Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [538,2,Mod(1,538)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(538, 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("538.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 538 = 2 \cdot 269 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 538.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: | \(4.29595162874\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 15x^{5} + 16x^{4} + 49x^{3} - 53x^{2} - 44x + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 538.1 |
$q$-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 | ||||||||
\(3\) | −2.60058 | −1.50145 | −0.750723 | − | 0.660617i | \(-0.770295\pi\) | ||||
−0.750723 | + | 0.660617i | \(0.770295\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.80694 | −1.70252 | −0.851258 | − | 0.524748i | \(-0.824160\pi\) | ||||
−0.851258 | + | 0.524748i | \(0.824160\pi\) | |||||||
\(6\) | −2.60058 | −1.06168 | ||||||||
\(7\) | 0.487379 | 0.184212 | 0.0921060 | − | 0.995749i | \(-0.470640\pi\) | ||||
0.0921060 | + | 0.995749i | \(0.470640\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.76302 | 1.25434 | ||||||||
\(10\) | −3.80694 | −1.20386 | ||||||||
\(11\) | 2.94230 | 0.887137 | 0.443569 | − | 0.896240i | \(-0.353712\pi\) | ||||
0.443569 | + | 0.896240i | \(0.353712\pi\) | |||||||
\(12\) | −2.60058 | −0.750723 | ||||||||
\(13\) | 1.21482 | 0.336930 | 0.168465 | − | 0.985708i | \(-0.446119\pi\) | ||||
0.168465 | + | 0.985708i | \(0.446119\pi\) | |||||||
\(14\) | 0.487379 | 0.130258 | ||||||||
\(15\) | 9.90026 | 2.55624 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.19066 | 0.773849 | 0.386924 | − | 0.922111i | \(-0.373537\pi\) | ||||
0.386924 | + | 0.922111i | \(0.373537\pi\) | |||||||
\(18\) | 3.76302 | 0.886953 | ||||||||
\(19\) | −2.02416 | −0.464374 | −0.232187 | − | 0.972671i | \(-0.574588\pi\) | ||||
−0.232187 | + | 0.972671i | \(0.574588\pi\) | |||||||
\(20\) | −3.80694 | −0.851258 | ||||||||
\(21\) | −1.26747 | −0.276585 | ||||||||
\(22\) | 2.94230 | 0.627301 | ||||||||
\(23\) | 7.20116 | 1.50155 | 0.750773 | − | 0.660560i | \(-0.229681\pi\) | ||||
0.750773 | + | 0.660560i | \(0.229681\pi\) | |||||||
\(24\) | −2.60058 | −0.530841 | ||||||||
\(25\) | 9.49279 | 1.89856 | ||||||||
\(26\) | 1.21482 | 0.238245 | ||||||||
\(27\) | −1.98430 | −0.381879 | ||||||||
\(28\) | 0.487379 | 0.0921060 | ||||||||
\(29\) | 3.48092 | 0.646390 | 0.323195 | − | 0.946332i | \(-0.395243\pi\) | ||||
0.323195 | + | 0.946332i | \(0.395243\pi\) | |||||||
\(30\) | 9.90026 | 1.80753 | ||||||||
\(31\) | −5.14753 | −0.924524 | −0.462262 | − | 0.886743i | \(-0.652962\pi\) | ||||
−0.462262 | + | 0.886743i | \(0.652962\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −7.65169 | −1.33199 | ||||||||
\(34\) | 3.19066 | 0.547194 | ||||||||
\(35\) | −1.85542 | −0.313624 | ||||||||
\(36\) | 3.76302 | 0.627170 | ||||||||
\(37\) | 1.03375 | 0.169947 | 0.0849733 | − | 0.996383i | \(-0.472919\pi\) | ||||
0.0849733 | + | 0.996383i | \(0.472919\pi\) | |||||||
\(38\) | −2.02416 | −0.328362 | ||||||||
\(39\) | −3.15923 | −0.505882 | ||||||||
\(40\) | −3.80694 | −0.601930 | ||||||||
\(41\) | 8.43673 | 1.31760 | 0.658798 | − | 0.752320i | \(-0.271065\pi\) | ||||
0.658798 | + | 0.752320i | \(0.271065\pi\) | |||||||
\(42\) | −1.26747 | −0.195575 | ||||||||
\(43\) | −1.24039 | −0.189158 | −0.0945788 | − | 0.995517i | \(-0.530150\pi\) | ||||
−0.0945788 | + | 0.995517i | \(0.530150\pi\) | |||||||
\(44\) | 2.94230 | 0.443569 | ||||||||
\(45\) | −14.3256 | −2.13553 | ||||||||
\(46\) | 7.20116 | 1.06175 | ||||||||
\(47\) | 4.41272 | 0.643661 | 0.321830 | − | 0.946797i | \(-0.395702\pi\) | ||||
0.321830 | + | 0.946797i | \(0.395702\pi\) | |||||||
\(48\) | −2.60058 | −0.375362 | ||||||||
\(49\) | −6.76246 | −0.966066 | ||||||||
\(50\) | 9.49279 | 1.34248 | ||||||||
\(51\) | −8.29757 | −1.16189 | ||||||||
\(52\) | 1.21482 | 0.168465 | ||||||||
\(53\) | 1.19619 | 0.164309 | 0.0821544 | − | 0.996620i | \(-0.473820\pi\) | ||||
0.0821544 | + | 0.996620i | \(0.473820\pi\) | |||||||
\(54\) | −1.98430 | −0.270029 | ||||||||
\(55\) | −11.2012 | −1.51036 | ||||||||
\(56\) | 0.487379 | 0.0651288 | ||||||||
\(57\) | 5.26399 | 0.697232 | ||||||||
\(58\) | 3.48092 | 0.457067 | ||||||||
\(59\) | −12.1673 | −1.58405 | −0.792026 | − | 0.610487i | \(-0.790974\pi\) | ||||
−0.792026 | + | 0.610487i | \(0.790974\pi\) | |||||||
\(60\) | 9.90026 | 1.27812 | ||||||||
\(61\) | 10.2849 | 1.31685 | 0.658423 | − | 0.752648i | \(-0.271224\pi\) | ||||
0.658423 | + | 0.752648i | \(0.271224\pi\) | |||||||
\(62\) | −5.14753 | −0.653737 | ||||||||
\(63\) | 1.83402 | 0.231065 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.62474 | −0.573628 | ||||||||
\(66\) | −7.65169 | −0.941858 | ||||||||
\(67\) | −11.3824 | −1.39058 | −0.695290 | − | 0.718730i | \(-0.744724\pi\) | ||||
−0.695290 | + | 0.718730i | \(0.744724\pi\) | |||||||
\(68\) | 3.19066 | 0.386924 | ||||||||
\(69\) | −18.7272 | −2.25449 | ||||||||
\(70\) | −1.85542 | −0.221766 | ||||||||
\(71\) | 8.87514 | 1.05329 | 0.526643 | − | 0.850087i | \(-0.323451\pi\) | ||||
0.526643 | + | 0.850087i | \(0.323451\pi\) | |||||||
\(72\) | 3.76302 | 0.443476 | ||||||||
\(73\) | 9.05652 | 1.05999 | 0.529993 | − | 0.848002i | \(-0.322195\pi\) | ||||
0.529993 | + | 0.848002i | \(0.322195\pi\) | |||||||
\(74\) | 1.03375 | 0.120170 | ||||||||
\(75\) | −24.6868 | −2.85058 | ||||||||
\(76\) | −2.02416 | −0.232187 | ||||||||
\(77\) | 1.43402 | 0.163421 | ||||||||
\(78\) | −3.15923 | −0.357713 | ||||||||
\(79\) | −7.41490 | −0.834241 | −0.417121 | − | 0.908851i | \(-0.636961\pi\) | ||||
−0.417121 | + | 0.908851i | \(0.636961\pi\) | |||||||
\(80\) | −3.80694 | −0.425629 | ||||||||
\(81\) | −6.12873 | −0.680970 | ||||||||
\(82\) | 8.43673 | 0.931680 | ||||||||
\(83\) | 6.48221 | 0.711514 | 0.355757 | − | 0.934578i | \(-0.384223\pi\) | ||||
0.355757 | + | 0.934578i | \(0.384223\pi\) | |||||||
\(84\) | −1.26747 | −0.138292 | ||||||||
\(85\) | −12.1467 | −1.31749 | ||||||||
\(86\) | −1.24039 | −0.133755 | ||||||||
\(87\) | −9.05241 | −0.970520 | ||||||||
\(88\) | 2.94230 | 0.313650 | ||||||||
\(89\) | 16.3474 | 1.73282 | 0.866412 | − | 0.499330i | \(-0.166420\pi\) | ||||
0.866412 | + | 0.499330i | \(0.166420\pi\) | |||||||
\(90\) | −14.3256 | −1.51005 | ||||||||
\(91\) | 0.592077 | 0.0620666 | ||||||||
\(92\) | 7.20116 | 0.750773 | ||||||||
\(93\) | 13.3866 | 1.38812 | ||||||||
\(94\) | 4.41272 | 0.455137 | ||||||||
\(95\) | 7.70585 | 0.790603 | ||||||||
\(96\) | −2.60058 | −0.265421 | ||||||||
\(97\) | −2.51050 | −0.254902 | −0.127451 | − | 0.991845i | \(-0.540680\pi\) | ||||
−0.127451 | + | 0.991845i | \(0.540680\pi\) | |||||||
\(98\) | −6.76246 | −0.683112 | ||||||||
\(99\) | 11.0719 | 1.11277 | ||||||||
\(100\) | 9.49279 | 0.949279 | ||||||||
\(101\) | 10.7868 | 1.07332 | 0.536662 | − | 0.843797i | \(-0.319685\pi\) | ||||
0.536662 | + | 0.843797i | \(0.319685\pi\) | |||||||
\(102\) | −8.29757 | −0.821582 | ||||||||
\(103\) | −7.88460 | −0.776893 | −0.388446 | − | 0.921471i | \(-0.626988\pi\) | ||||
−0.388446 | + | 0.921471i | \(0.626988\pi\) | |||||||
\(104\) | 1.21482 | 0.119123 | ||||||||
\(105\) | 4.82518 | 0.470889 | ||||||||
\(106\) | 1.19619 | 0.116184 | ||||||||
\(107\) | 11.9088 | 1.15126 | 0.575632 | − | 0.817709i | \(-0.304756\pi\) | ||||
0.575632 | + | 0.817709i | \(0.304756\pi\) | |||||||
\(108\) | −1.98430 | −0.190940 | ||||||||
\(109\) | 4.27981 | 0.409931 | 0.204966 | − | 0.978769i | \(-0.434292\pi\) | ||||
0.204966 | + | 0.978769i | \(0.434292\pi\) | |||||||
\(110\) | −11.2012 | −1.06799 | ||||||||
\(111\) | −2.68834 | −0.255166 | ||||||||
\(112\) | 0.487379 | 0.0460530 | ||||||||
\(113\) | 7.96219 | 0.749020 | 0.374510 | − | 0.927223i | \(-0.377811\pi\) | ||||
0.374510 | + | 0.927223i | \(0.377811\pi\) | |||||||
\(114\) | 5.26399 | 0.493017 | ||||||||
\(115\) | −27.4144 | −2.55641 | ||||||||
\(116\) | 3.48092 | 0.323195 | ||||||||
\(117\) | 4.57139 | 0.422625 | ||||||||
\(118\) | −12.1673 | −1.12009 | ||||||||
\(119\) | 1.55506 | 0.142552 | ||||||||
\(120\) | 9.90026 | 0.903766 | ||||||||
\(121\) | −2.34286 | −0.212988 | ||||||||
\(122\) | 10.2849 | 0.931150 | ||||||||
\(123\) | −21.9404 | −1.97830 | ||||||||
\(124\) | −5.14753 | −0.462262 | ||||||||
\(125\) | −17.1038 | −1.52981 | ||||||||
\(126\) | 1.83402 | 0.163387 | ||||||||
\(127\) | 18.5720 | 1.64800 | 0.824001 | − | 0.566588i | \(-0.191737\pi\) | ||||
0.824001 | + | 0.566588i | \(0.191737\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.22573 | 0.284010 | ||||||||
\(130\) | −4.62474 | −0.405616 | ||||||||
\(131\) | −21.8120 | −1.90573 | −0.952863 | − | 0.303402i | \(-0.901877\pi\) | ||||
−0.952863 | + | 0.303402i | \(0.901877\pi\) | |||||||
\(132\) | −7.65169 | −0.665994 | ||||||||
\(133\) | −0.986533 | −0.0855432 | ||||||||
\(134\) | −11.3824 | −0.983288 | ||||||||
\(135\) | 7.55412 | 0.650155 | ||||||||
\(136\) | 3.19066 | 0.273597 | ||||||||
\(137\) | −5.11308 | −0.436840 | −0.218420 | − | 0.975855i | \(-0.570090\pi\) | ||||
−0.218420 | + | 0.975855i | \(0.570090\pi\) | |||||||
\(138\) | −18.7272 | −1.59417 | ||||||||
\(139\) | −11.9663 | −1.01497 | −0.507483 | − | 0.861662i | \(-0.669424\pi\) | ||||
−0.507483 | + | 0.861662i | \(0.669424\pi\) | |||||||
\(140\) | −1.85542 | −0.156812 | ||||||||
\(141\) | −11.4756 | −0.966422 | ||||||||
\(142\) | 8.87514 | 0.744785 | ||||||||
\(143\) | 3.57436 | 0.298903 | ||||||||
\(144\) | 3.76302 | 0.313585 | ||||||||
\(145\) | −13.2516 | −1.10049 | ||||||||
\(146\) | 9.05652 | 0.749523 | ||||||||
\(147\) | 17.5863 | 1.45050 | ||||||||
\(148\) | 1.03375 | 0.0849733 | ||||||||
\(149\) | −23.7615 | −1.94662 | −0.973309 | − | 0.229497i | \(-0.926292\pi\) | ||||
−0.973309 | + | 0.229497i | \(0.926292\pi\) | |||||||
\(150\) | −24.6868 | −2.01567 | ||||||||
\(151\) | 6.87628 | 0.559584 | 0.279792 | − | 0.960061i | \(-0.409735\pi\) | ||||
0.279792 | + | 0.960061i | \(0.409735\pi\) | |||||||
\(152\) | −2.02416 | −0.164181 | ||||||||
\(153\) | 12.0065 | 0.970670 | ||||||||
\(154\) | 1.43402 | 0.115556 | ||||||||
\(155\) | 19.5963 | 1.57402 | ||||||||
\(156\) | −3.15923 | −0.252941 | ||||||||
\(157\) | 18.7809 | 1.49888 | 0.749439 | − | 0.662074i | \(-0.230323\pi\) | ||||
0.749439 | + | 0.662074i | \(0.230323\pi\) | |||||||
\(158\) | −7.41490 | −0.589898 | ||||||||
\(159\) | −3.11078 | −0.246701 | ||||||||
\(160\) | −3.80694 | −0.300965 | ||||||||
\(161\) | 3.50970 | 0.276603 | ||||||||
\(162\) | −6.12873 | −0.481518 | ||||||||
\(163\) | 12.4265 | 0.973317 | 0.486659 | − | 0.873592i | \(-0.338216\pi\) | ||||
0.486659 | + | 0.873592i | \(0.338216\pi\) | |||||||
\(164\) | 8.43673 | 0.658798 | ||||||||
\(165\) | 29.1295 | 2.26773 | ||||||||
\(166\) | 6.48221 | 0.503117 | ||||||||
\(167\) | 17.6213 | 1.36358 | 0.681789 | − | 0.731549i | \(-0.261202\pi\) | ||||
0.681789 | + | 0.731549i | \(0.261202\pi\) | |||||||
\(168\) | −1.26747 | −0.0977874 | ||||||||
\(169\) | −11.5242 | −0.886478 | ||||||||
\(170\) | −12.1467 | −0.931606 | ||||||||
\(171\) | −7.61695 | −0.582483 | ||||||||
\(172\) | −1.24039 | −0.0945788 | ||||||||
\(173\) | 6.38566 | 0.485493 | 0.242746 | − | 0.970090i | \(-0.421952\pi\) | ||||
0.242746 | + | 0.970090i | \(0.421952\pi\) | |||||||
\(174\) | −9.05241 | −0.686261 | ||||||||
\(175\) | 4.62659 | 0.349737 | ||||||||
\(176\) | 2.94230 | 0.221784 | ||||||||
\(177\) | 31.6421 | 2.37837 | ||||||||
\(178\) | 16.3474 | 1.22529 | ||||||||
\(179\) | −17.6175 | −1.31680 | −0.658399 | − | 0.752669i | \(-0.728766\pi\) | ||||
−0.658399 | + | 0.752669i | \(0.728766\pi\) | |||||||
\(180\) | −14.3256 | −1.06777 | ||||||||
\(181\) | 23.6018 | 1.75431 | 0.877155 | − | 0.480208i | \(-0.159439\pi\) | ||||
0.877155 | + | 0.480208i | \(0.159439\pi\) | |||||||
\(182\) | 0.592077 | 0.0438877 | ||||||||
\(183\) | −26.7467 | −1.97717 | ||||||||
\(184\) | 7.20116 | 0.530877 | ||||||||
\(185\) | −3.93541 | −0.289337 | ||||||||
\(186\) | 13.3866 | 0.981551 | ||||||||
\(187\) | 9.38788 | 0.686510 | ||||||||
\(188\) | 4.41272 | 0.321830 | ||||||||
\(189\) | −0.967108 | −0.0703467 | ||||||||
\(190\) | 7.70585 | 0.559041 | ||||||||
\(191\) | −2.26422 | −0.163833 | −0.0819165 | − | 0.996639i | \(-0.526104\pi\) | ||||
−0.0819165 | + | 0.996639i | \(0.526104\pi\) | |||||||
\(192\) | −2.60058 | −0.187681 | ||||||||
\(193\) | 9.40014 | 0.676637 | 0.338319 | − | 0.941032i | \(-0.390142\pi\) | ||||
0.338319 | + | 0.941032i | \(0.390142\pi\) | |||||||
\(194\) | −2.51050 | −0.180243 | ||||||||
\(195\) | 12.0270 | 0.861272 | ||||||||
\(196\) | −6.76246 | −0.483033 | ||||||||
\(197\) | 2.81802 | 0.200776 | 0.100388 | − | 0.994948i | \(-0.467992\pi\) | ||||
0.100388 | + | 0.994948i | \(0.467992\pi\) | |||||||
\(198\) | 11.0719 | 0.786849 | ||||||||
\(199\) | −14.8803 | −1.05483 | −0.527417 | − | 0.849606i | \(-0.676840\pi\) | ||||
−0.527417 | + | 0.849606i | \(0.676840\pi\) | |||||||
\(200\) | 9.49279 | 0.671242 | ||||||||
\(201\) | 29.6008 | 2.08788 | ||||||||
\(202\) | 10.7868 | 0.758955 | ||||||||
\(203\) | 1.69653 | 0.119073 | ||||||||
\(204\) | −8.29757 | −0.580946 | ||||||||
\(205\) | −32.1181 | −2.24323 | ||||||||
\(206\) | −7.88460 | −0.549346 | ||||||||
\(207\) | 27.0981 | 1.88345 | ||||||||
\(208\) | 1.21482 | 0.0842325 | ||||||||
\(209\) | −5.95568 | −0.411963 | ||||||||
\(210\) | 4.82518 | 0.332969 | ||||||||
\(211\) | −14.3512 | −0.987980 | −0.493990 | − | 0.869468i | \(-0.664462\pi\) | ||||
−0.493990 | + | 0.869468i | \(0.664462\pi\) | |||||||
\(212\) | 1.19619 | 0.0821544 | ||||||||
\(213\) | −23.0805 | −1.58145 | ||||||||
\(214\) | 11.9088 | 0.814066 | ||||||||
\(215\) | 4.72209 | 0.322044 | ||||||||
\(216\) | −1.98430 | −0.135015 | ||||||||
\(217\) | −2.50880 | −0.170308 | ||||||||
\(218\) | 4.27981 | 0.289865 | ||||||||
\(219\) | −23.5522 | −1.59151 | ||||||||
\(220\) | −11.2012 | −0.755182 | ||||||||
\(221\) | 3.87607 | 0.260733 | ||||||||
\(222\) | −2.68834 | −0.180429 | ||||||||
\(223\) | −4.41280 | −0.295503 | −0.147751 | − | 0.989025i | \(-0.547204\pi\) | ||||
−0.147751 | + | 0.989025i | \(0.547204\pi\) | |||||||
\(224\) | 0.487379 | 0.0325644 | ||||||||
\(225\) | 35.7216 | 2.38144 | ||||||||
\(226\) | 7.96219 | 0.529637 | ||||||||
\(227\) | −1.94853 | −0.129329 | −0.0646643 | − | 0.997907i | \(-0.520598\pi\) | ||||
−0.0646643 | + | 0.997907i | \(0.520598\pi\) | |||||||
\(228\) | 5.26399 | 0.348616 | ||||||||
\(229\) | 24.5536 | 1.62254 | 0.811272 | − | 0.584668i | \(-0.198775\pi\) | ||||
0.811272 | + | 0.584668i | \(0.198775\pi\) | |||||||
\(230\) | −27.4144 | −1.80765 | ||||||||
\(231\) | −3.72928 | −0.245368 | ||||||||
\(232\) | 3.48092 | 0.228533 | ||||||||
\(233\) | −21.7296 | −1.42355 | −0.711776 | − | 0.702406i | \(-0.752109\pi\) | ||||
−0.711776 | + | 0.702406i | \(0.752109\pi\) | |||||||
\(234\) | 4.57139 | 0.298841 | ||||||||
\(235\) | −16.7989 | −1.09584 | ||||||||
\(236\) | −12.1673 | −0.792026 | ||||||||
\(237\) | 19.2830 | 1.25257 | ||||||||
\(238\) | 1.55506 | 0.100800 | ||||||||
\(239\) | 11.3663 | 0.735227 | 0.367613 | − | 0.929979i | \(-0.380175\pi\) | ||||
0.367613 | + | 0.929979i | \(0.380175\pi\) | |||||||
\(240\) | 9.90026 | 0.639059 | ||||||||
\(241\) | 2.21590 | 0.142739 | 0.0713694 | − | 0.997450i | \(-0.477263\pi\) | ||||
0.0713694 | + | 0.997450i | \(0.477263\pi\) | |||||||
\(242\) | −2.34286 | −0.150605 | ||||||||
\(243\) | 21.8912 | 1.40432 | ||||||||
\(244\) | 10.2849 | 0.658423 | ||||||||
\(245\) | 25.7443 | 1.64474 | ||||||||
\(246\) | −21.9404 | −1.39887 | ||||||||
\(247\) | −2.45898 | −0.156461 | ||||||||
\(248\) | −5.14753 | −0.326869 | ||||||||
\(249\) | −16.8575 | −1.06830 | ||||||||
\(250\) | −17.1038 | −1.08174 | ||||||||
\(251\) | −7.23929 | −0.456940 | −0.228470 | − | 0.973551i | \(-0.573372\pi\) | ||||
−0.228470 | + | 0.973551i | \(0.573372\pi\) | |||||||
\(252\) | 1.83402 | 0.115532 | ||||||||
\(253\) | 21.1880 | 1.33208 | ||||||||
\(254\) | 18.5720 | 1.16531 | ||||||||
\(255\) | 31.5884 | 1.97814 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.7926 | −1.17225 | −0.586125 | − | 0.810221i | \(-0.699347\pi\) | ||||
−0.586125 | + | 0.810221i | \(0.699347\pi\) | |||||||
\(258\) | 3.22573 | 0.200825 | ||||||||
\(259\) | 0.503826 | 0.0313062 | ||||||||
\(260\) | −4.62474 | −0.286814 | ||||||||
\(261\) | 13.0988 | 0.810794 | ||||||||
\(262\) | −21.8120 | −1.34755 | ||||||||
\(263\) | −23.0460 | −1.42108 | −0.710538 | − | 0.703658i | \(-0.751549\pi\) | ||||
−0.710538 | + | 0.703658i | \(0.751549\pi\) | |||||||
\(264\) | −7.65169 | −0.470929 | ||||||||
\(265\) | −4.55381 | −0.279738 | ||||||||
\(266\) | −0.986533 | −0.0604882 | ||||||||
\(267\) | −42.5128 | −2.60174 | ||||||||
\(268\) | −11.3824 | −0.695290 | ||||||||
\(269\) | −1.00000 | −0.0609711 | ||||||||
\(270\) | 7.55412 | 0.459729 | ||||||||
\(271\) | −5.87186 | −0.356690 | −0.178345 | − | 0.983968i | \(-0.557074\pi\) | ||||
−0.178345 | + | 0.983968i | \(0.557074\pi\) | |||||||
\(272\) | 3.19066 | 0.193462 | ||||||||
\(273\) | −1.53974 | −0.0931896 | ||||||||
\(274\) | −5.11308 | −0.308892 | ||||||||
\(275\) | 27.9306 | 1.68428 | ||||||||
\(276\) | −18.7272 | −1.12725 | ||||||||
\(277\) | −5.00802 | −0.300903 | −0.150452 | − | 0.988617i | \(-0.548073\pi\) | ||||
−0.150452 | + | 0.988617i | \(0.548073\pi\) | |||||||
\(278\) | −11.9663 | −0.717689 | ||||||||
\(279\) | −19.3703 | −1.15967 | ||||||||
\(280\) | −1.85542 | −0.110883 | ||||||||
\(281\) | 24.4842 | 1.46061 | 0.730303 | − | 0.683124i | \(-0.239379\pi\) | ||||
0.730303 | + | 0.683124i | \(0.239379\pi\) | |||||||
\(282\) | −11.4756 | −0.683364 | ||||||||
\(283\) | −4.16006 | −0.247290 | −0.123645 | − | 0.992327i | \(-0.539458\pi\) | ||||
−0.123645 | + | 0.992327i | \(0.539458\pi\) | |||||||
\(284\) | 8.87514 | 0.526643 | ||||||||
\(285\) | −20.0397 | −1.18705 | ||||||||
\(286\) | 3.57436 | 0.211356 | ||||||||
\(287\) | 4.11189 | 0.242717 | ||||||||
\(288\) | 3.76302 | 0.221738 | ||||||||
\(289\) | −6.81969 | −0.401158 | ||||||||
\(290\) | −13.2516 | −0.778163 | ||||||||
\(291\) | 6.52875 | 0.382722 | ||||||||
\(292\) | 9.05652 | 0.529993 | ||||||||
\(293\) | −20.6328 | −1.20538 | −0.602691 | − | 0.797975i | \(-0.705905\pi\) | ||||
−0.602691 | + | 0.797975i | \(0.705905\pi\) | |||||||
\(294\) | 17.5863 | 1.02566 | ||||||||
\(295\) | 46.3203 | 2.69687 | ||||||||
\(296\) | 1.03375 | 0.0600852 | ||||||||
\(297\) | −5.83841 | −0.338779 | ||||||||
\(298\) | −23.7615 | −1.37647 | ||||||||
\(299\) | 8.74810 | 0.505916 | ||||||||
\(300\) | −24.6868 | −1.42529 | ||||||||
\(301\) | −0.604540 | −0.0348451 | ||||||||
\(302\) | 6.87628 | 0.395685 | ||||||||
\(303\) | −28.0519 | −1.61154 | ||||||||
\(304\) | −2.02416 | −0.116093 | ||||||||
\(305\) | −39.1540 | −2.24195 | ||||||||
\(306\) | 12.0065 | 0.686367 | ||||||||
\(307\) | 30.3443 | 1.73184 | 0.865919 | − | 0.500184i | \(-0.166734\pi\) | ||||
0.865919 | + | 0.500184i | \(0.166734\pi\) | |||||||
\(308\) | 1.43402 | 0.0817107 | ||||||||
\(309\) | 20.5045 | 1.16646 | ||||||||
\(310\) | 19.5963 | 1.11300 | ||||||||
\(311\) | −12.2874 | −0.696755 | −0.348377 | − | 0.937354i | \(-0.613267\pi\) | ||||
−0.348377 | + | 0.937354i | \(0.613267\pi\) | |||||||
\(312\) | −3.15923 | −0.178856 | ||||||||
\(313\) | −10.8210 | −0.611641 | −0.305821 | − | 0.952089i | \(-0.598931\pi\) | ||||
−0.305821 | + | 0.952089i | \(0.598931\pi\) | |||||||
\(314\) | 18.7809 | 1.05987 | ||||||||
\(315\) | −6.98200 | −0.393391 | ||||||||
\(316\) | −7.41490 | −0.417121 | ||||||||
\(317\) | −1.55660 | −0.0874273 | −0.0437137 | − | 0.999044i | \(-0.513919\pi\) | ||||
−0.0437137 | + | 0.999044i | \(0.513919\pi\) | |||||||
\(318\) | −3.11078 | −0.174444 | ||||||||
\(319\) | 10.2419 | 0.573437 | ||||||||
\(320\) | −3.80694 | −0.212814 | ||||||||
\(321\) | −30.9697 | −1.72856 | ||||||||
\(322\) | 3.50970 | 0.195588 | ||||||||
\(323\) | −6.45840 | −0.359355 | ||||||||
\(324\) | −6.12873 | −0.340485 | ||||||||
\(325\) | 11.5320 | 0.639681 | ||||||||
\(326\) | 12.4265 | 0.688239 | ||||||||
\(327\) | −11.1300 | −0.615490 | ||||||||
\(328\) | 8.43673 | 0.465840 | ||||||||
\(329\) | 2.15067 | 0.118570 | ||||||||
\(330\) | 29.1295 | 1.60353 | ||||||||
\(331\) | 4.76335 | 0.261818 | 0.130909 | − | 0.991394i | \(-0.458210\pi\) | ||||
0.130909 | + | 0.991394i | \(0.458210\pi\) | |||||||
\(332\) | 6.48221 | 0.355757 | ||||||||
\(333\) | 3.89001 | 0.213171 | ||||||||
\(334\) | 17.6213 | 0.964195 | ||||||||
\(335\) | 43.3320 | 2.36748 | ||||||||
\(336\) | −1.26747 | −0.0691461 | ||||||||
\(337\) | 20.9918 | 1.14350 | 0.571749 | − | 0.820429i | \(-0.306265\pi\) | ||||
0.571749 | + | 0.820429i | \(0.306265\pi\) | |||||||
\(338\) | −11.5242 | −0.626835 | ||||||||
\(339\) | −20.7063 | −1.12461 | ||||||||
\(340\) | −12.1467 | −0.658745 | ||||||||
\(341\) | −15.1456 | −0.820180 | ||||||||
\(342\) | −7.61695 | −0.411878 | ||||||||
\(343\) | −6.70754 | −0.362173 | ||||||||
\(344\) | −1.24039 | −0.0668773 | ||||||||
\(345\) | 71.2933 | 3.83830 | ||||||||
\(346\) | 6.38566 | 0.343295 | ||||||||
\(347\) | 28.6045 | 1.53557 | 0.767784 | − | 0.640709i | \(-0.221359\pi\) | ||||
0.767784 | + | 0.640709i | \(0.221359\pi\) | |||||||
\(348\) | −9.05241 | −0.485260 | ||||||||
\(349\) | −13.6612 | −0.731268 | −0.365634 | − | 0.930759i | \(-0.619148\pi\) | ||||
−0.365634 | + | 0.930759i | \(0.619148\pi\) | |||||||
\(350\) | 4.62659 | 0.247302 | ||||||||
\(351\) | −2.41057 | −0.128666 | ||||||||
\(352\) | 2.94230 | 0.156825 | ||||||||
\(353\) | 23.8109 | 1.26733 | 0.633664 | − | 0.773609i | \(-0.281550\pi\) | ||||
0.633664 | + | 0.773609i | \(0.281550\pi\) | |||||||
\(354\) | 31.6421 | 1.68176 | ||||||||
\(355\) | −33.7871 | −1.79323 | ||||||||
\(356\) | 16.3474 | 0.866412 | ||||||||
\(357\) | −4.04407 | −0.214035 | ||||||||
\(358\) | −17.6175 | −0.931116 | ||||||||
\(359\) | −11.2449 | −0.593483 | −0.296742 | − | 0.954958i | \(-0.595900\pi\) | ||||
−0.296742 | + | 0.954958i | \(0.595900\pi\) | |||||||
\(360\) | −14.3256 | −0.755025 | ||||||||
\(361\) | −14.9028 | −0.784357 | ||||||||
\(362\) | 23.6018 | 1.24048 | ||||||||
\(363\) | 6.09281 | 0.319790 | ||||||||
\(364\) | 0.592077 | 0.0310333 | ||||||||
\(365\) | −34.4776 | −1.80464 | ||||||||
\(366\) | −26.7467 | −1.39807 | ||||||||
\(367\) | −21.1011 | −1.10147 | −0.550735 | − | 0.834680i | \(-0.685653\pi\) | ||||
−0.550735 | + | 0.834680i | \(0.685653\pi\) | |||||||
\(368\) | 7.20116 | 0.375387 | ||||||||
\(369\) | 31.7476 | 1.65271 | ||||||||
\(370\) | −3.93541 | −0.204592 | ||||||||
\(371\) | 0.582997 | 0.0302677 | ||||||||
\(372\) | 13.3866 | 0.694062 | ||||||||
\(373\) | −33.9513 | −1.75793 | −0.878967 | − | 0.476883i | \(-0.841766\pi\) | ||||
−0.878967 | + | 0.476883i | \(0.841766\pi\) | |||||||
\(374\) | 9.38788 | 0.485436 | ||||||||
\(375\) | 44.4798 | 2.29693 | ||||||||
\(376\) | 4.41272 | 0.227569 | ||||||||
\(377\) | 4.22868 | 0.217788 | ||||||||
\(378\) | −0.967108 | −0.0497427 | ||||||||
\(379\) | 4.79211 | 0.246154 | 0.123077 | − | 0.992397i | \(-0.460724\pi\) | ||||
0.123077 | + | 0.992397i | \(0.460724\pi\) | |||||||
\(380\) | 7.70585 | 0.395302 | ||||||||
\(381\) | −48.2981 | −2.47439 | ||||||||
\(382\) | −2.26422 | −0.115847 | ||||||||
\(383\) | 32.6191 | 1.66676 | 0.833378 | − | 0.552704i | \(-0.186404\pi\) | ||||
0.833378 | + | 0.552704i | \(0.186404\pi\) | |||||||
\(384\) | −2.60058 | −0.132710 | ||||||||
\(385\) | −5.45922 | −0.278227 | ||||||||
\(386\) | 9.40014 | 0.478455 | ||||||||
\(387\) | −4.66761 | −0.237268 | ||||||||
\(388\) | −2.51050 | −0.127451 | ||||||||
\(389\) | 25.3685 | 1.28623 | 0.643117 | − | 0.765768i | \(-0.277641\pi\) | ||||
0.643117 | + | 0.765768i | \(0.277641\pi\) | |||||||
\(390\) | 12.0270 | 0.609011 | ||||||||
\(391\) | 22.9765 | 1.16197 | ||||||||
\(392\) | −6.76246 | −0.341556 | ||||||||
\(393\) | 56.7239 | 2.86134 | ||||||||
\(394\) | 2.81802 | 0.141970 | ||||||||
\(395\) | 28.2281 | 1.42031 | ||||||||
\(396\) | 11.0719 | 0.556386 | ||||||||
\(397\) | −28.8866 | −1.44978 | −0.724889 | − | 0.688866i | \(-0.758109\pi\) | ||||
−0.724889 | + | 0.688866i | \(0.758109\pi\) | |||||||
\(398\) | −14.8803 | −0.745881 | ||||||||
\(399\) | 2.56556 | 0.128439 | ||||||||
\(400\) | 9.49279 | 0.474639 | ||||||||
\(401\) | −16.8718 | −0.842536 | −0.421268 | − | 0.906936i | \(-0.638415\pi\) | ||||
−0.421268 | + | 0.906936i | \(0.638415\pi\) | |||||||
\(402\) | 29.6008 | 1.47635 | ||||||||
\(403\) | −6.25331 | −0.311500 | ||||||||
\(404\) | 10.7868 | 0.536662 | ||||||||
\(405\) | 23.3317 | 1.15936 | ||||||||
\(406\) | 1.69653 | 0.0841973 | ||||||||
\(407\) | 3.04159 | 0.150766 | ||||||||
\(408\) | −8.29757 | −0.410791 | ||||||||
\(409\) | −8.98467 | −0.444263 | −0.222132 | − | 0.975017i | \(-0.571301\pi\) | ||||
−0.222132 | + | 0.975017i | \(0.571301\pi\) | |||||||
\(410\) | −32.1181 | −1.58620 | ||||||||
\(411\) | 13.2970 | 0.655891 | ||||||||
\(412\) | −7.88460 | −0.388446 | ||||||||
\(413\) | −5.93011 | −0.291802 | ||||||||
\(414\) | 27.0981 | 1.33180 | ||||||||
\(415\) | −24.6774 | −1.21136 | ||||||||
\(416\) | 1.21482 | 0.0595614 | ||||||||
\(417\) | 31.1193 | 1.52392 | ||||||||
\(418\) | −5.95568 | −0.291302 | ||||||||
\(419\) | −32.3970 | −1.58270 | −0.791348 | − | 0.611366i | \(-0.790620\pi\) | ||||
−0.791348 | + | 0.611366i | \(0.790620\pi\) | |||||||
\(420\) | 4.82518 | 0.235445 | ||||||||
\(421\) | 6.47692 | 0.315666 | 0.157833 | − | 0.987466i | \(-0.449549\pi\) | ||||
0.157833 | + | 0.987466i | \(0.449549\pi\) | |||||||
\(422\) | −14.3512 | −0.698608 | ||||||||
\(423\) | 16.6052 | 0.807370 | ||||||||
\(424\) | 1.19619 | 0.0580919 | ||||||||
\(425\) | 30.2883 | 1.46920 | ||||||||
\(426\) | −23.0805 | −1.11826 | ||||||||
\(427\) | 5.01264 | 0.242579 | ||||||||
\(428\) | 11.9088 | 0.575632 | ||||||||
\(429\) | −9.29541 | −0.448787 | ||||||||
\(430\) | 4.72209 | 0.227719 | ||||||||
\(431\) | 12.7851 | 0.615836 | 0.307918 | − | 0.951413i | \(-0.400368\pi\) | ||||
0.307918 | + | 0.951413i | \(0.400368\pi\) | |||||||
\(432\) | −1.98430 | −0.0954698 | ||||||||
\(433\) | −17.4222 | −0.837256 | −0.418628 | − | 0.908158i | \(-0.637489\pi\) | ||||
−0.418628 | + | 0.908158i | \(0.637489\pi\) | |||||||
\(434\) | −2.50880 | −0.120426 | ||||||||
\(435\) | 34.4620 | 1.65233 | ||||||||
\(436\) | 4.27981 | 0.204966 | ||||||||
\(437\) | −14.5763 | −0.697278 | ||||||||
\(438\) | −23.5522 | −1.12537 | ||||||||
\(439\) | −4.52030 | −0.215742 | −0.107871 | − | 0.994165i | \(-0.534403\pi\) | ||||
−0.107871 | + | 0.994165i | \(0.534403\pi\) | |||||||
\(440\) | −11.2012 | −0.533994 | ||||||||
\(441\) | −25.4473 | −1.21178 | ||||||||
\(442\) | 3.87607 | 0.184366 | ||||||||
\(443\) | −13.2163 | −0.627926 | −0.313963 | − | 0.949435i | \(-0.601657\pi\) | ||||
−0.313963 | + | 0.949435i | \(0.601657\pi\) | |||||||
\(444\) | −2.68834 | −0.127583 | ||||||||
\(445\) | −62.2337 | −2.95016 | ||||||||
\(446\) | −4.41280 | −0.208952 | ||||||||
\(447\) | 61.7937 | 2.92274 | ||||||||
\(448\) | 0.487379 | 0.0230265 | ||||||||
\(449\) | −10.4441 | −0.492887 | −0.246443 | − | 0.969157i | \(-0.579262\pi\) | ||||
−0.246443 | + | 0.969157i | \(0.579262\pi\) | |||||||
\(450\) | 35.7216 | 1.68393 | ||||||||
\(451\) | 24.8234 | 1.16889 | ||||||||
\(452\) | 7.96219 | 0.374510 | ||||||||
\(453\) | −17.8823 | −0.840185 | ||||||||
\(454\) | −1.94853 | −0.0914491 | ||||||||
\(455\) | −2.25400 | −0.105669 | ||||||||
\(456\) | 5.26399 | 0.246509 | ||||||||
\(457\) | 10.7134 | 0.501153 | 0.250577 | − | 0.968097i | \(-0.419380\pi\) | ||||
0.250577 | + | 0.968097i | \(0.419380\pi\) | |||||||
\(458\) | 24.5536 | 1.14731 | ||||||||
\(459\) | −6.33123 | −0.295517 | ||||||||
\(460\) | −27.4144 | −1.27820 | ||||||||
\(461\) | −20.5805 | −0.958530 | −0.479265 | − | 0.877670i | \(-0.659097\pi\) | ||||
−0.479265 | + | 0.877670i | \(0.659097\pi\) | |||||||
\(462\) | −3.72928 | −0.173502 | ||||||||
\(463\) | −20.2894 | −0.942930 | −0.471465 | − | 0.881885i | \(-0.656275\pi\) | ||||
−0.471465 | + | 0.881885i | \(0.656275\pi\) | |||||||
\(464\) | 3.48092 | 0.161598 | ||||||||
\(465\) | −50.9619 | −2.36330 | ||||||||
\(466\) | −21.7296 | −1.00660 | ||||||||
\(467\) | −12.8280 | −0.593609 | −0.296805 | − | 0.954938i | \(-0.595921\pi\) | ||||
−0.296805 | + | 0.954938i | \(0.595921\pi\) | |||||||
\(468\) | 4.57139 | 0.211312 | ||||||||
\(469\) | −5.54754 | −0.256162 | ||||||||
\(470\) | −16.7989 | −0.774878 | ||||||||
\(471\) | −48.8412 | −2.25048 | ||||||||
\(472\) | −12.1673 | −0.560047 | ||||||||
\(473\) | −3.64960 | −0.167809 | ||||||||
\(474\) | 19.2830 | 0.885699 | ||||||||
\(475\) | −19.2149 | −0.881640 | ||||||||
\(476\) | 1.55506 | 0.0712762 | ||||||||
\(477\) | 4.50128 | 0.206099 | ||||||||
\(478\) | 11.3663 | 0.519884 | ||||||||
\(479\) | 36.1270 | 1.65069 | 0.825343 | − | 0.564631i | \(-0.190982\pi\) | ||||
0.825343 | + | 0.564631i | \(0.190982\pi\) | |||||||
\(480\) | 9.90026 | 0.451883 | ||||||||
\(481\) | 1.25581 | 0.0572601 | ||||||||
\(482\) | 2.21590 | 0.100932 | ||||||||
\(483\) | −9.12726 | −0.415304 | ||||||||
\(484\) | −2.34286 | −0.106494 | ||||||||
\(485\) | 9.55731 | 0.433975 | ||||||||
\(486\) | 21.8912 | 0.993003 | ||||||||
\(487\) | 11.1794 | 0.506586 | 0.253293 | − | 0.967390i | \(-0.418486\pi\) | ||||
0.253293 | + | 0.967390i | \(0.418486\pi\) | |||||||
\(488\) | 10.2849 | 0.465575 | ||||||||
\(489\) | −32.3161 | −1.46138 | ||||||||
\(490\) | 25.7443 | 1.16301 | ||||||||
\(491\) | 9.49758 | 0.428620 | 0.214310 | − | 0.976766i | \(-0.431250\pi\) | ||||
0.214310 | + | 0.976766i | \(0.431250\pi\) | |||||||
\(492\) | −21.9404 | −0.989149 | ||||||||
\(493\) | 11.1064 | 0.500208 | ||||||||
\(494\) | −2.45898 | −0.110635 | ||||||||
\(495\) | −42.1502 | −1.89451 | ||||||||
\(496\) | −5.14753 | −0.231131 | ||||||||
\(497\) | 4.32556 | 0.194028 | ||||||||
\(498\) | −16.8575 | −0.755403 | ||||||||
\(499\) | 20.4507 | 0.915498 | 0.457749 | − | 0.889081i | \(-0.348656\pi\) | ||||
0.457749 | + | 0.889081i | \(0.348656\pi\) | |||||||
\(500\) | −17.1038 | −0.764904 | ||||||||
\(501\) | −45.8257 | −2.04734 | ||||||||
\(502\) | −7.23929 | −0.323106 | ||||||||
\(503\) | −5.31796 | −0.237116 | −0.118558 | − | 0.992947i | \(-0.537827\pi\) | ||||
−0.118558 | + | 0.992947i | \(0.537827\pi\) | |||||||
\(504\) | 1.83402 | 0.0816937 | ||||||||
\(505\) | −41.0646 | −1.82735 | ||||||||
\(506\) | 21.1880 | 0.941921 | ||||||||
\(507\) | 29.9697 | 1.33100 | ||||||||
\(508\) | 18.5720 | 0.824001 | ||||||||
\(509\) | 17.2984 | 0.766738 | 0.383369 | − | 0.923595i | \(-0.374764\pi\) | ||||
0.383369 | + | 0.923595i | \(0.374764\pi\) | |||||||
\(510\) | 31.5884 | 1.39876 | ||||||||
\(511\) | 4.41396 | 0.195262 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.01654 | 0.177335 | ||||||||
\(514\) | −18.7926 | −0.828906 | ||||||||
\(515\) | 30.0162 | 1.32267 | ||||||||
\(516\) | 3.22573 | 0.142005 | ||||||||
\(517\) | 12.9835 | 0.571016 | ||||||||
\(518\) | 0.503826 | 0.0221368 | ||||||||
\(519\) | −16.6064 | −0.728941 | ||||||||
\(520\) | −4.62474 | −0.202808 | ||||||||
\(521\) | −38.1750 | −1.67248 | −0.836239 | − | 0.548364i | \(-0.815251\pi\) | ||||
−0.836239 | + | 0.548364i | \(0.815251\pi\) | |||||||
\(522\) | 13.0988 | 0.573318 | ||||||||
\(523\) | −29.2320 | −1.27823 | −0.639113 | − | 0.769113i | \(-0.720698\pi\) | ||||
−0.639113 | + | 0.769113i | \(0.720698\pi\) | |||||||
\(524\) | −21.8120 | −0.952863 | ||||||||
\(525\) | −12.0318 | −0.525112 | ||||||||
\(526\) | −23.0460 | −1.00485 | ||||||||
\(527\) | −16.4240 | −0.715442 | ||||||||
\(528\) | −7.65169 | −0.332997 | ||||||||
\(529\) | 28.8567 | 1.25464 | ||||||||
\(530\) | −4.55381 | −0.197805 | ||||||||
\(531\) | −45.7860 | −1.98694 | ||||||||
\(532\) | −0.986533 | −0.0427716 | ||||||||
\(533\) | 10.2491 | 0.443937 | ||||||||
\(534\) | −42.5128 | −1.83971 | ||||||||
\(535\) | −45.3359 | −1.96004 | ||||||||
\(536\) | −11.3824 | −0.491644 | ||||||||
\(537\) | 45.8159 | 1.97710 | ||||||||
\(538\) | −1.00000 | −0.0431131 | ||||||||
\(539\) | −19.8972 | −0.857033 | ||||||||
\(540\) | 7.55412 | 0.325077 | ||||||||
\(541\) | −33.8660 | −1.45601 | −0.728007 | − | 0.685569i | \(-0.759553\pi\) | ||||
−0.728007 | + | 0.685569i | \(0.759553\pi\) | |||||||
\(542\) | −5.87186 | −0.252218 | ||||||||
\(543\) | −61.3785 | −2.63400 | ||||||||
\(544\) | 3.19066 | 0.136798 | ||||||||
\(545\) | −16.2930 | −0.697915 | ||||||||
\(546\) | −1.53974 | −0.0658950 | ||||||||
\(547\) | −33.7387 | −1.44256 | −0.721280 | − | 0.692643i | \(-0.756446\pi\) | ||||
−0.721280 | + | 0.692643i | \(0.756446\pi\) | |||||||
\(548\) | −5.11308 | −0.218420 | ||||||||
\(549\) | 38.7023 | 1.65177 | ||||||||
\(550\) | 27.9306 | 1.19097 | ||||||||
\(551\) | −7.04593 | −0.300167 | ||||||||
\(552\) | −18.7272 | −0.797083 | ||||||||
\(553\) | −3.61387 | −0.153677 | ||||||||
\(554\) | −5.00802 | −0.212771 | ||||||||
\(555\) | 10.2343 | 0.434424 | ||||||||
\(556\) | −11.9663 | −0.507483 | ||||||||
\(557\) | −6.11043 | −0.258907 | −0.129454 | − | 0.991585i | \(-0.541322\pi\) | ||||
−0.129454 | + | 0.991585i | \(0.541322\pi\) | |||||||
\(558\) | −19.3703 | −0.820009 | ||||||||
\(559\) | −1.50685 | −0.0637329 | ||||||||
\(560\) | −1.85542 | −0.0784060 | ||||||||
\(561\) | −24.4140 | −1.03076 | ||||||||
\(562\) | 24.4842 | 1.03280 | ||||||||
\(563\) | 36.4999 | 1.53829 | 0.769143 | − | 0.639077i | \(-0.220683\pi\) | ||||
0.769143 | + | 0.639077i | \(0.220683\pi\) | |||||||
\(564\) | −11.4756 | −0.483211 | ||||||||
\(565\) | −30.3116 | −1.27522 | ||||||||
\(566\) | −4.16006 | −0.174861 | ||||||||
\(567\) | −2.98702 | −0.125443 | ||||||||
\(568\) | 8.87514 | 0.372393 | ||||||||
\(569\) | −12.5604 | −0.526558 | −0.263279 | − | 0.964720i | \(-0.584804\pi\) | ||||
−0.263279 | + | 0.964720i | \(0.584804\pi\) | |||||||
\(570\) | −20.0397 | −0.839370 | ||||||||
\(571\) | 29.0079 | 1.21394 | 0.606972 | − | 0.794724i | \(-0.292384\pi\) | ||||
0.606972 | + | 0.794724i | \(0.292384\pi\) | |||||||
\(572\) | 3.57436 | 0.149452 | ||||||||
\(573\) | 5.88828 | 0.245986 | ||||||||
\(574\) | 4.11189 | 0.171627 | ||||||||
\(575\) | 68.3591 | 2.85077 | ||||||||
\(576\) | 3.76302 | 0.156793 | ||||||||
\(577\) | −41.1128 | −1.71155 | −0.855775 | − | 0.517348i | \(-0.826919\pi\) | ||||
−0.855775 | + | 0.517348i | \(0.826919\pi\) | |||||||
\(578\) | −6.81969 | −0.283662 | ||||||||
\(579\) | −24.4458 | −1.01593 | ||||||||
\(580\) | −13.2516 | −0.550245 | ||||||||
\(581\) | 3.15929 | 0.131070 | ||||||||
\(582\) | 6.52875 | 0.270625 | ||||||||
\(583\) | 3.51954 | 0.145764 | ||||||||
\(584\) | 9.05652 | 0.374762 | ||||||||
\(585\) | −17.4030 | −0.719525 | ||||||||
\(586\) | −20.6328 | −0.852334 | ||||||||
\(587\) | −29.9889 | −1.23777 | −0.618887 | − | 0.785480i | \(-0.712416\pi\) | ||||
−0.618887 | + | 0.785480i | \(0.712416\pi\) | |||||||
\(588\) | 17.5863 | 0.725248 | ||||||||
\(589\) | 10.4194 | 0.429325 | ||||||||
\(590\) | 46.3203 | 1.90698 | ||||||||
\(591\) | −7.32849 | −0.301454 | ||||||||
\(592\) | 1.03375 | 0.0424867 | ||||||||
\(593\) | −4.55260 | −0.186953 | −0.0934765 | − | 0.995621i | \(-0.529798\pi\) | ||||
−0.0934765 | + | 0.995621i | \(0.529798\pi\) | |||||||
\(594\) | −5.83841 | −0.239553 | ||||||||
\(595\) | −5.92003 | −0.242697 | ||||||||
\(596\) | −23.7615 | −0.973309 | ||||||||
\(597\) | 38.6974 | 1.58378 | ||||||||
\(598\) | 8.74810 | 0.357736 | ||||||||
\(599\) | −39.5205 | −1.61477 | −0.807383 | − | 0.590028i | \(-0.799117\pi\) | ||||
−0.807383 | + | 0.590028i | \(0.799117\pi\) | |||||||
\(600\) | −24.6868 | −1.00783 | ||||||||
\(601\) | 32.0934 | 1.30912 | 0.654558 | − | 0.756011i | \(-0.272855\pi\) | ||||
0.654558 | + | 0.756011i | \(0.272855\pi\) | |||||||
\(602\) | −0.604540 | −0.0246392 | ||||||||
\(603\) | −42.8322 | −1.74426 | ||||||||
\(604\) | 6.87628 | 0.279792 | ||||||||
\(605\) | 8.91915 | 0.362615 | ||||||||
\(606\) | −28.0519 | −1.13953 | ||||||||
\(607\) | −4.60057 | −0.186732 | −0.0933658 | − | 0.995632i | \(-0.529763\pi\) | ||||
−0.0933658 | + | 0.995632i | \(0.529763\pi\) | |||||||
\(608\) | −2.02416 | −0.0820904 | ||||||||
\(609\) | −4.41196 | −0.178782 | ||||||||
\(610\) | −39.1540 | −1.58530 | ||||||||
\(611\) | 5.36065 | 0.216869 | ||||||||
\(612\) | 12.0065 | 0.485335 | ||||||||
\(613\) | 12.2463 | 0.494622 | 0.247311 | − | 0.968936i | \(-0.420453\pi\) | ||||
0.247311 | + | 0.968936i | \(0.420453\pi\) | |||||||
\(614\) | 30.3443 | 1.22459 | ||||||||
\(615\) | 83.5257 | 3.36808 | ||||||||
\(616\) | 1.43402 | 0.0577782 | ||||||||
\(617\) | 46.4794 | 1.87119 | 0.935595 | − | 0.353076i | \(-0.114864\pi\) | ||||
0.935595 | + | 0.353076i | \(0.114864\pi\) | |||||||
\(618\) | 20.5045 | 0.824814 | ||||||||
\(619\) | −36.5698 | −1.46986 | −0.734932 | − | 0.678141i | \(-0.762786\pi\) | ||||
−0.734932 | + | 0.678141i | \(0.762786\pi\) | |||||||
\(620\) | 19.5963 | 0.787008 | ||||||||
\(621\) | −14.2893 | −0.573409 | ||||||||
\(622\) | −12.2874 | −0.492680 | ||||||||
\(623\) | 7.96740 | 0.319207 | ||||||||
\(624\) | −3.15923 | −0.126471 | ||||||||
\(625\) | 17.6491 | 0.705964 | ||||||||
\(626\) | −10.8210 | −0.432496 | ||||||||
\(627\) | 15.4882 | 0.618540 | ||||||||
\(628\) | 18.7809 | 0.749439 | ||||||||
\(629\) | 3.29833 | 0.131513 | ||||||||
\(630\) | −6.98200 | −0.278170 | ||||||||
\(631\) | −21.2855 | −0.847363 | −0.423681 | − | 0.905811i | \(-0.639262\pi\) | ||||
−0.423681 | + | 0.905811i | \(0.639262\pi\) | |||||||
\(632\) | −7.41490 | −0.294949 | ||||||||
\(633\) | 37.3216 | 1.48340 | ||||||||
\(634\) | −1.55660 | −0.0618205 | ||||||||
\(635\) | −70.7026 | −2.80575 | ||||||||
\(636\) | −3.11078 | −0.123350 | ||||||||
\(637\) | −8.21516 | −0.325496 | ||||||||
\(638\) | 10.2419 | 0.405481 | ||||||||
\(639\) | 33.3974 | 1.32118 | ||||||||
\(640\) | −3.80694 | −0.150483 | ||||||||
\(641\) | 0.625521 | 0.0247066 | 0.0123533 | − | 0.999924i | \(-0.496068\pi\) | ||||
0.0123533 | + | 0.999924i | \(0.496068\pi\) | |||||||
\(642\) | −30.9697 | −1.22228 | ||||||||
\(643\) | 48.5331 | 1.91396 | 0.956980 | − | 0.290155i | \(-0.0937069\pi\) | ||||
0.956980 | + | 0.290155i | \(0.0937069\pi\) | |||||||
\(644\) | 3.50970 | 0.138301 | ||||||||
\(645\) | −12.2802 | −0.483531 | ||||||||
\(646\) | −6.45840 | −0.254102 | ||||||||
\(647\) | 18.6403 | 0.732825 | 0.366412 | − | 0.930453i | \(-0.380586\pi\) | ||||
0.366412 | + | 0.930453i | \(0.380586\pi\) | |||||||
\(648\) | −6.12873 | −0.240759 | ||||||||
\(649\) | −35.8000 | −1.40527 | ||||||||
\(650\) | 11.5320 | 0.452323 | ||||||||
\(651\) | 6.52434 | 0.255709 | ||||||||
\(652\) | 12.4265 | 0.486659 | ||||||||
\(653\) | 2.06115 | 0.0806589 | 0.0403294 | − | 0.999186i | \(-0.487159\pi\) | ||||
0.0403294 | + | 0.999186i | \(0.487159\pi\) | |||||||
\(654\) | −11.1300 | −0.435217 | ||||||||
\(655\) | 83.0370 | 3.24453 | ||||||||
\(656\) | 8.43673 | 0.329399 | ||||||||
\(657\) | 34.0799 | 1.32958 | ||||||||
\(658\) | 2.15067 | 0.0838417 | ||||||||
\(659\) | 16.6159 | 0.647263 | 0.323632 | − | 0.946183i | \(-0.395096\pi\) | ||||
0.323632 | + | 0.946183i | \(0.395096\pi\) | |||||||
\(660\) | 29.1295 | 1.13387 | ||||||||
\(661\) | −21.7435 | −0.845725 | −0.422863 | − | 0.906194i | \(-0.638975\pi\) | ||||
−0.422863 | + | 0.906194i | \(0.638975\pi\) | |||||||
\(662\) | 4.76335 | 0.185133 | ||||||||
\(663\) | −10.0800 | −0.391476 | ||||||||
\(664\) | 6.48221 | 0.251558 | ||||||||
\(665\) | 3.75567 | 0.145639 | ||||||||
\(666\) | 3.89001 | 0.150735 | ||||||||
\(667\) | 25.0667 | 0.970585 | ||||||||
\(668\) | 17.6213 | 0.681789 | ||||||||
\(669\) | 11.4758 | 0.443682 | ||||||||
\(670\) | 43.3320 | 1.67406 | ||||||||
\(671\) | 30.2612 | 1.16822 | ||||||||
\(672\) | −1.26747 | −0.0488937 | ||||||||
\(673\) | 22.4637 | 0.865913 | 0.432956 | − | 0.901415i | \(-0.357470\pi\) | ||||
0.432956 | + | 0.901415i | \(0.357470\pi\) | |||||||
\(674\) | 20.9918 | 0.808575 | ||||||||
\(675\) | −18.8366 | −0.725020 | ||||||||
\(676\) | −11.5242 | −0.443239 | ||||||||
\(677\) | −9.44261 | −0.362909 | −0.181454 | − | 0.983399i | \(-0.558080\pi\) | ||||
−0.181454 | + | 0.983399i | \(0.558080\pi\) | |||||||
\(678\) | −20.7063 | −0.795221 | ||||||||
\(679\) | −1.22356 | −0.0469561 | ||||||||
\(680\) | −12.1467 | −0.465803 | ||||||||
\(681\) | 5.06731 | 0.194180 | ||||||||
\(682\) | −15.1456 | −0.579954 | ||||||||
\(683\) | 9.14788 | 0.350034 | 0.175017 | − | 0.984565i | \(-0.444002\pi\) | ||||
0.175017 | + | 0.984565i | \(0.444002\pi\) | |||||||
\(684\) | −7.61695 | −0.291241 | ||||||||
\(685\) | 19.4652 | 0.743726 | ||||||||
\(686\) | −6.70754 | −0.256095 | ||||||||
\(687\) | −63.8535 | −2.43616 | ||||||||
\(688\) | −1.24039 | −0.0472894 | ||||||||
\(689\) | 1.45315 | 0.0553606 | ||||||||
\(690\) | 71.2933 | 2.71409 | ||||||||
\(691\) | −6.73151 | −0.256079 | −0.128039 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128039 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(692\) | 6.38566 | 0.242746 | ||||||||
\(693\) | 5.39624 | 0.204986 | ||||||||
\(694\) | 28.6045 | 1.08581 | ||||||||
\(695\) | 45.5549 | 1.72799 | ||||||||
\(696\) | −9.05241 | −0.343131 | ||||||||
\(697\) | 26.9187 | 1.01962 | ||||||||
\(698\) | −13.6612 | −0.517084 | ||||||||
\(699\) | 56.5095 | 2.13739 | ||||||||
\(700\) | 4.62659 | 0.174869 | ||||||||
\(701\) | 26.4298 | 0.998240 | 0.499120 | − | 0.866533i | \(-0.333657\pi\) | ||||
0.499120 | + | 0.866533i | \(0.333657\pi\) | |||||||
\(702\) | −2.41057 | −0.0909809 | ||||||||
\(703\) | −2.09246 | −0.0789187 | ||||||||
\(704\) | 2.94230 | 0.110892 | ||||||||
\(705\) | 43.6870 | 1.64535 | ||||||||
\(706\) | 23.8109 | 0.896136 | ||||||||
\(707\) | 5.25725 | 0.197719 | ||||||||
\(708\) | 31.6421 | 1.18918 | ||||||||
\(709\) | 14.0274 | 0.526810 | 0.263405 | − | 0.964685i | \(-0.415154\pi\) | ||||
0.263405 | + | 0.964685i | \(0.415154\pi\) | |||||||
\(710\) | −33.7871 | −1.26801 | ||||||||
\(711\) | −27.9024 | −1.04642 | ||||||||
\(712\) | 16.3474 | 0.612646 | ||||||||
\(713\) | −37.0682 | −1.38822 | ||||||||
\(714\) | −4.04407 | −0.151345 | ||||||||
\(715\) | −13.6074 | −0.508887 | ||||||||
\(716\) | −17.6175 | −0.658399 | ||||||||
\(717\) | −29.5591 | −1.10390 | ||||||||
\(718\) | −11.2449 | −0.419656 | ||||||||
\(719\) | −27.6353 | −1.03062 | −0.515312 | − | 0.857003i | \(-0.672324\pi\) | ||||
−0.515312 | + | 0.857003i | \(0.672324\pi\) | |||||||
\(720\) | −14.3256 | −0.533884 | ||||||||
\(721\) | −3.84279 | −0.143113 | ||||||||
\(722\) | −14.9028 | −0.554624 | ||||||||
\(723\) | −5.76263 | −0.214315 | ||||||||
\(724\) | 23.6018 | 0.877155 | ||||||||
\(725\) | 33.0436 | 1.22721 | ||||||||
\(726\) | 6.09281 | 0.226125 | ||||||||
\(727\) | −20.4908 | −0.759962 | −0.379981 | − | 0.924994i | \(-0.624070\pi\) | ||||
−0.379981 | + | 0.924994i | \(0.624070\pi\) | |||||||
\(728\) | 0.592077 | 0.0219438 | ||||||||
\(729\) | −38.5436 | −1.42754 | ||||||||
\(730\) | −34.4776 | −1.27607 | ||||||||
\(731\) | −3.95766 | −0.146379 | ||||||||
\(732\) | −26.7467 | −0.988586 | ||||||||
\(733\) | 23.4829 | 0.867360 | 0.433680 | − | 0.901067i | \(-0.357215\pi\) | ||||
0.433680 | + | 0.901067i | \(0.357215\pi\) | |||||||
\(734\) | −21.1011 | −0.778857 | ||||||||
\(735\) | −66.9501 | −2.46949 | ||||||||
\(736\) | 7.20116 | 0.265438 | ||||||||
\(737\) | −33.4904 | −1.23363 | ||||||||
\(738\) | 31.7476 | 1.16864 | ||||||||
\(739\) | −1.54880 | −0.0569737 | −0.0284868 | − | 0.999594i | \(-0.509069\pi\) | ||||
−0.0284868 | + | 0.999594i | \(0.509069\pi\) | |||||||
\(740\) | −3.93541 | −0.144668 | ||||||||
\(741\) | 6.39479 | 0.234918 | ||||||||
\(742\) | 0.582997 | 0.0214025 | ||||||||
\(743\) | 6.56645 | 0.240900 | 0.120450 | − | 0.992719i | \(-0.461566\pi\) | ||||
0.120450 | + | 0.992719i | \(0.461566\pi\) | |||||||
\(744\) | 13.3866 | 0.490776 | ||||||||
\(745\) | 90.4586 | 3.31415 | ||||||||
\(746\) | −33.9513 | −1.24305 | ||||||||
\(747\) | 24.3927 | 0.892482 | ||||||||
\(748\) | 9.38788 | 0.343255 | ||||||||
\(749\) | 5.80408 | 0.212077 | ||||||||
\(750\) | 44.4798 | 1.62417 | ||||||||
\(751\) | −29.3323 | −1.07035 | −0.535175 | − | 0.844741i | \(-0.679754\pi\) | ||||
−0.535175 | + | 0.844741i | \(0.679754\pi\) | |||||||
\(752\) | 4.41272 | 0.160915 | ||||||||
\(753\) | 18.8264 | 0.686071 | ||||||||
\(754\) | 4.22868 | 0.154000 | ||||||||
\(755\) | −26.1776 | −0.952700 | ||||||||
\(756\) | −0.967108 | −0.0351734 | ||||||||
\(757\) | 2.63020 | 0.0955962 | 0.0477981 | − | 0.998857i | \(-0.484780\pi\) | ||||
0.0477981 | + | 0.998857i | \(0.484780\pi\) | |||||||
\(758\) | 4.79211 | 0.174057 | ||||||||
\(759\) | −55.1011 | −2.00004 | ||||||||
\(760\) | 7.70585 | 0.279520 | ||||||||
\(761\) | −24.8658 | −0.901385 | −0.450693 | − | 0.892679i | \(-0.648823\pi\) | ||||
−0.450693 | + | 0.892679i | \(0.648823\pi\) | |||||||
\(762\) | −48.2981 | −1.74966 | ||||||||
\(763\) | 2.08589 | 0.0755143 | ||||||||
\(764\) | −2.26422 | −0.0819165 | ||||||||
\(765\) | −45.7081 | −1.65258 | ||||||||
\(766\) | 32.6191 | 1.17857 | ||||||||
\(767\) | −14.7811 | −0.533714 | ||||||||
\(768\) | −2.60058 | −0.0938404 | ||||||||
\(769\) | 37.4087 | 1.34899 | 0.674496 | − | 0.738279i | \(-0.264361\pi\) | ||||
0.674496 | + | 0.738279i | \(0.264361\pi\) | |||||||
\(770\) | −5.45922 | −0.196736 | ||||||||
\(771\) | 48.8717 | 1.76007 | ||||||||
\(772\) | 9.40014 | 0.338319 | ||||||||
\(773\) | −7.67556 | −0.276071 | −0.138035 | − | 0.990427i | \(-0.544079\pi\) | ||||
−0.138035 | + | 0.990427i | \(0.544079\pi\) | |||||||
\(774\) | −4.66761 | −0.167774 | ||||||||
\(775\) | −48.8644 | −1.75526 | ||||||||
\(776\) | −2.51050 | −0.0901215 | ||||||||
\(777\) | −1.31024 | −0.0470046 | ||||||||
\(778\) | 25.3685 | 0.909505 | ||||||||
\(779\) | −17.0773 | −0.611856 | ||||||||
\(780\) | 12.0270 | 0.430636 | ||||||||
\(781\) | 26.1133 | 0.934409 | ||||||||
\(782\) | 22.9765 | 0.821637 | ||||||||
\(783\) | −6.90719 | −0.246843 | ||||||||
\(784\) | −6.76246 | −0.241516 | ||||||||
\(785\) | −71.4977 | −2.55186 | ||||||||
\(786\) | 56.7239 | 2.02328 | ||||||||
\(787\) | −10.9680 | −0.390966 | −0.195483 | − | 0.980707i | \(-0.562627\pi\) | ||||
−0.195483 | + | 0.980707i | \(0.562627\pi\) | |||||||
\(788\) | 2.81802 | 0.100388 | ||||||||
\(789\) | 59.9330 | 2.13367 | ||||||||
\(790\) | 28.2281 | 1.00431 | ||||||||
\(791\) | 3.88061 | 0.137978 | ||||||||
\(792\) | 11.0719 | 0.393424 | ||||||||
\(793\) | 12.4943 | 0.443685 | ||||||||
\(794\) | −28.8866 | −1.02515 | ||||||||
\(795\) | 11.8426 | 0.420012 | ||||||||
\(796\) | −14.8803 | −0.527417 | ||||||||
\(797\) | 45.7135 | 1.61926 | 0.809628 | − | 0.586943i | \(-0.199669\pi\) | ||||
0.809628 | + | 0.586943i | \(0.199669\pi\) | |||||||
\(798\) | 2.56556 | 0.0908198 | ||||||||
\(799\) | 14.0795 | 0.498096 | ||||||||
\(800\) | 9.49279 | 0.335621 | ||||||||
\(801\) | 61.5157 | 2.17355 | ||||||||
\(802\) | −16.8718 | −0.595763 | ||||||||
\(803\) | 26.6470 | 0.940353 | ||||||||
\(804\) | 29.6008 | 1.04394 | ||||||||
\(805\) | −13.3612 | −0.470921 | ||||||||
\(806\) | −6.25331 | −0.220264 | ||||||||
\(807\) | 2.60058 | 0.0915448 | ||||||||
\(808\) | 10.7868 | 0.379478 | ||||||||
\(809\) | −12.8403 | −0.451441 | −0.225721 | − | 0.974192i | \(-0.572474\pi\) | ||||
−0.225721 | + | 0.974192i | \(0.572474\pi\) | |||||||
\(810\) | 23.3317 | 0.819792 | ||||||||
\(811\) | 44.9655 | 1.57895 | 0.789475 | − | 0.613782i | \(-0.210353\pi\) | ||||
0.789475 | + | 0.613782i | \(0.210353\pi\) | |||||||
\(812\) | 1.69653 | 0.0595365 | ||||||||
\(813\) | 15.2702 | 0.535551 | ||||||||
\(814\) | 3.04159 | 0.106608 | ||||||||
\(815\) | −47.3069 | −1.65709 | ||||||||
\(816\) | −8.29757 | −0.290473 | ||||||||
\(817\) | 2.51074 | 0.0878398 | ||||||||
\(818\) | −8.98467 | −0.314141 | ||||||||
\(819\) | 2.22800 | 0.0778526 | ||||||||
\(820\) | −32.1181 | −1.12161 | ||||||||
\(821\) | 48.4659 | 1.69147 | 0.845736 | − | 0.533602i | \(-0.179162\pi\) | ||||
0.845736 | + | 0.533602i | \(0.179162\pi\) | |||||||
\(822\) | 13.2970 | 0.463785 | ||||||||
\(823\) | −47.5382 | −1.65708 | −0.828539 | − | 0.559932i | \(-0.810827\pi\) | ||||
−0.828539 | + | 0.559932i | \(0.810827\pi\) | |||||||
\(824\) | −7.88460 | −0.274673 | ||||||||
\(825\) | −72.6359 | −2.52886 | ||||||||
\(826\) | −5.93011 | −0.206335 | ||||||||
\(827\) | −8.93030 | −0.310537 | −0.155268 | − | 0.987872i | \(-0.549624\pi\) | ||||
−0.155268 | + | 0.987872i | \(0.549624\pi\) | |||||||
\(828\) | 27.0981 | 0.941725 | ||||||||
\(829\) | 34.4302 | 1.19581 | 0.597905 | − | 0.801567i | \(-0.296000\pi\) | ||||
0.597905 | + | 0.801567i | \(0.296000\pi\) | |||||||
\(830\) | −24.6774 | −0.856564 | ||||||||
\(831\) | 13.0238 | 0.451790 | ||||||||
\(832\) | 1.21482 | 0.0421162 | ||||||||
\(833\) | −21.5767 | −0.747589 | ||||||||
\(834\) | 31.1193 | 1.07757 | ||||||||
\(835\) | −67.0833 | −2.32151 | ||||||||
\(836\) | −5.95568 | −0.205982 | ||||||||
\(837\) | 10.2143 | 0.353056 | ||||||||
\(838\) | −32.3970 | −1.11914 | ||||||||
\(839\) | 54.7089 | 1.88876 | 0.944381 | − | 0.328853i | \(-0.106662\pi\) | ||||
0.944381 | + | 0.328853i | \(0.106662\pi\) | |||||||
\(840\) | 4.82518 | 0.166485 | ||||||||
\(841\) | −16.8832 | −0.582180 | ||||||||
\(842\) | 6.47692 | 0.223209 | ||||||||
\(843\) | −63.6732 | −2.19302 | ||||||||
\(844\) | −14.3512 | −0.493990 | ||||||||
\(845\) | 43.8720 | 1.50924 | ||||||||
\(846\) | 16.6052 | 0.570897 | ||||||||
\(847\) | −1.14186 | −0.0392349 | ||||||||
\(848\) | 1.19619 | 0.0410772 | ||||||||
\(849\) | 10.8186 | 0.371293 | ||||||||
\(850\) | 30.2883 | 1.03888 | ||||||||
\(851\) | 7.44417 | 0.255183 | ||||||||
\(852\) | −23.0805 | −0.790726 | ||||||||
\(853\) | 52.4297 | 1.79516 | 0.897579 | − | 0.440853i | \(-0.145324\pi\) | ||||
0.897579 | + | 0.440853i | \(0.145324\pi\) | |||||||
\(854\) | 5.01264 | 0.171529 | ||||||||
\(855\) | 28.9973 | 0.991686 | ||||||||
\(856\) | 11.9088 | 0.407033 | ||||||||
\(857\) | 14.4635 | 0.494065 | 0.247033 | − | 0.969007i | \(-0.420545\pi\) | ||||
0.247033 | + | 0.969007i | \(0.420545\pi\) | |||||||
\(858\) | −9.29541 | −0.317340 | ||||||||
\(859\) | −14.5781 | −0.497398 | −0.248699 | − | 0.968581i | \(-0.580003\pi\) | ||||
−0.248699 | + | 0.968581i | \(0.580003\pi\) | |||||||
\(860\) | 4.72209 | 0.161022 | ||||||||
\(861\) | −10.6933 | −0.364426 | ||||||||
\(862\) | 12.7851 | 0.435462 | ||||||||
\(863\) | 45.1782 | 1.53788 | 0.768941 | − | 0.639319i | \(-0.220784\pi\) | ||||
0.768941 | + | 0.639319i | \(0.220784\pi\) | |||||||
\(864\) | −1.98430 | −0.0675073 | ||||||||
\(865\) | −24.3098 | −0.826558 | ||||||||
\(866\) | −17.4222 | −0.592030 | ||||||||
\(867\) | 17.7351 | 0.602317 | ||||||||
\(868\) | −2.50880 | −0.0851542 | ||||||||
\(869\) | −21.8169 | −0.740086 | ||||||||
\(870\) | 34.4620 | 1.16837 | ||||||||
\(871\) | −13.8275 | −0.468528 | ||||||||
\(872\) | 4.27981 | 0.144933 | ||||||||
\(873\) | −9.44705 | −0.319734 | ||||||||
\(874\) | −14.5763 | −0.493050 | ||||||||
\(875\) | −8.33603 | −0.281809 | ||||||||
\(876\) | −23.5522 | −0.795756 | ||||||||
\(877\) | 22.1120 | 0.746668 | 0.373334 | − | 0.927697i | \(-0.378214\pi\) | ||||
0.373334 | + | 0.927697i | \(0.378214\pi\) | |||||||
\(878\) | −4.52030 | −0.152553 | ||||||||
\(879\) | 53.6573 | 1.80982 | ||||||||
\(880\) | −11.2012 | −0.377591 | ||||||||
\(881\) | −23.7418 | −0.799882 | −0.399941 | − | 0.916541i | \(-0.630969\pi\) | ||||
−0.399941 | + | 0.916541i | \(0.630969\pi\) | |||||||
\(882\) | −25.4473 | −0.856855 | ||||||||
\(883\) | −6.97848 | −0.234844 | −0.117422 | − | 0.993082i | \(-0.537463\pi\) | ||||
−0.117422 | + | 0.993082i | \(0.537463\pi\) | |||||||
\(884\) | 3.87607 | 0.130366 | ||||||||
\(885\) | −120.460 | −4.04921 | ||||||||
\(886\) | −13.2163 | −0.444011 | ||||||||
\(887\) | −34.2177 | −1.14892 | −0.574459 | − | 0.818533i | \(-0.694788\pi\) | ||||
−0.574459 | + | 0.818533i | \(0.694788\pi\) | |||||||
\(888\) | −2.68834 | −0.0902147 | ||||||||
\(889\) | 9.05163 | 0.303582 | ||||||||
\(890\) | −62.2337 | −2.08608 | ||||||||
\(891\) | −18.0326 | −0.604114 | ||||||||
\(892\) | −4.41280 | −0.147751 | ||||||||
\(893\) | −8.93203 | −0.298899 | ||||||||
\(894\) | 61.7937 | 2.06669 | ||||||||
\(895\) | 67.0689 | 2.24187 | ||||||||
\(896\) | 0.487379 | 0.0162822 | ||||||||
\(897\) | −22.7501 | −0.759605 | ||||||||
\(898\) | −10.4441 | −0.348523 | ||||||||
\(899\) | −17.9181 | −0.597603 | ||||||||
\(900\) | 35.7216 | 1.19072 | ||||||||
\(901\) | 3.81662 | 0.127150 | ||||||||
\(902\) | 24.8234 | 0.826528 | ||||||||
\(903\) | 1.57216 | 0.0523181 | ||||||||
\(904\) | 7.96219 | 0.264818 | ||||||||
\(905\) | −89.8507 | −2.98674 | ||||||||
\(906\) | −17.8823 | −0.594100 | ||||||||
\(907\) | −21.2280 | −0.704864 | −0.352432 | − | 0.935837i | \(-0.614645\pi\) | ||||
−0.352432 | + | 0.935837i | \(0.614645\pi\) | |||||||
\(908\) | −1.94853 | −0.0646643 | ||||||||
\(909\) | 40.5909 | 1.34631 | ||||||||
\(910\) | −2.25400 | −0.0747195 | ||||||||
\(911\) | 0.586051 | 0.0194167 | 0.00970836 | − | 0.999953i | \(-0.496910\pi\) | ||||
0.00970836 | + | 0.999953i | \(0.496910\pi\) | |||||||
\(912\) | 5.26399 | 0.174308 | ||||||||
\(913\) | 19.0726 | 0.631211 | ||||||||
\(914\) | 10.7134 | 0.354369 | ||||||||
\(915\) | 101.823 | 3.36617 | ||||||||
\(916\) | 24.5536 | 0.811272 | ||||||||
\(917\) | −10.6307 | −0.351058 | ||||||||
\(918\) | −6.33123 | −0.208962 | ||||||||
\(919\) | 33.5346 | 1.10620 | 0.553102 | − | 0.833114i | \(-0.313444\pi\) | ||||
0.553102 | + | 0.833114i | \(0.313444\pi\) | |||||||
\(920\) | −27.4144 | −0.903826 | ||||||||
\(921\) | −78.9127 | −2.60026 | ||||||||
\(922\) | −20.5805 | −0.677783 | ||||||||
\(923\) | 10.7817 | 0.354883 | ||||||||
\(924\) | −3.72928 | −0.122684 | ||||||||
\(925\) | 9.81312 | 0.322654 | ||||||||
\(926\) | −20.2894 | −0.666752 | ||||||||
\(927\) | −29.6699 | −0.974489 | ||||||||
\(928\) | 3.48092 | 0.114267 | ||||||||
\(929\) | −13.7972 | −0.452672 | −0.226336 | − | 0.974049i | \(-0.572675\pi\) | ||||
−0.226336 | + | 0.974049i | \(0.572675\pi\) | |||||||
\(930\) | −50.9619 | −1.67111 | ||||||||
\(931\) | 13.6883 | 0.448616 | ||||||||
\(932\) | −21.7296 | −0.711776 | ||||||||
\(933\) | 31.9544 | 1.04614 | ||||||||
\(934\) | −12.8280 | −0.419745 | ||||||||
\(935\) | −35.7391 | −1.16879 | ||||||||
\(936\) | 4.57139 | 0.149420 | ||||||||
\(937\) | −22.6646 | −0.740419 | −0.370210 | − | 0.928948i | \(-0.620714\pi\) | ||||
−0.370210 | + | 0.928948i | \(0.620714\pi\) | |||||||
\(938\) | −5.54754 | −0.181134 | ||||||||
\(939\) | 28.1410 | 0.918346 | ||||||||
\(940\) | −16.7989 | −0.547921 | ||||||||
\(941\) | 26.4988 | 0.863836 | 0.431918 | − | 0.901913i | \(-0.357837\pi\) | ||||
0.431918 | + | 0.901913i | \(0.357837\pi\) | |||||||
\(942\) | −48.8412 | −1.59133 | ||||||||
\(943\) | 60.7542 | 1.97843 | ||||||||
\(944\) | −12.1673 | −0.396013 | ||||||||
\(945\) | 3.68172 | 0.119766 | ||||||||
\(946\) | −3.64960 | −0.118659 | ||||||||
\(947\) | 57.8561 | 1.88007 | 0.940035 | − | 0.341078i | \(-0.110792\pi\) | ||||
0.940035 | + | 0.341078i | \(0.110792\pi\) | |||||||
\(948\) | 19.2830 | 0.626284 | ||||||||
\(949\) | 11.0020 | 0.357141 | ||||||||
\(950\) | −19.2149 | −0.623414 | ||||||||
\(951\) | 4.04806 | 0.131267 | ||||||||
\(952\) | 1.55506 | 0.0503999 | ||||||||
\(953\) | −46.4902 | −1.50597 | −0.752983 | − | 0.658040i | \(-0.771386\pi\) | ||||
−0.752983 | + | 0.658040i | \(0.771386\pi\) | |||||||
\(954\) | 4.50128 | 0.145734 | ||||||||
\(955\) | 8.61974 | 0.278928 | ||||||||
\(956\) | 11.3663 | 0.367613 | ||||||||
\(957\) | −26.6349 | −0.860985 | ||||||||
\(958\) | 36.1270 | 1.16721 | ||||||||
\(959\) | −2.49201 | −0.0804711 | ||||||||
\(960\) | 9.90026 | 0.319529 | ||||||||
\(961\) | −4.50292 | −0.145255 | ||||||||
\(962\) | 1.25581 | 0.0404890 | ||||||||
\(963\) | 44.8129 | 1.44408 | ||||||||
\(964\) | 2.21590 | 0.0713694 | ||||||||
\(965\) | −35.7858 | −1.15199 | ||||||||
\(966\) | −9.12726 | −0.293665 | ||||||||
\(967\) | −5.69625 | −0.183179 | −0.0915895 | − | 0.995797i | \(-0.529195\pi\) | ||||
−0.0915895 | + | 0.995797i | \(0.529195\pi\) | |||||||
\(968\) | −2.34286 | −0.0753025 | ||||||||
\(969\) | 16.7956 | 0.539552 | ||||||||
\(970\) | 9.55731 | 0.306867 | ||||||||
\(971\) | 41.2535 | 1.32389 | 0.661944 | − | 0.749553i | \(-0.269732\pi\) | ||||
0.661944 | + | 0.749553i | \(0.269732\pi\) | |||||||
\(972\) | 21.8912 | 0.702159 | ||||||||
\(973\) | −5.83211 | −0.186969 | ||||||||
\(974\) | 11.1794 | 0.358210 | ||||||||
\(975\) | −29.9899 | −0.960447 | ||||||||
\(976\) | 10.2849 | 0.329211 | ||||||||
\(977\) | 21.7501 | 0.695848 | 0.347924 | − | 0.937523i | \(-0.386887\pi\) | ||||
0.347924 | + | 0.937523i | \(0.386887\pi\) | |||||||
\(978\) | −32.3161 | −1.03335 | ||||||||
\(979\) | 48.0991 | 1.53725 | ||||||||
\(980\) | 25.7443 | 0.822371 | ||||||||
\(981\) | 16.1050 | 0.514194 | ||||||||
\(982\) | 9.49758 | 0.303080 | ||||||||
\(983\) | −20.7357 | −0.661365 | −0.330682 | − | 0.943742i | \(-0.607279\pi\) | ||||
−0.330682 | + | 0.943742i | \(0.607279\pi\) | |||||||
\(984\) | −21.9404 | −0.699434 | ||||||||
\(985\) | −10.7280 | −0.341824 | ||||||||
\(986\) | 11.1064 | 0.353701 | ||||||||
\(987\) | −5.59299 | −0.178027 | ||||||||
\(988\) | −2.45898 | −0.0782307 | ||||||||
\(989\) | −8.93225 | −0.284029 | ||||||||
\(990\) | −42.1502 | −1.33962 | ||||||||
\(991\) | 14.2286 | 0.451987 | 0.225994 | − | 0.974129i | \(-0.427437\pi\) | ||||
0.225994 | + | 0.974129i | \(0.427437\pi\) | |||||||
\(992\) | −5.14753 | −0.163434 | ||||||||
\(993\) | −12.3875 | −0.393105 | ||||||||
\(994\) | 4.32556 | 0.137198 | ||||||||
\(995\) | 56.6483 | 1.79587 | ||||||||
\(996\) | −16.8575 | −0.534150 | ||||||||
\(997\) | 34.9594 | 1.10718 | 0.553588 | − | 0.832791i | \(-0.313258\pi\) | ||||
0.553588 | + | 0.832791i | \(0.313258\pi\) | |||||||
\(998\) | 20.4507 | 0.647355 | ||||||||
\(999\) | −2.05126 | −0.0648991 |
(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 | 538.2.a.e.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 4842.2.a.n.1.7 | 7 | |||
4.3 | odd | 2 | 4304.2.a.h.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
538.2.a.e.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
4304.2.a.h.1.6 | 7 | 4.3 | odd | 2 | |||
4842.2.a.n.1.7 | 7 | 3.2 | odd | 2 |