Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9576,2,Mod(1,9576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9576, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9576.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9576.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: | \(76.4647449756\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3192) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9576.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.41421 | 1.52688 | 0.763441 | − | 0.645877i | \(-0.223508\pi\) | ||||
0.763441 | + | 0.645877i | \(0.223508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.65685 | 1.56893 | 0.784465 | − | 0.620174i | \(-0.212938\pi\) | ||||
0.784465 | + | 0.620174i | \(0.212938\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.24264 | −0.543920 | −0.271960 | − | 0.962309i | \(-0.587672\pi\) | ||||
−0.271960 | + | 0.962309i | \(0.587672\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.48528 | 1.76930 | 0.884652 | − | 0.466252i | \(-0.154396\pi\) | ||||
0.884652 | + | 0.466252i | \(0.154396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.2426 | −1.90201 | −0.951005 | − | 0.309175i | \(-0.899947\pi\) | ||||
−0.951005 | + | 0.309175i | \(0.899947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.82843 | 1.58563 | 0.792816 | − | 0.609461i | \(-0.208614\pi\) | ||||
0.792816 | + | 0.609461i | \(0.208614\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.41421 | −0.577107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.82843 | 1.37877 | 0.689384 | − | 0.724396i | \(-0.257881\pi\) | ||||
0.689384 | + | 0.724396i | \(0.257881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.82843 | −1.34632 | −0.673161 | − | 0.739496i | \(-0.735064\pi\) | ||||
−0.673161 | + | 0.739496i | \(0.735064\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.5858 | 1.54410 | 0.772048 | − | 0.635564i | \(-0.219233\pi\) | ||||
0.772048 | + | 0.635564i | \(0.219233\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.07107 | 0.696565 | 0.348282 | − | 0.937390i | \(-0.386765\pi\) | ||||
0.348282 | + | 0.937390i | \(0.386765\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.65685 | 1.30213 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.34315 | 0.305052 | 0.152526 | − | 0.988299i | \(-0.451259\pi\) | ||||
0.152526 | + | 0.988299i | \(0.451259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.3137 | 2.39557 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.17157 | −1.12049 | −0.560243 | − | 0.828328i | \(-0.689292\pi\) | ||||
−0.560243 | + | 0.828328i | \(0.689292\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.7279 | −1.51053 | −0.755263 | − | 0.655422i | \(-0.772491\pi\) | ||||
−0.755263 | + | 0.655422i | \(0.772491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.82843 | −1.03329 | −0.516645 | − | 0.856200i | \(-0.672819\pi\) | ||||
−0.516645 | + | 0.856200i | \(0.672819\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.82843 | −0.322329 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.34315 | 0.263624 | 0.131812 | − | 0.991275i | \(-0.457920\pi\) | ||||
0.131812 | + | 0.991275i | \(0.457920\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2426 | 1.34380 | 0.671902 | − | 0.740640i | \(-0.265478\pi\) | ||||
0.671902 | + | 0.740640i | \(0.265478\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.8284 | 1.78381 | 0.891905 | − | 0.452223i | \(-0.149369\pi\) | ||||
0.891905 | + | 0.452223i | \(0.149369\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.65685 | −0.592999 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.41421 | 0.350291 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.343146 | −0.0348412 | −0.0174206 | − | 0.999848i | \(-0.505545\pi\) | ||||
−0.0174206 | + | 0.999848i | \(0.505545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.07107 | −0.902605 | −0.451302 | − | 0.892371i | \(-0.649040\pi\) | ||||
−0.451302 | + | 0.892371i | \(0.649040\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.7279 | 1.61715 | 0.808575 | − | 0.588394i | \(-0.200239\pi\) | ||||
0.808575 | + | 0.588394i | \(0.200239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.1421 | −1.54614 | −0.773068 | − | 0.634323i | \(-0.781279\pi\) | ||||
−0.773068 | + | 0.634323i | \(0.781279\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.58579 | −0.807683 | −0.403841 | − | 0.914829i | \(-0.632325\pi\) | ||||
−0.403841 | + | 0.914829i | \(0.632325\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.9706 | 2.70152 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.24264 | 0.205583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.48528 | −0.752947 | −0.376473 | − | 0.926427i | \(-0.622863\pi\) | ||||
−0.376473 | + | 0.926427i | \(0.622863\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.89949 | −0.864923 | −0.432461 | − | 0.901652i | \(-0.642355\pi\) | ||||
−0.432461 | + | 0.901652i | \(0.642355\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.6569 | 0.995912 | 0.497956 | − | 0.867202i | \(-0.334084\pi\) | ||||
0.497956 | + | 0.867202i | \(0.334084\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.4853 | −1.05899 | −0.529494 | − | 0.848314i | \(-0.677618\pi\) | ||||
−0.529494 | + | 0.848314i | \(0.677618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16.0000 | 1.33799 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −34.9706 | −2.90415 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.4853 | −1.51437 | −0.757187 | − | 0.653199i | \(-0.773427\pi\) | ||||
−0.757187 | + | 0.653199i | \(0.773427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.48528 | 0.690522 | 0.345261 | − | 0.938507i | \(-0.387790\pi\) | ||||
0.345261 | + | 0.938507i | \(0.387790\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.1421 | 2.42107 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.65685 | −0.611083 | −0.305542 | − | 0.952179i | \(-0.598838\pi\) | ||||
−0.305542 | + | 0.952179i | \(0.598838\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.48528 | −0.668734 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.51472 | −0.118642 | −0.0593210 | − | 0.998239i | \(-0.518894\pi\) | ||||
−0.0593210 | + | 0.998239i | \(0.518894\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.8284 | 1.76652 | 0.883258 | − | 0.468887i | \(-0.155345\pi\) | ||||
0.883258 | + | 0.468887i | \(0.155345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0000 | 1.46154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.17157 | 0.241130 | 0.120565 | − | 0.992705i | \(-0.461529\pi\) | ||||
0.120565 | + | 0.992705i | \(0.461529\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.65685 | −0.503211 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.07107 | −0.229542 | −0.114771 | − | 0.993392i | \(-0.536613\pi\) | ||||
−0.114771 | + | 0.993392i | \(0.536613\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.31371 | −0.692283 | −0.346141 | − | 0.938182i | \(-0.612508\pi\) | ||||
−0.346141 | + | 0.938182i | \(0.612508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.4853 | −1.50611 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.34315 | −0.463857 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.8284 | 1.07295 | 0.536474 | − | 0.843917i | \(-0.319756\pi\) | ||||
0.536474 | + | 0.843917i | \(0.319756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.343146 | −0.0247002 | −0.0123501 | − | 0.999924i | \(-0.503931\pi\) | ||||
−0.0123501 | + | 0.999924i | \(0.503931\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.9706 | −1.06661 | −0.533304 | − | 0.845924i | \(-0.679050\pi\) | ||||
−0.533304 | + | 0.845924i | \(0.679050\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.1421 | −1.00251 | −0.501255 | − | 0.865300i | \(-0.667128\pi\) | ||||
−0.501255 | + | 0.865300i | \(0.667128\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.2426 | 0.718892 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.1421 | 2.10522 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.82843 | 0.195646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.9706 | 1.99442 | 0.997208 | − | 0.0746754i | \(-0.0237921\pi\) | ||||
0.997208 | + | 0.0746754i | \(0.0237921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −30.1421 | −2.05568 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.82843 | −0.599313 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.6863 | −0.853372 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.828427 | −0.0554756 | −0.0277378 | − | 0.999615i | \(-0.508830\pi\) | ||||
−0.0277378 | + | 0.999615i | \(0.508830\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.5147 | −0.764259 | −0.382129 | − | 0.924109i | \(-0.624809\pi\) | ||||
−0.382129 | + | 0.924109i | \(0.624809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.4853 | 0.692887 | 0.346443 | − | 0.938071i | \(-0.387389\pi\) | ||||
0.346443 | + | 0.938071i | \(0.387389\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.4853 | −0.686914 | −0.343457 | − | 0.939168i | \(-0.611598\pi\) | ||||
−0.343457 | + | 0.939168i | \(0.611598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.1421 | 2.35765 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.34315 | 0.151565 | 0.0757827 | − | 0.997124i | \(-0.475854\pi\) | ||||
0.0757827 | + | 0.997124i | \(0.475854\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.41421 | 0.218126 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.65685 | 0.359937 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.24264 | 0.267793 | 0.133897 | − | 0.990995i | \(-0.457251\pi\) | ||||
0.133897 | + | 0.990995i | \(0.457251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.0000 | 1.50887 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0000 | 0.873296 | 0.436648 | − | 0.899632i | \(-0.356166\pi\) | ||||
0.436648 | + | 0.899632i | \(0.356166\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | 0.372822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.65685 | −0.102166 | −0.0510830 | − | 0.998694i | \(-0.516267\pi\) | ||||
−0.0510830 | + | 0.998694i | \(0.516267\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.3137 | 1.06357 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6569 | 0.710731 | 0.355365 | − | 0.934727i | \(-0.384356\pi\) | ||||
0.355365 | + | 0.934727i | \(0.384356\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.9706 | −1.03089 | −0.515444 | − | 0.856923i | \(-0.672373\pi\) | ||||
−0.515444 | + | 0.856923i | \(0.672373\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.8284 | 1.13540 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.3137 | −0.679775 | −0.339887 | − | 0.940466i | \(-0.610389\pi\) | ||||
−0.339887 | + | 0.940466i | \(0.610389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.75736 | −0.104835 | −0.0524176 | − | 0.998625i | \(-0.516693\pi\) | ||||
−0.0524176 | + | 0.998625i | \(0.516693\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.1421 | 0.840663 | 0.420331 | − | 0.907371i | \(-0.361914\pi\) | ||||
0.420331 | + | 0.907371i | \(0.361914\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.82843 | −0.521126 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9706 | −0.704151 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.51472 | −0.0884908 | −0.0442454 | − | 0.999021i | \(-0.514088\pi\) | ||||
−0.0442454 | + | 0.999021i | \(0.514088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 48.0000 | 2.77591 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.82843 | 0.508862 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.82843 | 0.390995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.1421 | −0.921280 | −0.460640 | − | 0.887587i | \(-0.652380\pi\) | ||||
−0.460640 | + | 0.887587i | \(0.652380\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.0416 | 1.59009 | 0.795047 | − | 0.606547i | \(-0.207446\pi\) | ||||
0.795047 | + | 0.606547i | \(0.207446\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.97056 | 0.167906 | 0.0839531 | − | 0.996470i | \(-0.473245\pi\) | ||||
0.0839531 | + | 0.996470i | \(0.473245\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.2132 | −1.52845 | −0.764223 | − | 0.644952i | \(-0.776877\pi\) | ||||
−0.764223 | + | 0.644952i | \(0.776877\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −28.9706 | −1.62204 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.24264 | −0.124784 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 37.6569 | 2.08883 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.5858 | −0.583613 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.1421 | −0.777322 | −0.388661 | − | 0.921381i | \(-0.627062\pi\) | ||||
−0.388661 | + | 0.921381i | \(0.627062\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −31.3137 | −1.71085 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.82843 | −0.480915 | −0.240458 | − | 0.970660i | \(-0.577297\pi\) | ||||
−0.240458 | + | 0.970660i | \(0.577297\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.9706 | 1.35223 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.9706 | −1.12576 | −0.562879 | − | 0.826539i | \(-0.690306\pi\) | ||||
−0.562879 | + | 0.826539i | \(0.690306\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.3137 | 1.56913 | 0.784563 | − | 0.620049i | \(-0.212887\pi\) | ||||
0.784563 | + | 0.620049i | \(0.212887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.100505 | −0.00534934 | −0.00267467 | − | 0.999996i | \(-0.500851\pi\) | ||||
−0.00267467 | + | 0.999996i | \(0.500851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.4558 | −2.30640 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.48528 | −0.236724 | −0.118362 | − | 0.992971i | \(-0.537764\pi\) | ||||
−0.118362 | + | 0.992971i | \(0.537764\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.1421 | −1.57771 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.85786 | 0.305778 | 0.152889 | − | 0.988243i | \(-0.451142\pi\) | ||||
0.152889 | + | 0.988243i | \(0.451142\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.07107 | −0.263277 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.3431 | 1.26044 | 0.630220 | − | 0.776416i | \(-0.282965\pi\) | ||||
0.630220 | + | 0.776416i | \(0.282965\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −57.9411 | −2.98412 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.8284 | 0.761685 | 0.380843 | − | 0.924640i | \(-0.375634\pi\) | ||||
0.380843 | + | 0.924640i | \(0.375634\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.4853 | 1.04675 | 0.523374 | − | 0.852103i | \(-0.324673\pi\) | ||||
0.523374 | + | 0.852103i | \(0.324673\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.65685 | −0.492159 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.4558 | −1.79768 | −0.898841 | − | 0.438274i | \(-0.855590\pi\) | ||||
−0.898841 | + | 0.438274i | \(0.855590\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.0294 | −0.962360 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.31371 | 0.0659331 | 0.0329666 | − | 0.999456i | \(-0.489505\pi\) | ||||
0.0329666 | + | 0.999456i | \(0.489505\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.3848 | 0.618466 | 0.309233 | − | 0.950986i | \(-0.399928\pi\) | ||||
0.309233 | + | 0.950986i | \(0.399928\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 49.9411 | 2.48774 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16.9706 | −0.841200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.6274 | −0.921066 | −0.460533 | − | 0.887642i | \(-0.652342\pi\) | ||||
−0.460533 | + | 0.887642i | \(0.652342\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.34315 | −0.115299 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.7990 | 2.05183 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.72792 | 0.230974 | 0.115487 | − | 0.993309i | \(-0.463157\pi\) | ||||
0.115487 | + | 0.993309i | \(0.463157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.51472 | −0.0738229 | −0.0369114 | − | 0.999319i | \(-0.511752\pi\) | ||||
−0.0369114 | + | 0.999319i | \(0.511752\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.9289 | −0.724160 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.00000 | −0.0967868 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.4142 | 1.60951 | 0.804753 | − | 0.593610i | \(-0.202298\pi\) | ||||
0.804753 | + | 0.593610i | \(0.202298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.62742 | 0.222379 | 0.111190 | − | 0.993799i | \(-0.464534\pi\) | ||||
0.111190 | + | 0.993799i | \(0.464534\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.48528 | 0.405906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.7990 | −1.99496 | −0.997478 | − | 0.0709697i | \(-0.977391\pi\) | ||||
−0.997478 | + | 0.0709697i | \(0.977391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.686292 | −0.0326067 | −0.0163033 | − | 0.999867i | \(-0.505190\pi\) | ||||
−0.0163033 | + | 0.999867i | \(0.505190\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 57.4558 | 2.72367 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.8701 | −0.796147 | −0.398074 | − | 0.917353i | \(-0.630321\pi\) | ||||
−0.398074 | + | 0.917353i | \(0.630321\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.9706 | 1.17582 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.3137 | −0.905441 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.3137 | −1.27768 | −0.638841 | − | 0.769339i | \(-0.720586\pi\) | ||||
−0.638841 | + | 0.769339i | \(0.720586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.5269 | 1.79438 | 0.897189 | − | 0.441648i | \(-0.145606\pi\) | ||||
0.897189 | + | 0.441648i | \(0.145606\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.89949 | −0.458094 | −0.229047 | − | 0.973415i | \(-0.573561\pi\) | ||||
−0.229047 | + | 0.973415i | \(0.573561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.17157 | 0.423504 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.9706 | −1.14815 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.65685 | 0.305437 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.727922 | 0.0332596 | 0.0166298 | − | 0.999862i | \(-0.494706\pi\) | ||||
0.0166298 | + | 0.999862i | \(0.494706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.9411 | −1.54758 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.17157 | −0.0531984 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0000 | 0.543772 | 0.271886 | − | 0.962329i | \(-0.412353\pi\) | ||||
0.271886 | + | 0.962329i | \(0.412353\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.65685 | 0.435808 | 0.217904 | − | 0.975970i | \(-0.430078\pi\) | ||||
0.217904 | + | 0.975970i | \(0.430078\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.9706 | 1.03454 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.7279 | 0.570925 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.5980 | 1.95171 | 0.975857 | − | 0.218411i | \(-0.0700874\pi\) | ||||
0.975857 | + | 0.218411i | \(0.0700874\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −42.1838 | −1.88088 | −0.940441 | − | 0.339958i | \(-0.889587\pi\) | ||||
−0.940441 | + | 0.339958i | \(0.889587\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.9706 | −1.37817 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.9706 | 0.663559 | 0.331779 | − | 0.943357i | \(-0.392351\pi\) | ||||
0.331779 | + | 0.943357i | \(0.392351\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.82843 | 0.390547 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.3137 | 1.20359 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.9411 | 1.31681 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.9706 | 1.70733 | 0.853666 | − | 0.520821i | \(-0.174374\pi\) | ||||
0.853666 | + | 0.520821i | \(0.174374\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.142136 | −0.00621516 | −0.00310758 | − | 0.999995i | \(-0.500989\pi\) | ||||
−0.00310758 | + | 0.999995i | \(0.500989\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.7990 | −0.862458 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 49.0000 | 2.13043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.9411 | 2.16319 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 57.1127 | 2.46920 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.82843 | 0.121829 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.0000 | −0.945854 | −0.472927 | − | 0.881102i | \(-0.656803\pi\) | ||||
−0.472927 | + | 0.881102i | \(0.656803\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −55.1127 | −2.36077 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.5980 | −1.52206 | −0.761030 | − | 0.648717i | \(-0.775306\pi\) | ||||
−0.761030 | + | 0.648717i | \(0.775306\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.2426 | −0.436351 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.34315 | −0.0996407 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.17157 | −0.134384 | −0.0671919 | − | 0.997740i | \(-0.521404\pi\) | ||||
−0.0671919 | + | 0.997740i | \(0.521404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −49.9411 | −2.11228 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.4853 | 1.03193 | 0.515966 | − | 0.856609i | \(-0.327433\pi\) | ||||
0.515966 | + | 0.856609i | \(0.327433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.3137 | −1.23324 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.5269 | 0.776689 | 0.388344 | − | 0.921514i | \(-0.373047\pi\) | ||||
0.388344 | + | 0.921514i | \(0.373047\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9706 | −0.542801 | −0.271401 | − | 0.962466i | \(-0.587487\pi\) | ||||
−0.271401 | + | 0.962466i | \(0.587487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 56.4853 | 2.35560 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.34315 | 0.180808 | 0.0904038 | − | 0.995905i | \(-0.471184\pi\) | ||||
0.0904038 | + | 0.995905i | \(0.471184\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.2426 | −0.507910 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.3431 | 0.594032 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.928932 | 0.0383411 | 0.0191706 | − | 0.999816i | \(-0.493897\pi\) | ||||
0.0191706 | + | 0.999816i | \(0.493897\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.82843 | 0.363769 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 48.3848 | 1.98692 | 0.993462 | − | 0.114161i | \(-0.0364178\pi\) | ||||
0.993462 | + | 0.114161i | \(0.0364178\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.65685 | 0.313900 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.1005 | −0.903002 | −0.451501 | − | 0.892271i | \(-0.649111\pi\) | ||||
−0.451501 | + | 0.892271i | \(0.649111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.31371 | −0.379914 | −0.189957 | − | 0.981792i | \(-0.560835\pi\) | ||||
−0.189957 | + | 0.981792i | \(0.560835\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.2426 | −0.416423 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.9411 | 1.05292 | 0.526459 | − | 0.850201i | \(-0.323519\pi\) | ||||
0.526459 | + | 0.850201i | \(0.323519\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 59.8823 | 2.42258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.2843 | −0.496157 | −0.248079 | − | 0.968740i | \(-0.579799\pi\) | ||||
−0.248079 | + | 0.968740i | \(0.579799\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.9411 | 1.44694 | 0.723468 | − | 0.690358i | \(-0.242547\pi\) | ||||
0.723468 | + | 0.690358i | \(0.242547\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.5147 | 0.462816 | 0.231408 | − | 0.972857i | \(-0.425667\pi\) | ||||
0.231408 | + | 0.972857i | \(0.425667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.8284 | −0.674217 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.4558 | 0.536520 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4558 | 0.615287 | 0.307644 | − | 0.951502i | \(-0.400460\pi\) | ||||
0.307644 | + | 0.951502i | \(0.400460\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −28.9706 | −1.14966 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.65685 | 0.224133 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −47.6985 | −1.88398 | −0.941988 | − | 0.335645i | \(-0.891046\pi\) | ||||
−0.941988 | + | 0.335645i | \(0.891046\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.1716 | 0.834925 | 0.417463 | − | 0.908694i | \(-0.362919\pi\) | ||||
0.417463 | + | 0.908694i | \(0.362919\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.727922 | −0.0286176 | −0.0143088 | − | 0.999898i | \(-0.504555\pi\) | ||||
−0.0143088 | + | 0.999898i | \(0.504555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.62742 | 0.260149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.5980 | −1.47132 | −0.735661 | − | 0.677350i | \(-0.763128\pi\) | ||||
−0.735661 | + | 0.677350i | \(0.763128\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.7990 | −1.32064 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.2426 | −0.632723 | −0.316362 | − | 0.948639i | \(-0.602461\pi\) | ||||
−0.316362 | + | 0.948639i | \(0.602461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0000 | 0.466746 | 0.233373 | − | 0.972387i | \(-0.425024\pi\) | ||||
0.233373 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.41421 | −0.132398 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −86.9117 | −3.36523 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.65685 | 0.218380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.3137 | 0.821583 | 0.410792 | − | 0.911729i | \(-0.365252\pi\) | ||||
0.410792 | + | 0.911729i | \(0.365252\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.9411 | −1.53506 | −0.767531 | − | 0.641012i | \(-0.778515\pi\) | ||||
−0.767531 | + | 0.641012i | \(0.778515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.343146 | 0.0131687 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.8995 | 0.837961 | 0.418980 | − | 0.907995i | \(-0.362388\pi\) | ||||
0.418980 | + | 0.907995i | \(0.362388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.7990 | 1.52064 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.6863 | 1.09286 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.9706 | 1.10209 | 0.551046 | − | 0.834475i | \(-0.314229\pi\) | ||||
0.551046 | + | 0.834475i | \(0.314229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −42.6274 | −1.61695 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.7990 | −0.749940 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −50.0000 | −1.88847 | −0.944237 | − | 0.329267i | \(-0.893198\pi\) | ||||
−0.944237 | + | 0.329267i | \(0.893198\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | −0.226294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.07107 | 0.341153 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.65685 | −0.0622245 | −0.0311122 | − | 0.999516i | \(-0.509905\pi\) | ||||
−0.0311122 | + | 0.999516i | \(0.509905\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 74.9117 | 2.80546 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 54.6274 | 2.04295 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.38478 | −0.238112 | −0.119056 | − | 0.992888i | \(-0.537987\pi\) | ||||
−0.119056 | + | 0.992888i | \(0.537987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −68.1838 | −2.53228 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.6274 | −0.987556 | −0.493778 | − | 0.869588i | \(-0.664385\pi\) | ||||
−0.493778 | + | 0.869588i | \(0.664385\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.7990 | 0.732292 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.8284 | −0.769316 | −0.384658 | − | 0.923059i | \(-0.625681\pi\) | ||||
−0.384658 | + | 0.923059i | \(0.625681\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.9411 | −0.955554 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.7990 | −1.39046 | −0.695229 | − | 0.718788i | \(-0.744697\pi\) | ||||
−0.695229 | + | 0.718788i | \(0.744697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.0711 | 1.43338 | 0.716689 | − | 0.697393i | \(-0.245657\pi\) | ||||
0.716689 | + | 0.697393i | \(0.245657\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −63.1127 | −2.31227 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.7279 | −0.611225 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.2010 | 0.445221 | 0.222611 | − | 0.974907i | \(-0.428542\pi\) | ||||
0.222611 | + | 0.974907i | \(0.428542\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.9706 | 1.05435 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.34315 | 0.157854 | 0.0789272 | − | 0.996880i | \(-0.474851\pi\) | ||||
0.0789272 | + | 0.996880i | \(0.474851\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −47.2132 | −1.71148 | −0.855739 | − | 0.517408i | \(-0.826897\pi\) | ||||
−0.855739 | + | 0.517408i | \(0.826897\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.1421 | 0.584385 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2548 | 0.478604 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.02944 | 0.0371225 | 0.0185612 | − | 0.999828i | \(-0.494091\pi\) | ||||
0.0185612 | + | 0.999828i | \(0.494091\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.5147 | 0.486091 | 0.243045 | − | 0.970015i | \(-0.421854\pi\) | ||||
0.243045 | + | 0.970015i | \(0.421854\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 58.7696 | 2.11106 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.82843 | 0.316311 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.1421 | −0.933053 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.1421 | 0.575405 | 0.287702 | − | 0.957720i | \(-0.407109\pi\) | ||||
0.287702 | + | 0.957720i | \(0.407109\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.58579 | 0.305275 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.3137 | 0.401762 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.48528 | −0.229720 | −0.114860 | − | 0.993382i | \(-0.536642\pi\) | ||||
−0.114860 | + | 0.993382i | \(0.536642\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.7401 | −0.839865 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.9706 | −0.881192 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.9706 | −1.02108 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.9706 | 0.948234 | 0.474117 | − | 0.880462i | \(-0.342767\pi\) | ||||
0.474117 | + | 0.880462i | \(0.342767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.9706 | −1.57913 | −0.789565 | − | 0.613667i | \(-0.789694\pi\) | ||||
−0.789565 | + | 0.613667i | \(0.789694\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.17157 | −0.181152 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.82843 | −0.308868 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.8284 | 0.587316 | 0.293658 | − | 0.955911i | \(-0.405127\pi\) | ||||
0.293658 | + | 0.955911i | \(0.405127\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.1421 | 1.53870 | 0.769349 | − | 0.638829i | \(-0.220581\pi\) | ||||
0.769349 | + | 0.638829i | \(0.220581\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.8995 | 0.761520 | 0.380760 | − | 0.924674i | \(-0.375662\pi\) | ||||
0.380760 | + | 0.924674i | \(0.375662\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.2843 | 1.74644 | 0.873222 | − | 0.487322i | \(-0.162026\pi\) | ||||
0.873222 | + | 0.487322i | \(0.162026\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.24264 | −0.0777029 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 77.9411 | 2.69726 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.2548 | −1.42428 | −0.712138 | − | 0.702040i | \(-0.752273\pi\) | ||||
−0.712138 | + | 0.702040i | \(0.752273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 75.9117 | 2.61764 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 64.8701 | 2.23160 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.00000 | 0.103081 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −50.9117 | −1.74523 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.02944 | 0.0352473 | 0.0176236 | − | 0.999845i | \(-0.494390\pi\) | ||||
0.0176236 | + | 0.999845i | \(0.494390\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.4853 | 0.904720 | 0.452360 | − | 0.891835i | \(-0.350582\pi\) | ||||
0.452360 | + | 0.891835i | \(0.350582\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.6569 | 1.83075 | 0.915374 | − | 0.402604i | \(-0.131895\pi\) | ||||
0.915374 | + | 0.402604i | \(0.131895\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.7574 | −0.944871 | −0.472436 | − | 0.881365i | \(-0.656625\pi\) | ||||
−0.472436 | + | 0.881365i | \(0.656625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.8284 | 0.368178 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.62742 | 0.224820 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −51.8823 | −1.75796 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.65685 | −0.191237 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.6863 | 0.630991 | 0.315496 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315496 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.3848 | −0.686781 | −0.343390 | − | 0.939193i | \(-0.611575\pi\) | ||||
−0.343390 | + | 0.939193i | \(0.611575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.4264 | 1.42454 | 0.712270 | − | 0.701906i | \(-0.247667\pi\) | ||||
0.712270 | + | 0.701906i | \(0.247667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.48528 | 0.284587 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.5858 | 0.354240 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.4853 | −0.350484 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −90.4264 | −3.01589 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.3726 | −0.378876 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.7990 | −1.05703 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.5980 | −1.04919 | −0.524597 | − | 0.851351i | \(-0.675784\pi\) | ||||
−0.524597 | + | 0.851351i | \(0.675784\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.4437 | 0.544802 | 0.272401 | − | 0.962184i | \(-0.412182\pi\) | ||||
0.272401 | + | 0.962184i | \(0.412182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.6274 | 1.14600 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.89949 | 0.326910 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.0000 | −0.791687 | −0.395843 | − | 0.918318i | \(-0.629548\pi\) | ||||
−0.395843 | + | 0.918318i | \(0.629548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −72.0000 | −2.36991 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.9411 | −1.31326 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.2132 | −1.41778 | −0.708890 | − | 0.705319i | \(-0.750804\pi\) | ||||
−0.708890 | + | 0.705319i | \(0.750804\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.6569 | −0.708255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.0294 | 0.817676 | 0.408838 | − | 0.912607i | \(-0.365934\pi\) | ||||
0.408838 | + | 0.912607i | \(0.365934\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.2843 | 0.987239 | 0.493620 | − | 0.869678i | \(-0.335674\pi\) | ||||
0.493620 | + | 0.869678i | \(0.335674\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 74.9117 | 2.43946 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.48528 | −0.145752 | −0.0728760 | − | 0.997341i | \(-0.523218\pi\) | ||||
−0.0728760 | + | 0.997341i | \(0.523218\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.9411 | −1.62116 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 50.0416 | 1.62101 | 0.810504 | − | 0.585734i | \(-0.199193\pi\) | ||||
0.810504 | + | 0.585734i | \(0.199193\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 50.6274 | 1.63826 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.6569 | −0.376419 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.9411 | 1.51423 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.17157 | −0.0377143 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.8284 | −0.798428 | −0.399214 | − | 0.916858i | \(-0.630717\pi\) | ||||
−0.399214 | + | 0.916858i | \(0.630717\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.6863 | 0.407122 | 0.203561 | − | 0.979062i | \(-0.434748\pi\) | ||||
0.203561 | + | 0.979062i | \(0.434748\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.4853 | 0.400260 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −61.1543 | −1.95650 | −0.978250 | − | 0.207429i | \(-0.933491\pi\) | ||||
−0.978250 | + | 0.207429i | \(0.933491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 47.5980 | 1.52124 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.2843 | −0.902128 | −0.451064 | − | 0.892492i | \(-0.648955\pi\) | ||||
−0.451064 | + | 0.892492i | \(0.648955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.1127 | −1.62859 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −74.9117 | −2.38205 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2843 | 0.771415 | 0.385708 | − | 0.922621i | \(-0.373957\pi\) | ||||
0.385708 | + | 0.922621i | \(0.373957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −48.2843 | −1.53071 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.6569 | 0.622539 | 0.311269 | − | 0.950322i | \(-0.399246\pi\) | ||||
0.311269 | + | 0.950322i | \(0.399246\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 9576.2.a.by.1.2 | 2 | ||
3.2 | odd | 2 | 3192.2.a.r.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 6384.2.a.bh.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3192.2.a.r.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
6384.2.a.bh.1.1 | 2 | 12.11 | even | 2 | |||
9576.2.a.by.1.2 | 2 | 1.1 | even | 1 | trivial |