Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(1,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, 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("3420.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.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: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1140) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.60555 | 1.74073 | 0.870367 | − | 0.492403i | \(-0.163881\pi\) | ||||
0.870367 | + | 0.492403i | \(0.163881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.60555 | −0.785603 | −0.392802 | − | 0.919623i | \(-0.628494\pi\) | ||||
−0.392802 | + | 0.919623i | \(0.628494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.60555 | −0.722650 | −0.361325 | − | 0.932440i | \(-0.617675\pi\) | ||||
−0.361325 | + | 0.932440i | \(0.617675\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.60555 | 0.855229 | 0.427615 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427615 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.60555 | 0.778480 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6056 | 1.74354 | 0.871771 | − | 0.489914i | \(-0.162972\pi\) | ||||
0.871771 | + | 0.489914i | \(0.162972\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.605551 | 0.0945712 | 0.0472856 | − | 0.998881i | \(-0.484943\pi\) | ||||
0.0472856 | + | 0.998881i | \(0.484943\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.39445 | 0.517649 | 0.258824 | − | 0.965924i | \(-0.416665\pi\) | ||||
0.258824 | + | 0.965924i | \(0.416665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.2111 | 2.03016 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.60555 | −0.351332 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.21110 | 1.19918 | 0.599592 | − | 0.800306i | \(-0.295330\pi\) | ||||
0.599592 | + | 0.800306i | \(0.295330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.21110 | 0.923287 | 0.461644 | − | 0.887066i | \(-0.347260\pi\) | ||||
0.461644 | + | 0.887066i | \(0.347260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.60555 | −0.323179 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.21110 | −0.618444 | −0.309222 | − | 0.950990i | \(-0.600069\pi\) | ||||
−0.309222 | + | 0.950990i | \(0.600069\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | 0.702247 | 0.351123 | − | 0.936329i | \(-0.385800\pi\) | ||||
0.351123 | + | 0.936329i | \(0.385800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.21110 | −0.352464 | −0.176232 | − | 0.984349i | \(-0.556391\pi\) | ||||
−0.176232 | + | 0.984349i | \(0.556391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.605551 | 0.0641883 | 0.0320942 | − | 0.999485i | \(-0.489782\pi\) | ||||
0.0320942 | + | 0.999485i | \(0.489782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.39445 | 0.953862 | 0.476931 | − | 0.878941i | \(-0.341749\pi\) | ||||
0.476931 | + | 0.878941i | \(0.341749\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.21110 | −0.717532 | −0.358766 | − | 0.933428i | \(-0.616802\pi\) | ||||
−0.358766 | + | 0.933428i | \(0.616802\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.4222 | −1.02693 | −0.513465 | − | 0.858110i | \(-0.671638\pi\) | ||||
−0.513465 | + | 0.858110i | \(0.671638\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.4222 | 1.00755 | 0.503776 | − | 0.863834i | \(-0.331944\pi\) | ||||
0.503776 | + | 0.863834i | \(0.331944\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.21110 | 0.307568 | 0.153784 | − | 0.988105i | \(-0.450854\pi\) | ||||
0.153784 | + | 0.988105i | \(0.450854\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.2111 | −1.24280 | −0.621398 | − | 0.783495i | \(-0.713435\pi\) | ||||
−0.621398 | + | 0.783495i | \(0.713435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.21110 | −0.844380 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.21110 | −0.382828 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.4222 | −0.924821 | −0.462411 | − | 0.886666i | \(-0.653015\pi\) | ||||
−0.462411 | + | 0.886666i | \(0.653015\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.6056 | 1.97506 | 0.987528 | − | 0.157443i | \(-0.0503250\pi\) | ||||
0.987528 | + | 0.157443i | \(0.0503250\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.60555 | −0.399352 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.4222 | −1.40304 | −0.701522 | − | 0.712648i | \(-0.747496\pi\) | ||||
−0.701522 | + | 0.712648i | \(0.747496\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.21110 | −0.442000 | −0.221000 | − | 0.975274i | \(-0.570932\pi\) | ||||
−0.221000 | + | 0.975274i | \(0.570932\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.78890 | 0.567716 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.60555 | 0.382470 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4222 | 1.01767 | 0.508833 | − | 0.860865i | \(-0.330077\pi\) | ||||
0.508833 | + | 0.860865i | \(0.330077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.788897 | 0.0629609 | 0.0314804 | − | 0.999504i | \(-0.489978\pi\) | ||||
0.0314804 | + | 0.999504i | \(0.489978\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.21110 | 0.725937 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.0278 | 1.49037 | 0.745184 | − | 0.666858i | \(-0.232361\pi\) | ||||
0.745184 | + | 0.666858i | \(0.232361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.2111 | 1.64136 | 0.820682 | − | 0.571385i | \(-0.193594\pi\) | ||||
0.820682 | + | 0.571385i | \(0.193594\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.21110 | −0.477777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.21110 | −0.396193 | −0.198096 | − | 0.980183i | \(-0.563476\pi\) | ||||
−0.198096 | + | 0.980183i | \(0.563476\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.60555 | 0.348147 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.78890 | 0.507426 | 0.253713 | − | 0.967280i | \(-0.418348\pi\) | ||||
0.253713 | + | 0.967280i | \(0.418348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.2111 | −1.13063 | −0.565316 | − | 0.824874i | \(-0.691246\pi\) | ||||
−0.565316 | + | 0.824874i | \(0.691246\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.6056 | 0.779736 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.21110 | 0.381074 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.8167 | −1.14445 | −0.572226 | − | 0.820096i | \(-0.693920\pi\) | ||||
−0.572226 | + | 0.820096i | \(0.693920\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.60555 | 0.475478 | 0.237739 | − | 0.971329i | \(-0.423594\pi\) | ||||
0.237739 | + | 0.971329i | \(0.423594\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.0000 | −0.997459 | −0.498729 | − | 0.866758i | \(-0.666200\pi\) | ||||
−0.498729 | + | 0.866758i | \(0.666200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.78890 | 0.197700 | 0.0988498 | − | 0.995102i | \(-0.468484\pi\) | ||||
0.0988498 | + | 0.995102i | \(0.468484\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.2111 | 1.48873 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.605551 | 0.0422935 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.60555 | 0.180230 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.39445 | 0.231499 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.4222 | 1.25058 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.21110 | 0.350537 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.4222 | 1.23364 | 0.616821 | − | 0.787103i | \(-0.288420\pi\) | ||||
0.616821 | + | 0.787103i | \(0.288420\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.21110 | −0.0803837 | −0.0401918 | − | 0.999192i | \(-0.512797\pi\) | ||||
−0.0401918 | + | 0.999192i | \(0.512797\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.2111 | 0.740851 | 0.370425 | − | 0.928862i | \(-0.379212\pi\) | ||||
0.370425 | + | 0.928862i | \(0.379212\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.4222 | −0.813806 | −0.406903 | − | 0.913471i | \(-0.633391\pi\) | ||||
−0.406903 | + | 0.913471i | \(0.633391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.18335 | −0.270598 | −0.135299 | − | 0.990805i | \(-0.543200\pi\) | ||||
−0.135299 | + | 0.990805i | \(0.543200\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.2111 | 0.907914 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.60555 | 0.165787 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.8167 | 1.75577 | 0.877886 | − | 0.478870i | \(-0.158953\pi\) | ||||
0.877886 | + | 0.478870i | \(0.158953\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.21110 | −0.327619 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.2111 | −1.07360 | −0.536800 | − | 0.843710i | \(-0.680367\pi\) | ||||
−0.536800 | + | 0.843710i | \(0.680367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 48.8444 | 3.03504 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.21110 | 0.444656 | 0.222328 | − | 0.974972i | \(-0.428634\pi\) | ||||
0.222328 | + | 0.974972i | \(0.428634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.6056 | 1.50023 | 0.750113 | − | 0.661309i | \(-0.229999\pi\) | ||||
0.750113 | + | 0.661309i | \(0.229999\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.6333 | −1.92159 | −0.960793 | − | 0.277266i | \(-0.910572\pi\) | ||||
−0.960793 | + | 0.277266i | \(0.910572\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.60555 | −0.157121 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.2389 | 1.92321 | 0.961605 | − | 0.274439i | \(-0.0884921\pi\) | ||||
0.961605 | + | 0.274439i | \(0.0884921\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.3944 | −0.677330 | −0.338665 | − | 0.940907i | \(-0.609975\pi\) | ||||
−0.338665 | + | 0.940907i | \(0.609975\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.78890 | 0.164623 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.6333 | 1.38067 | 0.690336 | − | 0.723489i | \(-0.257463\pi\) | ||||
0.690336 | + | 0.723489i | \(0.257463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.21110 | 0.536291 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.21110 | −0.301366 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6333 | 0.901089 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.21110 | 0.412907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.6333 | 1.80541 | 0.902704 | − | 0.430262i | \(-0.141579\pi\) | ||||
0.902704 | + | 0.430262i | \(0.141579\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.39445 | −0.532710 | −0.266355 | − | 0.963875i | \(-0.585819\pi\) | ||||
−0.266355 | + | 0.963875i | \(0.585819\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.2111 | 0.859782 | 0.429891 | − | 0.902881i | \(-0.358552\pi\) | ||||
0.429891 | + | 0.902881i | \(0.358552\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.4222 | −1.25936 | −0.629678 | − | 0.776856i | \(-0.716813\pi\) | ||||
−0.629678 | + | 0.776856i | \(0.716813\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | 0.111283 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.60555 | −0.144530 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.6333 | −1.52347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.0278 | −1.79914 | −0.899568 | − | 0.436780i | \(-0.856119\pi\) | ||||
−0.899568 | + | 0.436780i | \(0.856119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.4222 | −0.564394 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 33.2111 | 1.79323 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.6333 | 1.16134 | 0.580668 | − | 0.814140i | \(-0.302791\pi\) | ||||
0.580668 | + | 0.814140i | \(0.302791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.8444 | −1.22283 | −0.611417 | − | 0.791309i | \(-0.709400\pi\) | ||||
−0.611417 | + | 0.791309i | \(0.709400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.4222 | 1.51276 | 0.756381 | − | 0.654132i | \(-0.226966\pi\) | ||||
0.756381 | + | 0.654132i | \(0.226966\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.21110 | −0.276577 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.81665 | −0.412547 | −0.206274 | − | 0.978494i | \(-0.566134\pi\) | ||||
−0.206274 | + | 0.978494i | \(0.566134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0278 | −0.575644 | −0.287822 | − | 0.957684i | \(-0.592931\pi\) | ||||
−0.287822 | + | 0.957684i | \(0.592931\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.39445 | 0.486426 | 0.243213 | − | 0.969973i | \(-0.421799\pi\) | ||||
0.243213 | + | 0.969973i | \(0.421799\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.0000 | −0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.42221 | −0.124420 | −0.0622102 | − | 0.998063i | \(-0.519815\pi\) | ||||
−0.0622102 | + | 0.998063i | \(0.519815\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | 0.613171 | 0.306586 | − | 0.951843i | \(-0.400813\pi\) | ||||
0.306586 | + | 0.951843i | \(0.400813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | −0.611577 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.57779 | −0.384209 | −0.192105 | − | 0.981374i | \(-0.561531\pi\) | ||||
−0.192105 | + | 0.981374i | \(0.561531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.4222 | −1.82798 | −0.913989 | − | 0.405739i | \(-0.867014\pi\) | ||||
−0.913989 | + | 0.405739i | \(0.867014\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.6056 | −1.62824 | −0.814122 | − | 0.580694i | \(-0.802781\pi\) | ||||
−0.814122 | + | 0.580694i | \(0.802781\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.4222 | −0.519167 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.6333 | −1.36973 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.2111 | −1.34550 | −0.672751 | − | 0.739869i | \(-0.734888\pi\) | ||||
−0.672751 | + | 0.739869i | \(0.734888\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 42.4222 | 2.08746 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.21110 | −0.157627 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.0278 | −1.41810 | −0.709049 | − | 0.705159i | \(-0.750876\pi\) | ||||
−0.709049 | + | 0.705159i | \(0.750876\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.4222 | 0.995317 | 0.497659 | − | 0.867373i | \(-0.334193\pi\) | ||||
0.497659 | + | 0.867373i | \(0.334193\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | −0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.2111 | 1.60720 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.21110 | −0.251010 | −0.125505 | − | 0.992093i | \(-0.540055\pi\) | ||||
−0.125505 | + | 0.992093i | \(0.540055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.39445 | −0.451468 | −0.225734 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225734 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.00000 | −0.0956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.57779 | 0.266214 | 0.133107 | − | 0.991102i | \(-0.457505\pi\) | ||||
0.133107 | + | 0.991102i | \(0.457505\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.8444 | 1.84555 | 0.922777 | − | 0.385335i | \(-0.125914\pi\) | ||||
0.922777 | + | 0.385335i | \(0.125914\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.605551 | 0.0287059 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.2389 | −1.52145 | −0.760723 | − | 0.649077i | \(-0.775155\pi\) | ||||
−0.760723 | + | 0.649077i | \(0.775155\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.57779 | −0.0742955 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | −0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −40.0555 | −1.87372 | −0.936859 | − | 0.349708i | \(-0.886281\pi\) | ||||
−0.936859 | + | 0.349708i | \(0.886281\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.8444 | −1.62287 | −0.811433 | − | 0.584445i | \(-0.801312\pi\) | ||||
−0.811433 | + | 0.584445i | \(0.801312\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.02776 | −0.140712 | −0.0703559 | − | 0.997522i | \(-0.522413\pi\) | ||||
−0.0703559 | + | 0.997522i | \(0.522413\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.8444 | 1.61241 | 0.806204 | − | 0.591638i | \(-0.201519\pi\) | ||||
0.806204 | + | 0.591638i | \(0.201519\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.4222 | 0.850658 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.84441 | −0.406666 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.3944 | −0.977537 | −0.488769 | − | 0.872413i | \(-0.662554\pi\) | ||||
−0.488769 | + | 0.872413i | \(0.662554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.6333 | −1.25997 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.39445 | 0.426580 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 43.6333 | 1.97721 | 0.988607 | − | 0.150520i | \(-0.0480948\pi\) | ||||
0.988607 | + | 0.150520i | \(0.0480948\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.2389 | −1.72570 | −0.862848 | − | 0.505464i | \(-0.831321\pi\) | ||||
−0.862848 | + | 0.505464i | \(0.831321\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.21110 | −0.414847 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.0000 | −1.07655 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.6333 | 0.699843 | 0.349921 | − | 0.936779i | \(-0.386208\pi\) | ||||
0.349921 | + | 0.936779i | \(0.386208\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.2111 | −1.21328 | −0.606642 | − | 0.794975i | \(-0.707484\pi\) | ||||
−0.606642 | + | 0.794975i | \(0.707484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.21110 | −0.320890 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.4500 | −1.30535 | −0.652673 | − | 0.757639i | \(-0.726353\pi\) | ||||
−0.652673 | + | 0.757639i | \(0.726353\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.6333 | 1.22243 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.4222 | −0.459257 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.6333 | 0.687552 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.8167 | 1.13105 | 0.565524 | − | 0.824732i | \(-0.308674\pi\) | ||||
0.565524 | + | 0.824732i | \(0.308674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.7889 | −0.471766 | −0.235883 | − | 0.971782i | \(-0.575798\pi\) | ||||
−0.235883 | + | 0.971782i | \(0.575798\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | −0.348485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.57779 | −0.0683419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.4222 | 0.450591 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.0278 | −1.59490 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.21110 | 0.137549 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.2111 | −1.59103 | −0.795516 | − | 0.605933i | \(-0.792800\pi\) | ||||
−0.795516 | + | 0.605933i | \(0.792800\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.60555 | −0.196203 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.8444 | 1.56678 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.4222 | −1.03480 | −0.517401 | − | 0.855743i | \(-0.673100\pi\) | ||||
−0.517401 | + | 0.855743i | \(0.673100\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.84441 | −0.374079 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.6333 | 0.490285 | 0.245143 | − | 0.969487i | \(-0.421165\pi\) | ||||
0.245143 | + | 0.969487i | \(0.421165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.2111 | −0.555795 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.4500 | 1.06692 | 0.533459 | − | 0.845826i | \(-0.320892\pi\) | ||||
0.533459 | + | 0.845826i | \(0.320892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.6333 | −1.49121 | −0.745604 | − | 0.666390i | \(-0.767839\pi\) | ||||
−0.745604 | + | 0.666390i | \(0.767839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.00000 | 0.0834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.78890 | −0.365887 | −0.182943 | − | 0.983123i | \(-0.558562\pi\) | ||||
−0.182943 | + | 0.983123i | \(0.558562\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.7889 | −0.613547 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.4222 | 0.677817 | 0.338908 | − | 0.940819i | \(-0.389942\pi\) | ||||
0.338908 | + | 0.940819i | \(0.389942\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.4222 | 1.33142 | 0.665710 | − | 0.746210i | \(-0.268129\pi\) | ||||
0.665710 | + | 0.746210i | \(0.268129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.21110 | −0.377618 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.8444 | 0.851680 | 0.425840 | − | 0.904799i | \(-0.359979\pi\) | ||||
0.425840 | + | 0.904799i | \(0.359979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2111 | 0.783637 | 0.391819 | − | 0.920042i | \(-0.371846\pi\) | ||||
0.391819 | + | 0.920042i | \(0.371846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.21110 | −0.171206 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.6333 | 0.796891 | 0.398446 | − | 0.917192i | \(-0.369550\pi\) | ||||
0.398446 | + | 0.917192i | \(0.369550\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.6333 | 0.632456 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2111 | 0.775929 | 0.387965 | − | 0.921674i | \(-0.373178\pi\) | ||||
0.387965 | + | 0.921674i | \(0.373178\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.0000 | −1.36879 | −0.684394 | − | 0.729112i | \(-0.739933\pi\) | ||||
−0.684394 | + | 0.729112i | \(0.739933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.6333 | −1.91454 | −0.957272 | − | 0.289189i | \(-0.906615\pi\) | ||||
−0.957272 | + | 0.289189i | \(0.906615\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.78890 | 0.111735 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.2111 | −0.845742 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.8444 | −0.829803 | −0.414901 | − | 0.909866i | \(-0.636184\pi\) | ||||
−0.414901 | + | 0.909866i | \(0.636184\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.4222 | −0.413593 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.0278 | −1.46709 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.4500 | 1.16320 | 0.581602 | − | 0.813474i | \(-0.302426\pi\) | ||||
0.581602 | + | 0.813474i | \(0.302426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.6056 | 0.497114 | 0.248557 | − | 0.968617i | \(-0.420044\pi\) | ||||
0.248557 | + | 0.968617i | \(0.420044\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.6333 | 1.79403 | 0.897015 | − | 0.442000i | \(-0.145731\pi\) | ||||
0.897015 | + | 0.442000i | \(0.145731\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −42.0000 | −1.64359 | −0.821794 | − | 0.569785i | \(-0.807026\pi\) | ||||
−0.821794 | + | 0.569785i | \(0.807026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.6056 | 0.883272 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7889 | −0.653012 | −0.326506 | − | 0.945195i | \(-0.605871\pi\) | ||||
−0.326506 | + | 0.945195i | \(0.605871\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.60555 | −0.178596 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.21110 | 0.356655 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.7889 | −0.725337 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.3944 | 1.13307 | 0.566536 | − | 0.824037i | \(-0.308283\pi\) | ||||
0.566536 | + | 0.824037i | \(0.308283\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.4222 | 0.708023 | 0.354011 | − | 0.935241i | \(-0.384817\pi\) | ||||
0.354011 | + | 0.935241i | \(0.384817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 43.2666 | 1.66042 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.0000 | 1.83667 | 0.918334 | − | 0.395805i | \(-0.129534\pi\) | ||||
0.918334 | + | 0.395805i | \(0.129534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.4222 | −0.627460 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0555 | 1.14337 | 0.571683 | − | 0.820475i | \(-0.306291\pi\) | ||||
0.571683 | + | 0.820475i | \(0.306291\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.21110 | −0.197668 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.21110 | −0.0458738 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6056 | −0.399996 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.2111 | −1.24903 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.6333 | 0.662233 | 0.331116 | − | 0.943590i | \(-0.392575\pi\) | ||||
0.331116 | + | 0.943590i | \(0.392575\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.00000 | 0.299602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.78890 | 0.253890 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.2389 | 1.27689 | 0.638447 | − | 0.769666i | \(-0.279577\pi\) | ||||
0.638447 | + | 0.769666i | \(0.279577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.0000 | −1.78761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.60555 | 0.171046 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.6056 | −0.912569 | −0.456285 | − | 0.889834i | \(-0.650820\pi\) | ||||
−0.456285 | + | 0.889834i | \(0.650820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.78890 | −0.251096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.42221 | 0.163338 | 0.0816689 | − | 0.996660i | \(-0.473975\pi\) | ||||
0.0816689 | + | 0.996660i | \(0.473975\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.4222 | −0.383907 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.57779 | 0.352325 | 0.176162 | − | 0.984361i | \(-0.443632\pi\) | ||||
0.176162 | + | 0.984361i | \(0.443632\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.0000 | 0.733729 | 0.366864 | − | 0.930274i | \(-0.380431\pi\) | ||||
0.366864 | + | 0.930274i | \(0.380431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4222 | 0.455114 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.0000 | 1.75388 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8444 | −0.614661 | −0.307331 | − | 0.951603i | \(-0.599436\pi\) | ||||
−0.307331 | + | 0.951603i | \(0.599436\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | −0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.0555 | 1.31046 | 0.655230 | − | 0.755429i | \(-0.272572\pi\) | ||||
0.655230 | + | 0.755429i | \(0.272572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.7889 | 0.535394 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −24.0000 | −0.866590 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.42221 | 0.303712 | 0.151856 | − | 0.988403i | \(-0.451475\pi\) | ||||
0.151856 | + | 0.988403i | \(0.451475\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −43.2666 | −1.55619 | −0.778096 | − | 0.628145i | \(-0.783814\pi\) | ||||
−0.778096 | + | 0.628145i | \(0.783814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00000 | 0.143684 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.605551 | −0.0216961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.5778 | 0.485852 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.788897 | 0.0281570 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.6333 | 0.842436 | 0.421218 | − | 0.906959i | \(-0.361603\pi\) | ||||
0.421218 | + | 0.906959i | \(0.361603\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −60.8444 | −2.16338 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.7889 | −0.667213 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.78890 | −0.0987878 | −0.0493939 | − | 0.998779i | \(-0.515729\pi\) | ||||
−0.0493939 | + | 0.998779i | \(0.515729\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.6333 | −0.551687 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.21110 | 0.324649 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5778 | 0.688319 | 0.344159 | − | 0.938911i | \(-0.388164\pi\) | ||||
0.344159 | + | 0.938911i | \(0.388164\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.8444 | 0.591487 | 0.295744 | − | 0.955267i | \(-0.404433\pi\) | ||||
0.295744 | + | 0.955267i | \(0.404433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.0278 | 0.666513 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.39445 | −0.118757 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.7889 | −1.00474 | −0.502370 | − | 0.864653i | \(-0.667538\pi\) | ||||
−0.502370 | + | 0.864653i | \(0.667538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.1833 | −0.912694 | −0.456347 | − | 0.889802i | \(-0.650842\pi\) | ||||
−0.456347 | + | 0.889802i | \(0.650842\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.6333 | −0.543623 | −0.271812 | − | 0.962350i | \(-0.587623\pi\) | ||||
−0.271812 | + | 0.962350i | \(0.587623\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.788897 | 0.0273995 | 0.0136998 | − | 0.999906i | \(-0.495639\pi\) | ||||
0.0136998 | + | 0.999906i | \(0.495639\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.4222 | −0.984771 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.2111 | 0.734040 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.6333 | 0.539722 | 0.269861 | − | 0.962899i | \(-0.413022\pi\) | ||||
0.269861 | + | 0.962899i | \(0.413022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.21110 | −0.213668 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −19.3944 | −0.666401 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.2111 | 0.727107 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.6333 | −0.466796 | −0.233398 | − | 0.972381i | \(-0.574984\pi\) | ||||
−0.233398 | + | 0.972381i | \(0.574984\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.4222 | 0.765928 | 0.382964 | − | 0.923763i | \(-0.374903\pi\) | ||||
0.382964 | + | 0.923763i | \(0.374903\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.8444 | −1.66655 | −0.833275 | − | 0.552859i | \(-0.813537\pi\) | ||||
−0.833275 | + | 0.552859i | \(0.813537\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.4222 | 0.763261 | 0.381630 | − | 0.924315i | \(-0.375363\pi\) | ||||
0.381630 | + | 0.924315i | \(0.375363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.21110 | −0.177183 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.8444 | −0.707098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.4222 | −0.353143 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.60555 | 0.155696 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.02776 | −0.304846 | −0.152423 | − | 0.988315i | \(-0.548708\pi\) | ||||
−0.152423 | + | 0.988315i | \(0.548708\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44.7889 | −1.50898 | −0.754488 | − | 0.656314i | \(-0.772115\pi\) | ||||
−0.754488 | + | 0.656314i | \(0.772115\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.18335 | 0.208086 | 0.104043 | − | 0.994573i | \(-0.466822\pi\) | ||||
0.104043 | + | 0.994573i | \(0.466822\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.8444 | −1.23711 | −0.618557 | − | 0.785740i | \(-0.712282\pi\) | ||||
−0.618557 | + | 0.785740i | \(0.712282\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.0000 | −1.60987 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.00000 | 0.200782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.78890 | 0.226928 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.4222 | 0.614415 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.2111 | −0.505634 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.0555 | −1.39643 | −0.698215 | − | 0.715888i | \(-0.746022\pi\) | ||||
−0.698215 | + | 0.715888i | \(0.746022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.4222 | 0.610355 | 0.305177 | − | 0.952296i | \(-0.401284\pi\) | ||||
0.305177 | + | 0.952296i | \(0.401284\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.36669 | 0.276897 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 104.111 | 3.43805 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.5778 | 0.446919 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.6056 | 0.348708 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.36669 | 0.0776487 | 0.0388243 | − | 0.999246i | \(-0.487639\pi\) | ||||
0.0388243 | + | 0.999246i | \(0.487639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.2111 | −0.465750 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.21110 | 0.170421 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.78890 | −0.156446 | −0.0782232 | − | 0.996936i | \(-0.524925\pi\) | ||||
−0.0782232 | + | 0.996936i | \(0.524925\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.2389 | −0.659768 | −0.329884 | − | 0.944021i | \(-0.607010\pi\) | ||||
−0.329884 | + | 0.944021i | \(0.607010\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.21110 | 0.0394389 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.21110 | −0.234329 | −0.117165 | − | 0.993113i | \(-0.537381\pi\) | ||||
−0.117165 | + | 0.993113i | \(0.537381\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.6333 | −0.507479 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.21110 | 0.298377 | 0.149188 | − | 0.988809i | \(-0.452334\pi\) | ||||
0.149188 | + | 0.988809i | \(0.452334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.8167 | −0.511815 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −75.6333 | −2.44233 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.60555 | 0.212640 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2389 | 0.779469 | 0.389735 | − | 0.920927i | \(-0.372567\pi\) | ||||
0.389735 | + | 0.920927i | \(0.372567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.0000 | −0.769405 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.4222 | 0.717350 | 0.358675 | − | 0.933463i | \(-0.383229\pi\) | ||||
0.358675 | + | 0.933463i | \(0.383229\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.57779 | −0.0504265 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.21110 | −0.166208 | −0.0831042 | − | 0.996541i | \(-0.526483\pi\) | ||||
−0.0831042 | + | 0.996541i | \(0.526483\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.0000 | −0.446077 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.78890 | 0.215874 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5778 | 0.685441 | 0.342721 | − | 0.939437i | \(-0.388652\pi\) | ||||
0.342721 | + | 0.939437i | \(0.388652\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.78890 | 0.0884140 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.3667 | −0.581679 | −0.290839 | − | 0.956772i | \(-0.593935\pi\) | ||||
−0.290839 | + | 0.956772i | \(0.593935\pi\) | |||||||
\(998\) | 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 | 3420.2.a.i.1.2 | 2 | ||
3.2 | odd | 2 | 1140.2.a.e.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 4560.2.a.bl.1.1 | 2 | |||
15.2 | even | 4 | 5700.2.f.n.3649.4 | 4 | |||
15.8 | even | 4 | 5700.2.f.n.3649.1 | 4 | |||
15.14 | odd | 2 | 5700.2.a.u.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.a.e.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
3420.2.a.i.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4560.2.a.bl.1.1 | 2 | 12.11 | even | 2 | |||
5700.2.a.u.1.1 | 2 | 15.14 | odd | 2 | |||
5700.2.f.n.3649.1 | 4 | 15.8 | even | 4 | |||
5700.2.f.n.3649.4 | 4 | 15.2 | even | 4 |