Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10000,2,Mod(1,10000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10000, 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("10000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 10000.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: | \(79.8504020213\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 9x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 50) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.34841\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10000.1 |
$q$-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 | ||||||||
\(3\) | −1.34841 | −0.778507 | −0.389254 | − | 0.921131i | \(-0.627267\pi\) | ||||
−0.389254 | + | 0.921131i | \(0.627267\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.833366 | −0.314983 | −0.157491 | − | 0.987520i | \(-0.550341\pi\) | ||||
−0.157491 | + | 0.987520i | \(0.550341\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.18178 | −0.393927 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.833366 | −0.251269 | −0.125635 | − | 0.992077i | \(-0.540097\pi\) | ||||
−0.125635 | + | 0.992077i | \(0.540097\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.56375 | −1.26576 | −0.632878 | − | 0.774252i | \(-0.718126\pi\) | ||||
−0.632878 | + | 0.774252i | \(0.718126\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.45140 | −1.32216 | −0.661079 | − | 0.750316i | \(-0.729901\pi\) | ||||
−0.661079 | + | 0.750316i | \(0.729901\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.65392 | 1.98534 | 0.992672 | − | 0.120838i | \(-0.0385583\pi\) | ||||
0.992672 | + | 0.120838i | \(0.0385583\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.12372 | 0.245216 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.53019 | 0.736096 | 0.368048 | − | 0.929807i | \(-0.380026\pi\) | ||||
0.368048 | + | 0.929807i | \(0.380026\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.63877 | 1.08518 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.26962 | 0.607153 | 0.303577 | − | 0.952807i | \(-0.401819\pi\) | ||||
0.303577 | + | 0.952807i | \(0.401819\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.00233 | −1.07805 | −0.539025 | − | 0.842290i | \(-0.681207\pi\) | ||||
−0.539025 | + | 0.842290i | \(0.681207\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.12372 | 0.195615 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.31486 | −1.20256 | −0.601278 | − | 0.799040i | \(-0.705342\pi\) | ||||
−0.601278 | + | 0.799040i | \(0.705342\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.15382 | 0.985400 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.86692 | 0.291564 | 0.145782 | − | 0.989317i | \(-0.453430\pi\) | ||||
0.145782 | + | 0.989317i | \(0.453430\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.63877 | −0.249910 | −0.124955 | − | 0.992162i | \(-0.539879\pi\) | ||||
−0.124955 | + | 0.992162i | \(0.539879\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.833366 | −0.121559 | −0.0607794 | − | 0.998151i | \(-0.519359\pi\) | ||||
−0.0607794 | + | 0.998151i | \(0.519359\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.30550 | −0.900786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.35074 | 1.02931 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.42721 | −0.882845 | −0.441422 | − | 0.897299i | \(-0.645526\pi\) | ||||
−0.441422 | + | 0.897299i | \(0.645526\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.6691 | −1.54560 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.5325 | −1.76178 | −0.880892 | − | 0.473317i | \(-0.843057\pi\) | ||||
−0.880892 | + | 0.473317i | \(0.843057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.88420 | 0.753394 | 0.376697 | − | 0.926336i | \(-0.377060\pi\) | ||||
0.376697 | + | 0.926336i | \(0.377060\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.984855 | 0.124080 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.49990 | 0.183242 | 0.0916212 | − | 0.995794i | \(-0.470795\pi\) | ||||
0.0916212 | + | 0.995794i | \(0.470795\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.76016 | −0.573056 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.36123 | 0.280226 | 0.140113 | − | 0.990135i | \(-0.455253\pi\) | ||||
0.140113 | + | 0.990135i | \(0.455253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.33001 | 0.389748 | 0.194874 | − | 0.980828i | \(-0.437570\pi\) | ||||
0.194874 | + | 0.980828i | \(0.437570\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.694498 | 0.0791454 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.16896 | −0.581554 | −0.290777 | − | 0.956791i | \(-0.593914\pi\) | ||||
−0.290777 | + | 0.956791i | \(0.593914\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.05806 | −0.450895 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.3356 | −1.35401 | −0.677004 | − | 0.735979i | \(-0.736722\pi\) | ||||
−0.677004 | + | 0.735979i | \(0.736722\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.40880 | −0.472673 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.00579 | −0.742612 | −0.371306 | − | 0.928511i | \(-0.621090\pi\) | ||||
−0.371306 | + | 0.928511i | \(0.621090\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.80327 | 0.398691 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.09363 | 0.839270 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0902 | −1.12604 | −0.563018 | − | 0.826445i | \(-0.690360\pi\) | ||||
−0.563018 | + | 0.826445i | \(0.690360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.984855 | 0.0989816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7085 | 1.26454 | 0.632272 | − | 0.774746i | \(-0.282122\pi\) | ||||
0.632272 | + | 0.774746i | \(0.282122\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.01515 | 0.691223 | 0.345611 | − | 0.938378i | \(-0.387672\pi\) | ||||
0.345611 | + | 0.938378i | \(0.387672\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.7700 | −1.04118 | −0.520589 | − | 0.853807i | \(-0.674288\pi\) | ||||
−0.520589 | + | 0.853807i | \(0.674288\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.6355 | −1.01870 | −0.509349 | − | 0.860560i | \(-0.670114\pi\) | ||||
−0.509349 | + | 0.860560i | \(0.670114\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.86346 | 0.936198 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.74176 | −0.163851 | −0.0819253 | − | 0.996638i | \(-0.526107\pi\) | ||||
−0.0819253 | + | 0.996638i | \(0.526107\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.39334 | 0.498615 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.54301 | 0.416457 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3055 | −0.936864 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.51738 | −0.226984 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.66673 | 0.502841 | 0.251421 | − | 0.967878i | \(-0.419102\pi\) | ||||
0.251421 | + | 0.967878i | \(0.419102\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.20974 | 0.194557 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4745 | 1.43938 | 0.719690 | − | 0.694295i | \(-0.244284\pi\) | ||||
0.719690 | + | 0.694295i | \(0.244284\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.21188 | −0.625349 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.89324 | 0.247187 | 0.123593 | − | 0.992333i | \(-0.460558\pi\) | ||||
0.123593 | + | 0.992333i | \(0.460558\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.98951 | −0.423205 | −0.211603 | − | 0.977356i | \(-0.567868\pi\) | ||||
−0.211603 | + | 0.977356i | \(0.567868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.12372 | 0.0946345 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.80327 | 0.318045 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.50243 | 0.701268 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00579 | 0.164320 | 0.0821602 | − | 0.996619i | \(-0.473818\pi\) | ||||
0.0821602 | + | 0.996619i | \(0.473818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.96971 | 0.160293 | 0.0801463 | − | 0.996783i | \(-0.474461\pi\) | ||||
0.0801463 | + | 0.996783i | \(0.474461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.44235 | 0.520833 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.78467 | −0.621284 | −0.310642 | − | 0.950527i | \(-0.600544\pi\) | ||||
−0.310642 | + | 0.950527i | \(0.600544\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.66654 | 0.687301 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.94194 | −0.231858 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0960 | 1.10408 | 0.552040 | − | 0.833817i | \(-0.313849\pi\) | ||||
0.552040 | + | 0.833817i | \(0.313849\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.15615 | −0.631142 | −0.315571 | − | 0.948902i | \(-0.602196\pi\) | ||||
−0.315571 | + | 0.948902i | \(0.602196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.82777 | 0.602137 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.2270 | −0.782080 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.50336 | 0.190327 | 0.0951634 | − | 0.995462i | \(-0.469663\pi\) | ||||
0.0951634 | + | 0.995462i | \(0.469663\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.2474 | 1.37156 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.0326 | 1.49731 | 0.748654 | − | 0.662961i | \(-0.230700\pi\) | ||||
0.748654 | + | 0.662961i | \(0.230700\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.87829 | 0.585589 | 0.292794 | − | 0.956175i | \(-0.405415\pi\) | ||||
0.292794 | + | 0.956175i | \(0.405415\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.93434 | −0.586523 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.54301 | 0.332218 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.69916 | −0.341813 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.27521 | 0.381701 | 0.190850 | − | 0.981619i | \(-0.438875\pi\) | ||||
0.190850 | + | 0.981619i | \(0.438875\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.4461 | 0.967873 | 0.483937 | − | 0.875103i | \(-0.339207\pi\) | ||||
0.483937 | + | 0.875103i | \(0.339207\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.43858 | 0.387483 | 0.193742 | − | 0.981053i | \(-0.437938\pi\) | ||||
0.193742 | + | 0.981053i | \(0.437938\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.4090 | 1.23409 | 0.617045 | − | 0.786927i | \(-0.288329\pi\) | ||||
0.617045 | + | 0.786927i | \(0.288329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.02249 | −0.142655 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.72479 | −0.191243 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.17191 | −0.289968 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.21188 | −0.498856 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.269934 | 0.0185830 | 0.00929151 | − | 0.999957i | \(-0.497042\pi\) | ||||
0.00929151 | + | 0.999957i | \(0.497042\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.18392 | −0.218158 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.00214 | 0.339567 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.49023 | −0.303422 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.8788 | 1.67353 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.1713 | 1.55166 | 0.775832 | − | 0.630939i | \(-0.217330\pi\) | ||||
0.775832 | + | 0.630939i | \(0.217330\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.252653 | −0.0167692 | −0.00838459 | − | 0.999965i | \(-0.502669\pi\) | ||||
−0.00838459 | + | 0.999965i | \(0.502669\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.0904 | −1.39369 | −0.696845 | − | 0.717222i | \(-0.745414\pi\) | ||||
−0.696845 | + | 0.717222i | \(0.745414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.936471 | −0.0616153 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.6075 | 0.956972 | 0.478486 | − | 0.878095i | \(-0.341186\pi\) | ||||
0.478486 | + | 0.878095i | \(0.341186\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.96990 | 0.452744 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.81822 | −0.376349 | −0.188175 | − | 0.982136i | \(-0.560257\pi\) | ||||
−0.188175 | + | 0.982136i | \(0.560257\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7291 | 0.884371 | 0.442186 | − | 0.896924i | \(-0.354203\pi\) | ||||
0.442186 | + | 0.896924i | \(0.354203\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.4444 | −0.734157 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −39.4943 | −2.51296 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.6335 | 1.05410 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.8938 | 1.00320 | 0.501602 | − | 0.865098i | \(-0.332744\pi\) | ||||
0.501602 | + | 0.865098i | \(0.332744\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.94194 | −0.184958 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.31253 | 0.144252 | 0.0721259 | − | 0.997396i | \(-0.477022\pi\) | ||||
0.0721259 | + | 0.997396i | \(0.477022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.09595 | 0.378784 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.86397 | −0.239174 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.4593 | −1.32324 | −0.661619 | − | 0.749840i | \(-0.730130\pi\) | ||||
−0.661619 | + | 0.749840i | \(0.730130\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.44670 | 0.578129 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.3864 | 1.30395 | 0.651977 | − | 0.758239i | \(-0.273940\pi\) | ||||
0.651977 | + | 0.758239i | \(0.273940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.1305 | 1.58732 | 0.793658 | − | 0.608364i | \(-0.208174\pi\) | ||||
0.793658 | + | 0.608364i | \(0.208174\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.12838 | −0.310384 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.6469 | 1.12038 | 0.560191 | − | 0.828363i | \(-0.310728\pi\) | ||||
0.560191 | + | 0.828363i | \(0.310728\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.09343 | 0.424673 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.8187 | 0.884011 | 0.442006 | − | 0.897012i | \(-0.354267\pi\) | ||||
0.442006 | + | 0.897012i | \(0.354267\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.7800 | 0.938022 | 0.469011 | − | 0.883192i | \(-0.344611\pi\) | ||||
0.469011 | + | 0.883192i | \(0.344611\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.55583 | −0.0918375 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.7178 | 0.748103 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.9541 | 0.876627 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.4003 | −1.07496 | −0.537479 | − | 0.843277i | \(-0.680623\pi\) | ||||
−0.537479 | + | 0.843277i | \(0.680623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.69916 | −0.272673 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.1109 | −0.931718 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.36569 | 0.0787173 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.1363 | −0.984457 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.1179 | −1.94721 | −0.973606 | − | 0.228237i | \(-0.926704\pi\) | ||||
−0.973606 | + | 0.228237i | \(0.926704\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.45932 | −0.538122 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0379 | 0.739311 | 0.369656 | − | 0.929169i | \(-0.379476\pi\) | ||||
0.369656 | + | 0.929169i | \(0.379476\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.48262 | −0.196849 | −0.0984247 | − | 0.995144i | \(-0.531380\pi\) | ||||
−0.0984247 | + | 0.995144i | \(0.531380\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.82036 | −0.270738 | −0.135369 | − | 0.990795i | \(-0.543222\pi\) | ||||
−0.135369 | + | 0.990795i | \(0.543222\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.72479 | −0.152559 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.5225 | 0.810565 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −47.1760 | −2.62494 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.3411 | 0.793063 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.694498 | 0.0382889 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.56343 | −0.470689 | −0.235344 | − | 0.971912i | \(-0.575622\pi\) | ||||
−0.235344 | + | 0.971912i | \(0.575622\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.64456 | 0.473719 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.6712 | 0.799191 | 0.399596 | − | 0.916692i | \(-0.369151\pi\) | ||||
0.399596 | + | 0.916692i | \(0.369151\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.34861 | 0.127559 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.00214 | 0.270881 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0883 | 0.598715 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.9872 | −1.23402 | −0.617008 | − | 0.786957i | \(-0.711656\pi\) | ||||
−0.617008 | + | 0.786957i | \(0.711656\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.55023 | 0.190040 | 0.0950198 | − | 0.995475i | \(-0.469709\pi\) | ||||
0.0950198 | + | 0.995475i | \(0.469709\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.7339 | −1.37357 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.64110 | 0.300245 | 0.150123 | − | 0.988667i | \(-0.452033\pi\) | ||||
0.150123 | + | 0.988667i | \(0.452033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.12586 | −0.324215 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.9066 | 0.892295 | 0.446147 | − | 0.894960i | \(-0.352796\pi\) | ||||
0.446147 | + | 0.894960i | \(0.352796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 55.8903 | 2.94159 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.8961 | 0.729355 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.6133 | −0.658411 | −0.329205 | − | 0.944258i | \(-0.606781\pi\) | ||||
−0.329205 | + | 0.944258i | \(0.606781\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.20629 | −0.114855 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.35621 | 0.278081 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.2496 | −0.686037 | −0.343019 | − | 0.939329i | \(-0.611449\pi\) | ||||
−0.343019 | + | 0.939329i | \(0.611449\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.9217 | −0.768507 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3360 | −1.14732 | −0.573661 | − | 0.819093i | \(-0.694477\pi\) | ||||
−0.573661 | + | 0.819093i | \(0.694477\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.64110 | −0.391465 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.3529 | 1.24437 | 0.622187 | − | 0.782869i | \(-0.286244\pi\) | ||||
0.622187 | + | 0.782869i | \(0.286244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.93667 | 0.0984462 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.1116 | 1.52672 | 0.763360 | − | 0.645974i | \(-0.223548\pi\) | ||||
0.763360 | + | 0.645974i | \(0.223548\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.2445 | −0.973236 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.2144 | −1.12057 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.3704 | −1.77519 | −0.887594 | − | 0.460627i | \(-0.847624\pi\) | ||||
−0.887594 | + | 0.460627i | \(0.847624\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.72459 | 0.486839 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.66794 | −0.283043 | −0.141522 | − | 0.989935i | \(-0.545199\pi\) | ||||
−0.141522 | + | 0.989935i | \(0.545199\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.3931 | 1.36455 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.09595 | 0.302165 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.3676 | 0.957668 | 0.478834 | − | 0.877905i | \(-0.341060\pi\) | ||||
0.478834 | + | 0.877905i | \(0.341060\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.90129 | −0.192437 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.2775 | 0.554931 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.72793 | 0.329468 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.9792 | −1.12261 | −0.561304 | − | 0.827610i | \(-0.689700\pi\) | ||||
−0.561304 | + | 0.827610i | \(0.689700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.1272 | −0.493568 | −0.246784 | − | 0.969070i | \(-0.579374\pi\) | ||||
−0.246784 | + | 0.969070i | \(0.579374\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.984855 | 0.0478853 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.90369 | −0.237306 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.12838 | −0.247601 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.5024 | 1.37291 | 0.686457 | − | 0.727171i | \(-0.259165\pi\) | ||||
0.686457 | + | 0.727171i | \(0.259165\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.8897 | −0.763609 | −0.381804 | − | 0.924243i | \(-0.624697\pi\) | ||||
−0.381804 | + | 0.924243i | \(0.624697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.5500 | 1.46140 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.94660 | −0.140634 | −0.0703168 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703168 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.45171 | 0.354844 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.27327 | −0.250541 | −0.125270 | − | 0.992123i | \(-0.539980\pi\) | ||||
−0.125270 | + | 0.992123i | \(0.539980\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.70463 | −0.127925 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.81659 | −0.321695 | −0.160847 | − | 0.986979i | \(-0.551423\pi\) | ||||
−0.160847 | + | 0.986979i | \(0.551423\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.55583 | −0.0732609 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.65598 | −0.124789 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.17712 | −0.195397 | −0.0976987 | − | 0.995216i | \(-0.531148\pi\) | ||||
−0.0976987 | + | 0.995216i | \(0.531148\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −30.7392 | −1.43478 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.4342 | −1.74348 | −0.871742 | − | 0.489965i | \(-0.837010\pi\) | ||||
−0.871742 | + | 0.489965i | \(0.837010\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.8788 | −0.645003 | −0.322501 | − | 0.946569i | \(-0.604524\pi\) | ||||
−0.322501 | + | 0.946569i | \(0.604524\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.8606 | 0.641391 | 0.320696 | − | 0.947182i | \(-0.396083\pi\) | ||||
0.320696 | + | 0.947182i | \(0.396083\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.24997 | −0.0577181 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.4970 | 0.483674 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.36569 | 0.0627947 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.59554 | 0.347776 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.7974 | −1.31579 | −0.657894 | − | 0.753110i | \(-0.728553\pi\) | ||||
−0.657894 | + | 0.753110i | \(0.728553\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33.3832 | 1.52214 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.96696 | 0.180503 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.9513 | 1.76505 | 0.882525 | − | 0.470265i | \(-0.155842\pi\) | ||||
0.882525 | + | 0.470265i | \(0.155842\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.0072 | −0.859535 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.5069 | 1.06085 | 0.530426 | − | 0.847731i | \(-0.322032\pi\) | ||||
0.530426 | + | 0.847731i | \(0.322032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.8240 | −0.802753 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.96777 | −0.0882665 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.2651 | −1.26532 | −0.632660 | − | 0.774430i | \(-0.718037\pi\) | ||||
−0.632660 | + | 0.774430i | \(0.718037\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.9979 | 0.491348 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.90424 | 0.307845 | 0.153922 | − | 0.988083i | \(-0.450809\pi\) | ||||
0.153922 | + | 0.988083i | \(0.450809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.5551 | −0.468768 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.5390 | 1.48659 | 0.743295 | − | 0.668964i | \(-0.233262\pi\) | ||||
0.743295 | + | 0.668964i | \(0.233262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.77511 | −0.122764 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 48.7974 | 2.15446 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.694498 | 0.0305440 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.37556 | −0.148171 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.23342 | 0.0540373 | 0.0270186 | − | 0.999635i | \(-0.491399\pi\) | ||||
0.0270186 | + | 0.999635i | \(0.491399\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.0305 | 1.00705 | 0.503526 | − | 0.863980i | \(-0.332036\pi\) | ||||
0.503526 | + | 0.863980i | \(0.332036\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.7211 | 1.42535 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.5377 | −0.458162 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.9925 | 0.694014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.52014 | −0.369048 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.0123 | −1.16567 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.25479 | 0.226340 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.7700 | −1.15093 | −0.575466 | − | 0.817826i | \(-0.695179\pi\) | ||||
−0.575466 | + | 0.817826i | \(0.695179\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.6232 | −0.455885 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.42689 | 0.274794 | 0.137397 | − | 0.990516i | \(-0.456126\pi\) | ||||
0.137397 | + | 0.990516i | \(0.456126\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.95383 | −0.296782 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.2950 | 1.20541 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.30764 | 0.183179 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.0843 | −1.86791 | −0.933957 | − | 0.357386i | \(-0.883668\pi\) | ||||
−0.933957 | + | 0.357386i | \(0.883668\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.47893 | 0.316325 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.12586 | −0.258634 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.0779 | 0.846181 | 0.423091 | − | 0.906087i | \(-0.360945\pi\) | ||||
0.423091 | + | 0.906087i | \(0.360945\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.38185 | 0.142024 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.9339 | −1.25489 | −0.627447 | − | 0.778659i | \(-0.715900\pi\) | ||||
−0.627447 | + | 0.778659i | \(0.715900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2396 | 0.595911 | 0.297955 | − | 0.954580i | \(-0.403695\pi\) | ||||
0.297955 | + | 0.954580i | \(0.403695\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.11317 | −0.297157 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.2089 | 0.758048 | 0.379024 | − | 0.925387i | \(-0.376260\pi\) | ||||
0.379024 | + | 0.925387i | \(0.376260\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.1309 | −0.753496 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.2801 | 0.426489 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.35621 | 0.221832 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.16430 | 0.213154 | 0.106577 | − | 0.994304i | \(-0.466011\pi\) | ||||
0.106577 | + | 0.994304i | \(0.466011\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51.9437 | −2.14030 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.33346 | −0.301658 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.6286 | 1.46309 | 0.731546 | − | 0.681793i | \(-0.238799\pi\) | ||||
0.731546 | + | 0.681793i | \(0.238799\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.4745 | −0.960749 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.8284 | 1.30047 | 0.650236 | − | 0.759733i | \(-0.274670\pi\) | ||||
0.650236 | + | 0.759733i | \(0.274670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.6378 | −0.515508 | −0.257754 | − | 0.966211i | \(-0.582982\pi\) | ||||
−0.257754 | + | 0.966211i | \(0.582982\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.77255 | −0.0721840 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.9481 | 1.41850 | 0.709250 | − | 0.704957i | \(-0.249034\pi\) | ||||
0.709250 | + | 0.704957i | \(0.249034\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.67414 | 0.148884 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.80327 | 0.153864 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.12279 | −0.287687 | −0.143843 | − | 0.989600i | \(-0.545946\pi\) | ||||
−0.143843 | + | 0.989600i | \(0.545946\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.0870 | 0.647639 | 0.323820 | − | 0.946119i | \(-0.395033\pi\) | ||||
0.323820 | + | 0.946119i | \(0.395033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.750421 | 0.0301619 | 0.0150810 | − | 0.999886i | \(-0.495199\pi\) | ||||
0.0150810 | + | 0.999886i | \(0.495199\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.9060 | 0.798798 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.83838 | 0.233910 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.72459 | 0.388363 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.8762 | 1.58997 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.3756 | 0.612092 | 0.306046 | − | 0.952017i | \(-0.400994\pi\) | ||||
0.306046 | + | 0.952017i | \(0.400994\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.363983 | −0.0144670 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.7767 | 1.14017 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.79045 | −0.110389 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.45385 | 0.373405 | 0.186702 | − | 0.982417i | \(-0.440220\pi\) | ||||
0.186702 | + | 0.982417i | \(0.440220\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.8334 | 1.29482 | 0.647411 | − | 0.762141i | \(-0.275852\pi\) | ||||
0.647411 | + | 0.762141i | \(0.275852\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.8681 | 0.702468 | 0.351234 | − | 0.936288i | \(-0.385762\pi\) | ||||
0.351234 | + | 0.936288i | \(0.385762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2775 | 0.442682 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.74495 | −0.264355 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.9642 | 1.25086 | 0.625428 | − | 0.780282i | \(-0.284924\pi\) | ||||
0.625428 | + | 0.780282i | \(0.284924\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.93534 | −0.153532 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.3989 | 0.444037 | 0.222018 | − | 0.975042i | \(-0.428736\pi\) | ||||
0.222018 | + | 0.975042i | \(0.428736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.33427 | 0.285270 | 0.142635 | − | 0.989775i | \(-0.454442\pi\) | ||||
0.142635 | + | 0.989775i | \(0.454442\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.5469 | −1.30285 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.5424 | 0.446923 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31.2445 | −1.20798 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.90369 | −0.189305 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.7630 | 1.26292 | 0.631460 | − | 0.775408i | \(-0.282456\pi\) | ||||
0.631460 | + | 0.775408i | \(0.282456\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.5826 | 1.25225 | 0.626126 | − | 0.779722i | \(-0.284640\pi\) | ||||
0.626126 | + | 0.779722i | \(0.284640\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.24217 | 0.354682 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.340681 | 0.0130549 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.34942 | −0.166426 | −0.0832130 | − | 0.996532i | \(-0.526518\pi\) | ||||
−0.0832130 | + | 0.996532i | \(0.526518\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.4385 | 1.08500 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.3321 | 1.11747 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2595 | 0.770708 | 0.385354 | − | 0.922769i | \(-0.374079\pi\) | ||||
0.385354 | + | 0.922769i | \(0.374079\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.820744 | −0.0311775 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.1773 | −0.385493 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.6970 | −0.745010 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.5964 | 0.475758 | 0.237879 | − | 0.971295i | \(-0.423548\pi\) | ||||
0.237879 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −63.3022 | −2.38749 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.5908 | −0.398310 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.4781 | 1.10707 | 0.553537 | − | 0.832825i | \(-0.313278\pi\) | ||||
0.553537 | + | 0.832825i | \(0.313278\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.10858 | 0.229090 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.1894 | −0.793549 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.84537 | 0.292991 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.1585 | 1.12472 | 0.562361 | − | 0.826892i | \(-0.309893\pi\) | ||||
0.562361 | + | 0.826892i | \(0.309893\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.84618 | −0.217723 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.5126 | −0.688489 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.94735 | 0.220575 | 0.110287 | − | 0.993900i | \(-0.464823\pi\) | ||||
0.110287 | + | 0.993900i | \(0.464823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.6059 | 1.02244 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.93359 | 0.330421 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.1763 | −0.375871 | −0.187935 | − | 0.982181i | \(-0.560180\pi\) | ||||
−0.187935 | + | 0.982181i | \(0.560180\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.24997 | −0.0460432 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.3198 | −1.33605 | −0.668023 | − | 0.744140i | \(-0.732859\pi\) | ||||
−0.668023 | + | 0.744140i | \(0.732859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53.2546 | 1.95636 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.84832 | 0.104495 | 0.0522473 | − | 0.998634i | \(-0.483362\pi\) | ||||
0.0522473 | + | 0.998634i | \(0.483362\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.5780 | 0.533380 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.97537 | 0.327953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.5502 | 1.15128 | 0.575641 | − | 0.817702i | \(-0.304752\pi\) | ||||
0.575641 | + | 0.817702i | \(0.304752\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.4314 | −0.781002 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.6446 | 1.65898 | 0.829491 | − | 0.558520i | \(-0.188631\pi\) | ||||
0.829491 | + | 0.558520i | \(0.188631\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.96696 | 0.143991 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.07879 | 0.329106 | 0.164553 | − | 0.986368i | \(-0.447382\pi\) | ||||
0.164553 | + | 0.986368i | \(0.447382\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.86327 | 0.320872 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 61.7590 | 2.22999 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.4585 | −0.918057 | −0.459029 | − | 0.888421i | \(-0.651802\pi\) | ||||
−0.459029 | + | 0.888421i | \(0.651802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.11825 | −0.112301 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.1523 | −0.616924 | −0.308462 | − | 0.951237i | \(-0.599814\pi\) | ||||
−0.308462 | + | 0.951237i | \(0.599814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.21987 | −0.294886 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16.1561 | 0.578854 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.96777 | −0.0704123 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.4366 | 0.658872 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.2729 | 0.401835 | 0.200917 | − | 0.979608i | \(-0.435608\pi\) | ||||
0.200917 | + | 0.979608i | \(0.435608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.9360 | 1.03015 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.45152 | 0.0516101 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.8540 | −0.953613 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.6713 | 0.944745 | 0.472372 | − | 0.881399i | \(-0.343398\pi\) | ||||
0.472372 | + | 0.881399i | \(0.343398\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.54301 | 0.160720 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.27929 | 0.292534 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.77511 | −0.0979316 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.8378 | −1.01514 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.9742 | 0.385832 | 0.192916 | − | 0.981215i | \(-0.438206\pi\) | ||||
0.192916 | + | 0.981215i | \(0.438206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.86618 | 0.346448 | 0.173224 | − | 0.984882i | \(-0.444581\pi\) | ||||
0.173224 | + | 0.984882i | \(0.444581\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −35.2348 | −1.23574 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1818 | −0.496158 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.49463 | −0.157055 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.29790 | −0.0801971 | −0.0400985 | − | 0.999196i | \(-0.512767\pi\) | ||||
−0.0400985 | + | 0.999196i | \(0.512767\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.805405 | 0.0280746 | 0.0140373 | − | 0.999901i | \(-0.495532\pi\) | ||||
0.0140373 | + | 0.999901i | \(0.495532\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.4543 | 1.26764 | 0.633820 | − | 0.773480i | \(-0.281486\pi\) | ||||
0.633820 | + | 0.773480i | \(0.281486\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.5705 | 1.02703 | 0.513514 | − | 0.858081i | \(-0.328344\pi\) | ||||
0.513514 | + | 0.858081i | \(0.328344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.1437 | −0.872226 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34.3738 | 1.19098 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33.8458 | −1.16988 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 43.5273 | 1.50273 | 0.751365 | − | 0.659887i | \(-0.229396\pi\) | ||||
0.751365 | + | 0.659887i | \(0.229396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.3096 | −0.631365 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.9818 | −0.688209 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.58825 | 0.295096 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.2779 | −0.730257 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.8229 | −0.885197 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −50.6065 | −1.73273 | −0.866367 | − | 0.499408i | \(-0.833551\pi\) | ||||
−0.866367 | + | 0.499408i | \(0.833551\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.1589 | −1.16684 | −0.583422 | − | 0.812169i | \(-0.698287\pi\) | ||||
−0.583422 | + | 0.812169i | \(0.698287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.9872 | −0.374878 | −0.187439 | − | 0.982276i | \(-0.560019\pi\) | ||||
−0.187439 | + | 0.982276i | \(0.560019\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.09790 | 0.0714961 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.3080 | −1.57634 | −0.788172 | − | 0.615455i | \(-0.788972\pi\) | ||||
−0.788172 | + | 0.615455i | \(0.788972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.1488 | −0.582404 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.30764 | 0.146127 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.84518 | −0.231940 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.1061 | 0.443576 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.9772 | −0.708350 | −0.354175 | − | 0.935179i | \(-0.615238\pi\) | ||||
−0.354175 | + | 0.935179i | \(0.615238\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.8113 | 0.836863 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.8631 | −1.71362 | −0.856811 | − | 0.515631i | \(-0.827558\pi\) | ||||
−0.856811 | + | 0.515631i | \(0.827558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.0893 | −1.65199 | −0.825994 | − | 0.563680i | \(-0.809385\pi\) | ||||
−0.825994 | + | 0.563680i | \(0.809385\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.9694 | −1.24131 | −0.620655 | − | 0.784084i | \(-0.713133\pi\) | ||||
−0.620655 | + | 0.784084i | \(0.713133\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.72246 | −0.158386 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.38185 | 0.113296 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.21188 | −0.241336 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.7242 | 0.725349 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.6253 | −0.654542 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.0373 | 1.16726 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.84152 | −0.0612820 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 44.9718 | 1.49326 | 0.746632 | − | 0.665237i | \(-0.231670\pi\) | ||||
0.746632 | + | 0.665237i | \(0.231670\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.0187 | −0.498138 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.9495 | 0.892876 | 0.446438 | − | 0.894815i | \(-0.352692\pi\) | ||||
0.446438 | + | 0.894815i | \(0.352692\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.2801 | 0.340220 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.7293 | −0.453380 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.9013 | −1.05233 | −0.526163 | − | 0.850384i | \(-0.676370\pi\) | ||||
−0.526163 | + | 0.850384i | \(0.676370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.0050 | 1.51592 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.7761 | −0.354698 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.29036 | −0.272291 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.25536 | −0.205232 | −0.102616 | − | 0.994721i | \(-0.532721\pi\) | ||||
−0.102616 | + | 0.994721i | \(0.532721\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54.5673 | −1.78837 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.5805 | −0.575559 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.9195 | 1.01010 | 0.505049 | − | 0.863091i | \(-0.331475\pi\) | ||||
0.505049 | + | 0.863091i | \(0.331475\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.69602 | 0.153249 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.6341 | −0.835647 | −0.417823 | − | 0.908528i | \(-0.637207\pi\) | ||||
−0.417823 | + | 0.908528i | \(0.637207\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.59058 | 0.214619 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.2123 | −1.46920 | −0.734601 | − | 0.678500i | \(-0.762630\pi\) | ||||
−0.734601 | + | 0.678500i | \(0.762630\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.1973 | −0.493325 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.49984 | 0.210772 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.6040 | 0.667428 | 0.333714 | − | 0.942674i | \(-0.391698\pi\) | ||||
0.333714 | + | 0.942674i | \(0.391698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.67414 | 0.118768 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.41113 | −0.0778595 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.02796 | 0.162192 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.7278 | 0.410148 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.0957 | −1.64313 | −0.821564 | − | 0.570116i | \(-0.806898\pi\) | ||||
−0.821564 | + | 0.570116i | \(0.806898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 63.6127 | 2.04353 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.6139 | −0.468982 | −0.234491 | − | 0.972118i | \(-0.575342\pi\) | ||||
−0.234491 | + | 0.972118i | \(0.575342\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.15809 | 0.133302 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.2556 | 1.67181 | 0.835903 | − | 0.548877i | \(-0.184945\pi\) | ||||
0.835903 | + | 0.548877i | \(0.184945\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.83838 | 0.186595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.5688 | 0.401292 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.6089 | 0.944376 | 0.472188 | − | 0.881498i | \(-0.343464\pi\) | ||||
0.472188 | + | 0.881498i | \(0.343464\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.936471 | −0.0298082 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.78518 | −0.183958 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.8753 | −0.472531 | −0.236265 | − | 0.971689i | \(-0.575923\pi\) | ||||
−0.236265 | + | 0.971689i | \(0.575923\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.5471 | 0.366435 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.7746 | 0.974640 | 0.487320 | − | 0.873223i | \(-0.337974\pi\) | ||||
0.487320 | + | 0.873223i | \(0.337974\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −41.2468 | −1.30499 |
(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 | 10000.2.a.x.1.2 | 4 | ||
4.3 | odd | 2 | 1250.2.a.f.1.3 | 4 | |||
5.4 | even | 2 | 10000.2.a.t.1.3 | 4 | |||
20.3 | even | 4 | 1250.2.b.e.1249.7 | 8 | |||
20.7 | even | 4 | 1250.2.b.e.1249.2 | 8 | |||
20.19 | odd | 2 | 1250.2.a.l.1.2 | 4 | |||
25.9 | even | 10 | 400.2.u.d.81.1 | 8 | |||
25.14 | even | 10 | 400.2.u.d.321.1 | 8 | |||
100.11 | odd | 10 | 250.2.d.d.101.1 | 8 | |||
100.23 | even | 20 | 250.2.e.c.149.4 | 16 | |||
100.27 | even | 20 | 250.2.e.c.149.1 | 16 | |||
100.39 | odd | 10 | 50.2.d.b.21.2 | ✓ | 8 | ||
100.59 | odd | 10 | 50.2.d.b.31.2 | yes | 8 | ||
100.63 | even | 20 | 250.2.e.c.99.1 | 16 | |||
100.87 | even | 20 | 250.2.e.c.99.4 | 16 | |||
100.91 | odd | 10 | 250.2.d.d.151.1 | 8 | |||
300.59 | even | 10 | 450.2.h.e.181.2 | 8 | |||
300.239 | even | 10 | 450.2.h.e.271.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.2.d.b.21.2 | ✓ | 8 | 100.39 | odd | 10 | ||
50.2.d.b.31.2 | yes | 8 | 100.59 | odd | 10 | ||
250.2.d.d.101.1 | 8 | 100.11 | odd | 10 | |||
250.2.d.d.151.1 | 8 | 100.91 | odd | 10 | |||
250.2.e.c.99.1 | 16 | 100.63 | even | 20 | |||
250.2.e.c.99.4 | 16 | 100.87 | even | 20 | |||
250.2.e.c.149.1 | 16 | 100.27 | even | 20 | |||
250.2.e.c.149.4 | 16 | 100.23 | even | 20 | |||
400.2.u.d.81.1 | 8 | 25.9 | even | 10 | |||
400.2.u.d.321.1 | 8 | 25.14 | even | 10 | |||
450.2.h.e.181.2 | 8 | 300.59 | even | 10 | |||
450.2.h.e.271.2 | 8 | 300.239 | even | 10 | |||
1250.2.a.f.1.3 | 4 | 4.3 | odd | 2 | |||
1250.2.a.l.1.2 | 4 | 20.19 | odd | 2 | |||
1250.2.b.e.1249.2 | 8 | 20.7 | even | 4 | |||
1250.2.b.e.1249.7 | 8 | 20.3 | even | 4 | |||
10000.2.a.t.1.3 | 4 | 5.4 | even | 2 | |||
10000.2.a.x.1.2 | 4 | 1.1 | even | 1 | trivial |