Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,2,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, 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("2009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(16.0419457661\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 287) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.76801\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76801 | −1.95728 | −0.978640 | − | 0.205583i | \(-0.934091\pi\) | ||||
−0.978640 | + | 0.205583i | \(0.934091\pi\) | |||||||
\(3\) | −2.85049 | −1.64573 | −0.822866 | − | 0.568236i | \(-0.807626\pi\) | ||||
−0.822866 | + | 0.568236i | \(0.807626\pi\) | |||||||
\(4\) | 5.66188 | 2.83094 | ||||||||
\(5\) | −3.02107 | −1.35106 | −0.675531 | − | 0.737332i | \(-0.736086\pi\) | ||||
−0.675531 | + | 0.737332i | \(0.736086\pi\) | |||||||
\(6\) | 7.89019 | 3.22116 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −10.1361 | −3.58367 | ||||||||
\(9\) | 5.12530 | 1.70843 | ||||||||
\(10\) | 8.36234 | 2.64441 | ||||||||
\(11\) | −0.809408 | −0.244046 | −0.122023 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122023 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(12\) | −16.1392 | −4.65897 | ||||||||
\(13\) | −3.86586 | −1.07220 | −0.536098 | − | 0.844156i | \(-0.680102\pi\) | ||||
−0.536098 | + | 0.844156i | \(0.680102\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.61152 | 2.22349 | ||||||||
\(16\) | 16.7332 | 4.18329 | ||||||||
\(17\) | −0.828004 | −0.200821 | −0.100410 | − | 0.994946i | \(-0.532016\pi\) | ||||
−0.100410 | + | 0.994946i | \(0.532016\pi\) | |||||||
\(18\) | −14.1869 | −3.34388 | ||||||||
\(19\) | −1.89207 | −0.434069 | −0.217035 | − | 0.976164i | \(-0.569638\pi\) | ||||
−0.217035 | + | 0.976164i | \(0.569638\pi\) | |||||||
\(20\) | −17.1049 | −3.82478 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.24045 | 0.477665 | ||||||||
\(23\) | −0.475366 | −0.0991206 | −0.0495603 | − | 0.998771i | \(-0.515782\pi\) | ||||
−0.0495603 | + | 0.998771i | \(0.515782\pi\) | |||||||
\(24\) | 28.8930 | 5.89775 | ||||||||
\(25\) | 4.12684 | 0.825368 | ||||||||
\(26\) | 10.7007 | 2.09859 | ||||||||
\(27\) | −6.05815 | −1.16589 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.61064 | −0.484784 | −0.242392 | − | 0.970178i | \(-0.577932\pi\) | ||||
−0.242392 | + | 0.970178i | \(0.577932\pi\) | |||||||
\(30\) | −23.8368 | −4.35198 | ||||||||
\(31\) | 0.449043 | 0.0806505 | 0.0403253 | − | 0.999187i | \(-0.487161\pi\) | ||||
0.0403253 | + | 0.999187i | \(0.487161\pi\) | |||||||
\(32\) | −26.0453 | −4.60421 | ||||||||
\(33\) | 2.30721 | 0.401634 | ||||||||
\(34\) | 2.29192 | 0.393062 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 29.0189 | 4.83648 | ||||||||
\(37\) | 3.25880 | 0.535743 | 0.267871 | − | 0.963455i | \(-0.413680\pi\) | ||||
0.267871 | + | 0.963455i | \(0.413680\pi\) | |||||||
\(38\) | 5.23726 | 0.849595 | ||||||||
\(39\) | 11.0196 | 1.76455 | ||||||||
\(40\) | 30.6219 | 4.84175 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.10120 | −0.930425 | −0.465212 | − | 0.885199i | \(-0.654022\pi\) | ||||
−0.465212 | + | 0.885199i | \(0.654022\pi\) | |||||||
\(44\) | −4.58277 | −0.690879 | ||||||||
\(45\) | −15.4839 | −2.30820 | ||||||||
\(46\) | 1.31582 | 0.194007 | ||||||||
\(47\) | −5.67973 | −0.828474 | −0.414237 | − | 0.910169i | \(-0.635952\pi\) | ||||
−0.414237 | + | 0.910169i | \(0.635952\pi\) | |||||||
\(48\) | −47.6977 | −6.88458 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −11.4231 | −1.61548 | ||||||||
\(51\) | 2.36022 | 0.330497 | ||||||||
\(52\) | −21.8880 | −3.03532 | ||||||||
\(53\) | −13.0084 | −1.78684 | −0.893422 | − | 0.449218i | \(-0.851703\pi\) | ||||
−0.893422 | + | 0.449218i | \(0.851703\pi\) | |||||||
\(54\) | 16.7690 | 2.28197 | ||||||||
\(55\) | 2.44527 | 0.329721 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.39331 | 0.714362 | ||||||||
\(58\) | 7.22629 | 0.948858 | ||||||||
\(59\) | −9.52954 | −1.24064 | −0.620321 | − | 0.784348i | \(-0.712997\pi\) | ||||
−0.620321 | + | 0.784348i | \(0.712997\pi\) | |||||||
\(60\) | 48.7574 | 6.29456 | ||||||||
\(61\) | −11.7095 | −1.49925 | −0.749623 | − | 0.661865i | \(-0.769765\pi\) | ||||
−0.749623 | + | 0.661865i | \(0.769765\pi\) | |||||||
\(62\) | −1.24296 | −0.157856 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 38.6274 | 4.82842 | ||||||||
\(65\) | 11.6790 | 1.44860 | ||||||||
\(66\) | −6.38638 | −0.786109 | ||||||||
\(67\) | 5.13357 | 0.627165 | 0.313583 | − | 0.949561i | \(-0.398471\pi\) | ||||
0.313583 | + | 0.949561i | \(0.398471\pi\) | |||||||
\(68\) | −4.68806 | −0.568511 | ||||||||
\(69\) | 1.35503 | 0.163126 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.45987 | −0.173255 | −0.0866273 | − | 0.996241i | \(-0.527609\pi\) | ||||
−0.0866273 | + | 0.996241i | \(0.527609\pi\) | |||||||
\(72\) | −51.9507 | −6.12245 | ||||||||
\(73\) | 8.74088 | 1.02304 | 0.511521 | − | 0.859271i | \(-0.329082\pi\) | ||||
0.511521 | + | 0.859271i | \(0.329082\pi\) | |||||||
\(74\) | −9.02038 | −1.04860 | ||||||||
\(75\) | −11.7635 | −1.35833 | ||||||||
\(76\) | −10.7127 | −1.22883 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −30.5023 | −3.45371 | ||||||||
\(79\) | −10.6884 | −1.20254 | −0.601269 | − | 0.799047i | \(-0.705338\pi\) | ||||
−0.601269 | + | 0.799047i | \(0.705338\pi\) | |||||||
\(80\) | −50.5520 | −5.65189 | ||||||||
\(81\) | 1.89279 | 0.210310 | ||||||||
\(82\) | −2.76801 | −0.305676 | ||||||||
\(83\) | −6.30118 | −0.691644 | −0.345822 | − | 0.938300i | \(-0.612400\pi\) | ||||
−0.345822 | + | 0.938300i | \(0.612400\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.50146 | 0.271321 | ||||||||
\(86\) | 16.8882 | 1.82110 | ||||||||
\(87\) | 7.44162 | 0.797825 | ||||||||
\(88\) | 8.20427 | 0.874578 | ||||||||
\(89\) | −3.07544 | −0.325996 | −0.162998 | − | 0.986626i | \(-0.552116\pi\) | ||||
−0.162998 | + | 0.986626i | \(0.552116\pi\) | |||||||
\(90\) | 42.8595 | 4.51779 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.69147 | −0.280605 | ||||||||
\(93\) | −1.27999 | −0.132729 | ||||||||
\(94\) | 15.7216 | 1.62156 | ||||||||
\(95\) | 5.71605 | 0.586455 | ||||||||
\(96\) | 74.2419 | 7.57729 | ||||||||
\(97\) | −15.8551 | −1.60984 | −0.804918 | − | 0.593386i | \(-0.797791\pi\) | ||||
−0.804918 | + | 0.593386i | \(0.797791\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.14846 | −0.416936 | ||||||||
\(100\) | 23.3657 | 2.33657 | ||||||||
\(101\) | 2.85892 | 0.284474 | 0.142237 | − | 0.989833i | \(-0.454571\pi\) | ||||
0.142237 | + | 0.989833i | \(0.454571\pi\) | |||||||
\(102\) | −6.53311 | −0.646874 | ||||||||
\(103\) | −9.74855 | −0.960553 | −0.480277 | − | 0.877117i | \(-0.659464\pi\) | ||||
−0.480277 | + | 0.877117i | \(0.659464\pi\) | |||||||
\(104\) | 39.1848 | 3.84239 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 36.0075 | 3.49735 | ||||||||
\(107\) | −14.8849 | −1.43898 | −0.719489 | − | 0.694504i | \(-0.755624\pi\) | ||||
−0.719489 | + | 0.694504i | \(0.755624\pi\) | |||||||
\(108\) | −34.3005 | −3.30057 | ||||||||
\(109\) | −9.75957 | −0.934798 | −0.467399 | − | 0.884047i | \(-0.654809\pi\) | ||||
−0.467399 | + | 0.884047i | \(0.654809\pi\) | |||||||
\(110\) | −6.76855 | −0.645356 | ||||||||
\(111\) | −9.28917 | −0.881689 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.3338 | −1.91284 | −0.956420 | − | 0.291996i | \(-0.905681\pi\) | ||||
−0.956420 | + | 0.291996i | \(0.905681\pi\) | |||||||
\(114\) | −14.9288 | −1.39821 | ||||||||
\(115\) | 1.43611 | 0.133918 | ||||||||
\(116\) | −14.7812 | −1.37240 | ||||||||
\(117\) | −19.8137 | −1.83177 | ||||||||
\(118\) | 26.3779 | 2.42828 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −87.2876 | −7.96823 | ||||||||
\(121\) | −10.3449 | −0.940442 | ||||||||
\(122\) | 32.4120 | 2.93444 | ||||||||
\(123\) | −2.85049 | −0.257020 | ||||||||
\(124\) | 2.54243 | 0.228317 | ||||||||
\(125\) | 2.63787 | 0.235939 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.82133 | 0.694031 | 0.347015 | − | 0.937859i | \(-0.387195\pi\) | ||||
0.347015 | + | 0.937859i | \(0.387195\pi\) | |||||||
\(128\) | −54.8304 | −4.84637 | ||||||||
\(129\) | 17.3914 | 1.53123 | ||||||||
\(130\) | −32.3276 | −2.83532 | ||||||||
\(131\) | −2.45252 | −0.214278 | −0.107139 | − | 0.994244i | \(-0.534169\pi\) | ||||
−0.107139 | + | 0.994244i | \(0.534169\pi\) | |||||||
\(132\) | 13.0632 | 1.13700 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14.2098 | −1.22754 | ||||||||
\(135\) | 18.3021 | 1.57519 | ||||||||
\(136\) | 8.39276 | 0.719674 | ||||||||
\(137\) | 13.3576 | 1.14121 | 0.570607 | − | 0.821223i | \(-0.306708\pi\) | ||||
0.570607 | + | 0.821223i | \(0.306708\pi\) | |||||||
\(138\) | −3.75073 | −0.319283 | ||||||||
\(139\) | −9.08568 | −0.770638 | −0.385319 | − | 0.922784i | \(-0.625909\pi\) | ||||
−0.385319 | + | 0.922784i | \(0.625909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.1900 | 1.36345 | ||||||||
\(142\) | 4.04093 | 0.339108 | ||||||||
\(143\) | 3.12905 | 0.261665 | ||||||||
\(144\) | 85.7625 | 7.14687 | ||||||||
\(145\) | 7.88693 | 0.654974 | ||||||||
\(146\) | −24.1949 | −2.00238 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.4509 | 1.51666 | ||||||||
\(149\) | 2.94081 | 0.240921 | 0.120460 | − | 0.992718i | \(-0.461563\pi\) | ||||
0.120460 | + | 0.992718i | \(0.461563\pi\) | |||||||
\(150\) | 32.5616 | 2.65864 | ||||||||
\(151\) | 1.91810 | 0.156093 | 0.0780464 | − | 0.996950i | \(-0.475132\pi\) | ||||
0.0780464 | + | 0.996950i | \(0.475132\pi\) | |||||||
\(152\) | 19.1782 | 1.55556 | ||||||||
\(153\) | −4.24377 | −0.343088 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.35659 | −0.108964 | ||||||||
\(156\) | 62.3916 | 4.99533 | ||||||||
\(157\) | 10.5089 | 0.838702 | 0.419351 | − | 0.907824i | \(-0.362258\pi\) | ||||
0.419351 | + | 0.907824i | \(0.362258\pi\) | |||||||
\(158\) | 29.5856 | 2.35370 | ||||||||
\(159\) | 37.0804 | 2.94067 | ||||||||
\(160\) | 78.6846 | 6.22057 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.23927 | −0.411636 | ||||||||
\(163\) | 18.0875 | 1.41672 | 0.708362 | − | 0.705849i | \(-0.249434\pi\) | ||||
0.708362 | + | 0.705849i | \(0.249434\pi\) | |||||||
\(164\) | 5.66188 | 0.442119 | ||||||||
\(165\) | −6.97023 | −0.542632 | ||||||||
\(166\) | 17.4417 | 1.35374 | ||||||||
\(167\) | 19.0456 | 1.47380 | 0.736898 | − | 0.676004i | \(-0.236290\pi\) | ||||
0.736898 | + | 0.676004i | \(0.236290\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.94485 | 0.149604 | ||||||||
\(170\) | −6.92406 | −0.531051 | ||||||||
\(171\) | −9.69740 | −0.741579 | ||||||||
\(172\) | −34.5443 | −2.63398 | ||||||||
\(173\) | −4.63435 | −0.352343 | −0.176172 | − | 0.984359i | \(-0.556371\pi\) | ||||
−0.176172 | + | 0.984359i | \(0.556371\pi\) | |||||||
\(174\) | −20.5985 | −1.56157 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.5440 | −1.02091 | ||||||||
\(177\) | 27.1639 | 2.04176 | ||||||||
\(178\) | 8.51284 | 0.638065 | ||||||||
\(179\) | −10.7836 | −0.806002 | −0.403001 | − | 0.915200i | \(-0.632033\pi\) | ||||
−0.403001 | + | 0.915200i | \(0.632033\pi\) | |||||||
\(180\) | −87.6679 | −6.53438 | ||||||||
\(181\) | 19.6683 | 1.46193 | 0.730965 | − | 0.682415i | \(-0.239070\pi\) | ||||
0.730965 | + | 0.682415i | \(0.239070\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 33.3778 | 2.46736 | ||||||||
\(184\) | 4.81837 | 0.355215 | ||||||||
\(185\) | −9.84504 | −0.723822 | ||||||||
\(186\) | 3.54304 | 0.259788 | ||||||||
\(187\) | 0.670193 | 0.0490094 | ||||||||
\(188\) | −32.1580 | −2.34536 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.8221 | −1.14786 | ||||||||
\(191\) | 23.2230 | 1.68035 | 0.840177 | − | 0.542312i | \(-0.182451\pi\) | ||||
0.840177 | + | 0.542312i | \(0.182451\pi\) | |||||||
\(192\) | −110.107 | −7.94629 | ||||||||
\(193\) | −14.7682 | −1.06304 | −0.531518 | − | 0.847047i | \(-0.678378\pi\) | ||||
−0.531518 | + | 0.847047i | \(0.678378\pi\) | |||||||
\(194\) | 43.8870 | 3.15090 | ||||||||
\(195\) | −33.2909 | −2.38401 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.0210 | −1.56893 | −0.784466 | − | 0.620172i | \(-0.787063\pi\) | ||||
−0.784466 | + | 0.620172i | \(0.787063\pi\) | |||||||
\(198\) | 11.4830 | 0.816059 | ||||||||
\(199\) | −7.15240 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(200\) | −41.8302 | −2.95784 | ||||||||
\(201\) | −14.6332 | −1.03215 | ||||||||
\(202\) | −7.91353 | −0.556794 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 13.3633 | 0.935617 | ||||||||
\(205\) | −3.02107 | −0.211000 | ||||||||
\(206\) | 26.9841 | 1.88007 | ||||||||
\(207\) | −2.43639 | −0.169341 | ||||||||
\(208\) | −64.6880 | −4.48531 | ||||||||
\(209\) | 1.53145 | 0.105933 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.5087 | 1.20535 | 0.602673 | − | 0.797988i | \(-0.294102\pi\) | ||||
0.602673 | + | 0.797988i | \(0.294102\pi\) | |||||||
\(212\) | −73.6522 | −5.05845 | ||||||||
\(213\) | 4.16134 | 0.285131 | ||||||||
\(214\) | 41.2016 | 2.81648 | ||||||||
\(215\) | 18.4321 | 1.25706 | ||||||||
\(216\) | 61.4062 | 4.17816 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 27.0146 | 1.82966 | ||||||||
\(219\) | −24.9158 | −1.68365 | ||||||||
\(220\) | 13.8449 | 0.933420 | ||||||||
\(221\) | 3.20095 | 0.215319 | ||||||||
\(222\) | 25.7125 | 1.72571 | ||||||||
\(223\) | 9.22671 | 0.617866 | 0.308933 | − | 0.951084i | \(-0.400028\pi\) | ||||
0.308933 | + | 0.951084i | \(0.400028\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 21.1513 | 1.41009 | ||||||||
\(226\) | 56.2841 | 3.74396 | ||||||||
\(227\) | 21.8853 | 1.45258 | 0.726290 | − | 0.687388i | \(-0.241243\pi\) | ||||
0.726290 | + | 0.687388i | \(0.241243\pi\) | |||||||
\(228\) | 30.5363 | 2.02232 | ||||||||
\(229\) | −8.91465 | −0.589097 | −0.294548 | − | 0.955637i | \(-0.595169\pi\) | ||||
−0.294548 | + | 0.955637i | \(0.595169\pi\) | |||||||
\(230\) | −3.97517 | −0.262115 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 26.4618 | 1.73730 | ||||||||
\(233\) | 0.537037 | 0.0351825 | 0.0175912 | − | 0.999845i | \(-0.494400\pi\) | ||||
0.0175912 | + | 0.999845i | \(0.494400\pi\) | |||||||
\(234\) | 54.8445 | 3.58529 | ||||||||
\(235\) | 17.1588 | 1.11932 | ||||||||
\(236\) | −53.9552 | −3.51218 | ||||||||
\(237\) | 30.4672 | 1.97906 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.2066 | 0.918951 | 0.459476 | − | 0.888190i | \(-0.348037\pi\) | ||||
0.459476 | + | 0.888190i | \(0.348037\pi\) | |||||||
\(240\) | 144.098 | 9.30149 | ||||||||
\(241\) | −7.18725 | −0.462972 | −0.231486 | − | 0.972838i | \(-0.574359\pi\) | ||||
−0.231486 | + | 0.972838i | \(0.574359\pi\) | |||||||
\(242\) | 28.6347 | 1.84071 | ||||||||
\(243\) | 12.7790 | 0.819776 | ||||||||
\(244\) | −66.2978 | −4.24428 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.89019 | 0.503060 | ||||||||
\(247\) | 7.31445 | 0.465407 | ||||||||
\(248\) | −4.55156 | −0.289025 | ||||||||
\(249\) | 17.9614 | 1.13826 | ||||||||
\(250\) | −7.30166 | −0.461798 | ||||||||
\(251\) | 7.54012 | 0.475928 | 0.237964 | − | 0.971274i | \(-0.423520\pi\) | ||||
0.237964 | + | 0.971274i | \(0.423520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.384765 | 0.0241900 | ||||||||
\(254\) | −21.6495 | −1.35841 | ||||||||
\(255\) | −7.13038 | −0.446521 | ||||||||
\(256\) | 74.5164 | 4.65727 | ||||||||
\(257\) | 19.7370 | 1.23116 | 0.615579 | − | 0.788075i | \(-0.288922\pi\) | ||||
0.615579 | + | 0.788075i | \(0.288922\pi\) | |||||||
\(258\) | −48.1397 | −2.99704 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 66.1252 | 4.10091 | ||||||||
\(261\) | −13.3803 | −0.828222 | ||||||||
\(262\) | 6.78860 | 0.419401 | ||||||||
\(263\) | 0.286751 | 0.0176818 | 0.00884092 | − | 0.999961i | \(-0.497186\pi\) | ||||
0.00884092 | + | 0.999961i | \(0.497186\pi\) | |||||||
\(264\) | −23.3862 | −1.43932 | ||||||||
\(265\) | 39.2993 | 2.41414 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.76651 | 0.536501 | ||||||||
\(268\) | 29.0657 | 1.77547 | ||||||||
\(269\) | −18.2027 | −1.10984 | −0.554920 | − | 0.831904i | \(-0.687251\pi\) | ||||
−0.554920 | + | 0.831904i | \(0.687251\pi\) | |||||||
\(270\) | −50.6603 | −3.08309 | ||||||||
\(271\) | −4.82169 | −0.292897 | −0.146448 | − | 0.989218i | \(-0.546784\pi\) | ||||
−0.146448 | + | 0.989218i | \(0.546784\pi\) | |||||||
\(272\) | −13.8551 | −0.840091 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −36.9739 | −2.23367 | ||||||||
\(275\) | −3.34030 | −0.201427 | ||||||||
\(276\) | 7.67200 | 0.461800 | ||||||||
\(277\) | −14.4367 | −0.867416 | −0.433708 | − | 0.901054i | \(-0.642795\pi\) | ||||
−0.433708 | + | 0.901054i | \(0.642795\pi\) | |||||||
\(278\) | 25.1493 | 1.50835 | ||||||||
\(279\) | 2.30148 | 0.137786 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.23994 | −0.252934 | −0.126467 | − | 0.991971i | \(-0.540364\pi\) | ||||
−0.126467 | + | 0.991971i | \(0.540364\pi\) | |||||||
\(282\) | −44.8142 | −2.66864 | ||||||||
\(283\) | −22.5254 | −1.33900 | −0.669498 | − | 0.742813i | \(-0.733491\pi\) | ||||
−0.669498 | + | 0.742813i | \(0.733491\pi\) | |||||||
\(284\) | −8.26561 | −0.490474 | ||||||||
\(285\) | −16.2936 | −0.965147 | ||||||||
\(286\) | −8.66126 | −0.512151 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −133.490 | −7.86598 | ||||||||
\(289\) | −16.3144 | −0.959671 | ||||||||
\(290\) | −21.8311 | −1.28197 | ||||||||
\(291\) | 45.1947 | 2.64936 | ||||||||
\(292\) | 49.4899 | 2.89617 | ||||||||
\(293\) | 13.5665 | 0.792565 | 0.396282 | − | 0.918129i | \(-0.370300\pi\) | ||||
0.396282 | + | 0.918129i | \(0.370300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 28.7894 | 1.67618 | ||||||||
\(296\) | −33.0316 | −1.91992 | ||||||||
\(297\) | 4.90351 | 0.284531 | ||||||||
\(298\) | −8.14019 | −0.471549 | ||||||||
\(299\) | 1.83770 | 0.106277 | ||||||||
\(300\) | −66.6037 | −3.84537 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5.30932 | −0.305517 | ||||||||
\(303\) | −8.14934 | −0.468167 | ||||||||
\(304\) | −31.6602 | −1.81584 | ||||||||
\(305\) | 35.3751 | 2.02557 | ||||||||
\(306\) | 11.7468 | 0.671520 | ||||||||
\(307\) | −26.6357 | −1.52018 | −0.760090 | − | 0.649817i | \(-0.774845\pi\) | ||||
−0.760090 | + | 0.649817i | \(0.774845\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.7882 | 1.58081 | ||||||||
\(310\) | 3.75505 | 0.213273 | ||||||||
\(311\) | 9.43307 | 0.534900 | 0.267450 | − | 0.963572i | \(-0.413819\pi\) | ||||
0.267450 | + | 0.963572i | \(0.413819\pi\) | |||||||
\(312\) | −111.696 | −6.32354 | ||||||||
\(313\) | −12.1547 | −0.687023 | −0.343511 | − | 0.939148i | \(-0.611616\pi\) | ||||
−0.343511 | + | 0.939148i | \(0.611616\pi\) | |||||||
\(314\) | −29.0888 | −1.64157 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −60.5165 | −3.40432 | ||||||||
\(317\) | 14.4001 | 0.808789 | 0.404394 | − | 0.914585i | \(-0.367482\pi\) | ||||
0.404394 | + | 0.914585i | \(0.367482\pi\) | |||||||
\(318\) | −102.639 | −5.75571 | ||||||||
\(319\) | 2.11308 | 0.118310 | ||||||||
\(320\) | −116.696 | −6.52350 | ||||||||
\(321\) | 42.4293 | 2.36817 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.56664 | 0.0871701 | ||||||||
\(324\) | 10.7168 | 0.595377 | ||||||||
\(325\) | −15.9538 | −0.884956 | ||||||||
\(326\) | −50.0665 | −2.77292 | ||||||||
\(327\) | 27.8196 | 1.53843 | ||||||||
\(328\) | −10.1361 | −0.559675 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 19.2937 | 1.06208 | ||||||||
\(331\) | −4.76156 | −0.261719 | −0.130859 | − | 0.991401i | \(-0.541774\pi\) | ||||
−0.130859 | + | 0.991401i | \(0.541774\pi\) | |||||||
\(332\) | −35.6765 | −1.95800 | ||||||||
\(333\) | 16.7023 | 0.915281 | ||||||||
\(334\) | −52.7185 | −2.88463 | ||||||||
\(335\) | −15.5088 | −0.847339 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.79898 | −0.479311 | −0.239655 | − | 0.970858i | \(-0.577034\pi\) | ||||
−0.239655 | + | 0.970858i | \(0.577034\pi\) | |||||||
\(338\) | −5.38335 | −0.292816 | ||||||||
\(339\) | 57.9612 | 3.14802 | ||||||||
\(340\) | 14.1630 | 0.768094 | ||||||||
\(341\) | −0.363459 | −0.0196824 | ||||||||
\(342\) | 26.8425 | 1.45148 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 61.8426 | 3.33433 | ||||||||
\(345\) | −4.09362 | −0.220393 | ||||||||
\(346\) | 12.8279 | 0.689634 | ||||||||
\(347\) | −26.0201 | −1.39683 | −0.698416 | − | 0.715692i | \(-0.746112\pi\) | ||||
−0.698416 | + | 0.715692i | \(0.746112\pi\) | |||||||
\(348\) | 42.1336 | 2.25860 | ||||||||
\(349\) | −14.7488 | −0.789488 | −0.394744 | − | 0.918791i | \(-0.629167\pi\) | ||||
−0.394744 | + | 0.918791i | \(0.629167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.4199 | 1.25006 | ||||||||
\(352\) | 21.0813 | 1.12364 | ||||||||
\(353\) | 11.0539 | 0.588341 | 0.294170 | − | 0.955753i | \(-0.404957\pi\) | ||||
0.294170 | + | 0.955753i | \(0.404957\pi\) | |||||||
\(354\) | −75.1899 | −3.99630 | ||||||||
\(355\) | 4.41036 | 0.234078 | ||||||||
\(356\) | −17.4128 | −0.922875 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 29.8490 | 1.57757 | ||||||||
\(359\) | 23.7540 | 1.25369 | 0.626845 | − | 0.779144i | \(-0.284346\pi\) | ||||
0.626845 | + | 0.779144i | \(0.284346\pi\) | |||||||
\(360\) | 156.947 | 8.27181 | ||||||||
\(361\) | −15.4201 | −0.811584 | ||||||||
\(362\) | −54.4420 | −2.86141 | ||||||||
\(363\) | 29.4879 | 1.54771 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.4068 | −1.38219 | ||||||||
\(366\) | −92.3901 | −4.82931 | ||||||||
\(367\) | 21.1330 | 1.10313 | 0.551567 | − | 0.834130i | \(-0.314030\pi\) | ||||
0.551567 | + | 0.834130i | \(0.314030\pi\) | |||||||
\(368\) | −7.95438 | −0.414650 | ||||||||
\(369\) | 5.12530 | 0.266812 | ||||||||
\(370\) | 27.2512 | 1.41672 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.24718 | −0.375749 | ||||||||
\(373\) | 8.91618 | 0.461662 | 0.230831 | − | 0.972994i | \(-0.425855\pi\) | ||||
0.230831 | + | 0.972994i | \(0.425855\pi\) | |||||||
\(374\) | −1.85510 | −0.0959250 | ||||||||
\(375\) | −7.51923 | −0.388292 | ||||||||
\(376\) | 57.5705 | 2.96897 | ||||||||
\(377\) | 10.0924 | 0.519784 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.48486 | 0.127639 | 0.0638194 | − | 0.997961i | \(-0.479672\pi\) | ||||
0.0638194 | + | 0.997961i | \(0.479672\pi\) | |||||||
\(380\) | 32.3636 | 1.66022 | ||||||||
\(381\) | −22.2946 | −1.14219 | ||||||||
\(382\) | −64.2814 | −3.28892 | ||||||||
\(383\) | −12.1522 | −0.620950 | −0.310475 | − | 0.950582i | \(-0.600488\pi\) | ||||
−0.310475 | + | 0.950582i | \(0.600488\pi\) | |||||||
\(384\) | 156.294 | 7.97582 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 40.8785 | 2.08066 | ||||||||
\(387\) | −31.2705 | −1.58957 | ||||||||
\(388\) | −89.7695 | −4.55735 | ||||||||
\(389\) | −33.0103 | −1.67369 | −0.836844 | − | 0.547441i | \(-0.815602\pi\) | ||||
−0.836844 | + | 0.547441i | \(0.815602\pi\) | |||||||
\(390\) | 92.1496 | 4.66618 | ||||||||
\(391\) | 0.393605 | 0.0199055 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.99088 | 0.352643 | ||||||||
\(394\) | 60.9544 | 3.07084 | ||||||||
\(395\) | 32.2903 | 1.62470 | ||||||||
\(396\) | −23.4881 | −1.18032 | ||||||||
\(397\) | 17.1194 | 0.859198 | 0.429599 | − | 0.903020i | \(-0.358655\pi\) | ||||
0.429599 | + | 0.903020i | \(0.358655\pi\) | |||||||
\(398\) | 19.7979 | 0.992380 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 69.0551 | 3.45276 | ||||||||
\(401\) | 15.5316 | 0.775611 | 0.387805 | − | 0.921741i | \(-0.373233\pi\) | ||||
0.387805 | + | 0.921741i | \(0.373233\pi\) | |||||||
\(402\) | 40.5048 | 2.02020 | ||||||||
\(403\) | −1.73594 | −0.0864732 | ||||||||
\(404\) | 16.1869 | 0.805328 | ||||||||
\(405\) | −5.71826 | −0.284142 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.63770 | −0.130746 | ||||||||
\(408\) | −23.9235 | −1.18439 | ||||||||
\(409\) | 1.10843 | 0.0548083 | 0.0274041 | − | 0.999624i | \(-0.491276\pi\) | ||||
0.0274041 | + | 0.999624i | \(0.491276\pi\) | |||||||
\(410\) | 8.36234 | 0.412987 | ||||||||
\(411\) | −38.0756 | −1.87813 | ||||||||
\(412\) | −55.1952 | −2.71927 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.74396 | 0.331448 | ||||||||
\(415\) | 19.0363 | 0.934454 | ||||||||
\(416\) | 100.687 | 4.93661 | ||||||||
\(417\) | 25.8987 | 1.26826 | ||||||||
\(418\) | −4.23908 | −0.207340 | ||||||||
\(419\) | −5.74205 | −0.280518 | −0.140259 | − | 0.990115i | \(-0.544793\pi\) | ||||
−0.140259 | + | 0.990115i | \(0.544793\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.9380 | −1.21541 | −0.607703 | − | 0.794165i | \(-0.707909\pi\) | ||||
−0.607703 | + | 0.794165i | \(0.707909\pi\) | |||||||
\(422\) | −48.4641 | −2.35920 | ||||||||
\(423\) | −29.1103 | −1.41539 | ||||||||
\(424\) | 131.855 | 6.40345 | ||||||||
\(425\) | −3.41704 | −0.165751 | ||||||||
\(426\) | −11.5186 | −0.558080 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −84.2766 | −4.07367 | ||||||||
\(429\) | −8.91934 | −0.430630 | ||||||||
\(430\) | −51.0204 | −2.46042 | ||||||||
\(431\) | 15.8925 | 0.765517 | 0.382758 | − | 0.923848i | \(-0.374974\pi\) | ||||
0.382758 | + | 0.923848i | \(0.374974\pi\) | |||||||
\(432\) | −101.372 | −4.87726 | ||||||||
\(433\) | 6.34096 | 0.304727 | 0.152364 | − | 0.988325i | \(-0.451312\pi\) | ||||
0.152364 | + | 0.988325i | \(0.451312\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.4816 | −1.07791 | ||||||||
\(436\) | −55.2576 | −2.64636 | ||||||||
\(437\) | 0.899423 | 0.0430252 | ||||||||
\(438\) | 68.9672 | 3.29538 | ||||||||
\(439\) | −30.3726 | −1.44961 | −0.724803 | − | 0.688956i | \(-0.758069\pi\) | ||||
−0.724803 | + | 0.688956i | \(0.758069\pi\) | |||||||
\(440\) | −24.7856 | −1.18161 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.86025 | −0.421439 | ||||||||
\(443\) | 29.3469 | 1.39431 | 0.697157 | − | 0.716918i | \(-0.254448\pi\) | ||||
0.697157 | + | 0.716918i | \(0.254448\pi\) | |||||||
\(444\) | −52.5942 | −2.49601 | ||||||||
\(445\) | 9.29110 | 0.440440 | ||||||||
\(446\) | −25.5396 | −1.20934 | ||||||||
\(447\) | −8.38275 | −0.396491 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.1178 | 1.65731 | 0.828656 | − | 0.559758i | \(-0.189106\pi\) | ||||
0.828656 | + | 0.559758i | \(0.189106\pi\) | |||||||
\(450\) | −58.5470 | −2.75993 | ||||||||
\(451\) | −0.809408 | −0.0381135 | ||||||||
\(452\) | −115.127 | −5.41514 | ||||||||
\(453\) | −5.46753 | −0.256887 | ||||||||
\(454\) | −60.5788 | −2.84310 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −54.6674 | −2.56003 | ||||||||
\(457\) | 4.90137 | 0.229276 | 0.114638 | − | 0.993407i | \(-0.463429\pi\) | ||||
0.114638 | + | 0.993407i | \(0.463429\pi\) | |||||||
\(458\) | 24.6759 | 1.15303 | ||||||||
\(459\) | 5.01617 | 0.234135 | ||||||||
\(460\) | 8.13110 | 0.379114 | ||||||||
\(461\) | 1.55339 | 0.0723486 | 0.0361743 | − | 0.999345i | \(-0.488483\pi\) | ||||
0.0361743 | + | 0.999345i | \(0.488483\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.30847 | −0.293179 | −0.146590 | − | 0.989197i | \(-0.546830\pi\) | ||||
−0.146590 | + | 0.989197i | \(0.546830\pi\) | |||||||
\(464\) | −43.6843 | −2.02799 | ||||||||
\(465\) | 3.86695 | 0.179325 | ||||||||
\(466\) | −1.48652 | −0.0688619 | ||||||||
\(467\) | 21.0062 | 0.972049 | 0.486024 | − | 0.873945i | \(-0.338447\pi\) | ||||
0.486024 | + | 0.873945i | \(0.338447\pi\) | |||||||
\(468\) | −112.183 | −5.18565 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −47.4959 | −2.19082 | ||||||||
\(471\) | −29.9555 | −1.38028 | ||||||||
\(472\) | 96.5928 | 4.44604 | ||||||||
\(473\) | 4.93836 | 0.227066 | ||||||||
\(474\) | −84.3335 | −3.87356 | ||||||||
\(475\) | −7.80825 | −0.358267 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −66.6721 | −3.05270 | ||||||||
\(478\) | −39.3241 | −1.79864 | ||||||||
\(479\) | −0.510272 | −0.0233149 | −0.0116575 | − | 0.999932i | \(-0.503711\pi\) | ||||
−0.0116575 | + | 0.999932i | \(0.503711\pi\) | |||||||
\(480\) | −224.290 | −10.2374 | ||||||||
\(481\) | −12.5980 | −0.574421 | ||||||||
\(482\) | 19.8944 | 0.906165 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −58.5714 | −2.66234 | ||||||||
\(485\) | 47.8992 | 2.17499 | ||||||||
\(486\) | −35.3725 | −1.60453 | ||||||||
\(487\) | 10.9455 | 0.495988 | 0.247994 | − | 0.968762i | \(-0.420229\pi\) | ||||
0.247994 | + | 0.968762i | \(0.420229\pi\) | |||||||
\(488\) | 118.689 | 5.37280 | ||||||||
\(489\) | −51.5583 | −2.33155 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.52841 | 0.0689760 | 0.0344880 | − | 0.999405i | \(-0.489020\pi\) | ||||
0.0344880 | + | 0.999405i | \(0.489020\pi\) | |||||||
\(492\) | −16.1392 | −0.727609 | ||||||||
\(493\) | 2.16162 | 0.0973546 | ||||||||
\(494\) | −20.2465 | −0.910932 | ||||||||
\(495\) | 12.5328 | 0.563306 | ||||||||
\(496\) | 7.51392 | 0.337385 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −49.7175 | −2.22789 | ||||||||
\(499\) | −29.5904 | −1.32465 | −0.662324 | − | 0.749218i | \(-0.730430\pi\) | ||||
−0.662324 | + | 0.749218i | \(0.730430\pi\) | |||||||
\(500\) | 14.9353 | 0.667928 | ||||||||
\(501\) | −54.2894 | −2.42547 | ||||||||
\(502\) | −20.8711 | −0.931525 | ||||||||
\(503\) | 29.9673 | 1.33618 | 0.668088 | − | 0.744082i | \(-0.267113\pi\) | ||||
0.668088 | + | 0.744082i | \(0.267113\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.63700 | −0.384341 | ||||||||
\(506\) | −1.06503 | −0.0473465 | ||||||||
\(507\) | −5.54377 | −0.246207 | ||||||||
\(508\) | 44.2835 | 1.96476 | ||||||||
\(509\) | −9.94634 | −0.440864 | −0.220432 | − | 0.975402i | \(-0.570747\pi\) | ||||
−0.220432 | + | 0.975402i | \(0.570747\pi\) | |||||||
\(510\) | 19.7370 | 0.873967 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −96.6013 | −4.26922 | ||||||||
\(513\) | 11.4624 | 0.506078 | ||||||||
\(514\) | −54.6321 | −2.40972 | ||||||||
\(515\) | 29.4510 | 1.29777 | ||||||||
\(516\) | 98.4682 | 4.33482 | ||||||||
\(517\) | 4.59722 | 0.202185 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.2102 | 0.579862 | ||||||||
\(520\) | −118.380 | −5.19131 | ||||||||
\(521\) | −31.9204 | −1.39846 | −0.699230 | − | 0.714897i | \(-0.746474\pi\) | ||||
−0.699230 | + | 0.714897i | \(0.746474\pi\) | |||||||
\(522\) | 37.0369 | 1.62106 | ||||||||
\(523\) | 13.5725 | 0.593484 | 0.296742 | − | 0.954958i | \(-0.404100\pi\) | ||||
0.296742 | + | 0.954958i | \(0.404100\pi\) | |||||||
\(524\) | −13.8859 | −0.606607 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.793731 | −0.0346083 | ||||||||
\(527\) | −0.371810 | −0.0161963 | ||||||||
\(528\) | 38.6069 | 1.68015 | ||||||||
\(529\) | −22.7740 | −0.990175 | ||||||||
\(530\) | −108.781 | −4.72514 | ||||||||
\(531\) | −48.8418 | −2.11955 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.86586 | −0.167449 | ||||||||
\(534\) | −24.2658 | −1.05008 | ||||||||
\(535\) | 44.9683 | 1.94415 | ||||||||
\(536\) | −52.0345 | −2.24755 | ||||||||
\(537\) | 30.7385 | 1.32646 | ||||||||
\(538\) | 50.3854 | 2.17227 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 103.624 | 4.45927 | ||||||||
\(541\) | −3.85715 | −0.165832 | −0.0829159 | − | 0.996557i | \(-0.526423\pi\) | ||||
−0.0829159 | + | 0.996557i | \(0.526423\pi\) | |||||||
\(542\) | 13.3465 | 0.573280 | ||||||||
\(543\) | −56.0642 | −2.40595 | ||||||||
\(544\) | 21.5656 | 0.924619 | ||||||||
\(545\) | 29.4843 | 1.26297 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.96156 | 0.169384 | 0.0846920 | − | 0.996407i | \(-0.473009\pi\) | ||||
0.0846920 | + | 0.996407i | \(0.473009\pi\) | |||||||
\(548\) | 75.6290 | 3.23071 | ||||||||
\(549\) | −60.0146 | −2.56136 | ||||||||
\(550\) | 9.24598 | 0.394250 | ||||||||
\(551\) | 4.93951 | 0.210430 | ||||||||
\(552\) | −13.7347 | −0.584589 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 39.9609 | 1.69777 | ||||||||
\(555\) | 28.0632 | 1.19122 | ||||||||
\(556\) | −51.4421 | −2.18163 | ||||||||
\(557\) | −7.17809 | −0.304145 | −0.152073 | − | 0.988369i | \(-0.548595\pi\) | ||||
−0.152073 | + | 0.988369i | \(0.548595\pi\) | |||||||
\(558\) | −6.37052 | −0.269686 | ||||||||
\(559\) | 23.5864 | 0.997597 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.91038 | −0.0806563 | ||||||||
\(562\) | 11.7362 | 0.495062 | ||||||||
\(563\) | −24.9483 | −1.05145 | −0.525723 | − | 0.850656i | \(-0.676205\pi\) | ||||
−0.525723 | + | 0.850656i | \(0.676205\pi\) | |||||||
\(564\) | 91.6660 | 3.85984 | ||||||||
\(565\) | 61.4296 | 2.58436 | ||||||||
\(566\) | 62.3506 | 2.62079 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.7974 | 0.620886 | ||||||||
\(569\) | −35.7525 | −1.49882 | −0.749412 | − | 0.662104i | \(-0.769664\pi\) | ||||
−0.749412 | + | 0.662104i | \(0.769664\pi\) | |||||||
\(570\) | 45.1008 | 1.88906 | ||||||||
\(571\) | 32.9225 | 1.37777 | 0.688883 | − | 0.724873i | \(-0.258101\pi\) | ||||
0.688883 | + | 0.724873i | \(0.258101\pi\) | |||||||
\(572\) | 17.7163 | 0.740758 | ||||||||
\(573\) | −66.1968 | −2.76541 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.96176 | −0.0818110 | ||||||||
\(576\) | 197.977 | 8.24904 | ||||||||
\(577\) | −13.0378 | −0.542770 | −0.271385 | − | 0.962471i | \(-0.587482\pi\) | ||||
−0.271385 | + | 0.962471i | \(0.587482\pi\) | |||||||
\(578\) | 45.1585 | 1.87834 | ||||||||
\(579\) | 42.0965 | 1.74947 | ||||||||
\(580\) | 44.6549 | 1.85419 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −125.099 | −5.18554 | ||||||||
\(583\) | 10.5291 | 0.436072 | ||||||||
\(584\) | −88.5988 | −3.66624 | ||||||||
\(585\) | 59.8584 | 2.47484 | ||||||||
\(586\) | −37.5523 | −1.55127 | ||||||||
\(587\) | 20.5144 | 0.846721 | 0.423360 | − | 0.905961i | \(-0.360850\pi\) | ||||
0.423360 | + | 0.905961i | \(0.360850\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.849619 | −0.0350079 | ||||||||
\(590\) | −79.6893 | −3.28076 | ||||||||
\(591\) | 62.7707 | 2.58204 | ||||||||
\(592\) | 54.5300 | 2.24117 | ||||||||
\(593\) | −25.8242 | −1.06047 | −0.530236 | − | 0.847850i | \(-0.677897\pi\) | ||||
−0.530236 | + | 0.847850i | \(0.677897\pi\) | |||||||
\(594\) | −13.5730 | −0.556906 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.6505 | 0.682032 | ||||||||
\(597\) | 20.3879 | 0.834419 | ||||||||
\(598\) | −5.08676 | −0.208013 | ||||||||
\(599\) | 8.13168 | 0.332252 | 0.166126 | − | 0.986105i | \(-0.446874\pi\) | ||||
0.166126 | + | 0.986105i | \(0.446874\pi\) | |||||||
\(600\) | 119.237 | 4.86782 | ||||||||
\(601\) | −16.8215 | −0.686163 | −0.343082 | − | 0.939306i | \(-0.611471\pi\) | ||||
−0.343082 | + | 0.939306i | \(0.611471\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 26.3111 | 1.07147 | ||||||||
\(604\) | 10.8601 | 0.441890 | ||||||||
\(605\) | 31.2525 | 1.27059 | ||||||||
\(606\) | 22.5575 | 0.916334 | ||||||||
\(607\) | 2.45843 | 0.0997848 | 0.0498924 | − | 0.998755i | \(-0.484112\pi\) | ||||
0.0498924 | + | 0.998755i | \(0.484112\pi\) | |||||||
\(608\) | 49.2794 | 1.99854 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −97.9188 | −3.96462 | ||||||||
\(611\) | 21.9570 | 0.888286 | ||||||||
\(612\) | −24.0277 | −0.971263 | ||||||||
\(613\) | 22.9107 | 0.925355 | 0.462678 | − | 0.886527i | \(-0.346889\pi\) | ||||
0.462678 | + | 0.886527i | \(0.346889\pi\) | |||||||
\(614\) | 73.7280 | 2.97542 | ||||||||
\(615\) | 8.61152 | 0.347250 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.6529 | −1.27430 | −0.637149 | − | 0.770741i | \(-0.719886\pi\) | ||||
−0.637149 | + | 0.770741i | \(0.719886\pi\) | |||||||
\(618\) | −76.9179 | −3.09409 | ||||||||
\(619\) | 4.60395 | 0.185049 | 0.0925243 | − | 0.995710i | \(-0.470506\pi\) | ||||
0.0925243 | + | 0.995710i | \(0.470506\pi\) | |||||||
\(620\) | −7.68085 | −0.308470 | ||||||||
\(621\) | 2.87984 | 0.115564 | ||||||||
\(622\) | −26.1108 | −1.04695 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 184.393 | 7.38161 | ||||||||
\(625\) | −28.6034 | −1.14414 | ||||||||
\(626\) | 33.6443 | 1.34470 | ||||||||
\(627\) | −4.36539 | −0.174337 | ||||||||
\(628\) | 59.5002 | 2.37432 | ||||||||
\(629\) | −2.69830 | −0.107588 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.46440 | −0.217534 | −0.108767 | − | 0.994067i | \(-0.534690\pi\) | ||||
−0.108767 | + | 0.994067i | \(0.534690\pi\) | |||||||
\(632\) | 108.339 | 4.30949 | ||||||||
\(633\) | −49.9083 | −1.98368 | ||||||||
\(634\) | −39.8596 | −1.58303 | ||||||||
\(635\) | −23.6288 | −0.937679 | ||||||||
\(636\) | 209.945 | 8.32486 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.84902 | −0.231565 | ||||||||
\(639\) | −7.48227 | −0.295994 | ||||||||
\(640\) | 165.646 | 6.54774 | ||||||||
\(641\) | 36.9536 | 1.45958 | 0.729789 | − | 0.683672i | \(-0.239618\pi\) | ||||
0.729789 | + | 0.683672i | \(0.239618\pi\) | |||||||
\(642\) | −117.445 | −4.63518 | ||||||||
\(643\) | 21.6513 | 0.853843 | 0.426922 | − | 0.904289i | \(-0.359598\pi\) | ||||
0.426922 | + | 0.904289i | \(0.359598\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −52.5406 | −2.06879 | ||||||||
\(646\) | −4.33647 | −0.170616 | ||||||||
\(647\) | −17.9487 | −0.705637 | −0.352818 | − | 0.935692i | \(-0.614777\pi\) | ||||
−0.352818 | + | 0.935692i | \(0.614777\pi\) | |||||||
\(648\) | −19.1856 | −0.753682 | ||||||||
\(649\) | 7.71329 | 0.302773 | ||||||||
\(650\) | 44.1602 | 1.73211 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 102.409 | 4.01066 | ||||||||
\(653\) | 35.3145 | 1.38196 | 0.690982 | − | 0.722872i | \(-0.257178\pi\) | ||||
0.690982 | + | 0.722872i | \(0.257178\pi\) | |||||||
\(654\) | −77.0049 | −3.01113 | ||||||||
\(655\) | 7.40922 | 0.289502 | ||||||||
\(656\) | 16.7332 | 0.653320 | ||||||||
\(657\) | 44.7996 | 1.74780 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.81071 | −0.226353 | −0.113177 | − | 0.993575i | \(-0.536103\pi\) | ||||
−0.113177 | + | 0.993575i | \(0.536103\pi\) | |||||||
\(660\) | −39.4647 | −1.53616 | ||||||||
\(661\) | 36.6871 | 1.42696 | 0.713482 | − | 0.700674i | \(-0.247117\pi\) | ||||
0.713482 | + | 0.700674i | \(0.247117\pi\) | |||||||
\(662\) | 13.1800 | 0.512257 | ||||||||
\(663\) | −9.12427 | −0.354357 | ||||||||
\(664\) | 63.8696 | 2.47862 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −46.2322 | −1.79146 | ||||||||
\(667\) | 1.24101 | 0.0480521 | ||||||||
\(668\) | 107.834 | 4.17223 | ||||||||
\(669\) | −26.3006 | −1.01684 | ||||||||
\(670\) | 42.9287 | 1.65848 | ||||||||
\(671\) | 9.47775 | 0.365885 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.8608 | −1.76780 | −0.883902 | − | 0.467672i | \(-0.845093\pi\) | ||||
−0.883902 | + | 0.467672i | \(0.845093\pi\) | |||||||
\(674\) | 24.3557 | 0.938145 | ||||||||
\(675\) | −25.0010 | −0.962289 | ||||||||
\(676\) | 11.0115 | 0.423519 | ||||||||
\(677\) | −19.8902 | −0.764441 | −0.382221 | − | 0.924071i | \(-0.624841\pi\) | ||||
−0.382221 | + | 0.924071i | \(0.624841\pi\) | |||||||
\(678\) | −160.437 | −6.16155 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −25.3551 | −0.972323 | ||||||||
\(681\) | −62.3839 | −2.39056 | ||||||||
\(682\) | 1.00606 | 0.0385240 | ||||||||
\(683\) | −8.49824 | −0.325176 | −0.162588 | − | 0.986694i | \(-0.551984\pi\) | ||||
−0.162588 | + | 0.986694i | \(0.551984\pi\) | |||||||
\(684\) | −54.9056 | −2.09937 | ||||||||
\(685\) | −40.3541 | −1.54185 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.4111 | 0.969496 | ||||||||
\(688\) | −102.092 | −3.89224 | ||||||||
\(689\) | 50.2887 | 1.91585 | ||||||||
\(690\) | 11.3312 | 0.431371 | ||||||||
\(691\) | 31.2384 | 1.18837 | 0.594183 | − | 0.804330i | \(-0.297476\pi\) | ||||
0.594183 | + | 0.804330i | \(0.297476\pi\) | |||||||
\(692\) | −26.2392 | −0.997463 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 72.0239 | 2.73399 | ||||||||
\(695\) | 27.4484 | 1.04118 | ||||||||
\(696\) | −75.4292 | −2.85914 | ||||||||
\(697\) | −0.828004 | −0.0313629 | ||||||||
\(698\) | 40.8250 | 1.54525 | ||||||||
\(699\) | −1.53082 | −0.0579009 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.3738 | 0.769508 | 0.384754 | − | 0.923019i | \(-0.374286\pi\) | ||||
0.384754 | + | 0.923019i | \(0.374286\pi\) | |||||||
\(702\) | −64.8266 | −2.44672 | ||||||||
\(703\) | −6.16585 | −0.232550 | ||||||||
\(704\) | −31.2653 | −1.17836 | ||||||||
\(705\) | −48.9111 | −1.84210 | ||||||||
\(706\) | −30.5974 | −1.15155 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 153.799 | 5.78011 | ||||||||
\(709\) | 48.0124 | 1.80314 | 0.901571 | − | 0.432630i | \(-0.142414\pi\) | ||||
0.901571 | + | 0.432630i | \(0.142414\pi\) | |||||||
\(710\) | −12.2079 | −0.458155 | ||||||||
\(711\) | −54.7812 | −2.05446 | ||||||||
\(712\) | 31.1730 | 1.16826 | ||||||||
\(713\) | −0.213460 | −0.00799413 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.45308 | −0.353525 | ||||||||
\(716\) | −61.0553 | −2.28174 | ||||||||
\(717\) | −40.4959 | −1.51235 | ||||||||
\(718\) | −65.7514 | −2.45382 | ||||||||
\(719\) | −3.33151 | −0.124244 | −0.0621221 | − | 0.998069i | \(-0.519787\pi\) | ||||
−0.0621221 | + | 0.998069i | \(0.519787\pi\) | |||||||
\(720\) | −259.094 | −9.65587 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 42.6830 | 1.58850 | ||||||||
\(723\) | 20.4872 | 0.761927 | ||||||||
\(724\) | 111.359 | 4.13864 | ||||||||
\(725\) | −10.7737 | −0.400126 | ||||||||
\(726\) | −81.6229 | −3.02931 | ||||||||
\(727\) | 32.9605 | 1.22244 | 0.611219 | − | 0.791461i | \(-0.290679\pi\) | ||||
0.611219 | + | 0.791461i | \(0.290679\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.1049 | −1.55944 | ||||||||
\(730\) | 73.0942 | 2.70534 | ||||||||
\(731\) | 5.05182 | 0.186848 | ||||||||
\(732\) | 188.981 | 6.98495 | ||||||||
\(733\) | −35.7714 | −1.32125 | −0.660623 | − | 0.750718i | \(-0.729708\pi\) | ||||
−0.660623 | + | 0.750718i | \(0.729708\pi\) | |||||||
\(734\) | −58.4964 | −2.15914 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.3811 | 0.456372 | ||||||||
\(737\) | −4.15515 | −0.153057 | ||||||||
\(738\) | −14.1869 | −0.522226 | ||||||||
\(739\) | 19.1912 | 0.705961 | 0.352980 | − | 0.935631i | \(-0.385168\pi\) | ||||
0.352980 | + | 0.935631i | \(0.385168\pi\) | |||||||
\(740\) | −55.7415 | −2.04910 | ||||||||
\(741\) | −20.8498 | −0.765936 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.15568 | 0.189144 | 0.0945718 | − | 0.995518i | \(-0.469852\pi\) | ||||
0.0945718 | + | 0.995518i | \(0.469852\pi\) | |||||||
\(744\) | 12.9742 | 0.475657 | ||||||||
\(745\) | −8.88438 | −0.325499 | ||||||||
\(746\) | −24.6801 | −0.903602 | ||||||||
\(747\) | −32.2954 | −1.18163 | ||||||||
\(748\) | 3.79456 | 0.138743 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 20.8133 | 0.759995 | ||||||||
\(751\) | 19.9981 | 0.729741 | 0.364871 | − | 0.931058i | \(-0.381113\pi\) | ||||
0.364871 | + | 0.931058i | \(0.381113\pi\) | |||||||
\(752\) | −95.0399 | −3.46575 | ||||||||
\(753\) | −21.4930 | −0.783250 | ||||||||
\(754\) | −27.9358 | −1.01736 | ||||||||
\(755\) | −5.79471 | −0.210891 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.81127 | −0.0658319 | −0.0329159 | − | 0.999458i | \(-0.510479\pi\) | ||||
−0.0329159 | + | 0.999458i | \(0.510479\pi\) | |||||||
\(758\) | −6.87813 | −0.249825 | ||||||||
\(759\) | −1.09677 | −0.0398102 | ||||||||
\(760\) | −57.9387 | −2.10166 | ||||||||
\(761\) | 23.7203 | 0.859860 | 0.429930 | − | 0.902862i | \(-0.358538\pi\) | ||||
0.429930 | + | 0.902862i | \(0.358538\pi\) | |||||||
\(762\) | 61.7118 | 2.23558 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 131.486 | 4.75698 | ||||||||
\(765\) | 12.8207 | 0.463534 | ||||||||
\(766\) | 33.6375 | 1.21537 | ||||||||
\(767\) | 36.8399 | 1.33021 | ||||||||
\(768\) | −212.408 | −7.66462 | ||||||||
\(769\) | −47.0762 | −1.69761 | −0.848806 | − | 0.528704i | \(-0.822678\pi\) | ||||
−0.848806 | + | 0.528704i | \(0.822678\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −56.2600 | −2.02615 | ||||||||
\(772\) | −83.6157 | −3.00939 | ||||||||
\(773\) | −26.4758 | −0.952268 | −0.476134 | − | 0.879373i | \(-0.657962\pi\) | ||||
−0.476134 | + | 0.879373i | \(0.657962\pi\) | |||||||
\(774\) | 86.5571 | 3.11123 | ||||||||
\(775\) | 1.85313 | 0.0665664 | ||||||||
\(776\) | 160.709 | 5.76912 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 91.3729 | 3.27588 | ||||||||
\(779\) | −1.89207 | −0.0677903 | ||||||||
\(780\) | −188.489 | −6.74900 | ||||||||
\(781\) | 1.18163 | 0.0422820 | ||||||||
\(782\) | −1.08950 | −0.0389605 | ||||||||
\(783\) | 15.8157 | 0.565206 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −31.7481 | −1.13314 | ||||||||
\(786\) | −19.3508 | −0.690221 | ||||||||
\(787\) | 50.7389 | 1.80865 | 0.904324 | − | 0.426848i | \(-0.140376\pi\) | ||||
0.904324 | + | 0.426848i | \(0.140376\pi\) | |||||||
\(788\) | −124.680 | −4.44156 | ||||||||
\(789\) | −0.817382 | −0.0290996 | ||||||||
\(790\) | −89.3800 | −3.18000 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 42.0493 | 1.49416 | ||||||||
\(793\) | 45.2672 | 1.60749 | ||||||||
\(794\) | −47.3867 | −1.68169 | ||||||||
\(795\) | −112.022 | −3.97302 | ||||||||
\(796\) | −40.4961 | −1.43534 | ||||||||
\(797\) | 18.9700 | 0.671953 | 0.335976 | − | 0.941870i | \(-0.390934\pi\) | ||||
0.335976 | + | 0.941870i | \(0.390934\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.70284 | 0.166375 | ||||||||
\(800\) | −107.485 | −3.80016 | ||||||||
\(801\) | −15.7625 | −0.556942 | ||||||||
\(802\) | −42.9916 | −1.51809 | ||||||||
\(803\) | −7.07494 | −0.249669 | ||||||||
\(804\) | −82.8514 | −2.92194 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.80509 | 0.169252 | ||||||||
\(807\) | 51.8867 | 1.82650 | ||||||||
\(808\) | −28.9784 | −1.01946 | ||||||||
\(809\) | 43.5429 | 1.53089 | 0.765443 | − | 0.643503i | \(-0.222520\pi\) | ||||
0.765443 | + | 0.643503i | \(0.222520\pi\) | |||||||
\(810\) | 15.8282 | 0.556146 | ||||||||
\(811\) | 32.9946 | 1.15860 | 0.579298 | − | 0.815116i | \(-0.303327\pi\) | ||||
0.579298 | + | 0.815116i | \(0.303327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.7442 | 0.482029 | ||||||||
\(814\) | 7.30117 | 0.255906 | ||||||||
\(815\) | −54.6436 | −1.91408 | ||||||||
\(816\) | 39.4939 | 1.38256 | ||||||||
\(817\) | 11.5439 | 0.403869 | ||||||||
\(818\) | −3.06814 | −0.107275 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.1049 | −0.597330 | ||||||||
\(821\) | 34.7604 | 1.21315 | 0.606573 | − | 0.795028i | \(-0.292544\pi\) | ||||
0.606573 | + | 0.795028i | \(0.292544\pi\) | |||||||
\(822\) | 105.394 | 3.67603 | ||||||||
\(823\) | 21.5711 | 0.751922 | 0.375961 | − | 0.926636i | \(-0.377313\pi\) | ||||
0.375961 | + | 0.926636i | \(0.377313\pi\) | |||||||
\(824\) | 98.8127 | 3.44230 | ||||||||
\(825\) | 9.52149 | 0.331496 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.59470 | −0.0554532 | −0.0277266 | − | 0.999616i | \(-0.508827\pi\) | ||||
−0.0277266 | + | 0.999616i | \(0.508827\pi\) | |||||||
\(828\) | −13.7946 | −0.479394 | ||||||||
\(829\) | 36.1338 | 1.25498 | 0.627489 | − | 0.778626i | \(-0.284083\pi\) | ||||
0.627489 | + | 0.778626i | \(0.284083\pi\) | |||||||
\(830\) | −52.6926 | −1.82899 | ||||||||
\(831\) | 41.1516 | 1.42753 | ||||||||
\(832\) | −149.328 | −5.17701 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −71.6878 | −2.48234 | ||||||||
\(835\) | −57.5381 | −1.99119 | ||||||||
\(836\) | 8.67091 | 0.299890 | ||||||||
\(837\) | −2.72037 | −0.0940297 | ||||||||
\(838\) | 15.8941 | 0.549052 | ||||||||
\(839\) | 3.43446 | 0.118571 | 0.0592853 | − | 0.998241i | \(-0.481118\pi\) | ||||
0.0592853 | + | 0.998241i | \(0.481118\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.1845 | −0.764984 | ||||||||
\(842\) | 69.0287 | 2.37889 | ||||||||
\(843\) | 12.0859 | 0.416261 | ||||||||
\(844\) | 99.1320 | 3.41226 | ||||||||
\(845\) | −5.87551 | −0.202124 | ||||||||
\(846\) | 80.5777 | 2.77032 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −217.672 | −7.47489 | ||||||||
\(849\) | 64.2085 | 2.20363 | ||||||||
\(850\) | 9.45841 | 0.324421 | ||||||||
\(851\) | −1.54912 | −0.0531032 | ||||||||
\(852\) | 23.5610 | 0.807188 | ||||||||
\(853\) | 5.93145 | 0.203089 | 0.101544 | − | 0.994831i | \(-0.467622\pi\) | ||||
0.101544 | + | 0.994831i | \(0.467622\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.2965 | 1.00192 | ||||||||
\(856\) | 150.875 | 5.15682 | ||||||||
\(857\) | 15.5223 | 0.530233 | 0.265117 | − | 0.964216i | \(-0.414590\pi\) | ||||
0.265117 | + | 0.964216i | \(0.414590\pi\) | |||||||
\(858\) | 24.6888 | 0.842863 | ||||||||
\(859\) | −20.6119 | −0.703268 | −0.351634 | − | 0.936138i | \(-0.614374\pi\) | ||||
−0.351634 | + | 0.936138i | \(0.614374\pi\) | |||||||
\(860\) | 104.361 | 3.55867 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43.9907 | −1.49833 | ||||||||
\(863\) | −29.6407 | −1.00898 | −0.504491 | − | 0.863417i | \(-0.668320\pi\) | ||||
−0.504491 | + | 0.863417i | \(0.668320\pi\) | |||||||
\(864\) | 157.786 | 5.36800 | ||||||||
\(865\) | 14.0007 | 0.476037 | ||||||||
\(866\) | −17.5519 | −0.596436 | ||||||||
\(867\) | 46.5041 | 1.57936 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.65127 | 0.293474 | ||||||||
\(870\) | 62.2294 | 2.10977 | ||||||||
\(871\) | −19.8456 | −0.672444 | ||||||||
\(872\) | 98.9244 | 3.35000 | ||||||||
\(873\) | −81.2619 | −2.75030 | ||||||||
\(874\) | −2.48961 | −0.0842124 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −141.070 | −4.76633 | ||||||||
\(877\) | −25.6980 | −0.867760 | −0.433880 | − | 0.900971i | \(-0.642856\pi\) | ||||
−0.433880 | + | 0.900971i | \(0.642856\pi\) | |||||||
\(878\) | 84.0718 | 2.83728 | ||||||||
\(879\) | −38.6712 | −1.30435 | ||||||||
\(880\) | 40.9172 | 1.37932 | ||||||||
\(881\) | 3.71565 | 0.125183 | 0.0625917 | − | 0.998039i | \(-0.480063\pi\) | ||||
0.0625917 | + | 0.998039i | \(0.480063\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.8979 | −0.400395 | −0.200198 | − | 0.979756i | \(-0.564158\pi\) | ||||
−0.200198 | + | 0.979756i | \(0.564158\pi\) | |||||||
\(884\) | 18.1234 | 0.609555 | ||||||||
\(885\) | −82.0639 | −2.75855 | ||||||||
\(886\) | −81.2326 | −2.72906 | ||||||||
\(887\) | −9.80933 | −0.329365 | −0.164683 | − | 0.986347i | \(-0.552660\pi\) | ||||
−0.164683 | + | 0.986347i | \(0.552660\pi\) | |||||||
\(888\) | 94.1563 | 3.15968 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −25.7179 | −0.862065 | ||||||||
\(891\) | −1.53204 | −0.0513253 | ||||||||
\(892\) | 52.2405 | 1.74914 | ||||||||
\(893\) | 10.7464 | 0.359615 | ||||||||
\(894\) | 23.2036 | 0.776043 | ||||||||
\(895\) | 32.5779 | 1.08896 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.23834 | −0.174903 | ||||||||
\(898\) | −97.2065 | −3.24382 | ||||||||
\(899\) | −1.17229 | −0.0390981 | ||||||||
\(900\) | 119.756 | 3.99187 | ||||||||
\(901\) | 10.7710 | 0.358835 | ||||||||
\(902\) | 2.24045 | 0.0745988 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 206.106 | 6.85498 | ||||||||
\(905\) | −59.4191 | −1.97516 | ||||||||
\(906\) | 15.1342 | 0.502799 | ||||||||
\(907\) | −22.3954 | −0.743628 | −0.371814 | − | 0.928307i | \(-0.621264\pi\) | ||||
−0.371814 | + | 0.928307i | \(0.621264\pi\) | |||||||
\(908\) | 123.912 | 4.11217 | ||||||||
\(909\) | 14.6528 | 0.486004 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.3926 | −0.874425 | −0.437213 | − | 0.899358i | \(-0.644034\pi\) | ||||
−0.437213 | + | 0.899358i | \(0.644034\pi\) | |||||||
\(912\) | 90.2472 | 2.98838 | ||||||||
\(913\) | 5.10022 | 0.168793 | ||||||||
\(914\) | −13.5670 | −0.448758 | ||||||||
\(915\) | −100.837 | −3.33355 | ||||||||
\(916\) | −50.4737 | −1.66770 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −13.8848 | −0.458267 | ||||||||
\(919\) | −50.3575 | −1.66114 | −0.830571 | − | 0.556913i | \(-0.811986\pi\) | ||||
−0.830571 | + | 0.556913i | \(0.811986\pi\) | |||||||
\(920\) | −14.5566 | −0.479918 | ||||||||
\(921\) | 75.9249 | 2.50181 | ||||||||
\(922\) | −4.29980 | −0.141606 | ||||||||
\(923\) | 5.64364 | 0.185763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.4485 | 0.442185 | ||||||||
\(926\) | 17.4619 | 0.573834 | ||||||||
\(927\) | −49.9642 | −1.64104 | ||||||||
\(928\) | 67.9950 | 2.23205 | ||||||||
\(929\) | 19.1637 | 0.628741 | 0.314371 | − | 0.949300i | \(-0.398207\pi\) | ||||
0.314371 | + | 0.949300i | \(0.398207\pi\) | |||||||
\(930\) | −10.7037 | −0.350990 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.04064 | 0.0995995 | ||||||||
\(933\) | −26.8889 | −0.880303 | ||||||||
\(934\) | −58.1453 | −1.90257 | ||||||||
\(935\) | −2.02470 | −0.0662147 | ||||||||
\(936\) | 200.834 | 6.56447 | ||||||||
\(937\) | 4.86054 | 0.158787 | 0.0793935 | − | 0.996843i | \(-0.474702\pi\) | ||||
0.0793935 | + | 0.996843i | \(0.474702\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 34.6468 | 1.13066 | ||||||||
\(940\) | 97.1514 | 3.16873 | ||||||||
\(941\) | 15.9427 | 0.519718 | 0.259859 | − | 0.965647i | \(-0.416324\pi\) | ||||
0.259859 | + | 0.965647i | \(0.416324\pi\) | |||||||
\(942\) | 82.9172 | 2.70159 | ||||||||
\(943\) | −0.475366 | −0.0154800 | ||||||||
\(944\) | −159.459 | −5.18996 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.6694 | −0.444432 | ||||||||
\(947\) | −32.7906 | −1.06555 | −0.532775 | − | 0.846257i | \(-0.678851\pi\) | ||||
−0.532775 | + | 0.846257i | \(0.678851\pi\) | |||||||
\(948\) | 172.502 | 5.60259 | ||||||||
\(949\) | −33.7910 | −1.09690 | ||||||||
\(950\) | 21.6133 | 0.701229 | ||||||||
\(951\) | −41.0473 | −1.33105 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.3086 | −0.593074 | −0.296537 | − | 0.955021i | \(-0.595832\pi\) | ||||
−0.296537 | + | 0.955021i | \(0.595832\pi\) | |||||||
\(954\) | 184.549 | 5.97499 | ||||||||
\(955\) | −70.1581 | −2.27026 | ||||||||
\(956\) | 80.4364 | 2.60150 | ||||||||
\(957\) | −6.02330 | −0.194706 | ||||||||
\(958\) | 1.41244 | 0.0456338 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 332.641 | 10.7359 | ||||||||
\(961\) | −30.7984 | −0.993495 | ||||||||
\(962\) | 34.8715 | 1.12430 | ||||||||
\(963\) | −76.2896 | −2.45840 | ||||||||
\(964\) | −40.6934 | −1.31065 | ||||||||
\(965\) | 44.6156 | 1.43623 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3394 | 0.686230 | 0.343115 | − | 0.939293i | \(-0.388518\pi\) | ||||
0.343115 | + | 0.939293i | \(0.388518\pi\) | |||||||
\(968\) | 104.857 | 3.37023 | ||||||||
\(969\) | −4.46569 | −0.143459 | ||||||||
\(970\) | −132.585 | −4.25706 | ||||||||
\(971\) | −37.6666 | −1.20878 | −0.604389 | − | 0.796690i | \(-0.706583\pi\) | ||||
−0.604389 | + | 0.796690i | \(0.706583\pi\) | |||||||
\(972\) | 72.3535 | 2.32074 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −30.2973 | −0.970787 | ||||||||
\(975\) | 45.4761 | 1.45640 | ||||||||
\(976\) | −195.937 | −6.27179 | ||||||||
\(977\) | −15.5512 | −0.497527 | −0.248764 | − | 0.968564i | \(-0.580024\pi\) | ||||
−0.248764 | + | 0.968564i | \(0.580024\pi\) | |||||||
\(978\) | 142.714 | 4.56349 | ||||||||
\(979\) | 2.48928 | 0.0795578 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −50.0207 | −1.59704 | ||||||||
\(982\) | −4.23065 | −0.135005 | ||||||||
\(983\) | −22.3641 | −0.713303 | −0.356652 | − | 0.934237i | \(-0.616082\pi\) | ||||
−0.356652 | + | 0.934237i | \(0.616082\pi\) | |||||||
\(984\) | 28.8930 | 0.921074 | ||||||||
\(985\) | 66.5269 | 2.11972 | ||||||||
\(986\) | −5.98340 | −0.190550 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 41.4136 | 1.31754 | ||||||||
\(989\) | 2.90030 | 0.0922243 | ||||||||
\(990\) | −34.6908 | −1.10255 | ||||||||
\(991\) | −15.1727 | −0.481977 | −0.240989 | − | 0.970528i | \(-0.577472\pi\) | ||||
−0.240989 | + | 0.970528i | \(0.577472\pi\) | |||||||
\(992\) | −11.6955 | −0.371332 | ||||||||
\(993\) | 13.5728 | 0.430719 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.6079 | 0.685016 | ||||||||
\(996\) | 101.696 | 3.22235 | ||||||||
\(997\) | −18.1532 | −0.574917 | −0.287458 | − | 0.957793i | \(-0.592810\pi\) | ||||
−0.287458 | + | 0.957793i | \(0.592810\pi\) | |||||||
\(998\) | 81.9065 | 2.59270 | ||||||||
\(999\) | −19.7423 | −0.624618 |
(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 | 2009.2.a.s.1.1 | 17 | ||
7.2 | even | 3 | 287.2.e.d.165.17 | ✓ | 34 | ||
7.4 | even | 3 | 287.2.e.d.247.17 | yes | 34 | ||
7.6 | odd | 2 | 2009.2.a.r.1.1 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.e.d.165.17 | ✓ | 34 | 7.2 | even | 3 | ||
287.2.e.d.247.17 | yes | 34 | 7.4 | even | 3 | ||
2009.2.a.r.1.1 | 17 | 7.6 | odd | 2 | |||
2009.2.a.s.1.1 | 17 | 1.1 | even | 1 | trivial |