Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9075,2,Mod(1,9075)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9075, 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("9075.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9075.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: | \(72.4642398343\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 825) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9075.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36333 | 0.964019 | 0.482009 | − | 0.876166i | \(-0.339907\pi\) | ||||
0.482009 | + | 0.876166i | \(0.339907\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.141336 | −0.0706681 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.36333 | −0.556576 | ||||||||
\(7\) | 2.50466 | 0.946674 | 0.473337 | − | 0.880881i | \(-0.343049\pi\) | ||||
0.473337 | + | 0.880881i | \(0.343049\pi\) | |||||||
\(8\) | −2.91934 | −1.03214 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.141336 | 0.0408002 | ||||||||
\(13\) | 1.14134 | 0.316550 | 0.158275 | − | 0.987395i | \(-0.449407\pi\) | ||||
0.158275 | + | 0.987395i | \(0.449407\pi\) | |||||||
\(14\) | 3.41468 | 0.912612 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.69735 | −0.924338 | ||||||||
\(17\) | 7.64600 | 1.85443 | 0.927214 | − | 0.374533i | \(-0.122197\pi\) | ||||
0.927214 | + | 0.374533i | \(0.122197\pi\) | |||||||
\(18\) | 1.36333 | 0.321340 | ||||||||
\(19\) | −1.77801 | −0.407903 | −0.203951 | − | 0.978981i | \(-0.565378\pi\) | ||||
−0.203951 | + | 0.978981i | \(0.565378\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.50466 | −0.546563 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.41468 | −0.294981 | −0.147491 | − | 0.989063i | \(-0.547120\pi\) | ||||
−0.147491 | + | 0.989063i | \(0.547120\pi\) | |||||||
\(24\) | 2.91934 | 0.595909 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.55602 | 0.305160 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.354000 | −0.0668996 | ||||||||
\(29\) | 0.726656 | 0.134937 | 0.0674684 | − | 0.997721i | \(-0.478508\pi\) | ||||
0.0674684 | + | 0.997721i | \(0.478508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.85866 | 0.513431 | 0.256716 | − | 0.966487i | \(-0.417360\pi\) | ||||
0.256716 | + | 0.966487i | \(0.417360\pi\) | |||||||
\(32\) | 0.797984 | 0.141065 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.4240 | 1.78770 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.141336 | −0.0235560 | ||||||||
\(37\) | 8.42401 | 1.38490 | 0.692449 | − | 0.721467i | \(-0.256532\pi\) | ||||
0.692449 | + | 0.721467i | \(0.256532\pi\) | |||||||
\(38\) | −2.42401 | −0.393226 | ||||||||
\(39\) | −1.14134 | −0.182760 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.636672 | −0.0994314 | −0.0497157 | − | 0.998763i | \(-0.515832\pi\) | ||||
−0.0497157 | + | 0.998763i | \(0.515832\pi\) | |||||||
\(42\) | −3.41468 | −0.526897 | ||||||||
\(43\) | −12.6974 | −1.93633 | −0.968164 | − | 0.250317i | \(-0.919465\pi\) | ||||
−0.968164 | + | 0.250317i | \(0.919465\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.92867 | −0.284367 | ||||||||
\(47\) | −6.14134 | −0.895806 | −0.447903 | − | 0.894082i | \(-0.647829\pi\) | ||||
−0.447903 | + | 0.894082i | \(0.647829\pi\) | |||||||
\(48\) | 3.69735 | 0.533667 | ||||||||
\(49\) | −0.726656 | −0.103808 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.64600 | −1.07065 | ||||||||
\(52\) | −0.161312 | −0.0223700 | ||||||||
\(53\) | 12.0187 | 1.65089 | 0.825445 | − | 0.564483i | \(-0.190924\pi\) | ||||
0.825445 | + | 0.564483i | \(0.190924\pi\) | |||||||
\(54\) | −1.36333 | −0.185525 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.31198 | −0.977104 | ||||||||
\(57\) | 1.77801 | 0.235503 | ||||||||
\(58\) | 0.990671 | 0.130082 | ||||||||
\(59\) | −3.41468 | −0.444553 | −0.222277 | − | 0.974984i | \(-0.571349\pi\) | ||||
−0.222277 | + | 0.974984i | \(0.571349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.59465 | −0.588285 | −0.294142 | − | 0.955762i | \(-0.595034\pi\) | ||||
−0.294142 | + | 0.955762i | \(0.595034\pi\) | |||||||
\(62\) | 3.89730 | 0.494957 | ||||||||
\(63\) | 2.50466 | 0.315558 | ||||||||
\(64\) | 8.48262 | 1.06033 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.32131 | 1.13878 | 0.569389 | − | 0.822068i | \(-0.307180\pi\) | ||||
0.569389 | + | 0.822068i | \(0.307180\pi\) | |||||||
\(68\) | −1.08066 | −0.131049 | ||||||||
\(69\) | 1.41468 | 0.170307 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.85866 | 0.695295 | 0.347648 | − | 0.937625i | \(-0.386981\pi\) | ||||
0.347648 | + | 0.937625i | \(0.386981\pi\) | |||||||
\(72\) | −2.91934 | −0.344048 | ||||||||
\(73\) | 7.55602 | 0.884365 | 0.442182 | − | 0.896925i | \(-0.354204\pi\) | ||||
0.442182 | + | 0.896925i | \(0.354204\pi\) | |||||||
\(74\) | 11.4847 | 1.33507 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.251297 | 0.0288257 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.55602 | −0.176184 | ||||||||
\(79\) | −6.91934 | −0.778487 | −0.389244 | − | 0.921135i | \(-0.627264\pi\) | ||||
−0.389244 | + | 0.921135i | \(0.627264\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.867993 | −0.0958537 | ||||||||
\(83\) | −6.17997 | −0.678340 | −0.339170 | − | 0.940725i | \(-0.610146\pi\) | ||||
−0.339170 | + | 0.940725i | \(0.610146\pi\) | |||||||
\(84\) | 0.354000 | 0.0386245 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −17.3107 | −1.86666 | ||||||||
\(87\) | −0.726656 | −0.0779058 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.45331 | 0.366050 | 0.183025 | − | 0.983108i | \(-0.441411\pi\) | ||||
0.183025 | + | 0.983108i | \(0.441411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.85866 | 0.299669 | ||||||||
\(92\) | 0.199945 | 0.0208457 | ||||||||
\(93\) | −2.85866 | −0.296430 | ||||||||
\(94\) | −8.37266 | −0.863574 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.797984 | −0.0814439 | ||||||||
\(97\) | 19.4626 | 1.97613 | 0.988066 | − | 0.154032i | \(-0.0492257\pi\) | ||||
0.988066 | + | 0.154032i | \(0.0492257\pi\) | |||||||
\(98\) | −0.990671 | −0.100073 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.37266 | 0.833111 | 0.416555 | − | 0.909110i | \(-0.363237\pi\) | ||||
0.416555 | + | 0.909110i | \(0.363237\pi\) | |||||||
\(102\) | −10.4240 | −1.03213 | ||||||||
\(103\) | −2.54669 | −0.250933 | −0.125466 | − | 0.992098i | \(-0.540043\pi\) | ||||
−0.125466 | + | 0.992098i | \(0.540043\pi\) | |||||||
\(104\) | −3.33195 | −0.326725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.3854 | 1.59149 | ||||||||
\(107\) | −14.5653 | −1.40808 | −0.704042 | − | 0.710158i | \(-0.748624\pi\) | ||||
−0.704042 | + | 0.710158i | \(0.748624\pi\) | |||||||
\(108\) | 0.141336 | 0.0136001 | ||||||||
\(109\) | −2.41468 | −0.231284 | −0.115642 | − | 0.993291i | \(-0.536893\pi\) | ||||
−0.115642 | + | 0.993291i | \(0.536893\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.42401 | −0.799571 | ||||||||
\(112\) | −9.26063 | −0.875047 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 2.42401 | 0.227029 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.102703 | −0.00953572 | ||||||||
\(117\) | 1.14134 | 0.105517 | ||||||||
\(118\) | −4.65533 | −0.428558 | ||||||||
\(119\) | 19.1507 | 1.75554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −6.26401 | −0.567117 | ||||||||
\(123\) | 0.636672 | 0.0574068 | ||||||||
\(124\) | −0.404032 | −0.0362832 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.41468 | 0.304204 | ||||||||
\(127\) | −15.2020 | −1.34896 | −0.674480 | − | 0.738293i | \(-0.735632\pi\) | ||||
−0.674480 | + | 0.738293i | \(0.735632\pi\) | |||||||
\(128\) | 9.96862 | 0.881110 | ||||||||
\(129\) | 12.6974 | 1.11794 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.7453 | −1.63779 | −0.818893 | − | 0.573946i | \(-0.805412\pi\) | ||||
−0.818893 | + | 0.573946i | \(0.805412\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.45331 | −0.386151 | ||||||||
\(134\) | 12.7080 | 1.09780 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −22.3213 | −1.91404 | ||||||||
\(137\) | −8.74531 | −0.747163 | −0.373581 | − | 0.927597i | \(-0.621870\pi\) | ||||
−0.373581 | + | 0.927597i | \(0.621870\pi\) | |||||||
\(138\) | 1.92867 | 0.164180 | ||||||||
\(139\) | 22.3013 | 1.89157 | 0.945787 | − | 0.324787i | \(-0.105293\pi\) | ||||
0.945787 | + | 0.324787i | \(0.105293\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.14134 | 0.517194 | ||||||||
\(142\) | 7.98728 | 0.670278 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.69735 | −0.308113 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.3013 | 0.852544 | ||||||||
\(147\) | 0.726656 | 0.0599336 | ||||||||
\(148\) | −1.19062 | −0.0978681 | ||||||||
\(149\) | 15.9287 | 1.30493 | 0.652464 | − | 0.757820i | \(-0.273735\pi\) | ||||
0.652464 | + | 0.757820i | \(0.273735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.88665 | 0.804564 | 0.402282 | − | 0.915516i | \(-0.368217\pi\) | ||||
0.402282 | + | 0.915516i | \(0.368217\pi\) | |||||||
\(152\) | 5.19062 | 0.421015 | ||||||||
\(153\) | 7.64600 | 0.618143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.161312 | 0.0129153 | ||||||||
\(157\) | 0.132007 | 0.0105353 | 0.00526767 | − | 0.999986i | \(-0.498323\pi\) | ||||
0.00526767 | + | 0.999986i | \(0.498323\pi\) | |||||||
\(158\) | −9.43334 | −0.750476 | ||||||||
\(159\) | −12.0187 | −0.953142 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.54330 | −0.279251 | ||||||||
\(162\) | 1.36333 | 0.107113 | ||||||||
\(163\) | 4.31198 | 0.337740 | 0.168870 | − | 0.985638i | \(-0.445988\pi\) | ||||
0.168870 | + | 0.985638i | \(0.445988\pi\) | |||||||
\(164\) | 0.0899847 | 0.00702663 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.42533 | −0.653932 | ||||||||
\(167\) | −11.2920 | −0.873801 | −0.436901 | − | 0.899510i | \(-0.643924\pi\) | ||||
−0.436901 | + | 0.899510i | \(0.643924\pi\) | |||||||
\(168\) | 7.31198 | 0.564131 | ||||||||
\(169\) | −11.6974 | −0.899796 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.77801 | −0.135968 | ||||||||
\(172\) | 1.79459 | 0.136837 | ||||||||
\(173\) | 21.6460 | 1.64571 | 0.822857 | − | 0.568248i | \(-0.192379\pi\) | ||||
0.822857 | + | 0.568248i | \(0.192379\pi\) | |||||||
\(174\) | −0.990671 | −0.0751026 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.41468 | 0.256663 | ||||||||
\(178\) | 4.70800 | 0.352879 | ||||||||
\(179\) | 16.1413 | 1.20646 | 0.603230 | − | 0.797567i | \(-0.293880\pi\) | ||||
0.603230 | + | 0.797567i | \(0.293880\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7546 | 1.54268 | 0.771340 | − | 0.636423i | \(-0.219587\pi\) | ||||
0.771340 | + | 0.636423i | \(0.219587\pi\) | |||||||
\(182\) | 3.89730 | 0.288887 | ||||||||
\(183\) | 4.59465 | 0.339646 | ||||||||
\(184\) | 4.12994 | 0.304463 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.89730 | −0.285764 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.867993 | 0.0633049 | ||||||||
\(189\) | −2.50466 | −0.182188 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.31198 | 0.239646 | 0.119823 | − | 0.992795i | \(-0.461767\pi\) | ||||
0.119823 | + | 0.992795i | \(0.461767\pi\) | |||||||
\(192\) | −8.48262 | −0.612180 | ||||||||
\(193\) | −2.13201 | −0.153465 | −0.0767326 | − | 0.997052i | \(-0.524449\pi\) | ||||
−0.0767326 | + | 0.997052i | \(0.524449\pi\) | |||||||
\(194\) | 26.5340 | 1.90503 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.102703 | 0.00733591 | ||||||||
\(197\) | 17.9287 | 1.27737 | 0.638683 | − | 0.769470i | \(-0.279480\pi\) | ||||
0.638683 | + | 0.769470i | \(0.279480\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.1600 | 1.07466 | 0.537332 | − | 0.843371i | \(-0.319432\pi\) | ||||
0.537332 | + | 0.843371i | \(0.319432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.32131 | −0.657474 | ||||||||
\(202\) | 11.4147 | 0.803134 | ||||||||
\(203\) | 1.82003 | 0.127741 | ||||||||
\(204\) | 1.08066 | 0.0756611 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.47197 | −0.241904 | ||||||||
\(207\) | −1.41468 | −0.0983270 | ||||||||
\(208\) | −4.21992 | −0.292599 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3213 | 0.917076 | 0.458538 | − | 0.888675i | \(-0.348373\pi\) | ||||
0.458538 | + | 0.888675i | \(0.348373\pi\) | |||||||
\(212\) | −1.69867 | −0.116665 | ||||||||
\(213\) | −5.85866 | −0.401429 | ||||||||
\(214\) | −19.8573 | −1.35742 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.91934 | 0.198636 | ||||||||
\(217\) | 7.15999 | 0.486052 | ||||||||
\(218\) | −3.29200 | −0.222962 | ||||||||
\(219\) | −7.55602 | −0.510588 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.72666 | 0.587018 | ||||||||
\(222\) | −11.4847 | −0.770802 | ||||||||
\(223\) | 12.2534 | 0.820546 | 0.410273 | − | 0.911963i | \(-0.365433\pi\) | ||||
0.410273 | + | 0.911963i | \(0.365433\pi\) | |||||||
\(224\) | 1.99868 | 0.133543 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.17997 | −0.544123 | ||||||||
\(227\) | 8.74531 | 0.580447 | 0.290223 | − | 0.956959i | \(-0.406270\pi\) | ||||
0.290223 | + | 0.956959i | \(0.406270\pi\) | |||||||
\(228\) | −0.251297 | −0.0166425 | ||||||||
\(229\) | −11.4626 | −0.757473 | −0.378736 | − | 0.925505i | \(-0.623641\pi\) | ||||
−0.378736 | + | 0.925505i | \(0.623641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.12136 | −0.139274 | ||||||||
\(233\) | 7.48469 | 0.490338 | 0.245169 | − | 0.969480i | \(-0.421157\pi\) | ||||
0.245169 | + | 0.969480i | \(0.421157\pi\) | |||||||
\(234\) | 1.55602 | 0.101720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.482618 | 0.0314157 | ||||||||
\(237\) | 6.91934 | 0.449460 | ||||||||
\(238\) | 26.1086 | 1.69237 | ||||||||
\(239\) | −12.9066 | −0.834860 | −0.417430 | − | 0.908709i | \(-0.637069\pi\) | ||||
−0.417430 | + | 0.908709i | \(0.637069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.8773 | 1.08716 | 0.543582 | − | 0.839356i | \(-0.317068\pi\) | ||||
0.543582 | + | 0.839356i | \(0.317068\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.649390 | 0.0415729 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.867993 | 0.0553412 | ||||||||
\(247\) | −2.02930 | −0.129122 | ||||||||
\(248\) | −8.34542 | −0.529935 | ||||||||
\(249\) | 6.17997 | 0.391640 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.28267 | 0.144081 | 0.0720405 | − | 0.997402i | \(-0.477049\pi\) | ||||
0.0720405 | + | 0.997402i | \(0.477049\pi\) | |||||||
\(252\) | −0.354000 | −0.0222999 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −20.7253 | −1.30042 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.37473 | −0.210920 | ||||||||
\(257\) | 26.8667 | 1.67590 | 0.837949 | − | 0.545749i | \(-0.183755\pi\) | ||||
0.837949 | + | 0.545749i | \(0.183755\pi\) | |||||||
\(258\) | 17.3107 | 1.07771 | ||||||||
\(259\) | 21.0993 | 1.31105 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.726656 | 0.0449789 | ||||||||
\(262\) | −25.5560 | −1.57886 | ||||||||
\(263\) | 12.0187 | 0.741102 | 0.370551 | − | 0.928812i | \(-0.379169\pi\) | ||||
0.370551 | + | 0.928812i | \(0.379169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.07133 | −0.372257 | ||||||||
\(267\) | −3.45331 | −0.211339 | ||||||||
\(268\) | −1.31744 | −0.0804753 | ||||||||
\(269\) | −14.3854 | −0.877092 | −0.438546 | − | 0.898709i | \(-0.644506\pi\) | ||||
−0.438546 | + | 0.898709i | \(0.644506\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.6553 | −1.74069 | −0.870344 | − | 0.492445i | \(-0.836103\pi\) | ||||
−0.870344 | + | 0.492445i | \(0.836103\pi\) | |||||||
\(272\) | −28.2700 | −1.71412 | ||||||||
\(273\) | −2.85866 | −0.173014 | ||||||||
\(274\) | −11.9227 | −0.720279 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.199945 | −0.0120353 | ||||||||
\(277\) | −29.1600 | −1.75205 | −0.876027 | − | 0.482262i | \(-0.839815\pi\) | ||||
−0.876027 | + | 0.482262i | \(0.839815\pi\) | |||||||
\(278\) | 30.4040 | 1.82351 | ||||||||
\(279\) | 2.85866 | 0.171144 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.36333 | 0.319949 | 0.159975 | − | 0.987121i | \(-0.448859\pi\) | ||||
0.159975 | + | 0.987121i | \(0.448859\pi\) | |||||||
\(282\) | 8.37266 | 0.498584 | ||||||||
\(283\) | −10.0420 | −0.596936 | −0.298468 | − | 0.954420i | \(-0.596476\pi\) | ||||
−0.298468 | + | 0.954420i | \(0.596476\pi\) | |||||||
\(284\) | −0.828041 | −0.0491352 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.59465 | −0.0941292 | ||||||||
\(288\) | 0.797984 | 0.0470216 | ||||||||
\(289\) | 41.4613 | 2.43890 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.4626 | −1.14092 | ||||||||
\(292\) | −1.06794 | −0.0624963 | ||||||||
\(293\) | 20.3540 | 1.18909 | 0.594547 | − | 0.804061i | \(-0.297332\pi\) | ||||
0.594547 | + | 0.804061i | \(0.297332\pi\) | |||||||
\(294\) | 0.990671 | 0.0577771 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −24.5926 | −1.42941 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.7160 | 1.25797 | ||||||||
\(299\) | −1.61462 | −0.0933762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.8026 | −1.83307 | ||||||||
\(302\) | 13.4787 | 0.775615 | ||||||||
\(303\) | −8.37266 | −0.480997 | ||||||||
\(304\) | 6.57392 | 0.377040 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.4240 | 0.595901 | ||||||||
\(307\) | 25.6226 | 1.46236 | 0.731181 | − | 0.682184i | \(-0.238970\pi\) | ||||
0.731181 | + | 0.682184i | \(0.238970\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.54669 | 0.144876 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.9414 | 0.677134 | 0.338567 | − | 0.940942i | \(-0.390058\pi\) | ||||
0.338567 | + | 0.940942i | \(0.390058\pi\) | |||||||
\(312\) | 3.33195 | 0.188635 | ||||||||
\(313\) | −17.1986 | −0.972124 | −0.486062 | − | 0.873924i | \(-0.661567\pi\) | ||||
−0.486062 | + | 0.873924i | \(0.661567\pi\) | |||||||
\(314\) | 0.179969 | 0.0101563 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.977953 | 0.0550142 | ||||||||
\(317\) | 22.7453 | 1.27750 | 0.638752 | − | 0.769413i | \(-0.279451\pi\) | ||||
0.638752 | + | 0.769413i | \(0.279451\pi\) | |||||||
\(318\) | −16.3854 | −0.918846 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.5653 | 0.812958 | ||||||||
\(322\) | −4.83068 | −0.269203 | ||||||||
\(323\) | −13.5946 | −0.756427 | ||||||||
\(324\) | −0.141336 | −0.00785201 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.87864 | 0.325588 | ||||||||
\(327\) | 2.41468 | 0.133532 | ||||||||
\(328\) | 1.85866 | 0.102628 | ||||||||
\(329\) | −15.3820 | −0.848036 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.2733 | 1.38915 | 0.694574 | − | 0.719421i | \(-0.255593\pi\) | ||||
0.694574 | + | 0.719421i | \(0.255593\pi\) | |||||||
\(332\) | 0.873453 | 0.0479370 | ||||||||
\(333\) | 8.42401 | 0.461633 | ||||||||
\(334\) | −15.3947 | −0.842361 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.26063 | 0.505209 | ||||||||
\(337\) | −17.6880 | −0.963528 | −0.481764 | − | 0.876301i | \(-0.660004\pi\) | ||||
−0.481764 | + | 0.876301i | \(0.660004\pi\) | |||||||
\(338\) | −15.9473 | −0.867420 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.42401 | −0.131075 | ||||||||
\(343\) | −19.3527 | −1.04495 | ||||||||
\(344\) | 37.0679 | 1.99857 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 29.5106 | 1.58650 | ||||||||
\(347\) | 20.1027 | 1.07917 | 0.539585 | − | 0.841931i | \(-0.318581\pi\) | ||||
0.539585 | + | 0.841931i | \(0.318581\pi\) | |||||||
\(348\) | 0.102703 | 0.00550545 | ||||||||
\(349\) | 10.9907 | 0.588317 | 0.294159 | − | 0.955757i | \(-0.404961\pi\) | ||||
0.294159 | + | 0.955757i | \(0.404961\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.14134 | −0.0609200 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.7267 | −0.890270 | −0.445135 | − | 0.895463i | \(-0.646844\pi\) | ||||
−0.445135 | + | 0.895463i | \(0.646844\pi\) | |||||||
\(354\) | 4.65533 | 0.247428 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.488078 | −0.0258681 | ||||||||
\(357\) | −19.1507 | −1.01356 | ||||||||
\(358\) | 22.0059 | 1.16305 | ||||||||
\(359\) | 13.5933 | 0.717429 | 0.358714 | − | 0.933447i | \(-0.383215\pi\) | ||||
0.358714 | + | 0.933447i | \(0.383215\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.8387 | −0.833615 | ||||||||
\(362\) | 28.2954 | 1.48717 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.404032 | −0.0211771 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.26401 | 0.327425 | ||||||||
\(367\) | −28.9987 | −1.51372 | −0.756859 | − | 0.653578i | \(-0.773267\pi\) | ||||
−0.756859 | + | 0.653578i | \(0.773267\pi\) | |||||||
\(368\) | 5.23057 | 0.272662 | ||||||||
\(369\) | −0.636672 | −0.0331438 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.1027 | 1.56285 | ||||||||
\(372\) | 0.404032 | 0.0209481 | ||||||||
\(373\) | −17.8867 | −0.926136 | −0.463068 | − | 0.886323i | \(-0.653251\pi\) | ||||
−0.463068 | + | 0.886323i | \(0.653251\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.9287 | 0.924601 | ||||||||
\(377\) | 0.829359 | 0.0427142 | ||||||||
\(378\) | −3.41468 | −0.175632 | ||||||||
\(379\) | 23.7839 | 1.22170 | 0.610850 | − | 0.791747i | \(-0.290828\pi\) | ||||
0.610850 | + | 0.791747i | \(0.290828\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.2020 | 0.778823 | ||||||||
\(382\) | 4.51531 | 0.231023 | ||||||||
\(383\) | 31.7360 | 1.62163 | 0.810817 | − | 0.585300i | \(-0.199023\pi\) | ||||
0.810817 | + | 0.585300i | \(0.199023\pi\) | |||||||
\(384\) | −9.96862 | −0.508709 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.90663 | −0.147943 | ||||||||
\(387\) | −12.6974 | −0.645443 | ||||||||
\(388\) | −2.75077 | −0.139649 | ||||||||
\(389\) | 25.7546 | 1.30581 | 0.652906 | − | 0.757439i | \(-0.273550\pi\) | ||||
0.652906 | + | 0.757439i | \(0.273550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.8166 | −0.547021 | ||||||||
\(392\) | 2.12136 | 0.107145 | ||||||||
\(393\) | 18.7453 | 0.945576 | ||||||||
\(394\) | 24.4427 | 1.23140 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.03863 | 0.152505 | 0.0762523 | − | 0.997089i | \(-0.475705\pi\) | ||||
0.0762523 | + | 0.997089i | \(0.475705\pi\) | |||||||
\(398\) | 20.6680 | 1.03600 | ||||||||
\(399\) | 4.45331 | 0.222945 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.1800 | −0.907864 | −0.453932 | − | 0.891036i | \(-0.649979\pi\) | ||||
−0.453932 | + | 0.891036i | \(0.649979\pi\) | |||||||
\(402\) | −12.7080 | −0.633817 | ||||||||
\(403\) | 3.26270 | 0.162526 | ||||||||
\(404\) | −1.18336 | −0.0588743 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.48130 | 0.123145 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 22.3213 | 1.10507 | ||||||||
\(409\) | 20.5946 | 1.01834 | 0.509170 | − | 0.860666i | \(-0.329952\pi\) | ||||
0.509170 | + | 0.860666i | \(0.329952\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.74531 | 0.431375 | ||||||||
\(412\) | 0.359939 | 0.0177329 | ||||||||
\(413\) | −8.55263 | −0.420847 | ||||||||
\(414\) | −1.92867 | −0.0947891 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.910768 | 0.0446541 | ||||||||
\(417\) | −22.3013 | −1.09210 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.7253 | 1.59874 | 0.799369 | − | 0.600841i | \(-0.205167\pi\) | ||||
0.799369 | + | 0.600841i | \(0.205167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.5640 | 1.58707 | 0.793537 | − | 0.608522i | \(-0.208237\pi\) | ||||
0.793537 | + | 0.608522i | \(0.208237\pi\) | |||||||
\(422\) | 18.1613 | 0.884079 | ||||||||
\(423\) | −6.14134 | −0.298602 | ||||||||
\(424\) | −35.0866 | −1.70396 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.98728 | −0.386985 | ||||||||
\(427\) | −11.5081 | −0.556914 | ||||||||
\(428\) | 2.05861 | 0.0995066 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.82003 | −0.0876678 | −0.0438339 | − | 0.999039i | \(-0.513957\pi\) | ||||
−0.0438339 | + | 0.999039i | \(0.513957\pi\) | |||||||
\(432\) | 3.69735 | 0.177889 | ||||||||
\(433\) | 29.8280 | 1.43344 | 0.716722 | − | 0.697359i | \(-0.245642\pi\) | ||||
0.716722 | + | 0.697359i | \(0.245642\pi\) | |||||||
\(434\) | 9.76142 | 0.468563 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.341281 | 0.0163444 | ||||||||
\(437\) | 2.51531 | 0.120324 | ||||||||
\(438\) | −10.3013 | −0.492217 | ||||||||
\(439\) | −18.2220 | −0.869688 | −0.434844 | − | 0.900506i | \(-0.643197\pi\) | ||||
−0.434844 | + | 0.900506i | \(0.643197\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.726656 | −0.0346027 | ||||||||
\(442\) | 11.8973 | 0.565897 | ||||||||
\(443\) | 22.2627 | 1.05773 | 0.528866 | − | 0.848705i | \(-0.322617\pi\) | ||||
0.528866 | + | 0.848705i | \(0.322617\pi\) | |||||||
\(444\) | 1.19062 | 0.0565042 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.7054 | 0.791022 | ||||||||
\(447\) | −15.9287 | −0.753400 | ||||||||
\(448\) | 21.2461 | 1.00378 | ||||||||
\(449\) | 25.8760 | 1.22116 | 0.610582 | − | 0.791953i | \(-0.290936\pi\) | ||||
0.610582 | + | 0.791953i | \(0.290936\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.848017 | 0.0398874 | ||||||||
\(453\) | −9.88665 | −0.464515 | ||||||||
\(454\) | 11.9227 | 0.559562 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.19062 | −0.243073 | ||||||||
\(457\) | −10.4626 | −0.489422 | −0.244711 | − | 0.969596i | \(-0.578693\pi\) | ||||
−0.244711 | + | 0.969596i | \(0.578693\pi\) | |||||||
\(458\) | −15.6273 | −0.730218 | ||||||||
\(459\) | −7.64600 | −0.356885 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.8387 | −0.551383 | −0.275691 | − | 0.961246i | \(-0.588907\pi\) | ||||
−0.275691 | + | 0.961246i | \(0.588907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.7546 | −1.28987 | −0.644934 | − | 0.764238i | \(-0.723115\pi\) | ||||
−0.644934 | + | 0.764238i | \(0.723115\pi\) | |||||||
\(464\) | −2.68670 | −0.124727 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.2041 | 0.472695 | ||||||||
\(467\) | −20.8294 | −0.963868 | −0.481934 | − | 0.876208i | \(-0.660065\pi\) | ||||
−0.481934 | + | 0.876208i | \(0.660065\pi\) | |||||||
\(468\) | −0.161312 | −0.00745665 | ||||||||
\(469\) | 23.3467 | 1.07805 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.132007 | −0.00608258 | ||||||||
\(472\) | 9.96862 | 0.458843 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 9.43334 | 0.433288 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.70668 | −0.124061 | ||||||||
\(477\) | 12.0187 | 0.550297 | ||||||||
\(478\) | −17.5960 | −0.804821 | ||||||||
\(479\) | −2.64939 | −0.121054 | −0.0605269 | − | 0.998167i | \(-0.519278\pi\) | ||||
−0.0605269 | + | 0.998167i | \(0.519278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.61462 | 0.438389 | ||||||||
\(482\) | 23.0093 | 1.04805 | ||||||||
\(483\) | 3.54330 | 0.161226 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.36333 | −0.0618418 | ||||||||
\(487\) | −40.5360 | −1.83686 | −0.918432 | − | 0.395580i | \(-0.870544\pi\) | ||||
−0.918432 | + | 0.395580i | \(0.870544\pi\) | |||||||
\(488\) | 13.4134 | 0.607194 | ||||||||
\(489\) | −4.31198 | −0.194994 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.1214 | 0.727547 | 0.363773 | − | 0.931487i | \(-0.381488\pi\) | ||||
0.363773 | + | 0.931487i | \(0.381488\pi\) | |||||||
\(492\) | −0.0899847 | −0.00405682 | ||||||||
\(493\) | 5.55602 | 0.250230 | ||||||||
\(494\) | −2.76661 | −0.124476 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.5695 | −0.474584 | ||||||||
\(497\) | 14.6740 | 0.658218 | ||||||||
\(498\) | 8.42533 | 0.377548 | ||||||||
\(499\) | −28.0666 | −1.25643 | −0.628217 | − | 0.778038i | \(-0.716215\pi\) | ||||
−0.628217 | + | 0.778038i | \(0.716215\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.2920 | 0.504489 | ||||||||
\(502\) | 3.11203 | 0.138897 | ||||||||
\(503\) | 0.906626 | 0.0404245 | 0.0202122 | − | 0.999796i | \(-0.493566\pi\) | ||||
0.0202122 | + | 0.999796i | \(0.493566\pi\) | |||||||
\(504\) | −7.31198 | −0.325701 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.6974 | 0.519498 | ||||||||
\(508\) | 2.14859 | 0.0953284 | ||||||||
\(509\) | −14.3013 | −0.633895 | −0.316948 | − | 0.948443i | \(-0.602658\pi\) | ||||
−0.316948 | + | 0.948443i | \(0.602658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.9253 | 0.837205 | ||||||||
\(512\) | −24.5381 | −1.08444 | ||||||||
\(513\) | 1.77801 | 0.0785010 | ||||||||
\(514\) | 36.6281 | 1.61560 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.79459 | −0.0790026 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 28.7653 | 1.26387 | ||||||||
\(519\) | −21.6460 | −0.950154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.1214 | 0.881533 | 0.440766 | − | 0.897622i | \(-0.354707\pi\) | ||||
0.440766 | + | 0.897622i | \(0.354707\pi\) | |||||||
\(522\) | 0.990671 | 0.0433605 | ||||||||
\(523\) | −12.8459 | −0.561714 | −0.280857 | − | 0.959750i | \(-0.590619\pi\) | ||||
−0.280857 | + | 0.959750i | \(0.590619\pi\) | |||||||
\(524\) | 2.64939 | 0.115739 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.3854 | 0.714436 | ||||||||
\(527\) | 21.8573 | 0.952121 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9987 | −0.912986 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.41468 | −0.148184 | ||||||||
\(532\) | 0.629414 | 0.0272886 | ||||||||
\(533\) | −0.726656 | −0.0314750 | ||||||||
\(534\) | −4.70800 | −0.203735 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −27.2121 | −1.17538 | ||||||||
\(537\) | −16.1413 | −0.696550 | ||||||||
\(538\) | −19.6120 | −0.845533 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.6040 | −0.756854 | −0.378427 | − | 0.925631i | \(-0.623535\pi\) | ||||
−0.378427 | + | 0.925631i | \(0.623535\pi\) | |||||||
\(542\) | −39.0666 | −1.67805 | ||||||||
\(543\) | −20.7546 | −0.890667 | ||||||||
\(544\) | 6.10138 | 0.261595 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.89730 | −0.166789 | ||||||||
\(547\) | 19.9873 | 0.854594 | 0.427297 | − | 0.904111i | \(-0.359466\pi\) | ||||
0.427297 | + | 0.904111i | \(0.359466\pi\) | |||||||
\(548\) | 1.23603 | 0.0528005 | ||||||||
\(549\) | −4.59465 | −0.196095 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.29200 | −0.0550411 | ||||||||
\(552\) | −4.12994 | −0.175782 | ||||||||
\(553\) | −17.3306 | −0.736974 | ||||||||
\(554\) | −39.7546 | −1.68901 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.15198 | −0.133674 | ||||||||
\(557\) | −41.5933 | −1.76237 | −0.881183 | − | 0.472775i | \(-0.843252\pi\) | ||||
−0.881183 | + | 0.472775i | \(0.843252\pi\) | |||||||
\(558\) | 3.89730 | 0.164986 | ||||||||
\(559\) | −14.4919 | −0.612944 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.31198 | 0.308437 | ||||||||
\(563\) | 2.28267 | 0.0962032 | 0.0481016 | − | 0.998842i | \(-0.484683\pi\) | ||||
0.0481016 | + | 0.998842i | \(0.484683\pi\) | |||||||
\(564\) | −0.867993 | −0.0365491 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.6906 | −0.575458 | ||||||||
\(567\) | 2.50466 | 0.105186 | ||||||||
\(568\) | −17.1035 | −0.717645 | ||||||||
\(569\) | 2.37266 | 0.0994670 | 0.0497335 | − | 0.998763i | \(-0.484163\pi\) | ||||
0.0497335 | + | 0.998763i | \(0.484163\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.9053 | 1.33520 | 0.667598 | − | 0.744522i | \(-0.267323\pi\) | ||||
0.667598 | + | 0.744522i | \(0.267323\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.31198 | −0.138360 | ||||||||
\(574\) | −2.17403 | −0.0907423 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.48262 | 0.353442 | ||||||||
\(577\) | −3.28267 | −0.136659 | −0.0683297 | − | 0.997663i | \(-0.521767\pi\) | ||||
−0.0683297 | + | 0.997663i | \(0.521767\pi\) | |||||||
\(578\) | 56.5254 | 2.35115 | ||||||||
\(579\) | 2.13201 | 0.0886032 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.4787 | −0.642167 | ||||||||
\(582\) | −26.5340 | −1.09987 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −22.0586 | −0.912792 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.7492 | 1.14631 | ||||||||
\(587\) | −26.3400 | −1.08717 | −0.543583 | − | 0.839355i | \(-0.682933\pi\) | ||||
−0.543583 | + | 0.839355i | \(0.682933\pi\) | |||||||
\(588\) | −0.102703 | −0.00423539 | ||||||||
\(589\) | −5.08273 | −0.209430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.9287 | −0.737487 | ||||||||
\(592\) | −31.1465 | −1.28011 | ||||||||
\(593\) | −32.9694 | −1.35389 | −0.676945 | − | 0.736034i | \(-0.736697\pi\) | ||||
−0.676945 | + | 0.736034i | \(0.736697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.25130 | −0.0922167 | ||||||||
\(597\) | −15.1600 | −0.620457 | ||||||||
\(598\) | −2.20126 | −0.0900164 | ||||||||
\(599\) | 24.5454 | 1.00290 | 0.501448 | − | 0.865188i | \(-0.332801\pi\) | ||||
0.501448 | + | 0.865188i | \(0.332801\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.70668 | 0.395944 | 0.197972 | − | 0.980208i | \(-0.436565\pi\) | ||||
0.197972 | + | 0.980208i | \(0.436565\pi\) | |||||||
\(602\) | −43.3574 | −1.76712 | ||||||||
\(603\) | 9.32131 | 0.379593 | ||||||||
\(604\) | −1.39734 | −0.0568570 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.4147 | −0.463690 | ||||||||
\(607\) | 1.73599 | 0.0704615 | 0.0352307 | − | 0.999379i | \(-0.488783\pi\) | ||||
0.0352307 | + | 0.999379i | \(0.488783\pi\) | |||||||
\(608\) | −1.41882 | −0.0575408 | ||||||||
\(609\) | −1.82003 | −0.0737514 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.00933 | −0.283567 | ||||||||
\(612\) | −1.08066 | −0.0436829 | ||||||||
\(613\) | 12.0187 | 0.485429 | 0.242715 | − | 0.970098i | \(-0.421962\pi\) | ||||
0.242715 | + | 0.970098i | \(0.421962\pi\) | |||||||
\(614\) | 34.9321 | 1.40974 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.1587 | −1.69724 | −0.848622 | − | 0.528999i | \(-0.822567\pi\) | ||||
−0.848622 | + | 0.528999i | \(0.822567\pi\) | |||||||
\(618\) | 3.47197 | 0.139663 | ||||||||
\(619\) | 9.03863 | 0.363293 | 0.181647 | − | 0.983364i | \(-0.441857\pi\) | ||||
0.181647 | + | 0.983364i | \(0.441857\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.41468 | 0.0567691 | ||||||||
\(622\) | 16.2800 | 0.652770 | ||||||||
\(623\) | 8.64939 | 0.346530 | ||||||||
\(624\) | 4.21992 | 0.168932 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −23.4474 | −0.937146 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.0186574 | −0.000744512 0 | ||||||||
\(629\) | 64.4100 | 2.56819 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9614 | 0.436365 | 0.218183 | − | 0.975908i | \(-0.429987\pi\) | ||||
0.218183 | + | 0.975908i | \(0.429987\pi\) | |||||||
\(632\) | 20.1999 | 0.803511 | ||||||||
\(633\) | −13.3213 | −0.529474 | ||||||||
\(634\) | 31.0093 | 1.23154 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.69867 | 0.0673567 | ||||||||
\(637\) | −0.829359 | −0.0328604 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.85866 | 0.231765 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −44.1587 | −1.74416 | −0.872081 | − | 0.489361i | \(-0.837230\pi\) | ||||
−0.872081 | + | 0.489361i | \(0.837230\pi\) | |||||||
\(642\) | 19.8573 | 0.783707 | ||||||||
\(643\) | −22.5840 | −0.890626 | −0.445313 | − | 0.895375i | \(-0.646908\pi\) | ||||
−0.445313 | + | 0.895375i | \(0.646908\pi\) | |||||||
\(644\) | 0.500796 | 0.0197341 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.5340 | −0.729209 | ||||||||
\(647\) | 13.3561 | 0.525081 | 0.262541 | − | 0.964921i | \(-0.415440\pi\) | ||||
0.262541 | + | 0.964921i | \(0.415440\pi\) | |||||||
\(648\) | −2.91934 | −0.114683 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.15999 | −0.280622 | ||||||||
\(652\) | −0.609438 | −0.0238674 | ||||||||
\(653\) | −37.5933 | −1.47114 | −0.735570 | − | 0.677448i | \(-0.763086\pi\) | ||||
−0.735570 | + | 0.677448i | \(0.763086\pi\) | |||||||
\(654\) | 3.29200 | 0.128727 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.35400 | 0.0919082 | ||||||||
\(657\) | 7.55602 | 0.294788 | ||||||||
\(658\) | −20.9707 | −0.817523 | ||||||||
\(659\) | −7.00933 | −0.273045 | −0.136522 | − | 0.990637i | \(-0.543593\pi\) | ||||
−0.136522 | + | 0.990637i | \(0.543593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.6226 | 1.03550 | 0.517750 | − | 0.855532i | \(-0.326770\pi\) | ||||
0.517750 | + | 0.855532i | \(0.326770\pi\) | |||||||
\(662\) | 34.4559 | 1.33917 | ||||||||
\(663\) | −8.72666 | −0.338915 | ||||||||
\(664\) | 18.0415 | 0.700144 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.4847 | 0.445023 | ||||||||
\(667\) | −1.02799 | −0.0398038 | ||||||||
\(668\) | 1.59597 | 0.0617498 | ||||||||
\(669\) | −12.2534 | −0.473743 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.99868 | −0.0771008 | ||||||||
\(673\) | 35.6960 | 1.37598 | 0.687990 | − | 0.725720i | \(-0.258493\pi\) | ||||
0.687990 | + | 0.725720i | \(0.258493\pi\) | |||||||
\(674\) | −24.1146 | −0.928859 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.65326 | 0.0635869 | ||||||||
\(677\) | 33.2920 | 1.27952 | 0.639758 | − | 0.768577i | \(-0.279035\pi\) | ||||
0.639758 | + | 0.768577i | \(0.279035\pi\) | |||||||
\(678\) | 8.17997 | 0.314150 | ||||||||
\(679\) | 48.7474 | 1.87075 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.74531 | −0.335121 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.1787 | 1.38434 | 0.692169 | − | 0.721736i | \(-0.256655\pi\) | ||||
0.692169 | + | 0.721736i | \(0.256655\pi\) | |||||||
\(684\) | 0.251297 | 0.00960857 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.3841 | −1.00735 | ||||||||
\(687\) | 11.4626 | 0.437327 | ||||||||
\(688\) | 46.9466 | 1.78982 | ||||||||
\(689\) | 13.7173 | 0.522589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.3293 | 1.34399 | 0.671995 | − | 0.740555i | \(-0.265438\pi\) | ||||
0.671995 | + | 0.740555i | \(0.265438\pi\) | |||||||
\(692\) | −3.05936 | −0.116299 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.4066 | 1.04034 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.12136 | 0.0804100 | ||||||||
\(697\) | −4.86799 | −0.184388 | ||||||||
\(698\) | 14.9839 | 0.567149 | ||||||||
\(699\) | −7.48469 | −0.283097 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.4006 | 1.86584 | 0.932918 | − | 0.360088i | \(-0.117253\pi\) | ||||
0.932918 | + | 0.360088i | \(0.117253\pi\) | |||||||
\(702\) | −1.55602 | −0.0587280 | ||||||||
\(703\) | −14.9780 | −0.564904 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.8039 | −0.858237 | ||||||||
\(707\) | 20.9707 | 0.788684 | ||||||||
\(708\) | −0.482618 | −0.0181379 | ||||||||
\(709\) | −11.1027 | −0.416971 | −0.208485 | − | 0.978025i | \(-0.566853\pi\) | ||||
−0.208485 | + | 0.978025i | \(0.566853\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.91934 | −0.259496 | ||||||||
\(712\) | −10.0814 | −0.377817 | ||||||||
\(713\) | −4.04409 | −0.151452 | ||||||||
\(714\) | −26.1086 | −0.977091 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.28135 | −0.0852582 | ||||||||
\(717\) | 12.9066 | 0.482007 | ||||||||
\(718\) | 18.5322 | 0.691614 | ||||||||
\(719\) | −43.9787 | −1.64013 | −0.820064 | − | 0.572271i | \(-0.806062\pi\) | ||||
−0.820064 | + | 0.572271i | \(0.806062\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.37860 | −0.237551 | ||||||||
\(722\) | −21.5933 | −0.803621 | ||||||||
\(723\) | −16.8773 | −0.627674 | ||||||||
\(724\) | −2.93338 | −0.109018 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 44.1880 | 1.63884 | 0.819421 | − | 0.573193i | \(-0.194295\pi\) | ||||
0.819421 | + | 0.573193i | \(0.194295\pi\) | |||||||
\(728\) | −8.34542 | −0.309302 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −97.0840 | −3.59078 | ||||||||
\(732\) | −0.649390 | −0.0240021 | ||||||||
\(733\) | −47.3879 | −1.75031 | −0.875156 | − | 0.483840i | \(-0.839242\pi\) | ||||
−0.875156 | + | 0.483840i | \(0.839242\pi\) | |||||||
\(734\) | −39.5347 | −1.45925 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.12889 | −0.0416115 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.867993 | −0.0319512 | ||||||||
\(739\) | 13.0407 | 0.479710 | 0.239855 | − | 0.970809i | \(-0.422900\pi\) | ||||
0.239855 | + | 0.970809i | \(0.422900\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.02930 | 0.0745484 | ||||||||
\(742\) | 41.0399 | 1.50662 | ||||||||
\(743\) | −14.1800 | −0.520213 | −0.260106 | − | 0.965580i | \(-0.583758\pi\) | ||||
−0.260106 | + | 0.965580i | \(0.583758\pi\) | |||||||
\(744\) | 8.34542 | 0.305958 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −24.3854 | −0.892812 | ||||||||
\(747\) | −6.17997 | −0.226113 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −36.4813 | −1.33300 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.1120 | 0.697408 | 0.348704 | − | 0.937233i | \(-0.386622\pi\) | ||||
0.348704 | + | 0.937233i | \(0.386622\pi\) | |||||||
\(752\) | 22.7067 | 0.828027 | ||||||||
\(753\) | −2.28267 | −0.0831852 | ||||||||
\(754\) | 1.13069 | 0.0411773 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.354000 | 0.0128748 | ||||||||
\(757\) | −24.7347 | −0.898997 | −0.449498 | − | 0.893281i | \(-0.648397\pi\) | ||||
−0.449498 | + | 0.893281i | \(0.648397\pi\) | |||||||
\(758\) | 32.4253 | 1.17774 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.82003 | 0.355976 | 0.177988 | − | 0.984033i | \(-0.443041\pi\) | ||||
0.177988 | + | 0.984033i | \(0.443041\pi\) | |||||||
\(762\) | 20.7253 | 0.750800 | ||||||||
\(763\) | −6.04796 | −0.218951 | ||||||||
\(764\) | −0.468102 | −0.0169353 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43.2666 | 1.56328 | ||||||||
\(767\) | −3.89730 | −0.140723 | ||||||||
\(768\) | 3.37473 | 0.121775 | ||||||||
\(769\) | 15.3026 | 0.551828 | 0.275914 | − | 0.961182i | \(-0.411020\pi\) | ||||
0.275914 | + | 0.961182i | \(0.411020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.8667 | −0.967580 | ||||||||
\(772\) | 0.301330 | 0.0108451 | ||||||||
\(773\) | −5.36927 | −0.193119 | −0.0965596 | − | 0.995327i | \(-0.530784\pi\) | ||||
−0.0965596 | + | 0.995327i | \(0.530784\pi\) | |||||||
\(774\) | −17.3107 | −0.622219 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −56.8181 | −2.03965 | ||||||||
\(777\) | −21.0993 | −0.756934 | ||||||||
\(778\) | 35.1120 | 1.25883 | ||||||||
\(779\) | 1.13201 | 0.0405584 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −14.7466 | −0.527338 | ||||||||
\(783\) | −0.726656 | −0.0259686 | ||||||||
\(784\) | 2.68670 | 0.0959537 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 25.5560 | 0.911553 | ||||||||
\(787\) | 15.4767 | 0.551684 | 0.275842 | − | 0.961203i | \(-0.411043\pi\) | ||||
0.275842 | + | 0.961203i | \(0.411043\pi\) | |||||||
\(788\) | −2.53397 | −0.0902689 | ||||||||
\(789\) | −12.0187 | −0.427876 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.0280 | −0.534334 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.24404 | −0.186221 | ||||||||
\(794\) | 4.14265 | 0.147017 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.14265 | −0.0759444 | ||||||||
\(797\) | 43.6774 | 1.54713 | 0.773566 | − | 0.633716i | \(-0.218471\pi\) | ||||
0.773566 | + | 0.633716i | \(0.218471\pi\) | |||||||
\(798\) | 6.07133 | 0.214923 | ||||||||
\(799\) | −46.9567 | −1.66121 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.45331 | 0.122017 | ||||||||
\(802\) | −24.7853 | −0.875198 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 1.31744 | 0.0464624 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.44813 | 0.156679 | ||||||||
\(807\) | 14.3854 | 0.506389 | ||||||||
\(808\) | −24.4427 | −0.859890 | ||||||||
\(809\) | 26.9966 | 0.949150 | 0.474575 | − | 0.880215i | \(-0.342602\pi\) | ||||
0.474575 | + | 0.880215i | \(0.342602\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.2220 | 0.499402 | 0.249701 | − | 0.968323i | \(-0.419668\pi\) | ||||
0.249701 | + | 0.968323i | \(0.419668\pi\) | |||||||
\(812\) | −0.257236 | −0.00902722 | ||||||||
\(813\) | 28.6553 | 1.00499 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 28.2700 | 0.989646 | ||||||||
\(817\) | 22.5760 | 0.789834 | ||||||||
\(818\) | 28.0773 | 0.981699 | ||||||||
\(819\) | 2.85866 | 0.0998898 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.7801 | −0.829930 | −0.414965 | − | 0.909837i | \(-0.636206\pi\) | ||||
−0.414965 | + | 0.909837i | \(0.636206\pi\) | |||||||
\(822\) | 11.9227 | 0.415853 | ||||||||
\(823\) | 1.84934 | 0.0644638 | 0.0322319 | − | 0.999480i | \(-0.489738\pi\) | ||||
0.0322319 | + | 0.999480i | \(0.489738\pi\) | |||||||
\(824\) | 7.43466 | 0.258998 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.6600 | −0.405705 | ||||||||
\(827\) | 15.6987 | 0.545896 | 0.272948 | − | 0.962029i | \(-0.412001\pi\) | ||||
0.272948 | + | 0.962029i | \(0.412001\pi\) | |||||||
\(828\) | 0.199945 | 0.00694858 | ||||||||
\(829\) | −4.34128 | −0.150779 | −0.0753895 | − | 0.997154i | \(-0.524020\pi\) | ||||
−0.0753895 | + | 0.997154i | \(0.524020\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.1600 | 1.01155 | ||||||||
\(832\) | 9.68152 | 0.335646 | ||||||||
\(833\) | −5.55602 | −0.192505 | ||||||||
\(834\) | −30.4040 | −1.05281 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.85866 | −0.0988099 | ||||||||
\(838\) | 44.6154 | 1.54121 | ||||||||
\(839\) | 28.3013 | 0.977070 | 0.488535 | − | 0.872544i | \(-0.337531\pi\) | ||||
0.488535 | + | 0.872544i | \(0.337531\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4720 | −0.981792 | ||||||||
\(842\) | 44.3955 | 1.52997 | ||||||||
\(843\) | −5.36333 | −0.184723 | ||||||||
\(844\) | −1.88278 | −0.0648080 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.37266 | −0.287858 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −44.4372 | −1.52598 | ||||||||
\(849\) | 10.0420 | 0.344641 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.9173 | −0.408519 | ||||||||
\(852\) | 0.828041 | 0.0283682 | ||||||||
\(853\) | −35.7653 | −1.22458 | −0.612290 | − | 0.790633i | \(-0.709752\pi\) | ||||
−0.612290 | + | 0.790633i | \(0.709752\pi\) | |||||||
\(854\) | −15.6893 | −0.536875 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 42.5213 | 1.45335 | ||||||||
\(857\) | −24.7513 | −0.845487 | −0.422743 | − | 0.906249i | \(-0.638933\pi\) | ||||
−0.422743 | + | 0.906249i | \(0.638933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.8039 | −0.368625 | −0.184313 | − | 0.982868i | \(-0.559006\pi\) | ||||
−0.184313 | + | 0.982868i | \(0.559006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.59465 | 0.0543455 | ||||||||
\(862\) | −2.48130 | −0.0845134 | ||||||||
\(863\) | 16.6027 | 0.565161 | 0.282581 | − | 0.959244i | \(-0.408810\pi\) | ||||
0.282581 | + | 0.959244i | \(0.408810\pi\) | |||||||
\(864\) | −0.797984 | −0.0271480 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 40.6654 | 1.38187 | ||||||||
\(867\) | −41.4613 | −1.40810 | ||||||||
\(868\) | −1.01197 | −0.0343484 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.6387 | 0.360480 | ||||||||
\(872\) | 7.04928 | 0.238719 | ||||||||
\(873\) | 19.4626 | 0.658711 | ||||||||
\(874\) | 3.42920 | 0.115994 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.06794 | 0.0360823 | ||||||||
\(877\) | −11.1600 | −0.376846 | −0.188423 | − | 0.982088i | \(-0.560338\pi\) | ||||
−0.188423 | + | 0.982088i | \(0.560338\pi\) | |||||||
\(878\) | −24.8426 | −0.838396 | ||||||||
\(879\) | −20.3540 | −0.686523 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.5254 | 1.83701 | 0.918504 | − | 0.395413i | \(-0.129398\pi\) | ||||
0.918504 | + | 0.395413i | \(0.129398\pi\) | |||||||
\(882\) | −0.990671 | −0.0333576 | ||||||||
\(883\) | −12.7746 | −0.429900 | −0.214950 | − | 0.976625i | \(-0.568959\pi\) | ||||
−0.214950 | + | 0.976625i | \(0.568959\pi\) | |||||||
\(884\) | −1.23339 | −0.0414835 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.3514 | 1.01967 | ||||||||
\(887\) | −47.1053 | −1.58164 | −0.790820 | − | 0.612049i | \(-0.790345\pi\) | ||||
−0.790820 | + | 0.612049i | \(0.790345\pi\) | |||||||
\(888\) | 24.5926 | 0.825273 | ||||||||
\(889\) | −38.0759 | −1.27703 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.73184 | −0.0579864 | ||||||||
\(893\) | 10.9193 | 0.365402 | ||||||||
\(894\) | −21.7160 | −0.726292 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 24.9681 | 0.834124 | ||||||||
\(897\) | 1.61462 | 0.0539108 | ||||||||
\(898\) | 35.2775 | 1.17722 | ||||||||
\(899\) | 2.07727 | 0.0692807 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 91.8947 | 3.06146 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.8026 | 1.05832 | ||||||||
\(904\) | 17.5161 | 0.582576 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −13.4787 | −0.447801 | ||||||||
\(907\) | 24.7826 | 0.822894 | 0.411447 | − | 0.911434i | \(-0.365024\pi\) | ||||
0.411447 | + | 0.911434i | \(0.365024\pi\) | |||||||
\(908\) | −1.23603 | −0.0410191 | ||||||||
\(909\) | 8.37266 | 0.277704 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.08273 | −0.201530 | −0.100765 | − | 0.994910i | \(-0.532129\pi\) | ||||
−0.100765 | + | 0.994910i | \(0.532129\pi\) | |||||||
\(912\) | −6.57392 | −0.217684 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −14.2640 | −0.471812 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.62009 | 0.0535291 | ||||||||
\(917\) | −46.9507 | −1.55045 | ||||||||
\(918\) | −10.4240 | −0.344044 | ||||||||
\(919\) | −17.9953 | −0.593610 | −0.296805 | − | 0.954938i | \(-0.595921\pi\) | ||||
−0.296805 | + | 0.954938i | \(0.595921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.6226 | −0.844295 | ||||||||
\(922\) | −16.1400 | −0.531543 | ||||||||
\(923\) | 6.68670 | 0.220096 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −37.8387 | −1.24346 | ||||||||
\(927\) | −2.54669 | −0.0836442 | ||||||||
\(928\) | 0.579860 | 0.0190348 | ||||||||
\(929\) | −16.7453 | −0.549396 | −0.274698 | − | 0.961531i | \(-0.588578\pi\) | ||||
−0.274698 | + | 0.961531i | \(0.588578\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.29200 | 0.0423436 | ||||||||
\(932\) | −1.05786 | −0.0346513 | ||||||||
\(933\) | −11.9414 | −0.390944 | ||||||||
\(934\) | −28.3973 | −0.929187 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.33195 | −0.108908 | ||||||||
\(937\) | −31.5853 | −1.03185 | −0.515924 | − | 0.856635i | \(-0.672551\pi\) | ||||
−0.515924 | + | 0.856635i | \(0.672551\pi\) | |||||||
\(938\) | 31.8293 | 1.03926 | ||||||||
\(939\) | 17.1986 | 0.561256 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.8421 | 0.483838 | 0.241919 | − | 0.970296i | \(-0.422223\pi\) | ||||
0.241919 | + | 0.970296i | \(0.422223\pi\) | |||||||
\(942\) | −0.179969 | −0.00586372 | ||||||||
\(943\) | 0.900687 | 0.0293304 | ||||||||
\(944\) | 12.6253 | 0.410918 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.68802 | −0.0873490 | −0.0436745 | − | 0.999046i | \(-0.513906\pi\) | ||||
−0.0436745 | + | 0.999046i | \(0.513906\pi\) | |||||||
\(948\) | −0.977953 | −0.0317624 | ||||||||
\(949\) | 8.62395 | 0.279945 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.7453 | −0.737567 | ||||||||
\(952\) | −55.9074 | −1.81197 | ||||||||
\(953\) | 14.2700 | 0.462249 | 0.231125 | − | 0.972924i | \(-0.425760\pi\) | ||||
0.231125 | + | 0.972924i | \(0.425760\pi\) | |||||||
\(954\) | 16.3854 | 0.530496 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.82417 | 0.0589980 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.61199 | −0.116698 | ||||||||
\(959\) | −21.9041 | −0.707320 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.8280 | −0.736388 | ||||||||
\(962\) | 13.1079 | 0.422615 | ||||||||
\(963\) | −14.5653 | −0.469362 | ||||||||
\(964\) | −2.38538 | −0.0768278 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.83068 | 0.155425 | ||||||||
\(967\) | 10.0586 | 0.323463 | 0.161732 | − | 0.986835i | \(-0.448292\pi\) | ||||
0.161732 | + | 0.986835i | \(0.448292\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.5946 | 0.436723 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.4520 | −0.431695 | −0.215848 | − | 0.976427i | \(-0.569251\pi\) | ||||
−0.215848 | + | 0.976427i | \(0.569251\pi\) | |||||||
\(972\) | 0.141336 | 0.00453336 | ||||||||
\(973\) | 55.8573 | 1.79070 | ||||||||
\(974\) | −55.2639 | −1.77077 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.9880 | 0.543774 | ||||||||
\(977\) | 32.8294 | 1.05030 | 0.525152 | − | 0.851008i | \(-0.324008\pi\) | ||||
0.525152 | + | 0.851008i | \(0.324008\pi\) | |||||||
\(978\) | −5.87864 | −0.187978 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.41468 | −0.0770948 | ||||||||
\(982\) | 21.9787 | 0.701369 | ||||||||
\(983\) | −43.7746 | −1.39619 | −0.698097 | − | 0.716003i | \(-0.745969\pi\) | ||||
−0.698097 | + | 0.716003i | \(0.745969\pi\) | |||||||
\(984\) | −1.85866 | −0.0592520 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.57467 | 0.241227 | ||||||||
\(987\) | 15.3820 | 0.489614 | ||||||||
\(988\) | 0.286814 | 0.00912477 | ||||||||
\(989\) | 17.9627 | 0.571180 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.1507 | 1.33896 | 0.669480 | − | 0.742830i | \(-0.266517\pi\) | ||||
0.669480 | + | 0.742830i | \(0.266517\pi\) | |||||||
\(992\) | 2.28117 | 0.0724271 | ||||||||
\(993\) | −25.2733 | −0.802025 | ||||||||
\(994\) | 20.0055 | 0.634535 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.873453 | −0.0276764 | ||||||||
\(997\) | −17.4347 | −0.552161 | −0.276081 | − | 0.961135i | \(-0.589036\pi\) | ||||
−0.276081 | + | 0.961135i | \(0.589036\pi\) | |||||||
\(998\) | −38.2640 | −1.21123 | ||||||||
\(999\) | −8.42401 | −0.266524 |
(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 | 9075.2.a.cj.1.2 | 3 | ||
5.4 | even | 2 | 9075.2.a.cd.1.2 | 3 | |||
11.10 | odd | 2 | 825.2.a.i.1.2 | ✓ | 3 | ||
33.32 | even | 2 | 2475.2.a.bd.1.2 | 3 | |||
55.32 | even | 4 | 825.2.c.f.199.3 | 6 | |||
55.43 | even | 4 | 825.2.c.f.199.4 | 6 | |||
55.54 | odd | 2 | 825.2.a.m.1.2 | yes | 3 | ||
165.32 | odd | 4 | 2475.2.c.q.199.4 | 6 | |||
165.98 | odd | 4 | 2475.2.c.q.199.3 | 6 | |||
165.164 | even | 2 | 2475.2.a.z.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.a.i.1.2 | ✓ | 3 | 11.10 | odd | 2 | ||
825.2.a.m.1.2 | yes | 3 | 55.54 | odd | 2 | ||
825.2.c.f.199.3 | 6 | 55.32 | even | 4 | |||
825.2.c.f.199.4 | 6 | 55.43 | even | 4 | |||
2475.2.a.z.1.2 | 3 | 165.164 | even | 2 | |||
2475.2.a.bd.1.2 | 3 | 33.32 | even | 2 | |||
2475.2.c.q.199.3 | 6 | 165.98 | odd | 4 | |||
2475.2.c.q.199.4 | 6 | 165.32 | odd | 4 | |||
9075.2.a.cd.1.2 | 3 | 5.4 | even | 2 | |||
9075.2.a.cj.1.2 | 3 | 1.1 | even | 1 | trivial |