | 0.974985i | \(0.428653\pi\) | |||||||
\(798\) | 4.84585 | 0.171541 | ||||||||
\(799\) | −14.4898 | −0.512614 | ||||||||
\(800\) | −4.80900 | −0.170024 | ||||||||
\(801\) | −42.7494 | −1.51048 | ||||||||
\(802\) | 37.9560 | 1.34027 | ||||||||
\(803\) | −12.9335 | −0.456415 | ||||||||
\(804\) | −1.56210 | −0.0550912 | ||||||||
\(805\) | −0.533524 | −0.0188042 | ||||||||
\(806\) | 41.6354 | 1.46654 | ||||||||
\(807\) | −4.56641 | −0.160745 | ||||||||
\(808\) | 2.18445 | 0.0768486 | ||||||||
\(809\) | −30.4565 | −1.07079 | −0.535397 | − | 0.844601i | \(-0.679838\pi\) | ||||
−0.535397 | + | 0.844601i | \(0.679838\pi\) | |||||||
\(810\) | −1.74947 | −0.0614700 | ||||||||
\(811\) | 24.9265 | 0.875286 | 0.437643 | − | 0.899149i | \(-0.355813\pi\) | ||||
0.437643 | + | 0.899149i | \(0.355813\pi\) | |||||||
\(812\) | −25.1791 | −0.883612 | ||||||||
\(813\) | −0.506814 | −0.0177748 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.23816 | 0.288570 | ||||||||
\(816\) | 1.70027 | 0.0595215 | ||||||||
\(817\) | 6.09955 | 0.213396 | ||||||||
\(818\) | −6.62852 | −0.231761 | ||||||||
\(819\) | 67.9169 | 2.37321 | ||||||||
\(820\) | 4.00559 | 0.139881 | ||||||||
\(821\) | 35.9315 | 1.25402 | 0.627008 | − | 0.779013i | \(-0.284279\pi\) | ||||
0.627008 | + | 0.779013i | \(0.284279\pi\) | |||||||
\(822\) | −4.85669 | −0.169397 | ||||||||
\(823\) | 8.77287 | 0.305803 | 0.152902 | − | 0.988241i | \(-0.451138\pi\) | ||||
0.152902 | + | 0.988241i | \(0.451138\pi\) | |||||||
\(824\) | −6.49235 | −0.226172 | ||||||||
\(825\) | −6.68471 | −0.232732 | ||||||||
\(826\) | 65.4705 | 2.27801 | ||||||||
\(827\) | 2.05039 | 0.0712992 | 0.0356496 | − | 0.999364i | \(-0.488650\pi\) | ||||
0.0356496 | + | 0.999364i | \(0.488650\pi\) | |||||||
\(828\) | 0.636820 | 0.0221310 | ||||||||
\(829\) | −4.74434 | −0.164778 | −0.0823888 | − | 0.996600i | \(-0.526255\pi\) | ||||
−0.0823888 | + | 0.996600i | \(0.526255\pi\) | |||||||
\(830\) | 3.60545 | 0.125147 | ||||||||
\(831\) | −10.5986 | −0.367662 | ||||||||
\(832\) | 6.12279 | 0.212269 | ||||||||
\(833\) | −31.4547 | −1.08984 | ||||||||
\(834\) | 4.85632 | 0.168161 | ||||||||
\(835\) | 3.50110 | 0.121160 | ||||||||
\(836\) | −2.45714 | −0.0849819 | ||||||||
\(837\) | 28.3415 | 0.979627 | ||||||||
\(838\) | 10.5288 | 0.363711 | ||||||||
\(839\) | 38.6738 | 1.33517 | 0.667584 | − | 0.744535i | \(-0.267329\pi\) | ||||
0.667584 | + | 0.744535i | \(0.267329\pi\) | |||||||
\(840\) | −1.55388 | −0.0536139 | ||||||||
\(841\) | 0.815037 | 0.0281047 | ||||||||
\(842\) | −17.2148 | −0.593262 | ||||||||
\(843\) | −13.9275 | −0.479689 | ||||||||
\(844\) | −8.39000 | −0.288796 | ||||||||
\(845\) | −10.7025 | −0.368177 | ||||||||
\(846\) | −15.8061 | −0.543425 | ||||||||
\(847\) | 35.7365 | 1.22792 | ||||||||
\(848\) | 8.81762 | 0.302798 | ||||||||
\(849\) | −2.05368 | −0.0704821 | ||||||||
\(850\) | 10.6047 | 0.363740 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −8.45328 | −0.289605 | ||||||||
\(853\) | −21.4284 | −0.733693 | −0.366846 | − | 0.930282i | \(-0.619563\pi\) | ||||
−0.366846 | + | 0.930282i | \(0.619563\pi\) | |||||||
\(854\) | −16.6103 | −0.568392 | ||||||||
\(855\) | 1.43286 | 0.0490027 | ||||||||
\(856\) | −13.5439 | −0.462920 | ||||||||
\(857\) | 31.0899 | 1.06201 | 0.531006 | − | 0.847368i | \(-0.321814\pi\) | ||||
0.531006 | + | 0.847368i | \(0.321814\pi\) | |||||||
\(858\) | 8.51094 | 0.290559 | ||||||||
\(859\) | −12.3979 | −0.423010 | −0.211505 | − | 0.977377i | \(-0.567836\pi\) | ||||
−0.211505 | + | 0.977377i | \(0.567836\pi\) | |||||||
\(860\) | −1.95589 | −0.0666954 | ||||||||
\(861\) | −32.5867 | −1.11055 | ||||||||
\(862\) | −38.3116 | −1.30490 | ||||||||
\(863\) | −37.7541 | −1.28516 | −0.642582 | − | 0.766217i | \(-0.722137\pi\) | ||||
−0.642582 | + | 0.766217i | \(0.722137\pi\) | |||||||
\(864\) | 4.16783 | 0.141792 | ||||||||
\(865\) | 10.3914 | 0.353320 | ||||||||
\(866\) | −18.6148 | −0.632557 | ||||||||
\(867\) | 9.35815 | 0.317819 | ||||||||
\(868\) | −31.3571 | −1.06433 | ||||||||
\(869\) | −21.8128 | −0.739949 | ||||||||
\(870\) | 1.83998 | 0.0623811 | ||||||||
\(871\) | 12.4047 | 0.420317 | ||||||||
\(872\) | 14.7429 | 0.499257 | ||||||||
\(873\) | −9.90710 | −0.335305 | ||||||||
\(874\) | −0.360815 | −0.0122047 | ||||||||
\(875\) | −19.7683 | −0.668289 | ||||||||
\(876\) | −5.53141 | −0.186889 | ||||||||
\(877\) | −6.49746 | −0.219404 | −0.109702 | − | 0.993965i | \(-0.534990\pi\) | ||||
−0.109702 | + | 0.993965i | \(0.534990\pi\) | |||||||
\(878\) | 10.0078 | 0.337746 | ||||||||
\(879\) | −14.0452 | −0.473734 | ||||||||
\(880\) | 0.787910 | 0.0265604 | ||||||||
\(881\) | 7.92161 | 0.266886 | 0.133443 | − | 0.991057i | \(-0.457397\pi\) | ||||
0.133443 | + | 0.991057i | \(0.457397\pi\) | |||||||
\(882\) | −34.3120 | −1.15534 | ||||||||
\(883\) | 32.1806 | 1.08296 | 0.541481 | − | 0.840713i | \(-0.317864\pi\) | ||||
0.541481 | + | 0.840713i | \(0.317864\pi\) | |||||||
\(884\) | −13.5019 | −0.454118 | ||||||||
\(885\) | −4.78431 | −0.160823 | ||||||||
\(886\) | 28.9727 | 0.973358 | ||||||||
\(887\) | −0.113136 | −0.00379873 | −0.00189937 | − | 0.999998i | \(-0.500605\pi\) | ||||
−0.00189937 | + | 0.999998i | \(0.500605\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −70.1859 | −2.35396 | ||||||||
\(890\) | −7.76687 | −0.260346 | ||||||||
\(891\) | −7.21670 | −0.241769 | ||||||||
\(892\) | 14.8715 | 0.497935 | ||||||||
\(893\) | 8.95556 | 0.299686 | ||||||||
\(894\) | −16.5289 | −0.552810 | ||||||||
\(895\) | −1.51306 | −0.0505760 | ||||||||
\(896\) | −4.61128 | −0.154052 | ||||||||
\(897\) | 1.24978 | 0.0417288 | ||||||||
\(898\) | −9.39644 | −0.313563 | ||||||||
\(899\) | 37.1305 | 1.23837 | ||||||||
\(900\) | 11.5681 | 0.385602 | ||||||||
\(901\) | −19.4445 | −0.647791 | ||||||||
\(902\) | 16.5234 | 0.550170 | ||||||||
\(903\) | 15.9118 | 0.529510 | ||||||||
\(904\) | 4.86809 | 0.161910 | ||||||||
\(905\) | 2.15209 | 0.0715380 | ||||||||
\(906\) | 11.4165 | 0.379289 | ||||||||
\(907\) | 50.2529 | 1.66862 | 0.834310 | − | 0.551295i | \(-0.185866\pi\) | ||||
0.834310 | + | 0.551295i | \(0.185866\pi\) | |||||||
\(908\) | −10.0974 | −0.335093 | ||||||||
\(909\) | −5.25470 | −0.174287 | ||||||||
\(910\) | 12.3394 | 0.409046 | ||||||||
\(911\) | 35.7354 | 1.18397 | 0.591983 | − | 0.805951i | \(-0.298345\pi\) | ||||
0.591983 | + | 0.805951i | \(0.298345\pi\) | |||||||
\(912\) | −1.05087 | −0.0347977 | ||||||||
\(913\) | 14.8728 | 0.492217 | ||||||||
\(914\) | −27.0123 | −0.893488 | ||||||||
\(915\) | 1.21381 | 0.0401273 | ||||||||
\(916\) | 1.50284 | 0.0496551 | ||||||||
\(917\) | 10.9740 | 0.362394 | ||||||||
\(918\) | −9.19085 | −0.303343 | ||||||||
\(919\) | 12.5483 | 0.413932 | 0.206966 | − | 0.978348i | \(-0.433641\pi\) | ||||
0.206966 | + | 0.978348i | \(0.433641\pi\) | |||||||
\(920\) | 0.115700 | 0.00381450 | ||||||||
\(921\) | −7.50002 | −0.247134 | ||||||||
\(922\) | 27.6922 | 0.911995 | ||||||||
\(923\) | 67.1276 | 2.20953 | ||||||||
\(924\) | −6.40988 | −0.210870 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 27.7284 | 0.911211 | ||||||||
\(927\) | 15.6174 | 0.512942 | ||||||||
\(928\) | 5.46031 | 0.179244 | ||||||||
\(929\) | 26.0839 | 0.855783 | 0.427892 | − | 0.903830i | \(-0.359256\pi\) | ||||
0.427892 | + | 0.903830i | \(0.359256\pi\) | |||||||
\(930\) | 2.29144 | 0.0751393 | ||||||||
\(931\) | 19.4408 | 0.637146 | ||||||||
\(932\) | −3.35874 | −0.110019 | ||||||||
\(933\) | −12.2217 | −0.400121 | ||||||||
\(934\) | 5.72621 | 0.187367 | ||||||||
\(935\) | −1.73749 | −0.0568220 | ||||||||
\(936\) | −14.7284 | −0.481413 | ||||||||
\(937\) | 22.2574 | 0.727119 | 0.363560 | − | 0.931571i | \(-0.381561\pi\) | ||||
0.363560 | + | 0.931571i | \(0.381561\pi\) | |||||||
\(938\) | −9.34240 | −0.305040 | ||||||||
\(939\) | −0.395034 | −0.0128914 | ||||||||
\(940\) | −2.87171 | −0.0936647 | ||||||||
\(941\) | 1.07662 | 0.0350967 | 0.0175484 | − | 0.999846i | \(-0.494414\pi\) | ||||
0.0175484 | + | 0.999846i | \(0.494414\pi\) | |||||||
\(942\) | −10.7019 | −0.348688 | ||||||||
\(943\) | 2.42636 | 0.0790131 | ||||||||
\(944\) | −14.1979 | −0.462102 | ||||||||
\(945\) | 8.39950 | 0.273236 | ||||||||
\(946\) | −8.06822 | −0.262320 | ||||||||
\(947\) | −27.9357 | −0.907787 | −0.453894 | − | 0.891056i | \(-0.649965\pi\) | ||||
−0.453894 | + | 0.891056i | \(0.649965\pi\) | |||||||
\(948\) | −9.32890 | −0.302988 | ||||||||
\(949\) | 43.9250 | 1.42587 | ||||||||
\(950\) | −6.55434 | −0.212651 | ||||||||
\(951\) | 21.3393 | 0.691973 | ||||||||
\(952\) | 10.1687 | 0.329571 | ||||||||
\(953\) | 34.7908 | 1.12698 | 0.563492 | − | 0.826122i | \(-0.309458\pi\) | ||||
0.563492 | + | 0.826122i | \(0.309458\pi\) | |||||||
\(954\) | −21.2109 | −0.686727 | ||||||||
\(955\) | 8.43277 | 0.272878 | ||||||||
\(956\) | −5.36999 | −0.173678 | ||||||||
\(957\) | 7.59007 | 0.245352 | ||||||||
\(958\) | 16.3598 | 0.528560 | ||||||||
\(959\) | −29.0462 | −0.937950 | ||||||||
\(960\) | 0.336973 | 0.0108758 | ||||||||
\(961\) | 15.2410 | 0.491645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 32.5799 | 1.04987 | ||||||||
\(964\) | 6.94226 | 0.223595 | ||||||||
\(965\) | −1.24694 | −0.0401403 | ||||||||
\(966\) | −0.941250 | −0.0302842 | ||||||||
\(967\) | 20.3517 | 0.654467 | 0.327233 | − | 0.944944i | \(-0.393884\pi\) | ||||
0.327233 | + | 0.944944i | \(0.393884\pi\) | |||||||
\(968\) | −7.74980 | −0.249088 | ||||||||
\(969\) | 2.31736 | 0.0744444 | ||||||||
\(970\) | −1.79996 | −0.0577931 | ||||||||
\(971\) | −26.5861 | −0.853189 | −0.426594 | − | 0.904443i | \(-0.640287\pi\) | ||||
−0.426594 | + | 0.904443i | \(0.640287\pi\) | |||||||
\(972\) | −15.5899 | −0.500047 | ||||||||
\(973\) | 29.0439 | 0.931106 | ||||||||
\(974\) | −17.8331 | −0.571410 | ||||||||
\(975\) | 22.7027 | 0.727067 | ||||||||
\(976\) | 3.60210 | 0.115300 | ||||||||
\(977\) | 24.9760 | 0.799054 | 0.399527 | − | 0.916721i | \(-0.369174\pi\) | ||||
0.399527 | + | 0.916721i | \(0.369174\pi\) | |||||||
\(978\) | 14.5339 | 0.464742 | ||||||||
\(979\) | −32.0390 | −1.02397 | ||||||||
\(980\) | −6.23392 | −0.199135 | ||||||||
\(981\) | −35.4641 | −1.13228 | ||||||||
\(982\) | −6.51454 | −0.207887 | ||||||||
\(983\) | −26.3797 | −0.841383 | −0.420692 | − | 0.907204i | \(-0.638213\pi\) | ||||
−0.420692 | + | 0.907204i | \(0.638213\pi\) | |||||||
\(984\) | 7.06673 | 0.225279 | ||||||||
\(985\) | 1.95467 | 0.0622809 | ||||||||
\(986\) | −12.0410 | −0.383464 | ||||||||
\(987\) | 23.3622 | 0.743626 | ||||||||
\(988\) | 8.34495 | 0.265488 | ||||||||
\(989\) | −1.18477 | −0.0376734 | ||||||||
\(990\) | −1.89532 | −0.0602373 | ||||||||
\(991\) | 3.41775 | 0.108568 | 0.0542842 | − | 0.998526i | \(-0.482712\pi\) | ||||
0.0542842 | + | 0.998526i | \(0.482712\pi\) | |||||||
\(992\) | 6.80007 | 0.215903 | ||||||||
\(993\) | 10.9165 | 0.346426 | ||||||||
\(994\) | −50.5561 | −1.60354 | ||||||||
\(995\) | 3.50102 | 0.110990 | ||||||||
\(996\) | 6.36079 | 0.201549 | ||||||||
\(997\) | 14.4208 | 0.456712 | 0.228356 | − | 0.973578i | \(-0.426665\pi\) | ||||
0.228356 | + | 0.973578i | \(0.426665\pi\) | |||||||
\(998\) | −2.43802 | −0.0771743 | ||||||||
\(999\) | 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 | 2738.2.a.x.1.7 | yes | 18 | |
37.36 | even | 2 | 2738.2.a.w.1.7 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2738.2.a.w.1.7 | ✓ | 18 | 37.36 | even | 2 | ||
2738.2.a.x.1.7 | yes | 18 | 1.1 | even | 1 | trivial |