Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3822,2,Mod(1,3822)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3822, 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("3822.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3822.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: | \(30.5188236525\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 7 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3822.1 |
$q$-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 | ||||||||
\(5\) | 1.64575 | 0.736002 | 0.368001 | − | 0.929825i | \(-0.380042\pi\) | ||||
0.368001 | + | 0.929825i | \(0.380042\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.64575 | −0.520432 | ||||||||
\(11\) | −4.64575 | −1.40075 | −0.700373 | − | 0.713777i | \(-0.746983\pi\) | ||||
−0.700373 | + | 0.713777i | \(0.746983\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.64575 | 0.424931 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.35425 | −0.328454 | −0.164227 | − | 0.986423i | \(-0.552513\pi\) | ||||
−0.164227 | + | 0.986423i | \(0.552513\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 5.00000 | 1.14708 | 0.573539 | − | 0.819178i | \(-0.305570\pi\) | ||||
0.573539 | + | 0.819178i | \(0.305570\pi\) | |||||||
\(20\) | 1.64575 | 0.368001 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.64575 | 0.990478 | ||||||||
\(23\) | −7.64575 | −1.59425 | −0.797125 | − | 0.603815i | \(-0.793647\pi\) | ||||
−0.797125 | + | 0.603815i | \(0.793647\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −2.29150 | −0.458301 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.29150 | −1.16830 | −0.584151 | − | 0.811645i | \(-0.698573\pi\) | ||||
−0.584151 | + | 0.811645i | \(0.698573\pi\) | |||||||
\(30\) | −1.64575 | −0.300472 | ||||||||
\(31\) | −7.29150 | −1.30959 | −0.654796 | − | 0.755805i | \(-0.727246\pi\) | ||||
−0.654796 | + | 0.755805i | \(0.727246\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.64575 | −0.808721 | ||||||||
\(34\) | 1.35425 | 0.232252 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.354249 | 0.0582381 | 0.0291191 | − | 0.999576i | \(-0.490730\pi\) | ||||
0.0291191 | + | 0.999576i | \(0.490730\pi\) | |||||||
\(38\) | −5.00000 | −0.811107 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −1.64575 | −0.260216 | ||||||||
\(41\) | −7.64575 | −1.19407 | −0.597033 | − | 0.802217i | \(-0.703654\pi\) | ||||
−0.597033 | + | 0.802217i | \(0.703654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.29150 | 0.806947 | 0.403473 | − | 0.914991i | \(-0.367803\pi\) | ||||
0.403473 | + | 0.914991i | \(0.367803\pi\) | |||||||
\(44\) | −4.64575 | −0.700373 | ||||||||
\(45\) | 1.64575 | 0.245334 | ||||||||
\(46\) | 7.64575 | 1.12730 | ||||||||
\(47\) | 3.00000 | 0.437595 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.29150 | 0.324067 | ||||||||
\(51\) | −1.35425 | −0.189633 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −7.64575 | −1.03095 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | 6.29150 | 0.826115 | ||||||||
\(59\) | 7.93725 | 1.03334 | 0.516671 | − | 0.856184i | \(-0.327171\pi\) | ||||
0.516671 | + | 0.856184i | \(0.327171\pi\) | |||||||
\(60\) | 1.64575 | 0.212466 | ||||||||
\(61\) | 3.93725 | 0.504114 | 0.252057 | − | 0.967712i | \(-0.418893\pi\) | ||||
0.252057 | + | 0.967712i | \(0.418893\pi\) | |||||||
\(62\) | 7.29150 | 0.926022 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.64575 | 0.204130 | ||||||||
\(66\) | 4.64575 | 0.571852 | ||||||||
\(67\) | −13.5830 | −1.65943 | −0.829714 | − | 0.558189i | \(-0.811497\pi\) | ||||
−0.829714 | + | 0.558189i | \(0.811497\pi\) | |||||||
\(68\) | −1.35425 | −0.164227 | ||||||||
\(69\) | −7.64575 | −0.920440 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.70850 | 0.677474 | 0.338737 | − | 0.940881i | \(-0.390000\pi\) | ||||
0.338737 | + | 0.940881i | \(0.390000\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −8.35425 | −0.977791 | −0.488895 | − | 0.872342i | \(-0.662600\pi\) | ||||
−0.488895 | + | 0.872342i | \(0.662600\pi\) | |||||||
\(74\) | −0.354249 | −0.0411806 | ||||||||
\(75\) | −2.29150 | −0.264600 | ||||||||
\(76\) | 5.00000 | 0.573539 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.00000 | −0.113228 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 1.64575 | 0.184001 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.64575 | 0.844332 | ||||||||
\(83\) | −2.70850 | −0.297296 | −0.148648 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148648 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.22876 | −0.241743 | ||||||||
\(86\) | −5.29150 | −0.570597 | ||||||||
\(87\) | −6.29150 | −0.674520 | ||||||||
\(88\) | 4.64575 | 0.495239 | ||||||||
\(89\) | 1.06275 | 0.112651 | 0.0563254 | − | 0.998412i | \(-0.482062\pi\) | ||||
0.0563254 | + | 0.998412i | \(0.482062\pi\) | |||||||
\(90\) | −1.64575 | −0.173477 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.64575 | −0.797125 | ||||||||
\(93\) | −7.29150 | −0.756094 | ||||||||
\(94\) | −3.00000 | −0.309426 | ||||||||
\(95\) | 8.22876 | 0.844253 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −14.9373 | −1.51665 | −0.758324 | − | 0.651878i | \(-0.773982\pi\) | ||||
−0.758324 | + | 0.651878i | \(0.773982\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.64575 | −0.466916 | ||||||||
\(100\) | −2.29150 | −0.229150 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 1.35425 | 0.134091 | ||||||||
\(103\) | 5.29150 | 0.521387 | 0.260694 | − | 0.965422i | \(-0.416049\pi\) | ||||
0.260694 | + | 0.965422i | \(0.416049\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 7.64575 | 0.728994 | ||||||||
\(111\) | 0.354249 | 0.0336238 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.2288 | −1.05631 | −0.528156 | − | 0.849147i | \(-0.677116\pi\) | ||||
−0.528156 | + | 0.849147i | \(0.677116\pi\) | |||||||
\(114\) | −5.00000 | −0.468293 | ||||||||
\(115\) | −12.5830 | −1.17337 | ||||||||
\(116\) | −6.29150 | −0.584151 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −7.93725 | −0.730683 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.64575 | −0.150236 | ||||||||
\(121\) | 10.5830 | 0.962091 | ||||||||
\(122\) | −3.93725 | −0.356462 | ||||||||
\(123\) | −7.64575 | −0.689394 | ||||||||
\(124\) | −7.29150 | −0.654796 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.2288 | 1.44007 | 0.720035 | − | 0.693938i | \(-0.244126\pi\) | ||||
0.720035 | + | 0.693938i | \(0.244126\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.29150 | 0.465891 | ||||||||
\(130\) | −1.64575 | −0.144342 | ||||||||
\(131\) | −4.93725 | −0.431370 | −0.215685 | − | 0.976463i | \(-0.569198\pi\) | ||||
−0.215685 | + | 0.976463i | \(0.569198\pi\) | |||||||
\(132\) | −4.64575 | −0.404361 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.5830 | 1.17339 | ||||||||
\(135\) | 1.64575 | 0.141644 | ||||||||
\(136\) | 1.35425 | 0.116126 | ||||||||
\(137\) | 17.5203 | 1.49686 | 0.748428 | − | 0.663216i | \(-0.230809\pi\) | ||||
0.748428 | + | 0.663216i | \(0.230809\pi\) | |||||||
\(138\) | 7.64575 | 0.650850 | ||||||||
\(139\) | 4.22876 | 0.358678 | 0.179339 | − | 0.983787i | \(-0.442604\pi\) | ||||
0.179339 | + | 0.983787i | \(0.442604\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | −5.70850 | −0.479046 | ||||||||
\(143\) | −4.64575 | −0.388497 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −10.3542 | −0.859874 | ||||||||
\(146\) | 8.35425 | 0.691403 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.354249 | 0.0291191 | ||||||||
\(149\) | −22.9373 | −1.87909 | −0.939547 | − | 0.342421i | \(-0.888753\pi\) | ||||
−0.939547 | + | 0.342421i | \(0.888753\pi\) | |||||||
\(150\) | 2.29150 | 0.187100 | ||||||||
\(151\) | 21.9373 | 1.78523 | 0.892614 | − | 0.450821i | \(-0.148869\pi\) | ||||
0.892614 | + | 0.450821i | \(0.148869\pi\) | |||||||
\(152\) | −5.00000 | −0.405554 | ||||||||
\(153\) | −1.35425 | −0.109485 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.0000 | −0.963863 | ||||||||
\(156\) | 1.00000 | 0.0800641 | ||||||||
\(157\) | −2.64575 | −0.211154 | −0.105577 | − | 0.994411i | \(-0.533669\pi\) | ||||
−0.105577 | + | 0.994411i | \(0.533669\pi\) | |||||||
\(158\) | 10.0000 | 0.795557 | ||||||||
\(159\) | −3.00000 | −0.237915 | ||||||||
\(160\) | −1.64575 | −0.130108 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 23.5830 | 1.84716 | 0.923582 | − | 0.383402i | \(-0.125247\pi\) | ||||
0.923582 | + | 0.383402i | \(0.125247\pi\) | |||||||
\(164\) | −7.64575 | −0.597033 | ||||||||
\(165\) | −7.64575 | −0.595221 | ||||||||
\(166\) | 2.70850 | 0.210220 | ||||||||
\(167\) | 24.8745 | 1.92485 | 0.962424 | − | 0.271553i | \(-0.0875371\pi\) | ||||
0.962424 | + | 0.271553i | \(0.0875371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 2.22876 | 0.170938 | ||||||||
\(171\) | 5.00000 | 0.382360 | ||||||||
\(172\) | 5.29150 | 0.403473 | ||||||||
\(173\) | −11.7085 | −0.890181 | −0.445090 | − | 0.895486i | \(-0.646828\pi\) | ||||
−0.445090 | + | 0.895486i | \(0.646828\pi\) | |||||||
\(174\) | 6.29150 | 0.476958 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.64575 | −0.350187 | ||||||||
\(177\) | 7.93725 | 0.596601 | ||||||||
\(178\) | −1.06275 | −0.0796562 | ||||||||
\(179\) | −6.00000 | −0.448461 | −0.224231 | − | 0.974536i | \(-0.571987\pi\) | ||||
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(180\) | 1.64575 | 0.122667 | ||||||||
\(181\) | 9.35425 | 0.695296 | 0.347648 | − | 0.937625i | \(-0.386980\pi\) | ||||
0.347648 | + | 0.937625i | \(0.386980\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.93725 | 0.291050 | ||||||||
\(184\) | 7.64575 | 0.563652 | ||||||||
\(185\) | 0.583005 | 0.0428634 | ||||||||
\(186\) | 7.29150 | 0.534639 | ||||||||
\(187\) | 6.29150 | 0.460080 | ||||||||
\(188\) | 3.00000 | 0.218797 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.22876 | −0.596977 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 3.06275 | 0.220461 | 0.110231 | − | 0.993906i | \(-0.464841\pi\) | ||||
0.110231 | + | 0.993906i | \(0.464841\pi\) | |||||||
\(194\) | 14.9373 | 1.07243 | ||||||||
\(195\) | 1.64575 | 0.117855 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.8118 | 1.48278 | 0.741388 | − | 0.671076i | \(-0.234168\pi\) | ||||
0.741388 | + | 0.671076i | \(0.234168\pi\) | |||||||
\(198\) | 4.64575 | 0.330159 | ||||||||
\(199\) | 4.22876 | 0.299769 | 0.149884 | − | 0.988704i | \(-0.452110\pi\) | ||||
0.149884 | + | 0.988704i | \(0.452110\pi\) | |||||||
\(200\) | 2.29150 | 0.162034 | ||||||||
\(201\) | −13.5830 | −0.958071 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.35425 | −0.0948164 | ||||||||
\(205\) | −12.5830 | −0.878835 | ||||||||
\(206\) | −5.29150 | −0.368676 | ||||||||
\(207\) | −7.64575 | −0.531416 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | −23.2288 | −1.60677 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.6458 | −0.801727 | −0.400863 | − | 0.916138i | \(-0.631290\pi\) | ||||
−0.400863 | + | 0.916138i | \(0.631290\pi\) | |||||||
\(212\) | −3.00000 | −0.206041 | ||||||||
\(213\) | 5.70850 | 0.391140 | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 8.70850 | 0.593915 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.00000 | 0.270914 | ||||||||
\(219\) | −8.35425 | −0.564528 | ||||||||
\(220\) | −7.64575 | −0.515476 | ||||||||
\(221\) | −1.35425 | −0.0910966 | ||||||||
\(222\) | −0.354249 | −0.0237756 | ||||||||
\(223\) | 16.5203 | 1.10628 | 0.553139 | − | 0.833089i | \(-0.313430\pi\) | ||||
0.553139 | + | 0.833089i | \(0.313430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.29150 | −0.152767 | ||||||||
\(226\) | 11.2288 | 0.746926 | ||||||||
\(227\) | −15.2915 | −1.01493 | −0.507466 | − | 0.861672i | \(-0.669418\pi\) | ||||
−0.507466 | + | 0.861672i | \(0.669418\pi\) | |||||||
\(228\) | 5.00000 | 0.331133 | ||||||||
\(229\) | −26.4575 | −1.74836 | −0.874181 | − | 0.485601i | \(-0.838601\pi\) | ||||
−0.874181 | + | 0.485601i | \(0.838601\pi\) | |||||||
\(230\) | 12.5830 | 0.829699 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.29150 | 0.413057 | ||||||||
\(233\) | −4.64575 | −0.304353 | −0.152177 | − | 0.988353i | \(-0.548628\pi\) | ||||
−0.152177 | + | 0.988353i | \(0.548628\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | 4.93725 | 0.322071 | ||||||||
\(236\) | 7.93725 | 0.516671 | ||||||||
\(237\) | −10.0000 | −0.649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.00000 | 0.194054 | 0.0970269 | − | 0.995282i | \(-0.469067\pi\) | ||||
0.0970269 | + | 0.995282i | \(0.469067\pi\) | |||||||
\(240\) | 1.64575 | 0.106233 | ||||||||
\(241\) | 17.8745 | 1.15140 | 0.575699 | − | 0.817662i | \(-0.304730\pi\) | ||||
0.575699 | + | 0.817662i | \(0.304730\pi\) | |||||||
\(242\) | −10.5830 | −0.680301 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.93725 | 0.252057 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.64575 | 0.487475 | ||||||||
\(247\) | 5.00000 | 0.318142 | ||||||||
\(248\) | 7.29150 | 0.463011 | ||||||||
\(249\) | −2.70850 | −0.171644 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | −2.70850 | −0.170959 | −0.0854794 | − | 0.996340i | \(-0.527242\pi\) | ||||
−0.0854794 | + | 0.996340i | \(0.527242\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35.5203 | 2.23314 | ||||||||
\(254\) | −16.2288 | −1.01828 | ||||||||
\(255\) | −2.22876 | −0.139570 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.8745 | 0.990225 | 0.495112 | − | 0.868829i | \(-0.335127\pi\) | ||||
0.495112 | + | 0.868829i | \(0.335127\pi\) | |||||||
\(258\) | −5.29150 | −0.329435 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.64575 | 0.102065 | ||||||||
\(261\) | −6.29150 | −0.389434 | ||||||||
\(262\) | 4.93725 | 0.305025 | ||||||||
\(263\) | 1.64575 | 0.101481 | 0.0507407 | − | 0.998712i | \(-0.483842\pi\) | ||||
0.0507407 | + | 0.998712i | \(0.483842\pi\) | |||||||
\(264\) | 4.64575 | 0.285926 | ||||||||
\(265\) | −4.93725 | −0.303293 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.06275 | 0.0650390 | ||||||||
\(268\) | −13.5830 | −0.829714 | ||||||||
\(269\) | −24.8745 | −1.51663 | −0.758313 | − | 0.651891i | \(-0.773976\pi\) | ||||
−0.758313 | + | 0.651891i | \(0.773976\pi\) | |||||||
\(270\) | −1.64575 | −0.100157 | ||||||||
\(271\) | −17.3542 | −1.05420 | −0.527098 | − | 0.849805i | \(-0.676720\pi\) | ||||
−0.527098 | + | 0.849805i | \(0.676720\pi\) | |||||||
\(272\) | −1.35425 | −0.0821134 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.5203 | −1.05844 | ||||||||
\(275\) | 10.6458 | 0.641963 | ||||||||
\(276\) | −7.64575 | −0.460220 | ||||||||
\(277\) | −18.5203 | −1.11277 | −0.556387 | − | 0.830923i | \(-0.687813\pi\) | ||||
−0.556387 | + | 0.830923i | \(0.687813\pi\) | |||||||
\(278\) | −4.22876 | −0.253624 | ||||||||
\(279\) | −7.29150 | −0.436531 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5830 | 1.10857 | 0.554285 | − | 0.832327i | \(-0.312992\pi\) | ||||
0.554285 | + | 0.832327i | \(0.312992\pi\) | |||||||
\(282\) | −3.00000 | −0.178647 | ||||||||
\(283\) | −26.9373 | −1.60125 | −0.800627 | − | 0.599163i | \(-0.795500\pi\) | ||||
−0.800627 | + | 0.599163i | \(0.795500\pi\) | |||||||
\(284\) | 5.70850 | 0.338737 | ||||||||
\(285\) | 8.22876 | 0.487429 | ||||||||
\(286\) | 4.64575 | 0.274709 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.1660 | −0.892118 | ||||||||
\(290\) | 10.3542 | 0.608022 | ||||||||
\(291\) | −14.9373 | −0.875637 | ||||||||
\(292\) | −8.35425 | −0.488895 | ||||||||
\(293\) | −29.5203 | −1.72459 | −0.862296 | − | 0.506405i | \(-0.830974\pi\) | ||||
−0.862296 | + | 0.506405i | \(0.830974\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.0627 | 0.760542 | ||||||||
\(296\) | −0.354249 | −0.0205903 | ||||||||
\(297\) | −4.64575 | −0.269574 | ||||||||
\(298\) | 22.9373 | 1.32872 | ||||||||
\(299\) | −7.64575 | −0.442165 | ||||||||
\(300\) | −2.29150 | −0.132300 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −21.9373 | −1.26235 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | 6.47974 | 0.371029 | ||||||||
\(306\) | 1.35425 | 0.0774172 | ||||||||
\(307\) | 11.5830 | 0.661077 | 0.330539 | − | 0.943793i | \(-0.392770\pi\) | ||||
0.330539 | + | 0.943793i | \(0.392770\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.29150 | 0.301023 | ||||||||
\(310\) | 12.0000 | 0.681554 | ||||||||
\(311\) | −16.9373 | −0.960424 | −0.480212 | − | 0.877153i | \(-0.659440\pi\) | ||||
−0.480212 | + | 0.877153i | \(0.659440\pi\) | |||||||
\(312\) | −1.00000 | −0.0566139 | ||||||||
\(313\) | −29.1660 | −1.64856 | −0.824280 | − | 0.566182i | \(-0.808420\pi\) | ||||
−0.824280 | + | 0.566182i | \(0.808420\pi\) | |||||||
\(314\) | 2.64575 | 0.149308 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0000 | −0.562544 | ||||||||
\(317\) | −2.70850 | −0.152124 | −0.0760622 | − | 0.997103i | \(-0.524235\pi\) | ||||
−0.0760622 | + | 0.997103i | \(0.524235\pi\) | |||||||
\(318\) | 3.00000 | 0.168232 | ||||||||
\(319\) | 29.2288 | 1.63650 | ||||||||
\(320\) | 1.64575 | 0.0920003 | ||||||||
\(321\) | −12.0000 | −0.669775 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.77124 | −0.376762 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.29150 | −0.127110 | ||||||||
\(326\) | −23.5830 | −1.30614 | ||||||||
\(327\) | −4.00000 | −0.221201 | ||||||||
\(328\) | 7.64575 | 0.422166 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.64575 | 0.420885 | ||||||||
\(331\) | 32.5830 | 1.79092 | 0.895462 | − | 0.445138i | \(-0.146845\pi\) | ||||
0.895462 | + | 0.445138i | \(0.146845\pi\) | |||||||
\(332\) | −2.70850 | −0.148648 | ||||||||
\(333\) | 0.354249 | 0.0194127 | ||||||||
\(334\) | −24.8745 | −1.36107 | ||||||||
\(335\) | −22.3542 | −1.22134 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.58301 | 0.304126 | 0.152063 | − | 0.988371i | \(-0.451408\pi\) | ||||
0.152063 | + | 0.988371i | \(0.451408\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | −11.2288 | −0.609862 | ||||||||
\(340\) | −2.22876 | −0.120871 | ||||||||
\(341\) | 33.8745 | 1.83441 | ||||||||
\(342\) | −5.00000 | −0.270369 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.29150 | −0.285299 | ||||||||
\(345\) | −12.5830 | −0.677446 | ||||||||
\(346\) | 11.7085 | 0.629453 | ||||||||
\(347\) | −26.2288 | −1.40803 | −0.704017 | − | 0.710183i | \(-0.748612\pi\) | ||||
−0.704017 | + | 0.710183i | \(0.748612\pi\) | |||||||
\(348\) | −6.29150 | −0.337260 | ||||||||
\(349\) | 3.06275 | 0.163945 | 0.0819725 | − | 0.996635i | \(-0.473878\pi\) | ||||
0.0819725 | + | 0.996635i | \(0.473878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 4.64575 | 0.247619 | ||||||||
\(353\) | 0.583005 | 0.0310302 | 0.0155151 | − | 0.999880i | \(-0.495061\pi\) | ||||
0.0155151 | + | 0.999880i | \(0.495061\pi\) | |||||||
\(354\) | −7.93725 | −0.421860 | ||||||||
\(355\) | 9.39477 | 0.498622 | ||||||||
\(356\) | 1.06275 | 0.0563254 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | 0.317110 | ||||||||
\(359\) | −6.00000 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(360\) | −1.64575 | −0.0867387 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | −9.35425 | −0.491648 | ||||||||
\(363\) | 10.5830 | 0.555464 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.7490 | −0.719656 | ||||||||
\(366\) | −3.93725 | −0.205804 | ||||||||
\(367\) | 20.5830 | 1.07442 | 0.537212 | − | 0.843447i | \(-0.319477\pi\) | ||||
0.537212 | + | 0.843447i | \(0.319477\pi\) | |||||||
\(368\) | −7.64575 | −0.398562 | ||||||||
\(369\) | −7.64575 | −0.398022 | ||||||||
\(370\) | −0.583005 | −0.0303090 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −7.29150 | −0.378047 | ||||||||
\(373\) | 9.35425 | 0.484345 | 0.242172 | − | 0.970233i | \(-0.422140\pi\) | ||||
0.242172 | + | 0.970233i | \(0.422140\pi\) | |||||||
\(374\) | −6.29150 | −0.325326 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | −3.00000 | −0.154713 | ||||||||
\(377\) | −6.29150 | −0.324029 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.1660 | 1.70362 | 0.851812 | − | 0.523848i | \(-0.175504\pi\) | ||||
0.851812 | + | 0.523848i | \(0.175504\pi\) | |||||||
\(380\) | 8.22876 | 0.422126 | ||||||||
\(381\) | 16.2288 | 0.831424 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.7490 | −1.92888 | −0.964442 | − | 0.264293i | \(-0.914861\pi\) | ||||
−0.964442 | + | 0.264293i | \(0.914861\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.06275 | −0.155890 | ||||||||
\(387\) | 5.29150 | 0.268982 | ||||||||
\(388\) | −14.9373 | −0.758324 | ||||||||
\(389\) | 18.2915 | 0.927416 | 0.463708 | − | 0.885988i | \(-0.346519\pi\) | ||||
0.463708 | + | 0.885988i | \(0.346519\pi\) | |||||||
\(390\) | −1.64575 | −0.0833359 | ||||||||
\(391\) | 10.3542 | 0.523637 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.93725 | −0.249052 | ||||||||
\(394\) | −20.8118 | −1.04848 | ||||||||
\(395\) | −16.4575 | −0.828067 | ||||||||
\(396\) | −4.64575 | −0.233458 | ||||||||
\(397\) | 0.937254 | 0.0470394 | 0.0235197 | − | 0.999723i | \(-0.492513\pi\) | ||||
0.0235197 | + | 0.999723i | \(0.492513\pi\) | |||||||
\(398\) | −4.22876 | −0.211968 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.29150 | −0.114575 | ||||||||
\(401\) | 8.22876 | 0.410924 | 0.205462 | − | 0.978665i | \(-0.434130\pi\) | ||||
0.205462 | + | 0.978665i | \(0.434130\pi\) | |||||||
\(402\) | 13.5830 | 0.677459 | ||||||||
\(403\) | −7.29150 | −0.363216 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.64575 | 0.0817780 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.64575 | −0.0815769 | ||||||||
\(408\) | 1.35425 | 0.0670453 | ||||||||
\(409\) | −11.0627 | −0.547018 | −0.273509 | − | 0.961870i | \(-0.588184\pi\) | ||||
−0.273509 | + | 0.961870i | \(0.588184\pi\) | |||||||
\(410\) | 12.5830 | 0.621430 | ||||||||
\(411\) | 17.5203 | 0.864211 | ||||||||
\(412\) | 5.29150 | 0.260694 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.64575 | 0.375768 | ||||||||
\(415\) | −4.45751 | −0.218811 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 4.22876 | 0.207083 | ||||||||
\(418\) | 23.2288 | 1.13616 | ||||||||
\(419\) | −22.4575 | −1.09712 | −0.548561 | − | 0.836111i | \(-0.684824\pi\) | ||||
−0.548561 | + | 0.836111i | \(0.684824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.6458 | −1.44485 | −0.722423 | − | 0.691452i | \(-0.756972\pi\) | ||||
−0.722423 | + | 0.691452i | \(0.756972\pi\) | |||||||
\(422\) | 11.6458 | 0.566906 | ||||||||
\(423\) | 3.00000 | 0.145865 | ||||||||
\(424\) | 3.00000 | 0.145693 | ||||||||
\(425\) | 3.10326 | 0.150530 | ||||||||
\(426\) | −5.70850 | −0.276578 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | −4.64575 | −0.224299 | ||||||||
\(430\) | −8.70850 | −0.419961 | ||||||||
\(431\) | −0.583005 | −0.0280824 | −0.0140412 | − | 0.999901i | \(-0.504470\pi\) | ||||
−0.0140412 | + | 0.999901i | \(0.504470\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −12.4170 | −0.596723 | −0.298361 | − | 0.954453i | \(-0.596440\pi\) | ||||
−0.298361 | + | 0.954453i | \(0.596440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.3542 | −0.496448 | ||||||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | −38.2288 | −1.82873 | ||||||||
\(438\) | 8.35425 | 0.399181 | ||||||||
\(439\) | 18.3542 | 0.876000 | 0.438000 | − | 0.898975i | \(-0.355687\pi\) | ||||
0.438000 | + | 0.898975i | \(0.355687\pi\) | |||||||
\(440\) | 7.64575 | 0.364497 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.35425 | 0.0644150 | ||||||||
\(443\) | 34.9373 | 1.65992 | 0.829960 | − | 0.557824i | \(-0.188363\pi\) | ||||
0.829960 | + | 0.557824i | \(0.188363\pi\) | |||||||
\(444\) | 0.354249 | 0.0168119 | ||||||||
\(445\) | 1.74902 | 0.0829113 | ||||||||
\(446\) | −16.5203 | −0.782257 | ||||||||
\(447\) | −22.9373 | −1.08489 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.0000 | 0.566315 | 0.283158 | − | 0.959073i | \(-0.408618\pi\) | ||||
0.283158 | + | 0.959073i | \(0.408618\pi\) | |||||||
\(450\) | 2.29150 | 0.108022 | ||||||||
\(451\) | 35.5203 | 1.67258 | ||||||||
\(452\) | −11.2288 | −0.528156 | ||||||||
\(453\) | 21.9373 | 1.03070 | ||||||||
\(454\) | 15.2915 | 0.717666 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.00000 | −0.234146 | ||||||||
\(457\) | 5.77124 | 0.269967 | 0.134984 | − | 0.990848i | \(-0.456902\pi\) | ||||
0.134984 | + | 0.990848i | \(0.456902\pi\) | |||||||
\(458\) | 26.4575 | 1.23628 | ||||||||
\(459\) | −1.35425 | −0.0632109 | ||||||||
\(460\) | −12.5830 | −0.586686 | ||||||||
\(461\) | 16.4575 | 0.766503 | 0.383251 | − | 0.923644i | \(-0.374804\pi\) | ||||
0.383251 | + | 0.923644i | \(0.374804\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.1660 | −0.797772 | −0.398886 | − | 0.917000i | \(-0.630603\pi\) | ||||
−0.398886 | + | 0.917000i | \(0.630603\pi\) | |||||||
\(464\) | −6.29150 | −0.292076 | ||||||||
\(465\) | −12.0000 | −0.556487 | ||||||||
\(466\) | 4.64575 | 0.215210 | ||||||||
\(467\) | −0.479741 | −0.0221998 | −0.0110999 | − | 0.999938i | \(-0.503533\pi\) | ||||
−0.0110999 | + | 0.999938i | \(0.503533\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.93725 | −0.227739 | ||||||||
\(471\) | −2.64575 | −0.121910 | ||||||||
\(472\) | −7.93725 | −0.365342 | ||||||||
\(473\) | −24.5830 | −1.13033 | ||||||||
\(474\) | 10.0000 | 0.459315 | ||||||||
\(475\) | −11.4575 | −0.525707 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00000 | −0.137361 | ||||||||
\(478\) | −3.00000 | −0.137217 | ||||||||
\(479\) | 28.7490 | 1.31358 | 0.656788 | − | 0.754075i | \(-0.271915\pi\) | ||||
0.656788 | + | 0.754075i | \(0.271915\pi\) | |||||||
\(480\) | −1.64575 | −0.0751179 | ||||||||
\(481\) | 0.354249 | 0.0161523 | ||||||||
\(482\) | −17.8745 | −0.814162 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.5830 | 0.481046 | ||||||||
\(485\) | −24.5830 | −1.11626 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −8.06275 | −0.365358 | −0.182679 | − | 0.983173i | \(-0.558477\pi\) | ||||
−0.182679 | + | 0.983173i | \(0.558477\pi\) | |||||||
\(488\) | −3.93725 | −0.178231 | ||||||||
\(489\) | 23.5830 | 1.06646 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.1660 | −1.40650 | −0.703251 | − | 0.710941i | \(-0.748269\pi\) | ||||
−0.703251 | + | 0.710941i | \(0.748269\pi\) | |||||||
\(492\) | −7.64575 | −0.344697 | ||||||||
\(493\) | 8.52026 | 0.383733 | ||||||||
\(494\) | −5.00000 | −0.224961 | ||||||||
\(495\) | −7.64575 | −0.343651 | ||||||||
\(496\) | −7.29150 | −0.327398 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.70850 | 0.121371 | ||||||||
\(499\) | −18.7085 | −0.837507 | −0.418754 | − | 0.908100i | \(-0.637533\pi\) | ||||
−0.418754 | + | 0.908100i | \(0.637533\pi\) | |||||||
\(500\) | −12.0000 | −0.536656 | ||||||||
\(501\) | 24.8745 | 1.11131 | ||||||||
\(502\) | 2.70850 | 0.120886 | ||||||||
\(503\) | −16.4575 | −0.733804 | −0.366902 | − | 0.930260i | \(-0.619582\pi\) | ||||
−0.366902 | + | 0.930260i | \(0.619582\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −35.5203 | −1.57907 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 16.2288 | 0.720035 | ||||||||
\(509\) | 24.0000 | 1.06378 | 0.531891 | − | 0.846813i | \(-0.321482\pi\) | ||||
0.531891 | + | 0.846813i | \(0.321482\pi\) | |||||||
\(510\) | 2.22876 | 0.0986910 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.00000 | 0.220755 | ||||||||
\(514\) | −15.8745 | −0.700195 | ||||||||
\(515\) | 8.70850 | 0.383742 | ||||||||
\(516\) | 5.29150 | 0.232945 | ||||||||
\(517\) | −13.9373 | −0.612960 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.7085 | −0.513946 | ||||||||
\(520\) | −1.64575 | −0.0721710 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 6.29150 | 0.275372 | ||||||||
\(523\) | −37.2915 | −1.63064 | −0.815322 | − | 0.579008i | \(-0.803440\pi\) | ||||
−0.815322 | + | 0.579008i | \(0.803440\pi\) | |||||||
\(524\) | −4.93725 | −0.215685 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.64575 | −0.0717582 | ||||||||
\(527\) | 9.87451 | 0.430140 | ||||||||
\(528\) | −4.64575 | −0.202180 | ||||||||
\(529\) | 35.4575 | 1.54163 | ||||||||
\(530\) | 4.93725 | 0.214461 | ||||||||
\(531\) | 7.93725 | 0.344447 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.64575 | −0.331174 | ||||||||
\(534\) | −1.06275 | −0.0459895 | ||||||||
\(535\) | −19.7490 | −0.853824 | ||||||||
\(536\) | 13.5830 | 0.586696 | ||||||||
\(537\) | −6.00000 | −0.258919 | ||||||||
\(538\) | 24.8745 | 1.07242 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.64575 | 0.0708219 | ||||||||
\(541\) | 36.3542 | 1.56299 | 0.781496 | − | 0.623911i | \(-0.214457\pi\) | ||||
0.781496 | + | 0.623911i | \(0.214457\pi\) | |||||||
\(542\) | 17.3542 | 0.745429 | ||||||||
\(543\) | 9.35425 | 0.401429 | ||||||||
\(544\) | 1.35425 | 0.0580629 | ||||||||
\(545\) | −6.58301 | −0.281985 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.06275 | −0.216467 | −0.108234 | − | 0.994125i | \(-0.534519\pi\) | ||||
−0.108234 | + | 0.994125i | \(0.534519\pi\) | |||||||
\(548\) | 17.5203 | 0.748428 | ||||||||
\(549\) | 3.93725 | 0.168038 | ||||||||
\(550\) | −10.6458 | −0.453936 | ||||||||
\(551\) | −31.4575 | −1.34014 | ||||||||
\(552\) | 7.64575 | 0.325425 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 18.5203 | 0.786850 | ||||||||
\(555\) | 0.583005 | 0.0247472 | ||||||||
\(556\) | 4.22876 | 0.179339 | ||||||||
\(557\) | −31.1660 | −1.32055 | −0.660273 | − | 0.751026i | \(-0.729559\pi\) | ||||
−0.660273 | + | 0.751026i | \(0.729559\pi\) | |||||||
\(558\) | 7.29150 | 0.308674 | ||||||||
\(559\) | 5.29150 | 0.223807 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.29150 | 0.265627 | ||||||||
\(562\) | −18.5830 | −0.783877 | ||||||||
\(563\) | 47.0405 | 1.98252 | 0.991261 | − | 0.131917i | \(-0.0421133\pi\) | ||||
0.991261 | + | 0.131917i | \(0.0421133\pi\) | |||||||
\(564\) | 3.00000 | 0.126323 | ||||||||
\(565\) | −18.4797 | −0.777449 | ||||||||
\(566\) | 26.9373 | 1.13226 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.70850 | −0.239523 | ||||||||
\(569\) | −6.77124 | −0.283865 | −0.141933 | − | 0.989876i | \(-0.545332\pi\) | ||||
−0.141933 | + | 0.989876i | \(0.545332\pi\) | |||||||
\(570\) | −8.22876 | −0.344665 | ||||||||
\(571\) | −16.0000 | −0.669579 | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | −4.64575 | −0.194249 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.5203 | 0.730645 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 8.58301 | 0.357315 | 0.178658 | − | 0.983911i | \(-0.442825\pi\) | ||||
0.178658 | + | 0.983911i | \(0.442825\pi\) | |||||||
\(578\) | 15.1660 | 0.630823 | ||||||||
\(579\) | 3.06275 | 0.127283 | ||||||||
\(580\) | −10.3542 | −0.429937 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 14.9373 | 0.619169 | ||||||||
\(583\) | 13.9373 | 0.577222 | ||||||||
\(584\) | 8.35425 | 0.345701 | ||||||||
\(585\) | 1.64575 | 0.0680434 | ||||||||
\(586\) | 29.5203 | 1.21947 | ||||||||
\(587\) | 16.0627 | 0.662980 | 0.331490 | − | 0.943459i | \(-0.392449\pi\) | ||||
0.331490 | + | 0.943459i | \(0.392449\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.4575 | −1.50221 | ||||||||
\(590\) | −13.0627 | −0.537785 | ||||||||
\(591\) | 20.8118 | 0.856081 | ||||||||
\(592\) | 0.354249 | 0.0145595 | ||||||||
\(593\) | 6.47974 | 0.266091 | 0.133046 | − | 0.991110i | \(-0.457524\pi\) | ||||
0.133046 | + | 0.991110i | \(0.457524\pi\) | |||||||
\(594\) | 4.64575 | 0.190617 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.9373 | −0.939547 | ||||||||
\(597\) | 4.22876 | 0.173071 | ||||||||
\(598\) | 7.64575 | 0.312658 | ||||||||
\(599\) | 14.8118 | 0.605192 | 0.302596 | − | 0.953119i | \(-0.402147\pi\) | ||||
0.302596 | + | 0.953119i | \(0.402147\pi\) | |||||||
\(600\) | 2.29150 | 0.0935502 | ||||||||
\(601\) | −16.8745 | −0.688326 | −0.344163 | − | 0.938910i | \(-0.611837\pi\) | ||||
−0.344163 | + | 0.938910i | \(0.611837\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.5830 | −0.553143 | ||||||||
\(604\) | 21.9373 | 0.892614 | ||||||||
\(605\) | 17.4170 | 0.708102 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.8118 | −1.25061 | −0.625305 | − | 0.780380i | \(-0.715026\pi\) | ||||
−0.625305 | + | 0.780380i | \(0.715026\pi\) | |||||||
\(608\) | −5.00000 | −0.202777 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.47974 | −0.262357 | ||||||||
\(611\) | 3.00000 | 0.121367 | ||||||||
\(612\) | −1.35425 | −0.0547423 | ||||||||
\(613\) | 10.1255 | 0.408965 | 0.204482 | − | 0.978870i | \(-0.434449\pi\) | ||||
0.204482 | + | 0.978870i | \(0.434449\pi\) | |||||||
\(614\) | −11.5830 | −0.467452 | ||||||||
\(615\) | −12.5830 | −0.507396 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.2915 | −0.857164 | −0.428582 | − | 0.903503i | \(-0.640987\pi\) | ||||
−0.428582 | + | 0.903503i | \(0.640987\pi\) | |||||||
\(618\) | −5.29150 | −0.212855 | ||||||||
\(619\) | 21.7490 | 0.874167 | 0.437083 | − | 0.899421i | \(-0.356011\pi\) | ||||
0.437083 | + | 0.899421i | \(0.356011\pi\) | |||||||
\(620\) | −12.0000 | −0.481932 | ||||||||
\(621\) | −7.64575 | −0.306813 | ||||||||
\(622\) | 16.9373 | 0.679122 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −8.29150 | −0.331660 | ||||||||
\(626\) | 29.1660 | 1.16571 | ||||||||
\(627\) | −23.2288 | −0.927667 | ||||||||
\(628\) | −2.64575 | −0.105577 | ||||||||
\(629\) | −0.479741 | −0.0191285 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.4575 | −1.53097 | −0.765485 | − | 0.643454i | \(-0.777501\pi\) | ||||
−0.765485 | + | 0.643454i | \(0.777501\pi\) | |||||||
\(632\) | 10.0000 | 0.397779 | ||||||||
\(633\) | −11.6458 | −0.462877 | ||||||||
\(634\) | 2.70850 | 0.107568 | ||||||||
\(635\) | 26.7085 | 1.05989 | ||||||||
\(636\) | −3.00000 | −0.118958 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −29.2288 | −1.15718 | ||||||||
\(639\) | 5.70850 | 0.225825 | ||||||||
\(640\) | −1.64575 | −0.0650540 | ||||||||
\(641\) | −42.5830 | −1.68193 | −0.840964 | − | 0.541091i | \(-0.818011\pi\) | ||||
−0.840964 | + | 0.541091i | \(0.818011\pi\) | |||||||
\(642\) | 12.0000 | 0.473602 | ||||||||
\(643\) | 20.8745 | 0.823210 | 0.411605 | − | 0.911362i | \(-0.364968\pi\) | ||||
0.411605 | + | 0.911362i | \(0.364968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.70850 | 0.342897 | ||||||||
\(646\) | 6.77124 | 0.266411 | ||||||||
\(647\) | −37.7490 | −1.48407 | −0.742033 | − | 0.670363i | \(-0.766138\pi\) | ||||
−0.742033 | + | 0.670363i | \(0.766138\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −36.8745 | −1.44745 | ||||||||
\(650\) | 2.29150 | 0.0898801 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 23.5830 | 0.923582 | ||||||||
\(653\) | 12.0000 | 0.469596 | 0.234798 | − | 0.972044i | \(-0.424557\pi\) | ||||
0.234798 | + | 0.972044i | \(0.424557\pi\) | |||||||
\(654\) | 4.00000 | 0.156412 | ||||||||
\(655\) | −8.12549 | −0.317489 | ||||||||
\(656\) | −7.64575 | −0.298516 | ||||||||
\(657\) | −8.35425 | −0.325930 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.06275 | −0.0413987 | −0.0206994 | − | 0.999786i | \(-0.506589\pi\) | ||||
−0.0206994 | + | 0.999786i | \(0.506589\pi\) | |||||||
\(660\) | −7.64575 | −0.297610 | ||||||||
\(661\) | −21.5203 | −0.837041 | −0.418521 | − | 0.908207i | \(-0.637451\pi\) | ||||
−0.418521 | + | 0.908207i | \(0.637451\pi\) | |||||||
\(662\) | −32.5830 | −1.26637 | ||||||||
\(663\) | −1.35425 | −0.0525947 | ||||||||
\(664\) | 2.70850 | 0.105110 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.354249 | −0.0137269 | ||||||||
\(667\) | 48.1033 | 1.86257 | ||||||||
\(668\) | 24.8745 | 0.962424 | ||||||||
\(669\) | 16.5203 | 0.638710 | ||||||||
\(670\) | 22.3542 | 0.863620 | ||||||||
\(671\) | −18.2915 | −0.706136 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5830 | 0.562134 | 0.281067 | − | 0.959688i | \(-0.409312\pi\) | ||||
0.281067 | + | 0.959688i | \(0.409312\pi\) | |||||||
\(674\) | −5.58301 | −0.215049 | ||||||||
\(675\) | −2.29150 | −0.0882000 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −22.1660 | −0.851909 | −0.425954 | − | 0.904745i | \(-0.640062\pi\) | ||||
−0.425954 | + | 0.904745i | \(0.640062\pi\) | |||||||
\(678\) | 11.2288 | 0.431238 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.22876 | 0.0854689 | ||||||||
\(681\) | −15.2915 | −0.585972 | ||||||||
\(682\) | −33.8745 | −1.29712 | ||||||||
\(683\) | 8.70850 | 0.333221 | 0.166611 | − | 0.986023i | \(-0.446718\pi\) | ||||
0.166611 | + | 0.986023i | \(0.446718\pi\) | |||||||
\(684\) | 5.00000 | 0.191180 | ||||||||
\(685\) | 28.8340 | 1.10169 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.4575 | −1.00942 | ||||||||
\(688\) | 5.29150 | 0.201737 | ||||||||
\(689\) | −3.00000 | −0.114291 | ||||||||
\(690\) | 12.5830 | 0.479027 | ||||||||
\(691\) | 34.0405 | 1.29496 | 0.647481 | − | 0.762081i | \(-0.275822\pi\) | ||||
0.647481 | + | 0.762081i | \(0.275822\pi\) | |||||||
\(692\) | −11.7085 | −0.445090 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.2288 | 0.995630 | ||||||||
\(695\) | 6.95948 | 0.263988 | ||||||||
\(696\) | 6.29150 | 0.238479 | ||||||||
\(697\) | 10.3542 | 0.392195 | ||||||||
\(698\) | −3.06275 | −0.115927 | ||||||||
\(699\) | −4.64575 | −0.175718 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | −1.00000 | −0.0377426 | ||||||||
\(703\) | 1.77124 | 0.0668037 | ||||||||
\(704\) | −4.64575 | −0.175093 | ||||||||
\(705\) | 4.93725 | 0.185948 | ||||||||
\(706\) | −0.583005 | −0.0219417 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7.93725 | 0.298300 | ||||||||
\(709\) | 43.5203 | 1.63444 | 0.817219 | − | 0.576328i | \(-0.195515\pi\) | ||||
0.817219 | + | 0.576328i | \(0.195515\pi\) | |||||||
\(710\) | −9.39477 | −0.352579 | ||||||||
\(711\) | −10.0000 | −0.375029 | ||||||||
\(712\) | −1.06275 | −0.0398281 | ||||||||
\(713\) | 55.7490 | 2.08782 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.64575 | −0.285935 | ||||||||
\(716\) | −6.00000 | −0.224231 | ||||||||
\(717\) | 3.00000 | 0.112037 | ||||||||
\(718\) | 6.00000 | 0.223918 | ||||||||
\(719\) | 23.4170 | 0.873307 | 0.436653 | − | 0.899630i | \(-0.356164\pi\) | ||||
0.436653 | + | 0.899630i | \(0.356164\pi\) | |||||||
\(720\) | 1.64575 | 0.0613335 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.00000 | −0.223297 | ||||||||
\(723\) | 17.8745 | 0.664760 | ||||||||
\(724\) | 9.35425 | 0.347648 | ||||||||
\(725\) | 14.4170 | 0.535434 | ||||||||
\(726\) | −10.5830 | −0.392772 | ||||||||
\(727\) | 36.4575 | 1.35213 | 0.676067 | − | 0.736840i | \(-0.263683\pi\) | ||||
0.676067 | + | 0.736840i | \(0.263683\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 13.7490 | 0.508874 | ||||||||
\(731\) | −7.16601 | −0.265044 | ||||||||
\(732\) | 3.93725 | 0.145525 | ||||||||
\(733\) | −12.2288 | −0.451679 | −0.225840 | − | 0.974164i | \(-0.572513\pi\) | ||||
−0.225840 | + | 0.974164i | \(0.572513\pi\) | |||||||
\(734\) | −20.5830 | −0.759733 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.64575 | 0.281826 | ||||||||
\(737\) | 63.1033 | 2.32444 | ||||||||
\(738\) | 7.64575 | 0.281444 | ||||||||
\(739\) | −6.70850 | −0.246776 | −0.123388 | − | 0.992359i | \(-0.539376\pi\) | ||||
−0.123388 | + | 0.992359i | \(0.539376\pi\) | |||||||
\(740\) | 0.583005 | 0.0214317 | ||||||||
\(741\) | 5.00000 | 0.183680 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.45751 | 0.0534710 | 0.0267355 | − | 0.999643i | \(-0.491489\pi\) | ||||
0.0267355 | + | 0.999643i | \(0.491489\pi\) | |||||||
\(744\) | 7.29150 | 0.267319 | ||||||||
\(745\) | −37.7490 | −1.38302 | ||||||||
\(746\) | −9.35425 | −0.342483 | ||||||||
\(747\) | −2.70850 | −0.0990987 | ||||||||
\(748\) | 6.29150 | 0.230040 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 12.0000 | 0.438178 | ||||||||
\(751\) | 9.16601 | 0.334472 | 0.167236 | − | 0.985917i | \(-0.446516\pi\) | ||||
0.167236 | + | 0.985917i | \(0.446516\pi\) | |||||||
\(752\) | 3.00000 | 0.109399 | ||||||||
\(753\) | −2.70850 | −0.0987031 | ||||||||
\(754\) | 6.29150 | 0.229123 | ||||||||
\(755\) | 36.1033 | 1.31393 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.3542 | 0.776133 | 0.388067 | − | 0.921631i | \(-0.373143\pi\) | ||||
0.388067 | + | 0.921631i | \(0.373143\pi\) | |||||||
\(758\) | −33.1660 | −1.20464 | ||||||||
\(759\) | 35.5203 | 1.28930 | ||||||||
\(760\) | −8.22876 | −0.298488 | ||||||||
\(761\) | −3.29150 | −0.119317 | −0.0596584 | − | 0.998219i | \(-0.519001\pi\) | ||||
−0.0596584 | + | 0.998219i | \(0.519001\pi\) | |||||||
\(762\) | −16.2288 | −0.587906 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.22876 | −0.0805809 | ||||||||
\(766\) | 37.7490 | 1.36393 | ||||||||
\(767\) | 7.93725 | 0.286598 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 0.354249 | 0.0127745 | 0.00638727 | − | 0.999980i | \(-0.497967\pi\) | ||||
0.00638727 | + | 0.999980i | \(0.497967\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.8745 | 0.571706 | ||||||||
\(772\) | 3.06275 | 0.110231 | ||||||||
\(773\) | −44.3320 | −1.59451 | −0.797256 | − | 0.603641i | \(-0.793716\pi\) | ||||
−0.797256 | + | 0.603641i | \(0.793716\pi\) | |||||||
\(774\) | −5.29150 | −0.190199 | ||||||||
\(775\) | 16.7085 | 0.600187 | ||||||||
\(776\) | 14.9373 | 0.536216 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.2915 | −0.655782 | ||||||||
\(779\) | −38.2288 | −1.36969 | ||||||||
\(780\) | 1.64575 | 0.0589273 | ||||||||
\(781\) | −26.5203 | −0.948969 | ||||||||
\(782\) | −10.3542 | −0.370267 | ||||||||
\(783\) | −6.29150 | −0.224840 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.35425 | −0.155410 | ||||||||
\(786\) | 4.93725 | 0.176106 | ||||||||
\(787\) | −42.6235 | −1.51936 | −0.759682 | − | 0.650294i | \(-0.774646\pi\) | ||||
−0.759682 | + | 0.650294i | \(0.774646\pi\) | |||||||
\(788\) | 20.8118 | 0.741388 | ||||||||
\(789\) | 1.64575 | 0.0585903 | ||||||||
\(790\) | 16.4575 | 0.585532 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.64575 | 0.165080 | ||||||||
\(793\) | 3.93725 | 0.139816 | ||||||||
\(794\) | −0.937254 | −0.0332619 | ||||||||
\(795\) | −4.93725 | −0.175106 | ||||||||
\(796\) | 4.22876 | 0.149884 | ||||||||
\(797\) | −14.1255 | −0.500351 | −0.250175 | − | 0.968201i | \(-0.580488\pi\) | ||||
−0.250175 | + | 0.968201i | \(0.580488\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.06275 | −0.143730 | ||||||||
\(800\) | 2.29150 | 0.0810169 | ||||||||
\(801\) | 1.06275 | 0.0375503 | ||||||||
\(802\) | −8.22876 | −0.290567 | ||||||||
\(803\) | 38.8118 | 1.36964 | ||||||||
\(804\) | −13.5830 | −0.479036 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.29150 | 0.256832 | ||||||||
\(807\) | −24.8745 | −0.875624 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.8118 | −0.837177 | −0.418588 | − | 0.908176i | \(-0.637475\pi\) | ||||
−0.418588 | + | 0.908176i | \(0.637475\pi\) | |||||||
\(810\) | −1.64575 | −0.0578258 | ||||||||
\(811\) | 38.0000 | 1.33436 | 0.667180 | − | 0.744896i | \(-0.267501\pi\) | ||||
0.667180 | + | 0.744896i | \(0.267501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.3542 | −0.608640 | ||||||||
\(814\) | 1.64575 | 0.0576836 | ||||||||
\(815\) | 38.8118 | 1.35952 | ||||||||
\(816\) | −1.35425 | −0.0474082 | ||||||||
\(817\) | 26.4575 | 0.925631 | ||||||||
\(818\) | 11.0627 | 0.386800 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.5830 | −0.439418 | ||||||||
\(821\) | −32.2288 | −1.12479 | −0.562396 | − | 0.826868i | \(-0.690120\pi\) | ||||
−0.562396 | + | 0.826868i | \(0.690120\pi\) | |||||||
\(822\) | −17.5203 | −0.611089 | ||||||||
\(823\) | −21.5203 | −0.750149 | −0.375075 | − | 0.926995i | \(-0.622383\pi\) | ||||
−0.375075 | + | 0.926995i | \(0.622383\pi\) | |||||||
\(824\) | −5.29150 | −0.184338 | ||||||||
\(825\) | 10.6458 | 0.370637 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.6458 | 1.41339 | 0.706696 | − | 0.707518i | \(-0.250185\pi\) | ||||
0.706696 | + | 0.707518i | \(0.250185\pi\) | |||||||
\(828\) | −7.64575 | −0.265708 | ||||||||
\(829\) | 20.7712 | 0.721415 | 0.360708 | − | 0.932679i | \(-0.382535\pi\) | ||||
0.360708 | + | 0.932679i | \(0.382535\pi\) | |||||||
\(830\) | 4.45751 | 0.154723 | ||||||||
\(831\) | −18.5203 | −0.642461 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.22876 | −0.146430 | ||||||||
\(835\) | 40.9373 | 1.41669 | ||||||||
\(836\) | −23.2288 | −0.803383 | ||||||||
\(837\) | −7.29150 | −0.252031 | ||||||||
\(838\) | 22.4575 | 0.775782 | ||||||||
\(839\) | 21.0000 | 0.725001 | 0.362500 | − | 0.931984i | \(-0.381923\pi\) | ||||
0.362500 | + | 0.931984i | \(0.381923\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.5830 | 0.364931 | ||||||||
\(842\) | 29.6458 | 1.02166 | ||||||||
\(843\) | 18.5830 | 0.640033 | ||||||||
\(844\) | −11.6458 | −0.400863 | ||||||||
\(845\) | 1.64575 | 0.0566156 | ||||||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | −26.9373 | −0.924484 | ||||||||
\(850\) | −3.10326 | −0.106441 | ||||||||
\(851\) | −2.70850 | −0.0928461 | ||||||||
\(852\) | 5.70850 | 0.195570 | ||||||||
\(853\) | 38.1033 | 1.30463 | 0.652315 | − | 0.757948i | \(-0.273798\pi\) | ||||
0.652315 | + | 0.757948i | \(0.273798\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.22876 | 0.281418 | ||||||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | −1.93725 | −0.0661753 | −0.0330877 | − | 0.999452i | \(-0.510534\pi\) | ||||
−0.0330877 | + | 0.999452i | \(0.510534\pi\) | |||||||
\(858\) | 4.64575 | 0.158603 | ||||||||
\(859\) | −8.45751 | −0.288567 | −0.144283 | − | 0.989536i | \(-0.546088\pi\) | ||||
−0.144283 | + | 0.989536i | \(0.546088\pi\) | |||||||
\(860\) | 8.70850 | 0.296957 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.583005 | 0.0198572 | ||||||||
\(863\) | −31.7490 | −1.08075 | −0.540375 | − | 0.841425i | \(-0.681717\pi\) | ||||
−0.540375 | + | 0.841425i | \(0.681717\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −19.2693 | −0.655175 | ||||||||
\(866\) | 12.4170 | 0.421947 | ||||||||
\(867\) | −15.1660 | −0.515065 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.4575 | 1.57596 | ||||||||
\(870\) | 10.3542 | 0.351042 | ||||||||
\(871\) | −13.5830 | −0.460243 | ||||||||
\(872\) | 4.00000 | 0.135457 | ||||||||
\(873\) | −14.9373 | −0.505549 | ||||||||
\(874\) | 38.2288 | 1.29311 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.35425 | −0.282264 | ||||||||
\(877\) | −7.18824 | −0.242730 | −0.121365 | − | 0.992608i | \(-0.538727\pi\) | ||||
−0.121365 | + | 0.992608i | \(0.538727\pi\) | |||||||
\(878\) | −18.3542 | −0.619426 | ||||||||
\(879\) | −29.5203 | −0.995694 | ||||||||
\(880\) | −7.64575 | −0.257738 | ||||||||
\(881\) | −21.2915 | −0.717329 | −0.358664 | − | 0.933467i | \(-0.616768\pi\) | ||||
−0.358664 | + | 0.933467i | \(0.616768\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.9373 | −1.51226 | −0.756130 | − | 0.654422i | \(-0.772912\pi\) | ||||
−0.756130 | + | 0.654422i | \(0.772912\pi\) | |||||||
\(884\) | −1.35425 | −0.0455483 | ||||||||
\(885\) | 13.0627 | 0.439099 | ||||||||
\(886\) | −34.9373 | −1.17374 | ||||||||
\(887\) | −0.583005 | −0.0195754 | −0.00978770 | − | 0.999952i | \(-0.503116\pi\) | ||||
−0.00978770 | + | 0.999952i | \(0.503116\pi\) | |||||||
\(888\) | −0.354249 | −0.0118878 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.74902 | −0.0586271 | ||||||||
\(891\) | −4.64575 | −0.155639 | ||||||||
\(892\) | 16.5203 | 0.553139 | ||||||||
\(893\) | 15.0000 | 0.501956 | ||||||||
\(894\) | 22.9373 | 0.767137 | ||||||||
\(895\) | −9.87451 | −0.330068 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.64575 | −0.255284 | ||||||||
\(898\) | −12.0000 | −0.400445 | ||||||||
\(899\) | 45.8745 | 1.53000 | ||||||||
\(900\) | −2.29150 | −0.0763834 | ||||||||
\(901\) | 4.06275 | 0.135350 | ||||||||
\(902\) | −35.5203 | −1.18270 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.2288 | 0.373463 | ||||||||
\(905\) | 15.3948 | 0.511739 | ||||||||
\(906\) | −21.9373 | −0.728816 | ||||||||
\(907\) | −30.2288 | −1.00373 | −0.501865 | − | 0.864946i | \(-0.667352\pi\) | ||||
−0.501865 | + | 0.864946i | \(0.667352\pi\) | |||||||
\(908\) | −15.2915 | −0.507466 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.7490 | 0.853103 | 0.426551 | − | 0.904463i | \(-0.359728\pi\) | ||||
0.426551 | + | 0.904463i | \(0.359728\pi\) | |||||||
\(912\) | 5.00000 | 0.165567 | ||||||||
\(913\) | 12.5830 | 0.416437 | ||||||||
\(914\) | −5.77124 | −0.190896 | ||||||||
\(915\) | 6.47974 | 0.214214 | ||||||||
\(916\) | −26.4575 | −0.874181 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.35425 | 0.0446969 | ||||||||
\(919\) | 16.1255 | 0.531931 | 0.265965 | − | 0.963983i | \(-0.414309\pi\) | ||||
0.265965 | + | 0.963983i | \(0.414309\pi\) | |||||||
\(920\) | 12.5830 | 0.414849 | ||||||||
\(921\) | 11.5830 | 0.381673 | ||||||||
\(922\) | −16.4575 | −0.541999 | ||||||||
\(923\) | 5.70850 | 0.187897 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.811762 | −0.0266906 | ||||||||
\(926\) | 17.1660 | 0.564110 | ||||||||
\(927\) | 5.29150 | 0.173796 | ||||||||
\(928\) | 6.29150 | 0.206529 | ||||||||
\(929\) | 49.7490 | 1.63221 | 0.816106 | − | 0.577902i | \(-0.196128\pi\) | ||||
0.816106 | + | 0.577902i | \(0.196128\pi\) | |||||||
\(930\) | 12.0000 | 0.393496 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.64575 | −0.152177 | ||||||||
\(933\) | −16.9373 | −0.554501 | ||||||||
\(934\) | 0.479741 | 0.0156976 | ||||||||
\(935\) | 10.3542 | 0.338620 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 21.4575 | 0.700986 | 0.350493 | − | 0.936565i | \(-0.386014\pi\) | ||||
0.350493 | + | 0.936565i | \(0.386014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29.1660 | −0.951797 | ||||||||
\(940\) | 4.93725 | 0.161035 | ||||||||
\(941\) | 25.1660 | 0.820388 | 0.410194 | − | 0.911998i | \(-0.365461\pi\) | ||||
0.410194 | + | 0.911998i | \(0.365461\pi\) | |||||||
\(942\) | 2.64575 | 0.0862032 | ||||||||
\(943\) | 58.4575 | 1.90364 | ||||||||
\(944\) | 7.93725 | 0.258336 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.5830 | 0.799262 | ||||||||
\(947\) | 26.5203 | 0.861793 | 0.430896 | − | 0.902401i | \(-0.358197\pi\) | ||||
0.430896 | + | 0.902401i | \(0.358197\pi\) | |||||||
\(948\) | −10.0000 | −0.324785 | ||||||||
\(949\) | −8.35425 | −0.271190 | ||||||||
\(950\) | 11.4575 | 0.371731 | ||||||||
\(951\) | −2.70850 | −0.0878290 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.1033 | 1.07232 | 0.536160 | − | 0.844116i | \(-0.319874\pi\) | ||||
0.536160 | + | 0.844116i | \(0.319874\pi\) | |||||||
\(954\) | 3.00000 | 0.0971286 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | 0.0970269 | ||||||||
\(957\) | 29.2288 | 0.944832 | ||||||||
\(958\) | −28.7490 | −0.928839 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.64575 | 0.0531164 | ||||||||
\(961\) | 22.1660 | 0.715033 | ||||||||
\(962\) | −0.354249 | −0.0114214 | ||||||||
\(963\) | −12.0000 | −0.386695 | ||||||||
\(964\) | 17.8745 | 0.575699 | ||||||||
\(965\) | 5.04052 | 0.162260 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.1033 | −1.57905 | −0.789527 | − | 0.613715i | \(-0.789674\pi\) | ||||
−0.789527 | + | 0.613715i | \(0.789674\pi\) | |||||||
\(968\) | −10.5830 | −0.340151 | ||||||||
\(969\) | −6.77124 | −0.217524 | ||||||||
\(970\) | 24.5830 | 0.789313 | ||||||||
\(971\) | 1.06275 | 0.0341051 | 0.0170526 | − | 0.999855i | \(-0.494572\pi\) | ||||
0.0170526 | + | 0.999855i | \(0.494572\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.06275 | 0.258347 | ||||||||
\(975\) | −2.29150 | −0.0733868 | ||||||||
\(976\) | 3.93725 | 0.126028 | ||||||||
\(977\) | 51.8745 | 1.65961 | 0.829806 | − | 0.558052i | \(-0.188451\pi\) | ||||
0.829806 | + | 0.558052i | \(0.188451\pi\) | |||||||
\(978\) | −23.5830 | −0.754101 | ||||||||
\(979\) | −4.93725 | −0.157795 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.00000 | −0.127710 | ||||||||
\(982\) | 31.1660 | 0.994547 | ||||||||
\(983\) | 44.0405 | 1.40467 | 0.702337 | − | 0.711844i | \(-0.252140\pi\) | ||||
0.702337 | + | 0.711844i | \(0.252140\pi\) | |||||||
\(984\) | 7.64575 | 0.243738 | ||||||||
\(985\) | 34.2510 | 1.09133 | ||||||||
\(986\) | −8.52026 | −0.271340 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.00000 | 0.159071 | ||||||||
\(989\) | −40.4575 | −1.28647 | ||||||||
\(990\) | 7.64575 | 0.242998 | ||||||||
\(991\) | 26.5830 | 0.844437 | 0.422218 | − | 0.906494i | \(-0.361252\pi\) | ||||
0.422218 | + | 0.906494i | \(0.361252\pi\) | |||||||
\(992\) | 7.29150 | 0.231505 | ||||||||
\(993\) | 32.5830 | 1.03399 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.95948 | 0.220630 | ||||||||
\(996\) | −2.70850 | −0.0858220 | ||||||||
\(997\) | 25.2288 | 0.799003 | 0.399501 | − | 0.916733i | \(-0.369183\pi\) | ||||
0.399501 | + | 0.916733i | \(0.369183\pi\) | |||||||
\(998\) | 18.7085 | 0.592207 | ||||||||
\(999\) | 0.354249 | 0.0112079 |
(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 | 3822.2.a.bk.1.2 | 2 | ||
7.2 | even | 3 | 546.2.i.j.235.1 | yes | 4 | ||
7.4 | even | 3 | 546.2.i.j.79.1 | ✓ | 4 | ||
7.6 | odd | 2 | 3822.2.a.bi.1.1 | 2 | |||
21.2 | odd | 6 | 1638.2.j.k.235.2 | 4 | |||
21.11 | odd | 6 | 1638.2.j.k.1171.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.i.j.79.1 | ✓ | 4 | 7.4 | even | 3 | ||
546.2.i.j.235.1 | yes | 4 | 7.2 | even | 3 | ||
1638.2.j.k.235.2 | 4 | 21.2 | odd | 6 | |||
1638.2.j.k.1171.2 | 4 | 21.11 | odd | 6 | |||
3822.2.a.bi.1.1 | 2 | 7.6 | odd | 2 | |||
3822.2.a.bk.1.2 | 2 | 1.1 | even | 1 | trivial |