Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(79\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25482 | −1.59440 | −0.797198 | − | 0.603718i | \(-0.793685\pi\) | ||||
−0.797198 | + | 0.603718i | \(0.793685\pi\) | |||||||
\(3\) | −0.982243 | −0.567098 | −0.283549 | − | 0.958958i | \(-0.591512\pi\) | ||||
−0.283549 | + | 0.958958i | \(0.591512\pi\) | |||||||
\(4\) | 3.08420 | 1.54210 | ||||||||
\(5\) | 2.20296 | 0.985195 | 0.492598 | − | 0.870257i | \(-0.336047\pi\) | ||||
0.492598 | + | 0.870257i | \(0.336047\pi\) | |||||||
\(6\) | 2.21478 | 0.904179 | ||||||||
\(7\) | 0.164703 | 0.0622519 | 0.0311260 | − | 0.999515i | \(-0.490091\pi\) | ||||
0.0311260 | + | 0.999515i | \(0.490091\pi\) | |||||||
\(8\) | −2.44467 | −0.864320 | ||||||||
\(9\) | −2.03520 | −0.678400 | ||||||||
\(10\) | −4.96728 | −1.57079 | ||||||||
\(11\) | −1.46838 | −0.442734 | −0.221367 | − | 0.975191i | \(-0.571052\pi\) | ||||
−0.221367 | + | 0.975191i | \(0.571052\pi\) | |||||||
\(12\) | −3.02943 | −0.874521 | ||||||||
\(13\) | −5.51963 | −1.53087 | −0.765435 | − | 0.643513i | \(-0.777476\pi\) | ||||
−0.765435 | + | 0.643513i | \(0.777476\pi\) | |||||||
\(14\) | −0.371375 | −0.0992542 | ||||||||
\(15\) | −2.16385 | −0.558703 | ||||||||
\(16\) | −0.656123 | −0.164031 | ||||||||
\(17\) | −5.86965 | −1.42360 | −0.711800 | − | 0.702383i | \(-0.752120\pi\) | ||||
−0.711800 | + | 0.702383i | \(0.752120\pi\) | |||||||
\(18\) | 4.58900 | 1.08164 | ||||||||
\(19\) | 2.55171 | 0.585402 | 0.292701 | − | 0.956204i | \(-0.405446\pi\) | ||||
0.292701 | + | 0.956204i | \(0.405446\pi\) | |||||||
\(20\) | 6.79437 | 1.51927 | ||||||||
\(21\) | −0.161778 | −0.0353029 | ||||||||
\(22\) | 3.31093 | 0.705893 | ||||||||
\(23\) | 4.06900 | 0.848446 | 0.424223 | − | 0.905558i | \(-0.360547\pi\) | ||||
0.424223 | + | 0.905558i | \(0.360547\pi\) | |||||||
\(24\) | 2.40126 | 0.490154 | ||||||||
\(25\) | −0.146950 | −0.0293899 | ||||||||
\(26\) | 12.4458 | 2.44081 | ||||||||
\(27\) | 4.94579 | 0.951817 | ||||||||
\(28\) | 0.507977 | 0.0959986 | ||||||||
\(29\) | 5.77836 | 1.07301 | 0.536507 | − | 0.843896i | \(-0.319743\pi\) | ||||
0.536507 | + | 0.843896i | \(0.319743\pi\) | |||||||
\(30\) | 4.87908 | 0.890793 | ||||||||
\(31\) | 7.63079 | 1.37053 | 0.685265 | − | 0.728294i | \(-0.259686\pi\) | ||||
0.685265 | + | 0.728294i | \(0.259686\pi\) | |||||||
\(32\) | 6.36877 | 1.12585 | ||||||||
\(33\) | 1.44231 | 0.251074 | ||||||||
\(34\) | 13.2350 | 2.26978 | ||||||||
\(35\) | 0.362835 | 0.0613303 | ||||||||
\(36\) | −6.27695 | −1.04616 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | −5.75364 | −0.933363 | ||||||||
\(39\) | 5.42162 | 0.868154 | ||||||||
\(40\) | −5.38551 | −0.851524 | ||||||||
\(41\) | 7.80952 | 1.21964 | 0.609821 | − | 0.792539i | \(-0.291241\pi\) | ||||
0.609821 | + | 0.792539i | \(0.291241\pi\) | |||||||
\(42\) | 0.364781 | 0.0562869 | ||||||||
\(43\) | 8.43068 | 1.28567 | 0.642833 | − | 0.766006i | \(-0.277759\pi\) | ||||
0.642833 | + | 0.766006i | \(0.277759\pi\) | |||||||
\(44\) | −4.52878 | −0.682739 | ||||||||
\(45\) | −4.48347 | −0.668356 | ||||||||
\(46\) | −9.17485 | −1.35276 | ||||||||
\(47\) | −0.369843 | −0.0539472 | −0.0269736 | − | 0.999636i | \(-0.508587\pi\) | ||||
−0.0269736 | + | 0.999636i | \(0.508587\pi\) | |||||||
\(48\) | 0.644472 | 0.0930216 | ||||||||
\(49\) | −6.97287 | −0.996125 | ||||||||
\(50\) | 0.331344 | 0.0468592 | ||||||||
\(51\) | 5.76542 | 0.807321 | ||||||||
\(52\) | −17.0236 | −2.36075 | ||||||||
\(53\) | −8.21907 | −1.12898 | −0.564488 | − | 0.825441i | \(-0.690926\pi\) | ||||
−0.564488 | + | 0.825441i | \(0.690926\pi\) | |||||||
\(54\) | −11.1518 | −1.51757 | ||||||||
\(55\) | −3.23479 | −0.436180 | ||||||||
\(56\) | −0.402644 | −0.0538055 | ||||||||
\(57\) | −2.50640 | −0.331981 | ||||||||
\(58\) | −13.0291 | −1.71081 | ||||||||
\(59\) | 9.69520 | 1.26221 | 0.631104 | − | 0.775698i | \(-0.282602\pi\) | ||||
0.631104 | + | 0.775698i | \(0.282602\pi\) | |||||||
\(60\) | −6.67373 | −0.861574 | ||||||||
\(61\) | 3.52752 | 0.451653 | 0.225826 | − | 0.974168i | \(-0.427492\pi\) | ||||
0.225826 | + | 0.974168i | \(0.427492\pi\) | |||||||
\(62\) | −17.2060 | −2.18517 | ||||||||
\(63\) | −0.335203 | −0.0422317 | ||||||||
\(64\) | −13.0482 | −1.63102 | ||||||||
\(65\) | −12.1595 | −1.50821 | ||||||||
\(66\) | −3.25214 | −0.400311 | ||||||||
\(67\) | 3.90371 | 0.476914 | 0.238457 | − | 0.971153i | \(-0.423358\pi\) | ||||
0.238457 | + | 0.971153i | \(0.423358\pi\) | |||||||
\(68\) | −18.1032 | −2.19533 | ||||||||
\(69\) | −3.99675 | −0.481152 | ||||||||
\(70\) | −0.818126 | −0.0977848 | ||||||||
\(71\) | −5.46321 | −0.648364 | −0.324182 | − | 0.945995i | \(-0.605089\pi\) | ||||
−0.324182 | + | 0.945995i | \(0.605089\pi\) | |||||||
\(72\) | 4.97538 | 0.586354 | ||||||||
\(73\) | 4.24726 | 0.497104 | 0.248552 | − | 0.968618i | \(-0.420045\pi\) | ||||
0.248552 | + | 0.968618i | \(0.420045\pi\) | |||||||
\(74\) | 2.25482 | 0.262117 | ||||||||
\(75\) | 0.144340 | 0.0166670 | ||||||||
\(76\) | 7.86998 | 0.902748 | ||||||||
\(77\) | −0.241847 | −0.0275610 | ||||||||
\(78\) | −12.2248 | −1.38418 | ||||||||
\(79\) | 2.31589 | 0.260558 | 0.130279 | − | 0.991477i | \(-0.458413\pi\) | ||||
0.130279 | + | 0.991477i | \(0.458413\pi\) | |||||||
\(80\) | −1.44542 | −0.161602 | ||||||||
\(81\) | 1.24763 | 0.138626 | ||||||||
\(82\) | −17.6090 | −1.94459 | ||||||||
\(83\) | −7.50362 | −0.823629 | −0.411814 | − | 0.911268i | \(-0.635105\pi\) | ||||
−0.411814 | + | 0.911268i | \(0.635105\pi\) | |||||||
\(84\) | −0.498957 | −0.0544406 | ||||||||
\(85\) | −12.9306 | −1.40252 | ||||||||
\(86\) | −19.0096 | −2.04986 | ||||||||
\(87\) | −5.67575 | −0.608504 | ||||||||
\(88\) | 3.58970 | 0.382664 | ||||||||
\(89\) | −1.80665 | −0.191504 | −0.0957522 | − | 0.995405i | \(-0.530526\pi\) | ||||
−0.0957522 | + | 0.995405i | \(0.530526\pi\) | |||||||
\(90\) | 10.1094 | 1.06562 | ||||||||
\(91\) | −0.909100 | −0.0952996 | ||||||||
\(92\) | 12.5496 | 1.30839 | ||||||||
\(93\) | −7.49529 | −0.777225 | ||||||||
\(94\) | 0.833929 | 0.0860132 | ||||||||
\(95\) | 5.62133 | 0.576736 | ||||||||
\(96\) | −6.25568 | −0.638467 | ||||||||
\(97\) | 5.91157 | 0.600229 | 0.300114 | − | 0.953903i | \(-0.402975\pi\) | ||||
0.300114 | + | 0.953903i | \(0.402975\pi\) | |||||||
\(98\) | 15.7225 | 1.58822 | ||||||||
\(99\) | 2.98845 | 0.300351 | ||||||||
\(100\) | −0.453221 | −0.0453221 | ||||||||
\(101\) | −2.83089 | −0.281684 | −0.140842 | − | 0.990032i | \(-0.544981\pi\) | ||||
−0.140842 | + | 0.990032i | \(0.544981\pi\) | |||||||
\(102\) | −13.0000 | −1.28719 | ||||||||
\(103\) | −8.84765 | −0.871785 | −0.435893 | − | 0.899999i | \(-0.643567\pi\) | ||||
−0.435893 | + | 0.899999i | \(0.643567\pi\) | |||||||
\(104\) | 13.4936 | 1.32316 | ||||||||
\(105\) | −0.356392 | −0.0347803 | ||||||||
\(106\) | 18.5325 | 1.80004 | ||||||||
\(107\) | −8.73896 | −0.844827 | −0.422413 | − | 0.906403i | \(-0.638817\pi\) | ||||
−0.422413 | + | 0.906403i | \(0.638817\pi\) | |||||||
\(108\) | 15.2538 | 1.46780 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 7.29387 | 0.695443 | ||||||||
\(111\) | 0.982243 | 0.0932304 | ||||||||
\(112\) | −0.108065 | −0.0102112 | ||||||||
\(113\) | 1.52099 | 0.143083 | 0.0715413 | − | 0.997438i | \(-0.477208\pi\) | ||||
0.0715413 | + | 0.997438i | \(0.477208\pi\) | |||||||
\(114\) | 5.65147 | 0.529309 | ||||||||
\(115\) | 8.96387 | 0.835885 | ||||||||
\(116\) | 17.8216 | 1.65469 | ||||||||
\(117\) | 11.2335 | 1.03854 | ||||||||
\(118\) | −21.8609 | −2.01246 | ||||||||
\(119\) | −0.966749 | −0.0886218 | ||||||||
\(120\) | 5.28988 | 0.482898 | ||||||||
\(121\) | −8.84385 | −0.803987 | ||||||||
\(122\) | −7.95391 | −0.720113 | ||||||||
\(123\) | −7.67085 | −0.691657 | ||||||||
\(124\) | 23.5349 | 2.11349 | ||||||||
\(125\) | −11.3385 | −1.01415 | ||||||||
\(126\) | 0.755822 | 0.0673340 | ||||||||
\(127\) | −5.06517 | −0.449461 | −0.224731 | − | 0.974421i | \(-0.572150\pi\) | ||||
−0.224731 | + | 0.974421i | \(0.572150\pi\) | |||||||
\(128\) | 16.6837 | 1.47464 | ||||||||
\(129\) | −8.28098 | −0.729099 | ||||||||
\(130\) | 27.4175 | 2.40468 | ||||||||
\(131\) | 9.21320 | 0.804961 | 0.402480 | − | 0.915429i | \(-0.368148\pi\) | ||||
0.402480 | + | 0.915429i | \(0.368148\pi\) | |||||||
\(132\) | 4.44836 | 0.387180 | ||||||||
\(133\) | 0.420274 | 0.0364424 | ||||||||
\(134\) | −8.80215 | −0.760390 | ||||||||
\(135\) | 10.8954 | 0.937726 | ||||||||
\(136\) | 14.3493 | 1.23044 | ||||||||
\(137\) | 12.2131 | 1.04343 | 0.521716 | − | 0.853119i | \(-0.325292\pi\) | ||||
0.521716 | + | 0.853119i | \(0.325292\pi\) | |||||||
\(138\) | 9.01193 | 0.767147 | ||||||||
\(139\) | −5.06124 | −0.429289 | −0.214644 | − | 0.976692i | \(-0.568859\pi\) | ||||
−0.214644 | + | 0.976692i | \(0.568859\pi\) | |||||||
\(140\) | 1.11905 | 0.0945774 | ||||||||
\(141\) | 0.363276 | 0.0305934 | ||||||||
\(142\) | 12.3185 | 1.03375 | ||||||||
\(143\) | 8.10493 | 0.677768 | ||||||||
\(144\) | 1.33534 | 0.111278 | ||||||||
\(145\) | 12.7295 | 1.05713 | ||||||||
\(146\) | −9.57680 | −0.792581 | ||||||||
\(147\) | 6.84906 | 0.564901 | ||||||||
\(148\) | −3.08420 | −0.253519 | ||||||||
\(149\) | −21.9792 | −1.80061 | −0.900305 | − | 0.435261i | \(-0.856656\pi\) | ||||
−0.900305 | + | 0.435261i | \(0.856656\pi\) | |||||||
\(150\) | −0.325461 | −0.0265737 | ||||||||
\(151\) | −6.96943 | −0.567165 | −0.283582 | − | 0.958948i | \(-0.591523\pi\) | ||||
−0.283582 | + | 0.958948i | \(0.591523\pi\) | |||||||
\(152\) | −6.23808 | −0.505975 | ||||||||
\(153\) | 11.9459 | 0.965769 | ||||||||
\(154\) | 0.545321 | 0.0439432 | ||||||||
\(155\) | 16.8104 | 1.35024 | ||||||||
\(156\) | 16.7213 | 1.33878 | ||||||||
\(157\) | −5.70152 | −0.455031 | −0.227516 | − | 0.973774i | \(-0.573060\pi\) | ||||
−0.227516 | + | 0.973774i | \(0.573060\pi\) | |||||||
\(158\) | −5.22191 | −0.415433 | ||||||||
\(159\) | 8.07313 | 0.640241 | ||||||||
\(160\) | 14.0302 | 1.10918 | ||||||||
\(161\) | 0.670177 | 0.0528174 | ||||||||
\(162\) | −2.81318 | −0.221024 | ||||||||
\(163\) | −21.1576 | −1.65719 | −0.828597 | − | 0.559845i | \(-0.810861\pi\) | ||||
−0.828597 | + | 0.559845i | \(0.810861\pi\) | |||||||
\(164\) | 24.0861 | 1.88081 | ||||||||
\(165\) | 3.17735 | 0.247357 | ||||||||
\(166\) | 16.9193 | 1.31319 | ||||||||
\(167\) | −21.1413 | −1.63596 | −0.817980 | − | 0.575247i | \(-0.804906\pi\) | ||||
−0.817980 | + | 0.575247i | \(0.804906\pi\) | |||||||
\(168\) | 0.395494 | 0.0305130 | ||||||||
\(169\) | 17.4663 | 1.34356 | ||||||||
\(170\) | 29.1562 | 2.23618 | ||||||||
\(171\) | −5.19324 | −0.397137 | ||||||||
\(172\) | 26.0019 | 1.98262 | ||||||||
\(173\) | −1.56608 | −0.119067 | −0.0595334 | − | 0.998226i | \(-0.518961\pi\) | ||||
−0.0595334 | + | 0.998226i | \(0.518961\pi\) | |||||||
\(174\) | 12.7978 | 0.970197 | ||||||||
\(175\) | −0.0242030 | −0.00182958 | ||||||||
\(176\) | 0.963440 | 0.0726220 | ||||||||
\(177\) | −9.52304 | −0.715796 | ||||||||
\(178\) | 4.07366 | 0.305334 | ||||||||
\(179\) | −9.43139 | −0.704935 | −0.352468 | − | 0.935824i | \(-0.614657\pi\) | ||||
−0.352468 | + | 0.935824i | \(0.614657\pi\) | |||||||
\(180\) | −13.8279 | −1.03067 | ||||||||
\(181\) | −15.9628 | −1.18651 | −0.593254 | − | 0.805015i | \(-0.702157\pi\) | ||||
−0.593254 | + | 0.805015i | \(0.702157\pi\) | |||||||
\(182\) | 2.04985 | 0.151945 | ||||||||
\(183\) | −3.46488 | −0.256131 | ||||||||
\(184\) | −9.94735 | −0.733328 | ||||||||
\(185\) | −2.20296 | −0.161965 | ||||||||
\(186\) | 16.9005 | 1.23920 | ||||||||
\(187\) | 8.61889 | 0.630276 | ||||||||
\(188\) | −1.14067 | −0.0831919 | ||||||||
\(189\) | 0.814587 | 0.0592525 | ||||||||
\(190\) | −12.6751 | −0.919545 | ||||||||
\(191\) | −19.1227 | −1.38367 | −0.691835 | − | 0.722056i | \(-0.743197\pi\) | ||||
−0.691835 | + | 0.722056i | \(0.743197\pi\) | |||||||
\(192\) | 12.8165 | 0.924948 | ||||||||
\(193\) | −11.9264 | −0.858484 | −0.429242 | − | 0.903190i | \(-0.641219\pi\) | ||||
−0.429242 | + | 0.903190i | \(0.641219\pi\) | |||||||
\(194\) | −13.3295 | −0.957002 | ||||||||
\(195\) | 11.9436 | 0.855301 | ||||||||
\(196\) | −21.5057 | −1.53612 | ||||||||
\(197\) | −5.73361 | −0.408502 | −0.204251 | − | 0.978919i | \(-0.565476\pi\) | ||||
−0.204251 | + | 0.978919i | \(0.565476\pi\) | |||||||
\(198\) | −6.73841 | −0.478878 | ||||||||
\(199\) | 14.4102 | 1.02151 | 0.510755 | − | 0.859727i | \(-0.329366\pi\) | ||||
0.510755 | + | 0.859727i | \(0.329366\pi\) | |||||||
\(200\) | 0.359242 | 0.0254023 | ||||||||
\(201\) | −3.83439 | −0.270457 | ||||||||
\(202\) | 6.38313 | 0.449115 | ||||||||
\(203\) | 0.951713 | 0.0667972 | ||||||||
\(204\) | 17.7817 | 1.24497 | ||||||||
\(205\) | 17.2041 | 1.20159 | ||||||||
\(206\) | 19.9498 | 1.38997 | ||||||||
\(207\) | −8.28123 | −0.575585 | ||||||||
\(208\) | 3.62156 | 0.251110 | ||||||||
\(209\) | −3.74689 | −0.259178 | ||||||||
\(210\) | 0.803599 | 0.0554536 | ||||||||
\(211\) | 23.7280 | 1.63351 | 0.816753 | − | 0.576987i | \(-0.195772\pi\) | ||||
0.816753 | + | 0.576987i | \(0.195772\pi\) | |||||||
\(212\) | −25.3492 | −1.74099 | ||||||||
\(213\) | 5.36620 | 0.367686 | ||||||||
\(214\) | 19.7047 | 1.34699 | ||||||||
\(215\) | 18.5725 | 1.26663 | ||||||||
\(216\) | −12.0908 | −0.822674 | ||||||||
\(217\) | 1.25681 | 0.0853181 | ||||||||
\(218\) | 2.25482 | 0.152715 | ||||||||
\(219\) | −4.17184 | −0.281907 | ||||||||
\(220\) | −9.97674 | −0.672632 | ||||||||
\(221\) | 32.3983 | 2.17934 | ||||||||
\(222\) | −2.21478 | −0.148646 | ||||||||
\(223\) | −3.79616 | −0.254210 | −0.127105 | − | 0.991889i | \(-0.540568\pi\) | ||||
−0.127105 | + | 0.991889i | \(0.540568\pi\) | |||||||
\(224\) | 1.04896 | 0.0700863 | ||||||||
\(225\) | 0.299072 | 0.0199381 | ||||||||
\(226\) | −3.42955 | −0.228130 | ||||||||
\(227\) | −12.8835 | −0.855106 | −0.427553 | − | 0.903990i | \(-0.640624\pi\) | ||||
−0.427553 | + | 0.903990i | \(0.640624\pi\) | |||||||
\(228\) | −7.73023 | −0.511947 | ||||||||
\(229\) | 2.83708 | 0.187480 | 0.0937398 | − | 0.995597i | \(-0.470118\pi\) | ||||
0.0937398 | + | 0.995597i | \(0.470118\pi\) | |||||||
\(230\) | −20.2119 | −1.33273 | ||||||||
\(231\) | 0.237553 | 0.0156298 | ||||||||
\(232\) | −14.1262 | −0.927427 | ||||||||
\(233\) | 1.37489 | 0.0900719 | 0.0450359 | − | 0.998985i | \(-0.485660\pi\) | ||||
0.0450359 | + | 0.998985i | \(0.485660\pi\) | |||||||
\(234\) | −25.3296 | −1.65585 | ||||||||
\(235\) | −0.814752 | −0.0531485 | ||||||||
\(236\) | 29.9019 | 1.94645 | ||||||||
\(237\) | −2.27477 | −0.147762 | ||||||||
\(238\) | 2.17984 | 0.141298 | ||||||||
\(239\) | −18.8303 | −1.21803 | −0.609017 | − | 0.793157i | \(-0.708436\pi\) | ||||
−0.609017 | + | 0.793157i | \(0.708436\pi\) | |||||||
\(240\) | 1.41975 | 0.0916444 | ||||||||
\(241\) | 13.2071 | 0.850743 | 0.425372 | − | 0.905019i | \(-0.360143\pi\) | ||||
0.425372 | + | 0.905019i | \(0.360143\pi\) | |||||||
\(242\) | 19.9413 | 1.28187 | ||||||||
\(243\) | −16.0628 | −1.03043 | ||||||||
\(244\) | 10.8796 | 0.696493 | ||||||||
\(245\) | −15.3610 | −0.981378 | ||||||||
\(246\) | 17.2964 | 1.10278 | ||||||||
\(247\) | −14.0845 | −0.896175 | ||||||||
\(248\) | −18.6547 | −1.18458 | ||||||||
\(249\) | 7.37037 | 0.467078 | ||||||||
\(250\) | 25.5663 | 1.61696 | ||||||||
\(251\) | −24.4842 | −1.54543 | −0.772715 | − | 0.634753i | \(-0.781102\pi\) | ||||
−0.772715 | + | 0.634753i | \(0.781102\pi\) | |||||||
\(252\) | −1.03383 | −0.0651254 | ||||||||
\(253\) | −5.97485 | −0.375636 | ||||||||
\(254\) | 11.4210 | 0.716619 | ||||||||
\(255\) | 12.7010 | 0.795369 | ||||||||
\(256\) | −11.5223 | −0.720142 | ||||||||
\(257\) | 7.50671 | 0.468256 | 0.234128 | − | 0.972206i | \(-0.424777\pi\) | ||||
0.234128 | + | 0.972206i | \(0.424777\pi\) | |||||||
\(258\) | 18.6721 | 1.16247 | ||||||||
\(259\) | −0.164703 | −0.0102342 | ||||||||
\(260\) | −37.5024 | −2.32580 | ||||||||
\(261\) | −11.7601 | −0.727932 | ||||||||
\(262\) | −20.7741 | −1.28343 | ||||||||
\(263\) | −12.2348 | −0.754427 | −0.377214 | − | 0.926126i | \(-0.623118\pi\) | ||||
−0.377214 | + | 0.926126i | \(0.623118\pi\) | |||||||
\(264\) | −3.52596 | −0.217008 | ||||||||
\(265\) | −18.1063 | −1.11226 | ||||||||
\(266\) | −0.947642 | −0.0581036 | ||||||||
\(267\) | 1.77457 | 0.108602 | ||||||||
\(268\) | 12.0398 | 0.735448 | ||||||||
\(269\) | 23.1546 | 1.41176 | 0.705881 | − | 0.708330i | \(-0.250551\pi\) | ||||
0.705881 | + | 0.708330i | \(0.250551\pi\) | |||||||
\(270\) | −24.5671 | −1.49511 | ||||||||
\(271\) | 8.65013 | 0.525458 | 0.262729 | − | 0.964870i | \(-0.415377\pi\) | ||||
0.262729 | + | 0.964870i | \(0.415377\pi\) | |||||||
\(272\) | 3.85121 | 0.233514 | ||||||||
\(273\) | 0.892957 | 0.0540442 | ||||||||
\(274\) | −27.5382 | −1.66364 | ||||||||
\(275\) | 0.215778 | 0.0130119 | ||||||||
\(276\) | −12.3268 | −0.741984 | ||||||||
\(277\) | 21.0793 | 1.26653 | 0.633266 | − | 0.773934i | \(-0.281714\pi\) | ||||
0.633266 | + | 0.773934i | \(0.281714\pi\) | |||||||
\(278\) | 11.4122 | 0.684456 | ||||||||
\(279\) | −15.5302 | −0.929767 | ||||||||
\(280\) | −0.887010 | −0.0530090 | ||||||||
\(281\) | −30.6679 | −1.82949 | −0.914747 | − | 0.404027i | \(-0.867610\pi\) | ||||
−0.914747 | + | 0.404027i | \(0.867610\pi\) | |||||||
\(282\) | −0.819121 | −0.0487779 | ||||||||
\(283\) | 0.587072 | 0.0348978 | 0.0174489 | − | 0.999848i | \(-0.494446\pi\) | ||||
0.0174489 | + | 0.999848i | \(0.494446\pi\) | |||||||
\(284\) | −16.8496 | −0.999840 | ||||||||
\(285\) | −5.52151 | −0.327066 | ||||||||
\(286\) | −18.2751 | −1.08063 | ||||||||
\(287\) | 1.28625 | 0.0759251 | ||||||||
\(288\) | −12.9617 | −0.763776 | ||||||||
\(289\) | 17.4528 | 1.02663 | ||||||||
\(290\) | −28.7027 | −1.68548 | ||||||||
\(291\) | −5.80659 | −0.340389 | ||||||||
\(292\) | 13.0994 | 0.766584 | ||||||||
\(293\) | −12.7241 | −0.743353 | −0.371676 | − | 0.928362i | \(-0.621217\pi\) | ||||
−0.371676 | + | 0.928362i | \(0.621217\pi\) | |||||||
\(294\) | −15.4434 | −0.900675 | ||||||||
\(295\) | 21.3582 | 1.24352 | ||||||||
\(296\) | 2.44467 | 0.142093 | ||||||||
\(297\) | −7.26231 | −0.421402 | ||||||||
\(298\) | 49.5591 | 2.87088 | ||||||||
\(299\) | −22.4594 | −1.29886 | ||||||||
\(300\) | 0.445173 | 0.0257021 | ||||||||
\(301\) | 1.38856 | 0.0800352 | ||||||||
\(302\) | 15.7148 | 0.904285 | ||||||||
\(303\) | 2.78062 | 0.159742 | ||||||||
\(304\) | −1.67424 | −0.0960240 | ||||||||
\(305\) | 7.77100 | 0.444966 | ||||||||
\(306\) | −26.9358 | −1.53982 | ||||||||
\(307\) | −5.09662 | −0.290880 | −0.145440 | − | 0.989367i | \(-0.546460\pi\) | ||||
−0.145440 | + | 0.989367i | \(0.546460\pi\) | |||||||
\(308\) | −0.745904 | −0.0425018 | ||||||||
\(309\) | 8.69054 | 0.494388 | ||||||||
\(310\) | −37.9043 | −2.15282 | ||||||||
\(311\) | 13.7564 | 0.780053 | 0.390026 | − | 0.920804i | \(-0.372466\pi\) | ||||
0.390026 | + | 0.920804i | \(0.372466\pi\) | |||||||
\(312\) | −13.2540 | −0.750362 | ||||||||
\(313\) | 3.00027 | 0.169585 | 0.0847927 | − | 0.996399i | \(-0.472977\pi\) | ||||
0.0847927 | + | 0.996399i | \(0.472977\pi\) | |||||||
\(314\) | 12.8559 | 0.725500 | ||||||||
\(315\) | −0.738441 | −0.0416064 | ||||||||
\(316\) | 7.14267 | 0.401807 | ||||||||
\(317\) | −31.0840 | −1.74585 | −0.872925 | − | 0.487854i | \(-0.837780\pi\) | ||||
−0.872925 | + | 0.487854i | \(0.837780\pi\) | |||||||
\(318\) | −18.2034 | −1.02080 | ||||||||
\(319\) | −8.48484 | −0.475060 | ||||||||
\(320\) | −28.7446 | −1.60687 | ||||||||
\(321\) | 8.58378 | 0.479100 | ||||||||
\(322\) | −1.51113 | −0.0842118 | ||||||||
\(323\) | −14.9776 | −0.833378 | ||||||||
\(324\) | 3.84794 | 0.213774 | ||||||||
\(325\) | 0.811107 | 0.0449921 | ||||||||
\(326\) | 47.7066 | 2.64222 | ||||||||
\(327\) | 0.982243 | 0.0543182 | ||||||||
\(328\) | −19.0917 | −1.05416 | ||||||||
\(329\) | −0.0609143 | −0.00335832 | ||||||||
\(330\) | −7.16435 | −0.394384 | ||||||||
\(331\) | 5.25452 | 0.288815 | 0.144407 | − | 0.989518i | \(-0.453872\pi\) | ||||
0.144407 | + | 0.989518i | \(0.453872\pi\) | |||||||
\(332\) | −23.1426 | −1.27012 | ||||||||
\(333\) | 2.03520 | 0.111528 | ||||||||
\(334\) | 47.6697 | 2.60837 | ||||||||
\(335\) | 8.59973 | 0.469853 | ||||||||
\(336\) | 0.106147 | 0.00579077 | ||||||||
\(337\) | −3.28474 | −0.178931 | −0.0894656 | − | 0.995990i | \(-0.528516\pi\) | ||||
−0.0894656 | + | 0.995990i | \(0.528516\pi\) | |||||||
\(338\) | −39.3833 | −2.14217 | ||||||||
\(339\) | −1.49398 | −0.0811419 | ||||||||
\(340\) | −39.8806 | −2.16283 | ||||||||
\(341\) | −11.2049 | −0.606780 | ||||||||
\(342\) | 11.7098 | 0.633193 | ||||||||
\(343\) | −2.30138 | −0.124263 | ||||||||
\(344\) | −20.6102 | −1.11123 | ||||||||
\(345\) | −8.80469 | −0.474029 | ||||||||
\(346\) | 3.53122 | 0.189840 | ||||||||
\(347\) | 14.0046 | 0.751808 | 0.375904 | − | 0.926659i | \(-0.377332\pi\) | ||||
0.375904 | + | 0.926659i | \(0.377332\pi\) | |||||||
\(348\) | −17.5051 | −0.938374 | ||||||||
\(349\) | 20.4532 | 1.09483 | 0.547417 | − | 0.836860i | \(-0.315611\pi\) | ||||
0.547417 | + | 0.836860i | \(0.315611\pi\) | |||||||
\(350\) | 0.0545734 | 0.00291707 | ||||||||
\(351\) | −27.2989 | −1.45711 | ||||||||
\(352\) | −9.35179 | −0.498452 | ||||||||
\(353\) | −19.7082 | −1.04896 | −0.524481 | − | 0.851422i | \(-0.675741\pi\) | ||||
−0.524481 | + | 0.851422i | \(0.675741\pi\) | |||||||
\(354\) | 21.4727 | 1.14126 | ||||||||
\(355\) | −12.0353 | −0.638765 | ||||||||
\(356\) | −5.57206 | −0.295319 | ||||||||
\(357\) | 0.949583 | 0.0502572 | ||||||||
\(358\) | 21.2661 | 1.12395 | ||||||||
\(359\) | −1.72725 | −0.0911609 | −0.0455805 | − | 0.998961i | \(-0.514514\pi\) | ||||
−0.0455805 | + | 0.998961i | \(0.514514\pi\) | |||||||
\(360\) | 10.9606 | 0.577673 | ||||||||
\(361\) | −12.4888 | −0.657304 | ||||||||
\(362\) | 35.9933 | 1.89176 | ||||||||
\(363\) | 8.68681 | 0.455939 | ||||||||
\(364\) | −2.80384 | −0.146961 | ||||||||
\(365\) | 9.35657 | 0.489745 | ||||||||
\(366\) | 7.81267 | 0.408375 | ||||||||
\(367\) | −31.6988 | −1.65466 | −0.827332 | − | 0.561713i | \(-0.810142\pi\) | ||||
−0.827332 | + | 0.561713i | \(0.810142\pi\) | |||||||
\(368\) | −2.66977 | −0.139171 | ||||||||
\(369\) | −15.8939 | −0.827405 | ||||||||
\(370\) | 4.96728 | 0.258237 | ||||||||
\(371\) | −1.35371 | −0.0702809 | ||||||||
\(372\) | −23.1170 | −1.19856 | ||||||||
\(373\) | 11.8488 | 0.613509 | 0.306754 | − | 0.951789i | \(-0.400757\pi\) | ||||
0.306754 | + | 0.951789i | \(0.400757\pi\) | |||||||
\(374\) | −19.4340 | −1.00491 | ||||||||
\(375\) | 11.1372 | 0.575123 | ||||||||
\(376\) | 0.904143 | 0.0466276 | ||||||||
\(377\) | −31.8944 | −1.64265 | ||||||||
\(378\) | −1.83674 | −0.0944719 | ||||||||
\(379\) | −10.1128 | −0.519459 | −0.259729 | − | 0.965681i | \(-0.583633\pi\) | ||||
−0.259729 | + | 0.965681i | \(0.583633\pi\) | |||||||
\(380\) | 17.3373 | 0.889383 | ||||||||
\(381\) | 4.97523 | 0.254889 | ||||||||
\(382\) | 43.1181 | 2.20612 | ||||||||
\(383\) | −21.9162 | −1.11987 | −0.559933 | − | 0.828538i | \(-0.689173\pi\) | ||||
−0.559933 | + | 0.828538i | \(0.689173\pi\) | |||||||
\(384\) | −16.3874 | −0.836266 | ||||||||
\(385\) | −0.532780 | −0.0271530 | ||||||||
\(386\) | 26.8919 | 1.36876 | ||||||||
\(387\) | −17.1581 | −0.872196 | ||||||||
\(388\) | 18.2324 | 0.925612 | ||||||||
\(389\) | −28.8889 | −1.46472 | −0.732362 | − | 0.680915i | \(-0.761582\pi\) | ||||
−0.732362 | + | 0.680915i | \(0.761582\pi\) | |||||||
\(390\) | −26.9307 | −1.36369 | ||||||||
\(391\) | −23.8836 | −1.20785 | ||||||||
\(392\) | 17.0463 | 0.860970 | ||||||||
\(393\) | −9.04960 | −0.456492 | ||||||||
\(394\) | 12.9282 | 0.651315 | ||||||||
\(395\) | 5.10183 | 0.256701 | ||||||||
\(396\) | 9.21697 | 0.463170 | ||||||||
\(397\) | 4.43968 | 0.222821 | 0.111411 | − | 0.993774i | \(-0.464463\pi\) | ||||
0.111411 | + | 0.993774i | \(0.464463\pi\) | |||||||
\(398\) | −32.4923 | −1.62869 | ||||||||
\(399\) | −0.412812 | −0.0206664 | ||||||||
\(400\) | 0.0964170 | 0.00482085 | ||||||||
\(401\) | 17.2839 | 0.863119 | 0.431559 | − | 0.902085i | \(-0.357964\pi\) | ||||
0.431559 | + | 0.902085i | \(0.357964\pi\) | |||||||
\(402\) | 8.64585 | 0.431216 | ||||||||
\(403\) | −42.1191 | −2.09810 | ||||||||
\(404\) | −8.73101 | −0.434384 | ||||||||
\(405\) | 2.74848 | 0.136573 | ||||||||
\(406\) | −2.14594 | −0.106501 | ||||||||
\(407\) | 1.46838 | 0.0727850 | ||||||||
\(408\) | −14.0945 | −0.697783 | ||||||||
\(409\) | 24.8549 | 1.22900 | 0.614498 | − | 0.788918i | \(-0.289359\pi\) | ||||
0.614498 | + | 0.788918i | \(0.289359\pi\) | |||||||
\(410\) | −38.7921 | −1.91580 | ||||||||
\(411\) | −11.9962 | −0.591729 | ||||||||
\(412\) | −27.2879 | −1.34438 | ||||||||
\(413\) | 1.59683 | 0.0785748 | ||||||||
\(414\) | 18.6726 | 0.917711 | ||||||||
\(415\) | −16.5302 | −0.811435 | ||||||||
\(416\) | −35.1532 | −1.72353 | ||||||||
\(417\) | 4.97136 | 0.243449 | ||||||||
\(418\) | 8.44854 | 0.413232 | ||||||||
\(419\) | −9.44275 | −0.461309 | −0.230654 | − | 0.973036i | \(-0.574087\pi\) | ||||
−0.230654 | + | 0.973036i | \(0.574087\pi\) | |||||||
\(420\) | −1.09918 | −0.0536347 | ||||||||
\(421\) | 1.50629 | 0.0734120 | 0.0367060 | − | 0.999326i | \(-0.488313\pi\) | ||||
0.0367060 | + | 0.999326i | \(0.488313\pi\) | |||||||
\(422\) | −53.5024 | −2.60446 | ||||||||
\(423\) | 0.752705 | 0.0365978 | ||||||||
\(424\) | 20.0929 | 0.975796 | ||||||||
\(425\) | 0.862542 | 0.0418394 | ||||||||
\(426\) | −12.0998 | −0.586237 | ||||||||
\(427\) | 0.580994 | 0.0281162 | ||||||||
\(428\) | −26.9527 | −1.30281 | ||||||||
\(429\) | −7.96101 | −0.384361 | ||||||||
\(430\) | −41.8775 | −2.01951 | ||||||||
\(431\) | −13.2053 | −0.636075 | −0.318038 | − | 0.948078i | \(-0.603024\pi\) | ||||
−0.318038 | + | 0.948078i | \(0.603024\pi\) | |||||||
\(432\) | −3.24505 | −0.156127 | ||||||||
\(433\) | 18.0813 | 0.868932 | 0.434466 | − | 0.900688i | \(-0.356937\pi\) | ||||
0.434466 | + | 0.900688i | \(0.356937\pi\) | |||||||
\(434\) | −2.83389 | −0.136031 | ||||||||
\(435\) | −12.5035 | −0.599496 | ||||||||
\(436\) | −3.08420 | −0.147706 | ||||||||
\(437\) | 10.3829 | 0.496682 | ||||||||
\(438\) | 9.40674 | 0.449472 | ||||||||
\(439\) | −14.2156 | −0.678472 | −0.339236 | − | 0.940701i | \(-0.610168\pi\) | ||||
−0.339236 | + | 0.940701i | \(0.610168\pi\) | |||||||
\(440\) | 7.90799 | 0.376999 | ||||||||
\(441\) | 14.1912 | 0.675771 | ||||||||
\(442\) | −73.0522 | −3.47474 | ||||||||
\(443\) | −10.6497 | −0.505984 | −0.252992 | − | 0.967468i | \(-0.581415\pi\) | ||||
−0.252992 | + | 0.967468i | \(0.581415\pi\) | |||||||
\(444\) | 3.02943 | 0.143770 | ||||||||
\(445\) | −3.97998 | −0.188669 | ||||||||
\(446\) | 8.55965 | 0.405311 | ||||||||
\(447\) | 21.5889 | 1.02112 | ||||||||
\(448\) | −2.14907 | −0.101534 | ||||||||
\(449\) | 13.6692 | 0.645089 | 0.322544 | − | 0.946554i | \(-0.395462\pi\) | ||||
0.322544 | + | 0.946554i | \(0.395462\pi\) | |||||||
\(450\) | −0.674351 | −0.0317892 | ||||||||
\(451\) | −11.4674 | −0.539977 | ||||||||
\(452\) | 4.69103 | 0.220647 | ||||||||
\(453\) | 6.84568 | 0.321638 | ||||||||
\(454\) | 29.0499 | 1.36338 | ||||||||
\(455\) | −2.00271 | −0.0938887 | ||||||||
\(456\) | 6.12731 | 0.286937 | ||||||||
\(457\) | −0.00708470 | −0.000331408 0 | −0.000165704 | − | 1.00000i | \(-0.500053\pi\) | ||||
−0.000165704 | 1.00000i | \(0.500053\pi\) | ||||||||
\(458\) | −6.39710 | −0.298917 | ||||||||
\(459\) | −29.0300 | −1.35501 | ||||||||
\(460\) | 27.6463 | 1.28902 | ||||||||
\(461\) | 9.63524 | 0.448758 | 0.224379 | − | 0.974502i | \(-0.427965\pi\) | ||||
0.224379 | + | 0.974502i | \(0.427965\pi\) | |||||||
\(462\) | −0.535638 | −0.0249201 | ||||||||
\(463\) | 24.1464 | 1.12218 | 0.561089 | − | 0.827755i | \(-0.310382\pi\) | ||||
0.561089 | + | 0.827755i | \(0.310382\pi\) | |||||||
\(464\) | −3.79131 | −0.176007 | ||||||||
\(465\) | −16.5119 | −0.765719 | ||||||||
\(466\) | −3.10012 | −0.143610 | ||||||||
\(467\) | 26.2685 | 1.21556 | 0.607780 | − | 0.794105i | \(-0.292060\pi\) | ||||
0.607780 | + | 0.794105i | \(0.292060\pi\) | |||||||
\(468\) | 34.6465 | 1.60153 | ||||||||
\(469\) | 0.642953 | 0.0296888 | ||||||||
\(470\) | 1.83712 | 0.0847398 | ||||||||
\(471\) | 5.60028 | 0.258047 | ||||||||
\(472\) | −23.7015 | −1.09095 | ||||||||
\(473\) | −12.3795 | −0.569208 | ||||||||
\(474\) | 5.12919 | 0.235591 | ||||||||
\(475\) | −0.374973 | −0.0172049 | ||||||||
\(476\) | −2.98165 | −0.136663 | ||||||||
\(477\) | 16.7274 | 0.765897 | ||||||||
\(478\) | 42.4590 | 1.94203 | ||||||||
\(479\) | 36.0550 | 1.64739 | 0.823697 | − | 0.567030i | \(-0.191908\pi\) | ||||
0.823697 | + | 0.567030i | \(0.191908\pi\) | |||||||
\(480\) | −13.7810 | −0.629015 | ||||||||
\(481\) | 5.51963 | 0.251673 | ||||||||
\(482\) | −29.7796 | −1.35642 | ||||||||
\(483\) | −0.658277 | −0.0299526 | ||||||||
\(484\) | −27.2762 | −1.23983 | ||||||||
\(485\) | 13.0230 | 0.591342 | ||||||||
\(486\) | 36.2188 | 1.64292 | ||||||||
\(487\) | 39.5869 | 1.79385 | 0.896926 | − | 0.442180i | \(-0.145795\pi\) | ||||
0.896926 | + | 0.442180i | \(0.145795\pi\) | |||||||
\(488\) | −8.62361 | −0.390372 | ||||||||
\(489\) | 20.7819 | 0.939792 | ||||||||
\(490\) | 34.6362 | 1.56470 | ||||||||
\(491\) | −0.832067 | −0.0375507 | −0.0187753 | − | 0.999824i | \(-0.505977\pi\) | ||||
−0.0187753 | + | 0.999824i | \(0.505977\pi\) | |||||||
\(492\) | −23.6584 | −1.06660 | ||||||||
\(493\) | −33.9169 | −1.52754 | ||||||||
\(494\) | 31.7579 | 1.42886 | ||||||||
\(495\) | 6.58345 | 0.295904 | ||||||||
\(496\) | −5.00674 | −0.224809 | ||||||||
\(497\) | −0.899807 | −0.0403619 | ||||||||
\(498\) | −16.6188 | −0.744708 | ||||||||
\(499\) | −16.5920 | −0.742759 | −0.371380 | − | 0.928481i | \(-0.621115\pi\) | ||||
−0.371380 | + | 0.928481i | \(0.621115\pi\) | |||||||
\(500\) | −34.9703 | −1.56392 | ||||||||
\(501\) | 20.7659 | 0.927750 | ||||||||
\(502\) | 55.2074 | 2.46403 | ||||||||
\(503\) | 21.0814 | 0.939973 | 0.469986 | − | 0.882674i | \(-0.344259\pi\) | ||||
0.469986 | + | 0.882674i | \(0.344259\pi\) | |||||||
\(504\) | 0.819460 | 0.0365017 | ||||||||
\(505\) | −6.23634 | −0.277513 | ||||||||
\(506\) | 13.4722 | 0.598912 | ||||||||
\(507\) | −17.1562 | −0.761932 | ||||||||
\(508\) | −15.6220 | −0.693114 | ||||||||
\(509\) | −16.3778 | −0.725935 | −0.362967 | − | 0.931802i | \(-0.618236\pi\) | ||||
−0.362967 | + | 0.931802i | \(0.618236\pi\) | |||||||
\(510\) | −28.6385 | −1.26813 | ||||||||
\(511\) | 0.699537 | 0.0309457 | ||||||||
\(512\) | −7.38670 | −0.326449 | ||||||||
\(513\) | 12.6202 | 0.557196 | ||||||||
\(514\) | −16.9263 | −0.746585 | ||||||||
\(515\) | −19.4911 | −0.858879 | ||||||||
\(516\) | −25.5402 | −1.12434 | ||||||||
\(517\) | 0.543072 | 0.0238843 | ||||||||
\(518\) | 0.371375 | 0.0163173 | ||||||||
\(519\) | 1.53827 | 0.0675226 | ||||||||
\(520\) | 29.7260 | 1.30357 | ||||||||
\(521\) | −18.6781 | −0.818301 | −0.409150 | − | 0.912467i | \(-0.634175\pi\) | ||||
−0.409150 | + | 0.912467i | \(0.634175\pi\) | |||||||
\(522\) | 26.5169 | 1.16061 | ||||||||
\(523\) | −24.3894 | −1.06647 | −0.533236 | − | 0.845966i | \(-0.679024\pi\) | ||||
−0.533236 | + | 0.845966i | \(0.679024\pi\) | |||||||
\(524\) | 28.4153 | 1.24133 | ||||||||
\(525\) | 0.0237733 | 0.00103755 | ||||||||
\(526\) | 27.5871 | 1.20286 | ||||||||
\(527\) | −44.7901 | −1.95109 | ||||||||
\(528\) | −0.946332 | −0.0411838 | ||||||||
\(529\) | −6.44322 | −0.280140 | ||||||||
\(530\) | 40.8264 | 1.77339 | ||||||||
\(531\) | −19.7317 | −0.856281 | ||||||||
\(532\) | 1.29621 | 0.0561978 | ||||||||
\(533\) | −43.1057 | −1.86711 | ||||||||
\(534\) | −4.00133 | −0.173154 | ||||||||
\(535\) | −19.2516 | −0.832320 | ||||||||
\(536\) | −9.54326 | −0.412206 | ||||||||
\(537\) | 9.26392 | 0.399768 | ||||||||
\(538\) | −52.2094 | −2.25091 | ||||||||
\(539\) | 10.2388 | 0.441018 | ||||||||
\(540\) | 33.6035 | 1.44607 | ||||||||
\(541\) | −26.5119 | −1.13984 | −0.569919 | − | 0.821701i | \(-0.693025\pi\) | ||||
−0.569919 | + | 0.821701i | \(0.693025\pi\) | |||||||
\(542\) | −19.5045 | −0.837788 | ||||||||
\(543\) | 15.6794 | 0.672867 | ||||||||
\(544\) | −37.3824 | −1.60276 | ||||||||
\(545\) | −2.20296 | −0.0943646 | ||||||||
\(546\) | −2.01345 | −0.0861679 | ||||||||
\(547\) | −10.2219 | −0.437058 | −0.218529 | − | 0.975830i | \(-0.570126\pi\) | ||||
−0.218529 | + | 0.975830i | \(0.570126\pi\) | |||||||
\(548\) | 37.6675 | 1.60908 | ||||||||
\(549\) | −7.17921 | −0.306401 | ||||||||
\(550\) | −0.486540 | −0.0207461 | ||||||||
\(551\) | 14.7447 | 0.628145 | ||||||||
\(552\) | 9.77071 | 0.415869 | ||||||||
\(553\) | 0.381435 | 0.0162203 | ||||||||
\(554\) | −47.5299 | −2.01935 | ||||||||
\(555\) | 2.16385 | 0.0918501 | ||||||||
\(556\) | −15.6099 | −0.662005 | ||||||||
\(557\) | −7.30882 | −0.309684 | −0.154842 | − | 0.987939i | \(-0.549487\pi\) | ||||
−0.154842 | + | 0.987939i | \(0.549487\pi\) | |||||||
\(558\) | 35.0177 | 1.48242 | ||||||||
\(559\) | −46.5342 | −1.96819 | ||||||||
\(560\) | −0.238064 | −0.0100601 | ||||||||
\(561\) | −8.46584 | −0.357428 | ||||||||
\(562\) | 69.1505 | 2.91694 | ||||||||
\(563\) | 3.67009 | 0.154676 | 0.0773378 | − | 0.997005i | \(-0.475358\pi\) | ||||
0.0773378 | + | 0.997005i | \(0.475358\pi\) | |||||||
\(564\) | 1.12041 | 0.0471780 | ||||||||
\(565\) | 3.35068 | 0.140964 | ||||||||
\(566\) | −1.32374 | −0.0556409 | ||||||||
\(567\) | 0.205489 | 0.00862971 | ||||||||
\(568\) | 13.3557 | 0.560393 | ||||||||
\(569\) | 37.1544 | 1.55759 | 0.778797 | − | 0.627276i | \(-0.215830\pi\) | ||||
0.778797 | + | 0.627276i | \(0.215830\pi\) | |||||||
\(570\) | 12.4500 | 0.521472 | ||||||||
\(571\) | −11.8237 | −0.494805 | −0.247402 | − | 0.968913i | \(-0.579577\pi\) | ||||
−0.247402 | + | 0.968913i | \(0.579577\pi\) | |||||||
\(572\) | 24.9972 | 1.04519 | ||||||||
\(573\) | 18.7831 | 0.784676 | ||||||||
\(574\) | −2.90026 | −0.121055 | ||||||||
\(575\) | −0.597938 | −0.0249357 | ||||||||
\(576\) | 26.5556 | 1.10648 | ||||||||
\(577\) | −23.5618 | −0.980889 | −0.490444 | − | 0.871472i | \(-0.663166\pi\) | ||||
−0.490444 | + | 0.871472i | \(0.663166\pi\) | |||||||
\(578\) | −39.3528 | −1.63686 | ||||||||
\(579\) | 11.7147 | 0.486845 | ||||||||
\(580\) | 39.2603 | 1.63020 | ||||||||
\(581\) | −1.23587 | −0.0512725 | ||||||||
\(582\) | 13.0928 | 0.542714 | ||||||||
\(583\) | 12.0687 | 0.499836 | ||||||||
\(584\) | −10.3831 | −0.429657 | ||||||||
\(585\) | 24.7471 | 1.02317 | ||||||||
\(586\) | 28.6906 | 1.18520 | ||||||||
\(587\) | 6.98323 | 0.288229 | 0.144114 | − | 0.989561i | \(-0.453967\pi\) | ||||
0.144114 | + | 0.989561i | \(0.453967\pi\) | |||||||
\(588\) | 21.1238 | 0.871132 | ||||||||
\(589\) | 19.4716 | 0.802312 | ||||||||
\(590\) | −48.1588 | −1.98266 | ||||||||
\(591\) | 5.63179 | 0.231661 | ||||||||
\(592\) | 0.656123 | 0.0269665 | ||||||||
\(593\) | −13.3384 | −0.547741 | −0.273871 | − | 0.961767i | \(-0.588304\pi\) | ||||
−0.273871 | + | 0.961767i | \(0.588304\pi\) | |||||||
\(594\) | 16.3752 | 0.671882 | ||||||||
\(595\) | −2.12971 | −0.0873098 | ||||||||
\(596\) | −67.7883 | −2.77672 | ||||||||
\(597\) | −14.1543 | −0.579296 | ||||||||
\(598\) | 50.6418 | 2.07090 | ||||||||
\(599\) | 2.33637 | 0.0954615 | 0.0477308 | − | 0.998860i | \(-0.484801\pi\) | ||||
0.0477308 | + | 0.998860i | \(0.484801\pi\) | |||||||
\(600\) | −0.352863 | −0.0144056 | ||||||||
\(601\) | 26.4783 | 1.08007 | 0.540037 | − | 0.841641i | \(-0.318410\pi\) | ||||
0.540037 | + | 0.841641i | \(0.318410\pi\) | |||||||
\(602\) | −3.13095 | −0.127608 | ||||||||
\(603\) | −7.94482 | −0.323538 | ||||||||
\(604\) | −21.4951 | −0.874624 | ||||||||
\(605\) | −19.4827 | −0.792084 | ||||||||
\(606\) | −6.26978 | −0.254692 | ||||||||
\(607\) | 9.19531 | 0.373226 | 0.186613 | − | 0.982434i | \(-0.440249\pi\) | ||||
0.186613 | + | 0.982434i | \(0.440249\pi\) | |||||||
\(608\) | 16.2512 | 0.659075 | ||||||||
\(609\) | −0.934814 | −0.0378806 | ||||||||
\(610\) | −17.5222 | −0.709452 | ||||||||
\(611\) | 2.04140 | 0.0825861 | ||||||||
\(612\) | 36.8435 | 1.48931 | ||||||||
\(613\) | −11.1909 | −0.451998 | −0.225999 | − | 0.974128i | \(-0.572565\pi\) | ||||
−0.225999 | + | 0.974128i | \(0.572565\pi\) | |||||||
\(614\) | 11.4920 | 0.463777 | ||||||||
\(615\) | −16.8986 | −0.681417 | ||||||||
\(616\) | 0.591235 | 0.0238215 | ||||||||
\(617\) | −25.6710 | −1.03348 | −0.516739 | − | 0.856143i | \(-0.672854\pi\) | ||||
−0.516739 | + | 0.856143i | \(0.672854\pi\) | |||||||
\(618\) | −19.5956 | −0.788250 | ||||||||
\(619\) | 0.103921 | 0.00417695 | 0.00208847 | − | 0.999998i | \(-0.499335\pi\) | ||||
0.00208847 | + | 0.999998i | \(0.499335\pi\) | |||||||
\(620\) | 51.8464 | 2.08220 | ||||||||
\(621\) | 20.1244 | 0.807565 | ||||||||
\(622\) | −31.0181 | −1.24371 | ||||||||
\(623\) | −0.297561 | −0.0119215 | ||||||||
\(624\) | −3.55725 | −0.142404 | ||||||||
\(625\) | −24.2437 | −0.969746 | ||||||||
\(626\) | −6.76506 | −0.270386 | ||||||||
\(627\) | 3.68035 | 0.146979 | ||||||||
\(628\) | −17.5846 | −0.701703 | ||||||||
\(629\) | 5.86965 | 0.234038 | ||||||||
\(630\) | 1.66505 | 0.0663372 | ||||||||
\(631\) | 31.5390 | 1.25555 | 0.627774 | − | 0.778395i | \(-0.283966\pi\) | ||||
0.627774 | + | 0.778395i | \(0.283966\pi\) | |||||||
\(632\) | −5.66158 | −0.225206 | ||||||||
\(633\) | −23.3067 | −0.926358 | ||||||||
\(634\) | 70.0887 | 2.78358 | ||||||||
\(635\) | −11.1584 | −0.442807 | ||||||||
\(636\) | 24.8991 | 0.987314 | ||||||||
\(637\) | 38.4877 | 1.52494 | ||||||||
\(638\) | 19.1318 | 0.757434 | ||||||||
\(639\) | 11.1187 | 0.439850 | ||||||||
\(640\) | 36.7535 | 1.45281 | ||||||||
\(641\) | −18.2427 | −0.720545 | −0.360272 | − | 0.932847i | \(-0.617316\pi\) | ||||
−0.360272 | + | 0.932847i | \(0.617316\pi\) | |||||||
\(642\) | −19.3548 | −0.763875 | ||||||||
\(643\) | −10.6664 | −0.420641 | −0.210321 | − | 0.977632i | \(-0.567451\pi\) | ||||
−0.210321 | + | 0.977632i | \(0.567451\pi\) | |||||||
\(644\) | 2.06696 | 0.0814496 | ||||||||
\(645\) | −18.2427 | −0.718305 | ||||||||
\(646\) | 33.7718 | 1.32874 | ||||||||
\(647\) | −16.0421 | −0.630680 | −0.315340 | − | 0.948979i | \(-0.602119\pi\) | ||||
−0.315340 | + | 0.948979i | \(0.602119\pi\) | |||||||
\(648\) | −3.05004 | −0.119817 | ||||||||
\(649\) | −14.2363 | −0.558822 | ||||||||
\(650\) | −1.82890 | −0.0717353 | ||||||||
\(651\) | −1.23450 | −0.0483838 | ||||||||
\(652\) | −65.2543 | −2.55556 | ||||||||
\(653\) | −8.69012 | −0.340071 | −0.170035 | − | 0.985438i | \(-0.554388\pi\) | ||||
−0.170035 | + | 0.985438i | \(0.554388\pi\) | |||||||
\(654\) | −2.21478 | −0.0866047 | ||||||||
\(655\) | 20.2963 | 0.793044 | ||||||||
\(656\) | −5.12401 | −0.200059 | ||||||||
\(657\) | −8.64402 | −0.337235 | ||||||||
\(658\) | 0.137351 | 0.00535449 | ||||||||
\(659\) | 12.6363 | 0.492241 | 0.246121 | − | 0.969239i | \(-0.420844\pi\) | ||||
0.246121 | + | 0.969239i | \(0.420844\pi\) | |||||||
\(660\) | 9.79958 | 0.381448 | ||||||||
\(661\) | 7.58047 | 0.294846 | 0.147423 | − | 0.989074i | \(-0.452902\pi\) | ||||
0.147423 | + | 0.989074i | \(0.452902\pi\) | |||||||
\(662\) | −11.8480 | −0.460485 | ||||||||
\(663\) | −31.8230 | −1.23590 | ||||||||
\(664\) | 18.3438 | 0.711879 | ||||||||
\(665\) | 0.925849 | 0.0359029 | ||||||||
\(666\) | −4.58900 | −0.177820 | ||||||||
\(667\) | 23.5122 | 0.910394 | ||||||||
\(668\) | −65.2038 | −2.52281 | ||||||||
\(669\) | 3.72875 | 0.144162 | ||||||||
\(670\) | −19.3908 | −0.749132 | ||||||||
\(671\) | −5.17975 | −0.199962 | ||||||||
\(672\) | −1.03033 | −0.0397458 | ||||||||
\(673\) | 21.8094 | 0.840691 | 0.420346 | − | 0.907364i | \(-0.361909\pi\) | ||||
0.420346 | + | 0.907364i | \(0.361909\pi\) | |||||||
\(674\) | 7.40649 | 0.285287 | ||||||||
\(675\) | −0.726781 | −0.0279738 | ||||||||
\(676\) | 53.8695 | 2.07191 | ||||||||
\(677\) | 1.00890 | 0.0387752 | 0.0193876 | − | 0.999812i | \(-0.493828\pi\) | ||||
0.0193876 | + | 0.999812i | \(0.493828\pi\) | |||||||
\(678\) | 3.36865 | 0.129372 | ||||||||
\(679\) | 0.973653 | 0.0373654 | ||||||||
\(680\) | 31.6111 | 1.21223 | ||||||||
\(681\) | 12.6547 | 0.484929 | ||||||||
\(682\) | 25.2650 | 0.967448 | ||||||||
\(683\) | 0.173423 | 0.00663583 | 0.00331791 | − | 0.999994i | \(-0.498944\pi\) | ||||
0.00331791 | + | 0.999994i | \(0.498944\pi\) | |||||||
\(684\) | −16.0170 | −0.612424 | ||||||||
\(685\) | 26.9049 | 1.02798 | ||||||||
\(686\) | 5.18918 | 0.198124 | ||||||||
\(687\) | −2.78670 | −0.106319 | ||||||||
\(688\) | −5.53156 | −0.210889 | ||||||||
\(689\) | 45.3662 | 1.72832 | ||||||||
\(690\) | 19.8530 | 0.755790 | ||||||||
\(691\) | 32.6202 | 1.24093 | 0.620466 | − | 0.784233i | \(-0.286943\pi\) | ||||
0.620466 | + | 0.784233i | \(0.286943\pi\) | |||||||
\(692\) | −4.83010 | −0.183613 | ||||||||
\(693\) | 0.492207 | 0.0186974 | ||||||||
\(694\) | −31.5779 | −1.19868 | ||||||||
\(695\) | −11.1497 | −0.422933 | ||||||||
\(696\) | 13.8753 | 0.525942 | ||||||||
\(697\) | −45.8391 | −1.73628 | ||||||||
\(698\) | −46.1182 | −1.74560 | ||||||||
\(699\) | −1.35047 | −0.0510796 | ||||||||
\(700\) | −0.0746469 | −0.00282139 | ||||||||
\(701\) | 47.6177 | 1.79850 | 0.899248 | − | 0.437439i | \(-0.144114\pi\) | ||||
0.899248 | + | 0.437439i | \(0.144114\pi\) | |||||||
\(702\) | 61.5541 | 2.32321 | ||||||||
\(703\) | −2.55171 | −0.0962396 | ||||||||
\(704\) | 19.1597 | 0.722108 | ||||||||
\(705\) | 0.800284 | 0.0301404 | ||||||||
\(706\) | 44.4384 | 1.67246 | ||||||||
\(707\) | −0.466255 | −0.0175353 | ||||||||
\(708\) | −29.3709 | −1.10383 | ||||||||
\(709\) | 36.8959 | 1.38565 | 0.692827 | − | 0.721103i | \(-0.256365\pi\) | ||||
0.692827 | + | 0.721103i | \(0.256365\pi\) | |||||||
\(710\) | 27.1373 | 1.01844 | ||||||||
\(711\) | −4.71330 | −0.176763 | ||||||||
\(712\) | 4.41665 | 0.165521 | ||||||||
\(713\) | 31.0497 | 1.16282 | ||||||||
\(714\) | −2.14113 | −0.0801299 | ||||||||
\(715\) | 17.8549 | 0.667734 | ||||||||
\(716\) | −29.0883 | −1.08708 | ||||||||
\(717\) | 18.4960 | 0.690745 | ||||||||
\(718\) | 3.89464 | 0.145347 | ||||||||
\(719\) | −44.3594 | −1.65432 | −0.827162 | − | 0.561963i | \(-0.810046\pi\) | ||||
−0.827162 | + | 0.561963i | \(0.810046\pi\) | |||||||
\(720\) | 2.94171 | 0.109631 | ||||||||
\(721\) | −1.45724 | −0.0542703 | ||||||||
\(722\) | 28.1599 | 1.04800 | ||||||||
\(723\) | −12.9726 | −0.482455 | ||||||||
\(724\) | −49.2325 | −1.82971 | ||||||||
\(725\) | −0.849127 | −0.0315358 | ||||||||
\(726\) | −19.5872 | −0.726948 | ||||||||
\(727\) | −0.821279 | −0.0304595 | −0.0152298 | − | 0.999884i | \(-0.504848\pi\) | ||||
−0.0152298 | + | 0.999884i | \(0.504848\pi\) | |||||||
\(728\) | 2.22244 | 0.0823693 | ||||||||
\(729\) | 12.0347 | 0.445730 | ||||||||
\(730\) | −21.0973 | −0.780848 | ||||||||
\(731\) | −49.4851 | −1.83027 | ||||||||
\(732\) | −10.6864 | −0.394980 | ||||||||
\(733\) | −13.6899 | −0.505646 | −0.252823 | − | 0.967513i | \(-0.581359\pi\) | ||||
−0.252823 | + | 0.967513i | \(0.581359\pi\) | |||||||
\(734\) | 71.4750 | 2.63819 | ||||||||
\(735\) | 15.0882 | 0.556537 | ||||||||
\(736\) | 25.9145 | 0.955222 | ||||||||
\(737\) | −5.73214 | −0.211146 | ||||||||
\(738\) | 35.8379 | 1.31921 | ||||||||
\(739\) | 10.2102 | 0.375589 | 0.187795 | − | 0.982208i | \(-0.439866\pi\) | ||||
0.187795 | + | 0.982208i | \(0.439866\pi\) | |||||||
\(740\) | −6.79437 | −0.249766 | ||||||||
\(741\) | 13.8344 | 0.508219 | ||||||||
\(742\) | 3.05236 | 0.112056 | ||||||||
\(743\) | −8.70952 | −0.319521 | −0.159761 | − | 0.987156i | \(-0.551072\pi\) | ||||
−0.159761 | + | 0.987156i | \(0.551072\pi\) | |||||||
\(744\) | 18.3235 | 0.671771 | ||||||||
\(745\) | −48.4195 | −1.77395 | ||||||||
\(746\) | −26.7169 | −0.978176 | ||||||||
\(747\) | 15.2714 | 0.558749 | ||||||||
\(748\) | 26.5824 | 0.971947 | ||||||||
\(749\) | −1.43933 | −0.0525921 | ||||||||
\(750\) | −25.1124 | −0.916974 | ||||||||
\(751\) | 21.2111 | 0.774004 | 0.387002 | − | 0.922079i | \(-0.373511\pi\) | ||||
0.387002 | + | 0.922079i | \(0.373511\pi\) | |||||||
\(752\) | 0.242663 | 0.00884900 | ||||||||
\(753\) | 24.0495 | 0.876411 | ||||||||
\(754\) | 71.9160 | 2.61903 | ||||||||
\(755\) | −15.3534 | −0.558768 | ||||||||
\(756\) | 2.51235 | 0.0913731 | ||||||||
\(757\) | −43.6388 | −1.58608 | −0.793039 | − | 0.609171i | \(-0.791502\pi\) | ||||
−0.793039 | + | 0.609171i | \(0.791502\pi\) | |||||||
\(758\) | 22.8025 | 0.828223 | ||||||||
\(759\) | 5.86876 | 0.213022 | ||||||||
\(760\) | −13.7423 | −0.498484 | ||||||||
\(761\) | −8.35977 | −0.303041 | −0.151521 | − | 0.988454i | \(-0.548417\pi\) | ||||
−0.151521 | + | 0.988454i | \(0.548417\pi\) | |||||||
\(762\) | −11.2182 | −0.406394 | ||||||||
\(763\) | −0.164703 | −0.00596265 | ||||||||
\(764\) | −58.9781 | −2.13375 | ||||||||
\(765\) | 26.3164 | 0.951471 | ||||||||
\(766\) | 49.4171 | 1.78551 | ||||||||
\(767\) | −53.5139 | −1.93228 | ||||||||
\(768\) | 11.3177 | 0.408391 | ||||||||
\(769\) | 12.1551 | 0.438323 | 0.219161 | − | 0.975689i | \(-0.429668\pi\) | ||||
0.219161 | + | 0.975689i | \(0.429668\pi\) | |||||||
\(770\) | 1.20132 | 0.0432926 | ||||||||
\(771\) | −7.37341 | −0.265547 | ||||||||
\(772\) | −36.7835 | −1.32387 | ||||||||
\(773\) | −21.2250 | −0.763411 | −0.381705 | − | 0.924284i | \(-0.624663\pi\) | ||||
−0.381705 | + | 0.924284i | \(0.624663\pi\) | |||||||
\(774\) | 38.6884 | 1.39063 | ||||||||
\(775\) | −1.12134 | −0.0402798 | ||||||||
\(776\) | −14.4518 | −0.518789 | ||||||||
\(777\) | 0.161778 | 0.00580377 | ||||||||
\(778\) | 65.1391 | 2.33535 | ||||||||
\(779\) | 19.9276 | 0.713981 | ||||||||
\(780\) | 36.8365 | 1.31896 | ||||||||
\(781\) | 8.02208 | 0.287053 | ||||||||
\(782\) | 53.8532 | 1.92579 | ||||||||
\(783\) | 28.5785 | 1.02131 | ||||||||
\(784\) | 4.57506 | 0.163395 | ||||||||
\(785\) | −12.5603 | −0.448295 | ||||||||
\(786\) | 20.4052 | 0.727829 | ||||||||
\(787\) | −43.3762 | −1.54619 | −0.773096 | − | 0.634288i | \(-0.781293\pi\) | ||||
−0.773096 | + | 0.634288i | \(0.781293\pi\) | |||||||
\(788\) | −17.6836 | −0.629951 | ||||||||
\(789\) | 12.0175 | 0.427834 | ||||||||
\(790\) | −11.5037 | −0.409283 | ||||||||
\(791\) | 0.250511 | 0.00890716 | ||||||||
\(792\) | −7.30576 | −0.259599 | ||||||||
\(793\) | −19.4706 | −0.691422 | ||||||||
\(794\) | −10.0107 | −0.355265 | ||||||||
\(795\) | 17.7848 | 0.630762 | ||||||||
\(796\) | 44.4438 | 1.57527 | ||||||||
\(797\) | −6.90142 | −0.244461 | −0.122231 | − | 0.992502i | \(-0.539005\pi\) | ||||
−0.122231 | + | 0.992502i | \(0.539005\pi\) | |||||||
\(798\) | 0.930814 | 0.0329505 | ||||||||
\(799\) | 2.17085 | 0.0767992 | ||||||||
\(800\) | −0.935887 | −0.0330886 | ||||||||
\(801\) | 3.67689 | 0.129917 | ||||||||
\(802\) | −38.9721 | −1.37615 | ||||||||
\(803\) | −6.23661 | −0.220085 | ||||||||
\(804\) | −11.8260 | −0.417071 | ||||||||
\(805\) | 1.47638 | 0.0520354 | ||||||||
\(806\) | 94.9709 | 3.34521 | ||||||||
\(807\) | −22.7435 | −0.800608 | ||||||||
\(808\) | 6.92057 | 0.243465 | ||||||||
\(809\) | 17.6983 | 0.622238 | 0.311119 | − | 0.950371i | \(-0.399296\pi\) | ||||
0.311119 | + | 0.950371i | \(0.399296\pi\) | |||||||
\(810\) | −6.19733 | −0.217752 | ||||||||
\(811\) | 39.0802 | 1.37229 | 0.686145 | − | 0.727465i | \(-0.259302\pi\) | ||||
0.686145 | + | 0.727465i | \(0.259302\pi\) | |||||||
\(812\) | 2.93527 | 0.103008 | ||||||||
\(813\) | −8.49653 | −0.297986 | ||||||||
\(814\) | −3.31093 | −0.116048 | ||||||||
\(815\) | −46.6095 | −1.63266 | ||||||||
\(816\) | −3.78283 | −0.132425 | ||||||||
\(817\) | 21.5126 | 0.752632 | ||||||||
\(818\) | −56.0433 | −1.95951 | ||||||||
\(819\) | 1.85020 | 0.0646512 | ||||||||
\(820\) | 53.0608 | 1.85296 | ||||||||
\(821\) | 32.5810 | 1.13708 | 0.568542 | − | 0.822655i | \(-0.307508\pi\) | ||||
0.568542 | + | 0.822655i | \(0.307508\pi\) | |||||||
\(822\) | 27.0492 | 0.943450 | ||||||||
\(823\) | 47.1518 | 1.64361 | 0.821804 | − | 0.569770i | \(-0.192968\pi\) | ||||
0.821804 | + | 0.569770i | \(0.192968\pi\) | |||||||
\(824\) | 21.6295 | 0.753501 | ||||||||
\(825\) | −0.211947 | −0.00737903 | ||||||||
\(826\) | −3.60056 | −0.125279 | ||||||||
\(827\) | −44.4088 | −1.54425 | −0.772123 | − | 0.635473i | \(-0.780805\pi\) | ||||
−0.772123 | + | 0.635473i | \(0.780805\pi\) | |||||||
\(828\) | −25.5409 | −0.887609 | ||||||||
\(829\) | 24.8458 | 0.862931 | 0.431466 | − | 0.902129i | \(-0.357997\pi\) | ||||
0.431466 | + | 0.902129i | \(0.357997\pi\) | |||||||
\(830\) | 37.2726 | 1.29375 | ||||||||
\(831\) | −20.7050 | −0.718248 | ||||||||
\(832\) | 72.0210 | 2.49688 | ||||||||
\(833\) | 40.9283 | 1.41808 | ||||||||
\(834\) | −11.2095 | −0.388154 | ||||||||
\(835\) | −46.5734 | −1.61174 | ||||||||
\(836\) | −11.5561 | −0.399677 | ||||||||
\(837\) | 37.7403 | 1.30449 | ||||||||
\(838\) | 21.2917 | 0.735509 | ||||||||
\(839\) | −27.7744 | −0.958879 | −0.479440 | − | 0.877575i | \(-0.659160\pi\) | ||||
−0.479440 | + | 0.877575i | \(0.659160\pi\) | |||||||
\(840\) | 0.871259 | 0.0300613 | ||||||||
\(841\) | 4.38943 | 0.151360 | ||||||||
\(842\) | −3.39640 | −0.117048 | ||||||||
\(843\) | 30.1233 | 1.03750 | ||||||||
\(844\) | 73.1820 | 2.51903 | ||||||||
\(845\) | 38.4776 | 1.32367 | ||||||||
\(846\) | −1.69721 | −0.0583513 | ||||||||
\(847\) | −1.45661 | −0.0500497 | ||||||||
\(848\) | 5.39272 | 0.185187 | ||||||||
\(849\) | −0.576647 | −0.0197905 | ||||||||
\(850\) | −1.94487 | −0.0667086 | ||||||||
\(851\) | −4.06900 | −0.139484 | ||||||||
\(852\) | 16.5504 | 0.567008 | ||||||||
\(853\) | −12.8093 | −0.438581 | −0.219291 | − | 0.975660i | \(-0.570374\pi\) | ||||
−0.219291 | + | 0.975660i | \(0.570374\pi\) | |||||||
\(854\) | −1.31003 | −0.0448284 | ||||||||
\(855\) | −11.4405 | −0.391257 | ||||||||
\(856\) | 21.3638 | 0.730200 | ||||||||
\(857\) | 16.8746 | 0.576424 | 0.288212 | − | 0.957567i | \(-0.406939\pi\) | ||||
0.288212 | + | 0.957567i | \(0.406939\pi\) | |||||||
\(858\) | 17.9506 | 0.612824 | ||||||||
\(859\) | 5.81471 | 0.198395 | 0.0991977 | − | 0.995068i | \(-0.468372\pi\) | ||||
0.0991977 | + | 0.995068i | \(0.468372\pi\) | |||||||
\(860\) | 57.2812 | 1.95327 | ||||||||
\(861\) | −1.26341 | −0.0430570 | ||||||||
\(862\) | 29.7754 | 1.01416 | ||||||||
\(863\) | −8.25272 | −0.280926 | −0.140463 | − | 0.990086i | \(-0.544859\pi\) | ||||
−0.140463 | + | 0.990086i | \(0.544859\pi\) | |||||||
\(864\) | 31.4986 | 1.07160 | ||||||||
\(865\) | −3.45002 | −0.117304 | ||||||||
\(866\) | −40.7700 | −1.38542 | ||||||||
\(867\) | −17.1429 | −0.582203 | ||||||||
\(868\) | 3.87626 | 0.131569 | ||||||||
\(869\) | −3.40062 | −0.115358 | ||||||||
\(870\) | 28.1930 | 0.955834 | ||||||||
\(871\) | −21.5470 | −0.730093 | ||||||||
\(872\) | 2.44467 | 0.0827868 | ||||||||
\(873\) | −12.0312 | −0.407195 | ||||||||
\(874\) | −23.4116 | −0.791908 | ||||||||
\(875\) | −1.86749 | −0.0631328 | ||||||||
\(876\) | −12.8668 | −0.434728 | ||||||||
\(877\) | 39.6619 | 1.33929 | 0.669644 | − | 0.742682i | \(-0.266447\pi\) | ||||
0.669644 | + | 0.742682i | \(0.266447\pi\) | |||||||
\(878\) | 32.0535 | 1.08175 | ||||||||
\(879\) | 12.4982 | 0.421554 | ||||||||
\(880\) | 2.12242 | 0.0715469 | ||||||||
\(881\) | −15.0032 | −0.505471 | −0.252736 | − | 0.967535i | \(-0.581330\pi\) | ||||
−0.252736 | + | 0.967535i | \(0.581330\pi\) | |||||||
\(882\) | −31.9985 | −1.07745 | ||||||||
\(883\) | 16.3675 | 0.550811 | 0.275405 | − | 0.961328i | \(-0.411188\pi\) | ||||
0.275405 | + | 0.961328i | \(0.411188\pi\) | |||||||
\(884\) | 99.9227 | 3.36076 | ||||||||
\(885\) | −20.9789 | −0.705199 | ||||||||
\(886\) | 24.0132 | 0.806739 | ||||||||
\(887\) | 2.05599 | 0.0690333 | 0.0345166 | − | 0.999404i | \(-0.489011\pi\) | ||||
0.0345166 | + | 0.999404i | \(0.489011\pi\) | |||||||
\(888\) | −2.40126 | −0.0805808 | ||||||||
\(889\) | −0.834250 | −0.0279798 | ||||||||
\(890\) | 8.97413 | 0.300814 | ||||||||
\(891\) | −1.83200 | −0.0613743 | ||||||||
\(892\) | −11.7081 | −0.392016 | ||||||||
\(893\) | −0.943733 | −0.0315808 | ||||||||
\(894\) | −48.6791 | −1.62807 | ||||||||
\(895\) | −20.7770 | −0.694499 | ||||||||
\(896\) | 2.74785 | 0.0917992 | ||||||||
\(897\) | 22.0606 | 0.736581 | ||||||||
\(898\) | −30.8215 | −1.02853 | ||||||||
\(899\) | 44.0934 | 1.47060 | ||||||||
\(900\) | 0.922396 | 0.0307465 | ||||||||
\(901\) | 48.2431 | 1.60721 | ||||||||
\(902\) | 25.8568 | 0.860937 | ||||||||
\(903\) | −1.36390 | −0.0453878 | ||||||||
\(904\) | −3.71831 | −0.123669 | ||||||||
\(905\) | −35.1656 | −1.16894 | ||||||||
\(906\) | −15.4357 | −0.512818 | ||||||||
\(907\) | 21.7334 | 0.721644 | 0.360822 | − | 0.932635i | \(-0.382496\pi\) | ||||
0.360822 | + | 0.932635i | \(0.382496\pi\) | |||||||
\(908\) | −39.7352 | −1.31866 | ||||||||
\(909\) | 5.76141 | 0.191094 | ||||||||
\(910\) | 4.51575 | 0.149696 | ||||||||
\(911\) | 42.7574 | 1.41661 | 0.708307 | − | 0.705904i | \(-0.249459\pi\) | ||||
0.708307 | + | 0.705904i | \(0.249459\pi\) | |||||||
\(912\) | 1.64451 | 0.0544550 | ||||||||
\(913\) | 11.0182 | 0.364648 | ||||||||
\(914\) | 0.0159747 | 0.000528396 0 | ||||||||
\(915\) | −7.63301 | −0.252340 | ||||||||
\(916\) | 8.75011 | 0.289112 | ||||||||
\(917\) | 1.51744 | 0.0501103 | ||||||||
\(918\) | 65.4574 | 2.16042 | ||||||||
\(919\) | −32.6042 | −1.07551 | −0.537757 | − | 0.843100i | \(-0.680728\pi\) | ||||
−0.537757 | + | 0.843100i | \(0.680728\pi\) | |||||||
\(920\) | −21.9136 | −0.722472 | ||||||||
\(921\) | 5.00612 | 0.164957 | ||||||||
\(922\) | −21.7257 | −0.715498 | ||||||||
\(923\) | 30.1549 | 0.992560 | ||||||||
\(924\) | 0.732659 | 0.0241027 | ||||||||
\(925\) | 0.146950 | 0.00483167 | ||||||||
\(926\) | −54.4457 | −1.78920 | ||||||||
\(927\) | 18.0067 | 0.591419 | ||||||||
\(928\) | 36.8010 | 1.20805 | ||||||||
\(929\) | −4.16366 | −0.136605 | −0.0683026 | − | 0.997665i | \(-0.521758\pi\) | ||||
−0.0683026 | + | 0.997665i | \(0.521758\pi\) | |||||||
\(930\) | 37.2312 | 1.22086 | ||||||||
\(931\) | −17.7927 | −0.583134 | ||||||||
\(932\) | 4.24042 | 0.138900 | ||||||||
\(933\) | −13.5121 | −0.442367 | ||||||||
\(934\) | −59.2306 | −1.93808 | ||||||||
\(935\) | 18.9871 | 0.620945 | ||||||||
\(936\) | −27.4622 | −0.897632 | ||||||||
\(937\) | −15.9896 | −0.522359 | −0.261179 | − | 0.965290i | \(-0.584111\pi\) | ||||
−0.261179 | + | 0.965290i | \(0.584111\pi\) | |||||||
\(938\) | −1.44974 | −0.0473357 | ||||||||
\(939\) | −2.94699 | −0.0961715 | ||||||||
\(940\) | −2.51285 | −0.0819603 | ||||||||
\(941\) | −55.9491 | −1.82389 | −0.911944 | − | 0.410315i | \(-0.865419\pi\) | ||||
−0.911944 | + | 0.410315i | \(0.865419\pi\) | |||||||
\(942\) | −12.6276 | −0.411430 | ||||||||
\(943\) | 31.7770 | 1.03480 | ||||||||
\(944\) | −6.36124 | −0.207041 | ||||||||
\(945\) | 1.79450 | 0.0583752 | ||||||||
\(946\) | 27.9134 | 0.907543 | ||||||||
\(947\) | −38.4339 | −1.24893 | −0.624467 | − | 0.781051i | \(-0.714684\pi\) | ||||
−0.624467 | + | 0.781051i | \(0.714684\pi\) | |||||||
\(948\) | −7.01584 | −0.227864 | ||||||||
\(949\) | −23.4433 | −0.761002 | ||||||||
\(950\) | 0.845494 | 0.0274315 | ||||||||
\(951\) | 30.5320 | 0.990069 | ||||||||
\(952\) | 2.36338 | 0.0765975 | ||||||||
\(953\) | −14.2452 | −0.461447 | −0.230723 | − | 0.973019i | \(-0.574109\pi\) | ||||
−0.230723 | + | 0.973019i | \(0.574109\pi\) | |||||||
\(954\) | −37.7173 | −1.22114 | ||||||||
\(955\) | −42.1266 | −1.36318 | ||||||||
\(956\) | −58.0765 | −1.87833 | ||||||||
\(957\) | 8.33417 | 0.269406 | ||||||||
\(958\) | −81.2974 | −2.62660 | ||||||||
\(959\) | 2.01153 | 0.0649557 | ||||||||
\(960\) | 28.2342 | 0.911255 | ||||||||
\(961\) | 27.2290 | 0.878354 | ||||||||
\(962\) | −12.4458 | −0.401267 | ||||||||
\(963\) | 17.7855 | 0.573130 | ||||||||
\(964\) | 40.7333 | 1.31193 | ||||||||
\(965\) | −26.2735 | −0.845774 | ||||||||
\(966\) | 1.48429 | 0.0477564 | ||||||||
\(967\) | −40.7272 | −1.30970 | −0.654849 | − | 0.755760i | \(-0.727268\pi\) | ||||
−0.654849 | + | 0.755760i | \(0.727268\pi\) | |||||||
\(968\) | 21.6203 | 0.694901 | ||||||||
\(969\) | 14.7117 | 0.472607 | ||||||||
\(970\) | −29.3644 | −0.942834 | ||||||||
\(971\) | 36.3446 | 1.16635 | 0.583177 | − | 0.812345i | \(-0.301810\pi\) | ||||
0.583177 | + | 0.812345i | \(0.301810\pi\) | |||||||
\(972\) | −49.5410 | −1.58903 | ||||||||
\(973\) | −0.833601 | −0.0267240 | ||||||||
\(974\) | −89.2611 | −2.86011 | ||||||||
\(975\) | −0.796704 | −0.0255150 | ||||||||
\(976\) | −2.31449 | −0.0740850 | ||||||||
\(977\) | 33.3523 | 1.06704 | 0.533518 | − | 0.845789i | \(-0.320870\pi\) | ||||
0.533518 | + | 0.845789i | \(0.320870\pi\) | |||||||
\(978\) | −46.8595 | −1.49840 | ||||||||
\(979\) | 2.65285 | 0.0847855 | ||||||||
\(980\) | −47.3763 | −1.51338 | ||||||||
\(981\) | 2.03520 | 0.0649789 | ||||||||
\(982\) | 1.87616 | 0.0598706 | ||||||||
\(983\) | 10.8504 | 0.346075 | 0.173038 | − | 0.984915i | \(-0.444642\pi\) | ||||
0.173038 | + | 0.984915i | \(0.444642\pi\) | |||||||
\(984\) | 18.7527 | 0.597813 | ||||||||
\(985\) | −12.6309 | −0.402455 | ||||||||
\(986\) | 76.4765 | 2.43551 | ||||||||
\(987\) | 0.0598327 | 0.00190450 | ||||||||
\(988\) | −43.4394 | −1.38199 | ||||||||
\(989\) | 34.3045 | 1.09082 | ||||||||
\(990\) | −14.8445 | −0.471788 | ||||||||
\(991\) | −31.5246 | −1.00141 | −0.500706 | − | 0.865618i | \(-0.666926\pi\) | ||||
−0.500706 | + | 0.865618i | \(0.666926\pi\) | |||||||
\(992\) | 48.5987 | 1.54301 | ||||||||
\(993\) | −5.16121 | −0.163786 | ||||||||
\(994\) | 2.02890 | 0.0643528 | ||||||||
\(995\) | 31.7451 | 1.00639 | ||||||||
\(996\) | 22.7317 | 0.720281 | ||||||||
\(997\) | 58.4676 | 1.85169 | 0.925844 | − | 0.377906i | \(-0.123356\pi\) | ||||
0.925844 | + | 0.377906i | \(0.123356\pi\) | |||||||
\(998\) | 37.4119 | 1.18425 | ||||||||
\(999\) | −4.94579 | −0.156478 |
(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 | 4033.2.a.d.1.12 | ✓ | 79 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.d.1.12 | ✓ | 79 | 1.1 | even | 1 | trivial |