Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 31x^{7} + 24x^{6} + 293x^{5} - 101x^{4} - 864x^{3} - 278x^{2} + 24x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2004) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.111665\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-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 | ||||||||
\(5\) | −0.111665 | −0.0499380 | −0.0249690 | − | 0.999688i | \(-0.507949\pi\) | ||||
−0.0249690 | + | 0.999688i | \(0.507949\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.78430 | −1.43033 | −0.715166 | − | 0.698954i | \(-0.753649\pi\) | ||||
−0.715166 | + | 0.698954i | \(0.753649\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.64268 | 1.70133 | 0.850666 | − | 0.525707i | \(-0.176199\pi\) | ||||
0.850666 | + | 0.525707i | \(0.176199\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.56111 | 1.81972 | 0.909862 | − | 0.414911i | \(-0.136187\pi\) | ||||
0.909862 | + | 0.414911i | \(0.136187\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.37904 | 0.577003 | 0.288501 | − | 0.957479i | \(-0.406843\pi\) | ||||
0.288501 | + | 0.957479i | \(0.406843\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.46447 | 1.02422 | 0.512109 | − | 0.858920i | \(-0.328864\pi\) | ||||
0.512109 | + | 0.858920i | \(0.328864\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.90056 | 0.604809 | 0.302404 | − | 0.953180i | \(-0.402211\pi\) | ||||
0.302404 | + | 0.953180i | \(0.402211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.98753 | −0.997506 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.383613 | 0.0712351 | 0.0356175 | − | 0.999365i | \(-0.488660\pi\) | ||||
0.0356175 | + | 0.999365i | \(0.488660\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.50063 | −0.987943 | −0.493971 | − | 0.869478i | \(-0.664455\pi\) | ||||
−0.493971 | + | 0.869478i | \(0.664455\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.422573 | 0.0714280 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.40869 | 1.05358 | 0.526791 | − | 0.849995i | \(-0.323395\pi\) | ||||
0.526791 | + | 0.849995i | \(0.323395\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.20918 | −0.657364 | −0.328682 | − | 0.944441i | \(-0.606604\pi\) | ||||
−0.328682 | + | 0.944441i | \(0.606604\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.54888 | 0.541199 | 0.270600 | − | 0.962692i | \(-0.412778\pi\) | ||||
0.270600 | + | 0.962692i | \(0.412778\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.255709 | 0.0372990 | 0.0186495 | − | 0.999826i | \(-0.494063\pi\) | ||||
0.0186495 | + | 0.999826i | \(0.494063\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.32096 | 1.04585 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1901 | −1.67443 | −0.837217 | − | 0.546870i | \(-0.815819\pi\) | ||||
−0.837217 | + | 0.546870i | \(0.815819\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.630088 | −0.0849611 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.65173 | −1.25655 | −0.628274 | − | 0.777992i | \(-0.716238\pi\) | ||||
−0.628274 | + | 0.777992i | \(0.716238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.24962 | −0.288034 | −0.144017 | − | 0.989575i | \(-0.546002\pi\) | ||||
−0.144017 | + | 0.989575i | \(0.546002\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.732645 | −0.0908734 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6436 | 1.30032 | 0.650161 | − | 0.759796i | \(-0.274701\pi\) | ||||
0.650161 | + | 0.759796i | \(0.274701\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.99033 | 0.829600 | 0.414800 | − | 0.909913i | \(-0.363852\pi\) | ||||
0.414800 | + | 0.909913i | \(0.363852\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.95501 | 0.228817 | 0.114408 | − | 0.993434i | \(-0.463503\pi\) | ||||
0.114408 | + | 0.993434i | \(0.463503\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −21.3536 | −2.43347 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0719 | 1.58321 | 0.791606 | − | 0.611031i | \(-0.209245\pi\) | ||||
0.791606 | + | 0.611031i | \(0.209245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.74400 | −0.301193 | −0.150596 | − | 0.988595i | \(-0.548119\pi\) | ||||
−0.150596 | + | 0.988595i | \(0.548119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.265655 | −0.0288144 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.44387 | −1.00105 | −0.500524 | − | 0.865723i | \(-0.666859\pi\) | ||||
−0.500524 | + | 0.865723i | \(0.666859\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −24.8292 | −2.60281 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.498524 | −0.0511474 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.83182 | −0.693666 | −0.346833 | − | 0.937927i | \(-0.612743\pi\) | ||||
−0.346833 | + | 0.937927i | \(0.612743\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.7721 | 1.76839 | 0.884197 | − | 0.467113i | \(-0.154706\pi\) | ||||
0.884197 | + | 0.467113i | \(0.154706\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.33419 | −0.427061 | −0.213530 | − | 0.976936i | \(-0.568496\pi\) | ||||
−0.213530 | + | 0.976936i | \(0.568496\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.79832 | 0.657219 | 0.328609 | − | 0.944466i | \(-0.393420\pi\) | ||||
0.328609 | + | 0.944466i | \(0.393420\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.55808 | 0.149237 | 0.0746187 | − | 0.997212i | \(-0.476226\pi\) | ||||
0.0746187 | + | 0.997212i | \(0.476226\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.86093 | −0.927638 | −0.463819 | − | 0.885930i | \(-0.653521\pi\) | ||||
−0.463819 | + | 0.885930i | \(0.653521\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.323891 | −0.0302029 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.00302 | −0.825306 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8398 | 1.89453 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.11526 | 0.0997515 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.1734 | 1.61263 | 0.806313 | − | 0.591489i | \(-0.201459\pi\) | ||||
0.806313 | + | 0.591489i | \(0.201459\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.0741 | −1.75389 | −0.876943 | − | 0.480595i | \(-0.840421\pi\) | ||||
−0.876943 | + | 0.480595i | \(0.840421\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.8949 | −1.46497 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.79003 | 0.409240 | 0.204620 | − | 0.978841i | \(-0.434404\pi\) | ||||
0.204620 | + | 0.978841i | \(0.434404\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.465853 | −0.0395132 | −0.0197566 | − | 0.999805i | \(-0.506289\pi\) | ||||
−0.0197566 | + | 0.999805i | \(0.506289\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 37.0222 | 3.09595 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0428360 | −0.00355734 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.48816 | −0.285761 | −0.142880 | − | 0.989740i | \(-0.545636\pi\) | ||||
−0.142880 | + | 0.989740i | \(0.545636\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.1406 | 1.80177 | 0.900887 | − | 0.434054i | \(-0.142917\pi\) | ||||
0.900887 | + | 0.434054i | \(0.142917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.614227 | 0.0493359 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.55137 | −0.762282 | −0.381141 | − | 0.924517i | \(-0.624469\pi\) | ||||
−0.381141 | + | 0.924517i | \(0.624469\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.9766 | −0.865078 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.60472 | 0.517322 | 0.258661 | − | 0.965968i | \(-0.416719\pi\) | ||||
0.258661 | + | 0.965968i | \(0.416719\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.0481 | 2.31140 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.21939 | 0.624909 | 0.312454 | − | 0.949933i | \(-0.398849\pi\) | ||||
0.312454 | + | 0.949933i | \(0.398849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 18.8743 | 1.42677 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.9969 | −1.19567 | −0.597834 | − | 0.801620i | \(-0.703972\pi\) | ||||
−0.597834 | + | 0.801620i | \(0.703972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.74031 | −0.426674 | −0.213337 | − | 0.976979i | \(-0.568433\pi\) | ||||
−0.213337 | + | 0.976979i | \(0.568433\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.715625 | −0.0526138 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.4242 | 0.981673 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.80254 | −0.419857 | −0.209929 | − | 0.977717i | \(-0.567323\pi\) | ||||
−0.209929 | + | 0.977717i | \(0.567323\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.18082 | −0.516887 | −0.258443 | − | 0.966026i | \(-0.583210\pi\) | ||||
−0.258443 | + | 0.966026i | \(0.583210\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.2091 | 1.79607 | 0.898036 | − | 0.439922i | \(-0.144994\pi\) | ||||
0.898036 | + | 0.439922i | \(0.144994\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.7651 | 1.61377 | 0.806887 | − | 0.590705i | \(-0.201150\pi\) | ||||
0.806887 | + | 0.590705i | \(0.201150\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.45171 | −0.101890 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.470017 | 0.0328274 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.1915 | 1.74254 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.86999 | 0.679478 | 0.339739 | − | 0.940520i | \(-0.389661\pi\) | ||||
0.339739 | + | 0.940520i | \(0.389661\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.396285 | −0.0270264 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.8161 | 1.41309 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.6092 | 1.04999 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.5826 | −0.842595 | −0.421298 | − | 0.906922i | \(-0.638425\pi\) | ||||
−0.421298 | + | 0.906922i | \(0.638425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.4014 | 0.690366 | 0.345183 | − | 0.938535i | \(-0.387817\pi\) | ||||
0.345183 | + | 0.938535i | \(0.387817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.9538 | 1.05426 | 0.527129 | − | 0.849785i | \(-0.323268\pi\) | ||||
0.527129 | + | 0.849785i | \(0.323268\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.2954 | −0.739989 | −0.369994 | − | 0.929034i | \(-0.620640\pi\) | ||||
−0.369994 | + | 0.929034i | \(0.620640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.0285537 | −0.00186264 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.08621 | 0.0702609 | 0.0351305 | − | 0.999383i | \(-0.488815\pi\) | ||||
0.0351305 | + | 0.999383i | \(0.488815\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.60646 | 0.618806 | 0.309403 | − | 0.950931i | \(-0.399871\pi\) | ||||
0.309403 | + | 0.950931i | \(0.399871\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.817493 | −0.0522277 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.2919 | 1.86380 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.2234 | 1.71833 | 0.859163 | − | 0.511702i | \(-0.170985\pi\) | ||||
0.859163 | + | 0.511702i | \(0.170985\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.3669 | 1.02898 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.40522 | 0.212412 | 0.106206 | − | 0.994344i | \(-0.466130\pi\) | ||||
0.106206 | + | 0.994344i | \(0.466130\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.2524 | −1.50697 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.5618 | 1.88452 | 0.942260 | − | 0.334883i | \(-0.108697\pi\) | ||||
0.942260 | + | 0.334883i | \(0.108697\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.36120 | 0.0836179 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.0375 | −1.58754 | −0.793768 | − | 0.608221i | \(-0.791883\pi\) | ||||
−0.793768 | + | 0.608221i | \(0.791883\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.1407 | 1.34495 | 0.672476 | − | 0.740119i | \(-0.265231\pi\) | ||||
0.672476 | + | 0.740119i | \(0.265231\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.1430 | −1.69709 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.894169 | 0.0537254 | 0.0268627 | − | 0.999639i | \(-0.491448\pi\) | ||||
0.0268627 | + | 0.999639i | \(0.491448\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.2159 | 1.86219 | 0.931093 | − | 0.364781i | \(-0.118856\pi\) | ||||
0.931093 | + | 0.364781i | \(0.118856\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.65557 | 0.455076 | 0.227538 | − | 0.973769i | \(-0.426932\pi\) | ||||
0.227538 | + | 0.973769i | \(0.426932\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.9288 | 0.940249 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.3402 | −0.667068 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.1688 | −1.11985 | −0.559926 | − | 0.828543i | \(-0.689170\pi\) | ||||
−0.559926 | + | 0.828543i | \(0.689170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.07776 | 0.0627495 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 19.0309 | 1.10059 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.4301 | −0.774095 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.251203 | 0.0143839 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.8020 | −0.616504 | −0.308252 | − | 0.951305i | \(-0.599744\pi\) | ||||
−0.308252 | + | 0.951305i | \(0.599744\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.9080 | 1.18558 | 0.592791 | − | 0.805356i | \(-0.298026\pi\) | ||||
0.592791 | + | 0.805356i | \(0.298026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.96365 | −0.337085 | −0.168543 | − | 0.985694i | \(-0.553906\pi\) | ||||
−0.168543 | + | 0.985694i | \(0.553906\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.6322 | −0.934155 | −0.467078 | − | 0.884216i | \(-0.654693\pi\) | ||||
−0.467078 | + | 0.884216i | \(0.654693\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.16460 | 0.121194 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.6212 | 0.590977 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −32.7237 | −1.81519 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.967680 | −0.0533499 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.3573 | −1.83348 | −0.916741 | − | 0.399483i | \(-0.869190\pi\) | ||||
−0.916741 | + | 0.399483i | \(0.869190\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.18852 | −0.0649355 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.8458 | −1.84370 | −0.921848 | − | 0.387552i | \(-0.873321\pi\) | ||||
−0.921848 | + | 0.387552i | \(0.873321\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −31.0383 | −1.68082 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.21461 | −0.0655829 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.7213 | 1.32711 | 0.663553 | − | 0.748129i | \(-0.269048\pi\) | ||||
0.663553 | + | 0.748129i | \(0.269048\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.75243 | 0.361449 | 0.180725 | − | 0.983534i | \(-0.442156\pi\) | ||||
0.180725 | + | 0.983534i | \(0.442156\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.6342 | −0.725673 | −0.362837 | − | 0.931853i | \(-0.618192\pi\) | ||||
−0.362837 | + | 0.931853i | \(0.618192\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.780574 | −0.0414285 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.36561 | −0.494298 | −0.247149 | − | 0.968978i | \(-0.579494\pi\) | ||||
−0.247149 | + | 0.968978i | \(0.579494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.931464 | 0.0490244 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.218306 | −0.0114267 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.1131 | −0.997696 | −0.498848 | − | 0.866690i | \(-0.666243\pi\) | ||||
−0.498848 | + | 0.866690i | \(0.666243\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 46.1309 | 2.39500 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.2383 | 1.30679 | 0.653394 | − | 0.757018i | \(-0.273344\pi\) | ||||
0.653394 | + | 0.757018i | \(0.273344\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.51692 | 0.129628 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.57586 | −0.440513 | −0.220256 | − | 0.975442i | \(-0.570689\pi\) | ||||
−0.220256 | + | 0.975442i | \(0.570689\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.9850 | −0.612403 | −0.306202 | − | 0.951967i | \(-0.599058\pi\) | ||||
−0.306202 | + | 0.951967i | \(0.599058\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.38445 | 0.121523 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.72072 | −0.188648 | −0.0943240 | − | 0.995542i | \(-0.530069\pi\) | ||||
−0.0943240 | + | 0.995542i | \(0.530069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.90056 | 0.348976 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.57134 | −0.0790625 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8404 | −0.544065 | −0.272032 | − | 0.962288i | \(-0.587696\pi\) | ||||
−0.272032 | + | 0.962288i | \(0.587696\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.14250 | −0.406617 | −0.203308 | − | 0.979115i | \(-0.565169\pi\) | ||||
−0.203308 | + | 0.979115i | \(0.565169\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.0902 | −1.79778 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.1622 | 1.79249 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.26565 | −0.0625821 | −0.0312911 | − | 0.999510i | \(-0.509962\pi\) | ||||
−0.0312911 | + | 0.999510i | \(0.509962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.5251 | 1.79728 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.306408 | 0.0150410 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.4317 | 1.04701 | 0.523503 | − | 0.852024i | \(-0.324625\pi\) | ||||
0.523503 | + | 0.852024i | \(0.324625\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.89122 | 0.0921722 | 0.0460861 | − | 0.998937i | \(-0.485325\pi\) | ||||
0.0460861 | + | 0.998937i | \(0.485325\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.8656 | −0.575564 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.51325 | 0.411985 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.7831 | −1.19376 | −0.596880 | − | 0.802330i | \(-0.703593\pi\) | ||||
−0.596880 | + | 0.802330i | \(0.703593\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.1885 | 0.826027 | 0.413013 | − | 0.910725i | \(-0.364476\pi\) | ||||
0.413013 | + | 0.910725i | \(0.364476\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.9495 | 0.619457 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0523 | 1.33886 | 0.669432 | − | 0.742873i | \(-0.266537\pi\) | ||||
0.669432 | + | 0.742873i | \(0.266537\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.02151 | −0.143556 | −0.0717782 | − | 0.997421i | \(-0.522867\pi\) | ||||
−0.0717782 | + | 0.997421i | \(0.522867\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.05455 | 0.0499903 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.17729 | 0.385910 | 0.192955 | − | 0.981208i | \(-0.438193\pi\) | ||||
0.192955 | + | 0.981208i | \(0.438193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.7511 | −1.11839 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.77255 | 0.129979 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.58642 | 0.401656 | 0.200828 | − | 0.979627i | \(-0.435637\pi\) | ||||
0.200828 | + | 0.979627i | \(0.435637\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.243997 | −0.0113641 | −0.00568204 | − | 0.999984i | \(-0.501809\pi\) | ||||
−0.00568204 | + | 0.999984i | \(0.501809\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.5035 | −1.60351 | −0.801757 | − | 0.597650i | \(-0.796101\pi\) | ||||
−0.801757 | + | 0.597650i | \(0.796101\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.5335 | −1.13528 | −0.567638 | − | 0.823278i | \(-0.692143\pi\) | ||||
−0.567638 | + | 0.823278i | \(0.692143\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −40.2786 | −1.85989 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20.0252 | 0.920760 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.2667 | −1.02166 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.8205 | −1.31684 | −0.658421 | − | 0.752649i | \(-0.728776\pi\) | ||||
−0.658421 | + | 0.752649i | \(0.728776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 42.0481 | 1.91723 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.762874 | 0.0346403 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.3903 | 0.606772 | 0.303386 | − | 0.952868i | \(-0.401883\pi\) | ||||
0.303386 | + | 0.952868i | \(0.401883\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.2208 | −1.31872 | −0.659358 | − | 0.751829i | \(-0.729172\pi\) | ||||
−0.659358 | + | 0.751829i | \(0.729172\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.912631 | 0.0411028 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −26.4535 | −1.18660 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −43.4891 | −1.94684 | −0.973419 | − | 0.229030i | \(-0.926445\pi\) | ||||
−0.973419 | + | 0.229030i | \(0.926445\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.9720 | 0.979683 | 0.489841 | − | 0.871812i | \(-0.337055\pi\) | ||||
0.489841 | + | 0.871812i | \(0.337055\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.98452 | −0.0883101 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.71792 | 0.209118 | 0.104559 | − | 0.994519i | \(-0.466657\pi\) | ||||
0.104559 | + | 0.994519i | \(0.466657\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.39836 | −0.327284 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.483977 | 0.0213266 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.44288 | 0.0634579 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.2758 | −0.537814 | −0.268907 | − | 0.963166i | \(-0.586662\pi\) | ||||
−0.268907 | + | 0.963166i | \(0.586662\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.7110 | −1.21172 | −0.605859 | − | 0.795572i | \(-0.707170\pi\) | ||||
−0.605859 | + | 0.795572i | \(0.707170\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.0862 | −0.570046 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.5867 | −0.634206 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.6169 | −1.19622 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.759133 | −0.0328202 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41.3098 | 1.77934 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.8180 | 1.62592 | 0.812962 | − | 0.582317i | \(-0.197854\pi\) | ||||
0.812962 | + | 0.582317i | \(0.197854\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.173983 | −0.00745262 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.9100 | 1.53540 | 0.767701 | − | 0.640808i | \(-0.221401\pi\) | ||||
0.767701 | + | 0.640808i | \(0.221401\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.71263 | 0.0729603 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −53.2524 | −2.26452 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.6341 | 0.492951 | 0.246475 | − | 0.969149i | \(-0.420728\pi\) | ||||
0.246475 | + | 0.969149i | \(0.420728\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.2846 | 0.984834 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.3452 | −0.731013 | −0.365506 | − | 0.930809i | \(-0.619104\pi\) | ||||
−0.365506 | + | 0.930809i | \(0.619104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.10112 | 0.0463244 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.42505 | −0.311274 | −0.155637 | − | 0.987814i | \(-0.549743\pi\) | ||||
−0.155637 | + | 0.987814i | \(0.549743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.8276 | 0.829761 | 0.414881 | − | 0.909876i | \(-0.363823\pi\) | ||||
0.414881 | + | 0.909876i | \(0.363823\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.4666 | −0.603301 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.3484 | 0.847113 | 0.423557 | − | 0.905870i | \(-0.360781\pi\) | ||||
0.423557 | + | 0.905870i | \(0.360781\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.3841 | 0.430806 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −68.7846 | −2.84877 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.3887 | 1.08918 | 0.544590 | − | 0.838702i | \(-0.316685\pi\) | ||||
0.544590 | + | 0.838702i | \(0.316685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.5574 | −1.01187 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.98631 | 0.0815679 | 0.0407839 | − | 0.999168i | \(-0.487014\pi\) | ||||
0.0407839 | + | 0.999168i | \(0.487014\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.00532 | 0.0412141 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.4186 | −0.793422 | −0.396711 | − | 0.917943i | \(-0.629849\pi\) | ||||
−0.396711 | + | 0.917943i | \(0.629849\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.95870 | 0.283851 | 0.141926 | − | 0.989877i | \(-0.454671\pi\) | ||||
0.141926 | + | 0.989877i | \(0.454671\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.32707 | −0.0946090 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0403 | 0.772822 | 0.386411 | − | 0.922327i | \(-0.373715\pi\) | ||||
0.386411 | + | 0.922327i | \(0.373715\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.67773 | 0.0678738 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.3275 | −0.740242 | −0.370121 | − | 0.928984i | \(-0.620684\pi\) | ||||
−0.370121 | + | 0.928984i | \(0.620684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.68917 | −0.108262 | −0.0541310 | − | 0.998534i | \(-0.517239\pi\) | ||||
−0.0541310 | + | 0.998534i | \(0.517239\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.7700 | −1.23675 | −0.618376 | − | 0.785882i | \(-0.712209\pi\) | ||||
−0.618376 | + | 0.785882i | \(0.712209\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.7385 | 1.43183 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8131 | 0.992525 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.2465 | 0.607920 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.0018 | 1.43321 | 0.716604 | − | 0.697480i | \(-0.245695\pi\) | ||||
0.716604 | + | 0.697480i | \(0.245695\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.02933 | −0.0805314 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 48.0336 | 1.90316 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.1562 | 1.46758 | 0.733790 | − | 0.679376i | \(-0.237750\pi\) | ||||
0.733790 | + | 0.679376i | \(0.237750\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.1189 | 1.77931 | 0.889657 | − | 0.456630i | \(-0.150944\pi\) | ||||
0.889657 | + | 0.456630i | \(0.150944\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.7005 | 0.695879 | 0.347939 | − | 0.937517i | \(-0.386882\pi\) | ||||
0.347939 | + | 0.937517i | \(0.386882\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −54.4616 | −2.13780 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.14301 | −0.162129 | −0.0810643 | − | 0.996709i | \(-0.525832\pi\) | ||||
−0.0810643 | + | 0.996709i | \(0.525832\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.24157 | 0.0875855 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.7952 | −0.926930 | −0.463465 | − | 0.886115i | \(-0.653394\pi\) | ||||
−0.463465 | + | 0.886115i | \(0.653394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.35583 | −0.363900 | −0.181950 | − | 0.983308i | \(-0.558241\pi\) | ||||
−0.181950 | + | 0.983308i | \(0.558241\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.88657 | 0.0731579 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.11269 | 0.0430836 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.6939 | −0.490042 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.8403 | 0.456410 | 0.228205 | − | 0.973613i | \(-0.426714\pi\) | ||||
0.228205 | + | 0.973613i | \(0.426714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.85878 | −0.225171 | −0.112586 | − | 0.993642i | \(-0.535913\pi\) | ||||
−0.112586 | + | 0.993642i | \(0.535913\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.8537 | 0.992174 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.1803 | 0.886968 | 0.443484 | − | 0.896282i | \(-0.353742\pi\) | ||||
0.443484 | + | 0.896282i | \(0.353742\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.534878 | −0.0204366 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −79.9804 | −3.04701 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.7086 | 1.09213 | 0.546063 | − | 0.837744i | \(-0.316126\pi\) | ||||
0.546063 | + | 0.837744i | \(0.316126\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0520194 | 0.00197321 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.0138 | −0.379301 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.3971 | −1.86570 | −0.932851 | − | 0.360261i | \(-0.882688\pi\) | ||||
−0.932851 | + | 0.360261i | \(0.882688\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.6114 | 1.07910 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −67.2552 | −2.52939 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.82705 | 0.369063 | 0.184531 | − | 0.982827i | \(-0.440923\pi\) | ||||
0.184531 | + | 0.982827i | \(0.440923\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.9549 | −0.597516 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.13408 | −0.154606 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.3562 | 1.69150 | 0.845751 | − | 0.533578i | \(-0.179153\pi\) | ||||
0.845751 | + | 0.533578i | \(0.179153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.4019 | 0.610839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.91328 | −0.0710574 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.9767 | 1.55683 | 0.778414 | − | 0.627751i | \(-0.216024\pi\) | ||||
0.778414 | + | 0.627751i | \(0.216024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.44294 | 0.312274 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.1292 | 0.891234 | 0.445617 | − | 0.895224i | \(-0.352984\pi\) | ||||
0.445617 | + | 0.895224i | \(0.352984\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 60.0584 | 2.21228 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.4710 | −0.569108 | −0.284554 | − | 0.958660i | \(-0.591846\pi\) | ||||
−0.284554 | + | 0.958660i | \(0.591846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.61820 | 0.0960525 | 0.0480263 | − | 0.998846i | \(-0.484707\pi\) | ||||
0.0480263 | + | 0.998846i | \(0.484707\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.389504 | 0.0142703 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.7269 | −0.940041 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.3233 | −0.705116 | −0.352558 | − | 0.935790i | \(-0.614688\pi\) | ||||
−0.352558 | + | 0.935790i | \(0.614688\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.47232 | −0.0899770 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.3807 | 0.813441 | 0.406720 | − | 0.913553i | \(-0.366672\pi\) | ||||
0.406720 | + | 0.913553i | \(0.366672\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.3260 | 1.17182 | 0.585909 | − | 0.810377i | \(-0.300738\pi\) | ||||
0.585909 | + | 0.810377i | \(0.300738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.89627 | −0.213459 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −63.3260 | −2.28657 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.1841 | −1.05241 | −0.526203 | − | 0.850359i | \(-0.676385\pi\) | ||||
−0.526203 | + | 0.850359i | \(0.676385\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.4024 | 0.805757 | 0.402878 | − | 0.915253i | \(-0.368010\pi\) | ||||
0.402878 | + | 0.915253i | \(0.368010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.4346 | 0.985479 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18.7917 | −0.673284 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.4442 | 1.41142 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.06655 | 0.0380669 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6867 | 0.452230 | 0.226115 | − | 0.974101i | \(-0.427397\pi\) | ||||
0.226115 | + | 0.974101i | \(0.427397\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.3168 | 1.32683 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.7600 | −0.524143 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 39.8473 | 1.41146 | 0.705732 | − | 0.708479i | \(-0.250618\pi\) | ||||
0.705732 | + | 0.708479i | \(0.250618\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.608342 | 0.0215216 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.0315 | 0.389293 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.22570 | 0.0432003 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.9994 | −1.26567 | −0.632835 | − | 0.774286i | \(-0.718109\pi\) | ||||
−0.632835 | + | 0.774286i | \(0.718109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.4720 | 1.07002 | 0.535009 | − | 0.844846i | \(-0.320308\pi\) | ||||
0.535009 | + | 0.844846i | \(0.320308\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.737515 | −0.0258340 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.8439 | 0.554307 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.6784 | −0.512278 | −0.256139 | − | 0.966640i | \(-0.582451\pi\) | ||||
−0.256139 | + | 0.966640i | \(0.582451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.7719 | 1.03778 | 0.518891 | − | 0.854840i | \(-0.326345\pi\) | ||||
0.518891 | + | 0.854840i | \(0.326345\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.393491 | −0.0136830 | −0.00684152 | − | 0.999977i | \(-0.502178\pi\) | ||||
−0.00684152 | + | 0.999977i | \(0.502178\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.3936 | −0.708299 | −0.354149 | − | 0.935189i | \(-0.615230\pi\) | ||||
−0.354149 | + | 0.935189i | \(0.615230\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.4169 | 0.603459 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.111665 | −0.00386432 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.2050 | −1.04279 | −0.521396 | − | 0.853315i | \(-0.674589\pi\) | ||||
−0.521396 | + | 0.853315i | \(0.674589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8528 | −0.994926 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.35532 | −0.115426 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −78.8642 | −2.70981 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.5888 | 0.637216 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.9989 | 1.16410 | 0.582051 | − | 0.813153i | \(-0.302251\pi\) | ||||
0.582051 | + | 0.813153i | \(0.302251\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.110035 | −0.00375871 | −0.00187935 | − | 0.999998i | \(-0.500598\pi\) | ||||
−0.00187935 | + | 0.999998i | \(0.500598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.0084 | −0.546199 | −0.273100 | − | 0.961986i | \(-0.588049\pi\) | ||||
−0.273100 | + | 0.961986i | \(0.588049\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.6719 | 1.52065 | 0.760325 | − | 0.649542i | \(-0.225040\pi\) | ||||
0.760325 | + | 0.649542i | \(0.225040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.917816 | −0.0312067 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 79.4032 | 2.69357 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 69.8338 | 2.36623 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.22047 | −0.142678 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.4516 | −0.623067 | −0.311533 | − | 0.950235i | \(-0.600843\pi\) | ||||
−0.311533 | + | 0.950235i | \(0.600843\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.5042 | −1.12879 | −0.564393 | − | 0.825506i | \(-0.690890\pi\) | ||||
−0.564393 | + | 0.825506i | \(0.690890\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.7850 | −1.06965 | −0.534826 | − | 0.844962i | \(-0.679623\pi\) | ||||
−0.534826 | + | 0.844962i | \(0.679623\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.0665 | 1.07669 | 0.538344 | − | 0.842725i | \(-0.319050\pi\) | ||||
0.538344 | + | 0.842725i | \(0.319050\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −68.7736 | −2.30659 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.14160 | 0.0382023 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.78629 | 0.0597092 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.11011 | −0.0703762 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.0007 | −0.966153 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.640990 | 0.0213072 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.9240 | −0.528747 | −0.264373 | − | 0.964420i | \(-0.585165\pi\) | ||||
−0.264373 | + | 0.964420i | \(0.585165\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.50065 | −0.215376 | −0.107688 | − | 0.994185i | \(-0.534345\pi\) | ||||
−0.107688 | + | 0.994185i | \(0.534345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.4835 | −0.512429 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 75.9667 | 2.50864 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.81381 | 0.158793 | 0.0793965 | − | 0.996843i | \(-0.474701\pi\) | ||||
0.0793965 | + | 0.996843i | \(0.474701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.8643 | 1.50964 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −31.9635 | −1.05095 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.8321 | −1.76617 | −0.883087 | − | 0.469210i | \(-0.844539\pi\) | ||||
−0.883087 | + | 0.469210i | \(0.844539\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.6842 | 1.07118 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.49901 | −0.0490228 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.0027 | 0.751465 | 0.375732 | − | 0.926728i | \(-0.377391\pi\) | ||||
0.375732 | + | 0.926728i | \(0.377391\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.83773 | 0.190304 | 0.0951522 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951522 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.2090 | −0.397579 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.9102 | 1.65436 | 0.827180 | − | 0.561937i | \(-0.189944\pi\) | ||||
0.827180 | + | 0.561937i | \(0.189944\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.8270 | 0.416383 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.7272 | 1.57843 | 0.789215 | − | 0.614117i | \(-0.210488\pi\) | ||||
0.789215 | + | 0.614117i | \(0.210488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.647939 | 0.0209668 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.1269 | −0.585350 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.743054 | −0.0239695 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.801844 | 0.0258123 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.3000 | −1.29596 | −0.647981 | − | 0.761656i | \(-0.724386\pi\) | ||||
−0.647981 | + | 0.761656i | \(0.724386\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15.3107 | 0.491345 | 0.245672 | − | 0.969353i | \(-0.420991\pi\) | ||||
0.245672 | + | 0.969353i | \(0.420991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.76293 | 0.0565170 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.4387 | −0.333963 | −0.166982 | − | 0.985960i | \(-0.553402\pi\) | ||||
−0.166982 | + | 0.985960i | \(0.553402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.2887 | −1.70311 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −52.6192 | −1.67829 | −0.839146 | − | 0.543906i | \(-0.816945\pi\) | ||||
−0.839146 | + | 0.543906i | \(0.816945\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.81497 | −0.0896923 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.2938 | 0.327322 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.26644 | 0.0402298 | 0.0201149 | − | 0.999798i | \(-0.493597\pi\) | ||||
0.0201149 | + | 0.999798i | \(0.493597\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.54206 | −0.0805887 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.4566 | 1.75633 | 0.878164 | − | 0.478359i | \(-0.158768\pi\) | ||||
0.878164 | + | 0.478359i | \(0.158768\pi\) | |||||||
\(998\) | 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 | 6012.2.a.i.1.4 | 9 | ||
3.2 | odd | 2 | 2004.2.a.c.1.6 | ✓ | 9 | ||
12.11 | even | 2 | 8016.2.a.bc.1.6 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.2.a.c.1.6 | ✓ | 9 | 3.2 | odd | 2 | ||
6012.2.a.i.1.4 | 9 | 1.1 | even | 1 | trivial | ||
8016.2.a.bc.1.6 | 9 | 12.11 | even | 2 |