Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.143376304.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 12x^{4} + 22x^{2} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.65047\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | −2.80150 | −1.61745 | −0.808725 | − | 0.588187i | \(-0.799842\pi\) | ||||
−0.808725 | + | 0.588187i | \(0.799842\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.50896 | −1.70423 | −0.852113 | − | 0.523357i | \(-0.824679\pi\) | ||||
−0.852113 | + | 0.523357i | \(0.824679\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.84843 | 1.61614 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.10479 | 1.23764 | 0.618820 | − | 0.785533i | \(-0.287611\pi\) | ||||
0.618820 | + | 0.785533i | \(0.287611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.10245 | −1.13781 | −0.568907 | − | 0.822402i | \(-0.692634\pi\) | ||||
−0.568907 | + | 0.822402i | \(0.692634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.26588 | −0.549556 | −0.274778 | − | 0.961508i | \(-0.588604\pi\) | ||||
−0.274778 | + | 0.961508i | \(0.588604\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.77484 | −1.55425 | −0.777127 | − | 0.629343i | \(-0.783324\pi\) | ||||
−0.777127 | + | 0.629343i | \(0.783324\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.6319 | 2.75650 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.17837 | −0.996579 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.13863 | 0.768525 | 0.384263 | − | 0.923224i | \(-0.374456\pi\) | ||||
0.384263 | + | 0.923224i | \(0.374456\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.84124 | −0.330697 | −0.165349 | − | 0.986235i | \(-0.552875\pi\) | ||||
−0.165349 | + | 0.986235i | \(0.552875\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.4996 | −2.00182 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.1155 | 1.82738 | 0.913690 | − | 0.406411i | \(-0.133220\pi\) | ||||
0.913690 | + | 0.406411i | \(0.133220\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.4930 | 1.84036 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.36833 | 1.30691 | 0.653457 | − | 0.756964i | \(-0.273318\pi\) | ||||
0.653457 | + | 0.756964i | \(0.273318\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.43473 | −0.828789 | −0.414395 | − | 0.910097i | \(-0.636007\pi\) | ||||
−0.414395 | + | 0.910097i | \(0.636007\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.593285 | 0.0865396 | 0.0432698 | − | 0.999063i | \(-0.486222\pi\) | ||||
0.0432698 | + | 0.999063i | \(0.486222\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.3307 | 1.90439 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.34787 | 0.888879 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.70512 | 0.234216 | 0.117108 | − | 0.993119i | \(-0.462638\pi\) | ||||
0.117108 | + | 0.993119i | \(0.462638\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.9797 | 2.51393 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.19772 | −0.806874 | −0.403437 | − | 0.915007i | \(-0.632185\pi\) | ||||
−0.403437 | + | 0.915007i | \(0.632185\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.3814 | −1.45724 | −0.728620 | − | 0.684919i | \(-0.759838\pi\) | ||||
−0.728620 | + | 0.684919i | \(0.759838\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −21.8614 | −2.75427 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.78978 | 0.707335 | 0.353667 | − | 0.935371i | \(-0.384934\pi\) | ||||
0.353667 | + | 0.935371i | \(0.384934\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.80150 | 0.337261 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9915 | 1.42312 | 0.711562 | − | 0.702623i | \(-0.247988\pi\) | ||||
0.711562 | + | 0.702623i | \(0.247988\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.363592 | −0.0425552 | −0.0212776 | − | 0.999774i | \(-0.506773\pi\) | ||||
−0.0212776 | + | 0.999774i | \(0.506773\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.5083 | −2.10922 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.75692 | −0.197669 | −0.0988344 | − | 0.995104i | \(-0.531511\pi\) | ||||
−0.0988344 | + | 0.995104i | \(0.531511\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.0380417 | −0.00422685 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.72171 | 1.06710 | 0.533548 | − | 0.845770i | \(-0.320858\pi\) | ||||
0.533548 | + | 0.845770i | \(0.320858\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.5944 | −1.24305 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.2208 | −1.82540 | −0.912698 | − | 0.408634i | \(-0.866005\pi\) | ||||
−0.912698 | + | 0.408634i | \(0.866005\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 18.4978 | 1.93909 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.15825 | 0.534886 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.38314 | 0.445040 | 0.222520 | − | 0.974928i | \(-0.428572\pi\) | ||||
0.222520 | + | 0.974928i | \(0.428572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.9018 | 2.00020 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.21428 | −0.319833 | −0.159917 | − | 0.987131i | \(-0.551123\pi\) | ||||
−0.159917 | + | 0.987131i | \(0.551123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.09140 | 0.206072 | 0.103036 | − | 0.994678i | \(-0.467144\pi\) | ||||
0.103036 | + | 0.994678i | \(0.467144\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.81411 | 0.175377 | 0.0876885 | − | 0.996148i | \(-0.472052\pi\) | ||||
0.0876885 | + | 0.996148i | \(0.472052\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.16716 | 0.303359 | 0.151679 | − | 0.988430i | \(-0.451532\pi\) | ||||
0.151679 | + | 0.988430i | \(0.451532\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −31.1402 | −2.95570 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.0407 | −1.22677 | −0.613384 | − | 0.789785i | \(-0.710192\pi\) | ||||
−0.613384 | + | 0.789785i | \(0.710192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19.8904 | −1.83887 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.2168 | 0.936568 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.84927 | 0.531752 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −23.4439 | −2.11387 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0290 | 1.06740 | 0.533700 | − | 0.845674i | \(-0.320801\pi\) | ||||
0.533700 | + | 0.845674i | \(0.320801\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.2254 | 1.34052 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.33814 | −0.116914 | −0.0584571 | − | 0.998290i | \(-0.518618\pi\) | ||||
−0.0584571 | + | 0.998290i | \(0.518618\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.5475 | 2.64880 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.53176 | 0.728917 | 0.364459 | − | 0.931220i | \(-0.381254\pi\) | ||||
0.364459 | + | 0.931220i | \(0.381254\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.2021 | 1.62870 | 0.814352 | − | 0.580371i | \(-0.197092\pi\) | ||||
0.814352 | + | 0.580371i | \(0.197092\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.66209 | −0.139973 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.8397 | −1.40820 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −37.3461 | −3.08025 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.9657 | −1.14412 | −0.572058 | − | 0.820213i | \(-0.693855\pi\) | ||||
−0.572058 | + | 0.820213i | \(0.693855\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.38572 | 0.763799 | 0.381900 | − | 0.924204i | \(-0.375270\pi\) | ||||
0.381900 | + | 0.924204i | \(0.375270\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.9859 | −0.888161 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.3649 | 1.78491 | 0.892457 | − | 0.451133i | \(-0.148980\pi\) | ||||
0.892457 | + | 0.451133i | \(0.148980\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.77690 | −0.378833 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.50896 | 0.355356 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.91327 | 0.463163 | 0.231581 | − | 0.972816i | \(-0.425610\pi\) | ||||
0.231581 | + | 0.972816i | \(0.425610\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.73957 | 0.676288 | 0.338144 | − | 0.941094i | \(-0.390201\pi\) | ||||
0.338144 | + | 0.941094i | \(0.390201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.83010 | 0.294623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −32.8473 | −2.51190 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5284 | 0.800462 | 0.400231 | − | 0.916414i | \(-0.368930\pi\) | ||||
0.400231 | + | 0.916414i | \(0.368930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 17.3629 | 1.30508 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.29655 | 0.246396 | 0.123198 | − | 0.992382i | \(-0.460685\pi\) | ||||
0.123198 | + | 0.992382i | \(0.460685\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7994 | 1.17436 | 0.587180 | − | 0.809456i | \(-0.300238\pi\) | ||||
0.587180 | + | 0.809456i | \(0.300238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.8850 | 2.35701 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.30095 | −0.680153 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 23.3491 | 1.69840 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.9965 | 1.44689 | 0.723447 | − | 0.690380i | \(-0.242557\pi\) | ||||
0.723447 | + | 0.690380i | \(0.242557\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.613407 | −0.0441540 | −0.0220770 | − | 0.999756i | \(-0.507028\pi\) | ||||
−0.0220770 | + | 0.999756i | \(0.507028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.63996 | 0.330584 | 0.165292 | − | 0.986245i | \(-0.447143\pi\) | ||||
0.165292 | + | 0.986245i | \(0.447143\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1446 | 0.931795 | 0.465898 | − | 0.884839i | \(-0.345731\pi\) | ||||
0.465898 | + | 0.884839i | \(0.345731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.2201 | −1.14408 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.6609 | −1.30974 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.84843 | −0.336989 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −27.8093 | −1.92361 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.76863 | 0.465972 | 0.232986 | − | 0.972480i | \(-0.425150\pi\) | ||||
0.232986 | + | 0.972480i | \(0.425150\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −33.5941 | −2.30183 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.30209 | 0.563583 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.01860 | 0.0688308 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.29565 | 0.625293 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.46851 | 0.366199 | 0.183099 | − | 0.983094i | \(-0.441387\pi\) | ||||
0.183099 | + | 0.983094i | \(0.441387\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.55927 | 0.368981 | 0.184491 | − | 0.982834i | \(-0.440936\pi\) | ||||
0.184491 | + | 0.982834i | \(0.440936\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.33693 | −0.418756 | −0.209378 | − | 0.977835i | \(-0.567144\pi\) | ||||
−0.209378 | + | 0.977835i | \(0.567144\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 51.8511 | 3.41155 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.84557 | 0.645005 | 0.322502 | − | 0.946569i | \(-0.395476\pi\) | ||||
0.322502 | + | 0.946569i | \(0.395476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.92201 | 0.319719 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.9526 | −1.67873 | −0.839366 | − | 0.543567i | \(-0.817074\pi\) | ||||
−0.839366 | + | 0.543567i | \(0.817074\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.3220 | −0.793729 | −0.396865 | − | 0.917877i | \(-0.629902\pi\) | ||||
−0.396865 | + | 0.917877i | \(0.629902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.6417 | 1.00342 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.7934 | 1.76845 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −27.2354 | −1.72597 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.68797 | 0.485261 | 0.242630 | − | 0.970119i | \(-0.421990\pi\) | ||||
0.242630 | + | 0.970119i | \(0.421990\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.10479 | −0.258066 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −19.7126 | −1.22964 | −0.614818 | − | 0.788669i | \(-0.710771\pi\) | ||||
−0.614818 | + | 0.788669i | \(0.710771\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −50.1195 | −3.11427 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.0659 | 1.24205 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.96836 | 0.183037 | 0.0915183 | − | 0.995803i | \(-0.470828\pi\) | ||||
0.0915183 | + | 0.995803i | \(0.470828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 48.2440 | 2.95249 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.417916 | 0.0254808 | 0.0127404 | − | 0.999919i | \(-0.495944\pi\) | ||||
0.0127404 | + | 0.999919i | \(0.495944\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.1776 | −0.618245 | −0.309122 | − | 0.951022i | \(-0.600035\pi\) | ||||
−0.309122 | + | 0.951022i | \(0.600035\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −51.8216 | −3.13639 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.8176 | 1.13064 | 0.565321 | − | 0.824871i | \(-0.308752\pi\) | ||||
0.565321 | + | 0.824871i | \(0.308752\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.92713 | −0.534454 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.9609 | −1.54870 | −0.774350 | − | 0.632757i | \(-0.781923\pi\) | ||||
−0.774350 | + | 0.632757i | \(0.781923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.2612 | −1.32329 | −0.661646 | − | 0.749817i | \(-0.730142\pi\) | ||||
−0.661646 | + | 0.749817i | \(0.730142\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −37.7325 | −2.22728 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8658 | −0.697988 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2794 | −0.719830 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.21032 | 0.129128 | 0.0645641 | − | 0.997914i | \(-0.479434\pi\) | ||||
0.0645641 | + | 0.997914i | \(0.479434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.2561 | −1.23341 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.10245 | 0.237251 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.5050 | 1.41244 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.00483 | 0.517314 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.7730 | −1.12851 | −0.564253 | − | 0.825602i | \(-0.690836\pi\) | ||||
−0.564253 | + | 0.825602i | \(0.690836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.85906 | −0.333310 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.1593 | −0.689490 | −0.344745 | − | 0.938696i | \(-0.612035\pi\) | ||||
−0.344745 | + | 0.938696i | \(0.612035\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.0793 | −1.92628 | −0.963139 | − | 0.269003i | \(-0.913306\pi\) | ||||
−0.963139 | + | 0.269003i | \(0.913306\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.66161 | 0.205657 | 0.102828 | − | 0.994699i | \(-0.467211\pi\) | ||||
0.102828 | + | 0.994699i | \(0.467211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.9882 | 0.951157 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.08225 | −0.283663 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.3510 | 0.854150 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.87281 | −0.490667 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.67510 | −0.147483 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.50062 | −0.192412 | −0.0962058 | − | 0.995361i | \(-0.530671\pi\) | ||||
−0.0962058 | + | 0.995361i | \(0.530671\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 53.8928 | 2.95331 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.3643 | −1.81747 | −0.908735 | − | 0.417373i | \(-0.862951\pi\) | ||||
−0.908735 | + | 0.417373i | \(0.862951\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.5336 | 1.98423 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.55791 | −0.409284 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −28.5450 | −1.54128 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.80416 | −0.311584 | −0.155792 | − | 0.987790i | \(-0.549793\pi\) | ||||
−0.155792 | + | 0.987790i | \(0.549793\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.496058 | −0.0265534 | −0.0132767 | − | 0.999912i | \(-0.504226\pi\) | ||||
−0.0132767 | + | 0.999912i | \(0.504226\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.2440 | 1.13392 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.80547 | −0.308994 | −0.154497 | − | 0.987993i | \(-0.549376\pi\) | ||||
−0.154497 | + | 0.987993i | \(0.549376\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −28.6223 | −1.51485 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.3473 | −1.49611 | −0.748057 | − | 0.663635i | \(-0.769013\pi\) | ||||
−0.748057 | + | 0.663635i | \(0.769013\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.8984 | 1.41571 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.3868 | −0.860081 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.2615 | −1.26644 | −0.633219 | − | 0.773972i | \(-0.718267\pi\) | ||||
−0.633219 | + | 0.773972i | \(0.718267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 40.5732 | 2.11216 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.68832 | −0.399158 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6261 | 1.17153 | 0.585767 | − | 0.810479i | \(-0.300793\pi\) | ||||
0.585767 | + | 0.810479i | \(0.300793\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.9785 | −0.874439 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.43791 | −0.330693 | −0.165347 | − | 0.986236i | \(-0.552874\pi\) | ||||
−0.165347 | + | 0.986236i | \(0.552874\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −33.6993 | −1.72647 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5145 | −0.741657 | −0.370829 | − | 0.928701i | \(-0.620926\pi\) | ||||
−0.370829 | + | 0.928701i | \(0.620926\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.3499 | −1.33944 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.1850 | −1.32763 | −0.663815 | − | 0.747897i | \(-0.731064\pi\) | ||||
−0.663815 | + | 0.747897i | \(0.731064\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.26588 | 0.114590 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.74882 | 0.189103 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.6074 | 1.03426 | 0.517129 | − | 0.855908i | \(-0.327001\pi\) | ||||
0.517129 | + | 0.855908i | \(0.327001\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −85.5789 | −4.28430 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.4900 | 0.623719 | 0.311859 | − | 0.950128i | \(-0.399048\pi\) | ||||
0.311859 | + | 0.950128i | \(0.399048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.55361 | 0.376272 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.6268 | 2.26164 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.11740 | 0.450826 | 0.225413 | − | 0.974263i | \(-0.427627\pi\) | ||||
0.225413 | + | 0.974263i | \(0.427627\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.9018 | −1.17899 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.9453 | 1.37510 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −53.7949 | −2.63435 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.12358 | 0.348010 | 0.174005 | − | 0.984745i | \(-0.444329\pi\) | ||||
0.174005 | + | 0.984745i | \(0.444329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.13707 | 0.347840 | 0.173920 | − | 0.984760i | \(-0.444357\pi\) | ||||
0.173920 | + | 0.984760i | \(0.444357\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.87650 | 0.139860 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 51.3183 | 2.48347 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 47.1764 | 2.27770 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.2840 | 0.688036 | 0.344018 | − | 0.938963i | \(-0.388212\pi\) | ||||
0.344018 | + | 0.938963i | \(0.388212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.5102 | −0.841485 | −0.420743 | − | 0.907180i | \(-0.638230\pi\) | ||||
−0.420743 | + | 0.907180i | \(0.638230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.77484 | 0.324084 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.991828 | −0.0473374 | −0.0236687 | − | 0.999720i | \(-0.507535\pi\) | ||||
−0.0236687 | + | 0.999720i | \(0.507535\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 64.6330 | 3.07776 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.99095 | −0.142105 | −0.0710523 | − | 0.997473i | \(-0.522636\pi\) | ||||
−0.0710523 | + | 0.997473i | \(0.522636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 39.1250 | 1.85055 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.8981 | 0.986244 | 0.493122 | − | 0.869960i | \(-0.335856\pi\) | ||||
0.493122 | + | 0.869960i | \(0.335856\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.3502 | 1.61749 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −26.2941 | −1.23541 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.4482 | −1.56464 | −0.782320 | − | 0.622877i | \(-0.785964\pi\) | ||||
−0.782320 | + | 0.622877i | \(0.785964\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.7336 | 0.547676 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.53331 | 0.397436 | 0.198718 | − | 0.980057i | \(-0.436322\pi\) | ||||
0.198718 | + | 0.980057i | \(0.436322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.5937 | −0.631751 | −0.315876 | − | 0.948801i | \(-0.602298\pi\) | ||||
−0.315876 | + | 0.948801i | \(0.602298\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.3442 | −1.45044 | −0.725219 | − | 0.688518i | \(-0.758262\pi\) | ||||
−0.725219 | + | 0.688518i | \(0.758262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26.1059 | −1.20546 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −62.6554 | −2.88701 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.3084 | −1.02574 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.26715 | 0.378527 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −20.0701 | −0.917027 | −0.458513 | − | 0.888687i | \(-0.651618\pi\) | ||||
−0.458513 | + | 0.888687i | \(0.651618\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −45.6009 | −2.07922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.6319 | −0.574770 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.8679 | −1.21750 | −0.608750 | − | 0.793362i | \(-0.708329\pi\) | ||||
−0.608750 | + | 0.793362i | \(0.708329\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.5660 | −0.749143 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.2592 | −1.50097 | −0.750483 | − | 0.660890i | \(-0.770179\pi\) | ||||
−0.750483 | + | 0.660890i | \(0.770179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.37764 | −0.422348 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −54.0690 | −2.42533 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.4726 | 1.09554 | 0.547772 | − | 0.836627i | \(-0.315476\pi\) | ||||
0.547772 | + | 0.836627i | \(0.315476\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.4839 | −1.09386 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.8607 | 1.77730 | 0.888650 | − | 0.458585i | \(-0.151644\pi\) | ||||
0.888650 | + | 0.458585i | \(0.151644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.7300 | −0.476537 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.4456 | 0.906237 | 0.453119 | − | 0.891450i | \(-0.350311\pi\) | ||||
0.453119 | + | 0.891450i | \(0.350311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.63942 | 0.0725237 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.0826 | 1.54894 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.43531 | 0.107105 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.4955 | −1.29471 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.3985 | −1.33178 | −0.665892 | − | 0.746048i | \(-0.731949\pi\) | ||||
−0.665892 | + | 0.746048i | \(0.731949\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.27912 | 0.187113 | 0.0935564 | − | 0.995614i | \(-0.470176\pi\) | ||||
0.0935564 | + | 0.995614i | \(0.470176\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.17203 | 0.181737 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.0492 | −1.30402 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.3306 | −1.48703 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.23529 | −0.398532 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 54.7198 | 2.35695 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.60876 | −0.155153 | −0.0775764 | − | 0.996986i | \(-0.524718\pi\) | ||||
−0.0775764 | + | 0.996986i | \(0.524718\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −44.2621 | −1.89947 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.6519 | −1.31058 | −0.655290 | − | 0.755377i | \(-0.727454\pi\) | ||||
−0.655290 | + | 0.755377i | \(0.727454\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −55.1819 | −2.35511 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.0386 | −1.19448 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.92187 | 0.336872 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −45.9504 | −1.94698 | −0.973491 | − | 0.228725i | \(-0.926544\pi\) | ||||
−0.973491 | + | 0.228725i | \(0.926544\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2957 | 0.943009 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 26.0566 | 1.10011 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.30591 | −0.181472 | −0.0907362 | − | 0.995875i | \(-0.528922\pi\) | ||||
−0.0907362 | + | 0.995875i | \(0.528922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.171528 | 0.00720351 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.4627 | 1.23514 | 0.617571 | − | 0.786515i | \(-0.288117\pi\) | ||||
0.617571 | + | 0.786515i | \(0.288117\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.7317 | 1.32793 | 0.663966 | − | 0.747763i | \(-0.268872\pi\) | ||||
0.663966 | + | 0.747763i | \(0.268872\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −56.0202 | −2.34028 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.1386 | 1.00490 | 0.502451 | − | 0.864606i | \(-0.332432\pi\) | ||||
0.502451 | + | 0.864606i | \(0.332432\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.71846 | 0.0714169 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −43.8348 | −1.81857 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.99915 | 0.289875 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.9551 | −1.40148 | −0.700738 | − | 0.713419i | \(-0.747146\pi\) | ||||
−0.700738 | + | 0.713419i | \(0.747146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.4741 | 0.513988 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9989 | −0.534702 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.84201 | −0.280968 | −0.140484 | − | 0.990083i | \(-0.544866\pi\) | ||||
−0.140484 | + | 0.990083i | \(0.544866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.8246 | −1.50713 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6172 | −1.08755 | −0.543775 | − | 0.839231i | \(-0.683005\pi\) | ||||
−0.543775 | + | 0.839231i | \(0.683005\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0702 | 0.614728 | 0.307364 | − | 0.951592i | \(-0.400553\pi\) | ||||
0.307364 | + | 0.951592i | \(0.400553\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28.0713 | 1.14315 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.4205 | −1.76238 | −0.881191 | − | 0.472761i | \(-0.843258\pi\) | ||||
−0.881191 | + | 0.472761i | \(0.843258\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 52.2787 | 2.11844 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.43392 | −0.0984660 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.59633 | 0.185644 | 0.0928220 | − | 0.995683i | \(-0.470411\pi\) | ||||
0.0928220 | + | 0.995683i | \(0.470411\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.4809 | 1.22712 | 0.613558 | − | 0.789650i | \(-0.289738\pi\) | ||||
0.613558 | + | 0.789650i | \(0.289738\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.0511 | 1.48921 | 0.744605 | − | 0.667506i | \(-0.232638\pi\) | ||||
0.744605 | + | 0.667506i | \(0.232638\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.17837 | 0.207801 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 77.6477 | 3.11089 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 77.9078 | 3.11134 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.1864 | −1.00425 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.3035 | 1.16655 | 0.583276 | − | 0.812274i | \(-0.301770\pi\) | ||||
0.583276 | + | 0.812274i | \(0.301770\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.9624 | −0.753686 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −54.6886 | −2.16684 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 58.1397 | 2.29997 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.3307 | −0.447536 | −0.223768 | − | 0.974642i | \(-0.571836\pi\) | ||||
−0.223768 | + | 0.974642i | \(0.571836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.2340 | −1.11344 | −0.556721 | − | 0.830700i | \(-0.687941\pi\) | ||||
−0.556721 | + | 0.830700i | \(0.687941\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.0192 | −1.18018 | −0.590089 | − | 0.807338i | \(-0.700907\pi\) | ||||
−0.590089 | + | 0.807338i | \(0.700907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.4403 | −0.998619 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.2584 | −0.911567 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.7192 | 0.928204 | 0.464102 | − | 0.885782i | \(-0.346377\pi\) | ||||
0.464102 | + | 0.885782i | \(0.346377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.76285 | −0.0687752 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.8488 | 0.656336 | 0.328168 | − | 0.944619i | \(-0.393569\pi\) | ||||
0.328168 | + | 0.944619i | \(0.393569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.4941 | −0.913816 | −0.456908 | − | 0.889514i | \(-0.651043\pi\) | ||||
−0.456908 | + | 0.889514i | \(0.651043\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26.0418 | −1.01138 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.13863 | −0.160249 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.3201 | −0.592308 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −46.7182 | −1.80354 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.9329 | −0.768358 | −0.384179 | − | 0.923259i | \(-0.625515\pi\) | ||||
−0.384179 | + | 0.923259i | \(0.625515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.9965 | −1.30659 | −0.653296 | − | 0.757102i | \(-0.726614\pi\) | ||||
−0.653296 | + | 0.757102i | \(0.726614\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.7634 | −0.758450 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.5743 | −0.596809 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.8223 | −0.452367 | −0.226183 | − | 0.974085i | \(-0.572625\pi\) | ||||
−0.226183 | + | 0.974085i | \(0.572625\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.7529 | 0.677316 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.99517 | −0.266495 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0765 | 1.48654 | 0.743271 | − | 0.668991i | \(-0.233273\pi\) | ||||
0.743271 | + | 0.668991i | \(0.233273\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −89.7362 | −3.40880 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.9616 | −0.718222 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.5824 | −1.04326 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.3454 | −1.37275 | −0.686373 | − | 0.727250i | \(-0.740798\pi\) | ||||
−0.686373 | + | 0.727250i | \(0.740798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −75.3059 | −2.84021 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.4931 | 0.545068 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.6781 | −0.626359 | −0.313179 | − | 0.949694i | \(-0.601394\pi\) | ||||
−0.313179 | + | 0.949694i | \(0.601394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.51829 | −0.319461 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.84124 | 0.0689551 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 72.7062 | 2.71526 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.1134 | 0.899278 | 0.449639 | − | 0.893210i | \(-0.351553\pi\) | ||||
0.449639 | + | 0.893210i | \(0.351553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.43003 | −0.351193 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.5201 | 1.28382 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.05594 | −0.113339 | −0.0566693 | − | 0.998393i | \(-0.518048\pi\) | ||||
−0.0566693 | + | 0.998393i | \(0.518048\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7062 | −1.61875 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.3144 | 0.455466 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.2230 | 1.81809 | 0.909046 | − | 0.416696i | \(-0.136812\pi\) | ||||
0.909046 | + | 0.416696i | \(0.136812\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.7658 | 0.875425 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1179 | −0.482548 | −0.241274 | − | 0.970457i | \(-0.577565\pi\) | ||||
−0.241274 | + | 0.970457i | \(0.577565\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −77.8634 | −2.86038 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.9149 | 0.547173 | 0.273587 | − | 0.961847i | \(-0.411790\pi\) | ||||
0.273587 | + | 0.961847i | \(0.411790\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 47.1350 | 1.72458 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.17977 | −0.298882 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.40642 | −0.270264 | −0.135132 | − | 0.990828i | \(-0.543146\pi\) | ||||
−0.135132 | + | 0.990828i | \(0.543146\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21.5379 | −0.784884 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.37246 | −0.0498831 | −0.0249415 | − | 0.999689i | \(-0.507940\pi\) | ||||
−0.0249415 | + | 0.999689i | \(0.507940\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.4996 | 0.417408 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.9083 | −1.22918 | −0.614588 | − | 0.788849i | \(-0.710678\pi\) | ||||
−0.614588 | + | 0.788849i | \(0.710678\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.2806 | −0.516992 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.4258 | 0.918073 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.17267 | 0.258653 | 0.129327 | − | 0.991602i | \(-0.458718\pi\) | ||||
0.129327 | + | 0.991602i | \(0.458718\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.2248 | 1.98887 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.13634 | −0.112806 | −0.0564031 | − | 0.998408i | \(-0.517963\pi\) | ||||
−0.0564031 | + | 0.998408i | \(0.517963\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 140.410 | 5.03718 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −56.6941 | −2.03128 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.2224 | 1.76131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.4314 | −0.765896 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.546252 | −0.0194718 | −0.00973589 | − | 0.999953i | \(-0.503099\pi\) | ||||
−0.00973589 | + | 0.999953i | \(0.503099\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.31586 | −0.296052 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 58.8001 | 2.09069 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.6916 | 1.65807 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.0453 | 1.59559 | 0.797794 | − | 0.602931i | \(-0.206000\pi\) | ||||
0.797794 | + | 0.602931i | \(0.206000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.34431 | −0.0475584 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −83.4936 | −2.95010 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.49247 | −0.0526680 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.17079 | −0.0412139 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.0227 | 1.47744 | 0.738719 | − | 0.674013i | \(-0.235431\pi\) | ||||
0.738719 | + | 0.674013i | \(0.235431\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.9218 | −0.523974 | −0.261987 | − | 0.965071i | \(-0.584378\pi\) | ||||
−0.261987 | + | 0.965071i | \(0.584378\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.5126 | 0.999980 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.8194 | 1.28815 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 89.6851 | 3.13385 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.2317 | 1.12489 | 0.562447 | − | 0.826833i | \(-0.309860\pi\) | ||||
0.562447 | + | 0.826833i | \(0.309860\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.3609 | −1.09317 | −0.546586 | − | 0.837403i | \(-0.684073\pi\) | ||||
−0.546586 | + | 0.837403i | \(0.684073\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −29.6787 | −1.03203 | −0.516015 | − | 0.856580i | \(-0.672585\pi\) | ||||
−0.516015 | + | 0.856580i | \(0.672585\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.4868 | 0.607342 | 0.303671 | − | 0.952777i | \(-0.401788\pi\) | ||||
0.303671 | + | 0.952777i | \(0.401788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −52.7177 | −1.82876 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30.2058 | −1.04657 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.53465 | 0.329566 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.2177 | −0.767039 | −0.383520 | − | 0.923533i | \(-0.625288\pi\) | ||||
−0.383520 | + | 0.923533i | \(0.625288\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.8717 | −0.409369 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 72.7297 | 2.50494 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.3741 | −0.906225 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 62.3649 | 2.14036 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.1155 | −0.381035 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.5885 | 0.910374 | 0.455187 | − | 0.890396i | \(-0.349572\pi\) | ||||
0.455187 | + | 0.890396i | \(0.349572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0394 | 0.718692 | 0.359346 | − | 0.933204i | \(-0.383000\pi\) | ||||
0.359346 | + | 0.933204i | \(0.383000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.7924 | 1.46006 | 0.730028 | − | 0.683417i | \(-0.239507\pi\) | ||||
0.730028 | + | 0.683417i | \(0.239507\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 105.708 | 3.60251 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.5471 | 1.51640 | 0.758200 | − | 0.652022i | \(-0.226079\pi\) | ||||
0.758200 | + | 0.652022i | \(0.226079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33.2421 | 1.12896 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.21177 | −0.244643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.7523 | −0.804816 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.2513 | 0.719249 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.1814 | −0.411336 | −0.205668 | − | 0.978622i | \(-0.565937\pi\) | ||||
−0.205668 | + | 0.978622i | \(0.565937\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.19222 | −0.208858 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.3075 | −0.515723 | −0.257862 | − | 0.966182i | \(-0.583018\pi\) | ||||
−0.257862 | + | 0.966182i | \(0.583018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.1308 | −0.812065 | −0.406033 | − | 0.913859i | \(-0.633088\pi\) | ||||
−0.406033 | + | 0.913859i | \(0.633088\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.9353 | 0.602210 | 0.301105 | − | 0.953591i | \(-0.402645\pi\) | ||||
0.301105 | + | 0.953591i | \(0.402645\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −54.2383 | −1.81909 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.156153 | −0.00523132 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.01941 | −0.134505 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.4930 | −0.383741 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.62024 | −0.254149 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.86359 | −0.128715 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −68.6509 | −2.28456 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.7750 | 1.75236 | 0.876182 | − | 0.481980i | \(-0.160082\pi\) | ||||
0.876182 | + | 0.481980i | \(0.160082\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.5842 | −0.516896 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.2848 | −0.771461 | −0.385731 | − | 0.922611i | \(-0.626051\pi\) | ||||
−0.385731 | + | 0.922611i | \(0.626051\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.9055 | 1.32068 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6.03364 | 0.199248 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.79940 | 0.323253 | 0.161626 | − | 0.986852i | \(-0.448326\pi\) | ||||
0.161626 | + | 0.986852i | \(0.448326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 55.3942 | 1.82530 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −49.1944 | −1.61925 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.1400 | 0.333041 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −33.0707 | −1.08501 | −0.542507 | − | 0.840051i | \(-0.682525\pi\) | ||||
−0.542507 | + | 0.840051i | \(0.682525\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −90.3135 | −2.95990 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.0643 | 1.11521 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31.0078 | −1.01298 | −0.506491 | − | 0.862245i | \(-0.669058\pi\) | ||||
−0.506491 | + | 0.862245i | \(0.669058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 95.4734 | 3.11566 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.6560 | 0.542971 | 0.271486 | − | 0.962442i | \(-0.412485\pi\) | ||||
0.271486 | + | 0.962442i | \(0.412485\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.36833 | −0.272510 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.3503 | −0.531312 | −0.265656 | − | 0.964068i | \(-0.585589\pi\) | ||||
−0.265656 | + | 0.964068i | \(0.585589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.49162 | 0.0484199 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.2580 | −0.332639 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.2223 | −0.460704 | −0.230352 | − | 0.973107i | \(-0.573988\pi\) | ||||
−0.230352 | + | 0.973107i | \(0.573988\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.5925 | −1.53845 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.4693 | −1.24224 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6098 | −0.890639 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.79560 | 0.283434 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.2933 | 1.00632 | 0.503162 | − | 0.864192i | \(-0.332170\pi\) | ||||
0.503162 | + | 0.864192i | \(0.332170\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −43.0058 | −1.38154 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.4671 | 1.00983 | 0.504914 | − | 0.863170i | \(-0.331524\pi\) | ||||
0.504914 | + | 0.863170i | \(0.331524\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −86.5817 | −2.77568 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.8139 | 0.889846 | 0.444923 | − | 0.895569i | \(-0.353231\pi\) | ||||
0.444923 | + | 0.895569i | \(0.353231\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −70.6875 | −2.25918 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.3557 | 0.490271 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.5702 | 1.83621 | 0.918103 | − | 0.396343i | \(-0.129721\pi\) | ||||
0.918103 | + | 0.396343i | \(0.129721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.49431 | 0.238546 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.43473 | 0.172814 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 48.4772 | 1.53993 | 0.769964 | − | 0.638088i | \(-0.220274\pi\) | ||||
0.769964 | + | 0.638088i | \(0.220274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.80701 | 0.311216 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.6703 | 0.654634 | 0.327317 | − | 0.944915i | \(-0.393856\pi\) | ||||
0.327317 | + | 0.944915i | \(0.393856\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −57.5603 | −1.82113 |
(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 | 9200.2.a.cx.1.2 | 6 | ||
4.3 | odd | 2 | 2300.2.a.o.1.5 | 6 | |||
5.2 | odd | 4 | 1840.2.e.f.369.11 | 12 | |||
5.3 | odd | 4 | 1840.2.e.f.369.2 | 12 | |||
5.4 | even | 2 | 9200.2.a.cy.1.5 | 6 | |||
20.3 | even | 4 | 460.2.c.a.369.11 | yes | 12 | ||
20.7 | even | 4 | 460.2.c.a.369.2 | ✓ | 12 | ||
20.19 | odd | 2 | 2300.2.a.n.1.2 | 6 | |||
60.23 | odd | 4 | 4140.2.f.b.829.12 | 12 | |||
60.47 | odd | 4 | 4140.2.f.b.829.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.c.a.369.2 | ✓ | 12 | 20.7 | even | 4 | ||
460.2.c.a.369.11 | yes | 12 | 20.3 | even | 4 | ||
1840.2.e.f.369.2 | 12 | 5.3 | odd | 4 | |||
1840.2.e.f.369.11 | 12 | 5.2 | odd | 4 | |||
2300.2.a.n.1.2 | 6 | 20.19 | odd | 2 | |||
2300.2.a.o.1.5 | 6 | 4.3 | odd | 2 | |||
4140.2.f.b.829.11 | 12 | 60.47 | odd | 4 | |||
4140.2.f.b.829.12 | 12 | 60.23 | odd | 4 | |||
9200.2.a.cx.1.2 | 6 | 1.1 | even | 1 | trivial | ||
9200.2.a.cy.1.5 | 6 | 5.4 | even | 2 |