Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6930,2,Mod(1,6930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6930.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6930.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: | \(55.3363286007\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.347296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6930.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.694593 | −0.192645 | −0.0963227 | − | 0.995350i | \(-0.530708\pi\) | ||||
−0.0963227 | + | 0.995350i | \(0.530708\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.69459 | −0.653535 | −0.326767 | − | 0.945105i | \(-0.605959\pi\) | ||||
−0.326767 | + | 0.945105i | \(0.605959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.51754 | 1.26581 | 0.632905 | − | 0.774229i | \(-0.281862\pi\) | ||||
0.632905 | + | 0.774229i | \(0.281862\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −7.43376 | −1.55005 | −0.775023 | − | 0.631933i | \(-0.782262\pi\) | ||||
−0.775023 | + | 0.631933i | \(0.782262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.694593 | −0.136221 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −0.610815 | −0.113425 | −0.0567127 | − | 0.998391i | \(-0.518062\pi\) | ||||
−0.0567127 | + | 0.998391i | \(0.518062\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.51754 | −1.35019 | −0.675095 | − | 0.737731i | \(-0.735897\pi\) | ||||
−0.675095 | + | 0.737731i | \(0.735897\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.69459 | −0.462119 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.30541 | −0.214608 | −0.107304 | − | 0.994226i | \(-0.534222\pi\) | ||||
−0.107304 | + | 0.994226i | \(0.534222\pi\) | |||||||
\(38\) | 5.51754 | 0.895063 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −9.51754 | −1.48639 | −0.743195 | − | 0.669075i | \(-0.766691\pi\) | ||||
−0.743195 | + | 0.669075i | \(0.766691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.51754 | 0.841417 | 0.420709 | − | 0.907196i | \(-0.361782\pi\) | ||||
0.420709 | + | 0.907196i | \(0.361782\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.43376 | −1.09605 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.694593 | −0.0963227 | ||||||||
\(53\) | 4.12836 | 0.567073 | 0.283537 | − | 0.958961i | \(-0.408492\pi\) | ||||
0.283537 | + | 0.958961i | \(0.408492\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.610815 | −0.0802039 | ||||||||
\(59\) | 3.51754 | 0.457945 | 0.228972 | − | 0.973433i | \(-0.426463\pi\) | ||||
0.228972 | + | 0.973433i | \(0.426463\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | −0.512148 | −0.256074 | − | 0.966657i | \(-0.582429\pi\) | ||||
−0.256074 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(62\) | −7.51754 | −0.954729 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.694593 | 0.0861536 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.95130 | −1.09358 | −0.546788 | − | 0.837271i | \(-0.684150\pi\) | ||||
−0.546788 | + | 0.837271i | \(0.684150\pi\) | |||||||
\(68\) | −2.69459 | −0.326767 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −4.77837 | −0.567088 | −0.283544 | − | 0.958959i | \(-0.591510\pi\) | ||||
−0.283544 | + | 0.958959i | \(0.591510\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.51754 | 0.645779 | 0.322890 | − | 0.946437i | \(-0.395346\pi\) | ||||
0.322890 | + | 0.946437i | \(0.395346\pi\) | |||||||
\(74\) | −1.30541 | −0.151751 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.51754 | 0.632905 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.77837 | −0.312591 | −0.156296 | − | 0.987710i | \(-0.549955\pi\) | ||||
−0.156296 | + | 0.987710i | \(0.549955\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.51754 | −1.05104 | ||||||||
\(83\) | 4.73917 | 0.520192 | 0.260096 | − | 0.965583i | \(-0.416246\pi\) | ||||
0.260096 | + | 0.965583i | \(0.416246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.69459 | 0.292270 | ||||||||
\(86\) | 5.51754 | 0.594972 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −8.04458 | −0.852724 | −0.426362 | − | 0.904553i | \(-0.640205\pi\) | ||||
−0.426362 | + | 0.904553i | \(0.640205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.694593 | −0.0728131 | ||||||||
\(92\) | −7.43376 | −0.775023 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | −0.618853 | ||||||||
\(95\) | −5.51754 | −0.566088 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.90673 | −0.701272 | −0.350636 | − | 0.936512i | \(-0.614035\pi\) | ||||
−0.350636 | + | 0.936512i | \(0.614035\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.64590 | 0.760795 | 0.380398 | − | 0.924823i | \(-0.375787\pi\) | ||||
0.380398 | + | 0.924823i | \(0.375787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.51754 | −0.740725 | −0.370363 | − | 0.928887i | \(-0.620767\pi\) | ||||
−0.370363 | + | 0.928887i | \(0.620767\pi\) | |||||||
\(104\) | −0.694593 | −0.0681104 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.12836 | 0.400981 | ||||||||
\(107\) | 17.1634 | 1.65925 | 0.829626 | − | 0.558319i | \(-0.188554\pi\) | ||||
0.829626 | + | 0.558319i | \(0.188554\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.91622 | −0.183541 | −0.0917704 | − | 0.995780i | \(-0.529253\pi\) | ||||
−0.0917704 | + | 0.995780i | \(0.529253\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −12.2121 | −1.14882 | −0.574410 | − | 0.818567i | \(-0.694769\pi\) | ||||
−0.574410 | + | 0.818567i | \(0.694769\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.43376 | 0.693202 | ||||||||
\(116\) | −0.610815 | −0.0567127 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.51754 | 0.323816 | ||||||||
\(119\) | −2.69459 | −0.247013 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.00000 | −0.362143 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.51754 | −0.675095 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.5175 | 1.02202 | 0.511008 | − | 0.859576i | \(-0.329272\pi\) | ||||
0.511008 | + | 0.859576i | \(0.329272\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.694593 | 0.0609198 | ||||||||
\(131\) | −5.38919 | −0.470855 | −0.235428 | − | 0.971892i | \(-0.575649\pi\) | ||||
−0.235428 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.51754 | 0.478431 | ||||||||
\(134\) | −8.95130 | −0.773275 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.69459 | −0.231059 | ||||||||
\(137\) | −13.4338 | −1.14772 | −0.573862 | − | 0.818952i | \(-0.694555\pi\) | ||||
−0.573862 | + | 0.818952i | \(0.694555\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.9067 | −1.60365 | −0.801824 | − | 0.597561i | \(-0.796137\pi\) | ||||
−0.801824 | + | 0.597561i | \(0.796137\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.77837 | −0.400992 | ||||||||
\(143\) | 0.694593 | 0.0580848 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.610815 | 0.0507254 | ||||||||
\(146\) | 5.51754 | 0.456635 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.30541 | −0.107304 | ||||||||
\(149\) | 0.610815 | 0.0500399 | 0.0250199 | − | 0.999687i | \(-0.492035\pi\) | ||||
0.0250199 | + | 0.999687i | \(0.492035\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 5.51754 | 0.447532 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | 7.51754 | 0.603823 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.5526 | 1.95951 | 0.979756 | − | 0.200194i | \(-0.0641572\pi\) | ||||
0.979756 | + | 0.200194i | \(0.0641572\pi\) | |||||||
\(158\) | −2.77837 | −0.221035 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −7.43376 | −0.585863 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.91622 | −0.150090 | −0.0750450 | − | 0.997180i | \(-0.523910\pi\) | ||||
−0.0750450 | + | 0.997180i | \(0.523910\pi\) | |||||||
\(164\) | −9.51754 | −0.743195 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.73917 | 0.367831 | ||||||||
\(167\) | −24.2121 | −1.87359 | −0.936796 | − | 0.349877i | \(-0.886223\pi\) | ||||
−0.936796 | + | 0.349877i | \(0.886223\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5175 | −0.962888 | ||||||||
\(170\) | 2.69459 | 0.206666 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.51754 | 0.420709 | ||||||||
\(173\) | −7.22163 | −0.549050 | −0.274525 | − | 0.961580i | \(-0.588521\pi\) | ||||
−0.274525 | + | 0.961580i | \(0.588521\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.04458 | −0.602967 | ||||||||
\(179\) | −14.2959 | −1.06853 | −0.534263 | − | 0.845318i | \(-0.679411\pi\) | ||||
−0.534263 | + | 0.845318i | \(0.679411\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.52704 | −0.187833 | −0.0939166 | − | 0.995580i | \(-0.529939\pi\) | ||||
−0.0939166 | + | 0.995580i | \(0.529939\pi\) | |||||||
\(182\) | −0.694593 | −0.0514866 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.43376 | −0.548024 | ||||||||
\(185\) | 1.30541 | 0.0959755 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.69459 | 0.197048 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.51754 | −0.400284 | ||||||||
\(191\) | 0.610815 | 0.0441970 | 0.0220985 | − | 0.999756i | \(-0.492965\pi\) | ||||
0.0220985 | + | 0.999756i | \(0.492965\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.51754 | −0.109235 | −0.0546175 | − | 0.998507i | \(-0.517394\pi\) | ||||
−0.0546175 | + | 0.998507i | \(0.517394\pi\) | |||||||
\(194\) | −6.90673 | −0.495874 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 10.7392 | 0.765134 | 0.382567 | − | 0.923928i | \(-0.375040\pi\) | ||||
0.382567 | + | 0.923928i | \(0.375040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.906726 | −0.0642761 | −0.0321381 | − | 0.999483i | \(-0.510232\pi\) | ||||
−0.0321381 | + | 0.999483i | \(0.510232\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.64590 | 0.537963 | ||||||||
\(203\) | −0.610815 | −0.0428708 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.51754 | 0.664734 | ||||||||
\(206\) | −7.51754 | −0.523772 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.694593 | −0.0481613 | ||||||||
\(209\) | −5.51754 | −0.381656 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.3756 | −1.88461 | −0.942306 | − | 0.334753i | \(-0.891347\pi\) | ||||
−0.942306 | + | 0.334753i | \(0.891347\pi\) | |||||||
\(212\) | 4.12836 | 0.283537 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.1634 | 1.17327 | ||||||||
\(215\) | −5.51754 | −0.376293 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.51754 | −0.510324 | ||||||||
\(218\) | −1.91622 | −0.129783 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 1.87164 | 0.125900 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.6459 | 1.44952 | 0.724758 | − | 0.689003i | \(-0.241951\pi\) | ||||
0.724758 | + | 0.689003i | \(0.241951\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.2121 | −0.812339 | ||||||||
\(227\) | −11.3500 | −0.753325 | −0.376662 | − | 0.926351i | \(-0.622928\pi\) | ||||
−0.376662 | + | 0.926351i | \(0.622928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.69459 | −0.442391 | −0.221196 | − | 0.975229i | \(-0.570996\pi\) | ||||
−0.221196 | + | 0.975229i | \(0.570996\pi\) | |||||||
\(230\) | 7.43376 | 0.490168 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.610815 | −0.0401019 | ||||||||
\(233\) | −14.2567 | −0.933988 | −0.466994 | − | 0.884260i | \(-0.654663\pi\) | ||||
−0.466994 | + | 0.884260i | \(0.654663\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | 0.391397 | ||||||||
\(236\) | 3.51754 | 0.228972 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.69459 | −0.174665 | ||||||||
\(239\) | 3.72967 | 0.241253 | 0.120626 | − | 0.992698i | \(-0.461510\pi\) | ||||
0.120626 | + | 0.992698i | \(0.461510\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7392 | −0.949433 | −0.474717 | − | 0.880139i | \(-0.657449\pi\) | ||||
−0.474717 | + | 0.880139i | \(0.657449\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.83244 | −0.243853 | ||||||||
\(248\) | −7.51754 | −0.477364 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −18.3851 | −1.16046 | −0.580228 | − | 0.814454i | \(-0.697036\pi\) | ||||
−0.580228 | + | 0.814454i | \(0.697036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.43376 | 0.467357 | ||||||||
\(254\) | 11.5175 | 0.722675 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.09327 | −0.192953 | −0.0964766 | − | 0.995335i | \(-0.530757\pi\) | ||||
−0.0964766 | + | 0.995335i | \(0.530757\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.30541 | −0.0811141 | ||||||||
\(260\) | 0.694593 | 0.0430768 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.38919 | −0.332945 | ||||||||
\(263\) | 6.61081 | 0.407640 | 0.203820 | − | 0.979008i | \(-0.434664\pi\) | ||||
0.203820 | + | 0.979008i | \(0.434664\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.12836 | −0.253603 | ||||||||
\(266\) | 5.51754 | 0.338302 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.95130 | −0.546788 | ||||||||
\(269\) | 6.00000 | 0.365826 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.8135 | 0.839107 | 0.419554 | − | 0.907730i | \(-0.362187\pi\) | ||||
0.419554 | + | 0.907730i | \(0.362187\pi\) | |||||||
\(272\) | −2.69459 | −0.163384 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.4338 | −0.811563 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.1634 | 1.51192 | 0.755962 | − | 0.654615i | \(-0.227169\pi\) | ||||
0.755962 | + | 0.654615i | \(0.227169\pi\) | |||||||
\(278\) | −18.9067 | −1.13395 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 15.9162 | 0.949482 | 0.474741 | − | 0.880125i | \(-0.342542\pi\) | ||||
0.474741 | + | 0.880125i | \(0.342542\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2121 | −0.607048 | −0.303524 | − | 0.952824i | \(-0.598163\pi\) | ||||
−0.303524 | + | 0.952824i | \(0.598163\pi\) | |||||||
\(284\) | −4.77837 | −0.283544 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.694593 | 0.0410721 | ||||||||
\(287\) | −9.51754 | −0.561803 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.73917 | −0.572892 | ||||||||
\(290\) | 0.610815 | 0.0358683 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.51754 | 0.322890 | ||||||||
\(293\) | 26.6810 | 1.55872 | 0.779360 | − | 0.626577i | \(-0.215545\pi\) | ||||
0.779360 | + | 0.626577i | \(0.215545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.51754 | −0.204799 | ||||||||
\(296\) | −1.30541 | −0.0758753 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.610815 | 0.0353835 | ||||||||
\(299\) | 5.16344 | 0.298609 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.51754 | 0.318026 | ||||||||
\(302\) | 8.00000 | 0.460348 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.51754 | 0.316453 | ||||||||
\(305\) | 4.00000 | 0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.2472 | −0.984351 | −0.492175 | − | 0.870496i | \(-0.663798\pi\) | ||||
−0.492175 | + | 0.870496i | \(0.663798\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.51754 | 0.426968 | ||||||||
\(311\) | −12.1729 | −0.690264 | −0.345132 | − | 0.938554i | \(-0.612166\pi\) | ||||
−0.345132 | + | 0.938554i | \(0.612166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.6810 | −1.05591 | −0.527956 | − | 0.849272i | \(-0.677041\pi\) | ||||
−0.527956 | + | 0.849272i | \(0.677041\pi\) | |||||||
\(314\) | 24.5526 | 1.38558 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.77837 | −0.156296 | ||||||||
\(317\) | −29.7743 | −1.67229 | −0.836144 | − | 0.548510i | \(-0.815195\pi\) | ||||
−0.836144 | + | 0.548510i | \(0.815195\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.610815 | 0.0341991 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.43376 | −0.414267 | ||||||||
\(323\) | −14.8675 | −0.827251 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.694593 | −0.0385291 | ||||||||
\(326\) | −1.91622 | −0.106130 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.51754 | −0.525518 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.25671 | 0.233970 | 0.116985 | − | 0.993134i | \(-0.462677\pi\) | ||||
0.116985 | + | 0.993134i | \(0.462677\pi\) | |||||||
\(332\) | 4.73917 | 0.260096 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −24.2121 | −1.32483 | ||||||||
\(335\) | 8.95130 | 0.489062 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.64590 | 0.198605 | 0.0993023 | − | 0.995057i | \(-0.468339\pi\) | ||||
0.0993023 | + | 0.995057i | \(0.468339\pi\) | |||||||
\(338\) | −12.5175 | −0.680864 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.69459 | 0.146135 | ||||||||
\(341\) | 7.51754 | 0.407098 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 5.51754 | 0.297486 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.22163 | −0.388237 | ||||||||
\(347\) | 27.9418 | 1.49999 | 0.749997 | − | 0.661441i | \(-0.230055\pi\) | ||||
0.749997 | + | 0.661441i | \(0.230055\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.4783 | −1.36382 | −0.681912 | − | 0.731434i | \(-0.738851\pi\) | ||||
−0.681912 | + | 0.731434i | \(0.738851\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | 17.1634 | 0.913518 | 0.456759 | − | 0.889591i | \(-0.349010\pi\) | ||||
0.456759 | + | 0.889591i | \(0.349010\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.77837 | 0.253610 | ||||||||
\(356\) | −8.04458 | −0.426362 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.2959 | −0.755562 | ||||||||
\(359\) | 31.8188 | 1.67933 | 0.839667 | − | 0.543102i | \(-0.182750\pi\) | ||||
0.839667 | + | 0.543102i | \(0.182750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.4433 | 0.602277 | ||||||||
\(362\) | −2.52704 | −0.132818 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.694593 | −0.0364066 | ||||||||
\(365\) | −5.51754 | −0.288801 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.7743 | −1.44980 | −0.724902 | − | 0.688852i | \(-0.758115\pi\) | ||||
−0.724902 | + | 0.688852i | \(0.758115\pi\) | |||||||
\(368\) | −7.43376 | −0.387512 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.30541 | 0.0678649 | ||||||||
\(371\) | 4.12836 | 0.214334 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.739170 | 0.0382728 | 0.0191364 | − | 0.999817i | \(-0.493908\pi\) | ||||
0.0191364 | + | 0.999817i | \(0.493908\pi\) | |||||||
\(374\) | 2.69459 | 0.139334 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | 0.424267 | 0.0218509 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.5134 | 1.25917 | 0.629585 | − | 0.776932i | \(-0.283225\pi\) | ||||
0.629585 | + | 0.776932i | \(0.283225\pi\) | |||||||
\(380\) | −5.51754 | −0.283044 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.610815 | 0.0312520 | ||||||||
\(383\) | −6.00000 | −0.306586 | −0.153293 | − | 0.988181i | \(-0.548988\pi\) | ||||
−0.153293 | + | 0.988181i | \(0.548988\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.00000 | 0.0509647 | ||||||||
\(386\) | −1.51754 | −0.0772408 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.90673 | −0.350636 | ||||||||
\(389\) | −6.65002 | −0.337169 | −0.168585 | − | 0.985687i | \(-0.553920\pi\) | ||||
−0.168585 | + | 0.985687i | \(0.553920\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.0310 | 1.01301 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.7392 | 0.541032 | ||||||||
\(395\) | 2.77837 | 0.139795 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.9067 | 1.75192 | 0.875959 | − | 0.482385i | \(-0.160229\pi\) | ||||
0.875959 | + | 0.482385i | \(0.160229\pi\) | |||||||
\(398\) | −0.906726 | −0.0454501 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.22163 | 0.260108 | ||||||||
\(404\) | 7.64590 | 0.380398 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.610815 | −0.0303142 | ||||||||
\(407\) | 1.30541 | 0.0647066 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.64590 | 0.180278 | 0.0901390 | − | 0.995929i | \(-0.471269\pi\) | ||||
0.0901390 | + | 0.995929i | \(0.471269\pi\) | |||||||
\(410\) | 9.51754 | 0.470038 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.51754 | −0.370363 | ||||||||
\(413\) | 3.51754 | 0.173087 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.73917 | −0.232637 | ||||||||
\(416\) | −0.694593 | −0.0340552 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.51754 | −0.269872 | ||||||||
\(419\) | −18.3851 | −0.898169 | −0.449085 | − | 0.893489i | \(-0.648250\pi\) | ||||
−0.449085 | + | 0.893489i | \(0.648250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | −27.3756 | −1.33262 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.12836 | 0.200491 | ||||||||
\(425\) | −2.69459 | −0.130707 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | −0.193574 | ||||||||
\(428\) | 17.1634 | 0.829626 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.51754 | −0.266079 | ||||||||
\(431\) | −15.3054 | −0.737236 | −0.368618 | − | 0.929581i | \(-0.620169\pi\) | ||||
−0.368618 | + | 0.929581i | \(0.620169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.34998 | −0.449332 | −0.224666 | − | 0.974436i | \(-0.572129\pi\) | ||||
−0.224666 | + | 0.974436i | \(0.572129\pi\) | |||||||
\(434\) | −7.51754 | −0.360854 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.91622 | −0.0917704 | ||||||||
\(437\) | −41.0161 | −1.96207 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.5526 | 1.45820 | 0.729099 | − | 0.684409i | \(-0.239940\pi\) | ||||
0.729099 | + | 0.684409i | \(0.239940\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.87164 | 0.0890250 | ||||||||
\(443\) | −36.1985 | −1.71984 | −0.859922 | − | 0.510426i | \(-0.829488\pi\) | ||||
−0.859922 | + | 0.510426i | \(0.829488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.04458 | 0.381350 | ||||||||
\(446\) | 21.6459 | 1.02496 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 1.22163 | 0.0576522 | 0.0288261 | − | 0.999584i | \(-0.490823\pi\) | ||||
0.0288261 | + | 0.999584i | \(0.490823\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.51754 | 0.448164 | ||||||||
\(452\) | −12.2121 | −0.574410 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.3500 | −0.532681 | ||||||||
\(455\) | 0.694593 | 0.0325630 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0743 | −0.518033 | −0.259017 | − | 0.965873i | \(-0.583398\pi\) | ||||
−0.259017 | + | 0.965873i | \(0.583398\pi\) | |||||||
\(458\) | −6.69459 | −0.312818 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.43376 | 0.346601 | ||||||||
\(461\) | 7.87164 | 0.366619 | 0.183310 | − | 0.983055i | \(-0.441319\pi\) | ||||
0.183310 | + | 0.983055i | \(0.441319\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.1676 | 1.12316 | 0.561581 | − | 0.827422i | \(-0.310193\pi\) | ||||
0.561581 | + | 0.827422i | \(0.310193\pi\) | |||||||
\(464\) | −0.610815 | −0.0283564 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.2567 | −0.660429 | ||||||||
\(467\) | −27.5175 | −1.27336 | −0.636680 | − | 0.771128i | \(-0.719693\pi\) | ||||
−0.636680 | + | 0.771128i | \(0.719693\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.95130 | −0.413333 | ||||||||
\(470\) | 6.00000 | 0.276759 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.51754 | 0.161908 | ||||||||
\(473\) | −5.51754 | −0.253697 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.51754 | 0.253162 | ||||||||
\(476\) | −2.69459 | −0.123506 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.72967 | 0.170591 | ||||||||
\(479\) | −26.0702 | −1.19118 | −0.595588 | − | 0.803290i | \(-0.703081\pi\) | ||||
−0.595588 | + | 0.803290i | \(0.703081\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.906726 | 0.0413432 | ||||||||
\(482\) | −14.7392 | −0.671351 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 6.90673 | 0.313618 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9649 | 0.587497 | 0.293748 | − | 0.955883i | \(-0.405097\pi\) | ||||
0.293748 | + | 0.955883i | \(0.405097\pi\) | |||||||
\(488\) | −4.00000 | −0.181071 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 36.4243 | 1.64380 | 0.821902 | − | 0.569629i | \(-0.192913\pi\) | ||||
0.821902 | + | 0.569629i | \(0.192913\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.64590 | 0.0741275 | ||||||||
\(494\) | −3.83244 | −0.172430 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.51754 | −0.337548 | ||||||||
\(497\) | −4.77837 | −0.214339 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.1242 | 0.856118 | 0.428059 | − | 0.903751i | \(-0.359197\pi\) | ||||
0.428059 | + | 0.903751i | \(0.359197\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.3851 | −0.820566 | ||||||||
\(503\) | −21.7689 | −0.970626 | −0.485313 | − | 0.874340i | \(-0.661294\pi\) | ||||
−0.485313 | + | 0.874340i | \(0.661294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.64590 | −0.340238 | ||||||||
\(506\) | 7.43376 | 0.330471 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.5175 | 0.511008 | ||||||||
\(509\) | −22.1676 | −0.982560 | −0.491280 | − | 0.871002i | \(-0.663471\pi\) | ||||
−0.491280 | + | 0.871002i | \(0.663471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.51754 | 0.244082 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.09327 | −0.136438 | ||||||||
\(515\) | 7.51754 | 0.331262 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | −1.30541 | −0.0573563 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.694593 | 0.0304599 | ||||||||
\(521\) | 32.4688 | 1.42249 | 0.711243 | − | 0.702946i | \(-0.248133\pi\) | ||||
0.711243 | + | 0.702946i | \(0.248133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.60132 | −0.157475 | −0.0787373 | − | 0.996895i | \(-0.525089\pi\) | ||||
−0.0787373 | + | 0.996895i | \(0.525089\pi\) | |||||||
\(524\) | −5.38919 | −0.235428 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.61081 | 0.288245 | ||||||||
\(527\) | 20.2567 | 0.882396 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.2608 | 1.40264 | ||||||||
\(530\) | −4.12836 | −0.179324 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.51754 | 0.239216 | ||||||||
\(533\) | 6.61081 | 0.286346 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.1634 | −0.742040 | ||||||||
\(536\) | −8.95130 | −0.386637 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.00000 | 0.258678 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.951304 | 0.0408997 | 0.0204499 | − | 0.999791i | \(-0.493490\pi\) | ||||
0.0204499 | + | 0.999791i | \(0.493490\pi\) | |||||||
\(542\) | 13.8135 | 0.593339 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.69459 | −0.115530 | ||||||||
\(545\) | 1.91622 | 0.0820819 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.1985 | 1.63325 | 0.816625 | − | 0.577168i | \(-0.195842\pi\) | ||||
0.816625 | + | 0.577168i | \(0.195842\pi\) | |||||||
\(548\) | −13.4338 | −0.573862 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −3.37019 | −0.143575 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.77837 | −0.118148 | ||||||||
\(554\) | 25.1634 | 1.06909 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.9067 | −0.801824 | ||||||||
\(557\) | −8.29591 | −0.351509 | −0.175755 | − | 0.984434i | \(-0.556237\pi\) | ||||
−0.175755 | + | 0.984434i | \(0.556237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.83244 | −0.162095 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.9162 | 0.671385 | ||||||||
\(563\) | 15.0933 | 0.636106 | 0.318053 | − | 0.948073i | \(-0.396971\pi\) | ||||
0.318053 | + | 0.948073i | \(0.396971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.2121 | 0.513768 | ||||||||
\(566\) | −10.2121 | −0.429248 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.77837 | −0.200496 | ||||||||
\(569\) | −43.2080 | −1.81137 | −0.905687 | − | 0.423947i | \(-0.860644\pi\) | ||||
−0.905687 | + | 0.423947i | \(0.860644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5621 | 0.567557 | 0.283778 | − | 0.958890i | \(-0.408412\pi\) | ||||
0.283778 | + | 0.958890i | \(0.408412\pi\) | |||||||
\(572\) | 0.694593 | 0.0290424 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.51754 | −0.397254 | ||||||||
\(575\) | −7.43376 | −0.310009 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.3892 | 0.807182 | 0.403591 | − | 0.914939i | \(-0.367762\pi\) | ||||
0.403591 | + | 0.914939i | \(0.367762\pi\) | |||||||
\(578\) | −9.73917 | −0.405096 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.610815 | 0.0253627 | ||||||||
\(581\) | 4.73917 | 0.196614 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.12836 | −0.170979 | ||||||||
\(584\) | 5.51754 | 0.228317 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.6810 | 1.10218 | ||||||||
\(587\) | −28.7392 | −1.18619 | −0.593096 | − | 0.805132i | \(-0.702095\pi\) | ||||
−0.593096 | + | 0.805132i | \(0.702095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −41.4783 | −1.70909 | ||||||||
\(590\) | −3.51754 | −0.144815 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.30541 | −0.0536519 | ||||||||
\(593\) | −30.7837 | −1.26414 | −0.632068 | − | 0.774913i | \(-0.717794\pi\) | ||||
−0.632068 | + | 0.774913i | \(0.717794\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.69459 | 0.110468 | ||||||||
\(596\) | 0.610815 | 0.0250199 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.16344 | 0.211149 | ||||||||
\(599\) | 5.20264 | 0.212574 | 0.106287 | − | 0.994335i | \(-0.466104\pi\) | ||||
0.106287 | + | 0.994335i | \(0.466104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.68098 | −0.272523 | −0.136261 | − | 0.990673i | \(-0.543509\pi\) | ||||
−0.136261 | + | 0.990673i | \(0.543509\pi\) | |||||||
\(602\) | 5.51754 | 0.224878 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.8324 | 0.642619 | 0.321310 | − | 0.946974i | \(-0.395877\pi\) | ||||
0.321310 | + | 0.946974i | \(0.395877\pi\) | |||||||
\(608\) | 5.51754 | 0.223766 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.00000 | 0.161955 | ||||||||
\(611\) | 4.16756 | 0.168601 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.7202 | −0.756101 | −0.378050 | − | 0.925785i | \(-0.623405\pi\) | ||||
−0.378050 | + | 0.925785i | \(0.623405\pi\) | |||||||
\(614\) | −17.2472 | −0.696041 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 15.0797 | 0.607084 | 0.303542 | − | 0.952818i | \(-0.401831\pi\) | ||||
0.303542 | + | 0.952818i | \(0.401831\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −45.1498 | −1.81472 | −0.907362 | − | 0.420349i | \(-0.861907\pi\) | ||||
−0.907362 | + | 0.420349i | \(0.861907\pi\) | |||||||
\(620\) | 7.51754 | 0.301912 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.1729 | −0.488090 | ||||||||
\(623\) | −8.04458 | −0.322299 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.6810 | −0.746642 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.5526 | 0.979756 | ||||||||
\(629\) | 3.51754 | 0.140254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.42839 | 0.295719 | 0.147860 | − | 0.989008i | \(-0.452762\pi\) | ||||
0.147860 | + | 0.989008i | \(0.452762\pi\) | |||||||
\(632\) | −2.77837 | −0.110518 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −29.7743 | −1.18249 | ||||||||
\(635\) | −11.5175 | −0.457060 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.694593 | −0.0275208 | ||||||||
\(638\) | 0.610815 | 0.0241824 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 36.8485 | 1.45543 | 0.727715 | − | 0.685880i | \(-0.240582\pi\) | ||||
0.727715 | + | 0.685880i | \(0.240582\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.5134 | −1.28220 | −0.641102 | − | 0.767456i | \(-0.721522\pi\) | ||||
−0.641102 | + | 0.767456i | \(0.721522\pi\) | |||||||
\(644\) | −7.43376 | −0.292931 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.8675 | −0.584955 | ||||||||
\(647\) | 3.47834 | 0.136748 | 0.0683738 | − | 0.997660i | \(-0.478219\pi\) | ||||
0.0683738 | + | 0.997660i | \(0.478219\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.51754 | −0.138076 | ||||||||
\(650\) | −0.694593 | −0.0272442 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.91622 | −0.0750450 | ||||||||
\(653\) | 20.7202 | 0.810843 | 0.405422 | − | 0.914130i | \(-0.367125\pi\) | ||||
0.405422 | + | 0.914130i | \(0.367125\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.38919 | 0.210573 | ||||||||
\(656\) | −9.51754 | −0.371598 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | −8.25671 | −0.321636 | −0.160818 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160818 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.5972 | −1.57905 | −0.789524 | − | 0.613720i | \(-0.789673\pi\) | ||||
−0.789524 | + | 0.613720i | \(0.789673\pi\) | |||||||
\(662\) | 4.25671 | 0.165442 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.73917 | 0.183915 | ||||||||
\(665\) | −5.51754 | −0.213961 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.54065 | 0.175815 | ||||||||
\(668\) | −24.2121 | −0.936796 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.95130 | 0.345819 | ||||||||
\(671\) | 4.00000 | 0.154418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.3459 | −0.861370 | −0.430685 | − | 0.902502i | \(-0.641728\pi\) | ||||
−0.430685 | + | 0.902502i | \(0.641728\pi\) | |||||||
\(674\) | 3.64590 | 0.140435 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.5175 | −0.481444 | ||||||||
\(677\) | −15.9026 | −0.611187 | −0.305593 | − | 0.952162i | \(-0.598855\pi\) | ||||
−0.305593 | + | 0.952162i | \(0.598855\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.90673 | −0.265056 | ||||||||
\(680\) | 2.69459 | 0.103333 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.51754 | 0.287862 | ||||||||
\(683\) | 33.2526 | 1.27238 | 0.636188 | − | 0.771534i | \(-0.280510\pi\) | ||||
0.636188 | + | 0.771534i | \(0.280510\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.4338 | 0.513278 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.51754 | 0.210354 | ||||||||
\(689\) | −2.86753 | −0.109244 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.7338 | 0.408333 | 0.204166 | − | 0.978936i | \(-0.434552\pi\) | ||||
0.204166 | + | 0.978936i | \(0.434552\pi\) | |||||||
\(692\) | −7.22163 | −0.274525 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.9418 | 1.06066 | ||||||||
\(695\) | 18.9067 | 0.717173 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.6459 | 0.971408 | ||||||||
\(698\) | −25.4783 | −0.964369 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 37.4593 | 1.41482 | 0.707410 | − | 0.706803i | \(-0.249863\pi\) | ||||
0.707410 | + | 0.706803i | \(0.249863\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.20264 | −0.271653 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.1634 | 0.645954 | ||||||||
\(707\) | 7.64590 | 0.287554 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8135 | 0.744110 | 0.372055 | − | 0.928211i | \(-0.378653\pi\) | ||||
0.372055 | + | 0.928211i | \(0.378653\pi\) | |||||||
\(710\) | 4.77837 | 0.179329 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.04458 | −0.301483 | ||||||||
\(713\) | 55.8836 | 2.09286 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.694593 | −0.0259763 | ||||||||
\(716\) | −14.2959 | −0.534263 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 31.8188 | 1.18747 | ||||||||
\(719\) | −32.0838 | −1.19652 | −0.598262 | − | 0.801301i | \(-0.704142\pi\) | ||||
−0.598262 | + | 0.801301i | \(0.704142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.51754 | −0.279968 | ||||||||
\(722\) | 11.4433 | 0.425874 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.52704 | −0.0939166 | ||||||||
\(725\) | −0.610815 | −0.0226851 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.8675 | 1.29316 | 0.646582 | − | 0.762844i | \(-0.276198\pi\) | ||||
0.646582 | + | 0.762844i | \(0.276198\pi\) | |||||||
\(728\) | −0.694593 | −0.0257433 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.51754 | −0.204213 | ||||||||
\(731\) | −14.8675 | −0.549895 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.0405 | 1.07263 | 0.536317 | − | 0.844017i | \(-0.319815\pi\) | ||||
0.536317 | + | 0.844017i | \(0.319815\pi\) | |||||||
\(734\) | −27.7743 | −1.02517 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.43376 | −0.274012 | ||||||||
\(737\) | 8.95130 | 0.329726 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.4107 | 1.85439 | 0.927193 | − | 0.374584i | \(-0.122215\pi\) | ||||
0.927193 | + | 0.374584i | \(0.122215\pi\) | |||||||
\(740\) | 1.30541 | 0.0479877 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.12836 | 0.151557 | ||||||||
\(743\) | 10.7784 | 0.395420 | 0.197710 | − | 0.980261i | \(-0.436650\pi\) | ||||
0.197710 | + | 0.980261i | \(0.436650\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.610815 | −0.0223785 | ||||||||
\(746\) | 0.739170 | 0.0270629 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.69459 | 0.0985241 | ||||||||
\(749\) | 17.1634 | 0.627138 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.94181 | −0.289801 | −0.144900 | − | 0.989446i | \(-0.546286\pi\) | ||||
−0.144900 | + | 0.989446i | \(0.546286\pi\) | |||||||
\(752\) | −6.00000 | −0.218797 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.424267 | 0.0154509 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.3946 | 0.777599 | 0.388799 | − | 0.921322i | \(-0.372890\pi\) | ||||
0.388799 | + | 0.921322i | \(0.372890\pi\) | |||||||
\(758\) | 24.5134 | 0.890368 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.51754 | −0.200142 | ||||||||
\(761\) | 29.7743 | 1.07932 | 0.539658 | − | 0.841884i | \(-0.318554\pi\) | ||||
0.539658 | + | 0.841884i | \(0.318554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.91622 | −0.0693719 | ||||||||
\(764\) | 0.610815 | 0.0220985 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.00000 | −0.216789 | ||||||||
\(767\) | −2.44326 | −0.0882209 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.9459 | −0.466842 | −0.233421 | − | 0.972376i | \(-0.574992\pi\) | ||||
−0.233421 | + | 0.972376i | \(0.574992\pi\) | |||||||
\(770\) | 1.00000 | 0.0360375 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.51754 | −0.0546175 | ||||||||
\(773\) | −2.90673 | −0.104548 | −0.0522738 | − | 0.998633i | \(-0.516647\pi\) | ||||
−0.0522738 | + | 0.998633i | \(0.516647\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.51754 | −0.270038 | ||||||||
\(776\) | −6.90673 | −0.247937 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.65002 | −0.238415 | ||||||||
\(779\) | −52.5134 | −1.88149 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.77837 | 0.170984 | ||||||||
\(782\) | 20.0310 | 0.716306 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −24.5526 | −0.876321 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.1581 | 1.03937 | 0.519686 | − | 0.854357i | \(-0.326049\pi\) | ||||
0.519686 | + | 0.854357i | \(0.326049\pi\) | |||||||
\(788\) | 10.7392 | 0.382567 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.77837 | 0.0988500 | ||||||||
\(791\) | −12.2121 | −0.434213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.77837 | 0.0986628 | ||||||||
\(794\) | 34.9067 | 1.23879 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.906726 | −0.0321381 | ||||||||
\(797\) | −25.6851 | −0.909813 | −0.454906 | − | 0.890539i | \(-0.650327\pi\) | ||||
−0.454906 | + | 0.890539i | \(0.650327\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.1676 | 0.571967 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.51754 | −0.194710 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.43376 | 0.262006 | ||||||||
\(806\) | 5.22163 | 0.183924 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.64590 | 0.268982 | ||||||||
\(809\) | −32.4296 | −1.14017 | −0.570083 | − | 0.821587i | \(-0.693089\pi\) | ||||
−0.570083 | + | 0.821587i | \(0.693089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.2175 | 0.569474 | 0.284737 | − | 0.958606i | \(-0.408094\pi\) | ||||
0.284737 | + | 0.958606i | \(0.408094\pi\) | |||||||
\(812\) | −0.610815 | −0.0214354 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.30541 | 0.0457545 | ||||||||
\(815\) | 1.91622 | 0.0671223 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.4433 | 1.06507 | ||||||||
\(818\) | 3.64590 | 0.127476 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.51754 | 0.332367 | ||||||||
\(821\) | 16.7000 | 0.582833 | 0.291416 | − | 0.956596i | \(-0.405873\pi\) | ||||
0.291416 | + | 0.956596i | \(0.405873\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.9810 | 0.626779 | 0.313389 | − | 0.949625i | \(-0.398536\pi\) | ||||
0.313389 | + | 0.949625i | \(0.398536\pi\) | |||||||
\(824\) | −7.51754 | −0.261886 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.51754 | 0.122391 | ||||||||
\(827\) | 11.4284 | 0.397404 | 0.198702 | − | 0.980060i | \(-0.436327\pi\) | ||||
0.198702 | + | 0.980060i | \(0.436327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.2431 | 0.772535 | 0.386267 | − | 0.922387i | \(-0.373764\pi\) | ||||
0.386267 | + | 0.922387i | \(0.373764\pi\) | |||||||
\(830\) | −4.73917 | −0.164499 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.694593 | −0.0240807 | ||||||||
\(833\) | −2.69459 | −0.0933621 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.2121 | 0.837895 | ||||||||
\(836\) | −5.51754 | −0.190828 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.3851 | −0.635102 | ||||||||
\(839\) | 13.8972 | 0.479786 | 0.239893 | − | 0.970799i | \(-0.422888\pi\) | ||||
0.239893 | + | 0.970799i | \(0.422888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6269 | −0.987135 | ||||||||
\(842\) | 14.0000 | 0.482472 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −27.3756 | −0.942306 | ||||||||
\(845\) | 12.5175 | 0.430617 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 4.12836 | 0.141768 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.69459 | −0.0924238 | ||||||||
\(851\) | 9.70409 | 0.332652 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.5972 | 0.910671 | 0.455335 | − | 0.890320i | \(-0.349519\pi\) | ||||
0.455335 | + | 0.890320i | \(0.349519\pi\) | |||||||
\(854\) | −4.00000 | −0.136877 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.1634 | 0.586634 | ||||||||
\(857\) | 3.91622 | 0.133776 | 0.0668878 | − | 0.997761i | \(-0.478693\pi\) | ||||
0.0668878 | + | 0.997761i | \(0.478693\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.4688 | −0.425431 | −0.212716 | − | 0.977114i | \(-0.568231\pi\) | ||||
−0.212716 | + | 0.977114i | \(0.568231\pi\) | |||||||
\(860\) | −5.51754 | −0.188147 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.3054 | −0.521304 | ||||||||
\(863\) | 37.5931 | 1.27968 | 0.639842 | − | 0.768507i | \(-0.279000\pi\) | ||||
0.639842 | + | 0.768507i | \(0.279000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.22163 | 0.245543 | ||||||||
\(866\) | −9.34998 | −0.317725 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.51754 | −0.255162 | ||||||||
\(869\) | 2.77837 | 0.0942498 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.21751 | 0.210672 | ||||||||
\(872\) | −1.91622 | −0.0648915 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −41.0161 | −1.38739 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.7202 | −1.03735 | −0.518673 | − | 0.854972i | \(-0.673574\pi\) | ||||
−0.518673 | + | 0.854972i | \(0.673574\pi\) | |||||||
\(878\) | 30.5526 | 1.03110 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 3.95542 | 0.133262 | 0.0666308 | − | 0.997778i | \(-0.478775\pi\) | ||||
0.0666308 | + | 0.997778i | \(0.478775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.3756 | 1.66162 | 0.830810 | − | 0.556556i | \(-0.187878\pi\) | ||||
0.830810 | + | 0.556556i | \(0.187878\pi\) | |||||||
\(884\) | 1.87164 | 0.0629502 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.1985 | −1.21611 | ||||||||
\(887\) | −4.30129 | −0.144423 | −0.0722116 | − | 0.997389i | \(-0.523006\pi\) | ||||
−0.0722116 | + | 0.997389i | \(0.523006\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.5175 | 0.386286 | ||||||||
\(890\) | 8.04458 | 0.269655 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.6459 | 0.724758 | ||||||||
\(893\) | −33.1052 | −1.10782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.2959 | 0.477860 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.22163 | 0.0407663 | ||||||||
\(899\) | 4.59182 | 0.153146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.1242 | −0.370602 | ||||||||
\(902\) | 9.51754 | 0.316899 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.2121 | −0.406170 | ||||||||
\(905\) | 2.52704 | 0.0840015 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6946 | 0.554335 | 0.277167 | − | 0.960822i | \(-0.410604\pi\) | ||||
0.277167 | + | 0.960822i | \(0.410604\pi\) | |||||||
\(908\) | −11.3500 | −0.376662 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.694593 | 0.0230255 | ||||||||
\(911\) | 22.9649 | 0.760862 | 0.380431 | − | 0.924809i | \(-0.375776\pi\) | ||||
0.380431 | + | 0.924809i | \(0.375776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.73917 | −0.156844 | ||||||||
\(914\) | −11.0743 | −0.366305 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.69459 | −0.221196 | ||||||||
\(917\) | −5.38919 | −0.177967 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.5836 | −1.53665 | −0.768325 | − | 0.640059i | \(-0.778910\pi\) | ||||
−0.768325 | + | 0.640059i | \(0.778910\pi\) | |||||||
\(920\) | 7.43376 | 0.245084 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.87164 | 0.259239 | ||||||||
\(923\) | 3.31902 | 0.109247 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.30541 | −0.0429215 | ||||||||
\(926\) | 24.1676 | 0.794195 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.610815 | −0.0200510 | ||||||||
\(929\) | −39.5039 | −1.29608 | −0.648041 | − | 0.761606i | \(-0.724411\pi\) | ||||
−0.648041 | + | 0.761606i | \(0.724411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.51754 | 0.180830 | ||||||||
\(932\) | −14.2567 | −0.466994 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27.5175 | −0.900401 | ||||||||
\(935\) | −2.69459 | −0.0881226 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.0743 | 0.492455 | 0.246228 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246228 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(938\) | −8.95130 | −0.292270 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.00000 | 0.195698 | ||||||||
\(941\) | 22.1676 | 0.722642 | 0.361321 | − | 0.932442i | \(-0.382326\pi\) | ||||
0.361321 | + | 0.932442i | \(0.382326\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70.7511 | 2.30397 | ||||||||
\(944\) | 3.51754 | 0.114486 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.51754 | −0.179391 | ||||||||
\(947\) | 5.61493 | 0.182461 | 0.0912304 | − | 0.995830i | \(-0.470920\pi\) | ||||
0.0912304 | + | 0.995830i | \(0.470920\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.83244 | −0.124406 | ||||||||
\(950\) | 5.51754 | 0.179013 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.69459 | −0.0873323 | ||||||||
\(953\) | 17.5757 | 0.569334 | 0.284667 | − | 0.958626i | \(-0.408117\pi\) | ||||
0.284667 | + | 0.958626i | \(0.408117\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.610815 | −0.0197655 | ||||||||
\(956\) | 3.72967 | 0.120626 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.0702 | −0.842289 | ||||||||
\(959\) | −13.4338 | −0.433799 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.5134 | 0.823014 | ||||||||
\(962\) | 0.906726 | 0.0292340 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.7392 | −0.474717 | ||||||||
\(965\) | 1.51754 | 0.0488514 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.5175 | 0.370379 | 0.185190 | − | 0.982703i | \(-0.440710\pi\) | ||||
0.185190 | + | 0.982703i | \(0.440710\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.90673 | 0.221762 | ||||||||
\(971\) | −24.2257 | −0.777441 | −0.388721 | − | 0.921356i | \(-0.627083\pi\) | ||||
−0.388721 | + | 0.921356i | \(0.627083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.9067 | −0.606122 | ||||||||
\(974\) | 12.9649 | 0.415423 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | −0.128037 | ||||||||
\(977\) | 14.7338 | 0.471376 | 0.235688 | − | 0.971829i | \(-0.424266\pi\) | ||||
0.235688 | + | 0.971829i | \(0.424266\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.04458 | 0.257106 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.4243 | 1.16235 | ||||||||
\(983\) | −6.00000 | −0.191370 | −0.0956851 | − | 0.995412i | \(-0.530504\pi\) | ||||
−0.0956851 | + | 0.995412i | \(0.530504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.7392 | −0.342178 | ||||||||
\(986\) | 1.64590 | 0.0524160 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.83244 | −0.121926 | ||||||||
\(989\) | −41.0161 | −1.30424 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.3500 | 1.37706 | 0.688529 | − | 0.725209i | \(-0.258257\pi\) | ||||
0.688529 | + | 0.725209i | \(0.258257\pi\) | |||||||
\(992\) | −7.51754 | −0.238682 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.77837 | −0.151561 | ||||||||
\(995\) | 0.906726 | 0.0287452 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.34049 | −0.0741240 | −0.0370620 | − | 0.999313i | \(-0.511800\pi\) | ||||
−0.0370620 | + | 0.999313i | \(0.511800\pi\) | |||||||
\(998\) | 19.1242 | 0.605367 | ||||||||
\(999\) | 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 | 6930.2.a.cj.1.2 | yes | 3 | |
3.2 | odd | 2 | 6930.2.a.ci.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6930.2.a.ci.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
6930.2.a.cj.1.2 | yes | 3 | 1.1 | even | 1 | trivial |