Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, 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("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.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: | \(32.1158316930\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.45431 | −0.839645 | −0.419823 | − | 0.907606i | \(-0.637908\pi\) | ||||
−0.419823 | + | 0.907606i | \(0.637908\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.49956 | −1.11784 | −0.558919 | − | 0.829222i | \(-0.688784\pi\) | ||||
−0.558919 | + | 0.829222i | \(0.688784\pi\) | |||||||
\(6\) | −1.45431 | −0.593719 | ||||||||
\(7\) | −3.69872 | −1.39799 | −0.698993 | − | 0.715129i | \(-0.746368\pi\) | ||||
−0.698993 | + | 0.715129i | \(0.746368\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.884987 | −0.294996 | ||||||||
\(10\) | −2.49956 | −0.790431 | ||||||||
\(11\) | −3.95977 | −1.19392 | −0.596958 | − | 0.802273i | \(-0.703624\pi\) | ||||
−0.596958 | + | 0.802273i | \(0.703624\pi\) | |||||||
\(12\) | −1.45431 | −0.419823 | ||||||||
\(13\) | −4.27037 | −1.18439 | −0.592193 | − | 0.805796i | \(-0.701738\pi\) | ||||
−0.592193 | + | 0.805796i | \(0.701738\pi\) | |||||||
\(14\) | −3.69872 | −0.988525 | ||||||||
\(15\) | 3.63513 | 0.938588 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.57289 | 0.624017 | 0.312009 | − | 0.950079i | \(-0.398998\pi\) | ||||
0.312009 | + | 0.950079i | \(0.398998\pi\) | |||||||
\(18\) | −0.884987 | −0.208593 | ||||||||
\(19\) | −6.17964 | −1.41771 | −0.708853 | − | 0.705356i | \(-0.750787\pi\) | ||||
−0.708853 | + | 0.705356i | \(0.750787\pi\) | |||||||
\(20\) | −2.49956 | −0.558919 | ||||||||
\(21\) | 5.37908 | 1.17381 | ||||||||
\(22\) | −3.95977 | −0.844225 | ||||||||
\(23\) | 2.01625 | 0.420417 | 0.210208 | − | 0.977657i | \(-0.432586\pi\) | ||||
0.210208 | + | 0.977657i | \(0.432586\pi\) | |||||||
\(24\) | −1.45431 | −0.296859 | ||||||||
\(25\) | 1.24781 | 0.249563 | ||||||||
\(26\) | −4.27037 | −0.837488 | ||||||||
\(27\) | 5.64997 | 1.08734 | ||||||||
\(28\) | −3.69872 | −0.698993 | ||||||||
\(29\) | 0.563494 | 0.104638 | 0.0523191 | − | 0.998630i | \(-0.483339\pi\) | ||||
0.0523191 | + | 0.998630i | \(0.483339\pi\) | |||||||
\(30\) | 3.63513 | 0.663682 | ||||||||
\(31\) | −6.95868 | −1.24982 | −0.624908 | − | 0.780699i | \(-0.714863\pi\) | ||||
−0.624908 | + | 0.780699i | \(0.714863\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.75872 | 1.00247 | ||||||||
\(34\) | 2.57289 | 0.441247 | ||||||||
\(35\) | 9.24519 | 1.56272 | ||||||||
\(36\) | −0.884987 | −0.147498 | ||||||||
\(37\) | −7.95922 | −1.30849 | −0.654244 | − | 0.756283i | \(-0.727013\pi\) | ||||
−0.654244 | + | 0.756283i | \(0.727013\pi\) | |||||||
\(38\) | −6.17964 | −1.00247 | ||||||||
\(39\) | 6.21043 | 0.994465 | ||||||||
\(40\) | −2.49956 | −0.395216 | ||||||||
\(41\) | −5.61346 | −0.876675 | −0.438337 | − | 0.898811i | \(-0.644432\pi\) | ||||
−0.438337 | + | 0.898811i | \(0.644432\pi\) | |||||||
\(42\) | 5.37908 | 0.830010 | ||||||||
\(43\) | −7.70471 | −1.17496 | −0.587479 | − | 0.809240i | \(-0.699879\pi\) | ||||
−0.587479 | + | 0.809240i | \(0.699879\pi\) | |||||||
\(44\) | −3.95977 | −0.596958 | ||||||||
\(45\) | 2.21208 | 0.329757 | ||||||||
\(46\) | 2.01625 | 0.297280 | ||||||||
\(47\) | 3.56019 | 0.519307 | 0.259654 | − | 0.965702i | \(-0.416392\pi\) | ||||
0.259654 | + | 0.965702i | \(0.416392\pi\) | |||||||
\(48\) | −1.45431 | −0.209911 | ||||||||
\(49\) | 6.68055 | 0.954364 | ||||||||
\(50\) | 1.24781 | 0.176467 | ||||||||
\(51\) | −3.74177 | −0.523953 | ||||||||
\(52\) | −4.27037 | −0.592193 | ||||||||
\(53\) | −14.2373 | −1.95564 | −0.977821 | − | 0.209444i | \(-0.932835\pi\) | ||||
−0.977821 | + | 0.209444i | \(0.932835\pi\) | |||||||
\(54\) | 5.64997 | 0.768863 | ||||||||
\(55\) | 9.89769 | 1.33460 | ||||||||
\(56\) | −3.69872 | −0.494263 | ||||||||
\(57\) | 8.98710 | 1.19037 | ||||||||
\(58\) | 0.563494 | 0.0739903 | ||||||||
\(59\) | 10.6070 | 1.38091 | 0.690456 | − | 0.723374i | \(-0.257410\pi\) | ||||
0.690456 | + | 0.723374i | \(0.257410\pi\) | |||||||
\(60\) | 3.63513 | 0.469294 | ||||||||
\(61\) | −9.71533 | −1.24392 | −0.621960 | − | 0.783049i | \(-0.713663\pi\) | ||||
−0.621960 | + | 0.783049i | \(0.713663\pi\) | |||||||
\(62\) | −6.95868 | −0.883753 | ||||||||
\(63\) | 3.27332 | 0.412400 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.6740 | 1.32395 | ||||||||
\(66\) | 5.75872 | 0.708850 | ||||||||
\(67\) | −0.780231 | −0.0953204 | −0.0476602 | − | 0.998864i | \(-0.515176\pi\) | ||||
−0.0476602 | + | 0.998864i | \(0.515176\pi\) | |||||||
\(68\) | 2.57289 | 0.312009 | ||||||||
\(69\) | −2.93225 | −0.353001 | ||||||||
\(70\) | 9.24519 | 1.10501 | ||||||||
\(71\) | 7.96118 | 0.944818 | 0.472409 | − | 0.881379i | \(-0.343385\pi\) | ||||
0.472409 | + | 0.881379i | \(0.343385\pi\) | |||||||
\(72\) | −0.884987 | −0.104297 | ||||||||
\(73\) | 15.9875 | 1.87120 | 0.935599 | − | 0.353066i | \(-0.114861\pi\) | ||||
0.935599 | + | 0.353066i | \(0.114861\pi\) | |||||||
\(74\) | −7.95922 | −0.925241 | ||||||||
\(75\) | −1.81470 | −0.209544 | ||||||||
\(76\) | −6.17964 | −0.708853 | ||||||||
\(77\) | 14.6461 | 1.66908 | ||||||||
\(78\) | 6.21043 | 0.703193 | ||||||||
\(79\) | 13.5629 | 1.52594 | 0.762971 | − | 0.646433i | \(-0.223740\pi\) | ||||
0.762971 | + | 0.646433i | \(0.223740\pi\) | |||||||
\(80\) | −2.49956 | −0.279460 | ||||||||
\(81\) | −5.56184 | −0.617982 | ||||||||
\(82\) | −5.61346 | −0.619903 | ||||||||
\(83\) | −5.77362 | −0.633737 | −0.316869 | − | 0.948469i | \(-0.602631\pi\) | ||||
−0.316869 | + | 0.948469i | \(0.602631\pi\) | |||||||
\(84\) | 5.37908 | 0.586906 | ||||||||
\(85\) | −6.43110 | −0.697550 | ||||||||
\(86\) | −7.70471 | −0.830820 | ||||||||
\(87\) | −0.819494 | −0.0878589 | ||||||||
\(88\) | −3.95977 | −0.422113 | ||||||||
\(89\) | 16.5453 | 1.75380 | 0.876901 | − | 0.480672i | \(-0.159607\pi\) | ||||
0.876901 | + | 0.480672i | \(0.159607\pi\) | |||||||
\(90\) | 2.21208 | 0.233174 | ||||||||
\(91\) | 15.7949 | 1.65576 | ||||||||
\(92\) | 2.01625 | 0.210208 | ||||||||
\(93\) | 10.1201 | 1.04940 | ||||||||
\(94\) | 3.56019 | 0.367206 | ||||||||
\(95\) | 15.4464 | 1.58477 | ||||||||
\(96\) | −1.45431 | −0.148430 | ||||||||
\(97\) | 8.78153 | 0.891629 | 0.445815 | − | 0.895125i | \(-0.352914\pi\) | ||||
0.445815 | + | 0.895125i | \(0.352914\pi\) | |||||||
\(98\) | 6.68055 | 0.674837 | ||||||||
\(99\) | 3.50434 | 0.352200 | ||||||||
\(100\) | 1.24781 | 0.124781 | ||||||||
\(101\) | 1.36973 | 0.136294 | 0.0681469 | − | 0.997675i | \(-0.478291\pi\) | ||||
0.0681469 | + | 0.997675i | \(0.478291\pi\) | |||||||
\(102\) | −3.74177 | −0.370491 | ||||||||
\(103\) | −5.63186 | −0.554924 | −0.277462 | − | 0.960737i | \(-0.589493\pi\) | ||||
−0.277462 | + | 0.960737i | \(0.589493\pi\) | |||||||
\(104\) | −4.27037 | −0.418744 | ||||||||
\(105\) | −13.4454 | −1.31213 | ||||||||
\(106\) | −14.2373 | −1.38285 | ||||||||
\(107\) | 18.2872 | 1.76789 | 0.883945 | − | 0.467590i | \(-0.154878\pi\) | ||||
0.883945 | + | 0.467590i | \(0.154878\pi\) | |||||||
\(108\) | 5.64997 | 0.543669 | ||||||||
\(109\) | −14.6610 | −1.40427 | −0.702135 | − | 0.712044i | \(-0.747770\pi\) | ||||
−0.702135 | + | 0.712044i | \(0.747770\pi\) | |||||||
\(110\) | 9.89769 | 0.943708 | ||||||||
\(111\) | 11.5752 | 1.09867 | ||||||||
\(112\) | −3.69872 | −0.349496 | ||||||||
\(113\) | −17.0292 | −1.60197 | −0.800987 | − | 0.598682i | \(-0.795691\pi\) | ||||
−0.800987 | + | 0.598682i | \(0.795691\pi\) | |||||||
\(114\) | 8.98710 | 0.841719 | ||||||||
\(115\) | −5.03974 | −0.469958 | ||||||||
\(116\) | 0.563494 | 0.0523191 | ||||||||
\(117\) | 3.77922 | 0.349389 | ||||||||
\(118\) | 10.6070 | 0.976452 | ||||||||
\(119\) | −9.51640 | −0.872367 | ||||||||
\(120\) | 3.63513 | 0.331841 | ||||||||
\(121\) | 4.67976 | 0.425433 | ||||||||
\(122\) | −9.71533 | −0.879584 | ||||||||
\(123\) | 8.16370 | 0.736096 | ||||||||
\(124\) | −6.95868 | −0.624908 | ||||||||
\(125\) | 9.37883 | 0.838868 | ||||||||
\(126\) | 3.27332 | 0.291611 | ||||||||
\(127\) | −12.2429 | −1.08638 | −0.543191 | − | 0.839609i | \(-0.682784\pi\) | ||||
−0.543191 | + | 0.839609i | \(0.682784\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 11.2050 | 0.986547 | ||||||||
\(130\) | 10.6740 | 0.936176 | ||||||||
\(131\) | −3.81360 | −0.333195 | −0.166598 | − | 0.986025i | \(-0.553278\pi\) | ||||
−0.166598 | + | 0.986025i | \(0.553278\pi\) | |||||||
\(132\) | 5.75872 | 0.501233 | ||||||||
\(133\) | 22.8568 | 1.98193 | ||||||||
\(134\) | −0.780231 | −0.0674017 | ||||||||
\(135\) | −14.1225 | −1.21547 | ||||||||
\(136\) | 2.57289 | 0.220623 | ||||||||
\(137\) | −15.8322 | −1.35264 | −0.676320 | − | 0.736608i | \(-0.736426\pi\) | ||||
−0.676320 | + | 0.736608i | \(0.736426\pi\) | |||||||
\(138\) | −2.93225 | −0.249609 | ||||||||
\(139\) | −10.2425 | −0.868759 | −0.434380 | − | 0.900730i | \(-0.643032\pi\) | ||||
−0.434380 | + | 0.900730i | \(0.643032\pi\) | |||||||
\(140\) | 9.24519 | 0.781361 | ||||||||
\(141\) | −5.17762 | −0.436034 | ||||||||
\(142\) | 7.96118 | 0.668087 | ||||||||
\(143\) | 16.9097 | 1.41406 | ||||||||
\(144\) | −0.884987 | −0.0737489 | ||||||||
\(145\) | −1.40849 | −0.116969 | ||||||||
\(146\) | 15.9875 | 1.32314 | ||||||||
\(147\) | −9.71557 | −0.801327 | ||||||||
\(148\) | −7.95922 | −0.654244 | ||||||||
\(149\) | −11.7499 | −0.962593 | −0.481296 | − | 0.876558i | \(-0.659834\pi\) | ||||
−0.481296 | + | 0.876558i | \(0.659834\pi\) | |||||||
\(150\) | −1.81470 | −0.148170 | ||||||||
\(151\) | 5.76900 | 0.469474 | 0.234737 | − | 0.972059i | \(-0.424577\pi\) | ||||
0.234737 | + | 0.972059i | \(0.424577\pi\) | |||||||
\(152\) | −6.17964 | −0.501235 | ||||||||
\(153\) | −2.27697 | −0.184082 | ||||||||
\(154\) | 14.6461 | 1.18021 | ||||||||
\(155\) | 17.3937 | 1.39709 | ||||||||
\(156\) | 6.21043 | 0.497232 | ||||||||
\(157\) | −5.17265 | −0.412823 | −0.206411 | − | 0.978465i | \(-0.566179\pi\) | ||||
−0.206411 | + | 0.978465i | \(0.566179\pi\) | |||||||
\(158\) | 13.5629 | 1.07900 | ||||||||
\(159\) | 20.7054 | 1.64205 | ||||||||
\(160\) | −2.49956 | −0.197608 | ||||||||
\(161\) | −7.45754 | −0.587737 | ||||||||
\(162\) | −5.56184 | −0.436979 | ||||||||
\(163\) | −4.43532 | −0.347401 | −0.173700 | − | 0.984799i | \(-0.555572\pi\) | ||||
−0.173700 | + | 0.984799i | \(0.555572\pi\) | |||||||
\(164\) | −5.61346 | −0.438337 | ||||||||
\(165\) | −14.3943 | −1.12059 | ||||||||
\(166\) | −5.77362 | −0.448120 | ||||||||
\(167\) | −2.90902 | −0.225107 | −0.112554 | − | 0.993646i | \(-0.535903\pi\) | ||||
−0.112554 | + | 0.993646i | \(0.535903\pi\) | |||||||
\(168\) | 5.37908 | 0.415005 | ||||||||
\(169\) | 5.23603 | 0.402771 | ||||||||
\(170\) | −6.43110 | −0.493243 | ||||||||
\(171\) | 5.46890 | 0.418217 | ||||||||
\(172\) | −7.70471 | −0.587479 | ||||||||
\(173\) | −12.1386 | −0.922882 | −0.461441 | − | 0.887171i | \(-0.652667\pi\) | ||||
−0.461441 | + | 0.887171i | \(0.652667\pi\) | |||||||
\(174\) | −0.819494 | −0.0621257 | ||||||||
\(175\) | −4.61531 | −0.348885 | ||||||||
\(176\) | −3.95977 | −0.298479 | ||||||||
\(177\) | −15.4258 | −1.15948 | ||||||||
\(178\) | 16.5453 | 1.24012 | ||||||||
\(179\) | 22.6815 | 1.69530 | 0.847648 | − | 0.530560i | \(-0.178018\pi\) | ||||
0.847648 | + | 0.530560i | \(0.178018\pi\) | |||||||
\(180\) | 2.21208 | 0.164879 | ||||||||
\(181\) | −5.22540 | −0.388401 | −0.194201 | − | 0.980962i | \(-0.562211\pi\) | ||||
−0.194201 | + | 0.980962i | \(0.562211\pi\) | |||||||
\(182\) | 15.7949 | 1.17080 | ||||||||
\(183\) | 14.1291 | 1.04445 | ||||||||
\(184\) | 2.01625 | 0.148640 | ||||||||
\(185\) | 19.8946 | 1.46268 | ||||||||
\(186\) | 10.1201 | 0.742039 | ||||||||
\(187\) | −10.1880 | −0.745023 | ||||||||
\(188\) | 3.56019 | 0.259654 | ||||||||
\(189\) | −20.8977 | −1.52008 | ||||||||
\(190\) | 15.4464 | 1.12060 | ||||||||
\(191\) | −8.67170 | −0.627462 | −0.313731 | − | 0.949512i | \(-0.601579\pi\) | ||||
−0.313731 | + | 0.949512i | \(0.601579\pi\) | |||||||
\(192\) | −1.45431 | −0.104956 | ||||||||
\(193\) | −3.45130 | −0.248430 | −0.124215 | − | 0.992255i | \(-0.539641\pi\) | ||||
−0.124215 | + | 0.992255i | \(0.539641\pi\) | |||||||
\(194\) | 8.78153 | 0.630477 | ||||||||
\(195\) | −15.5234 | −1.11165 | ||||||||
\(196\) | 6.68055 | 0.477182 | ||||||||
\(197\) | 2.83509 | 0.201992 | 0.100996 | − | 0.994887i | \(-0.467797\pi\) | ||||
0.100996 | + | 0.994887i | \(0.467797\pi\) | |||||||
\(198\) | 3.50434 | 0.249043 | ||||||||
\(199\) | −11.0882 | −0.786024 | −0.393012 | − | 0.919533i | \(-0.628567\pi\) | ||||
−0.393012 | + | 0.919533i | \(0.628567\pi\) | |||||||
\(200\) | 1.24781 | 0.0882337 | ||||||||
\(201\) | 1.13470 | 0.0800353 | ||||||||
\(202\) | 1.36973 | 0.0963742 | ||||||||
\(203\) | −2.08421 | −0.146283 | ||||||||
\(204\) | −3.74177 | −0.261977 | ||||||||
\(205\) | 14.0312 | 0.979980 | ||||||||
\(206\) | −5.63186 | −0.392391 | ||||||||
\(207\) | −1.78435 | −0.124021 | ||||||||
\(208\) | −4.27037 | −0.296097 | ||||||||
\(209\) | 24.4699 | 1.69262 | ||||||||
\(210\) | −13.4454 | −0.927818 | ||||||||
\(211\) | 6.12946 | 0.421970 | 0.210985 | − | 0.977489i | \(-0.432333\pi\) | ||||
0.210985 | + | 0.977489i | \(0.432333\pi\) | |||||||
\(212\) | −14.2373 | −0.977821 | ||||||||
\(213\) | −11.5780 | −0.793312 | ||||||||
\(214\) | 18.2872 | 1.25009 | ||||||||
\(215\) | 19.2584 | 1.31341 | ||||||||
\(216\) | 5.64997 | 0.384432 | ||||||||
\(217\) | 25.7382 | 1.74722 | ||||||||
\(218\) | −14.6610 | −0.992969 | ||||||||
\(219\) | −23.2508 | −1.57114 | ||||||||
\(220\) | 9.89769 | 0.667302 | ||||||||
\(221\) | −10.9872 | −0.739077 | ||||||||
\(222\) | 11.5752 | 0.776874 | ||||||||
\(223\) | 24.4239 | 1.63554 | 0.817772 | − | 0.575542i | \(-0.195209\pi\) | ||||
0.817772 | + | 0.575542i | \(0.195209\pi\) | |||||||
\(224\) | −3.69872 | −0.247131 | ||||||||
\(225\) | −1.10430 | −0.0736199 | ||||||||
\(226\) | −17.0292 | −1.13277 | ||||||||
\(227\) | 18.8628 | 1.25197 | 0.625985 | − | 0.779835i | \(-0.284697\pi\) | ||||
0.625985 | + | 0.779835i | \(0.284697\pi\) | |||||||
\(228\) | 8.98710 | 0.595185 | ||||||||
\(229\) | 5.51478 | 0.364427 | 0.182213 | − | 0.983259i | \(-0.441674\pi\) | ||||
0.182213 | + | 0.983259i | \(0.441674\pi\) | |||||||
\(230\) | −5.03974 | −0.332311 | ||||||||
\(231\) | −21.2999 | −1.40143 | ||||||||
\(232\) | 0.563494 | 0.0369952 | ||||||||
\(233\) | 3.77347 | 0.247209 | 0.123604 | − | 0.992332i | \(-0.460555\pi\) | ||||
0.123604 | + | 0.992332i | \(0.460555\pi\) | |||||||
\(234\) | 3.77922 | 0.247055 | ||||||||
\(235\) | −8.89892 | −0.580502 | ||||||||
\(236\) | 10.6070 | 0.690456 | ||||||||
\(237\) | −19.7246 | −1.28125 | ||||||||
\(238\) | −9.51640 | −0.616857 | ||||||||
\(239\) | −13.1769 | −0.852345 | −0.426172 | − | 0.904642i | \(-0.640138\pi\) | ||||
−0.426172 | + | 0.904642i | \(0.640138\pi\) | |||||||
\(240\) | 3.63513 | 0.234647 | ||||||||
\(241\) | −16.5754 | −1.06771 | −0.533856 | − | 0.845575i | \(-0.679258\pi\) | ||||
−0.533856 | + | 0.845575i | \(0.679258\pi\) | |||||||
\(242\) | 4.67976 | 0.300827 | ||||||||
\(243\) | −8.86128 | −0.568451 | ||||||||
\(244\) | −9.71533 | −0.621960 | ||||||||
\(245\) | −16.6984 | −1.06682 | ||||||||
\(246\) | 8.16370 | 0.520498 | ||||||||
\(247\) | 26.3893 | 1.67911 | ||||||||
\(248\) | −6.95868 | −0.441877 | ||||||||
\(249\) | 8.39663 | 0.532115 | ||||||||
\(250\) | 9.37883 | 0.593169 | ||||||||
\(251\) | −29.1200 | −1.83804 | −0.919018 | − | 0.394215i | \(-0.871017\pi\) | ||||
−0.919018 | + | 0.394215i | \(0.871017\pi\) | |||||||
\(252\) | 3.27332 | 0.206200 | ||||||||
\(253\) | −7.98388 | −0.501942 | ||||||||
\(254\) | −12.2429 | −0.768188 | ||||||||
\(255\) | 9.35280 | 0.585695 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.7742 | −1.29586 | −0.647931 | − | 0.761699i | \(-0.724365\pi\) | ||||
−0.647931 | + | 0.761699i | \(0.724365\pi\) | |||||||
\(258\) | 11.2050 | 0.697594 | ||||||||
\(259\) | 29.4390 | 1.82925 | ||||||||
\(260\) | 10.6740 | 0.661976 | ||||||||
\(261\) | −0.498685 | −0.0308678 | ||||||||
\(262\) | −3.81360 | −0.235605 | ||||||||
\(263\) | −20.9500 | −1.29183 | −0.645915 | − | 0.763410i | \(-0.723524\pi\) | ||||
−0.645915 | + | 0.763410i | \(0.723524\pi\) | |||||||
\(264\) | 5.75872 | 0.354425 | ||||||||
\(265\) | 35.5870 | 2.18609 | ||||||||
\(266\) | 22.8568 | 1.40144 | ||||||||
\(267\) | −24.0620 | −1.47257 | ||||||||
\(268\) | −0.780231 | −0.0476602 | ||||||||
\(269\) | −5.65226 | −0.344624 | −0.172312 | − | 0.985042i | \(-0.555124\pi\) | ||||
−0.172312 | + | 0.985042i | \(0.555124\pi\) | |||||||
\(270\) | −14.1225 | −0.859465 | ||||||||
\(271\) | −11.9929 | −0.728518 | −0.364259 | − | 0.931298i | \(-0.618678\pi\) | ||||
−0.364259 | + | 0.931298i | \(0.618678\pi\) | |||||||
\(272\) | 2.57289 | 0.156004 | ||||||||
\(273\) | −22.9707 | −1.39025 | ||||||||
\(274\) | −15.8322 | −0.956461 | ||||||||
\(275\) | −4.94105 | −0.297957 | ||||||||
\(276\) | −2.93225 | −0.176501 | ||||||||
\(277\) | −1.12905 | −0.0678379 | −0.0339190 | − | 0.999425i | \(-0.510799\pi\) | ||||
−0.0339190 | + | 0.999425i | \(0.510799\pi\) | |||||||
\(278\) | −10.2425 | −0.614306 | ||||||||
\(279\) | 6.15834 | 0.368690 | ||||||||
\(280\) | 9.24519 | 0.552506 | ||||||||
\(281\) | 21.8794 | 1.30522 | 0.652608 | − | 0.757695i | \(-0.273675\pi\) | ||||
0.652608 | + | 0.757695i | \(0.273675\pi\) | |||||||
\(282\) | −5.17762 | −0.308323 | ||||||||
\(283\) | 25.2573 | 1.50139 | 0.750695 | − | 0.660649i | \(-0.229719\pi\) | ||||
0.750695 | + | 0.660649i | \(0.229719\pi\) | |||||||
\(284\) | 7.96118 | 0.472409 | ||||||||
\(285\) | −22.4638 | −1.33064 | ||||||||
\(286\) | 16.9097 | 0.999889 | ||||||||
\(287\) | 20.7626 | 1.22558 | ||||||||
\(288\) | −0.884987 | −0.0521484 | ||||||||
\(289\) | −10.3802 | −0.610603 | ||||||||
\(290\) | −1.40849 | −0.0827092 | ||||||||
\(291\) | −12.7711 | −0.748652 | ||||||||
\(292\) | 15.9875 | 0.935599 | ||||||||
\(293\) | −5.94045 | −0.347045 | −0.173522 | − | 0.984830i | \(-0.555515\pi\) | ||||
−0.173522 | + | 0.984830i | \(0.555515\pi\) | |||||||
\(294\) | −9.71557 | −0.566624 | ||||||||
\(295\) | −26.5128 | −1.54364 | ||||||||
\(296\) | −7.95922 | −0.462621 | ||||||||
\(297\) | −22.3726 | −1.29819 | ||||||||
\(298\) | −11.7499 | −0.680656 | ||||||||
\(299\) | −8.61012 | −0.497936 | ||||||||
\(300\) | −1.81470 | −0.104772 | ||||||||
\(301\) | 28.4976 | 1.64257 | ||||||||
\(302\) | 5.76900 | 0.331968 | ||||||||
\(303\) | −1.99202 | −0.114438 | ||||||||
\(304\) | −6.17964 | −0.354427 | ||||||||
\(305\) | 24.2841 | 1.39050 | ||||||||
\(306\) | −2.27697 | −0.130166 | ||||||||
\(307\) | 10.4116 | 0.594224 | 0.297112 | − | 0.954843i | \(-0.403977\pi\) | ||||
0.297112 | + | 0.954843i | \(0.403977\pi\) | |||||||
\(308\) | 14.6461 | 0.834538 | ||||||||
\(309\) | 8.19047 | 0.465939 | ||||||||
\(310\) | 17.3937 | 0.987893 | ||||||||
\(311\) | 33.2987 | 1.88820 | 0.944098 | − | 0.329665i | \(-0.106936\pi\) | ||||
0.944098 | + | 0.329665i | \(0.106936\pi\) | |||||||
\(312\) | 6.21043 | 0.351596 | ||||||||
\(313\) | 6.47296 | 0.365873 | 0.182937 | − | 0.983125i | \(-0.441440\pi\) | ||||
0.182937 | + | 0.983125i | \(0.441440\pi\) | |||||||
\(314\) | −5.17265 | −0.291910 | ||||||||
\(315\) | −8.18187 | −0.460996 | ||||||||
\(316\) | 13.5629 | 0.762971 | ||||||||
\(317\) | 19.4944 | 1.09491 | 0.547457 | − | 0.836834i | \(-0.315596\pi\) | ||||
0.547457 | + | 0.836834i | \(0.315596\pi\) | |||||||
\(318\) | 20.7054 | 1.16110 | ||||||||
\(319\) | −2.23130 | −0.124929 | ||||||||
\(320\) | −2.49956 | −0.139730 | ||||||||
\(321\) | −26.5952 | −1.48440 | ||||||||
\(322\) | −7.45754 | −0.415593 | ||||||||
\(323\) | −15.8995 | −0.884673 | ||||||||
\(324\) | −5.56184 | −0.308991 | ||||||||
\(325\) | −5.32862 | −0.295579 | ||||||||
\(326\) | −4.43532 | −0.245650 | ||||||||
\(327\) | 21.3216 | 1.17909 | ||||||||
\(328\) | −5.61346 | −0.309951 | ||||||||
\(329\) | −13.1682 | −0.725984 | ||||||||
\(330\) | −14.3943 | −0.792380 | ||||||||
\(331\) | 3.65322 | 0.200799 | 0.100400 | − | 0.994947i | \(-0.467988\pi\) | ||||
0.100400 | + | 0.994947i | \(0.467988\pi\) | |||||||
\(332\) | −5.77362 | −0.316869 | ||||||||
\(333\) | 7.04381 | 0.385998 | ||||||||
\(334\) | −2.90902 | −0.159175 | ||||||||
\(335\) | 1.95024 | 0.106553 | ||||||||
\(336\) | 5.37908 | 0.293453 | ||||||||
\(337\) | −19.3565 | −1.05442 | −0.527208 | − | 0.849736i | \(-0.676761\pi\) | ||||
−0.527208 | + | 0.849736i | \(0.676761\pi\) | |||||||
\(338\) | 5.23603 | 0.284802 | ||||||||
\(339\) | 24.7657 | 1.34509 | ||||||||
\(340\) | −6.43110 | −0.348775 | ||||||||
\(341\) | 27.5548 | 1.49217 | ||||||||
\(342\) | 5.46890 | 0.295724 | ||||||||
\(343\) | 1.18157 | 0.0637990 | ||||||||
\(344\) | −7.70471 | −0.415410 | ||||||||
\(345\) | 7.32934 | 0.394598 | ||||||||
\(346\) | −12.1386 | −0.652576 | ||||||||
\(347\) | −32.2125 | −1.72926 | −0.864628 | − | 0.502413i | \(-0.832446\pi\) | ||||
−0.864628 | + | 0.502413i | \(0.832446\pi\) | |||||||
\(348\) | −0.819494 | −0.0439295 | ||||||||
\(349\) | 6.54921 | 0.350571 | 0.175286 | − | 0.984518i | \(-0.443915\pi\) | ||||
0.175286 | + | 0.984518i | \(0.443915\pi\) | |||||||
\(350\) | −4.61531 | −0.246699 | ||||||||
\(351\) | −24.1274 | −1.28783 | ||||||||
\(352\) | −3.95977 | −0.211056 | ||||||||
\(353\) | 25.0982 | 1.33584 | 0.667922 | − | 0.744231i | \(-0.267184\pi\) | ||||
0.667922 | + | 0.744231i | \(0.267184\pi\) | |||||||
\(354\) | −15.4258 | −0.819874 | ||||||||
\(355\) | −19.8995 | −1.05615 | ||||||||
\(356\) | 16.5453 | 0.876901 | ||||||||
\(357\) | 13.8398 | 0.732479 | ||||||||
\(358\) | 22.6815 | 1.19875 | ||||||||
\(359\) | −7.88624 | −0.416220 | −0.208110 | − | 0.978105i | \(-0.566731\pi\) | ||||
−0.208110 | + | 0.978105i | \(0.566731\pi\) | |||||||
\(360\) | 2.21208 | 0.116587 | ||||||||
\(361\) | 19.1880 | 1.00989 | ||||||||
\(362\) | −5.22540 | −0.274641 | ||||||||
\(363\) | −6.80582 | −0.357213 | ||||||||
\(364\) | 15.7949 | 0.827878 | ||||||||
\(365\) | −39.9618 | −2.09170 | ||||||||
\(366\) | 14.1291 | 0.738539 | ||||||||
\(367\) | −10.9855 | −0.573440 | −0.286720 | − | 0.958014i | \(-0.592565\pi\) | ||||
−0.286720 | + | 0.958014i | \(0.592565\pi\) | |||||||
\(368\) | 2.01625 | 0.105104 | ||||||||
\(369\) | 4.96784 | 0.258615 | ||||||||
\(370\) | 19.8946 | 1.03427 | ||||||||
\(371\) | 52.6598 | 2.73396 | ||||||||
\(372\) | 10.1201 | 0.524701 | ||||||||
\(373\) | −2.84154 | −0.147130 | −0.0735648 | − | 0.997290i | \(-0.523438\pi\) | ||||
−0.0735648 | + | 0.997290i | \(0.523438\pi\) | |||||||
\(374\) | −10.1880 | −0.526811 | ||||||||
\(375\) | −13.6397 | −0.704351 | ||||||||
\(376\) | 3.56019 | 0.183603 | ||||||||
\(377\) | −2.40632 | −0.123932 | ||||||||
\(378\) | −20.8977 | −1.07486 | ||||||||
\(379\) | −21.7288 | −1.11613 | −0.558066 | − | 0.829797i | \(-0.688456\pi\) | ||||
−0.558066 | + | 0.829797i | \(0.688456\pi\) | |||||||
\(380\) | 15.4464 | 0.792384 | ||||||||
\(381\) | 17.8050 | 0.912176 | ||||||||
\(382\) | −8.67170 | −0.443683 | ||||||||
\(383\) | −22.9149 | −1.17090 | −0.585448 | − | 0.810710i | \(-0.699081\pi\) | ||||
−0.585448 | + | 0.810710i | \(0.699081\pi\) | |||||||
\(384\) | −1.45431 | −0.0742149 | ||||||||
\(385\) | −36.6088 | −1.86576 | ||||||||
\(386\) | −3.45130 | −0.175666 | ||||||||
\(387\) | 6.81857 | 0.346607 | ||||||||
\(388\) | 8.78153 | 0.445815 | ||||||||
\(389\) | −31.2393 | −1.58390 | −0.791948 | − | 0.610589i | \(-0.790933\pi\) | ||||
−0.791948 | + | 0.610589i | \(0.790933\pi\) | |||||||
\(390\) | −15.5234 | −0.786056 | ||||||||
\(391\) | 5.18758 | 0.262347 | ||||||||
\(392\) | 6.68055 | 0.337418 | ||||||||
\(393\) | 5.54614 | 0.279766 | ||||||||
\(394\) | 2.83509 | 0.142830 | ||||||||
\(395\) | −33.9012 | −1.70576 | ||||||||
\(396\) | 3.50434 | 0.176100 | ||||||||
\(397\) | 20.5339 | 1.03057 | 0.515283 | − | 0.857020i | \(-0.327687\pi\) | ||||
0.515283 | + | 0.857020i | \(0.327687\pi\) | |||||||
\(398\) | −11.0882 | −0.555803 | ||||||||
\(399\) | −33.2408 | −1.66412 | ||||||||
\(400\) | 1.24781 | 0.0623907 | ||||||||
\(401\) | −25.4113 | −1.26898 | −0.634489 | − | 0.772932i | \(-0.718789\pi\) | ||||
−0.634489 | + | 0.772932i | \(0.718789\pi\) | |||||||
\(402\) | 1.13470 | 0.0565935 | ||||||||
\(403\) | 29.7161 | 1.48026 | ||||||||
\(404\) | 1.36973 | 0.0681469 | ||||||||
\(405\) | 13.9022 | 0.690804 | ||||||||
\(406\) | −2.08421 | −0.103437 | ||||||||
\(407\) | 31.5167 | 1.56222 | ||||||||
\(408\) | −3.74177 | −0.185245 | ||||||||
\(409\) | −2.49880 | −0.123558 | −0.0617790 | − | 0.998090i | \(-0.519677\pi\) | ||||
−0.0617790 | + | 0.998090i | \(0.519677\pi\) | |||||||
\(410\) | 14.0312 | 0.692951 | ||||||||
\(411\) | 23.0250 | 1.13574 | ||||||||
\(412\) | −5.63186 | −0.277462 | ||||||||
\(413\) | −39.2323 | −1.93050 | ||||||||
\(414\) | −1.78435 | −0.0876962 | ||||||||
\(415\) | 14.4315 | 0.708416 | ||||||||
\(416\) | −4.27037 | −0.209372 | ||||||||
\(417\) | 14.8958 | 0.729450 | ||||||||
\(418\) | 24.4699 | 1.19686 | ||||||||
\(419\) | −22.0519 | −1.07730 | −0.538652 | − | 0.842528i | \(-0.681066\pi\) | ||||
−0.538652 | + | 0.842528i | \(0.681066\pi\) | |||||||
\(420\) | −13.4454 | −0.656066 | ||||||||
\(421\) | 37.9420 | 1.84918 | 0.924589 | − | 0.380966i | \(-0.124408\pi\) | ||||
0.924589 | + | 0.380966i | \(0.124408\pi\) | |||||||
\(422\) | 6.12946 | 0.298378 | ||||||||
\(423\) | −3.15072 | −0.153193 | ||||||||
\(424\) | −14.2373 | −0.691424 | ||||||||
\(425\) | 3.21048 | 0.155731 | ||||||||
\(426\) | −11.5780 | −0.560956 | ||||||||
\(427\) | 35.9343 | 1.73898 | ||||||||
\(428\) | 18.2872 | 0.883945 | ||||||||
\(429\) | −24.5919 | −1.18731 | ||||||||
\(430\) | 19.2584 | 0.928723 | ||||||||
\(431\) | 15.8101 | 0.761544 | 0.380772 | − | 0.924669i | \(-0.375658\pi\) | ||||
0.380772 | + | 0.924669i | \(0.375658\pi\) | |||||||
\(432\) | 5.64997 | 0.271834 | ||||||||
\(433\) | 23.1500 | 1.11252 | 0.556258 | − | 0.831010i | \(-0.312237\pi\) | ||||
0.556258 | + | 0.831010i | \(0.312237\pi\) | |||||||
\(434\) | 25.7382 | 1.23547 | ||||||||
\(435\) | 2.04838 | 0.0982121 | ||||||||
\(436\) | −14.6610 | −0.702135 | ||||||||
\(437\) | −12.4597 | −0.596028 | ||||||||
\(438\) | −23.2508 | −1.11097 | ||||||||
\(439\) | −10.3378 | −0.493398 | −0.246699 | − | 0.969092i | \(-0.579346\pi\) | ||||
−0.246699 | + | 0.969092i | \(0.579346\pi\) | |||||||
\(440\) | 9.89769 | 0.471854 | ||||||||
\(441\) | −5.91220 | −0.281533 | ||||||||
\(442\) | −10.9872 | −0.522607 | ||||||||
\(443\) | −31.8458 | −1.51304 | −0.756520 | − | 0.653971i | \(-0.773102\pi\) | ||||
−0.756520 | + | 0.653971i | \(0.773102\pi\) | |||||||
\(444\) | 11.5752 | 0.549333 | ||||||||
\(445\) | −41.3561 | −1.96047 | ||||||||
\(446\) | 24.4239 | 1.15650 | ||||||||
\(447\) | 17.0880 | 0.808236 | ||||||||
\(448\) | −3.69872 | −0.174748 | ||||||||
\(449\) | −8.92406 | −0.421153 | −0.210576 | − | 0.977577i | \(-0.567534\pi\) | ||||
−0.210576 | + | 0.977577i | \(0.567534\pi\) | |||||||
\(450\) | −1.10430 | −0.0520571 | ||||||||
\(451\) | 22.2280 | 1.04667 | ||||||||
\(452\) | −17.0292 | −0.800987 | ||||||||
\(453\) | −8.38990 | −0.394192 | ||||||||
\(454\) | 18.8628 | 0.885277 | ||||||||
\(455\) | −39.4803 | −1.85087 | ||||||||
\(456\) | 8.98710 | 0.420860 | ||||||||
\(457\) | −35.3746 | −1.65475 | −0.827376 | − | 0.561648i | \(-0.810168\pi\) | ||||
−0.827376 | + | 0.561648i | \(0.810168\pi\) | |||||||
\(458\) | 5.51478 | 0.257689 | ||||||||
\(459\) | 14.5367 | 0.678517 | ||||||||
\(460\) | −5.03974 | −0.234979 | ||||||||
\(461\) | −16.7319 | −0.779281 | −0.389640 | − | 0.920967i | \(-0.627401\pi\) | ||||
−0.389640 | + | 0.920967i | \(0.627401\pi\) | |||||||
\(462\) | −21.2999 | −0.990962 | ||||||||
\(463\) | 5.46233 | 0.253856 | 0.126928 | − | 0.991912i | \(-0.459488\pi\) | ||||
0.126928 | + | 0.991912i | \(0.459488\pi\) | |||||||
\(464\) | 0.563494 | 0.0261595 | ||||||||
\(465\) | −25.2957 | −1.17306 | ||||||||
\(466\) | 3.77347 | 0.174803 | ||||||||
\(467\) | −22.9179 | −1.06051 | −0.530257 | − | 0.847837i | \(-0.677905\pi\) | ||||
−0.530257 | + | 0.847837i | \(0.677905\pi\) | |||||||
\(468\) | 3.77922 | 0.174694 | ||||||||
\(469\) | 2.88586 | 0.133257 | ||||||||
\(470\) | −8.89892 | −0.410477 | ||||||||
\(471\) | 7.52263 | 0.346625 | ||||||||
\(472\) | 10.6070 | 0.488226 | ||||||||
\(473\) | 30.5089 | 1.40280 | ||||||||
\(474\) | −19.7246 | −0.905980 | ||||||||
\(475\) | −7.71104 | −0.353807 | ||||||||
\(476\) | −9.51640 | −0.436183 | ||||||||
\(477\) | 12.5998 | 0.576906 | ||||||||
\(478\) | −13.1769 | −0.602699 | ||||||||
\(479\) | −27.0543 | −1.23614 | −0.618070 | − | 0.786123i | \(-0.712085\pi\) | ||||
−0.618070 | + | 0.786123i | \(0.712085\pi\) | |||||||
\(480\) | 3.63513 | 0.165920 | ||||||||
\(481\) | 33.9888 | 1.54976 | ||||||||
\(482\) | −16.5754 | −0.754987 | ||||||||
\(483\) | 10.8456 | 0.493490 | ||||||||
\(484\) | 4.67976 | 0.212717 | ||||||||
\(485\) | −21.9500 | −0.996697 | ||||||||
\(486\) | −8.86128 | −0.401956 | ||||||||
\(487\) | 25.6673 | 1.16310 | 0.581548 | − | 0.813512i | \(-0.302447\pi\) | ||||
0.581548 | + | 0.813512i | \(0.302447\pi\) | |||||||
\(488\) | −9.71533 | −0.439792 | ||||||||
\(489\) | 6.45032 | 0.291694 | ||||||||
\(490\) | −16.6984 | −0.754359 | ||||||||
\(491\) | 22.4322 | 1.01235 | 0.506176 | − | 0.862430i | \(-0.331059\pi\) | ||||
0.506176 | + | 0.862430i | \(0.331059\pi\) | |||||||
\(492\) | 8.16370 | 0.368048 | ||||||||
\(493\) | 1.44981 | 0.0652960 | ||||||||
\(494\) | 26.3893 | 1.18731 | ||||||||
\(495\) | −8.75933 | −0.393702 | ||||||||
\(496\) | −6.95868 | −0.312454 | ||||||||
\(497\) | −29.4462 | −1.32084 | ||||||||
\(498\) | 8.39663 | 0.376262 | ||||||||
\(499\) | −11.9870 | −0.536612 | −0.268306 | − | 0.963334i | \(-0.586464\pi\) | ||||
−0.268306 | + | 0.963334i | \(0.586464\pi\) | |||||||
\(500\) | 9.37883 | 0.419434 | ||||||||
\(501\) | 4.23062 | 0.189010 | ||||||||
\(502\) | −29.1200 | −1.29969 | ||||||||
\(503\) | 10.7759 | 0.480473 | 0.240237 | − | 0.970714i | \(-0.422775\pi\) | ||||
0.240237 | + | 0.970714i | \(0.422775\pi\) | |||||||
\(504\) | 3.27332 | 0.145805 | ||||||||
\(505\) | −3.42374 | −0.152354 | ||||||||
\(506\) | −7.98388 | −0.354927 | ||||||||
\(507\) | −7.61480 | −0.338185 | ||||||||
\(508\) | −12.2429 | −0.543191 | ||||||||
\(509\) | 10.6066 | 0.470131 | 0.235065 | − | 0.971980i | \(-0.424470\pi\) | ||||
0.235065 | + | 0.971980i | \(0.424470\pi\) | |||||||
\(510\) | 9.35280 | 0.414149 | ||||||||
\(511\) | −59.1334 | −2.61591 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −34.9148 | −1.54153 | ||||||||
\(514\) | −20.7742 | −0.916312 | ||||||||
\(515\) | 14.0772 | 0.620315 | ||||||||
\(516\) | 11.2050 | 0.493274 | ||||||||
\(517\) | −14.0975 | −0.620009 | ||||||||
\(518\) | 29.4390 | 1.29347 | ||||||||
\(519\) | 17.6533 | 0.774894 | ||||||||
\(520\) | 10.6740 | 0.468088 | ||||||||
\(521\) | −9.89862 | −0.433666 | −0.216833 | − | 0.976209i | \(-0.569573\pi\) | ||||
−0.216833 | + | 0.976209i | \(0.569573\pi\) | |||||||
\(522\) | −0.498685 | −0.0218268 | ||||||||
\(523\) | −32.0225 | −1.40025 | −0.700124 | − | 0.714022i | \(-0.746872\pi\) | ||||
−0.700124 | + | 0.714022i | \(0.746872\pi\) | |||||||
\(524\) | −3.81360 | −0.166598 | ||||||||
\(525\) | 6.71209 | 0.292940 | ||||||||
\(526\) | −20.9500 | −0.913461 | ||||||||
\(527\) | −17.9039 | −0.779906 | ||||||||
\(528\) | 5.75872 | 0.250616 | ||||||||
\(529\) | −18.9347 | −0.823250 | ||||||||
\(530\) | 35.5870 | 1.54580 | ||||||||
\(531\) | −9.38704 | −0.407363 | ||||||||
\(532\) | 22.8568 | 0.990967 | ||||||||
\(533\) | 23.9715 | 1.03832 | ||||||||
\(534\) | −24.0620 | −1.04126 | ||||||||
\(535\) | −45.7100 | −1.97622 | ||||||||
\(536\) | −0.780231 | −0.0337009 | ||||||||
\(537\) | −32.9859 | −1.42345 | ||||||||
\(538\) | −5.65226 | −0.243686 | ||||||||
\(539\) | −26.4534 | −1.13943 | ||||||||
\(540\) | −14.1225 | −0.607734 | ||||||||
\(541\) | −17.6071 | −0.756987 | −0.378494 | − | 0.925604i | \(-0.623558\pi\) | ||||
−0.378494 | + | 0.925604i | \(0.623558\pi\) | |||||||
\(542\) | −11.9929 | −0.515140 | ||||||||
\(543\) | 7.59935 | 0.326119 | ||||||||
\(544\) | 2.57289 | 0.110312 | ||||||||
\(545\) | 36.6461 | 1.56975 | ||||||||
\(546\) | −22.9707 | −0.983053 | ||||||||
\(547\) | −39.6926 | −1.69713 | −0.848567 | − | 0.529088i | \(-0.822534\pi\) | ||||
−0.848567 | + | 0.529088i | \(0.822534\pi\) | |||||||
\(548\) | −15.8322 | −0.676320 | ||||||||
\(549\) | 8.59794 | 0.366951 | ||||||||
\(550\) | −4.94105 | −0.210687 | ||||||||
\(551\) | −3.48219 | −0.148346 | ||||||||
\(552\) | −2.93225 | −0.124805 | ||||||||
\(553\) | −50.1653 | −2.13324 | ||||||||
\(554\) | −1.12905 | −0.0479687 | ||||||||
\(555\) | −28.9329 | −1.22813 | ||||||||
\(556\) | −10.2425 | −0.434380 | ||||||||
\(557\) | 10.6074 | 0.449450 | 0.224725 | − | 0.974422i | \(-0.427852\pi\) | ||||
0.224725 | + | 0.974422i | \(0.427852\pi\) | |||||||
\(558\) | 6.15834 | 0.260703 | ||||||||
\(559\) | 32.9019 | 1.39160 | ||||||||
\(560\) | 9.24519 | 0.390680 | ||||||||
\(561\) | 14.8166 | 0.625555 | ||||||||
\(562\) | 21.8794 | 0.922927 | ||||||||
\(563\) | 39.8934 | 1.68131 | 0.840653 | − | 0.541574i | \(-0.182171\pi\) | ||||
0.840653 | + | 0.541574i | \(0.182171\pi\) | |||||||
\(564\) | −5.17762 | −0.218017 | ||||||||
\(565\) | 42.5656 | 1.79075 | ||||||||
\(566\) | 25.2573 | 1.06164 | ||||||||
\(567\) | 20.5717 | 0.863930 | ||||||||
\(568\) | 7.96118 | 0.334044 | ||||||||
\(569\) | 2.62368 | 0.109990 | 0.0549951 | − | 0.998487i | \(-0.482486\pi\) | ||||
0.0549951 | + | 0.998487i | \(0.482486\pi\) | |||||||
\(570\) | −22.4638 | −0.940906 | ||||||||
\(571\) | −17.7392 | −0.742362 | −0.371181 | − | 0.928560i | \(-0.621047\pi\) | ||||
−0.371181 | + | 0.928560i | \(0.621047\pi\) | |||||||
\(572\) | 16.9097 | 0.707028 | ||||||||
\(573\) | 12.6113 | 0.526845 | ||||||||
\(574\) | 20.7626 | 0.866615 | ||||||||
\(575\) | 2.51590 | 0.104920 | ||||||||
\(576\) | −0.884987 | −0.0368745 | ||||||||
\(577\) | 1.88691 | 0.0785531 | 0.0392766 | − | 0.999228i | \(-0.487495\pi\) | ||||
0.0392766 | + | 0.999228i | \(0.487495\pi\) | |||||||
\(578\) | −10.3802 | −0.431761 | ||||||||
\(579\) | 5.01925 | 0.208593 | ||||||||
\(580\) | −1.40849 | −0.0584843 | ||||||||
\(581\) | 21.3550 | 0.885956 | ||||||||
\(582\) | −12.7711 | −0.529377 | ||||||||
\(583\) | 56.3763 | 2.33487 | ||||||||
\(584\) | 15.9875 | 0.661568 | ||||||||
\(585\) | −9.44639 | −0.390560 | ||||||||
\(586\) | −5.94045 | −0.245398 | ||||||||
\(587\) | 45.8692 | 1.89323 | 0.946613 | − | 0.322373i | \(-0.104481\pi\) | ||||
0.946613 | + | 0.322373i | \(0.104481\pi\) | |||||||
\(588\) | −9.71557 | −0.400663 | ||||||||
\(589\) | 43.0021 | 1.77187 | ||||||||
\(590\) | −26.5128 | −1.09152 | ||||||||
\(591\) | −4.12309 | −0.169601 | ||||||||
\(592\) | −7.95922 | −0.327122 | ||||||||
\(593\) | −22.7125 | −0.932691 | −0.466346 | − | 0.884603i | \(-0.654430\pi\) | ||||
−0.466346 | + | 0.884603i | \(0.654430\pi\) | |||||||
\(594\) | −22.3726 | −0.917958 | ||||||||
\(595\) | 23.7868 | 0.975165 | ||||||||
\(596\) | −11.7499 | −0.481296 | ||||||||
\(597\) | 16.1257 | 0.659982 | ||||||||
\(598\) | −8.61012 | −0.352094 | ||||||||
\(599\) | −1.39791 | −0.0571172 | −0.0285586 | − | 0.999592i | \(-0.509092\pi\) | ||||
−0.0285586 | + | 0.999592i | \(0.509092\pi\) | |||||||
\(600\) | −1.81470 | −0.0740850 | ||||||||
\(601\) | 1.32460 | 0.0540316 | 0.0270158 | − | 0.999635i | \(-0.491400\pi\) | ||||
0.0270158 | + | 0.999635i | \(0.491400\pi\) | |||||||
\(602\) | 28.4976 | 1.16147 | ||||||||
\(603\) | 0.690494 | 0.0281191 | ||||||||
\(604\) | 5.76900 | 0.234737 | ||||||||
\(605\) | −11.6974 | −0.475566 | ||||||||
\(606\) | −1.99202 | −0.0809202 | ||||||||
\(607\) | 16.0726 | 0.652367 | 0.326183 | − | 0.945306i | \(-0.394237\pi\) | ||||
0.326183 | + | 0.945306i | \(0.394237\pi\) | |||||||
\(608\) | −6.17964 | −0.250618 | ||||||||
\(609\) | 3.03108 | 0.122826 | ||||||||
\(610\) | 24.2841 | 0.983233 | ||||||||
\(611\) | −15.2033 | −0.615061 | ||||||||
\(612\) | −2.27697 | −0.0920412 | ||||||||
\(613\) | 10.4160 | 0.420698 | 0.210349 | − | 0.977626i | \(-0.432540\pi\) | ||||
0.210349 | + | 0.977626i | \(0.432540\pi\) | |||||||
\(614\) | 10.4116 | 0.420180 | ||||||||
\(615\) | −20.4057 | −0.822836 | ||||||||
\(616\) | 14.6461 | 0.590107 | ||||||||
\(617\) | −15.1751 | −0.610927 | −0.305463 | − | 0.952204i | \(-0.598811\pi\) | ||||
−0.305463 | + | 0.952204i | \(0.598811\pi\) | |||||||
\(618\) | 8.19047 | 0.329469 | ||||||||
\(619\) | 44.0206 | 1.76934 | 0.884668 | − | 0.466221i | \(-0.154385\pi\) | ||||
0.884668 | + | 0.466221i | \(0.154385\pi\) | |||||||
\(620\) | 17.3937 | 0.698546 | ||||||||
\(621\) | 11.3917 | 0.457135 | ||||||||
\(622\) | 33.2987 | 1.33516 | ||||||||
\(623\) | −61.1966 | −2.45179 | ||||||||
\(624\) | 6.21043 | 0.248616 | ||||||||
\(625\) | −29.6820 | −1.18728 | ||||||||
\(626\) | 6.47296 | 0.258711 | ||||||||
\(627\) | −35.5868 | −1.42120 | ||||||||
\(628\) | −5.17265 | −0.206411 | ||||||||
\(629\) | −20.4782 | −0.816519 | ||||||||
\(630\) | −8.18187 | −0.325974 | ||||||||
\(631\) | −35.4807 | −1.41247 | −0.706233 | − | 0.707980i | \(-0.749607\pi\) | ||||
−0.706233 | + | 0.707980i | \(0.749607\pi\) | |||||||
\(632\) | 13.5629 | 0.539502 | ||||||||
\(633\) | −8.91413 | −0.354305 | ||||||||
\(634\) | 19.4944 | 0.774221 | ||||||||
\(635\) | 30.6019 | 1.21440 | ||||||||
\(636\) | 20.7054 | 0.821023 | ||||||||
\(637\) | −28.5284 | −1.13034 | ||||||||
\(638\) | −2.23130 | −0.0883382 | ||||||||
\(639\) | −7.04554 | −0.278717 | ||||||||
\(640\) | −2.49956 | −0.0988039 | ||||||||
\(641\) | −0.285736 | −0.0112859 | −0.00564295 | − | 0.999984i | \(-0.501796\pi\) | ||||
−0.00564295 | + | 0.999984i | \(0.501796\pi\) | |||||||
\(642\) | −26.5952 | −1.04963 | ||||||||
\(643\) | 29.4910 | 1.16301 | 0.581505 | − | 0.813543i | \(-0.302464\pi\) | ||||
0.581505 | + | 0.813543i | \(0.302464\pi\) | |||||||
\(644\) | −7.45754 | −0.293868 | ||||||||
\(645\) | −28.0077 | −1.10280 | ||||||||
\(646\) | −15.8995 | −0.625558 | ||||||||
\(647\) | 16.8892 | 0.663984 | 0.331992 | − | 0.943282i | \(-0.392279\pi\) | ||||
0.331992 | + | 0.943282i | \(0.392279\pi\) | |||||||
\(648\) | −5.56184 | −0.218490 | ||||||||
\(649\) | −42.0012 | −1.64869 | ||||||||
\(650\) | −5.32862 | −0.209006 | ||||||||
\(651\) | −37.4313 | −1.46705 | ||||||||
\(652\) | −4.43532 | −0.173700 | ||||||||
\(653\) | −17.5616 | −0.687237 | −0.343618 | − | 0.939109i | \(-0.611653\pi\) | ||||
−0.343618 | + | 0.939109i | \(0.611653\pi\) | |||||||
\(654\) | 21.3216 | 0.833741 | ||||||||
\(655\) | 9.53232 | 0.372459 | ||||||||
\(656\) | −5.61346 | −0.219169 | ||||||||
\(657\) | −14.1487 | −0.551995 | ||||||||
\(658\) | −13.1682 | −0.513348 | ||||||||
\(659\) | 43.8588 | 1.70850 | 0.854248 | − | 0.519865i | \(-0.174018\pi\) | ||||
0.854248 | + | 0.519865i | \(0.174018\pi\) | |||||||
\(660\) | −14.3943 | −0.560297 | ||||||||
\(661\) | 14.8547 | 0.577780 | 0.288890 | − | 0.957362i | \(-0.406714\pi\) | ||||
0.288890 | + | 0.957362i | \(0.406714\pi\) | |||||||
\(662\) | 3.65322 | 0.141986 | ||||||||
\(663\) | 15.9787 | 0.620563 | ||||||||
\(664\) | −5.77362 | −0.224060 | ||||||||
\(665\) | −57.1319 | −2.21548 | ||||||||
\(666\) | 7.04381 | 0.272942 | ||||||||
\(667\) | 1.13614 | 0.0439916 | ||||||||
\(668\) | −2.90902 | −0.112554 | ||||||||
\(669\) | −35.5199 | −1.37328 | ||||||||
\(670\) | 1.95024 | 0.0753442 | ||||||||
\(671\) | 38.4704 | 1.48513 | ||||||||
\(672\) | 5.37908 | 0.207503 | ||||||||
\(673\) | −17.1289 | −0.660269 | −0.330134 | − | 0.943934i | \(-0.607094\pi\) | ||||
−0.330134 | + | 0.943934i | \(0.607094\pi\) | |||||||
\(674\) | −19.3565 | −0.745584 | ||||||||
\(675\) | 7.05011 | 0.271359 | ||||||||
\(676\) | 5.23603 | 0.201386 | ||||||||
\(677\) | 3.11713 | 0.119801 | 0.0599005 | − | 0.998204i | \(-0.480922\pi\) | ||||
0.0599005 | + | 0.998204i | \(0.480922\pi\) | |||||||
\(678\) | 24.7657 | 0.951122 | ||||||||
\(679\) | −32.4804 | −1.24648 | ||||||||
\(680\) | −6.43110 | −0.246621 | ||||||||
\(681\) | −27.4324 | −1.05121 | ||||||||
\(682\) | 27.5548 | 1.05513 | ||||||||
\(683\) | 3.47425 | 0.132939 | 0.0664693 | − | 0.997788i | \(-0.478827\pi\) | ||||
0.0664693 | + | 0.997788i | \(0.478827\pi\) | |||||||
\(684\) | 5.46890 | 0.209109 | ||||||||
\(685\) | 39.5737 | 1.51203 | ||||||||
\(686\) | 1.18157 | 0.0451127 | ||||||||
\(687\) | −8.02019 | −0.305989 | ||||||||
\(688\) | −7.70471 | −0.293739 | ||||||||
\(689\) | 60.7984 | 2.31624 | ||||||||
\(690\) | 7.32934 | 0.279023 | ||||||||
\(691\) | −16.6611 | −0.633819 | −0.316910 | − | 0.948456i | \(-0.602645\pi\) | ||||
−0.316910 | + | 0.948456i | \(0.602645\pi\) | |||||||
\(692\) | −12.1386 | −0.461441 | ||||||||
\(693\) | −12.9616 | −0.492370 | ||||||||
\(694\) | −32.2125 | −1.22277 | ||||||||
\(695\) | 25.6018 | 0.971133 | ||||||||
\(696\) | −0.819494 | −0.0310628 | ||||||||
\(697\) | −14.4428 | −0.547060 | ||||||||
\(698\) | 6.54921 | 0.247891 | ||||||||
\(699\) | −5.48780 | −0.207568 | ||||||||
\(700\) | −4.61531 | −0.174442 | ||||||||
\(701\) | −30.9722 | −1.16980 | −0.584902 | − | 0.811104i | \(-0.698867\pi\) | ||||
−0.584902 | + | 0.811104i | \(0.698867\pi\) | |||||||
\(702\) | −24.1274 | −0.910631 | ||||||||
\(703\) | 49.1852 | 1.85505 | ||||||||
\(704\) | −3.95977 | −0.149239 | ||||||||
\(705\) | 12.9418 | 0.487416 | ||||||||
\(706\) | 25.0982 | 0.944584 | ||||||||
\(707\) | −5.06627 | −0.190537 | ||||||||
\(708\) | −15.4258 | −0.579738 | ||||||||
\(709\) | −13.6250 | −0.511698 | −0.255849 | − | 0.966717i | \(-0.582355\pi\) | ||||
−0.255849 | + | 0.966717i | \(0.582355\pi\) | |||||||
\(710\) | −19.8995 | −0.746813 | ||||||||
\(711\) | −12.0030 | −0.450146 | ||||||||
\(712\) | 16.5453 | 0.620062 | ||||||||
\(713\) | −14.0304 | −0.525444 | ||||||||
\(714\) | 13.8398 | 0.517941 | ||||||||
\(715\) | −42.2668 | −1.58069 | ||||||||
\(716\) | 22.6815 | 0.847648 | ||||||||
\(717\) | 19.1633 | 0.715667 | ||||||||
\(718\) | −7.88624 | −0.294312 | ||||||||
\(719\) | 27.5495 | 1.02742 | 0.513711 | − | 0.857963i | \(-0.328270\pi\) | ||||
0.513711 | + | 0.857963i | \(0.328270\pi\) | |||||||
\(720\) | 2.21208 | 0.0824394 | ||||||||
\(721\) | 20.8307 | 0.775776 | ||||||||
\(722\) | 19.1880 | 0.714102 | ||||||||
\(723\) | 24.1057 | 0.896500 | ||||||||
\(724\) | −5.22540 | −0.194201 | ||||||||
\(725\) | 0.703135 | 0.0261138 | ||||||||
\(726\) | −6.80582 | −0.252588 | ||||||||
\(727\) | −17.7917 | −0.659856 | −0.329928 | − | 0.944006i | \(-0.607025\pi\) | ||||
−0.329928 | + | 0.944006i | \(0.607025\pi\) | |||||||
\(728\) | 15.7949 | 0.585398 | ||||||||
\(729\) | 29.5725 | 1.09528 | ||||||||
\(730\) | −39.9618 | −1.47905 | ||||||||
\(731\) | −19.8234 | −0.733193 | ||||||||
\(732\) | 14.1291 | 0.522226 | ||||||||
\(733\) | 24.5244 | 0.905830 | 0.452915 | − | 0.891554i | \(-0.350384\pi\) | ||||
0.452915 | + | 0.891554i | \(0.350384\pi\) | |||||||
\(734\) | −10.9855 | −0.405483 | ||||||||
\(735\) | 24.2847 | 0.895754 | ||||||||
\(736\) | 2.01625 | 0.0743199 | ||||||||
\(737\) | 3.08953 | 0.113804 | ||||||||
\(738\) | 4.96784 | 0.182869 | ||||||||
\(739\) | 14.0201 | 0.515737 | 0.257869 | − | 0.966180i | \(-0.416980\pi\) | ||||
0.257869 | + | 0.966180i | \(0.416980\pi\) | |||||||
\(740\) | 19.8946 | 0.731339 | ||||||||
\(741\) | −38.3782 | −1.40986 | ||||||||
\(742\) | 52.6598 | 1.93320 | ||||||||
\(743\) | 47.0278 | 1.72528 | 0.862641 | − | 0.505817i | \(-0.168809\pi\) | ||||
0.862641 | + | 0.505817i | \(0.168809\pi\) | |||||||
\(744\) | 10.1201 | 0.371020 | ||||||||
\(745\) | 29.3697 | 1.07602 | ||||||||
\(746\) | −2.84154 | −0.104036 | ||||||||
\(747\) | 5.10958 | 0.186950 | ||||||||
\(748\) | −10.1880 | −0.372512 | ||||||||
\(749\) | −67.6393 | −2.47149 | ||||||||
\(750\) | −13.6397 | −0.498052 | ||||||||
\(751\) | 39.6133 | 1.44551 | 0.722755 | − | 0.691105i | \(-0.242876\pi\) | ||||
0.722755 | + | 0.691105i | \(0.242876\pi\) | |||||||
\(752\) | 3.56019 | 0.129827 | ||||||||
\(753\) | 42.3494 | 1.54330 | ||||||||
\(754\) | −2.40632 | −0.0876332 | ||||||||
\(755\) | −14.4200 | −0.524796 | ||||||||
\(756\) | −20.8977 | −0.760041 | ||||||||
\(757\) | −10.9455 | −0.397820 | −0.198910 | − | 0.980018i | \(-0.563740\pi\) | ||||
−0.198910 | + | 0.980018i | \(0.563740\pi\) | |||||||
\(758\) | −21.7288 | −0.789225 | ||||||||
\(759\) | 11.6110 | 0.421453 | ||||||||
\(760\) | 15.4464 | 0.560300 | ||||||||
\(761\) | −27.4110 | −0.993650 | −0.496825 | − | 0.867851i | \(-0.665501\pi\) | ||||
−0.496825 | + | 0.867851i | \(0.665501\pi\) | |||||||
\(762\) | 17.8050 | 0.645006 | ||||||||
\(763\) | 54.2270 | 1.96315 | ||||||||
\(764\) | −8.67170 | −0.313731 | ||||||||
\(765\) | 5.69144 | 0.205774 | ||||||||
\(766\) | −22.9149 | −0.827949 | ||||||||
\(767\) | −45.2957 | −1.63553 | ||||||||
\(768\) | −1.45431 | −0.0524778 | ||||||||
\(769\) | −0.681540 | −0.0245770 | −0.0122885 | − | 0.999924i | \(-0.503912\pi\) | ||||
−0.0122885 | + | 0.999924i | \(0.503912\pi\) | |||||||
\(770\) | −36.6088 | −1.31929 | ||||||||
\(771\) | 30.2121 | 1.08806 | ||||||||
\(772\) | −3.45130 | −0.124215 | ||||||||
\(773\) | −48.1630 | −1.73230 | −0.866152 | − | 0.499781i | \(-0.833414\pi\) | ||||
−0.866152 | + | 0.499781i | \(0.833414\pi\) | |||||||
\(774\) | 6.81857 | 0.245088 | ||||||||
\(775\) | −8.68313 | −0.311907 | ||||||||
\(776\) | 8.78153 | 0.315239 | ||||||||
\(777\) | −42.8133 | −1.53592 | ||||||||
\(778\) | −31.2393 | −1.11998 | ||||||||
\(779\) | 34.6891 | 1.24287 | ||||||||
\(780\) | −15.5234 | −0.555825 | ||||||||
\(781\) | −31.5244 | −1.12803 | ||||||||
\(782\) | 5.18758 | 0.185508 | ||||||||
\(783\) | 3.18372 | 0.113777 | ||||||||
\(784\) | 6.68055 | 0.238591 | ||||||||
\(785\) | 12.9294 | 0.461469 | ||||||||
\(786\) | 5.54614 | 0.197824 | ||||||||
\(787\) | −9.07799 | −0.323595 | −0.161798 | − | 0.986824i | \(-0.551729\pi\) | ||||
−0.161798 | + | 0.986824i | \(0.551729\pi\) | |||||||
\(788\) | 2.83509 | 0.100996 | ||||||||
\(789\) | 30.4677 | 1.08468 | ||||||||
\(790\) | −33.9012 | −1.20615 | ||||||||
\(791\) | 62.9863 | 2.23954 | ||||||||
\(792\) | 3.50434 | 0.124521 | ||||||||
\(793\) | 41.4880 | 1.47328 | ||||||||
\(794\) | 20.5339 | 0.728720 | ||||||||
\(795\) | −51.7545 | −1.83554 | ||||||||
\(796\) | −11.0882 | −0.393012 | ||||||||
\(797\) | −18.1718 | −0.643677 | −0.321838 | − | 0.946795i | \(-0.604301\pi\) | ||||
−0.321838 | + | 0.946795i | \(0.604301\pi\) | |||||||
\(798\) | −33.2408 | −1.17671 | ||||||||
\(799\) | 9.15998 | 0.324057 | ||||||||
\(800\) | 1.24781 | 0.0441169 | ||||||||
\(801\) | −14.6424 | −0.517364 | ||||||||
\(802\) | −25.4113 | −0.897303 | ||||||||
\(803\) | −63.3069 | −2.23405 | ||||||||
\(804\) | 1.13470 | 0.0400177 | ||||||||
\(805\) | 18.6406 | 0.656995 | ||||||||
\(806\) | 29.7161 | 1.04671 | ||||||||
\(807\) | 8.22012 | 0.289362 | ||||||||
\(808\) | 1.36973 | 0.0481871 | ||||||||
\(809\) | 16.3207 | 0.573806 | 0.286903 | − | 0.957960i | \(-0.407374\pi\) | ||||
0.286903 | + | 0.957960i | \(0.407374\pi\) | |||||||
\(810\) | 13.9022 | 0.488472 | ||||||||
\(811\) | 15.8896 | 0.557958 | 0.278979 | − | 0.960297i | \(-0.410004\pi\) | ||||
0.278979 | + | 0.960297i | \(0.410004\pi\) | |||||||
\(812\) | −2.08421 | −0.0731413 | ||||||||
\(813\) | 17.4414 | 0.611697 | ||||||||
\(814\) | 31.5167 | 1.10466 | ||||||||
\(815\) | 11.0864 | 0.388338 | ||||||||
\(816\) | −3.74177 | −0.130988 | ||||||||
\(817\) | 47.6123 | 1.66574 | ||||||||
\(818\) | −2.49880 | −0.0873686 | ||||||||
\(819\) | −13.9783 | −0.488441 | ||||||||
\(820\) | 14.0312 | 0.489990 | ||||||||
\(821\) | −32.8837 | −1.14765 | −0.573825 | − | 0.818978i | \(-0.694541\pi\) | ||||
−0.573825 | + | 0.818978i | \(0.694541\pi\) | |||||||
\(822\) | 23.0250 | 0.803088 | ||||||||
\(823\) | 46.1868 | 1.60997 | 0.804986 | − | 0.593294i | \(-0.202173\pi\) | ||||
0.804986 | + | 0.593294i | \(0.202173\pi\) | |||||||
\(824\) | −5.63186 | −0.196195 | ||||||||
\(825\) | 7.18581 | 0.250178 | ||||||||
\(826\) | −39.2323 | −1.36507 | ||||||||
\(827\) | −7.83901 | −0.272589 | −0.136294 | − | 0.990668i | \(-0.543519\pi\) | ||||
−0.136294 | + | 0.990668i | \(0.543519\pi\) | |||||||
\(828\) | −1.78435 | −0.0620106 | ||||||||
\(829\) | −25.7021 | −0.892670 | −0.446335 | − | 0.894866i | \(-0.647271\pi\) | ||||
−0.446335 | + | 0.894866i | \(0.647271\pi\) | |||||||
\(830\) | 14.4315 | 0.500926 | ||||||||
\(831\) | 1.64198 | 0.0569598 | ||||||||
\(832\) | −4.27037 | −0.148048 | ||||||||
\(833\) | 17.1883 | 0.595539 | ||||||||
\(834\) | 14.8958 | 0.515799 | ||||||||
\(835\) | 7.27129 | 0.251633 | ||||||||
\(836\) | 24.4699 | 0.846311 | ||||||||
\(837\) | −39.3163 | −1.35897 | ||||||||
\(838\) | −22.0519 | −0.761770 | ||||||||
\(839\) | −49.8165 | −1.71986 | −0.859929 | − | 0.510414i | \(-0.829492\pi\) | ||||
−0.859929 | + | 0.510414i | \(0.829492\pi\) | |||||||
\(840\) | −13.4454 | −0.463909 | ||||||||
\(841\) | −28.6825 | −0.989051 | ||||||||
\(842\) | 37.9420 | 1.30757 | ||||||||
\(843\) | −31.8194 | −1.09592 | ||||||||
\(844\) | 6.12946 | 0.210985 | ||||||||
\(845\) | −13.0878 | −0.450233 | ||||||||
\(846\) | −3.15072 | −0.108324 | ||||||||
\(847\) | −17.3092 | −0.594749 | ||||||||
\(848\) | −14.2373 | −0.488910 | ||||||||
\(849\) | −36.7319 | −1.26064 | ||||||||
\(850\) | 3.21048 | 0.110119 | ||||||||
\(851\) | −16.0478 | −0.550111 | ||||||||
\(852\) | −11.5780 | −0.396656 | ||||||||
\(853\) | 9.85602 | 0.337464 | 0.168732 | − | 0.985662i | \(-0.446033\pi\) | ||||
0.168732 | + | 0.985662i | \(0.446033\pi\) | |||||||
\(854\) | 35.9343 | 1.22965 | ||||||||
\(855\) | −13.6699 | −0.467499 | ||||||||
\(856\) | 18.2872 | 0.625044 | ||||||||
\(857\) | 26.1024 | 0.891641 | 0.445821 | − | 0.895122i | \(-0.352912\pi\) | ||||
0.445821 | + | 0.895122i | \(0.352912\pi\) | |||||||
\(858\) | −24.5919 | −0.839552 | ||||||||
\(859\) | 8.02377 | 0.273768 | 0.136884 | − | 0.990587i | \(-0.456291\pi\) | ||||
0.136884 | + | 0.990587i | \(0.456291\pi\) | |||||||
\(860\) | 19.2584 | 0.656706 | ||||||||
\(861\) | −30.1952 | −1.02905 | ||||||||
\(862\) | 15.8101 | 0.538493 | ||||||||
\(863\) | 31.7409 | 1.08047 | 0.540236 | − | 0.841514i | \(-0.318335\pi\) | ||||
0.540236 | + | 0.841514i | \(0.318335\pi\) | |||||||
\(864\) | 5.64997 | 0.192216 | ||||||||
\(865\) | 30.3412 | 1.03163 | ||||||||
\(866\) | 23.1500 | 0.786668 | ||||||||
\(867\) | 15.0961 | 0.512690 | ||||||||
\(868\) | 25.7382 | 0.873612 | ||||||||
\(869\) | −53.7058 | −1.82184 | ||||||||
\(870\) | 2.04838 | 0.0694464 | ||||||||
\(871\) | 3.33187 | 0.112896 | ||||||||
\(872\) | −14.6610 | −0.496484 | ||||||||
\(873\) | −7.77154 | −0.263027 | ||||||||
\(874\) | −12.4597 | −0.421455 | ||||||||
\(875\) | −34.6897 | −1.17272 | ||||||||
\(876\) | −23.2508 | −0.785571 | ||||||||
\(877\) | 19.8898 | 0.671630 | 0.335815 | − | 0.941928i | \(-0.390988\pi\) | ||||
0.335815 | + | 0.941928i | \(0.390988\pi\) | |||||||
\(878\) | −10.3378 | −0.348885 | ||||||||
\(879\) | 8.63925 | 0.291395 | ||||||||
\(880\) | 9.89769 | 0.333651 | ||||||||
\(881\) | −20.3517 | −0.685667 | −0.342833 | − | 0.939396i | \(-0.611387\pi\) | ||||
−0.342833 | + | 0.939396i | \(0.611387\pi\) | |||||||
\(882\) | −5.91220 | −0.199074 | ||||||||
\(883\) | 16.2450 | 0.546689 | 0.273344 | − | 0.961916i | \(-0.411870\pi\) | ||||
0.273344 | + | 0.961916i | \(0.411870\pi\) | |||||||
\(884\) | −10.9872 | −0.369539 | ||||||||
\(885\) | 38.5578 | 1.29611 | ||||||||
\(886\) | −31.8458 | −1.06988 | ||||||||
\(887\) | −24.0745 | −0.808343 | −0.404172 | − | 0.914683i | \(-0.632440\pi\) | ||||
−0.404172 | + | 0.914683i | \(0.632440\pi\) | |||||||
\(888\) | 11.5752 | 0.388437 | ||||||||
\(889\) | 45.2831 | 1.51875 | ||||||||
\(890\) | −41.3561 | −1.38626 | ||||||||
\(891\) | 22.0236 | 0.737818 | ||||||||
\(892\) | 24.4239 | 0.817772 | ||||||||
\(893\) | −22.0007 | −0.736226 | ||||||||
\(894\) | 17.0880 | 0.571509 | ||||||||
\(895\) | −56.6938 | −1.89507 | ||||||||
\(896\) | −3.69872 | −0.123566 | ||||||||
\(897\) | 12.5218 | 0.418090 | ||||||||
\(898\) | −8.92406 | −0.297800 | ||||||||
\(899\) | −3.92117 | −0.130778 | ||||||||
\(900\) | −1.10430 | −0.0368099 | ||||||||
\(901\) | −36.6309 | −1.22035 | ||||||||
\(902\) | 22.2280 | 0.740111 | ||||||||
\(903\) | −41.4443 | −1.37918 | ||||||||
\(904\) | −17.0292 | −0.566383 | ||||||||
\(905\) | 13.0612 | 0.434170 | ||||||||
\(906\) | −8.38990 | −0.278736 | ||||||||
\(907\) | 49.6591 | 1.64890 | 0.824452 | − | 0.565932i | \(-0.191484\pi\) | ||||
0.824452 | + | 0.565932i | \(0.191484\pi\) | |||||||
\(908\) | 18.8628 | 0.625985 | ||||||||
\(909\) | −1.21220 | −0.0402061 | ||||||||
\(910\) | −39.4803 | −1.30876 | ||||||||
\(911\) | −45.4012 | −1.50421 | −0.752105 | − | 0.659044i | \(-0.770961\pi\) | ||||
−0.752105 | + | 0.659044i | \(0.770961\pi\) | |||||||
\(912\) | 8.98710 | 0.297593 | ||||||||
\(913\) | 22.8622 | 0.756629 | ||||||||
\(914\) | −35.3746 | −1.17009 | ||||||||
\(915\) | −35.3165 | −1.16753 | ||||||||
\(916\) | 5.51478 | 0.182213 | ||||||||
\(917\) | 14.1054 | 0.465802 | ||||||||
\(918\) | 14.5367 | 0.479784 | ||||||||
\(919\) | 47.1125 | 1.55410 | 0.777050 | − | 0.629439i | \(-0.216715\pi\) | ||||
0.777050 | + | 0.629439i | \(0.216715\pi\) | |||||||
\(920\) | −5.03974 | −0.166155 | ||||||||
\(921\) | −15.1417 | −0.498937 | ||||||||
\(922\) | −16.7319 | −0.551035 | ||||||||
\(923\) | −33.9971 | −1.11903 | ||||||||
\(924\) | −21.2999 | −0.700716 | ||||||||
\(925\) | −9.93162 | −0.326550 | ||||||||
\(926\) | 5.46233 | 0.179503 | ||||||||
\(927\) | 4.98413 | 0.163700 | ||||||||
\(928\) | 0.563494 | 0.0184976 | ||||||||
\(929\) | 24.1684 | 0.792940 | 0.396470 | − | 0.918048i | \(-0.370235\pi\) | ||||
0.396470 | + | 0.918048i | \(0.370235\pi\) | |||||||
\(930\) | −25.2957 | −0.829480 | ||||||||
\(931\) | −41.2834 | −1.35301 | ||||||||
\(932\) | 3.77347 | 0.123604 | ||||||||
\(933\) | −48.4266 | −1.58542 | ||||||||
\(934\) | −22.9179 | −0.749897 | ||||||||
\(935\) | 25.4656 | 0.832816 | ||||||||
\(936\) | 3.77922 | 0.123528 | ||||||||
\(937\) | 41.6540 | 1.36078 | 0.680388 | − | 0.732852i | \(-0.261811\pi\) | ||||
0.680388 | + | 0.732852i | \(0.261811\pi\) | |||||||
\(938\) | 2.88586 | 0.0942266 | ||||||||
\(939\) | −9.41367 | −0.307204 | ||||||||
\(940\) | −8.89892 | −0.290251 | ||||||||
\(941\) | 15.3158 | 0.499282 | 0.249641 | − | 0.968339i | \(-0.419687\pi\) | ||||
0.249641 | + | 0.968339i | \(0.419687\pi\) | |||||||
\(942\) | 7.52263 | 0.245101 | ||||||||
\(943\) | −11.3181 | −0.368569 | ||||||||
\(944\) | 10.6070 | 0.345228 | ||||||||
\(945\) | 52.2350 | 1.69921 | ||||||||
\(946\) | 30.5089 | 0.991929 | ||||||||
\(947\) | 38.8651 | 1.26295 | 0.631473 | − | 0.775398i | \(-0.282451\pi\) | ||||
0.631473 | + | 0.775398i | \(0.282451\pi\) | |||||||
\(948\) | −19.7246 | −0.640625 | ||||||||
\(949\) | −68.2725 | −2.21622 | ||||||||
\(950\) | −7.71104 | −0.250179 | ||||||||
\(951\) | −28.3508 | −0.919339 | ||||||||
\(952\) | −9.51640 | −0.308428 | ||||||||
\(953\) | 47.0994 | 1.52570 | 0.762849 | − | 0.646577i | \(-0.223800\pi\) | ||||
0.762849 | + | 0.646577i | \(0.223800\pi\) | |||||||
\(954\) | 12.5998 | 0.407934 | ||||||||
\(955\) | 21.6754 | 0.701401 | ||||||||
\(956\) | −13.1769 | −0.426172 | ||||||||
\(957\) | 3.24500 | 0.104896 | ||||||||
\(958\) | −27.0543 | −0.874084 | ||||||||
\(959\) | 58.5591 | 1.89097 | ||||||||
\(960\) | 3.63513 | 0.117323 | ||||||||
\(961\) | 17.4232 | 0.562039 | ||||||||
\(962\) | 33.9888 | 1.09584 | ||||||||
\(963\) | −16.1839 | −0.521520 | ||||||||
\(964\) | −16.5754 | −0.533856 | ||||||||
\(965\) | 8.62673 | 0.277704 | ||||||||
\(966\) | 10.8456 | 0.348950 | ||||||||
\(967\) | −33.7240 | −1.08449 | −0.542245 | − | 0.840221i | \(-0.682425\pi\) | ||||
−0.542245 | + | 0.840221i | \(0.682425\pi\) | |||||||
\(968\) | 4.67976 | 0.150413 | ||||||||
\(969\) | 23.1228 | 0.742812 | ||||||||
\(970\) | −21.9500 | −0.704771 | ||||||||
\(971\) | −32.4877 | −1.04258 | −0.521290 | − | 0.853380i | \(-0.674549\pi\) | ||||
−0.521290 | + | 0.853380i | \(0.674549\pi\) | |||||||
\(972\) | −8.86128 | −0.284226 | ||||||||
\(973\) | 37.8842 | 1.21451 | ||||||||
\(974\) | 25.6673 | 0.822432 | ||||||||
\(975\) | 7.74946 | 0.248181 | ||||||||
\(976\) | −9.71533 | −0.310980 | ||||||||
\(977\) | 12.5170 | 0.400454 | 0.200227 | − | 0.979750i | \(-0.435832\pi\) | ||||
0.200227 | + | 0.979750i | \(0.435832\pi\) | |||||||
\(978\) | 6.45032 | 0.206259 | ||||||||
\(979\) | −65.5157 | −2.09389 | ||||||||
\(980\) | −16.6984 | −0.533412 | ||||||||
\(981\) | 12.9748 | 0.414253 | ||||||||
\(982\) | 22.4322 | 0.715841 | ||||||||
\(983\) | −10.1862 | −0.324888 | −0.162444 | − | 0.986718i | \(-0.551938\pi\) | ||||
−0.162444 | + | 0.986718i | \(0.551938\pi\) | |||||||
\(984\) | 8.16370 | 0.260249 | ||||||||
\(985\) | −7.08648 | −0.225794 | ||||||||
\(986\) | 1.44981 | 0.0461712 | ||||||||
\(987\) | 19.1506 | 0.609569 | ||||||||
\(988\) | 26.3893 | 0.839556 | ||||||||
\(989\) | −15.5346 | −0.493972 | ||||||||
\(990\) | −8.75933 | −0.278390 | ||||||||
\(991\) | −2.41835 | −0.0768215 | −0.0384108 | − | 0.999262i | \(-0.512230\pi\) | ||||
−0.0384108 | + | 0.999262i | \(0.512230\pi\) | |||||||
\(992\) | −6.95868 | −0.220938 | ||||||||
\(993\) | −5.31291 | −0.168600 | ||||||||
\(994\) | −29.4462 | −0.933976 | ||||||||
\(995\) | 27.7157 | 0.878648 | ||||||||
\(996\) | 8.39663 | 0.266057 | ||||||||
\(997\) | 44.8902 | 1.42169 | 0.710844 | − | 0.703350i | \(-0.248313\pi\) | ||||
0.710844 | + | 0.703350i | \(0.248313\pi\) | |||||||
\(998\) | −11.9870 | −0.379442 | ||||||||
\(999\) | −44.9694 | −1.42277 |
(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 | 4022.2.a.f.1.14 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.f.1.14 | ✓ | 50 | 1.1 | even | 1 | trivial |