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: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | 1.16 | ||
Root | \(2.31259\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.31259 | 1.63525 | 0.817625 | − | 0.575751i | \(-0.195290\pi\) | ||||
0.817625 | + | 0.575751i | \(0.195290\pi\) | |||||||
\(3\) | 2.69989 | 1.55878 | 0.779391 | − | 0.626538i | \(-0.215529\pi\) | ||||
0.779391 | + | 0.626538i | \(0.215529\pi\) | |||||||
\(4\) | 3.34809 | 1.67404 | ||||||||
\(5\) | 2.53973 | 1.13580 | 0.567902 | − | 0.823096i | \(-0.307755\pi\) | ||||
0.567902 | + | 0.823096i | \(0.307755\pi\) | |||||||
\(6\) | 6.24374 | 2.54900 | ||||||||
\(7\) | −2.18729 | −0.826718 | −0.413359 | − | 0.910568i | \(-0.635645\pi\) | ||||
−0.413359 | + | 0.910568i | \(0.635645\pi\) | |||||||
\(8\) | 3.11758 | 1.10223 | ||||||||
\(9\) | 4.28939 | 1.42980 | ||||||||
\(10\) | 5.87337 | 1.85732 | ||||||||
\(11\) | −3.12200 | −0.941318 | −0.470659 | − | 0.882315i | \(-0.655984\pi\) | ||||
−0.470659 | + | 0.882315i | \(0.655984\pi\) | |||||||
\(12\) | 9.03946 | 2.60947 | ||||||||
\(13\) | 3.44204 | 0.954651 | 0.477325 | − | 0.878727i | \(-0.341606\pi\) | ||||
0.477325 | + | 0.878727i | \(0.341606\pi\) | |||||||
\(14\) | −5.05832 | −1.35189 | ||||||||
\(15\) | 6.85700 | 1.77047 | ||||||||
\(16\) | 0.513513 | 0.128378 | ||||||||
\(17\) | −2.33435 | −0.566163 | −0.283081 | − | 0.959096i | \(-0.591357\pi\) | ||||
−0.283081 | + | 0.959096i | \(0.591357\pi\) | |||||||
\(18\) | 9.91963 | 2.33808 | ||||||||
\(19\) | 3.38242 | 0.775979 | 0.387990 | − | 0.921664i | \(-0.373170\pi\) | ||||
0.387990 | + | 0.921664i | \(0.373170\pi\) | |||||||
\(20\) | 8.50325 | 1.90138 | ||||||||
\(21\) | −5.90544 | −1.28867 | ||||||||
\(22\) | −7.21991 | −1.53929 | ||||||||
\(23\) | −6.58244 | −1.37253 | −0.686267 | − | 0.727350i | \(-0.740752\pi\) | ||||
−0.686267 | + | 0.727350i | \(0.740752\pi\) | |||||||
\(24\) | 8.41711 | 1.71814 | ||||||||
\(25\) | 1.45025 | 0.290049 | ||||||||
\(26\) | 7.96004 | 1.56109 | ||||||||
\(27\) | 3.48122 | 0.669961 | ||||||||
\(28\) | −7.32324 | −1.38396 | ||||||||
\(29\) | −5.41020 | −1.00465 | −0.502325 | − | 0.864679i | \(-0.667522\pi\) | ||||
−0.502325 | + | 0.864679i | \(0.667522\pi\) | |||||||
\(30\) | 15.8574 | 2.89516 | ||||||||
\(31\) | 2.13081 | 0.382705 | 0.191353 | − | 0.981521i | \(-0.438713\pi\) | ||||
0.191353 | + | 0.981521i | \(0.438713\pi\) | |||||||
\(32\) | −5.04761 | −0.892299 | ||||||||
\(33\) | −8.42904 | −1.46731 | ||||||||
\(34\) | −5.39840 | −0.925818 | ||||||||
\(35\) | −5.55514 | −0.938990 | ||||||||
\(36\) | 14.3613 | 2.39354 | ||||||||
\(37\) | −3.47929 | −0.571991 | −0.285996 | − | 0.958231i | \(-0.592324\pi\) | ||||
−0.285996 | + | 0.958231i | \(0.592324\pi\) | |||||||
\(38\) | 7.82215 | 1.26892 | ||||||||
\(39\) | 9.29313 | 1.48809 | ||||||||
\(40\) | 7.91782 | 1.25192 | ||||||||
\(41\) | 2.13473 | 0.333388 | 0.166694 | − | 0.986009i | \(-0.446691\pi\) | ||||
0.166694 | + | 0.986009i | \(0.446691\pi\) | |||||||
\(42\) | −13.6569 | −2.10730 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −10.4527 | −1.57581 | ||||||||
\(45\) | 10.8939 | 1.62397 | ||||||||
\(46\) | −15.2225 | −2.24444 | ||||||||
\(47\) | −1.16939 | −0.170573 | −0.0852867 | − | 0.996356i | \(-0.527181\pi\) | ||||
−0.0852867 | + | 0.996356i | \(0.527181\pi\) | |||||||
\(48\) | 1.38643 | 0.200114 | ||||||||
\(49\) | −2.21576 | −0.316537 | ||||||||
\(50\) | 3.35383 | 0.474304 | ||||||||
\(51\) | −6.30248 | −0.882523 | ||||||||
\(52\) | 11.5243 | 1.59813 | ||||||||
\(53\) | 10.4019 | 1.42880 | 0.714402 | − | 0.699735i | \(-0.246699\pi\) | ||||
0.714402 | + | 0.699735i | \(0.246699\pi\) | |||||||
\(54\) | 8.05065 | 1.09555 | ||||||||
\(55\) | −7.92904 | −1.06915 | ||||||||
\(56\) | −6.81905 | −0.911234 | ||||||||
\(57\) | 9.13214 | 1.20958 | ||||||||
\(58\) | −12.5116 | −1.64285 | ||||||||
\(59\) | 6.14435 | 0.799926 | 0.399963 | − | 0.916531i | \(-0.369023\pi\) | ||||
0.399963 | + | 0.916531i | \(0.369023\pi\) | |||||||
\(60\) | 22.9578 | 2.96384 | ||||||||
\(61\) | −2.50141 | −0.320272 | −0.160136 | − | 0.987095i | \(-0.551193\pi\) | ||||
−0.160136 | + | 0.987095i | \(0.551193\pi\) | |||||||
\(62\) | 4.92770 | 0.625819 | ||||||||
\(63\) | −9.38216 | −1.18204 | ||||||||
\(64\) | −12.7001 | −1.58751 | ||||||||
\(65\) | 8.74187 | 1.08430 | ||||||||
\(66\) | −19.4929 | −2.39942 | ||||||||
\(67\) | 10.3393 | 1.26315 | 0.631575 | − | 0.775315i | \(-0.282409\pi\) | ||||
0.631575 | + | 0.775315i | \(0.282409\pi\) | |||||||
\(68\) | −7.81560 | −0.947781 | ||||||||
\(69\) | −17.7718 | −2.13948 | ||||||||
\(70\) | −12.8468 | −1.53548 | ||||||||
\(71\) | 11.3311 | 1.34476 | 0.672378 | − | 0.740208i | \(-0.265273\pi\) | ||||
0.672378 | + | 0.740208i | \(0.265273\pi\) | |||||||
\(72\) | 13.3725 | 1.57597 | ||||||||
\(73\) | −8.36206 | −0.978705 | −0.489352 | − | 0.872086i | \(-0.662767\pi\) | ||||
−0.489352 | + | 0.872086i | \(0.662767\pi\) | |||||||
\(74\) | −8.04617 | −0.935349 | ||||||||
\(75\) | 3.91551 | 0.452124 | ||||||||
\(76\) | 11.3246 | 1.29902 | ||||||||
\(77\) | 6.82872 | 0.778205 | ||||||||
\(78\) | 21.4912 | 2.43340 | ||||||||
\(79\) | 9.81573 | 1.10436 | 0.552178 | − | 0.833726i | \(-0.313797\pi\) | ||||
0.552178 | + | 0.833726i | \(0.313797\pi\) | |||||||
\(80\) | 1.30419 | 0.145812 | ||||||||
\(81\) | −3.46928 | −0.385475 | ||||||||
\(82\) | 4.93675 | 0.545173 | ||||||||
\(83\) | 2.86913 | 0.314928 | 0.157464 | − | 0.987525i | \(-0.449668\pi\) | ||||
0.157464 | + | 0.987525i | \(0.449668\pi\) | |||||||
\(84\) | −19.7719 | −2.15729 | ||||||||
\(85\) | −5.92862 | −0.643049 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.6069 | −1.56603 | ||||||||
\(88\) | −9.73307 | −1.03755 | ||||||||
\(89\) | 14.9948 | 1.58944 | 0.794722 | − | 0.606973i | \(-0.207617\pi\) | ||||
0.794722 | + | 0.606973i | \(0.207617\pi\) | |||||||
\(90\) | 25.1932 | 2.65560 | ||||||||
\(91\) | −7.52875 | −0.789227 | ||||||||
\(92\) | −22.0386 | −2.29768 | ||||||||
\(93\) | 5.75295 | 0.596553 | ||||||||
\(94\) | −2.70433 | −0.278930 | ||||||||
\(95\) | 8.59043 | 0.881360 | ||||||||
\(96\) | −13.6280 | −1.39090 | ||||||||
\(97\) | −4.22212 | −0.428691 | −0.214346 | − | 0.976758i | \(-0.568762\pi\) | ||||
−0.214346 | + | 0.976758i | \(0.568762\pi\) | |||||||
\(98\) | −5.12414 | −0.517617 | ||||||||
\(99\) | −13.3915 | −1.34589 | ||||||||
\(100\) | 4.85555 | 0.485555 | ||||||||
\(101\) | 0.0929930 | 0.00925315 | 0.00462658 | − | 0.999989i | \(-0.498527\pi\) | ||||
0.00462658 | + | 0.999989i | \(0.498527\pi\) | |||||||
\(102\) | −14.5751 | −1.44315 | ||||||||
\(103\) | −14.3782 | −1.41672 | −0.708361 | − | 0.705851i | \(-0.750565\pi\) | ||||
−0.708361 | + | 0.705851i | \(0.750565\pi\) | |||||||
\(104\) | 10.7308 | 1.05224 | ||||||||
\(105\) | −14.9982 | −1.46368 | ||||||||
\(106\) | 24.0553 | 2.33645 | ||||||||
\(107\) | 12.6274 | 1.22074 | 0.610369 | − | 0.792117i | \(-0.291021\pi\) | ||||
0.610369 | + | 0.792117i | \(0.291021\pi\) | |||||||
\(108\) | 11.6554 | 1.12154 | ||||||||
\(109\) | 14.4274 | 1.38189 | 0.690946 | − | 0.722906i | \(-0.257194\pi\) | ||||
0.690946 | + | 0.722906i | \(0.257194\pi\) | |||||||
\(110\) | −18.3367 | −1.74833 | ||||||||
\(111\) | −9.39368 | −0.891609 | ||||||||
\(112\) | −1.12320 | −0.106133 | ||||||||
\(113\) | −12.2090 | −1.14853 | −0.574265 | − | 0.818670i | \(-0.694712\pi\) | ||||
−0.574265 | + | 0.818670i | \(0.694712\pi\) | |||||||
\(114\) | 21.1189 | 1.97797 | ||||||||
\(115\) | −16.7176 | −1.55893 | ||||||||
\(116\) | −18.1138 | −1.68183 | ||||||||
\(117\) | 14.7643 | 1.36496 | ||||||||
\(118\) | 14.2094 | 1.30808 | ||||||||
\(119\) | 5.10590 | 0.468057 | ||||||||
\(120\) | 21.3772 | 1.95146 | ||||||||
\(121\) | −1.25313 | −0.113921 | ||||||||
\(122\) | −5.78474 | −0.523725 | ||||||||
\(123\) | 5.76352 | 0.519679 | ||||||||
\(124\) | 7.13414 | 0.640665 | ||||||||
\(125\) | −9.01543 | −0.806364 | ||||||||
\(126\) | −21.6971 | −1.93293 | ||||||||
\(127\) | 6.77907 | 0.601545 | 0.300773 | − | 0.953696i | \(-0.402755\pi\) | ||||
0.300773 | + | 0.953696i | \(0.402755\pi\) | |||||||
\(128\) | −19.2749 | −1.70368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 20.2164 | 1.77309 | ||||||||
\(131\) | 2.62055 | 0.228958 | 0.114479 | − | 0.993426i | \(-0.463480\pi\) | ||||
0.114479 | + | 0.993426i | \(0.463480\pi\) | |||||||
\(132\) | −28.2212 | −2.45634 | ||||||||
\(133\) | −7.39833 | −0.641516 | ||||||||
\(134\) | 23.9107 | 2.06557 | ||||||||
\(135\) | 8.84138 | 0.760944 | ||||||||
\(136\) | −7.27751 | −0.624041 | ||||||||
\(137\) | −3.76383 | −0.321566 | −0.160783 | − | 0.986990i | \(-0.551402\pi\) | ||||
−0.160783 | + | 0.986990i | \(0.551402\pi\) | |||||||
\(138\) | −41.0990 | −3.49858 | ||||||||
\(139\) | −18.3182 | −1.55373 | −0.776863 | − | 0.629670i | \(-0.783190\pi\) | ||||
−0.776863 | + | 0.629670i | \(0.783190\pi\) | |||||||
\(140\) | −18.5991 | −1.57191 | ||||||||
\(141\) | −3.15723 | −0.265887 | ||||||||
\(142\) | 26.2043 | 2.19901 | ||||||||
\(143\) | −10.7460 | −0.898630 | ||||||||
\(144\) | 2.20266 | 0.183555 | ||||||||
\(145\) | −13.7405 | −1.14108 | ||||||||
\(146\) | −19.3380 | −1.60043 | ||||||||
\(147\) | −5.98229 | −0.493411 | ||||||||
\(148\) | −11.6490 | −0.957538 | ||||||||
\(149\) | 12.2136 | 1.00058 | 0.500288 | − | 0.865859i | \(-0.333227\pi\) | ||||
0.500288 | + | 0.865859i | \(0.333227\pi\) | |||||||
\(150\) | 9.05497 | 0.739335 | ||||||||
\(151\) | 8.48724 | 0.690681 | 0.345341 | − | 0.938477i | \(-0.387763\pi\) | ||||
0.345341 | + | 0.938477i | \(0.387763\pi\) | |||||||
\(152\) | 10.5449 | 0.855308 | ||||||||
\(153\) | −10.0129 | −0.809498 | ||||||||
\(154\) | 15.7920 | 1.27256 | ||||||||
\(155\) | 5.41169 | 0.434678 | ||||||||
\(156\) | 31.1142 | 2.49113 | ||||||||
\(157\) | −19.9629 | −1.59321 | −0.796605 | − | 0.604500i | \(-0.793373\pi\) | ||||
−0.796605 | + | 0.604500i | \(0.793373\pi\) | |||||||
\(158\) | 22.6998 | 1.80590 | ||||||||
\(159\) | 28.0838 | 2.22719 | ||||||||
\(160\) | −12.8196 | −1.01348 | ||||||||
\(161\) | 14.3977 | 1.13470 | ||||||||
\(162\) | −8.02303 | −0.630348 | ||||||||
\(163\) | 15.4322 | 1.20874 | 0.604371 | − | 0.796703i | \(-0.293424\pi\) | ||||
0.604371 | + | 0.796703i | \(0.293424\pi\) | |||||||
\(164\) | 7.14725 | 0.558106 | ||||||||
\(165\) | −21.4075 | −1.66657 | ||||||||
\(166\) | 6.63514 | 0.514986 | ||||||||
\(167\) | 14.5053 | 1.12246 | 0.561228 | − | 0.827661i | \(-0.310329\pi\) | ||||
0.561228 | + | 0.827661i | \(0.310329\pi\) | |||||||
\(168\) | −18.4107 | −1.42041 | ||||||||
\(169\) | −1.15235 | −0.0886420 | ||||||||
\(170\) | −13.7105 | −1.05155 | ||||||||
\(171\) | 14.5085 | 1.10949 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.57561 | −0.271849 | −0.135924 | − | 0.990719i | \(-0.543400\pi\) | ||||
−0.135924 | + | 0.990719i | \(0.543400\pi\) | |||||||
\(174\) | −33.7799 | −2.56085 | ||||||||
\(175\) | −3.17211 | −0.239789 | ||||||||
\(176\) | −1.60319 | −0.120845 | ||||||||
\(177\) | 16.5890 | 1.24691 | ||||||||
\(178\) | 34.6768 | 2.59914 | ||||||||
\(179\) | −2.36482 | −0.176755 | −0.0883776 | − | 0.996087i | \(-0.528168\pi\) | ||||
−0.0883776 | + | 0.996087i | \(0.528168\pi\) | |||||||
\(180\) | 36.4738 | 2.71860 | ||||||||
\(181\) | −13.0290 | −0.968436 | −0.484218 | − | 0.874947i | \(-0.660896\pi\) | ||||
−0.484218 | + | 0.874947i | \(0.660896\pi\) | |||||||
\(182\) | −17.4109 | −1.29058 | ||||||||
\(183\) | −6.75352 | −0.499234 | ||||||||
\(184\) | −20.5213 | −1.51285 | ||||||||
\(185\) | −8.83646 | −0.649670 | ||||||||
\(186\) | 13.3042 | 0.975514 | ||||||||
\(187\) | 7.28783 | 0.532939 | ||||||||
\(188\) | −3.91523 | −0.285547 | ||||||||
\(189\) | −7.61445 | −0.553869 | ||||||||
\(190\) | 19.8662 | 1.44124 | ||||||||
\(191\) | −3.73795 | −0.270469 | −0.135234 | − | 0.990814i | \(-0.543179\pi\) | ||||
−0.135234 | + | 0.990814i | \(0.543179\pi\) | |||||||
\(192\) | −34.2888 | −2.47458 | ||||||||
\(193\) | −16.0669 | −1.15652 | −0.578260 | − | 0.815853i | \(-0.696268\pi\) | ||||
−0.578260 | + | 0.815853i | \(0.696268\pi\) | |||||||
\(194\) | −9.76404 | −0.701017 | ||||||||
\(195\) | 23.6021 | 1.69018 | ||||||||
\(196\) | −7.41854 | −0.529896 | ||||||||
\(197\) | −20.2217 | −1.44074 | −0.720368 | − | 0.693592i | \(-0.756027\pi\) | ||||
−0.720368 | + | 0.693592i | \(0.756027\pi\) | |||||||
\(198\) | −30.9690 | −2.20087 | ||||||||
\(199\) | 9.28127 | 0.657932 | 0.328966 | − | 0.944342i | \(-0.393300\pi\) | ||||
0.328966 | + | 0.944342i | \(0.393300\pi\) | |||||||
\(200\) | 4.52126 | 0.319701 | ||||||||
\(201\) | 27.9150 | 1.96897 | ||||||||
\(202\) | 0.215055 | 0.0151312 | ||||||||
\(203\) | 11.8337 | 0.830562 | ||||||||
\(204\) | −21.1012 | −1.47738 | ||||||||
\(205\) | 5.42164 | 0.378664 | ||||||||
\(206\) | −33.2508 | −2.31669 | ||||||||
\(207\) | −28.2347 | −1.96245 | ||||||||
\(208\) | 1.76753 | 0.122556 | ||||||||
\(209\) | −10.5599 | −0.730443 | ||||||||
\(210\) | −34.6848 | −2.39348 | ||||||||
\(211\) | 10.0993 | 0.695262 | 0.347631 | − | 0.937631i | \(-0.386986\pi\) | ||||
0.347631 | + | 0.937631i | \(0.386986\pi\) | |||||||
\(212\) | 34.8263 | 2.39188 | ||||||||
\(213\) | 30.5927 | 2.09618 | ||||||||
\(214\) | 29.2021 | 1.99621 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 10.8530 | 0.738451 | ||||||||
\(217\) | −4.66071 | −0.316389 | ||||||||
\(218\) | 33.3647 | 2.25974 | ||||||||
\(219\) | −22.5766 | −1.52559 | ||||||||
\(220\) | −26.5471 | −1.78981 | ||||||||
\(221\) | −8.03492 | −0.540488 | ||||||||
\(222\) | −21.7238 | −1.45800 | ||||||||
\(223\) | 10.7183 | 0.717753 | 0.358876 | − | 0.933385i | \(-0.383160\pi\) | ||||
0.358876 | + | 0.933385i | \(0.383160\pi\) | |||||||
\(224\) | 11.0406 | 0.737680 | ||||||||
\(225\) | 6.22068 | 0.414712 | ||||||||
\(226\) | −28.2345 | −1.87813 | ||||||||
\(227\) | 16.9907 | 1.12771 | 0.563856 | − | 0.825873i | \(-0.309317\pi\) | ||||
0.563856 | + | 0.825873i | \(0.309317\pi\) | |||||||
\(228\) | 30.5752 | 2.02489 | ||||||||
\(229\) | −1.16971 | −0.0772965 | −0.0386482 | − | 0.999253i | \(-0.512305\pi\) | ||||
−0.0386482 | + | 0.999253i | \(0.512305\pi\) | |||||||
\(230\) | −38.6611 | −2.54924 | ||||||||
\(231\) | 18.4368 | 1.21305 | ||||||||
\(232\) | −16.8667 | −1.10735 | ||||||||
\(233\) | −18.6761 | −1.22351 | −0.611754 | − | 0.791048i | \(-0.709536\pi\) | ||||
−0.611754 | + | 0.791048i | \(0.709536\pi\) | |||||||
\(234\) | 34.1438 | 2.23205 | ||||||||
\(235\) | −2.96994 | −0.193738 | ||||||||
\(236\) | 20.5718 | 1.33911 | ||||||||
\(237\) | 26.5014 | 1.72145 | ||||||||
\(238\) | 11.8079 | 0.765390 | ||||||||
\(239\) | 15.8598 | 1.02589 | 0.512944 | − | 0.858422i | \(-0.328555\pi\) | ||||
0.512944 | + | 0.858422i | \(0.328555\pi\) | |||||||
\(240\) | 3.52116 | 0.227290 | ||||||||
\(241\) | 3.07702 | 0.198209 | 0.0991043 | − | 0.995077i | \(-0.468402\pi\) | ||||
0.0991043 | + | 0.995077i | \(0.468402\pi\) | |||||||
\(242\) | −2.89798 | −0.186289 | ||||||||
\(243\) | −19.8103 | −1.27083 | ||||||||
\(244\) | −8.37493 | −0.536150 | ||||||||
\(245\) | −5.62743 | −0.359523 | ||||||||
\(246\) | 13.3287 | 0.849806 | ||||||||
\(247\) | 11.6424 | 0.740789 | ||||||||
\(248\) | 6.64297 | 0.421829 | ||||||||
\(249\) | 7.74634 | 0.490904 | ||||||||
\(250\) | −20.8490 | −1.31861 | ||||||||
\(251\) | −11.6194 | −0.733412 | −0.366706 | − | 0.930337i | \(-0.619515\pi\) | ||||
−0.366706 | + | 0.930337i | \(0.619515\pi\) | |||||||
\(252\) | −31.4123 | −1.97879 | ||||||||
\(253\) | 20.5504 | 1.29199 | ||||||||
\(254\) | 15.6772 | 0.983677 | ||||||||
\(255\) | −16.0066 | −1.00237 | ||||||||
\(256\) | −19.1749 | −1.19843 | ||||||||
\(257\) | 24.8591 | 1.55067 | 0.775335 | − | 0.631550i | \(-0.217581\pi\) | ||||
0.775335 | + | 0.631550i | \(0.217581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.61021 | 0.472876 | ||||||||
\(260\) | 29.2685 | 1.81516 | ||||||||
\(261\) | −23.2065 | −1.43645 | ||||||||
\(262\) | 6.06026 | 0.374404 | ||||||||
\(263\) | −3.69195 | −0.227655 | −0.113828 | − | 0.993501i | \(-0.536311\pi\) | ||||
−0.113828 | + | 0.993501i | \(0.536311\pi\) | |||||||
\(264\) | −26.2782 | −1.61731 | ||||||||
\(265\) | 26.4179 | 1.62284 | ||||||||
\(266\) | −17.1093 | −1.04904 | ||||||||
\(267\) | 40.4842 | 2.47760 | ||||||||
\(268\) | 34.6170 | 2.11457 | ||||||||
\(269\) | 22.2263 | 1.35516 | 0.677581 | − | 0.735449i | \(-0.263029\pi\) | ||||
0.677581 | + | 0.735449i | \(0.263029\pi\) | |||||||
\(270\) | 20.4465 | 1.24433 | ||||||||
\(271\) | 7.29626 | 0.443216 | 0.221608 | − | 0.975136i | \(-0.428869\pi\) | ||||
0.221608 | + | 0.975136i | \(0.428869\pi\) | |||||||
\(272\) | −1.19872 | −0.0726830 | ||||||||
\(273\) | −20.3268 | −1.23023 | ||||||||
\(274\) | −8.70421 | −0.525841 | ||||||||
\(275\) | −4.52767 | −0.273029 | ||||||||
\(276\) | −59.5017 | −3.58158 | ||||||||
\(277\) | −7.37520 | −0.443133 | −0.221566 | − | 0.975145i | \(-0.571117\pi\) | ||||
−0.221566 | + | 0.975145i | \(0.571117\pi\) | |||||||
\(278\) | −42.3624 | −2.54073 | ||||||||
\(279\) | 9.13989 | 0.547191 | ||||||||
\(280\) | −17.3186 | −1.03498 | ||||||||
\(281\) | −19.1235 | −1.14081 | −0.570407 | − | 0.821362i | \(-0.693215\pi\) | ||||
−0.570407 | + | 0.821362i | \(0.693215\pi\) | |||||||
\(282\) | −7.30138 | −0.434791 | ||||||||
\(283\) | 19.7995 | 1.17696 | 0.588480 | − | 0.808512i | \(-0.299727\pi\) | ||||
0.588480 | + | 0.808512i | \(0.299727\pi\) | |||||||
\(284\) | 37.9375 | 2.25118 | ||||||||
\(285\) | 23.1932 | 1.37385 | ||||||||
\(286\) | −24.8512 | −1.46948 | ||||||||
\(287\) | −4.66927 | −0.275618 | ||||||||
\(288\) | −21.6512 | −1.27581 | ||||||||
\(289\) | −11.5508 | −0.679460 | ||||||||
\(290\) | −31.7761 | −1.86596 | ||||||||
\(291\) | −11.3992 | −0.668235 | ||||||||
\(292\) | −27.9969 | −1.63839 | ||||||||
\(293\) | 10.9778 | 0.641329 | 0.320664 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320664 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(294\) | −13.8346 | −0.806851 | ||||||||
\(295\) | 15.6050 | 0.908558 | ||||||||
\(296\) | −10.8469 | −0.630466 | ||||||||
\(297\) | −10.8684 | −0.630647 | ||||||||
\(298\) | 28.2451 | 1.63619 | ||||||||
\(299\) | −22.6570 | −1.31029 | ||||||||
\(300\) | 13.1095 | 0.756875 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 19.6275 | 1.12944 | ||||||||
\(303\) | 0.251071 | 0.0144236 | ||||||||
\(304\) | 1.73691 | 0.0996189 | ||||||||
\(305\) | −6.35291 | −0.363766 | ||||||||
\(306\) | −23.1559 | −1.32373 | ||||||||
\(307\) | −0.809531 | −0.0462024 | −0.0231012 | − | 0.999733i | \(-0.507354\pi\) | ||||
−0.0231012 | + | 0.999733i | \(0.507354\pi\) | |||||||
\(308\) | 22.8631 | 1.30275 | ||||||||
\(309\) | −38.8194 | −2.20836 | ||||||||
\(310\) | 12.5150 | 0.710807 | ||||||||
\(311\) | −10.8980 | −0.617971 | −0.308986 | − | 0.951067i | \(-0.599989\pi\) | ||||
−0.308986 | + | 0.951067i | \(0.599989\pi\) | |||||||
\(312\) | 28.9720 | 1.64022 | ||||||||
\(313\) | −16.0839 | −0.909113 | −0.454557 | − | 0.890718i | \(-0.650202\pi\) | ||||
−0.454557 | + | 0.890718i | \(0.650202\pi\) | |||||||
\(314\) | −46.1660 | −2.60530 | ||||||||
\(315\) | −23.8282 | −1.34257 | ||||||||
\(316\) | 32.8639 | 1.84874 | ||||||||
\(317\) | −1.34177 | −0.0753611 | −0.0376805 | − | 0.999290i | \(-0.511997\pi\) | ||||
−0.0376805 | + | 0.999290i | \(0.511997\pi\) | |||||||
\(318\) | 64.9465 | 3.64202 | ||||||||
\(319\) | 16.8906 | 0.945694 | ||||||||
\(320\) | −32.2548 | −1.80310 | ||||||||
\(321\) | 34.0926 | 1.90286 | ||||||||
\(322\) | 33.2960 | 1.85552 | ||||||||
\(323\) | −7.89573 | −0.439330 | ||||||||
\(324\) | −11.6154 | −0.645302 | ||||||||
\(325\) | 4.99181 | 0.276896 | ||||||||
\(326\) | 35.6884 | 1.97660 | ||||||||
\(327\) | 38.9523 | 2.15407 | ||||||||
\(328\) | 6.65517 | 0.367471 | ||||||||
\(329\) | 2.55780 | 0.141016 | ||||||||
\(330\) | −49.5069 | −2.72527 | ||||||||
\(331\) | 31.0480 | 1.70655 | 0.853276 | − | 0.521459i | \(-0.174612\pi\) | ||||
0.853276 | + | 0.521459i | \(0.174612\pi\) | |||||||
\(332\) | 9.60611 | 0.527204 | ||||||||
\(333\) | −14.9240 | −0.817832 | ||||||||
\(334\) | 33.5449 | 1.83550 | ||||||||
\(335\) | 26.2591 | 1.43469 | ||||||||
\(336\) | −3.03252 | −0.165438 | ||||||||
\(337\) | 17.5883 | 0.958094 | 0.479047 | − | 0.877789i | \(-0.340982\pi\) | ||||
0.479047 | + | 0.877789i | \(0.340982\pi\) | |||||||
\(338\) | −2.66491 | −0.144952 | ||||||||
\(339\) | −32.9630 | −1.79031 | ||||||||
\(340\) | −19.8495 | −1.07649 | ||||||||
\(341\) | −6.65239 | −0.360247 | ||||||||
\(342\) | 33.5523 | 1.81430 | ||||||||
\(343\) | 20.1575 | 1.08841 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −45.1357 | −2.43003 | ||||||||
\(346\) | −8.26894 | −0.444541 | ||||||||
\(347\) | 10.3838 | 0.557430 | 0.278715 | − | 0.960374i | \(-0.410092\pi\) | ||||
0.278715 | + | 0.960374i | \(0.410092\pi\) | |||||||
\(348\) | −48.9053 | −2.62160 | ||||||||
\(349\) | −3.01731 | −0.161513 | −0.0807564 | − | 0.996734i | \(-0.525734\pi\) | ||||
−0.0807564 | + | 0.996734i | \(0.525734\pi\) | |||||||
\(350\) | −7.33581 | −0.392115 | ||||||||
\(351\) | 11.9825 | 0.639579 | ||||||||
\(352\) | 15.7586 | 0.839937 | ||||||||
\(353\) | −27.2819 | −1.45207 | −0.726034 | − | 0.687659i | \(-0.758638\pi\) | ||||
−0.726034 | + | 0.687659i | \(0.758638\pi\) | |||||||
\(354\) | 38.3637 | 2.03901 | ||||||||
\(355\) | 28.7780 | 1.52738 | ||||||||
\(356\) | 50.2039 | 2.66080 | ||||||||
\(357\) | 13.7854 | 0.729598 | ||||||||
\(358\) | −5.46887 | −0.289039 | ||||||||
\(359\) | −11.0931 | −0.585470 | −0.292735 | − | 0.956194i | \(-0.594565\pi\) | ||||
−0.292735 | + | 0.956194i | \(0.594565\pi\) | |||||||
\(360\) | 33.9626 | 1.78999 | ||||||||
\(361\) | −7.55927 | −0.397856 | ||||||||
\(362\) | −30.1307 | −1.58364 | ||||||||
\(363\) | −3.38331 | −0.177578 | ||||||||
\(364\) | −25.2069 | −1.32120 | ||||||||
\(365\) | −21.2374 | −1.11162 | ||||||||
\(366\) | −15.6181 | −0.816373 | ||||||||
\(367\) | −27.3444 | −1.42737 | −0.713683 | − | 0.700469i | \(-0.752974\pi\) | ||||
−0.713683 | + | 0.700469i | \(0.752974\pi\) | |||||||
\(368\) | −3.38017 | −0.176203 | ||||||||
\(369\) | 9.15668 | 0.476678 | ||||||||
\(370\) | −20.4351 | −1.06237 | ||||||||
\(371\) | −22.7519 | −1.18122 | ||||||||
\(372\) | 19.2614 | 0.998656 | ||||||||
\(373\) | −1.07805 | −0.0558192 | −0.0279096 | − | 0.999610i | \(-0.508885\pi\) | ||||
−0.0279096 | + | 0.999610i | \(0.508885\pi\) | |||||||
\(374\) | 16.8538 | 0.871488 | ||||||||
\(375\) | −24.3406 | −1.25695 | ||||||||
\(376\) | −3.64567 | −0.188011 | ||||||||
\(377\) | −18.6221 | −0.959089 | ||||||||
\(378\) | −17.6091 | −0.905715 | ||||||||
\(379\) | −3.02350 | −0.155307 | −0.0776534 | − | 0.996980i | \(-0.524743\pi\) | ||||
−0.0776534 | + | 0.996980i | \(0.524743\pi\) | |||||||
\(380\) | 28.7615 | 1.47543 | ||||||||
\(381\) | 18.3027 | 0.937677 | ||||||||
\(382\) | −8.64436 | −0.442284 | ||||||||
\(383\) | −20.1617 | −1.03022 | −0.515108 | − | 0.857125i | \(-0.672248\pi\) | ||||
−0.515108 | + | 0.857125i | \(0.672248\pi\) | |||||||
\(384\) | −52.0401 | −2.65566 | ||||||||
\(385\) | 17.3431 | 0.883888 | ||||||||
\(386\) | −37.1562 | −1.89120 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.1360 | −0.717647 | ||||||||
\(389\) | 9.10714 | 0.461750 | 0.230875 | − | 0.972983i | \(-0.425841\pi\) | ||||
0.230875 | + | 0.972983i | \(0.425841\pi\) | |||||||
\(390\) | 54.5820 | 2.76387 | ||||||||
\(391\) | 15.3657 | 0.777077 | ||||||||
\(392\) | −6.90779 | −0.348896 | ||||||||
\(393\) | 7.07518 | 0.356896 | ||||||||
\(394\) | −46.7646 | −2.35596 | ||||||||
\(395\) | 24.9293 | 1.25433 | ||||||||
\(396\) | −44.8358 | −2.25309 | ||||||||
\(397\) | −23.8136 | −1.19517 | −0.597586 | − | 0.801805i | \(-0.703873\pi\) | ||||
−0.597586 | + | 0.801805i | \(0.703873\pi\) | |||||||
\(398\) | 21.4638 | 1.07588 | ||||||||
\(399\) | −19.9747 | −0.999984 | ||||||||
\(400\) | 0.744721 | 0.0372361 | ||||||||
\(401\) | 5.89688 | 0.294476 | 0.147238 | − | 0.989101i | \(-0.452962\pi\) | ||||
0.147238 | + | 0.989101i | \(0.452962\pi\) | |||||||
\(402\) | 64.5561 | 3.21977 | ||||||||
\(403\) | 7.33434 | 0.365350 | ||||||||
\(404\) | 0.311349 | 0.0154902 | ||||||||
\(405\) | −8.81104 | −0.437824 | ||||||||
\(406\) | 27.3665 | 1.35818 | ||||||||
\(407\) | 10.8623 | 0.538425 | ||||||||
\(408\) | −19.6485 | −0.972744 | ||||||||
\(409\) | −28.0492 | −1.38694 | −0.693471 | − | 0.720485i | \(-0.743919\pi\) | ||||
−0.693471 | + | 0.720485i | \(0.743919\pi\) | |||||||
\(410\) | 12.5380 | 0.619210 | ||||||||
\(411\) | −10.1619 | −0.501251 | ||||||||
\(412\) | −48.1393 | −2.37165 | ||||||||
\(413\) | −13.4395 | −0.661313 | ||||||||
\(414\) | −65.2953 | −3.20909 | ||||||||
\(415\) | 7.28683 | 0.357697 | ||||||||
\(416\) | −17.3741 | −0.851834 | ||||||||
\(417\) | −49.4570 | −2.42192 | ||||||||
\(418\) | −24.4207 | −1.19446 | ||||||||
\(419\) | 18.6673 | 0.911957 | 0.455979 | − | 0.889991i | \(-0.349289\pi\) | ||||
0.455979 | + | 0.889991i | \(0.349289\pi\) | |||||||
\(420\) | −50.2154 | −2.45026 | ||||||||
\(421\) | −29.7726 | −1.45103 | −0.725514 | − | 0.688208i | \(-0.758398\pi\) | ||||
−0.725514 | + | 0.688208i | \(0.758398\pi\) | |||||||
\(422\) | 23.3555 | 1.13693 | ||||||||
\(423\) | −5.01598 | −0.243886 | ||||||||
\(424\) | 32.4286 | 1.57487 | ||||||||
\(425\) | −3.38538 | −0.164215 | ||||||||
\(426\) | 70.7485 | 3.42778 | ||||||||
\(427\) | 5.47131 | 0.264775 | ||||||||
\(428\) | 42.2777 | 2.04357 | ||||||||
\(429\) | −29.0131 | −1.40077 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.00624 | −0.241142 | −0.120571 | − | 0.992705i | \(-0.538473\pi\) | ||||
−0.120571 | + | 0.992705i | \(0.538473\pi\) | |||||||
\(432\) | 1.78765 | 0.0860085 | ||||||||
\(433\) | 11.6589 | 0.560289 | 0.280145 | − | 0.959958i | \(-0.409618\pi\) | ||||
0.280145 | + | 0.959958i | \(0.409618\pi\) | |||||||
\(434\) | −10.7783 | −0.517376 | ||||||||
\(435\) | −37.0977 | −1.77870 | ||||||||
\(436\) | 48.3041 | 2.31335 | ||||||||
\(437\) | −22.2645 | −1.06506 | ||||||||
\(438\) | −52.2105 | −2.49472 | ||||||||
\(439\) | −1.56426 | −0.0746582 | −0.0373291 | − | 0.999303i | \(-0.511885\pi\) | ||||
−0.0373291 | + | 0.999303i | \(0.511885\pi\) | |||||||
\(440\) | −24.7194 | −1.17845 | ||||||||
\(441\) | −9.50425 | −0.452583 | ||||||||
\(442\) | −18.5815 | −0.883832 | ||||||||
\(443\) | −11.1007 | −0.527409 | −0.263704 | − | 0.964604i | \(-0.584944\pi\) | ||||
−0.263704 | + | 0.964604i | \(0.584944\pi\) | |||||||
\(444\) | −31.4509 | −1.49259 | ||||||||
\(445\) | 38.0828 | 1.80530 | ||||||||
\(446\) | 24.7871 | 1.17371 | ||||||||
\(447\) | 32.9753 | 1.55968 | ||||||||
\(448\) | 27.7788 | 1.31242 | ||||||||
\(449\) | 27.7667 | 1.31039 | 0.655196 | − | 0.755459i | \(-0.272586\pi\) | ||||
0.655196 | + | 0.755459i | \(0.272586\pi\) | |||||||
\(450\) | 14.3859 | 0.678158 | ||||||||
\(451\) | −6.66461 | −0.313824 | ||||||||
\(452\) | −40.8769 | −1.92269 | ||||||||
\(453\) | 22.9146 | 1.07662 | ||||||||
\(454\) | 39.2926 | 1.84409 | ||||||||
\(455\) | −19.1210 | −0.896407 | ||||||||
\(456\) | 28.4702 | 1.33324 | ||||||||
\(457\) | 26.9832 | 1.26222 | 0.631111 | − | 0.775692i | \(-0.282599\pi\) | ||||
0.631111 | + | 0.775692i | \(0.282599\pi\) | |||||||
\(458\) | −2.70506 | −0.126399 | ||||||||
\(459\) | −8.12638 | −0.379307 | ||||||||
\(460\) | −55.9721 | −2.60971 | ||||||||
\(461\) | 25.9146 | 1.20696 | 0.603482 | − | 0.797377i | \(-0.293780\pi\) | ||||
0.603482 | + | 0.797377i | \(0.293780\pi\) | |||||||
\(462\) | 42.6368 | 1.98364 | ||||||||
\(463\) | −10.3116 | −0.479220 | −0.239610 | − | 0.970869i | \(-0.577020\pi\) | ||||
−0.239610 | + | 0.970869i | \(0.577020\pi\) | |||||||
\(464\) | −2.77821 | −0.128975 | ||||||||
\(465\) | 14.6110 | 0.677567 | ||||||||
\(466\) | −43.1901 | −2.00074 | ||||||||
\(467\) | 6.82555 | 0.315849 | 0.157924 | − | 0.987451i | \(-0.449520\pi\) | ||||
0.157924 | + | 0.987451i | \(0.449520\pi\) | |||||||
\(468\) | 49.4321 | 2.28500 | ||||||||
\(469\) | −22.6151 | −1.04427 | ||||||||
\(470\) | −6.86827 | −0.316810 | ||||||||
\(471\) | −53.8975 | −2.48347 | ||||||||
\(472\) | 19.1555 | 0.881702 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 61.2869 | 2.81500 | ||||||||
\(475\) | 4.90534 | 0.225072 | ||||||||
\(476\) | 17.0950 | 0.783548 | ||||||||
\(477\) | 44.6177 | 2.04290 | ||||||||
\(478\) | 36.6773 | 1.67758 | ||||||||
\(479\) | 14.4974 | 0.662405 | 0.331203 | − | 0.943560i | \(-0.392546\pi\) | ||||
0.331203 | + | 0.943560i | \(0.392546\pi\) | |||||||
\(480\) | −34.6114 | −1.57979 | ||||||||
\(481\) | −11.9759 | −0.546052 | ||||||||
\(482\) | 7.11590 | 0.324121 | ||||||||
\(483\) | 38.8722 | 1.76875 | ||||||||
\(484\) | −4.19559 | −0.190709 | ||||||||
\(485\) | −10.7231 | −0.486909 | ||||||||
\(486\) | −45.8132 | −2.07813 | ||||||||
\(487\) | −3.07378 | −0.139286 | −0.0696431 | − | 0.997572i | \(-0.522186\pi\) | ||||
−0.0696431 | + | 0.997572i | \(0.522186\pi\) | |||||||
\(488\) | −7.79833 | −0.353014 | ||||||||
\(489\) | 41.6652 | 1.88416 | ||||||||
\(490\) | −13.0140 | −0.587911 | ||||||||
\(491\) | −1.64163 | −0.0740855 | −0.0370428 | − | 0.999314i | \(-0.511794\pi\) | ||||
−0.0370428 | + | 0.999314i | \(0.511794\pi\) | |||||||
\(492\) | 19.2968 | 0.869966 | ||||||||
\(493\) | 12.6293 | 0.568795 | ||||||||
\(494\) | 26.9242 | 1.21138 | ||||||||
\(495\) | −34.0108 | −1.52867 | ||||||||
\(496\) | 1.09420 | 0.0491310 | ||||||||
\(497\) | −24.7844 | −1.11173 | ||||||||
\(498\) | 17.9141 | 0.802751 | ||||||||
\(499\) | −34.1945 | −1.53076 | −0.765378 | − | 0.643581i | \(-0.777448\pi\) | ||||
−0.765378 | + | 0.643581i | \(0.777448\pi\) | |||||||
\(500\) | −30.1844 | −1.34989 | ||||||||
\(501\) | 39.1628 | 1.74966 | ||||||||
\(502\) | −26.8710 | −1.19931 | ||||||||
\(503\) | 25.1640 | 1.12201 | 0.561004 | − | 0.827813i | \(-0.310415\pi\) | ||||
0.561004 | + | 0.827813i | \(0.310415\pi\) | |||||||
\(504\) | −29.2496 | −1.30288 | ||||||||
\(505\) | 0.236178 | 0.0105098 | ||||||||
\(506\) | 47.5246 | 2.11273 | ||||||||
\(507\) | −3.11120 | −0.138173 | ||||||||
\(508\) | 22.6969 | 1.00701 | ||||||||
\(509\) | 5.14565 | 0.228077 | 0.114038 | − | 0.993476i | \(-0.463621\pi\) | ||||
0.114038 | + | 0.993476i | \(0.463621\pi\) | |||||||
\(510\) | −37.0168 | −1.63913 | ||||||||
\(511\) | 18.2903 | 0.809113 | ||||||||
\(512\) | −5.79385 | −0.256054 | ||||||||
\(513\) | 11.7749 | 0.519876 | ||||||||
\(514\) | 57.4891 | 2.53573 | ||||||||
\(515\) | −36.5167 | −1.60912 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.65084 | 0.160564 | ||||||||
\(518\) | 17.5993 | 0.773270 | ||||||||
\(519\) | −9.65376 | −0.423753 | ||||||||
\(520\) | 27.2535 | 1.19514 | ||||||||
\(521\) | 23.9214 | 1.04801 | 0.524007 | − | 0.851714i | \(-0.324437\pi\) | ||||
0.524007 | + | 0.851714i | \(0.324437\pi\) | |||||||
\(522\) | −53.6672 | −2.34895 | ||||||||
\(523\) | 31.0987 | 1.35985 | 0.679925 | − | 0.733282i | \(-0.262012\pi\) | ||||
0.679925 | + | 0.733282i | \(0.262012\pi\) | |||||||
\(524\) | 8.77382 | 0.383286 | ||||||||
\(525\) | −8.56435 | −0.373779 | ||||||||
\(526\) | −8.53798 | −0.372274 | ||||||||
\(527\) | −4.97406 | −0.216673 | ||||||||
\(528\) | −4.32842 | −0.188371 | ||||||||
\(529\) | 20.3285 | 0.883847 | ||||||||
\(530\) | 61.0939 | 2.65375 | ||||||||
\(531\) | 26.3555 | 1.14373 | ||||||||
\(532\) | −24.7702 | −1.07393 | ||||||||
\(533\) | 7.34782 | 0.318269 | ||||||||
\(534\) | 93.6236 | 4.05149 | ||||||||
\(535\) | 32.0703 | 1.38652 | ||||||||
\(536\) | 32.2336 | 1.39228 | ||||||||
\(537\) | −6.38476 | −0.275523 | ||||||||
\(538\) | 51.4004 | 2.21603 | ||||||||
\(539\) | 6.91759 | 0.297962 | ||||||||
\(540\) | 29.6017 | 1.27385 | ||||||||
\(541\) | 39.6765 | 1.70582 | 0.852912 | − | 0.522054i | \(-0.174834\pi\) | ||||
0.852912 | + | 0.522054i | \(0.174834\pi\) | |||||||
\(542\) | 16.8733 | 0.724769 | ||||||||
\(543\) | −35.1768 | −1.50958 | ||||||||
\(544\) | 11.7829 | 0.505186 | ||||||||
\(545\) | 36.6417 | 1.56956 | ||||||||
\(546\) | −47.0076 | −2.01174 | ||||||||
\(547\) | −32.5243 | −1.39064 | −0.695319 | − | 0.718701i | \(-0.744737\pi\) | ||||
−0.695319 | + | 0.718701i | \(0.744737\pi\) | |||||||
\(548\) | −12.6016 | −0.538315 | ||||||||
\(549\) | −10.7295 | −0.457925 | ||||||||
\(550\) | −10.4707 | −0.446470 | ||||||||
\(551\) | −18.2995 | −0.779587 | ||||||||
\(552\) | −55.4051 | −2.35820 | ||||||||
\(553\) | −21.4699 | −0.912992 | ||||||||
\(554\) | −17.0558 | −0.724633 | ||||||||
\(555\) | −23.8575 | −1.01269 | ||||||||
\(556\) | −61.3308 | −2.60100 | ||||||||
\(557\) | 3.13152 | 0.132687 | 0.0663434 | − | 0.997797i | \(-0.478867\pi\) | ||||
0.0663434 | + | 0.997797i | \(0.478867\pi\) | |||||||
\(558\) | 21.1369 | 0.894794 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.85264 | −0.120546 | ||||||||
\(561\) | 19.6763 | 0.830735 | ||||||||
\(562\) | −44.2250 | −1.86552 | ||||||||
\(563\) | −30.2154 | −1.27343 | −0.636713 | − | 0.771101i | \(-0.719706\pi\) | ||||
−0.636713 | + | 0.771101i | \(0.719706\pi\) | |||||||
\(564\) | −10.5707 | −0.445106 | ||||||||
\(565\) | −31.0077 | −1.30450 | ||||||||
\(566\) | 45.7882 | 1.92462 | ||||||||
\(567\) | 7.58832 | 0.318679 | ||||||||
\(568\) | 35.3256 | 1.48223 | ||||||||
\(569\) | 8.25304 | 0.345986 | 0.172993 | − | 0.984923i | \(-0.444656\pi\) | ||||
0.172993 | + | 0.984923i | \(0.444656\pi\) | |||||||
\(570\) | 53.6365 | 2.24658 | ||||||||
\(571\) | 29.0155 | 1.21426 | 0.607131 | − | 0.794601i | \(-0.292320\pi\) | ||||
0.607131 | + | 0.794601i | \(0.292320\pi\) | |||||||
\(572\) | −35.9787 | −1.50435 | ||||||||
\(573\) | −10.0920 | −0.421601 | ||||||||
\(574\) | −10.7981 | −0.450705 | ||||||||
\(575\) | −9.54616 | −0.398103 | ||||||||
\(576\) | −54.4757 | −2.26982 | ||||||||
\(577\) | 16.3515 | 0.680724 | 0.340362 | − | 0.940295i | \(-0.389450\pi\) | ||||
0.340362 | + | 0.940295i | \(0.389450\pi\) | |||||||
\(578\) | −26.7123 | −1.11109 | ||||||||
\(579\) | −43.3788 | −1.80276 | ||||||||
\(580\) | −46.0043 | −1.91022 | ||||||||
\(581\) | −6.27563 | −0.260357 | ||||||||
\(582\) | −26.3618 | −1.09273 | ||||||||
\(583\) | −32.4746 | −1.34496 | ||||||||
\(584\) | −26.0694 | −1.07876 | ||||||||
\(585\) | 37.4973 | 1.55032 | ||||||||
\(586\) | 25.3871 | 1.04873 | ||||||||
\(587\) | 24.0047 | 0.990781 | 0.495390 | − | 0.868670i | \(-0.335025\pi\) | ||||
0.495390 | + | 0.868670i | \(0.335025\pi\) | |||||||
\(588\) | −20.0292 | −0.825992 | ||||||||
\(589\) | 7.20729 | 0.296971 | ||||||||
\(590\) | 36.0880 | 1.48572 | ||||||||
\(591\) | −54.5963 | −2.24579 | ||||||||
\(592\) | −1.78666 | −0.0734312 | ||||||||
\(593\) | −41.5922 | −1.70799 | −0.853993 | − | 0.520285i | \(-0.825826\pi\) | ||||
−0.853993 | + | 0.520285i | \(0.825826\pi\) | |||||||
\(594\) | −25.1341 | −1.03126 | ||||||||
\(595\) | 12.9676 | 0.531621 | ||||||||
\(596\) | 40.8921 | 1.67501 | ||||||||
\(597\) | 25.0584 | 1.02557 | ||||||||
\(598\) | −52.3965 | −2.14265 | ||||||||
\(599\) | −16.7776 | −0.685512 | −0.342756 | − | 0.939424i | \(-0.611360\pi\) | ||||
−0.342756 | + | 0.939424i | \(0.611360\pi\) | |||||||
\(600\) | 12.2069 | 0.498344 | ||||||||
\(601\) | −3.26297 | −0.133099 | −0.0665496 | − | 0.997783i | \(-0.521199\pi\) | ||||
−0.0665496 | + | 0.997783i | \(0.521199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 44.3495 | 1.80605 | ||||||||
\(604\) | 28.4160 | 1.15623 | ||||||||
\(605\) | −3.18262 | −0.129392 | ||||||||
\(606\) | 0.580625 | 0.0235863 | ||||||||
\(607\) | −35.6329 | −1.44630 | −0.723148 | − | 0.690693i | \(-0.757306\pi\) | ||||
−0.723148 | + | 0.690693i | \(0.757306\pi\) | |||||||
\(608\) | −17.0731 | −0.692406 | ||||||||
\(609\) | 31.9496 | 1.29466 | ||||||||
\(610\) | −14.6917 | −0.594849 | ||||||||
\(611\) | −4.02510 | −0.162838 | ||||||||
\(612\) | −33.5242 | −1.35514 | ||||||||
\(613\) | 21.7996 | 0.880476 | 0.440238 | − | 0.897881i | \(-0.354894\pi\) | ||||
0.440238 | + | 0.897881i | \(0.354894\pi\) | |||||||
\(614\) | −1.87212 | −0.0755525 | ||||||||
\(615\) | 14.6378 | 0.590254 | ||||||||
\(616\) | 21.2891 | 0.857761 | ||||||||
\(617\) | 10.4546 | 0.420887 | 0.210443 | − | 0.977606i | \(-0.432509\pi\) | ||||
0.210443 | + | 0.977606i | \(0.432509\pi\) | |||||||
\(618\) | −89.7735 | −3.61122 | ||||||||
\(619\) | −35.5916 | −1.43055 | −0.715273 | − | 0.698845i | \(-0.753698\pi\) | ||||
−0.715273 | + | 0.698845i | \(0.753698\pi\) | |||||||
\(620\) | 18.1188 | 0.727670 | ||||||||
\(621\) | −22.9149 | −0.919544 | ||||||||
\(622\) | −25.2027 | −1.01054 | ||||||||
\(623\) | −32.7980 | −1.31402 | ||||||||
\(624\) | 4.77214 | 0.191039 | ||||||||
\(625\) | −30.1480 | −1.20592 | ||||||||
\(626\) | −37.1954 | −1.48663 | ||||||||
\(627\) | −28.5105 | −1.13860 | ||||||||
\(628\) | −66.8374 | −2.66710 | ||||||||
\(629\) | 8.12187 | 0.323840 | ||||||||
\(630\) | −55.1049 | −2.19543 | ||||||||
\(631\) | 2.50556 | 0.0997447 | 0.0498724 | − | 0.998756i | \(-0.484119\pi\) | ||||
0.0498724 | + | 0.998756i | \(0.484119\pi\) | |||||||
\(632\) | 30.6013 | 1.21725 | ||||||||
\(633\) | 27.2669 | 1.08376 | ||||||||
\(634\) | −3.10296 | −0.123234 | ||||||||
\(635\) | 17.2170 | 0.683237 | ||||||||
\(636\) | 94.0271 | 3.72842 | ||||||||
\(637\) | −7.62673 | −0.302182 | ||||||||
\(638\) | 39.0612 | 1.54645 | ||||||||
\(639\) | 48.6036 | 1.92273 | ||||||||
\(640\) | −48.9532 | −1.93504 | ||||||||
\(641\) | 18.3108 | 0.723232 | 0.361616 | − | 0.932327i | \(-0.382225\pi\) | ||||
0.361616 | + | 0.932327i | \(0.382225\pi\) | |||||||
\(642\) | 78.8424 | 3.11166 | ||||||||
\(643\) | −39.3116 | −1.55030 | −0.775150 | − | 0.631778i | \(-0.782326\pi\) | ||||
−0.775150 | + | 0.631778i | \(0.782326\pi\) | |||||||
\(644\) | 48.2048 | 1.89953 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.2596 | −0.718415 | ||||||||
\(647\) | 20.1378 | 0.791697 | 0.395848 | − | 0.918316i | \(-0.370451\pi\) | ||||
0.395848 | + | 0.918316i | \(0.370451\pi\) | |||||||
\(648\) | −10.8157 | −0.424882 | ||||||||
\(649\) | −19.1826 | −0.752984 | ||||||||
\(650\) | 11.5440 | 0.452794 | ||||||||
\(651\) | −12.5834 | −0.493182 | ||||||||
\(652\) | 51.6683 | 2.02349 | ||||||||
\(653\) | 17.4768 | 0.683920 | 0.341960 | − | 0.939714i | \(-0.388909\pi\) | ||||
0.341960 | + | 0.939714i | \(0.388909\pi\) | |||||||
\(654\) | 90.0809 | 3.52244 | ||||||||
\(655\) | 6.65549 | 0.260052 | ||||||||
\(656\) | 1.09621 | 0.0427998 | ||||||||
\(657\) | −35.8682 | −1.39935 | ||||||||
\(658\) | 5.91515 | 0.230597 | ||||||||
\(659\) | 22.2409 | 0.866382 | 0.433191 | − | 0.901302i | \(-0.357388\pi\) | ||||
0.433191 | + | 0.901302i | \(0.357388\pi\) | |||||||
\(660\) | −71.6743 | −2.78992 | ||||||||
\(661\) | −35.6536 | −1.38676 | −0.693382 | − | 0.720570i | \(-0.743880\pi\) | ||||
−0.693382 | + | 0.720570i | \(0.743880\pi\) | |||||||
\(662\) | 71.8014 | 2.79064 | ||||||||
\(663\) | −21.6934 | −0.842502 | ||||||||
\(664\) | 8.94474 | 0.347123 | ||||||||
\(665\) | −18.7898 | −0.728637 | ||||||||
\(666\) | −34.5132 | −1.33736 | ||||||||
\(667\) | 35.6123 | 1.37891 | ||||||||
\(668\) | 48.5651 | 1.87904 | ||||||||
\(669\) | 28.9383 | 1.11882 | ||||||||
\(670\) | 60.7267 | 2.34608 | ||||||||
\(671\) | 7.80939 | 0.301478 | ||||||||
\(672\) | 29.8084 | 1.14988 | ||||||||
\(673\) | −50.1296 | −1.93236 | −0.966178 | − | 0.257876i | \(-0.916977\pi\) | ||||
−0.966178 | + | 0.257876i | \(0.916977\pi\) | |||||||
\(674\) | 40.6745 | 1.56672 | ||||||||
\(675\) | 5.04863 | 0.194322 | ||||||||
\(676\) | −3.85815 | −0.148391 | ||||||||
\(677\) | −19.7657 | −0.759657 | −0.379829 | − | 0.925057i | \(-0.624017\pi\) | ||||
−0.379829 | + | 0.925057i | \(0.624017\pi\) | |||||||
\(678\) | −76.2301 | −2.92760 | ||||||||
\(679\) | 9.23500 | 0.354407 | ||||||||
\(680\) | −18.4829 | −0.708788 | ||||||||
\(681\) | 45.8730 | 1.75786 | ||||||||
\(682\) | −15.3843 | −0.589094 | ||||||||
\(683\) | −35.3877 | −1.35407 | −0.677036 | − | 0.735949i | \(-0.736736\pi\) | ||||
−0.677036 | + | 0.735949i | \(0.736736\pi\) | |||||||
\(684\) | 48.5758 | 1.85734 | ||||||||
\(685\) | −9.55913 | −0.365236 | ||||||||
\(686\) | 46.6162 | 1.77981 | ||||||||
\(687\) | −3.15808 | −0.120488 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35.8036 | 1.36401 | ||||||||
\(690\) | −104.381 | −3.97370 | ||||||||
\(691\) | 3.97384 | 0.151172 | 0.0755860 | − | 0.997139i | \(-0.475917\pi\) | ||||
0.0755860 | + | 0.997139i | \(0.475917\pi\) | |||||||
\(692\) | −11.9715 | −0.455087 | ||||||||
\(693\) | 29.2911 | 1.11268 | ||||||||
\(694\) | 24.0134 | 0.911537 | ||||||||
\(695\) | −46.5232 | −1.76473 | ||||||||
\(696\) | −45.5382 | −1.72612 | ||||||||
\(697\) | −4.98319 | −0.188752 | ||||||||
\(698\) | −6.97781 | −0.264114 | ||||||||
\(699\) | −50.4232 | −1.90718 | ||||||||
\(700\) | −10.6205 | −0.401418 | ||||||||
\(701\) | 46.4746 | 1.75532 | 0.877660 | − | 0.479284i | \(-0.159104\pi\) | ||||
0.877660 | + | 0.479284i | \(0.159104\pi\) | |||||||
\(702\) | 27.7107 | 1.04587 | ||||||||
\(703\) | −11.7684 | −0.443853 | ||||||||
\(704\) | 39.6496 | 1.49435 | ||||||||
\(705\) | −8.01852 | −0.301995 | ||||||||
\(706\) | −63.0919 | −2.37449 | ||||||||
\(707\) | −0.203403 | −0.00764975 | ||||||||
\(708\) | 55.5416 | 2.08738 | ||||||||
\(709\) | −5.22052 | −0.196061 | −0.0980303 | − | 0.995183i | \(-0.531254\pi\) | ||||
−0.0980303 | + | 0.995183i | \(0.531254\pi\) | |||||||
\(710\) | 66.5518 | 2.49765 | ||||||||
\(711\) | 42.1036 | 1.57901 | ||||||||
\(712\) | 46.7474 | 1.75193 | ||||||||
\(713\) | −14.0259 | −0.525275 | ||||||||
\(714\) | 31.8799 | 1.19308 | ||||||||
\(715\) | −27.2921 | −1.02067 | ||||||||
\(716\) | −7.91763 | −0.295896 | ||||||||
\(717\) | 42.8198 | 1.59913 | ||||||||
\(718\) | −25.6538 | −0.957390 | ||||||||
\(719\) | −33.9396 | −1.26573 | −0.632866 | − | 0.774261i | \(-0.718122\pi\) | ||||
−0.632866 | + | 0.774261i | \(0.718122\pi\) | |||||||
\(720\) | 5.59417 | 0.208482 | ||||||||
\(721\) | 31.4492 | 1.17123 | ||||||||
\(722\) | −17.4815 | −0.650594 | ||||||||
\(723\) | 8.30762 | 0.308964 | ||||||||
\(724\) | −43.6221 | −1.62120 | ||||||||
\(725\) | −7.84613 | −0.291398 | ||||||||
\(726\) | −7.82422 | −0.290384 | ||||||||
\(727\) | −11.6162 | −0.430821 | −0.215411 | − | 0.976524i | \(-0.569109\pi\) | ||||
−0.215411 | + | 0.976524i | \(0.569109\pi\) | |||||||
\(728\) | −23.4715 | −0.869910 | ||||||||
\(729\) | −43.0778 | −1.59547 | ||||||||
\(730\) | −49.1135 | −1.81777 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −22.6114 | −0.835740 | ||||||||
\(733\) | 25.0539 | 0.925386 | 0.462693 | − | 0.886519i | \(-0.346883\pi\) | ||||
0.462693 | + | 0.886519i | \(0.346883\pi\) | |||||||
\(734\) | −63.2365 | −2.33410 | ||||||||
\(735\) | −15.1934 | −0.560418 | ||||||||
\(736\) | 33.2256 | 1.22471 | ||||||||
\(737\) | −32.2794 | −1.18903 | ||||||||
\(738\) | 21.1757 | 0.779488 | ||||||||
\(739\) | 38.1121 | 1.40198 | 0.700988 | − | 0.713173i | \(-0.252743\pi\) | ||||
0.700988 | + | 0.713173i | \(0.252743\pi\) | |||||||
\(740\) | −29.5852 | −1.08758 | ||||||||
\(741\) | 31.4332 | 1.15473 | ||||||||
\(742\) | −52.6159 | −1.93159 | ||||||||
\(743\) | −31.8156 | −1.16720 | −0.583600 | − | 0.812041i | \(-0.698357\pi\) | ||||
−0.583600 | + | 0.812041i | \(0.698357\pi\) | |||||||
\(744\) | 17.9353 | 0.657539 | ||||||||
\(745\) | 31.0193 | 1.13646 | ||||||||
\(746\) | −2.49309 | −0.0912784 | ||||||||
\(747\) | 12.3068 | 0.450284 | ||||||||
\(748\) | 24.4003 | 0.892163 | ||||||||
\(749\) | −27.6199 | −1.00921 | ||||||||
\(750\) | −56.2900 | −2.05542 | ||||||||
\(751\) | 5.66453 | 0.206702 | 0.103351 | − | 0.994645i | \(-0.467044\pi\) | ||||
0.103351 | + | 0.994645i | \(0.467044\pi\) | |||||||
\(752\) | −0.600498 | −0.0218979 | ||||||||
\(753\) | −31.3712 | −1.14323 | ||||||||
\(754\) | −43.0654 | −1.56835 | ||||||||
\(755\) | 21.5553 | 0.784478 | ||||||||
\(756\) | −25.4938 | −0.927202 | ||||||||
\(757\) | 34.1137 | 1.23988 | 0.619941 | − | 0.784648i | \(-0.287157\pi\) | ||||
0.619941 | + | 0.784648i | \(0.287157\pi\) | |||||||
\(758\) | −6.99213 | −0.253966 | ||||||||
\(759\) | 55.4837 | 2.01393 | ||||||||
\(760\) | 26.7813 | 0.971461 | ||||||||
\(761\) | 4.91016 | 0.177993 | 0.0889966 | − | 0.996032i | \(-0.471634\pi\) | ||||
0.0889966 | + | 0.996032i | \(0.471634\pi\) | |||||||
\(762\) | 42.3268 | 1.53334 | ||||||||
\(763\) | −31.5569 | −1.14244 | ||||||||
\(764\) | −12.5150 | −0.452776 | ||||||||
\(765\) | −25.4302 | −0.919431 | ||||||||
\(766\) | −46.6259 | −1.68466 | ||||||||
\(767\) | 21.1491 | 0.763650 | ||||||||
\(768\) | −51.7700 | −1.86809 | ||||||||
\(769\) | −30.4099 | −1.09661 | −0.548305 | − | 0.836278i | \(-0.684727\pi\) | ||||
−0.548305 | + | 0.836278i | \(0.684727\pi\) | |||||||
\(770\) | 40.1076 | 1.44538 | ||||||||
\(771\) | 67.1169 | 2.41715 | ||||||||
\(772\) | −53.7933 | −1.93606 | ||||||||
\(773\) | 30.0965 | 1.08250 | 0.541248 | − | 0.840863i | \(-0.317952\pi\) | ||||
0.541248 | + | 0.840863i | \(0.317952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.09020 | 0.111003 | ||||||||
\(776\) | −13.1628 | −0.472516 | ||||||||
\(777\) | 20.5467 | 0.737110 | ||||||||
\(778\) | 21.0611 | 0.755077 | ||||||||
\(779\) | 7.22053 | 0.258702 | ||||||||
\(780\) | 79.0218 | 2.82943 | ||||||||
\(781\) | −35.3757 | −1.26584 | ||||||||
\(782\) | 35.5346 | 1.27072 | ||||||||
\(783\) | −18.8341 | −0.673076 | ||||||||
\(784\) | −1.13782 | −0.0406364 | ||||||||
\(785\) | −50.7004 | −1.80957 | ||||||||
\(786\) | 16.3620 | 0.583614 | ||||||||
\(787\) | −14.4153 | −0.513850 | −0.256925 | − | 0.966431i | \(-0.582709\pi\) | ||||
−0.256925 | + | 0.966431i | \(0.582709\pi\) | |||||||
\(788\) | −67.7040 | −2.41186 | ||||||||
\(789\) | −9.96785 | −0.354865 | ||||||||
\(790\) | 57.6514 | 2.05115 | ||||||||
\(791\) | 26.7047 | 0.949511 | ||||||||
\(792\) | −41.7490 | −1.48349 | ||||||||
\(793\) | −8.60995 | −0.305748 | ||||||||
\(794\) | −55.0712 | −1.95440 | ||||||||
\(795\) | 71.3255 | 2.52965 | ||||||||
\(796\) | 31.0745 | 1.10141 | ||||||||
\(797\) | 33.4165 | 1.18367 | 0.591837 | − | 0.806058i | \(-0.298403\pi\) | ||||
0.591837 | + | 0.806058i | \(0.298403\pi\) | |||||||
\(798\) | −46.1933 | −1.63522 | ||||||||
\(799\) | 2.72977 | 0.0965723 | ||||||||
\(800\) | −7.32028 | −0.258811 | ||||||||
\(801\) | 64.3186 | 2.27258 | ||||||||
\(802\) | 13.6371 | 0.481542 | ||||||||
\(803\) | 26.1063 | 0.921272 | ||||||||
\(804\) | 93.4619 | 3.29615 | ||||||||
\(805\) | 36.5663 | 1.28879 | ||||||||
\(806\) | 16.9614 | 0.597438 | ||||||||
\(807\) | 60.0085 | 2.11240 | ||||||||
\(808\) | 0.289913 | 0.0101991 | ||||||||
\(809\) | 3.68957 | 0.129719 | 0.0648593 | − | 0.997894i | \(-0.479340\pi\) | ||||
0.0648593 | + | 0.997894i | \(0.479340\pi\) | |||||||
\(810\) | −20.3763 | −0.715952 | ||||||||
\(811\) | −11.1422 | −0.391257 | −0.195628 | − | 0.980678i | \(-0.562675\pi\) | ||||
−0.195628 | + | 0.980678i | \(0.562675\pi\) | |||||||
\(812\) | 39.6202 | 1.39040 | ||||||||
\(813\) | 19.6991 | 0.690877 | ||||||||
\(814\) | 25.1201 | 0.880460 | ||||||||
\(815\) | 39.1936 | 1.37289 | ||||||||
\(816\) | −3.23641 | −0.113297 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −64.8663 | −2.26800 | ||||||||
\(819\) | −32.2938 | −1.12844 | ||||||||
\(820\) | 18.1521 | 0.633899 | ||||||||
\(821\) | 21.8105 | 0.761190 | 0.380595 | − | 0.924742i | \(-0.375719\pi\) | ||||
0.380595 | + | 0.924742i | \(0.375719\pi\) | |||||||
\(822\) | −23.5004 | −0.819671 | ||||||||
\(823\) | −2.33873 | −0.0815231 | −0.0407616 | − | 0.999169i | \(-0.512978\pi\) | ||||
−0.0407616 | + | 0.999169i | \(0.512978\pi\) | |||||||
\(824\) | −44.8250 | −1.56155 | ||||||||
\(825\) | −12.2242 | −0.425592 | ||||||||
\(826\) | −31.0800 | −1.08141 | ||||||||
\(827\) | −0.335711 | −0.0116738 | −0.00583691 | − | 0.999983i | \(-0.501858\pi\) | ||||
−0.00583691 | + | 0.999983i | \(0.501858\pi\) | |||||||
\(828\) | −94.5321 | −3.28522 | ||||||||
\(829\) | 48.9122 | 1.69879 | 0.849395 | − | 0.527758i | \(-0.176967\pi\) | ||||
0.849395 | + | 0.527758i | \(0.176967\pi\) | |||||||
\(830\) | 16.8515 | 0.584923 | ||||||||
\(831\) | −19.9122 | −0.690747 | ||||||||
\(832\) | −43.7142 | −1.51552 | ||||||||
\(833\) | 5.17235 | 0.179211 | ||||||||
\(834\) | −114.374 | −3.96044 | ||||||||
\(835\) | 36.8397 | 1.27489 | ||||||||
\(836\) | −35.3554 | −1.22279 | ||||||||
\(837\) | 7.41783 | 0.256398 | ||||||||
\(838\) | 43.1699 | 1.49128 | ||||||||
\(839\) | −9.35601 | −0.323005 | −0.161503 | − | 0.986872i | \(-0.551634\pi\) | ||||
−0.161503 | + | 0.986872i | \(0.551634\pi\) | |||||||
\(840\) | −46.7582 | −1.61331 | ||||||||
\(841\) | 0.270269 | 0.00931962 | ||||||||
\(842\) | −68.8519 | −2.37279 | ||||||||
\(843\) | −51.6314 | −1.77828 | ||||||||
\(844\) | 33.8132 | 1.16390 | ||||||||
\(845\) | −2.92665 | −0.100680 | ||||||||
\(846\) | −11.5999 | −0.398814 | ||||||||
\(847\) | 2.74096 | 0.0941805 | ||||||||
\(848\) | 5.34149 | 0.183427 | ||||||||
\(849\) | 53.4565 | 1.83462 | ||||||||
\(850\) | −7.82901 | −0.268533 | ||||||||
\(851\) | 22.9022 | 0.785077 | ||||||||
\(852\) | 102.427 | 3.50910 | ||||||||
\(853\) | 1.88280 | 0.0644660 | 0.0322330 | − | 0.999480i | \(-0.489738\pi\) | ||||
0.0322330 | + | 0.999480i | \(0.489738\pi\) | |||||||
\(854\) | 12.6529 | 0.432973 | ||||||||
\(855\) | 36.8478 | 1.26017 | ||||||||
\(856\) | 39.3670 | 1.34553 | ||||||||
\(857\) | −47.0757 | −1.60807 | −0.804037 | − | 0.594579i | \(-0.797319\pi\) | ||||
−0.804037 | + | 0.594579i | \(0.797319\pi\) | |||||||
\(858\) | −67.0956 | −2.29060 | ||||||||
\(859\) | −22.8236 | −0.778731 | −0.389365 | − | 0.921083i | \(-0.627306\pi\) | ||||
−0.389365 | + | 0.921083i | \(0.627306\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.6065 | −0.429628 | ||||||||
\(862\) | −11.5774 | −0.394327 | ||||||||
\(863\) | 5.93754 | 0.202116 | 0.101058 | − | 0.994881i | \(-0.467777\pi\) | ||||
0.101058 | + | 0.994881i | \(0.467777\pi\) | |||||||
\(864\) | −17.5718 | −0.597806 | ||||||||
\(865\) | −9.08111 | −0.308767 | ||||||||
\(866\) | 26.9622 | 0.916213 | ||||||||
\(867\) | −31.1859 | −1.05913 | ||||||||
\(868\) | −15.6045 | −0.529650 | ||||||||
\(869\) | −30.6447 | −1.03955 | ||||||||
\(870\) | −85.7919 | −2.90862 | ||||||||
\(871\) | 35.5884 | 1.20587 | ||||||||
\(872\) | 44.9785 | 1.52316 | ||||||||
\(873\) | −18.1103 | −0.612942 | ||||||||
\(874\) | −51.4888 | −1.74164 | ||||||||
\(875\) | 19.7194 | 0.666636 | ||||||||
\(876\) | −75.5885 | −2.55390 | ||||||||
\(877\) | −0.987134 | −0.0333331 | −0.0166666 | − | 0.999861i | \(-0.505305\pi\) | ||||
−0.0166666 | + | 0.999861i | \(0.505305\pi\) | |||||||
\(878\) | −3.61751 | −0.122085 | ||||||||
\(879\) | 29.6388 | 0.999691 | ||||||||
\(880\) | −4.07167 | −0.137256 | ||||||||
\(881\) | 19.9638 | 0.672596 | 0.336298 | − | 0.941756i | \(-0.390825\pi\) | ||||
0.336298 | + | 0.941756i | \(0.390825\pi\) | |||||||
\(882\) | −21.9795 | −0.740087 | ||||||||
\(883\) | 1.27698 | 0.0429737 | 0.0214869 | − | 0.999769i | \(-0.493160\pi\) | ||||
0.0214869 | + | 0.999769i | \(0.493160\pi\) | |||||||
\(884\) | −26.9016 | −0.904800 | ||||||||
\(885\) | 42.1318 | 1.41624 | ||||||||
\(886\) | −25.6713 | −0.862445 | ||||||||
\(887\) | 6.66827 | 0.223899 | 0.111949 | − | 0.993714i | \(-0.464291\pi\) | ||||
0.111949 | + | 0.993714i | \(0.464291\pi\) | |||||||
\(888\) | −29.2855 | −0.982758 | ||||||||
\(889\) | −14.8278 | −0.497308 | ||||||||
\(890\) | 88.0700 | 2.95211 | ||||||||
\(891\) | 10.8311 | 0.362855 | ||||||||
\(892\) | 35.8859 | 1.20155 | ||||||||
\(893\) | −3.95537 | −0.132361 | ||||||||
\(894\) | 76.2585 | 2.55047 | ||||||||
\(895\) | −6.00602 | −0.200759 | ||||||||
\(896\) | 42.1599 | 1.40846 | ||||||||
\(897\) | −61.1714 | −2.04245 | ||||||||
\(898\) | 64.2131 | 2.14282 | ||||||||
\(899\) | −11.5281 | −0.384484 | ||||||||
\(900\) | 20.8274 | 0.694246 | ||||||||
\(901\) | −24.2815 | −0.808936 | ||||||||
\(902\) | −15.4125 | −0.513181 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −38.0626 | −1.26594 | ||||||||
\(905\) | −33.0901 | −1.09995 | ||||||||
\(906\) | 52.9921 | 1.76054 | ||||||||
\(907\) | −6.03846 | −0.200504 | −0.100252 | − | 0.994962i | \(-0.531965\pi\) | ||||
−0.100252 | + | 0.994962i | \(0.531965\pi\) | |||||||
\(908\) | 56.8863 | 1.88784 | ||||||||
\(909\) | 0.398884 | 0.0132301 | ||||||||
\(910\) | −44.2191 | −1.46585 | ||||||||
\(911\) | 43.2321 | 1.43234 | 0.716172 | − | 0.697924i | \(-0.245892\pi\) | ||||
0.716172 | + | 0.697924i | \(0.245892\pi\) | |||||||
\(912\) | 4.68947 | 0.155284 | ||||||||
\(913\) | −8.95743 | −0.296448 | ||||||||
\(914\) | 62.4012 | 2.06405 | ||||||||
\(915\) | −17.1521 | −0.567032 | ||||||||
\(916\) | −3.91629 | −0.129398 | ||||||||
\(917\) | −5.73190 | −0.189284 | ||||||||
\(918\) | −18.7930 | −0.620262 | ||||||||
\(919\) | −13.6010 | −0.448655 | −0.224327 | − | 0.974514i | \(-0.572018\pi\) | ||||
−0.224327 | + | 0.974514i | \(0.572018\pi\) | |||||||
\(920\) | −52.1185 | −1.71830 | ||||||||
\(921\) | −2.18564 | −0.0720194 | ||||||||
\(922\) | 59.9299 | 1.97369 | ||||||||
\(923\) | 39.0022 | 1.28377 | ||||||||
\(924\) | 61.7279 | 2.03070 | ||||||||
\(925\) | −5.04583 | −0.165906 | ||||||||
\(926\) | −23.8465 | −0.783645 | ||||||||
\(927\) | −61.6736 | −2.02563 | ||||||||
\(928\) | 27.3086 | 0.896448 | ||||||||
\(929\) | −10.2628 | −0.336710 | −0.168355 | − | 0.985726i | \(-0.553845\pi\) | ||||
−0.168355 | + | 0.985726i | \(0.553845\pi\) | |||||||
\(930\) | 33.7892 | 1.10799 | ||||||||
\(931\) | −7.49461 | −0.245626 | ||||||||
\(932\) | −62.5291 | −2.04821 | ||||||||
\(933\) | −29.4235 | −0.963282 | ||||||||
\(934\) | 15.7847 | 0.516492 | ||||||||
\(935\) | 18.5091 | 0.605314 | ||||||||
\(936\) | 46.0288 | 1.50450 | ||||||||
\(937\) | 46.2018 | 1.50935 | 0.754673 | − | 0.656101i | \(-0.227796\pi\) | ||||
0.754673 | + | 0.656101i | \(0.227796\pi\) | |||||||
\(938\) | −52.2996 | −1.70764 | ||||||||
\(939\) | −43.4246 | −1.41711 | ||||||||
\(940\) | −9.94363 | −0.324326 | ||||||||
\(941\) | −23.4844 | −0.765568 | −0.382784 | − | 0.923838i | \(-0.625035\pi\) | ||||
−0.382784 | + | 0.923838i | \(0.625035\pi\) | |||||||
\(942\) | −124.643 | −4.06109 | ||||||||
\(943\) | −14.0517 | −0.457586 | ||||||||
\(944\) | 3.15520 | 0.102693 | ||||||||
\(945\) | −19.3387 | −0.629087 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.6686 | −1.28906 | −0.644528 | − | 0.764580i | \(-0.722946\pi\) | ||||
−0.644528 | + | 0.764580i | \(0.722946\pi\) | |||||||
\(948\) | 88.7289 | 2.88178 | ||||||||
\(949\) | −28.7826 | −0.934321 | ||||||||
\(950\) | 11.3441 | 0.368050 | ||||||||
\(951\) | −3.62262 | −0.117471 | ||||||||
\(952\) | 15.9180 | 0.515906 | ||||||||
\(953\) | −22.5856 | −0.731619 | −0.365809 | − | 0.930690i | \(-0.619208\pi\) | ||||
−0.365809 | + | 0.930690i | \(0.619208\pi\) | |||||||
\(954\) | 103.182 | 3.34066 | ||||||||
\(955\) | −9.49340 | −0.307199 | ||||||||
\(956\) | 53.1001 | 1.71738 | ||||||||
\(957\) | 45.6028 | 1.47413 | ||||||||
\(958\) | 33.5267 | 1.08320 | ||||||||
\(959\) | 8.23260 | 0.265845 | ||||||||
\(960\) | −87.0845 | −2.81064 | ||||||||
\(961\) | −26.4596 | −0.853537 | ||||||||
\(962\) | −27.6953 | −0.892931 | ||||||||
\(963\) | 54.1640 | 1.74541 | ||||||||
\(964\) | 10.3021 | 0.331810 | ||||||||
\(965\) | −40.8056 | −1.31358 | ||||||||
\(966\) | 89.8956 | 2.89234 | ||||||||
\(967\) | 43.7263 | 1.40614 | 0.703071 | − | 0.711119i | \(-0.251811\pi\) | ||||
0.703071 | + | 0.711119i | \(0.251811\pi\) | |||||||
\(968\) | −3.90673 | −0.125567 | ||||||||
\(969\) | −21.3176 | −0.684820 | ||||||||
\(970\) | −24.7981 | −0.796218 | ||||||||
\(971\) | −1.74534 | −0.0560106 | −0.0280053 | − | 0.999608i | \(-0.508916\pi\) | ||||
−0.0280053 | + | 0.999608i | \(0.508916\pi\) | |||||||
\(972\) | −66.3267 | −2.12743 | ||||||||
\(973\) | 40.0671 | 1.28449 | ||||||||
\(974\) | −7.10839 | −0.227768 | ||||||||
\(975\) | 13.4773 | 0.431620 | ||||||||
\(976\) | −1.28451 | −0.0411160 | ||||||||
\(977\) | −31.6577 | −1.01282 | −0.506409 | − | 0.862293i | \(-0.669027\pi\) | ||||
−0.506409 | + | 0.862293i | \(0.669027\pi\) | |||||||
\(978\) | 96.3546 | 3.08108 | ||||||||
\(979\) | −46.8137 | −1.49617 | ||||||||
\(980\) | −18.8411 | −0.601858 | ||||||||
\(981\) | 61.8848 | 1.97583 | ||||||||
\(982\) | −3.79641 | −0.121148 | ||||||||
\(983\) | 1.95919 | 0.0624886 | 0.0312443 | − | 0.999512i | \(-0.490053\pi\) | ||||
0.0312443 | + | 0.999512i | \(0.490053\pi\) | |||||||
\(984\) | 17.9682 | 0.572806 | ||||||||
\(985\) | −51.3577 | −1.63639 | ||||||||
\(986\) | 29.2064 | 0.930122 | ||||||||
\(987\) | 6.90578 | 0.219813 | ||||||||
\(988\) | 38.9798 | 1.24011 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −78.6531 | −2.49976 | ||||||||
\(991\) | −60.3980 | −1.91861 | −0.959303 | − | 0.282377i | \(-0.908877\pi\) | ||||
−0.959303 | + | 0.282377i | \(0.908877\pi\) | |||||||
\(992\) | −10.7555 | −0.341487 | ||||||||
\(993\) | 83.8261 | 2.66014 | ||||||||
\(994\) | −57.3163 | −1.81796 | ||||||||
\(995\) | 23.5719 | 0.747281 | ||||||||
\(996\) | 25.9354 | 0.821795 | ||||||||
\(997\) | 4.37427 | 0.138534 | 0.0692672 | − | 0.997598i | \(-0.477934\pi\) | ||||
0.0692672 | + | 0.997598i | \(0.477934\pi\) | |||||||
\(998\) | −79.0779 | −2.50317 | ||||||||
\(999\) | −12.1122 | −0.383212 |
(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.o.1.16 | 18 | ||
43.3 | odd | 42 | 43.2.g.a.9.1 | ✓ | 36 | ||
43.29 | odd | 42 | 43.2.g.a.24.1 | yes | 36 | ||
43.42 | odd | 2 | 1849.2.a.n.1.3 | 18 | |||
129.29 | even | 42 | 387.2.y.c.325.3 | 36 | |||
129.89 | even | 42 | 387.2.y.c.181.3 | 36 | |||
172.3 | even | 42 | 688.2.bg.c.353.1 | 36 | |||
172.115 | even | 42 | 688.2.bg.c.497.1 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.g.a.9.1 | ✓ | 36 | 43.3 | odd | 42 | ||
43.2.g.a.24.1 | yes | 36 | 43.29 | odd | 42 | ||
387.2.y.c.181.3 | 36 | 129.89 | even | 42 | |||
387.2.y.c.325.3 | 36 | 129.29 | even | 42 | |||
688.2.bg.c.353.1 | 36 | 172.3 | even | 42 | |||
688.2.bg.c.497.1 | 36 | 172.115 | even | 42 | |||
1849.2.a.n.1.3 | 18 | 43.42 | odd | 2 | |||
1849.2.a.o.1.16 | 18 | 1.1 | even | 1 | trivial |