Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7623,2,Mod(1,7623)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7623, 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("7623.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7623.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: | \(60.8699614608\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7488.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2541) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.326909\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7623.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.05896 | 1.45590 | 0.727952 | − | 0.685628i | \(-0.240472\pi\) | ||||
0.727952 | + | 0.685628i | \(0.240472\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.23931 | 1.11966 | ||||||||
\(5\) | 1.05896 | 0.473581 | 0.236791 | − | 0.971561i | \(-0.423904\pi\) | ||||
0.236791 | + | 0.971561i | \(0.423904\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.492737 | 0.174209 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.18035 | 0.689489 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.80554 | −1.05547 | −0.527733 | − | 0.849410i | \(-0.676958\pi\) | ||||
−0.527733 | + | 0.849410i | \(0.676958\pi\) | |||||||
\(14\) | 2.05896 | 0.550280 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.46410 | −0.866025 | ||||||||
\(17\) | −2.56622 | −0.622400 | −0.311200 | − | 0.950344i | \(-0.600731\pi\) | ||||
−0.311200 | + | 0.950344i | \(0.600731\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.180354 | 0.0413761 | 0.0206881 | − | 0.999786i | \(-0.493414\pi\) | ||||
0.0206881 | + | 0.999786i | \(0.493414\pi\) | |||||||
\(20\) | 2.37134 | 0.530248 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.433778 | −0.0904489 | −0.0452245 | − | 0.998977i | \(-0.514400\pi\) | ||||
−0.0452245 | + | 0.998977i | \(0.514400\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.87861 | −0.775721 | ||||||||
\(26\) | −7.83544 | −1.53666 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.23931 | 0.423191 | ||||||||
\(29\) | −9.03032 | −1.67689 | −0.838445 | − | 0.544987i | \(-0.816535\pi\) | ||||
−0.838445 | + | 0.544987i | \(0.816535\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.492737 | −0.0884982 | −0.0442491 | − | 0.999021i | \(-0.514090\pi\) | ||||
−0.0442491 | + | 0.999021i | \(0.514090\pi\) | |||||||
\(32\) | −8.11792 | −1.43506 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.28375 | −0.906155 | ||||||||
\(35\) | 1.05896 | 0.178997 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.775212 | −0.127444 | −0.0637220 | − | 0.997968i | \(-0.520297\pi\) | ||||
−0.0637220 | + | 0.997968i | \(0.520297\pi\) | |||||||
\(38\) | 0.371342 | 0.0602397 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.521789 | 0.0825020 | ||||||||
\(41\) | −3.09276 | −0.483008 | −0.241504 | − | 0.970400i | \(-0.577641\pi\) | ||||
−0.241504 | + | 0.970400i | \(0.577641\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.61413 | 0.246153 | 0.123076 | − | 0.992397i | \(-0.460724\pi\) | ||||
0.123076 | + | 0.992397i | \(0.460724\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.893131 | −0.131685 | ||||||||
\(47\) | −0.502098 | −0.0732386 | −0.0366193 | − | 0.999329i | \(-0.511659\pi\) | ||||
−0.0366193 | + | 0.999329i | \(0.511659\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −7.98589 | −1.12938 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.52179 | −1.18176 | ||||||||
\(53\) | 9.94273 | 1.36574 | 0.682869 | − | 0.730540i | \(-0.260732\pi\) | ||||
0.682869 | + | 0.730540i | \(0.260732\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.492737 | 0.0658448 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −18.5931 | −2.44139 | ||||||||
\(59\) | −13.4513 | −1.75121 | −0.875603 | − | 0.483032i | \(-0.839535\pi\) | ||||
−0.875603 | + | 0.483032i | \(0.839535\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.93756 | −0.760227 | −0.380114 | − | 0.924940i | \(-0.624115\pi\) | ||||
−0.380114 | + | 0.924940i | \(0.624115\pi\) | |||||||
\(62\) | −1.01453 | −0.128845 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.78626 | −1.22328 | ||||||||
\(65\) | −4.02991 | −0.499849 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.4068 | −1.76007 | −0.880037 | − | 0.474905i | \(-0.842483\pi\) | ||||
−0.880037 | + | 0.474905i | \(0.842483\pi\) | |||||||
\(68\) | −5.74658 | −0.696875 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.18035 | 0.260602 | ||||||||
\(71\) | 12.4990 | 1.48336 | 0.741681 | − | 0.670752i | \(-0.234029\pi\) | ||||
0.741681 | + | 0.670752i | \(0.234029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.27383 | 0.500214 | 0.250107 | − | 0.968218i | \(-0.419534\pi\) | ||||
0.250107 | + | 0.968218i | \(0.419534\pi\) | |||||||
\(74\) | −1.59613 | −0.185546 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.403870 | 0.0463271 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.37176 | −0.154335 | −0.0771674 | − | 0.997018i | \(-0.524588\pi\) | ||||
−0.0771674 | + | 0.997018i | \(0.524588\pi\) | |||||||
\(80\) | −3.66834 | −0.410133 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.36787 | −0.703213 | ||||||||
\(83\) | −7.47346 | −0.820319 | −0.410160 | − | 0.912014i | \(-0.634527\pi\) | ||||
−0.410160 | + | 0.912014i | \(0.634527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.71753 | −0.294757 | ||||||||
\(86\) | 3.32343 | 0.358375 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.1341 | 1.71021 | 0.855107 | − | 0.518451i | \(-0.173491\pi\) | ||||
0.855107 | + | 0.518451i | \(0.173491\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.80554 | −0.398929 | ||||||||
\(92\) | −0.971364 | −0.101272 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.03380 | −0.106628 | ||||||||
\(95\) | 0.190988 | 0.0195949 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.6158 | 1.48401 | 0.742006 | − | 0.670393i | \(-0.233875\pi\) | ||||
0.742006 | + | 0.670393i | \(0.233875\pi\) | |||||||
\(98\) | 2.05896 | 0.207986 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.68541 | −0.868541 | ||||||||
\(101\) | −6.10856 | −0.607824 | −0.303912 | − | 0.952700i | \(-0.598293\pi\) | ||||
−0.303912 | + | 0.952700i | \(0.598293\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.56275 | −0.942245 | −0.471123 | − | 0.882068i | \(-0.656151\pi\) | ||||
−0.471123 | + | 0.882068i | \(0.656151\pi\) | |||||||
\(104\) | −1.87513 | −0.183872 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 20.4717 | 1.98838 | ||||||||
\(107\) | −4.59486 | −0.444202 | −0.222101 | − | 0.975024i | \(-0.571291\pi\) | ||||
−0.222101 | + | 0.975024i | \(0.571291\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.99009 | 0.190616 | 0.0953079 | − | 0.995448i | \(-0.469616\pi\) | ||||
0.0953079 | + | 0.995448i | \(0.469616\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.46410 | −0.327327 | ||||||||
\(113\) | −8.61527 | −0.810456 | −0.405228 | − | 0.914216i | \(-0.632808\pi\) | ||||
−0.405228 | + | 0.914216i | \(0.632808\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.459353 | −0.0428349 | ||||||||
\(116\) | −20.2217 | −1.87754 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −27.6956 | −2.54959 | ||||||||
\(119\) | −2.56622 | −0.235245 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −12.2252 | −1.10682 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.10339 | −0.0990876 | ||||||||
\(125\) | −9.40208 | −0.840948 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.1294 | −1.69746 | −0.848729 | − | 0.528828i | \(-0.822632\pi\) | ||||
−0.848729 | + | 0.528828i | \(0.822632\pi\) | |||||||
\(128\) | −3.91368 | −0.345923 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.29742 | −0.727732 | ||||||||
\(131\) | 6.91998 | 0.604601 | 0.302301 | − | 0.953213i | \(-0.402245\pi\) | ||||
0.302301 | + | 0.953213i | \(0.402245\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.180354 | 0.0156387 | ||||||||
\(134\) | −29.6631 | −2.56250 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.26447 | −0.108428 | ||||||||
\(137\) | −6.81197 | −0.581986 | −0.290993 | − | 0.956725i | \(-0.593986\pi\) | ||||
−0.290993 | + | 0.956725i | \(0.593986\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.6013 | 1.66256 | 0.831280 | − | 0.555854i | \(-0.187609\pi\) | ||||
0.831280 | + | 0.555854i | \(0.187609\pi\) | |||||||
\(140\) | 2.37134 | 0.200415 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 25.7350 | 2.15963 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.56275 | −0.794143 | ||||||||
\(146\) | 8.79965 | 0.728264 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.73594 | −0.142694 | ||||||||
\(149\) | 8.18721 | 0.670722 | 0.335361 | − | 0.942090i | \(-0.391142\pi\) | ||||
0.335361 | + | 0.942090i | \(0.391142\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.1576 | 1.39627 | 0.698133 | − | 0.715968i | \(-0.254014\pi\) | ||||
0.698133 | + | 0.715968i | \(0.254014\pi\) | |||||||
\(152\) | 0.0888673 | 0.00720809 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.521789 | −0.0419111 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.02864 | 0.401329 | 0.200664 | − | 0.979660i | \(-0.435690\pi\) | ||||
0.200664 | + | 0.979660i | \(0.435690\pi\) | |||||||
\(158\) | −2.82439 | −0.224697 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.59655 | −0.679617 | ||||||||
\(161\) | −0.433778 | −0.0341865 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.2469 | 1.19423 | 0.597114 | − | 0.802156i | \(-0.296314\pi\) | ||||
0.597114 | + | 0.802156i | \(0.296314\pi\) | |||||||
\(164\) | −6.92566 | −0.540803 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.3876 | −1.19431 | ||||||||
\(167\) | 4.43072 | 0.342859 | 0.171430 | − | 0.985196i | \(-0.445161\pi\) | ||||
0.171430 | + | 0.985196i | \(0.445161\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.48210 | 0.114008 | ||||||||
\(170\) | −5.59527 | −0.429138 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.61455 | 0.275607 | ||||||||
\(173\) | −10.7124 | −0.814446 | −0.407223 | − | 0.913329i | \(-0.633503\pi\) | ||||
−0.407223 | + | 0.913329i | \(0.633503\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.87861 | −0.293195 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 33.2195 | 2.48991 | ||||||||
\(179\) | −11.4546 | −0.856157 | −0.428079 | − | 0.903741i | \(-0.640809\pi\) | ||||
−0.428079 | + | 0.903741i | \(0.640809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.5252 | 1.22831 | 0.614153 | − | 0.789187i | \(-0.289498\pi\) | ||||
0.614153 | + | 0.789187i | \(0.289498\pi\) | |||||||
\(182\) | −7.83544 | −0.580802 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.213738 | −0.0157570 | ||||||||
\(185\) | −0.820918 | −0.0603551 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.12436 | −0.0820021 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.393236 | 0.0285284 | ||||||||
\(191\) | 2.19794 | 0.159037 | 0.0795187 | − | 0.996833i | \(-0.474662\pi\) | ||||
0.0795187 | + | 0.996833i | \(0.474662\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −25.1481 | −1.81020 | −0.905100 | − | 0.425198i | \(-0.860204\pi\) | ||||
−0.905100 | + | 0.425198i | \(0.860204\pi\) | |||||||
\(194\) | 30.0934 | 2.16058 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.23931 | 0.159951 | ||||||||
\(197\) | 6.13203 | 0.436889 | 0.218444 | − | 0.975849i | \(-0.429902\pi\) | ||||
0.218444 | + | 0.975849i | \(0.429902\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.4956 | 1.45289 | 0.726446 | − | 0.687224i | \(-0.241171\pi\) | ||||
0.726446 | + | 0.687224i | \(0.241171\pi\) | |||||||
\(200\) | −1.91113 | −0.135137 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.5773 | −0.884934 | ||||||||
\(203\) | −9.03032 | −0.633804 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.27511 | −0.228743 | ||||||||
\(206\) | −19.6893 | −1.37182 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.1828 | 0.914060 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.82942 | 0.607843 | 0.303921 | − | 0.952697i | \(-0.401704\pi\) | ||||
0.303921 | + | 0.952697i | \(0.401704\pi\) | |||||||
\(212\) | 22.2649 | 1.52916 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.46063 | −0.646715 | ||||||||
\(215\) | 1.70930 | 0.116573 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.492737 | −0.0334492 | ||||||||
\(218\) | 4.09751 | 0.277518 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.76585 | 0.656922 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.6012 | −1.37956 | −0.689778 | − | 0.724021i | \(-0.742292\pi\) | ||||
−0.689778 | + | 0.724021i | \(0.742292\pi\) | |||||||
\(224\) | −8.11792 | −0.542401 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.7385 | −1.17995 | ||||||||
\(227\) | −17.4349 | −1.15720 | −0.578598 | − | 0.815613i | \(-0.696400\pi\) | ||||
−0.578598 | + | 0.815613i | \(0.696400\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.4477 | 1.54946 | 0.774732 | − | 0.632289i | \(-0.217885\pi\) | ||||
0.774732 | + | 0.632289i | \(0.217885\pi\) | |||||||
\(230\) | −0.945789 | −0.0623635 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.44958 | −0.292129 | ||||||||
\(233\) | 14.8692 | 0.974117 | 0.487058 | − | 0.873369i | \(-0.338070\pi\) | ||||
0.487058 | + | 0.873369i | \(0.338070\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.531702 | −0.0346844 | ||||||||
\(236\) | −30.1216 | −1.96075 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.28375 | −0.342494 | ||||||||
\(239\) | −22.5721 | −1.46007 | −0.730034 | − | 0.683411i | \(-0.760496\pi\) | ||||
−0.730034 | + | 0.683411i | \(0.760496\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.20245 | 0.141872 | 0.0709362 | − | 0.997481i | \(-0.477401\pi\) | ||||
0.0709362 | + | 0.997481i | \(0.477401\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.2961 | −0.851194 | ||||||||
\(245\) | 1.05896 | 0.0676544 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.686345 | −0.0436711 | ||||||||
\(248\) | −0.242790 | −0.0154172 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −19.3585 | −1.22434 | ||||||||
\(251\) | −7.39733 | −0.466916 | −0.233458 | − | 0.972367i | \(-0.575004\pi\) | ||||
−0.233458 | + | 0.972367i | \(0.575004\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −39.3866 | −2.47134 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.5144 | 0.719651 | ||||||||
\(257\) | −6.29786 | −0.392850 | −0.196425 | − | 0.980519i | \(-0.562933\pi\) | ||||
−0.196425 | + | 0.980519i | \(0.562933\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.775212 | −0.0481693 | ||||||||
\(260\) | −9.02423 | −0.559659 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.2480 | 0.880242 | ||||||||
\(263\) | −32.2131 | −1.98634 | −0.993172 | − | 0.116659i | \(-0.962782\pi\) | ||||
−0.993172 | + | 0.116659i | \(0.962782\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.5289 | 0.646788 | ||||||||
\(266\) | 0.371342 | 0.0227685 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −32.2614 | −1.97068 | ||||||||
\(269\) | −27.6136 | −1.68363 | −0.841816 | − | 0.539765i | \(-0.818513\pi\) | ||||
−0.841816 | + | 0.539765i | \(0.818513\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.9678 | −1.88116 | −0.940580 | − | 0.339573i | \(-0.889717\pi\) | ||||
−0.940580 | + | 0.339573i | \(0.889717\pi\) | |||||||
\(272\) | 8.88965 | 0.539014 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.0256 | −0.847316 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.420940 | 0.0252919 | 0.0126459 | − | 0.999920i | \(-0.495975\pi\) | ||||
0.0126459 | + | 0.999920i | \(0.495975\pi\) | |||||||
\(278\) | 40.3583 | 2.42053 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.521789 | 0.0311828 | ||||||||
\(281\) | −19.8996 | −1.18711 | −0.593554 | − | 0.804794i | \(-0.702276\pi\) | ||||
−0.593554 | + | 0.804794i | \(0.702276\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.3641 | 1.44829 | 0.724147 | − | 0.689645i | \(-0.242234\pi\) | ||||
0.724147 | + | 0.689645i | \(0.242234\pi\) | |||||||
\(284\) | 27.9893 | 1.66086 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.09276 | −0.182560 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.4145 | −0.612618 | ||||||||
\(290\) | −19.6893 | −1.15620 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.57046 | 0.560069 | ||||||||
\(293\) | 17.4662 | 1.02039 | 0.510193 | − | 0.860060i | \(-0.329574\pi\) | ||||
0.510193 | + | 0.860060i | \(0.329574\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.2443 | −0.829338 | ||||||||
\(296\) | −0.381976 | −0.0222019 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.8571 | 0.976507 | ||||||||
\(299\) | 1.65076 | 0.0954657 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.61413 | 0.0930370 | ||||||||
\(302\) | 35.3268 | 2.03283 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.624766 | −0.0358328 | ||||||||
\(305\) | −6.28764 | −0.360029 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.9239 | 0.623458 | 0.311729 | − | 0.950171i | \(-0.399092\pi\) | ||||
0.311729 | + | 0.950171i | \(0.399092\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.07434 | −0.0610185 | ||||||||
\(311\) | −3.51662 | −0.199409 | −0.0997047 | − | 0.995017i | \(-0.531790\pi\) | ||||
−0.0997047 | + | 0.995017i | \(0.531790\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.9789 | 1.46842 | 0.734208 | − | 0.678924i | \(-0.237554\pi\) | ||||
0.734208 | + | 0.678924i | \(0.237554\pi\) | |||||||
\(314\) | 10.3538 | 0.584296 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.07180 | −0.172802 | ||||||||
\(317\) | 3.72269 | 0.209087 | 0.104544 | − | 0.994520i | \(-0.466662\pi\) | ||||
0.104544 | + | 0.994520i | \(0.466662\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −10.3633 | −0.579323 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.893131 | −0.0497722 | ||||||||
\(323\) | −0.462829 | −0.0257525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.7602 | 0.818747 | ||||||||
\(326\) | 31.3927 | 1.73868 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.52392 | −0.0841443 | ||||||||
\(329\) | −0.502098 | −0.0276816 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.7683 | 0.976632 | 0.488316 | − | 0.872667i | \(-0.337611\pi\) | ||||
0.488316 | + | 0.872667i | \(0.337611\pi\) | |||||||
\(332\) | −16.7354 | −0.918476 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.12267 | 0.499170 | ||||||||
\(335\) | −15.2562 | −0.833538 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.1178 | 1.42273 | 0.711364 | − | 0.702824i | \(-0.248078\pi\) | ||||
0.711364 | + | 0.702824i | \(0.248078\pi\) | |||||||
\(338\) | 3.05159 | 0.165985 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.08539 | −0.330027 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.795343 | 0.0428820 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.0563 | −1.18575 | ||||||||
\(347\) | −0.794486 | −0.0426503 | −0.0213251 | − | 0.999773i | \(-0.506789\pi\) | ||||
−0.0213251 | + | 0.999773i | \(0.506789\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.7816 | 0.630657 | 0.315329 | − | 0.948983i | \(-0.397885\pi\) | ||||
0.315329 | + | 0.948983i | \(0.397885\pi\) | |||||||
\(350\) | −7.98589 | −0.426864 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.45041 | −0.343321 | −0.171660 | − | 0.985156i | \(-0.554913\pi\) | ||||
−0.171660 | + | 0.985156i | \(0.554913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.2360 | 0.702493 | ||||||||
\(356\) | 36.1294 | 1.91485 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23.5846 | −1.24648 | ||||||||
\(359\) | −5.87916 | −0.310290 | −0.155145 | − | 0.987892i | \(-0.549584\pi\) | ||||
−0.155145 | + | 0.987892i | \(0.549584\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9675 | −0.998288 | ||||||||
\(362\) | 34.0246 | 1.78830 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.52179 | −0.446663 | ||||||||
\(365\) | 4.52582 | 0.236892 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.3478 | −1.53194 | −0.765971 | − | 0.642876i | \(-0.777741\pi\) | ||||
−0.765971 | + | 0.642876i | \(0.777741\pi\) | |||||||
\(368\) | 1.50265 | 0.0783311 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.69024 | −0.0878712 | ||||||||
\(371\) | 9.94273 | 0.516201 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.83207 | −0.457307 | −0.228654 | − | 0.973508i | \(-0.573432\pi\) | ||||
−0.228654 | + | 0.973508i | \(0.573432\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.247402 | −0.0127588 | ||||||||
\(377\) | 34.3652 | 1.76990 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.7171 | −0.601867 | −0.300934 | − | 0.953645i | \(-0.597298\pi\) | ||||
−0.300934 | + | 0.953645i | \(0.597298\pi\) | |||||||
\(380\) | 0.427682 | 0.0219396 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.52547 | 0.231543 | ||||||||
\(383\) | −30.6516 | −1.56622 | −0.783112 | − | 0.621881i | \(-0.786369\pi\) | ||||
−0.783112 | + | 0.621881i | \(0.786369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −51.7789 | −2.63548 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 32.7294 | 1.66158 | ||||||||
\(389\) | 3.61107 | 0.183089 | 0.0915443 | − | 0.995801i | \(-0.470820\pi\) | ||||
0.0915443 | + | 0.995801i | \(0.470820\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.11317 | 0.0562954 | ||||||||
\(392\) | 0.492737 | 0.0248870 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.6256 | 0.636068 | ||||||||
\(395\) | −1.45264 | −0.0730901 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.10339 | 0.155755 | 0.0778774 | − | 0.996963i | \(-0.475186\pi\) | ||||
0.0778774 | + | 0.996963i | \(0.475186\pi\) | |||||||
\(398\) | 42.1995 | 2.11527 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.4359 | 0.671794 | ||||||||
\(401\) | −29.8141 | −1.48884 | −0.744422 | − | 0.667709i | \(-0.767275\pi\) | ||||
−0.744422 | + | 0.667709i | \(0.767275\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.87513 | 0.0934068 | ||||||||
\(404\) | −13.6790 | −0.680555 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.5931 | −0.922759 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.0348 | 0.941212 | 0.470606 | − | 0.882343i | \(-0.344035\pi\) | ||||
0.470606 | + | 0.882343i | \(0.344035\pi\) | |||||||
\(410\) | −6.74331 | −0.333028 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.4140 | −1.05499 | ||||||||
\(413\) | −13.4513 | −0.661893 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.91409 | −0.388488 | ||||||||
\(416\) | 30.8930 | 1.51466 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.05476 | −0.295795 | −0.147897 | − | 0.989003i | \(-0.547250\pi\) | ||||
−0.147897 | + | 0.989003i | \(0.547250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.2007 | 1.42315 | 0.711577 | − | 0.702608i | \(-0.247981\pi\) | ||||
0.711577 | + | 0.702608i | \(0.247981\pi\) | |||||||
\(422\) | 18.1794 | 0.884960 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.89915 | 0.237924 | ||||||||
\(425\) | 9.95336 | 0.482809 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.93756 | −0.287339 | ||||||||
\(428\) | −10.2893 | −0.497353 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.51938 | 0.169720 | ||||||||
\(431\) | −15.3401 | −0.738905 | −0.369452 | − | 0.929250i | \(-0.620455\pi\) | ||||
−0.369452 | + | 0.929250i | \(0.620455\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.47808 | 0.215203 | 0.107601 | − | 0.994194i | \(-0.465683\pi\) | ||||
0.107601 | + | 0.994194i | \(0.465683\pi\) | |||||||
\(434\) | −1.01453 | −0.0486988 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.45643 | 0.213424 | ||||||||
\(437\) | −0.0782337 | −0.00374242 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.4717 | 1.26342 | 0.631712 | − | 0.775203i | \(-0.282353\pi\) | ||||
0.631712 | + | 0.775203i | \(0.282353\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.1075 | 0.956416 | ||||||||
\(443\) | 3.86545 | 0.183653 | 0.0918266 | − | 0.995775i | \(-0.470729\pi\) | ||||
0.0918266 | + | 0.995775i | \(0.470729\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.0854 | 0.809925 | ||||||||
\(446\) | −42.4169 | −2.00850 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.78626 | −0.462357 | ||||||||
\(449\) | 7.26530 | 0.342871 | 0.171435 | − | 0.985195i | \(-0.445159\pi\) | ||||
0.171435 | + | 0.985195i | \(0.445159\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −19.2923 | −0.907433 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −35.8978 | −1.68477 | ||||||||
\(455\) | −4.02991 | −0.188925 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.7449 | −1.20430 | −0.602148 | − | 0.798384i | \(-0.705688\pi\) | ||||
−0.602148 | + | 0.798384i | \(0.705688\pi\) | |||||||
\(458\) | 48.2778 | 2.25587 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.02864 | −0.0479604 | ||||||||
\(461\) | −22.9619 | −1.06944 | −0.534721 | − | 0.845029i | \(-0.679583\pi\) | ||||
−0.534721 | + | 0.845029i | \(0.679583\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.68972 | 0.217950 | 0.108975 | − | 0.994044i | \(-0.465243\pi\) | ||||
0.108975 | + | 0.994044i | \(0.465243\pi\) | |||||||
\(464\) | 31.2820 | 1.45223 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 30.6152 | 1.41822 | ||||||||
\(467\) | 32.8849 | 1.52173 | 0.760867 | − | 0.648908i | \(-0.224774\pi\) | ||||
0.760867 | + | 0.648908i | \(0.224774\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.4068 | −0.665246 | ||||||||
\(470\) | −1.09475 | −0.0504972 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.62794 | −0.305076 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.699523 | −0.0320963 | ||||||||
\(476\) | −5.74658 | −0.263394 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −46.4751 | −2.12572 | ||||||||
\(479\) | −10.3796 | −0.474255 | −0.237127 | − | 0.971479i | \(-0.576206\pi\) | ||||
−0.237127 | + | 0.971479i | \(0.576206\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.95010 | 0.134513 | ||||||||
\(482\) | 4.53476 | 0.206553 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.4776 | 0.702800 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.4384 | 1.28867 | 0.644334 | − | 0.764744i | \(-0.277135\pi\) | ||||
0.644334 | + | 0.764744i | \(0.277135\pi\) | |||||||
\(488\) | −2.92566 | −0.132438 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.18035 | 0.0984984 | ||||||||
\(491\) | −30.9474 | −1.39664 | −0.698318 | − | 0.715788i | \(-0.746068\pi\) | ||||
−0.698318 | + | 0.715788i | \(0.746068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.1738 | 1.04370 | ||||||||
\(494\) | −1.41316 | −0.0635809 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.70689 | 0.0766417 | ||||||||
\(497\) | 12.4990 | 0.560658 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.2751 | −1.53436 | −0.767182 | − | 0.641429i | \(-0.778342\pi\) | ||||
−0.767182 | + | 0.641429i | \(0.778342\pi\) | |||||||
\(500\) | −21.0542 | −0.941573 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15.2308 | −0.679784 | ||||||||
\(503\) | −13.0742 | −0.582950 | −0.291475 | − | 0.956578i | \(-0.594146\pi\) | ||||
−0.291475 | + | 0.956578i | \(0.594146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.46871 | −0.287854 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −42.8367 | −1.90057 | ||||||||
\(509\) | 32.5765 | 1.44393 | 0.721963 | − | 0.691932i | \(-0.243240\pi\) | ||||
0.721963 | + | 0.691932i | \(0.243240\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.27383 | 0.189063 | ||||||||
\(512\) | 31.5351 | 1.39367 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.9670 | −0.571951 | ||||||||
\(515\) | −10.1266 | −0.446230 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.59613 | −0.0701299 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.98569 | −0.0870781 | ||||||||
\(521\) | −11.0109 | −0.482397 | −0.241198 | − | 0.970476i | \(-0.577540\pi\) | ||||
−0.241198 | + | 0.970476i | \(0.577540\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.20204 | 0.402377 | 0.201189 | − | 0.979553i | \(-0.435520\pi\) | ||||
0.201189 | + | 0.979553i | \(0.435520\pi\) | |||||||
\(524\) | 15.4960 | 0.676946 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −66.3254 | −2.89193 | ||||||||
\(527\) | 1.26447 | 0.0550813 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8118 | −0.991819 | ||||||||
\(530\) | 21.6787 | 0.941661 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.403870 | 0.0175100 | ||||||||
\(533\) | 11.7696 | 0.509798 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.86577 | −0.210365 | ||||||||
\(536\) | −7.09878 | −0.306621 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −56.8553 | −2.45121 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.28585 | 0.399230 | 0.199615 | − | 0.979874i | \(-0.436031\pi\) | ||||
0.199615 | + | 0.979874i | \(0.436031\pi\) | |||||||
\(542\) | −63.7614 | −2.73879 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.8324 | 0.893181 | ||||||||
\(545\) | 2.10742 | 0.0902720 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.40335 | 0.231031 | 0.115515 | − | 0.993306i | \(-0.463148\pi\) | ||||
0.115515 | + | 0.993306i | \(0.463148\pi\) | |||||||
\(548\) | −15.2541 | −0.651625 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.62866 | −0.0693832 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.37176 | −0.0583331 | ||||||||
\(554\) | 0.866699 | 0.0368225 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 43.8934 | 1.86150 | ||||||||
\(557\) | −23.3870 | −0.990939 | −0.495470 | − | 0.868625i | \(-0.665004\pi\) | ||||
−0.495470 | + | 0.868625i | \(0.665004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.14264 | −0.259806 | ||||||||
\(560\) | −3.66834 | −0.155016 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −40.9724 | −1.72832 | ||||||||
\(563\) | 24.5311 | 1.03386 | 0.516930 | − | 0.856028i | \(-0.327075\pi\) | ||||
0.516930 | + | 0.856028i | \(0.327075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.12322 | −0.383817 | ||||||||
\(566\) | 50.1647 | 2.10858 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.15874 | 0.258415 | ||||||||
\(569\) | 39.4165 | 1.65243 | 0.826213 | − | 0.563358i | \(-0.190491\pi\) | ||||
0.826213 | + | 0.563358i | \(0.190491\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −41.0006 | −1.71582 | −0.857911 | − | 0.513798i | \(-0.828238\pi\) | ||||
−0.857911 | + | 0.513798i | \(0.828238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.36787 | −0.265790 | ||||||||
\(575\) | 1.68245 | 0.0701631 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.1963 | −1.83992 | −0.919959 | − | 0.392015i | \(-0.871778\pi\) | ||||
−0.919959 | + | 0.392015i | \(0.871778\pi\) | |||||||
\(578\) | −21.4430 | −0.891913 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.4140 | −0.889167 | ||||||||
\(581\) | −7.47346 | −0.310051 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.10588 | 0.0871418 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 35.9622 | 1.48559 | ||||||||
\(587\) | 2.75552 | 0.113733 | 0.0568663 | − | 0.998382i | \(-0.481889\pi\) | ||||
0.0568663 | + | 0.998382i | \(0.481889\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0888673 | −0.00366171 | ||||||||
\(590\) | −29.3285 | −1.20744 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.68541 | 0.110370 | ||||||||
\(593\) | 30.8619 | 1.26735 | 0.633673 | − | 0.773601i | \(-0.281547\pi\) | ||||
0.633673 | + | 0.773601i | \(0.281547\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.71753 | −0.111408 | ||||||||
\(596\) | 18.3337 | 0.750979 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.39884 | 0.138989 | ||||||||
\(599\) | 13.3297 | 0.544638 | 0.272319 | − | 0.962207i | \(-0.412209\pi\) | ||||
0.272319 | + | 0.962207i | \(0.412209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.4395 | −0.670582 | −0.335291 | − | 0.942115i | \(-0.608835\pi\) | ||||
−0.335291 | + | 0.942115i | \(0.608835\pi\) | |||||||
\(602\) | 3.32343 | 0.135453 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 38.4213 | 1.56334 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.2669 | −0.984962 | −0.492481 | − | 0.870323i | \(-0.663910\pi\) | ||||
−0.492481 | + | 0.870323i | \(0.663910\pi\) | |||||||
\(608\) | −1.46410 | −0.0593772 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.9460 | −0.524168 | ||||||||
\(611\) | 1.91075 | 0.0773008 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.5773 | −0.992668 | −0.496334 | − | 0.868132i | \(-0.665321\pi\) | ||||
−0.496334 | + | 0.868132i | \(0.665321\pi\) | |||||||
\(614\) | 22.4918 | 0.907695 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.4094 | 0.620358 | 0.310179 | − | 0.950678i | \(-0.399611\pi\) | ||||
0.310179 | + | 0.950678i | \(0.399611\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.6568 | 1.43317 | 0.716583 | − | 0.697501i | \(-0.245705\pi\) | ||||
0.716583 | + | 0.697501i | \(0.245705\pi\) | |||||||
\(620\) | −1.16845 | −0.0469260 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.24059 | −0.290321 | ||||||||
\(623\) | 16.1341 | 0.646400 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.43660 | 0.377464 | ||||||||
\(626\) | 53.4896 | 2.13787 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.2607 | 0.449351 | ||||||||
\(629\) | 1.98937 | 0.0793212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.6305 | 0.463003 | 0.231502 | − | 0.972834i | \(-0.425636\pi\) | ||||
0.231502 | + | 0.972834i | \(0.425636\pi\) | |||||||
\(632\) | −0.675916 | −0.0268865 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.66487 | 0.304411 | ||||||||
\(635\) | −20.2572 | −0.803884 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.80554 | −0.150781 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.14443 | −0.163823 | ||||||||
\(641\) | −36.8237 | −1.45445 | −0.727225 | − | 0.686399i | \(-0.759190\pi\) | ||||
−0.727225 | + | 0.686399i | \(0.759190\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.4049 | 1.90890 | 0.954452 | − | 0.298366i | \(-0.0964415\pi\) | ||||
0.954452 | + | 0.298366i | \(0.0964415\pi\) | |||||||
\(644\) | −0.971364 | −0.0382771 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.952947 | −0.0374932 | ||||||||
\(647\) | 26.2987 | 1.03391 | 0.516954 | − | 0.856013i | \(-0.327066\pi\) | ||||
0.516954 | + | 0.856013i | \(0.327066\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 30.3906 | 1.19202 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 34.1426 | 1.33713 | ||||||||
\(653\) | 23.9772 | 0.938302 | 0.469151 | − | 0.883118i | \(-0.344560\pi\) | ||||
0.469151 | + | 0.883118i | \(0.344560\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.32798 | 0.286328 | ||||||||
\(656\) | 10.7136 | 0.418297 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.03380 | −0.0403017 | ||||||||
\(659\) | −5.02206 | −0.195632 | −0.0978159 | − | 0.995205i | \(-0.531186\pi\) | ||||
−0.0978159 | + | 0.995205i | \(0.531186\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.2645 | −0.515928 | −0.257964 | − | 0.966155i | \(-0.583052\pi\) | ||||
−0.257964 | + | 0.966155i | \(0.583052\pi\) | |||||||
\(662\) | 36.5841 | 1.42188 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.68245 | −0.142907 | ||||||||
\(665\) | 0.190988 | 0.00740619 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.91715 | 0.151673 | ||||||||
\(668\) | 9.92177 | 0.383885 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −31.4120 | −1.21355 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.2097 | −1.39578 | −0.697892 | − | 0.716203i | \(-0.745878\pi\) | ||||
−0.697892 | + | 0.716203i | \(0.745878\pi\) | |||||||
\(674\) | 53.7755 | 2.07136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.31889 | 0.127650 | ||||||||
\(677\) | 8.90851 | 0.342382 | 0.171191 | − | 0.985238i | \(-0.445238\pi\) | ||||
0.171191 | + | 0.985238i | \(0.445238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.6158 | 0.560904 | ||||||||
\(680\) | −1.33903 | −0.0513493 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.2377 | 0.889166 | 0.444583 | − | 0.895738i | \(-0.353352\pi\) | ||||
0.444583 | + | 0.895738i | \(0.353352\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.21360 | −0.275618 | ||||||||
\(686\) | 2.05896 | 0.0786114 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.59152 | −0.213175 | ||||||||
\(689\) | −37.8374 | −1.44149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.2034 | 1.11095 | 0.555475 | − | 0.831533i | \(-0.312536\pi\) | ||||
0.555475 | + | 0.831533i | \(0.312536\pi\) | |||||||
\(692\) | −23.9883 | −0.911900 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.63582 | −0.0620947 | ||||||||
\(695\) | 20.7570 | 0.787357 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.93671 | 0.300624 | ||||||||
\(698\) | 24.2579 | 0.918176 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.68541 | −0.328278 | ||||||||
\(701\) | −45.7062 | −1.72630 | −0.863150 | − | 0.504947i | \(-0.831512\pi\) | ||||
−0.863150 | + | 0.504947i | \(0.831512\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.139813 | −0.00527314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.2811 | −0.499842 | ||||||||
\(707\) | −6.10856 | −0.229736 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.12487 | −0.192469 | −0.0962343 | − | 0.995359i | \(-0.530680\pi\) | ||||
−0.0962343 | + | 0.995359i | \(0.530680\pi\) | |||||||
\(710\) | 27.2523 | 1.02276 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.94989 | 0.297935 | ||||||||
\(713\) | 0.213738 | 0.00800457 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.6505 | −0.958602 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.1049 | −0.451753 | ||||||||
\(719\) | −2.68899 | −0.100282 | −0.0501412 | − | 0.998742i | \(-0.515967\pi\) | ||||
−0.0501412 | + | 0.998742i | \(0.515967\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.56275 | −0.356135 | ||||||||
\(722\) | −39.0533 | −1.45341 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 37.0050 | 1.37528 | ||||||||
\(725\) | 35.0251 | 1.30080 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.17656 | 0.0436363 | 0.0218181 | − | 0.999762i | \(-0.493055\pi\) | ||||
0.0218181 | + | 0.999762i | \(0.493055\pi\) | |||||||
\(728\) | −1.87513 | −0.0694969 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 9.31847 | 0.344892 | ||||||||
\(731\) | −4.14222 | −0.153206 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.2128 | −0.598833 | −0.299416 | − | 0.954123i | \(-0.596792\pi\) | ||||
−0.299416 | + | 0.954123i | \(0.596792\pi\) | |||||||
\(734\) | −60.4259 | −2.23036 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.52137 | 0.129800 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.2564 | 1.37050 | 0.685249 | − | 0.728309i | \(-0.259693\pi\) | ||||
0.685249 | + | 0.728309i | \(0.259693\pi\) | |||||||
\(740\) | −1.83829 | −0.0675770 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.4717 | 0.751539 | ||||||||
\(743\) | −31.9013 | −1.17034 | −0.585172 | − | 0.810909i | \(-0.698973\pi\) | ||||
−0.585172 | + | 0.810909i | \(0.698973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.66992 | 0.317641 | ||||||||
\(746\) | −18.1849 | −0.665795 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.59486 | −0.167892 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.2186 | 0.810767 | 0.405384 | − | 0.914147i | \(-0.367138\pi\) | ||||
0.405384 | + | 0.914147i | \(0.367138\pi\) | |||||||
\(752\) | 1.73932 | 0.0634265 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 70.7566 | 2.57680 | ||||||||
\(755\) | 18.1692 | 0.661245 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.8014 | −1.41026 | −0.705131 | − | 0.709077i | \(-0.749112\pi\) | ||||
−0.705131 | + | 0.709077i | \(0.749112\pi\) | |||||||
\(758\) | −24.1251 | −0.876261 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.0941068 | 0.00341361 | ||||||||
\(761\) | −49.4020 | −1.79082 | −0.895410 | − | 0.445242i | \(-0.853118\pi\) | ||||
−0.895410 | + | 0.445242i | \(0.853118\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.99009 | 0.0720460 | ||||||||
\(764\) | 4.92188 | 0.178067 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −63.1104 | −2.28027 | ||||||||
\(767\) | 51.1893 | 1.84834 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.2939 | −0.587575 | −0.293787 | − | 0.955871i | \(-0.594916\pi\) | ||||
−0.293787 | + | 0.955871i | \(0.594916\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −56.3145 | −2.02680 | ||||||||
\(773\) | 47.5351 | 1.70972 | 0.854860 | − | 0.518858i | \(-0.173643\pi\) | ||||
0.854860 | + | 0.518858i | \(0.173643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.91113 | 0.0686499 | ||||||||
\(776\) | 7.20176 | 0.258528 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.43505 | 0.266559 | ||||||||
\(779\) | −0.557792 | −0.0199850 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 2.29197 | 0.0819608 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.46410 | −0.123718 | ||||||||
\(785\) | 5.32512 | 0.190062 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.8753 | 1.67093 | 0.835463 | − | 0.549547i | \(-0.185200\pi\) | ||||
0.835463 | + | 0.549547i | \(0.185200\pi\) | |||||||
\(788\) | 13.7315 | 0.489166 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.99092 | −0.106412 | ||||||||
\(791\) | −8.61527 | −0.306324 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.5956 | 0.802394 | ||||||||
\(794\) | 6.38976 | 0.226764 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.8960 | 1.62674 | ||||||||
\(797\) | 22.5463 | 0.798631 | 0.399315 | − | 0.916814i | \(-0.369248\pi\) | ||||
0.399315 | + | 0.916814i | \(0.369248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.28850 | 0.0455837 | ||||||||
\(800\) | 31.4862 | 1.11321 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −61.3860 | −2.16761 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.459353 | −0.0161901 | ||||||||
\(806\) | 3.86081 | 0.135991 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.00991 | −0.105888 | ||||||||
\(809\) | −12.8111 | −0.450416 | −0.225208 | − | 0.974311i | \(-0.572306\pi\) | ||||
−0.225208 | + | 0.974311i | \(0.572306\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.65327 | 0.163398 | 0.0816991 | − | 0.996657i | \(-0.473965\pi\) | ||||
0.0816991 | + | 0.996657i | \(0.473965\pi\) | |||||||
\(812\) | −20.2217 | −0.709644 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.1458 | 0.565564 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.291116 | 0.0101848 | ||||||||
\(818\) | 39.1920 | 1.37031 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.33399 | −0.256114 | ||||||||
\(821\) | −45.9133 | −1.60238 | −0.801192 | − | 0.598407i | \(-0.795801\pi\) | ||||
−0.801192 | + | 0.598407i | \(0.795801\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.0742 | 1.36204 | 0.681021 | − | 0.732264i | \(-0.261536\pi\) | ||||
0.681021 | + | 0.732264i | \(0.261536\pi\) | |||||||
\(824\) | −4.71192 | −0.164148 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.6956 | −0.963653 | ||||||||
\(827\) | −43.9735 | −1.52911 | −0.764554 | − | 0.644560i | \(-0.777041\pi\) | ||||
−0.764554 | + | 0.644560i | \(0.777041\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.9035 | 0.587082 | 0.293541 | − | 0.955946i | \(-0.405166\pi\) | ||||
0.293541 | + | 0.955946i | \(0.405166\pi\) | |||||||
\(830\) | −16.2948 | −0.565601 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 37.2420 | 1.29113 | ||||||||
\(833\) | −2.56622 | −0.0889143 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.69195 | 0.162372 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.4665 | −0.430648 | ||||||||
\(839\) | 16.2627 | 0.561450 | 0.280725 | − | 0.959788i | \(-0.409425\pi\) | ||||
0.280725 | + | 0.959788i | \(0.409425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.5467 | 1.81196 | ||||||||
\(842\) | 60.1230 | 2.07197 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19.7718 | 0.680575 | ||||||||
\(845\) | 1.56949 | 0.0539920 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −34.4426 | −1.18276 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 20.4936 | 0.702924 | ||||||||
\(851\) | 0.336270 | 0.0115272 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.70771 | 0.161189 | 0.0805945 | − | 0.996747i | \(-0.474318\pi\) | ||||
0.0805945 | + | 0.996747i | \(0.474318\pi\) | |||||||
\(854\) | −12.2252 | −0.418338 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.26406 | −0.0773839 | ||||||||
\(857\) | −27.6135 | −0.943259 | −0.471629 | − | 0.881797i | \(-0.656334\pi\) | ||||
−0.471629 | + | 0.881797i | \(0.656334\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.1645 | 0.619763 | 0.309882 | − | 0.950775i | \(-0.399711\pi\) | ||||
0.309882 | + | 0.950775i | \(0.399711\pi\) | |||||||
\(860\) | 3.82766 | 0.130522 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −31.5846 | −1.07577 | ||||||||
\(863\) | 31.2285 | 1.06303 | 0.531515 | − | 0.847049i | \(-0.321623\pi\) | ||||
0.531515 | + | 0.847049i | \(0.321623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3440 | −0.385706 | ||||||||
\(866\) | 9.22018 | 0.313314 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.10339 | −0.0374516 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 54.8257 | 1.85770 | ||||||||
\(872\) | 0.980590 | 0.0332070 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.161080 | −0.00544861 | ||||||||
\(875\) | −9.40208 | −0.317848 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.4419 | 0.521436 | 0.260718 | − | 0.965415i | \(-0.416041\pi\) | ||||
0.260718 | + | 0.965415i | \(0.416041\pi\) | |||||||
\(878\) | 54.5041 | 1.83942 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.5879 | 1.60328 | 0.801639 | − | 0.597808i | \(-0.203962\pi\) | ||||
0.801639 | + | 0.597808i | \(0.203962\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.2786 | −0.749734 | −0.374867 | − | 0.927079i | \(-0.622312\pi\) | ||||
−0.374867 | + | 0.927079i | \(0.622312\pi\) | |||||||
\(884\) | 21.8688 | 0.735527 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.95881 | 0.267381 | ||||||||
\(887\) | −25.5643 | −0.858365 | −0.429183 | − | 0.903218i | \(-0.641198\pi\) | ||||
−0.429183 | + | 0.903218i | \(0.641198\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.1294 | −0.641579 | ||||||||
\(890\) | 35.1781 | 1.17917 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −46.1325 | −1.54463 | ||||||||
\(893\) | −0.0905556 | −0.00303033 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.1300 | −0.405460 | ||||||||
\(896\) | −3.91368 | −0.130747 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.9590 | 0.499187 | ||||||||
\(899\) | 4.44958 | 0.148402 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.5153 | −0.850036 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.24506 | −0.141189 | ||||||||
\(905\) | 17.4995 | 0.581702 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.08704 | 0.102504 | 0.0512518 | − | 0.998686i | \(-0.483679\pi\) | ||||
0.0512518 | + | 0.998686i | \(0.483679\pi\) | |||||||
\(908\) | −39.0422 | −1.29566 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.29742 | −0.275057 | ||||||||
\(911\) | 5.06946 | 0.167959 | 0.0839793 | − | 0.996467i | \(-0.473237\pi\) | ||||
0.0839793 | + | 0.996467i | \(0.473237\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −53.0078 | −1.75334 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 52.5066 | 1.73487 | ||||||||
\(917\) | 6.91998 | 0.228518 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.7870 | 1.08154 | 0.540771 | − | 0.841170i | \(-0.318132\pi\) | ||||
0.540771 | + | 0.841170i | \(0.318132\pi\) | |||||||
\(920\) | −0.226340 | −0.00746222 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −47.2776 | −1.55701 | ||||||||
\(923\) | −47.5655 | −1.56564 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00674 | 0.0988610 | ||||||||
\(926\) | 9.65595 | 0.317314 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 73.3074 | 2.40643 | ||||||||
\(929\) | −22.3901 | −0.734595 | −0.367298 | − | 0.930103i | \(-0.619717\pi\) | ||||
−0.367298 | + | 0.930103i | \(0.619717\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.180354 | 0.00591087 | ||||||||
\(932\) | 33.2969 | 1.09068 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 67.7088 | 2.21550 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.67075 | 0.217924 | 0.108962 | − | 0.994046i | \(-0.465247\pi\) | ||||
0.108962 | + | 0.994046i | \(0.465247\pi\) | |||||||
\(938\) | −29.6631 | −0.968534 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.19065 | −0.0388346 | ||||||||
\(941\) | −8.84967 | −0.288491 | −0.144245 | − | 0.989542i | \(-0.546075\pi\) | ||||
−0.144245 | + | 0.989542i | \(0.546075\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.34157 | 0.0436875 | ||||||||
\(944\) | 46.5965 | 1.51659 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.9296 | −1.13506 | −0.567530 | − | 0.823352i | \(-0.692101\pi\) | ||||
−0.567530 | + | 0.823352i | \(0.692101\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.2642 | −0.527959 | ||||||||
\(950\) | −1.44029 | −0.0467292 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.26447 | −0.0409818 | ||||||||
\(953\) | 3.36257 | 0.108924 | 0.0544621 | − | 0.998516i | \(-0.482656\pi\) | ||||
0.0544621 | + | 0.998516i | \(0.482656\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.32753 | 0.0753171 | ||||||||
\(956\) | −50.5460 | −1.63478 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.3711 | −0.690469 | ||||||||
\(959\) | −6.81197 | −0.219970 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7572 | −0.992168 | ||||||||
\(962\) | 6.07413 | 0.195838 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.93198 | 0.158849 | ||||||||
\(965\) | −26.6308 | −0.857277 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.65340 | −0.213959 | −0.106979 | − | 0.994261i | \(-0.534118\pi\) | ||||
−0.106979 | + | 0.994261i | \(0.534118\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 31.8677 | 1.02321 | ||||||||
\(971\) | −13.3090 | −0.427106 | −0.213553 | − | 0.976931i | \(-0.568504\pi\) | ||||
−0.213553 | + | 0.976931i | \(0.568504\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.6013 | 0.628389 | ||||||||
\(974\) | 58.5536 | 1.87618 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 20.5683 | 0.658376 | ||||||||
\(977\) | −1.37314 | −0.0439307 | −0.0219654 | − | 0.999759i | \(-0.506992\pi\) | ||||
−0.0219654 | + | 0.999759i | \(0.506992\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 2.37134 | 0.0757497 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −63.7194 | −2.03337 | ||||||||
\(983\) | 10.7743 | 0.343646 | 0.171823 | − | 0.985128i | \(-0.445034\pi\) | ||||
0.171823 | + | 0.985128i | \(0.445034\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.49357 | 0.206902 | ||||||||
\(986\) | 47.7139 | 1.51952 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.53694 | −0.0488966 | ||||||||
\(989\) | −0.700175 | −0.0222643 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.59499 | 0.177731 | 0.0888654 | − | 0.996044i | \(-0.471676\pi\) | ||||
0.0888654 | + | 0.996044i | \(0.471676\pi\) | |||||||
\(992\) | 4.00000 | 0.127000 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.7350 | 0.816265 | ||||||||
\(995\) | 21.7040 | 0.688062 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.7503 | −1.44893 | −0.724463 | − | 0.689314i | \(-0.757912\pi\) | ||||
−0.724463 | + | 0.689314i | \(0.757912\pi\) | |||||||
\(998\) | −70.5711 | −2.23389 | ||||||||
\(999\) | 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 | 7623.2.a.cf.1.4 | 4 | ||
3.2 | odd | 2 | 2541.2.a.bo.1.1 | yes | 4 | ||
11.10 | odd | 2 | 7623.2.a.cm.1.1 | 4 | |||
33.32 | even | 2 | 2541.2.a.bk.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2541.2.a.bk.1.4 | ✓ | 4 | 33.32 | even | 2 | ||
2541.2.a.bo.1.1 | yes | 4 | 3.2 | odd | 2 | ||
7623.2.a.cf.1.4 | 4 | 1.1 | even | 1 | trivial | ||
7623.2.a.cm.1.1 | 4 | 11.10 | odd | 2 |