Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(0\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.02903 | −1.43474 | −0.717369 | − | 0.696694i | \(-0.754654\pi\) | ||||
−0.717369 | + | 0.696694i | \(0.754654\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.11694 | 1.05847 | ||||||||
\(5\) | 4.33739 | 1.93974 | 0.969870 | − | 0.243625i | \(-0.0783366\pi\) | ||||
0.969870 | + | 0.243625i | \(0.0783366\pi\) | |||||||
\(6\) | −2.02903 | −0.828346 | ||||||||
\(7\) | −3.04221 | −1.14985 | −0.574923 | − | 0.818207i | \(-0.694968\pi\) | ||||
−0.574923 | + | 0.818207i | \(0.694968\pi\) | |||||||
\(8\) | −0.237280 | −0.0838912 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −8.80067 | −2.78302 | ||||||||
\(11\) | −2.48095 | −0.748036 | −0.374018 | − | 0.927422i | \(-0.622020\pi\) | ||||
−0.374018 | + | 0.927422i | \(0.622020\pi\) | |||||||
\(12\) | 2.11694 | 0.611109 | ||||||||
\(13\) | −2.83592 | −0.786544 | −0.393272 | − | 0.919422i | \(-0.628657\pi\) | ||||
−0.393272 | + | 0.919422i | \(0.628657\pi\) | |||||||
\(14\) | 6.17272 | 1.64973 | ||||||||
\(15\) | 4.33739 | 1.11991 | ||||||||
\(16\) | −3.75244 | −0.938110 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −2.02903 | −0.478246 | ||||||||
\(19\) | −1.71391 | −0.393198 | −0.196599 | − | 0.980484i | \(-0.562990\pi\) | ||||
−0.196599 | + | 0.980484i | \(0.562990\pi\) | |||||||
\(20\) | 9.18200 | 2.05316 | ||||||||
\(21\) | −3.04221 | −0.663864 | ||||||||
\(22\) | 5.03392 | 1.07323 | ||||||||
\(23\) | −2.49567 | −0.520384 | −0.260192 | − | 0.965557i | \(-0.583786\pi\) | ||||
−0.260192 | + | 0.965557i | \(0.583786\pi\) | |||||||
\(24\) | −0.237280 | −0.0484346 | ||||||||
\(25\) | 13.8129 | 2.76259 | ||||||||
\(26\) | 5.75416 | 1.12848 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −6.44018 | −1.21708 | ||||||||
\(29\) | −2.97228 | −0.551939 | −0.275970 | − | 0.961166i | \(-0.588999\pi\) | ||||
−0.275970 | + | 0.961166i | \(0.588999\pi\) | |||||||
\(30\) | −8.80067 | −1.60678 | ||||||||
\(31\) | −0.206606 | −0.0371076 | −0.0185538 | − | 0.999828i | \(-0.505906\pi\) | ||||
−0.0185538 | + | 0.999828i | \(0.505906\pi\) | |||||||
\(32\) | 8.08835 | 1.42983 | ||||||||
\(33\) | −2.48095 | −0.431879 | ||||||||
\(34\) | −2.02903 | −0.347975 | ||||||||
\(35\) | −13.1952 | −2.23040 | ||||||||
\(36\) | 2.11694 | 0.352824 | ||||||||
\(37\) | 10.5877 | 1.74061 | 0.870305 | − | 0.492512i | \(-0.163921\pi\) | ||||
0.870305 | + | 0.492512i | \(0.163921\pi\) | |||||||
\(38\) | 3.47757 | 0.564136 | ||||||||
\(39\) | −2.83592 | −0.454111 | ||||||||
\(40\) | −1.02918 | −0.162727 | ||||||||
\(41\) | 4.56632 | 0.713140 | 0.356570 | − | 0.934269i | \(-0.383946\pi\) | ||||
0.356570 | + | 0.934269i | \(0.383946\pi\) | |||||||
\(42\) | 6.17272 | 0.952471 | ||||||||
\(43\) | 10.7284 | 1.63607 | 0.818033 | − | 0.575171i | \(-0.195065\pi\) | ||||
0.818033 | + | 0.575171i | \(0.195065\pi\) | |||||||
\(44\) | −5.25204 | −0.791774 | ||||||||
\(45\) | 4.33739 | 0.646580 | ||||||||
\(46\) | 5.06378 | 0.746614 | ||||||||
\(47\) | −1.56364 | −0.228081 | −0.114040 | − | 0.993476i | \(-0.536379\pi\) | ||||
−0.114040 | + | 0.993476i | \(0.536379\pi\) | |||||||
\(48\) | −3.75244 | −0.541618 | ||||||||
\(49\) | 2.25503 | 0.322147 | ||||||||
\(50\) | −28.0268 | −3.96359 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −6.00349 | −0.832534 | ||||||||
\(53\) | −3.33236 | −0.457735 | −0.228867 | − | 0.973458i | \(-0.573502\pi\) | ||||
−0.228867 | + | 0.973458i | \(0.573502\pi\) | |||||||
\(54\) | −2.02903 | −0.276115 | ||||||||
\(55\) | −10.7609 | −1.45099 | ||||||||
\(56\) | 0.721856 | 0.0964620 | ||||||||
\(57\) | −1.71391 | −0.227013 | ||||||||
\(58\) | 6.03084 | 0.791888 | ||||||||
\(59\) | −11.5571 | −1.50461 | −0.752304 | − | 0.658816i | \(-0.771057\pi\) | ||||
−0.752304 | + | 0.658816i | \(0.771057\pi\) | |||||||
\(60\) | 9.18200 | 1.18539 | ||||||||
\(61\) | 13.3272 | 1.70637 | 0.853187 | − | 0.521605i | \(-0.174666\pi\) | ||||
0.853187 | + | 0.521605i | \(0.174666\pi\) | |||||||
\(62\) | 0.419209 | 0.0532396 | ||||||||
\(63\) | −3.04221 | −0.383282 | ||||||||
\(64\) | −8.90659 | −1.11332 | ||||||||
\(65\) | −12.3005 | −1.52569 | ||||||||
\(66\) | 5.03392 | 0.619632 | ||||||||
\(67\) | −3.95247 | −0.482871 | −0.241435 | − | 0.970417i | \(-0.577618\pi\) | ||||
−0.241435 | + | 0.970417i | \(0.577618\pi\) | |||||||
\(68\) | 2.11694 | 0.256717 | ||||||||
\(69\) | −2.49567 | −0.300444 | ||||||||
\(70\) | 26.7735 | 3.20004 | ||||||||
\(71\) | 7.14457 | 0.847905 | 0.423952 | − | 0.905684i | \(-0.360642\pi\) | ||||
0.423952 | + | 0.905684i | \(0.360642\pi\) | |||||||
\(72\) | −0.237280 | −0.0279637 | ||||||||
\(73\) | −10.4608 | −1.22434 | −0.612172 | − | 0.790724i | \(-0.709704\pi\) | ||||
−0.612172 | + | 0.790724i | \(0.709704\pi\) | |||||||
\(74\) | −21.4828 | −2.49732 | ||||||||
\(75\) | 13.8129 | 1.59498 | ||||||||
\(76\) | −3.62825 | −0.416189 | ||||||||
\(77\) | 7.54758 | 0.860126 | ||||||||
\(78\) | 5.75416 | 0.651530 | ||||||||
\(79\) | −3.69072 | −0.415238 | −0.207619 | − | 0.978210i | \(-0.566571\pi\) | ||||
−0.207619 | + | 0.978210i | \(0.566571\pi\) | |||||||
\(80\) | −16.2758 | −1.81969 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.26519 | −1.02317 | ||||||||
\(83\) | −1.81049 | −0.198727 | −0.0993636 | − | 0.995051i | \(-0.531681\pi\) | ||||
−0.0993636 | + | 0.995051i | \(0.531681\pi\) | |||||||
\(84\) | −6.44018 | −0.702681 | ||||||||
\(85\) | 4.33739 | 0.470456 | ||||||||
\(86\) | −21.7682 | −2.34733 | ||||||||
\(87\) | −2.97228 | −0.318662 | ||||||||
\(88\) | 0.588681 | 0.0627536 | ||||||||
\(89\) | 16.6642 | 1.76640 | 0.883200 | − | 0.468997i | \(-0.155384\pi\) | ||||
0.883200 | + | 0.468997i | \(0.155384\pi\) | |||||||
\(90\) | −8.80067 | −0.927672 | ||||||||
\(91\) | 8.62747 | 0.904404 | ||||||||
\(92\) | −5.28320 | −0.550811 | ||||||||
\(93\) | −0.206606 | −0.0214241 | ||||||||
\(94\) | 3.17267 | 0.327236 | ||||||||
\(95\) | −7.43390 | −0.762702 | ||||||||
\(96\) | 8.08835 | 0.825514 | ||||||||
\(97\) | 9.74805 | 0.989764 | 0.494882 | − | 0.868960i | \(-0.335211\pi\) | ||||
0.494882 | + | 0.868960i | \(0.335211\pi\) | |||||||
\(98\) | −4.57551 | −0.462196 | ||||||||
\(99\) | −2.48095 | −0.249345 | ||||||||
\(100\) | 29.2412 | 2.92412 | ||||||||
\(101\) | −7.84278 | −0.780386 | −0.390193 | − | 0.920733i | \(-0.627592\pi\) | ||||
−0.390193 | + | 0.920733i | \(0.627592\pi\) | |||||||
\(102\) | −2.02903 | −0.200903 | ||||||||
\(103\) | −4.23429 | −0.417217 | −0.208608 | − | 0.977999i | \(-0.566893\pi\) | ||||
−0.208608 | + | 0.977999i | \(0.566893\pi\) | |||||||
\(104\) | 0.672908 | 0.0659841 | ||||||||
\(105\) | −13.1952 | −1.28772 | ||||||||
\(106\) | 6.76144 | 0.656729 | ||||||||
\(107\) | −1.84744 | −0.178599 | −0.0892996 | − | 0.996005i | \(-0.528463\pi\) | ||||
−0.0892996 | + | 0.996005i | \(0.528463\pi\) | |||||||
\(108\) | 2.11694 | 0.203703 | ||||||||
\(109\) | 17.9716 | 1.72137 | 0.860683 | − | 0.509141i | \(-0.170037\pi\) | ||||
0.860683 | + | 0.509141i | \(0.170037\pi\) | |||||||
\(110\) | 21.8341 | 2.08180 | ||||||||
\(111\) | 10.5877 | 1.00494 | ||||||||
\(112\) | 11.4157 | 1.07868 | ||||||||
\(113\) | 10.4247 | 0.980674 | 0.490337 | − | 0.871533i | \(-0.336874\pi\) | ||||
0.490337 | + | 0.871533i | \(0.336874\pi\) | |||||||
\(114\) | 3.47757 | 0.325704 | ||||||||
\(115\) | −10.8247 | −1.00941 | ||||||||
\(116\) | −6.29216 | −0.584212 | ||||||||
\(117\) | −2.83592 | −0.262181 | ||||||||
\(118\) | 23.4497 | 2.15872 | ||||||||
\(119\) | −3.04221 | −0.278879 | ||||||||
\(120\) | −1.02918 | −0.0939505 | ||||||||
\(121\) | −4.84487 | −0.440443 | ||||||||
\(122\) | −27.0412 | −2.44820 | ||||||||
\(123\) | 4.56632 | 0.411732 | ||||||||
\(124\) | −0.437373 | −0.0392773 | ||||||||
\(125\) | 38.2251 | 3.41896 | ||||||||
\(126\) | 6.17272 | 0.549909 | ||||||||
\(127\) | −17.0834 | −1.51591 | −0.757953 | − | 0.652309i | \(-0.773800\pi\) | ||||
−0.757953 | + | 0.652309i | \(0.773800\pi\) | |||||||
\(128\) | 1.89500 | 0.167496 | ||||||||
\(129\) | 10.7284 | 0.944583 | ||||||||
\(130\) | 24.9580 | 2.18896 | ||||||||
\(131\) | 14.6619 | 1.28101 | 0.640507 | − | 0.767952i | \(-0.278724\pi\) | ||||
0.640507 | + | 0.767952i | \(0.278724\pi\) | |||||||
\(132\) | −5.25204 | −0.457131 | ||||||||
\(133\) | 5.21407 | 0.452117 | ||||||||
\(134\) | 8.01965 | 0.692793 | ||||||||
\(135\) | 4.33739 | 0.373303 | ||||||||
\(136\) | −0.237280 | −0.0203466 | ||||||||
\(137\) | −17.4703 | −1.49259 | −0.746295 | − | 0.665615i | \(-0.768169\pi\) | ||||
−0.746295 | + | 0.665615i | \(0.768169\pi\) | |||||||
\(138\) | 5.06378 | 0.431058 | ||||||||
\(139\) | −12.3183 | −1.04482 | −0.522412 | − | 0.852693i | \(-0.674968\pi\) | ||||
−0.522412 | + | 0.852693i | \(0.674968\pi\) | |||||||
\(140\) | −27.9336 | −2.36082 | ||||||||
\(141\) | −1.56364 | −0.131682 | ||||||||
\(142\) | −14.4965 | −1.21652 | ||||||||
\(143\) | 7.03579 | 0.588363 | ||||||||
\(144\) | −3.75244 | −0.312703 | ||||||||
\(145\) | −12.8919 | −1.07062 | ||||||||
\(146\) | 21.2252 | 1.75661 | ||||||||
\(147\) | 2.25503 | 0.185992 | ||||||||
\(148\) | 22.4136 | 1.84239 | ||||||||
\(149\) | 0.702898 | 0.0575837 | 0.0287918 | − | 0.999585i | \(-0.490834\pi\) | ||||
0.0287918 | + | 0.999585i | \(0.490834\pi\) | |||||||
\(150\) | −28.0268 | −2.28838 | ||||||||
\(151\) | −23.4715 | −1.91008 | −0.955041 | − | 0.296475i | \(-0.904189\pi\) | ||||
−0.955041 | + | 0.296475i | \(0.904189\pi\) | |||||||
\(152\) | 0.406677 | 0.0329859 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −15.3142 | −1.23406 | ||||||||
\(155\) | −0.896131 | −0.0719790 | ||||||||
\(156\) | −6.00349 | −0.480664 | ||||||||
\(157\) | 1.00000 | 0.0798087 | ||||||||
\(158\) | 7.48856 | 0.595758 | ||||||||
\(159\) | −3.33236 | −0.264273 | ||||||||
\(160\) | 35.0823 | 2.77350 | ||||||||
\(161\) | 7.59236 | 0.598361 | ||||||||
\(162\) | −2.02903 | −0.159415 | ||||||||
\(163\) | 13.5041 | 1.05772 | 0.528861 | − | 0.848708i | \(-0.322619\pi\) | ||||
0.528861 | + | 0.848708i | \(0.322619\pi\) | |||||||
\(164\) | 9.66665 | 0.754838 | ||||||||
\(165\) | −10.7609 | −0.837732 | ||||||||
\(166\) | 3.67353 | 0.285121 | ||||||||
\(167\) | 24.3642 | 1.88536 | 0.942679 | − | 0.333701i | \(-0.108298\pi\) | ||||
0.942679 | + | 0.333701i | \(0.108298\pi\) | |||||||
\(168\) | 0.721856 | 0.0556924 | ||||||||
\(169\) | −4.95754 | −0.381349 | ||||||||
\(170\) | −8.80067 | −0.674981 | ||||||||
\(171\) | −1.71391 | −0.131066 | ||||||||
\(172\) | 22.7114 | 1.73173 | ||||||||
\(173\) | 2.75723 | 0.209628 | 0.104814 | − | 0.994492i | \(-0.466575\pi\) | ||||
0.104814 | + | 0.994492i | \(0.466575\pi\) | |||||||
\(174\) | 6.03084 | 0.457197 | ||||||||
\(175\) | −42.0218 | −3.17655 | ||||||||
\(176\) | 9.30963 | 0.701739 | ||||||||
\(177\) | −11.5571 | −0.868686 | ||||||||
\(178\) | −33.8120 | −2.53432 | ||||||||
\(179\) | 21.1616 | 1.58169 | 0.790845 | − | 0.612016i | \(-0.209641\pi\) | ||||
0.790845 | + | 0.612016i | \(0.209641\pi\) | |||||||
\(180\) | 9.18200 | 0.684386 | ||||||||
\(181\) | 24.0748 | 1.78947 | 0.894735 | − | 0.446598i | \(-0.147365\pi\) | ||||
0.894735 | + | 0.446598i | \(0.147365\pi\) | |||||||
\(182\) | −17.5053 | −1.29758 | ||||||||
\(183\) | 13.3272 | 0.985176 | ||||||||
\(184\) | 0.592174 | 0.0436556 | ||||||||
\(185\) | 45.9231 | 3.37633 | ||||||||
\(186\) | 0.419209 | 0.0307379 | ||||||||
\(187\) | −2.48095 | −0.181425 | ||||||||
\(188\) | −3.31014 | −0.241417 | ||||||||
\(189\) | −3.04221 | −0.221288 | ||||||||
\(190\) | 15.0836 | 1.09428 | ||||||||
\(191\) | 12.0618 | 0.872762 | 0.436381 | − | 0.899762i | \(-0.356260\pi\) | ||||
0.436381 | + | 0.899762i | \(0.356260\pi\) | |||||||
\(192\) | −8.90659 | −0.642778 | ||||||||
\(193\) | −18.3096 | −1.31796 | −0.658978 | − | 0.752163i | \(-0.729011\pi\) | ||||
−0.658978 | + | 0.752163i | \(0.729011\pi\) | |||||||
\(194\) | −19.7790 | −1.42005 | ||||||||
\(195\) | −12.3005 | −0.880857 | ||||||||
\(196\) | 4.77377 | 0.340983 | ||||||||
\(197\) | 0.950036 | 0.0676873 | 0.0338436 | − | 0.999427i | \(-0.489225\pi\) | ||||
0.0338436 | + | 0.999427i | \(0.489225\pi\) | |||||||
\(198\) | 5.03392 | 0.357745 | ||||||||
\(199\) | 11.6263 | 0.824164 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(200\) | −3.27754 | −0.231757 | ||||||||
\(201\) | −3.95247 | −0.278786 | ||||||||
\(202\) | 15.9132 | 1.11965 | ||||||||
\(203\) | 9.04231 | 0.634645 | ||||||||
\(204\) | 2.11694 | 0.148216 | ||||||||
\(205\) | 19.8059 | 1.38331 | ||||||||
\(206\) | 8.59148 | 0.598596 | ||||||||
\(207\) | −2.49567 | −0.173461 | ||||||||
\(208\) | 10.6416 | 0.737864 | ||||||||
\(209\) | 4.25213 | 0.294126 | ||||||||
\(210\) | 26.7735 | 1.84754 | ||||||||
\(211\) | 26.4117 | 1.81825 | 0.909127 | − | 0.416519i | \(-0.136750\pi\) | ||||
0.909127 | + | 0.416519i | \(0.136750\pi\) | |||||||
\(212\) | −7.05441 | −0.484499 | ||||||||
\(213\) | 7.14457 | 0.489538 | ||||||||
\(214\) | 3.74851 | 0.256243 | ||||||||
\(215\) | 46.5332 | 3.17354 | ||||||||
\(216\) | −0.237280 | −0.0161449 | ||||||||
\(217\) | 0.628539 | 0.0426680 | ||||||||
\(218\) | −36.4648 | −2.46971 | ||||||||
\(219\) | −10.4608 | −0.706876 | ||||||||
\(220\) | −22.7801 | −1.53584 | ||||||||
\(221\) | −2.83592 | −0.190765 | ||||||||
\(222\) | −21.4828 | −1.44183 | ||||||||
\(223\) | 24.8083 | 1.66129 | 0.830643 | − | 0.556805i | \(-0.187973\pi\) | ||||
0.830643 | + | 0.556805i | \(0.187973\pi\) | |||||||
\(224\) | −24.6064 | −1.64409 | ||||||||
\(225\) | 13.8129 | 0.920863 | ||||||||
\(226\) | −21.1520 | −1.40701 | ||||||||
\(227\) | 3.66507 | 0.243259 | 0.121630 | − | 0.992576i | \(-0.461188\pi\) | ||||
0.121630 | + | 0.992576i | \(0.461188\pi\) | |||||||
\(228\) | −3.62825 | −0.240287 | ||||||||
\(229\) | 18.0273 | 1.19128 | 0.595640 | − | 0.803252i | \(-0.296899\pi\) | ||||
0.595640 | + | 0.803252i | \(0.296899\pi\) | |||||||
\(230\) | 21.9636 | 1.44824 | ||||||||
\(231\) | 7.54758 | 0.496594 | ||||||||
\(232\) | 0.705264 | 0.0463029 | ||||||||
\(233\) | 4.05523 | 0.265667 | 0.132834 | − | 0.991138i | \(-0.457592\pi\) | ||||
0.132834 | + | 0.991138i | \(0.457592\pi\) | |||||||
\(234\) | 5.75416 | 0.376161 | ||||||||
\(235\) | −6.78212 | −0.442417 | ||||||||
\(236\) | −24.4657 | −1.59258 | ||||||||
\(237\) | −3.69072 | −0.239738 | ||||||||
\(238\) | 6.17272 | 0.400118 | ||||||||
\(239\) | −19.7857 | −1.27983 | −0.639916 | − | 0.768445i | \(-0.721031\pi\) | ||||
−0.639916 | + | 0.768445i | \(0.721031\pi\) | |||||||
\(240\) | −16.2758 | −1.05060 | ||||||||
\(241\) | 17.9625 | 1.15707 | 0.578533 | − | 0.815659i | \(-0.303626\pi\) | ||||
0.578533 | + | 0.815659i | \(0.303626\pi\) | |||||||
\(242\) | 9.83036 | 0.631919 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 28.2129 | 1.80615 | ||||||||
\(245\) | 9.78093 | 0.624881 | ||||||||
\(246\) | −9.26519 | −0.590727 | ||||||||
\(247\) | 4.86052 | 0.309267 | ||||||||
\(248\) | 0.0490235 | 0.00311300 | ||||||||
\(249\) | −1.81049 | −0.114735 | ||||||||
\(250\) | −77.5598 | −4.90531 | ||||||||
\(251\) | 7.45092 | 0.470298 | 0.235149 | − | 0.971959i | \(-0.424442\pi\) | ||||
0.235149 | + | 0.971959i | \(0.424442\pi\) | |||||||
\(252\) | −6.44018 | −0.405693 | ||||||||
\(253\) | 6.19165 | 0.389266 | ||||||||
\(254\) | 34.6626 | 2.17493 | ||||||||
\(255\) | 4.33739 | 0.271618 | ||||||||
\(256\) | 13.9682 | 0.873012 | ||||||||
\(257\) | 21.8356 | 1.36207 | 0.681033 | − | 0.732253i | \(-0.261531\pi\) | ||||
0.681033 | + | 0.732253i | \(0.261531\pi\) | |||||||
\(258\) | −21.7682 | −1.35523 | ||||||||
\(259\) | −32.2101 | −2.00144 | ||||||||
\(260\) | −26.0395 | −1.61490 | ||||||||
\(261\) | −2.97228 | −0.183980 | ||||||||
\(262\) | −29.7493 | −1.83792 | ||||||||
\(263\) | −9.79833 | −0.604191 | −0.302095 | − | 0.953278i | \(-0.597686\pi\) | ||||
−0.302095 | + | 0.953278i | \(0.597686\pi\) | |||||||
\(264\) | 0.588681 | 0.0362308 | ||||||||
\(265\) | −14.4537 | −0.887886 | ||||||||
\(266\) | −10.5795 | −0.648670 | ||||||||
\(267\) | 16.6642 | 1.01983 | ||||||||
\(268\) | −8.36715 | −0.511105 | ||||||||
\(269\) | 29.0279 | 1.76986 | 0.884930 | − | 0.465724i | \(-0.154206\pi\) | ||||
0.884930 | + | 0.465724i | \(0.154206\pi\) | |||||||
\(270\) | −8.80067 | −0.535592 | ||||||||
\(271\) | −13.3293 | −0.809697 | −0.404849 | − | 0.914384i | \(-0.632676\pi\) | ||||
−0.404849 | + | 0.914384i | \(0.632676\pi\) | |||||||
\(272\) | −3.75244 | −0.227525 | ||||||||
\(273\) | 8.62747 | 0.522158 | ||||||||
\(274\) | 35.4477 | 2.14148 | ||||||||
\(275\) | −34.2693 | −2.06651 | ||||||||
\(276\) | −5.28320 | −0.318011 | ||||||||
\(277\) | 25.2409 | 1.51658 | 0.758288 | − | 0.651919i | \(-0.226036\pi\) | ||||
0.758288 | + | 0.651919i | \(0.226036\pi\) | |||||||
\(278\) | 24.9941 | 1.49905 | ||||||||
\(279\) | −0.206606 | −0.0123692 | ||||||||
\(280\) | 3.13097 | 0.187111 | ||||||||
\(281\) | −24.6239 | −1.46894 | −0.734470 | − | 0.678641i | \(-0.762569\pi\) | ||||
−0.734470 | + | 0.678641i | \(0.762569\pi\) | |||||||
\(282\) | 3.17267 | 0.188930 | ||||||||
\(283\) | −6.67364 | −0.396707 | −0.198353 | − | 0.980131i | \(-0.563559\pi\) | ||||
−0.198353 | + | 0.980131i | \(0.563559\pi\) | |||||||
\(284\) | 15.1247 | 0.897483 | ||||||||
\(285\) | −7.43390 | −0.440346 | ||||||||
\(286\) | −14.2758 | −0.844146 | ||||||||
\(287\) | −13.8917 | −0.820002 | ||||||||
\(288\) | 8.08835 | 0.476611 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 26.1581 | 1.53606 | ||||||||
\(291\) | 9.74805 | 0.571441 | ||||||||
\(292\) | −22.1449 | −1.29593 | ||||||||
\(293\) | 6.40980 | 0.374464 | 0.187232 | − | 0.982316i | \(-0.440048\pi\) | ||||
0.187232 | + | 0.982316i | \(0.440048\pi\) | |||||||
\(294\) | −4.57551 | −0.266849 | ||||||||
\(295\) | −50.1277 | −2.91855 | ||||||||
\(296\) | −2.51226 | −0.146022 | ||||||||
\(297\) | −2.48095 | −0.143960 | ||||||||
\(298\) | −1.42620 | −0.0826174 | ||||||||
\(299\) | 7.07754 | 0.409305 | ||||||||
\(300\) | 29.2412 | 1.68824 | ||||||||
\(301\) | −32.6380 | −1.88122 | ||||||||
\(302\) | 47.6242 | 2.74046 | ||||||||
\(303\) | −7.84278 | −0.450556 | ||||||||
\(304\) | 6.43134 | 0.368863 | ||||||||
\(305\) | 57.8053 | 3.30992 | ||||||||
\(306\) | −2.02903 | −0.115992 | ||||||||
\(307\) | −5.50105 | −0.313961 | −0.156981 | − | 0.987602i | \(-0.550176\pi\) | ||||
−0.156981 | + | 0.987602i | \(0.550176\pi\) | |||||||
\(308\) | 15.9778 | 0.910419 | ||||||||
\(309\) | −4.23429 | −0.240880 | ||||||||
\(310\) | 1.81827 | 0.103271 | ||||||||
\(311\) | −19.5463 | −1.10837 | −0.554186 | − | 0.832393i | \(-0.686970\pi\) | ||||
−0.554186 | + | 0.832393i | \(0.686970\pi\) | |||||||
\(312\) | 0.672908 | 0.0380959 | ||||||||
\(313\) | 16.6493 | 0.941076 | 0.470538 | − | 0.882380i | \(-0.344060\pi\) | ||||
0.470538 | + | 0.882380i | \(0.344060\pi\) | |||||||
\(314\) | −2.02903 | −0.114505 | ||||||||
\(315\) | −13.1952 | −0.743467 | ||||||||
\(316\) | −7.81304 | −0.439518 | ||||||||
\(317\) | −1.84809 | −0.103799 | −0.0518994 | − | 0.998652i | \(-0.516528\pi\) | ||||
−0.0518994 | + | 0.998652i | \(0.516528\pi\) | |||||||
\(318\) | 6.76144 | 0.379163 | ||||||||
\(319\) | 7.37410 | 0.412870 | ||||||||
\(320\) | −38.6314 | −2.15956 | ||||||||
\(321\) | −1.84744 | −0.103114 | ||||||||
\(322\) | −15.4051 | −0.858492 | ||||||||
\(323\) | −1.71391 | −0.0953645 | ||||||||
\(324\) | 2.11694 | 0.117608 | ||||||||
\(325\) | −39.1724 | −2.17290 | ||||||||
\(326\) | −27.4001 | −1.51755 | ||||||||
\(327\) | 17.9716 | 0.993831 | ||||||||
\(328\) | −1.08350 | −0.0598262 | ||||||||
\(329\) | 4.75692 | 0.262258 | ||||||||
\(330\) | 21.8341 | 1.20193 | ||||||||
\(331\) | −2.38003 | −0.130819 | −0.0654093 | − | 0.997859i | \(-0.520835\pi\) | ||||
−0.0654093 | + | 0.997859i | \(0.520835\pi\) | |||||||
\(332\) | −3.83271 | −0.210347 | ||||||||
\(333\) | 10.5877 | 0.580204 | ||||||||
\(334\) | −49.4356 | −2.70499 | ||||||||
\(335\) | −17.1434 | −0.936643 | ||||||||
\(336\) | 11.4157 | 0.622777 | ||||||||
\(337\) | −17.6299 | −0.960362 | −0.480181 | − | 0.877170i | \(-0.659429\pi\) | ||||
−0.480181 | + | 0.877170i | \(0.659429\pi\) | |||||||
\(338\) | 10.0590 | 0.547136 | ||||||||
\(339\) | 10.4247 | 0.566193 | ||||||||
\(340\) | 9.18200 | 0.497964 | ||||||||
\(341\) | 0.512580 | 0.0277578 | ||||||||
\(342\) | 3.47757 | 0.188045 | ||||||||
\(343\) | 14.4352 | 0.779427 | ||||||||
\(344\) | −2.54564 | −0.137252 | ||||||||
\(345\) | −10.8247 | −0.582782 | ||||||||
\(346\) | −5.59449 | −0.300761 | ||||||||
\(347\) | 20.9777 | 1.12614 | 0.563072 | − | 0.826408i | \(-0.309619\pi\) | ||||
0.563072 | + | 0.826408i | \(0.309619\pi\) | |||||||
\(348\) | −6.29216 | −0.337295 | ||||||||
\(349\) | 11.2771 | 0.603647 | 0.301824 | − | 0.953364i | \(-0.402405\pi\) | ||||
0.301824 | + | 0.953364i | \(0.402405\pi\) | |||||||
\(350\) | 85.2633 | 4.55752 | ||||||||
\(351\) | −2.83592 | −0.151370 | ||||||||
\(352\) | −20.0668 | −1.06957 | ||||||||
\(353\) | 2.69501 | 0.143441 | 0.0717204 | − | 0.997425i | \(-0.477151\pi\) | ||||
0.0717204 | + | 0.997425i | \(0.477151\pi\) | |||||||
\(354\) | 23.4497 | 1.24634 | ||||||||
\(355\) | 30.9888 | 1.64471 | ||||||||
\(356\) | 35.2771 | 1.86968 | ||||||||
\(357\) | −3.04221 | −0.161011 | ||||||||
\(358\) | −42.9374 | −2.26931 | ||||||||
\(359\) | −2.50405 | −0.132159 | −0.0660793 | − | 0.997814i | \(-0.521049\pi\) | ||||
−0.0660793 | + | 0.997814i | \(0.521049\pi\) | |||||||
\(360\) | −1.02918 | −0.0542424 | ||||||||
\(361\) | −16.0625 | −0.845395 | ||||||||
\(362\) | −48.8485 | −2.56742 | ||||||||
\(363\) | −4.84487 | −0.254290 | ||||||||
\(364\) | 18.2639 | 0.957286 | ||||||||
\(365\) | −45.3726 | −2.37491 | ||||||||
\(366\) | −27.0412 | −1.41347 | ||||||||
\(367\) | −12.9267 | −0.674770 | −0.337385 | − | 0.941367i | \(-0.609542\pi\) | ||||
−0.337385 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(368\) | 9.36486 | 0.488177 | ||||||||
\(369\) | 4.56632 | 0.237713 | ||||||||
\(370\) | −93.1790 | −4.84415 | ||||||||
\(371\) | 10.1377 | 0.526325 | ||||||||
\(372\) | −0.437373 | −0.0226768 | ||||||||
\(373\) | −18.1284 | −0.938655 | −0.469327 | − | 0.883024i | \(-0.655504\pi\) | ||||
−0.469327 | + | 0.883024i | \(0.655504\pi\) | |||||||
\(374\) | 5.03392 | 0.260298 | ||||||||
\(375\) | 38.2251 | 1.97394 | ||||||||
\(376\) | 0.371021 | 0.0191340 | ||||||||
\(377\) | 8.42917 | 0.434124 | ||||||||
\(378\) | 6.17272 | 0.317490 | ||||||||
\(379\) | 28.8584 | 1.48236 | 0.741179 | − | 0.671308i | \(-0.234267\pi\) | ||||
0.741179 | + | 0.671308i | \(0.234267\pi\) | |||||||
\(380\) | −15.7371 | −0.807298 | ||||||||
\(381\) | −17.0834 | −0.875209 | ||||||||
\(382\) | −24.4737 | −1.25218 | ||||||||
\(383\) | 16.3185 | 0.833835 | 0.416917 | − | 0.908944i | \(-0.363110\pi\) | ||||
0.416917 | + | 0.908944i | \(0.363110\pi\) | |||||||
\(384\) | 1.89500 | 0.0967036 | ||||||||
\(385\) | 32.7368 | 1.66842 | ||||||||
\(386\) | 37.1507 | 1.89092 | ||||||||
\(387\) | 10.7284 | 0.545355 | ||||||||
\(388\) | 20.6361 | 1.04764 | ||||||||
\(389\) | −16.9161 | −0.857678 | −0.428839 | − | 0.903381i | \(-0.641077\pi\) | ||||
−0.428839 | + | 0.903381i | \(0.641077\pi\) | |||||||
\(390\) | 24.9580 | 1.26380 | ||||||||
\(391\) | −2.49567 | −0.126212 | ||||||||
\(392\) | −0.535074 | −0.0270253 | ||||||||
\(393\) | 14.6619 | 0.739594 | ||||||||
\(394\) | −1.92765 | −0.0971135 | ||||||||
\(395\) | −16.0081 | −0.805454 | ||||||||
\(396\) | −5.25204 | −0.263925 | ||||||||
\(397\) | 31.6534 | 1.58864 | 0.794320 | − | 0.607499i | \(-0.207827\pi\) | ||||
0.794320 | + | 0.607499i | \(0.207827\pi\) | |||||||
\(398\) | −23.5900 | −1.18246 | ||||||||
\(399\) | 5.21407 | 0.261030 | ||||||||
\(400\) | −51.8322 | −2.59161 | ||||||||
\(401\) | −2.83679 | −0.141663 | −0.0708313 | − | 0.997488i | \(-0.522565\pi\) | ||||
−0.0708313 | + | 0.997488i | \(0.522565\pi\) | |||||||
\(402\) | 8.01965 | 0.399984 | ||||||||
\(403\) | 0.585919 | 0.0291867 | ||||||||
\(404\) | −16.6027 | −0.826016 | ||||||||
\(405\) | 4.33739 | 0.215527 | ||||||||
\(406\) | −18.3471 | −0.910549 | ||||||||
\(407\) | −26.2676 | −1.30204 | ||||||||
\(408\) | −0.237280 | −0.0117471 | ||||||||
\(409\) | 6.77076 | 0.334793 | 0.167396 | − | 0.985890i | \(-0.446464\pi\) | ||||
0.167396 | + | 0.985890i | \(0.446464\pi\) | |||||||
\(410\) | −40.1867 | −1.98468 | ||||||||
\(411\) | −17.4703 | −0.861748 | ||||||||
\(412\) | −8.96374 | −0.441612 | ||||||||
\(413\) | 35.1591 | 1.73007 | ||||||||
\(414\) | 5.06378 | 0.248871 | ||||||||
\(415\) | −7.85280 | −0.385479 | ||||||||
\(416\) | −22.9379 | −1.12463 | ||||||||
\(417\) | −12.3183 | −0.603230 | ||||||||
\(418\) | −8.62769 | −0.421994 | ||||||||
\(419\) | 17.6732 | 0.863392 | 0.431696 | − | 0.902019i | \(-0.357915\pi\) | ||||
0.431696 | + | 0.902019i | \(0.357915\pi\) | |||||||
\(420\) | −27.9336 | −1.36302 | ||||||||
\(421\) | −34.4675 | −1.67984 | −0.839922 | − | 0.542707i | \(-0.817400\pi\) | ||||
−0.839922 | + | 0.542707i | \(0.817400\pi\) | |||||||
\(422\) | −53.5899 | −2.60872 | ||||||||
\(423\) | −1.56364 | −0.0760269 | ||||||||
\(424\) | 0.790703 | 0.0383999 | ||||||||
\(425\) | 13.8129 | 0.670026 | ||||||||
\(426\) | −14.4965 | −0.702359 | ||||||||
\(427\) | −40.5441 | −1.96207 | ||||||||
\(428\) | −3.91094 | −0.189042 | ||||||||
\(429\) | 7.03579 | 0.339691 | ||||||||
\(430\) | −94.4171 | −4.55320 | ||||||||
\(431\) | −0.390666 | −0.0188177 | −0.00940886 | − | 0.999956i | \(-0.502995\pi\) | ||||
−0.00940886 | + | 0.999956i | \(0.502995\pi\) | |||||||
\(432\) | −3.75244 | −0.180539 | ||||||||
\(433\) | −38.0307 | −1.82764 | −0.913820 | − | 0.406120i | \(-0.866881\pi\) | ||||
−0.913820 | + | 0.406120i | \(0.866881\pi\) | |||||||
\(434\) | −1.27532 | −0.0612174 | ||||||||
\(435\) | −12.8919 | −0.618122 | ||||||||
\(436\) | 38.0448 | 1.82202 | ||||||||
\(437\) | 4.27736 | 0.204614 | ||||||||
\(438\) | 21.2252 | 1.01418 | ||||||||
\(439\) | −5.60904 | −0.267705 | −0.133852 | − | 0.991001i | \(-0.542735\pi\) | ||||
−0.133852 | + | 0.991001i | \(0.542735\pi\) | |||||||
\(440\) | 2.55334 | 0.121726 | ||||||||
\(441\) | 2.25503 | 0.107382 | ||||||||
\(442\) | 5.75416 | 0.273697 | ||||||||
\(443\) | −0.359747 | −0.0170921 | −0.00854604 | − | 0.999963i | \(-0.502720\pi\) | ||||
−0.00854604 | + | 0.999963i | \(0.502720\pi\) | |||||||
\(444\) | 22.4136 | 1.06370 | ||||||||
\(445\) | 72.2790 | 3.42635 | ||||||||
\(446\) | −50.3367 | −2.38351 | ||||||||
\(447\) | 0.702898 | 0.0332459 | ||||||||
\(448\) | 27.0957 | 1.28015 | ||||||||
\(449\) | −15.5512 | −0.733908 | −0.366954 | − | 0.930239i | \(-0.619599\pi\) | ||||
−0.366954 | + | 0.930239i | \(0.619599\pi\) | |||||||
\(450\) | −28.0268 | −1.32120 | ||||||||
\(451\) | −11.3288 | −0.533454 | ||||||||
\(452\) | 22.0685 | 1.03802 | ||||||||
\(453\) | −23.4715 | −1.10279 | ||||||||
\(454\) | −7.43652 | −0.349013 | ||||||||
\(455\) | 37.4207 | 1.75431 | ||||||||
\(456\) | 0.406677 | 0.0190444 | ||||||||
\(457\) | −19.4379 | −0.909265 | −0.454632 | − | 0.890679i | \(-0.650229\pi\) | ||||
−0.454632 | + | 0.890679i | \(0.650229\pi\) | |||||||
\(458\) | −36.5779 | −1.70917 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −22.9153 | −1.06843 | ||||||||
\(461\) | 15.9970 | 0.745054 | 0.372527 | − | 0.928021i | \(-0.378491\pi\) | ||||
0.372527 | + | 0.928021i | \(0.378491\pi\) | |||||||
\(462\) | −15.3142 | −0.712482 | ||||||||
\(463\) | −27.4791 | −1.27706 | −0.638530 | − | 0.769597i | \(-0.720457\pi\) | ||||
−0.638530 | + | 0.769597i | \(0.720457\pi\) | |||||||
\(464\) | 11.1533 | 0.517780 | ||||||||
\(465\) | −0.896131 | −0.0415571 | ||||||||
\(466\) | −8.22817 | −0.381162 | ||||||||
\(467\) | −34.1414 | −1.57987 | −0.789937 | − | 0.613188i | \(-0.789887\pi\) | ||||
−0.789937 | + | 0.613188i | \(0.789887\pi\) | |||||||
\(468\) | −6.00349 | −0.277511 | ||||||||
\(469\) | 12.0242 | 0.555227 | ||||||||
\(470\) | 13.7611 | 0.634752 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 2.74227 | 0.126223 | ||||||||
\(473\) | −26.6167 | −1.22384 | ||||||||
\(474\) | 7.48856 | 0.343961 | ||||||||
\(475\) | −23.6741 | −1.08624 | ||||||||
\(476\) | −6.44018 | −0.295185 | ||||||||
\(477\) | −3.33236 | −0.152578 | ||||||||
\(478\) | 40.1457 | 1.83622 | ||||||||
\(479\) | 25.4012 | 1.16061 | 0.580306 | − | 0.814398i | \(-0.302933\pi\) | ||||
0.580306 | + | 0.814398i | \(0.302933\pi\) | |||||||
\(480\) | 35.0823 | 1.60128 | ||||||||
\(481\) | −30.0260 | −1.36907 | ||||||||
\(482\) | −36.4463 | −1.66008 | ||||||||
\(483\) | 7.59236 | 0.345464 | ||||||||
\(484\) | −10.2563 | −0.466196 | ||||||||
\(485\) | 42.2811 | 1.91988 | ||||||||
\(486\) | −2.02903 | −0.0920384 | ||||||||
\(487\) | 36.4125 | 1.65001 | 0.825004 | − | 0.565127i | \(-0.191173\pi\) | ||||
0.825004 | + | 0.565127i | \(0.191173\pi\) | |||||||
\(488\) | −3.16228 | −0.143150 | ||||||||
\(489\) | 13.5041 | 0.610676 | ||||||||
\(490\) | −19.8458 | −0.896540 | ||||||||
\(491\) | 22.0393 | 0.994620 | 0.497310 | − | 0.867573i | \(-0.334321\pi\) | ||||
0.497310 | + | 0.867573i | \(0.334321\pi\) | |||||||
\(492\) | 9.66665 | 0.435806 | ||||||||
\(493\) | −2.97228 | −0.133865 | ||||||||
\(494\) | −9.86212 | −0.443718 | ||||||||
\(495\) | −10.7609 | −0.483665 | ||||||||
\(496\) | 0.775277 | 0.0348109 | ||||||||
\(497\) | −21.7353 | −0.974960 | ||||||||
\(498\) | 3.67353 | 0.164615 | ||||||||
\(499\) | 30.7360 | 1.37593 | 0.687965 | − | 0.725743i | \(-0.258504\pi\) | ||||
0.687965 | + | 0.725743i | \(0.258504\pi\) | |||||||
\(500\) | 80.9204 | 3.61887 | ||||||||
\(501\) | 24.3642 | 1.08851 | ||||||||
\(502\) | −15.1181 | −0.674754 | ||||||||
\(503\) | 1.36067 | 0.0606694 | 0.0303347 | − | 0.999540i | \(-0.490343\pi\) | ||||
0.0303347 | + | 0.999540i | \(0.490343\pi\) | |||||||
\(504\) | 0.721856 | 0.0321540 | ||||||||
\(505\) | −34.0172 | −1.51374 | ||||||||
\(506\) | −12.5630 | −0.558494 | ||||||||
\(507\) | −4.95754 | −0.220172 | ||||||||
\(508\) | −36.1646 | −1.60454 | ||||||||
\(509\) | 4.91757 | 0.217967 | 0.108984 | − | 0.994044i | \(-0.465240\pi\) | ||||
0.108984 | + | 0.994044i | \(0.465240\pi\) | |||||||
\(510\) | −8.80067 | −0.389700 | ||||||||
\(511\) | 31.8239 | 1.40781 | ||||||||
\(512\) | −32.1318 | −1.42004 | ||||||||
\(513\) | −1.71391 | −0.0756710 | ||||||||
\(514\) | −44.3049 | −1.95421 | ||||||||
\(515\) | −18.3657 | −0.809292 | ||||||||
\(516\) | 22.7114 | 0.999814 | ||||||||
\(517\) | 3.87932 | 0.170612 | ||||||||
\(518\) | 65.3550 | 2.87153 | ||||||||
\(519\) | 2.75723 | 0.121029 | ||||||||
\(520\) | 2.91867 | 0.127992 | ||||||||
\(521\) | −36.7653 | −1.61072 | −0.805359 | − | 0.592787i | \(-0.798028\pi\) | ||||
−0.805359 | + | 0.592787i | \(0.798028\pi\) | |||||||
\(522\) | 6.03084 | 0.263963 | ||||||||
\(523\) | 22.1738 | 0.969592 | 0.484796 | − | 0.874627i | \(-0.338894\pi\) | ||||
0.484796 | + | 0.874627i | \(0.338894\pi\) | |||||||
\(524\) | 31.0383 | 1.35592 | ||||||||
\(525\) | −42.0218 | −1.83398 | ||||||||
\(526\) | 19.8811 | 0.866855 | ||||||||
\(527\) | −0.206606 | −0.00899990 | ||||||||
\(528\) | 9.30963 | 0.405149 | ||||||||
\(529\) | −16.7716 | −0.729201 | ||||||||
\(530\) | 29.3270 | 1.27388 | ||||||||
\(531\) | −11.5571 | −0.501536 | ||||||||
\(532\) | 11.0379 | 0.478553 | ||||||||
\(533\) | −12.9497 | −0.560916 | ||||||||
\(534\) | −33.8120 | −1.46319 | ||||||||
\(535\) | −8.01309 | −0.346436 | ||||||||
\(536\) | 0.937842 | 0.0405086 | ||||||||
\(537\) | 21.1616 | 0.913190 | ||||||||
\(538\) | −58.8983 | −2.53928 | ||||||||
\(539\) | −5.59462 | −0.240977 | ||||||||
\(540\) | 9.18200 | 0.395131 | ||||||||
\(541\) | −12.4314 | −0.534466 | −0.267233 | − | 0.963632i | \(-0.586109\pi\) | ||||
−0.267233 | + | 0.963632i | \(0.586109\pi\) | |||||||
\(542\) | 27.0455 | 1.16170 | ||||||||
\(543\) | 24.0748 | 1.03315 | ||||||||
\(544\) | 8.08835 | 0.346785 | ||||||||
\(545\) | 77.9497 | 3.33900 | ||||||||
\(546\) | −17.5053 | −0.749160 | ||||||||
\(547\) | 9.83134 | 0.420358 | 0.210179 | − | 0.977663i | \(-0.432595\pi\) | ||||
0.210179 | + | 0.977663i | \(0.432595\pi\) | |||||||
\(548\) | −36.9837 | −1.57986 | ||||||||
\(549\) | 13.3272 | 0.568792 | ||||||||
\(550\) | 69.5332 | 2.96491 | ||||||||
\(551\) | 5.09423 | 0.217021 | ||||||||
\(552\) | 0.592174 | 0.0252046 | ||||||||
\(553\) | 11.2279 | 0.477460 | ||||||||
\(554\) | −51.2144 | −2.17589 | ||||||||
\(555\) | 45.9231 | 1.94933 | ||||||||
\(556\) | −26.0771 | −1.10592 | ||||||||
\(557\) | −24.1835 | −1.02469 | −0.512343 | − | 0.858781i | \(-0.671222\pi\) | ||||
−0.512343 | + | 0.858781i | \(0.671222\pi\) | |||||||
\(558\) | 0.419209 | 0.0177465 | ||||||||
\(559\) | −30.4249 | −1.28684 | ||||||||
\(560\) | 49.5143 | 2.09236 | ||||||||
\(561\) | −2.48095 | −0.104746 | ||||||||
\(562\) | 49.9626 | 2.10754 | ||||||||
\(563\) | 12.1098 | 0.510368 | 0.255184 | − | 0.966893i | \(-0.417864\pi\) | ||||
0.255184 | + | 0.966893i | \(0.417864\pi\) | |||||||
\(564\) | −3.31014 | −0.139382 | ||||||||
\(565\) | 45.2160 | 1.90225 | ||||||||
\(566\) | 13.5410 | 0.569170 | ||||||||
\(567\) | −3.04221 | −0.127761 | ||||||||
\(568\) | −1.69527 | −0.0711318 | ||||||||
\(569\) | −14.3539 | −0.601749 | −0.300874 | − | 0.953664i | \(-0.597278\pi\) | ||||
−0.300874 | + | 0.953664i | \(0.597278\pi\) | |||||||
\(570\) | 15.0836 | 0.631781 | ||||||||
\(571\) | 30.3527 | 1.27022 | 0.635111 | − | 0.772421i | \(-0.280954\pi\) | ||||
0.635111 | + | 0.772421i | \(0.280954\pi\) | |||||||
\(572\) | 14.8944 | 0.622765 | ||||||||
\(573\) | 12.0618 | 0.503889 | ||||||||
\(574\) | 28.1866 | 1.17649 | ||||||||
\(575\) | −34.4726 | −1.43761 | ||||||||
\(576\) | −8.90659 | −0.371108 | ||||||||
\(577\) | 34.4598 | 1.43458 | 0.717290 | − | 0.696775i | \(-0.245382\pi\) | ||||
0.717290 | + | 0.696775i | \(0.245382\pi\) | |||||||
\(578\) | −2.02903 | −0.0843963 | ||||||||
\(579\) | −18.3096 | −0.760922 | ||||||||
\(580\) | −27.2915 | −1.13322 | ||||||||
\(581\) | 5.50789 | 0.228506 | ||||||||
\(582\) | −19.7790 | −0.819867 | ||||||||
\(583\) | 8.26743 | 0.342402 | ||||||||
\(584\) | 2.48214 | 0.102712 | ||||||||
\(585\) | −12.3005 | −0.508563 | ||||||||
\(586\) | −13.0056 | −0.537258 | ||||||||
\(587\) | 28.4278 | 1.17334 | 0.586670 | − | 0.809826i | \(-0.300439\pi\) | ||||
0.586670 | + | 0.809826i | \(0.300439\pi\) | |||||||
\(588\) | 4.77377 | 0.196867 | ||||||||
\(589\) | 0.354104 | 0.0145906 | ||||||||
\(590\) | 101.710 | 4.18735 | ||||||||
\(591\) | 0.950036 | 0.0390793 | ||||||||
\(592\) | −39.7298 | −1.63288 | ||||||||
\(593\) | 32.8256 | 1.34799 | 0.673993 | − | 0.738737i | \(-0.264578\pi\) | ||||
0.673993 | + | 0.738737i | \(0.264578\pi\) | |||||||
\(594\) | 5.03392 | 0.206544 | ||||||||
\(595\) | −13.1952 | −0.540952 | ||||||||
\(596\) | 1.48800 | 0.0609507 | ||||||||
\(597\) | 11.6263 | 0.475831 | ||||||||
\(598\) | −14.3605 | −0.587245 | ||||||||
\(599\) | −12.1815 | −0.497723 | −0.248862 | − | 0.968539i | \(-0.580056\pi\) | ||||
−0.248862 | + | 0.968539i | \(0.580056\pi\) | |||||||
\(600\) | −3.27754 | −0.133805 | ||||||||
\(601\) | −25.9996 | −1.06055 | −0.530273 | − | 0.847827i | \(-0.677911\pi\) | ||||
−0.530273 | + | 0.847827i | \(0.677911\pi\) | |||||||
\(602\) | 66.2234 | 2.69906 | ||||||||
\(603\) | −3.95247 | −0.160957 | ||||||||
\(604\) | −49.6878 | −2.02177 | ||||||||
\(605\) | −21.0141 | −0.854344 | ||||||||
\(606\) | 15.9132 | 0.646429 | ||||||||
\(607\) | −35.1807 | −1.42794 | −0.713971 | − | 0.700175i | \(-0.753105\pi\) | ||||
−0.713971 | + | 0.700175i | \(0.753105\pi\) | |||||||
\(608\) | −13.8627 | −0.562207 | ||||||||
\(609\) | 9.04231 | 0.366413 | ||||||||
\(610\) | −117.288 | −4.74887 | ||||||||
\(611\) | 4.43437 | 0.179395 | ||||||||
\(612\) | 2.11694 | 0.0855723 | ||||||||
\(613\) | 12.5541 | 0.507057 | 0.253529 | − | 0.967328i | \(-0.418409\pi\) | ||||
0.253529 | + | 0.967328i | \(0.418409\pi\) | |||||||
\(614\) | 11.1618 | 0.450452 | ||||||||
\(615\) | 19.8059 | 0.798652 | ||||||||
\(616\) | −1.79089 | −0.0721570 | ||||||||
\(617\) | 46.1072 | 1.85621 | 0.928103 | − | 0.372323i | \(-0.121439\pi\) | ||||
0.928103 | + | 0.372323i | \(0.121439\pi\) | |||||||
\(618\) | 8.59148 | 0.345600 | ||||||||
\(619\) | −28.4276 | −1.14260 | −0.571300 | − | 0.820741i | \(-0.693561\pi\) | ||||
−0.571300 | + | 0.820741i | \(0.693561\pi\) | |||||||
\(620\) | −1.89706 | −0.0761877 | ||||||||
\(621\) | −2.49567 | −0.100148 | ||||||||
\(622\) | 39.6600 | 1.59022 | ||||||||
\(623\) | −50.6959 | −2.03109 | ||||||||
\(624\) | 10.6416 | 0.426006 | ||||||||
\(625\) | 96.7326 | 3.86930 | ||||||||
\(626\) | −33.7819 | −1.35020 | ||||||||
\(627\) | 4.25213 | 0.169814 | ||||||||
\(628\) | 2.11694 | 0.0844752 | ||||||||
\(629\) | 10.5877 | 0.422160 | ||||||||
\(630\) | 26.7735 | 1.06668 | ||||||||
\(631\) | −7.69323 | −0.306263 | −0.153131 | − | 0.988206i | \(-0.548936\pi\) | ||||
−0.153131 | + | 0.988206i | \(0.548936\pi\) | |||||||
\(632\) | 0.875734 | 0.0348348 | ||||||||
\(633\) | 26.4117 | 1.04977 | ||||||||
\(634\) | 3.74981 | 0.148924 | ||||||||
\(635\) | −74.0973 | −2.94046 | ||||||||
\(636\) | −7.05441 | −0.279726 | ||||||||
\(637\) | −6.39509 | −0.253383 | ||||||||
\(638\) | −14.9622 | −0.592360 | ||||||||
\(639\) | 7.14457 | 0.282635 | ||||||||
\(640\) | 8.21934 | 0.324898 | ||||||||
\(641\) | −10.8466 | −0.428417 | −0.214208 | − | 0.976788i | \(-0.568717\pi\) | ||||
−0.214208 | + | 0.976788i | \(0.568717\pi\) | |||||||
\(642\) | 3.74851 | 0.147942 | ||||||||
\(643\) | 21.5341 | 0.849224 | 0.424612 | − | 0.905376i | \(-0.360411\pi\) | ||||
0.424612 | + | 0.905376i | \(0.360411\pi\) | |||||||
\(644\) | 16.0726 | 0.633349 | ||||||||
\(645\) | 46.5332 | 1.83224 | ||||||||
\(646\) | 3.47757 | 0.136823 | ||||||||
\(647\) | 27.6790 | 1.08817 | 0.544086 | − | 0.839029i | \(-0.316876\pi\) | ||||
0.544086 | + | 0.839029i | \(0.316876\pi\) | |||||||
\(648\) | −0.237280 | −0.00932125 | ||||||||
\(649\) | 28.6727 | 1.12550 | ||||||||
\(650\) | 79.4818 | 3.11753 | ||||||||
\(651\) | 0.628539 | 0.0246344 | ||||||||
\(652\) | 28.5874 | 1.11957 | ||||||||
\(653\) | 5.57383 | 0.218121 | 0.109060 | − | 0.994035i | \(-0.465216\pi\) | ||||
0.109060 | + | 0.994035i | \(0.465216\pi\) | |||||||
\(654\) | −36.4648 | −1.42589 | ||||||||
\(655\) | 63.5942 | 2.48483 | ||||||||
\(656\) | −17.1349 | −0.669004 | ||||||||
\(657\) | −10.4608 | −0.408115 | ||||||||
\(658\) | −9.65192 | −0.376271 | ||||||||
\(659\) | 24.5583 | 0.956654 | 0.478327 | − | 0.878182i | \(-0.341243\pi\) | ||||
0.478327 | + | 0.878182i | \(0.341243\pi\) | |||||||
\(660\) | −22.7801 | −0.886715 | ||||||||
\(661\) | −13.1731 | −0.512374 | −0.256187 | − | 0.966627i | \(-0.582466\pi\) | ||||
−0.256187 | + | 0.966627i | \(0.582466\pi\) | |||||||
\(662\) | 4.82915 | 0.187690 | ||||||||
\(663\) | −2.83592 | −0.110138 | ||||||||
\(664\) | 0.429594 | 0.0166715 | ||||||||
\(665\) | 22.6155 | 0.876990 | ||||||||
\(666\) | −21.4828 | −0.832440 | ||||||||
\(667\) | 7.41785 | 0.287220 | ||||||||
\(668\) | 51.5776 | 1.99560 | ||||||||
\(669\) | 24.8083 | 0.959144 | ||||||||
\(670\) | 34.7844 | 1.34384 | ||||||||
\(671\) | −33.0642 | −1.27643 | ||||||||
\(672\) | −24.6064 | −0.949214 | ||||||||
\(673\) | 39.0564 | 1.50551 | 0.752756 | − | 0.658300i | \(-0.228724\pi\) | ||||
0.752756 | + | 0.658300i | \(0.228724\pi\) | |||||||
\(674\) | 35.7715 | 1.37787 | ||||||||
\(675\) | 13.8129 | 0.531660 | ||||||||
\(676\) | −10.4948 | −0.403647 | ||||||||
\(677\) | 3.55016 | 0.136444 | 0.0682220 | − | 0.997670i | \(-0.478267\pi\) | ||||
0.0682220 | + | 0.997670i | \(0.478267\pi\) | |||||||
\(678\) | −21.1520 | −0.812338 | ||||||||
\(679\) | −29.6556 | −1.13808 | ||||||||
\(680\) | −1.02918 | −0.0394671 | ||||||||
\(681\) | 3.66507 | 0.140446 | ||||||||
\(682\) | −1.04004 | −0.0398251 | ||||||||
\(683\) | −19.8106 | −0.758032 | −0.379016 | − | 0.925390i | \(-0.623737\pi\) | ||||
−0.379016 | + | 0.925390i | \(0.623737\pi\) | |||||||
\(684\) | −3.62825 | −0.138730 | ||||||||
\(685\) | −75.7756 | −2.89524 | ||||||||
\(686\) | −29.2894 | −1.11827 | ||||||||
\(687\) | 18.0273 | 0.687786 | ||||||||
\(688\) | −40.2577 | −1.53481 | ||||||||
\(689\) | 9.45031 | 0.360028 | ||||||||
\(690\) | 21.9636 | 0.836140 | ||||||||
\(691\) | −7.72246 | −0.293776 | −0.146888 | − | 0.989153i | \(-0.546926\pi\) | ||||
−0.146888 | + | 0.989153i | \(0.546926\pi\) | |||||||
\(692\) | 5.83690 | 0.221886 | ||||||||
\(693\) | 7.54758 | 0.286709 | ||||||||
\(694\) | −42.5644 | −1.61572 | ||||||||
\(695\) | −53.4293 | −2.02669 | ||||||||
\(696\) | 0.705264 | 0.0267330 | ||||||||
\(697\) | 4.56632 | 0.172962 | ||||||||
\(698\) | −22.8814 | −0.866075 | ||||||||
\(699\) | 4.05523 | 0.153383 | ||||||||
\(700\) | −88.9578 | −3.36229 | ||||||||
\(701\) | −39.3642 | −1.48677 | −0.743383 | − | 0.668866i | \(-0.766780\pi\) | ||||
−0.743383 | + | 0.668866i | \(0.766780\pi\) | |||||||
\(702\) | 5.75416 | 0.217177 | ||||||||
\(703\) | −18.1464 | −0.684405 | ||||||||
\(704\) | 22.0968 | 0.832806 | ||||||||
\(705\) | −6.78212 | −0.255430 | ||||||||
\(706\) | −5.46824 | −0.205800 | ||||||||
\(707\) | 23.8594 | 0.897324 | ||||||||
\(708\) | −24.4657 | −0.919479 | ||||||||
\(709\) | −36.6393 | −1.37602 | −0.688009 | − | 0.725702i | \(-0.741515\pi\) | ||||
−0.688009 | + | 0.725702i | \(0.741515\pi\) | |||||||
\(710\) | −62.8770 | −2.35973 | ||||||||
\(711\) | −3.69072 | −0.138413 | ||||||||
\(712\) | −3.95408 | −0.148185 | ||||||||
\(713\) | 0.515621 | 0.0193102 | ||||||||
\(714\) | 6.17272 | 0.231008 | ||||||||
\(715\) | 30.5170 | 1.14127 | ||||||||
\(716\) | 44.7979 | 1.67417 | ||||||||
\(717\) | −19.7857 | −0.738912 | ||||||||
\(718\) | 5.08077 | 0.189613 | ||||||||
\(719\) | 11.3012 | 0.421464 | 0.210732 | − | 0.977544i | \(-0.432415\pi\) | ||||
0.210732 | + | 0.977544i | \(0.432415\pi\) | |||||||
\(720\) | −16.2758 | −0.606563 | ||||||||
\(721\) | 12.8816 | 0.479735 | ||||||||
\(722\) | 32.5912 | 1.21292 | ||||||||
\(723\) | 17.9625 | 0.668032 | ||||||||
\(724\) | 50.9651 | 1.89410 | ||||||||
\(725\) | −41.0560 | −1.52478 | ||||||||
\(726\) | 9.83036 | 0.364839 | ||||||||
\(727\) | 15.1101 | 0.560403 | 0.280202 | − | 0.959941i | \(-0.409599\pi\) | ||||
0.280202 | + | 0.959941i | \(0.409599\pi\) | |||||||
\(728\) | −2.04713 | −0.0758716 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 92.0621 | 3.40737 | ||||||||
\(731\) | 10.7284 | 0.396804 | ||||||||
\(732\) | 28.2129 | 1.04278 | ||||||||
\(733\) | 15.5737 | 0.575228 | 0.287614 | − | 0.957746i | \(-0.407138\pi\) | ||||
0.287614 | + | 0.957746i | \(0.407138\pi\) | |||||||
\(734\) | 26.2287 | 0.968117 | ||||||||
\(735\) | 9.78093 | 0.360775 | ||||||||
\(736\) | −20.1859 | −0.744061 | ||||||||
\(737\) | 9.80589 | 0.361205 | ||||||||
\(738\) | −9.26519 | −0.341056 | ||||||||
\(739\) | −10.7846 | −0.396717 | −0.198358 | − | 0.980130i | \(-0.563561\pi\) | ||||
−0.198358 | + | 0.980130i | \(0.563561\pi\) | |||||||
\(740\) | 97.2165 | 3.57375 | ||||||||
\(741\) | 4.86052 | 0.178556 | ||||||||
\(742\) | −20.5697 | −0.755138 | ||||||||
\(743\) | 8.16216 | 0.299440 | 0.149720 | − | 0.988728i | \(-0.452163\pi\) | ||||
0.149720 | + | 0.988728i | \(0.452163\pi\) | |||||||
\(744\) | 0.0490235 | 0.00179729 | ||||||||
\(745\) | 3.04874 | 0.111697 | ||||||||
\(746\) | 36.7830 | 1.34672 | ||||||||
\(747\) | −1.81049 | −0.0662424 | ||||||||
\(748\) | −5.25204 | −0.192034 | ||||||||
\(749\) | 5.62031 | 0.205362 | ||||||||
\(750\) | −77.5598 | −2.83208 | ||||||||
\(751\) | −24.4452 | −0.892016 | −0.446008 | − | 0.895029i | \(-0.647155\pi\) | ||||
−0.446008 | + | 0.895029i | \(0.647155\pi\) | |||||||
\(752\) | 5.86747 | 0.213965 | ||||||||
\(753\) | 7.45092 | 0.271527 | ||||||||
\(754\) | −17.1030 | −0.622854 | ||||||||
\(755\) | −101.805 | −3.70506 | ||||||||
\(756\) | −6.44018 | −0.234227 | ||||||||
\(757\) | 5.15457 | 0.187346 | 0.0936731 | − | 0.995603i | \(-0.470139\pi\) | ||||
0.0936731 | + | 0.995603i | \(0.470139\pi\) | |||||||
\(758\) | −58.5545 | −2.12679 | ||||||||
\(759\) | 6.19165 | 0.224743 | ||||||||
\(760\) | 1.76392 | 0.0639840 | ||||||||
\(761\) | 5.60100 | 0.203036 | 0.101518 | − | 0.994834i | \(-0.467630\pi\) | ||||
0.101518 | + | 0.994834i | \(0.467630\pi\) | |||||||
\(762\) | 34.6626 | 1.25569 | ||||||||
\(763\) | −54.6733 | −1.97931 | ||||||||
\(764\) | 25.5342 | 0.923793 | ||||||||
\(765\) | 4.33739 | 0.156819 | ||||||||
\(766\) | −33.1106 | −1.19633 | ||||||||
\(767\) | 32.7751 | 1.18344 | ||||||||
\(768\) | 13.9682 | 0.504034 | ||||||||
\(769\) | −34.1015 | −1.22973 | −0.614866 | − | 0.788631i | \(-0.710790\pi\) | ||||
−0.614866 | + | 0.788631i | \(0.710790\pi\) | |||||||
\(770\) | −66.4237 | −2.39375 | ||||||||
\(771\) | 21.8356 | 0.786389 | ||||||||
\(772\) | −38.7604 | −1.39502 | ||||||||
\(773\) | 38.1150 | 1.37090 | 0.685451 | − | 0.728118i | \(-0.259605\pi\) | ||||
0.685451 | + | 0.728118i | \(0.259605\pi\) | |||||||
\(774\) | −21.7682 | −0.782442 | ||||||||
\(775\) | −2.85384 | −0.102513 | ||||||||
\(776\) | −2.31302 | −0.0830325 | ||||||||
\(777\) | −32.2101 | −1.15553 | ||||||||
\(778\) | 34.3231 | 1.23054 | ||||||||
\(779\) | −7.82627 | −0.280405 | ||||||||
\(780\) | −26.0395 | −0.932362 | ||||||||
\(781\) | −17.7254 | −0.634263 | ||||||||
\(782\) | 5.06378 | 0.181081 | ||||||||
\(783\) | −2.97228 | −0.106221 | ||||||||
\(784\) | −8.46186 | −0.302209 | ||||||||
\(785\) | 4.33739 | 0.154808 | ||||||||
\(786\) | −29.7493 | −1.06112 | ||||||||
\(787\) | 14.1501 | 0.504396 | 0.252198 | − | 0.967676i | \(-0.418847\pi\) | ||||
0.252198 | + | 0.967676i | \(0.418847\pi\) | |||||||
\(788\) | 2.01117 | 0.0716451 | ||||||||
\(789\) | −9.79833 | −0.348830 | ||||||||
\(790\) | 32.4808 | 1.15561 | ||||||||
\(791\) | −31.7141 | −1.12762 | ||||||||
\(792\) | 0.588681 | 0.0209179 | ||||||||
\(793\) | −37.7950 | −1.34214 | ||||||||
\(794\) | −64.2256 | −2.27928 | ||||||||
\(795\) | −14.4537 | −0.512621 | ||||||||
\(796\) | 24.6121 | 0.872354 | ||||||||
\(797\) | 37.0314 | 1.31172 | 0.655860 | − | 0.754882i | \(-0.272306\pi\) | ||||
0.655860 | + | 0.754882i | \(0.272306\pi\) | |||||||
\(798\) | −10.5795 | −0.374510 | ||||||||
\(799\) | −1.56364 | −0.0553177 | ||||||||
\(800\) | 111.724 | 3.95004 | ||||||||
\(801\) | 16.6642 | 0.588800 | ||||||||
\(802\) | 5.75592 | 0.203249 | ||||||||
\(803\) | 25.9528 | 0.915854 | ||||||||
\(804\) | −8.36715 | −0.295087 | ||||||||
\(805\) | 32.9310 | 1.16067 | ||||||||
\(806\) | −1.18884 | −0.0418753 | ||||||||
\(807\) | 29.0279 | 1.02183 | ||||||||
\(808\) | 1.86094 | 0.0654675 | ||||||||
\(809\) | −18.3228 | −0.644195 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(810\) | −8.80067 | −0.309224 | ||||||||
\(811\) | −19.6896 | −0.691397 | −0.345698 | − | 0.938346i | \(-0.612358\pi\) | ||||
−0.345698 | + | 0.938346i | \(0.612358\pi\) | |||||||
\(812\) | 19.1420 | 0.671754 | ||||||||
\(813\) | −13.3293 | −0.467479 | ||||||||
\(814\) | 53.2977 | 1.86808 | ||||||||
\(815\) | 58.5725 | 2.05170 | ||||||||
\(816\) | −3.75244 | −0.131362 | ||||||||
\(817\) | −18.3875 | −0.643298 | ||||||||
\(818\) | −13.7380 | −0.480340 | ||||||||
\(819\) | 8.62747 | 0.301468 | ||||||||
\(820\) | 41.9280 | 1.46419 | ||||||||
\(821\) | −10.4932 | −0.366216 | −0.183108 | − | 0.983093i | \(-0.558616\pi\) | ||||
−0.183108 | + | 0.983093i | \(0.558616\pi\) | |||||||
\(822\) | 35.4477 | 1.23638 | ||||||||
\(823\) | −5.17633 | −0.180436 | −0.0902178 | − | 0.995922i | \(-0.528756\pi\) | ||||
−0.0902178 | + | 0.995922i | \(0.528756\pi\) | |||||||
\(824\) | 1.00471 | 0.0350008 | ||||||||
\(825\) | −34.2693 | −1.19310 | ||||||||
\(826\) | −71.3388 | −2.48219 | ||||||||
\(827\) | 33.2105 | 1.15484 | 0.577421 | − | 0.816447i | \(-0.304059\pi\) | ||||
0.577421 | + | 0.816447i | \(0.304059\pi\) | |||||||
\(828\) | −5.28320 | −0.183604 | ||||||||
\(829\) | −19.1621 | −0.665528 | −0.332764 | − | 0.943010i | \(-0.607981\pi\) | ||||
−0.332764 | + | 0.943010i | \(0.607981\pi\) | |||||||
\(830\) | 15.9335 | 0.553061 | ||||||||
\(831\) | 25.2409 | 0.875596 | ||||||||
\(832\) | 25.2584 | 0.875678 | ||||||||
\(833\) | 2.25503 | 0.0781321 | ||||||||
\(834\) | 24.9941 | 0.865477 | ||||||||
\(835\) | 105.677 | 3.65710 | ||||||||
\(836\) | 9.00152 | 0.311324 | ||||||||
\(837\) | −0.206606 | −0.00714135 | ||||||||
\(838\) | −35.8594 | −1.23874 | ||||||||
\(839\) | 22.2975 | 0.769794 | 0.384897 | − | 0.922960i | \(-0.374237\pi\) | ||||
0.384897 | + | 0.922960i | \(0.374237\pi\) | |||||||
\(840\) | 3.13097 | 0.108029 | ||||||||
\(841\) | −20.1655 | −0.695363 | ||||||||
\(842\) | 69.9355 | 2.41014 | ||||||||
\(843\) | −24.6239 | −0.848093 | ||||||||
\(844\) | 55.9120 | 1.92457 | ||||||||
\(845\) | −21.5028 | −0.739718 | ||||||||
\(846\) | 3.17267 | 0.109079 | ||||||||
\(847\) | 14.7391 | 0.506441 | ||||||||
\(848\) | 12.5045 | 0.429405 | ||||||||
\(849\) | −6.67364 | −0.229039 | ||||||||
\(850\) | −28.0268 | −0.961311 | ||||||||
\(851\) | −26.4235 | −0.905786 | ||||||||
\(852\) | 15.1247 | 0.518162 | ||||||||
\(853\) | 24.8370 | 0.850402 | 0.425201 | − | 0.905099i | \(-0.360203\pi\) | ||||
0.425201 | + | 0.905099i | \(0.360203\pi\) | |||||||
\(854\) | 82.2651 | 2.81505 | ||||||||
\(855\) | −7.43390 | −0.254234 | ||||||||
\(856\) | 0.438362 | 0.0149829 | ||||||||
\(857\) | 22.1234 | 0.755721 | 0.377861 | − | 0.925863i | \(-0.376660\pi\) | ||||
0.377861 | + | 0.925863i | \(0.376660\pi\) | |||||||
\(858\) | −14.2758 | −0.487368 | ||||||||
\(859\) | −27.7242 | −0.945936 | −0.472968 | − | 0.881080i | \(-0.656817\pi\) | ||||
−0.472968 | + | 0.881080i | \(0.656817\pi\) | |||||||
\(860\) | 98.5082 | 3.35910 | ||||||||
\(861\) | −13.8917 | −0.473428 | ||||||||
\(862\) | 0.792671 | 0.0269985 | ||||||||
\(863\) | −27.5512 | −0.937852 | −0.468926 | − | 0.883237i | \(-0.655359\pi\) | ||||
−0.468926 | + | 0.883237i | \(0.655359\pi\) | |||||||
\(864\) | 8.08835 | 0.275171 | ||||||||
\(865\) | 11.9592 | 0.406624 | ||||||||
\(866\) | 77.1653 | 2.62218 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 1.33058 | 0.0451628 | ||||||||
\(869\) | 9.15650 | 0.310613 | ||||||||
\(870\) | 26.1581 | 0.886842 | ||||||||
\(871\) | 11.2089 | 0.379799 | ||||||||
\(872\) | −4.26430 | −0.144407 | ||||||||
\(873\) | 9.74805 | 0.329921 | ||||||||
\(874\) | −8.67887 | −0.293567 | ||||||||
\(875\) | −116.289 | −3.93128 | ||||||||
\(876\) | −22.1449 | −0.748208 | ||||||||
\(877\) | 6.48081 | 0.218842 | 0.109421 | − | 0.993996i | \(-0.465100\pi\) | ||||
0.109421 | + | 0.993996i | \(0.465100\pi\) | |||||||
\(878\) | 11.3809 | 0.384086 | ||||||||
\(879\) | 6.40980 | 0.216197 | ||||||||
\(880\) | 40.3795 | 1.36119 | ||||||||
\(881\) | 21.9520 | 0.739581 | 0.369791 | − | 0.929115i | \(-0.379429\pi\) | ||||
0.369791 | + | 0.929115i | \(0.379429\pi\) | |||||||
\(882\) | −4.57551 | −0.154065 | ||||||||
\(883\) | 2.27900 | 0.0766944 | 0.0383472 | − | 0.999264i | \(-0.487791\pi\) | ||||
0.0383472 | + | 0.999264i | \(0.487791\pi\) | |||||||
\(884\) | −6.00349 | −0.201919 | ||||||||
\(885\) | −50.1277 | −1.68502 | ||||||||
\(886\) | 0.729935 | 0.0245227 | ||||||||
\(887\) | 30.2297 | 1.01502 | 0.507508 | − | 0.861647i | \(-0.330567\pi\) | ||||
0.507508 | + | 0.861647i | \(0.330567\pi\) | |||||||
\(888\) | −2.51226 | −0.0843058 | ||||||||
\(889\) | 51.9712 | 1.74306 | ||||||||
\(890\) | −146.656 | −4.91592 | ||||||||
\(891\) | −2.48095 | −0.0831151 | ||||||||
\(892\) | 52.5178 | 1.75842 | ||||||||
\(893\) | 2.67994 | 0.0896809 | ||||||||
\(894\) | −1.42620 | −0.0476992 | ||||||||
\(895\) | 91.7860 | 3.06807 | ||||||||
\(896\) | −5.76497 | −0.192594 | ||||||||
\(897\) | 7.07754 | 0.236312 | ||||||||
\(898\) | 31.5538 | 1.05297 | ||||||||
\(899\) | 0.614092 | 0.0204811 | ||||||||
\(900\) | 29.2412 | 0.974707 | ||||||||
\(901\) | −3.33236 | −0.111017 | ||||||||
\(902\) | 22.9865 | 0.765367 | ||||||||
\(903\) | −32.6380 | −1.08613 | ||||||||
\(904\) | −2.47358 | −0.0822700 | ||||||||
\(905\) | 104.422 | 3.47110 | ||||||||
\(906\) | 47.6242 | 1.58221 | ||||||||
\(907\) | 36.3444 | 1.20680 | 0.603398 | − | 0.797440i | \(-0.293813\pi\) | ||||
0.603398 | + | 0.797440i | \(0.293813\pi\) | |||||||
\(908\) | 7.75874 | 0.257483 | ||||||||
\(909\) | −7.84278 | −0.260129 | ||||||||
\(910\) | −75.9275 | −2.51697 | ||||||||
\(911\) | 55.9184 | 1.85266 | 0.926329 | − | 0.376716i | \(-0.122947\pi\) | ||||
0.926329 | + | 0.376716i | \(0.122947\pi\) | |||||||
\(912\) | 6.43134 | 0.212963 | ||||||||
\(913\) | 4.49174 | 0.148655 | ||||||||
\(914\) | 39.4399 | 1.30456 | ||||||||
\(915\) | 57.8053 | 1.91098 | ||||||||
\(916\) | 38.1628 | 1.26094 | ||||||||
\(917\) | −44.6045 | −1.47297 | ||||||||
\(918\) | −2.02903 | −0.0669678 | ||||||||
\(919\) | −14.7142 | −0.485376 | −0.242688 | − | 0.970104i | \(-0.578029\pi\) | ||||
−0.242688 | + | 0.970104i | \(0.578029\pi\) | |||||||
\(920\) | 2.56849 | 0.0846805 | ||||||||
\(921\) | −5.50105 | −0.181266 | ||||||||
\(922\) | −32.4583 | −1.06896 | ||||||||
\(923\) | −20.2615 | −0.666914 | ||||||||
\(924\) | 15.9778 | 0.525631 | ||||||||
\(925\) | 146.248 | 4.80859 | ||||||||
\(926\) | 55.7557 | 1.83225 | ||||||||
\(927\) | −4.23429 | −0.139072 | ||||||||
\(928\) | −24.0409 | −0.789180 | ||||||||
\(929\) | 29.2848 | 0.960804 | 0.480402 | − | 0.877048i | \(-0.340491\pi\) | ||||
0.480402 | + | 0.877048i | \(0.340491\pi\) | |||||||
\(930\) | 1.81827 | 0.0596235 | ||||||||
\(931\) | −3.86492 | −0.126668 | ||||||||
\(932\) | 8.58469 | 0.281201 | ||||||||
\(933\) | −19.5463 | −0.639918 | ||||||||
\(934\) | 69.2737 | 2.26670 | ||||||||
\(935\) | −10.7609 | −0.351918 | ||||||||
\(936\) | 0.672908 | 0.0219947 | ||||||||
\(937\) | 50.2976 | 1.64315 | 0.821576 | − | 0.570099i | \(-0.193095\pi\) | ||||
0.821576 | + | 0.570099i | \(0.193095\pi\) | |||||||
\(938\) | −24.3975 | −0.796605 | ||||||||
\(939\) | 16.6493 | 0.543330 | ||||||||
\(940\) | −14.3574 | −0.468286 | ||||||||
\(941\) | −54.1344 | −1.76473 | −0.882365 | − | 0.470566i | \(-0.844050\pi\) | ||||
−0.882365 | + | 0.470566i | \(0.844050\pi\) | |||||||
\(942\) | −2.02903 | −0.0661092 | ||||||||
\(943\) | −11.3961 | −0.371107 | ||||||||
\(944\) | 43.3673 | 1.41149 | ||||||||
\(945\) | −13.1952 | −0.429241 | ||||||||
\(946\) | 54.0059 | 1.75588 | ||||||||
\(947\) | −38.6745 | −1.25675 | −0.628377 | − | 0.777909i | \(-0.716280\pi\) | ||||
−0.628377 | + | 0.777909i | \(0.716280\pi\) | |||||||
\(948\) | −7.81304 | −0.253756 | ||||||||
\(949\) | 29.6660 | 0.963001 | ||||||||
\(950\) | 48.0354 | 1.55848 | ||||||||
\(951\) | −1.84809 | −0.0599283 | ||||||||
\(952\) | 0.721856 | 0.0233955 | ||||||||
\(953\) | 20.8108 | 0.674128 | 0.337064 | − | 0.941482i | \(-0.390566\pi\) | ||||
0.337064 | + | 0.941482i | \(0.390566\pi\) | |||||||
\(954\) | 6.76144 | 0.218910 | ||||||||
\(955\) | 52.3167 | 1.69293 | ||||||||
\(956\) | −41.8853 | −1.35467 | ||||||||
\(957\) | 7.37410 | 0.238371 | ||||||||
\(958\) | −51.5398 | −1.66517 | ||||||||
\(959\) | 53.1484 | 1.71625 | ||||||||
\(960\) | −38.6314 | −1.24682 | ||||||||
\(961\) | −30.9573 | −0.998623 | ||||||||
\(962\) | 60.9234 | 1.96425 | ||||||||
\(963\) | −1.84744 | −0.0595331 | ||||||||
\(964\) | 38.0256 | 1.22472 | ||||||||
\(965\) | −79.4159 | −2.55649 | ||||||||
\(966\) | −15.4051 | −0.495650 | ||||||||
\(967\) | 22.1259 | 0.711520 | 0.355760 | − | 0.934577i | \(-0.384222\pi\) | ||||
0.355760 | + | 0.934577i | \(0.384222\pi\) | |||||||
\(968\) | 1.14959 | 0.0369493 | ||||||||
\(969\) | −1.71391 | −0.0550587 | ||||||||
\(970\) | −85.7893 | −2.75453 | ||||||||
\(971\) | 36.4603 | 1.17007 | 0.585033 | − | 0.811009i | \(-0.301081\pi\) | ||||
0.585033 | + | 0.811009i | \(0.301081\pi\) | |||||||
\(972\) | 2.11694 | 0.0679010 | ||||||||
\(973\) | 37.4748 | 1.20139 | ||||||||
\(974\) | −73.8819 | −2.36733 | ||||||||
\(975\) | −39.1724 | −1.25452 | ||||||||
\(976\) | −50.0095 | −1.60077 | ||||||||
\(977\) | 31.2840 | 1.00086 | 0.500432 | − | 0.865776i | \(-0.333175\pi\) | ||||
0.500432 | + | 0.865776i | \(0.333175\pi\) | |||||||
\(978\) | −27.4001 | −0.876160 | ||||||||
\(979\) | −41.3431 | −1.32133 | ||||||||
\(980\) | 20.7057 | 0.661419 | ||||||||
\(981\) | 17.9716 | 0.573789 | ||||||||
\(982\) | −44.7183 | −1.42702 | ||||||||
\(983\) | −35.9301 | −1.14599 | −0.572996 | − | 0.819558i | \(-0.694219\pi\) | ||||
−0.572996 | + | 0.819558i | \(0.694219\pi\) | |||||||
\(984\) | −1.08350 | −0.0345407 | ||||||||
\(985\) | 4.12068 | 0.131296 | ||||||||
\(986\) | 6.03084 | 0.192061 | ||||||||
\(987\) | 4.75692 | 0.151415 | ||||||||
\(988\) | 10.2894 | 0.327351 | ||||||||
\(989\) | −26.7746 | −0.851382 | ||||||||
\(990\) | 21.8341 | 0.693932 | ||||||||
\(991\) | −8.39164 | −0.266569 | −0.133285 | − | 0.991078i | \(-0.542552\pi\) | ||||
−0.133285 | + | 0.991078i | \(0.542552\pi\) | |||||||
\(992\) | −1.67110 | −0.0530576 | ||||||||
\(993\) | −2.38003 | −0.0755281 | ||||||||
\(994\) | 44.1014 | 1.39881 | ||||||||
\(995\) | 50.4276 | 1.59866 | ||||||||
\(996\) | −3.83271 | −0.121444 | ||||||||
\(997\) | 25.7281 | 0.814818 | 0.407409 | − | 0.913246i | \(-0.366432\pi\) | ||||
0.407409 | + | 0.913246i | \(0.366432\pi\) | |||||||
\(998\) | −62.3640 | −1.97410 | ||||||||
\(999\) | 10.5877 | 0.334981 |
(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 | 8007.2.a.i.1.11 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.i.1.11 | ✓ | 63 | 1.1 | even | 1 | trivial |