Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3312,2,Mod(1,3312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3312.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3312 = 2^{4} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3312.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: | \(26.4464531494\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.44688.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 5x^{2} + 6x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1656) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.27733\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3312.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.64575 | −0.736002 | −0.368001 | − | 0.929825i | \(-0.619958\pi\) | ||||
−0.368001 | + | 0.929825i | \(0.619958\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.01109 | 0.382157 | 0.191078 | − | 0.981575i | \(-0.438802\pi\) | ||||
0.191078 | + | 0.981575i | \(0.438802\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.21151 | 1.57133 | 0.785665 | − | 0.618652i | \(-0.212321\pi\) | ||||
0.785665 | + | 0.618652i | \(0.212321\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.55467 | 0.708538 | 0.354269 | − | 0.935144i | \(-0.384730\pi\) | ||||
0.354269 | + | 0.935144i | \(0.384730\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.56576 | 0.864824 | 0.432412 | − | 0.901676i | \(-0.357663\pi\) | ||||
0.432412 | + | 0.901676i | \(0.357663\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.09108 | −0.709143 | −0.354571 | − | 0.935029i | \(-0.615373\pi\) | ||||
−0.354571 | + | 0.935029i | \(0.615373\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.29150 | −0.458301 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.44533 | 0.268391 | 0.134196 | − | 0.990955i | \(-0.457155\pi\) | ||||
0.134196 | + | 0.990955i | \(0.457155\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.44533 | −0.259589 | −0.129795 | − | 0.991541i | \(-0.541432\pi\) | ||||
−0.129795 | + | 0.991541i | \(0.541432\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.66401 | −0.281268 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.10217 | 1.00319 | 0.501596 | − | 0.865102i | \(-0.332747\pi\) | ||||
0.501596 | + | 0.865102i | \(0.332747\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.73683 | 0.739769 | 0.369885 | − | 0.929078i | \(-0.379397\pi\) | ||||
0.369885 | + | 0.929078i | \(0.379397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.3319 | −1.72810 | −0.864052 | − | 0.503402i | \(-0.832082\pi\) | ||||
−0.864052 | + | 0.503402i | \(0.832082\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.0221841 | −0.00323589 | −0.00161794 | − | 0.999999i | \(-0.500515\pi\) | ||||
−0.00161794 | + | 0.999999i | \(0.500515\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.97769 | −0.853956 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.66794 | 1.05327 | 0.526636 | − | 0.850091i | \(-0.323453\pi\) | ||||
0.526636 | + | 0.850091i | \(0.323453\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.57685 | −1.15650 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.28535 | 0.427716 | 0.213858 | − | 0.976865i | \(-0.431397\pi\) | ||||
0.213858 | + | 0.976865i | \(0.431397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.21151 | 0.923340 | 0.461670 | − | 0.887052i | \(-0.347251\pi\) | ||||
0.461670 | + | 0.887052i | \(0.347251\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.20435 | −0.521485 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.4919 | −1.40396 | −0.701981 | − | 0.712196i | \(-0.747701\pi\) | ||||
−0.701981 | + | 0.712196i | \(0.747701\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.736834 | −0.0874461 | −0.0437230 | − | 0.999044i | \(-0.513922\pi\) | ||||
−0.0437230 | + | 0.999044i | \(0.513922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6862 | 1.36777 | 0.683883 | − | 0.729592i | \(-0.260290\pi\) | ||||
0.683883 | + | 0.729592i | \(0.260290\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.26932 | 0.600495 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.12043 | 0.238567 | 0.119283 | − | 0.992860i | \(-0.461940\pi\) | ||||
0.119283 | + | 0.992860i | \(0.461940\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.21151 | 1.01109 | 0.505547 | − | 0.862799i | \(-0.331291\pi\) | ||||
0.505547 | + | 0.862799i | \(0.331291\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.86836 | −0.636513 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.96660 | −0.844458 | −0.422229 | − | 0.906489i | \(-0.638752\pi\) | ||||
−0.422229 | + | 0.906489i | \(0.638752\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.58301 | 0.270773 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.08715 | 0.521931 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.31369 | −0.742592 | −0.371296 | − | 0.928514i | \(-0.621087\pi\) | ||||
−0.371296 | + | 0.928514i | \(0.621087\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.42315 | 0.340616 | 0.170308 | − | 0.985391i | \(-0.445524\pi\) | ||||
0.170308 | + | 0.985391i | \(0.445524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.43412 | 0.732505 | 0.366253 | − | 0.930515i | \(-0.380641\pi\) | ||||
0.366253 | + | 0.930515i | \(0.380641\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.5252 | −1.01751 | −0.508755 | − | 0.860912i | \(-0.669894\pi\) | ||||
−0.508755 | + | 0.860912i | \(0.669894\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.7945 | 1.70441 | 0.852203 | − | 0.523212i | \(-0.175266\pi\) | ||||
0.852203 | + | 0.523212i | \(0.175266\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.835079 | 0.0785576 | 0.0392788 | − | 0.999228i | \(-0.487494\pi\) | ||||
0.0392788 | + | 0.999228i | \(0.487494\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.64575 | −0.153467 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.60531 | 0.330498 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.1599 | 1.46908 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.60519 | 0.763587 | 0.381794 | − | 0.924248i | \(-0.375307\pi\) | ||||
0.381794 | + | 0.924248i | \(0.375307\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3137 | 1.16322 | 0.581611 | − | 0.813467i | \(-0.302423\pi\) | ||||
0.581611 | + | 0.813467i | \(0.302423\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.12537 | −0.271004 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.8066 | 1.35045 | 0.675225 | − | 0.737612i | \(-0.264046\pi\) | ||||
0.675225 | + | 0.737612i | \(0.264046\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.3137 | 1.11335 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.37866 | −0.197537 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.9088 | 1.63099 | 0.815496 | − | 0.578763i | \(-0.196464\pi\) | ||||
0.815496 | + | 0.578763i | \(0.196464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0505 | −0.817900 | −0.408950 | − | 0.912557i | \(-0.634105\pi\) | ||||
−0.408950 | + | 0.912557i | \(0.634105\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.37866 | 0.191058 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.48083 | 0.357609 | 0.178805 | − | 0.983885i | \(-0.442777\pi\) | ||||
0.178805 | + | 0.983885i | \(0.442777\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.01109 | 0.0796852 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.1376 | 1.57729 | 0.788647 | − | 0.614846i | \(-0.210782\pi\) | ||||
0.788647 | + | 0.614846i | \(0.210782\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.9999 | −1.16073 | −0.580363 | − | 0.814358i | \(-0.697089\pi\) | ||||
−0.580363 | + | 0.814358i | \(0.697089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.47367 | −0.497974 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.29138 | −0.478325 | −0.239162 | − | 0.970980i | \(-0.576873\pi\) | ||||
−0.239162 | + | 0.970980i | \(0.576873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.31692 | −0.175143 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.2914 | 1.21767 | 0.608837 | − | 0.793295i | \(-0.291636\pi\) | ||||
0.608837 | + | 0.793295i | \(0.291636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.5252 | 0.930991 | 0.465495 | − | 0.885050i | \(-0.345876\pi\) | ||||
0.465495 | + | 0.885050i | \(0.345876\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.0427 | −0.738351 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.5830 | 1.35892 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.2693 | 0.960134 | 0.480067 | − | 0.877232i | \(-0.340612\pi\) | ||||
0.480067 | + | 0.877232i | \(0.340612\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50402 | 0.540152 | 0.270076 | − | 0.962839i | \(-0.412951\pi\) | ||||
0.270076 | + | 0.962839i | \(0.412951\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.75902 | −0.196572 | −0.0982859 | − | 0.995158i | \(-0.531336\pi\) | ||||
−0.0982859 | + | 0.995158i | \(0.531336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.2741 | −1.08275 | −0.541377 | − | 0.840780i | \(-0.682097\pi\) | ||||
−0.541377 | + | 0.840780i | \(0.682097\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.46136 | 0.102568 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.79565 | −0.544472 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.1092 | −1.11430 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.33587 | −0.505022 | −0.252511 | − | 0.967594i | \(-0.581256\pi\) | ||||
−0.252511 | + | 0.967594i | \(0.581256\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.6496 | 1.27189 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.46136 | −0.0992038 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.10934 | 0.612760 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1155 | 0.744348 | 0.372174 | − | 0.928163i | \(-0.378612\pi\) | ||||
0.372174 | + | 0.928163i | \(0.378612\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.1082 | −1.13551 | −0.567756 | − | 0.823197i | \(-0.692188\pi\) | ||||
−0.567756 | + | 0.823197i | \(0.692188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.7945 | −0.911567 | −0.455784 | − | 0.890091i | \(-0.650641\pi\) | ||||
−0.455784 | + | 0.890091i | \(0.650641\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.95563 | −0.259142 | −0.129571 | − | 0.991570i | \(-0.541360\pi\) | ||||
−0.129571 | + | 0.991570i | \(0.541360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0365096 | 0.00238162 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.04437 | 0.261608 | 0.130804 | − | 0.991408i | \(-0.458244\pi\) | ||||
0.130804 | + | 0.991408i | \(0.458244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3787 | −0.797379 | −0.398690 | − | 0.917086i | \(-0.630535\pi\) | ||||
−0.398690 | + | 0.917086i | \(0.630535\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.83780 | 0.628514 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.89669 | −0.502454 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.6852 | 1.17940 | 0.589699 | − | 0.807623i | \(-0.299246\pi\) | ||||
0.589699 | + | 0.807623i | \(0.299246\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.21151 | 0.327645 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.4169 | −1.27357 | −0.636785 | − | 0.771042i | \(-0.719736\pi\) | ||||
−0.636785 | + | 0.771042i | \(0.719736\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.16986 | 0.383376 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.10934 | −0.561706 | −0.280853 | − | 0.959751i | \(-0.590617\pi\) | ||||
−0.280853 | + | 0.959751i | \(0.590617\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.6195 | −0.775211 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.5607 | 1.19264 | 0.596318 | − | 0.802748i | \(-0.296630\pi\) | ||||
0.596318 | + | 0.802748i | \(0.296630\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.02218 | −0.122839 | −0.0614195 | − | 0.998112i | \(-0.519563\pi\) | ||||
−0.0614195 | + | 0.998112i | \(0.519563\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.9422 | −0.720141 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.4230 | −1.46744 | −0.733719 | − | 0.679453i | \(-0.762217\pi\) | ||||
−0.733719 | + | 0.679453i | \(0.762217\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4403 | 0.801779 | 0.400890 | − | 0.916126i | \(-0.368701\pi\) | ||||
0.400890 | + | 0.916126i | \(0.368701\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.13545 | 0.424159 | 0.212079 | − | 0.977252i | \(-0.431976\pi\) | ||||
0.212079 | + | 0.977252i | \(0.431976\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.78938 | 0.282708 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.28535 | −0.252079 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.2731 | 1.65173 | 0.825867 | − | 0.563865i | \(-0.190686\pi\) | ||||
0.825867 | + | 0.563865i | \(0.190686\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.40687 | −0.314800 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.55467 | 0.147740 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.4576 | −0.660407 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.8684 | −0.679580 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.07283 | 0.289522 | 0.144761 | − | 0.989467i | \(-0.453759\pi\) | ||||
0.144761 | + | 0.989467i | \(0.453759\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.9250 | −1.69689 | −0.848446 | − | 0.529281i | \(-0.822462\pi\) | ||||
−0.848446 | + | 0.529281i | \(0.822462\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.35806 | 0.415902 | 0.207951 | − | 0.978139i | \(-0.433321\pi\) | ||||
0.207951 | + | 0.978139i | \(0.433321\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.3563 | 1.76115 | 0.880574 | − | 0.473909i | \(-0.157157\pi\) | ||||
0.880574 | + | 0.473909i | \(0.157157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.53236 | 0.421731 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.0221 | −0.613284 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.85403 | −0.324723 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.0224302 | −0.00123662 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.8745 | 1.42219 | 0.711096 | − | 0.703095i | \(-0.248199\pi\) | ||||
0.711096 | + | 0.703095i | \(0.248199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.9128 | 1.03332 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.7811 | −1.62228 | −0.811139 | − | 0.584853i | \(-0.801152\pi\) | ||||
−0.811139 | + | 0.584853i | \(0.801152\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.53236 | −0.407900 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.1216 | −0.708502 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.2347 | −0.656793 | −0.328397 | − | 0.944540i | \(-0.606508\pi\) | ||||
−0.328397 | + | 0.944540i | \(0.606508\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.0221 | −1.12529 | −0.562643 | − | 0.826700i | \(-0.690215\pi\) | ||||
−0.562643 | + | 0.826700i | \(0.690215\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.91285 | −0.261484 | −0.130742 | − | 0.991416i | \(-0.541736\pi\) | ||||
−0.130742 | + | 0.991416i | \(0.541736\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.21265 | 0.0643605 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.15998 | −0.430667 | −0.215334 | − | 0.976541i | \(-0.569084\pi\) | ||||
−0.215334 | + | 0.976541i | \(0.569084\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.44521 | −0.497116 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.2326 | −1.00668 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.7034 | 1.28951 | 0.644754 | − | 0.764390i | \(-0.276960\pi\) | ||||
0.644754 | + | 0.764390i | \(0.276960\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.75299 | 0.402515 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.16087 | 0.215442 | 0.107721 | − | 0.994181i | \(-0.465645\pi\) | ||||
0.107721 | + | 0.994181i | \(0.465645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.69234 | 0.190165 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1276 | −0.571586 | −0.285793 | − | 0.958291i | \(-0.592257\pi\) | ||||
−0.285793 | + | 0.958291i | \(0.592257\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.89066 | −0.147706 | −0.0738530 | − | 0.997269i | \(-0.523530\pi\) | ||||
−0.0738530 | + | 0.997269i | \(0.523530\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.67199 | −0.441965 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.7266 | −0.898776 | −0.449388 | − | 0.893337i | \(-0.648358\pi\) | ||||
−0.449388 | + | 0.893337i | \(0.648358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.56576 | 0.180328 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.48970 | −0.175586 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.47367 | 0.375093 | 0.187546 | − | 0.982256i | \(-0.439947\pi\) | ||||
0.187546 | + | 0.982256i | \(0.439947\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.56576 | 0.178066 | 0.0890328 | − | 0.996029i | \(-0.471622\pi\) | ||||
0.0890328 | + | 0.996029i | \(0.471622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.69234 | −0.183929 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.8016 | 1.57634 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.7144 | 1.22205 | 0.611024 | − | 0.791612i | \(-0.290758\pi\) | ||||
0.611024 | + | 0.791612i | \(0.290758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.32179 | 0.163455 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.1599 | −0.744168 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.15282 | −0.154025 | −0.0770126 | − | 0.997030i | \(-0.524538\pi\) | ||||
−0.0770126 | + | 0.997030i | \(0.524538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0578 | −0.490187 | −0.245094 | − | 0.969499i | \(-0.578819\pi\) | ||||
−0.245094 | + | 0.969499i | \(0.578819\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.17095 | −0.396349 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.29150 | 0.352861 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.9494 | −0.623749 | −0.311874 | − | 0.950123i | \(-0.600957\pi\) | ||||
−0.311874 | + | 0.950123i | \(0.600957\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.5243 | 0.505766 | 0.252883 | − | 0.967497i | \(-0.418621\pi\) | ||||
0.252883 | + | 0.967497i | \(0.418621\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.09108 | −0.147867 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.6274 | 0.889036 | 0.444518 | − | 0.895770i | \(-0.353375\pi\) | ||||
0.444518 | + | 0.895770i | \(0.353375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.69234 | 0.175428 | 0.0877142 | − | 0.996146i | \(-0.472044\pi\) | ||||
0.0877142 | + | 0.996146i | \(0.472044\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1110 | 0.621523 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.1012 | −0.807054 | −0.403527 | − | 0.914968i | \(-0.632216\pi\) | ||||
−0.403527 | + | 0.914968i | \(0.632216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24.6861 | 1.16242 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.25098 | −0.199289 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.3137 | −1.65190 | −0.825952 | − | 0.563740i | \(-0.809362\pi\) | ||||
−0.825952 | + | 0.563740i | \(0.809362\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.7794 | 1.38696 | 0.693482 | − | 0.720474i | \(-0.256076\pi\) | ||||
0.693482 | + | 0.720474i | \(0.256076\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.17431 | 0.286944 | 0.143472 | − | 0.989654i | \(-0.454173\pi\) | ||||
0.143472 | + | 0.989654i | \(0.454173\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.1732 | 1.76644 | 0.883222 | − | 0.468955i | \(-0.155369\pi\) | ||||
0.883222 | + | 0.468955i | \(0.155369\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.6194 | −0.536534 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −59.0566 | −2.71542 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.08322 | 0.325001 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.80168 | −0.219394 | −0.109697 | − | 0.993965i | \(-0.534988\pi\) | ||||
−0.109697 | + | 0.993965i | \(0.534988\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.5890 | 0.710799 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.0365 | 0.546550 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.2104 | 1.14239 | 0.571196 | − | 0.820814i | \(-0.306480\pi\) | ||||
0.571196 | + | 0.820814i | \(0.306480\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4453 | −0.516521 | −0.258260 | − | 0.966075i | \(-0.583149\pi\) | ||||
−0.258260 | + | 0.966075i | \(0.583149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.15371 | 0.232111 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.745007 | −0.0334181 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.7083 | −1.37469 | −0.687345 | − | 0.726331i | \(-0.741224\pi\) | ||||
−0.687345 | + | 0.726331i | \(0.741224\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.2247 | −1.39224 | −0.696120 | − | 0.717925i | \(-0.745092\pi\) | ||||
−0.696120 | + | 0.717925i | \(0.745092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.63365 | −0.250694 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.7207 | −1.58329 | −0.791646 | − | 0.610981i | \(-0.790775\pi\) | ||||
−0.791646 | + | 0.610981i | \(0.790775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.8158 | 0.522701 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.2347 | −0.539126 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.115613 | −0.00508465 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.6446 | −1.12351 | −0.561756 | − | 0.827303i | \(-0.689874\pi\) | ||||
−0.561756 | + | 0.827303i | \(0.689874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.53026 | −0.285548 | −0.142774 | − | 0.989755i | \(-0.545602\pi\) | ||||
−0.142774 | + | 0.989755i | \(0.545602\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.15371 | −0.224499 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.1010 | 0.524154 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.3219 | 0.748889 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −31.1528 | −1.34185 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.61336 | 0.198344 | 0.0991720 | − | 0.995070i | \(-0.468381\pi\) | ||||
0.0991720 | + | 0.995070i | \(0.468381\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29.2854 | −1.25445 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6112 | −0.753001 | −0.376501 | − | 0.926416i | \(-0.622873\pi\) | ||||
−0.376501 | + | 0.926416i | \(0.622873\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.46764 | −0.190328 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.14395 | 0.0911700 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.44140 | 0.0610742 | 0.0305371 | − | 0.999534i | \(-0.490278\pi\) | ||||
0.0305371 | + | 0.999534i | \(0.490278\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.9494 | −1.22443 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.84718 | −0.372864 | −0.186432 | − | 0.982468i | \(-0.559692\pi\) | ||||
−0.186432 | + | 0.982468i | \(0.559692\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.37433 | −0.0578186 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.47861 | 0.187753 | 0.0938765 | − | 0.995584i | \(-0.470074\pi\) | ||||
0.0938765 | + | 0.995584i | \(0.470074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.49192 | 0.313527 | 0.156764 | − | 0.987636i | \(-0.449894\pi\) | ||||
0.156764 | + | 0.987636i | \(0.449894\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.29150 | −0.0955623 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.2265 | 0.592258 | 0.296129 | − | 0.955148i | \(-0.404304\pi\) | ||||
0.296129 | + | 0.955148i | \(0.404304\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.31369 | 0.386397 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.9615 | 1.65504 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.94131 | −0.0801263 | −0.0400631 | − | 0.999197i | \(-0.512756\pi\) | ||||
−0.0400631 | + | 0.999197i | \(0.512756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.46764 | 0.184086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.1659 | 1.64942 | 0.824708 | − | 0.565559i | \(-0.191340\pi\) | ||||
0.824708 | + | 0.565559i | \(0.191340\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.93345 | −0.243248 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.4170 | −0.711639 | −0.355820 | − | 0.934555i | \(-0.615798\pi\) | ||||
−0.355820 | + | 0.934555i | \(0.615798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.3925 | 1.77002 | 0.885009 | − | 0.465573i | \(-0.154152\pi\) | ||||
0.885009 | + | 0.465573i | \(0.154152\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.5951 | −1.08124 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.2692 | 0.822701 | 0.411351 | − | 0.911477i | \(-0.365057\pi\) | ||||
0.411351 | + | 0.911477i | \(0.365057\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0566731 | −0.00229275 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.6792 | 0.471716 | 0.235858 | − | 0.971787i | \(-0.424210\pi\) | ||||
0.235858 | + | 0.971787i | \(0.424210\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.6589 | −1.75764 | −0.878821 | − | 0.477151i | \(-0.841670\pi\) | ||||
−0.878821 | + | 0.477151i | \(0.841670\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.1193 | 0.406729 | 0.203364 | − | 0.979103i | \(-0.434812\pi\) | ||||
0.203364 | + | 0.979103i | \(0.434812\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.05497 | −0.322715 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.29150 | −0.331660 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.7589 | 0.867584 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.8188 | −1.70459 | −0.852295 | − | 0.523062i | \(-0.824790\pi\) | ||||
−0.852295 | + | 0.523062i | \(0.824790\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.1620 | −0.562002 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.2710 | −0.605060 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.13646 | 0.242376 | 0.121188 | − | 0.992630i | \(-0.461330\pi\) | ||||
0.121188 | + | 0.992630i | \(0.461330\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.3319 | −1.39336 | −0.696678 | − | 0.717384i | \(-0.745339\pi\) | ||||
−0.696678 | + | 0.717384i | \(0.745339\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.5403 | 0.571640 | 0.285820 | − | 0.958283i | \(-0.407734\pi\) | ||||
0.285820 | + | 0.958283i | \(0.407734\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.1216 | 0.672083 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.3136 | −0.794931 | −0.397466 | − | 0.917617i | \(-0.630110\pi\) | ||||
−0.397466 | + | 0.917617i | \(0.630110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.9110 | −0.856134 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.9605 | −1.12814 | −0.564071 | − | 0.825726i | \(-0.690766\pi\) | ||||
−0.564071 | + | 0.825726i | \(0.690766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1669 | −0.667715 | −0.333857 | − | 0.942624i | \(-0.608350\pi\) | ||||
−0.333857 | + | 0.942624i | \(0.608350\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.14358 | 0.199459 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.44533 | 0.0559635 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.5829 | 1.45087 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.3359 | 0.591154 | 0.295577 | − | 0.955319i | \(-0.404488\pi\) | ||||
0.295577 | + | 0.955319i | \(0.404488\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.79970 | 0.338200 | 0.169100 | − | 0.985599i | \(-0.445914\pi\) | ||||
0.169100 | + | 0.985599i | \(0.445914\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.39481 | −0.283787 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.6861 | −0.638475 | −0.319237 | − | 0.947675i | \(-0.603427\pi\) | ||||
−0.319237 | + | 0.947675i | \(0.603427\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.0138 | −0.993935 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.5890 | 0.746283 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.97154 | −0.113043 | −0.0565214 | − | 0.998401i | \(-0.518001\pi\) | ||||
−0.0565214 | + | 0.998401i | \(0.518001\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.58301 | 0.249708 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8904 | 0.639770 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.8216 | 1.08858 | 0.544289 | − | 0.838898i | \(-0.316799\pi\) | ||||
0.544289 | + | 0.838898i | \(0.316799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.8623 | −0.711406 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.46112 | 0.130169 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.6345 | 1.11295 | 0.556474 | − | 0.830865i | \(-0.312154\pi\) | ||||
0.556474 | + | 0.830865i | \(0.312154\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.44533 | −0.0541281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.9110 | −0.819426 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.0870 | −0.749120 | −0.374560 | − | 0.927203i | \(-0.622206\pi\) | ||||
−0.374560 | + | 0.927203i | \(0.622206\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.51658 | 0.279932 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.31198 | −0.123004 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.8227 | 0.735181 | 0.367591 | − | 0.929988i | \(-0.380183\pi\) | ||||
0.367591 | + | 0.929988i | \(0.380183\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.4070 | −1.49451 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.6343 | −1.61167 | −0.805835 | − | 0.592141i | \(-0.798283\pi\) | ||||
−0.805835 | + | 0.592141i | \(0.798283\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −59.8903 | −2.20609 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.4611 | −1.30446 | −0.652229 | − | 0.758022i | \(-0.726166\pi\) | ||||
−0.652229 | + | 0.758022i | \(0.726166\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.9431 | 0.805014 | 0.402507 | − | 0.915417i | \(-0.368139\pi\) | ||||
0.402507 | + | 0.915417i | \(0.368139\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.7649 | −1.20041 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.6419 | −0.388848 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.6445 | 1.62910 | 0.814550 | − | 0.580093i | \(-0.196984\pi\) | ||||
0.814550 | + | 0.580093i | \(0.196984\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.5407 | 0.601976 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.85346 | −0.0673650 | −0.0336825 | − | 0.999433i | \(-0.510724\pi\) | ||||
−0.0336825 | + | 0.999433i | \(0.510724\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.93345 | −0.0700874 | −0.0350437 | − | 0.999386i | \(-0.511157\pi\) | ||||
−0.0350437 | + | 0.999386i | \(0.511157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.9919 | 0.651350 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.39298 | 0.303053 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 37.8523 | 1.36499 | 0.682495 | − | 0.730890i | \(-0.260895\pi\) | ||||
0.682495 | + | 0.730890i | \(0.260895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.5568 | 0.991148 | 0.495574 | − | 0.868566i | \(-0.334958\pi\) | ||||
0.495574 | + | 0.868566i | \(0.334958\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.31198 | 0.118970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.6419 | −0.524602 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.84002 | −0.137407 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.37433 | −0.263201 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.3380 | −1.01014 | −0.505070 | − | 0.863079i | \(-0.668533\pi\) | ||||
−0.505070 | + | 0.863079i | \(0.668533\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.844342 | 0.0300213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.4230 | 0.654221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.73918 | 0.132449 | 0.0662243 | − | 0.997805i | \(-0.478905\pi\) | ||||
0.0662243 | + | 0.997805i | \(0.478905\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0791033 | −0.00279847 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 60.9027 | 2.14921 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.66401 | −0.0586485 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.0222 | −1.47742 | −0.738711 | − | 0.674023i | \(-0.764565\pi\) | ||||
−0.738711 | + | 0.674023i | \(0.764565\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.8382 | −1.01265 | −0.506323 | − | 0.862344i | \(-0.668996\pi\) | ||||
−0.506323 | + | 0.862344i | \(0.668996\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −33.1414 | −1.16089 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.0280 | 1.22547 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.269195 | 0.00939499 | 0.00469749 | − | 0.999989i | \(-0.498505\pi\) | ||||
0.00469749 | + | 0.999989i | \(0.498505\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.4007 | −1.51285 | −0.756427 | − | 0.654078i | \(-0.773057\pi\) | ||||
−0.756427 | + | 0.654078i | \(0.773057\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.7439 | −1.69499 | −0.847495 | − | 0.530803i | \(-0.821890\pi\) | ||||
−0.847495 | + | 0.530803i | \(0.821890\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.1758 | 1.60375 | 0.801875 | − | 0.597491i | \(-0.203836\pi\) | ||||
0.801875 | + | 0.597491i | \(0.203836\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.3150 | −0.738522 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.6861 | 0.854297 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −54.7571 | −1.89042 | −0.945212 | − | 0.326457i | \(-0.894145\pi\) | ||||
−0.945212 | + | 0.326457i | \(0.894145\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9110 | −0.927966 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.6540 | 0.366510 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.3391 | 0.561418 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.10217 | 0.209180 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.7811 | 1.01968 | 0.509842 | − | 0.860268i | \(-0.329704\pi\) | ||||
0.509842 | + | 0.860268i | \(0.329704\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.42930 | 0.185461 | 0.0927307 | − | 0.995691i | \(-0.470440\pi\) | ||||
0.0927307 | + | 0.995691i | \(0.470440\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.32801 | −0.250029 | −0.125014 | − | 0.992155i | \(-0.539898\pi\) | ||||
−0.125014 | + | 0.992155i | \(0.539898\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.5484 | 0.597354 | 0.298677 | − | 0.954354i | \(-0.403455\pi\) | ||||
0.298677 | + | 0.954354i | \(0.403455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.3540 | 0.352048 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.0506 | 0.374867 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.3581 | −0.994760 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.1331 | 0.410174 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.86062 | 0.0965963 | 0.0482981 | − | 0.998833i | \(-0.484620\pi\) | ||||
0.0482981 | + | 0.998833i | \(0.484620\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −55.1425 | −1.85780 | −0.928899 | − | 0.370334i | \(-0.879243\pi\) | ||||
−0.928899 | + | 0.370334i | \(0.879243\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.8622 | 0.466500 | 0.233250 | − | 0.972417i | \(-0.425064\pi\) | ||||
0.233250 | + | 0.972417i | \(0.425064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.6049 | −0.826153 | −0.413077 | − | 0.910696i | \(-0.635546\pi\) | ||||
−0.413077 | + | 0.910696i | \(0.635546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.70064 | 0.291810 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.0685730 | 0.00229471 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.8116 | −0.896212 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.08898 | −0.0696715 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.3420 | 0.910895 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.6134 | −0.685211 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.2571 | 1.07108 | 0.535540 | − | 0.844510i | \(-0.320108\pi\) | ||||
0.535540 | + | 0.844510i | \(0.320108\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.2041 | −0.868181 | −0.434090 | − | 0.900869i | \(-0.642930\pi\) | ||||
−0.434090 | + | 0.900869i | \(0.642930\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.0059 | 1.58876 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.4614 | 0.444533 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.9584 | −0.922263 | −0.461132 | − | 0.887332i | \(-0.652556\pi\) | ||||
−0.461132 | + | 0.887332i | \(0.652556\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.88237 | −0.0619589 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.9831 | −0.459763 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.7810 | 1.53483 | 0.767417 | − | 0.641149i | \(-0.221542\pi\) | ||||
0.767417 | + | 0.641149i | \(0.221542\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.4775 | 0.605577 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −30.5830 | −1.00017 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.8017 | −0.483550 | −0.241775 | − | 0.970332i | \(-0.577730\pi\) | ||||
−0.241775 | + | 0.970332i | \(0.577730\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.5951 | −0.866976 | −0.433488 | − | 0.901159i | \(-0.642717\pi\) | ||||
−0.433488 | + | 0.901159i | \(0.642717\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.73683 | 0.154253 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 57.0200 | 1.85290 | 0.926451 | − | 0.376415i | \(-0.122843\pi\) | ||||
0.926451 | + | 0.376415i | \(0.122843\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.8543 | 0.969113 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.1266 | 1.17025 | 0.585127 | − | 0.810941i | \(-0.301045\pi\) | ||||
0.585127 | + | 0.810941i | \(0.301045\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.8380 | −0.706661 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.9819 | 0.516084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9110 | −0.932613 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.3498 | −0.397553 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.2470 | 0.329522 | 0.164761 | − | 0.986334i | \(-0.447315\pi\) | ||||
0.164761 | + | 0.986334i | \(0.447315\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.37954 | −0.268912 | −0.134456 | − | 0.990920i | \(-0.542929\pi\) | ||||
−0.134456 | + | 0.990920i | \(0.542929\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.04437 | −0.129656 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.9280 | −1.62933 | −0.814666 | − | 0.579931i | \(-0.803080\pi\) | ||||
−0.814666 | + | 0.579931i | \(0.803080\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.5180 | −1.32692 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.9857 | −0.573654 | −0.286827 | − | 0.957982i | \(-0.592600\pi\) | ||||
−0.286827 | + | 0.957982i | \(0.592600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.54066 | 0.144677 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.3319 | −0.360335 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.0931 | −1.49596 | −0.747980 | − | 0.663721i | \(-0.768976\pi\) | ||||
−0.747980 | + | 0.663721i | \(0.768976\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.1374 | 0.796910 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.4391 | 0.457289 | 0.228645 | − | 0.973510i | \(-0.426571\pi\) | ||||
0.228645 | + | 0.973510i | \(0.426571\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3312.2.a.bh.1.2 | 4 | ||
3.2 | odd | 2 | 3312.2.a.bg.1.4 | 4 | |||
4.3 | odd | 2 | 1656.2.a.p.1.1 | yes | 4 | ||
12.11 | even | 2 | 1656.2.a.o.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1656.2.a.o.1.3 | ✓ | 4 | 12.11 | even | 2 | ||
1656.2.a.p.1.1 | yes | 4 | 4.3 | odd | 2 | ||
3312.2.a.bg.1.4 | 4 | 3.2 | odd | 2 | |||
3312.2.a.bh.1.2 | 4 | 1.1 | even | 1 | trivial |