Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} - 699 x^{6} - 297 x^{5} + 394 x^{4} + 89 x^{3} - 57 x^{2} - 17 x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.34497\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34497 | −1.65814 | −0.829071 | − | 0.559144i | \(-0.811130\pi\) | ||||
−0.829071 | + | 0.559144i | \(0.811130\pi\) | |||||||
\(3\) | 3.01587 | 1.74121 | 0.870605 | − | 0.491982i | \(-0.163727\pi\) | ||||
0.870605 | + | 0.491982i | \(0.163727\pi\) | |||||||
\(4\) | 3.49887 | 1.74943 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −7.07210 | −2.88717 | ||||||||
\(7\) | −1.32864 | −0.502180 | −0.251090 | − | 0.967964i | \(-0.580789\pi\) | ||||
−0.251090 | + | 0.967964i | \(0.580789\pi\) | |||||||
\(8\) | −3.51479 | −1.24267 | ||||||||
\(9\) | 6.09545 | 2.03182 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.04712 | −1.22025 | −0.610126 | − | 0.792304i | \(-0.708881\pi\) | ||||
−0.610126 | + | 0.792304i | \(0.708881\pi\) | |||||||
\(12\) | 10.5521 | 3.04613 | ||||||||
\(13\) | 3.88814 | 1.07838 | 0.539188 | − | 0.842186i | \(-0.318731\pi\) | ||||
0.539188 | + | 0.842186i | \(0.318731\pi\) | |||||||
\(14\) | 3.11562 | 0.832685 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.24433 | 0.311083 | ||||||||
\(17\) | −2.67658 | −0.649166 | −0.324583 | − | 0.945857i | \(-0.605224\pi\) | ||||
−0.324583 | + | 0.945857i | \(0.605224\pi\) | |||||||
\(18\) | −14.2936 | −3.36904 | ||||||||
\(19\) | −4.01370 | −0.920805 | −0.460402 | − | 0.887710i | \(-0.652295\pi\) | ||||
−0.460402 | + | 0.887710i | \(0.652295\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00701 | −0.874401 | ||||||||
\(22\) | 9.49035 | 2.02335 | ||||||||
\(23\) | 0.553005 | 0.115310 | 0.0576548 | − | 0.998337i | \(-0.481638\pi\) | ||||
0.0576548 | + | 0.998337i | \(0.481638\pi\) | |||||||
\(24\) | −10.6001 | −2.16374 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.11755 | −1.78810 | ||||||||
\(27\) | 9.33545 | 1.79661 | ||||||||
\(28\) | −4.64874 | −0.878530 | ||||||||
\(29\) | 2.20769 | 0.409958 | 0.204979 | − | 0.978766i | \(-0.434287\pi\) | ||||
0.204979 | + | 0.978766i | \(0.434287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.23013 | −1.29857 | −0.649285 | − | 0.760545i | \(-0.724932\pi\) | ||||
−0.649285 | + | 0.760545i | \(0.724932\pi\) | |||||||
\(32\) | 4.11166 | 0.726846 | ||||||||
\(33\) | −12.2056 | −2.12472 | ||||||||
\(34\) | 6.27649 | 1.07641 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 21.3272 | 3.55453 | ||||||||
\(37\) | 1.59215 | 0.261749 | 0.130874 | − | 0.991399i | \(-0.458222\pi\) | ||||
0.130874 | + | 0.991399i | \(0.458222\pi\) | |||||||
\(38\) | 9.41198 | 1.52682 | ||||||||
\(39\) | 11.7261 | 1.87768 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.02098 | −0.784145 | −0.392072 | − | 0.919934i | \(-0.628242\pi\) | ||||
−0.392072 | + | 0.919934i | \(0.628242\pi\) | |||||||
\(42\) | 9.39630 | 1.44988 | ||||||||
\(43\) | 3.61669 | 0.551540 | 0.275770 | − | 0.961224i | \(-0.411067\pi\) | ||||
0.275770 | + | 0.961224i | \(0.411067\pi\) | |||||||
\(44\) | −14.1603 | −2.13475 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.29678 | −0.191200 | ||||||||
\(47\) | 5.44306 | 0.793952 | 0.396976 | − | 0.917829i | \(-0.370060\pi\) | ||||
0.396976 | + | 0.917829i | \(0.370060\pi\) | |||||||
\(48\) | 3.75274 | 0.541661 | ||||||||
\(49\) | −5.23471 | −0.747815 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.07221 | −1.13033 | ||||||||
\(52\) | 13.6041 | 1.88655 | ||||||||
\(53\) | 0.894563 | 0.122878 | 0.0614388 | − | 0.998111i | \(-0.480431\pi\) | ||||
0.0614388 | + | 0.998111i | \(0.480431\pi\) | |||||||
\(54\) | −21.8913 | −2.97903 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.66990 | 0.624042 | ||||||||
\(57\) | −12.1048 | −1.60332 | ||||||||
\(58\) | −5.17696 | −0.679768 | ||||||||
\(59\) | −11.5371 | −1.50201 | −0.751003 | − | 0.660298i | \(-0.770430\pi\) | ||||
−0.751003 | + | 0.660298i | \(0.770430\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.61517 | 0.462876 | 0.231438 | − | 0.972850i | \(-0.425657\pi\) | ||||
0.231438 | + | 0.972850i | \(0.425657\pi\) | |||||||
\(62\) | 16.9544 | 2.15321 | ||||||||
\(63\) | −8.09867 | −1.02034 | ||||||||
\(64\) | −12.1304 | −1.51630 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 28.6216 | 3.52308 | ||||||||
\(67\) | −5.71261 | −0.697907 | −0.348953 | − | 0.937140i | \(-0.613463\pi\) | ||||
−0.348953 | + | 0.937140i | \(0.613463\pi\) | |||||||
\(68\) | −9.36499 | −1.13567 | ||||||||
\(69\) | 1.66779 | 0.200778 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.34797 | 0.159974 | 0.0799871 | − | 0.996796i | \(-0.474512\pi\) | ||||
0.0799871 | + | 0.996796i | \(0.474512\pi\) | |||||||
\(72\) | −21.4242 | −2.52487 | ||||||||
\(73\) | −5.19142 | −0.607610 | −0.303805 | − | 0.952734i | \(-0.598257\pi\) | ||||
−0.303805 | + | 0.952734i | \(0.598257\pi\) | |||||||
\(74\) | −3.73355 | −0.434016 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.0434 | −1.61089 | ||||||||
\(77\) | 5.37718 | 0.612786 | ||||||||
\(78\) | −27.4973 | −3.11346 | ||||||||
\(79\) | 10.0840 | 1.13454 | 0.567270 | − | 0.823532i | \(-0.308000\pi\) | ||||
0.567270 | + | 0.823532i | \(0.308000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.86813 | 1.09646 | ||||||||
\(82\) | 11.7740 | 1.30022 | ||||||||
\(83\) | −14.9857 | −1.64489 | −0.822446 | − | 0.568843i | \(-0.807391\pi\) | ||||
−0.822446 | + | 0.568843i | \(0.807391\pi\) | |||||||
\(84\) | −14.0200 | −1.52971 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.48101 | −0.914531 | ||||||||
\(87\) | 6.65810 | 0.713823 | ||||||||
\(88\) | 14.2248 | 1.51637 | ||||||||
\(89\) | −5.29556 | −0.561329 | −0.280664 | − | 0.959806i | \(-0.590555\pi\) | ||||
−0.280664 | + | 0.959806i | \(0.590555\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.16595 | −0.541538 | ||||||||
\(92\) | 1.93489 | 0.201726 | ||||||||
\(93\) | −21.8051 | −2.26108 | ||||||||
\(94\) | −12.7638 | −1.31649 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 12.4002 | 1.26559 | ||||||||
\(97\) | −5.86258 | −0.595255 | −0.297627 | − | 0.954682i | \(-0.596195\pi\) | ||||
−0.297627 | + | 0.954682i | \(0.596195\pi\) | |||||||
\(98\) | 12.2752 | 1.23998 | ||||||||
\(99\) | −24.6690 | −2.47933 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4274 | −1.33608 | −0.668039 | − | 0.744127i | \(-0.732866\pi\) | ||||
−0.668039 | + | 0.744127i | \(0.732866\pi\) | |||||||
\(102\) | 18.9290 | 1.87426 | ||||||||
\(103\) | 14.2030 | 1.39946 | 0.699730 | − | 0.714408i | \(-0.253304\pi\) | ||||
0.699730 | + | 0.714408i | \(0.253304\pi\) | |||||||
\(104\) | −13.6660 | −1.34006 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.09772 | −0.203749 | ||||||||
\(107\) | 2.11593 | 0.204554 | 0.102277 | − | 0.994756i | \(-0.467387\pi\) | ||||
0.102277 | + | 0.994756i | \(0.467387\pi\) | |||||||
\(108\) | 32.6635 | 3.14305 | ||||||||
\(109\) | 19.1134 | 1.83073 | 0.915366 | − | 0.402622i | \(-0.131901\pi\) | ||||
0.915366 | + | 0.402622i | \(0.131901\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.80172 | 0.455759 | ||||||||
\(112\) | −1.65327 | −0.156220 | ||||||||
\(113\) | −13.1598 | −1.23797 | −0.618987 | − | 0.785401i | \(-0.712457\pi\) | ||||
−0.618987 | + | 0.785401i | \(0.712457\pi\) | |||||||
\(114\) | 28.3853 | 2.65852 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.72442 | 0.717194 | ||||||||
\(117\) | 23.6999 | 2.19106 | ||||||||
\(118\) | 27.0542 | 2.49054 | ||||||||
\(119\) | 3.55622 | 0.325998 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.37916 | 0.489015 | ||||||||
\(122\) | −8.47746 | −0.767513 | ||||||||
\(123\) | −15.1426 | −1.36536 | ||||||||
\(124\) | −25.2973 | −2.27176 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 18.9911 | 1.69186 | ||||||||
\(127\) | −5.72538 | −0.508045 | −0.254023 | − | 0.967198i | \(-0.581754\pi\) | ||||
−0.254023 | + | 0.967198i | \(0.581754\pi\) | |||||||
\(128\) | 20.2220 | 1.78739 | ||||||||
\(129\) | 10.9074 | 0.960347 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.9467 | 1.48064 | 0.740319 | − | 0.672256i | \(-0.234675\pi\) | ||||
0.740319 | + | 0.672256i | \(0.234675\pi\) | |||||||
\(132\) | −42.7056 | −3.71705 | ||||||||
\(133\) | 5.33277 | 0.462410 | ||||||||
\(134\) | 13.3959 | 1.15723 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.40762 | 0.806697 | ||||||||
\(137\) | −19.3019 | −1.64907 | −0.824537 | − | 0.565808i | \(-0.808564\pi\) | ||||
−0.824537 | + | 0.565808i | \(0.808564\pi\) | |||||||
\(138\) | −3.91091 | −0.332919 | ||||||||
\(139\) | 5.79018 | 0.491116 | 0.245558 | − | 0.969382i | \(-0.421029\pi\) | ||||
0.245558 | + | 0.969382i | \(0.421029\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.4155 | 1.38244 | ||||||||
\(142\) | −3.16094 | −0.265260 | ||||||||
\(143\) | −15.7358 | −1.31589 | ||||||||
\(144\) | 7.58476 | 0.632063 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.1737 | 1.00750 | ||||||||
\(147\) | −15.7872 | −1.30210 | ||||||||
\(148\) | 5.57073 | 0.457912 | ||||||||
\(149\) | −7.06741 | −0.578985 | −0.289492 | − | 0.957180i | \(-0.593487\pi\) | ||||
−0.289492 | + | 0.957180i | \(0.593487\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.88032 | −0.397155 | −0.198577 | − | 0.980085i | \(-0.563632\pi\) | ||||
−0.198577 | + | 0.980085i | \(0.563632\pi\) | |||||||
\(152\) | 14.1073 | 1.14425 | ||||||||
\(153\) | −16.3150 | −1.31899 | ||||||||
\(154\) | −12.6093 | −1.01609 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 41.0281 | 3.28487 | ||||||||
\(157\) | −6.14143 | −0.490139 | −0.245070 | − | 0.969506i | \(-0.578811\pi\) | ||||
−0.245070 | + | 0.969506i | \(0.578811\pi\) | |||||||
\(158\) | −23.6467 | −1.88123 | ||||||||
\(159\) | 2.69788 | 0.213956 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.734747 | −0.0579062 | ||||||||
\(162\) | −23.1404 | −1.81808 | ||||||||
\(163\) | 17.6834 | 1.38507 | 0.692535 | − | 0.721385i | \(-0.256494\pi\) | ||||
0.692535 | + | 0.721385i | \(0.256494\pi\) | |||||||
\(164\) | −17.5677 | −1.37181 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 35.1409 | 2.72746 | ||||||||
\(167\) | −13.6648 | −1.05741 | −0.528705 | − | 0.848806i | \(-0.677322\pi\) | ||||
−0.528705 | + | 0.848806i | \(0.677322\pi\) | |||||||
\(168\) | 14.0838 | 1.08659 | ||||||||
\(169\) | 2.11762 | 0.162893 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.4653 | −1.87091 | ||||||||
\(172\) | 12.6543 | 0.964882 | ||||||||
\(173\) | −3.57596 | −0.271875 | −0.135938 | − | 0.990717i | \(-0.543405\pi\) | ||||
−0.135938 | + | 0.990717i | \(0.543405\pi\) | |||||||
\(174\) | −15.6130 | −1.18362 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.03596 | −0.379600 | ||||||||
\(177\) | −34.7944 | −2.61531 | ||||||||
\(178\) | 12.4179 | 0.930762 | ||||||||
\(179\) | −26.2632 | −1.96301 | −0.981503 | − | 0.191444i | \(-0.938683\pi\) | ||||
−0.981503 | + | 0.191444i | \(0.938683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.9729 | −1.18726 | −0.593630 | − | 0.804738i | \(-0.702306\pi\) | ||||
−0.593630 | + | 0.804738i | \(0.702306\pi\) | |||||||
\(182\) | 12.1140 | 0.897947 | ||||||||
\(183\) | 10.9029 | 0.805964 | ||||||||
\(184\) | −1.94370 | −0.143291 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 51.1322 | 3.74920 | ||||||||
\(187\) | 10.8324 | 0.792146 | ||||||||
\(188\) | 19.0445 | 1.38897 | ||||||||
\(189\) | −12.4035 | −0.902221 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.91575 | 0.645121 | 0.322560 | − | 0.946549i | \(-0.395456\pi\) | ||||
0.322560 | + | 0.946549i | \(0.395456\pi\) | |||||||
\(192\) | −36.5836 | −2.64019 | ||||||||
\(193\) | 8.53301 | 0.614219 | 0.307110 | − | 0.951674i | \(-0.400638\pi\) | ||||
0.307110 | + | 0.951674i | \(0.400638\pi\) | |||||||
\(194\) | 13.7475 | 0.987016 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.3155 | −1.30825 | ||||||||
\(197\) | −19.4714 | −1.38728 | −0.693641 | − | 0.720321i | \(-0.743994\pi\) | ||||
−0.693641 | + | 0.720321i | \(0.743994\pi\) | |||||||
\(198\) | 57.8479 | 4.11107 | ||||||||
\(199\) | 8.98881 | 0.637200 | 0.318600 | − | 0.947889i | \(-0.396787\pi\) | ||||
0.318600 | + | 0.947889i | \(0.396787\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −17.2285 | −1.21520 | ||||||||
\(202\) | 31.4868 | 2.21541 | ||||||||
\(203\) | −2.93323 | −0.205873 | ||||||||
\(204\) | −28.2436 | −1.97745 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −33.3055 | −2.32050 | ||||||||
\(207\) | 3.37081 | 0.234288 | ||||||||
\(208\) | 4.83813 | 0.335464 | ||||||||
\(209\) | 16.2439 | 1.12361 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.56061 | −0.451651 | −0.225825 | − | 0.974168i | \(-0.572508\pi\) | ||||
−0.225825 | + | 0.974168i | \(0.572508\pi\) | |||||||
\(212\) | 3.12996 | 0.214966 | ||||||||
\(213\) | 4.06529 | 0.278549 | ||||||||
\(214\) | −4.96178 | −0.339180 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −32.8122 | −2.23258 | ||||||||
\(217\) | 9.60627 | 0.652116 | ||||||||
\(218\) | −44.8203 | −3.03561 | ||||||||
\(219\) | −15.6566 | −1.05798 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4069 | −0.700045 | ||||||||
\(222\) | −11.2599 | −0.755714 | ||||||||
\(223\) | −3.89457 | −0.260800 | −0.130400 | − | 0.991461i | \(-0.541626\pi\) | ||||
−0.130400 | + | 0.991461i | \(0.541626\pi\) | |||||||
\(224\) | −5.46294 | −0.365008 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 30.8594 | 2.05274 | ||||||||
\(227\) | 11.0989 | 0.736659 | 0.368329 | − | 0.929695i | \(-0.379930\pi\) | ||||
0.368329 | + | 0.929695i | \(0.379930\pi\) | |||||||
\(228\) | −42.3530 | −2.80489 | ||||||||
\(229\) | −23.1814 | −1.53187 | −0.765935 | − | 0.642918i | \(-0.777724\pi\) | ||||
−0.765935 | + | 0.642918i | \(0.777724\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.2168 | 1.06699 | ||||||||
\(232\) | −7.75957 | −0.509441 | ||||||||
\(233\) | 18.8689 | 1.23614 | 0.618071 | − | 0.786123i | \(-0.287915\pi\) | ||||
0.618071 | + | 0.786123i | \(0.287915\pi\) | |||||||
\(234\) | −55.5755 | −3.63309 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −40.3669 | −2.62766 | ||||||||
\(237\) | 30.4120 | 1.97547 | ||||||||
\(238\) | −8.33922 | −0.540551 | ||||||||
\(239\) | −13.5375 | −0.875666 | −0.437833 | − | 0.899056i | \(-0.644254\pi\) | ||||
−0.437833 | + | 0.899056i | \(0.644254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | −12.6140 | −0.810855 | ||||||||
\(243\) | 1.75460 | 0.112558 | ||||||||
\(244\) | 12.6490 | 0.809770 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 35.5089 | 2.26396 | ||||||||
\(247\) | −15.6058 | −0.992973 | ||||||||
\(248\) | 25.4124 | 1.61369 | ||||||||
\(249\) | −45.1948 | −2.86410 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5451 | −1.29679 | −0.648397 | − | 0.761302i | \(-0.724560\pi\) | ||||
−0.648397 | + | 0.761302i | \(0.724560\pi\) | |||||||
\(252\) | −28.3362 | −1.78501 | ||||||||
\(253\) | −2.23808 | −0.140707 | ||||||||
\(254\) | 13.4258 | 0.842410 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −23.1591 | −1.44745 | ||||||||
\(257\) | −27.5851 | −1.72071 | −0.860356 | − | 0.509694i | \(-0.829759\pi\) | ||||
−0.860356 | + | 0.509694i | \(0.829759\pi\) | |||||||
\(258\) | −25.5776 | −1.59239 | ||||||||
\(259\) | −2.11541 | −0.131445 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.4569 | 0.832959 | ||||||||
\(262\) | −39.7394 | −2.45511 | ||||||||
\(263\) | −9.86377 | −0.608226 | −0.304113 | − | 0.952636i | \(-0.598360\pi\) | ||||
−0.304113 | + | 0.952636i | \(0.598360\pi\) | |||||||
\(264\) | 42.9000 | 2.64031 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.5052 | −0.766741 | ||||||||
\(267\) | −15.9707 | −0.977392 | ||||||||
\(268\) | −19.9877 | −1.22094 | ||||||||
\(269\) | 19.4589 | 1.18643 | 0.593214 | − | 0.805045i | \(-0.297859\pi\) | ||||
0.593214 | + | 0.805045i | \(0.297859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.0735 | −1.52310 | −0.761552 | − | 0.648104i | \(-0.775562\pi\) | ||||
−0.761552 | + | 0.648104i | \(0.775562\pi\) | |||||||
\(272\) | −3.33055 | −0.201944 | ||||||||
\(273\) | −15.5798 | −0.942933 | ||||||||
\(274\) | 45.2623 | 2.73440 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.83537 | 0.351248 | ||||||||
\(277\) | 27.5593 | 1.65588 | 0.827939 | − | 0.560819i | \(-0.189514\pi\) | ||||
0.827939 | + | 0.560819i | \(0.189514\pi\) | |||||||
\(278\) | −13.5778 | −0.814340 | ||||||||
\(279\) | −44.0709 | −2.63845 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.6910 | 1.77122 | 0.885609 | − | 0.464432i | \(-0.153741\pi\) | ||||
0.885609 | + | 0.464432i | \(0.153741\pi\) | |||||||
\(282\) | −38.4939 | −2.29228 | ||||||||
\(283\) | 20.1705 | 1.19901 | 0.599506 | − | 0.800370i | \(-0.295364\pi\) | ||||
0.599506 | + | 0.800370i | \(0.295364\pi\) | |||||||
\(284\) | 4.71636 | 0.279864 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 36.8998 | 2.18193 | ||||||||
\(287\) | 6.67109 | 0.393782 | ||||||||
\(288\) | 25.0624 | 1.47682 | ||||||||
\(289\) | −9.83592 | −0.578584 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.6807 | −1.03646 | ||||||||
\(292\) | −18.1641 | −1.06297 | ||||||||
\(293\) | −4.59568 | −0.268483 | −0.134241 | − | 0.990949i | \(-0.542860\pi\) | ||||
−0.134241 | + | 0.990949i | \(0.542860\pi\) | |||||||
\(294\) | 37.0204 | 2.15907 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.59609 | −0.325266 | ||||||||
\(297\) | −37.7817 | −2.19231 | ||||||||
\(298\) | 16.5728 | 0.960039 | ||||||||
\(299\) | 2.15016 | 0.124347 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.80529 | −0.276972 | ||||||||
\(302\) | 11.4442 | 0.658539 | ||||||||
\(303\) | −40.4953 | −2.32639 | ||||||||
\(304\) | −4.99437 | −0.286447 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 38.2580 | 2.18706 | ||||||||
\(307\) | 2.54946 | 0.145505 | 0.0727526 | − | 0.997350i | \(-0.476822\pi\) | ||||
0.0727526 | + | 0.997350i | \(0.476822\pi\) | |||||||
\(308\) | 18.8140 | 1.07203 | ||||||||
\(309\) | 42.8342 | 2.43675 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.5631 | −1.22273 | −0.611366 | − | 0.791348i | \(-0.709380\pi\) | ||||
−0.611366 | + | 0.791348i | \(0.709380\pi\) | |||||||
\(312\) | −41.2148 | −2.33333 | ||||||||
\(313\) | −33.2289 | −1.87821 | −0.939104 | − | 0.343633i | \(-0.888342\pi\) | ||||
−0.939104 | + | 0.343633i | \(0.888342\pi\) | |||||||
\(314\) | 14.4014 | 0.812720 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 35.2826 | 1.98480 | ||||||||
\(317\) | −21.5858 | −1.21238 | −0.606189 | − | 0.795321i | \(-0.707302\pi\) | ||||
−0.606189 | + | 0.795321i | \(0.707302\pi\) | |||||||
\(318\) | −6.32644 | −0.354769 | ||||||||
\(319\) | −8.93479 | −0.500252 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.38135 | 0.356172 | ||||||||
\(322\) | 1.72296 | 0.0960166 | ||||||||
\(323\) | 10.7430 | 0.597755 | ||||||||
\(324\) | 34.5273 | 1.91818 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −41.4669 | −2.29664 | ||||||||
\(327\) | 57.6435 | 3.18769 | ||||||||
\(328\) | 17.6477 | 0.974430 | ||||||||
\(329\) | −7.23189 | −0.398707 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.8718 | −0.872391 | −0.436196 | − | 0.899852i | \(-0.643674\pi\) | ||||
−0.436196 | + | 0.899852i | \(0.643674\pi\) | |||||||
\(332\) | −52.4329 | −2.87763 | ||||||||
\(333\) | 9.70489 | 0.531825 | ||||||||
\(334\) | 32.0434 | 1.75334 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.98605 | −0.272011 | ||||||||
\(337\) | 27.2339 | 1.48352 | 0.741762 | − | 0.670663i | \(-0.233990\pi\) | ||||
0.741762 | + | 0.670663i | \(0.233990\pi\) | |||||||
\(338\) | −4.96574 | −0.270100 | ||||||||
\(339\) | −39.6883 | −2.15557 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.2612 | 1.58458 | ||||||||
\(342\) | 57.3702 | 3.10223 | ||||||||
\(343\) | 16.2556 | 0.877718 | ||||||||
\(344\) | −12.7119 | −0.685380 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.38550 | 0.450807 | ||||||||
\(347\) | 31.7885 | 1.70650 | 0.853249 | − | 0.521503i | \(-0.174629\pi\) | ||||
0.853249 | + | 0.521503i | \(0.174629\pi\) | |||||||
\(348\) | 23.2958 | 1.24879 | ||||||||
\(349\) | −28.3944 | −1.51992 | −0.759958 | − | 0.649972i | \(-0.774781\pi\) | ||||
−0.759958 | + | 0.649972i | \(0.774781\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.2975 | 1.93742 | ||||||||
\(352\) | −16.6404 | −0.886936 | ||||||||
\(353\) | 22.2636 | 1.18497 | 0.592485 | − | 0.805582i | \(-0.298147\pi\) | ||||
0.592485 | + | 0.805582i | \(0.298147\pi\) | |||||||
\(354\) | 81.5918 | 4.33655 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.5285 | −0.982007 | ||||||||
\(357\) | 10.7251 | 0.567632 | ||||||||
\(358\) | 61.5864 | 3.25494 | ||||||||
\(359\) | 28.1144 | 1.48382 | 0.741910 | − | 0.670499i | \(-0.233920\pi\) | ||||
0.741910 | + | 0.670499i | \(0.233920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.89025 | −0.152118 | ||||||||
\(362\) | 37.4560 | 1.96864 | ||||||||
\(363\) | 16.2228 | 0.851478 | ||||||||
\(364\) | −18.0750 | −0.947385 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −25.5669 | −1.33640 | ||||||||
\(367\) | 10.5062 | 0.548420 | 0.274210 | − | 0.961670i | \(-0.411584\pi\) | ||||
0.274210 | + | 0.961670i | \(0.411584\pi\) | |||||||
\(368\) | 0.688122 | 0.0358708 | ||||||||
\(369\) | −30.6051 | −1.59324 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.18855 | −0.0617067 | ||||||||
\(372\) | −76.2932 | −3.95562 | ||||||||
\(373\) | −16.2726 | −0.842562 | −0.421281 | − | 0.906930i | \(-0.638419\pi\) | ||||
−0.421281 | + | 0.906930i | \(0.638419\pi\) | |||||||
\(374\) | −25.4017 | −1.31349 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.1312 | −0.986617 | ||||||||
\(377\) | 8.58381 | 0.442089 | ||||||||
\(378\) | 29.0858 | 1.49601 | ||||||||
\(379\) | 19.8759 | 1.02096 | 0.510478 | − | 0.859891i | \(-0.329469\pi\) | ||||
0.510478 | + | 0.859891i | \(0.329469\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.2670 | −0.884614 | ||||||||
\(382\) | −20.9071 | −1.06970 | ||||||||
\(383\) | −6.83677 | −0.349343 | −0.174671 | − | 0.984627i | \(-0.555886\pi\) | ||||
−0.174671 | + | 0.984627i | \(0.555886\pi\) | |||||||
\(384\) | 60.9868 | 3.11222 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.0096 | −1.01846 | ||||||||
\(387\) | 22.0453 | 1.12063 | ||||||||
\(388\) | −20.5124 | −1.04136 | ||||||||
\(389\) | −16.6018 | −0.841746 | −0.420873 | − | 0.907120i | \(-0.638276\pi\) | ||||
−0.420873 | + | 0.907120i | \(0.638276\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.48016 | −0.0748551 | ||||||||
\(392\) | 18.3989 | 0.929285 | ||||||||
\(393\) | 51.1089 | 2.57810 | ||||||||
\(394\) | 45.6598 | 2.30031 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −86.3135 | −4.33742 | ||||||||
\(397\) | 27.8469 | 1.39759 | 0.698797 | − | 0.715320i | \(-0.253719\pi\) | ||||
0.698797 | + | 0.715320i | \(0.253719\pi\) | |||||||
\(398\) | −21.0784 | −1.05657 | ||||||||
\(399\) | 16.0829 | 0.805153 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5265 | 0.875230 | 0.437615 | − | 0.899163i | \(-0.355823\pi\) | ||||
0.437615 | + | 0.899163i | \(0.355823\pi\) | |||||||
\(402\) | 40.4002 | 2.01498 | ||||||||
\(403\) | −28.1118 | −1.40035 | ||||||||
\(404\) | −46.9807 | −2.33738 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.87834 | 0.341366 | ||||||||
\(407\) | −6.44364 | −0.319399 | ||||||||
\(408\) | 28.3721 | 1.40463 | ||||||||
\(409\) | 31.8521 | 1.57498 | 0.787492 | − | 0.616325i | \(-0.211379\pi\) | ||||
0.787492 | + | 0.616325i | \(0.211379\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −58.2120 | −2.87139 | ||||||||
\(412\) | 49.6943 | 2.44826 | ||||||||
\(413\) | 15.3287 | 0.754278 | ||||||||
\(414\) | −7.90445 | −0.388482 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.9867 | 0.783813 | ||||||||
\(417\) | 17.4624 | 0.855137 | ||||||||
\(418\) | −38.0914 | −1.86311 | ||||||||
\(419\) | −6.43813 | −0.314523 | −0.157262 | − | 0.987557i | \(-0.550267\pi\) | ||||
−0.157262 | + | 0.987557i | \(0.550267\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.3455 | 1.62516 | 0.812581 | − | 0.582848i | \(-0.198062\pi\) | ||||
0.812581 | + | 0.582848i | \(0.198062\pi\) | |||||||
\(422\) | 15.3844 | 0.748901 | ||||||||
\(423\) | 33.1779 | 1.61316 | ||||||||
\(424\) | −3.14420 | −0.152696 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.53296 | −0.461874 | ||||||||
\(427\) | −4.80328 | −0.232447 | ||||||||
\(428\) | 7.40335 | 0.357854 | ||||||||
\(429\) | −47.4569 | −2.29124 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.7262 | −1.43186 | −0.715929 | − | 0.698173i | \(-0.753997\pi\) | ||||
−0.715929 | + | 0.698173i | \(0.753997\pi\) | |||||||
\(432\) | 11.6164 | 0.558894 | ||||||||
\(433\) | 17.4809 | 0.840077 | 0.420039 | − | 0.907506i | \(-0.362017\pi\) | ||||
0.420039 | + | 0.907506i | \(0.362017\pi\) | |||||||
\(434\) | −22.5264 | −1.08130 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 66.8753 | 3.20274 | ||||||||
\(437\) | −2.21960 | −0.106178 | ||||||||
\(438\) | 36.7142 | 1.75427 | ||||||||
\(439\) | −19.7835 | −0.944216 | −0.472108 | − | 0.881541i | \(-0.656507\pi\) | ||||
−0.472108 | + | 0.881541i | \(0.656507\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −31.9079 | −1.51942 | ||||||||
\(442\) | 24.4039 | 1.16077 | ||||||||
\(443\) | −2.71041 | −0.128775 | −0.0643877 | − | 0.997925i | \(-0.520509\pi\) | ||||
−0.0643877 | + | 0.997925i | \(0.520509\pi\) | |||||||
\(444\) | 16.8006 | 0.797321 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.13263 | 0.432443 | ||||||||
\(447\) | −21.3144 | −1.00814 | ||||||||
\(448\) | 16.1169 | 0.761454 | ||||||||
\(449\) | 27.9994 | 1.32137 | 0.660687 | − | 0.750662i | \(-0.270265\pi\) | ||||
0.660687 | + | 0.750662i | \(0.270265\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.3205 | 0.956854 | ||||||||
\(452\) | −46.0445 | −2.16575 | ||||||||
\(453\) | −14.7184 | −0.691531 | ||||||||
\(454\) | −26.0265 | −1.22148 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 42.5457 | 1.99239 | ||||||||
\(457\) | 18.7373 | 0.876492 | 0.438246 | − | 0.898855i | \(-0.355600\pi\) | ||||
0.438246 | + | 0.898855i | \(0.355600\pi\) | |||||||
\(458\) | 54.3596 | 2.54006 | ||||||||
\(459\) | −24.9871 | −1.16630 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.3566 | 1.13440 | 0.567200 | − | 0.823580i | \(-0.308027\pi\) | ||||
0.567200 | + | 0.823580i | \(0.308027\pi\) | |||||||
\(462\) | −38.0279 | −1.76922 | ||||||||
\(463\) | −20.0566 | −0.932111 | −0.466055 | − | 0.884756i | \(-0.654325\pi\) | ||||
−0.466055 | + | 0.884756i | \(0.654325\pi\) | |||||||
\(464\) | 2.74710 | 0.127531 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −44.2469 | −2.04970 | ||||||||
\(467\) | −21.0159 | −0.972501 | −0.486250 | − | 0.873819i | \(-0.661636\pi\) | ||||
−0.486250 | + | 0.873819i | \(0.661636\pi\) | |||||||
\(468\) | 82.9229 | 3.83311 | ||||||||
\(469\) | 7.59002 | 0.350475 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.5217 | −0.853436 | ||||||||
\(472\) | 40.5506 | 1.86649 | ||||||||
\(473\) | −14.6372 | −0.673017 | ||||||||
\(474\) | −71.3152 | −3.27561 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.4427 | 0.570312 | ||||||||
\(477\) | 5.45276 | 0.249665 | ||||||||
\(478\) | 31.7449 | 1.45198 | ||||||||
\(479\) | −14.8456 | −0.678314 | −0.339157 | − | 0.940730i | \(-0.610142\pi\) | ||||
−0.339157 | + | 0.940730i | \(0.610142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.19052 | 0.282263 | ||||||||
\(482\) | 2.34497 | 0.106810 | ||||||||
\(483\) | −2.21590 | −0.100827 | ||||||||
\(484\) | 18.8210 | 0.855498 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.11448 | −0.186637 | ||||||||
\(487\) | 3.38997 | 0.153614 | 0.0768072 | − | 0.997046i | \(-0.475527\pi\) | ||||
0.0768072 | + | 0.997046i | \(0.475527\pi\) | |||||||
\(488\) | −12.7066 | −0.575200 | ||||||||
\(489\) | 53.3307 | 2.41170 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.64393 | −0.390095 | −0.195048 | − | 0.980794i | \(-0.562486\pi\) | ||||
−0.195048 | + | 0.980794i | \(0.562486\pi\) | |||||||
\(492\) | −52.9819 | −2.38861 | ||||||||
\(493\) | −5.90906 | −0.266131 | ||||||||
\(494\) | 36.5951 | 1.64649 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.99668 | −0.403963 | ||||||||
\(497\) | −1.79097 | −0.0803359 | ||||||||
\(498\) | 105.980 | 4.74909 | ||||||||
\(499\) | −8.41032 | −0.376498 | −0.188249 | − | 0.982121i | \(-0.560281\pi\) | ||||
−0.188249 | + | 0.982121i | \(0.560281\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −41.2111 | −1.84117 | ||||||||
\(502\) | 48.1775 | 2.15027 | ||||||||
\(503\) | −5.09312 | −0.227091 | −0.113546 | − | 0.993533i | \(-0.536221\pi\) | ||||
−0.113546 | + | 0.993533i | \(0.536221\pi\) | |||||||
\(504\) | 28.4651 | 1.26794 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.24822 | 0.233312 | ||||||||
\(507\) | 6.38644 | 0.283632 | ||||||||
\(508\) | −20.0323 | −0.888791 | ||||||||
\(509\) | 25.7848 | 1.14289 | 0.571445 | − | 0.820641i | \(-0.306383\pi\) | ||||
0.571445 | + | 0.820641i | \(0.306383\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.89754 | 0.305129 | ||||||||
\(512\) | 13.8634 | 0.612682 | ||||||||
\(513\) | −37.4697 | −1.65433 | ||||||||
\(514\) | 64.6861 | 2.85318 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 38.1637 | 1.68006 | ||||||||
\(517\) | −22.0287 | −0.968822 | ||||||||
\(518\) | 4.96055 | 0.217954 | ||||||||
\(519\) | −10.7846 | −0.473392 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.7411 | 1.78490 | 0.892450 | − | 0.451146i | \(-0.148985\pi\) | ||||
0.892450 | + | 0.451146i | \(0.148985\pi\) | |||||||
\(522\) | −31.5559 | −1.38116 | ||||||||
\(523\) | −6.82084 | −0.298255 | −0.149127 | − | 0.988818i | \(-0.547646\pi\) | ||||
−0.149127 | + | 0.988818i | \(0.547646\pi\) | |||||||
\(524\) | 59.2941 | 2.59028 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.1302 | 1.00852 | ||||||||
\(527\) | 19.3520 | 0.842988 | ||||||||
\(528\) | −15.1878 | −0.660963 | ||||||||
\(529\) | −22.6942 | −0.986704 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −70.3240 | −3.05180 | ||||||||
\(532\) | 18.6586 | 0.808955 | ||||||||
\(533\) | −19.5222 | −0.845602 | ||||||||
\(534\) | 37.4508 | 1.62065 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20.0786 | 0.867265 | ||||||||
\(537\) | −79.2064 | −3.41801 | ||||||||
\(538\) | −45.6304 | −1.96726 | ||||||||
\(539\) | 21.1855 | 0.912523 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.5367 | −0.968929 | −0.484464 | − | 0.874811i | \(-0.660985\pi\) | ||||
−0.484464 | + | 0.874811i | \(0.660985\pi\) | |||||||
\(542\) | 58.7964 | 2.52552 | ||||||||
\(543\) | −48.1722 | −2.06727 | ||||||||
\(544\) | −11.0052 | −0.471844 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 36.5341 | 1.56352 | ||||||||
\(547\) | −13.6655 | −0.584295 | −0.292148 | − | 0.956373i | \(-0.594370\pi\) | ||||
−0.292148 | + | 0.956373i | \(0.594370\pi\) | |||||||
\(548\) | −67.5348 | −2.88494 | ||||||||
\(549\) | 22.0361 | 0.940478 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.86100 | −0.377491 | ||||||||
\(552\) | −5.86193 | −0.249500 | ||||||||
\(553\) | −13.3981 | −0.569743 | ||||||||
\(554\) | −64.6256 | −2.74568 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.2591 | 0.859175 | ||||||||
\(557\) | 34.1533 | 1.44712 | 0.723562 | − | 0.690260i | \(-0.242504\pi\) | ||||
0.723562 | + | 0.690260i | \(0.242504\pi\) | |||||||
\(558\) | 103.345 | 4.37493 | ||||||||
\(559\) | 14.0622 | 0.594767 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.6692 | 1.37929 | ||||||||
\(562\) | −69.6244 | −2.93693 | ||||||||
\(563\) | −3.98769 | −0.168061 | −0.0840306 | − | 0.996463i | \(-0.526779\pi\) | ||||
−0.0840306 | + | 0.996463i | \(0.526779\pi\) | |||||||
\(564\) | 57.4358 | 2.41848 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −47.2992 | −1.98813 | ||||||||
\(567\) | −13.1112 | −0.550620 | ||||||||
\(568\) | −4.73782 | −0.198795 | ||||||||
\(569\) | −41.4137 | −1.73615 | −0.868077 | − | 0.496429i | \(-0.834644\pi\) | ||||
−0.868077 | + | 0.496429i | \(0.834644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2699 | −0.848269 | −0.424135 | − | 0.905599i | \(-0.639422\pi\) | ||||
−0.424135 | + | 0.905599i | \(0.639422\pi\) | |||||||
\(572\) | −55.0573 | −2.30206 | ||||||||
\(573\) | 26.8887 | 1.12329 | ||||||||
\(574\) | −15.6435 | −0.652946 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −73.9401 | −3.08084 | ||||||||
\(577\) | 40.1443 | 1.67123 | 0.835615 | − | 0.549315i | \(-0.185111\pi\) | ||||
0.835615 | + | 0.549315i | \(0.185111\pi\) | |||||||
\(578\) | 23.0649 | 0.959373 | ||||||||
\(579\) | 25.7344 | 1.06949 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.9106 | 0.826032 | ||||||||
\(582\) | 41.4608 | 1.71860 | ||||||||
\(583\) | −3.62040 | −0.149942 | ||||||||
\(584\) | 18.2467 | 0.755056 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.7767 | 0.445182 | ||||||||
\(587\) | −14.4260 | −0.595425 | −0.297713 | − | 0.954656i | \(-0.596224\pi\) | ||||
−0.297713 | + | 0.954656i | \(0.596224\pi\) | |||||||
\(588\) | −55.2372 | −2.27794 | ||||||||
\(589\) | 29.0196 | 1.19573 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −58.7232 | −2.41555 | ||||||||
\(592\) | 1.98117 | 0.0814255 | ||||||||
\(593\) | 10.7886 | 0.443036 | 0.221518 | − | 0.975156i | \(-0.428899\pi\) | ||||
0.221518 | + | 0.975156i | \(0.428899\pi\) | |||||||
\(594\) | 88.5967 | 3.63517 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −24.7279 | −1.01290 | ||||||||
\(597\) | 27.1090 | 1.10950 | ||||||||
\(598\) | −5.04205 | −0.206185 | ||||||||
\(599\) | 11.7886 | 0.481669 | 0.240834 | − | 0.970566i | \(-0.422579\pi\) | ||||
0.240834 | + | 0.970566i | \(0.422579\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.9629 | 1.01826 | 0.509129 | − | 0.860690i | \(-0.329967\pi\) | ||||
0.509129 | + | 0.860690i | \(0.329967\pi\) | |||||||
\(602\) | 11.2682 | 0.459259 | ||||||||
\(603\) | −34.8209 | −1.41802 | ||||||||
\(604\) | −17.0756 | −0.694796 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 94.9600 | 3.85749 | ||||||||
\(607\) | 9.36804 | 0.380237 | 0.190119 | − | 0.981761i | \(-0.439113\pi\) | ||||
0.190119 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(608\) | −16.5030 | −0.669284 | ||||||||
\(609\) | −8.84624 | −0.358468 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.1634 | 0.856179 | ||||||||
\(612\) | −57.0838 | −2.30748 | ||||||||
\(613\) | 11.8795 | 0.479808 | 0.239904 | − | 0.970797i | \(-0.422884\pi\) | ||||
0.239904 | + | 0.970797i | \(0.422884\pi\) | |||||||
\(614\) | −5.97839 | −0.241268 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18.8996 | −0.761488 | ||||||||
\(617\) | 30.8556 | 1.24220 | 0.621100 | − | 0.783732i | \(-0.286686\pi\) | ||||
0.621100 | + | 0.783732i | \(0.286686\pi\) | |||||||
\(618\) | −100.445 | −4.04048 | ||||||||
\(619\) | 41.5695 | 1.67082 | 0.835409 | − | 0.549629i | \(-0.185231\pi\) | ||||
0.835409 | + | 0.549629i | \(0.185231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.16255 | 0.207166 | ||||||||
\(622\) | 50.5648 | 2.02746 | ||||||||
\(623\) | 7.03592 | 0.281888 | ||||||||
\(624\) | 14.5912 | 0.584114 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 77.9206 | 3.11433 | ||||||||
\(627\) | 48.9894 | 1.95645 | ||||||||
\(628\) | −21.4880 | −0.857466 | ||||||||
\(629\) | −4.26153 | −0.169918 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.426407 | 0.0169750 | 0.00848750 | − | 0.999964i | \(-0.497298\pi\) | ||||
0.00848750 | + | 0.999964i | \(0.497298\pi\) | |||||||
\(632\) | −35.4432 | −1.40985 | ||||||||
\(633\) | −19.7859 | −0.786419 | ||||||||
\(634\) | 50.6179 | 2.01029 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.43952 | 0.374301 | ||||||||
\(637\) | −20.3533 | −0.806426 | ||||||||
\(638\) | 20.9518 | 0.829489 | ||||||||
\(639\) | 8.21646 | 0.325038 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.82887 | 0.269724 | 0.134862 | − | 0.990864i | \(-0.456941\pi\) | ||||
0.134862 | + | 0.990864i | \(0.456941\pi\) | |||||||
\(642\) | −14.9641 | −0.590584 | ||||||||
\(643\) | 9.38104 | 0.369952 | 0.184976 | − | 0.982743i | \(-0.440779\pi\) | ||||
0.184976 | + | 0.982743i | \(0.440779\pi\) | |||||||
\(644\) | −2.57078 | −0.101303 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25.1919 | −0.991163 | ||||||||
\(647\) | −49.7829 | −1.95717 | −0.978584 | − | 0.205850i | \(-0.934004\pi\) | ||||
−0.978584 | + | 0.205850i | \(0.934004\pi\) | |||||||
\(648\) | −34.6844 | −1.36253 | ||||||||
\(649\) | 46.6921 | 1.83283 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.9712 | 1.13547 | ||||||||
\(652\) | 61.8718 | 2.42309 | ||||||||
\(653\) | 17.8648 | 0.699105 | 0.349553 | − | 0.936917i | \(-0.386334\pi\) | ||||
0.349553 | + | 0.936917i | \(0.386334\pi\) | |||||||
\(654\) | −135.172 | −5.28564 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.24776 | −0.243934 | ||||||||
\(657\) | −31.6440 | −1.23455 | ||||||||
\(658\) | 16.9585 | 0.661112 | ||||||||
\(659\) | −32.3949 | −1.26193 | −0.630963 | − | 0.775813i | \(-0.717340\pi\) | ||||
−0.630963 | + | 0.775813i | \(0.717340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.6604 | −1.15366 | −0.576828 | − | 0.816866i | \(-0.695710\pi\) | ||||
−0.576828 | + | 0.816866i | \(0.695710\pi\) | |||||||
\(662\) | 37.2188 | 1.44655 | ||||||||
\(663\) | −31.3858 | −1.21893 | ||||||||
\(664\) | 52.6715 | 2.04405 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −22.7576 | −0.881841 | ||||||||
\(667\) | 1.22087 | 0.0472721 | ||||||||
\(668\) | −47.8111 | −1.84987 | ||||||||
\(669\) | −11.7455 | −0.454107 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.6310 | −0.564825 | ||||||||
\(672\) | −16.4755 | −0.635555 | ||||||||
\(673\) | −21.9919 | −0.847724 | −0.423862 | − | 0.905727i | \(-0.639326\pi\) | ||||
−0.423862 | + | 0.905727i | \(0.639326\pi\) | |||||||
\(674\) | −63.8626 | −2.45989 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.40925 | 0.284971 | ||||||||
\(677\) | 4.39296 | 0.168835 | 0.0844175 | − | 0.996430i | \(-0.473097\pi\) | ||||
0.0844175 | + | 0.996430i | \(0.473097\pi\) | |||||||
\(678\) | 93.0678 | 3.57425 | ||||||||
\(679\) | 7.78927 | 0.298925 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.4727 | 1.28268 | ||||||||
\(682\) | −68.6165 | −2.62746 | ||||||||
\(683\) | −44.2158 | −1.69187 | −0.845935 | − | 0.533286i | \(-0.820957\pi\) | ||||
−0.845935 | + | 0.533286i | \(0.820957\pi\) | |||||||
\(684\) | −85.6007 | −3.27302 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −38.1187 | −1.45538 | ||||||||
\(687\) | −69.9120 | −2.66731 | ||||||||
\(688\) | 4.50036 | 0.171575 | ||||||||
\(689\) | 3.47818 | 0.132508 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.9956 | −0.684585 | −0.342292 | − | 0.939593i | \(-0.611203\pi\) | ||||
−0.342292 | + | 0.939593i | \(0.611203\pi\) | |||||||
\(692\) | −12.5118 | −0.475627 | ||||||||
\(693\) | 32.7763 | 1.24507 | ||||||||
\(694\) | −74.5431 | −2.82962 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −23.4018 | −0.887044 | ||||||||
\(697\) | 13.4390 | 0.509040 | ||||||||
\(698\) | 66.5839 | 2.52024 | ||||||||
\(699\) | 56.9060 | 2.15238 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.1833 | −1.55547 | −0.777735 | − | 0.628592i | \(-0.783631\pi\) | ||||
−0.777735 | + | 0.628592i | \(0.783631\pi\) | |||||||
\(702\) | −85.1165 | −3.21251 | ||||||||
\(703\) | −6.39042 | −0.241019 | ||||||||
\(704\) | 49.0931 | 1.85026 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −52.2073 | −1.96485 | ||||||||
\(707\) | 17.8402 | 0.670951 | ||||||||
\(708\) | −121.741 | −4.57531 | ||||||||
\(709\) | 31.3551 | 1.17757 | 0.588783 | − | 0.808291i | \(-0.299607\pi\) | ||||
0.588783 | + | 0.808291i | \(0.299607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 61.4666 | 2.30518 | ||||||||
\(712\) | 18.6128 | 0.697544 | ||||||||
\(713\) | −3.99830 | −0.149738 | ||||||||
\(714\) | −25.1500 | −0.941213 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −91.8916 | −3.43415 | ||||||||
\(717\) | −40.8272 | −1.52472 | ||||||||
\(718\) | −65.9273 | −2.46038 | ||||||||
\(719\) | −1.93864 | −0.0722989 | −0.0361494 | − | 0.999346i | \(-0.511509\pi\) | ||||
−0.0361494 | + | 0.999346i | \(0.511509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.8707 | −0.702780 | ||||||||
\(722\) | 6.77753 | 0.252234 | ||||||||
\(723\) | −3.01587 | −0.112161 | ||||||||
\(724\) | −55.8872 | −2.07703 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −38.0420 | −1.41187 | ||||||||
\(727\) | −0.936776 | −0.0347431 | −0.0173715 | − | 0.999849i | \(-0.505530\pi\) | ||||
−0.0173715 | + | 0.999849i | \(0.505530\pi\) | |||||||
\(728\) | 18.1572 | 0.672951 | ||||||||
\(729\) | −24.3128 | −0.900472 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.68035 | −0.358041 | ||||||||
\(732\) | 38.1477 | 1.40998 | ||||||||
\(733\) | −20.1520 | −0.744332 | −0.372166 | − | 0.928166i | \(-0.621385\pi\) | ||||
−0.372166 | + | 0.928166i | \(0.621385\pi\) | |||||||
\(734\) | −24.6367 | −0.909358 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.27377 | 0.0838124 | ||||||||
\(737\) | 23.1196 | 0.851622 | ||||||||
\(738\) | 71.7679 | 2.64181 | ||||||||
\(739\) | −8.45213 | −0.310917 | −0.155458 | − | 0.987842i | \(-0.549685\pi\) | ||||
−0.155458 | + | 0.987842i | \(0.549685\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −47.0650 | −1.72898 | ||||||||
\(742\) | 2.78712 | 0.102318 | ||||||||
\(743\) | 0.812941 | 0.0298239 | 0.0149120 | − | 0.999889i | \(-0.495253\pi\) | ||||
0.0149120 | + | 0.999889i | \(0.495253\pi\) | |||||||
\(744\) | 76.6404 | 2.80977 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 38.1587 | 1.39709 | ||||||||
\(747\) | −91.3444 | −3.34212 | ||||||||
\(748\) | 37.9012 | 1.38581 | ||||||||
\(749\) | −2.81131 | −0.102723 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.5689 | 0.714080 | 0.357040 | − | 0.934089i | \(-0.383786\pi\) | ||||
0.357040 | + | 0.934089i | \(0.383786\pi\) | |||||||
\(752\) | 6.77297 | 0.246985 | ||||||||
\(753\) | −61.9612 | −2.25799 | ||||||||
\(754\) | −20.1287 | −0.733045 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −43.3981 | −1.57837 | ||||||||
\(757\) | −15.0406 | −0.546661 | −0.273330 | − | 0.961920i | \(-0.588125\pi\) | ||||
−0.273330 | + | 0.961920i | \(0.588125\pi\) | |||||||
\(758\) | −46.6083 | −1.69289 | ||||||||
\(759\) | −6.74974 | −0.245000 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.0667 | −1.16242 | −0.581209 | − | 0.813754i | \(-0.697420\pi\) | ||||
−0.581209 | + | 0.813754i | \(0.697420\pi\) | |||||||
\(762\) | 40.4905 | 1.46681 | ||||||||
\(763\) | −25.3949 | −0.919357 | ||||||||
\(764\) | 31.1950 | 1.12860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.0320 | 0.579260 | ||||||||
\(767\) | −44.8580 | −1.61973 | ||||||||
\(768\) | −69.8449 | −2.52031 | ||||||||
\(769\) | 20.1660 | 0.727204 | 0.363602 | − | 0.931554i | \(-0.381547\pi\) | ||||
0.363602 | + | 0.931554i | \(0.381547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −83.1930 | −2.99612 | ||||||||
\(772\) | 29.8558 | 1.07454 | ||||||||
\(773\) | −9.25347 | −0.332824 | −0.166412 | − | 0.986056i | \(-0.553218\pi\) | ||||
−0.166412 | + | 0.986056i | \(0.553218\pi\) | |||||||
\(774\) | −51.6955 | −1.85816 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.6057 | 0.739703 | ||||||||
\(777\) | −6.37978 | −0.228873 | ||||||||
\(778\) | 38.9307 | 1.39573 | ||||||||
\(779\) | 20.1527 | 0.722044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.45538 | −0.195209 | ||||||||
\(782\) | 3.47093 | 0.124120 | ||||||||
\(783\) | 20.6098 | 0.736534 | ||||||||
\(784\) | −6.51371 | −0.232633 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −119.849 | −4.27486 | ||||||||
\(787\) | −2.93319 | −0.104557 | −0.0522784 | − | 0.998633i | \(-0.516648\pi\) | ||||
−0.0522784 | + | 0.998633i | \(0.516648\pi\) | |||||||
\(788\) | −68.1279 | −2.42696 | ||||||||
\(789\) | −29.7478 | −1.05905 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.4847 | 0.621686 | ||||||||
\(792\) | 86.7063 | 3.08098 | ||||||||
\(793\) | 14.0563 | 0.499154 | ||||||||
\(794\) | −65.3000 | −2.31741 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 31.4506 | 1.11474 | ||||||||
\(797\) | −27.3198 | −0.967718 | −0.483859 | − | 0.875146i | \(-0.660765\pi\) | ||||
−0.483859 | + | 0.875146i | \(0.660765\pi\) | |||||||
\(798\) | −37.7139 | −1.33506 | ||||||||
\(799\) | −14.5688 | −0.515407 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.2788 | −1.14052 | ||||||||
\(802\) | −41.0990 | −1.45125 | ||||||||
\(803\) | 21.0103 | 0.741437 | ||||||||
\(804\) | −60.2801 | −2.12592 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 65.9211 | 2.32197 | ||||||||
\(807\) | 58.6853 | 2.06582 | ||||||||
\(808\) | 47.1945 | 1.66030 | ||||||||
\(809\) | −2.27241 | −0.0798938 | −0.0399469 | − | 0.999202i | \(-0.512719\pi\) | ||||
−0.0399469 | + | 0.999202i | \(0.512719\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.79682 | −0.344013 | −0.172006 | − | 0.985096i | \(-0.555025\pi\) | ||||
−0.172006 | + | 0.985096i | \(0.555025\pi\) | |||||||
\(812\) | −10.2630 | −0.360160 | ||||||||
\(813\) | −75.6182 | −2.65205 | ||||||||
\(814\) | 15.1101 | 0.529609 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.0445 | −0.351628 | ||||||||
\(817\) | −14.5163 | −0.507861 | ||||||||
\(818\) | −74.6921 | −2.61155 | ||||||||
\(819\) | −31.4888 | −1.10031 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.5651 | 0.717726 | 0.358863 | − | 0.933390i | \(-0.383165\pi\) | ||||
0.358863 | + | 0.933390i | \(0.383165\pi\) | |||||||
\(822\) | 136.505 | 4.76116 | ||||||||
\(823\) | 10.5127 | 0.366449 | 0.183225 | − | 0.983071i | \(-0.441346\pi\) | ||||
0.183225 | + | 0.983071i | \(0.441346\pi\) | |||||||
\(824\) | −49.9204 | −1.73906 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.9454 | −1.25070 | ||||||||
\(827\) | −33.6008 | −1.16842 | −0.584208 | − | 0.811604i | \(-0.698595\pi\) | ||||
−0.584208 | + | 0.811604i | \(0.698595\pi\) | |||||||
\(828\) | 11.7940 | 0.409871 | ||||||||
\(829\) | 33.7332 | 1.17160 | 0.585801 | − | 0.810455i | \(-0.300780\pi\) | ||||
0.585801 | + | 0.810455i | \(0.300780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 83.1151 | 2.88323 | ||||||||
\(832\) | −47.1646 | −1.63514 | ||||||||
\(833\) | 14.0111 | 0.485456 | ||||||||
\(834\) | −40.9487 | −1.41794 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 56.8352 | 1.96569 | ||||||||
\(837\) | −67.4966 | −2.33302 | ||||||||
\(838\) | 15.0972 | 0.521524 | ||||||||
\(839\) | −50.5894 | −1.74654 | −0.873270 | − | 0.487237i | \(-0.838005\pi\) | ||||
−0.873270 | + | 0.487237i | \(0.838005\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.1261 | −0.831934 | ||||||||
\(842\) | −78.1941 | −2.69475 | ||||||||
\(843\) | 89.5441 | 3.08406 | ||||||||
\(844\) | −22.9547 | −0.790133 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −77.8010 | −2.67485 | ||||||||
\(847\) | −7.14699 | −0.245573 | ||||||||
\(848\) | 1.11313 | 0.0382251 | ||||||||
\(849\) | 60.8315 | 2.08773 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.880470 | 0.0301821 | ||||||||
\(852\) | 14.2239 | 0.487303 | ||||||||
\(853\) | −4.82513 | −0.165209 | −0.0826046 | − | 0.996582i | \(-0.526324\pi\) | ||||
−0.0826046 | + | 0.996582i | \(0.526324\pi\) | |||||||
\(854\) | 11.2635 | 0.385430 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.43704 | −0.254193 | ||||||||
\(857\) | 27.8017 | 0.949689 | 0.474844 | − | 0.880070i | \(-0.342504\pi\) | ||||
0.474844 | + | 0.880070i | \(0.342504\pi\) | |||||||
\(858\) | 111.285 | 3.79920 | ||||||||
\(859\) | −1.40326 | −0.0478785 | −0.0239392 | − | 0.999713i | \(-0.507621\pi\) | ||||
−0.0239392 | + | 0.999713i | \(0.507621\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.1191 | 0.685657 | ||||||||
\(862\) | 69.7068 | 2.37422 | ||||||||
\(863\) | −20.1198 | −0.684887 | −0.342444 | − | 0.939538i | \(-0.611255\pi\) | ||||
−0.342444 | + | 0.939538i | \(0.611255\pi\) | |||||||
\(864\) | 38.3842 | 1.30586 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −40.9921 | −1.39297 | ||||||||
\(867\) | −29.6638 | −1.00744 | ||||||||
\(868\) | 33.6110 | 1.14083 | ||||||||
\(869\) | −40.8112 | −1.38442 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.2114 | −0.752605 | ||||||||
\(872\) | −67.1796 | −2.27499 | ||||||||
\(873\) | −35.7350 | −1.20945 | ||||||||
\(874\) | 5.20488 | 0.176058 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −54.7804 | −1.85086 | ||||||||
\(877\) | 22.9122 | 0.773689 | 0.386845 | − | 0.922145i | \(-0.373565\pi\) | ||||
0.386845 | + | 0.922145i | \(0.373565\pi\) | |||||||
\(878\) | 46.3917 | 1.56564 | ||||||||
\(879\) | −13.8600 | −0.467485 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.6497 | 1.06631 | 0.533153 | − | 0.846019i | \(-0.321007\pi\) | ||||
0.533153 | + | 0.846019i | \(0.321007\pi\) | |||||||
\(882\) | 74.8229 | 2.51942 | ||||||||
\(883\) | 5.43312 | 0.182839 | 0.0914195 | − | 0.995812i | \(-0.470860\pi\) | ||||
0.0914195 | + | 0.995812i | \(0.470860\pi\) | |||||||
\(884\) | −36.4124 | −1.22468 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.35582 | 0.213528 | ||||||||
\(887\) | 28.1102 | 0.943847 | 0.471923 | − | 0.881640i | \(-0.343560\pi\) | ||||
0.471923 | + | 0.881640i | \(0.343560\pi\) | |||||||
\(888\) | −16.8771 | −0.566357 | ||||||||
\(889\) | 7.60698 | 0.255130 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −39.9375 | −1.33796 | ||||||||
\(892\) | −13.6266 | −0.456252 | ||||||||
\(893\) | −21.8468 | −0.731075 | ||||||||
\(894\) | 49.9815 | 1.67163 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −26.8678 | −0.897591 | ||||||||
\(897\) | 6.48460 | 0.216514 | ||||||||
\(898\) | −65.6577 | −2.19102 | ||||||||
\(899\) | −15.9619 | −0.532359 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.39437 | −0.0797680 | ||||||||
\(902\) | −47.6508 | −1.58660 | ||||||||
\(903\) | −14.4921 | −0.482267 | ||||||||
\(904\) | 46.2541 | 1.53839 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34.5141 | 1.14666 | ||||||||
\(907\) | 34.1991 | 1.13556 | 0.567781 | − | 0.823180i | \(-0.307802\pi\) | ||||
0.567781 | + | 0.823180i | \(0.307802\pi\) | |||||||
\(908\) | 38.8335 | 1.28874 | ||||||||
\(909\) | −81.8461 | −2.71466 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.4208 | −1.90244 | −0.951218 | − | 0.308519i | \(-0.900167\pi\) | ||||
−0.951218 | + | 0.308519i | \(0.900167\pi\) | |||||||
\(912\) | −15.0623 | −0.498764 | ||||||||
\(913\) | 60.6488 | 2.00718 | ||||||||
\(914\) | −43.9382 | −1.45335 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −81.1086 | −2.67990 | ||||||||
\(917\) | −22.5161 | −0.743546 | ||||||||
\(918\) | 58.5939 | 1.93389 | ||||||||
\(919\) | 2.33801 | 0.0771238 | 0.0385619 | − | 0.999256i | \(-0.487722\pi\) | ||||
0.0385619 | + | 0.999256i | \(0.487722\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.68882 | 0.253355 | ||||||||
\(922\) | −57.1154 | −1.88099 | ||||||||
\(923\) | 5.24108 | 0.172512 | ||||||||
\(924\) | 56.7405 | 1.86663 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 47.0321 | 1.54557 | ||||||||
\(927\) | 86.5734 | 2.84344 | ||||||||
\(928\) | 9.07729 | 0.297977 | ||||||||
\(929\) | 28.8794 | 0.947504 | 0.473752 | − | 0.880658i | \(-0.342899\pi\) | ||||
0.473752 | + | 0.880658i | \(0.342899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.0105 | 0.688592 | ||||||||
\(932\) | 66.0197 | 2.16255 | ||||||||
\(933\) | −65.0315 | −2.12903 | ||||||||
\(934\) | 49.2816 | 1.61254 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −83.3003 | −2.72276 | ||||||||
\(937\) | 56.3605 | 1.84122 | 0.920608 | − | 0.390487i | \(-0.127693\pi\) | ||||
0.920608 | + | 0.390487i | \(0.127693\pi\) | |||||||
\(938\) | −17.7983 | −0.581137 | ||||||||
\(939\) | −100.214 | −3.27036 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0489 | −0.881767 | −0.440884 | − | 0.897564i | \(-0.645335\pi\) | ||||
−0.440884 | + | 0.897564i | \(0.645335\pi\) | |||||||
\(942\) | 43.4328 | 1.41512 | ||||||||
\(943\) | −2.77663 | −0.0904194 | ||||||||
\(944\) | −14.3560 | −0.467249 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 34.3236 | 1.11596 | ||||||||
\(947\) | −9.75421 | −0.316969 | −0.158485 | − | 0.987361i | \(-0.550661\pi\) | ||||
−0.158485 | + | 0.987361i | \(0.550661\pi\) | |||||||
\(948\) | 106.408 | 3.45596 | ||||||||
\(949\) | −20.1850 | −0.655231 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −65.0998 | −2.11100 | ||||||||
\(952\) | −12.4994 | −0.405107 | ||||||||
\(953\) | −6.26546 | −0.202958 | −0.101479 | − | 0.994838i | \(-0.532357\pi\) | ||||
−0.101479 | + | 0.994838i | \(0.532357\pi\) | |||||||
\(954\) | −12.7865 | −0.413979 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −47.3658 | −1.53192 | ||||||||
\(957\) | −26.9461 | −0.871044 | ||||||||
\(958\) | 34.8125 | 1.12474 | ||||||||
\(959\) | 25.6454 | 0.828132 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.2748 | 0.686284 | ||||||||
\(962\) | −14.5165 | −0.468032 | ||||||||
\(963\) | 12.8975 | 0.415617 | ||||||||
\(964\) | −3.49887 | −0.112691 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.19621 | 0.167185 | ||||||||
\(967\) | 15.8446 | 0.509527 | 0.254763 | − | 0.967003i | \(-0.418002\pi\) | ||||
0.254763 | + | 0.967003i | \(0.418002\pi\) | |||||||
\(968\) | −18.9066 | −0.607682 | ||||||||
\(969\) | 32.3994 | 1.04082 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.9429 | 1.08928 | 0.544640 | − | 0.838670i | \(-0.316666\pi\) | ||||
0.544640 | + | 0.838670i | \(0.316666\pi\) | |||||||
\(972\) | 6.13911 | 0.196912 | ||||||||
\(973\) | −7.69308 | −0.246629 | ||||||||
\(974\) | −7.94937 | −0.254714 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.49847 | 0.143993 | ||||||||
\(977\) | 33.0383 | 1.05699 | 0.528495 | − | 0.848937i | \(-0.322757\pi\) | ||||
0.528495 | + | 0.848937i | \(0.322757\pi\) | |||||||
\(978\) | −125.059 | −3.99894 | ||||||||
\(979\) | 21.4318 | 0.684962 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 116.505 | 3.71971 | ||||||||
\(982\) | 20.2697 | 0.646833 | ||||||||
\(983\) | 13.6593 | 0.435663 | 0.217831 | − | 0.975986i | \(-0.430102\pi\) | ||||
0.217831 | + | 0.975986i | \(0.430102\pi\) | |||||||
\(984\) | 53.2230 | 1.69669 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.8566 | 0.441283 | ||||||||
\(987\) | −21.8104 | −0.694233 | ||||||||
\(988\) | −54.6026 | −1.73714 | ||||||||
\(989\) | 2.00005 | 0.0635978 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.7712 | −1.51750 | −0.758751 | − | 0.651381i | \(-0.774190\pi\) | ||||
−0.758751 | + | 0.651381i | \(0.774190\pi\) | |||||||
\(992\) | −29.7279 | −0.943861 | ||||||||
\(993\) | −47.8671 | −1.51902 | ||||||||
\(994\) | 4.19976 | 0.133208 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −158.131 | −5.01056 | ||||||||
\(997\) | −15.2848 | −0.484073 | −0.242036 | − | 0.970267i | \(-0.577815\pi\) | ||||
−0.242036 | + | 0.970267i | \(0.577815\pi\) | |||||||
\(998\) | 19.7219 | 0.624287 | ||||||||
\(999\) | 14.8635 | 0.470260 |
(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 | 6025.2.a.i.1.1 | 15 | ||
5.4 | even | 2 | 1205.2.a.c.1.15 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.c.1.15 | ✓ | 15 | 5.4 | even | 2 | ||
6025.2.a.i.1.1 | 15 | 1.1 | even | 1 | trivial |