Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(1,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, 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("731.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 2 x^{18} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + 7816 x^{11} - 19517 x^{10} - 13527 x^{9} + 40173 x^{8} + 8942 x^{7} - 41911 x^{6} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Root | \(2.66743\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 731.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.66743 | 1.88616 | 0.943080 | − | 0.332567i | \(-0.107915\pi\) | ||||
0.943080 | + | 0.332567i | \(0.107915\pi\) | |||||||
\(3\) | −1.22120 | −0.705062 | −0.352531 | − | 0.935800i | \(-0.614679\pi\) | ||||
−0.352531 | + | 0.935800i | \(0.614679\pi\) | |||||||
\(4\) | 5.11519 | 2.55760 | ||||||||
\(5\) | −1.15779 | −0.517781 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(6\) | −3.25748 | −1.32986 | ||||||||
\(7\) | 2.36958 | 0.895616 | 0.447808 | − | 0.894130i | \(-0.352205\pi\) | ||||
0.447808 | + | 0.894130i | \(0.352205\pi\) | |||||||
\(8\) | 8.30956 | 2.93787 | ||||||||
\(9\) | −1.50866 | −0.502888 | ||||||||
\(10\) | −3.08834 | −0.976617 | ||||||||
\(11\) | 6.51509 | 1.96437 | 0.982187 | − | 0.187905i | \(-0.0601698\pi\) | ||||
0.982187 | + | 0.187905i | \(0.0601698\pi\) | |||||||
\(12\) | −6.24669 | −1.80326 | ||||||||
\(13\) | −3.92858 | −1.08959 | −0.544796 | − | 0.838569i | \(-0.683393\pi\) | ||||
−0.544796 | + | 0.838569i | \(0.683393\pi\) | |||||||
\(14\) | 6.32068 | 1.68927 | ||||||||
\(15\) | 1.41390 | 0.365068 | ||||||||
\(16\) | 11.9348 | 2.98370 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −4.02426 | −0.948527 | ||||||||
\(19\) | 0.308012 | 0.0706629 | 0.0353315 | − | 0.999376i | \(-0.488751\pi\) | ||||
0.0353315 | + | 0.999376i | \(0.488751\pi\) | |||||||
\(20\) | −5.92234 | −1.32427 | ||||||||
\(21\) | −2.89373 | −0.631464 | ||||||||
\(22\) | 17.3786 | 3.70512 | ||||||||
\(23\) | 1.28661 | 0.268278 | 0.134139 | − | 0.990963i | \(-0.457173\pi\) | ||||
0.134139 | + | 0.990963i | \(0.457173\pi\) | |||||||
\(24\) | −10.1477 | −2.07138 | ||||||||
\(25\) | −3.65951 | −0.731903 | ||||||||
\(26\) | −10.4792 | −2.05514 | ||||||||
\(27\) | 5.50599 | 1.05963 | ||||||||
\(28\) | 12.1208 | 2.29062 | ||||||||
\(29\) | −2.29611 | −0.426377 | −0.213188 | − | 0.977011i | \(-0.568385\pi\) | ||||
−0.213188 | + | 0.977011i | \(0.568385\pi\) | |||||||
\(30\) | 3.77148 | 0.688576 | ||||||||
\(31\) | 5.07718 | 0.911889 | 0.455945 | − | 0.890008i | \(-0.349301\pi\) | ||||
0.455945 | + | 0.890008i | \(0.349301\pi\) | |||||||
\(32\) | 15.2162 | 2.68986 | ||||||||
\(33\) | −7.95625 | −1.38501 | ||||||||
\(34\) | 2.66743 | 0.457461 | ||||||||
\(35\) | −2.74348 | −0.463733 | ||||||||
\(36\) | −7.71711 | −1.28618 | ||||||||
\(37\) | −5.52176 | −0.907771 | −0.453886 | − | 0.891060i | \(-0.649963\pi\) | ||||
−0.453886 | + | 0.891060i | \(0.649963\pi\) | |||||||
\(38\) | 0.821602 | 0.133281 | ||||||||
\(39\) | 4.79759 | 0.768230 | ||||||||
\(40\) | −9.62076 | −1.52118 | ||||||||
\(41\) | −0.358377 | −0.0559691 | −0.0279846 | − | 0.999608i | \(-0.508909\pi\) | ||||
−0.0279846 | + | 0.999608i | \(0.508909\pi\) | |||||||
\(42\) | −7.71884 | −1.19104 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 33.3260 | 5.02408 | ||||||||
\(45\) | 1.74672 | 0.260386 | ||||||||
\(46\) | 3.43196 | 0.506014 | ||||||||
\(47\) | −7.52351 | −1.09742 | −0.548709 | − | 0.836014i | \(-0.684880\pi\) | ||||
−0.548709 | + | 0.836014i | \(0.684880\pi\) | |||||||
\(48\) | −14.5748 | −2.10369 | ||||||||
\(49\) | −1.38511 | −0.197873 | ||||||||
\(50\) | −9.76150 | −1.38049 | ||||||||
\(51\) | −1.22120 | −0.171003 | ||||||||
\(52\) | −20.0954 | −2.78674 | ||||||||
\(53\) | −0.0422801 | −0.00580761 | −0.00290381 | − | 0.999996i | \(-0.500924\pi\) | ||||
−0.00290381 | + | 0.999996i | \(0.500924\pi\) | |||||||
\(54\) | 14.6869 | 1.99863 | ||||||||
\(55\) | −7.54313 | −1.01712 | ||||||||
\(56\) | 19.6901 | 2.63121 | ||||||||
\(57\) | −0.376146 | −0.0498217 | ||||||||
\(58\) | −6.12471 | −0.804214 | ||||||||
\(59\) | −5.52410 | −0.719176 | −0.359588 | − | 0.933111i | \(-0.617083\pi\) | ||||
−0.359588 | + | 0.933111i | \(0.617083\pi\) | |||||||
\(60\) | 7.23237 | 0.933695 | ||||||||
\(61\) | −4.20526 | −0.538428 | −0.269214 | − | 0.963080i | \(-0.586764\pi\) | ||||
−0.269214 | + | 0.963080i | \(0.586764\pi\) | |||||||
\(62\) | 13.5430 | 1.71997 | ||||||||
\(63\) | −3.57489 | −0.450394 | ||||||||
\(64\) | 16.7185 | 2.08981 | ||||||||
\(65\) | 4.54848 | 0.564170 | ||||||||
\(66\) | −21.2228 | −2.61234 | ||||||||
\(67\) | 7.62209 | 0.931186 | 0.465593 | − | 0.884999i | \(-0.345841\pi\) | ||||
0.465593 | + | 0.884999i | \(0.345841\pi\) | |||||||
\(68\) | 5.11519 | 0.620308 | ||||||||
\(69\) | −1.57122 | −0.189152 | ||||||||
\(70\) | −7.31805 | −0.874674 | ||||||||
\(71\) | 6.07143 | 0.720546 | 0.360273 | − | 0.932847i | \(-0.382684\pi\) | ||||
0.360273 | + | 0.932847i | \(0.382684\pi\) | |||||||
\(72\) | −12.5363 | −1.47742 | ||||||||
\(73\) | −7.32893 | −0.857786 | −0.428893 | − | 0.903355i | \(-0.641096\pi\) | ||||
−0.428893 | + | 0.903355i | \(0.641096\pi\) | |||||||
\(74\) | −14.7289 | −1.71220 | ||||||||
\(75\) | 4.46901 | 0.516037 | ||||||||
\(76\) | 1.57554 | 0.180727 | ||||||||
\(77\) | 15.4380 | 1.75932 | ||||||||
\(78\) | 12.7973 | 1.44900 | ||||||||
\(79\) | −11.0101 | −1.23874 | −0.619368 | − | 0.785101i | \(-0.712611\pi\) | ||||
−0.619368 | + | 0.785101i | \(0.712611\pi\) | |||||||
\(80\) | −13.8180 | −1.54490 | ||||||||
\(81\) | −2.19794 | −0.244216 | ||||||||
\(82\) | −0.955947 | −0.105567 | ||||||||
\(83\) | −7.59813 | −0.834003 | −0.417002 | − | 0.908906i | \(-0.636919\pi\) | ||||
−0.417002 | + | 0.908906i | \(0.636919\pi\) | |||||||
\(84\) | −14.8020 | −1.61503 | ||||||||
\(85\) | −1.15779 | −0.125580 | ||||||||
\(86\) | −2.66743 | −0.287637 | ||||||||
\(87\) | 2.80401 | 0.300622 | ||||||||
\(88\) | 54.1376 | 5.77109 | ||||||||
\(89\) | −12.4245 | −1.31699 | −0.658497 | − | 0.752583i | \(-0.728808\pi\) | ||||
−0.658497 | + | 0.752583i | \(0.728808\pi\) | |||||||
\(90\) | 4.65926 | 0.491129 | ||||||||
\(91\) | −9.30907 | −0.975856 | ||||||||
\(92\) | 6.58128 | 0.686146 | ||||||||
\(93\) | −6.20027 | −0.642938 | ||||||||
\(94\) | −20.0685 | −2.06990 | ||||||||
\(95\) | −0.356615 | −0.0365879 | ||||||||
\(96\) | −18.5820 | −1.89652 | ||||||||
\(97\) | −17.8513 | −1.81252 | −0.906261 | − | 0.422718i | \(-0.861076\pi\) | ||||
−0.906261 | + | 0.422718i | \(0.861076\pi\) | |||||||
\(98\) | −3.69468 | −0.373219 | ||||||||
\(99\) | −9.82908 | −0.987860 | ||||||||
\(100\) | −18.7191 | −1.87191 | ||||||||
\(101\) | 5.07769 | 0.505249 | 0.252624 | − | 0.967564i | \(-0.418706\pi\) | ||||
0.252624 | + | 0.967564i | \(0.418706\pi\) | |||||||
\(102\) | −3.25748 | −0.322538 | ||||||||
\(103\) | 0.113534 | 0.0111868 | 0.00559342 | − | 0.999984i | \(-0.498220\pi\) | ||||
0.00559342 | + | 0.999984i | \(0.498220\pi\) | |||||||
\(104\) | −32.6448 | −3.20108 | ||||||||
\(105\) | 3.35035 | 0.326960 | ||||||||
\(106\) | −0.112779 | −0.0109541 | ||||||||
\(107\) | −11.0063 | −1.06402 | −0.532012 | − | 0.846737i | \(-0.678564\pi\) | ||||
−0.532012 | + | 0.846737i | \(0.678564\pi\) | |||||||
\(108\) | 28.1642 | 2.71010 | ||||||||
\(109\) | 15.2804 | 1.46360 | 0.731798 | − | 0.681522i | \(-0.238682\pi\) | ||||
0.731798 | + | 0.681522i | \(0.238682\pi\) | |||||||
\(110\) | −20.1208 | −1.91844 | ||||||||
\(111\) | 6.74319 | 0.640035 | ||||||||
\(112\) | 28.2804 | 2.67225 | ||||||||
\(113\) | 16.0296 | 1.50794 | 0.753969 | − | 0.656910i | \(-0.228137\pi\) | ||||
0.753969 | + | 0.656910i | \(0.228137\pi\) | |||||||
\(114\) | −1.00334 | −0.0939717 | ||||||||
\(115\) | −1.48963 | −0.138909 | ||||||||
\(116\) | −11.7450 | −1.09050 | ||||||||
\(117\) | 5.92691 | 0.547943 | ||||||||
\(118\) | −14.7352 | −1.35648 | ||||||||
\(119\) | 2.36958 | 0.217219 | ||||||||
\(120\) | 11.7489 | 1.07252 | ||||||||
\(121\) | 31.4464 | 2.85877 | ||||||||
\(122\) | −11.2172 | −1.01556 | ||||||||
\(123\) | 0.437651 | 0.0394617 | ||||||||
\(124\) | 25.9708 | 2.33224 | ||||||||
\(125\) | 10.0259 | 0.896746 | ||||||||
\(126\) | −9.53579 | −0.849515 | ||||||||
\(127\) | 17.2139 | 1.52749 | 0.763743 | − | 0.645521i | \(-0.223360\pi\) | ||||
0.763743 | + | 0.645521i | \(0.223360\pi\) | |||||||
\(128\) | 14.1630 | 1.25185 | ||||||||
\(129\) | 1.22120 | 0.107521 | ||||||||
\(130\) | 12.1328 | 1.06411 | ||||||||
\(131\) | −2.11340 | −0.184649 | −0.0923243 | − | 0.995729i | \(-0.529430\pi\) | ||||
−0.0923243 | + | 0.995729i | \(0.529430\pi\) | |||||||
\(132\) | −40.6977 | −3.54228 | ||||||||
\(133\) | 0.729859 | 0.0632868 | ||||||||
\(134\) | 20.3314 | 1.75637 | ||||||||
\(135\) | −6.37480 | −0.548656 | ||||||||
\(136\) | 8.30956 | 0.712539 | ||||||||
\(137\) | −13.1346 | −1.12217 | −0.561084 | − | 0.827759i | \(-0.689616\pi\) | ||||
−0.561084 | + | 0.827759i | \(0.689616\pi\) | |||||||
\(138\) | −4.19111 | −0.356771 | ||||||||
\(139\) | 21.0890 | 1.78875 | 0.894375 | − | 0.447318i | \(-0.147621\pi\) | ||||
0.894375 | + | 0.447318i | \(0.147621\pi\) | |||||||
\(140\) | −14.0334 | −1.18604 | ||||||||
\(141\) | 9.18774 | 0.773747 | ||||||||
\(142\) | 16.1951 | 1.35906 | ||||||||
\(143\) | −25.5951 | −2.14037 | ||||||||
\(144\) | −18.0056 | −1.50047 | ||||||||
\(145\) | 2.65842 | 0.220770 | ||||||||
\(146\) | −19.5494 | −1.61792 | ||||||||
\(147\) | 1.69150 | 0.139512 | ||||||||
\(148\) | −28.2449 | −2.32171 | ||||||||
\(149\) | −18.6209 | −1.52548 | −0.762741 | − | 0.646704i | \(-0.776147\pi\) | ||||
−0.762741 | + | 0.646704i | \(0.776147\pi\) | |||||||
\(150\) | 11.9208 | 0.973327 | ||||||||
\(151\) | 7.82065 | 0.636436 | 0.318218 | − | 0.948018i | \(-0.396916\pi\) | ||||
0.318218 | + | 0.948018i | \(0.396916\pi\) | |||||||
\(152\) | 2.55945 | 0.207599 | ||||||||
\(153\) | −1.50866 | −0.121968 | ||||||||
\(154\) | 41.1798 | 3.31837 | ||||||||
\(155\) | −5.87833 | −0.472159 | ||||||||
\(156\) | 24.5406 | 1.96482 | ||||||||
\(157\) | 19.0355 | 1.51920 | 0.759600 | − | 0.650391i | \(-0.225395\pi\) | ||||
0.759600 | + | 0.650391i | \(0.225395\pi\) | |||||||
\(158\) | −29.3688 | −2.33645 | ||||||||
\(159\) | 0.0516325 | 0.00409472 | ||||||||
\(160\) | −17.6172 | −1.39276 | ||||||||
\(161\) | 3.04873 | 0.240274 | ||||||||
\(162\) | −5.86286 | −0.460630 | ||||||||
\(163\) | −9.68110 | −0.758282 | −0.379141 | − | 0.925339i | \(-0.623781\pi\) | ||||
−0.379141 | + | 0.925339i | \(0.623781\pi\) | |||||||
\(164\) | −1.83317 | −0.143146 | ||||||||
\(165\) | 9.21169 | 0.717129 | ||||||||
\(166\) | −20.2675 | −1.57306 | ||||||||
\(167\) | −6.67564 | −0.516576 | −0.258288 | − | 0.966068i | \(-0.583158\pi\) | ||||
−0.258288 | + | 0.966068i | \(0.583158\pi\) | |||||||
\(168\) | −24.0457 | −1.85516 | ||||||||
\(169\) | 2.43374 | 0.187211 | ||||||||
\(170\) | −3.08834 | −0.236865 | ||||||||
\(171\) | −0.464687 | −0.0355355 | ||||||||
\(172\) | −5.11519 | −0.390030 | ||||||||
\(173\) | −2.47305 | −0.188023 | −0.0940113 | − | 0.995571i | \(-0.529969\pi\) | ||||
−0.0940113 | + | 0.995571i | \(0.529969\pi\) | |||||||
\(174\) | 7.47952 | 0.567021 | ||||||||
\(175\) | −8.67150 | −0.655504 | ||||||||
\(176\) | 77.7564 | 5.86111 | ||||||||
\(177\) | 6.74604 | 0.507064 | ||||||||
\(178\) | −33.1415 | −2.48406 | ||||||||
\(179\) | 18.3300 | 1.37005 | 0.685025 | − | 0.728520i | \(-0.259791\pi\) | ||||
0.685025 | + | 0.728520i | \(0.259791\pi\) | |||||||
\(180\) | 8.93482 | 0.665962 | ||||||||
\(181\) | 12.4942 | 0.928690 | 0.464345 | − | 0.885654i | \(-0.346290\pi\) | ||||
0.464345 | + | 0.885654i | \(0.346290\pi\) | |||||||
\(182\) | −24.8313 | −1.84062 | ||||||||
\(183\) | 5.13547 | 0.379625 | ||||||||
\(184\) | 10.6912 | 0.788166 | ||||||||
\(185\) | 6.39305 | 0.470027 | ||||||||
\(186\) | −16.5388 | −1.21268 | ||||||||
\(187\) | 6.51509 | 0.476431 | ||||||||
\(188\) | −38.4842 | −2.80675 | ||||||||
\(189\) | 13.0469 | 0.949020 | ||||||||
\(190\) | −0.951246 | −0.0690106 | ||||||||
\(191\) | 12.0780 | 0.873936 | 0.436968 | − | 0.899477i | \(-0.356052\pi\) | ||||
0.436968 | + | 0.899477i | \(0.356052\pi\) | |||||||
\(192\) | −20.4166 | −1.47344 | ||||||||
\(193\) | −22.5069 | −1.62008 | −0.810042 | − | 0.586372i | \(-0.800556\pi\) | ||||
−0.810042 | + | 0.586372i | \(0.800556\pi\) | |||||||
\(194\) | −47.6171 | −3.41871 | ||||||||
\(195\) | −5.55462 | −0.397775 | ||||||||
\(196\) | −7.08510 | −0.506078 | ||||||||
\(197\) | 8.66711 | 0.617506 | 0.308753 | − | 0.951142i | \(-0.400088\pi\) | ||||
0.308753 | + | 0.951142i | \(0.400088\pi\) | |||||||
\(198\) | −26.2184 | −1.86326 | ||||||||
\(199\) | −9.76275 | −0.692063 | −0.346032 | − | 0.938223i | \(-0.612471\pi\) | ||||
−0.346032 | + | 0.938223i | \(0.612471\pi\) | |||||||
\(200\) | −30.4090 | −2.15024 | ||||||||
\(201\) | −9.30812 | −0.656544 | ||||||||
\(202\) | 13.5444 | 0.952980 | ||||||||
\(203\) | −5.44080 | −0.381870 | ||||||||
\(204\) | −6.24669 | −0.437356 | ||||||||
\(205\) | 0.414927 | 0.0289798 | ||||||||
\(206\) | 0.302844 | 0.0211002 | ||||||||
\(207\) | −1.94107 | −0.134914 | ||||||||
\(208\) | −46.8869 | −3.25102 | ||||||||
\(209\) | 2.00673 | 0.138808 | ||||||||
\(210\) | 8.93682 | 0.616699 | ||||||||
\(211\) | −0.635111 | −0.0437229 | −0.0218614 | − | 0.999761i | \(-0.506959\pi\) | ||||
−0.0218614 | + | 0.999761i | \(0.506959\pi\) | |||||||
\(212\) | −0.216271 | −0.0148535 | ||||||||
\(213\) | −7.41445 | −0.508029 | ||||||||
\(214\) | −29.3587 | −2.00692 | ||||||||
\(215\) | 1.15779 | 0.0789609 | ||||||||
\(216\) | 45.7524 | 3.11306 | ||||||||
\(217\) | 12.0308 | 0.816702 | ||||||||
\(218\) | 40.7594 | 2.76057 | ||||||||
\(219\) | 8.95010 | 0.604792 | ||||||||
\(220\) | −38.5846 | −2.60137 | ||||||||
\(221\) | −3.92858 | −0.264265 | ||||||||
\(222\) | 17.9870 | 1.20721 | ||||||||
\(223\) | 23.6836 | 1.58597 | 0.792987 | − | 0.609239i | \(-0.208525\pi\) | ||||
0.792987 | + | 0.609239i | \(0.208525\pi\) | |||||||
\(224\) | 36.0559 | 2.40908 | ||||||||
\(225\) | 5.52098 | 0.368065 | ||||||||
\(226\) | 42.7579 | 2.84421 | ||||||||
\(227\) | 28.1558 | 1.86876 | 0.934381 | − | 0.356274i | \(-0.115953\pi\) | ||||
0.934381 | + | 0.356274i | \(0.115953\pi\) | |||||||
\(228\) | −1.92406 | −0.127424 | ||||||||
\(229\) | −0.785206 | −0.0518879 | −0.0259439 | − | 0.999663i | \(-0.508259\pi\) | ||||
−0.0259439 | + | 0.999663i | \(0.508259\pi\) | |||||||
\(230\) | −3.97350 | −0.262005 | ||||||||
\(231\) | −18.8529 | −1.24043 | ||||||||
\(232\) | −19.0797 | −1.25264 | ||||||||
\(233\) | −0.995090 | −0.0651905 | −0.0325953 | − | 0.999469i | \(-0.510377\pi\) | ||||
−0.0325953 | + | 0.999469i | \(0.510377\pi\) | |||||||
\(234\) | 15.8096 | 1.03351 | ||||||||
\(235\) | 8.71068 | 0.568222 | ||||||||
\(236\) | −28.2568 | −1.83936 | ||||||||
\(237\) | 13.4456 | 0.873385 | ||||||||
\(238\) | 6.32068 | 0.409709 | ||||||||
\(239\) | −7.10271 | −0.459436 | −0.229718 | − | 0.973257i | \(-0.573780\pi\) | ||||
−0.229718 | + | 0.973257i | \(0.573780\pi\) | |||||||
\(240\) | 16.8746 | 1.08925 | ||||||||
\(241\) | 29.9977 | 1.93232 | 0.966161 | − | 0.257940i | \(-0.0830438\pi\) | ||||
0.966161 | + | 0.257940i | \(0.0830438\pi\) | |||||||
\(242\) | 83.8812 | 5.39209 | ||||||||
\(243\) | −13.8338 | −0.887442 | ||||||||
\(244\) | −21.5107 | −1.37708 | ||||||||
\(245\) | 1.60367 | 0.102455 | ||||||||
\(246\) | 1.16741 | 0.0744310 | ||||||||
\(247\) | −1.21005 | −0.0769937 | ||||||||
\(248\) | 42.1892 | 2.67902 | ||||||||
\(249\) | 9.27886 | 0.588024 | ||||||||
\(250\) | 26.7435 | 1.69141 | ||||||||
\(251\) | −15.0432 | −0.949517 | −0.474759 | − | 0.880116i | \(-0.657465\pi\) | ||||
−0.474759 | + | 0.880116i | \(0.657465\pi\) | |||||||
\(252\) | −18.2863 | −1.15193 | ||||||||
\(253\) | 8.38241 | 0.526998 | ||||||||
\(254\) | 45.9169 | 2.88108 | ||||||||
\(255\) | 1.41390 | 0.0885419 | ||||||||
\(256\) | 4.34199 | 0.271375 | ||||||||
\(257\) | −13.1966 | −0.823181 | −0.411590 | − | 0.911369i | \(-0.635027\pi\) | ||||
−0.411590 | + | 0.911369i | \(0.635027\pi\) | |||||||
\(258\) | 3.25748 | 0.202802 | ||||||||
\(259\) | −13.0842 | −0.813014 | ||||||||
\(260\) | 23.2664 | 1.44292 | ||||||||
\(261\) | 3.46406 | 0.214420 | ||||||||
\(262\) | −5.63735 | −0.348277 | ||||||||
\(263\) | −9.40757 | −0.580095 | −0.290048 | − | 0.957012i | \(-0.593671\pi\) | ||||
−0.290048 | + | 0.957012i | \(0.593671\pi\) | |||||||
\(264\) | −66.1130 | −4.06897 | ||||||||
\(265\) | 0.0489516 | 0.00300707 | ||||||||
\(266\) | 1.94685 | 0.119369 | ||||||||
\(267\) | 15.1728 | 0.928562 | ||||||||
\(268\) | 38.9885 | 2.38160 | ||||||||
\(269\) | 23.7915 | 1.45059 | 0.725297 | − | 0.688436i | \(-0.241702\pi\) | ||||
0.725297 | + | 0.688436i | \(0.241702\pi\) | |||||||
\(270\) | −17.0044 | −1.03485 | ||||||||
\(271\) | 10.4516 | 0.634889 | 0.317445 | − | 0.948277i | \(-0.397175\pi\) | ||||
0.317445 | + | 0.948277i | \(0.397175\pi\) | |||||||
\(272\) | 11.9348 | 0.723654 | ||||||||
\(273\) | 11.3683 | 0.688039 | ||||||||
\(274\) | −35.0358 | −2.11659 | ||||||||
\(275\) | −23.8421 | −1.43773 | ||||||||
\(276\) | −8.03708 | −0.483775 | ||||||||
\(277\) | 28.7979 | 1.73030 | 0.865149 | − | 0.501515i | \(-0.167224\pi\) | ||||
0.865149 | + | 0.501515i | \(0.167224\pi\) | |||||||
\(278\) | 56.2536 | 3.37387 | ||||||||
\(279\) | −7.65977 | −0.458578 | ||||||||
\(280\) | −22.7971 | −1.36239 | ||||||||
\(281\) | −22.0010 | −1.31247 | −0.656234 | − | 0.754558i | \(-0.727851\pi\) | ||||
−0.656234 | + | 0.754558i | \(0.727851\pi\) | |||||||
\(282\) | 24.5077 | 1.45941 | ||||||||
\(283\) | 1.40000 | 0.0832211 | 0.0416106 | − | 0.999134i | \(-0.486751\pi\) | ||||
0.0416106 | + | 0.999134i | \(0.486751\pi\) | |||||||
\(284\) | 31.0565 | 1.84287 | ||||||||
\(285\) | 0.435499 | 0.0257967 | ||||||||
\(286\) | −68.2731 | −4.03707 | ||||||||
\(287\) | −0.849202 | −0.0501268 | ||||||||
\(288\) | −22.9561 | −1.35270 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 7.09115 | 0.416407 | ||||||||
\(291\) | 21.8000 | 1.27794 | ||||||||
\(292\) | −37.4889 | −2.19387 | ||||||||
\(293\) | −26.4316 | −1.54415 | −0.772074 | − | 0.635533i | \(-0.780781\pi\) | ||||
−0.772074 | + | 0.635533i | \(0.780781\pi\) | |||||||
\(294\) | 4.51196 | 0.263143 | ||||||||
\(295\) | 6.39576 | 0.372376 | ||||||||
\(296\) | −45.8834 | −2.66692 | ||||||||
\(297\) | 35.8721 | 2.08151 | ||||||||
\(298\) | −49.6699 | −2.87730 | ||||||||
\(299\) | −5.05457 | −0.292313 | ||||||||
\(300\) | 22.8598 | 1.31981 | ||||||||
\(301\) | −2.36958 | −0.136580 | ||||||||
\(302\) | 20.8611 | 1.20042 | ||||||||
\(303\) | −6.20089 | −0.356232 | ||||||||
\(304\) | 3.67607 | 0.210837 | ||||||||
\(305\) | 4.86882 | 0.278788 | ||||||||
\(306\) | −4.02426 | −0.230052 | ||||||||
\(307\) | 4.69458 | 0.267934 | 0.133967 | − | 0.990986i | \(-0.457228\pi\) | ||||
0.133967 | + | 0.990986i | \(0.457228\pi\) | |||||||
\(308\) | 78.9684 | 4.49964 | ||||||||
\(309\) | −0.138648 | −0.00788741 | ||||||||
\(310\) | −15.6800 | −0.890567 | ||||||||
\(311\) | −9.45381 | −0.536076 | −0.268038 | − | 0.963408i | \(-0.586375\pi\) | ||||
−0.268038 | + | 0.963408i | \(0.586375\pi\) | |||||||
\(312\) | 39.8659 | 2.25696 | ||||||||
\(313\) | 0.488917 | 0.0276352 | 0.0138176 | − | 0.999905i | \(-0.495602\pi\) | ||||
0.0138176 | + | 0.999905i | \(0.495602\pi\) | |||||||
\(314\) | 50.7760 | 2.86545 | ||||||||
\(315\) | 4.13899 | 0.233206 | ||||||||
\(316\) | −56.3189 | −3.16819 | ||||||||
\(317\) | 2.98536 | 0.167675 | 0.0838373 | − | 0.996479i | \(-0.473282\pi\) | ||||
0.0838373 | + | 0.996479i | \(0.473282\pi\) | |||||||
\(318\) | 0.137726 | 0.00772330 | ||||||||
\(319\) | −14.9594 | −0.837563 | ||||||||
\(320\) | −19.3565 | −1.08206 | ||||||||
\(321\) | 13.4410 | 0.750202 | ||||||||
\(322\) | 8.13228 | 0.453194 | ||||||||
\(323\) | 0.308012 | 0.0171383 | ||||||||
\(324\) | −11.2429 | −0.624605 | ||||||||
\(325\) | 14.3767 | 0.797476 | ||||||||
\(326\) | −25.8237 | −1.43024 | ||||||||
\(327\) | −18.6604 | −1.03193 | ||||||||
\(328\) | −2.97796 | −0.164430 | ||||||||
\(329\) | −17.8275 | −0.982864 | ||||||||
\(330\) | 24.5716 | 1.35262 | ||||||||
\(331\) | −6.43306 | −0.353593 | −0.176796 | − | 0.984247i | \(-0.556573\pi\) | ||||
−0.176796 | + | 0.984247i | \(0.556573\pi\) | |||||||
\(332\) | −38.8659 | −2.13304 | ||||||||
\(333\) | 8.33048 | 0.456507 | ||||||||
\(334\) | −17.8068 | −0.974345 | ||||||||
\(335\) | −8.82481 | −0.482151 | ||||||||
\(336\) | −34.5362 | −1.88410 | ||||||||
\(337\) | 31.9329 | 1.73950 | 0.869749 | − | 0.493494i | \(-0.164281\pi\) | ||||
0.869749 | + | 0.493494i | \(0.164281\pi\) | |||||||
\(338\) | 6.49184 | 0.353110 | ||||||||
\(339\) | −19.5754 | −1.06319 | ||||||||
\(340\) | −5.92234 | −0.321184 | ||||||||
\(341\) | 33.0783 | 1.79129 | ||||||||
\(342\) | −1.23952 | −0.0670257 | ||||||||
\(343\) | −19.8692 | −1.07283 | ||||||||
\(344\) | −8.30956 | −0.448022 | ||||||||
\(345\) | 1.81914 | 0.0979395 | ||||||||
\(346\) | −6.59669 | −0.354640 | ||||||||
\(347\) | −21.9876 | −1.18036 | −0.590179 | − | 0.807273i | \(-0.700943\pi\) | ||||
−0.590179 | + | 0.807273i | \(0.700943\pi\) | |||||||
\(348\) | 14.3431 | 0.768869 | ||||||||
\(349\) | 21.2791 | 1.13905 | 0.569523 | − | 0.821976i | \(-0.307128\pi\) | ||||
0.569523 | + | 0.821976i | \(0.307128\pi\) | |||||||
\(350\) | −23.1306 | −1.23638 | ||||||||
\(351\) | −21.6307 | −1.15456 | ||||||||
\(352\) | 99.1347 | 5.28390 | ||||||||
\(353\) | 29.6150 | 1.57625 | 0.788124 | − | 0.615517i | \(-0.211053\pi\) | ||||
0.788124 | + | 0.615517i | \(0.211053\pi\) | |||||||
\(354\) | 17.9946 | 0.956403 | ||||||||
\(355\) | −7.02946 | −0.373085 | ||||||||
\(356\) | −63.5537 | −3.36834 | ||||||||
\(357\) | −2.89373 | −0.153153 | ||||||||
\(358\) | 48.8940 | 2.58413 | ||||||||
\(359\) | 33.6193 | 1.77436 | 0.887180 | − | 0.461423i | \(-0.152661\pi\) | ||||
0.887180 | + | 0.461423i | \(0.152661\pi\) | |||||||
\(360\) | 14.5145 | 0.764981 | ||||||||
\(361\) | −18.9051 | −0.995007 | ||||||||
\(362\) | 33.3276 | 1.75166 | ||||||||
\(363\) | −38.4025 | −2.01561 | ||||||||
\(364\) | −47.6177 | −2.49584 | ||||||||
\(365\) | 8.48538 | 0.444145 | ||||||||
\(366\) | 13.6985 | 0.716033 | ||||||||
\(367\) | −8.84424 | −0.461666 | −0.230833 | − | 0.972993i | \(-0.574145\pi\) | ||||
−0.230833 | + | 0.972993i | \(0.574145\pi\) | |||||||
\(368\) | 15.3555 | 0.800461 | ||||||||
\(369\) | 0.540671 | 0.0281462 | ||||||||
\(370\) | 17.0530 | 0.886545 | ||||||||
\(371\) | −0.100186 | −0.00520139 | ||||||||
\(372\) | −31.7156 | −1.64438 | ||||||||
\(373\) | −36.6255 | −1.89640 | −0.948198 | − | 0.317679i | \(-0.897097\pi\) | ||||
−0.948198 | + | 0.317679i | \(0.897097\pi\) | |||||||
\(374\) | 17.3786 | 0.898624 | ||||||||
\(375\) | −12.2437 | −0.632262 | ||||||||
\(376\) | −62.5171 | −3.22407 | ||||||||
\(377\) | 9.02045 | 0.464577 | ||||||||
\(378\) | 34.8016 | 1.79000 | ||||||||
\(379\) | −9.39461 | −0.482569 | −0.241284 | − | 0.970454i | \(-0.577569\pi\) | ||||
−0.241284 | + | 0.970454i | \(0.577569\pi\) | |||||||
\(380\) | −1.82415 | −0.0935771 | ||||||||
\(381\) | −21.0216 | −1.07697 | ||||||||
\(382\) | 32.2173 | 1.64838 | ||||||||
\(383\) | 25.7441 | 1.31546 | 0.657730 | − | 0.753253i | \(-0.271517\pi\) | ||||
0.657730 | + | 0.753253i | \(0.271517\pi\) | |||||||
\(384\) | −17.2959 | −0.882629 | ||||||||
\(385\) | −17.8740 | −0.910945 | ||||||||
\(386\) | −60.0357 | −3.05574 | ||||||||
\(387\) | 1.50866 | 0.0766897 | ||||||||
\(388\) | −91.3127 | −4.63570 | ||||||||
\(389\) | −31.9152 | −1.61817 | −0.809083 | − | 0.587695i | \(-0.800036\pi\) | ||||
−0.809083 | + | 0.587695i | \(0.800036\pi\) | |||||||
\(390\) | −14.8166 | −0.750266 | ||||||||
\(391\) | 1.28661 | 0.0650669 | ||||||||
\(392\) | −11.5096 | −0.581325 | ||||||||
\(393\) | 2.58089 | 0.130189 | ||||||||
\(394\) | 23.1189 | 1.16471 | ||||||||
\(395\) | 12.7475 | 0.641394 | ||||||||
\(396\) | −50.2777 | −2.52655 | ||||||||
\(397\) | 5.89272 | 0.295747 | 0.147874 | − | 0.989006i | \(-0.452757\pi\) | ||||
0.147874 | + | 0.989006i | \(0.452757\pi\) | |||||||
\(398\) | −26.0415 | −1.30534 | ||||||||
\(399\) | −0.891306 | −0.0446211 | ||||||||
\(400\) | −43.6756 | −2.18378 | ||||||||
\(401\) | −20.7143 | −1.03442 | −0.517210 | − | 0.855858i | \(-0.673029\pi\) | ||||
−0.517210 | + | 0.855858i | \(0.673029\pi\) | |||||||
\(402\) | −24.8288 | −1.23835 | ||||||||
\(403\) | −19.9461 | −0.993587 | ||||||||
\(404\) | 25.9733 | 1.29222 | ||||||||
\(405\) | 2.54476 | 0.126450 | ||||||||
\(406\) | −14.5130 | −0.720267 | ||||||||
\(407\) | −35.9748 | −1.78320 | ||||||||
\(408\) | −10.1477 | −0.502384 | ||||||||
\(409\) | −36.5799 | −1.80876 | −0.904379 | − | 0.426731i | \(-0.859665\pi\) | ||||
−0.904379 | + | 0.426731i | \(0.859665\pi\) | |||||||
\(410\) | 1.10679 | 0.0546604 | ||||||||
\(411\) | 16.0401 | 0.791198 | ||||||||
\(412\) | 0.580749 | 0.0286114 | ||||||||
\(413\) | −13.0898 | −0.644105 | ||||||||
\(414\) | −5.17767 | −0.254468 | ||||||||
\(415\) | 8.79707 | 0.431831 | ||||||||
\(416\) | −59.7779 | −2.93085 | ||||||||
\(417\) | −25.7540 | −1.26118 | ||||||||
\(418\) | 5.35282 | 0.261815 | ||||||||
\(419\) | 7.11670 | 0.347674 | 0.173837 | − | 0.984774i | \(-0.444383\pi\) | ||||
0.173837 | + | 0.984774i | \(0.444383\pi\) | |||||||
\(420\) | 17.1377 | 0.836232 | ||||||||
\(421\) | 35.3632 | 1.72350 | 0.861748 | − | 0.507337i | \(-0.169370\pi\) | ||||
0.861748 | + | 0.507337i | \(0.169370\pi\) | |||||||
\(422\) | −1.69412 | −0.0824683 | ||||||||
\(423\) | 11.3505 | 0.551878 | ||||||||
\(424\) | −0.351329 | −0.0170620 | ||||||||
\(425\) | −3.65951 | −0.177513 | ||||||||
\(426\) | −19.7775 | −0.958224 | ||||||||
\(427\) | −9.96468 | −0.482225 | ||||||||
\(428\) | −56.2996 | −2.72134 | ||||||||
\(429\) | 31.2568 | 1.50909 | ||||||||
\(430\) | 3.08834 | 0.148933 | ||||||||
\(431\) | 8.88389 | 0.427922 | 0.213961 | − | 0.976842i | \(-0.431363\pi\) | ||||
0.213961 | + | 0.976842i | \(0.431363\pi\) | |||||||
\(432\) | 65.7130 | 3.16162 | ||||||||
\(433\) | 5.10237 | 0.245204 | 0.122602 | − | 0.992456i | \(-0.460876\pi\) | ||||
0.122602 | + | 0.992456i | \(0.460876\pi\) | |||||||
\(434\) | 32.0913 | 1.54043 | ||||||||
\(435\) | −3.24647 | −0.155656 | ||||||||
\(436\) | 78.1621 | 3.74329 | ||||||||
\(437\) | 0.396293 | 0.0189573 | ||||||||
\(438\) | 23.8738 | 1.14073 | ||||||||
\(439\) | 24.0015 | 1.14553 | 0.572764 | − | 0.819720i | \(-0.305871\pi\) | ||||
0.572764 | + | 0.819720i | \(0.305871\pi\) | |||||||
\(440\) | −62.6801 | −2.98816 | ||||||||
\(441\) | 2.08966 | 0.0995078 | ||||||||
\(442\) | −10.4792 | −0.498446 | ||||||||
\(443\) | 2.14142 | 0.101742 | 0.0508710 | − | 0.998705i | \(-0.483800\pi\) | ||||
0.0508710 | + | 0.998705i | \(0.483800\pi\) | |||||||
\(444\) | 34.4927 | 1.63695 | ||||||||
\(445\) | 14.3850 | 0.681915 | ||||||||
\(446\) | 63.1745 | 2.99140 | ||||||||
\(447\) | 22.7399 | 1.07556 | ||||||||
\(448\) | 39.6157 | 1.87166 | ||||||||
\(449\) | 13.9735 | 0.659448 | 0.329724 | − | 0.944077i | \(-0.393044\pi\) | ||||
0.329724 | + | 0.944077i | \(0.393044\pi\) | |||||||
\(450\) | 14.7268 | 0.694229 | ||||||||
\(451\) | −2.33486 | −0.109944 | ||||||||
\(452\) | 81.9945 | 3.85670 | ||||||||
\(453\) | −9.55060 | −0.448727 | ||||||||
\(454\) | 75.1035 | 3.52478 | ||||||||
\(455\) | 10.7780 | 0.505280 | ||||||||
\(456\) | −3.12561 | −0.146370 | ||||||||
\(457\) | 0.782294 | 0.0365942 | 0.0182971 | − | 0.999833i | \(-0.494176\pi\) | ||||
0.0182971 | + | 0.999833i | \(0.494176\pi\) | |||||||
\(458\) | −2.09448 | −0.0978688 | ||||||||
\(459\) | 5.50599 | 0.256998 | ||||||||
\(460\) | −7.61976 | −0.355273 | ||||||||
\(461\) | −38.4583 | −1.79118 | −0.895592 | − | 0.444877i | \(-0.853247\pi\) | ||||
−0.895592 | + | 0.444877i | \(0.853247\pi\) | |||||||
\(462\) | −50.2889 | −2.33965 | ||||||||
\(463\) | −4.07968 | −0.189599 | −0.0947994 | − | 0.995496i | \(-0.530221\pi\) | ||||
−0.0947994 | + | 0.995496i | \(0.530221\pi\) | |||||||
\(464\) | −27.4036 | −1.27218 | ||||||||
\(465\) | 7.17863 | 0.332901 | ||||||||
\(466\) | −2.65433 | −0.122960 | ||||||||
\(467\) | −21.9870 | −1.01744 | −0.508719 | − | 0.860932i | \(-0.669881\pi\) | ||||
−0.508719 | + | 0.860932i | \(0.669881\pi\) | |||||||
\(468\) | 30.3173 | 1.40142 | ||||||||
\(469\) | 18.0611 | 0.833985 | ||||||||
\(470\) | 23.2351 | 1.07176 | ||||||||
\(471\) | −23.2462 | −1.07113 | ||||||||
\(472\) | −45.9028 | −2.11285 | ||||||||
\(473\) | −6.51509 | −0.299564 | ||||||||
\(474\) | 35.8652 | 1.64734 | ||||||||
\(475\) | −1.12718 | −0.0517184 | ||||||||
\(476\) | 12.1208 | 0.555558 | ||||||||
\(477\) | 0.0637864 | 0.00292058 | ||||||||
\(478\) | −18.9460 | −0.866569 | ||||||||
\(479\) | −10.1140 | −0.462121 | −0.231061 | − | 0.972939i | \(-0.574220\pi\) | ||||
−0.231061 | + | 0.972939i | \(0.574220\pi\) | |||||||
\(480\) | 21.5141 | 0.981982 | ||||||||
\(481\) | 21.6927 | 0.989100 | ||||||||
\(482\) | 80.0168 | 3.64467 | ||||||||
\(483\) | −3.72312 | −0.169408 | ||||||||
\(484\) | 160.855 | 7.31157 | ||||||||
\(485\) | 20.6681 | 0.938490 | ||||||||
\(486\) | −36.9008 | −1.67386 | ||||||||
\(487\) | −34.1263 | −1.54641 | −0.773205 | − | 0.634157i | \(-0.781347\pi\) | ||||
−0.773205 | + | 0.634157i | \(0.781347\pi\) | |||||||
\(488\) | −34.9439 | −1.58183 | ||||||||
\(489\) | 11.8226 | 0.534636 | ||||||||
\(490\) | 4.27768 | 0.193246 | ||||||||
\(491\) | 8.07034 | 0.364209 | 0.182105 | − | 0.983279i | \(-0.441709\pi\) | ||||
0.182105 | + | 0.983279i | \(0.441709\pi\) | |||||||
\(492\) | 2.23867 | 0.100927 | ||||||||
\(493\) | −2.29611 | −0.103412 | ||||||||
\(494\) | −3.22773 | −0.145222 | ||||||||
\(495\) | 11.3801 | 0.511495 | ||||||||
\(496\) | 60.5952 | 2.72081 | ||||||||
\(497\) | 14.3867 | 0.645332 | ||||||||
\(498\) | 24.7507 | 1.10911 | ||||||||
\(499\) | 15.3883 | 0.688875 | 0.344437 | − | 0.938809i | \(-0.388070\pi\) | ||||
0.344437 | + | 0.938809i | \(0.388070\pi\) | |||||||
\(500\) | 51.2846 | 2.29352 | ||||||||
\(501\) | 8.15231 | 0.364218 | ||||||||
\(502\) | −40.1267 | −1.79094 | ||||||||
\(503\) | 26.7497 | 1.19271 | 0.596356 | − | 0.802720i | \(-0.296615\pi\) | ||||
0.596356 | + | 0.802720i | \(0.296615\pi\) | |||||||
\(504\) | −29.7058 | −1.32320 | ||||||||
\(505\) | −5.87891 | −0.261608 | ||||||||
\(506\) | 22.3595 | 0.994001 | ||||||||
\(507\) | −2.97209 | −0.131995 | ||||||||
\(508\) | 88.0524 | 3.90669 | ||||||||
\(509\) | 29.6718 | 1.31518 | 0.657589 | − | 0.753377i | \(-0.271576\pi\) | ||||
0.657589 | + | 0.753377i | \(0.271576\pi\) | |||||||
\(510\) | 3.77148 | 0.167004 | ||||||||
\(511\) | −17.3664 | −0.768246 | ||||||||
\(512\) | −16.7441 | −0.739991 | ||||||||
\(513\) | 1.69591 | 0.0748765 | ||||||||
\(514\) | −35.2010 | −1.55265 | ||||||||
\(515\) | −0.131449 | −0.00579233 | ||||||||
\(516\) | 6.24669 | 0.274995 | ||||||||
\(517\) | −49.0164 | −2.15574 | ||||||||
\(518\) | −34.9013 | −1.53347 | ||||||||
\(519\) | 3.02010 | 0.132567 | ||||||||
\(520\) | 37.7959 | 1.65746 | ||||||||
\(521\) | −30.3472 | −1.32953 | −0.664767 | − | 0.747051i | \(-0.731469\pi\) | ||||
−0.664767 | + | 0.747051i | \(0.731469\pi\) | |||||||
\(522\) | 9.24013 | 0.404430 | ||||||||
\(523\) | 27.5156 | 1.20317 | 0.601587 | − | 0.798807i | \(-0.294535\pi\) | ||||
0.601587 | + | 0.798807i | \(0.294535\pi\) | |||||||
\(524\) | −10.8105 | −0.472257 | ||||||||
\(525\) | 10.5897 | 0.462171 | ||||||||
\(526\) | −25.0940 | −1.09415 | ||||||||
\(527\) | 5.07718 | 0.221166 | ||||||||
\(528\) | −94.9563 | −4.13244 | ||||||||
\(529\) | −21.3446 | −0.928027 | ||||||||
\(530\) | 0.130575 | 0.00567181 | ||||||||
\(531\) | 8.33400 | 0.361665 | ||||||||
\(532\) | 3.73337 | 0.161862 | ||||||||
\(533\) | 1.40791 | 0.0609835 | ||||||||
\(534\) | 40.4725 | 1.75142 | ||||||||
\(535\) | 12.7431 | 0.550931 | ||||||||
\(536\) | 63.3362 | 2.73571 | ||||||||
\(537\) | −22.3847 | −0.965969 | ||||||||
\(538\) | 63.4622 | 2.73605 | ||||||||
\(539\) | −9.02411 | −0.388696 | ||||||||
\(540\) | −32.6083 | −1.40324 | ||||||||
\(541\) | 19.6595 | 0.845226 | 0.422613 | − | 0.906310i | \(-0.361113\pi\) | ||||
0.422613 | + | 0.906310i | \(0.361113\pi\) | |||||||
\(542\) | 27.8789 | 1.19750 | ||||||||
\(543\) | −15.2580 | −0.654784 | ||||||||
\(544\) | 15.2162 | 0.652388 | ||||||||
\(545\) | −17.6915 | −0.757822 | ||||||||
\(546\) | 30.3241 | 1.29775 | ||||||||
\(547\) | −9.16183 | −0.391732 | −0.195866 | − | 0.980631i | \(-0.562752\pi\) | ||||
−0.195866 | + | 0.980631i | \(0.562752\pi\) | |||||||
\(548\) | −67.1862 | −2.87005 | ||||||||
\(549\) | 6.34432 | 0.270769 | ||||||||
\(550\) | −63.5971 | −2.71179 | ||||||||
\(551\) | −0.707230 | −0.0301290 | ||||||||
\(552\) | −13.0561 | −0.555706 | ||||||||
\(553\) | −26.0893 | −1.10943 | ||||||||
\(554\) | 76.8164 | 3.26362 | ||||||||
\(555\) | −7.80722 | −0.331398 | ||||||||
\(556\) | 107.875 | 4.57490 | ||||||||
\(557\) | 25.8790 | 1.09653 | 0.548263 | − | 0.836306i | \(-0.315289\pi\) | ||||
0.548263 | + | 0.836306i | \(0.315289\pi\) | |||||||
\(558\) | −20.4319 | −0.864951 | ||||||||
\(559\) | 3.92858 | 0.166161 | ||||||||
\(560\) | −32.7429 | −1.38364 | ||||||||
\(561\) | −7.95625 | −0.335913 | ||||||||
\(562\) | −58.6861 | −2.47552 | ||||||||
\(563\) | 36.5929 | 1.54221 | 0.771103 | − | 0.636711i | \(-0.219706\pi\) | ||||
0.771103 | + | 0.636711i | \(0.219706\pi\) | |||||||
\(564\) | 46.9970 | 1.97893 | ||||||||
\(565\) | −18.5590 | −0.780782 | ||||||||
\(566\) | 3.73439 | 0.156968 | ||||||||
\(567\) | −5.20819 | −0.218723 | ||||||||
\(568\) | 50.4509 | 2.11687 | ||||||||
\(569\) | −22.5560 | −0.945596 | −0.472798 | − | 0.881171i | \(-0.656756\pi\) | ||||
−0.472798 | + | 0.881171i | \(0.656756\pi\) | |||||||
\(570\) | 1.16166 | 0.0486568 | ||||||||
\(571\) | 28.1823 | 1.17939 | 0.589696 | − | 0.807626i | \(-0.299248\pi\) | ||||
0.589696 | + | 0.807626i | \(0.299248\pi\) | |||||||
\(572\) | −130.924 | −5.47419 | ||||||||
\(573\) | −14.7497 | −0.616179 | ||||||||
\(574\) | −2.26519 | −0.0945472 | ||||||||
\(575\) | −4.70838 | −0.196353 | ||||||||
\(576\) | −25.2225 | −1.05094 | ||||||||
\(577\) | 7.01637 | 0.292095 | 0.146048 | − | 0.989278i | \(-0.453345\pi\) | ||||
0.146048 | + | 0.989278i | \(0.453345\pi\) | |||||||
\(578\) | 2.66743 | 0.110951 | ||||||||
\(579\) | 27.4855 | 1.14226 | ||||||||
\(580\) | 13.5983 | 0.564640 | ||||||||
\(581\) | −18.0043 | −0.746946 | ||||||||
\(582\) | 58.1501 | 2.41040 | ||||||||
\(583\) | −0.275458 | −0.0114083 | ||||||||
\(584\) | −60.9002 | −2.52007 | ||||||||
\(585\) | −6.86213 | −0.283714 | ||||||||
\(586\) | −70.5044 | −2.91251 | ||||||||
\(587\) | 3.53126 | 0.145751 | 0.0728753 | − | 0.997341i | \(-0.476782\pi\) | ||||
0.0728753 | + | 0.997341i | \(0.476782\pi\) | |||||||
\(588\) | 8.65234 | 0.356816 | ||||||||
\(589\) | 1.56384 | 0.0644368 | ||||||||
\(590\) | 17.0603 | 0.702360 | ||||||||
\(591\) | −10.5843 | −0.435380 | ||||||||
\(592\) | −65.9011 | −2.70852 | ||||||||
\(593\) | −16.2807 | −0.668569 | −0.334284 | − | 0.942472i | \(-0.608495\pi\) | ||||
−0.334284 | + | 0.942472i | \(0.608495\pi\) | |||||||
\(594\) | 95.6863 | 3.92605 | ||||||||
\(595\) | −2.74348 | −0.112472 | ||||||||
\(596\) | −95.2494 | −3.90157 | ||||||||
\(597\) | 11.9223 | 0.487947 | ||||||||
\(598\) | −13.4827 | −0.551349 | ||||||||
\(599\) | −43.2707 | −1.76799 | −0.883996 | − | 0.467495i | \(-0.845157\pi\) | ||||
−0.883996 | + | 0.467495i | \(0.845157\pi\) | |||||||
\(600\) | 37.1355 | 1.51605 | ||||||||
\(601\) | 42.0708 | 1.71611 | 0.858053 | − | 0.513561i | \(-0.171674\pi\) | ||||
0.858053 | + | 0.513561i | \(0.171674\pi\) | |||||||
\(602\) | −6.32068 | −0.257612 | ||||||||
\(603\) | −11.4992 | −0.468282 | ||||||||
\(604\) | 40.0042 | 1.62775 | ||||||||
\(605\) | −36.4085 | −1.48021 | ||||||||
\(606\) | −16.5404 | −0.671909 | ||||||||
\(607\) | −1.60950 | −0.0653275 | −0.0326638 | − | 0.999466i | \(-0.510399\pi\) | ||||
−0.0326638 | + | 0.999466i | \(0.510399\pi\) | |||||||
\(608\) | 4.68677 | 0.190074 | ||||||||
\(609\) | 6.64432 | 0.269242 | ||||||||
\(610\) | 12.9872 | 0.525838 | ||||||||
\(611\) | 29.5567 | 1.19574 | ||||||||
\(612\) | −7.71711 | −0.311946 | ||||||||
\(613\) | −29.3932 | −1.18718 | −0.593590 | − | 0.804767i | \(-0.702290\pi\) | ||||
−0.593590 | + | 0.804767i | \(0.702290\pi\) | |||||||
\(614\) | 12.5225 | 0.505366 | ||||||||
\(615\) | −0.506710 | −0.0204325 | ||||||||
\(616\) | 128.283 | 5.16867 | ||||||||
\(617\) | −33.5535 | −1.35081 | −0.675406 | − | 0.737446i | \(-0.736032\pi\) | ||||
−0.675406 | + | 0.737446i | \(0.736032\pi\) | |||||||
\(618\) | −0.369834 | −0.0148769 | ||||||||
\(619\) | 21.9301 | 0.881445 | 0.440723 | − | 0.897643i | \(-0.354722\pi\) | ||||
0.440723 | + | 0.897643i | \(0.354722\pi\) | |||||||
\(620\) | −30.0688 | −1.20759 | ||||||||
\(621\) | 7.08409 | 0.284275 | ||||||||
\(622\) | −25.2174 | −1.01113 | ||||||||
\(623\) | −29.4408 | −1.17952 | ||||||||
\(624\) | 57.2584 | 2.29217 | ||||||||
\(625\) | 6.68961 | 0.267585 | ||||||||
\(626\) | 1.30415 | 0.0521245 | ||||||||
\(627\) | −2.45062 | −0.0978685 | ||||||||
\(628\) | 97.3704 | 3.88550 | ||||||||
\(629\) | −5.52176 | −0.220167 | ||||||||
\(630\) | 11.0405 | 0.439863 | ||||||||
\(631\) | −2.89353 | −0.115190 | −0.0575949 | − | 0.998340i | \(-0.518343\pi\) | ||||
−0.0575949 | + | 0.998340i | \(0.518343\pi\) | |||||||
\(632\) | −91.4894 | −3.63925 | ||||||||
\(633\) | 0.775599 | 0.0308273 | ||||||||
\(634\) | 7.96325 | 0.316261 | ||||||||
\(635\) | −19.9301 | −0.790903 | ||||||||
\(636\) | 0.264110 | 0.0104727 | ||||||||
\(637\) | 5.44151 | 0.215600 | ||||||||
\(638\) | −39.9031 | −1.57978 | ||||||||
\(639\) | −9.15975 | −0.362354 | ||||||||
\(640\) | −16.3979 | −0.648183 | ||||||||
\(641\) | −6.49838 | −0.256671 | −0.128335 | − | 0.991731i | \(-0.540963\pi\) | ||||
−0.128335 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(642\) | 35.8529 | 1.41500 | ||||||||
\(643\) | −34.3274 | −1.35374 | −0.676869 | − | 0.736103i | \(-0.736664\pi\) | ||||
−0.676869 | + | 0.736103i | \(0.736664\pi\) | |||||||
\(644\) | 15.5948 | 0.614523 | ||||||||
\(645\) | −1.41390 | −0.0556723 | ||||||||
\(646\) | 0.821602 | 0.0323255 | ||||||||
\(647\) | −0.516741 | −0.0203152 | −0.0101576 | − | 0.999948i | \(-0.503233\pi\) | ||||
−0.0101576 | + | 0.999948i | \(0.503233\pi\) | |||||||
\(648\) | −18.2639 | −0.717475 | ||||||||
\(649\) | −35.9900 | −1.41273 | ||||||||
\(650\) | 38.3489 | 1.50417 | ||||||||
\(651\) | −14.6920 | −0.575826 | ||||||||
\(652\) | −49.5207 | −1.93938 | ||||||||
\(653\) | 3.02652 | 0.118437 | 0.0592184 | − | 0.998245i | \(-0.481139\pi\) | ||||
0.0592184 | + | 0.998245i | \(0.481139\pi\) | |||||||
\(654\) | −49.7755 | −1.94638 | ||||||||
\(655\) | 2.44688 | 0.0956076 | ||||||||
\(656\) | −4.27717 | −0.166995 | ||||||||
\(657\) | 11.0569 | 0.431370 | ||||||||
\(658\) | −47.5537 | −1.85384 | ||||||||
\(659\) | 24.7953 | 0.965887 | 0.482943 | − | 0.875652i | \(-0.339568\pi\) | ||||
0.482943 | + | 0.875652i | \(0.339568\pi\) | |||||||
\(660\) | 47.1196 | 1.83413 | ||||||||
\(661\) | 1.16506 | 0.0453156 | 0.0226578 | − | 0.999743i | \(-0.492787\pi\) | ||||
0.0226578 | + | 0.999743i | \(0.492787\pi\) | |||||||
\(662\) | −17.1597 | −0.666932 | ||||||||
\(663\) | 4.79759 | 0.186323 | ||||||||
\(664\) | −63.1371 | −2.45020 | ||||||||
\(665\) | −0.845026 | −0.0327687 | ||||||||
\(666\) | 22.2210 | 0.861045 | ||||||||
\(667\) | −2.95421 | −0.114387 | ||||||||
\(668\) | −34.1472 | −1.32119 | ||||||||
\(669\) | −28.9225 | −1.11821 | ||||||||
\(670\) | −23.5396 | −0.909413 | ||||||||
\(671\) | −27.3976 | −1.05767 | ||||||||
\(672\) | −44.0315 | −1.69855 | ||||||||
\(673\) | −15.3866 | −0.593109 | −0.296554 | − | 0.955016i | \(-0.595838\pi\) | ||||
−0.296554 | + | 0.955016i | \(0.595838\pi\) | |||||||
\(674\) | 85.1789 | 3.28097 | ||||||||
\(675\) | −20.1493 | −0.775545 | ||||||||
\(676\) | 12.4491 | 0.478810 | ||||||||
\(677\) | −28.6663 | −1.10174 | −0.550868 | − | 0.834592i | \(-0.685703\pi\) | ||||
−0.550868 | + | 0.834592i | \(0.685703\pi\) | |||||||
\(678\) | −52.2160 | −2.00534 | ||||||||
\(679\) | −42.3000 | −1.62332 | ||||||||
\(680\) | −9.62076 | −0.368939 | ||||||||
\(681\) | −34.3839 | −1.31759 | ||||||||
\(682\) | 88.2342 | 3.37866 | ||||||||
\(683\) | 14.2794 | 0.546385 | 0.273192 | − | 0.961959i | \(-0.411920\pi\) | ||||
0.273192 | + | 0.961959i | \(0.411920\pi\) | |||||||
\(684\) | −2.37697 | −0.0908855 | ||||||||
\(685\) | 15.2072 | 0.581037 | ||||||||
\(686\) | −52.9996 | −2.02353 | ||||||||
\(687\) | 0.958896 | 0.0365842 | ||||||||
\(688\) | −11.9348 | −0.455010 | ||||||||
\(689\) | 0.166101 | 0.00632793 | ||||||||
\(690\) | 4.85244 | 0.184729 | ||||||||
\(691\) | 36.2344 | 1.37842 | 0.689211 | − | 0.724561i | \(-0.257957\pi\) | ||||
0.689211 | + | 0.724561i | \(0.257957\pi\) | |||||||
\(692\) | −12.6501 | −0.480886 | ||||||||
\(693\) | −23.2908 | −0.884743 | ||||||||
\(694\) | −58.6505 | −2.22634 | ||||||||
\(695\) | −24.4168 | −0.926181 | ||||||||
\(696\) | 23.3001 | 0.883189 | ||||||||
\(697\) | −0.358377 | −0.0135745 | ||||||||
\(698\) | 56.7606 | 2.14842 | ||||||||
\(699\) | 1.21521 | 0.0459633 | ||||||||
\(700\) | −44.3564 | −1.67651 | ||||||||
\(701\) | 5.14395 | 0.194284 | 0.0971422 | − | 0.995271i | \(-0.469030\pi\) | ||||
0.0971422 | + | 0.995271i | \(0.469030\pi\) | |||||||
\(702\) | −57.6985 | −2.17769 | ||||||||
\(703\) | −1.70077 | −0.0641458 | ||||||||
\(704\) | 108.922 | 4.10516 | ||||||||
\(705\) | −10.6375 | −0.400631 | ||||||||
\(706\) | 78.9960 | 2.97305 | ||||||||
\(707\) | 12.0320 | 0.452509 | ||||||||
\(708\) | 34.5073 | 1.29686 | ||||||||
\(709\) | 7.73810 | 0.290610 | 0.145305 | − | 0.989387i | \(-0.453584\pi\) | ||||
0.145305 | + | 0.989387i | \(0.453584\pi\) | |||||||
\(710\) | −18.7506 | −0.703698 | ||||||||
\(711\) | 16.6106 | 0.622946 | ||||||||
\(712\) | −103.242 | −3.86916 | ||||||||
\(713\) | 6.53238 | 0.244639 | ||||||||
\(714\) | −7.71884 | −0.288870 | ||||||||
\(715\) | 29.6338 | 1.10824 | ||||||||
\(716\) | 93.7615 | 3.50403 | ||||||||
\(717\) | 8.67384 | 0.323931 | ||||||||
\(718\) | 89.6773 | 3.34673 | ||||||||
\(719\) | −6.85306 | −0.255576 | −0.127788 | − | 0.991802i | \(-0.540788\pi\) | ||||
−0.127788 | + | 0.991802i | \(0.540788\pi\) | |||||||
\(720\) | 20.8468 | 0.776914 | ||||||||
\(721\) | 0.269028 | 0.0100191 | ||||||||
\(722\) | −50.4281 | −1.87674 | ||||||||
\(723\) | −36.6333 | −1.36241 | ||||||||
\(724\) | 63.9105 | 2.37521 | ||||||||
\(725\) | 8.40264 | 0.312066 | ||||||||
\(726\) | −102.436 | −3.80175 | ||||||||
\(727\) | −25.9649 | −0.962983 | −0.481492 | − | 0.876451i | \(-0.659905\pi\) | ||||
−0.481492 | + | 0.876451i | \(0.659905\pi\) | |||||||
\(728\) | −77.3543 | −2.86694 | ||||||||
\(729\) | 23.4878 | 0.869917 | ||||||||
\(730\) | 22.6342 | 0.837729 | ||||||||
\(731\) | −1.00000 | −0.0369863 | ||||||||
\(732\) | 26.2689 | 0.970927 | ||||||||
\(733\) | 32.5717 | 1.20306 | 0.601531 | − | 0.798850i | \(-0.294558\pi\) | ||||
0.601531 | + | 0.798850i | \(0.294558\pi\) | |||||||
\(734\) | −23.5914 | −0.870775 | ||||||||
\(735\) | −1.95841 | −0.0722369 | ||||||||
\(736\) | 19.5773 | 0.721630 | ||||||||
\(737\) | 49.6586 | 1.82920 | ||||||||
\(738\) | 1.44220 | 0.0530882 | ||||||||
\(739\) | −22.9751 | −0.845151 | −0.422576 | − | 0.906328i | \(-0.638874\pi\) | ||||
−0.422576 | + | 0.906328i | \(0.638874\pi\) | |||||||
\(740\) | 32.7017 | 1.20214 | ||||||||
\(741\) | 1.47772 | 0.0542853 | ||||||||
\(742\) | −0.267239 | −0.00981065 | ||||||||
\(743\) | −2.51329 | −0.0922038 | −0.0461019 | − | 0.998937i | \(-0.514680\pi\) | ||||
−0.0461019 | + | 0.998937i | \(0.514680\pi\) | |||||||
\(744\) | −51.5216 | −1.88887 | ||||||||
\(745\) | 21.5591 | 0.789866 | ||||||||
\(746\) | −97.6960 | −3.57691 | ||||||||
\(747\) | 11.4630 | 0.419410 | ||||||||
\(748\) | 33.3260 | 1.21852 | ||||||||
\(749\) | −26.0804 | −0.952956 | ||||||||
\(750\) | −32.6592 | −1.19255 | ||||||||
\(751\) | −33.9701 | −1.23959 | −0.619794 | − | 0.784765i | \(-0.712784\pi\) | ||||
−0.619794 | + | 0.784765i | \(0.712784\pi\) | |||||||
\(752\) | −89.7917 | −3.27437 | ||||||||
\(753\) | 18.3708 | 0.669468 | ||||||||
\(754\) | 24.0614 | 0.876265 | ||||||||
\(755\) | −9.05470 | −0.329534 | ||||||||
\(756\) | 66.7372 | 2.42721 | ||||||||
\(757\) | 5.93628 | 0.215758 | 0.107879 | − | 0.994164i | \(-0.465594\pi\) | ||||
0.107879 | + | 0.994164i | \(0.465594\pi\) | |||||||
\(758\) | −25.0595 | −0.910201 | ||||||||
\(759\) | −10.2366 | −0.371566 | ||||||||
\(760\) | −2.96331 | −0.107491 | ||||||||
\(761\) | −8.61012 | −0.312116 | −0.156058 | − | 0.987748i | \(-0.549879\pi\) | ||||
−0.156058 | + | 0.987748i | \(0.549879\pi\) | |||||||
\(762\) | −56.0738 | −2.03134 | ||||||||
\(763\) | 36.2080 | 1.31082 | ||||||||
\(764\) | 61.7815 | 2.23518 | ||||||||
\(765\) | 1.74672 | 0.0631528 | ||||||||
\(766\) | 68.6706 | 2.48117 | ||||||||
\(767\) | 21.7019 | 0.783609 | ||||||||
\(768\) | −5.30245 | −0.191336 | ||||||||
\(769\) | 38.3439 | 1.38271 | 0.691357 | − | 0.722513i | \(-0.257013\pi\) | ||||
0.691357 | + | 0.722513i | \(0.257013\pi\) | |||||||
\(770\) | −47.6777 | −1.71819 | ||||||||
\(771\) | 16.1157 | 0.580393 | ||||||||
\(772\) | −115.127 | −4.14352 | ||||||||
\(773\) | −8.12687 | −0.292303 | −0.146152 | − | 0.989262i | \(-0.546689\pi\) | ||||
−0.146152 | + | 0.989262i | \(0.546689\pi\) | |||||||
\(774\) | 4.02426 | 0.144649 | ||||||||
\(775\) | −18.5800 | −0.667414 | ||||||||
\(776\) | −148.336 | −5.32496 | ||||||||
\(777\) | 15.9785 | 0.573225 | ||||||||
\(778\) | −85.1316 | −3.05212 | ||||||||
\(779\) | −0.110385 | −0.00395494 | ||||||||
\(780\) | −28.4130 | −1.01735 | ||||||||
\(781\) | 39.5559 | 1.41542 | ||||||||
\(782\) | 3.43196 | 0.122726 | ||||||||
\(783\) | −12.6424 | −0.451801 | ||||||||
\(784\) | −16.5310 | −0.590393 | ||||||||
\(785\) | −22.0392 | −0.786613 | ||||||||
\(786\) | 6.88435 | 0.245557 | ||||||||
\(787\) | 35.5439 | 1.26700 | 0.633502 | − | 0.773741i | \(-0.281617\pi\) | ||||
0.633502 | + | 0.773741i | \(0.281617\pi\) | |||||||
\(788\) | 44.3339 | 1.57933 | ||||||||
\(789\) | 11.4885 | 0.409003 | ||||||||
\(790\) | 34.0030 | 1.20977 | ||||||||
\(791\) | 37.9834 | 1.35053 | ||||||||
\(792\) | −81.6754 | −2.90221 | ||||||||
\(793\) | 16.5207 | 0.586667 | ||||||||
\(794\) | 15.7184 | 0.557826 | ||||||||
\(795\) | −0.0597798 | −0.00212017 | ||||||||
\(796\) | −49.9384 | −1.77002 | ||||||||
\(797\) | 0.405256 | 0.0143549 | 0.00717746 | − | 0.999974i | \(-0.497715\pi\) | ||||
0.00717746 | + | 0.999974i | \(0.497715\pi\) | |||||||
\(798\) | −2.37750 | −0.0841625 | ||||||||
\(799\) | −7.52351 | −0.266163 | ||||||||
\(800\) | −55.6838 | −1.96872 | ||||||||
\(801\) | 18.7444 | 0.662301 | ||||||||
\(802\) | −55.2539 | −1.95108 | ||||||||
\(803\) | −47.7486 | −1.68501 | ||||||||
\(804\) | −47.6128 | −1.67917 | ||||||||
\(805\) | −3.52980 | −0.124409 | ||||||||
\(806\) | −53.2049 | −1.87406 | ||||||||
\(807\) | −29.0543 | −1.02276 | ||||||||
\(808\) | 42.1934 | 1.48436 | ||||||||
\(809\) | −31.3337 | −1.10163 | −0.550817 | − | 0.834626i | \(-0.685684\pi\) | ||||
−0.550817 | + | 0.834626i | \(0.685684\pi\) | |||||||
\(810\) | 6.78798 | 0.238505 | ||||||||
\(811\) | 4.94465 | 0.173630 | 0.0868151 | − | 0.996224i | \(-0.472331\pi\) | ||||
0.0868151 | + | 0.996224i | \(0.472331\pi\) | |||||||
\(812\) | −27.8308 | −0.976668 | ||||||||
\(813\) | −12.7635 | −0.447636 | ||||||||
\(814\) | −95.9602 | −3.36340 | ||||||||
\(815\) | 11.2087 | 0.392624 | ||||||||
\(816\) | −14.5748 | −0.510221 | ||||||||
\(817\) | −0.308012 | −0.0107760 | ||||||||
\(818\) | −97.5743 | −3.41160 | ||||||||
\(819\) | 14.0443 | 0.490746 | ||||||||
\(820\) | 2.12243 | 0.0741185 | ||||||||
\(821\) | −5.52402 | −0.192790 | −0.0963948 | − | 0.995343i | \(-0.530731\pi\) | ||||
−0.0963948 | + | 0.995343i | \(0.530731\pi\) | |||||||
\(822\) | 42.7858 | 1.49233 | ||||||||
\(823\) | −3.26294 | −0.113739 | −0.0568694 | − | 0.998382i | \(-0.518112\pi\) | ||||
−0.0568694 | + | 0.998382i | \(0.518112\pi\) | |||||||
\(824\) | 0.943418 | 0.0328655 | ||||||||
\(825\) | 29.1160 | 1.01369 | ||||||||
\(826\) | −34.9161 | −1.21489 | ||||||||
\(827\) | −20.4127 | −0.709818 | −0.354909 | − | 0.934901i | \(-0.615488\pi\) | ||||
−0.354909 | + | 0.934901i | \(0.615488\pi\) | |||||||
\(828\) | −9.92894 | −0.345054 | ||||||||
\(829\) | 25.9529 | 0.901381 | 0.450691 | − | 0.892680i | \(-0.351178\pi\) | ||||
0.450691 | + | 0.892680i | \(0.351178\pi\) | |||||||
\(830\) | 23.4656 | 0.814502 | ||||||||
\(831\) | −35.1681 | −1.21997 | ||||||||
\(832\) | −65.6798 | −2.27704 | ||||||||
\(833\) | −1.38511 | −0.0479912 | ||||||||
\(834\) | −68.6971 | −2.37878 | ||||||||
\(835\) | 7.72901 | 0.267473 | ||||||||
\(836\) | 10.2648 | 0.355016 | ||||||||
\(837\) | 27.9549 | 0.966264 | ||||||||
\(838\) | 18.9833 | 0.655768 | ||||||||
\(839\) | 13.3088 | 0.459472 | 0.229736 | − | 0.973253i | \(-0.426214\pi\) | ||||
0.229736 | + | 0.973253i | \(0.426214\pi\) | |||||||
\(840\) | 27.8399 | 0.960568 | ||||||||
\(841\) | −23.7279 | −0.818203 | ||||||||
\(842\) | 94.3288 | 3.25079 | ||||||||
\(843\) | 26.8676 | 0.925370 | ||||||||
\(844\) | −3.24872 | −0.111825 | ||||||||
\(845\) | −2.81777 | −0.0969343 | ||||||||
\(846\) | 30.2766 | 1.04093 | ||||||||
\(847\) | 74.5147 | 2.56036 | ||||||||
\(848\) | −0.504604 | −0.0173282 | ||||||||
\(849\) | −1.70968 | −0.0586760 | ||||||||
\(850\) | −9.76150 | −0.334817 | ||||||||
\(851\) | −7.10437 | −0.243535 | ||||||||
\(852\) | −37.9263 | −1.29933 | ||||||||
\(853\) | −46.9946 | −1.60906 | −0.804532 | − | 0.593909i | \(-0.797584\pi\) | ||||
−0.804532 | + | 0.593909i | \(0.797584\pi\) | |||||||
\(854\) | −26.5801 | −0.909552 | ||||||||
\(855\) | 0.538012 | 0.0183996 | ||||||||
\(856\) | −91.4579 | −3.12597 | ||||||||
\(857\) | 2.55569 | 0.0873008 | 0.0436504 | − | 0.999047i | \(-0.486101\pi\) | ||||
0.0436504 | + | 0.999047i | \(0.486101\pi\) | |||||||
\(858\) | 83.3753 | 2.84639 | ||||||||
\(859\) | 6.56470 | 0.223985 | 0.111992 | − | 0.993709i | \(-0.464277\pi\) | ||||
0.111992 | + | 0.993709i | \(0.464277\pi\) | |||||||
\(860\) | 5.92234 | 0.201950 | ||||||||
\(861\) | 1.03705 | 0.0353425 | ||||||||
\(862\) | 23.6972 | 0.807129 | ||||||||
\(863\) | 10.0905 | 0.343484 | 0.171742 | − | 0.985142i | \(-0.445060\pi\) | ||||
0.171742 | + | 0.985142i | \(0.445060\pi\) | |||||||
\(864\) | 83.7801 | 2.85026 | ||||||||
\(865\) | 2.86328 | 0.0973545 | ||||||||
\(866\) | 13.6102 | 0.462494 | ||||||||
\(867\) | −1.22120 | −0.0414742 | ||||||||
\(868\) | 61.5397 | 2.08879 | ||||||||
\(869\) | −71.7320 | −2.43334 | ||||||||
\(870\) | −8.65974 | −0.293593 | ||||||||
\(871\) | −29.9440 | −1.01461 | ||||||||
\(872\) | 126.973 | 4.29986 | ||||||||
\(873\) | 26.9316 | 0.911496 | ||||||||
\(874\) | 1.05709 | 0.0357564 | ||||||||
\(875\) | 23.7572 | 0.803140 | ||||||||
\(876\) | 45.7815 | 1.54681 | ||||||||
\(877\) | −55.3115 | −1.86774 | −0.933868 | − | 0.357619i | \(-0.883589\pi\) | ||||
−0.933868 | + | 0.357619i | \(0.883589\pi\) | |||||||
\(878\) | 64.0223 | 2.16065 | ||||||||
\(879\) | 32.2783 | 1.08872 | ||||||||
\(880\) | −90.0258 | −3.03477 | ||||||||
\(881\) | 8.63268 | 0.290842 | 0.145421 | − | 0.989370i | \(-0.453546\pi\) | ||||
0.145421 | + | 0.989370i | \(0.453546\pi\) | |||||||
\(882\) | 5.57403 | 0.187687 | ||||||||
\(883\) | 20.1129 | 0.676854 | 0.338427 | − | 0.940993i | \(-0.390105\pi\) | ||||
0.338427 | + | 0.940993i | \(0.390105\pi\) | |||||||
\(884\) | −20.0954 | −0.675883 | ||||||||
\(885\) | −7.81052 | −0.262548 | ||||||||
\(886\) | 5.71210 | 0.191902 | ||||||||
\(887\) | −27.7739 | −0.932557 | −0.466279 | − | 0.884638i | \(-0.654406\pi\) | ||||
−0.466279 | + | 0.884638i | \(0.654406\pi\) | |||||||
\(888\) | 56.0329 | 1.88034 | ||||||||
\(889\) | 40.7896 | 1.36804 | ||||||||
\(890\) | 38.3710 | 1.28620 | ||||||||
\(891\) | −14.3198 | −0.479731 | ||||||||
\(892\) | 121.146 | 4.05628 | ||||||||
\(893\) | −2.31734 | −0.0775467 | ||||||||
\(894\) | 60.6571 | 2.02868 | ||||||||
\(895\) | −21.2224 | −0.709385 | ||||||||
\(896\) | 33.5604 | 1.12117 | ||||||||
\(897\) | 6.17265 | 0.206099 | ||||||||
\(898\) | 37.2732 | 1.24382 | ||||||||
\(899\) | −11.6578 | −0.388808 | ||||||||
\(900\) | 28.2409 | 0.941362 | ||||||||
\(901\) | −0.0422801 | −0.00140855 | ||||||||
\(902\) | −6.22808 | −0.207372 | ||||||||
\(903\) | 2.89373 | 0.0962974 | ||||||||
\(904\) | 133.199 | 4.43013 | ||||||||
\(905\) | −14.4658 | −0.480858 | ||||||||
\(906\) | −25.4756 | −0.846370 | ||||||||
\(907\) | 24.3607 | 0.808883 | 0.404442 | − | 0.914564i | \(-0.367466\pi\) | ||||
0.404442 | + | 0.914564i | \(0.367466\pi\) | |||||||
\(908\) | 144.022 | 4.77954 | ||||||||
\(909\) | −7.66052 | −0.254084 | ||||||||
\(910\) | 28.7495 | 0.953038 | ||||||||
\(911\) | −3.04070 | −0.100743 | −0.0503714 | − | 0.998731i | \(-0.516041\pi\) | ||||
−0.0503714 | + | 0.998731i | \(0.516041\pi\) | |||||||
\(912\) | −4.48923 | −0.148653 | ||||||||
\(913\) | −49.5025 | −1.63829 | ||||||||
\(914\) | 2.08672 | 0.0690224 | ||||||||
\(915\) | −5.94582 | −0.196563 | ||||||||
\(916\) | −4.01648 | −0.132708 | ||||||||
\(917\) | −5.00786 | −0.165374 | ||||||||
\(918\) | 14.6869 | 0.484739 | ||||||||
\(919\) | 32.3552 | 1.06730 | 0.533649 | − | 0.845706i | \(-0.320820\pi\) | ||||
0.533649 | + | 0.845706i | \(0.320820\pi\) | |||||||
\(920\) | −12.3782 | −0.408097 | ||||||||
\(921\) | −5.73303 | −0.188910 | ||||||||
\(922\) | −102.585 | −3.37846 | ||||||||
\(923\) | −23.8521 | −0.785101 | ||||||||
\(924\) | −96.4364 | −3.17252 | ||||||||
\(925\) | 20.2069 | 0.664400 | ||||||||
\(926\) | −10.8823 | −0.357614 | ||||||||
\(927\) | −0.171285 | −0.00562573 | ||||||||
\(928\) | −34.9380 | −1.14689 | ||||||||
\(929\) | 1.68345 | 0.0552321 | 0.0276161 | − | 0.999619i | \(-0.491208\pi\) | ||||
0.0276161 | + | 0.999619i | \(0.491208\pi\) | |||||||
\(930\) | 19.1485 | 0.627905 | ||||||||
\(931\) | −0.426631 | −0.0139823 | ||||||||
\(932\) | −5.09008 | −0.166731 | ||||||||
\(933\) | 11.5450 | 0.377967 | ||||||||
\(934\) | −58.6489 | −1.91905 | ||||||||
\(935\) | −7.54313 | −0.246687 | ||||||||
\(936\) | 49.2500 | 1.60979 | ||||||||
\(937\) | −20.5243 | −0.670500 | −0.335250 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335250 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(938\) | 48.1768 | 1.57303 | ||||||||
\(939\) | −0.597067 | −0.0194845 | ||||||||
\(940\) | 44.5568 | 1.45328 | ||||||||
\(941\) | 8.41695 | 0.274385 | 0.137192 | − | 0.990544i | \(-0.456192\pi\) | ||||
0.137192 | + | 0.990544i | \(0.456192\pi\) | |||||||
\(942\) | −62.0077 | −2.02032 | ||||||||
\(943\) | −0.461093 | −0.0150153 | ||||||||
\(944\) | −65.9290 | −2.14581 | ||||||||
\(945\) | −15.1056 | −0.491385 | ||||||||
\(946\) | −17.3786 | −0.565026 | ||||||||
\(947\) | 0.843099 | 0.0273970 | 0.0136985 | − | 0.999906i | \(-0.495639\pi\) | ||||
0.0136985 | + | 0.999906i | \(0.495639\pi\) | |||||||
\(948\) | 68.7768 | 2.23377 | ||||||||
\(949\) | 28.7923 | 0.934637 | ||||||||
\(950\) | −3.00667 | −0.0975491 | ||||||||
\(951\) | −3.64573 | −0.118221 | ||||||||
\(952\) | 19.6901 | 0.638161 | ||||||||
\(953\) | 10.6277 | 0.344266 | 0.172133 | − | 0.985074i | \(-0.444934\pi\) | ||||
0.172133 | + | 0.985074i | \(0.444934\pi\) | |||||||
\(954\) | 0.170146 | 0.00550867 | ||||||||
\(955\) | −13.9839 | −0.452507 | ||||||||
\(956\) | −36.3317 | −1.17505 | ||||||||
\(957\) | 18.2684 | 0.590534 | ||||||||
\(958\) | −26.9784 | −0.871634 | ||||||||
\(959\) | −31.1235 | −1.00503 | ||||||||
\(960\) | 23.6382 | 0.762921 | ||||||||
\(961\) | −5.22220 | −0.168458 | ||||||||
\(962\) | 57.8637 | 1.86560 | ||||||||
\(963\) | 16.6049 | 0.535085 | ||||||||
\(964\) | 153.444 | 4.94210 | ||||||||
\(965\) | 26.0584 | 0.838848 | ||||||||
\(966\) | −9.93116 | −0.319530 | ||||||||
\(967\) | −41.9531 | −1.34912 | −0.674561 | − | 0.738219i | \(-0.735667\pi\) | ||||
−0.674561 | + | 0.738219i | \(0.735667\pi\) | |||||||
\(968\) | 261.306 | 8.39870 | ||||||||
\(969\) | −0.376146 | −0.0120835 | ||||||||
\(970\) | 55.1307 | 1.77014 | ||||||||
\(971\) | −33.1186 | −1.06283 | −0.531414 | − | 0.847112i | \(-0.678339\pi\) | ||||
−0.531414 | + | 0.847112i | \(0.678339\pi\) | |||||||
\(972\) | −70.7628 | −2.26972 | ||||||||
\(973\) | 49.9721 | 1.60203 | ||||||||
\(974\) | −91.0295 | −2.91677 | ||||||||
\(975\) | −17.5569 | −0.562269 | ||||||||
\(976\) | −50.1889 | −1.60651 | ||||||||
\(977\) | −53.0473 | −1.69713 | −0.848566 | − | 0.529089i | \(-0.822534\pi\) | ||||
−0.848566 | + | 0.529089i | \(0.822534\pi\) | |||||||
\(978\) | 31.5359 | 1.00841 | ||||||||
\(979\) | −80.9468 | −2.58707 | ||||||||
\(980\) | 8.20308 | 0.262038 | ||||||||
\(981\) | −23.0530 | −0.736025 | ||||||||
\(982\) | 21.5271 | 0.686957 | ||||||||
\(983\) | 36.1599 | 1.15332 | 0.576661 | − | 0.816984i | \(-0.304356\pi\) | ||||
0.576661 | + | 0.816984i | \(0.304356\pi\) | |||||||
\(984\) | 3.63669 | 0.115933 | ||||||||
\(985\) | −10.0347 | −0.319733 | ||||||||
\(986\) | −6.12471 | −0.195051 | ||||||||
\(987\) | 21.7710 | 0.692980 | ||||||||
\(988\) | −6.18965 | −0.196919 | ||||||||
\(989\) | −1.28661 | −0.0409120 | ||||||||
\(990\) | 30.3555 | 0.964761 | ||||||||
\(991\) | 53.5511 | 1.70111 | 0.850554 | − | 0.525888i | \(-0.176267\pi\) | ||||
0.850554 | + | 0.525888i | \(0.176267\pi\) | |||||||
\(992\) | 77.2553 | 2.45286 | ||||||||
\(993\) | 7.85607 | 0.249305 | ||||||||
\(994\) | 38.3756 | 1.21720 | ||||||||
\(995\) | 11.3033 | 0.358337 | ||||||||
\(996\) | 47.4631 | 1.50393 | ||||||||
\(997\) | −23.1974 | −0.734668 | −0.367334 | − | 0.930089i | \(-0.619729\pi\) | ||||
−0.367334 | + | 0.930089i | \(0.619729\pi\) | |||||||
\(998\) | 41.0472 | 1.29933 | ||||||||
\(999\) | −30.4028 | −0.961901 |
(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 | 731.2.a.e.1.19 | ✓ | 19 | |
3.2 | odd | 2 | 6579.2.a.t.1.1 | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.a.e.1.19 | ✓ | 19 | 1.1 | even | 1 | trivial | |
6579.2.a.t.1.1 | 19 | 3.2 | odd | 2 |