Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, 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("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.915292\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.915292 | −0.528444 | −0.264222 | − | 0.964462i | \(-0.585115\pi\) | ||||
−0.264222 | + | 0.964462i | \(0.585115\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.31004 | −0.585868 | −0.292934 | − | 0.956133i | \(-0.594632\pi\) | ||||
−0.292934 | + | 0.956133i | \(0.594632\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.16224 | −0.720747 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.72778 | 0.822458 | 0.411229 | − | 0.911532i | \(-0.365100\pi\) | ||||
0.411229 | + | 0.911532i | \(0.365100\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.20323 | 1.72047 | 0.860233 | − | 0.509902i | \(-0.170318\pi\) | ||||
0.860233 | + | 0.509902i | \(0.170318\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19907 | 0.309598 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.76678 | −1.64118 | −0.820592 | − | 0.571514i | \(-0.806356\pi\) | ||||
−0.820592 | + | 0.571514i | \(0.806356\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.15682 | 1.18306 | 0.591528 | − | 0.806284i | \(-0.298525\pi\) | ||||
0.591528 | + | 0.806284i | \(0.298525\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.76186 | 1.40995 | 0.704973 | − | 0.709234i | \(-0.250959\pi\) | ||||
0.704973 | + | 0.709234i | \(0.250959\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.28379 | −0.656758 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.72496 | 0.909318 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.37080 | −1.18303 | −0.591514 | − | 0.806295i | \(-0.701470\pi\) | ||||
−0.591514 | + | 0.806295i | \(0.701470\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.28883 | 0.411086 | 0.205543 | − | 0.978648i | \(-0.434104\pi\) | ||||
0.205543 | + | 0.978648i | \(0.434104\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.49672 | −0.434623 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.35867 | 1.53856 | 0.769278 | − | 0.638915i | \(-0.220616\pi\) | ||||
0.769278 | + | 0.638915i | \(0.220616\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.67776 | −0.909169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.74692 | −1.02890 | −0.514448 | − | 0.857521i | \(-0.672003\pi\) | ||||
−0.514448 | + | 0.857521i | \(0.672003\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.83262 | 0.422263 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.15236 | 1.18914 | 0.594572 | − | 0.804042i | \(-0.297322\pi\) | ||||
0.594572 | + | 0.804042i | \(0.297322\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.19357 | 0.867274 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.5686 | −1.72643 | −0.863215 | − | 0.504837i | \(-0.831552\pi\) | ||||
−0.863215 | + | 0.504837i | \(0.831552\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.57351 | −0.481852 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.72000 | −0.625179 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.48363 | 0.193152 | 0.0965759 | − | 0.995326i | \(-0.469211\pi\) | ||||
0.0965759 | + | 0.995326i | \(0.469211\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.36836 | −0.303237 | −0.151619 | − | 0.988439i | \(-0.548449\pi\) | ||||
−0.151619 | + | 0.988439i | \(0.548449\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.12648 | −1.00797 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.61180 | 0.319083 | 0.159541 | − | 0.987191i | \(-0.448998\pi\) | ||||
0.159541 | + | 0.987191i | \(0.448998\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.18908 | −0.745077 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.28105 | −0.152033 | −0.0760164 | − | 0.997107i | \(-0.524220\pi\) | ||||
−0.0760164 | + | 0.997107i | \(0.524220\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.81398 | 0.446393 | 0.223196 | − | 0.974774i | \(-0.428351\pi\) | ||||
0.223196 | + | 0.974774i | \(0.428351\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00563 | 0.347060 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.28357 | 0.481940 | 0.240970 | − | 0.970533i | \(-0.422535\pi\) | ||||
0.240970 | + | 0.970533i | \(0.422535\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.16201 | 0.240223 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.35962 | −0.259002 | −0.129501 | − | 0.991579i | \(-0.541338\pi\) | ||||
−0.129501 | + | 0.991579i | \(0.541338\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.86476 | 0.961518 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.83114 | 0.625164 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.98293 | 0.422190 | 0.211095 | − | 0.977466i | \(-0.432297\pi\) | ||||
0.211095 | + | 0.977466i | \(0.432297\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.09495 | −0.217236 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.75565 | −0.693115 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.03488 | −0.714284 | −0.357142 | − | 0.934050i | \(-0.616249\pi\) | ||||
−0.357142 | + | 0.934050i | \(0.616249\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.89813 | −0.592784 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.24828 | −0.621727 | −0.310864 | − | 0.950455i | \(-0.600618\pi\) | ||||
−0.310864 | + | 0.950455i | \(0.600618\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.53553 | 0.742498 | 0.371249 | − | 0.928533i | \(-0.378930\pi\) | ||||
0.371249 | + | 0.928533i | \(0.378930\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.8145 | −1.72220 | −0.861098 | − | 0.508439i | \(-0.830223\pi\) | ||||
−0.861098 | + | 0.508439i | \(0.830223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.83067 | −0.750042 | −0.375021 | − | 0.927016i | \(-0.622365\pi\) | ||||
−0.375021 | + | 0.927016i | \(0.622365\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.56591 | −0.813040 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.31934 | 0.500401 | 0.250201 | − | 0.968194i | \(-0.419503\pi\) | ||||
0.250201 | + | 0.968194i | \(0.419503\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.85832 | −0.826042 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.4129 | −1.24002 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.55920 | −0.323563 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.915292 | 0.0825291 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8521 | 0.970642 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.66189 | 0.857354 | 0.428677 | − | 0.903458i | \(-0.358980\pi\) | ||||
0.428677 | + | 0.903458i | \(0.358980\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.17540 | 0.543714 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.2464 | 1.50683 | 0.753413 | − | 0.657547i | \(-0.228406\pi\) | ||||
0.753413 | + | 0.657547i | \(0.228406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.18989 | −0.532741 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.10990 | −0.692875 | −0.346438 | − | 0.938073i | \(-0.612609\pi\) | ||||
−0.346438 | + | 0.938073i | \(0.612609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.72783 | −0.231372 | −0.115686 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115686 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.46179 | −0.628396 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.9211 | 1.41501 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.34601 | 0.693099 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.82784 | −0.395512 | −0.197756 | − | 0.980251i | \(-0.563365\pi\) | ||||
−0.197756 | + | 0.980251i | \(0.563365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.35596 | 0.191726 | 0.0958628 | − | 0.995395i | \(-0.469439\pi\) | ||||
0.0958628 | + | 0.995395i | \(0.469439\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.6314 | 1.18288 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.99846 | −0.240842 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.6689 | 1.01109 | 0.505543 | − | 0.862801i | \(-0.331292\pi\) | ||||
0.505543 | + | 0.862801i | \(0.331292\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.5039 | 0.912321 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.78527 | 0.688115 | 0.344058 | − | 0.938949i | \(-0.388198\pi\) | ||||
0.344058 | + | 0.938949i | \(0.388198\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.27080 | 0.254632 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.24661 | −0.251230 | −0.125615 | − | 0.992079i | \(-0.540090\pi\) | ||||
−0.125615 | + | 0.992079i | \(0.540090\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.4800 | 1.96000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.1503 | −0.852684 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.370585 | −0.0281751 | −0.0140875 | − | 0.999901i | \(-0.504484\pi\) | ||||
−0.0140875 | + | 0.999901i | \(0.504484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.35795 | −0.102070 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.0644 | −1.79866 | −0.899330 | − | 0.437271i | \(-0.855945\pi\) | ||||
−0.899330 | + | 0.437271i | \(0.855945\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.03031 | −0.0765824 | −0.0382912 | − | 0.999267i | \(-0.512191\pi\) | ||||
−0.0382912 | + | 0.999267i | \(0.512191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.16774 | 0.160244 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.2602 | −0.901391 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.4583 | −1.34980 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.25690 | 0.597448 | 0.298724 | − | 0.954340i | \(-0.403439\pi\) | ||||
0.298724 | + | 0.954340i | \(0.403439\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.77019 | 0.703274 | 0.351637 | − | 0.936137i | \(-0.385625\pi\) | ||||
0.351637 | + | 0.936137i | \(0.385625\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.43810 | 0.532653 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.63912 | 0.188030 | 0.0940149 | − | 0.995571i | \(-0.470030\pi\) | ||||
0.0940149 | + | 0.995571i | \(0.470030\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.19404 | 0.509972 | 0.254986 | − | 0.966945i | \(-0.417929\pi\) | ||||
0.254986 | + | 0.966945i | \(0.417929\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.39056 | −0.168617 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.31004 | 0.0914972 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −14.6208 | −1.01621 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.0667 | 0.973014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.7516 | −1.35976 | −0.679879 | − | 0.733324i | \(-0.737968\pi\) | ||||
−0.679879 | + | 0.733324i | \(0.737968\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.17254 | 0.0803409 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.83875 | 0.602798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.49090 | −0.235893 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −41.9758 | −2.82360 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.8914 | 1.33203 | 0.666014 | − | 0.745939i | \(-0.267999\pi\) | ||||
0.666014 | + | 0.745939i | \(0.267999\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.10035 | 0.473357 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.0483 | 1.06516 | 0.532581 | − | 0.846379i | \(-0.321222\pi\) | ||||
0.532581 | + | 0.846379i | \(0.321222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.4940 | 1.35428 | 0.677142 | − | 0.735852i | \(-0.263218\pi\) | ||||
0.677142 | + | 0.735852i | \(0.263218\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.2859 | −1.00141 | −0.500705 | − | 0.865618i | \(-0.666926\pi\) | ||||
−0.500705 | + | 0.865618i | \(0.666926\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.6799 | −0.696682 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.92072 | −0.254678 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.3135 | 1.76676 | 0.883380 | − | 0.468657i | \(-0.155262\pi\) | ||||
0.883380 | + | 0.468657i | \(0.155262\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.7932 | −1.01733 | −0.508663 | − | 0.860965i | \(-0.669860\pi\) | ||||
−0.508663 | + | 0.860965i | \(0.669860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1537 | −1.03626 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.9889 | 2.03541 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.15974 | 0.136868 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.7718 | 0.995505 | 0.497753 | − | 0.867319i | \(-0.334159\pi\) | ||||
0.497753 | + | 0.867319i | \(0.334159\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.4449 | 1.15962 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.11384 | −0.508108 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.38691 | −0.460783 | −0.230391 | − | 0.973098i | \(-0.574001\pi\) | ||||
−0.230391 | + | 0.973098i | \(0.574001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.7752 | 0.852664 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.79849 | −0.480875 | −0.240438 | − | 0.970665i | \(-0.577291\pi\) | ||||
−0.240438 | + | 0.970665i | \(0.577291\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.4654 | 1.01146 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.64555 | −0.223104 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3794 | 0.693815 | 0.346907 | − | 0.937899i | \(-0.387232\pi\) | ||||
0.346907 | + | 0.937899i | \(0.387232\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.2606 | −1.23075 | −0.615373 | − | 0.788236i | \(-0.710995\pi\) | ||||
−0.615373 | + | 0.788236i | \(0.710995\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.95747 | −0.540156 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.4498 | 1.34888 | 0.674440 | − | 0.738330i | \(-0.264385\pi\) | ||||
0.674440 | + | 0.738330i | \(0.264385\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.94900 | −0.296289 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.7285 | 1.71380 | 0.856898 | − | 0.515485i | \(-0.172388\pi\) | ||||
0.856898 | + | 0.515485i | \(0.172388\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.3840 | 1.50892 | 0.754462 | − | 0.656344i | \(-0.227898\pi\) | ||||
0.754462 | + | 0.656344i | \(0.227898\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.18339 | 0.366272 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.7893 | 1.69349 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.43897 | 0.377459 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.3359 | 1.53856 | 0.769280 | − | 0.638912i | \(-0.220615\pi\) | ||||
0.769280 | + | 0.638912i | \(0.220615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.94361 | −0.113161 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.8887 | 0.747876 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 41.9454 | 2.42576 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.71900 | 0.328548 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.10265 | 0.177657 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.8539 | −1.70385 | −0.851926 | − | 0.523663i | \(-0.824565\pi\) | ||||
−0.851926 | + | 0.523663i | \(0.824565\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.89721 | −0.392369 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.09275 | 0.0619642 | 0.0309821 | − | 0.999520i | \(-0.490137\pi\) | ||||
0.0309821 | + | 0.999520i | \(0.490137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.8202 | 1.45945 | 0.729723 | − | 0.683743i | \(-0.239649\pi\) | ||||
0.729723 | + | 0.683743i | \(0.239649\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.09034 | 0.342067 | 0.171034 | − | 0.985265i | \(-0.445289\pi\) | ||||
0.171034 | + | 0.985265i | \(0.445289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.3782 | −0.972991 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.3055 | 0.910084 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −34.8951 | −1.94161 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −20.3701 | −1.12993 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.16735 | 0.396355 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.7596 | 0.756298 | 0.378149 | − | 0.925745i | \(-0.376561\pi\) | ||||
0.378149 | + | 0.925745i | \(0.376561\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.2357 | −1.10891 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.42157 | −0.186940 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.3125 | −1.54228 | −0.771141 | − | 0.636664i | \(-0.780314\pi\) | ||||
−0.771141 | + | 0.636664i | \(0.780314\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.86875 | −0.264434 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.24343 | 0.338101 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.10794 | 0.436517 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.3979 | −0.772920 | −0.386460 | − | 0.922306i | \(-0.626302\pi\) | ||||
−0.386460 | + | 0.922306i | \(0.626302\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.5569 | 0.832741 | 0.416371 | − | 0.909195i | \(-0.363302\pi\) | ||||
0.416371 | + | 0.909195i | \(0.363302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 29.3100 | 1.56445 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.63356 | 0.246620 | 0.123310 | − | 0.992368i | \(-0.460649\pi\) | ||||
0.123310 | + | 0.992368i | \(0.460649\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.67823 | 0.0890712 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.24826 | −0.329771 | −0.164885 | − | 0.986313i | \(-0.552725\pi\) | ||||
−0.164885 | + | 0.986313i | \(0.552725\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.59281 | 0.399622 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.25770 | 0.170985 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.99647 | −0.261527 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.2894 | 1.84209 | 0.921047 | − | 0.389452i | \(-0.127336\pi\) | ||||
0.921047 | + | 0.389452i | \(0.127336\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.16224 | 0.112562 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.5655 | 1.53084 | 0.765421 | − | 0.643530i | \(-0.222531\pi\) | ||||
0.765421 | + | 0.643530i | \(0.222531\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.93284 | −0.512930 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −39.5195 | −2.03536 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.02380 | −0.463522 | −0.231761 | − | 0.972773i | \(-0.574449\pi\) | ||||
−0.231761 | + | 0.972773i | \(0.574449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.84344 | −0.453063 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.0681 | −1.02543 | −0.512716 | − | 0.858559i | \(-0.671360\pi\) | ||||
−0.512716 | + | 0.858559i | \(0.671360\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.5885 | 0.741574 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.4162 | 1.79567 | 0.897836 | − | 0.440330i | \(-0.145139\pi\) | ||||
0.897836 | + | 0.440330i | \(0.145139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.7560 | −2.31398 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.7855 | −0.796273 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.61166 | −0.282353 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.8612 | 1.04699 | 0.523496 | − | 0.852028i | \(-0.324628\pi\) | ||||
0.523496 | + | 0.852028i | \(0.324628\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.68818 | 0.483805 | 0.241902 | − | 0.970301i | \(-0.422229\pi\) | ||||
0.241902 | + | 0.970301i | \(0.422229\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.1981 | 0.707259 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.83232 | −0.140739 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.5284 | 1.26540 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.5208 | −0.718009 | −0.359004 | − | 0.933336i | \(-0.616884\pi\) | ||||
−0.359004 | + | 0.933336i | \(0.616884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.42292 | 0.366146 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.09120 | 0.151741 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.49676 | 0.122267 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.75224 | −0.378721 | −0.189361 | − | 0.981908i | \(-0.560642\pi\) | ||||
−0.189361 | + | 0.981908i | \(0.560642\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.10905 | 0.297737 | 0.148869 | − | 0.988857i | \(-0.452437\pi\) | ||||
0.148869 | + | 0.988857i | \(0.452437\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.6274 | −0.857072 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 22.2207 | 1.07786 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.4877 | −0.747753 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.0724 | 0.966853 | 0.483427 | − | 0.875385i | \(-0.339392\pi\) | ||||
0.483427 | + | 0.875385i | \(0.339392\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0613 | 0.867973 | 0.433986 | − | 0.900919i | \(-0.357107\pi\) | ||||
0.433986 | + | 0.900919i | \(0.357107\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.63904 | −0.366264 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 34.8697 | 1.66804 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.24242 | −0.202480 | −0.101240 | − | 0.994862i | \(-0.532281\pi\) | ||||
−0.101240 | + | 0.994862i | \(0.532281\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3712 | 0.777819 | 0.388909 | − | 0.921276i | \(-0.372852\pi\) | ||||
0.388909 | + | 0.921276i | \(0.372852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.21781 | −0.247348 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.41888 | 0.209006 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.4030 | −0.679721 | −0.339860 | − | 0.940476i | \(-0.610380\pi\) | ||||
−0.339860 | + | 0.940476i | \(0.610380\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.72778 | −0.128446 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.15639 | −0.101316 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.7736 | −0.597523 | −0.298761 | − | 0.954328i | \(-0.596573\pi\) | ||||
−0.298761 | + | 0.954328i | \(0.596573\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −31.9727 | −1.49236 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.83939 | −0.178818 | −0.0894092 | − | 0.995995i | \(-0.528498\pi\) | ||||
−0.0894092 | + | 0.995995i | \(0.528498\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42.3474 | 1.96805 | 0.984025 | − | 0.178030i | \(-0.0569723\pi\) | ||||
0.984025 | + | 0.178030i | \(0.0569723\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.74447 | 0.127272 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.2929 | −1.26296 | −0.631482 | − | 0.775390i | \(-0.717553\pi\) | ||||
−0.631482 | + | 0.775390i | \(0.717553\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.5957 | −0.534302 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.4041 | −0.846224 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.9339 | −0.776982 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 27.1763 | 1.24432 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.9162 | 1.13845 | 0.569225 | − | 0.822182i | \(-0.307243\pi\) | ||||
0.569225 | + | 0.822182i | \(0.307243\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 58.0539 | 2.64703 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.21598 | 0.418476 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.1545 | 0.777346 | 0.388673 | − | 0.921376i | \(-0.372934\pi\) | ||||
0.388673 | + | 0.921376i | \(0.372934\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.04108 | −0.363630 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.8028 | 0.938815 | 0.469408 | − | 0.882982i | \(-0.344468\pi\) | ||||
0.469408 | + | 0.882982i | \(0.344468\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 43.1098 | 1.94157 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.72679 | 0.347293 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.8858 | 0.666380 | 0.333190 | − | 0.942860i | \(-0.391875\pi\) | ||||
0.333190 | + | 0.942860i | \(0.391875\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.97159 | 0.132761 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.55717 | −0.203194 | −0.101597 | − | 0.994826i | \(-0.532395\pi\) | ||||
−0.101597 | + | 0.994826i | \(0.532395\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.18550 | 0.364250 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.3216 | −1.03575 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.37084 | 0.238058 | 0.119029 | − | 0.992891i | \(-0.462022\pi\) | ||||
0.119029 | + | 0.992891i | \(0.462022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.3658 | 1.07577 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.87186 | −0.435006 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.2379 | 0.978021 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.339193 | 0.0148889 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.7276 | −0.645228 | −0.322614 | − | 0.946531i | \(-0.604562\pi\) | ||||
−0.322614 | + | 0.946531i | \(0.604562\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.0551 | −1.70776 | −0.853880 | − | 0.520470i | \(-0.825757\pi\) | ||||
−0.853880 | + | 0.520470i | \(0.825757\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.4880 | −0.674668 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7228 | 0.987947 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.20796 | −0.139214 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.20323 | −0.268692 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 23.3378 | 1.00898 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.0260 | 0.950490 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.7979 | −0.507230 | −0.253615 | − | 0.967305i | \(-0.581620\pi\) | ||||
−0.253615 | + | 0.967305i | \(0.581620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.943034 | 0.0404695 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.2585 | 0.439426 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4776 | −0.704530 | −0.352265 | − | 0.935900i | \(-0.614588\pi\) | ||||
−0.352265 | + | 0.935900i | \(0.614588\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.12097 | 0.218557 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.8531 | −1.39959 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.2217 | 0.476334 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.7784 | −1.26175 | −0.630876 | − | 0.775884i | \(-0.717304\pi\) | ||||
−0.630876 | + | 0.775884i | \(0.717304\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.8527 | −1.77018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.8947 | 0.713296 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.9737 | 1.17895 | 0.589476 | − | 0.807786i | \(-0.299334\pi\) | ||||
0.589476 | + | 0.807786i | \(0.299334\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.96856 | −0.293169 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −39.1698 | −1.64208 | −0.821041 | − | 0.570870i | \(-0.806606\pi\) | ||||
−0.821041 | + | 0.570870i | \(0.806606\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.58472 | −0.401108 | −0.200554 | − | 0.979683i | \(-0.564274\pi\) | ||||
−0.200554 | + | 0.979683i | \(0.564274\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.55747 | −0.315718 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.2045 | −0.925994 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.4043 | 0.724549 | 0.362275 | − | 0.932071i | \(-0.382000\pi\) | ||||
0.362275 | + | 0.932071i | \(0.382000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.94257 | −0.371641 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −34.2844 | −1.41991 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.5714 | 0.726488 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.8005 | 1.10617 | 0.553087 | − | 0.833123i | \(-0.313450\pi\) | ||||
0.553087 | + | 0.833123i | \(0.313450\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.8031 | 0.486338 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.41557 | −0.0993632 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.07921 | 0.167513 | 0.0837564 | − | 0.996486i | \(-0.473308\pi\) | ||||
0.0837564 | + | 0.996486i | \(0.473308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.58465 | −0.269492 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.348239 | 0.0142287 | 0.00711434 | − | 0.999975i | \(-0.497735\pi\) | ||||
0.00711434 | + | 0.999975i | \(0.497735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.9913 | 0.529924 | 0.264962 | − | 0.964259i | \(-0.414641\pi\) | ||||
0.264962 | + | 0.964259i | \(0.414641\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.64735 | −0.229978 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.66269 | 0.189565 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.8925 | −1.33506 | −0.667532 | − | 0.744581i | \(-0.732649\pi\) | ||||
−0.667532 | + | 0.744581i | \(0.732649\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 50.5709 | 2.04588 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.5587 | −1.92088 | −0.960439 | − | 0.278490i | \(-0.910166\pi\) | ||||
−0.960439 | + | 0.278490i | \(0.910166\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.19907 | −0.0483512 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3219 | 0.576578 | 0.288289 | − | 0.957544i | \(-0.406914\pi\) | ||||
0.288289 | + | 0.957544i | \(0.406914\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.567473 | 0.0228087 | 0.0114043 | − | 0.999935i | \(-0.496370\pi\) | ||||
0.0114043 | + | 0.999935i | \(0.496370\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 31.9495 | 1.28209 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.20225 | 0.0880900 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.8751 | −0.514183 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −63.3280 | −2.52505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.5021 | 0.776366 | 0.388183 | − | 0.921582i | \(-0.373103\pi\) | ||||
0.388183 | + | 0.921582i | \(0.373103\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.0785 | 0.718556 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.6575 | −0.502296 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.76994 | 0.109577 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.0255 | −0.751461 | −0.375731 | − | 0.926729i | \(-0.622608\pi\) | ||||
−0.375731 | + | 0.926729i | \(0.622608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.8947 | 1.77047 | 0.885237 | − | 0.465141i | \(-0.153996\pi\) | ||||
0.885237 | + | 0.465141i | \(0.153996\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.09003 | −0.318545 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.67864 | 0.223250 | 0.111625 | − | 0.993750i | \(-0.464394\pi\) | ||||
0.111625 | + | 0.993750i | \(0.464394\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.04701 | 0.158859 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.31189 | −0.168737 | −0.0843686 | − | 0.996435i | \(-0.526887\pi\) | ||||
−0.0843686 | + | 0.996435i | \(0.526887\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.5935 | −0.882802 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.24674 | −0.321736 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.9372 | 1.67260 | 0.836298 | − | 0.548275i | \(-0.184715\pi\) | ||||
0.836298 | + | 0.548275i | \(0.184715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.6588 | 0.570160 | 0.285080 | − | 0.958504i | \(-0.407980\pi\) | ||||
0.285080 | + | 0.958504i | \(0.407980\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 38.4201 | 1.49211 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −43.0785 | −1.66801 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.2065 | −0.703902 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.46037 | −0.249400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.0296 | −1.00337 | −0.501684 | − | 0.865051i | \(-0.667286\pi\) | ||||
−0.501684 | + | 0.865051i | \(0.667286\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −15.5158 | −0.597202 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.3578 | −1.39735 | −0.698673 | − | 0.715441i | \(-0.746226\pi\) | ||||
−0.698673 | + | 0.715441i | \(0.746226\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6889 | −0.562878 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.5708 | 0.672328 | 0.336164 | − | 0.941803i | \(-0.390870\pi\) | ||||
0.336164 | + | 0.941803i | \(0.390870\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.6243 | 0.405934 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.7580 | −0.715663 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −77.9658 | −2.97026 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.1288 | 0.955944 | 0.477972 | − | 0.878375i | \(-0.341372\pi\) | ||||
0.477972 | + | 0.878375i | \(0.341372\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.57357 | 0.135553 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.76678 | 0.256310 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.9910 | 0.529189 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.8610 | −0.485753 | −0.242877 | − | 0.970057i | \(-0.578091\pi\) | ||||
−0.242877 | + | 0.970057i | \(0.578091\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.2610 | 1.82020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.77525 | 0.368157 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.9369 | −0.898969 | −0.449484 | − | 0.893288i | \(-0.648392\pi\) | ||||
−0.449484 | + | 0.893288i | \(0.648392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.26212 | −0.347357 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.4767 | 0.579609 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.1673 | −0.829009 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.9998 | −0.933634 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.7742 | 1.44603 | 0.723017 | − | 0.690830i | \(-0.242755\pi\) | ||||
0.723017 | + | 0.690830i | \(0.242755\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.4553 | 0.537600 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.9204 | 0.776964 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.6322 | 0.728117 | 0.364059 | − | 0.931376i | \(-0.381391\pi\) | ||||
0.364059 | + | 0.931376i | \(0.381391\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.29935 | 0.307383 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.6549 | 1.68861 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.7663 | 1.32106 | 0.660529 | − | 0.750801i | \(-0.270332\pi\) | ||||
0.660529 | + | 0.750801i | \(0.270332\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.12444 | 0.262432 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.6233 | −0.832212 | −0.416106 | − | 0.909316i | \(-0.636606\pi\) | ||||
−0.416106 | + | 0.909316i | \(0.636606\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29.2792 | −1.07560 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.9685 | 0.622515 | 0.311257 | − | 0.950326i | \(-0.399250\pi\) | ||||
0.311257 | + | 0.950326i | \(0.399250\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.32467 | 0.231718 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.10207 | 0.186675 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.1262 | 1.39124 | 0.695622 | − | 0.718408i | \(-0.255129\pi\) | ||||
0.695622 | + | 0.718408i | \(0.255129\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.4358 | −0.526069 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.08641 | −0.112326 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.1230 | 0.549656 | 0.274828 | − | 0.961493i | \(-0.411379\pi\) | ||||
0.274828 | + | 0.961493i | \(0.411379\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.8825 | −0.612794 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −43.5322 | −1.57804 | −0.789020 | − | 0.614367i | \(-0.789411\pi\) | ||||
−0.789020 | + | 0.614367i | \(0.789411\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.1677 | −0.693011 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.20327 | 0.332311 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.22236 | 0.188323 | 0.0941616 | − | 0.995557i | \(-0.469983\pi\) | ||||
0.0941616 | + | 0.995557i | \(0.469983\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.76118 | 0.243498 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.83438 | −0.209848 | −0.104924 | − | 0.994480i | \(-0.533460\pi\) | ||||
−0.104924 | + | 0.994480i | \(0.533460\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.51604 | −0.269984 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.15682 | −0.184762 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.49443 | −0.125041 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −30.1018 | −1.07575 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.5967 | −0.592363 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −54.2719 | −1.93459 | −0.967293 | − | 0.253662i | \(-0.918365\pi\) | ||||
−0.967293 | + | 0.253662i | \(0.918365\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.13789 | 0.254116 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.6915 | −0.521709 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.0706 | −0.534500 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.7610 | 0.735393 | 0.367697 | − | 0.929946i | \(-0.380146\pi\) | ||||
0.367697 | + | 0.929946i | \(0.380146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.1652 | −1.95160 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.61206 | −0.304292 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.4037 | 0.367139 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.4155 | −0.366642 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.74903 | 0.0966509 | 0.0483254 | − | 0.998832i | \(-0.484612\pi\) | ||||
0.0483254 | + | 0.998832i | \(0.484612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.6188 | −1.35609 | −0.678045 | − | 0.735020i | \(-0.737173\pi\) | ||||
−0.678045 | + | 0.735020i | \(0.737173\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.5444 | 0.650380 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.5091 | −0.403145 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.7927 | −1.21724 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.0655 | 1.11910 | 0.559548 | − | 0.828798i | \(-0.310975\pi\) | ||||
0.559548 | + | 0.828798i | \(0.310975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.9174 | 0.868566 | 0.434283 | − | 0.900776i | \(-0.357002\pi\) | ||||
0.434283 | + | 0.900776i | \(0.357002\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.19870 | 0.285442 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0445 | 0.557924 | 0.278962 | − | 0.960302i | \(-0.410010\pi\) | ||||
0.278962 | + | 0.960302i | \(0.410010\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.2341 | −0.806955 | −0.403477 | − | 0.914990i | \(-0.632199\pi\) | ||||
−0.403477 | + | 0.914990i | \(0.632199\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.5481 | −0.712807 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.25319 | 0.147188 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.8146 | 0.373808 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.97240 | −0.344286 | −0.172143 | − | 0.985072i | \(-0.555069\pi\) | ||||
−0.172143 | + | 0.985072i | \(0.555069\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5871 | 0.399556 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.2949 | −0.905645 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33.3799 | −1.14830 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.2338 | −0.797382 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.2820 | 2.16928 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.8869 | 0.715155 | 0.357577 | − | 0.933883i | \(-0.383603\pi\) | ||||
0.357577 | + | 0.933883i | \(0.383603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.6073 | 0.499561 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.0377 | 0.855272 | 0.427636 | − | 0.903951i | \(-0.359347\pi\) | ||||
0.427636 | + | 0.903951i | \(0.359347\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.8628 | 1.15538 | 0.577692 | − | 0.816255i | \(-0.303953\pi\) | ||||
0.577692 | + | 0.816255i | \(0.303953\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.2687 | 1.60905 | 0.804523 | − | 0.593922i | \(-0.202421\pi\) | ||||
0.804523 | + | 0.593922i | \(0.202421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.485482 | 0.0165069 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.3506 | −0.894912 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.6847 | 0.396375 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.2016 | 0.548971 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.2111 | 0.514818 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.3287 | 0.821522 | 0.410761 | − | 0.911743i | \(-0.365263\pi\) | ||||
0.410761 | + | 0.911743i | \(0.365263\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −24.1050 | −0.813042 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.4242 | 1.56407 | 0.782035 | − | 0.623235i | \(-0.214182\pi\) | ||||
0.782035 | + | 0.623235i | \(0.214182\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.22330 | −0.142125 | −0.0710626 | − | 0.997472i | \(-0.522639\pi\) | ||||
−0.0710626 | + | 0.997472i | \(0.522639\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.77897 | 0.0597995 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.72536 | −0.192239 | −0.0961194 | − | 0.995370i | \(-0.530643\pi\) | ||||
−0.0961194 | + | 0.995370i | \(0.530643\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.89750 | 0.197574 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42.0403 | 1.40682 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.5254 | 1.05378 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −38.3922 | −1.28188 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.5817 | −0.486326 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 85.0489 | 2.83339 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.34975 | 0.0448672 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.2656 | −0.606501 | −0.303250 | − | 0.952911i | \(-0.598072\pi\) | ||||
−0.303250 | + | 0.952911i | \(0.598072\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.5103 | 0.448108 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.8893 | −0.758356 | −0.379178 | − | 0.925324i | \(-0.623793\pi\) | ||||
−0.379178 | + | 0.925324i | \(0.623793\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.43654 | −0.213018 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.83983 | −0.0938819 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.67612 | 0.154251 | 0.0771254 | − | 0.997021i | \(-0.475426\pi\) | ||||
0.0771254 | + | 0.997021i | \(0.475426\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 27.3250 | 0.900390 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.94665 | −0.261567 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.7319 | −1.01046 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.2936 | −0.535153 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.1752 | 1.08844 | 0.544222 | − | 0.838941i | \(-0.316825\pi\) | ||||
0.544222 | + | 0.838941i | \(0.316825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.00019 | −0.0327446 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.1811 | 0.790808 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −54.1119 | −1.76776 | −0.883879 | − | 0.467715i | \(-0.845077\pi\) | ||||
−0.883879 | + | 0.467715i | \(0.845077\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.6330 | −0.771235 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.1721 | −0.624993 | −0.312497 | − | 0.949919i | \(-0.601165\pi\) | ||||
−0.312497 | + | 0.949919i | \(0.601165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.76186 | −0.220197 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.20600 | −0.0391898 | −0.0195949 | − | 0.999808i | \(-0.506238\pi\) | ||||
−0.0195949 | + | 0.999808i | \(0.506238\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.6590 | 0.768003 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.57443 | −0.180763 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.0276 | 1.13466 | 0.567328 | − | 0.823492i | \(-0.307977\pi\) | ||||
0.567328 | + | 0.823492i | \(0.307977\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.8169 | −0.350026 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.9061 | 0.514171 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7613 | −0.831008 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.5193 | 1.24127 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.7993 | −0.412026 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.8246 | −1.18420 | −0.592099 | − | 0.805865i | \(-0.701701\pi\) | ||||
−0.592099 | + | 0.805865i | \(0.701701\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.9392 | 1.02603 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.28648 | −0.105468 | −0.0527341 | − | 0.998609i | \(-0.516794\pi\) | ||||
−0.0527341 | + | 0.998609i | \(0.516794\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.6446 | 0.597105 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.64478 | −0.308564 | −0.154282 | − | 0.988027i | \(-0.549306\pi\) | ||||
−0.154282 | + | 0.988027i | \(0.549306\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.8646 | 0.347234 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.9318 | 0.540591 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −29.4596 | −0.939615 | −0.469808 | − | 0.882769i | \(-0.655677\pi\) | ||||
−0.469808 | + | 0.882769i | \(0.655677\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.45736 | −0.110161 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45.6218 | −1.45069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9223 | −0.601086 | −0.300543 | − | 0.953768i | \(-0.597168\pi\) | ||||
−0.300543 | + | 0.953768i | \(0.597168\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.5941 | −0.399661 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.42449 | −0.298777 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.4615 | −1.59813 | −0.799066 | − | 0.601243i | \(-0.794672\pi\) | ||||
−0.799066 | + | 0.601243i | \(0.794672\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.2193 | 1.39904 |
(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 | 8036.2.a.t.1.7 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.14 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.14 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.7 | yes | 20 | 1.1 | even | 1 | trivial |