Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(1,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, 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("930.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
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 | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.56155 | −0.590211 | −0.295106 | − | 0.955465i | \(-0.595355\pi\) | ||||
−0.295106 | + | 0.955465i | \(0.595355\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.56155 | −0.470826 | −0.235413 | − | 0.971895i | \(-0.575644\pi\) | ||||
−0.235413 | + | 0.971895i | \(0.575644\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −1.56155 | −0.417343 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.12311 | 1.24254 | 0.621268 | − | 0.783598i | \(-0.286618\pi\) | ||||
0.621268 | + | 0.783598i | \(0.286618\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.68466 | 1.07473 | 0.537367 | − | 0.843348i | \(-0.319419\pi\) | ||||
0.537367 | + | 0.843348i | \(0.319419\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.56155 | 0.340759 | ||||||||
\(22\) | −1.56155 | −0.332924 | ||||||||
\(23\) | 5.56155 | 1.15966 | 0.579832 | − | 0.814736i | \(-0.303118\pi\) | ||||
0.579832 | + | 0.814736i | \(0.303118\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.56155 | −0.295106 | ||||||||
\(29\) | −1.12311 | −0.208555 | −0.104278 | − | 0.994548i | \(-0.533253\pi\) | ||||
−0.104278 | + | 0.994548i | \(0.533253\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.56155 | 0.271831 | ||||||||
\(34\) | 5.12311 | 0.878605 | ||||||||
\(35\) | −1.56155 | −0.263951 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.12311 | 0.842233 | 0.421117 | − | 0.907006i | \(-0.361638\pi\) | ||||
0.421117 | + | 0.907006i | \(0.361638\pi\) | |||||||
\(38\) | 4.68466 | 0.759952 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −1.12311 | −0.175400 | −0.0876998 | − | 0.996147i | \(-0.527952\pi\) | ||||
−0.0876998 | + | 0.996147i | \(0.527952\pi\) | |||||||
\(42\) | 1.56155 | 0.240953 | ||||||||
\(43\) | −7.80776 | −1.19067 | −0.595336 | − | 0.803477i | \(-0.702981\pi\) | ||||
−0.595336 | + | 0.803477i | \(0.702981\pi\) | |||||||
\(44\) | −1.56155 | −0.235413 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 5.56155 | 0.820006 | ||||||||
\(47\) | −3.12311 | −0.455552 | −0.227776 | − | 0.973714i | \(-0.573145\pi\) | ||||
−0.227776 | + | 0.973714i | \(0.573145\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −4.56155 | −0.651650 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −5.12311 | −0.717378 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 11.5616 | 1.58810 | 0.794051 | − | 0.607852i | \(-0.207968\pi\) | ||||
0.794051 | + | 0.607852i | \(0.207968\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −1.56155 | −0.210560 | ||||||||
\(56\) | −1.56155 | −0.208671 | ||||||||
\(57\) | −4.68466 | −0.620498 | ||||||||
\(58\) | −1.12311 | −0.147471 | ||||||||
\(59\) | −4.87689 | −0.634918 | −0.317459 | − | 0.948272i | \(-0.602830\pi\) | ||||
−0.317459 | + | 0.948272i | \(0.602830\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | −1.56155 | −0.196737 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 1.56155 | 0.192214 | ||||||||
\(67\) | 9.36932 | 1.14464 | 0.572322 | − | 0.820029i | \(-0.306043\pi\) | ||||
0.572322 | + | 0.820029i | \(0.306043\pi\) | |||||||
\(68\) | 5.12311 | 0.621268 | ||||||||
\(69\) | −5.56155 | −0.669532 | ||||||||
\(70\) | −1.56155 | −0.186641 | ||||||||
\(71\) | 4.68466 | 0.555967 | 0.277983 | − | 0.960586i | \(-0.410334\pi\) | ||||
0.277983 | + | 0.960586i | \(0.410334\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 9.80776 | 1.14791 | 0.573956 | − | 0.818886i | \(-0.305408\pi\) | ||||
0.573956 | + | 0.818886i | \(0.305408\pi\) | |||||||
\(74\) | 5.12311 | 0.595549 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 4.68466 | 0.537367 | ||||||||
\(77\) | 2.43845 | 0.277887 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | −16.6847 | −1.87717 | −0.938585 | − | 0.345047i | \(-0.887863\pi\) | ||||
−0.938585 | + | 0.345047i | \(0.887863\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.12311 | −0.124026 | ||||||||
\(83\) | −2.24621 | −0.246554 | −0.123277 | − | 0.992372i | \(-0.539340\pi\) | ||||
−0.123277 | + | 0.992372i | \(0.539340\pi\) | |||||||
\(84\) | 1.56155 | 0.170379 | ||||||||
\(85\) | 5.12311 | 0.555679 | ||||||||
\(86\) | −7.80776 | −0.841933 | ||||||||
\(87\) | 1.12311 | 0.120410 | ||||||||
\(88\) | −1.56155 | −0.166462 | ||||||||
\(89\) | −1.31534 | −0.139426 | −0.0697130 | − | 0.997567i | \(-0.522208\pi\) | ||||
−0.0697130 | + | 0.997567i | \(0.522208\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −3.12311 | −0.327390 | ||||||||
\(92\) | 5.56155 | 0.579832 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | −3.12311 | −0.322124 | ||||||||
\(95\) | 4.68466 | 0.480636 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | −4.56155 | −0.460786 | ||||||||
\(99\) | −1.56155 | −0.156942 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.56155 | 0.354388 | 0.177194 | − | 0.984176i | \(-0.443298\pi\) | ||||
0.177194 | + | 0.984176i | \(0.443298\pi\) | |||||||
\(102\) | −5.12311 | −0.507263 | ||||||||
\(103\) | −18.2462 | −1.79785 | −0.898926 | − | 0.438100i | \(-0.855652\pi\) | ||||
−0.898926 | + | 0.438100i | \(0.855652\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 1.56155 | 0.152392 | ||||||||
\(106\) | 11.5616 | 1.12296 | ||||||||
\(107\) | 1.56155 | 0.150961 | 0.0754805 | − | 0.997147i | \(-0.475951\pi\) | ||||
0.0754805 | + | 0.997147i | \(0.475951\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −19.3693 | −1.85524 | −0.927622 | − | 0.373520i | \(-0.878151\pi\) | ||||
−0.927622 | + | 0.373520i | \(0.878151\pi\) | |||||||
\(110\) | −1.56155 | −0.148888 | ||||||||
\(111\) | −5.12311 | −0.486264 | ||||||||
\(112\) | −1.56155 | −0.147553 | ||||||||
\(113\) | 10.6847 | 1.00513 | 0.502564 | − | 0.864540i | \(-0.332390\pi\) | ||||
0.502564 | + | 0.864540i | \(0.332390\pi\) | |||||||
\(114\) | −4.68466 | −0.438758 | ||||||||
\(115\) | 5.56155 | 0.518617 | ||||||||
\(116\) | −1.12311 | −0.104278 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | −4.87689 | −0.448955 | ||||||||
\(119\) | −8.00000 | −0.733359 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | 1.12311 | 0.101267 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.56155 | −0.139114 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 7.80776 | 0.687435 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | 9.36932 | 0.818601 | 0.409301 | − | 0.912400i | \(-0.365773\pi\) | ||||
0.409301 | + | 0.912400i | \(0.365773\pi\) | |||||||
\(132\) | 1.56155 | 0.135916 | ||||||||
\(133\) | −7.31534 | −0.634321 | ||||||||
\(134\) | 9.36932 | 0.809386 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 5.12311 | 0.439303 | ||||||||
\(137\) | 3.75379 | 0.320708 | 0.160354 | − | 0.987060i | \(-0.448736\pi\) | ||||
0.160354 | + | 0.987060i | \(0.448736\pi\) | |||||||
\(138\) | −5.56155 | −0.473431 | ||||||||
\(139\) | −8.87689 | −0.752928 | −0.376464 | − | 0.926431i | \(-0.622860\pi\) | ||||
−0.376464 | + | 0.926431i | \(0.622860\pi\) | |||||||
\(140\) | −1.56155 | −0.131975 | ||||||||
\(141\) | 3.12311 | 0.263013 | ||||||||
\(142\) | 4.68466 | 0.393128 | ||||||||
\(143\) | −3.12311 | −0.261167 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.12311 | −0.0932688 | ||||||||
\(146\) | 9.80776 | 0.811696 | ||||||||
\(147\) | 4.56155 | 0.376231 | ||||||||
\(148\) | 5.12311 | 0.421117 | ||||||||
\(149\) | −20.0540 | −1.64289 | −0.821443 | − | 0.570291i | \(-0.806830\pi\) | ||||
−0.821443 | + | 0.570291i | \(0.806830\pi\) | |||||||
\(150\) | −1.00000 | −0.0816497 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 4.68466 | 0.379976 | ||||||||
\(153\) | 5.12311 | 0.414179 | ||||||||
\(154\) | 2.43845 | 0.196496 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | −20.0540 | −1.60048 | −0.800241 | − | 0.599679i | \(-0.795295\pi\) | ||||
−0.800241 | + | 0.599679i | \(0.795295\pi\) | |||||||
\(158\) | −16.6847 | −1.32736 | ||||||||
\(159\) | −11.5616 | −0.916891 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −8.68466 | −0.684447 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 9.36932 | 0.733862 | 0.366931 | − | 0.930248i | \(-0.380409\pi\) | ||||
0.366931 | + | 0.930248i | \(0.380409\pi\) | |||||||
\(164\) | −1.12311 | −0.0876998 | ||||||||
\(165\) | 1.56155 | 0.121567 | ||||||||
\(166\) | −2.24621 | −0.174340 | ||||||||
\(167\) | −2.43845 | −0.188693 | −0.0943464 | − | 0.995539i | \(-0.530076\pi\) | ||||
−0.0943464 | + | 0.995539i | \(0.530076\pi\) | |||||||
\(168\) | 1.56155 | 0.120476 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 5.12311 | 0.392924 | ||||||||
\(171\) | 4.68466 | 0.358245 | ||||||||
\(172\) | −7.80776 | −0.595336 | ||||||||
\(173\) | −8.24621 | −0.626948 | −0.313474 | − | 0.949597i | \(-0.601493\pi\) | ||||
−0.313474 | + | 0.949597i | \(0.601493\pi\) | |||||||
\(174\) | 1.12311 | 0.0851424 | ||||||||
\(175\) | −1.56155 | −0.118042 | ||||||||
\(176\) | −1.56155 | −0.117706 | ||||||||
\(177\) | 4.87689 | 0.366570 | ||||||||
\(178\) | −1.31534 | −0.0985890 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 24.0540 | 1.78792 | 0.893959 | − | 0.448149i | \(-0.147917\pi\) | ||||
0.893959 | + | 0.448149i | \(0.147917\pi\) | |||||||
\(182\) | −3.12311 | −0.231500 | ||||||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | 5.56155 | 0.410003 | ||||||||
\(185\) | 5.12311 | 0.376658 | ||||||||
\(186\) | −1.00000 | −0.0733236 | ||||||||
\(187\) | −8.00000 | −0.585018 | ||||||||
\(188\) | −3.12311 | −0.227776 | ||||||||
\(189\) | 1.56155 | 0.113586 | ||||||||
\(190\) | 4.68466 | 0.339861 | ||||||||
\(191\) | 2.24621 | 0.162530 | 0.0812651 | − | 0.996693i | \(-0.474104\pi\) | ||||
0.0812651 | + | 0.996693i | \(0.474104\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −18.4924 | −1.33111 | −0.665557 | − | 0.746347i | \(-0.731806\pi\) | ||||
−0.665557 | + | 0.746347i | \(0.731806\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | −4.56155 | −0.325825 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | −1.56155 | −0.110975 | ||||||||
\(199\) | 3.80776 | 0.269925 | 0.134963 | − | 0.990851i | \(-0.456909\pi\) | ||||
0.134963 | + | 0.990851i | \(0.456909\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −9.36932 | −0.660861 | ||||||||
\(202\) | 3.56155 | 0.250590 | ||||||||
\(203\) | 1.75379 | 0.123092 | ||||||||
\(204\) | −5.12311 | −0.358689 | ||||||||
\(205\) | −1.12311 | −0.0784411 | ||||||||
\(206\) | −18.2462 | −1.27127 | ||||||||
\(207\) | 5.56155 | 0.386555 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | −7.31534 | −0.506013 | ||||||||
\(210\) | 1.56155 | 0.107757 | ||||||||
\(211\) | −11.3153 | −0.778980 | −0.389490 | − | 0.921031i | \(-0.627349\pi\) | ||||
−0.389490 | + | 0.921031i | \(0.627349\pi\) | |||||||
\(212\) | 11.5616 | 0.794051 | ||||||||
\(213\) | −4.68466 | −0.320988 | ||||||||
\(214\) | 1.56155 | 0.106746 | ||||||||
\(215\) | −7.80776 | −0.532485 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −1.56155 | −0.106005 | ||||||||
\(218\) | −19.3693 | −1.31186 | ||||||||
\(219\) | −9.80776 | −0.662747 | ||||||||
\(220\) | −1.56155 | −0.105280 | ||||||||
\(221\) | 10.2462 | 0.689235 | ||||||||
\(222\) | −5.12311 | −0.343840 | ||||||||
\(223\) | −12.8769 | −0.862301 | −0.431150 | − | 0.902280i | \(-0.641892\pi\) | ||||
−0.431150 | + | 0.902280i | \(0.641892\pi\) | |||||||
\(224\) | −1.56155 | −0.104336 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 10.6847 | 0.710733 | ||||||||
\(227\) | −4.68466 | −0.310932 | −0.155466 | − | 0.987841i | \(-0.549688\pi\) | ||||
−0.155466 | + | 0.987841i | \(0.549688\pi\) | |||||||
\(228\) | −4.68466 | −0.310249 | ||||||||
\(229\) | −12.4384 | −0.821956 | −0.410978 | − | 0.911645i | \(-0.634813\pi\) | ||||
−0.410978 | + | 0.911645i | \(0.634813\pi\) | |||||||
\(230\) | 5.56155 | 0.366718 | ||||||||
\(231\) | −2.43845 | −0.160438 | ||||||||
\(232\) | −1.12311 | −0.0737355 | ||||||||
\(233\) | 20.0540 | 1.31378 | 0.656890 | − | 0.753987i | \(-0.271872\pi\) | ||||
0.656890 | + | 0.753987i | \(0.271872\pi\) | |||||||
\(234\) | 2.00000 | 0.130744 | ||||||||
\(235\) | −3.12311 | −0.203729 | ||||||||
\(236\) | −4.87689 | −0.317459 | ||||||||
\(237\) | 16.6847 | 1.08379 | ||||||||
\(238\) | −8.00000 | −0.518563 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −4.24621 | −0.273523 | −0.136761 | − | 0.990604i | \(-0.543669\pi\) | ||||
−0.136761 | + | 0.990604i | \(0.543669\pi\) | |||||||
\(242\) | −8.56155 | −0.550357 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −4.56155 | −0.291427 | ||||||||
\(246\) | 1.12311 | 0.0716066 | ||||||||
\(247\) | 9.36932 | 0.596155 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | 2.24621 | 0.142348 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −16.4924 | −1.04099 | −0.520496 | − | 0.853864i | \(-0.674253\pi\) | ||||
−0.520496 | + | 0.853864i | \(0.674253\pi\) | |||||||
\(252\) | −1.56155 | −0.0983686 | ||||||||
\(253\) | −8.68466 | −0.546000 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.12311 | −0.320821 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.6847 | 0.666491 | 0.333245 | − | 0.942840i | \(-0.391856\pi\) | ||||
0.333245 | + | 0.942840i | \(0.391856\pi\) | |||||||
\(258\) | 7.80776 | 0.486090 | ||||||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | −1.12311 | −0.0695185 | ||||||||
\(262\) | 9.36932 | 0.578838 | ||||||||
\(263\) | 12.4924 | 0.770316 | 0.385158 | − | 0.922851i | \(-0.374147\pi\) | ||||
0.385158 | + | 0.922851i | \(0.374147\pi\) | |||||||
\(264\) | 1.56155 | 0.0961069 | ||||||||
\(265\) | 11.5616 | 0.710221 | ||||||||
\(266\) | −7.31534 | −0.448532 | ||||||||
\(267\) | 1.31534 | 0.0804976 | ||||||||
\(268\) | 9.36932 | 0.572322 | ||||||||
\(269\) | 16.2462 | 0.990549 | 0.495274 | − | 0.868737i | \(-0.335067\pi\) | ||||
0.495274 | + | 0.868737i | \(0.335067\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −10.0540 | −0.610736 | −0.305368 | − | 0.952234i | \(-0.598779\pi\) | ||||
−0.305368 | + | 0.952234i | \(0.598779\pi\) | |||||||
\(272\) | 5.12311 | 0.310634 | ||||||||
\(273\) | 3.12311 | 0.189019 | ||||||||
\(274\) | 3.75379 | 0.226775 | ||||||||
\(275\) | −1.56155 | −0.0941652 | ||||||||
\(276\) | −5.56155 | −0.334766 | ||||||||
\(277\) | 19.3693 | 1.16379 | 0.581895 | − | 0.813264i | \(-0.302312\pi\) | ||||
0.581895 | + | 0.813264i | \(0.302312\pi\) | |||||||
\(278\) | −8.87689 | −0.532401 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | −1.56155 | −0.0933206 | ||||||||
\(281\) | 13.1231 | 0.782859 | 0.391429 | − | 0.920208i | \(-0.371981\pi\) | ||||
0.391429 | + | 0.920208i | \(0.371981\pi\) | |||||||
\(282\) | 3.12311 | 0.185978 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 4.68466 | 0.277983 | ||||||||
\(285\) | −4.68466 | −0.277495 | ||||||||
\(286\) | −3.12311 | −0.184673 | ||||||||
\(287\) | 1.75379 | 0.103523 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 9.24621 | 0.543895 | ||||||||
\(290\) | −1.12311 | −0.0659510 | ||||||||
\(291\) | 6.00000 | 0.351726 | ||||||||
\(292\) | 9.80776 | 0.573956 | ||||||||
\(293\) | −6.49242 | −0.379291 | −0.189646 | − | 0.981853i | \(-0.560734\pi\) | ||||
−0.189646 | + | 0.981853i | \(0.560734\pi\) | |||||||
\(294\) | 4.56155 | 0.266035 | ||||||||
\(295\) | −4.87689 | −0.283944 | ||||||||
\(296\) | 5.12311 | 0.297774 | ||||||||
\(297\) | 1.56155 | 0.0906105 | ||||||||
\(298\) | −20.0540 | −1.16170 | ||||||||
\(299\) | 11.1231 | 0.643266 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 12.1922 | 0.702749 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.56155 | −0.204606 | ||||||||
\(304\) | 4.68466 | 0.268684 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | 5.12311 | 0.292868 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 2.43845 | 0.138943 | ||||||||
\(309\) | 18.2462 | 1.03799 | ||||||||
\(310\) | 1.00000 | 0.0567962 | ||||||||
\(311\) | −18.2462 | −1.03465 | −0.517324 | − | 0.855790i | \(-0.673072\pi\) | ||||
−0.517324 | + | 0.855790i | \(0.673072\pi\) | |||||||
\(312\) | −2.00000 | −0.113228 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | −20.0540 | −1.13171 | ||||||||
\(315\) | −1.56155 | −0.0879835 | ||||||||
\(316\) | −16.6847 | −0.938585 | ||||||||
\(317\) | 25.1231 | 1.41105 | 0.705527 | − | 0.708683i | \(-0.250710\pi\) | ||||
0.705527 | + | 0.708683i | \(0.250710\pi\) | |||||||
\(318\) | −11.5616 | −0.648340 | ||||||||
\(319\) | 1.75379 | 0.0981933 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −1.56155 | −0.0871574 | ||||||||
\(322\) | −8.68466 | −0.483977 | ||||||||
\(323\) | 24.0000 | 1.33540 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 9.36932 | 0.518918 | ||||||||
\(327\) | 19.3693 | 1.07113 | ||||||||
\(328\) | −1.12311 | −0.0620131 | ||||||||
\(329\) | 4.87689 | 0.268872 | ||||||||
\(330\) | 1.56155 | 0.0859607 | ||||||||
\(331\) | 10.2462 | 0.563183 | 0.281591 | − | 0.959534i | \(-0.409138\pi\) | ||||
0.281591 | + | 0.959534i | \(0.409138\pi\) | |||||||
\(332\) | −2.24621 | −0.123277 | ||||||||
\(333\) | 5.12311 | 0.280744 | ||||||||
\(334\) | −2.43845 | −0.133426 | ||||||||
\(335\) | 9.36932 | 0.511900 | ||||||||
\(336\) | 1.56155 | 0.0851897 | ||||||||
\(337\) | −10.0000 | −0.544735 | −0.272367 | − | 0.962193i | \(-0.587807\pi\) | ||||
−0.272367 | + | 0.962193i | \(0.587807\pi\) | |||||||
\(338\) | −9.00000 | −0.489535 | ||||||||
\(339\) | −10.6847 | −0.580311 | ||||||||
\(340\) | 5.12311 | 0.277839 | ||||||||
\(341\) | −1.56155 | −0.0845628 | ||||||||
\(342\) | 4.68466 | 0.253317 | ||||||||
\(343\) | 18.0540 | 0.974823 | ||||||||
\(344\) | −7.80776 | −0.420966 | ||||||||
\(345\) | −5.56155 | −0.299424 | ||||||||
\(346\) | −8.24621 | −0.443319 | ||||||||
\(347\) | −2.24621 | −0.120583 | −0.0602915 | − | 0.998181i | \(-0.519203\pi\) | ||||
−0.0602915 | + | 0.998181i | \(0.519203\pi\) | |||||||
\(348\) | 1.12311 | 0.0602048 | ||||||||
\(349\) | −19.3693 | −1.03682 | −0.518408 | − | 0.855133i | \(-0.673475\pi\) | ||||
−0.518408 | + | 0.855133i | \(0.673475\pi\) | |||||||
\(350\) | −1.56155 | −0.0834685 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | −1.56155 | −0.0832310 | ||||||||
\(353\) | 16.2462 | 0.864699 | 0.432349 | − | 0.901706i | \(-0.357685\pi\) | ||||
0.432349 | + | 0.901706i | \(0.357685\pi\) | |||||||
\(354\) | 4.87689 | 0.259204 | ||||||||
\(355\) | 4.68466 | 0.248636 | ||||||||
\(356\) | −1.31534 | −0.0697130 | ||||||||
\(357\) | 8.00000 | 0.423405 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −19.3153 | −1.01942 | −0.509712 | − | 0.860345i | \(-0.670248\pi\) | ||||
−0.509712 | + | 0.860345i | \(0.670248\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 2.94602 | 0.155054 | ||||||||
\(362\) | 24.0540 | 1.26425 | ||||||||
\(363\) | 8.56155 | 0.449365 | ||||||||
\(364\) | −3.12311 | −0.163695 | ||||||||
\(365\) | 9.80776 | 0.513362 | ||||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | −9.36932 | −0.489074 | −0.244537 | − | 0.969640i | \(-0.578636\pi\) | ||||
−0.244537 | + | 0.969640i | \(0.578636\pi\) | |||||||
\(368\) | 5.56155 | 0.289916 | ||||||||
\(369\) | −1.12311 | −0.0584665 | ||||||||
\(370\) | 5.12311 | 0.266338 | ||||||||
\(371\) | −18.0540 | −0.937316 | ||||||||
\(372\) | −1.00000 | −0.0518476 | ||||||||
\(373\) | 6.68466 | 0.346118 | 0.173059 | − | 0.984911i | \(-0.444635\pi\) | ||||
0.173059 | + | 0.984911i | \(0.444635\pi\) | |||||||
\(374\) | −8.00000 | −0.413670 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −3.12311 | −0.161062 | ||||||||
\(377\) | −2.24621 | −0.115686 | ||||||||
\(378\) | 1.56155 | 0.0803176 | ||||||||
\(379\) | 30.0540 | 1.54377 | 0.771885 | − | 0.635763i | \(-0.219314\pi\) | ||||
0.771885 | + | 0.635763i | \(0.219314\pi\) | |||||||
\(380\) | 4.68466 | 0.240318 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.24621 | 0.114926 | ||||||||
\(383\) | 6.24621 | 0.319166 | 0.159583 | − | 0.987184i | \(-0.448985\pi\) | ||||
0.159583 | + | 0.987184i | \(0.448985\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 2.43845 | 0.124275 | ||||||||
\(386\) | −18.4924 | −0.941240 | ||||||||
\(387\) | −7.80776 | −0.396891 | ||||||||
\(388\) | −6.00000 | −0.304604 | ||||||||
\(389\) | 24.2462 | 1.22933 | 0.614666 | − | 0.788788i | \(-0.289291\pi\) | ||||
0.614666 | + | 0.788788i | \(0.289291\pi\) | |||||||
\(390\) | −2.00000 | −0.101274 | ||||||||
\(391\) | 28.4924 | 1.44092 | ||||||||
\(392\) | −4.56155 | −0.230393 | ||||||||
\(393\) | −9.36932 | −0.472620 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | −16.6847 | −0.839496 | ||||||||
\(396\) | −1.56155 | −0.0784710 | ||||||||
\(397\) | −28.0540 | −1.40799 | −0.703994 | − | 0.710206i | \(-0.748602\pi\) | ||||
−0.703994 | + | 0.710206i | \(0.748602\pi\) | |||||||
\(398\) | 3.80776 | 0.190866 | ||||||||
\(399\) | 7.31534 | 0.366225 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.31534 | −0.0656850 | −0.0328425 | − | 0.999461i | \(-0.510456\pi\) | ||||
−0.0328425 | + | 0.999461i | \(0.510456\pi\) | |||||||
\(402\) | −9.36932 | −0.467299 | ||||||||
\(403\) | 2.00000 | 0.0996271 | ||||||||
\(404\) | 3.56155 | 0.177194 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 1.75379 | 0.0870391 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | −5.12311 | −0.253632 | ||||||||
\(409\) | −12.6307 | −0.624547 | −0.312274 | − | 0.949992i | \(-0.601091\pi\) | ||||
−0.312274 | + | 0.949992i | \(0.601091\pi\) | |||||||
\(410\) | −1.12311 | −0.0554662 | ||||||||
\(411\) | −3.75379 | −0.185161 | ||||||||
\(412\) | −18.2462 | −0.898926 | ||||||||
\(413\) | 7.61553 | 0.374736 | ||||||||
\(414\) | 5.56155 | 0.273335 | ||||||||
\(415\) | −2.24621 | −0.110262 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 8.87689 | 0.434703 | ||||||||
\(418\) | −7.31534 | −0.357805 | ||||||||
\(419\) | 22.2462 | 1.08680 | 0.543399 | − | 0.839474i | \(-0.317137\pi\) | ||||
0.543399 | + | 0.839474i | \(0.317137\pi\) | |||||||
\(420\) | 1.56155 | 0.0761960 | ||||||||
\(421\) | 18.4924 | 0.901266 | 0.450633 | − | 0.892709i | \(-0.351198\pi\) | ||||
0.450633 | + | 0.892709i | \(0.351198\pi\) | |||||||
\(422\) | −11.3153 | −0.550822 | ||||||||
\(423\) | −3.12311 | −0.151851 | ||||||||
\(424\) | 11.5616 | 0.561479 | ||||||||
\(425\) | 5.12311 | 0.248507 | ||||||||
\(426\) | −4.68466 | −0.226972 | ||||||||
\(427\) | −9.36932 | −0.453413 | ||||||||
\(428\) | 1.56155 | 0.0754805 | ||||||||
\(429\) | 3.12311 | 0.150785 | ||||||||
\(430\) | −7.80776 | −0.376524 | ||||||||
\(431\) | −13.7538 | −0.662497 | −0.331248 | − | 0.943544i | \(-0.607470\pi\) | ||||
−0.331248 | + | 0.943544i | \(0.607470\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −18.3002 | −0.879451 | −0.439725 | − | 0.898132i | \(-0.644924\pi\) | ||||
−0.439725 | + | 0.898132i | \(0.644924\pi\) | |||||||
\(434\) | −1.56155 | −0.0749569 | ||||||||
\(435\) | 1.12311 | 0.0538488 | ||||||||
\(436\) | −19.3693 | −0.927622 | ||||||||
\(437\) | 26.0540 | 1.24633 | ||||||||
\(438\) | −9.80776 | −0.468633 | ||||||||
\(439\) | −31.6155 | −1.50893 | −0.754463 | − | 0.656342i | \(-0.772103\pi\) | ||||
−0.754463 | + | 0.656342i | \(0.772103\pi\) | |||||||
\(440\) | −1.56155 | −0.0744441 | ||||||||
\(441\) | −4.56155 | −0.217217 | ||||||||
\(442\) | 10.2462 | 0.487363 | ||||||||
\(443\) | −14.0540 | −0.667725 | −0.333862 | − | 0.942622i | \(-0.608352\pi\) | ||||
−0.333862 | + | 0.942622i | \(0.608352\pi\) | |||||||
\(444\) | −5.12311 | −0.243132 | ||||||||
\(445\) | −1.31534 | −0.0623532 | ||||||||
\(446\) | −12.8769 | −0.609739 | ||||||||
\(447\) | 20.0540 | 0.948520 | ||||||||
\(448\) | −1.56155 | −0.0737764 | ||||||||
\(449\) | −22.4924 | −1.06148 | −0.530742 | − | 0.847534i | \(-0.678087\pi\) | ||||
−0.530742 | + | 0.847534i | \(0.678087\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 1.75379 | 0.0825827 | ||||||||
\(452\) | 10.6847 | 0.502564 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.68466 | −0.219862 | ||||||||
\(455\) | −3.12311 | −0.146413 | ||||||||
\(456\) | −4.68466 | −0.219379 | ||||||||
\(457\) | 24.7386 | 1.15722 | 0.578612 | − | 0.815603i | \(-0.303594\pi\) | ||||
0.578612 | + | 0.815603i | \(0.303594\pi\) | |||||||
\(458\) | −12.4384 | −0.581210 | ||||||||
\(459\) | −5.12311 | −0.239126 | ||||||||
\(460\) | 5.56155 | 0.259309 | ||||||||
\(461\) | −15.3693 | −0.715820 | −0.357910 | − | 0.933756i | \(-0.616511\pi\) | ||||
−0.357910 | + | 0.933756i | \(0.616511\pi\) | |||||||
\(462\) | −2.43845 | −0.113447 | ||||||||
\(463\) | −18.7386 | −0.870858 | −0.435429 | − | 0.900223i | \(-0.643403\pi\) | ||||
−0.435429 | + | 0.900223i | \(0.643403\pi\) | |||||||
\(464\) | −1.12311 | −0.0521389 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 20.0540 | 0.928982 | ||||||||
\(467\) | −26.2462 | −1.21453 | −0.607265 | − | 0.794499i | \(-0.707733\pi\) | ||||
−0.607265 | + | 0.794499i | \(0.707733\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −14.6307 | −0.675582 | ||||||||
\(470\) | −3.12311 | −0.144058 | ||||||||
\(471\) | 20.0540 | 0.924038 | ||||||||
\(472\) | −4.87689 | −0.224477 | ||||||||
\(473\) | 12.1922 | 0.560600 | ||||||||
\(474\) | 16.6847 | 0.766352 | ||||||||
\(475\) | 4.68466 | 0.214947 | ||||||||
\(476\) | −8.00000 | −0.366679 | ||||||||
\(477\) | 11.5616 | 0.529367 | ||||||||
\(478\) | 24.0000 | 1.09773 | ||||||||
\(479\) | 6.43845 | 0.294180 | 0.147090 | − | 0.989123i | \(-0.453009\pi\) | ||||
0.147090 | + | 0.989123i | \(0.453009\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 10.2462 | 0.467187 | ||||||||
\(482\) | −4.24621 | −0.193410 | ||||||||
\(483\) | 8.68466 | 0.395166 | ||||||||
\(484\) | −8.56155 | −0.389161 | ||||||||
\(485\) | −6.00000 | −0.272446 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 24.0000 | 1.08754 | 0.543772 | − | 0.839233i | \(-0.316996\pi\) | ||||
0.543772 | + | 0.839233i | \(0.316996\pi\) | |||||||
\(488\) | 6.00000 | 0.271607 | ||||||||
\(489\) | −9.36932 | −0.423695 | ||||||||
\(490\) | −4.56155 | −0.206070 | ||||||||
\(491\) | 2.93087 | 0.132268 | 0.0661341 | − | 0.997811i | \(-0.478933\pi\) | ||||
0.0661341 | + | 0.997811i | \(0.478933\pi\) | |||||||
\(492\) | 1.12311 | 0.0506335 | ||||||||
\(493\) | −5.75379 | −0.259138 | ||||||||
\(494\) | 9.36932 | 0.421545 | ||||||||
\(495\) | −1.56155 | −0.0701866 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −7.31534 | −0.328138 | ||||||||
\(498\) | 2.24621 | 0.100655 | ||||||||
\(499\) | 20.0000 | 0.895323 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 2.43845 | 0.108942 | ||||||||
\(502\) | −16.4924 | −0.736093 | ||||||||
\(503\) | 9.75379 | 0.434900 | 0.217450 | − | 0.976071i | \(-0.430226\pi\) | ||||
0.217450 | + | 0.976071i | \(0.430226\pi\) | |||||||
\(504\) | −1.56155 | −0.0695571 | ||||||||
\(505\) | 3.56155 | 0.158487 | ||||||||
\(506\) | −8.68466 | −0.386080 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.6155 | −0.958091 | −0.479046 | − | 0.877790i | \(-0.659017\pi\) | ||||
−0.479046 | + | 0.877790i | \(0.659017\pi\) | |||||||
\(510\) | −5.12311 | −0.226855 | ||||||||
\(511\) | −15.3153 | −0.677511 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.68466 | −0.206833 | ||||||||
\(514\) | 10.6847 | 0.471280 | ||||||||
\(515\) | −18.2462 | −0.804024 | ||||||||
\(516\) | 7.80776 | 0.343718 | ||||||||
\(517\) | 4.87689 | 0.214486 | ||||||||
\(518\) | −8.00000 | −0.351500 | ||||||||
\(519\) | 8.24621 | 0.361968 | ||||||||
\(520\) | 2.00000 | 0.0877058 | ||||||||
\(521\) | −15.7538 | −0.690186 | −0.345093 | − | 0.938568i | \(-0.612153\pi\) | ||||
−0.345093 | + | 0.938568i | \(0.612153\pi\) | |||||||
\(522\) | −1.12311 | −0.0491570 | ||||||||
\(523\) | 39.4233 | 1.72386 | 0.861930 | − | 0.507027i | \(-0.169256\pi\) | ||||
0.861930 | + | 0.507027i | \(0.169256\pi\) | |||||||
\(524\) | 9.36932 | 0.409301 | ||||||||
\(525\) | 1.56155 | 0.0681518 | ||||||||
\(526\) | 12.4924 | 0.544696 | ||||||||
\(527\) | 5.12311 | 0.223166 | ||||||||
\(528\) | 1.56155 | 0.0679579 | ||||||||
\(529\) | 7.93087 | 0.344820 | ||||||||
\(530\) | 11.5616 | 0.502202 | ||||||||
\(531\) | −4.87689 | −0.211639 | ||||||||
\(532\) | −7.31534 | −0.317160 | ||||||||
\(533\) | −2.24621 | −0.0972942 | ||||||||
\(534\) | 1.31534 | 0.0569204 | ||||||||
\(535\) | 1.56155 | 0.0675118 | ||||||||
\(536\) | 9.36932 | 0.404693 | ||||||||
\(537\) | 12.0000 | 0.517838 | ||||||||
\(538\) | 16.2462 | 0.700424 | ||||||||
\(539\) | 7.12311 | 0.306814 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 36.2462 | 1.55835 | 0.779173 | − | 0.626809i | \(-0.215639\pi\) | ||||
0.779173 | + | 0.626809i | \(0.215639\pi\) | |||||||
\(542\) | −10.0540 | −0.431855 | ||||||||
\(543\) | −24.0540 | −1.03225 | ||||||||
\(544\) | 5.12311 | 0.219651 | ||||||||
\(545\) | −19.3693 | −0.829690 | ||||||||
\(546\) | 3.12311 | 0.133657 | ||||||||
\(547\) | 35.1231 | 1.50176 | 0.750878 | − | 0.660441i | \(-0.229631\pi\) | ||||
0.750878 | + | 0.660441i | \(0.229631\pi\) | |||||||
\(548\) | 3.75379 | 0.160354 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | −1.56155 | −0.0665848 | ||||||||
\(551\) | −5.26137 | −0.224142 | ||||||||
\(552\) | −5.56155 | −0.236715 | ||||||||
\(553\) | 26.0540 | 1.10793 | ||||||||
\(554\) | 19.3693 | 0.822923 | ||||||||
\(555\) | −5.12311 | −0.217464 | ||||||||
\(556\) | −8.87689 | −0.376464 | ||||||||
\(557\) | −6.19224 | −0.262373 | −0.131187 | − | 0.991358i | \(-0.541879\pi\) | ||||
−0.131187 | + | 0.991358i | \(0.541879\pi\) | |||||||
\(558\) | 1.00000 | 0.0423334 | ||||||||
\(559\) | −15.6155 | −0.660466 | ||||||||
\(560\) | −1.56155 | −0.0659877 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 13.1231 | 0.553565 | ||||||||
\(563\) | −16.4924 | −0.695073 | −0.347536 | − | 0.937667i | \(-0.612982\pi\) | ||||
−0.347536 | + | 0.937667i | \(0.612982\pi\) | |||||||
\(564\) | 3.12311 | 0.131506 | ||||||||
\(565\) | 10.6847 | 0.449507 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.56155 | −0.0655791 | ||||||||
\(568\) | 4.68466 | 0.196564 | ||||||||
\(569\) | 10.1922 | 0.427281 | 0.213640 | − | 0.976912i | \(-0.431468\pi\) | ||||
0.213640 | + | 0.976912i | \(0.431468\pi\) | |||||||
\(570\) | −4.68466 | −0.196219 | ||||||||
\(571\) | 32.8769 | 1.37586 | 0.687928 | − | 0.725779i | \(-0.258521\pi\) | ||||
0.687928 | + | 0.725779i | \(0.258521\pi\) | |||||||
\(572\) | −3.12311 | −0.130584 | ||||||||
\(573\) | −2.24621 | −0.0938368 | ||||||||
\(574\) | 1.75379 | 0.0732017 | ||||||||
\(575\) | 5.56155 | 0.231933 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 6.87689 | 0.286289 | 0.143144 | − | 0.989702i | \(-0.454279\pi\) | ||||
0.143144 | + | 0.989702i | \(0.454279\pi\) | |||||||
\(578\) | 9.24621 | 0.384592 | ||||||||
\(579\) | 18.4924 | 0.768519 | ||||||||
\(580\) | −1.12311 | −0.0466344 | ||||||||
\(581\) | 3.50758 | 0.145519 | ||||||||
\(582\) | 6.00000 | 0.248708 | ||||||||
\(583\) | −18.0540 | −0.747719 | ||||||||
\(584\) | 9.80776 | 0.405848 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | −6.49242 | −0.268200 | ||||||||
\(587\) | 32.4924 | 1.34111 | 0.670553 | − | 0.741862i | \(-0.266057\pi\) | ||||
0.670553 | + | 0.741862i | \(0.266057\pi\) | |||||||
\(588\) | 4.56155 | 0.188115 | ||||||||
\(589\) | 4.68466 | 0.193028 | ||||||||
\(590\) | −4.87689 | −0.200779 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | 5.12311 | 0.210558 | ||||||||
\(593\) | −30.0000 | −1.23195 | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | 1.56155 | 0.0640713 | ||||||||
\(595\) | −8.00000 | −0.327968 | ||||||||
\(596\) | −20.0540 | −0.821443 | ||||||||
\(597\) | −3.80776 | −0.155841 | ||||||||
\(598\) | 11.1231 | 0.454858 | ||||||||
\(599\) | −23.4233 | −0.957050 | −0.478525 | − | 0.878074i | \(-0.658828\pi\) | ||||
−0.478525 | + | 0.878074i | \(0.658828\pi\) | |||||||
\(600\) | −1.00000 | −0.0408248 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | 12.1922 | 0.496918 | ||||||||
\(603\) | 9.36932 | 0.381548 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.56155 | −0.348077 | ||||||||
\(606\) | −3.56155 | −0.144678 | ||||||||
\(607\) | −30.0540 | −1.21985 | −0.609927 | − | 0.792458i | \(-0.708801\pi\) | ||||
−0.609927 | + | 0.792458i | \(0.708801\pi\) | |||||||
\(608\) | 4.68466 | 0.189988 | ||||||||
\(609\) | −1.75379 | −0.0710671 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −6.24621 | −0.252695 | ||||||||
\(612\) | 5.12311 | 0.207089 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.12311 | 0.0452880 | ||||||||
\(616\) | 2.43845 | 0.0982478 | ||||||||
\(617\) | −19.5616 | −0.787518 | −0.393759 | − | 0.919214i | \(-0.628826\pi\) | ||||
−0.393759 | + | 0.919214i | \(0.628826\pi\) | |||||||
\(618\) | 18.2462 | 0.733970 | ||||||||
\(619\) | −13.3693 | −0.537358 | −0.268679 | − | 0.963230i | \(-0.586587\pi\) | ||||
−0.268679 | + | 0.963230i | \(0.586587\pi\) | |||||||
\(620\) | 1.00000 | 0.0401610 | ||||||||
\(621\) | −5.56155 | −0.223177 | ||||||||
\(622\) | −18.2462 | −0.731606 | ||||||||
\(623\) | 2.05398 | 0.0822908 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | 7.31534 | 0.292147 | ||||||||
\(628\) | −20.0540 | −0.800241 | ||||||||
\(629\) | 26.2462 | 1.04650 | ||||||||
\(630\) | −1.56155 | −0.0622138 | ||||||||
\(631\) | −24.3002 | −0.967375 | −0.483688 | − | 0.875241i | \(-0.660703\pi\) | ||||
−0.483688 | + | 0.875241i | \(0.660703\pi\) | |||||||
\(632\) | −16.6847 | −0.663680 | ||||||||
\(633\) | 11.3153 | 0.449744 | ||||||||
\(634\) | 25.1231 | 0.997766 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.5616 | −0.458445 | ||||||||
\(637\) | −9.12311 | −0.361471 | ||||||||
\(638\) | 1.75379 | 0.0694332 | ||||||||
\(639\) | 4.68466 | 0.185322 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −38.4924 | −1.52036 | −0.760180 | − | 0.649713i | \(-0.774889\pi\) | ||||
−0.760180 | + | 0.649713i | \(0.774889\pi\) | |||||||
\(642\) | −1.56155 | −0.0616296 | ||||||||
\(643\) | 30.0540 | 1.18521 | 0.592607 | − | 0.805492i | \(-0.298099\pi\) | ||||
0.592607 | + | 0.805492i | \(0.298099\pi\) | |||||||
\(644\) | −8.68466 | −0.342223 | ||||||||
\(645\) | 7.80776 | 0.307430 | ||||||||
\(646\) | 24.0000 | 0.944267 | ||||||||
\(647\) | −17.0691 | −0.671057 | −0.335528 | − | 0.942030i | \(-0.608915\pi\) | ||||
−0.335528 | + | 0.942030i | \(0.608915\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 7.61553 | 0.298936 | ||||||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 1.56155 | 0.0612021 | ||||||||
\(652\) | 9.36932 | 0.366931 | ||||||||
\(653\) | 23.7538 | 0.929558 | 0.464779 | − | 0.885427i | \(-0.346134\pi\) | ||||
0.464779 | + | 0.885427i | \(0.346134\pi\) | |||||||
\(654\) | 19.3693 | 0.757400 | ||||||||
\(655\) | 9.36932 | 0.366090 | ||||||||
\(656\) | −1.12311 | −0.0438499 | ||||||||
\(657\) | 9.80776 | 0.382637 | ||||||||
\(658\) | 4.87689 | 0.190121 | ||||||||
\(659\) | 18.7386 | 0.729954 | 0.364977 | − | 0.931017i | \(-0.381077\pi\) | ||||
0.364977 | + | 0.931017i | \(0.381077\pi\) | |||||||
\(660\) | 1.56155 | 0.0607834 | ||||||||
\(661\) | −6.49242 | −0.252526 | −0.126263 | − | 0.991997i | \(-0.540298\pi\) | ||||
−0.126263 | + | 0.991997i | \(0.540298\pi\) | |||||||
\(662\) | 10.2462 | 0.398230 | ||||||||
\(663\) | −10.2462 | −0.397930 | ||||||||
\(664\) | −2.24621 | −0.0871699 | ||||||||
\(665\) | −7.31534 | −0.283677 | ||||||||
\(666\) | 5.12311 | 0.198516 | ||||||||
\(667\) | −6.24621 | −0.241854 | ||||||||
\(668\) | −2.43845 | −0.0943464 | ||||||||
\(669\) | 12.8769 | 0.497849 | ||||||||
\(670\) | 9.36932 | 0.361968 | ||||||||
\(671\) | −9.36932 | −0.361698 | ||||||||
\(672\) | 1.56155 | 0.0602382 | ||||||||
\(673\) | 28.2462 | 1.08881 | 0.544406 | − | 0.838822i | \(-0.316755\pi\) | ||||
0.544406 | + | 0.838822i | \(0.316755\pi\) | |||||||
\(674\) | −10.0000 | −0.385186 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −29.4233 | −1.13083 | −0.565414 | − | 0.824807i | \(-0.691284\pi\) | ||||
−0.565414 | + | 0.824807i | \(0.691284\pi\) | |||||||
\(678\) | −10.6847 | −0.410342 | ||||||||
\(679\) | 9.36932 | 0.359561 | ||||||||
\(680\) | 5.12311 | 0.196462 | ||||||||
\(681\) | 4.68466 | 0.179517 | ||||||||
\(682\) | −1.56155 | −0.0597949 | ||||||||
\(683\) | 19.3153 | 0.739081 | 0.369541 | − | 0.929215i | \(-0.379515\pi\) | ||||
0.369541 | + | 0.929215i | \(0.379515\pi\) | |||||||
\(684\) | 4.68466 | 0.179122 | ||||||||
\(685\) | 3.75379 | 0.143425 | ||||||||
\(686\) | 18.0540 | 0.689304 | ||||||||
\(687\) | 12.4384 | 0.474556 | ||||||||
\(688\) | −7.80776 | −0.297668 | ||||||||
\(689\) | 23.1231 | 0.880920 | ||||||||
\(690\) | −5.56155 | −0.211725 | ||||||||
\(691\) | −22.0540 | −0.838973 | −0.419486 | − | 0.907762i | \(-0.637790\pi\) | ||||
−0.419486 | + | 0.907762i | \(0.637790\pi\) | |||||||
\(692\) | −8.24621 | −0.313474 | ||||||||
\(693\) | 2.43845 | 0.0926289 | ||||||||
\(694\) | −2.24621 | −0.0852650 | ||||||||
\(695\) | −8.87689 | −0.336720 | ||||||||
\(696\) | 1.12311 | 0.0425712 | ||||||||
\(697\) | −5.75379 | −0.217940 | ||||||||
\(698\) | −19.3693 | −0.733139 | ||||||||
\(699\) | −20.0540 | −0.758511 | ||||||||
\(700\) | −1.56155 | −0.0590211 | ||||||||
\(701\) | 25.8078 | 0.974746 | 0.487373 | − | 0.873194i | \(-0.337955\pi\) | ||||
0.487373 | + | 0.873194i | \(0.337955\pi\) | |||||||
\(702\) | −2.00000 | −0.0754851 | ||||||||
\(703\) | 24.0000 | 0.905177 | ||||||||
\(704\) | −1.56155 | −0.0588532 | ||||||||
\(705\) | 3.12311 | 0.117623 | ||||||||
\(706\) | 16.2462 | 0.611434 | ||||||||
\(707\) | −5.56155 | −0.209164 | ||||||||
\(708\) | 4.87689 | 0.183285 | ||||||||
\(709\) | −20.0540 | −0.753143 | −0.376571 | − | 0.926388i | \(-0.622897\pi\) | ||||
−0.376571 | + | 0.926388i | \(0.622897\pi\) | |||||||
\(710\) | 4.68466 | 0.175812 | ||||||||
\(711\) | −16.6847 | −0.625724 | ||||||||
\(712\) | −1.31534 | −0.0492945 | ||||||||
\(713\) | 5.56155 | 0.208282 | ||||||||
\(714\) | 8.00000 | 0.299392 | ||||||||
\(715\) | −3.12311 | −0.116798 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | −24.0000 | −0.896296 | ||||||||
\(718\) | −19.3153 | −0.720842 | ||||||||
\(719\) | −43.1231 | −1.60822 | −0.804110 | − | 0.594480i | \(-0.797358\pi\) | ||||
−0.804110 | + | 0.594480i | \(0.797358\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 28.4924 | 1.06111 | ||||||||
\(722\) | 2.94602 | 0.109640 | ||||||||
\(723\) | 4.24621 | 0.157918 | ||||||||
\(724\) | 24.0540 | 0.893959 | ||||||||
\(725\) | −1.12311 | −0.0417111 | ||||||||
\(726\) | 8.56155 | 0.317749 | ||||||||
\(727\) | −14.0540 | −0.521233 | −0.260617 | − | 0.965442i | \(-0.583926\pi\) | ||||
−0.260617 | + | 0.965442i | \(0.583926\pi\) | |||||||
\(728\) | −3.12311 | −0.115750 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.80776 | 0.363002 | ||||||||
\(731\) | −40.0000 | −1.47945 | ||||||||
\(732\) | −6.00000 | −0.221766 | ||||||||
\(733\) | 26.4924 | 0.978520 | 0.489260 | − | 0.872138i | \(-0.337267\pi\) | ||||
0.489260 | + | 0.872138i | \(0.337267\pi\) | |||||||
\(734\) | −9.36932 | −0.345828 | ||||||||
\(735\) | 4.56155 | 0.168255 | ||||||||
\(736\) | 5.56155 | 0.205002 | ||||||||
\(737\) | −14.6307 | −0.538928 | ||||||||
\(738\) | −1.12311 | −0.0413421 | ||||||||
\(739\) | −12.9848 | −0.477655 | −0.238828 | − | 0.971062i | \(-0.576763\pi\) | ||||
−0.238828 | + | 0.971062i | \(0.576763\pi\) | |||||||
\(740\) | 5.12311 | 0.188329 | ||||||||
\(741\) | −9.36932 | −0.344190 | ||||||||
\(742\) | −18.0540 | −0.662782 | ||||||||
\(743\) | 11.4233 | 0.419080 | 0.209540 | − | 0.977800i | \(-0.432803\pi\) | ||||
0.209540 | + | 0.977800i | \(0.432803\pi\) | |||||||
\(744\) | −1.00000 | −0.0366618 | ||||||||
\(745\) | −20.0540 | −0.734721 | ||||||||
\(746\) | 6.68466 | 0.244743 | ||||||||
\(747\) | −2.24621 | −0.0821846 | ||||||||
\(748\) | −8.00000 | −0.292509 | ||||||||
\(749\) | −2.43845 | −0.0890989 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 36.8769 | 1.34566 | 0.672828 | − | 0.739798i | \(-0.265079\pi\) | ||||
0.672828 | + | 0.739798i | \(0.265079\pi\) | |||||||
\(752\) | −3.12311 | −0.113888 | ||||||||
\(753\) | 16.4924 | 0.601017 | ||||||||
\(754\) | −2.24621 | −0.0818022 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.56155 | 0.0567931 | ||||||||
\(757\) | 10.0000 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(758\) | 30.0540 | 1.09161 | ||||||||
\(759\) | 8.68466 | 0.315233 | ||||||||
\(760\) | 4.68466 | 0.169930 | ||||||||
\(761\) | 41.4233 | 1.50159 | 0.750797 | − | 0.660533i | \(-0.229670\pi\) | ||||
0.750797 | + | 0.660533i | \(0.229670\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.2462 | 1.09499 | ||||||||
\(764\) | 2.24621 | 0.0812651 | ||||||||
\(765\) | 5.12311 | 0.185226 | ||||||||
\(766\) | 6.24621 | 0.225685 | ||||||||
\(767\) | −9.75379 | −0.352189 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −16.4384 | −0.592786 | −0.296393 | − | 0.955066i | \(-0.595784\pi\) | ||||
−0.296393 | + | 0.955066i | \(0.595784\pi\) | |||||||
\(770\) | 2.43845 | 0.0878755 | ||||||||
\(771\) | −10.6847 | −0.384799 | ||||||||
\(772\) | −18.4924 | −0.665557 | ||||||||
\(773\) | −15.5616 | −0.559710 | −0.279855 | − | 0.960042i | \(-0.590286\pi\) | ||||
−0.279855 | + | 0.960042i | \(0.590286\pi\) | |||||||
\(774\) | −7.80776 | −0.280644 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 8.00000 | 0.286998 | ||||||||
\(778\) | 24.2462 | 0.869269 | ||||||||
\(779\) | −5.26137 | −0.188508 | ||||||||
\(780\) | −2.00000 | −0.0716115 | ||||||||
\(781\) | −7.31534 | −0.261764 | ||||||||
\(782\) | 28.4924 | 1.01889 | ||||||||
\(783\) | 1.12311 | 0.0401365 | ||||||||
\(784\) | −4.56155 | −0.162913 | ||||||||
\(785\) | −20.0540 | −0.715757 | ||||||||
\(786\) | −9.36932 | −0.334192 | ||||||||
\(787\) | 10.9309 | 0.389643 | 0.194822 | − | 0.980839i | \(-0.437587\pi\) | ||||
0.194822 | + | 0.980839i | \(0.437587\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | −12.4924 | −0.444742 | ||||||||
\(790\) | −16.6847 | −0.593614 | ||||||||
\(791\) | −16.6847 | −0.593238 | ||||||||
\(792\) | −1.56155 | −0.0554874 | ||||||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | −28.0540 | −0.995598 | ||||||||
\(795\) | −11.5616 | −0.410046 | ||||||||
\(796\) | 3.80776 | 0.134963 | ||||||||
\(797\) | 38.9848 | 1.38091 | 0.690457 | − | 0.723373i | \(-0.257409\pi\) | ||||
0.690457 | + | 0.723373i | \(0.257409\pi\) | |||||||
\(798\) | 7.31534 | 0.258960 | ||||||||
\(799\) | −16.0000 | −0.566039 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −1.31534 | −0.0464753 | ||||||||
\(802\) | −1.31534 | −0.0464463 | ||||||||
\(803\) | −15.3153 | −0.540467 | ||||||||
\(804\) | −9.36932 | −0.330430 | ||||||||
\(805\) | −8.68466 | −0.306094 | ||||||||
\(806\) | 2.00000 | 0.0704470 | ||||||||
\(807\) | −16.2462 | −0.571894 | ||||||||
\(808\) | 3.56155 | 0.125295 | ||||||||
\(809\) | −25.3153 | −0.890040 | −0.445020 | − | 0.895521i | \(-0.646803\pi\) | ||||
−0.445020 | + | 0.895521i | \(0.646803\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 53.6695 | 1.88459 | 0.942296 | − | 0.334782i | \(-0.108663\pi\) | ||||
0.942296 | + | 0.334782i | \(0.108663\pi\) | |||||||
\(812\) | 1.75379 | 0.0615459 | ||||||||
\(813\) | 10.0540 | 0.352608 | ||||||||
\(814\) | −8.00000 | −0.280400 | ||||||||
\(815\) | 9.36932 | 0.328193 | ||||||||
\(816\) | −5.12311 | −0.179345 | ||||||||
\(817\) | −36.5767 | −1.27966 | ||||||||
\(818\) | −12.6307 | −0.441621 | ||||||||
\(819\) | −3.12311 | −0.109130 | ||||||||
\(820\) | −1.12311 | −0.0392205 | ||||||||
\(821\) | −21.6155 | −0.754387 | −0.377194 | − | 0.926134i | \(-0.623111\pi\) | ||||
−0.377194 | + | 0.926134i | \(0.623111\pi\) | |||||||
\(822\) | −3.75379 | −0.130928 | ||||||||
\(823\) | 15.6155 | 0.544323 | 0.272162 | − | 0.962252i | \(-0.412261\pi\) | ||||
0.272162 | + | 0.962252i | \(0.412261\pi\) | |||||||
\(824\) | −18.2462 | −0.635637 | ||||||||
\(825\) | 1.56155 | 0.0543663 | ||||||||
\(826\) | 7.61553 | 0.264978 | ||||||||
\(827\) | 18.2462 | 0.634483 | 0.317241 | − | 0.948345i | \(-0.397243\pi\) | ||||
0.317241 | + | 0.948345i | \(0.397243\pi\) | |||||||
\(828\) | 5.56155 | 0.193277 | ||||||||
\(829\) | −37.4233 | −1.29976 | −0.649882 | − | 0.760035i | \(-0.725182\pi\) | ||||
−0.649882 | + | 0.760035i | \(0.725182\pi\) | |||||||
\(830\) | −2.24621 | −0.0779671 | ||||||||
\(831\) | −19.3693 | −0.671914 | ||||||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −23.3693 | −0.809699 | ||||||||
\(834\) | 8.87689 | 0.307382 | ||||||||
\(835\) | −2.43845 | −0.0843859 | ||||||||
\(836\) | −7.31534 | −0.253006 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 22.2462 | 0.768483 | ||||||||
\(839\) | 34.9309 | 1.20595 | 0.602974 | − | 0.797761i | \(-0.293982\pi\) | ||||
0.602974 | + | 0.797761i | \(0.293982\pi\) | |||||||
\(840\) | 1.56155 | 0.0538787 | ||||||||
\(841\) | −27.7386 | −0.956505 | ||||||||
\(842\) | 18.4924 | 0.637291 | ||||||||
\(843\) | −13.1231 | −0.451984 | ||||||||
\(844\) | −11.3153 | −0.389490 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | −3.12311 | −0.107375 | ||||||||
\(847\) | 13.3693 | 0.459375 | ||||||||
\(848\) | 11.5616 | 0.397025 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.12311 | 0.175721 | ||||||||
\(851\) | 28.4924 | 0.976708 | ||||||||
\(852\) | −4.68466 | −0.160494 | ||||||||
\(853\) | −38.7926 | −1.32823 | −0.664117 | − | 0.747629i | \(-0.731192\pi\) | ||||
−0.664117 | + | 0.747629i | \(0.731192\pi\) | |||||||
\(854\) | −9.36932 | −0.320611 | ||||||||
\(855\) | 4.68466 | 0.160212 | ||||||||
\(856\) | 1.56155 | 0.0533728 | ||||||||
\(857\) | −53.2311 | −1.81834 | −0.909169 | − | 0.416427i | \(-0.863282\pi\) | ||||
−0.909169 | + | 0.416427i | \(0.863282\pi\) | |||||||
\(858\) | 3.12311 | 0.106621 | ||||||||
\(859\) | −22.7386 | −0.775832 | −0.387916 | − | 0.921695i | \(-0.626805\pi\) | ||||
−0.387916 | + | 0.921695i | \(0.626805\pi\) | |||||||
\(860\) | −7.80776 | −0.266243 | ||||||||
\(861\) | −1.75379 | −0.0597690 | ||||||||
\(862\) | −13.7538 | −0.468456 | ||||||||
\(863\) | −30.5464 | −1.03981 | −0.519906 | − | 0.854224i | \(-0.674033\pi\) | ||||
−0.519906 | + | 0.854224i | \(0.674033\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −8.24621 | −0.280380 | ||||||||
\(866\) | −18.3002 | −0.621866 | ||||||||
\(867\) | −9.24621 | −0.314018 | ||||||||
\(868\) | −1.56155 | −0.0530026 | ||||||||
\(869\) | 26.0540 | 0.883821 | ||||||||
\(870\) | 1.12311 | 0.0380768 | ||||||||
\(871\) | 18.7386 | 0.634934 | ||||||||
\(872\) | −19.3693 | −0.655928 | ||||||||
\(873\) | −6.00000 | −0.203069 | ||||||||
\(874\) | 26.0540 | 0.881289 | ||||||||
\(875\) | −1.56155 | −0.0527901 | ||||||||
\(876\) | −9.80776 | −0.331374 | ||||||||
\(877\) | −50.0000 | −1.68838 | −0.844190 | − | 0.536044i | \(-0.819918\pi\) | ||||
−0.844190 | + | 0.536044i | \(0.819918\pi\) | |||||||
\(878\) | −31.6155 | −1.06697 | ||||||||
\(879\) | 6.49242 | 0.218984 | ||||||||
\(880\) | −1.56155 | −0.0526399 | ||||||||
\(881\) | 42.4924 | 1.43161 | 0.715803 | − | 0.698302i | \(-0.246061\pi\) | ||||
0.715803 | + | 0.698302i | \(0.246061\pi\) | |||||||
\(882\) | −4.56155 | −0.153595 | ||||||||
\(883\) | −31.4233 | −1.05748 | −0.528739 | − | 0.848784i | \(-0.677335\pi\) | ||||
−0.528739 | + | 0.848784i | \(0.677335\pi\) | |||||||
\(884\) | 10.2462 | 0.344617 | ||||||||
\(885\) | 4.87689 | 0.163935 | ||||||||
\(886\) | −14.0540 | −0.472153 | ||||||||
\(887\) | −57.3693 | −1.92627 | −0.963137 | − | 0.269013i | \(-0.913303\pi\) | ||||
−0.963137 | + | 0.269013i | \(0.913303\pi\) | |||||||
\(888\) | −5.12311 | −0.171920 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.31534 | −0.0440903 | ||||||||
\(891\) | −1.56155 | −0.0523140 | ||||||||
\(892\) | −12.8769 | −0.431150 | ||||||||
\(893\) | −14.6307 | −0.489597 | ||||||||
\(894\) | 20.0540 | 0.670705 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | −1.56155 | −0.0521678 | ||||||||
\(897\) | −11.1231 | −0.371390 | ||||||||
\(898\) | −22.4924 | −0.750582 | ||||||||
\(899\) | −1.12311 | −0.0374577 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 59.2311 | 1.97327 | ||||||||
\(902\) | 1.75379 | 0.0583948 | ||||||||
\(903\) | −12.1922 | −0.405732 | ||||||||
\(904\) | 10.6847 | 0.355366 | ||||||||
\(905\) | 24.0540 | 0.799581 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0000 | 0.796907 | 0.398453 | − | 0.917189i | \(-0.369547\pi\) | ||||
0.398453 | + | 0.917189i | \(0.369547\pi\) | |||||||
\(908\) | −4.68466 | −0.155466 | ||||||||
\(909\) | 3.56155 | 0.118129 | ||||||||
\(910\) | −3.12311 | −0.103530 | ||||||||
\(911\) | −44.4924 | −1.47410 | −0.737050 | − | 0.675838i | \(-0.763782\pi\) | ||||
−0.737050 | + | 0.675838i | \(0.763782\pi\) | |||||||
\(912\) | −4.68466 | −0.155125 | ||||||||
\(913\) | 3.50758 | 0.116084 | ||||||||
\(914\) | 24.7386 | 0.818281 | ||||||||
\(915\) | −6.00000 | −0.198354 | ||||||||
\(916\) | −12.4384 | −0.410978 | ||||||||
\(917\) | −14.6307 | −0.483148 | ||||||||
\(918\) | −5.12311 | −0.169088 | ||||||||
\(919\) | 39.6155 | 1.30680 | 0.653398 | − | 0.757015i | \(-0.273343\pi\) | ||||
0.653398 | + | 0.757015i | \(0.273343\pi\) | |||||||
\(920\) | 5.56155 | 0.183359 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.3693 | −0.506161 | ||||||||
\(923\) | 9.36932 | 0.308395 | ||||||||
\(924\) | −2.43845 | −0.0802190 | ||||||||
\(925\) | 5.12311 | 0.168447 | ||||||||
\(926\) | −18.7386 | −0.615790 | ||||||||
\(927\) | −18.2462 | −0.599284 | ||||||||
\(928\) | −1.12311 | −0.0368677 | ||||||||
\(929\) | 11.5616 | 0.379322 | 0.189661 | − | 0.981850i | \(-0.439261\pi\) | ||||
0.189661 | + | 0.981850i | \(0.439261\pi\) | |||||||
\(930\) | −1.00000 | −0.0327913 | ||||||||
\(931\) | −21.3693 | −0.700351 | ||||||||
\(932\) | 20.0540 | 0.656890 | ||||||||
\(933\) | 18.2462 | 0.597354 | ||||||||
\(934\) | −26.2462 | −0.858802 | ||||||||
\(935\) | −8.00000 | −0.261628 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | 16.6307 | 0.543301 | 0.271650 | − | 0.962396i | \(-0.412431\pi\) | ||||
0.271650 | + | 0.962396i | \(0.412431\pi\) | |||||||
\(938\) | −14.6307 | −0.477709 | ||||||||
\(939\) | 10.0000 | 0.326338 | ||||||||
\(940\) | −3.12311 | −0.101864 | ||||||||
\(941\) | 27.3693 | 0.892214 | 0.446107 | − | 0.894980i | \(-0.352810\pi\) | ||||
0.446107 | + | 0.894980i | \(0.352810\pi\) | |||||||
\(942\) | 20.0540 | 0.653394 | ||||||||
\(943\) | −6.24621 | −0.203405 | ||||||||
\(944\) | −4.87689 | −0.158729 | ||||||||
\(945\) | 1.56155 | 0.0507973 | ||||||||
\(946\) | 12.1922 | 0.396404 | ||||||||
\(947\) | −0.876894 | −0.0284952 | −0.0142476 | − | 0.999898i | \(-0.504535\pi\) | ||||
−0.0142476 | + | 0.999898i | \(0.504535\pi\) | |||||||
\(948\) | 16.6847 | 0.541893 | ||||||||
\(949\) | 19.6155 | 0.636747 | ||||||||
\(950\) | 4.68466 | 0.151990 | ||||||||
\(951\) | −25.1231 | −0.814673 | ||||||||
\(952\) | −8.00000 | −0.259281 | ||||||||
\(953\) | −58.1080 | −1.88230 | −0.941151 | − | 0.337988i | \(-0.890254\pi\) | ||||
−0.941151 | + | 0.337988i | \(0.890254\pi\) | |||||||
\(954\) | 11.5616 | 0.374319 | ||||||||
\(955\) | 2.24621 | 0.0726857 | ||||||||
\(956\) | 24.0000 | 0.776215 | ||||||||
\(957\) | −1.75379 | −0.0566919 | ||||||||
\(958\) | 6.43845 | 0.208017 | ||||||||
\(959\) | −5.86174 | −0.189285 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 10.2462 | 0.330351 | ||||||||
\(963\) | 1.56155 | 0.0503203 | ||||||||
\(964\) | −4.24621 | −0.136761 | ||||||||
\(965\) | −18.4924 | −0.595292 | ||||||||
\(966\) | 8.68466 | 0.279424 | ||||||||
\(967\) | −25.7538 | −0.828186 | −0.414093 | − | 0.910235i | \(-0.635901\pi\) | ||||
−0.414093 | + | 0.910235i | \(0.635901\pi\) | |||||||
\(968\) | −8.56155 | −0.275179 | ||||||||
\(969\) | −24.0000 | −0.770991 | ||||||||
\(970\) | −6.00000 | −0.192648 | ||||||||
\(971\) | −28.8769 | −0.926704 | −0.463352 | − | 0.886174i | \(-0.653353\pi\) | ||||
−0.463352 | + | 0.886174i | \(0.653353\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 13.8617 | 0.444387 | ||||||||
\(974\) | 24.0000 | 0.769010 | ||||||||
\(975\) | −2.00000 | −0.0640513 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | −22.9848 | −0.735350 | −0.367675 | − | 0.929954i | \(-0.619846\pi\) | ||||
−0.367675 | + | 0.929954i | \(0.619846\pi\) | |||||||
\(978\) | −9.36932 | −0.299598 | ||||||||
\(979\) | 2.05398 | 0.0656453 | ||||||||
\(980\) | −4.56155 | −0.145713 | ||||||||
\(981\) | −19.3693 | −0.618415 | ||||||||
\(982\) | 2.93087 | 0.0935278 | ||||||||
\(983\) | −24.9848 | −0.796893 | −0.398446 | − | 0.917192i | \(-0.630451\pi\) | ||||
−0.398446 | + | 0.917192i | \(0.630451\pi\) | |||||||
\(984\) | 1.12311 | 0.0358033 | ||||||||
\(985\) | 6.00000 | 0.191176 | ||||||||
\(986\) | −5.75379 | −0.183238 | ||||||||
\(987\) | −4.87689 | −0.155233 | ||||||||
\(988\) | 9.36932 | 0.298078 | ||||||||
\(989\) | −43.4233 | −1.38078 | ||||||||
\(990\) | −1.56155 | −0.0496294 | ||||||||
\(991\) | 23.3153 | 0.740636 | 0.370318 | − | 0.928905i | \(-0.379249\pi\) | ||||
0.370318 | + | 0.928905i | \(0.379249\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | −10.2462 | −0.325154 | ||||||||
\(994\) | −7.31534 | −0.232029 | ||||||||
\(995\) | 3.80776 | 0.120714 | ||||||||
\(996\) | 2.24621 | 0.0711739 | ||||||||
\(997\) | −62.4924 | −1.97915 | −0.989577 | − | 0.144002i | \(-0.954003\pi\) | ||||
−0.989577 | + | 0.144002i | \(0.954003\pi\) | |||||||
\(998\) | 20.0000 | 0.633089 | ||||||||
\(999\) | −5.12311 | −0.162088 |
(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 | 930.2.a.p.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 2790.2.a.be.1.1 | 2 | |||
4.3 | odd | 2 | 7440.2.a.bl.1.2 | 2 | |||
5.2 | odd | 4 | 4650.2.d.bd.3349.3 | 4 | |||
5.3 | odd | 4 | 4650.2.d.bd.3349.2 | 4 | |||
5.4 | even | 2 | 4650.2.a.ce.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.a.p.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
2790.2.a.be.1.1 | 2 | 3.2 | odd | 2 | |||
4650.2.a.ce.1.2 | 2 | 5.4 | even | 2 | |||
4650.2.d.bd.3349.2 | 4 | 5.3 | odd | 4 | |||
4650.2.d.bd.3349.3 | 4 | 5.2 | odd | 4 | |||
7440.2.a.bl.1.2 | 2 | 4.3 | odd | 2 |