Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,2,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(14.7643393337\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.80194\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80194 | −1.27416 | −0.637081 | − | 0.770797i | \(-0.719858\pi\) | ||||
−0.637081 | + | 0.770797i | \(0.719858\pi\) | |||||||
\(3\) | 1.24698 | 0.719944 | 0.359972 | − | 0.932963i | \(-0.382786\pi\) | ||||
0.359972 | + | 0.932963i | \(0.382786\pi\) | |||||||
\(4\) | 1.24698 | 0.623490 | ||||||||
\(5\) | −2.24698 | −1.00488 | −0.502440 | − | 0.864612i | \(-0.667564\pi\) | ||||
−0.502440 | + | 0.864612i | \(0.667564\pi\) | |||||||
\(6\) | −2.24698 | −0.917326 | ||||||||
\(7\) | −1.69202 | −0.639524 | −0.319762 | − | 0.947498i | \(-0.603603\pi\) | ||||
−0.319762 | + | 0.947498i | \(0.603603\pi\) | |||||||
\(8\) | 1.35690 | 0.479735 | ||||||||
\(9\) | −1.44504 | −0.481681 | ||||||||
\(10\) | 4.04892 | 1.28038 | ||||||||
\(11\) | −1.13706 | −0.342837 | −0.171419 | − | 0.985198i | \(-0.554835\pi\) | ||||
−0.171419 | + | 0.985198i | \(0.554835\pi\) | |||||||
\(12\) | 1.55496 | 0.448878 | ||||||||
\(13\) | −6.54288 | −1.81467 | −0.907334 | − | 0.420411i | \(-0.861886\pi\) | ||||
−0.907334 | + | 0.420411i | \(0.861886\pi\) | |||||||
\(14\) | 3.04892 | 0.814857 | ||||||||
\(15\) | −2.80194 | −0.723457 | ||||||||
\(16\) | −4.93900 | −1.23475 | ||||||||
\(17\) | −3.60388 | −0.874068 | −0.437034 | − | 0.899445i | \(-0.643971\pi\) | ||||
−0.437034 | + | 0.899445i | \(0.643971\pi\) | |||||||
\(18\) | 2.60388 | 0.613739 | ||||||||
\(19\) | 4.44504 | 1.01976 | 0.509881 | − | 0.860245i | \(-0.329689\pi\) | ||||
0.509881 | + | 0.860245i | \(0.329689\pi\) | |||||||
\(20\) | −2.80194 | −0.626532 | ||||||||
\(21\) | −2.10992 | −0.460421 | ||||||||
\(22\) | 2.04892 | 0.436831 | ||||||||
\(23\) | −3.71379 | −0.774379 | −0.387190 | − | 0.922000i | \(-0.626554\pi\) | ||||
−0.387190 | + | 0.922000i | \(0.626554\pi\) | |||||||
\(24\) | 1.69202 | 0.345382 | ||||||||
\(25\) | 0.0489173 | 0.00978347 | ||||||||
\(26\) | 11.7899 | 2.31218 | ||||||||
\(27\) | −5.54288 | −1.06673 | ||||||||
\(28\) | −2.10992 | −0.398737 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 5.04892 | 0.921802 | ||||||||
\(31\) | 10.3230 | 1.85407 | 0.927037 | − | 0.374971i | \(-0.122347\pi\) | ||||
0.927037 | + | 0.374971i | \(0.122347\pi\) | |||||||
\(32\) | 6.18598 | 1.09354 | ||||||||
\(33\) | −1.41789 | −0.246824 | ||||||||
\(34\) | 6.49396 | 1.11370 | ||||||||
\(35\) | 3.80194 | 0.642645 | ||||||||
\(36\) | −1.80194 | −0.300323 | ||||||||
\(37\) | −3.65279 | −0.600515 | −0.300258 | − | 0.953858i | \(-0.597073\pi\) | ||||
−0.300258 | + | 0.953858i | \(0.597073\pi\) | |||||||
\(38\) | −8.00969 | −1.29934 | ||||||||
\(39\) | −8.15883 | −1.30646 | ||||||||
\(40\) | −3.04892 | −0.482076 | ||||||||
\(41\) | 4.39612 | 0.686559 | 0.343280 | − | 0.939233i | \(-0.388462\pi\) | ||||
0.343280 | + | 0.939233i | \(0.388462\pi\) | |||||||
\(42\) | 3.80194 | 0.586652 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −1.41789 | −0.213756 | ||||||||
\(45\) | 3.24698 | 0.484031 | ||||||||
\(46\) | 6.69202 | 0.986685 | ||||||||
\(47\) | −3.14914 | −0.459350 | −0.229675 | − | 0.973267i | \(-0.573766\pi\) | ||||
−0.229675 | + | 0.973267i | \(0.573766\pi\) | |||||||
\(48\) | −6.15883 | −0.888951 | ||||||||
\(49\) | −4.13706 | −0.591009 | ||||||||
\(50\) | −0.0881460 | −0.0124657 | ||||||||
\(51\) | −4.49396 | −0.629280 | ||||||||
\(52\) | −8.15883 | −1.13143 | ||||||||
\(53\) | 11.1468 | 1.53112 | 0.765562 | − | 0.643362i | \(-0.222461\pi\) | ||||
0.765562 | + | 0.643362i | \(0.222461\pi\) | |||||||
\(54\) | 9.98792 | 1.35918 | ||||||||
\(55\) | 2.55496 | 0.344510 | ||||||||
\(56\) | −2.29590 | −0.306802 | ||||||||
\(57\) | 5.54288 | 0.734172 | ||||||||
\(58\) | −10.8116 | −1.41964 | ||||||||
\(59\) | 0.158834 | 0.0206784 | 0.0103392 | − | 0.999947i | \(-0.496709\pi\) | ||||
0.0103392 | + | 0.999947i | \(0.496709\pi\) | |||||||
\(60\) | −3.49396 | −0.451068 | ||||||||
\(61\) | 0.713792 | 0.0913917 | 0.0456958 | − | 0.998955i | \(-0.485449\pi\) | ||||
0.0456958 | + | 0.998955i | \(0.485449\pi\) | |||||||
\(62\) | −18.6015 | −2.36239 | ||||||||
\(63\) | 2.44504 | 0.308046 | ||||||||
\(64\) | −1.26875 | −0.158594 | ||||||||
\(65\) | 14.7017 | 1.82352 | ||||||||
\(66\) | 2.55496 | 0.314494 | ||||||||
\(67\) | −2.09783 | −0.256291 | −0.128146 | − | 0.991755i | \(-0.540902\pi\) | ||||
−0.128146 | + | 0.991755i | \(0.540902\pi\) | |||||||
\(68\) | −4.49396 | −0.544973 | ||||||||
\(69\) | −4.63102 | −0.557510 | ||||||||
\(70\) | −6.85086 | −0.818834 | ||||||||
\(71\) | 3.72587 | 0.442180 | 0.221090 | − | 0.975253i | \(-0.429039\pi\) | ||||
0.221090 | + | 0.975253i | \(0.429039\pi\) | |||||||
\(72\) | −1.96077 | −0.231079 | ||||||||
\(73\) | −1.43296 | −0.167715 | −0.0838577 | − | 0.996478i | \(-0.526724\pi\) | ||||
−0.0838577 | + | 0.996478i | \(0.526724\pi\) | |||||||
\(74\) | 6.58211 | 0.765154 | ||||||||
\(75\) | 0.0609989 | 0.00704355 | ||||||||
\(76\) | 5.54288 | 0.635812 | ||||||||
\(77\) | 1.92394 | 0.219253 | ||||||||
\(78\) | 14.7017 | 1.66464 | ||||||||
\(79\) | −0.0609989 | −0.00686292 | −0.00343146 | − | 0.999994i | \(-0.501092\pi\) | ||||
−0.00343146 | + | 0.999994i | \(0.501092\pi\) | |||||||
\(80\) | 11.0978 | 1.24078 | ||||||||
\(81\) | −2.57673 | −0.286303 | ||||||||
\(82\) | −7.92154 | −0.874788 | ||||||||
\(83\) | −12.2838 | −1.34832 | −0.674162 | − | 0.738584i | \(-0.735495\pi\) | ||||
−0.674162 | + | 0.738584i | \(0.735495\pi\) | |||||||
\(84\) | −2.63102 | −0.287068 | ||||||||
\(85\) | 8.09783 | 0.878333 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.48188 | 0.802141 | ||||||||
\(88\) | −1.54288 | −0.164471 | ||||||||
\(89\) | 10.6189 | 1.12561 | 0.562803 | − | 0.826591i | \(-0.309723\pi\) | ||||
0.562803 | + | 0.826591i | \(0.309723\pi\) | |||||||
\(90\) | −5.85086 | −0.616734 | ||||||||
\(91\) | 11.0707 | 1.16052 | ||||||||
\(92\) | −4.63102 | −0.482817 | ||||||||
\(93\) | 12.8726 | 1.33483 | ||||||||
\(94\) | 5.67456 | 0.585286 | ||||||||
\(95\) | −9.98792 | −1.02474 | ||||||||
\(96\) | 7.71379 | 0.787286 | ||||||||
\(97\) | 3.50365 | 0.355742 | 0.177871 | − | 0.984054i | \(-0.443079\pi\) | ||||
0.177871 | + | 0.984054i | \(0.443079\pi\) | |||||||
\(98\) | 7.45473 | 0.753042 | ||||||||
\(99\) | 1.64310 | 0.165138 | ||||||||
\(100\) | 0.0609989 | 0.00609989 | ||||||||
\(101\) | 12.8726 | 1.28087 | 0.640437 | − | 0.768011i | \(-0.278753\pi\) | ||||
0.640437 | + | 0.768011i | \(0.278753\pi\) | |||||||
\(102\) | 8.09783 | 0.801805 | ||||||||
\(103\) | 3.71379 | 0.365931 | 0.182965 | − | 0.983119i | \(-0.441430\pi\) | ||||
0.182965 | + | 0.983119i | \(0.441430\pi\) | |||||||
\(104\) | −8.87800 | −0.870560 | ||||||||
\(105\) | 4.74094 | 0.462668 | ||||||||
\(106\) | −20.0858 | −1.95090 | ||||||||
\(107\) | 5.04892 | 0.488097 | 0.244049 | − | 0.969763i | \(-0.421524\pi\) | ||||
0.244049 | + | 0.969763i | \(0.421524\pi\) | |||||||
\(108\) | −6.91185 | −0.665093 | ||||||||
\(109\) | 2.17629 | 0.208451 | 0.104225 | − | 0.994554i | \(-0.466764\pi\) | ||||
0.104225 | + | 0.994554i | \(0.466764\pi\) | |||||||
\(110\) | −4.60388 | −0.438962 | ||||||||
\(111\) | −4.55496 | −0.432337 | ||||||||
\(112\) | 8.35690 | 0.789652 | ||||||||
\(113\) | 11.7463 | 1.10500 | 0.552500 | − | 0.833513i | \(-0.313674\pi\) | ||||
0.552500 | + | 0.833513i | \(0.313674\pi\) | |||||||
\(114\) | −9.98792 | −0.935454 | ||||||||
\(115\) | 8.34481 | 0.778158 | ||||||||
\(116\) | 7.48188 | 0.694675 | ||||||||
\(117\) | 9.45473 | 0.874090 | ||||||||
\(118\) | −0.286208 | −0.0263476 | ||||||||
\(119\) | 6.09783 | 0.558988 | ||||||||
\(120\) | −3.80194 | −0.347068 | ||||||||
\(121\) | −9.70709 | −0.882462 | ||||||||
\(122\) | −1.28621 | −0.116448 | ||||||||
\(123\) | 5.48188 | 0.494284 | ||||||||
\(124\) | 12.8726 | 1.15600 | ||||||||
\(125\) | 11.1250 | 0.995049 | ||||||||
\(126\) | −4.40581 | −0.392501 | ||||||||
\(127\) | −20.2228 | −1.79448 | −0.897242 | − | 0.441538i | \(-0.854433\pi\) | ||||
−0.897242 | + | 0.441538i | \(0.854433\pi\) | |||||||
\(128\) | −10.0858 | −0.891463 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −26.4916 | −2.32346 | ||||||||
\(131\) | −2.05861 | −0.179861 | −0.0899306 | − | 0.995948i | \(-0.528665\pi\) | ||||
−0.0899306 | + | 0.995948i | \(0.528665\pi\) | |||||||
\(132\) | −1.76809 | −0.153892 | ||||||||
\(133\) | −7.52111 | −0.652163 | ||||||||
\(134\) | 3.78017 | 0.326557 | ||||||||
\(135\) | 12.4547 | 1.07193 | ||||||||
\(136\) | −4.89008 | −0.419321 | ||||||||
\(137\) | −15.6015 | −1.33292 | −0.666462 | − | 0.745539i | \(-0.732192\pi\) | ||||
−0.666462 | + | 0.745539i | \(0.732192\pi\) | |||||||
\(138\) | 8.34481 | 0.710358 | ||||||||
\(139\) | −7.07606 | −0.600184 | −0.300092 | − | 0.953910i | \(-0.597017\pi\) | ||||
−0.300092 | + | 0.953910i | \(0.597017\pi\) | |||||||
\(140\) | 4.74094 | 0.400682 | ||||||||
\(141\) | −3.92692 | −0.330706 | ||||||||
\(142\) | −6.71379 | −0.563409 | ||||||||
\(143\) | 7.43967 | 0.622136 | ||||||||
\(144\) | 7.13706 | 0.594755 | ||||||||
\(145\) | −13.4819 | −1.11961 | ||||||||
\(146\) | 2.58211 | 0.213697 | ||||||||
\(147\) | −5.15883 | −0.425493 | ||||||||
\(148\) | −4.55496 | −0.374415 | ||||||||
\(149\) | 5.80194 | 0.475313 | 0.237657 | − | 0.971349i | \(-0.423621\pi\) | ||||
0.237657 | + | 0.971349i | \(0.423621\pi\) | |||||||
\(150\) | −0.109916 | −0.00897463 | ||||||||
\(151\) | −7.44935 | −0.606220 | −0.303110 | − | 0.952956i | \(-0.598025\pi\) | ||||
−0.303110 | + | 0.952956i | \(0.598025\pi\) | |||||||
\(152\) | 6.03146 | 0.489216 | ||||||||
\(153\) | 5.20775 | 0.421022 | ||||||||
\(154\) | −3.46681 | −0.279364 | ||||||||
\(155\) | −23.1957 | −1.86312 | ||||||||
\(156\) | −10.1739 | −0.814564 | ||||||||
\(157\) | −13.2131 | −1.05452 | −0.527261 | − | 0.849703i | \(-0.676781\pi\) | ||||
−0.527261 | + | 0.849703i | \(0.676781\pi\) | |||||||
\(158\) | 0.109916 | 0.00874447 | ||||||||
\(159\) | 13.8998 | 1.10232 | ||||||||
\(160\) | −13.8998 | −1.09887 | ||||||||
\(161\) | 6.28382 | 0.495234 | ||||||||
\(162\) | 4.64310 | 0.364797 | ||||||||
\(163\) | 14.1860 | 1.11113 | 0.555566 | − | 0.831473i | \(-0.312502\pi\) | ||||
0.555566 | + | 0.831473i | \(0.312502\pi\) | |||||||
\(164\) | 5.48188 | 0.428063 | ||||||||
\(165\) | 3.18598 | 0.248028 | ||||||||
\(166\) | 22.1347 | 1.71798 | ||||||||
\(167\) | 9.47219 | 0.732980 | 0.366490 | − | 0.930422i | \(-0.380559\pi\) | ||||
0.366490 | + | 0.930422i | \(0.380559\pi\) | |||||||
\(168\) | −2.86294 | −0.220880 | ||||||||
\(169\) | 29.8092 | 2.29302 | ||||||||
\(170\) | −14.5918 | −1.11914 | ||||||||
\(171\) | −6.42327 | −0.491200 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.76271 | 0.362102 | 0.181051 | − | 0.983474i | \(-0.442050\pi\) | ||||
0.181051 | + | 0.983474i | \(0.442050\pi\) | |||||||
\(174\) | −13.4819 | −1.02206 | ||||||||
\(175\) | −0.0827692 | −0.00625676 | ||||||||
\(176\) | 5.61596 | 0.423319 | ||||||||
\(177\) | 0.198062 | 0.0148873 | ||||||||
\(178\) | −19.1347 | −1.43420 | ||||||||
\(179\) | −1.64742 | −0.123134 | −0.0615668 | − | 0.998103i | \(-0.519610\pi\) | ||||
−0.0615668 | + | 0.998103i | \(0.519610\pi\) | |||||||
\(180\) | 4.04892 | 0.301788 | ||||||||
\(181\) | 2.27652 | 0.169212 | 0.0846062 | − | 0.996414i | \(-0.473037\pi\) | ||||
0.0846062 | + | 0.996414i | \(0.473037\pi\) | |||||||
\(182\) | −19.9487 | −1.47870 | ||||||||
\(183\) | 0.890084 | 0.0657969 | ||||||||
\(184\) | −5.03923 | −0.371497 | ||||||||
\(185\) | 8.20775 | 0.603446 | ||||||||
\(186\) | −23.1957 | −1.70079 | ||||||||
\(187\) | 4.09783 | 0.299663 | ||||||||
\(188\) | −3.92692 | −0.286400 | ||||||||
\(189\) | 9.37867 | 0.682198 | ||||||||
\(190\) | 17.9976 | 1.30568 | ||||||||
\(191\) | 15.0315 | 1.08764 | 0.543819 | − | 0.839202i | \(-0.316978\pi\) | ||||
0.543819 | + | 0.839202i | \(0.316978\pi\) | |||||||
\(192\) | −1.58211 | −0.114179 | ||||||||
\(193\) | 9.85086 | 0.709080 | 0.354540 | − | 0.935041i | \(-0.384637\pi\) | ||||
0.354540 | + | 0.935041i | \(0.384637\pi\) | |||||||
\(194\) | −6.31336 | −0.453272 | ||||||||
\(195\) | 18.3327 | 1.31283 | ||||||||
\(196\) | −5.15883 | −0.368488 | ||||||||
\(197\) | 10.9608 | 0.780923 | 0.390461 | − | 0.920619i | \(-0.372316\pi\) | ||||
0.390461 | + | 0.920619i | \(0.372316\pi\) | |||||||
\(198\) | −2.96077 | −0.210413 | ||||||||
\(199\) | 24.3545 | 1.72644 | 0.863222 | − | 0.504824i | \(-0.168442\pi\) | ||||
0.863222 | + | 0.504824i | \(0.168442\pi\) | |||||||
\(200\) | 0.0663757 | 0.00469347 | ||||||||
\(201\) | −2.61596 | −0.184515 | ||||||||
\(202\) | −23.1957 | −1.63204 | ||||||||
\(203\) | −10.1521 | −0.712540 | ||||||||
\(204\) | −5.60388 | −0.392350 | ||||||||
\(205\) | −9.87800 | −0.689910 | ||||||||
\(206\) | −6.69202 | −0.466255 | ||||||||
\(207\) | 5.36658 | 0.373003 | ||||||||
\(208\) | 32.3153 | 2.24066 | ||||||||
\(209\) | −5.05429 | −0.349613 | ||||||||
\(210\) | −8.54288 | −0.589514 | ||||||||
\(211\) | −10.3110 | −0.709836 | −0.354918 | − | 0.934897i | \(-0.615491\pi\) | ||||
−0.354918 | + | 0.934897i | \(0.615491\pi\) | |||||||
\(212\) | 13.8998 | 0.954640 | ||||||||
\(213\) | 4.64609 | 0.318345 | ||||||||
\(214\) | −9.09783 | −0.621915 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.52111 | −0.511746 | ||||||||
\(217\) | −17.4668 | −1.18572 | ||||||||
\(218\) | −3.92154 | −0.265600 | ||||||||
\(219\) | −1.78687 | −0.120746 | ||||||||
\(220\) | 3.18598 | 0.214799 | ||||||||
\(221\) | 23.5797 | 1.58614 | ||||||||
\(222\) | 8.20775 | 0.550868 | ||||||||
\(223\) | −2.83340 | −0.189738 | −0.0948691 | − | 0.995490i | \(-0.530243\pi\) | ||||
−0.0948691 | + | 0.995490i | \(0.530243\pi\) | |||||||
\(224\) | −10.4668 | −0.699343 | ||||||||
\(225\) | −0.0706876 | −0.00471251 | ||||||||
\(226\) | −21.1661 | −1.40795 | ||||||||
\(227\) | 13.0640 | 0.867087 | 0.433543 | − | 0.901133i | \(-0.357263\pi\) | ||||
0.433543 | + | 0.901133i | \(0.357263\pi\) | |||||||
\(228\) | 6.91185 | 0.457749 | ||||||||
\(229\) | −17.9162 | −1.18393 | −0.591967 | − | 0.805962i | \(-0.701648\pi\) | ||||
−0.591967 | + | 0.805962i | \(0.701648\pi\) | |||||||
\(230\) | −15.0368 | −0.991500 | ||||||||
\(231\) | 2.39911 | 0.157850 | ||||||||
\(232\) | 8.14138 | 0.534507 | ||||||||
\(233\) | 9.34050 | 0.611917 | 0.305958 | − | 0.952045i | \(-0.401023\pi\) | ||||
0.305958 | + | 0.952045i | \(0.401023\pi\) | |||||||
\(234\) | −17.0368 | −1.11373 | ||||||||
\(235\) | 7.07606 | 0.461592 | ||||||||
\(236\) | 0.198062 | 0.0128928 | ||||||||
\(237\) | −0.0760644 | −0.00494091 | ||||||||
\(238\) | −10.9879 | −0.712241 | ||||||||
\(239\) | 7.24160 | 0.468420 | 0.234210 | − | 0.972186i | \(-0.424750\pi\) | ||||
0.234210 | + | 0.972186i | \(0.424750\pi\) | |||||||
\(240\) | 13.8388 | 0.893289 | ||||||||
\(241\) | 0.109916 | 0.00708033 | 0.00354016 | − | 0.999994i | \(-0.498873\pi\) | ||||
0.00354016 | + | 0.999994i | \(0.498873\pi\) | |||||||
\(242\) | 17.4916 | 1.12440 | ||||||||
\(243\) | 13.4155 | 0.860605 | ||||||||
\(244\) | 0.890084 | 0.0569818 | ||||||||
\(245\) | 9.29590 | 0.593893 | ||||||||
\(246\) | −9.87800 | −0.629798 | ||||||||
\(247\) | −29.0834 | −1.85053 | ||||||||
\(248\) | 14.0073 | 0.889464 | ||||||||
\(249\) | −15.3177 | −0.970718 | ||||||||
\(250\) | −20.0465 | −1.26785 | ||||||||
\(251\) | −27.8974 | −1.76087 | −0.880433 | − | 0.474170i | \(-0.842748\pi\) | ||||
−0.880433 | + | 0.474170i | \(0.842748\pi\) | |||||||
\(252\) | 3.04892 | 0.192064 | ||||||||
\(253\) | 4.22282 | 0.265486 | ||||||||
\(254\) | 36.4403 | 2.28647 | ||||||||
\(255\) | 10.0978 | 0.632351 | ||||||||
\(256\) | 20.7114 | 1.29446 | ||||||||
\(257\) | 2.66487 | 0.166230 | 0.0831151 | − | 0.996540i | \(-0.473513\pi\) | ||||
0.0831151 | + | 0.996540i | \(0.473513\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.18060 | 0.384044 | ||||||||
\(260\) | 18.3327 | 1.13695 | ||||||||
\(261\) | −8.67025 | −0.536675 | ||||||||
\(262\) | 3.70948 | 0.229172 | ||||||||
\(263\) | 24.1347 | 1.48821 | 0.744104 | − | 0.668064i | \(-0.232877\pi\) | ||||
0.744104 | + | 0.668064i | \(0.232877\pi\) | |||||||
\(264\) | −1.92394 | −0.118410 | ||||||||
\(265\) | −25.0465 | −1.53860 | ||||||||
\(266\) | 13.5526 | 0.830961 | ||||||||
\(267\) | 13.2416 | 0.810373 | ||||||||
\(268\) | −2.61596 | −0.159795 | ||||||||
\(269\) | 30.1511 | 1.83834 | 0.919171 | − | 0.393858i | \(-0.128860\pi\) | ||||
0.919171 | + | 0.393858i | \(0.128860\pi\) | |||||||
\(270\) | −22.4426 | −1.36582 | ||||||||
\(271\) | −13.6920 | −0.831731 | −0.415866 | − | 0.909426i | \(-0.636521\pi\) | ||||
−0.415866 | + | 0.909426i | \(0.636521\pi\) | |||||||
\(272\) | 17.7995 | 1.07926 | ||||||||
\(273\) | 13.8049 | 0.835512 | ||||||||
\(274\) | 28.1129 | 1.69836 | ||||||||
\(275\) | −0.0556221 | −0.00335414 | ||||||||
\(276\) | −5.77479 | −0.347602 | ||||||||
\(277\) | 18.5743 | 1.11602 | 0.558012 | − | 0.829833i | \(-0.311564\pi\) | ||||
0.558012 | + | 0.829833i | \(0.311564\pi\) | |||||||
\(278\) | 12.7506 | 0.764732 | ||||||||
\(279\) | −14.9172 | −0.893071 | ||||||||
\(280\) | 5.15883 | 0.308299 | ||||||||
\(281\) | −2.71618 | −0.162034 | −0.0810170 | − | 0.996713i | \(-0.525817\pi\) | ||||
−0.0810170 | + | 0.996713i | \(0.525817\pi\) | |||||||
\(282\) | 7.07606 | 0.421374 | ||||||||
\(283\) | 17.0121 | 1.01126 | 0.505632 | − | 0.862749i | \(-0.331259\pi\) | ||||
0.505632 | + | 0.862749i | \(0.331259\pi\) | |||||||
\(284\) | 4.64609 | 0.275695 | ||||||||
\(285\) | −12.4547 | −0.737755 | ||||||||
\(286\) | −13.4058 | −0.792702 | ||||||||
\(287\) | −7.43834 | −0.439071 | ||||||||
\(288\) | −8.93900 | −0.526736 | ||||||||
\(289\) | −4.01208 | −0.236005 | ||||||||
\(290\) | 24.2935 | 1.42656 | ||||||||
\(291\) | 4.36898 | 0.256114 | ||||||||
\(292\) | −1.78687 | −0.104569 | ||||||||
\(293\) | −11.0315 | −0.644465 | −0.322232 | − | 0.946661i | \(-0.604433\pi\) | ||||
−0.322232 | + | 0.946661i | \(0.604433\pi\) | |||||||
\(294\) | 9.29590 | 0.542148 | ||||||||
\(295\) | −0.356896 | −0.0207793 | ||||||||
\(296\) | −4.95646 | −0.288088 | ||||||||
\(297\) | 6.30260 | 0.365714 | ||||||||
\(298\) | −10.4547 | −0.605626 | ||||||||
\(299\) | 24.2989 | 1.40524 | ||||||||
\(300\) | 0.0760644 | 0.00439158 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.4233 | 0.772422 | ||||||||
\(303\) | 16.0519 | 0.922158 | ||||||||
\(304\) | −21.9541 | −1.25915 | ||||||||
\(305\) | −1.60388 | −0.0918376 | ||||||||
\(306\) | −9.38404 | −0.536450 | ||||||||
\(307\) | 15.7952 | 0.901482 | 0.450741 | − | 0.892655i | \(-0.351160\pi\) | ||||
0.450741 | + | 0.892655i | \(0.351160\pi\) | |||||||
\(308\) | 2.39911 | 0.136702 | ||||||||
\(309\) | 4.63102 | 0.263450 | ||||||||
\(310\) | 41.7972 | 2.37392 | ||||||||
\(311\) | −12.3666 | −0.701245 | −0.350622 | − | 0.936517i | \(-0.614030\pi\) | ||||
−0.350622 | + | 0.936517i | \(0.614030\pi\) | |||||||
\(312\) | −11.0707 | −0.626754 | ||||||||
\(313\) | 5.83446 | 0.329783 | 0.164892 | − | 0.986312i | \(-0.447273\pi\) | ||||
0.164892 | + | 0.986312i | \(0.447273\pi\) | |||||||
\(314\) | 23.8092 | 1.34363 | ||||||||
\(315\) | −5.49396 | −0.309550 | ||||||||
\(316\) | −0.0760644 | −0.00427896 | ||||||||
\(317\) | 26.1685 | 1.46977 | 0.734885 | − | 0.678191i | \(-0.237236\pi\) | ||||
0.734885 | + | 0.678191i | \(0.237236\pi\) | |||||||
\(318\) | −25.0465 | −1.40454 | ||||||||
\(319\) | −6.82238 | −0.381980 | ||||||||
\(320\) | 2.85086 | 0.159368 | ||||||||
\(321\) | 6.29590 | 0.351403 | ||||||||
\(322\) | −11.3230 | −0.631009 | ||||||||
\(323\) | −16.0194 | −0.891342 | ||||||||
\(324\) | −3.21313 | −0.178507 | ||||||||
\(325\) | −0.320060 | −0.0177537 | ||||||||
\(326\) | −25.5623 | −1.41576 | ||||||||
\(327\) | 2.71379 | 0.150073 | ||||||||
\(328\) | 5.96508 | 0.329367 | ||||||||
\(329\) | 5.32842 | 0.293765 | ||||||||
\(330\) | −5.74094 | −0.316028 | ||||||||
\(331\) | −18.2664 | −1.00401 | −0.502005 | − | 0.864865i | \(-0.667404\pi\) | ||||
−0.502005 | + | 0.864865i | \(0.667404\pi\) | |||||||
\(332\) | −15.3177 | −0.840666 | ||||||||
\(333\) | 5.27844 | 0.289257 | ||||||||
\(334\) | −17.0683 | −0.933936 | ||||||||
\(335\) | 4.71379 | 0.257542 | ||||||||
\(336\) | 10.4209 | 0.568506 | ||||||||
\(337\) | −7.09113 | −0.386278 | −0.193139 | − | 0.981171i | \(-0.561867\pi\) | ||||
−0.193139 | + | 0.981171i | \(0.561867\pi\) | |||||||
\(338\) | −53.7144 | −2.92168 | ||||||||
\(339\) | 14.6474 | 0.795538 | ||||||||
\(340\) | 10.0978 | 0.547632 | ||||||||
\(341\) | −11.7380 | −0.635646 | ||||||||
\(342\) | 11.5743 | 0.625868 | ||||||||
\(343\) | 18.8442 | 1.01749 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.4058 | 0.560230 | ||||||||
\(346\) | −8.58211 | −0.461377 | ||||||||
\(347\) | 3.21446 | 0.172561 | 0.0862805 | − | 0.996271i | \(-0.472502\pi\) | ||||
0.0862805 | + | 0.996271i | \(0.472502\pi\) | |||||||
\(348\) | 9.32975 | 0.500127 | ||||||||
\(349\) | −27.3502 | −1.46402 | −0.732011 | − | 0.681293i | \(-0.761418\pi\) | ||||
−0.732011 | + | 0.681293i | \(0.761418\pi\) | |||||||
\(350\) | 0.149145 | 0.00797213 | ||||||||
\(351\) | 36.2664 | 1.93575 | ||||||||
\(352\) | −7.03385 | −0.374906 | ||||||||
\(353\) | −23.0978 | −1.22937 | −0.614687 | − | 0.788771i | \(-0.710718\pi\) | ||||
−0.614687 | + | 0.788771i | \(0.710718\pi\) | |||||||
\(354\) | −0.356896 | −0.0189688 | ||||||||
\(355\) | −8.37196 | −0.444338 | ||||||||
\(356\) | 13.2416 | 0.701804 | ||||||||
\(357\) | 7.60388 | 0.402440 | ||||||||
\(358\) | 2.96854 | 0.156892 | ||||||||
\(359\) | −0.254749 | −0.0134452 | −0.00672258 | − | 0.999977i | \(-0.502140\pi\) | ||||
−0.00672258 | + | 0.999977i | \(0.502140\pi\) | |||||||
\(360\) | 4.40581 | 0.232207 | ||||||||
\(361\) | 0.758397 | 0.0399156 | ||||||||
\(362\) | −4.10215 | −0.215604 | ||||||||
\(363\) | −12.1045 | −0.635324 | ||||||||
\(364\) | 13.8049 | 0.723575 | ||||||||
\(365\) | 3.21983 | 0.168534 | ||||||||
\(366\) | −1.60388 | −0.0838359 | ||||||||
\(367\) | −14.8092 | −0.773036 | −0.386518 | − | 0.922282i | \(-0.626322\pi\) | ||||
−0.386518 | + | 0.922282i | \(0.626322\pi\) | |||||||
\(368\) | 18.3424 | 0.956165 | ||||||||
\(369\) | −6.35258 | −0.330702 | ||||||||
\(370\) | −14.7899 | −0.768888 | ||||||||
\(371\) | −18.8605 | −0.979191 | ||||||||
\(372\) | 16.0519 | 0.832252 | ||||||||
\(373\) | −22.4722 | −1.16357 | −0.581783 | − | 0.813344i | \(-0.697645\pi\) | ||||
−0.581783 | + | 0.813344i | \(0.697645\pi\) | |||||||
\(374\) | −7.38404 | −0.381820 | ||||||||
\(375\) | 13.8726 | 0.716379 | ||||||||
\(376\) | −4.27306 | −0.220366 | ||||||||
\(377\) | −39.2573 | −2.02185 | ||||||||
\(378\) | −16.8998 | −0.869230 | ||||||||
\(379\) | −26.0508 | −1.33814 | −0.669071 | − | 0.743199i | \(-0.733308\pi\) | ||||
−0.669071 | + | 0.743199i | \(0.733308\pi\) | |||||||
\(380\) | −12.4547 | −0.638914 | ||||||||
\(381\) | −25.2174 | −1.29193 | ||||||||
\(382\) | −27.0858 | −1.38583 | ||||||||
\(383\) | −12.3405 | −0.630570 | −0.315285 | − | 0.948997i | \(-0.602100\pi\) | ||||
−0.315285 | + | 0.948997i | \(0.602100\pi\) | |||||||
\(384\) | −12.5767 | −0.641803 | ||||||||
\(385\) | −4.32304 | −0.220323 | ||||||||
\(386\) | −17.7506 | −0.903483 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.36898 | 0.221801 | ||||||||
\(389\) | 19.9138 | 1.00967 | 0.504834 | − | 0.863216i | \(-0.331554\pi\) | ||||
0.504834 | + | 0.863216i | \(0.331554\pi\) | |||||||
\(390\) | −33.0344 | −1.67276 | ||||||||
\(391\) | 13.3840 | 0.676860 | ||||||||
\(392\) | −5.61356 | −0.283528 | ||||||||
\(393\) | −2.56704 | −0.129490 | ||||||||
\(394\) | −19.7506 | −0.995022 | ||||||||
\(395\) | 0.137063 | 0.00689641 | ||||||||
\(396\) | 2.04892 | 0.102962 | ||||||||
\(397\) | 9.12498 | 0.457970 | 0.228985 | − | 0.973430i | \(-0.426459\pi\) | ||||
0.228985 | + | 0.973430i | \(0.426459\pi\) | |||||||
\(398\) | −43.8853 | −2.19977 | ||||||||
\(399\) | −9.37867 | −0.469521 | ||||||||
\(400\) | −0.241603 | −0.0120801 | ||||||||
\(401\) | 0.0435405 | 0.00217431 | 0.00108716 | − | 0.999999i | \(-0.499654\pi\) | ||||
0.00108716 | + | 0.999999i | \(0.499654\pi\) | |||||||
\(402\) | 4.71379 | 0.235103 | ||||||||
\(403\) | −67.5424 | −3.36453 | ||||||||
\(404\) | 16.0519 | 0.798612 | ||||||||
\(405\) | 5.78986 | 0.287700 | ||||||||
\(406\) | 18.2935 | 0.907891 | ||||||||
\(407\) | 4.15346 | 0.205879 | ||||||||
\(408\) | −6.09783 | −0.301888 | ||||||||
\(409\) | 10.6866 | 0.528421 | 0.264210 | − | 0.964465i | \(-0.414889\pi\) | ||||
0.264210 | + | 0.964465i | \(0.414889\pi\) | |||||||
\(410\) | 17.7995 | 0.879057 | ||||||||
\(411\) | −19.4547 | −0.959631 | ||||||||
\(412\) | 4.63102 | 0.228154 | ||||||||
\(413\) | −0.268750 | −0.0132243 | ||||||||
\(414\) | −9.67025 | −0.475267 | ||||||||
\(415\) | 27.6015 | 1.35490 | ||||||||
\(416\) | −40.4741 | −1.98441 | ||||||||
\(417\) | −8.82371 | −0.432099 | ||||||||
\(418\) | 9.10752 | 0.445464 | ||||||||
\(419\) | 7.38106 | 0.360588 | 0.180294 | − | 0.983613i | \(-0.442295\pi\) | ||||
0.180294 | + | 0.983613i | \(0.442295\pi\) | |||||||
\(420\) | 5.91185 | 0.288469 | ||||||||
\(421\) | −9.79225 | −0.477245 | −0.238623 | − | 0.971112i | \(-0.576696\pi\) | ||||
−0.238623 | + | 0.971112i | \(0.576696\pi\) | |||||||
\(422\) | 18.5797 | 0.904446 | ||||||||
\(423\) | 4.55065 | 0.221260 | ||||||||
\(424\) | 15.1250 | 0.734534 | ||||||||
\(425\) | −0.176292 | −0.00855142 | ||||||||
\(426\) | −8.37196 | −0.405623 | ||||||||
\(427\) | −1.20775 | −0.0584472 | ||||||||
\(428\) | 6.29590 | 0.304324 | ||||||||
\(429\) | 9.27711 | 0.447903 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.3297 | 1.31643 | 0.658214 | − | 0.752831i | \(-0.271312\pi\) | ||||
0.658214 | + | 0.752831i | \(0.271312\pi\) | |||||||
\(432\) | 27.3763 | 1.31714 | ||||||||
\(433\) | 2.77777 | 0.133491 | 0.0667457 | − | 0.997770i | \(-0.478738\pi\) | ||||
0.0667457 | + | 0.997770i | \(0.478738\pi\) | |||||||
\(434\) | 31.4741 | 1.51081 | ||||||||
\(435\) | −16.8116 | −0.806056 | ||||||||
\(436\) | 2.71379 | 0.129967 | ||||||||
\(437\) | −16.5080 | −0.789683 | ||||||||
\(438\) | 3.21983 | 0.153850 | ||||||||
\(439\) | 9.58211 | 0.457329 | 0.228664 | − | 0.973505i | \(-0.426564\pi\) | ||||
0.228664 | + | 0.973505i | \(0.426564\pi\) | |||||||
\(440\) | 3.46681 | 0.165274 | ||||||||
\(441\) | 5.97823 | 0.284678 | ||||||||
\(442\) | −42.4892 | −2.02100 | ||||||||
\(443\) | 23.7754 | 1.12960 | 0.564801 | − | 0.825227i | \(-0.308953\pi\) | ||||
0.564801 | + | 0.825227i | \(0.308953\pi\) | |||||||
\(444\) | −5.67994 | −0.269558 | ||||||||
\(445\) | −23.8605 | −1.13110 | ||||||||
\(446\) | 5.10560 | 0.241757 | ||||||||
\(447\) | 7.23490 | 0.342199 | ||||||||
\(448\) | 2.14675 | 0.101424 | ||||||||
\(449\) | 18.3502 | 0.865999 | 0.433000 | − | 0.901394i | \(-0.357455\pi\) | ||||
0.433000 | + | 0.901394i | \(0.357455\pi\) | |||||||
\(450\) | 0.127375 | 0.00600450 | ||||||||
\(451\) | −4.99867 | −0.235378 | ||||||||
\(452\) | 14.6474 | 0.688956 | ||||||||
\(453\) | −9.28919 | −0.436444 | ||||||||
\(454\) | −23.5405 | −1.10481 | ||||||||
\(455\) | −24.8756 | −1.16619 | ||||||||
\(456\) | 7.52111 | 0.352208 | ||||||||
\(457\) | −39.8116 | −1.86231 | −0.931155 | − | 0.364624i | \(-0.881197\pi\) | ||||
−0.931155 | + | 0.364624i | \(0.881197\pi\) | |||||||
\(458\) | 32.2838 | 1.50852 | ||||||||
\(459\) | 19.9758 | 0.932392 | ||||||||
\(460\) | 10.4058 | 0.485174 | ||||||||
\(461\) | −19.2301 | −0.895636 | −0.447818 | − | 0.894125i | \(-0.647799\pi\) | ||||
−0.447818 | + | 0.894125i | \(0.647799\pi\) | |||||||
\(462\) | −4.32304 | −0.201126 | ||||||||
\(463\) | −14.9584 | −0.695175 | −0.347587 | − | 0.937648i | \(-0.612999\pi\) | ||||
−0.347587 | + | 0.937648i | \(0.612999\pi\) | |||||||
\(464\) | −29.6340 | −1.37572 | ||||||||
\(465\) | −28.9245 | −1.34134 | ||||||||
\(466\) | −16.8310 | −0.779681 | ||||||||
\(467\) | −25.7904 | −1.19344 | −0.596720 | − | 0.802450i | \(-0.703530\pi\) | ||||
−0.596720 | + | 0.802450i | \(0.703530\pi\) | |||||||
\(468\) | 11.7899 | 0.544986 | ||||||||
\(469\) | 3.54958 | 0.163904 | ||||||||
\(470\) | −12.7506 | −0.588143 | ||||||||
\(471\) | −16.4765 | −0.759197 | ||||||||
\(472\) | 0.215521 | 0.00992014 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.137063 | 0.00629553 | ||||||||
\(475\) | 0.217440 | 0.00997681 | ||||||||
\(476\) | 7.60388 | 0.348523 | ||||||||
\(477\) | −16.1075 | −0.737513 | ||||||||
\(478\) | −13.0489 | −0.596844 | ||||||||
\(479\) | −29.7157 | −1.35775 | −0.678873 | − | 0.734256i | \(-0.737531\pi\) | ||||
−0.678873 | + | 0.734256i | \(0.737531\pi\) | |||||||
\(480\) | −17.3327 | −0.791127 | ||||||||
\(481\) | 23.8998 | 1.08974 | ||||||||
\(482\) | −0.198062 | −0.00902149 | ||||||||
\(483\) | 7.83579 | 0.356541 | ||||||||
\(484\) | −12.1045 | −0.550206 | ||||||||
\(485\) | −7.87263 | −0.357478 | ||||||||
\(486\) | −24.1739 | −1.09655 | ||||||||
\(487\) | 1.52111 | 0.0689279 | 0.0344640 | − | 0.999406i | \(-0.489028\pi\) | ||||
0.0344640 | + | 0.999406i | \(0.489028\pi\) | |||||||
\(488\) | 0.968541 | 0.0438438 | ||||||||
\(489\) | 17.6896 | 0.799953 | ||||||||
\(490\) | −16.7506 | −0.756716 | ||||||||
\(491\) | −28.6631 | −1.29355 | −0.646773 | − | 0.762682i | \(-0.723882\pi\) | ||||
−0.646773 | + | 0.762682i | \(0.723882\pi\) | |||||||
\(492\) | 6.83579 | 0.308181 | ||||||||
\(493\) | −21.6233 | −0.973862 | ||||||||
\(494\) | 52.4064 | 2.35788 | ||||||||
\(495\) | −3.69202 | −0.165944 | ||||||||
\(496\) | −50.9855 | −2.28932 | ||||||||
\(497\) | −6.30426 | −0.282785 | ||||||||
\(498\) | 27.6015 | 1.23685 | ||||||||
\(499\) | 20.8159 | 0.931849 | 0.465925 | − | 0.884824i | \(-0.345722\pi\) | ||||
0.465925 | + | 0.884824i | \(0.345722\pi\) | |||||||
\(500\) | 13.8726 | 0.620403 | ||||||||
\(501\) | 11.8116 | 0.527705 | ||||||||
\(502\) | 50.2693 | 2.24363 | ||||||||
\(503\) | −3.65087 | −0.162784 | −0.0813922 | − | 0.996682i | \(-0.525937\pi\) | ||||
−0.0813922 | + | 0.996682i | \(0.525937\pi\) | |||||||
\(504\) | 3.31767 | 0.147781 | ||||||||
\(505\) | −28.9245 | −1.28712 | ||||||||
\(506\) | −7.60925 | −0.338273 | ||||||||
\(507\) | 37.1715 | 1.65084 | ||||||||
\(508\) | −25.2174 | −1.11884 | ||||||||
\(509\) | −6.27114 | −0.277964 | −0.138982 | − | 0.990295i | \(-0.544383\pi\) | ||||
−0.138982 | + | 0.990295i | \(0.544383\pi\) | |||||||
\(510\) | −18.1957 | −0.805718 | ||||||||
\(511\) | 2.42460 | 0.107258 | ||||||||
\(512\) | −17.1491 | −0.757892 | ||||||||
\(513\) | −24.6383 | −1.08781 | ||||||||
\(514\) | −4.80194 | −0.211804 | ||||||||
\(515\) | −8.34481 | −0.367716 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.58078 | 0.157482 | ||||||||
\(518\) | −11.1371 | −0.489334 | ||||||||
\(519\) | 5.93900 | 0.260693 | ||||||||
\(520\) | 19.9487 | 0.874808 | ||||||||
\(521\) | 0.128703 | 0.00563856 | 0.00281928 | − | 0.999996i | \(-0.499103\pi\) | ||||
0.00281928 | + | 0.999996i | \(0.499103\pi\) | |||||||
\(522\) | 15.6233 | 0.683811 | ||||||||
\(523\) | 21.6209 | 0.945414 | 0.472707 | − | 0.881220i | \(-0.343277\pi\) | ||||
0.472707 | + | 0.881220i | \(0.343277\pi\) | |||||||
\(524\) | −2.56704 | −0.112142 | ||||||||
\(525\) | −0.103211 | −0.00450452 | ||||||||
\(526\) | −43.4892 | −1.89622 | ||||||||
\(527\) | −37.2030 | −1.62059 | ||||||||
\(528\) | 7.00298 | 0.304766 | ||||||||
\(529\) | −9.20775 | −0.400337 | ||||||||
\(530\) | 45.1323 | 1.96042 | ||||||||
\(531\) | −0.229521 | −0.00996037 | ||||||||
\(532\) | −9.37867 | −0.406617 | ||||||||
\(533\) | −28.7633 | −1.24588 | ||||||||
\(534\) | −23.8605 | −1.03255 | ||||||||
\(535\) | −11.3448 | −0.490479 | ||||||||
\(536\) | −2.84654 | −0.122952 | ||||||||
\(537\) | −2.05429 | −0.0886493 | ||||||||
\(538\) | −54.3303 | −2.34235 | ||||||||
\(539\) | 4.70410 | 0.202620 | ||||||||
\(540\) | 15.5308 | 0.668339 | ||||||||
\(541\) | 14.0519 | 0.604138 | 0.302069 | − | 0.953286i | \(-0.402323\pi\) | ||||
0.302069 | + | 0.953286i | \(0.402323\pi\) | |||||||
\(542\) | 24.6722 | 1.05976 | ||||||||
\(543\) | 2.83877 | 0.121823 | ||||||||
\(544\) | −22.2935 | −0.955826 | ||||||||
\(545\) | −4.89008 | −0.209468 | ||||||||
\(546\) | −24.8756 | −1.06458 | ||||||||
\(547\) | −33.7318 | −1.44227 | −0.721135 | − | 0.692795i | \(-0.756379\pi\) | ||||
−0.721135 | + | 0.692795i | \(0.756379\pi\) | |||||||
\(548\) | −19.4547 | −0.831065 | ||||||||
\(549\) | −1.03146 | −0.0440216 | ||||||||
\(550\) | 0.100228 | 0.00427372 | ||||||||
\(551\) | 26.6703 | 1.13619 | ||||||||
\(552\) | −6.28382 | −0.267457 | ||||||||
\(553\) | 0.103211 | 0.00438900 | ||||||||
\(554\) | −33.4698 | −1.42200 | ||||||||
\(555\) | 10.2349 | 0.434447 | ||||||||
\(556\) | −8.82371 | −0.374209 | ||||||||
\(557\) | 25.4588 | 1.07872 | 0.539362 | − | 0.842074i | \(-0.318666\pi\) | ||||
0.539362 | + | 0.842074i | \(0.318666\pi\) | |||||||
\(558\) | 26.8799 | 1.13792 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −18.7778 | −0.793506 | ||||||||
\(561\) | 5.10992 | 0.215741 | ||||||||
\(562\) | 4.89440 | 0.206458 | ||||||||
\(563\) | −6.42327 | −0.270709 | −0.135354 | − | 0.990797i | \(-0.543217\pi\) | ||||
−0.135354 | + | 0.990797i | \(0.543217\pi\) | |||||||
\(564\) | −4.89679 | −0.206192 | ||||||||
\(565\) | −26.3937 | −1.11039 | ||||||||
\(566\) | −30.6547 | −1.28851 | ||||||||
\(567\) | 4.35988 | 0.183098 | ||||||||
\(568\) | 5.05562 | 0.212129 | ||||||||
\(569\) | −1.22414 | −0.0513188 | −0.0256594 | − | 0.999671i | \(-0.508169\pi\) | ||||
−0.0256594 | + | 0.999671i | \(0.508169\pi\) | |||||||
\(570\) | 22.4426 | 0.940019 | ||||||||
\(571\) | 36.9221 | 1.54514 | 0.772572 | − | 0.634928i | \(-0.218970\pi\) | ||||
0.772572 | + | 0.634928i | \(0.218970\pi\) | |||||||
\(572\) | 9.27711 | 0.387895 | ||||||||
\(573\) | 18.7439 | 0.783039 | ||||||||
\(574\) | 13.4034 | 0.559448 | ||||||||
\(575\) | −0.181669 | −0.00757611 | ||||||||
\(576\) | 1.83340 | 0.0763915 | ||||||||
\(577\) | 25.7904 | 1.07367 | 0.536835 | − | 0.843687i | \(-0.319620\pi\) | ||||
0.536835 | + | 0.843687i | \(0.319620\pi\) | |||||||
\(578\) | 7.22952 | 0.300708 | ||||||||
\(579\) | 12.2838 | 0.510498 | ||||||||
\(580\) | −16.8116 | −0.698065 | ||||||||
\(581\) | 20.7845 | 0.862286 | ||||||||
\(582\) | −7.87263 | −0.326331 | ||||||||
\(583\) | −12.6746 | −0.524927 | ||||||||
\(584\) | −1.94438 | −0.0804589 | ||||||||
\(585\) | −21.2446 | −0.878356 | ||||||||
\(586\) | 19.8780 | 0.821153 | ||||||||
\(587\) | −9.42519 | −0.389019 | −0.194510 | − | 0.980901i | \(-0.562312\pi\) | ||||
−0.194510 | + | 0.980901i | \(0.562312\pi\) | |||||||
\(588\) | −6.43296 | −0.265291 | ||||||||
\(589\) | 45.8864 | 1.89071 | ||||||||
\(590\) | 0.643104 | 0.0264762 | ||||||||
\(591\) | 13.6679 | 0.562221 | ||||||||
\(592\) | 18.0411 | 0.741487 | ||||||||
\(593\) | 8.71810 | 0.358010 | 0.179005 | − | 0.983848i | \(-0.442712\pi\) | ||||
0.179005 | + | 0.983848i | \(0.442712\pi\) | |||||||
\(594\) | −11.3569 | −0.465979 | ||||||||
\(595\) | −13.7017 | −0.561715 | ||||||||
\(596\) | 7.23490 | 0.296353 | ||||||||
\(597\) | 30.3696 | 1.24294 | ||||||||
\(598\) | −43.7851 | −1.79050 | ||||||||
\(599\) | 18.7791 | 0.767293 | 0.383647 | − | 0.923480i | \(-0.374668\pi\) | ||||
0.383647 | + | 0.923480i | \(0.374668\pi\) | |||||||
\(600\) | 0.0827692 | 0.00337904 | ||||||||
\(601\) | 13.5646 | 0.553313 | 0.276657 | − | 0.960969i | \(-0.410774\pi\) | ||||
0.276657 | + | 0.960969i | \(0.410774\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.03146 | 0.123451 | ||||||||
\(604\) | −9.28919 | −0.377972 | ||||||||
\(605\) | 21.8116 | 0.886769 | ||||||||
\(606\) | −28.9245 | −1.17498 | ||||||||
\(607\) | 30.1866 | 1.22524 | 0.612618 | − | 0.790379i | \(-0.290117\pi\) | ||||
0.612618 | + | 0.790379i | \(0.290117\pi\) | |||||||
\(608\) | 27.4969 | 1.11515 | ||||||||
\(609\) | −12.6595 | −0.512989 | ||||||||
\(610\) | 2.89008 | 0.117016 | ||||||||
\(611\) | 20.6045 | 0.833567 | ||||||||
\(612\) | 6.49396 | 0.262503 | ||||||||
\(613\) | 4.49694 | 0.181630 | 0.0908149 | − | 0.995868i | \(-0.471053\pi\) | ||||
0.0908149 | + | 0.995868i | \(0.471053\pi\) | |||||||
\(614\) | −28.4620 | −1.14863 | ||||||||
\(615\) | −12.3177 | −0.496696 | ||||||||
\(616\) | 2.61058 | 0.105183 | ||||||||
\(617\) | −28.5579 | −1.14970 | −0.574850 | − | 0.818259i | \(-0.694939\pi\) | ||||
−0.574850 | + | 0.818259i | \(0.694939\pi\) | |||||||
\(618\) | −8.34481 | −0.335678 | ||||||||
\(619\) | −2.90515 | −0.116768 | −0.0583839 | − | 0.998294i | \(-0.518595\pi\) | ||||
−0.0583839 | + | 0.998294i | \(0.518595\pi\) | |||||||
\(620\) | −28.9245 | −1.16164 | ||||||||
\(621\) | 20.5851 | 0.826051 | ||||||||
\(622\) | 22.2838 | 0.893500 | ||||||||
\(623\) | −17.9675 | −0.719852 | ||||||||
\(624\) | 40.2965 | 1.61315 | ||||||||
\(625\) | −25.2422 | −1.00969 | ||||||||
\(626\) | −10.5133 | −0.420197 | ||||||||
\(627\) | −6.30260 | −0.251702 | ||||||||
\(628\) | −16.4765 | −0.657484 | ||||||||
\(629\) | 13.1642 | 0.524891 | ||||||||
\(630\) | 9.89977 | 0.394416 | ||||||||
\(631\) | −15.1196 | −0.601902 | −0.300951 | − | 0.953640i | \(-0.597304\pi\) | ||||
−0.300951 | + | 0.953640i | \(0.597304\pi\) | |||||||
\(632\) | −0.0827692 | −0.00329238 | ||||||||
\(633\) | −12.8576 | −0.511042 | ||||||||
\(634\) | −47.1540 | −1.87273 | ||||||||
\(635\) | 45.4403 | 1.80324 | ||||||||
\(636\) | 17.3327 | 0.687288 | ||||||||
\(637\) | 27.0683 | 1.07248 | ||||||||
\(638\) | 12.2935 | 0.486704 | ||||||||
\(639\) | −5.38404 | −0.212989 | ||||||||
\(640\) | 22.6625 | 0.895813 | ||||||||
\(641\) | −3.40714 | −0.134574 | −0.0672870 | − | 0.997734i | \(-0.521434\pi\) | ||||
−0.0672870 | + | 0.997734i | \(0.521434\pi\) | |||||||
\(642\) | −11.3448 | −0.447744 | ||||||||
\(643\) | 0.977165 | 0.0385356 | 0.0192678 | − | 0.999814i | \(-0.493866\pi\) | ||||
0.0192678 | + | 0.999814i | \(0.493866\pi\) | |||||||
\(644\) | 7.83579 | 0.308773 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.8659 | 1.13571 | ||||||||
\(647\) | 16.4558 | 0.646944 | 0.323472 | − | 0.946238i | \(-0.395150\pi\) | ||||
0.323472 | + | 0.946238i | \(0.395150\pi\) | |||||||
\(648\) | −3.49635 | −0.137350 | ||||||||
\(649\) | −0.180604 | −0.00708932 | ||||||||
\(650\) | 0.576728 | 0.0226211 | ||||||||
\(651\) | −21.7808 | −0.853655 | ||||||||
\(652\) | 17.6896 | 0.692779 | ||||||||
\(653\) | −33.7077 | −1.31908 | −0.659542 | − | 0.751668i | \(-0.729250\pi\) | ||||
−0.659542 | + | 0.751668i | \(0.729250\pi\) | |||||||
\(654\) | −4.89008 | −0.191217 | ||||||||
\(655\) | 4.62565 | 0.180739 | ||||||||
\(656\) | −21.7125 | −0.847729 | ||||||||
\(657\) | 2.07069 | 0.0807852 | ||||||||
\(658\) | −9.60148 | −0.374305 | ||||||||
\(659\) | −35.1008 | −1.36733 | −0.683667 | − | 0.729794i | \(-0.739616\pi\) | ||||
−0.683667 | + | 0.729794i | \(0.739616\pi\) | |||||||
\(660\) | 3.97285 | 0.154643 | ||||||||
\(661\) | 2.10693 | 0.0819502 | 0.0409751 | − | 0.999160i | \(-0.486954\pi\) | ||||
0.0409751 | + | 0.999160i | \(0.486954\pi\) | |||||||
\(662\) | 32.9148 | 1.27927 | ||||||||
\(663\) | 29.4034 | 1.14193 | ||||||||
\(664\) | −16.6679 | −0.646838 | ||||||||
\(665\) | 16.8998 | 0.655345 | ||||||||
\(666\) | −9.51142 | −0.368560 | ||||||||
\(667\) | −22.2828 | −0.862792 | ||||||||
\(668\) | 11.8116 | 0.457006 | ||||||||
\(669\) | −3.53319 | −0.136601 | ||||||||
\(670\) | −8.49396 | −0.328150 | ||||||||
\(671\) | −0.811626 | −0.0313325 | ||||||||
\(672\) | −13.0519 | −0.503488 | ||||||||
\(673\) | −17.4964 | −0.674435 | −0.337217 | − | 0.941427i | \(-0.609486\pi\) | ||||
−0.337217 | + | 0.941427i | \(0.609486\pi\) | |||||||
\(674\) | 12.7778 | 0.492181 | ||||||||
\(675\) | −0.271143 | −0.0104363 | ||||||||
\(676\) | 37.1715 | 1.42967 | ||||||||
\(677\) | 29.4252 | 1.13090 | 0.565451 | − | 0.824782i | \(-0.308702\pi\) | ||||
0.565451 | + | 0.824782i | \(0.308702\pi\) | |||||||
\(678\) | −26.3937 | −1.01365 | ||||||||
\(679\) | −5.92825 | −0.227505 | ||||||||
\(680\) | 10.9879 | 0.421367 | ||||||||
\(681\) | 16.2905 | 0.624254 | ||||||||
\(682\) | 21.1511 | 0.809916 | ||||||||
\(683\) | −51.8504 | −1.98400 | −0.992000 | − | 0.126239i | \(-0.959709\pi\) | ||||
−0.992000 | + | 0.126239i | \(0.959709\pi\) | |||||||
\(684\) | −8.00969 | −0.306258 | ||||||||
\(685\) | 35.0562 | 1.33943 | ||||||||
\(686\) | −33.9560 | −1.29645 | ||||||||
\(687\) | −22.3411 | −0.852366 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −72.9318 | −2.77848 | ||||||||
\(690\) | −18.7506 | −0.713824 | ||||||||
\(691\) | −1.26337 | −0.0480610 | −0.0240305 | − | 0.999711i | \(-0.507650\pi\) | ||||
−0.0240305 | + | 0.999711i | \(0.507650\pi\) | |||||||
\(692\) | 5.93900 | 0.225767 | ||||||||
\(693\) | −2.78017 | −0.105610 | ||||||||
\(694\) | −5.79225 | −0.219871 | ||||||||
\(695\) | 15.8998 | 0.603113 | ||||||||
\(696\) | 10.1521 | 0.384815 | ||||||||
\(697\) | −15.8431 | −0.600100 | ||||||||
\(698\) | 49.2833 | 1.86540 | ||||||||
\(699\) | 11.6474 | 0.440546 | ||||||||
\(700\) | −0.103211 | −0.00390103 | ||||||||
\(701\) | 33.9922 | 1.28387 | 0.641934 | − | 0.766760i | \(-0.278132\pi\) | ||||
0.641934 | + | 0.766760i | \(0.278132\pi\) | |||||||
\(702\) | −65.3497 | −2.46647 | ||||||||
\(703\) | −16.2368 | −0.612383 | ||||||||
\(704\) | 1.44265 | 0.0543719 | ||||||||
\(705\) | 8.82371 | 0.332320 | ||||||||
\(706\) | 41.6209 | 1.56642 | ||||||||
\(707\) | −21.7808 | −0.819150 | ||||||||
\(708\) | 0.246980 | 0.00928206 | ||||||||
\(709\) | 35.1618 | 1.32053 | 0.660265 | − | 0.751033i | \(-0.270444\pi\) | ||||
0.660265 | + | 0.751033i | \(0.270444\pi\) | |||||||
\(710\) | 15.0858 | 0.566158 | ||||||||
\(711\) | 0.0881460 | 0.00330573 | ||||||||
\(712\) | 14.4088 | 0.539993 | ||||||||
\(713\) | −38.3376 | −1.43576 | ||||||||
\(714\) | −13.7017 | −0.512774 | ||||||||
\(715\) | −16.7168 | −0.625172 | ||||||||
\(716\) | −2.05429 | −0.0767726 | ||||||||
\(717\) | 9.03013 | 0.337236 | ||||||||
\(718\) | 0.459042 | 0.0171313 | ||||||||
\(719\) | 24.4983 | 0.913631 | 0.456816 | − | 0.889561i | \(-0.348990\pi\) | ||||
0.456816 | + | 0.889561i | \(0.348990\pi\) | |||||||
\(720\) | −16.0368 | −0.597658 | ||||||||
\(721\) | −6.28382 | −0.234022 | ||||||||
\(722\) | −1.36658 | −0.0508590 | ||||||||
\(723\) | 0.137063 | 0.00509744 | ||||||||
\(724\) | 2.83877 | 0.105502 | ||||||||
\(725\) | 0.293504 | 0.0109005 | ||||||||
\(726\) | 21.8116 | 0.809505 | ||||||||
\(727\) | 38.9855 | 1.44589 | 0.722947 | − | 0.690904i | \(-0.242787\pi\) | ||||
0.722947 | + | 0.690904i | \(0.242787\pi\) | |||||||
\(728\) | 15.0218 | 0.556744 | ||||||||
\(729\) | 24.4590 | 0.905890 | ||||||||
\(730\) | −5.80194 | −0.214739 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.10992 | 0.0410237 | ||||||||
\(733\) | 5.86294 | 0.216553 | 0.108276 | − | 0.994121i | \(-0.465467\pi\) | ||||
0.108276 | + | 0.994121i | \(0.465467\pi\) | |||||||
\(734\) | 26.6853 | 0.984973 | ||||||||
\(735\) | 11.5918 | 0.427570 | ||||||||
\(736\) | −22.9734 | −0.846812 | ||||||||
\(737\) | 2.38537 | 0.0878663 | ||||||||
\(738\) | 11.4470 | 0.421368 | ||||||||
\(739\) | 22.5840 | 0.830767 | 0.415383 | − | 0.909646i | \(-0.363647\pi\) | ||||
0.415383 | + | 0.909646i | \(0.363647\pi\) | |||||||
\(740\) | 10.2349 | 0.376242 | ||||||||
\(741\) | −36.2664 | −1.33228 | ||||||||
\(742\) | 33.9855 | 1.24765 | ||||||||
\(743\) | 44.8877 | 1.64677 | 0.823385 | − | 0.567483i | \(-0.192083\pi\) | ||||
0.823385 | + | 0.567483i | \(0.192083\pi\) | |||||||
\(744\) | 17.4668 | 0.640364 | ||||||||
\(745\) | −13.0368 | −0.477633 | ||||||||
\(746\) | 40.4935 | 1.48257 | ||||||||
\(747\) | 17.7506 | 0.649461 | ||||||||
\(748\) | 5.10992 | 0.186837 | ||||||||
\(749\) | −8.54288 | −0.312150 | ||||||||
\(750\) | −24.9976 | −0.912784 | ||||||||
\(751\) | 0.476501 | 0.0173878 | 0.00869388 | − | 0.999962i | \(-0.497233\pi\) | ||||
0.00869388 | + | 0.999962i | \(0.497233\pi\) | |||||||
\(752\) | 15.5536 | 0.567183 | ||||||||
\(753\) | −34.7875 | −1.26773 | ||||||||
\(754\) | 70.7391 | 2.57617 | ||||||||
\(755\) | 16.7385 | 0.609178 | ||||||||
\(756\) | 11.6950 | 0.425343 | ||||||||
\(757\) | 10.7855 | 0.392007 | 0.196004 | − | 0.980603i | \(-0.437204\pi\) | ||||
0.196004 | + | 0.980603i | \(0.437204\pi\) | |||||||
\(758\) | 46.9420 | 1.70501 | ||||||||
\(759\) | 5.26577 | 0.191135 | ||||||||
\(760\) | −13.5526 | −0.491603 | ||||||||
\(761\) | −8.87023 | −0.321546 | −0.160773 | − | 0.986991i | \(-0.551399\pi\) | ||||
−0.160773 | + | 0.986991i | \(0.551399\pi\) | |||||||
\(762\) | 45.4403 | 1.64613 | ||||||||
\(763\) | −3.68233 | −0.133309 | ||||||||
\(764\) | 18.7439 | 0.678131 | ||||||||
\(765\) | −11.7017 | −0.423076 | ||||||||
\(766\) | 22.2368 | 0.803449 | ||||||||
\(767\) | −1.03923 | −0.0375244 | ||||||||
\(768\) | 25.8267 | 0.931940 | ||||||||
\(769\) | 38.7928 | 1.39891 | 0.699453 | − | 0.714679i | \(-0.253427\pi\) | ||||
0.699453 | + | 0.714679i | \(0.253427\pi\) | |||||||
\(770\) | 7.78986 | 0.280727 | ||||||||
\(771\) | 3.32304 | 0.119677 | ||||||||
\(772\) | 12.2838 | 0.442104 | ||||||||
\(773\) | −44.4730 | −1.59958 | −0.799792 | − | 0.600277i | \(-0.795057\pi\) | ||||
−0.799792 | + | 0.600277i | \(0.795057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.504976 | 0.0181393 | ||||||||
\(776\) | 4.75409 | 0.170662 | ||||||||
\(777\) | 7.70709 | 0.276490 | ||||||||
\(778\) | −35.8834 | −1.28648 | ||||||||
\(779\) | 19.5410 | 0.700127 | ||||||||
\(780\) | 22.8605 | 0.818539 | ||||||||
\(781\) | −4.23655 | −0.151596 | ||||||||
\(782\) | −24.1172 | −0.862430 | ||||||||
\(783\) | −33.2573 | −1.18852 | ||||||||
\(784\) | 20.4330 | 0.729749 | ||||||||
\(785\) | 29.6896 | 1.05967 | ||||||||
\(786\) | 4.62565 | 0.164991 | ||||||||
\(787\) | −10.6243 | −0.378716 | −0.189358 | − | 0.981908i | \(-0.560641\pi\) | ||||
−0.189358 | + | 0.981908i | \(0.560641\pi\) | |||||||
\(788\) | 13.6679 | 0.486897 | ||||||||
\(789\) | 30.0954 | 1.07143 | ||||||||
\(790\) | −0.246980 | −0.00878714 | ||||||||
\(791\) | −19.8750 | −0.706674 | ||||||||
\(792\) | 2.22952 | 0.0792226 | ||||||||
\(793\) | −4.67025 | −0.165845 | ||||||||
\(794\) | −16.4426 | −0.583528 | ||||||||
\(795\) | −31.2325 | −1.10770 | ||||||||
\(796\) | 30.3696 | 1.07642 | ||||||||
\(797\) | 0.528402 | 0.0187170 | 0.00935848 | − | 0.999956i | \(-0.497021\pi\) | ||||
0.00935848 | + | 0.999956i | \(0.497021\pi\) | |||||||
\(798\) | 16.8998 | 0.598245 | ||||||||
\(799\) | 11.3491 | 0.401503 | ||||||||
\(800\) | 0.302602 | 0.0106986 | ||||||||
\(801\) | −15.3448 | −0.542182 | ||||||||
\(802\) | −0.0784573 | −0.00277042 | ||||||||
\(803\) | 1.62937 | 0.0574991 | ||||||||
\(804\) | −3.26205 | −0.115043 | ||||||||
\(805\) | −14.1196 | −0.497651 | ||||||||
\(806\) | 121.707 | 4.28695 | ||||||||
\(807\) | 37.5978 | 1.32350 | ||||||||
\(808\) | 17.4668 | 0.614480 | ||||||||
\(809\) | 10.7127 | 0.376639 | 0.188320 | − | 0.982108i | \(-0.439696\pi\) | ||||
0.188320 | + | 0.982108i | \(0.439696\pi\) | |||||||
\(810\) | −10.4330 | −0.366577 | ||||||||
\(811\) | 52.4782 | 1.84276 | 0.921379 | − | 0.388666i | \(-0.127064\pi\) | ||||
0.921379 | + | 0.388666i | \(0.127064\pi\) | |||||||
\(812\) | −12.6595 | −0.444261 | ||||||||
\(813\) | −17.0737 | −0.598800 | ||||||||
\(814\) | −7.48427 | −0.262324 | ||||||||
\(815\) | −31.8756 | −1.11655 | ||||||||
\(816\) | 22.1957 | 0.777004 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −19.2567 | −0.673294 | ||||||||
\(819\) | −15.9976 | −0.559002 | ||||||||
\(820\) | −12.3177 | −0.430152 | ||||||||
\(821\) | 14.1032 | 0.492205 | 0.246103 | − | 0.969244i | \(-0.420850\pi\) | ||||
0.246103 | + | 0.969244i | \(0.420850\pi\) | |||||||
\(822\) | 35.0562 | 1.22273 | ||||||||
\(823\) | 45.8146 | 1.59700 | 0.798498 | − | 0.601997i | \(-0.205628\pi\) | ||||
0.798498 | + | 0.601997i | \(0.205628\pi\) | |||||||
\(824\) | 5.03923 | 0.175550 | ||||||||
\(825\) | −0.0693596 | −0.00241479 | ||||||||
\(826\) | 0.484271 | 0.0168499 | ||||||||
\(827\) | −38.4655 | −1.33758 | −0.668788 | − | 0.743453i | \(-0.733187\pi\) | ||||
−0.668788 | + | 0.743453i | \(0.733187\pi\) | |||||||
\(828\) | 6.69202 | 0.232564 | ||||||||
\(829\) | −19.2849 | −0.669792 | −0.334896 | − | 0.942255i | \(-0.608701\pi\) | ||||
−0.334896 | + | 0.942255i | \(0.608701\pi\) | |||||||
\(830\) | −49.7362 | −1.72637 | ||||||||
\(831\) | 23.1618 | 0.803475 | ||||||||
\(832\) | 8.30127 | 0.287795 | ||||||||
\(833\) | 14.9095 | 0.516582 | ||||||||
\(834\) | 15.8998 | 0.550564 | ||||||||
\(835\) | −21.2838 | −0.736557 | ||||||||
\(836\) | −6.30260 | −0.217980 | ||||||||
\(837\) | −57.2194 | −1.97779 | ||||||||
\(838\) | −13.3002 | −0.459448 | ||||||||
\(839\) | 5.90946 | 0.204017 | 0.102009 | − | 0.994784i | \(-0.467473\pi\) | ||||
0.102009 | + | 0.994784i | \(0.467473\pi\) | |||||||
\(840\) | 6.43296 | 0.221958 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 17.6450 | 0.608088 | ||||||||
\(843\) | −3.38703 | −0.116655 | ||||||||
\(844\) | −12.8576 | −0.442575 | ||||||||
\(845\) | −66.9807 | −2.30421 | ||||||||
\(846\) | −8.19998 | −0.281921 | ||||||||
\(847\) | 16.4246 | 0.564356 | ||||||||
\(848\) | −55.0538 | −1.89056 | ||||||||
\(849\) | 21.2137 | 0.728053 | ||||||||
\(850\) | 0.317667 | 0.0108959 | ||||||||
\(851\) | 13.5657 | 0.465027 | ||||||||
\(852\) | 5.79358 | 0.198485 | ||||||||
\(853\) | 27.6021 | 0.945077 | 0.472538 | − | 0.881310i | \(-0.343338\pi\) | ||||
0.472538 | + | 0.881310i | \(0.343338\pi\) | |||||||
\(854\) | 2.17629 | 0.0744712 | ||||||||
\(855\) | 14.4330 | 0.493597 | ||||||||
\(856\) | 6.85086 | 0.234157 | ||||||||
\(857\) | 17.0683 | 0.583042 | 0.291521 | − | 0.956564i | \(-0.405839\pi\) | ||||
0.291521 | + | 0.956564i | \(0.405839\pi\) | |||||||
\(858\) | −16.7168 | −0.570701 | ||||||||
\(859\) | −4.80838 | −0.164060 | −0.0820299 | − | 0.996630i | \(-0.526140\pi\) | ||||
−0.0820299 | + | 0.996630i | \(0.526140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.27545 | −0.316107 | ||||||||
\(862\) | −49.2465 | −1.67734 | ||||||||
\(863\) | −54.3909 | −1.85149 | −0.925743 | − | 0.378153i | \(-0.876559\pi\) | ||||
−0.925743 | + | 0.378153i | \(0.876559\pi\) | |||||||
\(864\) | −34.2881 | −1.16651 | ||||||||
\(865\) | −10.7017 | −0.363869 | ||||||||
\(866\) | −5.00538 | −0.170090 | ||||||||
\(867\) | −5.00298 | −0.169910 | ||||||||
\(868\) | −21.7808 | −0.739287 | ||||||||
\(869\) | 0.0693596 | 0.00235286 | ||||||||
\(870\) | 30.2935 | 1.02705 | ||||||||
\(871\) | 13.7259 | 0.465083 | ||||||||
\(872\) | 2.95300 | 0.100001 | ||||||||
\(873\) | −5.06292 | −0.171354 | ||||||||
\(874\) | 29.7463 | 1.00618 | ||||||||
\(875\) | −18.8237 | −0.636357 | ||||||||
\(876\) | −2.22819 | −0.0752837 | ||||||||
\(877\) | −13.4940 | −0.455659 | −0.227829 | − | 0.973701i | \(-0.573163\pi\) | ||||
−0.227829 | + | 0.973701i | \(0.573163\pi\) | |||||||
\(878\) | −17.2664 | −0.582711 | ||||||||
\(879\) | −13.7560 | −0.463979 | ||||||||
\(880\) | −12.6189 | −0.425384 | ||||||||
\(881\) | −35.3564 | −1.19119 | −0.595594 | − | 0.803286i | \(-0.703083\pi\) | ||||
−0.595594 | + | 0.803286i | \(0.703083\pi\) | |||||||
\(882\) | −10.7724 | −0.362726 | ||||||||
\(883\) | 53.6902 | 1.80682 | 0.903410 | − | 0.428778i | \(-0.141056\pi\) | ||||
0.903410 | + | 0.428778i | \(0.141056\pi\) | |||||||
\(884\) | 29.4034 | 0.988944 | ||||||||
\(885\) | −0.445042 | −0.0149599 | ||||||||
\(886\) | −42.8418 | −1.43930 | ||||||||
\(887\) | 9.72156 | 0.326418 | 0.163209 | − | 0.986592i | \(-0.447816\pi\) | ||||
0.163209 | + | 0.986592i | \(0.447816\pi\) | |||||||
\(888\) | −6.18060 | −0.207407 | ||||||||
\(889\) | 34.2174 | 1.14762 | ||||||||
\(890\) | 42.9952 | 1.44120 | ||||||||
\(891\) | 2.92990 | 0.0981555 | ||||||||
\(892\) | −3.53319 | −0.118300 | ||||||||
\(893\) | −13.9981 | −0.468428 | ||||||||
\(894\) | −13.0368 | −0.436017 | ||||||||
\(895\) | 3.70171 | 0.123735 | ||||||||
\(896\) | 17.0653 | 0.570112 | ||||||||
\(897\) | 30.3002 | 1.01169 | ||||||||
\(898\) | −33.0659 | −1.10342 | ||||||||
\(899\) | 61.9383 | 2.06576 | ||||||||
\(900\) | −0.0881460 | −0.00293820 | ||||||||
\(901\) | −40.1715 | −1.33831 | ||||||||
\(902\) | 9.00730 | 0.299910 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.9385 | 0.530108 | ||||||||
\(905\) | −5.11529 | −0.170038 | ||||||||
\(906\) | 16.7385 | 0.556101 | ||||||||
\(907\) | −28.8455 | −0.957798 | −0.478899 | − | 0.877870i | \(-0.658964\pi\) | ||||
−0.478899 | + | 0.877870i | \(0.658964\pi\) | |||||||
\(908\) | 16.2905 | 0.540620 | ||||||||
\(909\) | −18.6015 | −0.616972 | ||||||||
\(910\) | 44.8243 | 1.48591 | ||||||||
\(911\) | −14.3274 | −0.474686 | −0.237343 | − | 0.971426i | \(-0.576277\pi\) | ||||
−0.237343 | + | 0.971426i | \(0.576277\pi\) | |||||||
\(912\) | −27.3763 | −0.906519 | ||||||||
\(913\) | 13.9675 | 0.462256 | ||||||||
\(914\) | 71.7381 | 2.37288 | ||||||||
\(915\) | −2.00000 | −0.0661180 | ||||||||
\(916\) | −22.3411 | −0.738171 | ||||||||
\(917\) | 3.48321 | 0.115026 | ||||||||
\(918\) | −35.9952 | −1.18802 | ||||||||
\(919\) | 42.9077 | 1.41539 | 0.707697 | − | 0.706517i | \(-0.249734\pi\) | ||||
0.707697 | + | 0.706517i | \(0.249734\pi\) | |||||||
\(920\) | 11.3230 | 0.373310 | ||||||||
\(921\) | 19.6963 | 0.649016 | ||||||||
\(922\) | 34.6515 | 1.14119 | ||||||||
\(923\) | −24.3779 | −0.802409 | ||||||||
\(924\) | 2.99164 | 0.0984177 | ||||||||
\(925\) | −0.178685 | −0.00587512 | ||||||||
\(926\) | 26.9541 | 0.885766 | ||||||||
\(927\) | −5.36658 | −0.176262 | ||||||||
\(928\) | 37.1159 | 1.21839 | ||||||||
\(929\) | 19.1919 | 0.629667 | 0.314834 | − | 0.949147i | \(-0.398051\pi\) | ||||
0.314834 | + | 0.949147i | \(0.398051\pi\) | |||||||
\(930\) | 52.1202 | 1.70909 | ||||||||
\(931\) | −18.3894 | −0.602689 | ||||||||
\(932\) | 11.6474 | 0.381524 | ||||||||
\(933\) | −15.4209 | −0.504857 | ||||||||
\(934\) | 46.4728 | 1.52064 | ||||||||
\(935\) | −9.20775 | −0.301126 | ||||||||
\(936\) | 12.8291 | 0.419332 | ||||||||
\(937\) | −35.0767 | −1.14590 | −0.572952 | − | 0.819589i | \(-0.694202\pi\) | ||||
−0.572952 | + | 0.819589i | \(0.694202\pi\) | |||||||
\(938\) | −6.39612 | −0.208841 | ||||||||
\(939\) | 7.27545 | 0.237425 | ||||||||
\(940\) | 8.82371 | 0.287798 | ||||||||
\(941\) | −8.92048 | −0.290799 | −0.145400 | − | 0.989373i | \(-0.546447\pi\) | ||||
−0.145400 | + | 0.989373i | \(0.546447\pi\) | |||||||
\(942\) | 29.6896 | 0.967340 | ||||||||
\(943\) | −16.3263 | −0.531657 | ||||||||
\(944\) | −0.784479 | −0.0255326 | ||||||||
\(945\) | −21.0737 | −0.685527 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.3672 | 0.889314 | 0.444657 | − | 0.895701i | \(-0.353326\pi\) | ||||
0.444657 | + | 0.895701i | \(0.353326\pi\) | |||||||
\(948\) | −0.0948508 | −0.00308061 | ||||||||
\(949\) | 9.37568 | 0.304348 | ||||||||
\(950\) | −0.391813 | −0.0127121 | ||||||||
\(951\) | 32.6316 | 1.05815 | ||||||||
\(952\) | 8.27413 | 0.268166 | ||||||||
\(953\) | 52.1221 | 1.68840 | 0.844200 | − | 0.536028i | \(-0.180076\pi\) | ||||
0.844200 | + | 0.536028i | \(0.180076\pi\) | |||||||
\(954\) | 29.0248 | 0.939711 | ||||||||
\(955\) | −33.7754 | −1.09295 | ||||||||
\(956\) | 9.03013 | 0.292055 | ||||||||
\(957\) | −8.50737 | −0.275004 | ||||||||
\(958\) | 53.5459 | 1.72999 | ||||||||
\(959\) | 26.3980 | 0.852437 | ||||||||
\(960\) | 3.55496 | 0.114736 | ||||||||
\(961\) | 75.5652 | 2.43759 | ||||||||
\(962\) | −43.0659 | −1.38850 | ||||||||
\(963\) | −7.29590 | −0.235107 | ||||||||
\(964\) | 0.137063 | 0.00441451 | ||||||||
\(965\) | −22.1347 | −0.712540 | ||||||||
\(966\) | −14.1196 | −0.454291 | ||||||||
\(967\) | 10.1618 | 0.326782 | 0.163391 | − | 0.986561i | \(-0.447757\pi\) | ||||
0.163391 | + | 0.986561i | \(0.447757\pi\) | |||||||
\(968\) | −13.1715 | −0.423348 | ||||||||
\(969\) | −19.9758 | −0.641716 | ||||||||
\(970\) | 14.1860 | 0.455484 | ||||||||
\(971\) | 7.46250 | 0.239483 | 0.119742 | − | 0.992805i | \(-0.461793\pi\) | ||||
0.119742 | + | 0.992805i | \(0.461793\pi\) | |||||||
\(972\) | 16.7289 | 0.536578 | ||||||||
\(973\) | 11.9729 | 0.383832 | ||||||||
\(974\) | −2.74094 | −0.0878253 | ||||||||
\(975\) | −0.399108 | −0.0127817 | ||||||||
\(976\) | −3.52542 | −0.112846 | ||||||||
\(977\) | −2.22414 | −0.0711567 | −0.0355783 | − | 0.999367i | \(-0.511327\pi\) | ||||
−0.0355783 | + | 0.999367i | \(0.511327\pi\) | |||||||
\(978\) | −31.8756 | −1.01927 | ||||||||
\(979\) | −12.0744 | −0.385900 | ||||||||
\(980\) | 11.5918 | 0.370286 | ||||||||
\(981\) | −3.14483 | −0.100407 | ||||||||
\(982\) | 51.6491 | 1.64819 | ||||||||
\(983\) | 21.5050 | 0.685902 | 0.342951 | − | 0.939353i | \(-0.388573\pi\) | ||||
0.342951 | + | 0.939353i | \(0.388573\pi\) | |||||||
\(984\) | 7.43834 | 0.237126 | ||||||||
\(985\) | −24.6286 | −0.784733 | ||||||||
\(986\) | 38.9638 | 1.24086 | ||||||||
\(987\) | 6.64443 | 0.211495 | ||||||||
\(988\) | −36.2664 | −1.15379 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 6.65279 | 0.211440 | ||||||||
\(991\) | −50.7900 | −1.61340 | −0.806698 | − | 0.590963i | \(-0.798748\pi\) | ||||
−0.806698 | + | 0.590963i | \(0.798748\pi\) | |||||||
\(992\) | 63.8582 | 2.02750 | ||||||||
\(993\) | −22.7778 | −0.722831 | ||||||||
\(994\) | 11.3599 | 0.360314 | ||||||||
\(995\) | −54.7241 | −1.73487 | ||||||||
\(996\) | −19.1008 | −0.605233 | ||||||||
\(997\) | 1.00059 | 0.0316890 | 0.0158445 | − | 0.999874i | \(-0.494956\pi\) | ||||
0.0158445 | + | 0.999874i | \(0.494956\pi\) | |||||||
\(998\) | −37.5090 | −1.18733 | ||||||||
\(999\) | 20.2470 | 0.640586 |
(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 | 1849.2.a.j.1.1 | 3 | ||
43.8 | odd | 14 | 43.2.e.a.21.1 | ✓ | 6 | ||
43.27 | odd | 14 | 43.2.e.a.41.1 | yes | 6 | ||
43.42 | odd | 2 | 1849.2.a.k.1.3 | 3 | |||
129.8 | even | 14 | 387.2.u.c.64.1 | 6 | |||
129.113 | even | 14 | 387.2.u.c.127.1 | 6 | |||
172.27 | even | 14 | 688.2.u.b.385.1 | 6 | |||
172.51 | even | 14 | 688.2.u.b.193.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.e.a.21.1 | ✓ | 6 | 43.8 | odd | 14 | ||
43.2.e.a.41.1 | yes | 6 | 43.27 | odd | 14 | ||
387.2.u.c.64.1 | 6 | 129.8 | even | 14 | |||
387.2.u.c.127.1 | 6 | 129.113 | even | 14 | |||
688.2.u.b.193.1 | 6 | 172.51 | even | 14 | |||
688.2.u.b.385.1 | 6 | 172.27 | even | 14 | |||
1849.2.a.j.1.1 | 3 | 1.1 | even | 1 | trivial | ||
1849.2.a.k.1.3 | 3 | 43.42 | odd | 2 |