Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 3x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.360409\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.41421 | 1.52688 | 0.763441 | − | 0.645877i | \(-0.223508\pi\) | ||||
0.763441 | + | 0.645877i | \(0.223508\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.41421 | 1.07967 | ||||||||
\(11\) | −0.298573 | −0.0900231 | −0.0450116 | − | 0.998986i | \(-0.514332\pi\) | ||||
−0.0450116 | + | 0.998986i | \(0.514332\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 4.72082 | 1.30932 | 0.654660 | − | 0.755924i | \(-0.272812\pi\) | ||||
0.654660 | + | 0.755924i | \(0.272812\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.54925 | 0.860819 | 0.430409 | − | 0.902634i | \(-0.358369\pi\) | ||||
0.430409 | + | 0.902634i | \(0.358369\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.98285 | −1.83139 | −0.915696 | − | 0.401872i | \(-0.868360\pi\) | ||||
−0.915696 | + | 0.401872i | \(0.868360\pi\) | |||||||
\(20\) | 3.41421 | 0.763441 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.298573 | −0.0636559 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 6.65685 | 1.33137 | ||||||||
\(26\) | 4.72082 | 0.925829 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.03878 | 1.49276 | 0.746382 | − | 0.665517i | \(-0.231789\pi\) | ||||
0.746382 | + | 0.665517i | \(0.231789\pi\) | |||||||
\(30\) | 3.41421 | 0.623347 | ||||||||
\(31\) | −9.98285 | −1.79297 | −0.896486 | − | 0.443071i | \(-0.853889\pi\) | ||||
−0.896486 | + | 0.443071i | \(0.853889\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.298573 | −0.0519749 | ||||||||
\(34\) | 3.54925 | 0.608691 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.54925 | −0.583492 | −0.291746 | − | 0.956496i | \(-0.594236\pi\) | ||||
−0.291746 | + | 0.956496i | \(0.594236\pi\) | |||||||
\(38\) | −7.98285 | −1.29499 | ||||||||
\(39\) | 4.72082 | 0.755936 | ||||||||
\(40\) | 3.41421 | 0.539835 | ||||||||
\(41\) | −0.817068 | −0.127605 | −0.0638023 | − | 0.997963i | \(-0.520323\pi\) | ||||
−0.0638023 | + | 0.997963i | \(0.520323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.99088 | −1.06610 | −0.533050 | − | 0.846084i | \(-0.678954\pi\) | ||||
−0.533050 | + | 0.846084i | \(0.678954\pi\) | |||||||
\(44\) | −0.298573 | −0.0450116 | ||||||||
\(45\) | 3.41421 | 0.508961 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 9.38571 | 1.36905 | 0.684523 | − | 0.728991i | \(-0.260011\pi\) | ||||
0.684523 | + | 0.728991i | \(0.260011\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.65685 | 0.941421 | ||||||||
\(51\) | 3.54925 | 0.496994 | ||||||||
\(52\) | 4.72082 | 0.654660 | ||||||||
\(53\) | 8.14639 | 1.11899 | 0.559496 | − | 0.828833i | \(-0.310995\pi\) | ||||
0.559496 | + | 0.828833i | \(0.310995\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.01939 | −0.137455 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.98285 | −1.05735 | ||||||||
\(58\) | 8.03878 | 1.05554 | ||||||||
\(59\) | 10.0388 | 1.30694 | 0.653469 | − | 0.756953i | \(-0.273313\pi\) | ||||
0.653469 | + | 0.756953i | \(0.273313\pi\) | |||||||
\(60\) | 3.41421 | 0.440773 | ||||||||
\(61\) | 5.18293 | 0.663606 | 0.331803 | − | 0.943349i | \(-0.392343\pi\) | ||||
0.331803 | + | 0.943349i | \(0.392343\pi\) | |||||||
\(62\) | −9.98285 | −1.26782 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 16.1179 | 1.99918 | ||||||||
\(66\) | −0.298573 | −0.0367518 | ||||||||
\(67\) | 15.2061 | 1.85772 | 0.928860 | − | 0.370430i | \(-0.120790\pi\) | ||||
0.928860 | + | 0.370430i | \(0.120790\pi\) | |||||||
\(68\) | 3.54925 | 0.430409 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.57775 | −0.661958 | −0.330979 | − | 0.943638i | \(-0.607379\pi\) | ||||
−0.330979 | + | 0.943638i | \(0.607379\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.776751 | 0.0909118 | 0.0454559 | − | 0.998966i | \(-0.485526\pi\) | ||||
0.0454559 | + | 0.998966i | \(0.485526\pi\) | |||||||
\(74\) | −3.54925 | −0.412591 | ||||||||
\(75\) | 6.65685 | 0.768667 | ||||||||
\(76\) | −7.98285 | −0.915696 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.72082 | 0.534527 | ||||||||
\(79\) | −14.0791 | −1.58402 | −0.792011 | − | 0.610506i | \(-0.790966\pi\) | ||||
−0.792011 | + | 0.610506i | \(0.790966\pi\) | |||||||
\(80\) | 3.41421 | 0.381721 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.817068 | −0.0902300 | ||||||||
\(83\) | −0.884359 | −0.0970710 | −0.0485355 | − | 0.998821i | \(-0.515455\pi\) | ||||
−0.0485355 | + | 0.998821i | \(0.515455\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.1179 | 1.31437 | ||||||||
\(86\) | −6.99088 | −0.753846 | ||||||||
\(87\) | 8.03878 | 0.861848 | ||||||||
\(88\) | −0.298573 | −0.0318280 | ||||||||
\(89\) | 2.43469 | 0.258077 | 0.129038 | − | 0.991640i | \(-0.458811\pi\) | ||||
0.129038 | + | 0.991640i | \(0.458811\pi\) | |||||||
\(90\) | 3.41421 | 0.359890 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −9.98285 | −1.03517 | ||||||||
\(94\) | 9.38571 | 0.968062 | ||||||||
\(95\) | −27.2552 | −2.79632 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −12.0345 | −1.22192 | −0.610961 | − | 0.791661i | \(-0.709217\pi\) | ||||
−0.610961 | + | 0.791661i | \(0.709217\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.298573 | −0.0300077 | ||||||||
\(100\) | 6.65685 | 0.665685 | ||||||||
\(101\) | −4.99088 | −0.496611 | −0.248306 | − | 0.968682i | \(-0.579874\pi\) | ||||
−0.248306 | + | 0.968682i | \(0.579874\pi\) | |||||||
\(102\) | 3.54925 | 0.351428 | ||||||||
\(103\) | −8.86721 | −0.873712 | −0.436856 | − | 0.899531i | \(-0.643908\pi\) | ||||
−0.436856 | + | 0.899531i | \(0.643908\pi\) | |||||||
\(104\) | 4.72082 | 0.462914 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.14639 | 0.791247 | ||||||||
\(107\) | −14.4956 | −1.40134 | −0.700669 | − | 0.713486i | \(-0.747115\pi\) | ||||
−0.700669 | + | 0.713486i | \(0.747115\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 10.0345 | 0.961133 | 0.480567 | − | 0.876958i | \(-0.340431\pi\) | ||||
0.480567 | + | 0.876958i | \(0.340431\pi\) | |||||||
\(110\) | −1.01939 | −0.0971952 | ||||||||
\(111\) | −3.54925 | −0.336880 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0194 | −1.41291 | −0.706453 | − | 0.707760i | \(-0.749706\pi\) | ||||
−0.706453 | + | 0.707760i | \(0.749706\pi\) | |||||||
\(114\) | −7.98285 | −0.747662 | ||||||||
\(115\) | 3.41421 | 0.318377 | ||||||||
\(116\) | 8.03878 | 0.746382 | ||||||||
\(117\) | 4.72082 | 0.436440 | ||||||||
\(118\) | 10.0388 | 0.924145 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.41421 | 0.311674 | ||||||||
\(121\) | −10.9109 | −0.991896 | ||||||||
\(122\) | 5.18293 | 0.469241 | ||||||||
\(123\) | −0.817068 | −0.0736725 | ||||||||
\(124\) | −9.98285 | −0.896486 | ||||||||
\(125\) | 5.65685 | 0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4820 | −1.01886 | −0.509429 | − | 0.860512i | \(-0.670143\pi\) | ||||
−0.509429 | + | 0.860512i | \(0.670143\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.99088 | −0.615513 | ||||||||
\(130\) | 16.1179 | 1.41363 | ||||||||
\(131\) | 14.7941 | 1.29257 | 0.646285 | − | 0.763097i | \(-0.276322\pi\) | ||||
0.646285 | + | 0.763097i | \(0.276322\pi\) | |||||||
\(132\) | −0.298573 | −0.0259874 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.2061 | 1.31361 | ||||||||
\(135\) | 3.41421 | 0.293849 | ||||||||
\(136\) | 3.54925 | 0.304345 | ||||||||
\(137\) | −2.90151 | −0.247893 | −0.123946 | − | 0.992289i | \(-0.539555\pi\) | ||||
−0.123946 | + | 0.992289i | \(0.539555\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 5.17157 | 0.438647 | 0.219324 | − | 0.975652i | \(-0.429615\pi\) | ||||
0.219324 | + | 0.975652i | \(0.429615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.38571 | 0.790419 | ||||||||
\(142\) | −5.57775 | −0.468075 | ||||||||
\(143\) | −1.40951 | −0.117869 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 27.4461 | 2.27928 | ||||||||
\(146\) | 0.776751 | 0.0642844 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.54925 | −0.291746 | ||||||||
\(149\) | 7.78053 | 0.637406 | 0.318703 | − | 0.947855i | \(-0.396753\pi\) | ||||
0.318703 | + | 0.947855i | \(0.396753\pi\) | |||||||
\(150\) | 6.65685 | 0.543530 | ||||||||
\(151\) | −20.6192 | −1.67797 | −0.838985 | − | 0.544155i | \(-0.816850\pi\) | ||||
−0.838985 | + | 0.544155i | \(0.816850\pi\) | |||||||
\(152\) | −7.98285 | −0.647495 | ||||||||
\(153\) | 3.54925 | 0.286940 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −34.0836 | −2.73766 | ||||||||
\(156\) | 4.72082 | 0.377968 | ||||||||
\(157\) | 22.9577 | 1.83222 | 0.916111 | − | 0.400925i | \(-0.131311\pi\) | ||||
0.916111 | + | 0.400925i | \(0.131311\pi\) | |||||||
\(158\) | −14.0791 | −1.12007 | ||||||||
\(159\) | 8.14639 | 0.646051 | ||||||||
\(160\) | 3.41421 | 0.269917 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −4.63746 | −0.363234 | −0.181617 | − | 0.983369i | \(-0.558133\pi\) | ||||
−0.181617 | + | 0.983369i | \(0.558133\pi\) | |||||||
\(164\) | −0.817068 | −0.0638023 | ||||||||
\(165\) | −1.01939 | −0.0793595 | ||||||||
\(166\) | −0.884359 | −0.0686396 | ||||||||
\(167\) | 22.1981 | 1.71774 | 0.858869 | − | 0.512195i | \(-0.171168\pi\) | ||||
0.858869 | + | 0.512195i | \(0.171168\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.28613 | 0.714318 | ||||||||
\(170\) | 12.1179 | 0.929399 | ||||||||
\(171\) | −7.98285 | −0.610464 | ||||||||
\(172\) | −6.99088 | −0.533050 | ||||||||
\(173\) | 3.16732 | 0.240807 | 0.120403 | − | 0.992725i | \(-0.461581\pi\) | ||||
0.120403 | + | 0.992725i | \(0.461581\pi\) | |||||||
\(174\) | 8.03878 | 0.609419 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.298573 | −0.0225058 | ||||||||
\(177\) | 10.0388 | 0.754561 | ||||||||
\(178\) | 2.43469 | 0.182488 | ||||||||
\(179\) | 13.5998 | 1.01650 | 0.508250 | − | 0.861210i | \(-0.330293\pi\) | ||||
0.508250 | + | 0.861210i | \(0.330293\pi\) | |||||||
\(180\) | 3.41421 | 0.254480 | ||||||||
\(181\) | 9.64549 | 0.716944 | 0.358472 | − | 0.933540i | \(-0.383298\pi\) | ||||
0.358472 | + | 0.933540i | \(0.383298\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.18293 | 0.383133 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −12.1179 | −0.890924 | ||||||||
\(186\) | −9.98285 | −0.731978 | ||||||||
\(187\) | −1.05971 | −0.0774936 | ||||||||
\(188\) | 9.38571 | 0.684523 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −27.2552 | −1.97730 | ||||||||
\(191\) | −2.13612 | −0.154564 | −0.0772820 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772820 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 21.9496 | 1.57997 | 0.789985 | − | 0.613127i | \(-0.210088\pi\) | ||||
0.789985 | + | 0.613127i | \(0.210088\pi\) | |||||||
\(194\) | −12.0345 | −0.864029 | ||||||||
\(195\) | 16.1179 | 1.15423 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.17490 | 0.439943 | 0.219972 | − | 0.975506i | \(-0.429403\pi\) | ||||
0.219972 | + | 0.975506i | \(0.429403\pi\) | |||||||
\(198\) | −0.298573 | −0.0212186 | ||||||||
\(199\) | −21.4644 | −1.52157 | −0.760784 | − | 0.649005i | \(-0.775185\pi\) | ||||
−0.760784 | + | 0.649005i | \(0.775185\pi\) | |||||||
\(200\) | 6.65685 | 0.470711 | ||||||||
\(201\) | 15.2061 | 1.07256 | ||||||||
\(202\) | −4.99088 | −0.351157 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.54925 | 0.248497 | ||||||||
\(205\) | −2.78964 | −0.194837 | ||||||||
\(206\) | −8.86721 | −0.617808 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 4.72082 | 0.327330 | ||||||||
\(209\) | 2.38346 | 0.164868 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.23461 | −0.635737 | −0.317868 | − | 0.948135i | \(-0.602967\pi\) | ||||
−0.317868 | + | 0.948135i | \(0.602967\pi\) | |||||||
\(212\) | 8.14639 | 0.559496 | ||||||||
\(213\) | −5.57775 | −0.382181 | ||||||||
\(214\) | −14.4956 | −0.990896 | ||||||||
\(215\) | −23.8684 | −1.62781 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.0345 | 0.679624 | ||||||||
\(219\) | 0.776751 | 0.0524880 | ||||||||
\(220\) | −1.01939 | −0.0687274 | ||||||||
\(221\) | 16.7553 | 1.12709 | ||||||||
\(222\) | −3.54925 | −0.238210 | ||||||||
\(223\) | 17.0265 | 1.14018 | 0.570089 | − | 0.821583i | \(-0.306909\pi\) | ||||
0.570089 | + | 0.821583i | \(0.306909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | −15.0194 | −0.999075 | ||||||||
\(227\) | −24.3563 | −1.61658 | −0.808291 | − | 0.588783i | \(-0.799607\pi\) | ||||
−0.808291 | + | 0.588783i | \(0.799607\pi\) | |||||||
\(228\) | −7.98285 | −0.528677 | ||||||||
\(229\) | −24.1923 | −1.59867 | −0.799335 | − | 0.600885i | \(-0.794815\pi\) | ||||
−0.799335 | + | 0.600885i | \(0.794815\pi\) | |||||||
\(230\) | 3.41421 | 0.225127 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.03878 | 0.527772 | ||||||||
\(233\) | −21.9109 | −1.43543 | −0.717714 | − | 0.696338i | \(-0.754811\pi\) | ||||
−0.717714 | + | 0.696338i | \(0.754811\pi\) | |||||||
\(234\) | 4.72082 | 0.308610 | ||||||||
\(235\) | 32.0448 | 2.09037 | ||||||||
\(236\) | 10.0388 | 0.653469 | ||||||||
\(237\) | −14.0791 | −0.914536 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.47926 | −0.419109 | −0.209554 | − | 0.977797i | \(-0.567201\pi\) | ||||
−0.209554 | + | 0.977797i | \(0.567201\pi\) | |||||||
\(240\) | 3.41421 | 0.220387 | ||||||||
\(241\) | −8.52832 | −0.549357 | −0.274679 | − | 0.961536i | \(-0.588571\pi\) | ||||
−0.274679 | + | 0.961536i | \(0.588571\pi\) | |||||||
\(242\) | −10.9109 | −0.701376 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.18293 | 0.331803 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.817068 | −0.0520943 | ||||||||
\(247\) | −37.6856 | −2.39788 | ||||||||
\(248\) | −9.98285 | −0.633912 | ||||||||
\(249\) | −0.884359 | −0.0560440 | ||||||||
\(250\) | 5.65685 | 0.357771 | ||||||||
\(251\) | 12.5024 | 0.789146 | 0.394573 | − | 0.918865i | \(-0.370892\pi\) | ||||
0.394573 | + | 0.918865i | \(0.370892\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.298573 | −0.0187711 | ||||||||
\(254\) | −11.4820 | −0.720442 | ||||||||
\(255\) | 12.1179 | 0.758851 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.79614 | 0.361553 | 0.180777 | − | 0.983524i | \(-0.442139\pi\) | ||||
0.180777 | + | 0.983524i | \(0.442139\pi\) | |||||||
\(258\) | −6.99088 | −0.435233 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.1179 | 0.999589 | ||||||||
\(261\) | 8.03878 | 0.497588 | ||||||||
\(262\) | 14.7941 | 0.913984 | ||||||||
\(263\) | −8.68629 | −0.535620 | −0.267810 | − | 0.963472i | \(-0.586300\pi\) | ||||
−0.267810 | + | 0.963472i | \(0.586300\pi\) | |||||||
\(264\) | −0.298573 | −0.0183759 | ||||||||
\(265\) | 27.8135 | 1.70857 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.43469 | 0.149001 | ||||||||
\(268\) | 15.2061 | 0.928860 | ||||||||
\(269\) | 28.4713 | 1.73593 | 0.867963 | − | 0.496629i | \(-0.165429\pi\) | ||||
0.867963 | + | 0.496629i | \(0.165429\pi\) | |||||||
\(270\) | 3.41421 | 0.207782 | ||||||||
\(271\) | −2.46211 | −0.149563 | −0.0747814 | − | 0.997200i | \(-0.523826\pi\) | ||||
−0.0747814 | + | 0.997200i | \(0.523826\pi\) | |||||||
\(272\) | 3.54925 | 0.215205 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.90151 | −0.175287 | ||||||||
\(275\) | −1.98756 | −0.119854 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −23.5192 | −1.41313 | −0.706566 | − | 0.707647i | \(-0.749757\pi\) | ||||
−0.706566 | + | 0.707647i | \(0.749757\pi\) | |||||||
\(278\) | 5.17157 | 0.310170 | ||||||||
\(279\) | −9.98285 | −0.597658 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.81236 | −0.167771 | −0.0838857 | − | 0.996475i | \(-0.526733\pi\) | ||||
−0.0838857 | + | 0.996475i | \(0.526733\pi\) | |||||||
\(282\) | 9.38571 | 0.558911 | ||||||||
\(283\) | −17.6800 | −1.05097 | −0.525484 | − | 0.850803i | \(-0.676116\pi\) | ||||
−0.525484 | + | 0.850803i | \(0.676116\pi\) | |||||||
\(284\) | −5.57775 | −0.330979 | ||||||||
\(285\) | −27.2552 | −1.61446 | ||||||||
\(286\) | −1.40951 | −0.0833460 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −4.40285 | −0.258991 | ||||||||
\(290\) | 27.4461 | 1.61169 | ||||||||
\(291\) | −12.0345 | −0.705476 | ||||||||
\(292\) | 0.776751 | 0.0454559 | ||||||||
\(293\) | −8.97373 | −0.524251 | −0.262126 | − | 0.965034i | \(-0.584423\pi\) | ||||
−0.262126 | + | 0.965034i | \(0.584423\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.2745 | 1.99554 | ||||||||
\(296\) | −3.54925 | −0.206296 | ||||||||
\(297\) | −0.298573 | −0.0173250 | ||||||||
\(298\) | 7.78053 | 0.450714 | ||||||||
\(299\) | 4.72082 | 0.273012 | ||||||||
\(300\) | 6.65685 | 0.384334 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −20.6192 | −1.18650 | ||||||||
\(303\) | −4.99088 | −0.286719 | ||||||||
\(304\) | −7.98285 | −0.457848 | ||||||||
\(305\) | 17.6956 | 1.01325 | ||||||||
\(306\) | 3.54925 | 0.202897 | ||||||||
\(307\) | 5.49648 | 0.313701 | 0.156850 | − | 0.987622i | \(-0.449866\pi\) | ||||
0.156850 | + | 0.987622i | \(0.449866\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.86721 | −0.504438 | ||||||||
\(310\) | −34.0836 | −1.93582 | ||||||||
\(311\) | −20.0277 | −1.13566 | −0.567832 | − | 0.823144i | \(-0.692218\pi\) | ||||
−0.567832 | + | 0.823144i | \(0.692218\pi\) | |||||||
\(312\) | 4.72082 | 0.267264 | ||||||||
\(313\) | −18.4004 | −1.04005 | −0.520026 | − | 0.854151i | \(-0.674078\pi\) | ||||
−0.520026 | + | 0.854151i | \(0.674078\pi\) | |||||||
\(314\) | 22.9577 | 1.29558 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.0791 | −0.792011 | ||||||||
\(317\) | −21.6468 | −1.21581 | −0.607903 | − | 0.794011i | \(-0.707989\pi\) | ||||
−0.607903 | + | 0.794011i | \(0.707989\pi\) | |||||||
\(318\) | 8.14639 | 0.456827 | ||||||||
\(319\) | −2.40016 | −0.134383 | ||||||||
\(320\) | 3.41421 | 0.190860 | ||||||||
\(321\) | −14.4956 | −0.809063 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.3331 | −1.57650 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 31.4258 | 1.74319 | ||||||||
\(326\) | −4.63746 | −0.256845 | ||||||||
\(327\) | 10.0345 | 0.554911 | ||||||||
\(328\) | −0.817068 | −0.0451150 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.01939 | −0.0561157 | ||||||||
\(331\) | 6.34315 | 0.348651 | 0.174325 | − | 0.984688i | \(-0.444226\pi\) | ||||
0.174325 | + | 0.984688i | \(0.444226\pi\) | |||||||
\(332\) | −0.884359 | −0.0485355 | ||||||||
\(333\) | −3.54925 | −0.194497 | ||||||||
\(334\) | 22.1981 | 1.21462 | ||||||||
\(335\) | 51.9169 | 2.83652 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.7150 | −0.583685 | −0.291842 | − | 0.956466i | \(-0.594268\pi\) | ||||
−0.291842 | + | 0.956466i | \(0.594268\pi\) | |||||||
\(338\) | 9.28613 | 0.505099 | ||||||||
\(339\) | −15.0194 | −0.815741 | ||||||||
\(340\) | 12.1179 | 0.657184 | ||||||||
\(341\) | 2.98061 | 0.161409 | ||||||||
\(342\) | −7.98285 | −0.431663 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6.99088 | −0.376923 | ||||||||
\(345\) | 3.41421 | 0.183815 | ||||||||
\(346\) | 3.16732 | 0.170276 | ||||||||
\(347\) | 22.9120 | 1.22998 | 0.614991 | − | 0.788534i | \(-0.289160\pi\) | ||||
0.614991 | + | 0.788534i | \(0.289160\pi\) | |||||||
\(348\) | 8.03878 | 0.430924 | ||||||||
\(349\) | −11.4922 | −0.615165 | −0.307582 | − | 0.951521i | \(-0.599520\pi\) | ||||
−0.307582 | + | 0.951521i | \(0.599520\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.72082 | 0.251979 | ||||||||
\(352\) | −0.298573 | −0.0159140 | ||||||||
\(353\) | 10.9510 | 0.582864 | 0.291432 | − | 0.956592i | \(-0.405868\pi\) | ||||
0.291432 | + | 0.956592i | \(0.405868\pi\) | |||||||
\(354\) | 10.0388 | 0.533555 | ||||||||
\(355\) | −19.0436 | −1.01073 | ||||||||
\(356\) | 2.43469 | 0.129038 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.5998 | 0.718774 | ||||||||
\(359\) | −4.63746 | −0.244756 | −0.122378 | − | 0.992484i | \(-0.539052\pi\) | ||||
−0.122378 | + | 0.992484i | \(0.539052\pi\) | |||||||
\(360\) | 3.41421 | 0.179945 | ||||||||
\(361\) | 44.7259 | 2.35400 | ||||||||
\(362\) | 9.64549 | 0.506956 | ||||||||
\(363\) | −10.9109 | −0.572671 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.65199 | 0.138812 | ||||||||
\(366\) | 5.18293 | 0.270916 | ||||||||
\(367\) | 15.5838 | 0.813466 | 0.406733 | − | 0.913547i | \(-0.366668\pi\) | ||||
0.406733 | + | 0.913547i | \(0.366668\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −0.817068 | −0.0425349 | ||||||||
\(370\) | −12.1179 | −0.629979 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −9.98285 | −0.517587 | ||||||||
\(373\) | −18.4650 | −0.956079 | −0.478040 | − | 0.878338i | \(-0.658653\pi\) | ||||
−0.478040 | + | 0.878338i | \(0.658653\pi\) | |||||||
\(374\) | −1.05971 | −0.0547962 | ||||||||
\(375\) | 5.65685 | 0.292119 | ||||||||
\(376\) | 9.38571 | 0.484031 | ||||||||
\(377\) | 37.9496 | 1.95451 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.2691 | 1.29799 | 0.648994 | − | 0.760793i | \(-0.275190\pi\) | ||||
0.648994 | + | 0.760793i | \(0.275190\pi\) | |||||||
\(380\) | −27.2552 | −1.39816 | ||||||||
\(381\) | −11.4820 | −0.588238 | ||||||||
\(382\) | −2.13612 | −0.109293 | ||||||||
\(383\) | 20.6983 | 1.05764 | 0.528818 | − | 0.848735i | \(-0.322636\pi\) | ||||
0.528818 | + | 0.848735i | \(0.322636\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.9496 | 1.11721 | ||||||||
\(387\) | −6.99088 | −0.355367 | ||||||||
\(388\) | −12.0345 | −0.610961 | ||||||||
\(389\) | −18.6638 | −0.946292 | −0.473146 | − | 0.880984i | \(-0.656882\pi\) | ||||
−0.473146 | + | 0.880984i | \(0.656882\pi\) | |||||||
\(390\) | 16.1179 | 0.816161 | ||||||||
\(391\) | 3.54925 | 0.179493 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.7941 | 0.746265 | ||||||||
\(394\) | 6.17490 | 0.311087 | ||||||||
\(395\) | −48.0691 | −2.41862 | ||||||||
\(396\) | −0.298573 | −0.0150039 | ||||||||
\(397\) | −23.4374 | −1.17629 | −0.588144 | − | 0.808756i | \(-0.700141\pi\) | ||||
−0.588144 | + | 0.808756i | \(0.700141\pi\) | |||||||
\(398\) | −21.4644 | −1.07591 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.65685 | 0.332843 | ||||||||
\(401\) | −6.24735 | −0.311978 | −0.155989 | − | 0.987759i | \(-0.549856\pi\) | ||||
−0.155989 | + | 0.987759i | \(0.549856\pi\) | |||||||
\(402\) | 15.2061 | 0.758411 | ||||||||
\(403\) | −47.1272 | −2.34757 | ||||||||
\(404\) | −4.99088 | −0.248306 | ||||||||
\(405\) | 3.41421 | 0.169654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.05971 | 0.0525278 | ||||||||
\(408\) | 3.54925 | 0.175714 | ||||||||
\(409\) | 29.9222 | 1.47956 | 0.739779 | − | 0.672850i | \(-0.234930\pi\) | ||||
0.739779 | + | 0.672850i | \(0.234930\pi\) | |||||||
\(410\) | −2.78964 | −0.137771 | ||||||||
\(411\) | −2.90151 | −0.143121 | ||||||||
\(412\) | −8.86721 | −0.436856 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −3.01939 | −0.148216 | ||||||||
\(416\) | 4.72082 | 0.231457 | ||||||||
\(417\) | 5.17157 | 0.253253 | ||||||||
\(418\) | 2.38346 | 0.116579 | ||||||||
\(419\) | 29.5827 | 1.44521 | 0.722604 | − | 0.691262i | \(-0.242945\pi\) | ||||
0.722604 | + | 0.691262i | \(0.242945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.970334 | 0.0472912 | 0.0236456 | − | 0.999720i | \(-0.492473\pi\) | ||||
0.0236456 | + | 0.999720i | \(0.492473\pi\) | |||||||
\(422\) | −9.23461 | −0.449534 | ||||||||
\(423\) | 9.38571 | 0.456349 | ||||||||
\(424\) | 8.14639 | 0.395624 | ||||||||
\(425\) | 23.6268 | 1.14607 | ||||||||
\(426\) | −5.57775 | −0.270243 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −14.4956 | −0.700669 | ||||||||
\(429\) | −1.40951 | −0.0680517 | ||||||||
\(430\) | −23.8684 | −1.15103 | ||||||||
\(431\) | 23.2246 | 1.11869 | 0.559344 | − | 0.828936i | \(-0.311053\pi\) | ||||
0.559344 | + | 0.828936i | \(0.311053\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 5.94724 | 0.285806 | 0.142903 | − | 0.989737i | \(-0.454356\pi\) | ||||
0.142903 | + | 0.989737i | \(0.454356\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 27.4461 | 1.31594 | ||||||||
\(436\) | 10.0345 | 0.480567 | ||||||||
\(437\) | −7.98285 | −0.381872 | ||||||||
\(438\) | 0.776751 | 0.0371146 | ||||||||
\(439\) | −17.8080 | −0.849927 | −0.424964 | − | 0.905210i | \(-0.639713\pi\) | ||||
−0.424964 | + | 0.905210i | \(0.639713\pi\) | |||||||
\(440\) | −1.01939 | −0.0485976 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.7553 | 0.796971 | ||||||||
\(443\) | 27.5983 | 1.31123 | 0.655617 | − | 0.755093i | \(-0.272408\pi\) | ||||
0.655617 | + | 0.755093i | \(0.272408\pi\) | |||||||
\(444\) | −3.54925 | −0.168440 | ||||||||
\(445\) | 8.31255 | 0.394053 | ||||||||
\(446\) | 17.0265 | 0.806228 | ||||||||
\(447\) | 7.78053 | 0.368006 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.9221 | −1.74246 | −0.871230 | − | 0.490875i | \(-0.836677\pi\) | ||||
−0.871230 | + | 0.490875i | \(0.836677\pi\) | |||||||
\(450\) | 6.65685 | 0.313807 | ||||||||
\(451\) | 0.243954 | 0.0114874 | ||||||||
\(452\) | −15.0194 | −0.706453 | ||||||||
\(453\) | −20.6192 | −0.968776 | ||||||||
\(454\) | −24.3563 | −1.14310 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.98285 | −0.373831 | ||||||||
\(457\) | −14.5971 | −0.682826 | −0.341413 | − | 0.939913i | \(-0.610905\pi\) | ||||
−0.341413 | + | 0.939913i | \(0.610905\pi\) | |||||||
\(458\) | −24.1923 | −1.13043 | ||||||||
\(459\) | 3.54925 | 0.165665 | ||||||||
\(460\) | 3.41421 | 0.159189 | ||||||||
\(461\) | −3.08668 | −0.143761 | −0.0718806 | − | 0.997413i | \(-0.522900\pi\) | ||||
−0.0718806 | + | 0.997413i | \(0.522900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −35.1190 | −1.63212 | −0.816060 | − | 0.577967i | \(-0.803846\pi\) | ||||
−0.816060 | + | 0.577967i | \(0.803846\pi\) | |||||||
\(464\) | 8.03878 | 0.373191 | ||||||||
\(465\) | −34.0836 | −1.58059 | ||||||||
\(466\) | −21.9109 | −1.01500 | ||||||||
\(467\) | 0.462114 | 0.0213841 | 0.0106920 | − | 0.999943i | \(-0.496597\pi\) | ||||
0.0106920 | + | 0.999943i | \(0.496597\pi\) | |||||||
\(468\) | 4.72082 | 0.218220 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 32.0448 | 1.47812 | ||||||||
\(471\) | 22.9577 | 1.05783 | ||||||||
\(472\) | 10.0388 | 0.462072 | ||||||||
\(473\) | 2.08729 | 0.0959736 | ||||||||
\(474\) | −14.0791 | −0.646674 | ||||||||
\(475\) | −53.1407 | −2.43826 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.14639 | 0.372998 | ||||||||
\(478\) | −6.47926 | −0.296355 | ||||||||
\(479\) | 19.3115 | 0.882367 | 0.441183 | − | 0.897417i | \(-0.354559\pi\) | ||||
0.441183 | + | 0.897417i | \(0.354559\pi\) | |||||||
\(480\) | 3.41421 | 0.155837 | ||||||||
\(481\) | −16.7553 | −0.763978 | ||||||||
\(482\) | −8.52832 | −0.388454 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9109 | −0.495948 | ||||||||
\(485\) | −41.0884 | −1.86573 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −10.4692 | −0.474406 | −0.237203 | − | 0.971460i | \(-0.576231\pi\) | ||||
−0.237203 | + | 0.971460i | \(0.576231\pi\) | |||||||
\(488\) | 5.18293 | 0.234620 | ||||||||
\(489\) | −4.63746 | −0.209713 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.2846 | 0.554396 | 0.277198 | − | 0.960813i | \(-0.410594\pi\) | ||||
0.277198 | + | 0.960813i | \(0.410594\pi\) | |||||||
\(492\) | −0.817068 | −0.0368363 | ||||||||
\(493\) | 28.5316 | 1.28500 | ||||||||
\(494\) | −37.6856 | −1.69555 | ||||||||
\(495\) | −1.01939 | −0.0458182 | ||||||||
\(496\) | −9.98285 | −0.448243 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.884359 | −0.0396291 | ||||||||
\(499\) | −6.37188 | −0.285245 | −0.142622 | − | 0.989777i | \(-0.545553\pi\) | ||||
−0.142622 | + | 0.989777i | \(0.545553\pi\) | |||||||
\(500\) | 5.65685 | 0.252982 | ||||||||
\(501\) | 22.1981 | 0.991737 | ||||||||
\(502\) | 12.5024 | 0.558011 | ||||||||
\(503\) | 9.94964 | 0.443632 | 0.221816 | − | 0.975088i | \(-0.428802\pi\) | ||||
0.221816 | + | 0.975088i | \(0.428802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0399 | −0.758267 | ||||||||
\(506\) | −0.298573 | −0.0132732 | ||||||||
\(507\) | 9.28613 | 0.412411 | ||||||||
\(508\) | −11.4820 | −0.509429 | ||||||||
\(509\) | −0.743537 | −0.0329567 | −0.0164784 | − | 0.999864i | \(-0.505245\pi\) | ||||
−0.0164784 | + | 0.999864i | \(0.505245\pi\) | |||||||
\(510\) | 12.1179 | 0.536589 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.98285 | −0.352451 | ||||||||
\(514\) | 5.79614 | 0.255657 | ||||||||
\(515\) | −30.2745 | −1.33406 | ||||||||
\(516\) | −6.99088 | −0.307756 | ||||||||
\(517\) | −2.80232 | −0.123246 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.16732 | 0.139030 | ||||||||
\(520\) | 16.1179 | 0.706816 | ||||||||
\(521\) | 12.6317 | 0.553404 | 0.276702 | − | 0.960956i | \(-0.410759\pi\) | ||||
0.276702 | + | 0.960956i | \(0.410759\pi\) | |||||||
\(522\) | 8.03878 | 0.351848 | ||||||||
\(523\) | 13.9441 | 0.609732 | 0.304866 | − | 0.952395i | \(-0.401388\pi\) | ||||
0.304866 | + | 0.952395i | \(0.401388\pi\) | |||||||
\(524\) | 14.7941 | 0.646285 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.68629 | −0.378740 | ||||||||
\(527\) | −35.4316 | −1.54342 | ||||||||
\(528\) | −0.298573 | −0.0129937 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 27.8135 | 1.20814 | ||||||||
\(531\) | 10.0388 | 0.435646 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.85723 | −0.167075 | ||||||||
\(534\) | 2.43469 | 0.105359 | ||||||||
\(535\) | −49.4909 | −2.13968 | ||||||||
\(536\) | 15.2061 | 0.656803 | ||||||||
\(537\) | 13.5998 | 0.586876 | ||||||||
\(538\) | 28.4713 | 1.22749 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.41421 | 0.146924 | ||||||||
\(541\) | 12.8263 | 0.551444 | 0.275722 | − | 0.961237i | \(-0.411083\pi\) | ||||
0.275722 | + | 0.961237i | \(0.411083\pi\) | |||||||
\(542\) | −2.46211 | −0.105757 | ||||||||
\(543\) | 9.64549 | 0.413928 | ||||||||
\(544\) | 3.54925 | 0.152173 | ||||||||
\(545\) | 34.2600 | 1.46754 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.4234 | −0.488429 | −0.244215 | − | 0.969721i | \(-0.578530\pi\) | ||||
−0.244215 | + | 0.969721i | \(0.578530\pi\) | |||||||
\(548\) | −2.90151 | −0.123946 | ||||||||
\(549\) | 5.18293 | 0.221202 | ||||||||
\(550\) | −1.98756 | −0.0847497 | ||||||||
\(551\) | −64.1724 | −2.73384 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −23.5192 | −0.999235 | ||||||||
\(555\) | −12.1179 | −0.514375 | ||||||||
\(556\) | 5.17157 | 0.219324 | ||||||||
\(557\) | −24.7026 | −1.04668 | −0.523341 | − | 0.852123i | \(-0.675315\pi\) | ||||
−0.523341 | + | 0.852123i | \(0.675315\pi\) | |||||||
\(558\) | −9.98285 | −0.422608 | ||||||||
\(559\) | −33.0027 | −1.39587 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.05971 | −0.0447409 | ||||||||
\(562\) | −2.81236 | −0.118632 | ||||||||
\(563\) | 36.6658 | 1.54528 | 0.772639 | − | 0.634846i | \(-0.218937\pi\) | ||||
0.772639 | + | 0.634846i | \(0.218937\pi\) | |||||||
\(564\) | 9.38571 | 0.395209 | ||||||||
\(565\) | −51.2794 | −2.15734 | ||||||||
\(566\) | −17.6800 | −0.743147 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.57775 | −0.234037 | ||||||||
\(569\) | −29.9430 | −1.25528 | −0.627638 | − | 0.778506i | \(-0.715978\pi\) | ||||
−0.627638 | + | 0.778506i | \(0.715978\pi\) | |||||||
\(570\) | −27.2552 | −1.14159 | ||||||||
\(571\) | 27.2837 | 1.14179 | 0.570893 | − | 0.821025i | \(-0.306597\pi\) | ||||
0.570893 | + | 0.821025i | \(0.306597\pi\) | |||||||
\(572\) | −1.40951 | −0.0589345 | ||||||||
\(573\) | −2.13612 | −0.0892376 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.65685 | 0.277610 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −6.84766 | −0.285072 | −0.142536 | − | 0.989790i | \(-0.545526\pi\) | ||||
−0.142536 | + | 0.989790i | \(0.545526\pi\) | |||||||
\(578\) | −4.40285 | −0.183135 | ||||||||
\(579\) | 21.9496 | 0.912196 | ||||||||
\(580\) | 27.4461 | 1.13964 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −12.0345 | −0.498847 | ||||||||
\(583\) | −2.43229 | −0.100735 | ||||||||
\(584\) | 0.776751 | 0.0321422 | ||||||||
\(585\) | 16.1179 | 0.666392 | ||||||||
\(586\) | −8.97373 | −0.370702 | ||||||||
\(587\) | 3.17823 | 0.131179 | 0.0655897 | − | 0.997847i | \(-0.479107\pi\) | ||||
0.0655897 | + | 0.997847i | \(0.479107\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 79.6916 | 3.28364 | ||||||||
\(590\) | 34.2745 | 1.41106 | ||||||||
\(591\) | 6.17490 | 0.254001 | ||||||||
\(592\) | −3.54925 | −0.145873 | ||||||||
\(593\) | −11.6433 | −0.478134 | −0.239067 | − | 0.971003i | \(-0.576842\pi\) | ||||
−0.239067 | + | 0.971003i | \(0.576842\pi\) | |||||||
\(594\) | −0.298573 | −0.0122506 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.78053 | 0.318703 | ||||||||
\(597\) | −21.4644 | −0.878478 | ||||||||
\(598\) | 4.72082 | 0.193049 | ||||||||
\(599\) | −21.0027 | −0.858147 | −0.429073 | − | 0.903270i | \(-0.641160\pi\) | ||||
−0.429073 | + | 0.903270i | \(0.641160\pi\) | |||||||
\(600\) | 6.65685 | 0.271765 | ||||||||
\(601\) | −25.5236 | −1.04113 | −0.520564 | − | 0.853822i | \(-0.674278\pi\) | ||||
−0.520564 | + | 0.853822i | \(0.674278\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.2061 | 0.619240 | ||||||||
\(604\) | −20.6192 | −0.838985 | ||||||||
\(605\) | −37.2520 | −1.51451 | ||||||||
\(606\) | −4.99088 | −0.202741 | ||||||||
\(607\) | 38.7124 | 1.57129 | 0.785644 | − | 0.618679i | \(-0.212332\pi\) | ||||
0.785644 | + | 0.618679i | \(0.212332\pi\) | |||||||
\(608\) | −7.98285 | −0.323747 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.6956 | 0.716475 | ||||||||
\(611\) | 44.3082 | 1.79252 | ||||||||
\(612\) | 3.54925 | 0.143470 | ||||||||
\(613\) | −4.91780 | −0.198628 | −0.0993141 | − | 0.995056i | \(-0.531665\pi\) | ||||
−0.0993141 | + | 0.995056i | \(0.531665\pi\) | |||||||
\(614\) | 5.49648 | 0.221820 | ||||||||
\(615\) | −2.78964 | −0.112489 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.196983 | 0.00793024 | 0.00396512 | − | 0.999992i | \(-0.498738\pi\) | ||||
0.00396512 | + | 0.999992i | \(0.498738\pi\) | |||||||
\(618\) | −8.86721 | −0.356692 | ||||||||
\(619\) | 11.2623 | 0.452668 | 0.226334 | − | 0.974050i | \(-0.427326\pi\) | ||||
0.226334 | + | 0.974050i | \(0.427326\pi\) | |||||||
\(620\) | −34.0836 | −1.36883 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | −20.0277 | −0.803036 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.72082 | 0.188984 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | −18.4004 | −0.735428 | ||||||||
\(627\) | 2.38346 | 0.0951863 | ||||||||
\(628\) | 22.9577 | 0.916111 | ||||||||
\(629\) | −12.5971 | −0.502281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.4067 | 1.25028 | 0.625141 | − | 0.780512i | \(-0.285042\pi\) | ||||
0.625141 | + | 0.780512i | \(0.285042\pi\) | |||||||
\(632\) | −14.0791 | −0.560037 | ||||||||
\(633\) | −9.23461 | −0.367043 | ||||||||
\(634\) | −21.6468 | −0.859705 | ||||||||
\(635\) | −39.2018 | −1.55568 | ||||||||
\(636\) | 8.14639 | 0.323025 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.40016 | −0.0950233 | ||||||||
\(639\) | −5.57775 | −0.220653 | ||||||||
\(640\) | 3.41421 | 0.134959 | ||||||||
\(641\) | −7.71387 | −0.304680 | −0.152340 | − | 0.988328i | \(-0.548681\pi\) | ||||
−0.152340 | + | 0.988328i | \(0.548681\pi\) | |||||||
\(642\) | −14.4956 | −0.572094 | ||||||||
\(643\) | −10.3260 | −0.407218 | −0.203609 | − | 0.979052i | \(-0.565267\pi\) | ||||
−0.203609 | + | 0.979052i | \(0.565267\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.8684 | −0.939816 | ||||||||
\(646\) | −28.3331 | −1.11475 | ||||||||
\(647\) | 11.4897 | 0.451706 | 0.225853 | − | 0.974161i | \(-0.427483\pi\) | ||||
0.225853 | + | 0.974161i | \(0.427483\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −2.99731 | −0.117655 | ||||||||
\(650\) | 31.4258 | 1.23262 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.63746 | −0.181617 | ||||||||
\(653\) | −36.4898 | −1.42795 | −0.713977 | − | 0.700169i | \(-0.753108\pi\) | ||||
−0.713977 | + | 0.700169i | \(0.753108\pi\) | |||||||
\(654\) | 10.0345 | 0.392381 | ||||||||
\(655\) | 50.5103 | 1.97360 | ||||||||
\(656\) | −0.817068 | −0.0319011 | ||||||||
\(657\) | 0.776751 | 0.0303039 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.5702 | 0.645482 | 0.322741 | − | 0.946487i | \(-0.395396\pi\) | ||||
0.322741 | + | 0.946487i | \(0.395396\pi\) | |||||||
\(660\) | −1.01939 | −0.0396798 | ||||||||
\(661\) | 43.7190 | 1.70047 | 0.850237 | − | 0.526401i | \(-0.176459\pi\) | ||||
0.850237 | + | 0.526401i | \(0.176459\pi\) | |||||||
\(662\) | 6.34315 | 0.246533 | ||||||||
\(663\) | 16.7553 | 0.650724 | ||||||||
\(664\) | −0.884359 | −0.0343198 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.54925 | −0.137530 | ||||||||
\(667\) | 8.03878 | 0.311263 | ||||||||
\(668\) | 22.1981 | 0.858869 | ||||||||
\(669\) | 17.0265 | 0.658282 | ||||||||
\(670\) | 51.9169 | 2.00572 | ||||||||
\(671\) | −1.54748 | −0.0597399 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.2745 | 1.55247 | 0.776235 | − | 0.630444i | \(-0.217127\pi\) | ||||
0.776235 | + | 0.630444i | \(0.217127\pi\) | |||||||
\(674\) | −10.7150 | −0.412727 | ||||||||
\(675\) | 6.65685 | 0.256222 | ||||||||
\(676\) | 9.28613 | 0.357159 | ||||||||
\(677\) | −27.9543 | −1.07437 | −0.537186 | − | 0.843464i | \(-0.680513\pi\) | ||||
−0.537186 | + | 0.843464i | \(0.680513\pi\) | |||||||
\(678\) | −15.0194 | −0.576816 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.1179 | 0.464700 | ||||||||
\(681\) | −24.3563 | −0.933334 | ||||||||
\(682\) | 2.98061 | 0.114133 | ||||||||
\(683\) | 25.8554 | 0.989328 | 0.494664 | − | 0.869084i | \(-0.335291\pi\) | ||||
0.494664 | + | 0.869084i | \(0.335291\pi\) | |||||||
\(684\) | −7.98285 | −0.305232 | ||||||||
\(685\) | −9.90637 | −0.378503 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.1923 | −0.922993 | ||||||||
\(688\) | −6.99088 | −0.266525 | ||||||||
\(689\) | 38.4576 | 1.46512 | ||||||||
\(690\) | 3.41421 | 0.129977 | ||||||||
\(691\) | −5.83777 | −0.222079 | −0.111040 | − | 0.993816i | \(-0.535418\pi\) | ||||
−0.111040 | + | 0.993816i | \(0.535418\pi\) | |||||||
\(692\) | 3.16732 | 0.120403 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.9120 | 0.869728 | ||||||||
\(695\) | 17.6569 | 0.669763 | ||||||||
\(696\) | 8.03878 | 0.304709 | ||||||||
\(697\) | −2.89997 | −0.109844 | ||||||||
\(698\) | −11.4922 | −0.434987 | ||||||||
\(699\) | −21.9109 | −0.828745 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.0394 | 0.945725 | 0.472862 | − | 0.881136i | \(-0.343221\pi\) | ||||
0.472862 | + | 0.881136i | \(0.343221\pi\) | |||||||
\(702\) | 4.72082 | 0.178176 | ||||||||
\(703\) | 28.3331 | 1.06860 | ||||||||
\(704\) | −0.298573 | −0.0112529 | ||||||||
\(705\) | 32.0448 | 1.20688 | ||||||||
\(706\) | 10.9510 | 0.412147 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10.0388 | 0.377281 | ||||||||
\(709\) | 6.97699 | 0.262026 | 0.131013 | − | 0.991381i | \(-0.458177\pi\) | ||||
0.131013 | + | 0.991381i | \(0.458177\pi\) | |||||||
\(710\) | −19.0436 | −0.714695 | ||||||||
\(711\) | −14.0791 | −0.528008 | ||||||||
\(712\) | 2.43469 | 0.0912439 | ||||||||
\(713\) | −9.98285 | −0.373861 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.81236 | −0.179972 | ||||||||
\(716\) | 13.5998 | 0.508250 | ||||||||
\(717\) | −6.47926 | −0.241972 | ||||||||
\(718\) | −4.63746 | −0.173069 | ||||||||
\(719\) | −7.63369 | −0.284688 | −0.142344 | − | 0.989817i | \(-0.545464\pi\) | ||||
−0.142344 | + | 0.989817i | \(0.545464\pi\) | |||||||
\(720\) | 3.41421 | 0.127240 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 44.7259 | 1.66453 | ||||||||
\(723\) | −8.52832 | −0.317172 | ||||||||
\(724\) | 9.64549 | 0.358472 | ||||||||
\(725\) | 53.5130 | 1.98742 | ||||||||
\(726\) | −10.9109 | −0.404940 | ||||||||
\(727\) | 9.08243 | 0.336849 | 0.168424 | − | 0.985715i | \(-0.446132\pi\) | ||||
0.168424 | + | 0.985715i | \(0.446132\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.65199 | 0.0981547 | ||||||||
\(731\) | −24.8124 | −0.917718 | ||||||||
\(732\) | 5.18293 | 0.191567 | ||||||||
\(733\) | 39.1874 | 1.44742 | 0.723710 | − | 0.690104i | \(-0.242435\pi\) | ||||
0.723710 | + | 0.690104i | \(0.242435\pi\) | |||||||
\(734\) | 15.5838 | 0.575208 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −4.54013 | −0.167238 | ||||||||
\(738\) | −0.817068 | −0.0300767 | ||||||||
\(739\) | 5.78325 | 0.212740 | 0.106370 | − | 0.994327i | \(-0.466077\pi\) | ||||
0.106370 | + | 0.994327i | \(0.466077\pi\) | |||||||
\(740\) | −12.1179 | −0.445462 | ||||||||
\(741\) | −37.6856 | −1.38441 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.6192 | −1.12331 | −0.561655 | − | 0.827371i | \(-0.689835\pi\) | ||||
−0.561655 | + | 0.827371i | \(0.689835\pi\) | |||||||
\(744\) | −9.98285 | −0.365989 | ||||||||
\(745\) | 26.5644 | 0.973244 | ||||||||
\(746\) | −18.4650 | −0.676050 | ||||||||
\(747\) | −0.884359 | −0.0323570 | ||||||||
\(748\) | −1.05971 | −0.0387468 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.65685 | 0.206559 | ||||||||
\(751\) | 7.75265 | 0.282898 | 0.141449 | − | 0.989946i | \(-0.454824\pi\) | ||||
0.141449 | + | 0.989946i | \(0.454824\pi\) | |||||||
\(752\) | 9.38571 | 0.342261 | ||||||||
\(753\) | 12.5024 | 0.455614 | ||||||||
\(754\) | 37.9496 | 1.38204 | ||||||||
\(755\) | −70.3985 | −2.56206 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.0617 | −1.16530 | −0.582652 | − | 0.812722i | \(-0.697985\pi\) | ||||
−0.582652 | + | 0.812722i | \(0.697985\pi\) | |||||||
\(758\) | 25.2691 | 0.917816 | ||||||||
\(759\) | −0.298573 | −0.0108375 | ||||||||
\(760\) | −27.2552 | −0.988648 | ||||||||
\(761\) | 27.4933 | 0.996632 | 0.498316 | − | 0.866996i | \(-0.333952\pi\) | ||||
0.498316 | + | 0.866996i | \(0.333952\pi\) | |||||||
\(762\) | −11.4820 | −0.415947 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.13612 | −0.0772820 | ||||||||
\(765\) | 12.1179 | 0.438123 | ||||||||
\(766\) | 20.6983 | 0.747861 | ||||||||
\(767\) | 47.3913 | 1.71120 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −30.3755 | −1.09537 | −0.547684 | − | 0.836685i | \(-0.684491\pi\) | ||||
−0.547684 | + | 0.836685i | \(0.684491\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.79614 | 0.208743 | ||||||||
\(772\) | 21.9496 | 0.789985 | ||||||||
\(773\) | −31.6645 | −1.13889 | −0.569447 | − | 0.822028i | \(-0.692842\pi\) | ||||
−0.569447 | + | 0.822028i | \(0.692842\pi\) | |||||||
\(774\) | −6.99088 | −0.251282 | ||||||||
\(775\) | −66.4544 | −2.38711 | ||||||||
\(776\) | −12.0345 | −0.432014 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.6638 | −0.669130 | ||||||||
\(779\) | 6.52253 | 0.233694 | ||||||||
\(780\) | 16.1179 | 0.577113 | ||||||||
\(781\) | 1.66537 | 0.0595915 | ||||||||
\(782\) | 3.54925 | 0.126921 | ||||||||
\(783\) | 8.03878 | 0.287283 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 78.3824 | 2.79759 | ||||||||
\(786\) | 14.7941 | 0.527689 | ||||||||
\(787\) | 15.0586 | 0.536782 | 0.268391 | − | 0.963310i | \(-0.413508\pi\) | ||||
0.268391 | + | 0.963310i | \(0.413508\pi\) | |||||||
\(788\) | 6.17490 | 0.219972 | ||||||||
\(789\) | −8.68629 | −0.309240 | ||||||||
\(790\) | −48.0691 | −1.71022 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.298573 | −0.0106093 | ||||||||
\(793\) | 24.4677 | 0.868873 | ||||||||
\(794\) | −23.4374 | −0.831762 | ||||||||
\(795\) | 27.8135 | 0.986444 | ||||||||
\(796\) | −21.4644 | −0.760784 | ||||||||
\(797\) | −9.68491 | −0.343057 | −0.171529 | − | 0.985179i | \(-0.554871\pi\) | ||||
−0.171529 | + | 0.985179i | \(0.554871\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.3122 | 1.17850 | ||||||||
\(800\) | 6.65685 | 0.235355 | ||||||||
\(801\) | 2.43469 | 0.0860255 | ||||||||
\(802\) | −6.24735 | −0.220601 | ||||||||
\(803\) | −0.231917 | −0.00818416 | ||||||||
\(804\) | 15.2061 | 0.536278 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −47.1272 | −1.65999 | ||||||||
\(807\) | 28.4713 | 1.00224 | ||||||||
\(808\) | −4.99088 | −0.175579 | ||||||||
\(809\) | −34.1649 | −1.20117 | −0.600586 | − | 0.799560i | \(-0.705066\pi\) | ||||
−0.600586 | + | 0.799560i | \(0.705066\pi\) | |||||||
\(810\) | 3.41421 | 0.119963 | ||||||||
\(811\) | −18.1649 | −0.637854 | −0.318927 | − | 0.947779i | \(-0.603323\pi\) | ||||
−0.318927 | + | 0.947779i | \(0.603323\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.46211 | −0.0863501 | ||||||||
\(814\) | 1.05971 | 0.0371428 | ||||||||
\(815\) | −15.8333 | −0.554616 | ||||||||
\(816\) | 3.54925 | 0.124248 | ||||||||
\(817\) | 55.8072 | 1.95245 | ||||||||
\(818\) | 29.9222 | 1.04621 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.78964 | −0.0974186 | ||||||||
\(821\) | 7.18610 | 0.250797 | 0.125398 | − | 0.992106i | \(-0.459979\pi\) | ||||
0.125398 | + | 0.992106i | \(0.459979\pi\) | |||||||
\(822\) | −2.90151 | −0.101202 | ||||||||
\(823\) | −31.5189 | −1.09868 | −0.549340 | − | 0.835599i | \(-0.685121\pi\) | ||||
−0.549340 | + | 0.835599i | \(0.685121\pi\) | |||||||
\(824\) | −8.86721 | −0.308904 | ||||||||
\(825\) | −1.98756 | −0.0691978 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.2594 | 1.08700 | 0.543498 | − | 0.839410i | \(-0.317099\pi\) | ||||
0.543498 | + | 0.839410i | \(0.317099\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −55.9338 | −1.94266 | −0.971331 | − | 0.237733i | \(-0.923596\pi\) | ||||
−0.971331 | + | 0.237733i | \(0.923596\pi\) | |||||||
\(830\) | −3.01939 | −0.104805 | ||||||||
\(831\) | −23.5192 | −0.815872 | ||||||||
\(832\) | 4.72082 | 0.163665 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 5.17157 | 0.179077 | ||||||||
\(835\) | 75.7889 | 2.62278 | ||||||||
\(836\) | 2.38346 | 0.0824338 | ||||||||
\(837\) | −9.98285 | −0.345058 | ||||||||
\(838\) | 29.5827 | 1.02192 | ||||||||
\(839\) | −28.3249 | −0.977885 | −0.488942 | − | 0.872316i | \(-0.662617\pi\) | ||||
−0.488942 | + | 0.872316i | \(0.662617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.6220 | 1.22835 | ||||||||
\(842\) | 0.970334 | 0.0334399 | ||||||||
\(843\) | −2.81236 | −0.0968629 | ||||||||
\(844\) | −9.23461 | −0.317868 | ||||||||
\(845\) | 31.7048 | 1.09068 | ||||||||
\(846\) | 9.38571 | 0.322687 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.14639 | 0.279748 | ||||||||
\(849\) | −17.6800 | −0.606777 | ||||||||
\(850\) | 23.6268 | 0.810393 | ||||||||
\(851\) | −3.54925 | −0.121667 | ||||||||
\(852\) | −5.57775 | −0.191091 | ||||||||
\(853\) | −29.6914 | −1.01661 | −0.508307 | − | 0.861176i | \(-0.669728\pi\) | ||||
−0.508307 | + | 0.861176i | \(0.669728\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.2552 | −0.932107 | ||||||||
\(856\) | −14.4956 | −0.495448 | ||||||||
\(857\) | −26.6467 | −0.910232 | −0.455116 | − | 0.890432i | \(-0.650402\pi\) | ||||
−0.455116 | + | 0.890432i | \(0.650402\pi\) | |||||||
\(858\) | −1.40951 | −0.0481198 | ||||||||
\(859\) | 28.5543 | 0.974261 | 0.487131 | − | 0.873329i | \(-0.338044\pi\) | ||||
0.487131 | + | 0.873329i | \(0.338044\pi\) | |||||||
\(860\) | −23.8684 | −0.813905 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23.2246 | 0.791032 | ||||||||
\(863\) | −6.82906 | −0.232464 | −0.116232 | − | 0.993222i | \(-0.537082\pi\) | ||||
−0.116232 | + | 0.993222i | \(0.537082\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 10.8139 | 0.367684 | ||||||||
\(866\) | 5.94724 | 0.202095 | ||||||||
\(867\) | −4.40285 | −0.149529 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.20364 | 0.142599 | ||||||||
\(870\) | 27.4461 | 0.930511 | ||||||||
\(871\) | 71.7852 | 2.43235 | ||||||||
\(872\) | 10.0345 | 0.339812 | ||||||||
\(873\) | −12.0345 | −0.407307 | ||||||||
\(874\) | −7.98285 | −0.270024 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.776751 | 0.0262440 | ||||||||
\(877\) | −46.7034 | −1.57706 | −0.788532 | − | 0.614994i | \(-0.789158\pi\) | ||||
−0.788532 | + | 0.614994i | \(0.789158\pi\) | |||||||
\(878\) | −17.8080 | −0.600989 | ||||||||
\(879\) | −8.97373 | −0.302677 | ||||||||
\(880\) | −1.01939 | −0.0343637 | ||||||||
\(881\) | 29.0805 | 0.979746 | 0.489873 | − | 0.871794i | \(-0.337043\pi\) | ||||
0.489873 | + | 0.871794i | \(0.337043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.0858 | 0.810550 | 0.405275 | − | 0.914195i | \(-0.367176\pi\) | ||||
0.405275 | + | 0.914195i | \(0.367176\pi\) | |||||||
\(884\) | 16.7553 | 0.563543 | ||||||||
\(885\) | 34.2745 | 1.15213 | ||||||||
\(886\) | 27.5983 | 0.927183 | ||||||||
\(887\) | −48.3629 | −1.62387 | −0.811934 | − | 0.583749i | \(-0.801585\pi\) | ||||
−0.811934 | + | 0.583749i | \(0.801585\pi\) | |||||||
\(888\) | −3.54925 | −0.119105 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.31255 | 0.278637 | ||||||||
\(891\) | −0.298573 | −0.0100026 | ||||||||
\(892\) | 17.0265 | 0.570089 | ||||||||
\(893\) | −74.9247 | −2.50726 | ||||||||
\(894\) | 7.78053 | 0.260220 | ||||||||
\(895\) | 46.4327 | 1.55208 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.72082 | 0.157624 | ||||||||
\(898\) | −36.9221 | −1.23211 | ||||||||
\(899\) | −80.2500 | −2.67649 | ||||||||
\(900\) | 6.65685 | 0.221895 | ||||||||
\(901\) | 28.9135 | 0.963250 | ||||||||
\(902\) | 0.243954 | 0.00812279 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.0194 | −0.499538 | ||||||||
\(905\) | 32.9318 | 1.09469 | ||||||||
\(906\) | −20.6192 | −0.685028 | ||||||||
\(907\) | −35.3606 | −1.17413 | −0.587065 | − | 0.809540i | \(-0.699717\pi\) | ||||
−0.587065 | + | 0.809540i | \(0.699717\pi\) | |||||||
\(908\) | −24.3563 | −0.808291 | ||||||||
\(909\) | −4.99088 | −0.165537 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.9926 | −1.02683 | −0.513416 | − | 0.858140i | \(-0.671620\pi\) | ||||
−0.513416 | + | 0.858140i | \(0.671620\pi\) | |||||||
\(912\) | −7.98285 | −0.264339 | ||||||||
\(913\) | 0.264046 | 0.00873864 | ||||||||
\(914\) | −14.5971 | −0.482831 | ||||||||
\(915\) | 17.6956 | 0.585000 | ||||||||
\(916\) | −24.1923 | −0.799335 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.54925 | 0.117143 | ||||||||
\(919\) | 27.9717 | 0.922702 | 0.461351 | − | 0.887218i | \(-0.347365\pi\) | ||||
0.461351 | + | 0.887218i | \(0.347365\pi\) | |||||||
\(920\) | 3.41421 | 0.112563 | ||||||||
\(921\) | 5.49648 | 0.181115 | ||||||||
\(922\) | −3.08668 | −0.101654 | ||||||||
\(923\) | −26.3316 | −0.866714 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.6268 | −0.776845 | ||||||||
\(926\) | −35.1190 | −1.15408 | ||||||||
\(927\) | −8.86721 | −0.291237 | ||||||||
\(928\) | 8.03878 | 0.263886 | ||||||||
\(929\) | −22.1696 | −0.727360 | −0.363680 | − | 0.931524i | \(-0.618480\pi\) | ||||
−0.363680 | + | 0.931524i | \(0.618480\pi\) | |||||||
\(930\) | −34.0836 | −1.11764 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −21.9109 | −0.717714 | ||||||||
\(933\) | −20.0277 | −0.655676 | ||||||||
\(934\) | 0.462114 | 0.0151208 | ||||||||
\(935\) | −3.61807 | −0.118324 | ||||||||
\(936\) | 4.72082 | 0.154305 | ||||||||
\(937\) | −32.8696 | −1.07380 | −0.536902 | − | 0.843645i | \(-0.680405\pi\) | ||||
−0.536902 | + | 0.843645i | \(0.680405\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.4004 | −0.600474 | ||||||||
\(940\) | 32.0448 | 1.04519 | ||||||||
\(941\) | −6.11920 | −0.199480 | −0.0997401 | − | 0.995014i | \(-0.531801\pi\) | ||||
−0.0997401 | + | 0.995014i | \(0.531801\pi\) | |||||||
\(942\) | 22.9577 | 0.748001 | ||||||||
\(943\) | −0.817068 | −0.0266074 | ||||||||
\(944\) | 10.0388 | 0.326735 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.08729 | 0.0678636 | ||||||||
\(947\) | 14.2943 | 0.464503 | 0.232251 | − | 0.972656i | \(-0.425391\pi\) | ||||
0.232251 | + | 0.972656i | \(0.425391\pi\) | |||||||
\(948\) | −14.0791 | −0.457268 | ||||||||
\(949\) | 3.66690 | 0.119033 | ||||||||
\(950\) | −53.1407 | −1.72411 | ||||||||
\(951\) | −21.6468 | −0.701946 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.54166 | 0.276692 | 0.138346 | − | 0.990384i | \(-0.455821\pi\) | ||||
0.138346 | + | 0.990384i | \(0.455821\pi\) | |||||||
\(954\) | 8.14639 | 0.263749 | ||||||||
\(955\) | −7.29316 | −0.236001 | ||||||||
\(956\) | −6.47926 | −0.209554 | ||||||||
\(957\) | −2.40016 | −0.0775862 | ||||||||
\(958\) | 19.3115 | 0.623928 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.41421 | 0.110193 | ||||||||
\(961\) | 68.6573 | 2.21475 | ||||||||
\(962\) | −16.7553 | −0.540214 | ||||||||
\(963\) | −14.4956 | −0.467113 | ||||||||
\(964\) | −8.52832 | −0.274679 | ||||||||
\(965\) | 74.9407 | 2.41243 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.5816 | 1.14423 | 0.572114 | − | 0.820174i | \(-0.306124\pi\) | ||||
0.572114 | + | 0.820174i | \(0.306124\pi\) | |||||||
\(968\) | −10.9109 | −0.350688 | ||||||||
\(969\) | −28.3331 | −0.910190 | ||||||||
\(970\) | −41.0884 | −1.31927 | ||||||||
\(971\) | −39.0732 | −1.25392 | −0.626959 | − | 0.779053i | \(-0.715700\pi\) | ||||
−0.626959 | + | 0.779053i | \(0.715700\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.4692 | −0.335455 | ||||||||
\(975\) | 31.4258 | 1.00643 | ||||||||
\(976\) | 5.18293 | 0.165902 | ||||||||
\(977\) | −12.1400 | −0.388392 | −0.194196 | − | 0.980963i | \(-0.562210\pi\) | ||||
−0.194196 | + | 0.980963i | \(0.562210\pi\) | |||||||
\(978\) | −4.63746 | −0.148290 | ||||||||
\(979\) | −0.726932 | −0.0232329 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0345 | 0.320378 | ||||||||
\(982\) | 12.2846 | 0.392017 | ||||||||
\(983\) | −56.4746 | −1.80126 | −0.900630 | − | 0.434587i | \(-0.856894\pi\) | ||||
−0.900630 | + | 0.434587i | \(0.856894\pi\) | |||||||
\(984\) | −0.817068 | −0.0260472 | ||||||||
\(985\) | 21.0824 | 0.671742 | ||||||||
\(986\) | 28.5316 | 0.908632 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −37.6856 | −1.19894 | ||||||||
\(989\) | −6.99088 | −0.222297 | ||||||||
\(990\) | −1.01939 | −0.0323984 | ||||||||
\(991\) | −48.3603 | −1.53622 | −0.768108 | − | 0.640321i | \(-0.778802\pi\) | ||||
−0.768108 | + | 0.640321i | \(0.778802\pi\) | |||||||
\(992\) | −9.98285 | −0.316956 | ||||||||
\(993\) | 6.34315 | 0.201294 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −73.2839 | −2.32326 | ||||||||
\(996\) | −0.884359 | −0.0280220 | ||||||||
\(997\) | −13.6999 | −0.433880 | −0.216940 | − | 0.976185i | \(-0.569608\pi\) | ||||
−0.216940 | + | 0.976185i | \(0.569608\pi\) | |||||||
\(998\) | −6.37188 | −0.201698 | ||||||||
\(999\) | −3.54925 | −0.112293 |
(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 | 6762.2.a.ct.1.3 | yes | 4 | |
7.6 | odd | 2 | 6762.2.a.ci.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.ci.1.1 | ✓ | 4 | 7.6 | odd | 2 | ||
6762.2.a.ct.1.3 | yes | 4 | 1.1 | even | 1 | trivial |