Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, 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("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.131472.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 19x^{2} + 20x + 52 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.32258\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 | ||||||||
\(7\) | 2.32258 | 0.877853 | 0.438926 | − | 0.898523i | \(-0.355359\pi\) | ||||
0.438926 | + | 0.898523i | \(0.355359\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 5.34541 | 1.61170 | 0.805850 | − | 0.592119i | \(-0.201709\pi\) | ||||
0.805850 | + | 0.592119i | \(0.201709\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.32258 | 0.620736 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.02283 | −0.922900 | −0.461450 | − | 0.887166i | \(-0.652671\pi\) | ||||
−0.461450 | + | 0.887166i | \(0.652671\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.32258 | 0.506828 | ||||||||
\(22\) | 5.34541 | 1.13964 | ||||||||
\(23\) | −4.93593 | −1.02921 | −0.514607 | − | 0.857426i | \(-0.672062\pi\) | ||||
−0.514607 | + | 0.857426i | \(0.672062\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.32258 | 0.438926 | ||||||||
\(29\) | 4.29078 | 0.796777 | 0.398388 | − | 0.917217i | \(-0.369570\pi\) | ||||
0.398388 | + | 0.917217i | \(0.369570\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 3.47183 | 0.623560 | 0.311780 | − | 0.950154i | \(-0.399075\pi\) | ||||
0.311780 | + | 0.950154i | \(0.399075\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 5.34541 | 0.930516 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | −2.32258 | −0.392588 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.14925 | −0.517734 | −0.258867 | − | 0.965913i | \(-0.583349\pi\) | ||||
−0.258867 | + | 0.965913i | \(0.583349\pi\) | |||||||
\(38\) | −4.02283 | −0.652589 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −2.64516 | −0.413104 | −0.206552 | − | 0.978436i | \(-0.566224\pi\) | ||||
−0.206552 | + | 0.978436i | \(0.566224\pi\) | |||||||
\(42\) | 2.32258 | 0.358382 | ||||||||
\(43\) | 12.2508 | 1.86823 | 0.934113 | − | 0.356976i | \(-0.116192\pi\) | ||||
0.934113 | + | 0.356976i | \(0.116192\pi\) | |||||||
\(44\) | 5.34541 | 0.805850 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −4.93593 | −0.727764 | ||||||||
\(47\) | 1.81894 | 0.265320 | 0.132660 | − | 0.991162i | \(-0.457648\pi\) | ||||
0.132660 | + | 0.991162i | \(0.457648\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.60562 | −0.229375 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 4.00000 | 0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.48693 | −0.753687 | −0.376844 | − | 0.926277i | \(-0.622991\pi\) | ||||
−0.376844 | + | 0.926277i | \(0.622991\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −5.34541 | −0.720774 | ||||||||
\(56\) | 2.32258 | 0.310368 | ||||||||
\(57\) | −4.02283 | −0.532836 | ||||||||
\(58\) | 4.29078 | 0.563406 | ||||||||
\(59\) | −6.78668 | −0.883551 | −0.441775 | − | 0.897126i | \(-0.645651\pi\) | ||||
−0.441775 | + | 0.897126i | \(0.645651\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 0.535898 | 0.0686148 | 0.0343074 | − | 0.999411i | \(-0.489077\pi\) | ||||
0.0343074 | + | 0.999411i | \(0.489077\pi\) | |||||||
\(62\) | 3.47183 | 0.440923 | ||||||||
\(63\) | 2.32258 | 0.292618 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.34541 | 0.657974 | ||||||||
\(67\) | −4.10926 | −0.502026 | −0.251013 | − | 0.967984i | \(-0.580764\pi\) | ||||
−0.251013 | + | 0.967984i | \(0.580764\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | −4.93593 | −0.594217 | ||||||||
\(70\) | −2.32258 | −0.277601 | ||||||||
\(71\) | 15.8719 | 1.88364 | 0.941822 | − | 0.336112i | \(-0.109112\pi\) | ||||
0.941822 | + | 0.336112i | \(0.109112\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 13.5734 | 1.58864 | 0.794321 | − | 0.607498i | \(-0.207827\pi\) | ||||
0.794321 | + | 0.607498i | \(0.207827\pi\) | |||||||
\(74\) | −3.14925 | −0.366093 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −4.02283 | −0.461450 | ||||||||
\(77\) | 12.4151 | 1.41484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.96774 | −0.896441 | −0.448220 | − | 0.893923i | \(-0.647942\pi\) | ||||
−0.448220 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.64516 | −0.292109 | ||||||||
\(83\) | −11.3360 | −1.24428 | −0.622142 | − | 0.782904i | \(-0.713737\pi\) | ||||
−0.622142 | + | 0.782904i | \(0.713737\pi\) | |||||||
\(84\) | 2.32258 | 0.253414 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 12.2508 | 1.32104 | ||||||||
\(87\) | 4.29078 | 0.460019 | ||||||||
\(88\) | 5.34541 | 0.569822 | ||||||||
\(89\) | −1.73978 | −0.184417 | −0.0922083 | − | 0.995740i | \(-0.529393\pi\) | ||||
−0.0922083 | + | 0.995740i | \(0.529393\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.93593 | −0.514607 | ||||||||
\(93\) | 3.47183 | 0.360012 | ||||||||
\(94\) | 1.81894 | 0.187610 | ||||||||
\(95\) | 4.02283 | 0.412733 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −16.1093 | −1.63565 | −0.817824 | − | 0.575469i | \(-0.804820\pi\) | ||||
−0.817824 | + | 0.575469i | \(0.804820\pi\) | |||||||
\(98\) | −1.60562 | −0.162192 | ||||||||
\(99\) | 5.34541 | 0.537233 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.6908 | 1.26278 | 0.631391 | − | 0.775464i | \(-0.282484\pi\) | ||||
0.631391 | + | 0.775464i | \(0.282484\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | 4.79612 | 0.472575 | 0.236288 | − | 0.971683i | \(-0.424069\pi\) | ||||
0.236288 | + | 0.971683i | \(0.424069\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.32258 | −0.226661 | ||||||||
\(106\) | −5.48693 | −0.532938 | ||||||||
\(107\) | 3.07180 | 0.296962 | 0.148481 | − | 0.988915i | \(-0.452562\pi\) | ||||
0.148481 | + | 0.988915i | \(0.452562\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −6.69081 | −0.640864 | −0.320432 | − | 0.947272i | \(-0.603828\pi\) | ||||
−0.320432 | + | 0.947272i | \(0.603828\pi\) | |||||||
\(110\) | −5.34541 | −0.509664 | ||||||||
\(111\) | −3.14925 | −0.298914 | ||||||||
\(112\) | 2.32258 | 0.219463 | ||||||||
\(113\) | −7.10972 | −0.668826 | −0.334413 | − | 0.942427i | \(-0.608538\pi\) | ||||
−0.334413 | + | 0.942427i | \(0.608538\pi\) | |||||||
\(114\) | −4.02283 | −0.376772 | ||||||||
\(115\) | 4.93593 | 0.460278 | ||||||||
\(116\) | 4.29078 | 0.398388 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.78668 | −0.624765 | ||||||||
\(119\) | 9.29032 | 0.851642 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 17.5734 | 1.59758 | ||||||||
\(122\) | 0.535898 | 0.0485180 | ||||||||
\(123\) | −2.64516 | −0.238506 | ||||||||
\(124\) | 3.47183 | 0.311780 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.32258 | 0.206912 | ||||||||
\(127\) | −2.13209 | −0.189192 | −0.0945961 | − | 0.995516i | \(-0.530156\pi\) | ||||
−0.0945961 | + | 0.995516i | \(0.530156\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 12.2508 | 1.07862 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.25851 | 0.109957 | 0.0549785 | − | 0.998488i | \(-0.482491\pi\) | ||||
0.0549785 | + | 0.998488i | \(0.482491\pi\) | |||||||
\(132\) | 5.34541 | 0.465258 | ||||||||
\(133\) | −9.34333 | −0.810170 | ||||||||
\(134\) | −4.10926 | −0.354986 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | −19.7149 | −1.68436 | −0.842178 | − | 0.539199i | \(-0.818727\pi\) | ||||
−0.842178 | + | 0.539199i | \(0.818727\pi\) | |||||||
\(138\) | −4.93593 | −0.420175 | ||||||||
\(139\) | 5.67742 | 0.481553 | 0.240776 | − | 0.970581i | \(-0.422598\pi\) | ||||
0.240776 | + | 0.970581i | \(0.422598\pi\) | |||||||
\(140\) | −2.32258 | −0.196294 | ||||||||
\(141\) | 1.81894 | 0.153183 | ||||||||
\(142\) | 15.8719 | 1.33194 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.29078 | −0.356329 | ||||||||
\(146\) | 13.5734 | 1.12334 | ||||||||
\(147\) | −1.60562 | −0.132430 | ||||||||
\(148\) | −3.14925 | −0.258867 | ||||||||
\(149\) | −19.4775 | −1.59566 | −0.797829 | − | 0.602884i | \(-0.794018\pi\) | ||||
−0.797829 | + | 0.602884i | \(0.794018\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −14.5170 | −1.18138 | −0.590690 | − | 0.806899i | \(-0.701144\pi\) | ||||
−0.590690 | + | 0.806899i | \(0.701144\pi\) | |||||||
\(152\) | −4.02283 | −0.326294 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | 12.4151 | 1.00044 | ||||||||
\(155\) | −3.47183 | −0.278864 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.3829 | 1.94596 | 0.972982 | − | 0.230879i | \(-0.0741602\pi\) | ||||
0.972982 | + | 0.230879i | \(0.0741602\pi\) | |||||||
\(158\) | −7.96774 | −0.633879 | ||||||||
\(159\) | −5.48693 | −0.435142 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −11.4641 | −0.903498 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −23.6267 | −1.85059 | −0.925295 | − | 0.379249i | \(-0.876182\pi\) | ||||
−0.925295 | + | 0.379249i | \(0.876182\pi\) | |||||||
\(164\) | −2.64516 | −0.206552 | ||||||||
\(165\) | −5.34541 | −0.416139 | ||||||||
\(166\) | −11.3360 | −0.879842 | ||||||||
\(167\) | 16.7471 | 1.29593 | 0.647967 | − | 0.761669i | \(-0.275620\pi\) | ||||
0.647967 | + | 0.761669i | \(0.275620\pi\) | |||||||
\(168\) | 2.32258 | 0.179191 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | −4.02283 | −0.307633 | ||||||||
\(172\) | 12.2508 | 0.934113 | ||||||||
\(173\) | 16.1321 | 1.22650 | 0.613250 | − | 0.789889i | \(-0.289862\pi\) | ||||
0.613250 | + | 0.789889i | \(0.289862\pi\) | |||||||
\(174\) | 4.29078 | 0.325283 | ||||||||
\(175\) | 2.32258 | 0.175571 | ||||||||
\(176\) | 5.34541 | 0.402925 | ||||||||
\(177\) | −6.78668 | −0.510118 | ||||||||
\(178\) | −1.73978 | −0.130402 | ||||||||
\(179\) | 7.32824 | 0.547738 | 0.273869 | − | 0.961767i | \(-0.411696\pi\) | ||||
0.273869 | + | 0.961767i | \(0.411696\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 19.5734 | 1.45488 | 0.727438 | − | 0.686173i | \(-0.240711\pi\) | ||||
0.727438 | + | 0.686173i | \(0.240711\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.535898 | 0.0396147 | ||||||||
\(184\) | −4.93593 | −0.363882 | ||||||||
\(185\) | 3.14925 | 0.231538 | ||||||||
\(186\) | 3.47183 | 0.254567 | ||||||||
\(187\) | 21.3816 | 1.56358 | ||||||||
\(188\) | 1.81894 | 0.132660 | ||||||||
\(189\) | 2.32258 | 0.168943 | ||||||||
\(190\) | 4.02283 | 0.291846 | ||||||||
\(191\) | −17.0375 | −1.23279 | −0.616394 | − | 0.787438i | \(-0.711407\pi\) | ||||
−0.616394 | + | 0.787438i | \(0.711407\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 6.15491 | 0.443040 | 0.221520 | − | 0.975156i | \(-0.428898\pi\) | ||||
0.221520 | + | 0.975156i | \(0.428898\pi\) | |||||||
\(194\) | −16.1093 | −1.15658 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.60562 | −0.114687 | ||||||||
\(197\) | 13.7867 | 0.982260 | 0.491130 | − | 0.871086i | \(-0.336584\pi\) | ||||
0.491130 | + | 0.871086i | \(0.336584\pi\) | |||||||
\(198\) | 5.34541 | 0.379881 | ||||||||
\(199\) | 2.28304 | 0.161841 | 0.0809203 | − | 0.996721i | \(-0.474214\pi\) | ||||
0.0809203 | + | 0.996721i | \(0.474214\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −4.10926 | −0.289845 | ||||||||
\(202\) | 12.6908 | 0.892922 | ||||||||
\(203\) | 9.96567 | 0.699453 | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | 2.64516 | 0.184746 | ||||||||
\(206\) | 4.79612 | 0.334161 | ||||||||
\(207\) | −4.93593 | −0.343071 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.5036 | −1.48744 | ||||||||
\(210\) | −2.32258 | −0.160273 | ||||||||
\(211\) | 22.4775 | 1.54741 | 0.773707 | − | 0.633543i | \(-0.218400\pi\) | ||||
0.773707 | + | 0.633543i | \(0.218400\pi\) | |||||||
\(212\) | −5.48693 | −0.376844 | ||||||||
\(213\) | 15.8719 | 1.08752 | ||||||||
\(214\) | 3.07180 | 0.209984 | ||||||||
\(215\) | −12.2508 | −0.835496 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 8.06361 | 0.547393 | ||||||||
\(218\) | −6.69081 | −0.453159 | ||||||||
\(219\) | 13.5734 | 0.917203 | ||||||||
\(220\) | −5.34541 | −0.360387 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.14925 | −0.211364 | ||||||||
\(223\) | −1.37891 | −0.0923389 | −0.0461694 | − | 0.998934i | \(-0.514701\pi\) | ||||
−0.0461694 | + | 0.998934i | \(0.514701\pi\) | |||||||
\(224\) | 2.32258 | 0.155184 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −7.10972 | −0.472931 | ||||||||
\(227\) | −19.3205 | −1.28235 | −0.641174 | − | 0.767396i | \(-0.721552\pi\) | ||||
−0.641174 | + | 0.767396i | \(0.721552\pi\) | |||||||
\(228\) | −4.02283 | −0.266418 | ||||||||
\(229\) | 15.7626 | 1.04162 | 0.520811 | − | 0.853672i | \(-0.325630\pi\) | ||||
0.520811 | + | 0.853672i | \(0.325630\pi\) | |||||||
\(230\) | 4.93593 | 0.325466 | ||||||||
\(231\) | 12.4151 | 0.816856 | ||||||||
\(232\) | 4.29078 | 0.281703 | ||||||||
\(233\) | 16.5549 | 1.08455 | 0.542275 | − | 0.840201i | \(-0.317563\pi\) | ||||
0.542275 | + | 0.840201i | \(0.317563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.81894 | −0.118655 | ||||||||
\(236\) | −6.78668 | −0.441775 | ||||||||
\(237\) | −7.96774 | −0.517560 | ||||||||
\(238\) | 9.29032 | 0.602202 | ||||||||
\(239\) | 26.2006 | 1.69477 | 0.847387 | − | 0.530976i | \(-0.178175\pi\) | ||||
0.847387 | + | 0.530976i | \(0.178175\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 15.6496 | 1.00808 | 0.504039 | − | 0.863681i | \(-0.331847\pi\) | ||||
0.504039 | + | 0.863681i | \(0.331847\pi\) | |||||||
\(242\) | 17.5734 | 1.12966 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.535898 | 0.0343074 | ||||||||
\(245\) | 1.60562 | 0.102580 | ||||||||
\(246\) | −2.64516 | −0.168649 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.47183 | 0.220462 | ||||||||
\(249\) | −11.3360 | −0.718388 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −28.3416 | −1.78891 | −0.894454 | − | 0.447160i | \(-0.852435\pi\) | ||||
−0.894454 | + | 0.447160i | \(0.852435\pi\) | |||||||
\(252\) | 2.32258 | 0.146309 | ||||||||
\(253\) | −26.3846 | −1.65878 | ||||||||
\(254\) | −2.13209 | −0.133779 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.5093 | −0.780309 | −0.390154 | − | 0.920750i | \(-0.627578\pi\) | ||||
−0.390154 | + | 0.920750i | \(0.627578\pi\) | |||||||
\(258\) | 12.2508 | 0.762700 | ||||||||
\(259\) | −7.31439 | −0.454494 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.29078 | 0.265592 | ||||||||
\(262\) | 1.25851 | 0.0777513 | ||||||||
\(263\) | −10.7059 | −0.660154 | −0.330077 | − | 0.943954i | \(-0.607075\pi\) | ||||
−0.330077 | + | 0.943954i | \(0.607075\pi\) | |||||||
\(264\) | 5.34541 | 0.328987 | ||||||||
\(265\) | 5.48693 | 0.337059 | ||||||||
\(266\) | −9.34333 | −0.572877 | ||||||||
\(267\) | −1.73978 | −0.106473 | ||||||||
\(268\) | −4.10926 | −0.251013 | ||||||||
\(269\) | 7.52522 | 0.458821 | 0.229410 | − | 0.973330i | \(-0.426320\pi\) | ||||
0.229410 | + | 0.973330i | \(0.426320\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 9.84868 | 0.598264 | 0.299132 | − | 0.954212i | \(-0.403303\pi\) | ||||
0.299132 | + | 0.954212i | \(0.403303\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −19.7149 | −1.19102 | ||||||||
\(275\) | 5.34541 | 0.322340 | ||||||||
\(276\) | −4.93593 | −0.297108 | ||||||||
\(277\) | 0.953101 | 0.0572663 | 0.0286331 | − | 0.999590i | \(-0.490885\pi\) | ||||
0.0286331 | + | 0.999590i | \(0.490885\pi\) | |||||||
\(278\) | 5.67742 | 0.340509 | ||||||||
\(279\) | 3.47183 | 0.207853 | ||||||||
\(280\) | −2.32258 | −0.138801 | ||||||||
\(281\) | 5.57336 | 0.332479 | 0.166239 | − | 0.986085i | \(-0.446838\pi\) | ||||
0.166239 | + | 0.986085i | \(0.446838\pi\) | |||||||
\(282\) | 1.81894 | 0.108316 | ||||||||
\(283\) | 22.0134 | 1.30856 | 0.654280 | − | 0.756252i | \(-0.272972\pi\) | ||||
0.654280 | + | 0.756252i | \(0.272972\pi\) | |||||||
\(284\) | 15.8719 | 0.941822 | ||||||||
\(285\) | 4.02283 | 0.238292 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.14359 | −0.362645 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | −4.29078 | −0.251963 | ||||||||
\(291\) | −16.1093 | −0.944342 | ||||||||
\(292\) | 13.5734 | 0.794321 | ||||||||
\(293\) | −6.84302 | −0.399773 | −0.199887 | − | 0.979819i | \(-0.564057\pi\) | ||||
−0.199887 | + | 0.979819i | \(0.564057\pi\) | |||||||
\(294\) | −1.60562 | −0.0936419 | ||||||||
\(295\) | 6.78668 | 0.395136 | ||||||||
\(296\) | −3.14925 | −0.183047 | ||||||||
\(297\) | 5.34541 | 0.310172 | ||||||||
\(298\) | −19.4775 | −1.12830 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 28.4534 | 1.64003 | ||||||||
\(302\) | −14.5170 | −0.835361 | ||||||||
\(303\) | 12.6908 | 0.729068 | ||||||||
\(304\) | −4.02283 | −0.230725 | ||||||||
\(305\) | −0.535898 | −0.0306855 | ||||||||
\(306\) | 4.00000 | 0.228665 | ||||||||
\(307\) | 4.75442 | 0.271349 | 0.135675 | − | 0.990753i | \(-0.456680\pi\) | ||||
0.135675 | + | 0.990753i | \(0.456680\pi\) | |||||||
\(308\) | 12.4151 | 0.707418 | ||||||||
\(309\) | 4.79612 | 0.272842 | ||||||||
\(310\) | −3.47183 | −0.197187 | ||||||||
\(311\) | −1.93639 | −0.109803 | −0.0549013 | − | 0.998492i | \(-0.517484\pi\) | ||||
−0.0549013 | + | 0.998492i | \(0.517484\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.5545 | 1.44443 | 0.722213 | − | 0.691671i | \(-0.243125\pi\) | ||||
0.722213 | + | 0.691671i | \(0.243125\pi\) | |||||||
\(314\) | 24.3829 | 1.37600 | ||||||||
\(315\) | −2.32258 | −0.130863 | ||||||||
\(316\) | −7.96774 | −0.448220 | ||||||||
\(317\) | −12.6667 | −0.711435 | −0.355717 | − | 0.934594i | \(-0.615763\pi\) | ||||
−0.355717 | + | 0.934594i | \(0.615763\pi\) | |||||||
\(318\) | −5.48693 | −0.307692 | ||||||||
\(319\) | 22.9359 | 1.28417 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 3.07180 | 0.171451 | ||||||||
\(322\) | −11.4641 | −0.638869 | ||||||||
\(323\) | −16.0913 | −0.895344 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.6267 | −1.30856 | ||||||||
\(327\) | −6.69081 | −0.370003 | ||||||||
\(328\) | −2.64516 | −0.146054 | ||||||||
\(329\) | 4.22464 | 0.232912 | ||||||||
\(330\) | −5.34541 | −0.294255 | ||||||||
\(331\) | −23.6981 | −1.30256 | −0.651282 | − | 0.758836i | \(-0.725769\pi\) | ||||
−0.651282 | + | 0.758836i | \(0.725769\pi\) | |||||||
\(332\) | −11.3360 | −0.622142 | ||||||||
\(333\) | −3.14925 | −0.172578 | ||||||||
\(334\) | 16.7471 | 0.916363 | ||||||||
\(335\) | 4.10926 | 0.224513 | ||||||||
\(336\) | 2.32258 | 0.126707 | ||||||||
\(337\) | −19.5554 | −1.06525 | −0.532625 | − | 0.846351i | \(-0.678795\pi\) | ||||
−0.532625 | + | 0.846351i | \(0.678795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.10972 | −0.386147 | ||||||||
\(340\) | −4.00000 | −0.216930 | ||||||||
\(341\) | 18.5584 | 1.00499 | ||||||||
\(342\) | −4.02283 | −0.217530 | ||||||||
\(343\) | −19.9872 | −1.07921 | ||||||||
\(344\) | 12.2508 | 0.660518 | ||||||||
\(345\) | 4.93593 | 0.265742 | ||||||||
\(346\) | 16.1321 | 0.867266 | ||||||||
\(347\) | −23.0375 | −1.23672 | −0.618358 | − | 0.785897i | \(-0.712202\pi\) | ||||
−0.618358 | + | 0.785897i | \(0.712202\pi\) | |||||||
\(348\) | 4.29078 | 0.230010 | ||||||||
\(349\) | 15.3205 | 0.820088 | 0.410044 | − | 0.912066i | \(-0.365513\pi\) | ||||
0.410044 | + | 0.912066i | \(0.365513\pi\) | |||||||
\(350\) | 2.32258 | 0.124147 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.34541 | 0.284911 | ||||||||
\(353\) | −28.4078 | −1.51199 | −0.755996 | − | 0.654576i | \(-0.772847\pi\) | ||||
−0.755996 | + | 0.654576i | \(0.772847\pi\) | |||||||
\(354\) | −6.78668 | −0.360708 | ||||||||
\(355\) | −15.8719 | −0.842391 | ||||||||
\(356\) | −1.73978 | −0.0922083 | ||||||||
\(357\) | 9.29032 | 0.491696 | ||||||||
\(358\) | 7.32824 | 0.387309 | ||||||||
\(359\) | −23.5734 | −1.24415 | −0.622077 | − | 0.782956i | \(-0.713711\pi\) | ||||
−0.622077 | + | 0.782956i | \(0.713711\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | −2.81687 | −0.148256 | ||||||||
\(362\) | 19.5734 | 1.02875 | ||||||||
\(363\) | 17.5734 | 0.922362 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.5734 | −0.710462 | ||||||||
\(366\) | 0.535898 | 0.0280119 | ||||||||
\(367\) | 27.4909 | 1.43501 | 0.717506 | − | 0.696552i | \(-0.245283\pi\) | ||||
0.717506 | + | 0.696552i | \(0.245283\pi\) | |||||||
\(368\) | −4.93593 | −0.257303 | ||||||||
\(369\) | −2.64516 | −0.137701 | ||||||||
\(370\) | 3.14925 | 0.163722 | ||||||||
\(371\) | −12.7438 | −0.661627 | ||||||||
\(372\) | 3.47183 | 0.180006 | ||||||||
\(373\) | 26.3421 | 1.36394 | 0.681971 | − | 0.731379i | \(-0.261123\pi\) | ||||
0.681971 | + | 0.731379i | \(0.261123\pi\) | |||||||
\(374\) | 21.3816 | 1.10562 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 1.81894 | 0.0938048 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.32258 | 0.119461 | ||||||||
\(379\) | −0.448551 | −0.0230405 | −0.0115202 | − | 0.999934i | \(-0.503667\pi\) | ||||
−0.0115202 | + | 0.999934i | \(0.503667\pi\) | |||||||
\(380\) | 4.02283 | 0.206367 | ||||||||
\(381\) | −2.13209 | −0.109230 | ||||||||
\(382\) | −17.0375 | −0.871713 | ||||||||
\(383\) | 12.1227 | 0.619439 | 0.309719 | − | 0.950828i | \(-0.399765\pi\) | ||||
0.309719 | + | 0.950828i | \(0.399765\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −12.4151 | −0.632734 | ||||||||
\(386\) | 6.15491 | 0.313277 | ||||||||
\(387\) | 12.2508 | 0.622742 | ||||||||
\(388\) | −16.1093 | −0.817824 | ||||||||
\(389\) | −18.6195 | −0.944045 | −0.472022 | − | 0.881587i | \(-0.656476\pi\) | ||||
−0.472022 | + | 0.881587i | \(0.656476\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.7437 | −0.998484 | ||||||||
\(392\) | −1.60562 | −0.0810962 | ||||||||
\(393\) | 1.25851 | 0.0634837 | ||||||||
\(394\) | 13.7867 | 0.694563 | ||||||||
\(395\) | 7.96774 | 0.400900 | ||||||||
\(396\) | 5.34541 | 0.268617 | ||||||||
\(397\) | −11.3042 | −0.567340 | −0.283670 | − | 0.958922i | \(-0.591552\pi\) | ||||
−0.283670 | + | 0.958922i | \(0.591552\pi\) | |||||||
\(398\) | 2.28304 | 0.114439 | ||||||||
\(399\) | −9.34333 | −0.467752 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.50580 | −0.0751959 | −0.0375980 | − | 0.999293i | \(-0.511971\pi\) | ||||
−0.0375980 | + | 0.999293i | \(0.511971\pi\) | |||||||
\(402\) | −4.10926 | −0.204951 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12.6908 | 0.631391 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 9.96567 | 0.494588 | ||||||||
\(407\) | −16.8340 | −0.834432 | ||||||||
\(408\) | 4.00000 | 0.198030 | ||||||||
\(409\) | 11.1394 | 0.550806 | 0.275403 | − | 0.961329i | \(-0.411189\pi\) | ||||
0.275403 | + | 0.961329i | \(0.411189\pi\) | |||||||
\(410\) | 2.64516 | 0.130635 | ||||||||
\(411\) | −19.7149 | −0.972464 | ||||||||
\(412\) | 4.79612 | 0.236288 | ||||||||
\(413\) | −15.7626 | −0.775627 | ||||||||
\(414\) | −4.93593 | −0.242588 | ||||||||
\(415\) | 11.3360 | 0.556461 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.67742 | 0.278024 | ||||||||
\(418\) | −21.5036 | −1.05178 | ||||||||
\(419\) | −15.5098 | −0.757701 | −0.378851 | − | 0.925458i | \(-0.623681\pi\) | ||||
−0.378851 | + | 0.925458i | \(0.623681\pi\) | |||||||
\(420\) | −2.32258 | −0.113330 | ||||||||
\(421\) | −39.4452 | −1.92244 | −0.961221 | − | 0.275778i | \(-0.911065\pi\) | ||||
−0.961221 | + | 0.275778i | \(0.911065\pi\) | |||||||
\(422\) | 22.4775 | 1.09419 | ||||||||
\(423\) | 1.81894 | 0.0884400 | ||||||||
\(424\) | −5.48693 | −0.266469 | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 15.8719 | 0.768995 | ||||||||
\(427\) | 1.24467 | 0.0602336 | ||||||||
\(428\) | 3.07180 | 0.148481 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12.2508 | −0.590785 | ||||||||
\(431\) | −2.15491 | −0.103799 | −0.0518993 | − | 0.998652i | \(-0.516527\pi\) | ||||
−0.0518993 | + | 0.998652i | \(0.516527\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 1.33938 | 0.0643664 | 0.0321832 | − | 0.999482i | \(-0.489754\pi\) | ||||
0.0321832 | + | 0.999482i | \(0.489754\pi\) | |||||||
\(434\) | 8.06361 | 0.387066 | ||||||||
\(435\) | −4.29078 | −0.205727 | ||||||||
\(436\) | −6.69081 | −0.320432 | ||||||||
\(437\) | 19.8564 | 0.949861 | ||||||||
\(438\) | 13.5734 | 0.648560 | ||||||||
\(439\) | −31.6981 | −1.51287 | −0.756434 | − | 0.654071i | \(-0.773060\pi\) | ||||
−0.756434 | + | 0.654071i | \(0.773060\pi\) | |||||||
\(440\) | −5.34541 | −0.254832 | ||||||||
\(441\) | −1.60562 | −0.0764583 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.0904 | −1.33461 | −0.667307 | − | 0.744782i | \(-0.732553\pi\) | ||||
−0.667307 | + | 0.744782i | \(0.732553\pi\) | |||||||
\(444\) | −3.14925 | −0.149457 | ||||||||
\(445\) | 1.73978 | 0.0824736 | ||||||||
\(446\) | −1.37891 | −0.0652935 | ||||||||
\(447\) | −19.4775 | −0.921254 | ||||||||
\(448\) | 2.32258 | 0.109732 | ||||||||
\(449\) | −28.9167 | −1.36466 | −0.682332 | − | 0.731043i | \(-0.739034\pi\) | ||||
−0.682332 | + | 0.731043i | \(0.739034\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −14.1395 | −0.665801 | ||||||||
\(452\) | −7.10972 | −0.334413 | ||||||||
\(453\) | −14.5170 | −0.682070 | ||||||||
\(454\) | −19.3205 | −0.906756 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.02283 | −0.188386 | ||||||||
\(457\) | −9.69900 | −0.453700 | −0.226850 | − | 0.973930i | \(-0.572843\pi\) | ||||
−0.226850 | + | 0.973930i | \(0.572843\pi\) | |||||||
\(458\) | 15.7626 | 0.736538 | ||||||||
\(459\) | 4.00000 | 0.186704 | ||||||||
\(460\) | 4.93593 | 0.230139 | ||||||||
\(461\) | 11.9979 | 0.558799 | 0.279400 | − | 0.960175i | \(-0.409865\pi\) | ||||
0.279400 | + | 0.960175i | \(0.409865\pi\) | |||||||
\(462\) | 12.4151 | 0.577604 | ||||||||
\(463\) | −6.42664 | −0.298671 | −0.149336 | − | 0.988787i | \(-0.547713\pi\) | ||||
−0.149336 | + | 0.988787i | \(0.547713\pi\) | |||||||
\(464\) | 4.29078 | 0.199194 | ||||||||
\(465\) | −3.47183 | −0.161002 | ||||||||
\(466\) | 16.5549 | 0.766893 | ||||||||
\(467\) | −26.2642 | −1.21536 | −0.607681 | − | 0.794182i | \(-0.707900\pi\) | ||||
−0.607681 | + | 0.794182i | \(0.707900\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.54409 | −0.440705 | ||||||||
\(470\) | −1.81894 | −0.0839015 | ||||||||
\(471\) | 24.3829 | 1.12350 | ||||||||
\(472\) | −6.78668 | −0.312382 | ||||||||
\(473\) | 65.4854 | 3.01102 | ||||||||
\(474\) | −7.96774 | −0.365970 | ||||||||
\(475\) | −4.02283 | −0.184580 | ||||||||
\(476\) | 9.29032 | 0.425821 | ||||||||
\(477\) | −5.48693 | −0.251229 | ||||||||
\(478\) | 26.2006 | 1.19839 | ||||||||
\(479\) | −25.6826 | −1.17347 | −0.586735 | − | 0.809779i | \(-0.699587\pi\) | ||||
−0.586735 | + | 0.809779i | \(0.699587\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 15.6496 | 0.712818 | ||||||||
\(483\) | −11.4641 | −0.521635 | ||||||||
\(484\) | 17.5734 | 0.798789 | ||||||||
\(485\) | 16.1093 | 0.731484 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −9.37891 | −0.424999 | −0.212500 | − | 0.977161i | \(-0.568160\pi\) | ||||
−0.212500 | + | 0.977161i | \(0.568160\pi\) | |||||||
\(488\) | 0.535898 | 0.0242590 | ||||||||
\(489\) | −23.6267 | −1.06844 | ||||||||
\(490\) | 1.60562 | 0.0725347 | ||||||||
\(491\) | −7.73854 | −0.349235 | −0.174618 | − | 0.984636i | \(-0.555869\pi\) | ||||
−0.174618 | + | 0.984636i | \(0.555869\pi\) | |||||||
\(492\) | −2.64516 | −0.119253 | ||||||||
\(493\) | 17.1631 | 0.772987 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.34541 | −0.240258 | ||||||||
\(496\) | 3.47183 | 0.155890 | ||||||||
\(497\) | 36.8637 | 1.65356 | ||||||||
\(498\) | −11.3360 | −0.507977 | ||||||||
\(499\) | 3.18106 | 0.142404 | 0.0712019 | − | 0.997462i | \(-0.477317\pi\) | ||||
0.0712019 | + | 0.997462i | \(0.477317\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 16.7471 | 0.748207 | ||||||||
\(502\) | −28.3416 | −1.26495 | ||||||||
\(503\) | −35.0758 | −1.56395 | −0.781975 | − | 0.623309i | \(-0.785788\pi\) | ||||
−0.781975 | + | 0.623309i | \(0.785788\pi\) | |||||||
\(504\) | 2.32258 | 0.103456 | ||||||||
\(505\) | −12.6908 | −0.564734 | ||||||||
\(506\) | −26.3846 | −1.17294 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.13209 | −0.0945961 | ||||||||
\(509\) | 18.7867 | 0.832705 | 0.416353 | − | 0.909203i | \(-0.363308\pi\) | ||||
0.416353 | + | 0.909203i | \(0.363308\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | 31.5252 | 1.39459 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −4.02283 | −0.177612 | ||||||||
\(514\) | −12.5093 | −0.551761 | ||||||||
\(515\) | −4.79612 | −0.211342 | ||||||||
\(516\) | 12.2508 | 0.539311 | ||||||||
\(517\) | 9.72298 | 0.427616 | ||||||||
\(518\) | −7.31439 | −0.321376 | ||||||||
\(519\) | 16.1321 | 0.708120 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.28512 | 0.231545 | 0.115773 | − | 0.993276i | \(-0.463066\pi\) | ||||
0.115773 | + | 0.993276i | \(0.463066\pi\) | |||||||
\(522\) | 4.29078 | 0.187802 | ||||||||
\(523\) | −20.7523 | −0.907437 | −0.453718 | − | 0.891145i | \(-0.649903\pi\) | ||||
−0.453718 | + | 0.891145i | \(0.649903\pi\) | |||||||
\(524\) | 1.25851 | 0.0549785 | ||||||||
\(525\) | 2.32258 | 0.101366 | ||||||||
\(526\) | −10.7059 | −0.466800 | ||||||||
\(527\) | 13.8873 | 0.604942 | ||||||||
\(528\) | 5.34541 | 0.232629 | ||||||||
\(529\) | 1.36345 | 0.0592805 | ||||||||
\(530\) | 5.48693 | 0.238337 | ||||||||
\(531\) | −6.78668 | −0.294517 | ||||||||
\(532\) | −9.34333 | −0.405085 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.73978 | −0.0752877 | ||||||||
\(535\) | −3.07180 | −0.132805 | ||||||||
\(536\) | −4.10926 | −0.177493 | ||||||||
\(537\) | 7.32824 | 0.316237 | ||||||||
\(538\) | 7.52522 | 0.324435 | ||||||||
\(539\) | −8.58271 | −0.369683 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 28.7365 | 1.23548 | 0.617739 | − | 0.786384i | \(-0.288049\pi\) | ||||
0.617739 | + | 0.786384i | \(0.288049\pi\) | |||||||
\(542\) | 9.84868 | 0.423037 | ||||||||
\(543\) | 19.5734 | 0.839973 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 6.69081 | 0.286603 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.3768 | 0.785737 | 0.392869 | − | 0.919595i | \(-0.371483\pi\) | ||||
0.392869 | + | 0.919595i | \(0.371483\pi\) | |||||||
\(548\) | −19.7149 | −0.842178 | ||||||||
\(549\) | 0.535898 | 0.0228716 | ||||||||
\(550\) | 5.34541 | 0.227929 | ||||||||
\(551\) | −17.2610 | −0.735345 | ||||||||
\(552\) | −4.93593 | −0.210087 | ||||||||
\(553\) | −18.5057 | −0.786943 | ||||||||
\(554\) | 0.953101 | 0.0404934 | ||||||||
\(555\) | 3.14925 | 0.133678 | ||||||||
\(556\) | 5.67742 | 0.240776 | ||||||||
\(557\) | 26.5386 | 1.12448 | 0.562238 | − | 0.826975i | \(-0.309940\pi\) | ||||
0.562238 | + | 0.826975i | \(0.309940\pi\) | |||||||
\(558\) | 3.47183 | 0.146974 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.32258 | −0.0981469 | ||||||||
\(561\) | 21.3816 | 0.902733 | ||||||||
\(562\) | 5.57336 | 0.235098 | ||||||||
\(563\) | −6.06111 | −0.255446 | −0.127723 | − | 0.991810i | \(-0.540767\pi\) | ||||
−0.127723 | + | 0.991810i | \(0.540767\pi\) | |||||||
\(564\) | 1.81894 | 0.0765913 | ||||||||
\(565\) | 7.10972 | 0.299108 | ||||||||
\(566\) | 22.0134 | 0.925292 | ||||||||
\(567\) | 2.32258 | 0.0975392 | ||||||||
\(568\) | 15.8719 | 0.665969 | ||||||||
\(569\) | −14.4964 | −0.607719 | −0.303860 | − | 0.952717i | \(-0.598275\pi\) | ||||
−0.303860 | + | 0.952717i | \(0.598275\pi\) | |||||||
\(570\) | 4.02283 | 0.168498 | ||||||||
\(571\) | 2.90413 | 0.121534 | 0.0607670 | − | 0.998152i | \(-0.480645\pi\) | ||||
0.0607670 | + | 0.998152i | \(0.480645\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.0375 | −0.711750 | ||||||||
\(574\) | −6.14359 | −0.256429 | ||||||||
\(575\) | −4.93593 | −0.205843 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −18.8180 | −0.783405 | −0.391702 | − | 0.920092i | \(-0.628114\pi\) | ||||
−0.391702 | + | 0.920092i | \(0.628114\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 6.15491 | 0.255789 | ||||||||
\(580\) | −4.29078 | −0.178165 | ||||||||
\(581\) | −26.3287 | −1.09230 | ||||||||
\(582\) | −16.1093 | −0.667750 | ||||||||
\(583\) | −29.3299 | −1.21472 | ||||||||
\(584\) | 13.5734 | 0.561670 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.84302 | −0.282682 | ||||||||
\(587\) | 3.93639 | 0.162472 | 0.0812361 | − | 0.996695i | \(-0.474113\pi\) | ||||
0.0812361 | + | 0.996695i | \(0.474113\pi\) | |||||||
\(588\) | −1.60562 | −0.0662148 | ||||||||
\(589\) | −13.9666 | −0.575483 | ||||||||
\(590\) | 6.78668 | 0.279403 | ||||||||
\(591\) | 13.7867 | 0.567108 | ||||||||
\(592\) | −3.14925 | −0.129434 | ||||||||
\(593\) | −20.1227 | −0.826338 | −0.413169 | − | 0.910654i | \(-0.635578\pi\) | ||||
−0.413169 | + | 0.910654i | \(0.635578\pi\) | |||||||
\(594\) | 5.34541 | 0.219325 | ||||||||
\(595\) | −9.29032 | −0.380866 | ||||||||
\(596\) | −19.4775 | −0.797829 | ||||||||
\(597\) | 2.28304 | 0.0934388 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 48.1172 | 1.96601 | 0.983007 | − | 0.183567i | \(-0.0587644\pi\) | ||||
0.983007 | + | 0.183567i | \(0.0587644\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −4.24217 | −0.173042 | −0.0865209 | − | 0.996250i | \(-0.527575\pi\) | ||||
−0.0865209 | + | 0.996250i | \(0.527575\pi\) | |||||||
\(602\) | 28.4534 | 1.15967 | ||||||||
\(603\) | −4.10926 | −0.167342 | ||||||||
\(604\) | −14.5170 | −0.590690 | ||||||||
\(605\) | −17.5734 | −0.714459 | ||||||||
\(606\) | 12.6908 | 0.515529 | ||||||||
\(607\) | 12.0685 | 0.489844 | 0.244922 | − | 0.969543i | \(-0.421238\pi\) | ||||
0.244922 | + | 0.969543i | \(0.421238\pi\) | |||||||
\(608\) | −4.02283 | −0.163147 | ||||||||
\(609\) | 9.96567 | 0.403829 | ||||||||
\(610\) | −0.535898 | −0.0216979 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | −41.7421 | −1.68595 | −0.842974 | − | 0.537954i | \(-0.819197\pi\) | ||||
−0.842974 | + | 0.537954i | \(0.819197\pi\) | |||||||
\(614\) | 4.75442 | 0.191873 | ||||||||
\(615\) | 2.64516 | 0.106663 | ||||||||
\(616\) | 12.4151 | 0.500220 | ||||||||
\(617\) | −33.4586 | −1.34699 | −0.673497 | − | 0.739190i | \(-0.735208\pi\) | ||||
−0.673497 | + | 0.739190i | \(0.735208\pi\) | |||||||
\(618\) | 4.79612 | 0.192928 | ||||||||
\(619\) | −38.0978 | −1.53128 | −0.765639 | − | 0.643270i | \(-0.777577\pi\) | ||||
−0.765639 | + | 0.643270i | \(0.777577\pi\) | |||||||
\(620\) | −3.47183 | −0.139432 | ||||||||
\(621\) | −4.93593 | −0.198072 | ||||||||
\(622\) | −1.93639 | −0.0776422 | ||||||||
\(623\) | −4.04078 | −0.161891 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 25.5545 | 1.02136 | ||||||||
\(627\) | −21.5036 | −0.858773 | ||||||||
\(628\) | 24.3829 | 0.972982 | ||||||||
\(629\) | −12.5970 | −0.502276 | ||||||||
\(630\) | −2.32258 | −0.0925338 | ||||||||
\(631\) | 24.8001 | 0.987275 | 0.493638 | − | 0.869668i | \(-0.335667\pi\) | ||||
0.493638 | + | 0.869668i | \(0.335667\pi\) | |||||||
\(632\) | −7.96774 | −0.316940 | ||||||||
\(633\) | 22.4775 | 0.893400 | ||||||||
\(634\) | −12.6667 | −0.503060 | ||||||||
\(635\) | 2.13209 | 0.0846093 | ||||||||
\(636\) | −5.48693 | −0.217571 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.9359 | 0.908042 | ||||||||
\(639\) | 15.8719 | 0.627881 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 4.08519 | 0.161355 | 0.0806776 | − | 0.996740i | \(-0.474292\pi\) | ||||
0.0806776 | + | 0.996740i | \(0.474292\pi\) | |||||||
\(642\) | 3.07180 | 0.121234 | ||||||||
\(643\) | −36.5816 | −1.44264 | −0.721318 | − | 0.692604i | \(-0.756463\pi\) | ||||
−0.721318 | + | 0.692604i | \(0.756463\pi\) | |||||||
\(644\) | −11.4641 | −0.451749 | ||||||||
\(645\) | −12.2508 | −0.482374 | ||||||||
\(646\) | −16.0913 | −0.633104 | ||||||||
\(647\) | 17.2341 | 0.677541 | 0.338771 | − | 0.940869i | \(-0.389989\pi\) | ||||
0.338771 | + | 0.940869i | \(0.389989\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −36.2776 | −1.42402 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.06361 | 0.316038 | ||||||||
\(652\) | −23.6267 | −0.925295 | ||||||||
\(653\) | −21.9274 | −0.858085 | −0.429042 | − | 0.903284i | \(-0.641149\pi\) | ||||
−0.429042 | + | 0.903284i | \(0.641149\pi\) | |||||||
\(654\) | −6.69081 | −0.261631 | ||||||||
\(655\) | −1.25851 | −0.0491742 | ||||||||
\(656\) | −2.64516 | −0.103276 | ||||||||
\(657\) | 13.5734 | 0.529547 | ||||||||
\(658\) | 4.22464 | 0.164694 | ||||||||
\(659\) | −48.4759 | −1.88835 | −0.944176 | − | 0.329441i | \(-0.893140\pi\) | ||||
−0.944176 | + | 0.329441i | \(0.893140\pi\) | |||||||
\(660\) | −5.34541 | −0.208070 | ||||||||
\(661\) | −29.8221 | −1.15994 | −0.579972 | − | 0.814636i | \(-0.696937\pi\) | ||||
−0.579972 | + | 0.814636i | \(0.696937\pi\) | |||||||
\(662\) | −23.6981 | −0.921052 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.3360 | −0.439921 | ||||||||
\(665\) | 9.34333 | 0.362319 | ||||||||
\(666\) | −3.14925 | −0.122031 | ||||||||
\(667\) | −21.1790 | −0.820054 | ||||||||
\(668\) | 16.7471 | 0.647967 | ||||||||
\(669\) | −1.37891 | −0.0533119 | ||||||||
\(670\) | 4.10926 | 0.158755 | ||||||||
\(671\) | 2.86459 | 0.110586 | ||||||||
\(672\) | 2.32258 | 0.0895955 | ||||||||
\(673\) | −30.6719 | −1.18232 | −0.591158 | − | 0.806556i | \(-0.701329\pi\) | ||||
−0.591158 | + | 0.806556i | \(0.701329\pi\) | |||||||
\(674\) | −19.5554 | −0.753246 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.0831 | 0.810290 | 0.405145 | − | 0.914252i | \(-0.367221\pi\) | ||||
0.405145 | + | 0.914252i | \(0.367221\pi\) | |||||||
\(678\) | −7.10972 | −0.273047 | ||||||||
\(679\) | −37.4150 | −1.43586 | ||||||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | −19.3205 | −0.740363 | ||||||||
\(682\) | 18.5584 | 0.710636 | ||||||||
\(683\) | 13.3360 | 0.510287 | 0.255143 | − | 0.966903i | \(-0.417877\pi\) | ||||
0.255143 | + | 0.966903i | \(0.417877\pi\) | |||||||
\(684\) | −4.02283 | −0.153817 | ||||||||
\(685\) | 19.7149 | 0.753267 | ||||||||
\(686\) | −19.9872 | −0.763117 | ||||||||
\(687\) | 15.7626 | 0.601381 | ||||||||
\(688\) | 12.2508 | 0.467057 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.93593 | 0.187908 | ||||||||
\(691\) | 34.9054 | 1.32786 | 0.663932 | − | 0.747793i | \(-0.268887\pi\) | ||||
0.663932 | + | 0.747793i | \(0.268887\pi\) | |||||||
\(692\) | 16.1321 | 0.613250 | ||||||||
\(693\) | 12.4151 | 0.471612 | ||||||||
\(694\) | −23.0375 | −0.874490 | ||||||||
\(695\) | −5.67742 | −0.215357 | ||||||||
\(696\) | 4.29078 | 0.162641 | ||||||||
\(697\) | −10.5806 | −0.400770 | ||||||||
\(698\) | 15.3205 | 0.579890 | ||||||||
\(699\) | 16.5549 | 0.626166 | ||||||||
\(700\) | 2.32258 | 0.0877853 | ||||||||
\(701\) | −39.6715 | −1.49837 | −0.749186 | − | 0.662360i | \(-0.769555\pi\) | ||||
−0.749186 | + | 0.662360i | \(0.769555\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.6689 | 0.477817 | ||||||||
\(704\) | 5.34541 | 0.201463 | ||||||||
\(705\) | −1.81894 | −0.0685053 | ||||||||
\(706\) | −28.4078 | −1.06914 | ||||||||
\(707\) | 29.4754 | 1.10854 | ||||||||
\(708\) | −6.78668 | −0.255059 | ||||||||
\(709\) | −2.83441 | −0.106448 | −0.0532242 | − | 0.998583i | \(-0.516950\pi\) | ||||
−0.0532242 | + | 0.998583i | \(0.516950\pi\) | |||||||
\(710\) | −15.8719 | −0.595661 | ||||||||
\(711\) | −7.96774 | −0.298814 | ||||||||
\(712\) | −1.73978 | −0.0652011 | ||||||||
\(713\) | −17.1367 | −0.641776 | ||||||||
\(714\) | 9.29032 | 0.347681 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.32824 | 0.273869 | ||||||||
\(717\) | 26.2006 | 0.978478 | ||||||||
\(718\) | −23.5734 | −0.879750 | ||||||||
\(719\) | −43.7128 | −1.63021 | −0.815106 | − | 0.579311i | \(-0.803322\pi\) | ||||
−0.815106 | + | 0.579311i | \(0.803322\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 11.1394 | 0.414852 | ||||||||
\(722\) | −2.81687 | −0.104833 | ||||||||
\(723\) | 15.6496 | 0.582014 | ||||||||
\(724\) | 19.5734 | 0.727438 | ||||||||
\(725\) | 4.29078 | 0.159355 | ||||||||
\(726\) | 17.5734 | 0.652209 | ||||||||
\(727\) | 16.2568 | 0.602932 | 0.301466 | − | 0.953477i | \(-0.402524\pi\) | ||||
0.301466 | + | 0.953477i | \(0.402524\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −13.5734 | −0.502373 | ||||||||
\(731\) | 49.0031 | 1.81245 | ||||||||
\(732\) | 0.535898 | 0.0198074 | ||||||||
\(733\) | 4.96774 | 0.183488 | 0.0917438 | − | 0.995783i | \(-0.470756\pi\) | ||||
0.0917438 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(734\) | 27.4909 | 1.01471 | ||||||||
\(735\) | 1.60562 | 0.0592243 | ||||||||
\(736\) | −4.93593 | −0.181941 | ||||||||
\(737\) | −21.9657 | −0.809116 | ||||||||
\(738\) | −2.64516 | −0.0973697 | ||||||||
\(739\) | 49.6875 | 1.82778 | 0.913892 | − | 0.405957i | \(-0.133062\pi\) | ||||
0.913892 | + | 0.405957i | \(0.133062\pi\) | |||||||
\(740\) | 3.14925 | 0.115769 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.7438 | −0.467841 | ||||||||
\(743\) | −21.5420 | −0.790300 | −0.395150 | − | 0.918617i | \(-0.629307\pi\) | ||||
−0.395150 | + | 0.918617i | \(0.629307\pi\) | |||||||
\(744\) | 3.47183 | 0.127284 | ||||||||
\(745\) | 19.4775 | 0.713600 | ||||||||
\(746\) | 26.3421 | 0.964452 | ||||||||
\(747\) | −11.3360 | −0.414761 | ||||||||
\(748\) | 21.3816 | 0.781790 | ||||||||
\(749\) | 7.13449 | 0.260689 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −6.34872 | −0.231668 | −0.115834 | − | 0.993269i | \(-0.536954\pi\) | ||||
−0.115834 | + | 0.993269i | \(0.536954\pi\) | |||||||
\(752\) | 1.81894 | 0.0663300 | ||||||||
\(753\) | −28.3416 | −1.03283 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.5170 | 0.528329 | ||||||||
\(756\) | 2.32258 | 0.0844714 | ||||||||
\(757\) | −48.1107 | −1.74861 | −0.874307 | − | 0.485373i | \(-0.838684\pi\) | ||||
−0.874307 | + | 0.485373i | \(0.838684\pi\) | |||||||
\(758\) | −0.448551 | −0.0162921 | ||||||||
\(759\) | −26.3846 | −0.957699 | ||||||||
\(760\) | 4.02283 | 0.145923 | ||||||||
\(761\) | −33.6866 | −1.22114 | −0.610569 | − | 0.791963i | \(-0.709059\pi\) | ||||
−0.610569 | + | 0.791963i | \(0.709059\pi\) | |||||||
\(762\) | −2.13209 | −0.0772374 | ||||||||
\(763\) | −15.5399 | −0.562584 | ||||||||
\(764\) | −17.0375 | −0.616394 | ||||||||
\(765\) | −4.00000 | −0.144620 | ||||||||
\(766\) | 12.1227 | 0.438009 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 5.98886 | 0.215964 | 0.107982 | − | 0.994153i | \(-0.465561\pi\) | ||||
0.107982 | + | 0.994153i | \(0.465561\pi\) | |||||||
\(770\) | −12.4151 | −0.447410 | ||||||||
\(771\) | −12.5093 | −0.450511 | ||||||||
\(772\) | 6.15491 | 0.221520 | ||||||||
\(773\) | 13.4882 | 0.485136 | 0.242568 | − | 0.970134i | \(-0.422010\pi\) | ||||
0.242568 | + | 0.970134i | \(0.422010\pi\) | |||||||
\(774\) | 12.2508 | 0.440345 | ||||||||
\(775\) | 3.47183 | 0.124712 | ||||||||
\(776\) | −16.1093 | −0.578289 | ||||||||
\(777\) | −7.31439 | −0.262402 | ||||||||
\(778\) | −18.6195 | −0.667540 | ||||||||
\(779\) | 10.6410 | 0.381254 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 84.8416 | 3.03587 | ||||||||
\(782\) | −19.7437 | −0.706035 | ||||||||
\(783\) | 4.29078 | 0.153340 | ||||||||
\(784\) | −1.60562 | −0.0573437 | ||||||||
\(785\) | −24.3829 | −0.870262 | ||||||||
\(786\) | 1.25851 | 0.0448897 | ||||||||
\(787\) | 54.6487 | 1.94802 | 0.974009 | − | 0.226510i | \(-0.0727317\pi\) | ||||
0.974009 | + | 0.226510i | \(0.0727317\pi\) | |||||||
\(788\) | 13.7867 | 0.491130 | ||||||||
\(789\) | −10.7059 | −0.381140 | ||||||||
\(790\) | 7.96774 | 0.283479 | ||||||||
\(791\) | −16.5129 | −0.587131 | ||||||||
\(792\) | 5.34541 | 0.189941 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −11.3042 | −0.401170 | ||||||||
\(795\) | 5.48693 | 0.194601 | ||||||||
\(796\) | 2.28304 | 0.0809203 | ||||||||
\(797\) | −38.3244 | −1.35752 | −0.678760 | − | 0.734361i | \(-0.737482\pi\) | ||||
−0.678760 | + | 0.734361i | \(0.737482\pi\) | |||||||
\(798\) | −9.34333 | −0.330750 | ||||||||
\(799\) | 7.27577 | 0.257398 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −1.73978 | −0.0614722 | ||||||||
\(802\) | −1.50580 | −0.0531716 | ||||||||
\(803\) | 72.5551 | 2.56041 | ||||||||
\(804\) | −4.10926 | −0.144922 | ||||||||
\(805\) | 11.4641 | 0.404056 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.52522 | 0.264900 | ||||||||
\(808\) | 12.6908 | 0.446461 | ||||||||
\(809\) | 11.3816 | 0.400157 | 0.200078 | − | 0.979780i | \(-0.435880\pi\) | ||||
0.200078 | + | 0.979780i | \(0.435880\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | −10.8899 | −0.382397 | −0.191198 | − | 0.981551i | \(-0.561237\pi\) | ||||
−0.191198 | + | 0.981551i | \(0.561237\pi\) | |||||||
\(812\) | 9.96567 | 0.349726 | ||||||||
\(813\) | 9.84868 | 0.345408 | ||||||||
\(814\) | −16.8340 | −0.590033 | ||||||||
\(815\) | 23.6267 | 0.827609 | ||||||||
\(816\) | 4.00000 | 0.140028 | ||||||||
\(817\) | −49.2828 | −1.72419 | ||||||||
\(818\) | 11.1394 | 0.389479 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.64516 | 0.0923730 | ||||||||
\(821\) | 1.68810 | 0.0589152 | 0.0294576 | − | 0.999566i | \(-0.490622\pi\) | ||||
0.0294576 | + | 0.999566i | \(0.490622\pi\) | |||||||
\(822\) | −19.7149 | −0.687636 | ||||||||
\(823\) | 6.77816 | 0.236272 | 0.118136 | − | 0.992997i | \(-0.462308\pi\) | ||||
0.118136 | + | 0.992997i | \(0.462308\pi\) | |||||||
\(824\) | 4.79612 | 0.167081 | ||||||||
\(825\) | 5.34541 | 0.186103 | ||||||||
\(826\) | −15.7626 | −0.548451 | ||||||||
\(827\) | 30.2298 | 1.05119 | 0.525597 | − | 0.850733i | \(-0.323842\pi\) | ||||
0.525597 | + | 0.850733i | \(0.323842\pi\) | |||||||
\(828\) | −4.93593 | −0.171536 | ||||||||
\(829\) | −10.4405 | −0.362612 | −0.181306 | − | 0.983427i | \(-0.558032\pi\) | ||||
−0.181306 | + | 0.983427i | \(0.558032\pi\) | |||||||
\(830\) | 11.3360 | 0.393477 | ||||||||
\(831\) | 0.953101 | 0.0330627 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.42249 | −0.222526 | ||||||||
\(834\) | 5.67742 | 0.196593 | ||||||||
\(835\) | −16.7471 | −0.579559 | ||||||||
\(836\) | −21.5036 | −0.743719 | ||||||||
\(837\) | 3.47183 | 0.120004 | ||||||||
\(838\) | −15.5098 | −0.535776 | ||||||||
\(839\) | −11.1965 | −0.386547 | −0.193273 | − | 0.981145i | \(-0.561910\pi\) | ||||
−0.193273 | + | 0.981145i | \(0.561910\pi\) | |||||||
\(840\) | −2.32258 | −0.0801366 | ||||||||
\(841\) | −10.5892 | −0.365146 | ||||||||
\(842\) | −39.4452 | −1.35937 | ||||||||
\(843\) | 5.57336 | 0.191957 | ||||||||
\(844\) | 22.4775 | 0.773707 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.81894 | 0.0625365 | ||||||||
\(847\) | 40.8155 | 1.40244 | ||||||||
\(848\) | −5.48693 | −0.188422 | ||||||||
\(849\) | 22.0134 | 0.755498 | ||||||||
\(850\) | 4.00000 | 0.137199 | ||||||||
\(851\) | 15.5445 | 0.532859 | ||||||||
\(852\) | 15.8719 | 0.543761 | ||||||||
\(853\) | −21.8185 | −0.747051 | −0.373525 | − | 0.927620i | \(-0.621851\pi\) | ||||
−0.373525 | + | 0.927620i | \(0.621851\pi\) | |||||||
\(854\) | 1.24467 | 0.0425916 | ||||||||
\(855\) | 4.02283 | 0.137578 | ||||||||
\(856\) | 3.07180 | 0.104992 | ||||||||
\(857\) | 9.42369 | 0.321907 | 0.160954 | − | 0.986962i | \(-0.448543\pi\) | ||||
0.160954 | + | 0.986962i | \(0.448543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.4775 | 0.835161 | 0.417581 | − | 0.908640i | \(-0.362878\pi\) | ||||
0.417581 | + | 0.908640i | \(0.362878\pi\) | |||||||
\(860\) | −12.2508 | −0.417748 | ||||||||
\(861\) | −6.14359 | −0.209373 | ||||||||
\(862\) | −2.15491 | −0.0733966 | ||||||||
\(863\) | −29.7873 | −1.01397 | −0.506986 | − | 0.861954i | \(-0.669240\pi\) | ||||
−0.506986 | + | 0.861954i | \(0.669240\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −16.1321 | −0.548507 | ||||||||
\(866\) | 1.33938 | 0.0455139 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 8.06361 | 0.273697 | ||||||||
\(869\) | −42.5908 | −1.44479 | ||||||||
\(870\) | −4.29078 | −0.145471 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.69081 | −0.226579 | ||||||||
\(873\) | −16.1093 | −0.545216 | ||||||||
\(874\) | 19.8564 | 0.671653 | ||||||||
\(875\) | −2.32258 | −0.0785175 | ||||||||
\(876\) | 13.5734 | 0.458601 | ||||||||
\(877\) | 1.90979 | 0.0644890 | 0.0322445 | − | 0.999480i | \(-0.489734\pi\) | ||||
0.0322445 | + | 0.999480i | \(0.489734\pi\) | |||||||
\(878\) | −31.6981 | −1.06976 | ||||||||
\(879\) | −6.84302 | −0.230809 | ||||||||
\(880\) | −5.34541 | −0.180194 | ||||||||
\(881\) | 6.36823 | 0.214551 | 0.107276 | − | 0.994229i | \(-0.465787\pi\) | ||||
0.107276 | + | 0.994229i | \(0.465787\pi\) | |||||||
\(882\) | −1.60562 | −0.0540642 | ||||||||
\(883\) | 34.9897 | 1.17750 | 0.588749 | − | 0.808316i | \(-0.299621\pi\) | ||||
0.588749 | + | 0.808316i | \(0.299621\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.78668 | 0.228132 | ||||||||
\(886\) | −28.0904 | −0.943715 | ||||||||
\(887\) | 21.4001 | 0.718546 | 0.359273 | − | 0.933233i | \(-0.383025\pi\) | ||||
0.359273 | + | 0.933233i | \(0.383025\pi\) | |||||||
\(888\) | −3.14925 | −0.105682 | ||||||||
\(889\) | −4.95194 | −0.166083 | ||||||||
\(890\) | 1.73978 | 0.0583176 | ||||||||
\(891\) | 5.34541 | 0.179078 | ||||||||
\(892\) | −1.37891 | −0.0461694 | ||||||||
\(893\) | −7.31729 | −0.244864 | ||||||||
\(894\) | −19.4775 | −0.651425 | ||||||||
\(895\) | −7.32824 | −0.244956 | ||||||||
\(896\) | 2.32258 | 0.0775919 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.9167 | −0.964963 | ||||||||
\(899\) | 14.8969 | 0.496838 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −21.9477 | −0.731184 | ||||||||
\(902\) | −14.1395 | −0.470792 | ||||||||
\(903\) | 28.4534 | 0.946871 | ||||||||
\(904\) | −7.10972 | −0.236466 | ||||||||
\(905\) | −19.5734 | −0.650641 | ||||||||
\(906\) | −14.5170 | −0.482296 | ||||||||
\(907\) | 32.4693 | 1.07813 | 0.539063 | − | 0.842266i | \(-0.318779\pi\) | ||||
0.539063 | + | 0.842266i | \(0.318779\pi\) | |||||||
\(908\) | −19.3205 | −0.641174 | ||||||||
\(909\) | 12.6908 | 0.420928 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.4380 | 1.14098 | 0.570490 | − | 0.821304i | \(-0.306753\pi\) | ||||
0.570490 | + | 0.821304i | \(0.306753\pi\) | |||||||
\(912\) | −4.02283 | −0.133209 | ||||||||
\(913\) | −60.5954 | −2.00541 | ||||||||
\(914\) | −9.69900 | −0.320814 | ||||||||
\(915\) | −0.535898 | −0.0177163 | ||||||||
\(916\) | 15.7626 | 0.520811 | ||||||||
\(917\) | 2.92300 | 0.0965260 | ||||||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | 36.4827 | 1.20345 | 0.601727 | − | 0.798702i | \(-0.294480\pi\) | ||||
0.601727 | + | 0.798702i | \(0.294480\pi\) | |||||||
\(920\) | 4.93593 | 0.162733 | ||||||||
\(921\) | 4.75442 | 0.156663 | ||||||||
\(922\) | 11.9979 | 0.395131 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.4151 | 0.408428 | ||||||||
\(925\) | −3.14925 | −0.103547 | ||||||||
\(926\) | −6.42664 | −0.211192 | ||||||||
\(927\) | 4.79612 | 0.157525 | ||||||||
\(928\) | 4.29078 | 0.140852 | ||||||||
\(929\) | 49.9100 | 1.63749 | 0.818747 | − | 0.574155i | \(-0.194669\pi\) | ||||
0.818747 | + | 0.574155i | \(0.194669\pi\) | |||||||
\(930\) | −3.47183 | −0.113846 | ||||||||
\(931\) | 6.45914 | 0.211690 | ||||||||
\(932\) | 16.5549 | 0.542275 | ||||||||
\(933\) | −1.93639 | −0.0633946 | ||||||||
\(934\) | −26.2642 | −0.859390 | ||||||||
\(935\) | −21.3816 | −0.699254 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.8873 | −0.519017 | −0.259508 | − | 0.965741i | \(-0.583560\pi\) | ||||
−0.259508 | + | 0.965741i | \(0.583560\pi\) | |||||||
\(938\) | −9.54409 | −0.311625 | ||||||||
\(939\) | 25.5545 | 0.833939 | ||||||||
\(940\) | −1.81894 | −0.0593274 | ||||||||
\(941\) | 6.99273 | 0.227956 | 0.113978 | − | 0.993483i | \(-0.463641\pi\) | ||||
0.113978 | + | 0.993483i | \(0.463641\pi\) | |||||||
\(942\) | 24.3829 | 0.794437 | ||||||||
\(943\) | 13.0563 | 0.425173 | ||||||||
\(944\) | −6.78668 | −0.220888 | ||||||||
\(945\) | −2.32258 | −0.0755535 | ||||||||
\(946\) | 65.4854 | 2.12911 | ||||||||
\(947\) | −52.3064 | −1.69973 | −0.849865 | − | 0.527000i | \(-0.823317\pi\) | ||||
−0.849865 | + | 0.527000i | \(0.823317\pi\) | |||||||
\(948\) | −7.96774 | −0.258780 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −4.02283 | −0.130518 | ||||||||
\(951\) | −12.6667 | −0.410747 | ||||||||
\(952\) | 9.29032 | 0.301101 | ||||||||
\(953\) | 28.8827 | 0.935603 | 0.467802 | − | 0.883833i | \(-0.345046\pi\) | ||||
0.467802 | + | 0.883833i | \(0.345046\pi\) | |||||||
\(954\) | −5.48693 | −0.177646 | ||||||||
\(955\) | 17.0375 | 0.551319 | ||||||||
\(956\) | 26.2006 | 0.847387 | ||||||||
\(957\) | 22.9359 | 0.741413 | ||||||||
\(958\) | −25.6826 | −0.829768 | ||||||||
\(959\) | −45.7894 | −1.47862 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −18.9464 | −0.611173 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.07180 | 0.0989873 | ||||||||
\(964\) | 15.6496 | 0.504039 | ||||||||
\(965\) | −6.15491 | −0.198134 | ||||||||
\(966\) | −11.4641 | −0.368851 | ||||||||
\(967\) | 10.8610 | 0.349265 | 0.174633 | − | 0.984634i | \(-0.444126\pi\) | ||||
0.174633 | + | 0.984634i | \(0.444126\pi\) | |||||||
\(968\) | 17.5734 | 0.564829 | ||||||||
\(969\) | −16.0913 | −0.516927 | ||||||||
\(970\) | 16.1093 | 0.517237 | ||||||||
\(971\) | −24.9979 | −0.802222 | −0.401111 | − | 0.916030i | \(-0.631376\pi\) | ||||
−0.401111 | + | 0.916030i | \(0.631376\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 13.1863 | 0.422732 | ||||||||
\(974\) | −9.37891 | −0.300520 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.535898 | 0.0171537 | ||||||||
\(977\) | 42.7653 | 1.36818 | 0.684092 | − | 0.729396i | \(-0.260199\pi\) | ||||
0.684092 | + | 0.729396i | \(0.260199\pi\) | |||||||
\(978\) | −23.6267 | −0.755500 | ||||||||
\(979\) | −9.29984 | −0.297224 | ||||||||
\(980\) | 1.60562 | 0.0512898 | ||||||||
\(981\) | −6.69081 | −0.213621 | ||||||||
\(982\) | −7.73854 | −0.246947 | ||||||||
\(983\) | 10.1288 | 0.323058 | 0.161529 | − | 0.986868i | \(-0.448358\pi\) | ||||
0.161529 | + | 0.986868i | \(0.448358\pi\) | |||||||
\(984\) | −2.64516 | −0.0843246 | ||||||||
\(985\) | −13.7867 | −0.439280 | ||||||||
\(986\) | 17.1631 | 0.546584 | ||||||||
\(987\) | 4.22464 | 0.134472 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −60.4691 | −1.92280 | ||||||||
\(990\) | −5.34541 | −0.169888 | ||||||||
\(991\) | 20.2483 | 0.643208 | 0.321604 | − | 0.946874i | \(-0.395778\pi\) | ||||
0.321604 | + | 0.946874i | \(0.395778\pi\) | |||||||
\(992\) | 3.47183 | 0.110231 | ||||||||
\(993\) | −23.6981 | −0.752036 | ||||||||
\(994\) | 36.8637 | 1.16924 | ||||||||
\(995\) | −2.28304 | −0.0723774 | ||||||||
\(996\) | −11.3360 | −0.359194 | ||||||||
\(997\) | −20.7961 | −0.658620 | −0.329310 | − | 0.944222i | \(-0.606816\pi\) | ||||
−0.329310 | + | 0.944222i | \(0.606816\pi\) | |||||||
\(998\) | 3.18106 | 0.100695 | ||||||||
\(999\) | −3.14925 | −0.0996380 |
(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 | 5070.2.a.ca.1.3 | 4 | ||
13.5 | odd | 4 | 5070.2.b.ba.1351.3 | 8 | |||
13.6 | odd | 12 | 390.2.bb.c.361.1 | yes | 8 | ||
13.8 | odd | 4 | 5070.2.b.ba.1351.6 | 8 | |||
13.11 | odd | 12 | 390.2.bb.c.121.1 | ✓ | 8 | ||
13.12 | even | 2 | 5070.2.a.bz.1.2 | 4 | |||
39.11 | even | 12 | 1170.2.bs.f.901.3 | 8 | |||
39.32 | even | 12 | 1170.2.bs.f.361.3 | 8 | |||
65.19 | odd | 12 | 1950.2.bc.g.751.4 | 8 | |||
65.24 | odd | 12 | 1950.2.bc.g.901.4 | 8 | |||
65.32 | even | 12 | 1950.2.y.j.49.2 | 8 | |||
65.37 | even | 12 | 1950.2.y.k.199.3 | 8 | |||
65.58 | even | 12 | 1950.2.y.k.49.3 | 8 | |||
65.63 | even | 12 | 1950.2.y.j.199.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.c.121.1 | ✓ | 8 | 13.11 | odd | 12 | ||
390.2.bb.c.361.1 | yes | 8 | 13.6 | odd | 12 | ||
1170.2.bs.f.361.3 | 8 | 39.32 | even | 12 | |||
1170.2.bs.f.901.3 | 8 | 39.11 | even | 12 | |||
1950.2.y.j.49.2 | 8 | 65.32 | even | 12 | |||
1950.2.y.j.199.2 | 8 | 65.63 | even | 12 | |||
1950.2.y.k.49.3 | 8 | 65.58 | even | 12 | |||
1950.2.y.k.199.3 | 8 | 65.37 | even | 12 | |||
1950.2.bc.g.751.4 | 8 | 65.19 | odd | 12 | |||
1950.2.bc.g.901.4 | 8 | 65.24 | odd | 12 | |||
5070.2.a.bz.1.2 | 4 | 13.12 | even | 2 | |||
5070.2.a.ca.1.3 | 4 | 1.1 | even | 1 | trivial | ||
5070.2.b.ba.1351.3 | 8 | 13.5 | odd | 4 | |||
5070.2.b.ba.1351.6 | 8 | 13.8 | odd | 4 |