Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1075,2,Mod(1,1075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1075, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1075 = 5^{2} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1075.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: | \(8.58391821729\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.282109865.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 11x^{4} + 8x^{3} + 34x^{2} - 12x - 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.66064\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.66064 | −1.17425 | −0.587125 | − | 0.809497i | \(-0.699740\pi\) | ||||
−0.587125 | + | 0.809497i | \(0.699740\pi\) | |||||||
\(3\) | −3.28593 | −1.89713 | −0.948567 | − | 0.316577i | \(-0.897466\pi\) | ||||
−0.948567 | + | 0.316577i | \(0.897466\pi\) | |||||||
\(4\) | 0.757722 | 0.378861 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.45675 | 2.22771 | ||||||||
\(7\) | −0.418362 | −0.158126 | −0.0790629 | − | 0.996870i | \(-0.525193\pi\) | ||||
−0.0790629 | + | 0.996870i | \(0.525193\pi\) | |||||||
\(8\) | 2.06297 | 0.729372 | ||||||||
\(9\) | 7.79735 | 2.59912 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.03535 | −0.312169 | −0.156084 | − | 0.987744i | \(-0.549887\pi\) | ||||
−0.156084 | + | 0.987744i | \(0.549887\pi\) | |||||||
\(12\) | −2.48982 | −0.718750 | ||||||||
\(13\) | −1.83145 | −0.507954 | −0.253977 | − | 0.967210i | \(-0.581739\pi\) | ||||
−0.253977 | + | 0.967210i | \(0.581739\pi\) | |||||||
\(14\) | 0.694748 | 0.185679 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.94130 | −1.23533 | ||||||||
\(17\) | 5.10985 | 1.23932 | 0.619660 | − | 0.784870i | \(-0.287270\pi\) | ||||
0.619660 | + | 0.784870i | \(0.287270\pi\) | |||||||
\(18\) | −12.9486 | −3.05201 | ||||||||
\(19\) | 3.10985 | 0.713448 | 0.356724 | − | 0.934210i | \(-0.383894\pi\) | ||||
0.356724 | + | 0.934210i | \(0.383894\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.37471 | 0.299986 | ||||||||
\(22\) | 1.71934 | 0.366564 | ||||||||
\(23\) | −8.80565 | −1.83611 | −0.918053 | − | 0.396458i | \(-0.870239\pi\) | ||||
−0.918053 | + | 0.396458i | \(0.870239\pi\) | |||||||
\(24\) | −6.77879 | −1.38372 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.04138 | 0.596465 | ||||||||
\(27\) | −15.7637 | −3.03373 | ||||||||
\(28\) | −0.317002 | −0.0599078 | ||||||||
\(29\) | −1.66368 | −0.308937 | −0.154469 | − | 0.987998i | \(-0.549367\pi\) | ||||
−0.154469 | + | 0.987998i | \(0.549367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.86680 | −0.694498 | −0.347249 | − | 0.937773i | \(-0.612884\pi\) | ||||
−0.347249 | + | 0.937773i | \(0.612884\pi\) | |||||||
\(32\) | 4.07977 | 0.721208 | ||||||||
\(33\) | 3.40208 | 0.592226 | ||||||||
\(34\) | −8.48561 | −1.45527 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.90822 | 0.984704 | ||||||||
\(37\) | 5.86984 | 0.964996 | 0.482498 | − | 0.875897i | \(-0.339730\pi\) | ||||
0.482498 | + | 0.875897i | \(0.339730\pi\) | |||||||
\(38\) | −5.16433 | −0.837766 | ||||||||
\(39\) | 6.01803 | 0.963657 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.8578 | −1.69570 | −0.847851 | − | 0.530234i | \(-0.822104\pi\) | ||||
−0.847851 | + | 0.530234i | \(0.822104\pi\) | |||||||
\(42\) | −2.28289 | −0.352258 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | −0.784506 | −0.118269 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.6230 | 2.15605 | ||||||||
\(47\) | −0.275355 | −0.0401647 | −0.0200823 | − | 0.999798i | \(-0.506393\pi\) | ||||
−0.0200823 | + | 0.999798i | \(0.506393\pi\) | |||||||
\(48\) | 16.2368 | 2.34358 | ||||||||
\(49\) | −6.82497 | −0.974996 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.7906 | −2.35116 | ||||||||
\(52\) | −1.38773 | −0.192444 | ||||||||
\(53\) | 7.35014 | 1.00962 | 0.504810 | − | 0.863230i | \(-0.331563\pi\) | ||||
0.504810 | + | 0.863230i | \(0.331563\pi\) | |||||||
\(54\) | 26.1779 | 3.56236 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.863070 | −0.115333 | ||||||||
\(57\) | −10.2187 | −1.35351 | ||||||||
\(58\) | 2.76277 | 0.362769 | ||||||||
\(59\) | 10.0095 | 1.30313 | 0.651566 | − | 0.758592i | \(-0.274112\pi\) | ||||
0.651566 | + | 0.758592i | \(0.274112\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.84598 | −0.492427 | −0.246214 | − | 0.969216i | \(-0.579186\pi\) | ||||
−0.246214 | + | 0.969216i | \(0.579186\pi\) | |||||||
\(62\) | 6.42136 | 0.815514 | ||||||||
\(63\) | −3.26211 | −0.410987 | ||||||||
\(64\) | 3.10758 | 0.388447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.64963 | −0.695421 | ||||||||
\(67\) | 6.49513 | 0.793507 | 0.396753 | − | 0.917925i | \(-0.370137\pi\) | ||||
0.396753 | + | 0.917925i | \(0.370137\pi\) | |||||||
\(68\) | 3.87185 | 0.469530 | ||||||||
\(69\) | 28.9348 | 3.48334 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.25380 | 0.742190 | 0.371095 | − | 0.928595i | \(-0.378982\pi\) | ||||
0.371095 | + | 0.928595i | \(0.378982\pi\) | |||||||
\(72\) | 16.0857 | 1.89572 | ||||||||
\(73\) | 2.78582 | 0.326056 | 0.163028 | − | 0.986621i | \(-0.447874\pi\) | ||||
0.163028 | + | 0.986621i | \(0.447874\pi\) | |||||||
\(74\) | −9.74768 | −1.13315 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.35640 | 0.270298 | ||||||||
\(77\) | 0.433149 | 0.0493620 | ||||||||
\(78\) | −9.99378 | −1.13157 | ||||||||
\(79\) | −16.3754 | −1.84238 | −0.921190 | − | 0.389114i | \(-0.872781\pi\) | ||||
−0.921190 | + | 0.389114i | \(0.872781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 28.4066 | 3.15628 | ||||||||
\(82\) | 18.0309 | 1.99118 | ||||||||
\(83\) | 6.13740 | 0.673667 | 0.336834 | − | 0.941564i | \(-0.390644\pi\) | ||||
0.336834 | + | 0.941564i | \(0.390644\pi\) | |||||||
\(84\) | 1.04165 | 0.113653 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.66064 | 0.179071 | ||||||||
\(87\) | 5.46673 | 0.586095 | ||||||||
\(88\) | −2.13589 | −0.227687 | ||||||||
\(89\) | 15.3732 | 1.62956 | 0.814780 | − | 0.579770i | \(-0.196858\pi\) | ||||
0.814780 | + | 0.579770i | \(0.196858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.766210 | 0.0803207 | ||||||||
\(92\) | −6.67224 | −0.695629 | ||||||||
\(93\) | 12.7060 | 1.31756 | ||||||||
\(94\) | 0.457265 | 0.0471633 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −13.4058 | −1.36823 | ||||||||
\(97\) | 9.11314 | 0.925299 | 0.462649 | − | 0.886541i | \(-0.346899\pi\) | ||||
0.462649 | + | 0.886541i | \(0.346899\pi\) | |||||||
\(98\) | 11.3338 | 1.14489 | ||||||||
\(99\) | −8.07296 | −0.811363 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3938 | 1.33273 | 0.666365 | − | 0.745626i | \(-0.267849\pi\) | ||||
0.666365 | + | 0.745626i | \(0.267849\pi\) | |||||||
\(102\) | 27.8831 | 2.76084 | ||||||||
\(103\) | −16.1555 | −1.59185 | −0.795925 | − | 0.605396i | \(-0.793015\pi\) | ||||
−0.795925 | + | 0.605396i | \(0.793015\pi\) | |||||||
\(104\) | −3.77824 | −0.370487 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.2059 | −1.18555 | ||||||||
\(107\) | 1.25504 | 0.121329 | 0.0606647 | − | 0.998158i | \(-0.480678\pi\) | ||||
0.0606647 | + | 0.998158i | \(0.480678\pi\) | |||||||
\(108\) | −11.9445 | −1.14936 | ||||||||
\(109\) | −7.35341 | −0.704329 | −0.352164 | − | 0.935938i | \(-0.614554\pi\) | ||||
−0.352164 | + | 0.935938i | \(0.614554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.2879 | −1.83073 | ||||||||
\(112\) | 2.06725 | 0.195337 | ||||||||
\(113\) | 9.56479 | 0.899780 | 0.449890 | − | 0.893084i | \(-0.351463\pi\) | ||||
0.449890 | + | 0.893084i | \(0.351463\pi\) | |||||||
\(114\) | 16.9696 | 1.58935 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.26061 | −0.117044 | ||||||||
\(117\) | −14.2805 | −1.32023 | ||||||||
\(118\) | −16.6222 | −1.53020 | ||||||||
\(119\) | −2.13776 | −0.195969 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.92806 | −0.902551 | ||||||||
\(122\) | 6.38678 | 0.578232 | ||||||||
\(123\) | 35.6780 | 3.21697 | ||||||||
\(124\) | −2.92996 | −0.263118 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.41719 | 0.482601 | ||||||||
\(127\) | −7.99151 | −0.709132 | −0.354566 | − | 0.935031i | \(-0.615371\pi\) | ||||
−0.354566 | + | 0.935031i | \(0.615371\pi\) | |||||||
\(128\) | −13.3201 | −1.17734 | ||||||||
\(129\) | 3.28593 | 0.289310 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.86435 | 0.512371 | 0.256185 | − | 0.966628i | \(-0.417534\pi\) | ||||
0.256185 | + | 0.966628i | \(0.417534\pi\) | |||||||
\(132\) | 2.57783 | 0.224371 | ||||||||
\(133\) | −1.30104 | −0.112815 | ||||||||
\(134\) | −10.7861 | −0.931775 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.5415 | 0.903925 | ||||||||
\(137\) | −19.6872 | −1.68199 | −0.840995 | − | 0.541042i | \(-0.818030\pi\) | ||||
−0.840995 | + | 0.541042i | \(0.818030\pi\) | |||||||
\(138\) | −48.0502 | −4.09031 | ||||||||
\(139\) | −12.1919 | −1.03410 | −0.517051 | − | 0.855955i | \(-0.672970\pi\) | ||||
−0.517051 | + | 0.855955i | \(0.672970\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.904798 | 0.0761977 | ||||||||
\(142\) | −10.3853 | −0.871516 | ||||||||
\(143\) | 1.89619 | 0.158567 | ||||||||
\(144\) | −38.5290 | −3.21075 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.62624 | −0.382870 | ||||||||
\(147\) | 22.4264 | 1.84970 | ||||||||
\(148\) | 4.44771 | 0.365599 | ||||||||
\(149\) | 21.2313 | 1.73933 | 0.869666 | − | 0.493641i | \(-0.164334\pi\) | ||||
0.869666 | + | 0.493641i | \(0.164334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.9612 | 1.94993 | 0.974966 | − | 0.222355i | \(-0.0713743\pi\) | ||||
0.974966 | + | 0.222355i | \(0.0713743\pi\) | |||||||
\(152\) | 6.41554 | 0.520369 | ||||||||
\(153\) | 39.8432 | 3.22114 | ||||||||
\(154\) | −0.719305 | −0.0579632 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.56000 | 0.365092 | ||||||||
\(157\) | 4.60922 | 0.367856 | 0.183928 | − | 0.982940i | \(-0.441119\pi\) | ||||
0.183928 | + | 0.982940i | \(0.441119\pi\) | |||||||
\(158\) | 27.1937 | 2.16341 | ||||||||
\(159\) | −24.1521 | −1.91538 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.68395 | 0.290336 | ||||||||
\(162\) | −47.1731 | −3.70626 | ||||||||
\(163\) | −8.79982 | −0.689255 | −0.344628 | − | 0.938739i | \(-0.611995\pi\) | ||||
−0.344628 | + | 0.938739i | \(0.611995\pi\) | |||||||
\(164\) | −8.22719 | −0.642436 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.1920 | −0.791053 | ||||||||
\(167\) | 17.4290 | 1.34870 | 0.674348 | − | 0.738413i | \(-0.264425\pi\) | ||||
0.674348 | + | 0.738413i | \(0.264425\pi\) | |||||||
\(168\) | 2.83599 | 0.218801 | ||||||||
\(169\) | −9.64578 | −0.741983 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.2486 | 1.85433 | ||||||||
\(172\) | −0.757722 | −0.0577758 | ||||||||
\(173\) | 1.56459 | 0.118953 | 0.0594767 | − | 0.998230i | \(-0.481057\pi\) | ||||
0.0594767 | + | 0.998230i | \(0.481057\pi\) | |||||||
\(174\) | −9.07826 | −0.688221 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.11596 | 0.385630 | ||||||||
\(177\) | −32.8907 | −2.47221 | ||||||||
\(178\) | −25.5294 | −1.91351 | ||||||||
\(179\) | −7.25355 | −0.542156 | −0.271078 | − | 0.962557i | \(-0.587380\pi\) | ||||
−0.271078 | + | 0.962557i | \(0.587380\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6732 | 1.23931 | 0.619656 | − | 0.784873i | \(-0.287272\pi\) | ||||
0.619656 | + | 0.784873i | \(0.287272\pi\) | |||||||
\(182\) | −1.27240 | −0.0943165 | ||||||||
\(183\) | 12.6376 | 0.934200 | ||||||||
\(184\) | −18.1658 | −1.33920 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −21.1002 | −1.54714 | ||||||||
\(187\) | −5.29046 | −0.386877 | ||||||||
\(188\) | −0.208643 | −0.0152168 | ||||||||
\(189\) | 6.59495 | 0.479712 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.5312 | 0.762014 | 0.381007 | − | 0.924572i | \(-0.375577\pi\) | ||||
0.381007 | + | 0.924572i | \(0.375577\pi\) | |||||||
\(192\) | −10.2113 | −0.736936 | ||||||||
\(193\) | −3.40684 | −0.245229 | −0.122615 | − | 0.992454i | \(-0.539128\pi\) | ||||
−0.122615 | + | 0.992454i | \(0.539128\pi\) | |||||||
\(194\) | −15.1336 | −1.08653 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.17144 | −0.369388 | ||||||||
\(197\) | 12.7570 | 0.908897 | 0.454449 | − | 0.890773i | \(-0.349836\pi\) | ||||
0.454449 | + | 0.890773i | \(0.349836\pi\) | |||||||
\(198\) | 13.4063 | 0.952742 | ||||||||
\(199\) | 17.0212 | 1.20660 | 0.603300 | − | 0.797515i | \(-0.293852\pi\) | ||||
0.603300 | + | 0.797515i | \(0.293852\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −21.3426 | −1.50539 | ||||||||
\(202\) | −22.2422 | −1.56496 | ||||||||
\(203\) | 0.696019 | 0.0488509 | ||||||||
\(204\) | −12.7226 | −0.890762 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 26.8285 | 1.86923 | ||||||||
\(207\) | −68.6607 | −4.77225 | ||||||||
\(208\) | 9.04977 | 0.627488 | ||||||||
\(209\) | −3.21977 | −0.222716 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.9014 | 1.09470 | 0.547348 | − | 0.836905i | \(-0.315637\pi\) | ||||
0.547348 | + | 0.836905i | \(0.315637\pi\) | |||||||
\(212\) | 5.56937 | 0.382506 | ||||||||
\(213\) | −20.5496 | −1.40803 | ||||||||
\(214\) | −2.08417 | −0.142471 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −32.5202 | −2.21272 | ||||||||
\(217\) | 1.61772 | 0.109818 | ||||||||
\(218\) | 12.2114 | 0.827057 | ||||||||
\(219\) | −9.15401 | −0.618571 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.35845 | −0.629518 | ||||||||
\(222\) | 32.0302 | 2.14973 | ||||||||
\(223\) | 6.51336 | 0.436167 | 0.218083 | − | 0.975930i | \(-0.430020\pi\) | ||||
0.218083 | + | 0.975930i | \(0.430020\pi\) | |||||||
\(224\) | −1.70682 | −0.114042 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.8837 | −1.05657 | ||||||||
\(227\) | 18.2375 | 1.21047 | 0.605234 | − | 0.796047i | \(-0.293079\pi\) | ||||
0.605234 | + | 0.796047i | \(0.293079\pi\) | |||||||
\(228\) | −7.74297 | −0.512791 | ||||||||
\(229\) | −0.680942 | −0.0449979 | −0.0224989 | − | 0.999747i | \(-0.507162\pi\) | ||||
−0.0224989 | + | 0.999747i | \(0.507162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.42330 | −0.0936462 | ||||||||
\(232\) | −3.43212 | −0.225330 | ||||||||
\(233\) | −19.9212 | −1.30508 | −0.652540 | − | 0.757754i | \(-0.726297\pi\) | ||||
−0.652540 | + | 0.757754i | \(0.726297\pi\) | |||||||
\(234\) | 23.7147 | 1.55028 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.58446 | 0.493706 | ||||||||
\(237\) | 53.8085 | 3.49524 | ||||||||
\(238\) | 3.55005 | 0.230116 | ||||||||
\(239\) | 14.9202 | 0.965110 | 0.482555 | − | 0.875866i | \(-0.339709\pi\) | ||||
0.482555 | + | 0.875866i | \(0.339709\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8540 | −0.699169 | −0.349584 | − | 0.936905i | \(-0.613677\pi\) | ||||
−0.349584 | + | 0.936905i | \(0.613677\pi\) | |||||||
\(242\) | 16.4869 | 1.05982 | ||||||||
\(243\) | −46.0508 | −2.95416 | ||||||||
\(244\) | −2.91419 | −0.186562 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −59.2482 | −3.77753 | ||||||||
\(247\) | −5.69554 | −0.362399 | ||||||||
\(248\) | −7.97711 | −0.506547 | ||||||||
\(249\) | −20.1671 | −1.27804 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.1535 | −0.767124 | −0.383562 | − | 0.923515i | \(-0.625303\pi\) | ||||
−0.383562 | + | 0.923515i | \(0.625303\pi\) | |||||||
\(252\) | −2.47177 | −0.155707 | ||||||||
\(253\) | 9.11691 | 0.573175 | ||||||||
\(254\) | 13.2710 | 0.832698 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.9047 | 0.994046 | ||||||||
\(257\) | −21.4603 | −1.33866 | −0.669328 | − | 0.742967i | \(-0.733418\pi\) | ||||
−0.669328 | + | 0.742967i | \(0.733418\pi\) | |||||||
\(258\) | −5.45675 | −0.339722 | ||||||||
\(259\) | −2.45572 | −0.152591 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.9723 | −0.802963 | ||||||||
\(262\) | −9.73857 | −0.601651 | ||||||||
\(263\) | −1.04713 | −0.0645691 | −0.0322846 | − | 0.999479i | \(-0.510278\pi\) | ||||
−0.0322846 | + | 0.999479i | \(0.510278\pi\) | |||||||
\(264\) | 7.01840 | 0.431953 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.16056 | 0.132472 | ||||||||
\(267\) | −50.5154 | −3.09149 | ||||||||
\(268\) | 4.92151 | 0.300629 | ||||||||
\(269\) | 24.6494 | 1.50290 | 0.751450 | − | 0.659790i | \(-0.229355\pi\) | ||||
0.751450 | + | 0.659790i | \(0.229355\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9212 | 0.663418 | 0.331709 | − | 0.943382i | \(-0.392375\pi\) | ||||
0.331709 | + | 0.943382i | \(0.392375\pi\) | |||||||
\(272\) | −25.2493 | −1.53096 | ||||||||
\(273\) | −2.51771 | −0.152379 | ||||||||
\(274\) | 32.6933 | 1.97508 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 21.9245 | 1.31970 | ||||||||
\(277\) | 17.2987 | 1.03938 | 0.519690 | − | 0.854355i | \(-0.326047\pi\) | ||||
0.519690 | + | 0.854355i | \(0.326047\pi\) | |||||||
\(278\) | 20.2463 | 1.21429 | ||||||||
\(279\) | −30.1508 | −1.80508 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0056 | 0.835504 | 0.417752 | − | 0.908561i | \(-0.362818\pi\) | ||||
0.417752 | + | 0.908561i | \(0.362818\pi\) | |||||||
\(282\) | −1.50254 | −0.0894751 | ||||||||
\(283\) | −5.90394 | −0.350953 | −0.175476 | − | 0.984484i | \(-0.556147\pi\) | ||||
−0.175476 | + | 0.984484i | \(0.556147\pi\) | |||||||
\(284\) | 4.73865 | 0.281187 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.14889 | −0.186198 | ||||||||
\(287\) | 4.54248 | 0.268134 | ||||||||
\(288\) | 31.8114 | 1.87450 | ||||||||
\(289\) | 9.11054 | 0.535914 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29.9451 | −1.75542 | ||||||||
\(292\) | 2.11088 | 0.123530 | ||||||||
\(293\) | 2.93453 | 0.171437 | 0.0857184 | − | 0.996319i | \(-0.472681\pi\) | ||||
0.0857184 | + | 0.996319i | \(0.472681\pi\) | |||||||
\(294\) | −37.2422 | −2.17201 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.1093 | 0.703840 | ||||||||
\(297\) | 16.3209 | 0.947037 | ||||||||
\(298\) | −35.2575 | −2.04241 | ||||||||
\(299\) | 16.1272 | 0.932657 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.418362 | 0.0241140 | ||||||||
\(302\) | −39.7908 | −2.28971 | ||||||||
\(303\) | −44.0110 | −2.52837 | ||||||||
\(304\) | −15.3667 | −0.881340 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −66.1653 | −3.78242 | ||||||||
\(307\) | 7.24809 | 0.413670 | 0.206835 | − | 0.978376i | \(-0.433684\pi\) | ||||
0.206835 | + | 0.978376i | \(0.433684\pi\) | |||||||
\(308\) | 0.328207 | 0.0187013 | ||||||||
\(309\) | 53.0859 | 3.01995 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5821 | 0.770171 | 0.385085 | − | 0.922881i | \(-0.374172\pi\) | ||||
0.385085 | + | 0.922881i | \(0.374172\pi\) | |||||||
\(312\) | 12.4151 | 0.702864 | ||||||||
\(313\) | 2.63634 | 0.149015 | 0.0745073 | − | 0.997220i | \(-0.476262\pi\) | ||||
0.0745073 | + | 0.997220i | \(0.476262\pi\) | |||||||
\(314\) | −7.65425 | −0.431954 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.4080 | −0.698006 | ||||||||
\(317\) | 14.4272 | 0.810312 | 0.405156 | − | 0.914247i | \(-0.367217\pi\) | ||||
0.405156 | + | 0.914247i | \(0.367217\pi\) | |||||||
\(318\) | 40.1079 | 2.24914 | ||||||||
\(319\) | 1.72248 | 0.0964405 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.12398 | −0.230178 | ||||||||
\(322\) | −6.11771 | −0.340926 | ||||||||
\(323\) | 15.8908 | 0.884190 | ||||||||
\(324\) | 21.5243 | 1.19579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.6133 | 0.809357 | ||||||||
\(327\) | 24.1628 | 1.33621 | ||||||||
\(328\) | −22.3994 | −1.23680 | ||||||||
\(329\) | 0.115198 | 0.00635107 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3003 | 0.786016 | 0.393008 | − | 0.919535i | \(-0.371434\pi\) | ||||
0.393008 | + | 0.919535i | \(0.371434\pi\) | |||||||
\(332\) | 4.65045 | 0.255226 | ||||||||
\(333\) | 45.7692 | 2.50813 | ||||||||
\(334\) | −28.9433 | −1.58371 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.79285 | −0.370580 | ||||||||
\(337\) | 23.0364 | 1.25487 | 0.627436 | − | 0.778669i | \(-0.284105\pi\) | ||||
0.627436 | + | 0.778669i | \(0.284105\pi\) | |||||||
\(338\) | 16.0182 | 0.871273 | ||||||||
\(339\) | −31.4293 | −1.70700 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00348 | 0.216801 | ||||||||
\(342\) | −40.2681 | −2.17745 | ||||||||
\(343\) | 5.78384 | 0.312298 | ||||||||
\(344\) | −2.06297 | −0.111228 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.59821 | −0.139681 | ||||||||
\(347\) | −1.03484 | −0.0555531 | −0.0277766 | − | 0.999614i | \(-0.508843\pi\) | ||||
−0.0277766 | + | 0.999614i | \(0.508843\pi\) | |||||||
\(348\) | 4.14226 | 0.222049 | ||||||||
\(349\) | 15.0905 | 0.807777 | 0.403889 | − | 0.914808i | \(-0.367658\pi\) | ||||
0.403889 | + | 0.914808i | \(0.367658\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.8706 | 1.54100 | ||||||||
\(352\) | −4.22398 | −0.225139 | ||||||||
\(353\) | 32.6499 | 1.73778 | 0.868888 | − | 0.495008i | \(-0.164835\pi\) | ||||
0.868888 | + | 0.495008i | \(0.164835\pi\) | |||||||
\(354\) | 54.6196 | 2.90300 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.6486 | 0.617377 | ||||||||
\(357\) | 7.02455 | 0.371778 | ||||||||
\(358\) | 12.0455 | 0.636626 | ||||||||
\(359\) | −9.63690 | −0.508616 | −0.254308 | − | 0.967123i | \(-0.581848\pi\) | ||||
−0.254308 | + | 0.967123i | \(0.581848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.32885 | −0.490992 | ||||||||
\(362\) | −27.6883 | −1.45526 | ||||||||
\(363\) | 32.6229 | 1.71226 | ||||||||
\(364\) | 0.580575 | 0.0304304 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.9865 | −1.09698 | ||||||||
\(367\) | −6.54305 | −0.341544 | −0.170772 | − | 0.985311i | \(-0.554626\pi\) | ||||
−0.170772 | + | 0.985311i | \(0.554626\pi\) | |||||||
\(368\) | 43.5114 | 2.26819 | ||||||||
\(369\) | −84.6620 | −4.40733 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.07502 | −0.159647 | ||||||||
\(372\) | 9.62765 | 0.499171 | ||||||||
\(373\) | 25.3361 | 1.31185 | 0.655927 | − | 0.754824i | \(-0.272278\pi\) | ||||
0.655927 | + | 0.754824i | \(0.272278\pi\) | |||||||
\(374\) | 8.78555 | 0.454290 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.568051 | −0.0292950 | ||||||||
\(377\) | 3.04695 | 0.156926 | ||||||||
\(378\) | −10.9518 | −0.563301 | ||||||||
\(379\) | −9.44773 | −0.485297 | −0.242649 | − | 0.970114i | \(-0.578016\pi\) | ||||
−0.242649 | + | 0.970114i | \(0.578016\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.2596 | 1.34532 | ||||||||
\(382\) | −17.4886 | −0.894795 | ||||||||
\(383\) | 27.7715 | 1.41906 | 0.709530 | − | 0.704675i | \(-0.248907\pi\) | ||||
0.709530 | + | 0.704675i | \(0.248907\pi\) | |||||||
\(384\) | 43.7690 | 2.23357 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.65753 | 0.287960 | ||||||||
\(387\) | −7.79735 | −0.396361 | ||||||||
\(388\) | 6.90523 | 0.350560 | ||||||||
\(389\) | 15.8897 | 0.805638 | 0.402819 | − | 0.915280i | \(-0.368030\pi\) | ||||
0.402819 | + | 0.915280i | \(0.368030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −44.9955 | −2.27552 | ||||||||
\(392\) | −14.0797 | −0.711135 | ||||||||
\(393\) | −19.2699 | −0.972036 | ||||||||
\(394\) | −21.1847 | −1.06727 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.11706 | −0.307394 | ||||||||
\(397\) | −7.27891 | −0.365318 | −0.182659 | − | 0.983176i | \(-0.558470\pi\) | ||||
−0.182659 | + | 0.983176i | \(0.558470\pi\) | |||||||
\(398\) | −28.2660 | −1.41685 | ||||||||
\(399\) | 4.27513 | 0.214024 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.0688 | −1.80119 | −0.900595 | − | 0.434659i | \(-0.856869\pi\) | ||||
−0.900595 | + | 0.434659i | \(0.856869\pi\) | |||||||
\(402\) | 35.4423 | 1.76770 | ||||||||
\(403\) | 7.08187 | 0.352773 | ||||||||
\(404\) | 10.1488 | 0.504920 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.15584 | −0.0573632 | ||||||||
\(407\) | −6.07732 | −0.301242 | ||||||||
\(408\) | −34.6386 | −1.71487 | ||||||||
\(409\) | −2.84173 | −0.140515 | −0.0702573 | − | 0.997529i | \(-0.522382\pi\) | ||||
−0.0702573 | + | 0.997529i | \(0.522382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 64.6908 | 3.19096 | ||||||||
\(412\) | −12.2414 | −0.603090 | ||||||||
\(413\) | −4.18761 | −0.206059 | ||||||||
\(414\) | 114.021 | 5.60381 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.47191 | −0.366341 | ||||||||
\(417\) | 40.0617 | 1.96183 | ||||||||
\(418\) | 5.34688 | 0.261524 | ||||||||
\(419\) | −29.8465 | −1.45810 | −0.729049 | − | 0.684462i | \(-0.760037\pi\) | ||||
−0.729049 | + | 0.684462i | \(0.760037\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.8518 | 1.40615 | 0.703075 | − | 0.711116i | \(-0.251810\pi\) | ||||
0.703075 | + | 0.711116i | \(0.251810\pi\) | |||||||
\(422\) | −26.4064 | −1.28545 | ||||||||
\(423\) | −2.14704 | −0.104393 | ||||||||
\(424\) | 15.1632 | 0.736388 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 34.1254 | 1.65338 | ||||||||
\(427\) | 1.60901 | 0.0778655 | ||||||||
\(428\) | 0.950973 | 0.0459670 | ||||||||
\(429\) | −6.23075 | −0.300824 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.38096 | 0.114687 | 0.0573435 | − | 0.998355i | \(-0.481737\pi\) | ||||
0.0573435 | + | 0.998355i | \(0.481737\pi\) | |||||||
\(432\) | 77.8934 | 3.74765 | ||||||||
\(433\) | −20.6586 | −0.992790 | −0.496395 | − | 0.868097i | \(-0.665343\pi\) | ||||
−0.496395 | + | 0.868097i | \(0.665343\pi\) | |||||||
\(434\) | −2.68645 | −0.128954 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.57184 | −0.266843 | ||||||||
\(437\) | −27.3842 | −1.30997 | ||||||||
\(438\) | 15.2015 | 0.726356 | ||||||||
\(439\) | 23.2249 | 1.10846 | 0.554231 | − | 0.832363i | \(-0.313012\pi\) | ||||
0.554231 | + | 0.832363i | \(0.313012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −53.2167 | −2.53413 | ||||||||
\(442\) | 15.5410 | 0.739211 | ||||||||
\(443\) | −36.2317 | −1.72142 | −0.860710 | − | 0.509095i | \(-0.829980\pi\) | ||||
−0.860710 | + | 0.509095i | \(0.829980\pi\) | |||||||
\(444\) | −14.6149 | −0.693591 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.8163 | −0.512168 | ||||||||
\(447\) | −69.7644 | −3.29974 | ||||||||
\(448\) | −1.30009 | −0.0614235 | ||||||||
\(449\) | −31.7118 | −1.49657 | −0.748286 | − | 0.663377i | \(-0.769123\pi\) | ||||
−0.748286 | + | 0.663377i | \(0.769123\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.2416 | 0.529345 | ||||||||
\(452\) | 7.24746 | 0.340892 | ||||||||
\(453\) | −78.7347 | −3.69928 | ||||||||
\(454\) | −30.2860 | −1.42139 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −21.0810 | −0.987209 | ||||||||
\(457\) | 15.4209 | 0.721358 | 0.360679 | − | 0.932690i | \(-0.382545\pi\) | ||||
0.360679 | + | 0.932690i | \(0.382545\pi\) | |||||||
\(458\) | 1.13080 | 0.0528387 | ||||||||
\(459\) | −80.5504 | −3.75977 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.98422 | −0.138989 | −0.0694945 | − | 0.997582i | \(-0.522139\pi\) | ||||
−0.0694945 | + | 0.997582i | \(0.522139\pi\) | |||||||
\(462\) | 2.36359 | 0.109964 | ||||||||
\(463\) | 23.3271 | 1.08410 | 0.542052 | − | 0.840345i | \(-0.317648\pi\) | ||||
0.542052 | + | 0.840345i | \(0.317648\pi\) | |||||||
\(464\) | 8.22073 | 0.381638 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 33.0819 | 1.53249 | ||||||||
\(467\) | 12.3447 | 0.571243 | 0.285621 | − | 0.958343i | \(-0.407800\pi\) | ||||
0.285621 | + | 0.958343i | \(0.407800\pi\) | |||||||
\(468\) | −10.8206 | −0.500184 | ||||||||
\(469\) | −2.71731 | −0.125474 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.1456 | −0.697871 | ||||||||
\(472\) | 20.6494 | 0.950467 | ||||||||
\(473\) | 1.03535 | 0.0476053 | ||||||||
\(474\) | −89.3566 | −4.10428 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.61983 | −0.0742449 | ||||||||
\(477\) | 57.3116 | 2.62412 | ||||||||
\(478\) | −24.7771 | −1.13328 | ||||||||
\(479\) | 15.9091 | 0.726903 | 0.363452 | − | 0.931613i | \(-0.381598\pi\) | ||||
0.363452 | + | 0.931613i | \(0.381598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.7503 | −0.490173 | ||||||||
\(482\) | 18.0246 | 0.820999 | ||||||||
\(483\) | −12.1052 | −0.550806 | ||||||||
\(484\) | −7.52271 | −0.341941 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 76.4737 | 3.46892 | ||||||||
\(487\) | −8.15431 | −0.369507 | −0.184753 | − | 0.982785i | \(-0.559149\pi\) | ||||
−0.184753 | + | 0.982785i | \(0.559149\pi\) | |||||||
\(488\) | −7.93416 | −0.359163 | ||||||||
\(489\) | 28.9156 | 1.30761 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.4997 | 1.69234 | 0.846169 | − | 0.532915i | \(-0.178904\pi\) | ||||
0.846169 | + | 0.532915i | \(0.178904\pi\) | |||||||
\(492\) | 27.0340 | 1.21879 | ||||||||
\(493\) | −8.50114 | −0.382872 | ||||||||
\(494\) | 9.45824 | 0.425546 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.1070 | 0.857931 | ||||||||
\(497\) | −2.61635 | −0.117359 | ||||||||
\(498\) | 33.4902 | 1.50073 | ||||||||
\(499\) | −16.3210 | −0.730629 | −0.365315 | − | 0.930884i | \(-0.619039\pi\) | ||||
−0.365315 | + | 0.930884i | \(0.619039\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −57.2705 | −2.55866 | ||||||||
\(502\) | 20.1826 | 0.900795 | ||||||||
\(503\) | 7.34030 | 0.327288 | 0.163644 | − | 0.986519i | \(-0.447675\pi\) | ||||
0.163644 | + | 0.986519i | \(0.447675\pi\) | |||||||
\(504\) | −6.72965 | −0.299762 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.1399 | −0.673050 | ||||||||
\(507\) | 31.6954 | 1.40764 | ||||||||
\(508\) | −6.05535 | −0.268663 | ||||||||
\(509\) | 27.1292 | 1.20248 | 0.601240 | − | 0.799069i | \(-0.294674\pi\) | ||||
0.601240 | + | 0.799069i | \(0.294674\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.16548 | −0.0515578 | ||||||||
\(512\) | 0.228189 | 0.0100846 | ||||||||
\(513\) | −49.0229 | −2.16441 | ||||||||
\(514\) | 35.6378 | 1.57192 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.48982 | 0.109608 | ||||||||
\(517\) | 0.285088 | 0.0125382 | ||||||||
\(518\) | 4.07806 | 0.179180 | ||||||||
\(519\) | −5.14113 | −0.225670 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.6617 | 1.64999 | 0.824995 | − | 0.565140i | \(-0.191178\pi\) | ||||
0.824995 | + | 0.565140i | \(0.191178\pi\) | |||||||
\(522\) | 21.5423 | 0.942879 | ||||||||
\(523\) | −18.4289 | −0.805841 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(524\) | 4.44355 | 0.194117 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.73891 | 0.0758202 | ||||||||
\(527\) | −19.7588 | −0.860705 | ||||||||
\(528\) | −16.8107 | −0.731592 | ||||||||
\(529\) | 54.5395 | 2.37128 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 78.0479 | 3.38699 | ||||||||
\(532\) | −0.985828 | −0.0427411 | ||||||||
\(533\) | 19.8856 | 0.861339 | ||||||||
\(534\) | 83.8879 | 3.63018 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 13.3993 | 0.578761 | ||||||||
\(537\) | 23.8347 | 1.02854 | ||||||||
\(538\) | −40.9338 | −1.76478 | ||||||||
\(539\) | 7.06622 | 0.304363 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.53559 | −0.237994 | −0.118997 | − | 0.992895i | \(-0.537968\pi\) | ||||
−0.118997 | + | 0.992895i | \(0.537968\pi\) | |||||||
\(542\) | −18.1362 | −0.779018 | ||||||||
\(543\) | −54.7872 | −2.35114 | ||||||||
\(544\) | 20.8470 | 0.893808 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.18101 | 0.178931 | ||||||||
\(547\) | −26.4946 | −1.13283 | −0.566413 | − | 0.824121i | \(-0.691669\pi\) | ||||
−0.566413 | + | 0.824121i | \(0.691669\pi\) | |||||||
\(548\) | −14.9174 | −0.637241 | ||||||||
\(549\) | −29.9884 | −1.27988 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.17378 | −0.220411 | ||||||||
\(552\) | 59.6917 | 2.54065 | ||||||||
\(553\) | 6.85085 | 0.291328 | ||||||||
\(554\) | −28.7270 | −1.22049 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.23807 | −0.391781 | ||||||||
\(557\) | −39.4417 | −1.67120 | −0.835599 | − | 0.549340i | \(-0.814879\pi\) | ||||
−0.835599 | + | 0.549340i | \(0.814879\pi\) | |||||||
\(558\) | 50.0696 | 2.11961 | ||||||||
\(559\) | 1.83145 | 0.0774623 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.3841 | 0.733957 | ||||||||
\(562\) | −23.2583 | −0.981090 | ||||||||
\(563\) | 16.1786 | 0.681847 | 0.340923 | − | 0.940091i | \(-0.389260\pi\) | ||||
0.340923 | + | 0.940091i | \(0.389260\pi\) | |||||||
\(564\) | 0.685586 | 0.0288684 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.80431 | 0.412106 | ||||||||
\(567\) | −11.8842 | −0.499090 | ||||||||
\(568\) | 12.9014 | 0.541332 | ||||||||
\(569\) | 24.1001 | 1.01033 | 0.505164 | − | 0.863023i | \(-0.331432\pi\) | ||||
0.505164 | + | 0.863023i | \(0.331432\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.47727 | 0.0618217 | 0.0309109 | − | 0.999522i | \(-0.490159\pi\) | ||||
0.0309109 | + | 0.999522i | \(0.490159\pi\) | |||||||
\(572\) | 1.43679 | 0.0600750 | ||||||||
\(573\) | −34.6050 | −1.44564 | ||||||||
\(574\) | −7.54343 | −0.314857 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.2309 | 1.00962 | ||||||||
\(577\) | 28.0608 | 1.16819 | 0.584094 | − | 0.811686i | \(-0.301450\pi\) | ||||
0.584094 | + | 0.811686i | \(0.301450\pi\) | |||||||
\(578\) | −15.1293 | −0.629297 | ||||||||
\(579\) | 11.1946 | 0.465233 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.56765 | −0.106524 | ||||||||
\(582\) | 49.7281 | 2.06129 | ||||||||
\(583\) | −7.60995 | −0.315172 | ||||||||
\(584\) | 5.74708 | 0.237816 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.87319 | −0.201310 | ||||||||
\(587\) | −0.883090 | −0.0364490 | −0.0182245 | − | 0.999834i | \(-0.505801\pi\) | ||||
−0.0182245 | + | 0.999834i | \(0.505801\pi\) | |||||||
\(588\) | 16.9930 | 0.700779 | ||||||||
\(589\) | −12.0252 | −0.495488 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.9186 | −1.72430 | ||||||||
\(592\) | −29.0046 | −1.19208 | ||||||||
\(593\) | 1.46230 | 0.0600494 | 0.0300247 | − | 0.999549i | \(-0.490441\pi\) | ||||
0.0300247 | + | 0.999549i | \(0.490441\pi\) | |||||||
\(594\) | −27.1032 | −1.11206 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.0874 | 0.658965 | ||||||||
\(597\) | −55.9304 | −2.28908 | ||||||||
\(598\) | −26.7814 | −1.09517 | ||||||||
\(599\) | 39.1820 | 1.60093 | 0.800467 | − | 0.599376i | \(-0.204585\pi\) | ||||
0.800467 | + | 0.599376i | \(0.204585\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5220 | −0.510782 | −0.255391 | − | 0.966838i | \(-0.582204\pi\) | ||||
−0.255391 | + | 0.966838i | \(0.582204\pi\) | |||||||
\(602\) | −0.694748 | −0.0283158 | ||||||||
\(603\) | 50.6448 | 2.06242 | ||||||||
\(604\) | 18.1559 | 0.738754 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 73.0864 | 2.96893 | ||||||||
\(607\) | 31.4913 | 1.27819 | 0.639097 | − | 0.769126i | \(-0.279308\pi\) | ||||
0.639097 | + | 0.769126i | \(0.279308\pi\) | |||||||
\(608\) | 12.6875 | 0.514544 | ||||||||
\(609\) | −2.28707 | −0.0926767 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.504300 | 0.0204018 | ||||||||
\(612\) | 30.1901 | 1.22036 | ||||||||
\(613\) | 8.81861 | 0.356180 | 0.178090 | − | 0.984014i | \(-0.443008\pi\) | ||||
0.178090 | + | 0.984014i | \(0.443008\pi\) | |||||||
\(614\) | −12.0365 | −0.485752 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.893576 | 0.0360032 | ||||||||
\(617\) | −0.0225984 | −0.000909776 0 | −0.000454888 | − | 1.00000i | \(-0.500145\pi\) | ||||
−0.000454888 | 1.00000i | \(0.500145\pi\) | ||||||||
\(618\) | −88.1565 | −3.54618 | ||||||||
\(619\) | −35.2045 | −1.41499 | −0.707495 | − | 0.706719i | \(-0.750175\pi\) | ||||
−0.707495 | + | 0.706719i | \(0.750175\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 138.810 | 5.57026 | ||||||||
\(622\) | −22.5550 | −0.904372 | ||||||||
\(623\) | −6.43157 | −0.257676 | ||||||||
\(624\) | −29.7369 | −1.19043 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.37801 | −0.174980 | ||||||||
\(627\) | 10.5799 | 0.422522 | ||||||||
\(628\) | 3.49251 | 0.139366 | ||||||||
\(629\) | 29.9940 | 1.19594 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.6406 | −1.37902 | −0.689511 | − | 0.724275i | \(-0.742174\pi\) | ||||
−0.689511 | + | 0.724275i | \(0.742174\pi\) | |||||||
\(632\) | −33.7821 | −1.34378 | ||||||||
\(633\) | −52.2508 | −2.07678 | ||||||||
\(634\) | −23.9584 | −0.951509 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −18.3006 | −0.725665 | ||||||||
\(637\) | 12.4996 | 0.495253 | ||||||||
\(638\) | −2.86042 | −0.113245 | ||||||||
\(639\) | 48.7631 | 1.92904 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.72453 | 0.226105 | 0.113053 | − | 0.993589i | \(-0.463937\pi\) | ||||
0.113053 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(642\) | 6.84844 | 0.270287 | ||||||||
\(643\) | −5.48384 | −0.216262 | −0.108131 | − | 0.994137i | \(-0.534487\pi\) | ||||
−0.108131 | + | 0.994137i | \(0.534487\pi\) | |||||||
\(644\) | 2.79141 | 0.109997 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26.3890 | −1.03826 | ||||||||
\(647\) | 12.4219 | 0.488357 | 0.244178 | − | 0.969730i | \(-0.421482\pi\) | ||||
0.244178 | + | 0.969730i | \(0.421482\pi\) | |||||||
\(648\) | 58.6020 | 2.30210 | ||||||||
\(649\) | −10.3634 | −0.406797 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.31572 | −0.208340 | ||||||||
\(652\) | −6.66782 | −0.261132 | ||||||||
\(653\) | −29.0925 | −1.13848 | −0.569238 | − | 0.822173i | \(-0.692762\pi\) | ||||
−0.569238 | + | 0.822173i | \(0.692762\pi\) | |||||||
\(654\) | −40.1257 | −1.56904 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 53.6516 | 2.09474 | ||||||||
\(657\) | 21.7220 | 0.847456 | ||||||||
\(658\) | −0.191302 | −0.00745774 | ||||||||
\(659\) | −8.60292 | −0.335122 | −0.167561 | − | 0.985862i | \(-0.553589\pi\) | ||||
−0.167561 | + | 0.985862i | \(0.553589\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.394246 | −0.0153344 | −0.00766719 | − | 0.999971i | \(-0.502441\pi\) | ||||
−0.00766719 | + | 0.999971i | \(0.502441\pi\) | |||||||
\(662\) | −23.7476 | −0.922978 | ||||||||
\(663\) | 30.7512 | 1.19428 | ||||||||
\(664\) | 12.6613 | 0.491354 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −76.0061 | −2.94518 | ||||||||
\(667\) | 14.6498 | 0.567241 | ||||||||
\(668\) | 13.2063 | 0.510969 | ||||||||
\(669\) | −21.4024 | −0.827466 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.98192 | 0.153720 | ||||||||
\(672\) | 5.60849 | 0.216352 | ||||||||
\(673\) | −18.8806 | −0.727794 | −0.363897 | − | 0.931439i | \(-0.618554\pi\) | ||||
−0.363897 | + | 0.931439i | \(0.618554\pi\) | |||||||
\(674\) | −38.2551 | −1.47353 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.30882 | −0.281108 | ||||||||
\(677\) | 18.7810 | 0.721814 | 0.360907 | − | 0.932602i | \(-0.382467\pi\) | ||||
0.360907 | + | 0.932602i | \(0.382467\pi\) | |||||||
\(678\) | 52.1927 | 2.00445 | ||||||||
\(679\) | −3.81259 | −0.146314 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −59.9273 | −2.29642 | ||||||||
\(682\) | −6.64834 | −0.254578 | ||||||||
\(683\) | 28.7666 | 1.10072 | 0.550361 | − | 0.834927i | \(-0.314490\pi\) | ||||
0.550361 | + | 0.834927i | \(0.314490\pi\) | |||||||
\(684\) | 18.3737 | 0.702535 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.60487 | −0.366716 | ||||||||
\(687\) | 2.23753 | 0.0853670 | ||||||||
\(688\) | 4.94130 | 0.188385 | ||||||||
\(689\) | −13.4615 | −0.512841 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.9619 | −0.721346 | −0.360673 | − | 0.932692i | \(-0.617453\pi\) | ||||
−0.360673 | + | 0.932692i | \(0.617453\pi\) | |||||||
\(692\) | 1.18552 | 0.0450668 | ||||||||
\(693\) | 3.37742 | 0.128297 | ||||||||
\(694\) | 1.71850 | 0.0652332 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 11.2777 | 0.427481 | ||||||||
\(697\) | −55.4817 | −2.10152 | ||||||||
\(698\) | −25.0599 | −0.948532 | ||||||||
\(699\) | 65.4597 | 2.47591 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.4331 | −0.658438 | −0.329219 | − | 0.944254i | \(-0.606785\pi\) | ||||
−0.329219 | + | 0.944254i | \(0.606785\pi\) | |||||||
\(702\) | −47.9436 | −1.80952 | ||||||||
\(703\) | 18.2543 | 0.688474 | ||||||||
\(704\) | −3.21742 | −0.121261 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −54.2196 | −2.04058 | ||||||||
\(707\) | −5.60344 | −0.210739 | ||||||||
\(708\) | −24.9220 | −0.936626 | ||||||||
\(709\) | −23.2515 | −0.873228 | −0.436614 | − | 0.899649i | \(-0.643822\pi\) | ||||
−0.436614 | + | 0.899649i | \(0.643822\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −127.685 | −4.78856 | ||||||||
\(712\) | 31.7146 | 1.18856 | ||||||||
\(713\) | 34.0497 | 1.27517 | ||||||||
\(714\) | −11.6652 | −0.436561 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.49618 | −0.205402 | ||||||||
\(717\) | −49.0269 | −1.83094 | ||||||||
\(718\) | 16.0034 | 0.597242 | ||||||||
\(719\) | 19.8428 | 0.740013 | 0.370006 | − | 0.929029i | \(-0.379355\pi\) | ||||
0.370006 | + | 0.929029i | \(0.379355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.75885 | 0.251713 | ||||||||
\(722\) | 15.4919 | 0.576547 | ||||||||
\(723\) | 35.6656 | 1.32642 | ||||||||
\(724\) | 12.6337 | 0.469528 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −54.1749 | −2.01062 | ||||||||
\(727\) | −9.98392 | −0.370283 | −0.185142 | − | 0.982712i | \(-0.559274\pi\) | ||||
−0.185142 | + | 0.982712i | \(0.559274\pi\) | |||||||
\(728\) | 1.58067 | 0.0585836 | ||||||||
\(729\) | 66.1000 | 2.44815 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.10985 | −0.188995 | ||||||||
\(732\) | 9.57581 | 0.353932 | ||||||||
\(733\) | 5.80810 | 0.214527 | 0.107264 | − | 0.994231i | \(-0.465791\pi\) | ||||
0.107264 | + | 0.994231i | \(0.465791\pi\) | |||||||
\(734\) | 10.8656 | 0.401058 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35.9250 | −1.32421 | ||||||||
\(737\) | −6.72471 | −0.247708 | ||||||||
\(738\) | 140.593 | 5.17530 | ||||||||
\(739\) | −24.2801 | −0.893157 | −0.446579 | − | 0.894744i | \(-0.647358\pi\) | ||||
−0.446579 | + | 0.894744i | \(0.647358\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.7152 | 0.687519 | ||||||||
\(742\) | 5.10650 | 0.187465 | ||||||||
\(743\) | −42.5948 | −1.56265 | −0.781326 | − | 0.624123i | \(-0.785457\pi\) | ||||
−0.781326 | + | 0.624123i | \(0.785457\pi\) | |||||||
\(744\) | 26.2122 | 0.960988 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −42.0742 | −1.54044 | ||||||||
\(747\) | 47.8554 | 1.75094 | ||||||||
\(748\) | −4.00870 | −0.146573 | ||||||||
\(749\) | −0.525061 | −0.0191853 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0708 | 0.367487 | 0.183744 | − | 0.982974i | \(-0.441178\pi\) | ||||
0.183744 | + | 0.982974i | \(0.441178\pi\) | |||||||
\(752\) | 1.36061 | 0.0496164 | ||||||||
\(753\) | 39.9357 | 1.45534 | ||||||||
\(754\) | −5.05988 | −0.184270 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.99714 | 0.181744 | ||||||||
\(757\) | −28.3498 | −1.03039 | −0.515195 | − | 0.857073i | \(-0.672280\pi\) | ||||
−0.515195 | + | 0.857073i | \(0.672280\pi\) | |||||||
\(758\) | 15.6893 | 0.569860 | ||||||||
\(759\) | −29.9575 | −1.08739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.1916 | −0.913195 | −0.456598 | − | 0.889673i | \(-0.650932\pi\) | ||||
−0.456598 | + | 0.889673i | \(0.650932\pi\) | |||||||
\(762\) | −43.6077 | −1.57974 | ||||||||
\(763\) | 3.07638 | 0.111373 | ||||||||
\(764\) | 7.97976 | 0.288698 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −46.1185 | −1.66633 | ||||||||
\(767\) | −18.3320 | −0.661931 | ||||||||
\(768\) | −52.2619 | −1.88584 | ||||||||
\(769\) | 48.9390 | 1.76479 | 0.882394 | − | 0.470512i | \(-0.155931\pi\) | ||||
0.882394 | + | 0.470512i | \(0.155931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 70.5170 | 2.53961 | ||||||||
\(772\) | −2.58144 | −0.0929079 | ||||||||
\(773\) | −47.5716 | −1.71103 | −0.855517 | − | 0.517775i | \(-0.826760\pi\) | ||||
−0.855517 | + | 0.517775i | \(0.826760\pi\) | |||||||
\(774\) | 12.9486 | 0.465427 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.8002 | 0.674887 | ||||||||
\(777\) | 8.06931 | 0.289485 | ||||||||
\(778\) | −26.3870 | −0.946020 | ||||||||
\(779\) | −33.7661 | −1.20980 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.47486 | −0.231689 | ||||||||
\(782\) | 74.7214 | 2.67203 | ||||||||
\(783\) | 26.2258 | 0.937233 | ||||||||
\(784\) | 33.7243 | 1.20444 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 32.0003 | 1.14141 | ||||||||
\(787\) | 43.9966 | 1.56831 | 0.784155 | − | 0.620564i | \(-0.213096\pi\) | ||||
0.784155 | + | 0.620564i | \(0.213096\pi\) | |||||||
\(788\) | 9.66625 | 0.344346 | ||||||||
\(789\) | 3.44081 | 0.122496 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.00154 | −0.142278 | ||||||||
\(792\) | −16.6543 | −0.591785 | ||||||||
\(793\) | 7.04374 | 0.250130 | ||||||||
\(794\) | 12.0876 | 0.428974 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.8973 | 0.457134 | ||||||||
\(797\) | 0.857030 | 0.0303576 | 0.0151788 | − | 0.999885i | \(-0.495168\pi\) | ||||
0.0151788 | + | 0.999885i | \(0.495168\pi\) | |||||||
\(798\) | −7.09945 | −0.251318 | ||||||||
\(799\) | −1.40702 | −0.0497769 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 119.870 | 4.23541 | ||||||||
\(802\) | 59.8973 | 2.11505 | ||||||||
\(803\) | −2.88429 | −0.101784 | ||||||||
\(804\) | −16.1717 | −0.570333 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.7604 | −0.414243 | ||||||||
\(807\) | −80.9962 | −2.85120 | ||||||||
\(808\) | 27.6310 | 0.972056 | ||||||||
\(809\) | −12.4204 | −0.436677 | −0.218338 | − | 0.975873i | \(-0.570064\pi\) | ||||
−0.218338 | + | 0.975873i | \(0.570064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.0981 | −0.740855 | −0.370427 | − | 0.928861i | \(-0.620789\pi\) | ||||
−0.370427 | + | 0.928861i | \(0.620789\pi\) | |||||||
\(812\) | 0.527389 | 0.0185077 | ||||||||
\(813\) | −35.8864 | −1.25859 | ||||||||
\(814\) | 10.0922 | 0.353733 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 82.9675 | 2.90444 | ||||||||
\(817\) | −3.10985 | −0.108800 | ||||||||
\(818\) | 4.71909 | 0.164999 | ||||||||
\(819\) | 5.97441 | 0.208763 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.1333 | −1.36576 | −0.682881 | − | 0.730529i | \(-0.739273\pi\) | ||||
−0.682881 | + | 0.730529i | \(0.739273\pi\) | |||||||
\(822\) | −107.428 | −3.74698 | ||||||||
\(823\) | −17.1258 | −0.596966 | −0.298483 | − | 0.954415i | \(-0.596481\pi\) | ||||
−0.298483 | + | 0.954415i | \(0.596481\pi\) | |||||||
\(824\) | −33.3284 | −1.16105 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.95411 | 0.241964 | ||||||||
\(827\) | 3.68695 | 0.128208 | 0.0641039 | − | 0.997943i | \(-0.479581\pi\) | ||||
0.0641039 | + | 0.997943i | \(0.479581\pi\) | |||||||
\(828\) | −52.0258 | −1.80802 | ||||||||
\(829\) | 1.80157 | 0.0625711 | 0.0312855 | − | 0.999510i | \(-0.490040\pi\) | ||||
0.0312855 | + | 0.999510i | \(0.490040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −56.8425 | −1.97184 | ||||||||
\(832\) | −5.69139 | −0.197313 | ||||||||
\(833\) | −34.8746 | −1.20833 | ||||||||
\(834\) | −66.5280 | −2.30368 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.43969 | −0.0843785 | ||||||||
\(837\) | 60.9553 | 2.10692 | ||||||||
\(838\) | 49.5643 | 1.71217 | ||||||||
\(839\) | 23.5253 | 0.812184 | 0.406092 | − | 0.913832i | \(-0.366891\pi\) | ||||
0.406092 | + | 0.913832i | \(0.366891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2322 | −0.904558 | ||||||||
\(842\) | −47.9124 | −1.65117 | ||||||||
\(843\) | −46.0215 | −1.58506 | ||||||||
\(844\) | 12.0488 | 0.414738 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.56546 | 0.122583 | ||||||||
\(847\) | 4.15352 | 0.142717 | ||||||||
\(848\) | −36.3193 | −1.24721 | ||||||||
\(849\) | 19.3999 | 0.665804 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −51.6878 | −1.77183 | ||||||||
\(852\) | −15.5709 | −0.533449 | ||||||||
\(853\) | 34.8867 | 1.19450 | 0.597249 | − | 0.802056i | \(-0.296260\pi\) | ||||
0.597249 | + | 0.802056i | \(0.296260\pi\) | |||||||
\(854\) | −2.67199 | −0.0914335 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.58912 | 0.0884943 | ||||||||
\(857\) | −3.91889 | −0.133867 | −0.0669333 | − | 0.997757i | \(-0.521321\pi\) | ||||
−0.0669333 | + | 0.997757i | \(0.521321\pi\) | |||||||
\(858\) | 10.3470 | 0.353242 | ||||||||
\(859\) | 39.2696 | 1.33986 | 0.669931 | − | 0.742424i | \(-0.266324\pi\) | ||||
0.669931 | + | 0.742424i | \(0.266324\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.9263 | −0.508687 | ||||||||
\(862\) | −3.95392 | −0.134671 | ||||||||
\(863\) | 25.1270 | 0.855332 | 0.427666 | − | 0.903937i | \(-0.359336\pi\) | ||||
0.427666 | + | 0.903937i | \(0.359336\pi\) | |||||||
\(864\) | −64.3125 | −2.18795 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.3065 | 1.16578 | ||||||||
\(867\) | −29.9366 | −1.01670 | ||||||||
\(868\) | 1.22578 | 0.0416058 | ||||||||
\(869\) | 16.9542 | 0.575133 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.8955 | −0.403065 | ||||||||
\(872\) | −15.1699 | −0.513717 | ||||||||
\(873\) | 71.0583 | 2.40496 | ||||||||
\(874\) | 45.4753 | 1.53823 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.93620 | −0.234353 | ||||||||
\(877\) | −27.5451 | −0.930130 | −0.465065 | − | 0.885276i | \(-0.653969\pi\) | ||||
−0.465065 | + | 0.885276i | \(0.653969\pi\) | |||||||
\(878\) | −38.5681 | −1.30161 | ||||||||
\(879\) | −9.64265 | −0.325239 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.6072 | 0.593203 | 0.296602 | − | 0.955001i | \(-0.404147\pi\) | ||||
0.296602 | + | 0.955001i | \(0.404147\pi\) | |||||||
\(882\) | 88.3737 | 2.97570 | ||||||||
\(883\) | −44.8242 | −1.50845 | −0.754227 | − | 0.656614i | \(-0.771988\pi\) | ||||
−0.754227 | + | 0.656614i | \(0.771988\pi\) | |||||||
\(884\) | −7.09111 | −0.238500 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 60.1678 | 2.02138 | ||||||||
\(887\) | −7.46972 | −0.250809 | −0.125404 | − | 0.992106i | \(-0.540023\pi\) | ||||
−0.125404 | + | 0.992106i | \(0.540023\pi\) | |||||||
\(888\) | −39.7904 | −1.33528 | ||||||||
\(889\) | 3.34334 | 0.112132 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −29.4106 | −0.985294 | ||||||||
\(892\) | 4.93532 | 0.165247 | ||||||||
\(893\) | −0.856312 | −0.0286554 | ||||||||
\(894\) | 115.854 | 3.87472 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.57262 | 0.186168 | ||||||||
\(897\) | −52.9927 | −1.76938 | ||||||||
\(898\) | 52.6618 | 1.75735 | ||||||||
\(899\) | 6.43311 | 0.214556 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.5581 | 1.25124 | ||||||||
\(902\) | −18.6682 | −0.621584 | ||||||||
\(903\) | −1.37471 | −0.0457474 | ||||||||
\(904\) | 19.7319 | 0.656274 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 130.750 | 4.34388 | ||||||||
\(907\) | 43.4335 | 1.44219 | 0.721093 | − | 0.692838i | \(-0.243640\pi\) | ||||
0.721093 | + | 0.692838i | \(0.243640\pi\) | |||||||
\(908\) | 13.8190 | 0.458600 | ||||||||
\(909\) | 104.436 | 3.46392 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.1269 | 0.567440 | 0.283720 | − | 0.958907i | \(-0.408431\pi\) | ||||
0.283720 | + | 0.958907i | \(0.408431\pi\) | |||||||
\(912\) | 50.4939 | 1.67202 | ||||||||
\(913\) | −6.35434 | −0.210298 | ||||||||
\(914\) | −25.6085 | −0.847054 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.515965 | −0.0170480 | ||||||||
\(917\) | −2.45342 | −0.0810191 | ||||||||
\(918\) | 133.765 | 4.41491 | ||||||||
\(919\) | −17.0359 | −0.561964 | −0.280982 | − | 0.959713i | \(-0.590660\pi\) | ||||
−0.280982 | + | 0.959713i | \(0.590660\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.8167 | −0.784787 | ||||||||
\(922\) | 4.95571 | 0.163208 | ||||||||
\(923\) | −11.4536 | −0.376998 | ||||||||
\(924\) | −1.07847 | −0.0354789 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −38.7379 | −1.27301 | ||||||||
\(927\) | −125.970 | −4.13740 | ||||||||
\(928\) | −6.78742 | −0.222808 | ||||||||
\(929\) | −6.23233 | −0.204476 | −0.102238 | − | 0.994760i | \(-0.532600\pi\) | ||||
−0.102238 | + | 0.994760i | \(0.532600\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.2246 | −0.695609 | ||||||||
\(932\) | −15.0947 | −0.494445 | ||||||||
\(933\) | −44.6299 | −1.46112 | ||||||||
\(934\) | −20.5000 | −0.670781 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −29.4603 | −0.962939 | ||||||||
\(937\) | 3.88579 | 0.126943 | 0.0634717 | − | 0.997984i | \(-0.479783\pi\) | ||||
0.0634717 | + | 0.997984i | \(0.479783\pi\) | |||||||
\(938\) | 4.51248 | 0.147338 | ||||||||
\(939\) | −8.66283 | −0.282701 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.7775 | 0.546932 | 0.273466 | − | 0.961882i | \(-0.411830\pi\) | ||||
0.273466 | + | 0.961882i | \(0.411830\pi\) | |||||||
\(942\) | 25.1513 | 0.819475 | ||||||||
\(943\) | 95.6100 | 3.11349 | ||||||||
\(944\) | −49.4602 | −1.60979 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.71934 | −0.0559005 | ||||||||
\(947\) | 3.90586 | 0.126923 | 0.0634617 | − | 0.997984i | \(-0.479786\pi\) | ||||
0.0634617 | + | 0.997984i | \(0.479786\pi\) | |||||||
\(948\) | 40.7719 | 1.32421 | ||||||||
\(949\) | −5.10210 | −0.165621 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.4068 | −1.53727 | ||||||||
\(952\) | −4.41015 | −0.142934 | ||||||||
\(953\) | −30.0787 | −0.974345 | −0.487173 | − | 0.873306i | \(-0.661972\pi\) | ||||
−0.487173 | + | 0.873306i | \(0.661972\pi\) | |||||||
\(954\) | −95.1739 | −3.08137 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.3054 | 0.365643 | ||||||||
\(957\) | −5.65996 | −0.182961 | ||||||||
\(958\) | −26.4192 | −0.853566 | ||||||||
\(959\) | 8.23637 | 0.265966 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.0478 | −0.517673 | ||||||||
\(962\) | 17.8524 | 0.575586 | ||||||||
\(963\) | 9.78599 | 0.315349 | ||||||||
\(964\) | −8.22434 | −0.264888 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 20.1024 | 0.646783 | ||||||||
\(967\) | 50.4756 | 1.62319 | 0.811593 | − | 0.584223i | \(-0.198601\pi\) | ||||
0.811593 | + | 0.584223i | \(0.198601\pi\) | |||||||
\(968\) | −20.4813 | −0.658295 | ||||||||
\(969\) | −52.2162 | −1.67743 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.3772 | −1.64877 | −0.824387 | − | 0.566026i | \(-0.808480\pi\) | ||||
−0.824387 | + | 0.566026i | \(0.808480\pi\) | |||||||
\(972\) | −34.8937 | −1.11922 | ||||||||
\(973\) | 5.10062 | 0.163518 | ||||||||
\(974\) | 13.5414 | 0.433893 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.0041 | 0.608308 | ||||||||
\(977\) | −7.93563 | −0.253883 | −0.126942 | − | 0.991910i | \(-0.540516\pi\) | ||||
−0.126942 | + | 0.991910i | \(0.540516\pi\) | |||||||
\(978\) | −48.0184 | −1.53546 | ||||||||
\(979\) | −15.9166 | −0.508698 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −57.3371 | −1.83063 | ||||||||
\(982\) | −62.2734 | −1.98723 | ||||||||
\(983\) | 9.69159 | 0.309114 | 0.154557 | − | 0.987984i | \(-0.450605\pi\) | ||||
0.154557 | + | 0.987984i | \(0.450605\pi\) | |||||||
\(984\) | 73.6027 | 2.34637 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 14.1173 | 0.449587 | ||||||||
\(987\) | −0.378533 | −0.0120488 | ||||||||
\(988\) | −4.31564 | −0.137299 | ||||||||
\(989\) | 8.80565 | 0.280003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.9030 | −0.918136 | −0.459068 | − | 0.888401i | \(-0.651816\pi\) | ||||
−0.459068 | + | 0.888401i | \(0.651816\pi\) | |||||||
\(992\) | −15.7757 | −0.500878 | ||||||||
\(993\) | −46.9898 | −1.49118 | ||||||||
\(994\) | 4.34482 | 0.137809 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15.2810 | −0.484198 | ||||||||
\(997\) | −12.1891 | −0.386034 | −0.193017 | − | 0.981195i | \(-0.561827\pi\) | ||||
−0.193017 | + | 0.981195i | \(0.561827\pi\) | |||||||
\(998\) | 27.1033 | 0.857941 | ||||||||
\(999\) | −92.5307 | −2.92754 |
(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 | 1075.2.a.r.1.2 | yes | 6 | |
3.2 | odd | 2 | 9675.2.a.cj.1.5 | 6 | |||
5.2 | odd | 4 | 1075.2.b.j.474.4 | 12 | |||
5.3 | odd | 4 | 1075.2.b.j.474.9 | 12 | |||
5.4 | even | 2 | 1075.2.a.q.1.5 | ✓ | 6 | ||
15.14 | odd | 2 | 9675.2.a.ck.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1075.2.a.q.1.5 | ✓ | 6 | 5.4 | even | 2 | ||
1075.2.a.r.1.2 | yes | 6 | 1.1 | even | 1 | trivial | |
1075.2.b.j.474.4 | 12 | 5.2 | odd | 4 | |||
1075.2.b.j.474.9 | 12 | 5.3 | odd | 4 | |||
9675.2.a.cj.1.5 | 6 | 3.2 | odd | 2 | |||
9675.2.a.ck.1.2 | 6 | 15.14 | odd | 2 |