Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, 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("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 275) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-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 | ||||||||
\(3\) | 0.381966 | 0.220528 | 0.110264 | − | 0.993902i | \(-0.464830\pi\) | ||||
0.110264 | + | 0.993902i | \(0.464830\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.85410 | 1.45671 | 0.728357 | − | 0.685198i | \(-0.240284\pi\) | ||||
0.728357 | + | 0.685198i | \(0.240284\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.76393 | −0.489227 | −0.244613 | − | 0.969621i | \(-0.578661\pi\) | ||||
−0.244613 | + | 0.969621i | \(0.578661\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.61803 | −0.392431 | −0.196215 | − | 0.980561i | \(-0.562865\pi\) | ||||
−0.196215 | + | 0.980561i | \(0.562865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.70820 | −1.53897 | −0.769484 | − | 0.638666i | \(-0.779486\pi\) | ||||
−0.769484 | + | 0.638666i | \(0.779486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.47214 | 0.321246 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.09017 | 1.47840 | 0.739201 | − | 0.673485i | \(-0.235203\pi\) | ||||
0.739201 | + | 0.673485i | \(0.235203\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.61803 | −0.671852 | −0.335926 | − | 0.941888i | \(-0.609049\pi\) | ||||
−0.335926 | + | 0.941888i | \(0.609049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.381966 | −0.0664917 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.76393 | −0.947585 | −0.473792 | − | 0.880637i | \(-0.657115\pi\) | ||||
−0.473792 | + | 0.880637i | \(0.657115\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.673762 | −0.107888 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.94427 | −0.867061 | −0.433531 | − | 0.901139i | \(-0.642732\pi\) | ||||
−0.433531 | + | 0.901139i | \(0.642732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.85410 | 1.12201 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.618034 | −0.0865421 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.32624 | 0.868976 | 0.434488 | − | 0.900678i | \(-0.356929\pi\) | ||||
0.434488 | + | 0.900678i | \(0.356929\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.56231 | −0.339386 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.47214 | −1.23317 | −0.616584 | − | 0.787289i | \(-0.711484\pi\) | ||||
−0.616584 | + | 0.787289i | \(0.711484\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0902 | −1.41995 | −0.709975 | − | 0.704226i | \(-0.751294\pi\) | ||||
−0.709975 | + | 0.704226i | \(0.751294\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.0000 | −1.38587 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | 0.977356 | 0.488678 | − | 0.872464i | \(-0.337479\pi\) | ||||
0.488678 | + | 0.872464i | \(0.337479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.70820 | 0.326029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.1803 | 1.68290 | 0.841448 | − | 0.540338i | \(-0.181703\pi\) | ||||
0.841448 | + | 0.540338i | \(0.181703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.6180 | −1.47683 | −0.738415 | − | 0.674347i | \(-0.764425\pi\) | ||||
−0.738415 | + | 0.674347i | \(0.764425\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.85410 | −0.439216 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.854102 | 0.0960940 | 0.0480470 | − | 0.998845i | \(-0.484700\pi\) | ||||
0.0480470 | + | 0.998845i | \(0.484700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.8541 | −1.84998 | −0.924989 | − | 0.379994i | \(-0.875926\pi\) | ||||
−0.924989 | + | 0.379994i | \(0.875926\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.38197 | −0.148162 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18.0902 | −1.91755 | −0.958777 | − | 0.284159i | \(-0.908286\pi\) | ||||
−0.958777 | + | 0.284159i | \(0.908286\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.79837 | −0.712663 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.14590 | 0.118824 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.618034 | 0.0627518 | 0.0313759 | − | 0.999508i | \(-0.490011\pi\) | ||||
0.0313759 | + | 0.999508i | \(0.490011\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.85410 | 0.286848 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.09017 | 0.506491 | 0.253245 | − | 0.967402i | \(-0.418502\pi\) | ||||
0.253245 | + | 0.967402i | \(0.418502\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.61803 | 0.750627 | 0.375314 | − | 0.926898i | \(-0.377535\pi\) | ||||
0.375314 | + | 0.926898i | \(0.377535\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.236068 | 0.0228216 | 0.0114108 | − | 0.999935i | \(-0.496368\pi\) | ||||
0.0114108 | + | 0.999935i | \(0.496368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.09017 | 0.774898 | 0.387449 | − | 0.921891i | \(-0.373356\pi\) | ||||
0.387449 | + | 0.921891i | \(0.373356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.20163 | −0.208969 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.6525 | −1.84875 | −0.924375 | − | 0.381486i | \(-0.875413\pi\) | ||||
−0.924375 | + | 0.381486i | \(0.875413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.03444 | 0.465434 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.23607 | −0.571659 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.14590 | −0.103322 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.61803 | 0.143577 | 0.0717886 | − | 0.997420i | \(-0.477129\pi\) | ||||
0.0717886 | + | 0.997420i | \(0.477129\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.29180 | −0.201781 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.09017 | 0.0952486 | 0.0476243 | − | 0.998865i | \(-0.484835\pi\) | ||||
0.0476243 | + | 0.998865i | \(0.484835\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.8541 | −2.24183 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.5623 | 1.24414 | 0.622071 | − | 0.782961i | \(-0.286292\pi\) | ||||
0.622071 | + | 0.782961i | \(0.286292\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.7082 | 1.41717 | 0.708586 | − | 0.705625i | \(-0.249334\pi\) | ||||
0.708586 | + | 0.705625i | \(0.249334\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.27051 | −0.191211 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.76393 | 0.147507 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.00000 | 0.247436 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.94427 | 0.732743 | 0.366372 | − | 0.930469i | \(-0.380600\pi\) | ||||
0.366372 | + | 0.930469i | \(0.380600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00000 | 0.244137 | 0.122068 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122068 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.61803 | 0.373346 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.4164 | −1.70922 | −0.854608 | − | 0.519274i | \(-0.826202\pi\) | ||||
−0.854608 | + | 0.519274i | \(0.826202\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.41641 | 0.191634 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.3262 | 2.15361 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.145898 | −0.0114276 | −0.00571381 | − | 0.999984i | \(-0.501819\pi\) | ||||
−0.00571381 | + | 0.999984i | \(0.501819\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.7082 | −1.44768 | −0.723842 | − | 0.689966i | \(-0.757626\pi\) | ||||
−0.723842 | + | 0.689966i | \(0.757626\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.88854 | −0.760657 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.1459 | 1.46412 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.47214 | −0.263982 | −0.131991 | − | 0.991251i | \(-0.542137\pi\) | ||||
−0.131991 | + | 0.991251i | \(0.542137\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.61803 | −0.271948 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.3820 | 0.850728 | 0.425364 | − | 0.905022i | \(-0.360146\pi\) | ||||
0.425364 | + | 0.905022i | \(0.360146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.09017 | 0.378349 | 0.189175 | − | 0.981943i | \(-0.439419\pi\) | ||||
0.189175 | + | 0.981943i | \(0.439419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.23607 | −0.313139 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.61803 | 0.118322 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.61803 | −0.626870 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.90983 | 0.717050 | 0.358525 | − | 0.933520i | \(-0.383280\pi\) | ||||
0.358525 | + | 0.933520i | \(0.383280\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.94427 | 0.355896 | 0.177948 | − | 0.984040i | \(-0.443054\pi\) | ||||
0.177948 | + | 0.984040i | \(0.443054\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.90983 | 0.634799 | 0.317400 | − | 0.948292i | \(-0.397190\pi\) | ||||
0.317400 | + | 0.948292i | \(0.397190\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.09017 | −0.573497 | −0.286748 | − | 0.958006i | \(-0.592574\pi\) | ||||
−0.286748 | + | 0.958006i | \(0.592574\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.05573 | 0.215534 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.9443 | −0.978696 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.2361 | −1.40650 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.70820 | 0.464016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.0000 | −1.17033 | −0.585164 | − | 0.810915i | \(-0.698970\pi\) | ||||
−0.585164 | + | 0.810915i | \(0.698970\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.41641 | 0.371126 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.5623 | 0.784900 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.81966 | −0.325682 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.85410 | 0.191988 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.8885 | −1.26487 | −0.632435 | − | 0.774613i | \(-0.717945\pi\) | ||||
−0.632435 | + | 0.774613i | \(0.717945\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.03444 | 0.334148 | 0.167074 | − | 0.985944i | \(-0.446568\pi\) | ||||
0.167074 | + | 0.985944i | \(0.446568\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.0344 | −1.12567 | −0.562834 | − | 0.826570i | \(-0.690289\pi\) | ||||
−0.562834 | + | 0.826570i | \(0.690289\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.47214 | −0.0968594 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.5066 | 1.47445 | 0.737227 | − | 0.675645i | \(-0.236135\pi\) | ||||
0.737227 | + | 0.675645i | \(0.236135\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.326238 | 0.0211914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.61803 | −0.557454 | −0.278727 | − | 0.960370i | \(-0.589913\pi\) | ||||
−0.278727 | + | 0.960370i | \(0.589913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.2705 | −0.790413 | −0.395207 | − | 0.918592i | \(-0.629327\pi\) | ||||
−0.395207 | + | 0.918592i | \(0.629327\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.65248 | 0.619207 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.8328 | 0.752904 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.43769 | −0.407972 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.27051 | −0.395791 | −0.197896 | − | 0.980223i | \(-0.563411\pi\) | ||||
−0.197896 | + | 0.980223i | \(0.563411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.09017 | −0.445755 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.94427 | −0.433172 | −0.216586 | − | 0.976264i | \(-0.569492\pi\) | ||||
−0.216586 | + | 0.976264i | \(0.569492\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.2148 | −1.38036 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.3262 | 0.639178 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.0000 | −1.29492 | −0.647458 | − | 0.762101i | \(-0.724168\pi\) | ||||
−0.647458 | + | 0.762101i | \(0.724168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.90983 | −0.422875 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.6738 | 0.894675 | 0.447338 | − | 0.894365i | \(-0.352372\pi\) | ||||
0.447338 | + | 0.894365i | \(0.352372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.18034 | 0.557666 | 0.278833 | − | 0.960340i | \(-0.410052\pi\) | ||||
0.278833 | + | 0.960340i | \(0.410052\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.59675 | −0.157162 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.52786 | 0.151885 | 0.0759423 | − | 0.997112i | \(-0.475804\pi\) | ||||
0.0759423 | + | 0.997112i | \(0.475804\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.56231 | −0.512612 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.3607 | 1.15496 | 0.577481 | − | 0.816404i | \(-0.304036\pi\) | ||||
0.577481 | + | 0.816404i | \(0.304036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.61803 | −0.571733 | −0.285866 | − | 0.958269i | \(-0.592281\pi\) | ||||
−0.285866 | + | 0.958269i | \(0.592281\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.5623 | −0.682501 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3820 | −0.845998 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.236068 | 0.0138385 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.8885 | −0.694536 | −0.347268 | − | 0.937766i | \(-0.612891\pi\) | ||||
−0.347268 | + | 0.937766i | \(0.612891\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.23607 | 0.129750 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.5066 | −0.723274 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.1246 | −1.33288 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.94427 | 0.111696 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.4508 | −1.28134 | −0.640669 | − | 0.767817i | \(-0.721343\pi\) | ||||
−0.640669 | + | 0.767817i | \(0.721343\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.90983 | 0.165534 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.18034 | −0.180341 | −0.0901703 | − | 0.995926i | \(-0.528741\pi\) | ||||
−0.0901703 | + | 0.995926i | \(0.528741\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.23607 | −0.0698667 | −0.0349333 | − | 0.999390i | \(-0.511122\pi\) | ||||
−0.0349333 | + | 0.999390i | \(0.511122\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.3820 | −0.807772 | −0.403886 | − | 0.914809i | \(-0.632341\pi\) | ||||
−0.403886 | + | 0.914809i | \(0.632341\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.61803 | 0.202571 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.0901699 | 0.00503280 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.8541 | 0.603938 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.09017 | 0.170887 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.9098 | −1.26306 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.18034 | −0.174807 | −0.0874036 | − | 0.996173i | \(-0.527857\pi\) | ||||
−0.0874036 | + | 0.996173i | \(0.527857\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.4508 | 0.901501 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.4164 | 1.38452 | 0.692260 | − | 0.721648i | \(-0.256615\pi\) | ||||
0.692260 | + | 0.721648i | \(0.256615\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.50658 | −0.407701 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | −0.162459 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.29180 | 0.177740 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.437694 | 0.0234967 | 0.0117483 | − | 0.999931i | \(-0.496260\pi\) | ||||
0.0117483 | + | 0.999931i | \(0.496260\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.8328 | −1.70397 | −0.851986 | − | 0.523565i | \(-0.824602\pi\) | ||||
−0.851986 | + | 0.523565i | \(0.824602\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.94427 | 0.210530 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.3607 | 1.24336 | 0.621682 | − | 0.783270i | \(-0.286450\pi\) | ||||
0.621682 | + | 0.783270i | \(0.286450\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.38197 | −0.126067 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.47214 | −0.236030 | −0.118015 | − | 0.993012i | \(-0.537653\pi\) | ||||
−0.118015 | + | 0.993012i | \(0.537653\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.0000 | 1.36842 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.381966 | 0.0200480 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.8541 | 0.723178 | 0.361589 | − | 0.932338i | \(-0.382234\pi\) | ||||
0.361589 | + | 0.932338i | \(0.382234\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.56231 | 0.445736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.3820 | 1.26585 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.1803 | −1.30379 | −0.651894 | − | 0.758310i | \(-0.726025\pi\) | ||||
−0.651894 | + | 0.758310i | \(0.726025\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.38197 | 0.328688 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2361 | 1.14219 | 0.571095 | − | 0.820884i | \(-0.306519\pi\) | ||||
0.571095 | + | 0.820884i | \(0.306519\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.618034 | 0.0316628 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.9443 | 1.17240 | 0.586199 | − | 0.810167i | \(-0.300624\pi\) | ||||
0.586199 | + | 0.810167i | \(0.300624\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.1246 | 0.870493 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.4721 | 0.733766 | 0.366883 | − | 0.930267i | \(-0.380425\pi\) | ||||
0.366883 | + | 0.930267i | \(0.380425\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.4721 | −0.580171 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.416408 | 0.0210050 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.0902 | −1.30943 | −0.654714 | − | 0.755877i | \(-0.727211\pi\) | ||||
−0.654714 | + | 0.755877i | \(0.727211\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.87539 | −0.494388 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.3607 | −0.517388 | −0.258694 | − | 0.965959i | \(-0.583292\pi\) | ||||
−0.258694 | + | 0.965959i | \(0.583292\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.29180 | −0.263603 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.76393 | 0.285708 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.1246 | −0.995098 | −0.497549 | − | 0.867436i | \(-0.665767\pi\) | ||||
−0.497549 | + | 0.867436i | \(0.665767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.56231 | 0.274368 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.5066 | −1.79637 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.38197 | 0.312526 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.18034 | 0.0576634 | 0.0288317 | − | 0.999584i | \(-0.490821\pi\) | ||||
0.0288317 | + | 0.999584i | \(0.490821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.2705 | 1.03666 | 0.518331 | − | 0.855180i | \(-0.326554\pi\) | ||||
0.518331 | + | 0.855180i | \(0.326554\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.9656 | 0.824894 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.7426 | −2.06846 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.673762 | 0.0325295 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.1803 | −1.11656 | −0.558279 | − | 0.829653i | \(-0.688538\pi\) | ||||
−0.558279 | + | 0.829653i | \(0.688538\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.8885 | −0.811612 | −0.405806 | − | 0.913959i | \(-0.633009\pi\) | ||||
−0.405806 | + | 0.913959i | \(0.633009\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −47.5623 | −2.27521 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.2705 | 1.63564 | 0.817821 | − | 0.575473i | \(-0.195182\pi\) | ||||
0.817821 | + | 0.575473i | \(0.195182\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.4164 | −1.06745 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.34752 | −0.254069 | −0.127034 | − | 0.991898i | \(-0.540546\pi\) | ||||
−0.127034 | + | 0.991898i | \(0.540546\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.41641 | 0.161591 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.326238 | 0.0153961 | 0.00769806 | − | 0.999970i | \(-0.497550\pi\) | ||||
0.00769806 | + | 0.999970i | \(0.497550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00000 | 0.141264 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.14590 | 0.0538390 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −38.9787 | −1.82335 | −0.911674 | − | 0.410915i | \(-0.865209\pi\) | ||||
−0.911674 | + | 0.410915i | \(0.865209\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.61803 | 0.168875 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.1803 | 0.613870 | 0.306935 | − | 0.951731i | \(-0.400697\pi\) | ||||
0.306935 | + | 0.951731i | \(0.400697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.3607 | −1.55040 | −0.775201 | − | 0.631714i | \(-0.782352\pi\) | ||||
−0.775201 | + | 0.631714i | \(0.782352\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.5279 | 1.32011 | 0.660056 | − | 0.751216i | \(-0.270533\pi\) | ||||
0.660056 | + | 0.751216i | \(0.270533\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.8328 | 1.42373 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.18034 | −0.376930 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | 0.275880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.0557 | −0.826715 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.58359 | −0.0723562 | −0.0361781 | − | 0.999345i | \(-0.511518\pi\) | ||||
−0.0361781 | + | 0.999345i | \(0.511518\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.1672 | 0.463584 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.4377 | 0.474932 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.58359 | −0.162388 | −0.0811940 | − | 0.996698i | \(-0.525873\pi\) | ||||
−0.0811940 | + | 0.996698i | \(0.525873\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0557281 | −0.00252011 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.1803 | 1.31689 | 0.658445 | − | 0.752629i | \(-0.271214\pi\) | ||||
0.658445 | + | 0.752629i | \(0.271214\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.85410 | 0.263655 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 54.6525 | 2.45150 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.20163 | −0.232857 | −0.116428 | − | 0.993199i | \(-0.537145\pi\) | ||||
−0.116428 | + | 0.993199i | \(0.537145\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.14590 | −0.319255 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.6525 | 1.09920 | 0.549600 | − | 0.835428i | \(-0.314780\pi\) | ||||
0.549600 | + | 0.835428i | \(0.314780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.77709 | −0.167746 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.6180 | 0.825230 | 0.412615 | − | 0.910906i | \(-0.364616\pi\) | ||||
0.412615 | + | 0.910906i | \(0.364616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.6312 | −2.15132 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.0000 | 0.662266 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.94427 | 0.261429 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.32624 | −0.0582154 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.1803 | −1.05936 | −0.529680 | − | 0.848198i | \(-0.677688\pi\) | ||||
−0.529680 | + | 0.848198i | \(0.677688\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.05573 | 0.221072 | 0.110536 | − | 0.993872i | \(-0.464743\pi\) | ||||
0.110536 | + | 0.993872i | \(0.464743\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.85410 | −0.211448 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.2705 | 1.18567 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.0344 | 1.17319 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.29180 | 0.229213 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.34752 | 0.187610 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.85410 | −0.338300 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.72949 | −0.375310 | −0.187655 | − | 0.982235i | \(-0.560089\pi\) | ||||
−0.187655 | + | 0.982235i | \(0.560089\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.94427 | 0.0834367 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.8541 | −1.19096 | −0.595478 | − | 0.803372i | \(-0.703037\pi\) | ||||
−0.595478 | + | 0.803372i | \(0.703037\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.6525 | 1.35089 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.2705 | 1.03396 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.29180 | 0.139981 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.2361 | 0.603202 | 0.301601 | − | 0.953434i | \(-0.402479\pi\) | ||||
0.301601 | + | 0.953434i | \(0.402479\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.5836 | 0.447638 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.618034 | 0.0260934 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.0344 | 0.675771 | 0.337886 | − | 0.941187i | \(-0.390288\pi\) | ||||
0.337886 | + | 0.941187i | \(0.390288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 29.7082 | 1.24763 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.6180 | 1.19973 | 0.599865 | − | 0.800101i | \(-0.295221\pi\) | ||||
0.599865 | + | 0.800101i | \(0.295221\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.72949 | −0.114226 | −0.0571128 | − | 0.998368i | \(-0.518189\pi\) | ||||
−0.0571128 | + | 0.998368i | \(0.518189\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.78522 | 0.158130 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.56231 | 0.189931 | 0.0949656 | − | 0.995481i | \(-0.469726\pi\) | ||||
0.0949656 | + | 0.995481i | \(0.469726\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.88854 | 0.0784852 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −64.9574 | −2.69489 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.32624 | −0.262006 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.0344 | 1.03328 | 0.516641 | − | 0.856202i | \(-0.327182\pi\) | ||||
0.516641 | + | 0.856202i | \(0.327182\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.1246 | −0.829220 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.40325 | 0.139991 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.00000 | −0.369586 | −0.184793 | − | 0.982777i | \(-0.559161\pi\) | ||||
−0.184793 | + | 0.982777i | \(0.559161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.09017 | −0.126472 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.3262 | 0.626213 | 0.313107 | − | 0.949718i | \(-0.398630\pi\) | ||||
0.313107 | + | 0.949718i | \(0.398630\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2705 | 0.459734 | 0.229867 | − | 0.973222i | \(-0.426171\pi\) | ||||
0.229867 | + | 0.973222i | \(0.426171\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.8328 | −0.929824 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.4721 | 0.506228 | 0.253114 | − | 0.967436i | \(-0.418545\pi\) | ||||
0.253114 | + | 0.967436i | \(0.418545\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.32624 | −0.215830 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.4853 | 0.424189 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.5623 | −1.07284 | −0.536421 | − | 0.843951i | \(-0.680224\pi\) | ||||
−0.536421 | + | 0.843951i | \(0.680224\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.8197 | 0.636876 | 0.318438 | − | 0.947944i | \(-0.396842\pi\) | ||||
0.318438 | + | 0.947944i | \(0.396842\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.8885 | −0.518034 | −0.259017 | − | 0.965873i | \(-0.583399\pi\) | ||||
−0.259017 | + | 0.965873i | \(0.583399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.8541 | −0.636203 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −69.7214 | −2.79333 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.56231 | 0.102329 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.32624 | 0.371861 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.72949 | −0.108659 | −0.0543296 | − | 0.998523i | \(-0.517302\pi\) | ||||
−0.0543296 | + | 0.998523i | \(0.517302\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.49342 | −0.258090 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.8541 | −0.548920 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.4721 | −1.60105 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.00000 | −0.118493 | −0.0592464 | − | 0.998243i | \(-0.518870\pi\) | ||||
−0.0592464 | + | 0.998243i | \(0.518870\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 37.4164 | 1.47556 | 0.737780 | − | 0.675042i | \(-0.235874\pi\) | ||||
0.737780 | + | 0.675042i | \(0.235874\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.6525 | 1.71616 | 0.858078 | − | 0.513519i | \(-0.171659\pi\) | ||||
0.858078 | + | 0.513519i | \(0.171659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.47214 | 0.371814 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.41641 | 0.173093 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.7426 | 1.35958 | 0.679792 | − | 0.733405i | \(-0.262070\pi\) | ||||
0.679792 | + | 0.733405i | \(0.262070\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.0132 | 1.40501 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.2705 | 0.945445 | 0.472722 | − | 0.881211i | \(-0.343271\pi\) | ||||
0.472722 | + | 0.881211i | \(0.343271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.8197 | −1.04316 | −0.521582 | − | 0.853201i | \(-0.674658\pi\) | ||||
−0.521582 | + | 0.853201i | \(0.674658\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.09017 | 0.0423387 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.6525 | −0.993268 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.21478 | −0.278940 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.0902 | 0.428131 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.4164 | 0.941183 | 0.470592 | − | 0.882351i | \(-0.344040\pi\) | ||||
0.470592 | + | 0.882351i | \(0.344040\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.65248 | 0.101943 | 0.0509715 | − | 0.998700i | \(-0.483768\pi\) | ||||
0.0509715 | + | 0.998700i | \(0.483768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.38197 | 0.0914115 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.92299 | 0.0736890 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.36068 | 0.0520650 | 0.0260325 | − | 0.999661i | \(-0.491713\pi\) | ||||
0.0260325 | + | 0.999661i | \(0.491713\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.50658 | −0.248241 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.1591 | −0.425126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.9098 | −0.719364 | −0.359682 | − | 0.933075i | \(-0.617115\pi\) | ||||
−0.359682 | + | 0.933075i | \(0.617115\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.0000 | 0.417855 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.85410 | 0.183862 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.59675 | 0.325159 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.3607 | 1.67548 | 0.837740 | − | 0.546070i | \(-0.183877\pi\) | ||||
0.837740 | + | 0.546070i | \(0.183877\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.6656 | 1.45830 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.6180 | 0.737812 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.3050 | 0.800124 | 0.400062 | − | 0.916488i | \(-0.368989\pi\) | ||||
0.400062 | + | 0.916488i | \(0.368989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.43769 | −0.0914207 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21.2705 | 0.796587 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.29180 | −0.122934 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.6525 | −0.583739 | −0.291869 | − | 0.956458i | \(-0.594277\pi\) | ||||
−0.291869 | + | 0.956458i | \(0.594277\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.3607 | 1.09345 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.68692 | −0.174308 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.72949 | −0.286671 | −0.143335 | − | 0.989674i | \(-0.545783\pi\) | ||||
−0.143335 | + | 0.989674i | \(0.545783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.70820 | 0.359071 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.83282 | 0.289312 | 0.144656 | − | 0.989482i | \(-0.453793\pi\) | ||||
0.144656 | + | 0.989482i | \(0.453793\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.00000 | −0.294684 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.8541 | 1.31891 | 0.659457 | − | 0.751742i | \(-0.270786\pi\) | ||||
0.659457 | + | 0.751742i | \(0.270786\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.51973 | 0.166037 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.3262 | 1.25931 | 0.629654 | − | 0.776876i | \(-0.283197\pi\) | ||||
0.629654 | + | 0.776876i | \(0.283197\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 48.1033 | 1.76001 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.909830 | 0.0332445 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.2705 | 0.812662 | 0.406331 | − | 0.913726i | \(-0.366808\pi\) | ||||
0.406331 | + | 0.913726i | \(0.366808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.39512 | −0.0872831 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.5279 | 0.455333 | 0.227666 | − | 0.973739i | \(-0.426890\pi\) | ||||
0.227666 | + | 0.973739i | \(0.426890\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.70820 | −0.0983016 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.0000 | 0.435000 | 0.217500 | − | 0.976060i | \(-0.430210\pi\) | ||||
0.217500 | + | 0.976060i | \(0.430210\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.1803 | 1.12880 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.7082 | 0.603298 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.65248 | −0.0955266 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.20163 | −0.330959 | −0.165480 | − | 0.986213i | \(-0.552917\pi\) | ||||
−0.165480 | + | 0.986213i | \(0.552917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.48529 | −0.304408 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.1246 | 0.721039 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.1803 | −0.507412 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.09017 | 0.289119 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.7082 | 1.23721 | 0.618607 | − | 0.785701i | \(-0.287697\pi\) | ||||
0.618607 | + | 0.785701i | \(0.287697\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.02129 | −0.285565 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −75.7426 | −2.69310 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.5623 | 0.694678 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.7984 | −0.984669 | −0.492334 | − | 0.870406i | \(-0.663856\pi\) | ||||
−0.492334 | + | 0.870406i | \(0.663856\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.61803 | 0.340262 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 51.6312 | 1.82430 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 12.6180 | 0.445281 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.60488 | 0.197301 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.4164 | −1.52644 | −0.763220 | − | 0.646139i | \(-0.776383\pi\) | ||||
−0.763220 | + | 0.646139i | \(0.776383\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.0000 | −0.596951 | −0.298475 | − | 0.954417i | \(-0.596478\pi\) | ||||
−0.298475 | + | 0.954417i | \(0.596478\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.50658 | 0.122981 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.2492 | 1.40814 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 19.4033 | 0.678005 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −40.3607 | −1.40860 | −0.704299 | − | 0.709904i | \(-0.748738\pi\) | ||||
−0.704299 | + | 0.709904i | \(0.748738\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.583592 | 0.0203427 | 0.0101714 | − | 0.999948i | \(-0.496762\pi\) | ||||
0.0101714 | + | 0.999948i | \(0.496762\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.0689 | −0.906504 | −0.453252 | − | 0.891382i | \(-0.649736\pi\) | ||||
−0.453252 | + | 0.891382i | \(0.649736\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.1033 | 1.77489 | 0.887446 | − | 0.460912i | \(-0.152478\pi\) | ||||
0.887446 | + | 0.460912i | \(0.152478\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.965558 | 0.0334948 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.7082 | −0.440313 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.70820 | −0.231869 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −43.3394 | −1.49624 | −0.748121 | − | 0.663562i | \(-0.769044\pi\) | ||||
−0.748121 | + | 0.663562i | \(0.769044\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9098 | −0.548615 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.39512 | 0.254702 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.85410 | 0.132429 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.67376 | −0.126083 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40.8673 | −1.40091 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −43.1459 | −1.47729 | −0.738644 | − | 0.674096i | \(-0.764533\pi\) | ||||
−0.738644 | + | 0.674096i | \(0.764533\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30.8197 | 1.05278 | 0.526390 | − | 0.850243i | \(-0.323545\pi\) | ||||
0.526390 | + | 0.850243i | \(0.323545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.18034 | 0.210870 | 0.105435 | − | 0.994426i | \(-0.466376\pi\) | ||||
0.105435 | + | 0.994426i | \(0.466376\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.41641 | −0.150511 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48.5967 | 1.65425 | 0.827126 | − | 0.562016i | \(-0.189974\pi\) | ||||
0.827126 | + | 0.562016i | \(0.189974\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.49342 | −0.186566 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.854102 | −0.0289734 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.1115 | −0.478148 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.76393 | −0.0597001 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.4164 | −1.06086 | −0.530428 | − | 0.847730i | \(-0.677969\pi\) | ||||
−0.530428 | + | 0.847730i | \(0.677969\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.54102 | −0.153165 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.09017 | −0.0367288 | −0.0183644 | − | 0.999831i | \(-0.505846\pi\) | ||||
−0.0183644 | + | 0.999831i | \(0.505846\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.347524 | −0.0116951 | −0.00584756 | − | 0.999983i | \(-0.501861\pi\) | ||||
−0.00584756 | + | 0.999983i | \(0.501861\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.7771 | −1.43631 | −0.718157 | − | 0.695881i | \(-0.755014\pi\) | ||||
−0.718157 | + | 0.695881i | \(0.755014\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.23607 | 0.209151 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.70820 | −0.258235 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.8754 | 1.33438 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.77709 | −0.159502 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.8541 | −0.362005 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.2361 | −0.341013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.83282 | −0.293938 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.8328 | −1.28942 | −0.644711 | − | 0.764426i | \(-0.723022\pi\) | ||||
−0.644711 | + | 0.764426i | \(0.723022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.5279 | −0.481859 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.0000 | 0.596367 | 0.298183 | − | 0.954509i | \(-0.403619\pi\) | ||||
0.298183 | + | 0.954509i | \(0.403619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.8541 | 0.557789 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.20163 | 0.138750 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.41641 | 0.112697 | 0.0563484 | − | 0.998411i | \(-0.482054\pi\) | ||||
0.0563484 | + | 0.998411i | \(0.482054\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.57546 | −0.282571 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.0132 | −0.823318 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.7426 | −0.714122 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.40325 | 0.177275 | 0.0886375 | − | 0.996064i | \(-0.471749\pi\) | ||||
0.0886375 | + | 0.996064i | \(0.471749\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −52.6869 | −1.72674 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.21478 | −0.0397702 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.8328 | −0.484567 | −0.242283 | − | 0.970206i | \(-0.577896\pi\) | ||||
−0.242283 | + | 0.970206i | \(0.577896\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.472136 | −0.0154076 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −47.7214 | −1.55567 | −0.777836 | − | 0.628467i | \(-0.783683\pi\) | ||||
−0.777836 | + | 0.628467i | \(0.783683\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.2705 | −0.692663 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.36068 | 0.174199 | 0.0870993 | − | 0.996200i | \(-0.472240\pi\) | ||||
0.0870993 | + | 0.996200i | \(0.472240\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.2574 | 0.722504 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.49342 | −0.178136 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.472136 | 0.0152940 | 0.00764699 | − | 0.999971i | \(-0.497566\pi\) | ||||
0.00764699 | + | 0.999971i | \(0.497566\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.38197 | 0.0446726 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 56.1246 | 1.81236 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.673762 | −0.0217117 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.72949 | 0.119932 | 0.0599662 | − | 0.998200i | \(-0.480901\pi\) | ||||
0.0599662 | + | 0.998200i | \(0.480901\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.14590 | 0.133185 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.0902 | −1.12610 | −0.563049 | − | 0.826424i | \(-0.690372\pi\) | ||||
−0.563049 | + | 0.826424i | \(0.690372\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 64.3951 | 2.06441 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.06888 | 0.0341966 | 0.0170983 | − | 0.999854i | \(-0.494557\pi\) | ||||
0.0170983 | + | 0.999854i | \(0.494557\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0902 | 0.578164 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.0902 | −0.737212 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.4721 | −0.334009 | −0.167005 | − | 0.985956i | \(-0.553409\pi\) | ||||
−0.167005 | + | 0.985956i | \(0.553409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.75078 | −0.278540 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −42.5410 | −1.35273 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.2705 | 0.389786 | 0.194893 | − | 0.980825i | \(-0.437564\pi\) | ||||
0.194893 | + | 0.980825i | \(0.437564\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.21478 | −0.0385499 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.8541 | −1.23052 | −0.615261 | − | 0.788324i | \(-0.710949\pi\) | ||||
−0.615261 | + | 0.788324i | \(0.710949\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.8885 | 0.407775 |
(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 | 4400.2.a.bv.1.1 | 2 | ||
4.3 | odd | 2 | 275.2.a.d.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 4400.2.b.x.4049.2 | 4 | |||
5.3 | odd | 4 | 4400.2.b.x.4049.3 | 4 | |||
5.4 | even | 2 | 4400.2.a.bg.1.2 | 2 | |||
12.11 | even | 2 | 2475.2.a.s.1.1 | 2 | |||
20.3 | even | 4 | 275.2.b.e.199.2 | 4 | |||
20.7 | even | 4 | 275.2.b.e.199.3 | 4 | |||
20.19 | odd | 2 | 275.2.a.g.1.1 | yes | 2 | ||
44.43 | even | 2 | 3025.2.a.m.1.1 | 2 | |||
60.23 | odd | 4 | 2475.2.c.p.199.3 | 4 | |||
60.47 | odd | 4 | 2475.2.c.p.199.2 | 4 | |||
60.59 | even | 2 | 2475.2.a.n.1.2 | 2 | |||
220.219 | even | 2 | 3025.2.a.i.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
275.2.a.d.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
275.2.a.g.1.1 | yes | 2 | 20.19 | odd | 2 | ||
275.2.b.e.199.2 | 4 | 20.3 | even | 4 | |||
275.2.b.e.199.3 | 4 | 20.7 | even | 4 | |||
2475.2.a.n.1.2 | 2 | 60.59 | even | 2 | |||
2475.2.a.s.1.1 | 2 | 12.11 | even | 2 | |||
2475.2.c.p.199.2 | 4 | 60.47 | odd | 4 | |||
2475.2.c.p.199.3 | 4 | 60.23 | odd | 4 | |||
3025.2.a.i.1.2 | 2 | 220.219 | even | 2 | |||
3025.2.a.m.1.1 | 2 | 44.43 | even | 2 | |||
4400.2.a.bg.1.2 | 2 | 5.4 | even | 2 | |||
4400.2.a.bv.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4400.2.b.x.4049.2 | 4 | 5.2 | odd | 4 | |||
4400.2.b.x.4049.3 | 4 | 5.3 | odd | 4 |