Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5929,2,Mod(1,5929)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5929, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5929.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5929 = 7^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5929.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: | \(47.3433033584\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 847) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5929.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.30278 | −1.62831 | −0.814154 | − | 0.580649i | \(-0.802799\pi\) | ||||
−0.814154 | + | 0.580649i | \(0.802799\pi\) | |||||||
\(3\) | 2.30278 | 1.32951 | 0.664754 | − | 0.747062i | \(-0.268536\pi\) | ||||
0.664754 | + | 0.747062i | \(0.268536\pi\) | |||||||
\(4\) | 3.30278 | 1.65139 | ||||||||
\(5\) | −3.60555 | −1.61245 | −0.806226 | − | 0.591608i | \(-0.798493\pi\) | ||||
−0.806226 | + | 0.591608i | \(0.798493\pi\) | |||||||
\(6\) | −5.30278 | −2.16485 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00000 | −1.06066 | ||||||||
\(9\) | 2.30278 | 0.767592 | ||||||||
\(10\) | 8.30278 | 2.62557 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 7.60555 | 2.19553 | ||||||||
\(13\) | 6.60555 | 1.83205 | 0.916025 | − | 0.401121i | \(-0.131379\pi\) | ||||
0.916025 | + | 0.401121i | \(0.131379\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.30278 | −2.14377 | ||||||||
\(16\) | 0.302776 | 0.0756939 | ||||||||
\(17\) | 2.69722 | 0.654173 | 0.327086 | − | 0.944994i | \(-0.393933\pi\) | ||||
0.327086 | + | 0.944994i | \(0.393933\pi\) | |||||||
\(18\) | −5.30278 | −1.24988 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | −11.9083 | −2.66278 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.69722 | −0.562410 | −0.281205 | − | 0.959648i | \(-0.590734\pi\) | ||||
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(24\) | −6.90833 | −1.41016 | ||||||||
\(25\) | 8.00000 | 1.60000 | ||||||||
\(26\) | −15.2111 | −2.98314 | ||||||||
\(27\) | −1.60555 | −0.308988 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.69722 | −0.872253 | −0.436126 | − | 0.899885i | \(-0.643650\pi\) | ||||
−0.436126 | + | 0.899885i | \(0.643650\pi\) | |||||||
\(30\) | 19.1194 | 3.49071 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | 5.30278 | 0.937407 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.21110 | −1.06520 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.60555 | 1.26759 | ||||||||
\(37\) | −5.21110 | −0.856700 | −0.428350 | − | 0.903613i | \(-0.640905\pi\) | ||||
−0.428350 | + | 0.903613i | \(0.640905\pi\) | |||||||
\(38\) | 6.90833 | 1.12068 | ||||||||
\(39\) | 15.2111 | 2.43573 | ||||||||
\(40\) | 10.8167 | 1.71026 | ||||||||
\(41\) | 7.00000 | 1.09322 | 0.546608 | − | 0.837389i | \(-0.315919\pi\) | ||||
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.69722 | −0.258824 | −0.129412 | − | 0.991591i | \(-0.541309\pi\) | ||||
−0.129412 | + | 0.991591i | \(0.541309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.30278 | −1.23770 | ||||||||
\(46\) | 6.21110 | 0.915777 | ||||||||
\(47\) | 1.90833 | 0.278358 | 0.139179 | − | 0.990267i | \(-0.455554\pi\) | ||||
0.139179 | + | 0.990267i | \(0.455554\pi\) | |||||||
\(48\) | 0.697224 | 0.100636 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −18.4222 | −2.60529 | ||||||||
\(51\) | 6.21110 | 0.869728 | ||||||||
\(52\) | 21.8167 | 3.02543 | ||||||||
\(53\) | −12.9083 | −1.77310 | −0.886548 | − | 0.462638i | \(-0.846903\pi\) | ||||
−0.886548 | + | 0.462638i | \(0.846903\pi\) | |||||||
\(54\) | 3.69722 | 0.503129 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.90833 | −0.915030 | ||||||||
\(58\) | 10.8167 | 1.42030 | ||||||||
\(59\) | −6.69722 | −0.871904 | −0.435952 | − | 0.899970i | \(-0.643588\pi\) | ||||
−0.435952 | + | 0.899970i | \(0.643588\pi\) | |||||||
\(60\) | −27.4222 | −3.54019 | ||||||||
\(61\) | −4.30278 | −0.550914 | −0.275457 | − | 0.961313i | \(-0.588829\pi\) | ||||
−0.275457 | + | 0.961313i | \(0.588829\pi\) | |||||||
\(62\) | 2.30278 | 0.292453 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.8167 | −1.60208 | ||||||||
\(65\) | −23.8167 | −2.95409 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.51388 | 1.04014 | 0.520068 | − | 0.854125i | \(-0.325907\pi\) | ||||
0.520068 | + | 0.854125i | \(0.325907\pi\) | |||||||
\(68\) | 8.90833 | 1.08029 | ||||||||
\(69\) | −6.21110 | −0.747729 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.30278 | −0.510646 | −0.255323 | − | 0.966856i | \(-0.582182\pi\) | ||||
−0.255323 | + | 0.966856i | \(0.582182\pi\) | |||||||
\(72\) | −6.90833 | −0.814154 | ||||||||
\(73\) | −5.00000 | −0.585206 | −0.292603 | − | 0.956234i | \(-0.594521\pi\) | ||||
−0.292603 | + | 0.956234i | \(0.594521\pi\) | |||||||
\(74\) | 12.0000 | 1.39497 | ||||||||
\(75\) | 18.4222 | 2.12721 | ||||||||
\(76\) | −9.90833 | −1.13656 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −35.0278 | −3.96611 | ||||||||
\(79\) | 8.30278 | 0.934135 | 0.467068 | − | 0.884222i | \(-0.345310\pi\) | ||||
0.467068 | + | 0.884222i | \(0.345310\pi\) | |||||||
\(80\) | −1.09167 | −0.122053 | ||||||||
\(81\) | −10.6056 | −1.17839 | ||||||||
\(82\) | −16.1194 | −1.78009 | ||||||||
\(83\) | 3.00000 | 0.329293 | 0.164646 | − | 0.986353i | \(-0.447352\pi\) | ||||
0.164646 | + | 0.986353i | \(0.447352\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.72498 | −1.05482 | ||||||||
\(86\) | 3.90833 | 0.421446 | ||||||||
\(87\) | −10.8167 | −1.15967 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.7250 | 1.56084 | 0.780422 | − | 0.625253i | \(-0.215004\pi\) | ||||
0.780422 | + | 0.625253i | \(0.215004\pi\) | |||||||
\(90\) | 19.1194 | 2.01536 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.90833 | −0.928757 | ||||||||
\(93\) | −2.30278 | −0.238787 | ||||||||
\(94\) | −4.39445 | −0.453253 | ||||||||
\(95\) | 10.8167 | 1.10977 | ||||||||
\(96\) | 12.2111 | 1.24629 | ||||||||
\(97\) | 3.60555 | 0.366088 | 0.183044 | − | 0.983105i | \(-0.441405\pi\) | ||||
0.183044 | + | 0.983105i | \(0.441405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 26.4222 | 2.64222 | ||||||||
\(101\) | −5.30278 | −0.527646 | −0.263823 | − | 0.964571i | \(-0.584983\pi\) | ||||
−0.263823 | + | 0.964571i | \(0.584983\pi\) | |||||||
\(102\) | −14.3028 | −1.41619 | ||||||||
\(103\) | 14.3028 | 1.40929 | 0.704647 | − | 0.709558i | \(-0.251105\pi\) | ||||
0.704647 | + | 0.709558i | \(0.251105\pi\) | |||||||
\(104\) | −19.8167 | −1.94318 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 29.7250 | 2.88715 | ||||||||
\(107\) | −12.3944 | −1.19822 | −0.599108 | − | 0.800668i | \(-0.704478\pi\) | ||||
−0.599108 | + | 0.800668i | \(0.704478\pi\) | |||||||
\(108\) | −5.30278 | −0.510260 | ||||||||
\(109\) | 8.00000 | 0.766261 | 0.383131 | − | 0.923694i | \(-0.374846\pi\) | ||||
0.383131 | + | 0.923694i | \(0.374846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.6972 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667828\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667828\pi\) | |||||||
\(114\) | 15.9083 | 1.48995 | ||||||||
\(115\) | 9.72498 | 0.906859 | ||||||||
\(116\) | −15.5139 | −1.44043 | ||||||||
\(117\) | 15.2111 | 1.40627 | ||||||||
\(118\) | 15.4222 | 1.41973 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 24.9083 | 2.27381 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.90833 | 0.897058 | ||||||||
\(123\) | 16.1194 | 1.45344 | ||||||||
\(124\) | −3.30278 | −0.296598 | ||||||||
\(125\) | −10.8167 | −0.967471 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | 18.9083 | 1.67128 | ||||||||
\(129\) | −3.90833 | −0.344109 | ||||||||
\(130\) | 54.8444 | 4.81017 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −19.6056 | −1.69366 | ||||||||
\(135\) | 5.78890 | 0.498229 | ||||||||
\(136\) | −8.09167 | −0.693855 | ||||||||
\(137\) | −10.1194 | −0.864561 | −0.432281 | − | 0.901739i | \(-0.642291\pi\) | ||||
−0.432281 | + | 0.901739i | \(0.642291\pi\) | |||||||
\(138\) | 14.3028 | 1.21753 | ||||||||
\(139\) | 21.6056 | 1.83256 | 0.916279 | − | 0.400540i | \(-0.131177\pi\) | ||||
0.916279 | + | 0.400540i | \(0.131177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.39445 | 0.370079 | ||||||||
\(142\) | 9.90833 | 0.831488 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.697224 | 0.0581020 | ||||||||
\(145\) | 16.9361 | 1.40647 | ||||||||
\(146\) | 11.5139 | 0.952895 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.2111 | −1.41474 | ||||||||
\(149\) | 4.90833 | 0.402106 | 0.201053 | − | 0.979580i | \(-0.435564\pi\) | ||||
0.201053 | + | 0.979580i | \(0.435564\pi\) | |||||||
\(150\) | −42.4222 | −3.46376 | ||||||||
\(151\) | 0.211103 | 0.0171793 | 0.00858964 | − | 0.999963i | \(-0.497266\pi\) | ||||
0.00858964 | + | 0.999963i | \(0.497266\pi\) | |||||||
\(152\) | 9.00000 | 0.729996 | ||||||||
\(153\) | 6.21110 | 0.502138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.60555 | 0.289605 | ||||||||
\(156\) | 50.2389 | 4.02233 | ||||||||
\(157\) | −7.21110 | −0.575509 | −0.287754 | − | 0.957704i | \(-0.592909\pi\) | ||||
−0.287754 | + | 0.957704i | \(0.592909\pi\) | |||||||
\(158\) | −19.1194 | −1.52106 | ||||||||
\(159\) | −29.7250 | −2.35734 | ||||||||
\(160\) | −19.1194 | −1.51152 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 24.4222 | 1.91879 | ||||||||
\(163\) | 2.81665 | 0.220617 | 0.110309 | − | 0.993897i | \(-0.464816\pi\) | ||||
0.110309 | + | 0.993897i | \(0.464816\pi\) | |||||||
\(164\) | 23.1194 | 1.80532 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.90833 | −0.536190 | ||||||||
\(167\) | −5.21110 | −0.403247 | −0.201624 | − | 0.979463i | \(-0.564622\pi\) | ||||
−0.201624 | + | 0.979463i | \(0.564622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.6333 | 2.35641 | ||||||||
\(170\) | 22.3944 | 1.71758 | ||||||||
\(171\) | −6.90833 | −0.528293 | ||||||||
\(172\) | −5.60555 | −0.427419 | ||||||||
\(173\) | −1.30278 | −0.0990482 | −0.0495241 | − | 0.998773i | \(-0.515770\pi\) | ||||
−0.0495241 | + | 0.998773i | \(0.515770\pi\) | |||||||
\(174\) | 24.9083 | 1.88830 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −15.4222 | −1.15920 | ||||||||
\(178\) | −33.9083 | −2.54154 | ||||||||
\(179\) | −6.39445 | −0.477944 | −0.238972 | − | 0.971027i | \(-0.576810\pi\) | ||||
−0.238972 | + | 0.971027i | \(0.576810\pi\) | |||||||
\(180\) | −27.4222 | −2.04393 | ||||||||
\(181\) | 25.2111 | 1.87393 | 0.936963 | − | 0.349428i | \(-0.113624\pi\) | ||||
0.936963 | + | 0.349428i | \(0.113624\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.90833 | −0.732445 | ||||||||
\(184\) | 8.09167 | 0.596526 | ||||||||
\(185\) | 18.7889 | 1.38139 | ||||||||
\(186\) | 5.30278 | 0.388818 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.30278 | 0.459677 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.9083 | −1.80704 | ||||||||
\(191\) | −26.8167 | −1.94038 | −0.970192 | − | 0.242336i | \(-0.922086\pi\) | ||||
−0.970192 | + | 0.242336i | \(0.922086\pi\) | |||||||
\(192\) | −29.5139 | −2.12998 | ||||||||
\(193\) | 2.11943 | 0.152560 | 0.0762799 | − | 0.997086i | \(-0.475696\pi\) | ||||
0.0762799 | + | 0.997086i | \(0.475696\pi\) | |||||||
\(194\) | −8.30278 | −0.596105 | ||||||||
\(195\) | −54.8444 | −3.92749 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6056 | 0.755614 | 0.377807 | − | 0.925884i | \(-0.376678\pi\) | ||||
0.377807 | + | 0.925884i | \(0.376678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.4222 | −1.37680 | −0.688402 | − | 0.725330i | \(-0.741687\pi\) | ||||
−0.688402 | + | 0.725330i | \(0.741687\pi\) | |||||||
\(200\) | −24.0000 | −1.69706 | ||||||||
\(201\) | 19.6056 | 1.38287 | ||||||||
\(202\) | 12.2111 | 0.859170 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 20.5139 | 1.43626 | ||||||||
\(205\) | −25.2389 | −1.76276 | ||||||||
\(206\) | −32.9361 | −2.29477 | ||||||||
\(207\) | −6.21110 | −0.431701 | ||||||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5139 | −1.06802 | −0.534010 | − | 0.845478i | \(-0.679315\pi\) | ||||
−0.534010 | + | 0.845478i | \(0.679315\pi\) | |||||||
\(212\) | −42.6333 | −2.92807 | ||||||||
\(213\) | −9.90833 | −0.678907 | ||||||||
\(214\) | 28.5416 | 1.95107 | ||||||||
\(215\) | 6.11943 | 0.417342 | ||||||||
\(216\) | 4.81665 | 0.327732 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −18.4222 | −1.24771 | ||||||||
\(219\) | −11.5139 | −0.778036 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.8167 | 1.19848 | ||||||||
\(222\) | 27.6333 | 1.85463 | ||||||||
\(223\) | −13.9083 | −0.931370 | −0.465685 | − | 0.884950i | \(-0.654192\pi\) | ||||
−0.465685 | + | 0.884950i | \(0.654192\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.4222 | 1.22815 | ||||||||
\(226\) | 24.6333 | 1.63858 | ||||||||
\(227\) | 6.51388 | 0.432341 | 0.216171 | − | 0.976356i | \(-0.430643\pi\) | ||||
0.216171 | + | 0.976356i | \(0.430643\pi\) | |||||||
\(228\) | −22.8167 | −1.51107 | ||||||||
\(229\) | 2.60555 | 0.172180 | 0.0860898 | − | 0.996287i | \(-0.472563\pi\) | ||||
0.0860898 | + | 0.996287i | \(0.472563\pi\) | |||||||
\(230\) | −22.3944 | −1.47665 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.0917 | 0.925164 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | −35.0278 | −2.28984 | ||||||||
\(235\) | −6.88057 | −0.448839 | ||||||||
\(236\) | −22.1194 | −1.43985 | ||||||||
\(237\) | 19.1194 | 1.24194 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.3305 | −1.70318 | −0.851590 | − | 0.524208i | \(-0.824361\pi\) | ||||
−0.851590 | + | 0.524208i | \(0.824361\pi\) | |||||||
\(240\) | −2.51388 | −0.162270 | ||||||||
\(241\) | 0.486122 | 0.0313139 | 0.0156569 | − | 0.999877i | \(-0.495016\pi\) | ||||
0.0156569 | + | 0.999877i | \(0.495016\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −19.6056 | −1.25770 | ||||||||
\(244\) | −14.2111 | −0.909773 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −37.1194 | −2.36665 | ||||||||
\(247\) | −19.8167 | −1.26090 | ||||||||
\(248\) | 3.00000 | 0.190500 | ||||||||
\(249\) | 6.90833 | 0.437797 | ||||||||
\(250\) | 24.9083 | 1.57534 | ||||||||
\(251\) | −4.39445 | −0.277375 | −0.138688 | − | 0.990336i | \(-0.544288\pi\) | ||||
−0.138688 | + | 0.990336i | \(0.544288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.60555 | 0.288978 | ||||||||
\(255\) | −22.3944 | −1.40239 | ||||||||
\(256\) | −17.9083 | −1.11927 | ||||||||
\(257\) | −6.48612 | −0.404593 | −0.202297 | − | 0.979324i | \(-0.564840\pi\) | ||||
−0.202297 | + | 0.979324i | \(0.564840\pi\) | |||||||
\(258\) | 9.00000 | 0.560316 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −78.6611 | −4.87835 | ||||||||
\(261\) | −10.8167 | −0.669534 | ||||||||
\(262\) | 13.8167 | 0.853596 | ||||||||
\(263\) | −20.2389 | −1.24798 | −0.623991 | − | 0.781432i | \(-0.714490\pi\) | ||||
−0.623991 | + | 0.781432i | \(0.714490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 46.5416 | 2.85903 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.9083 | 2.07516 | ||||||||
\(268\) | 28.1194 | 1.71767 | ||||||||
\(269\) | −16.1194 | −0.982819 | −0.491409 | − | 0.870929i | \(-0.663518\pi\) | ||||
−0.491409 | + | 0.870929i | \(0.663518\pi\) | |||||||
\(270\) | −13.3305 | −0.811270 | ||||||||
\(271\) | −28.5139 | −1.73209 | −0.866047 | − | 0.499962i | \(-0.833347\pi\) | ||||
−0.866047 | + | 0.499962i | \(0.833347\pi\) | |||||||
\(272\) | 0.816654 | 0.0495169 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.3028 | 1.40777 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −20.5139 | −1.23479 | ||||||||
\(277\) | −29.9361 | −1.79868 | −0.899342 | − | 0.437245i | \(-0.855954\pi\) | ||||
−0.899342 | + | 0.437245i | \(0.855954\pi\) | |||||||
\(278\) | −49.7527 | −2.98397 | ||||||||
\(279\) | −2.30278 | −0.137864 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.39445 | −0.381461 | −0.190730 | − | 0.981642i | \(-0.561086\pi\) | ||||
−0.190730 | + | 0.981642i | \(0.561086\pi\) | |||||||
\(282\) | −10.1194 | −0.602603 | ||||||||
\(283\) | 4.39445 | 0.261223 | 0.130611 | − | 0.991434i | \(-0.458306\pi\) | ||||
0.130611 | + | 0.991434i | \(0.458306\pi\) | |||||||
\(284\) | −14.2111 | −0.843274 | ||||||||
\(285\) | 24.9083 | 1.47544 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 12.2111 | 0.719546 | ||||||||
\(289\) | −9.72498 | −0.572058 | ||||||||
\(290\) | −39.0000 | −2.29016 | ||||||||
\(291\) | 8.30278 | 0.486717 | ||||||||
\(292\) | −16.5139 | −0.966402 | ||||||||
\(293\) | 4.81665 | 0.281392 | 0.140696 | − | 0.990053i | \(-0.455066\pi\) | ||||
0.140696 | + | 0.990053i | \(0.455066\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.1472 | 1.40590 | ||||||||
\(296\) | 15.6333 | 0.908668 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.3028 | −0.654752 | ||||||||
\(299\) | −17.8167 | −1.03036 | ||||||||
\(300\) | 60.8444 | 3.51285 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.486122 | −0.0279732 | ||||||||
\(303\) | −12.2111 | −0.701510 | ||||||||
\(304\) | −0.908327 | −0.0520961 | ||||||||
\(305\) | 15.5139 | 0.888322 | ||||||||
\(306\) | −14.3028 | −0.817635 | ||||||||
\(307\) | −16.6333 | −0.949313 | −0.474657 | − | 0.880171i | \(-0.657428\pi\) | ||||
−0.474657 | + | 0.880171i | \(0.657428\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 32.9361 | 1.87367 | ||||||||
\(310\) | −8.30278 | −0.471566 | ||||||||
\(311\) | −6.39445 | −0.362596 | −0.181298 | − | 0.983428i | \(-0.558030\pi\) | ||||
−0.181298 | + | 0.983428i | \(0.558030\pi\) | |||||||
\(312\) | −45.6333 | −2.58348 | ||||||||
\(313\) | −15.3028 | −0.864964 | −0.432482 | − | 0.901643i | \(-0.642362\pi\) | ||||
−0.432482 | + | 0.901643i | \(0.642362\pi\) | |||||||
\(314\) | 16.6056 | 0.937105 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 27.4222 | 1.54262 | ||||||||
\(317\) | 17.3028 | 0.971821 | 0.485910 | − | 0.874009i | \(-0.338488\pi\) | ||||
0.485910 | + | 0.874009i | \(0.338488\pi\) | |||||||
\(318\) | 68.4500 | 3.83848 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 46.2111 | 2.58328 | ||||||||
\(321\) | −28.5416 | −1.59304 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.09167 | −0.450233 | ||||||||
\(324\) | −35.0278 | −1.94599 | ||||||||
\(325\) | 52.8444 | 2.93128 | ||||||||
\(326\) | −6.48612 | −0.359233 | ||||||||
\(327\) | 18.4222 | 1.01875 | ||||||||
\(328\) | −21.0000 | −1.15953 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.8167 | 1.30908 | 0.654541 | − | 0.756027i | \(-0.272862\pi\) | ||||
0.654541 | + | 0.756027i | \(0.272862\pi\) | |||||||
\(332\) | 9.90833 | 0.543790 | ||||||||
\(333\) | −12.0000 | −0.657596 | ||||||||
\(334\) | 12.0000 | 0.656611 | ||||||||
\(335\) | −30.6972 | −1.67717 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7889 | −0.642182 | −0.321091 | − | 0.947048i | \(-0.604050\pi\) | ||||
−0.321091 | + | 0.947048i | \(0.604050\pi\) | |||||||
\(338\) | −70.5416 | −3.83696 | ||||||||
\(339\) | −24.6333 | −1.33790 | ||||||||
\(340\) | −32.1194 | −1.74192 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 15.9083 | 0.860224 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.09167 | 0.274525 | ||||||||
\(345\) | 22.3944 | 1.20568 | ||||||||
\(346\) | 3.00000 | 0.161281 | ||||||||
\(347\) | −9.60555 | −0.515653 | −0.257827 | − | 0.966191i | \(-0.583006\pi\) | ||||
−0.257827 | + | 0.966191i | \(0.583006\pi\) | |||||||
\(348\) | −35.7250 | −1.91506 | ||||||||
\(349\) | −4.69722 | −0.251437 | −0.125718 | − | 0.992066i | \(-0.540124\pi\) | ||||
−0.125718 | + | 0.992066i | \(0.540124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.6056 | −0.566082 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.09167 | −0.271002 | −0.135501 | − | 0.990777i | \(-0.543264\pi\) | ||||
−0.135501 | + | 0.990777i | \(0.543264\pi\) | |||||||
\(354\) | 35.5139 | 1.88754 | ||||||||
\(355\) | 15.5139 | 0.823391 | ||||||||
\(356\) | 48.6333 | 2.57756 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.7250 | 0.778239 | ||||||||
\(359\) | 33.9361 | 1.79108 | 0.895539 | − | 0.444983i | \(-0.146790\pi\) | ||||
0.895539 | + | 0.444983i | \(0.146790\pi\) | |||||||
\(360\) | 24.9083 | 1.31278 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | −58.0555 | −3.05133 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.0278 | 0.943616 | ||||||||
\(366\) | 22.8167 | 1.19265 | ||||||||
\(367\) | 17.6333 | 0.920451 | 0.460226 | − | 0.887802i | \(-0.347769\pi\) | ||||
0.460226 | + | 0.887802i | \(0.347769\pi\) | |||||||
\(368\) | −0.816654 | −0.0425710 | ||||||||
\(369\) | 16.1194 | 0.839144 | ||||||||
\(370\) | −43.2666 | −2.24932 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.60555 | −0.394329 | ||||||||
\(373\) | 20.1194 | 1.04174 | 0.520872 | − | 0.853635i | \(-0.325607\pi\) | ||||
0.520872 | + | 0.853635i | \(0.325607\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −24.9083 | −1.28626 | ||||||||
\(376\) | −5.72498 | −0.295243 | ||||||||
\(377\) | −31.0278 | −1.59801 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.8167 | −0.812447 | −0.406223 | − | 0.913774i | \(-0.633155\pi\) | ||||
−0.406223 | + | 0.913774i | \(0.633155\pi\) | |||||||
\(380\) | 35.7250 | 1.83265 | ||||||||
\(381\) | −4.60555 | −0.235950 | ||||||||
\(382\) | 61.7527 | 3.15954 | ||||||||
\(383\) | −38.6333 | −1.97407 | −0.987035 | − | 0.160506i | \(-0.948687\pi\) | ||||
−0.987035 | + | 0.160506i | \(0.948687\pi\) | |||||||
\(384\) | 43.5416 | 2.22197 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.88057 | −0.248414 | ||||||||
\(387\) | −3.90833 | −0.198671 | ||||||||
\(388\) | 11.9083 | 0.604554 | ||||||||
\(389\) | −7.81665 | −0.396320 | −0.198160 | − | 0.980170i | \(-0.563497\pi\) | ||||
−0.198160 | + | 0.980170i | \(0.563497\pi\) | |||||||
\(390\) | 126.294 | 6.39516 | ||||||||
\(391\) | −7.27502 | −0.367914 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.8167 | −0.696958 | ||||||||
\(394\) | −24.4222 | −1.23037 | ||||||||
\(395\) | −29.9361 | −1.50625 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.2111 | −1.51625 | −0.758126 | − | 0.652108i | \(-0.773885\pi\) | ||||
−0.758126 | + | 0.652108i | \(0.773885\pi\) | |||||||
\(398\) | 44.7250 | 2.24186 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.42221 | 0.121110 | ||||||||
\(401\) | −21.2111 | −1.05923 | −0.529616 | − | 0.848238i | \(-0.677664\pi\) | ||||
−0.529616 | + | 0.848238i | \(0.677664\pi\) | |||||||
\(402\) | −45.1472 | −2.25174 | ||||||||
\(403\) | −6.60555 | −0.329046 | ||||||||
\(404\) | −17.5139 | −0.871348 | ||||||||
\(405\) | 38.2389 | 1.90010 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −18.6333 | −0.922486 | ||||||||
\(409\) | 20.6056 | 1.01888 | 0.509439 | − | 0.860506i | \(-0.329853\pi\) | ||||
0.509439 | + | 0.860506i | \(0.329853\pi\) | |||||||
\(410\) | 58.1194 | 2.87031 | ||||||||
\(411\) | −23.3028 | −1.14944 | ||||||||
\(412\) | 47.2389 | 2.32729 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 14.3028 | 0.702943 | ||||||||
\(415\) | −10.8167 | −0.530969 | ||||||||
\(416\) | 35.0278 | 1.71738 | ||||||||
\(417\) | 49.7527 | 2.43640 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.4222 | 1.87705 | 0.938524 | − | 0.345215i | \(-0.112194\pi\) | ||||
0.938524 | + | 0.345215i | \(0.112194\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.8167 | −1.06328 | −0.531639 | − | 0.846971i | \(-0.678424\pi\) | ||||
−0.531639 | + | 0.846971i | \(0.678424\pi\) | |||||||
\(422\) | 35.7250 | 1.73906 | ||||||||
\(423\) | 4.39445 | 0.213665 | ||||||||
\(424\) | 38.7250 | 1.88065 | ||||||||
\(425\) | 21.5778 | 1.04668 | ||||||||
\(426\) | 22.8167 | 1.10547 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −40.9361 | −1.97872 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.0917 | −0.679561 | ||||||||
\(431\) | 3.11943 | 0.150258 | 0.0751288 | − | 0.997174i | \(-0.476063\pi\) | ||||
0.0751288 | + | 0.997174i | \(0.476063\pi\) | |||||||
\(432\) | −0.486122 | −0.0233885 | ||||||||
\(433\) | −29.1472 | −1.40072 | −0.700362 | − | 0.713788i | \(-0.746978\pi\) | ||||
−0.700362 | + | 0.713788i | \(0.746978\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 39.0000 | 1.86991 | ||||||||
\(436\) | 26.4222 | 1.26539 | ||||||||
\(437\) | 8.09167 | 0.387077 | ||||||||
\(438\) | 26.5139 | 1.26688 | ||||||||
\(439\) | 27.7250 | 1.32324 | 0.661621 | − | 0.749839i | \(-0.269869\pi\) | ||||
0.661621 | + | 0.749839i | \(0.269869\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −41.0278 | −1.95149 | ||||||||
\(443\) | 26.9361 | 1.27977 | 0.639886 | − | 0.768470i | \(-0.278982\pi\) | ||||
0.639886 | + | 0.768470i | \(0.278982\pi\) | |||||||
\(444\) | −39.6333 | −1.88091 | ||||||||
\(445\) | −53.0917 | −2.51679 | ||||||||
\(446\) | 32.0278 | 1.51656 | ||||||||
\(447\) | 11.3028 | 0.534603 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.3305 | 1.90332 | 0.951658 | − | 0.307160i | \(-0.0993788\pi\) | ||||
0.951658 | + | 0.307160i | \(0.0993788\pi\) | |||||||
\(450\) | −42.4222 | −1.99980 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −35.3305 | −1.66181 | ||||||||
\(453\) | 0.486122 | 0.0228400 | ||||||||
\(454\) | −15.0000 | −0.703985 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 20.7250 | 0.970536 | ||||||||
\(457\) | −21.1194 | −0.987925 | −0.493963 | − | 0.869483i | \(-0.664452\pi\) | ||||
−0.493963 | + | 0.869483i | \(0.664452\pi\) | |||||||
\(458\) | −6.00000 | −0.280362 | ||||||||
\(459\) | −4.33053 | −0.202132 | ||||||||
\(460\) | 32.1194 | 1.49758 | ||||||||
\(461\) | 8.09167 | 0.376867 | 0.188433 | − | 0.982086i | \(-0.439659\pi\) | ||||
0.188433 | + | 0.982086i | \(0.439659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.8167 | −1.43217 | −0.716086 | − | 0.698012i | \(-0.754068\pi\) | ||||
−0.716086 | + | 0.698012i | \(0.754068\pi\) | |||||||
\(464\) | −1.42221 | −0.0660242 | ||||||||
\(465\) | 8.30278 | 0.385032 | ||||||||
\(466\) | 41.4500 | 1.92013 | ||||||||
\(467\) | 13.5416 | 0.626632 | 0.313316 | − | 0.949649i | \(-0.398560\pi\) | ||||
0.313316 | + | 0.949649i | \(0.398560\pi\) | |||||||
\(468\) | 50.2389 | 2.32229 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 15.8444 | 0.730848 | ||||||||
\(471\) | −16.6056 | −0.765143 | ||||||||
\(472\) | 20.0917 | 0.924794 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −44.0278 | −2.02226 | ||||||||
\(475\) | −24.0000 | −1.10120 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.7250 | −1.36101 | ||||||||
\(478\) | 60.6333 | 2.77330 | ||||||||
\(479\) | −28.6333 | −1.30829 | −0.654145 | − | 0.756370i | \(-0.726971\pi\) | ||||
−0.654145 | + | 0.756370i | \(0.726971\pi\) | |||||||
\(480\) | −44.0278 | −2.00958 | ||||||||
\(481\) | −34.4222 | −1.56952 | ||||||||
\(482\) | −1.11943 | −0.0509886 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0000 | −0.590300 | ||||||||
\(486\) | 45.1472 | 2.04792 | ||||||||
\(487\) | −2.81665 | −0.127635 | −0.0638174 | − | 0.997962i | \(-0.520328\pi\) | ||||
−0.0638174 | + | 0.997962i | \(0.520328\pi\) | |||||||
\(488\) | 12.9083 | 0.584333 | ||||||||
\(489\) | 6.48612 | 0.293313 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.6972 | 0.573018 | 0.286509 | − | 0.958078i | \(-0.407505\pi\) | ||||
0.286509 | + | 0.958078i | \(0.407505\pi\) | |||||||
\(492\) | 53.2389 | 2.40019 | ||||||||
\(493\) | −12.6695 | −0.570604 | ||||||||
\(494\) | 45.6333 | 2.05314 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.302776 | −0.0135950 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −15.9083 | −0.712869 | ||||||||
\(499\) | 2.90833 | 0.130195 | 0.0650973 | − | 0.997879i | \(-0.479264\pi\) | ||||
0.0650973 | + | 0.997879i | \(0.479264\pi\) | |||||||
\(500\) | −35.7250 | −1.59767 | ||||||||
\(501\) | −12.0000 | −0.536120 | ||||||||
\(502\) | 10.1194 | 0.451652 | ||||||||
\(503\) | 5.57779 | 0.248702 | 0.124351 | − | 0.992238i | \(-0.460315\pi\) | ||||
0.124351 | + | 0.992238i | \(0.460315\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.1194 | 0.850803 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 70.5416 | 3.13286 | ||||||||
\(508\) | −6.60555 | −0.293074 | ||||||||
\(509\) | −22.3028 | −0.988553 | −0.494277 | − | 0.869305i | \(-0.664567\pi\) | ||||
−0.494277 | + | 0.869305i | \(0.664567\pi\) | |||||||
\(510\) | 51.5694 | 2.28353 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.42221 | 0.151242 | ||||||||
\(513\) | 4.81665 | 0.212660 | ||||||||
\(514\) | 14.9361 | 0.658802 | ||||||||
\(515\) | −51.5694 | −2.27242 | ||||||||
\(516\) | −12.9083 | −0.568257 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.00000 | −0.131685 | ||||||||
\(520\) | 71.4500 | 3.13329 | ||||||||
\(521\) | −7.42221 | −0.325173 | −0.162586 | − | 0.986694i | \(-0.551984\pi\) | ||||
−0.162586 | + | 0.986694i | \(0.551984\pi\) | |||||||
\(522\) | 24.9083 | 1.09021 | ||||||||
\(523\) | −44.5416 | −1.94767 | −0.973835 | − | 0.227257i | \(-0.927024\pi\) | ||||
−0.973835 | + | 0.227257i | \(0.927024\pi\) | |||||||
\(524\) | −19.8167 | −0.865695 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 46.6056 | 2.03210 | ||||||||
\(527\) | −2.69722 | −0.117493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.7250 | −0.683695 | ||||||||
\(530\) | −107.175 | −4.65538 | ||||||||
\(531\) | −15.4222 | −0.669267 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 46.2389 | 2.00283 | ||||||||
\(534\) | −78.0833 | −3.37899 | ||||||||
\(535\) | 44.6888 | 1.93207 | ||||||||
\(536\) | −25.5416 | −1.10323 | ||||||||
\(537\) | −14.7250 | −0.635430 | ||||||||
\(538\) | 37.1194 | 1.60033 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.1194 | 0.822769 | ||||||||
\(541\) | 32.3944 | 1.39275 | 0.696373 | − | 0.717680i | \(-0.254796\pi\) | ||||
0.696373 | + | 0.717680i | \(0.254796\pi\) | |||||||
\(542\) | 65.6611 | 2.82038 | ||||||||
\(543\) | 58.0555 | 2.49140 | ||||||||
\(544\) | 14.3028 | 0.613226 | ||||||||
\(545\) | −28.8444 | −1.23556 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.9361 | 1.27997 | 0.639987 | − | 0.768386i | \(-0.278940\pi\) | ||||
0.639987 | + | 0.768386i | \(0.278940\pi\) | |||||||
\(548\) | −33.4222 | −1.42773 | ||||||||
\(549\) | −9.90833 | −0.422877 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.0917 | 0.600325 | ||||||||
\(552\) | 18.6333 | 0.793086 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 68.9361 | 2.92881 | ||||||||
\(555\) | 43.2666 | 1.83657 | ||||||||
\(556\) | 71.3583 | 3.02627 | ||||||||
\(557\) | −7.23886 | −0.306720 | −0.153360 | − | 0.988170i | \(-0.549009\pi\) | ||||
−0.153360 | + | 0.988170i | \(0.549009\pi\) | |||||||
\(558\) | 5.30278 | 0.224484 | ||||||||
\(559\) | −11.2111 | −0.474179 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.7250 | 0.621136 | ||||||||
\(563\) | −0.302776 | −0.0127605 | −0.00638024 | − | 0.999980i | \(-0.502031\pi\) | ||||
−0.00638024 | + | 0.999980i | \(0.502031\pi\) | |||||||
\(564\) | 14.5139 | 0.611145 | ||||||||
\(565\) | 38.5694 | 1.62263 | ||||||||
\(566\) | −10.1194 | −0.425351 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.9083 | 0.541621 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | −57.3583 | −2.40247 | ||||||||
\(571\) | −25.8444 | −1.08155 | −0.540777 | − | 0.841166i | \(-0.681870\pi\) | ||||
−0.540777 | + | 0.841166i | \(0.681870\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −61.7527 | −2.57976 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.5778 | −0.899856 | ||||||||
\(576\) | −29.5139 | −1.22974 | ||||||||
\(577\) | −2.21110 | −0.0920494 | −0.0460247 | − | 0.998940i | \(-0.514655\pi\) | ||||
−0.0460247 | + | 0.998940i | \(0.514655\pi\) | |||||||
\(578\) | 22.3944 | 0.931486 | ||||||||
\(579\) | 4.88057 | 0.202830 | ||||||||
\(580\) | 55.9361 | 2.32262 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −19.1194 | −0.792526 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 15.0000 | 0.620704 | ||||||||
\(585\) | −54.8444 | −2.26754 | ||||||||
\(586\) | −11.0917 | −0.458193 | ||||||||
\(587\) | 13.6056 | 0.561561 | 0.280781 | − | 0.959772i | \(-0.409407\pi\) | ||||
0.280781 | + | 0.959772i | \(0.409407\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.00000 | 0.123613 | ||||||||
\(590\) | −55.6056 | −2.28924 | ||||||||
\(591\) | 24.4222 | 1.00460 | ||||||||
\(592\) | −1.57779 | −0.0648470 | ||||||||
\(593\) | 22.6056 | 0.928299 | 0.464149 | − | 0.885757i | \(-0.346360\pi\) | ||||
0.464149 | + | 0.885757i | \(0.346360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.2111 | 0.664033 | ||||||||
\(597\) | −44.7250 | −1.83047 | ||||||||
\(598\) | 41.0278 | 1.67775 | ||||||||
\(599\) | −14.7889 | −0.604258 | −0.302129 | − | 0.953267i | \(-0.597697\pi\) | ||||
−0.302129 | + | 0.953267i | \(0.597697\pi\) | |||||||
\(600\) | −55.2666 | −2.25625 | ||||||||
\(601\) | −5.81665 | −0.237266 | −0.118633 | − | 0.992938i | \(-0.537851\pi\) | ||||
−0.118633 | + | 0.992938i | \(0.537851\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.6056 | 0.798400 | ||||||||
\(604\) | 0.697224 | 0.0283697 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 28.1194 | 1.14227 | ||||||||
\(607\) | −20.5416 | −0.833759 | −0.416880 | − | 0.908962i | \(-0.636876\pi\) | ||||
−0.416880 | + | 0.908962i | \(0.636876\pi\) | |||||||
\(608\) | −15.9083 | −0.645168 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −35.7250 | −1.44646 | ||||||||
\(611\) | 12.6056 | 0.509966 | ||||||||
\(612\) | 20.5139 | 0.829224 | ||||||||
\(613\) | 33.0555 | 1.33510 | 0.667550 | − | 0.744565i | \(-0.267343\pi\) | ||||
0.667550 | + | 0.744565i | \(0.267343\pi\) | |||||||
\(614\) | 38.3028 | 1.54577 | ||||||||
\(615\) | −58.1194 | −2.34360 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6333 | 0.870924 | 0.435462 | − | 0.900207i | \(-0.356585\pi\) | ||||
0.435462 | + | 0.900207i | \(0.356585\pi\) | |||||||
\(618\) | −75.8444 | −3.05091 | ||||||||
\(619\) | −39.8167 | −1.60037 | −0.800183 | − | 0.599756i | \(-0.795264\pi\) | ||||
−0.800183 | + | 0.599756i | \(0.795264\pi\) | |||||||
\(620\) | 11.9083 | 0.478250 | ||||||||
\(621\) | 4.33053 | 0.173778 | ||||||||
\(622\) | 14.7250 | 0.590418 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.60555 | 0.184370 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 35.2389 | 1.40843 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.8167 | −0.950388 | ||||||||
\(629\) | −14.0555 | −0.560430 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.0555 | −1.23630 | −0.618150 | − | 0.786060i | \(-0.712118\pi\) | ||||
−0.618150 | + | 0.786060i | \(0.712118\pi\) | |||||||
\(632\) | −24.9083 | −0.990800 | ||||||||
\(633\) | −35.7250 | −1.41994 | ||||||||
\(634\) | −39.8444 | −1.58242 | ||||||||
\(635\) | 7.21110 | 0.286164 | ||||||||
\(636\) | −98.1749 | −3.89289 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.90833 | −0.391967 | ||||||||
\(640\) | −68.1749 | −2.69485 | ||||||||
\(641\) | −28.8167 | −1.13819 | −0.569095 | − | 0.822272i | \(-0.692706\pi\) | ||||
−0.569095 | + | 0.822272i | \(0.692706\pi\) | |||||||
\(642\) | 65.7250 | 2.59396 | ||||||||
\(643\) | 1.23886 | 0.0488558 | 0.0244279 | − | 0.999702i | \(-0.492224\pi\) | ||||
0.0244279 | + | 0.999702i | \(0.492224\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.0917 | 0.554859 | ||||||||
\(646\) | 18.6333 | 0.733118 | ||||||||
\(647\) | −10.6056 | −0.416947 | −0.208474 | − | 0.978028i | \(-0.566850\pi\) | ||||
−0.208474 | + | 0.978028i | \(0.566850\pi\) | |||||||
\(648\) | 31.8167 | 1.24988 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −121.689 | −4.77303 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.30278 | 0.364325 | ||||||||
\(653\) | −6.81665 | −0.266756 | −0.133378 | − | 0.991065i | \(-0.542582\pi\) | ||||
−0.133378 | + | 0.991065i | \(0.542582\pi\) | |||||||
\(654\) | −42.4222 | −1.65884 | ||||||||
\(655\) | 21.6333 | 0.845283 | ||||||||
\(656\) | 2.11943 | 0.0827498 | ||||||||
\(657\) | −11.5139 | −0.449199 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.63331 | −0.180488 | −0.0902440 | − | 0.995920i | \(-0.528765\pi\) | ||||
−0.0902440 | + | 0.995920i | \(0.528765\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.3028 | 0.711895 | 0.355948 | − | 0.934506i | \(-0.384158\pi\) | ||||
0.355948 | + | 0.934506i | \(0.384158\pi\) | |||||||
\(662\) | −54.8444 | −2.13159 | ||||||||
\(663\) | 41.0278 | 1.59339 | ||||||||
\(664\) | −9.00000 | −0.349268 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 27.6333 | 1.07077 | ||||||||
\(667\) | 12.6695 | 0.490564 | ||||||||
\(668\) | −17.2111 | −0.665918 | ||||||||
\(669\) | −32.0278 | −1.23826 | ||||||||
\(670\) | 70.6888 | 2.73095 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.42221 | 0.324652 | 0.162326 | − | 0.986737i | \(-0.448100\pi\) | ||||
0.162326 | + | 0.986737i | \(0.448100\pi\) | |||||||
\(674\) | 27.1472 | 1.04567 | ||||||||
\(675\) | −12.8444 | −0.494382 | ||||||||
\(676\) | 101.175 | 3.89134 | ||||||||
\(677\) | 10.3028 | 0.395968 | 0.197984 | − | 0.980205i | \(-0.436561\pi\) | ||||
0.197984 | + | 0.980205i | \(0.436561\pi\) | |||||||
\(678\) | 56.7250 | 2.17851 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 29.1749 | 1.11881 | ||||||||
\(681\) | 15.0000 | 0.574801 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.6972 | 0.600638 | 0.300319 | − | 0.953839i | \(-0.402907\pi\) | ||||
0.300319 | + | 0.953839i | \(0.402907\pi\) | |||||||
\(684\) | −22.8167 | −0.872417 | ||||||||
\(685\) | 36.4861 | 1.39406 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | −0.513878 | −0.0195914 | ||||||||
\(689\) | −85.2666 | −3.24840 | ||||||||
\(690\) | −51.5694 | −1.96321 | ||||||||
\(691\) | 17.0278 | 0.647766 | 0.323883 | − | 0.946097i | \(-0.395012\pi\) | ||||
0.323883 | + | 0.946097i | \(0.395012\pi\) | |||||||
\(692\) | −4.30278 | −0.163567 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.1194 | 0.839642 | ||||||||
\(695\) | −77.8999 | −2.95491 | ||||||||
\(696\) | 32.4500 | 1.23001 | ||||||||
\(697\) | 18.8806 | 0.715153 | ||||||||
\(698\) | 10.8167 | 0.409416 | ||||||||
\(699\) | −41.4500 | −1.56778 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.1194 | 1.17536 | 0.587682 | − | 0.809092i | \(-0.300040\pi\) | ||||
0.587682 | + | 0.809092i | \(0.300040\pi\) | |||||||
\(702\) | 24.4222 | 0.921757 | ||||||||
\(703\) | 15.6333 | 0.589621 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.8444 | −0.596735 | ||||||||
\(706\) | 11.7250 | 0.441275 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −50.9361 | −1.91430 | ||||||||
\(709\) | 25.3305 | 0.951308 | 0.475654 | − | 0.879632i | \(-0.342211\pi\) | ||||
0.475654 | + | 0.879632i | \(0.342211\pi\) | |||||||
\(710\) | −35.7250 | −1.34073 | ||||||||
\(711\) | 19.1194 | 0.717035 | ||||||||
\(712\) | −44.1749 | −1.65553 | ||||||||
\(713\) | 2.69722 | 0.101012 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.1194 | −0.789270 | ||||||||
\(717\) | −60.6333 | −2.26439 | ||||||||
\(718\) | −78.1472 | −2.91643 | ||||||||
\(719\) | −21.2389 | −0.792076 | −0.396038 | − | 0.918234i | \(-0.629615\pi\) | ||||
−0.396038 | + | 0.918234i | \(0.629615\pi\) | |||||||
\(720\) | −2.51388 | −0.0936867 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 23.0278 | 0.857004 | ||||||||
\(723\) | 1.11943 | 0.0416320 | ||||||||
\(724\) | 83.2666 | 3.09458 | ||||||||
\(725\) | −37.5778 | −1.39560 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.1194 | −0.894540 | −0.447270 | − | 0.894399i | \(-0.647604\pi\) | ||||
−0.447270 | + | 0.894399i | \(0.647604\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.3305 | −0.493723 | ||||||||
\(730\) | −41.5139 | −1.53650 | ||||||||
\(731\) | −4.57779 | −0.169316 | ||||||||
\(732\) | −32.7250 | −1.20955 | ||||||||
\(733\) | −6.78890 | −0.250754 | −0.125377 | − | 0.992109i | \(-0.540014\pi\) | ||||
−0.125377 | + | 0.992109i | \(0.540014\pi\) | |||||||
\(734\) | −40.6056 | −1.49878 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.3028 | −0.527207 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −37.1194 | −1.36639 | ||||||||
\(739\) | 43.1194 | 1.58617 | 0.793087 | − | 0.609108i | \(-0.208473\pi\) | ||||
0.793087 | + | 0.609108i | \(0.208473\pi\) | |||||||
\(740\) | 62.0555 | 2.28121 | ||||||||
\(741\) | −45.6333 | −1.67638 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −44.9361 | −1.64855 | −0.824273 | − | 0.566193i | \(-0.808416\pi\) | ||||
−0.824273 | + | 0.566193i | \(0.808416\pi\) | |||||||
\(744\) | 6.90833 | 0.253272 | ||||||||
\(745\) | −17.6972 | −0.648376 | ||||||||
\(746\) | −46.3305 | −1.69628 | ||||||||
\(747\) | 6.90833 | 0.252762 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 57.3583 | 2.09443 | ||||||||
\(751\) | 7.63331 | 0.278543 | 0.139272 | − | 0.990254i | \(-0.455524\pi\) | ||||
0.139272 | + | 0.990254i | \(0.455524\pi\) | |||||||
\(752\) | 0.577795 | 0.0210700 | ||||||||
\(753\) | −10.1194 | −0.368773 | ||||||||
\(754\) | 71.4500 | 2.60205 | ||||||||
\(755\) | −0.761141 | −0.0277008 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.8167 | −0.865631 | −0.432816 | − | 0.901483i | \(-0.642480\pi\) | ||||
−0.432816 | + | 0.901483i | \(0.642480\pi\) | |||||||
\(758\) | 36.4222 | 1.32291 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −32.4500 | −1.17708 | ||||||||
\(761\) | 42.0000 | 1.52250 | 0.761249 | − | 0.648459i | \(-0.224586\pi\) | ||||
0.761249 | + | 0.648459i | \(0.224586\pi\) | |||||||
\(762\) | 10.6056 | 0.384199 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −88.5694 | −3.20433 | ||||||||
\(765\) | −22.3944 | −0.809673 | ||||||||
\(766\) | 88.9638 | 3.21439 | ||||||||
\(767\) | −44.2389 | −1.59737 | ||||||||
\(768\) | −41.2389 | −1.48808 | ||||||||
\(769\) | −39.3305 | −1.41830 | −0.709148 | − | 0.705060i | \(-0.750920\pi\) | ||||
−0.709148 | + | 0.705060i | \(0.750920\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.9361 | −0.537910 | ||||||||
\(772\) | 7.00000 | 0.251936 | ||||||||
\(773\) | −30.6333 | −1.10180 | −0.550902 | − | 0.834570i | \(-0.685716\pi\) | ||||
−0.550902 | + | 0.834570i | \(0.685716\pi\) | |||||||
\(774\) | 9.00000 | 0.323498 | ||||||||
\(775\) | −8.00000 | −0.287368 | ||||||||
\(776\) | −10.8167 | −0.388295 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.0000 | 0.645331 | ||||||||
\(779\) | −21.0000 | −0.752403 | ||||||||
\(780\) | −181.139 | −6.48581 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 16.7527 | 0.599077 | ||||||||
\(783\) | 7.54163 | 0.269516 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.0000 | 0.927980 | ||||||||
\(786\) | 31.8167 | 1.13486 | ||||||||
\(787\) | −22.4861 | −0.801544 | −0.400772 | − | 0.916178i | \(-0.631258\pi\) | ||||
−0.400772 | + | 0.916178i | \(0.631258\pi\) | |||||||
\(788\) | 35.0278 | 1.24781 | ||||||||
\(789\) | −46.6056 | −1.65920 | ||||||||
\(790\) | 68.9361 | 2.45264 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.4222 | −1.00930 | ||||||||
\(794\) | 69.5694 | 2.46893 | ||||||||
\(795\) | 107.175 | 3.80110 | ||||||||
\(796\) | −64.1472 | −2.27364 | ||||||||
\(797\) | 28.6333 | 1.01424 | 0.507122 | − | 0.861874i | \(-0.330709\pi\) | ||||
0.507122 | + | 0.861874i | \(0.330709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.14719 | 0.182094 | ||||||||
\(800\) | 42.4222 | 1.49985 | ||||||||
\(801\) | 33.9083 | 1.19809 | ||||||||
\(802\) | 48.8444 | 1.72476 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 64.7527 | 2.28365 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.2111 | 0.535788 | ||||||||
\(807\) | −37.1194 | −1.30667 | ||||||||
\(808\) | 15.9083 | 0.559653 | ||||||||
\(809\) | −8.09167 | −0.284488 | −0.142244 | − | 0.989832i | \(-0.545432\pi\) | ||||
−0.142244 | + | 0.989832i | \(0.545432\pi\) | |||||||
\(810\) | −88.0555 | −3.09396 | ||||||||
\(811\) | −40.8444 | −1.43424 | −0.717121 | − | 0.696949i | \(-0.754540\pi\) | ||||
−0.717121 | + | 0.696949i | \(0.754540\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −65.6611 | −2.30283 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.1556 | −0.355735 | ||||||||
\(816\) | 1.88057 | 0.0658331 | ||||||||
\(817\) | 5.09167 | 0.178135 | ||||||||
\(818\) | −47.4500 | −1.65905 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −83.3583 | −2.91100 | ||||||||
\(821\) | 27.4222 | 0.957042 | 0.478521 | − | 0.878076i | \(-0.341173\pi\) | ||||
0.478521 | + | 0.878076i | \(0.341173\pi\) | |||||||
\(822\) | 53.6611 | 1.87164 | ||||||||
\(823\) | 35.2111 | 1.22738 | 0.613691 | − | 0.789546i | \(-0.289684\pi\) | ||||
0.613691 | + | 0.789546i | \(0.289684\pi\) | |||||||
\(824\) | −42.9083 | −1.49478 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.1833 | 0.493203 | 0.246602 | − | 0.969117i | \(-0.420686\pi\) | ||||
0.246602 | + | 0.969117i | \(0.420686\pi\) | |||||||
\(828\) | −20.5139 | −0.712907 | ||||||||
\(829\) | −13.2750 | −0.461060 | −0.230530 | − | 0.973065i | \(-0.574046\pi\) | ||||
−0.230530 | + | 0.973065i | \(0.574046\pi\) | |||||||
\(830\) | 24.9083 | 0.864581 | ||||||||
\(831\) | −68.9361 | −2.39137 | ||||||||
\(832\) | −84.6611 | −2.93509 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −114.569 | −3.96721 | ||||||||
\(835\) | 18.7889 | 0.650217 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.60555 | 0.0554960 | ||||||||
\(838\) | −88.4777 | −3.05641 | ||||||||
\(839\) | −42.2111 | −1.45729 | −0.728645 | − | 0.684892i | \(-0.759849\pi\) | ||||
−0.728645 | + | 0.684892i | \(0.759849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.93608 | −0.239175 | ||||||||
\(842\) | 50.2389 | 1.73135 | ||||||||
\(843\) | −14.7250 | −0.507155 | ||||||||
\(844\) | −51.2389 | −1.76371 | ||||||||
\(845\) | −110.450 | −3.79959 | ||||||||
\(846\) | −10.1194 | −0.347913 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.90833 | −0.134212 | ||||||||
\(849\) | 10.1194 | 0.347298 | ||||||||
\(850\) | −49.6888 | −1.70431 | ||||||||
\(851\) | 14.0555 | 0.481817 | ||||||||
\(852\) | −32.7250 | −1.12114 | ||||||||
\(853\) | −45.7250 | −1.56559 | −0.782797 | − | 0.622277i | \(-0.786208\pi\) | ||||
−0.782797 | + | 0.622277i | \(0.786208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24.9083 | 0.851847 | ||||||||
\(856\) | 37.1833 | 1.27090 | ||||||||
\(857\) | 35.3583 | 1.20782 | 0.603908 | − | 0.797054i | \(-0.293609\pi\) | ||||
0.603908 | + | 0.797054i | \(0.293609\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.3028 | 0.863320 | 0.431660 | − | 0.902036i | \(-0.357928\pi\) | ||||
0.431660 | + | 0.902036i | \(0.357928\pi\) | |||||||
\(860\) | 20.2111 | 0.689193 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.18335 | −0.244666 | ||||||||
\(863\) | 31.4222 | 1.06962 | 0.534812 | − | 0.844971i | \(-0.320382\pi\) | ||||
0.534812 | + | 0.844971i | \(0.320382\pi\) | |||||||
\(864\) | −8.51388 | −0.289648 | ||||||||
\(865\) | 4.69722 | 0.159710 | ||||||||
\(866\) | 67.1194 | 2.28081 | ||||||||
\(867\) | −22.3944 | −0.760555 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −89.8082 | −3.04478 | ||||||||
\(871\) | 56.2389 | 1.90558 | ||||||||
\(872\) | −24.0000 | −0.812743 | ||||||||
\(873\) | 8.30278 | 0.281006 | ||||||||
\(874\) | −18.6333 | −0.630281 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −38.0278 | −1.28484 | ||||||||
\(877\) | −47.0555 | −1.58895 | −0.794476 | − | 0.607296i | \(-0.792254\pi\) | ||||
−0.794476 | + | 0.607296i | \(0.792254\pi\) | |||||||
\(878\) | −63.8444 | −2.15464 | ||||||||
\(879\) | 11.0917 | 0.374113 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.3305 | −1.15663 | −0.578313 | − | 0.815815i | \(-0.696289\pi\) | ||||
−0.578313 | + | 0.815815i | \(0.696289\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.72498 | −0.259966 | −0.129983 | − | 0.991516i | \(-0.541492\pi\) | ||||
−0.129983 | + | 0.991516i | \(0.541492\pi\) | |||||||
\(884\) | 58.8444 | 1.97915 | ||||||||
\(885\) | 55.6056 | 1.86916 | ||||||||
\(886\) | −62.0278 | −2.08386 | ||||||||
\(887\) | 44.1194 | 1.48139 | 0.740693 | − | 0.671844i | \(-0.234497\pi\) | ||||
0.740693 | + | 0.671844i | \(0.234497\pi\) | |||||||
\(888\) | 36.0000 | 1.20808 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 122.258 | 4.09810 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −45.9361 | −1.53805 | ||||||||
\(893\) | −5.72498 | −0.191579 | ||||||||
\(894\) | −26.0278 | −0.870498 | ||||||||
\(895\) | 23.0555 | 0.770661 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −41.0278 | −1.36988 | ||||||||
\(898\) | −92.8722 | −3.09918 | ||||||||
\(899\) | 4.69722 | 0.156661 | ||||||||
\(900\) | 60.8444 | 2.02815 | ||||||||
\(901\) | −34.8167 | −1.15991 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.0917 | 1.06735 | ||||||||
\(905\) | −90.8999 | −3.02162 | ||||||||
\(906\) | −1.11943 | −0.0371906 | ||||||||
\(907\) | 0.394449 | 0.0130975 | 0.00654873 | − | 0.999979i | \(-0.497915\pi\) | ||||
0.00654873 | + | 0.999979i | \(0.497915\pi\) | |||||||
\(908\) | 21.5139 | 0.713963 | ||||||||
\(909\) | −12.2111 | −0.405017 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.4500 | −1.67148 | −0.835741 | − | 0.549124i | \(-0.814961\pi\) | ||||
−0.835741 | + | 0.549124i | \(0.814961\pi\) | |||||||
\(912\) | −2.09167 | −0.0692622 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 48.6333 | 1.60865 | ||||||||
\(915\) | 35.7250 | 1.18103 | ||||||||
\(916\) | 8.60555 | 0.284335 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.97224 | 0.329133 | ||||||||
\(919\) | −55.4777 | −1.83004 | −0.915021 | − | 0.403407i | \(-0.867826\pi\) | ||||
−0.915021 | + | 0.403407i | \(0.867826\pi\) | |||||||
\(920\) | −29.1749 | −0.961869 | ||||||||
\(921\) | −38.3028 | −1.26212 | ||||||||
\(922\) | −18.6333 | −0.613655 | ||||||||
\(923\) | −28.4222 | −0.935528 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41.6888 | −1.37072 | ||||||||
\(926\) | 70.9638 | 2.33202 | ||||||||
\(927\) | 32.9361 | 1.08176 | ||||||||
\(928\) | −24.9083 | −0.817656 | ||||||||
\(929\) | 27.6333 | 0.906619 | 0.453310 | − | 0.891353i | \(-0.350243\pi\) | ||||
0.453310 | + | 0.891353i | \(0.350243\pi\) | |||||||
\(930\) | −19.1194 | −0.626951 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −59.4500 | −1.94735 | ||||||||
\(933\) | −14.7250 | −0.482074 | ||||||||
\(934\) | −31.1833 | −1.02035 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −45.6333 | −1.49157 | ||||||||
\(937\) | 31.6056 | 1.03251 | 0.516254 | − | 0.856435i | \(-0.327326\pi\) | ||||
0.516254 | + | 0.856435i | \(0.327326\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.2389 | −1.14998 | ||||||||
\(940\) | −22.7250 | −0.741207 | ||||||||
\(941\) | 37.4222 | 1.21993 | 0.609965 | − | 0.792429i | \(-0.291184\pi\) | ||||
0.609965 | + | 0.792429i | \(0.291184\pi\) | |||||||
\(942\) | 38.2389 | 1.24589 | ||||||||
\(943\) | −18.8806 | −0.614836 | ||||||||
\(944\) | −2.02776 | −0.0659978 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.6611 | 1.51628 | 0.758140 | − | 0.652091i | \(-0.226108\pi\) | ||||
0.758140 | + | 0.652091i | \(0.226108\pi\) | |||||||
\(948\) | 63.1472 | 2.05093 | ||||||||
\(949\) | −33.0278 | −1.07213 | ||||||||
\(950\) | 55.2666 | 1.79309 | ||||||||
\(951\) | 39.8444 | 1.29204 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.02776 | 0.195258 | 0.0976291 | − | 0.995223i | \(-0.468874\pi\) | ||||
0.0976291 | + | 0.995223i | \(0.468874\pi\) | |||||||
\(954\) | 68.4500 | 2.21615 | ||||||||
\(955\) | 96.6888 | 3.12878 | ||||||||
\(956\) | −86.9638 | −2.81261 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 65.9361 | 2.13030 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 106.414 | 3.43449 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 79.2666 | 2.55566 | ||||||||
\(963\) | −28.5416 | −0.919741 | ||||||||
\(964\) | 1.60555 | 0.0517113 | ||||||||
\(965\) | −7.64171 | −0.245995 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.5139 | −1.30284 | −0.651419 | − | 0.758718i | \(-0.725826\pi\) | ||||
−0.651419 | + | 0.758718i | \(0.725826\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.6333 | −0.598588 | ||||||||
\(970\) | 29.9361 | 0.961190 | ||||||||
\(971\) | 6.36669 | 0.204317 | 0.102158 | − | 0.994768i | \(-0.467425\pi\) | ||||
0.102158 | + | 0.994768i | \(0.467425\pi\) | |||||||
\(972\) | −64.7527 | −2.07695 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.48612 | 0.207829 | ||||||||
\(975\) | 121.689 | 3.89716 | ||||||||
\(976\) | −1.30278 | −0.0417008 | ||||||||
\(977\) | 40.0278 | 1.28060 | 0.640301 | − | 0.768124i | \(-0.278810\pi\) | ||||
0.640301 | + | 0.768124i | \(0.278810\pi\) | |||||||
\(978\) | −14.9361 | −0.477603 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.4222 | 0.588176 | ||||||||
\(982\) | −29.2389 | −0.933049 | ||||||||
\(983\) | 9.27502 | 0.295827 | 0.147914 | − | 0.989000i | \(-0.452744\pi\) | ||||
0.147914 | + | 0.989000i | \(0.452744\pi\) | |||||||
\(984\) | −48.3583 | −1.54161 | ||||||||
\(985\) | −38.2389 | −1.21839 | ||||||||
\(986\) | 29.1749 | 0.929119 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −65.4500 | −2.08224 | ||||||||
\(989\) | 4.57779 | 0.145565 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.7250 | −1.38897 | −0.694485 | − | 0.719507i | \(-0.744368\pi\) | ||||
−0.694485 | + | 0.719507i | \(0.744368\pi\) | |||||||
\(992\) | −5.30278 | −0.168363 | ||||||||
\(993\) | 54.8444 | 1.74043 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 70.0278 | 2.22003 | ||||||||
\(996\) | 22.8167 | 0.722973 | ||||||||
\(997\) | 45.6972 | 1.44725 | 0.723623 | − | 0.690196i | \(-0.242476\pi\) | ||||
0.723623 | + | 0.690196i | \(0.242476\pi\) | |||||||
\(998\) | −6.69722 | −0.211997 | ||||||||
\(999\) | 8.36669 | 0.264710 |
(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 | 5929.2.a.k.1.1 | 2 | ||
7.6 | odd | 2 | 847.2.a.e.1.1 | ✓ | 2 | ||
11.10 | odd | 2 | 5929.2.a.p.1.2 | 2 | |||
21.20 | even | 2 | 7623.2.a.bs.1.2 | 2 | |||
77.6 | even | 10 | 847.2.f.o.729.1 | 8 | |||
77.13 | even | 10 | 847.2.f.o.323.1 | 8 | |||
77.20 | odd | 10 | 847.2.f.r.323.2 | 8 | |||
77.27 | odd | 10 | 847.2.f.r.729.2 | 8 | |||
77.41 | even | 10 | 847.2.f.o.372.2 | 8 | |||
77.48 | odd | 10 | 847.2.f.r.148.1 | 8 | |||
77.62 | even | 10 | 847.2.f.o.148.2 | 8 | |||
77.69 | odd | 10 | 847.2.f.r.372.1 | 8 | |||
77.76 | even | 2 | 847.2.a.g.1.2 | yes | 2 | ||
231.230 | odd | 2 | 7623.2.a.bc.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.e.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
847.2.a.g.1.2 | yes | 2 | 77.76 | even | 2 | ||
847.2.f.o.148.2 | 8 | 77.62 | even | 10 | |||
847.2.f.o.323.1 | 8 | 77.13 | even | 10 | |||
847.2.f.o.372.2 | 8 | 77.41 | even | 10 | |||
847.2.f.o.729.1 | 8 | 77.6 | even | 10 | |||
847.2.f.r.148.1 | 8 | 77.48 | odd | 10 | |||
847.2.f.r.323.2 | 8 | 77.20 | odd | 10 | |||
847.2.f.r.372.1 | 8 | 77.69 | odd | 10 | |||
847.2.f.r.729.2 | 8 | 77.27 | odd | 10 | |||
5929.2.a.k.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5929.2.a.p.1.2 | 2 | 11.10 | odd | 2 | |||
7623.2.a.bc.1.1 | 2 | 231.230 | odd | 2 | |||
7623.2.a.bs.1.2 | 2 | 21.20 | even | 2 |