Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, 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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 10x^{5} + 8x^{4} + 22x^{3} - 5x^{2} - 7x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.19620\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.42067 | −1.71167 | −0.855835 | − | 0.517250i | \(-0.826956\pi\) | ||||
−0.855835 | + | 0.517250i | \(0.826956\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.85962 | 1.92981 | ||||||||
\(5\) | −2.85962 | −1.27886 | −0.639431 | − | 0.768849i | \(-0.720830\pi\) | ||||
−0.639431 | + | 0.768849i | \(0.720830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.49298 | −0.942258 | −0.471129 | − | 0.882064i | \(-0.656153\pi\) | ||||
−0.471129 | + | 0.882064i | \(0.656153\pi\) | |||||||
\(8\) | −4.50152 | −1.59153 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.92219 | 2.18899 | ||||||||
\(11\) | 1.12006 | 0.337710 | 0.168855 | − | 0.985641i | \(-0.445993\pi\) | ||||
0.168855 | + | 0.985641i | \(0.445993\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.971725 | −0.269508 | −0.134754 | − | 0.990879i | \(-0.543024\pi\) | ||||
−0.134754 | + | 0.990879i | \(0.543024\pi\) | |||||||
\(14\) | 6.03467 | 1.61283 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.17744 | 0.794359 | ||||||||
\(17\) | 7.78181 | 1.88737 | 0.943683 | − | 0.330851i | \(-0.107336\pi\) | ||||
0.943683 | + | 0.330851i | \(0.107336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.63600 | −1.06357 | −0.531786 | − | 0.846879i | \(-0.678479\pi\) | ||||
−0.531786 | + | 0.846879i | \(0.678479\pi\) | |||||||
\(20\) | −11.0371 | −2.46796 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.71129 | −0.578048 | ||||||||
\(23\) | −5.88790 | −1.22771 | −0.613856 | − | 0.789418i | \(-0.710382\pi\) | ||||
−0.613856 | + | 0.789418i | \(0.710382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.17744 | 0.635487 | ||||||||
\(26\) | 2.35222 | 0.461308 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −9.62196 | −1.81838 | ||||||||
\(29\) | 7.22556 | 1.34175 | 0.670877 | − | 0.741569i | \(-0.265918\pi\) | ||||
0.670877 | + | 0.741569i | \(0.265918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.96875 | 0.712809 | 0.356405 | − | 0.934332i | \(-0.384002\pi\) | ||||
0.356405 | + | 0.934332i | \(0.384002\pi\) | |||||||
\(32\) | 1.31153 | 0.231849 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −18.8372 | −3.23055 | ||||||||
\(35\) | 7.12898 | 1.20502 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.21281 | 1.02138 | 0.510690 | − | 0.859765i | \(-0.329390\pi\) | ||||
0.510690 | + | 0.859765i | \(0.329390\pi\) | |||||||
\(38\) | 11.2222 | 1.82048 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 12.8727 | 2.03534 | ||||||||
\(41\) | −10.8562 | −1.69545 | −0.847723 | − | 0.530439i | \(-0.822027\pi\) | ||||
−0.847723 | + | 0.530439i | \(0.822027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.3040 | 1.87635 | 0.938174 | − | 0.346165i | \(-0.112516\pi\) | ||||
0.938174 | + | 0.346165i | \(0.112516\pi\) | |||||||
\(44\) | 4.32300 | 0.651717 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.2526 | 2.10144 | ||||||||
\(47\) | 5.23663 | 0.763841 | 0.381920 | − | 0.924195i | \(-0.375263\pi\) | ||||
0.381920 | + | 0.924195i | \(0.375263\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.785046 | −0.112149 | ||||||||
\(50\) | −7.69151 | −1.08774 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.75049 | −0.520099 | ||||||||
\(53\) | 0.697008 | 0.0957414 | 0.0478707 | − | 0.998854i | \(-0.484756\pi\) | ||||
0.0478707 | + | 0.998854i | \(0.484756\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.20294 | −0.431885 | ||||||||
\(56\) | 11.2222 | 1.49963 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −17.4907 | −2.29664 | ||||||||
\(59\) | −7.55604 | −0.983713 | −0.491857 | − | 0.870676i | \(-0.663682\pi\) | ||||
−0.491857 | + | 0.870676i | \(0.663682\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.56381 | −0.328262 | −0.164131 | − | 0.986439i | \(-0.552482\pi\) | ||||
−0.164131 | + | 0.986439i | \(0.552482\pi\) | |||||||
\(62\) | −9.60703 | −1.22009 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −9.52966 | −1.19121 | ||||||||
\(65\) | 2.77876 | 0.344663 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.16648 | 0.753356 | 0.376678 | − | 0.926344i | \(-0.377066\pi\) | ||||
0.376678 | + | 0.926344i | \(0.377066\pi\) | |||||||
\(68\) | 30.0348 | 3.64226 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −17.2569 | −2.06259 | ||||||||
\(71\) | 3.64042 | 0.432038 | 0.216019 | − | 0.976389i | \(-0.430693\pi\) | ||||
0.216019 | + | 0.976389i | \(0.430693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.1915 | −1.54395 | −0.771977 | − | 0.635650i | \(-0.780732\pi\) | ||||
−0.771977 | + | 0.635650i | \(0.780732\pi\) | |||||||
\(74\) | −15.0391 | −1.74826 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.8932 | −2.05249 | ||||||||
\(77\) | −2.79229 | −0.318210 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4007 | 1.39519 | 0.697595 | − | 0.716492i | \(-0.254253\pi\) | ||||
0.697595 | + | 0.716492i | \(0.254253\pi\) | |||||||
\(80\) | −9.08627 | −1.01588 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 26.2791 | 2.90204 | ||||||||
\(83\) | −5.28871 | −0.580512 | −0.290256 | − | 0.956949i | \(-0.593740\pi\) | ||||
−0.290256 | + | 0.956949i | \(0.593740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.2530 | −2.41368 | ||||||||
\(86\) | −29.7840 | −3.21169 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.04197 | −0.537476 | ||||||||
\(89\) | 1.20236 | 0.127450 | 0.0637249 | − | 0.997968i | \(-0.479702\pi\) | ||||
0.0637249 | + | 0.997968i | \(0.479702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.42249 | 0.253946 | ||||||||
\(92\) | −22.7251 | −2.36925 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.6761 | −1.30744 | ||||||||
\(95\) | 13.2572 | 1.36016 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.49376 | −0.354737 | −0.177369 | − | 0.984144i | \(-0.556758\pi\) | ||||
−0.177369 | + | 0.984144i | \(0.556758\pi\) | |||||||
\(98\) | 1.90033 | 0.191963 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.2637 | 1.22637 | ||||||||
\(101\) | −14.7746 | −1.47013 | −0.735064 | − | 0.677998i | \(-0.762848\pi\) | ||||
−0.735064 | + | 0.677998i | \(0.762848\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.5456 | 1.53176 | 0.765879 | − | 0.642985i | \(-0.222304\pi\) | ||||
0.765879 | + | 0.642985i | \(0.222304\pi\) | |||||||
\(104\) | 4.37424 | 0.428930 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.68722 | −0.163878 | ||||||||
\(107\) | 4.63008 | 0.447607 | 0.223803 | − | 0.974634i | \(-0.428153\pi\) | ||||
0.223803 | + | 0.974634i | \(0.428153\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.46029 | −0.427218 | −0.213609 | − | 0.976919i | \(-0.568522\pi\) | ||||
−0.213609 | + | 0.976919i | \(0.568522\pi\) | |||||||
\(110\) | 7.75326 | 0.739244 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.92129 | −0.748491 | ||||||||
\(113\) | −1.22312 | −0.115062 | −0.0575309 | − | 0.998344i | \(-0.518323\pi\) | ||||
−0.0575309 | + | 0.998344i | \(0.518323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.8372 | 1.57007 | ||||||||
\(116\) | 27.8879 | 2.58933 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.2907 | 1.68379 | ||||||||
\(119\) | −19.3999 | −1.77839 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.74547 | −0.885952 | ||||||||
\(122\) | 6.20613 | 0.561877 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.3179 | 1.37559 | ||||||||
\(125\) | 5.21184 | 0.466161 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.92155 | 0.170510 | 0.0852549 | − | 0.996359i | \(-0.472830\pi\) | ||||
0.0852549 | + | 0.996359i | \(0.472830\pi\) | |||||||
\(128\) | 20.4450 | 1.80710 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.72646 | −0.589950 | ||||||||
\(131\) | −1.79786 | −0.157080 | −0.0785399 | − | 0.996911i | \(-0.525026\pi\) | ||||
−0.0785399 | + | 0.996911i | \(0.525026\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.5575 | 1.00216 | ||||||||
\(134\) | −14.9270 | −1.28950 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −35.0300 | −3.00380 | ||||||||
\(137\) | 9.30901 | 0.795322 | 0.397661 | − | 0.917532i | \(-0.369822\pi\) | ||||
0.397661 | + | 0.917532i | \(0.369822\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.9155 | −1.85885 | −0.929423 | − | 0.369016i | \(-0.879695\pi\) | ||||
−0.929423 | + | 0.369016i | \(0.879695\pi\) | |||||||
\(140\) | 27.5152 | 2.32546 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.81223 | −0.739506 | ||||||||
\(143\) | −1.08839 | −0.0910156 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.6624 | −1.71592 | ||||||||
\(146\) | 31.9323 | 2.64274 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 23.9791 | 1.97107 | ||||||||
\(149\) | −5.26452 | −0.431286 | −0.215643 | − | 0.976472i | \(-0.569185\pi\) | ||||
−0.215643 | + | 0.976472i | \(0.569185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9898 | 0.975715 | 0.487858 | − | 0.872923i | \(-0.337778\pi\) | ||||
0.487858 | + | 0.872923i | \(0.337778\pi\) | |||||||
\(152\) | 20.8691 | 1.69270 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.75919 | 0.544671 | ||||||||
\(155\) | −11.3491 | −0.911584 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0625 | −0.962688 | −0.481344 | − | 0.876532i | \(-0.659851\pi\) | ||||
−0.481344 | + | 0.876532i | \(0.659851\pi\) | |||||||
\(158\) | −30.0180 | −2.38811 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.75049 | −0.296502 | ||||||||
\(161\) | 14.6784 | 1.15682 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.5155 | −0.901964 | −0.450982 | − | 0.892533i | \(-0.648926\pi\) | ||||
−0.450982 | + | 0.892533i | \(0.648926\pi\) | |||||||
\(164\) | −41.9006 | −3.27189 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.8022 | 0.993644 | ||||||||
\(167\) | −9.51806 | −0.736530 | −0.368265 | − | 0.929721i | \(-0.620048\pi\) | ||||
−0.368265 | + | 0.929721i | \(0.620048\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0558 | −0.927365 | ||||||||
\(170\) | 53.8671 | 4.13142 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 47.4889 | 3.62100 | ||||||||
\(173\) | 18.3312 | 1.39370 | 0.696849 | − | 0.717218i | \(-0.254585\pi\) | ||||
0.696849 | + | 0.717218i | \(0.254585\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.92129 | −0.598793 | ||||||||
\(176\) | 3.55892 | 0.268263 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.91051 | −0.218152 | ||||||||
\(179\) | −9.47162 | −0.707942 | −0.353971 | − | 0.935256i | \(-0.615169\pi\) | ||||
−0.353971 | + | 0.935256i | \(0.615169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.52272 | −0.410501 | −0.205250 | − | 0.978710i | \(-0.565801\pi\) | ||||
−0.205250 | + | 0.978710i | \(0.565801\pi\) | |||||||
\(182\) | −5.86404 | −0.434672 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 26.5045 | 1.95394 | ||||||||
\(185\) | −17.7663 | −1.30620 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.71608 | 0.637383 | ||||||||
\(188\) | 20.2114 | 1.47407 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −32.0913 | −2.32815 | ||||||||
\(191\) | 12.2366 | 0.885411 | 0.442706 | − | 0.896667i | \(-0.354019\pi\) | ||||
0.442706 | + | 0.896667i | \(0.354019\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.57272 | −0.257170 | −0.128585 | − | 0.991698i | \(-0.541044\pi\) | ||||
−0.128585 | + | 0.991698i | \(0.541044\pi\) | |||||||
\(194\) | 8.45721 | 0.607193 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.02998 | −0.216427 | ||||||||
\(197\) | −14.9639 | −1.06614 | −0.533068 | − | 0.846072i | \(-0.678961\pi\) | ||||
−0.533068 | + | 0.846072i | \(0.678961\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.4882 | −0.885262 | −0.442631 | − | 0.896704i | \(-0.645955\pi\) | ||||
−0.442631 | + | 0.896704i | \(0.645955\pi\) | |||||||
\(200\) | −14.3033 | −1.01140 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 35.7644 | 2.51637 | ||||||||
\(203\) | −18.0132 | −1.26428 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.0445 | 2.16824 | ||||||||
\(206\) | −37.6308 | −2.62186 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.08759 | −0.214086 | ||||||||
\(209\) | −5.19259 | −0.359179 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.95186 | −0.616271 | −0.308136 | − | 0.951342i | \(-0.599705\pi\) | ||||
−0.308136 | + | 0.951342i | \(0.599705\pi\) | |||||||
\(212\) | 2.69019 | 0.184763 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.2079 | −0.766155 | ||||||||
\(215\) | −35.1849 | −2.39959 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.89403 | −0.671650 | ||||||||
\(218\) | 10.7969 | 0.731257 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.3622 | −0.833456 | ||||||||
\(221\) | −7.56178 | −0.508660 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6518 | −0.914190 | −0.457095 | − | 0.889418i | \(-0.651110\pi\) | ||||
−0.457095 | + | 0.889418i | \(0.651110\pi\) | |||||||
\(224\) | −3.26963 | −0.218461 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.96077 | 0.196948 | ||||||||
\(227\) | −2.30473 | −0.152971 | −0.0764853 | − | 0.997071i | \(-0.524370\pi\) | ||||
−0.0764853 | + | 0.997071i | \(0.524370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.1300 | 1.39631 | 0.698156 | − | 0.715945i | \(-0.254004\pi\) | ||||
0.698156 | + | 0.715945i | \(0.254004\pi\) | |||||||
\(230\) | −40.7571 | −2.68745 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −32.5260 | −2.13544 | ||||||||
\(233\) | −9.11468 | −0.597122 | −0.298561 | − | 0.954391i | \(-0.596507\pi\) | ||||
−0.298561 | + | 0.954391i | \(0.596507\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.9748 | −0.976847 | ||||||||
\(236\) | −29.1635 | −1.89838 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 46.9607 | 3.04401 | ||||||||
\(239\) | 1.00000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7038 | −0.947156 | −0.473578 | − | 0.880752i | \(-0.657038\pi\) | ||||
−0.473578 | + | 0.880752i | \(0.657038\pi\) | |||||||
\(242\) | 23.5905 | 1.51646 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.89534 | −0.633484 | ||||||||
\(245\) | 2.24494 | 0.143424 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.50492 | 0.286641 | ||||||||
\(248\) | −17.8654 | −1.13446 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.6161 | −0.797914 | ||||||||
\(251\) | −12.3028 | −0.776546 | −0.388273 | − | 0.921544i | \(-0.626928\pi\) | ||||
−0.388273 | + | 0.921544i | \(0.626928\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.59479 | −0.414611 | ||||||||
\(254\) | −4.65143 | −0.291856 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30.4313 | −1.90196 | ||||||||
\(257\) | −30.2278 | −1.88556 | −0.942779 | − | 0.333418i | \(-0.891798\pi\) | ||||
−0.942779 | + | 0.333418i | \(0.891798\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.4884 | −0.962403 | ||||||||
\(260\) | 10.7250 | 0.665135 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.35202 | 0.268869 | ||||||||
\(263\) | −14.7836 | −0.911595 | −0.455797 | − | 0.890084i | \(-0.650646\pi\) | ||||
−0.455797 | + | 0.890084i | \(0.650646\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.99318 | −0.122440 | ||||||||
\(266\) | −27.9768 | −1.71536 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 23.8003 | 1.45383 | ||||||||
\(269\) | 15.3623 | 0.936658 | 0.468329 | − | 0.883554i | \(-0.344856\pi\) | ||||
0.468329 | + | 0.883554i | \(0.344856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.71861 | −0.529618 | −0.264809 | − | 0.964301i | \(-0.585309\pi\) | ||||
−0.264809 | + | 0.964301i | \(0.585309\pi\) | |||||||
\(272\) | 24.7262 | 1.49925 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.5340 | −1.36133 | ||||||||
\(275\) | 3.55892 | 0.214611 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.47755 | −0.449282 | −0.224641 | − | 0.974442i | \(-0.572121\pi\) | ||||
−0.224641 | + | 0.974442i | \(0.572121\pi\) | |||||||
\(278\) | 53.0500 | 3.18173 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −32.0913 | −1.91782 | ||||||||
\(281\) | −19.3396 | −1.15371 | −0.576853 | − | 0.816848i | \(-0.695720\pi\) | ||||
−0.576853 | + | 0.816848i | \(0.695720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.53348 | 0.507263 | 0.253631 | − | 0.967301i | \(-0.418375\pi\) | ||||
0.253631 | + | 0.967301i | \(0.418375\pi\) | |||||||
\(284\) | 14.0506 | 0.833751 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.63463 | 0.155789 | ||||||||
\(287\) | 27.0642 | 1.59755 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 43.5566 | 2.56215 | ||||||||
\(290\) | 50.0167 | 2.93708 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −50.9144 | −2.97954 | ||||||||
\(293\) | −16.6219 | −0.971059 | −0.485529 | − | 0.874220i | \(-0.661373\pi\) | ||||
−0.485529 | + | 0.874220i | \(0.661373\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 21.6074 | 1.25803 | ||||||||
\(296\) | −27.9671 | −1.62555 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.7436 | 0.738220 | ||||||||
\(299\) | 5.72141 | 0.330878 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.6737 | −1.76800 | ||||||||
\(302\) | −29.0233 | −1.67010 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.7306 | −0.844858 | ||||||||
\(305\) | 7.33153 | 0.419802 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.5311 | −0.943480 | −0.471740 | − | 0.881738i | \(-0.656374\pi\) | ||||
−0.471740 | + | 0.881738i | \(0.656374\pi\) | |||||||
\(308\) | −10.7772 | −0.614086 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 27.4725 | 1.56033 | ||||||||
\(311\) | −13.7367 | −0.778939 | −0.389470 | − | 0.921039i | \(-0.627342\pi\) | ||||
−0.389470 | + | 0.921039i | \(0.627342\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6071 | 0.825641 | 0.412821 | − | 0.910812i | \(-0.364544\pi\) | ||||
0.412821 | + | 0.910812i | \(0.364544\pi\) | |||||||
\(314\) | 29.1992 | 1.64780 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 47.8621 | 2.69245 | ||||||||
\(317\) | −8.04568 | −0.451890 | −0.225945 | − | 0.974140i | \(-0.572547\pi\) | ||||
−0.225945 | + | 0.974140i | \(0.572547\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.09305 | 0.453124 | ||||||||
\(320\) | 27.2512 | 1.52339 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −35.5315 | −1.98009 | ||||||||
\(323\) | −36.0765 | −2.00735 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.08759 | −0.171269 | ||||||||
\(326\) | 27.8752 | 1.54386 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 48.8692 | 2.69835 | ||||||||
\(329\) | −13.0548 | −0.719735 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2686 | −1.22399 | −0.611997 | − | 0.790860i | \(-0.709634\pi\) | ||||
−0.611997 | + | 0.790860i | \(0.709634\pi\) | |||||||
\(332\) | −20.4124 | −1.12028 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 23.0400 | 1.26070 | ||||||||
\(335\) | −17.6338 | −0.963438 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.6136 | 1.72210 | 0.861052 | − | 0.508517i | \(-0.169806\pi\) | ||||
0.861052 | + | 0.508517i | \(0.169806\pi\) | |||||||
\(338\) | 29.1829 | 1.58734 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −85.8883 | −4.65795 | ||||||||
\(341\) | 4.44524 | 0.240723 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4080 | 1.04793 | ||||||||
\(344\) | −55.3869 | −2.98626 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −44.3738 | −2.38555 | ||||||||
\(347\) | 10.8188 | 0.580784 | 0.290392 | − | 0.956908i | \(-0.406214\pi\) | ||||
0.290392 | + | 0.956908i | \(0.406214\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.1766 | −1.88296 | −0.941479 | − | 0.337071i | \(-0.890564\pi\) | ||||
−0.941479 | + | 0.337071i | \(0.890564\pi\) | |||||||
\(350\) | 19.1748 | 1.02494 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.46899 | 0.0782977 | ||||||||
\(353\) | 17.1199 | 0.911203 | 0.455601 | − | 0.890184i | \(-0.349424\pi\) | ||||
0.455601 | + | 0.890184i | \(0.349424\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.4102 | −0.552517 | ||||||||
\(356\) | 4.64065 | 0.245954 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.9276 | 1.21176 | ||||||||
\(359\) | 11.2236 | 0.592361 | 0.296181 | − | 0.955132i | \(-0.404287\pi\) | ||||
0.296181 | + | 0.955132i | \(0.404287\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.49251 | 0.131185 | ||||||||
\(362\) | 13.3687 | 0.702641 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.34990 | 0.490068 | ||||||||
\(365\) | 37.7228 | 1.97450 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.31570 | 0.277477 | 0.138739 | − | 0.990329i | \(-0.455695\pi\) | ||||
0.138739 | + | 0.990329i | \(0.455695\pi\) | |||||||
\(368\) | −18.7084 | −0.975244 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 43.0062 | 2.23579 | ||||||||
\(371\) | −1.73763 | −0.0902131 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.01475 | 0.207876 | 0.103938 | − | 0.994584i | \(-0.466856\pi\) | ||||
0.103938 | + | 0.994584i | \(0.466856\pi\) | |||||||
\(374\) | −21.0987 | −1.09099 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.5728 | −1.21567 | ||||||||
\(377\) | −7.02126 | −0.361613 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0669 | 1.03077 | 0.515383 | − | 0.856960i | \(-0.327650\pi\) | ||||
0.515383 | + | 0.856960i | \(0.327650\pi\) | |||||||
\(380\) | 51.1678 | 2.62485 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −29.6208 | −1.51553 | ||||||||
\(383\) | −26.2363 | −1.34061 | −0.670306 | − | 0.742085i | \(-0.733837\pi\) | ||||
−0.670306 | + | 0.742085i | \(0.733837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.98488 | 0.406947 | ||||||||
\(386\) | 8.64837 | 0.440191 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.4846 | −0.684576 | ||||||||
\(389\) | −13.1624 | −0.667360 | −0.333680 | − | 0.942686i | \(-0.608291\pi\) | ||||
−0.333680 | + | 0.942686i | \(0.608291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.8185 | −2.31714 | ||||||||
\(392\) | 3.53390 | 0.178489 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 36.2227 | 1.82487 | ||||||||
\(395\) | −35.4614 | −1.78426 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.5087 | −1.48100 | −0.740500 | − | 0.672056i | \(-0.765411\pi\) | ||||
−0.740500 | + | 0.672056i | \(0.765411\pi\) | |||||||
\(398\) | 30.2297 | 1.51528 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.0961 | 0.504805 | ||||||||
\(401\) | −27.1474 | −1.35568 | −0.677839 | − | 0.735211i | \(-0.737083\pi\) | ||||
−0.677839 | + | 0.735211i | \(0.737083\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.85654 | −0.192108 | ||||||||
\(404\) | −57.0244 | −2.83707 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 43.6039 | 2.16403 | ||||||||
\(407\) | 6.95871 | 0.344931 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.8766 | −0.735599 | −0.367799 | − | 0.929905i | \(-0.619889\pi\) | ||||
−0.367799 | + | 0.929905i | \(0.619889\pi\) | |||||||
\(410\) | −75.1483 | −3.71131 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 60.0003 | 2.95600 | ||||||||
\(413\) | 18.8371 | 0.926912 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.1237 | 0.742394 | ||||||||
\(416\) | −1.27445 | −0.0624850 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12.5695 | 0.614796 | ||||||||
\(419\) | 21.1669 | 1.03407 | 0.517035 | − | 0.855964i | \(-0.327036\pi\) | ||||
0.517035 | + | 0.855964i | \(0.327036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.12081 | −0.395784 | −0.197892 | − | 0.980224i | \(-0.563410\pi\) | ||||
−0.197892 | + | 0.980224i | \(0.563410\pi\) | |||||||
\(422\) | 21.6695 | 1.05485 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.13760 | −0.152375 | ||||||||
\(425\) | 24.7262 | 1.19940 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.39153 | 0.309308 | ||||||||
\(428\) | 17.8704 | 0.863796 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 85.1708 | 4.10730 | ||||||||
\(431\) | 16.4514 | 0.792438 | 0.396219 | − | 0.918156i | \(-0.370322\pi\) | ||||
0.396219 | + | 0.918156i | \(0.370322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7856 | 0.758606 | 0.379303 | − | 0.925273i | \(-0.376164\pi\) | ||||
0.379303 | + | 0.925273i | \(0.376164\pi\) | |||||||
\(434\) | 23.9501 | 1.14964 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.2150 | −0.824451 | ||||||||
\(437\) | 27.2963 | 1.30576 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.441975 | 0.0210943 | 0.0105472 | − | 0.999944i | \(-0.496643\pi\) | ||||
0.0105472 | + | 0.999944i | \(0.496643\pi\) | |||||||
\(440\) | 14.4181 | 0.687357 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.3045 | 0.870658 | ||||||||
\(443\) | −34.6291 | −1.64528 | −0.822639 | − | 0.568564i | \(-0.807499\pi\) | ||||
−0.822639 | + | 0.568564i | \(0.807499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.43829 | −0.162991 | ||||||||
\(446\) | 33.0464 | 1.56479 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 23.7573 | 1.12242 | ||||||||
\(449\) | −27.3140 | −1.28903 | −0.644513 | − | 0.764593i | \(-0.722940\pi\) | ||||
−0.644513 | + | 0.764593i | \(0.722940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.1595 | −0.572570 | ||||||||
\(452\) | −4.72079 | −0.222047 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.57899 | 0.261835 | ||||||||
\(455\) | −6.92741 | −0.324762 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.4901 | −1.05204 | −0.526021 | − | 0.850472i | \(-0.676317\pi\) | ||||
−0.526021 | + | 0.850472i | \(0.676317\pi\) | |||||||
\(458\) | −51.1488 | −2.39003 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 64.9851 | 3.02994 | ||||||||
\(461\) | 34.2275 | 1.59413 | 0.797067 | − | 0.603891i | \(-0.206384\pi\) | ||||
0.797067 | + | 0.603891i | \(0.206384\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.5949 | −0.957125 | −0.478563 | − | 0.878053i | \(-0.658842\pi\) | ||||
−0.478563 | + | 0.878053i | \(0.658842\pi\) | |||||||
\(464\) | 22.9588 | 1.06583 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 22.0636 | 1.02208 | ||||||||
\(467\) | 18.8946 | 0.874338 | 0.437169 | − | 0.899379i | \(-0.355981\pi\) | ||||
0.437169 | + | 0.899379i | \(0.355981\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.3729 | −0.709856 | ||||||||
\(470\) | 36.2489 | 1.67204 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 34.0137 | 1.56561 | ||||||||
\(473\) | 13.7812 | 0.633662 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.7306 | −0.675886 | ||||||||
\(476\) | −74.8763 | −3.43195 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.42067 | −0.110719 | ||||||||
\(479\) | 33.5961 | 1.53504 | 0.767522 | − | 0.641023i | \(-0.221490\pi\) | ||||
0.767522 | + | 0.641023i | \(0.221490\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.03714 | −0.275270 | ||||||||
\(482\) | 35.5930 | 1.62122 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −37.6138 | −1.70972 | ||||||||
\(485\) | 9.99082 | 0.453660 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.7272 | 0.984553 | 0.492276 | − | 0.870439i | \(-0.336165\pi\) | ||||
0.492276 | + | 0.870439i | \(0.336165\pi\) | |||||||
\(488\) | 11.5411 | 0.522439 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.43424 | −0.245494 | ||||||||
\(491\) | 19.6300 | 0.885891 | 0.442946 | − | 0.896548i | \(-0.353933\pi\) | ||||
0.442946 | + | 0.896548i | \(0.353933\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 56.2279 | 2.53238 | ||||||||
\(494\) | −10.9049 | −0.490635 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.6105 | 0.566227 | ||||||||
\(497\) | −9.07549 | −0.407091 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.2445 | 1.21963 | 0.609816 | − | 0.792543i | \(-0.291243\pi\) | ||||
0.609816 | + | 0.792543i | \(0.291243\pi\) | |||||||
\(500\) | 20.1157 | 0.899603 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 29.7810 | 1.32919 | ||||||||
\(503\) | −11.8818 | −0.529782 | −0.264891 | − | 0.964278i | \(-0.585336\pi\) | ||||
−0.264891 | + | 0.964278i | \(0.585336\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 42.2498 | 1.88009 | ||||||||
\(506\) | 15.9638 | 0.709677 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.41645 | 0.329052 | ||||||||
\(509\) | 33.3751 | 1.47933 | 0.739663 | − | 0.672977i | \(-0.234985\pi\) | ||||
0.739663 | + | 0.672977i | \(0.234985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.8863 | 1.45480 | ||||||||
\(512\) | 32.7739 | 1.44842 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 73.1714 | 3.22745 | ||||||||
\(515\) | −44.4546 | −1.95891 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.86533 | 0.257957 | ||||||||
\(518\) | 37.4923 | 1.64732 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.5087 | −0.548542 | ||||||||
\(521\) | −23.8798 | −1.04619 | −0.523097 | − | 0.852273i | \(-0.675223\pi\) | ||||
−0.523097 | + | 0.852273i | \(0.675223\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.3692 | 1.89640 | 0.948202 | − | 0.317669i | \(-0.102900\pi\) | ||||
0.948202 | + | 0.317669i | \(0.102900\pi\) | |||||||
\(524\) | −6.93906 | −0.303134 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 35.7861 | 1.56035 | ||||||||
\(527\) | 30.8841 | 1.34533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.6673 | 0.507275 | ||||||||
\(530\) | 4.82482 | 0.209577 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 44.6074 | 1.93398 | ||||||||
\(533\) | 10.5492 | 0.456936 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.2403 | −0.572427 | ||||||||
\(536\) | −27.7586 | −1.19899 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −37.1871 | −1.60325 | ||||||||
\(539\) | −0.879298 | −0.0378740 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.3614 | 1.90724 | 0.953622 | − | 0.301008i | \(-0.0973230\pi\) | ||||
0.953622 | + | 0.301008i | \(0.0973230\pi\) | |||||||
\(542\) | 21.1048 | 0.906530 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.2061 | 0.437583 | ||||||||
\(545\) | 12.7547 | 0.546353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.4733 | −0.747103 | −0.373551 | − | 0.927610i | \(-0.621860\pi\) | ||||
−0.373551 | + | 0.927610i | \(0.621860\pi\) | |||||||
\(548\) | 35.9292 | 1.53482 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.61494 | −0.367342 | ||||||||
\(551\) | −33.4977 | −1.42705 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.9148 | −1.31463 | ||||||||
\(554\) | 18.1006 | 0.769022 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −84.5854 | −3.58722 | ||||||||
\(557\) | 26.1559 | 1.10826 | 0.554130 | − | 0.832430i | \(-0.313051\pi\) | ||||
0.554130 | + | 0.832430i | \(0.313051\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.9561 | −0.505691 | ||||||||
\(560\) | 22.6519 | 0.957217 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 46.8148 | 1.97476 | ||||||||
\(563\) | 39.7284 | 1.67435 | 0.837176 | − | 0.546933i | \(-0.184205\pi\) | ||||
0.837176 | + | 0.546933i | \(0.184205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.49767 | 0.147148 | ||||||||
\(566\) | −20.6567 | −0.868266 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.3874 | −0.687601 | ||||||||
\(569\) | −2.15075 | −0.0901640 | −0.0450820 | − | 0.998983i | \(-0.514355\pi\) | ||||
−0.0450820 | + | 0.998983i | \(0.514355\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.3630 | −0.726619 | −0.363310 | − | 0.931669i | \(-0.618353\pi\) | ||||
−0.363310 | + | 0.931669i | \(0.618353\pi\) | |||||||
\(572\) | −4.20077 | −0.175643 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −65.5133 | −2.73447 | ||||||||
\(575\) | −18.7084 | −0.780195 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.1707 | −0.922977 | −0.461489 | − | 0.887146i | \(-0.652684\pi\) | ||||
−0.461489 | + | 0.887146i | \(0.652684\pi\) | |||||||
\(578\) | −105.436 | −4.38555 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −79.7490 | −3.31139 | ||||||||
\(581\) | 13.1847 | 0.546992 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.780690 | 0.0323329 | ||||||||
\(584\) | 59.3820 | 2.45725 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 40.2359 | 1.66213 | ||||||||
\(587\) | −2.43336 | −0.100436 | −0.0502178 | − | 0.998738i | \(-0.515992\pi\) | ||||
−0.0502178 | + | 0.998738i | \(0.515992\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.3991 | −0.758124 | ||||||||
\(590\) | −52.3044 | −2.15334 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 19.7408 | 0.811342 | ||||||||
\(593\) | 15.5820 | 0.639874 | 0.319937 | − | 0.947439i | \(-0.396338\pi\) | ||||
0.319937 | + | 0.947439i | \(0.396338\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 55.4764 | 2.27431 | ||||||||
\(596\) | −20.3191 | −0.832301 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.8496 | −0.566354 | ||||||||
\(599\) | −13.6123 | −0.556181 | −0.278091 | − | 0.960555i | \(-0.589702\pi\) | ||||
−0.278091 | + | 0.960555i | \(0.589702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.30181 | −0.175475 | −0.0877373 | − | 0.996144i | \(-0.527964\pi\) | ||||
−0.0877373 | + | 0.996144i | \(0.527964\pi\) | |||||||
\(602\) | 74.2508 | 3.02624 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 46.2761 | 1.88295 | ||||||||
\(605\) | 27.8684 | 1.13301 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.1853 | 0.453997 | 0.226999 | − | 0.973895i | \(-0.427109\pi\) | ||||
0.226999 | + | 0.973895i | \(0.427109\pi\) | |||||||
\(608\) | −6.08027 | −0.246588 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17.7472 | −0.718562 | ||||||||
\(611\) | −5.08856 | −0.205861 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.7783 | 1.64702 | 0.823511 | − | 0.567301i | \(-0.192012\pi\) | ||||
0.823511 | + | 0.567301i | \(0.192012\pi\) | |||||||
\(614\) | 40.0163 | 1.61492 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.5695 | 0.506441 | ||||||||
\(617\) | −42.0334 | −1.69220 | −0.846100 | − | 0.533024i | \(-0.821056\pi\) | ||||
−0.846100 | + | 0.533024i | \(0.821056\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.0986 | −0.446090 | −0.223045 | − | 0.974808i | \(-0.571600\pi\) | ||||
−0.223045 | + | 0.974808i | \(0.571600\pi\) | |||||||
\(620\) | −43.8034 | −1.75919 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 33.2521 | 1.33329 | ||||||||
\(623\) | −2.99746 | −0.120091 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7911 | −1.23164 | ||||||||
\(626\) | −35.3589 | −1.41322 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −46.5565 | −1.85781 | ||||||||
\(629\) | 48.3469 | 1.92772 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.2393 | −1.04457 | −0.522285 | − | 0.852771i | \(-0.674920\pi\) | ||||
−0.522285 | + | 0.852771i | \(0.674920\pi\) | |||||||
\(632\) | −55.8222 | −2.22049 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.4759 | 0.773486 | ||||||||
\(635\) | −5.49490 | −0.218059 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.762849 | 0.0302252 | ||||||||
\(638\) | −19.5906 | −0.775598 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −58.4651 | −2.31104 | ||||||||
\(641\) | −12.1081 | −0.478240 | −0.239120 | − | 0.970990i | \(-0.576859\pi\) | ||||
−0.239120 | + | 0.970990i | \(0.576859\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.6604 | 1.05138 | 0.525692 | − | 0.850675i | \(-0.323806\pi\) | ||||
0.525692 | + | 0.850675i | \(0.323806\pi\) | |||||||
\(644\) | 56.6531 | 2.23245 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 87.3291 | 3.43592 | ||||||||
\(647\) | 29.7009 | 1.16766 | 0.583832 | − | 0.811875i | \(-0.301553\pi\) | ||||
0.583832 | + | 0.811875i | \(0.301553\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.46321 | −0.332210 | ||||||||
\(650\) | 7.47403 | 0.293156 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −44.4455 | −1.74062 | ||||||||
\(653\) | 9.28628 | 0.363400 | 0.181700 | − | 0.983354i | \(-0.441840\pi\) | ||||
0.181700 | + | 0.983354i | \(0.441840\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.14120 | 0.200883 | ||||||||
\(656\) | −34.4947 | −1.34679 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 31.6013 | 1.23195 | ||||||||
\(659\) | −16.1495 | −0.629094 | −0.314547 | − | 0.949242i | \(-0.601853\pi\) | ||||
−0.314547 | + | 0.949242i | \(0.601853\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.2682 | −1.21619 | −0.608097 | − | 0.793863i | \(-0.708067\pi\) | ||||
−0.608097 | + | 0.793863i | \(0.708067\pi\) | |||||||
\(662\) | 53.9049 | 2.09507 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.8073 | 0.923901 | ||||||||
\(665\) | −33.0500 | −1.28162 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −42.5434 | −1.64729 | ||||||||
\(668\) | −36.7361 | −1.42136 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 42.6856 | 1.64909 | ||||||||
\(671\) | −2.87162 | −0.110858 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.6955 | −0.720657 | −0.360329 | − | 0.932825i | \(-0.617335\pi\) | ||||
−0.360329 | + | 0.932825i | \(0.617335\pi\) | |||||||
\(674\) | −76.5260 | −2.94767 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −46.5306 | −1.78964 | ||||||||
\(677\) | −24.3890 | −0.937346 | −0.468673 | − | 0.883372i | \(-0.655268\pi\) | ||||
−0.468673 | + | 0.883372i | \(0.655268\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.70987 | 0.334254 | ||||||||
\(680\) | 100.173 | 3.84144 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.7604 | −0.412038 | ||||||||
\(683\) | −44.2443 | −1.69296 | −0.846481 | − | 0.532419i | \(-0.821283\pi\) | ||||
−0.846481 | + | 0.532419i | \(0.821283\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.6202 | −1.01711 | ||||||||
\(686\) | −46.9802 | −1.79371 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 39.0953 | 1.49049 | ||||||||
\(689\) | −0.677300 | −0.0258031 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.11643 | 0.118555 | 0.0592773 | − | 0.998242i | \(-0.481120\pi\) | ||||
0.0592773 | + | 0.998242i | \(0.481120\pi\) | |||||||
\(692\) | 70.7516 | 2.68957 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.1887 | −0.994110 | ||||||||
\(695\) | 62.6699 | 2.37721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −84.4805 | −3.19993 | ||||||||
\(698\) | 85.1507 | 3.22300 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −30.5732 | −1.15556 | ||||||||
\(701\) | 26.4851 | 1.00033 | 0.500164 | − | 0.865931i | \(-0.333273\pi\) | ||||
0.500164 | + | 0.865931i | \(0.333273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.8026 | −1.08631 | ||||||||
\(704\) | −10.6738 | −0.402283 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −41.4417 | −1.55968 | ||||||||
\(707\) | 36.8328 | 1.38524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.0210 | 0.714350 | 0.357175 | − | 0.934038i | \(-0.383740\pi\) | ||||
0.357175 | + | 0.934038i | \(0.383740\pi\) | |||||||
\(710\) | 25.1996 | 0.945726 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.41244 | −0.202840 | ||||||||
\(713\) | −23.3676 | −0.875124 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.11238 | 0.116396 | ||||||||
\(716\) | −36.5569 | −1.36619 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −27.1687 | −1.01393 | ||||||||
\(719\) | 31.3712 | 1.16995 | 0.584974 | − | 0.811052i | \(-0.301105\pi\) | ||||
0.584974 | + | 0.811052i | \(0.301105\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.7550 | −1.44331 | ||||||||
\(722\) | −6.03353 | −0.224545 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.3156 | −0.792189 | ||||||||
\(725\) | 22.9588 | 0.852667 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.3958 | −1.60946 | −0.804730 | − | 0.593641i | \(-0.797690\pi\) | ||||
−0.804730 | + | 0.593641i | \(0.797690\pi\) | |||||||
\(728\) | −10.9049 | −0.404162 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −91.3144 | −3.37970 | ||||||||
\(731\) | 95.7476 | 3.54135 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.8576 | −0.622649 | −0.311325 | − | 0.950304i | \(-0.600773\pi\) | ||||
−0.311325 | + | 0.950304i | \(0.600773\pi\) | |||||||
\(734\) | −12.8675 | −0.474949 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.72217 | −0.284643 | ||||||||
\(737\) | 6.90682 | 0.254416 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.0747 | 1.84203 | 0.921013 | − | 0.389531i | \(-0.127363\pi\) | ||||
0.921013 | + | 0.389531i | \(0.127363\pi\) | |||||||
\(740\) | −68.5711 | −2.52073 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.20621 | 0.154415 | ||||||||
\(743\) | 43.8762 | 1.60966 | 0.804831 | − | 0.593504i | \(-0.202256\pi\) | ||||
0.804831 | + | 0.593504i | \(0.202256\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.0545 | 0.551556 | ||||||||
\(746\) | −9.71837 | −0.355815 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 33.6408 | 1.23003 | ||||||||
\(749\) | −11.5427 | −0.421761 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.6107 | −0.898059 | −0.449029 | − | 0.893517i | \(-0.648230\pi\) | ||||
−0.449029 | + | 0.893517i | \(0.648230\pi\) | |||||||
\(752\) | 16.6391 | 0.606764 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.9961 | 0.618962 | ||||||||
\(755\) | −34.2863 | −1.24781 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.2113 | −1.71593 | −0.857963 | − | 0.513712i | \(-0.828270\pi\) | ||||
−0.857963 | + | 0.513712i | \(0.828270\pi\) | |||||||
\(758\) | −48.5752 | −1.76433 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −59.6776 | −2.16474 | ||||||||
\(761\) | −42.8822 | −1.55448 | −0.777239 | − | 0.629206i | \(-0.783380\pi\) | ||||
−0.777239 | + | 0.629206i | \(0.783380\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.1194 | 0.402550 | ||||||||
\(764\) | 47.2288 | 1.70868 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 63.5093 | 2.29469 | ||||||||
\(767\) | 7.34239 | 0.265118 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.8695 | −1.29349 | −0.646744 | − | 0.762707i | \(-0.723870\pi\) | ||||
−0.646744 | + | 0.762707i | \(0.723870\pi\) | |||||||
\(770\) | −19.3287 | −0.696559 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.7894 | −0.496290 | ||||||||
\(773\) | 5.98233 | 0.215170 | 0.107585 | − | 0.994196i | \(-0.465688\pi\) | ||||
0.107585 | + | 0.994196i | \(0.465688\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.6105 | 0.452981 | ||||||||
\(776\) | 15.7272 | 0.564574 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.8618 | 1.14230 | ||||||||
\(779\) | 50.3291 | 1.80323 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.07748 | 0.145904 | ||||||||
\(782\) | 110.911 | 3.96618 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.49443 | −0.0890870 | ||||||||
\(785\) | 34.4940 | 1.23115 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.5595 | 1.26756 | 0.633780 | − | 0.773513i | \(-0.281502\pi\) | ||||
0.633780 | + | 0.773513i | \(0.281502\pi\) | |||||||
\(788\) | −57.7552 | −2.05744 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 85.8402 | 3.05406 | ||||||||
\(791\) | 3.04922 | 0.108418 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.49132 | 0.0884693 | ||||||||
\(794\) | 71.4307 | 2.53498 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −48.1996 | −1.70839 | ||||||||
\(797\) | 13.1917 | 0.467273 | 0.233636 | − | 0.972324i | \(-0.424937\pi\) | ||||
0.233636 | + | 0.972324i | \(0.424937\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 40.7505 | 1.44165 | ||||||||
\(800\) | 4.16731 | 0.147337 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 65.7148 | 2.32047 | ||||||||
\(803\) | −14.7753 | −0.521409 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41.9747 | −1.47941 | ||||||||
\(806\) | 9.33538 | 0.328825 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 66.5082 | 2.33975 | ||||||||
\(809\) | 27.1698 | 0.955238 | 0.477619 | − | 0.878567i | \(-0.341500\pi\) | ||||
0.477619 | + | 0.878567i | \(0.341500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.2045 | −0.358329 | −0.179165 | − | 0.983819i | \(-0.557339\pi\) | ||||
−0.179165 | + | 0.983819i | \(0.557339\pi\) | |||||||
\(812\) | −69.5241 | −2.43982 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.8447 | −0.590407 | ||||||||
\(815\) | 32.9300 | 1.15349 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −57.0415 | −1.99563 | ||||||||
\(818\) | 36.0112 | 1.25910 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 119.820 | 4.18430 | ||||||||
\(821\) | −33.9031 | −1.18323 | −0.591613 | − | 0.806222i | \(-0.701509\pi\) | ||||
−0.591613 | + | 0.806222i | \(0.701509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.71662 | 0.303842 | 0.151921 | − | 0.988393i | \(-0.451454\pi\) | ||||
0.151921 | + | 0.988393i | \(0.451454\pi\) | |||||||
\(824\) | −69.9790 | −2.43783 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −45.5983 | −1.58657 | ||||||||
\(827\) | 4.52090 | 0.157207 | 0.0786036 | − | 0.996906i | \(-0.474954\pi\) | ||||
0.0786036 | + | 0.996906i | \(0.474954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.1324 | −0.490839 | −0.245419 | − | 0.969417i | \(-0.578926\pi\) | ||||
−0.245419 | + | 0.969417i | \(0.578926\pi\) | |||||||
\(830\) | −36.6095 | −1.27073 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.26020 | 0.321040 | ||||||||
\(833\) | −6.10908 | −0.211667 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.2181 | 0.941920 | ||||||||
\(836\) | −20.0414 | −0.693148 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −51.2379 | −1.76999 | ||||||||
\(839\) | −27.3228 | −0.943286 | −0.471643 | − | 0.881789i | \(-0.656339\pi\) | ||||
−0.471643 | + | 0.881789i | \(0.656339\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.2087 | 0.800302 | ||||||||
\(842\) | 19.6578 | 0.677452 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −34.5508 | −1.18929 | ||||||||
\(845\) | 34.4749 | 1.18597 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.2953 | 0.834795 | ||||||||
\(848\) | 2.21470 | 0.0760531 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −59.8539 | −2.05297 | ||||||||
\(851\) | −36.5804 | −1.25396 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.6150 | −0.979758 | −0.489879 | − | 0.871791i | \(-0.662959\pi\) | ||||
−0.489879 | + | 0.871791i | \(0.662959\pi\) | |||||||
\(854\) | −15.4718 | −0.529433 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.8424 | −0.712379 | ||||||||
\(857\) | 25.9084 | 0.885015 | 0.442507 | − | 0.896765i | \(-0.354089\pi\) | ||||
0.442507 | + | 0.896765i | \(0.354089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.3172 | 0.829693 | 0.414847 | − | 0.909891i | \(-0.363835\pi\) | ||||
0.414847 | + | 0.909891i | \(0.363835\pi\) | |||||||
\(860\) | −135.800 | −4.63075 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39.8234 | −1.35639 | ||||||||
\(863\) | 38.4808 | 1.30990 | 0.654952 | − | 0.755671i | \(-0.272689\pi\) | ||||
0.654952 | + | 0.755671i | \(0.272689\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52.4204 | −1.78235 | ||||||||
\(866\) | −38.2116 | −1.29848 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −38.1872 | −1.29616 | ||||||||
\(869\) | 13.8895 | 0.471171 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.99212 | −0.203035 | ||||||||
\(872\) | 20.0781 | 0.679930 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −66.0752 | −2.23503 | ||||||||
\(875\) | −12.9930 | −0.439244 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.81200 | 0.230025 | 0.115013 | − | 0.993364i | \(-0.463309\pi\) | ||||
0.115013 | + | 0.993364i | \(0.463309\pi\) | |||||||
\(878\) | −1.06987 | −0.0361065 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.1772 | −0.343072 | ||||||||
\(881\) | −51.1946 | −1.72479 | −0.862395 | − | 0.506235i | \(-0.831037\pi\) | ||||
−0.862395 | + | 0.506235i | \(0.831037\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.9388 | 0.805606 | 0.402803 | − | 0.915287i | \(-0.368036\pi\) | ||||
0.402803 | + | 0.915287i | \(0.368036\pi\) | |||||||
\(884\) | −29.1856 | −0.981618 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 83.8255 | 2.81617 | ||||||||
\(887\) | −22.9111 | −0.769278 | −0.384639 | − | 0.923067i | \(-0.625674\pi\) | ||||
−0.384639 | + | 0.923067i | \(0.625674\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.79038 | −0.160664 | ||||||||
\(890\) | 8.32295 | 0.278986 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −52.6907 | −1.76421 | ||||||||
\(893\) | −24.2770 | −0.812400 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.0853 | 0.905360 | ||||||||
\(896\) | −50.9691 | −1.70276 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 66.1180 | 2.20639 | ||||||||
\(899\) | 28.6765 | 0.956414 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.42398 | 0.180699 | ||||||||
\(902\) | 29.4342 | 0.980050 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.50592 | 0.183124 | ||||||||
\(905\) | 15.7929 | 0.524974 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.2708 | 1.00512 | 0.502562 | − | 0.864541i | \(-0.332391\pi\) | ||||
0.502562 | + | 0.864541i | \(0.332391\pi\) | |||||||
\(908\) | −8.89540 | −0.295204 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 16.7689 | 0.555885 | ||||||||
\(911\) | −49.9174 | −1.65384 | −0.826919 | − | 0.562322i | \(-0.809908\pi\) | ||||
−0.826919 | + | 0.562322i | \(0.809908\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.92367 | −0.196045 | ||||||||
\(914\) | 54.4409 | 1.80075 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 81.5540 | 2.69462 | ||||||||
\(917\) | 4.48203 | 0.148010 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2909 | −0.504400 | −0.252200 | − | 0.967675i | \(-0.581154\pi\) | ||||
−0.252200 | + | 0.967675i | \(0.581154\pi\) | |||||||
\(920\) | −75.7928 | −2.49882 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −82.8533 | −2.72863 | ||||||||
\(923\) | −3.53748 | −0.116438 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.7408 | 0.649074 | ||||||||
\(926\) | 49.8533 | 1.63828 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.47657 | 0.311084 | ||||||||
\(929\) | −18.9994 | −0.623349 | −0.311674 | − | 0.950189i | \(-0.600890\pi\) | ||||
−0.311674 | + | 0.950189i | \(0.600890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.63948 | 0.119279 | ||||||||
\(932\) | −35.1792 | −1.15233 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −45.7375 | −1.49658 | ||||||||
\(935\) | −24.9247 | −0.815125 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.8277 | −0.517068 | −0.258534 | − | 0.966002i | \(-0.583239\pi\) | ||||
−0.258534 | + | 0.966002i | \(0.583239\pi\) | |||||||
\(938\) | 37.2127 | 1.21504 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −57.7970 | −1.88513 | ||||||||
\(941\) | 48.8260 | 1.59168 | 0.795840 | − | 0.605506i | \(-0.207029\pi\) | ||||
0.795840 | + | 0.605506i | \(0.207029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 63.9199 | 2.08152 | ||||||||
\(944\) | −24.0089 | −0.781422 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.3598 | −1.08462 | ||||||||
\(947\) | −44.8868 | −1.45862 | −0.729312 | − | 0.684181i | \(-0.760160\pi\) | ||||
−0.729312 | + | 0.684181i | \(0.760160\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.8186 | 0.416108 | ||||||||
\(950\) | 35.6579 | 1.15689 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 87.3291 | 2.83035 | ||||||||
\(953\) | −37.1889 | −1.20467 | −0.602334 | − | 0.798244i | \(-0.705762\pi\) | ||||
−0.602334 | + | 0.798244i | \(0.705762\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.9921 | −1.13232 | ||||||||
\(956\) | 3.85962 | 0.124829 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −81.3249 | −2.62749 | ||||||||
\(959\) | −23.2072 | −0.749399 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2490 | −0.491903 | ||||||||
\(962\) | 14.6139 | 0.471171 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −56.7511 | −1.82783 | ||||||||
\(965\) | 10.2166 | 0.328885 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.40043 | 0.205824 | 0.102912 | − | 0.994690i | \(-0.467184\pi\) | ||||
0.102912 | + | 0.994690i | \(0.467184\pi\) | |||||||
\(968\) | 43.8694 | 1.41002 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.1844 | −0.776515 | ||||||||
\(971\) | −1.23491 | −0.0396301 | −0.0198150 | − | 0.999804i | \(-0.506308\pi\) | ||||
−0.0198150 | + | 0.999804i | \(0.506308\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 54.6348 | 1.75151 | ||||||||
\(974\) | −52.5943 | −1.68523 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.14635 | −0.260758 | ||||||||
\(977\) | 5.05273 | 0.161651 | 0.0808256 | − | 0.996728i | \(-0.474244\pi\) | ||||
0.0808256 | + | 0.996728i | \(0.474244\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.34671 | 0.0430411 | ||||||||
\(980\) | 8.66460 | 0.276781 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −47.5178 | −1.51635 | ||||||||
\(983\) | 60.0002 | 1.91371 | 0.956855 | − | 0.290566i | \(-0.0938436\pi\) | ||||
0.956855 | + | 0.290566i | \(0.0938436\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 42.7912 | 1.36344 | ||||||||
\(986\) | −136.109 | −4.33460 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.3873 | 0.553163 | ||||||||
\(989\) | −72.4449 | −2.30361 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.43534 | 0.172659 | 0.0863296 | − | 0.996267i | \(-0.472486\pi\) | ||||
0.0863296 | + | 0.996267i | \(0.472486\pi\) | |||||||
\(992\) | 5.20515 | 0.165264 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 21.9687 | 0.696805 | ||||||||
\(995\) | 35.7114 | 1.13213 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.7441 | −1.06869 | −0.534343 | − | 0.845268i | \(-0.679441\pi\) | ||||
−0.534343 | + | 0.845268i | \(0.679441\pi\) | |||||||
\(998\) | −65.9498 | −2.08760 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.2.a.f.1.1 | 7 | ||
3.2 | odd | 2 | 717.2.a.e.1.7 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.2.a.e.1.7 | ✓ | 7 | 3.2 | odd | 2 | ||
2151.2.a.f.1.1 | 7 | 1.1 | even | 1 | trivial |