Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1904,2,Mod(1,1904)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1904, 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("1904.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1904 = 2^{4} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1904.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: | \(15.2035165449\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.453749.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 10x^{2} + x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 119) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.32183\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1904.1 |
$q$-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 | ||||||||
\(3\) | −0.907578 | −0.523991 | −0.261995 | − | 0.965069i | \(-0.584380\pi\) | ||||
−0.261995 | + | 0.965069i | \(0.584380\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.03818 | 1.35872 | 0.679358 | − | 0.733807i | \(-0.262258\pi\) | ||||
0.679358 | + | 0.733807i | \(0.262258\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.17630 | −0.725434 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.78178 | −1.44176 | −0.720880 | − | 0.693060i | \(-0.756262\pi\) | ||||
−0.720880 | + | 0.693060i | \(0.756262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.39933 | −1.22015 | −0.610077 | − | 0.792342i | \(-0.708861\pi\) | ||||
−0.610077 | + | 0.792342i | \(0.708861\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.75739 | −0.711954 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.64366 | 0.606497 | 0.303248 | − | 0.952912i | \(-0.401929\pi\) | ||||
0.303248 | + | 0.952912i | \(0.401929\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.907578 | −0.198050 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.45881 | 1.76378 | 0.881892 | − | 0.471451i | \(-0.156270\pi\) | ||||
0.881892 | + | 0.471451i | \(0.156270\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.23054 | 0.846109 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.69790 | 0.904111 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.04298 | 1.30785 | 0.653925 | − | 0.756560i | \(-0.273121\pi\) | ||||
0.653925 | + | 0.756560i | \(0.273121\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.42063 | 0.614364 | 0.307182 | − | 0.951651i | \(-0.400614\pi\) | ||||
0.307182 | + | 0.951651i | \(0.400614\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.33984 | 0.755469 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.03818 | 0.513546 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.66977 | 1.58970 | 0.794850 | − | 0.606806i | \(-0.207549\pi\) | ||||
0.794850 | + | 0.606806i | \(0.207549\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.99273 | 0.639349 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.33675 | 0.208766 | 0.104383 | − | 0.994537i | \(-0.466713\pi\) | ||||
0.104383 | + | 0.994537i | \(0.466713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.52513 | −0.385078 | −0.192539 | − | 0.981289i | \(-0.561672\pi\) | ||||
−0.192539 | + | 0.981289i | \(0.561672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.61200 | −0.985659 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.57082 | 0.812588 | 0.406294 | − | 0.913742i | \(-0.366821\pi\) | ||||
0.406294 | + | 0.913742i | \(0.366821\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.907578 | −0.127086 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.17630 | 0.711020 | 0.355510 | − | 0.934673i | \(-0.384307\pi\) | ||||
0.355510 | + | 0.934673i | \(0.384307\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.5279 | −1.95894 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.39933 | −0.317799 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.28732 | −1.20911 | −0.604553 | − | 0.796565i | \(-0.706648\pi\) | ||||
−0.604553 | + | 0.796565i | \(0.706648\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.66325 | 0.853141 | 0.426571 | − | 0.904454i | \(-0.359722\pi\) | ||||
0.426571 | + | 0.904454i | \(0.359722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.17630 | −0.274188 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.3659 | −1.65784 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.28251 | −0.645362 | −0.322681 | − | 0.946508i | \(-0.604584\pi\) | ||||
−0.322681 | + | 0.946508i | \(0.604584\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.67704 | −0.924206 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9310 | 1.41595 | 0.707973 | − | 0.706239i | \(-0.249610\pi\) | ||||
0.707973 | + | 0.706239i | \(0.249610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.7155 | 1.48823 | 0.744116 | − | 0.668050i | \(-0.232871\pi\) | ||||
0.744116 | + | 0.668050i | \(0.232871\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.83955 | −0.443353 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.78178 | −0.544934 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.94051 | −0.218325 | −0.109162 | − | 0.994024i | \(-0.534817\pi\) | ||||
−0.109162 | + | 0.994024i | \(0.534817\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.26519 | 0.251688 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.58417 | 0.503178 | 0.251589 | − | 0.967834i | \(-0.419047\pi\) | ||||
0.251589 | + | 0.967834i | \(0.419047\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.03818 | 0.329537 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.39206 | −0.685301 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.3956 | −1.41993 | −0.709965 | − | 0.704237i | \(-0.751289\pi\) | ||||
−0.709965 | + | 0.704237i | \(0.751289\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.39933 | −0.461175 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.10449 | −0.321921 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.03191 | 0.824057 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.1668 | −1.53995 | −0.769976 | − | 0.638073i | \(-0.779732\pi\) | ||||
−0.769976 | + | 0.638073i | \(0.779732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.4066 | 1.04590 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.24786 | 0.323174 | 0.161587 | − | 0.986858i | \(-0.448339\pi\) | ||||
0.161587 | + | 0.986858i | \(0.448339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7031 | 1.25168 | 0.625839 | − | 0.779952i | \(-0.284757\pi\) | ||||
0.625839 | + | 0.779952i | \(0.284757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.75739 | −0.269093 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.91410 | −0.378390 | −0.189195 | − | 0.981940i | \(-0.560588\pi\) | ||||
−0.189195 | + | 0.981940i | \(0.560588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.56356 | −0.341327 | −0.170663 | − | 0.985329i | \(-0.554591\pi\) | ||||
−0.170663 | + | 0.985329i | \(0.554591\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.77607 | −0.832988 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.966622 | 0.0909322 | 0.0454661 | − | 0.998966i | \(-0.485523\pi\) | ||||
0.0454661 | + | 0.998966i | \(0.485523\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.6994 | 2.39648 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.57426 | 0.885141 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.8654 | 1.07867 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.21321 | −0.109391 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.33775 | −0.209095 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.55875 | 0.493260 | 0.246630 | − | 0.969110i | \(-0.420677\pi\) | ||||
0.246630 | + | 0.969110i | \(0.420677\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.29175 | 0.201777 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.51134 | 0.306787 | 0.153393 | − | 0.988165i | \(-0.450980\pi\) | ||||
0.153393 | + | 0.988165i | \(0.450980\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.64366 | 0.229234 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.2731 | 1.22843 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.93780 | −0.165557 | −0.0827786 | − | 0.996568i | \(-0.526379\pi\) | ||||
−0.0827786 | + | 0.996568i | \(0.526379\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.69834 | −0.398508 | −0.199254 | − | 0.979948i | \(-0.563852\pi\) | ||||
−0.199254 | + | 0.979948i | \(0.563852\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.05596 | −0.425789 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.0366 | 1.75917 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.3979 | 1.77700 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.907578 | −0.0748558 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.24162 | 0.347487 | 0.173743 | − | 0.984791i | \(-0.444414\pi\) | ||||
0.173743 | + | 0.984791i | \(0.444414\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.4584 | −1.01385 | −0.506924 | − | 0.861991i | \(-0.669217\pi\) | ||||
−0.506924 | + | 0.861991i | \(0.669217\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.17630 | −0.175944 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3925 | 0.834746 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.6472 | −1.40840 | −0.704199 | − | 0.710002i | \(-0.748694\pi\) | ||||
−0.704199 | + | 0.710002i | \(0.748694\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.69790 | −0.372568 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.45881 | 0.666648 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.67557 | 0.209567 | 0.104783 | − | 0.994495i | \(-0.466585\pi\) | ||||
0.104783 | + | 0.994495i | \(0.466585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.1852 | 1.02647 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.95783 | 0.151501 | 0.0757507 | − | 0.997127i | \(-0.475865\pi\) | ||||
0.0757507 | + | 0.997127i | \(0.475865\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.35407 | 0.488775 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.75340 | −0.439973 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.01732 | 0.457488 | 0.228744 | − | 0.973487i | \(-0.426538\pi\) | ||||
0.228744 | + | 0.973487i | \(0.426538\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.23054 | 0.319799 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.42897 | 0.633560 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.75112 | −0.130885 | −0.0654423 | − | 0.997856i | \(-0.520846\pi\) | ||||
−0.0654423 | + | 0.997856i | \(0.520846\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.76491 | 0.205514 | 0.102757 | − | 0.994707i | \(-0.467234\pi\) | ||||
0.102757 | + | 0.994707i | \(0.467234\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.04742 | −0.447038 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.3785 | 2.15995 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.78178 | −0.349678 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.69790 | 0.341722 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.8461 | −1.36365 | −0.681827 | − | 0.731514i | \(-0.738814\pi\) | ||||
−0.681827 | + | 0.731514i | \(0.738814\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.9107 | 0.857348 | 0.428674 | − | 0.903459i | \(-0.358981\pi\) | ||||
0.428674 | + | 0.903459i | \(0.358981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.1306 | 0.868693 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.2682 | −1.23031 | −0.615153 | − | 0.788408i | \(-0.710906\pi\) | ||||
−0.615153 | + | 0.788408i | \(0.710906\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2451 | 1.08070 | 0.540350 | − | 0.841440i | \(-0.318292\pi\) | ||||
0.540350 | + | 0.841440i | \(0.318292\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.79429 | 0.338163 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.04298 | 0.494321 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.06130 | 0.283653 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.4089 | −1.27951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.6414 | −0.874423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.51331 | −0.586080 | −0.293040 | − | 0.956100i | \(-0.594667\pi\) | ||||
−0.293040 | + | 0.956100i | \(0.594667\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.8283 | −0.741942 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.67179 | −0.523212 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.42063 | 0.232208 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.5403 | −0.779820 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.39933 | −0.295931 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.49093 | 0.166805 | 0.0834027 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834027 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.20694 | −0.613796 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9842 | 1.12728 | 0.563640 | − | 0.826020i | \(-0.309400\pi\) | ||||
0.563640 | + | 0.826020i | \(0.309400\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3303 | −1.07914 | −0.539568 | − | 0.841942i | \(-0.681413\pi\) | ||||
−0.539568 | + | 0.841942i | \(0.681413\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.33984 | 0.285540 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.77825 | −0.378546 | −0.189273 | − | 0.981925i | \(-0.560613\pi\) | ||||
−0.189273 | + | 0.981925i | \(0.560613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.9252 | 1.10408 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.76117 | 0.114400 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.44275 | −0.481432 | −0.240716 | − | 0.970596i | \(-0.577382\pi\) | ||||
−0.240716 | + | 0.970596i | \(0.577382\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.9036 | 1.41093 | 0.705467 | − | 0.708743i | \(-0.250737\pi\) | ||||
0.705467 | + | 0.708743i | \(0.250737\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1495 | −1.03599 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.03818 | 0.194102 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.6303 | −0.740019 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.16049 | −0.263661 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.5769 | −1.04632 | −0.523162 | − | 0.852233i | \(-0.675248\pi\) | ||||
−0.523162 | + | 0.852233i | \(0.675248\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −40.4482 | −2.54296 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.75739 | −0.172674 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.1158 | 0.755764 | 0.377882 | − | 0.925854i | \(-0.376653\pi\) | ||||
0.377882 | + | 0.925854i | \(0.376653\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.66977 | 0.600850 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.3277 | −0.948758 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.20135 | −0.197404 | −0.0987018 | − | 0.995117i | \(-0.531469\pi\) | ||||
−0.0987018 | + | 0.995117i | \(0.531469\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.7265 | 0.966074 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1575 | 0.744030 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.4400 | 0.941396 | 0.470698 | − | 0.882294i | \(-0.344002\pi\) | ||||
0.470698 | + | 0.882294i | \(0.344002\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.8878 | 1.51182 | 0.755912 | − | 0.654673i | \(-0.227194\pi\) | ||||
0.755912 | + | 0.654673i | \(0.227194\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.99273 | 0.241651 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.2295 | −1.21989 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2870 | −0.678172 | −0.339086 | − | 0.940755i | \(-0.610118\pi\) | ||||
−0.339086 | + | 0.940755i | \(0.610118\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.44433 | −0.445680 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0332 | 0.777495 | 0.388747 | − | 0.921344i | \(-0.372908\pi\) | ||||
0.388747 | + | 0.921344i | \(0.372908\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.7190 | −1.29106 | −0.645531 | − | 0.763734i | \(-0.723364\pi\) | ||||
−0.645531 | + | 0.763734i | \(0.723364\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.28959 | −0.431798 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.33675 | 0.0789061 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.7650 | 0.806920 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.9400 | −1.69069 | −0.845346 | − | 0.534219i | \(-0.820606\pi\) | ||||
−0.845346 | + | 0.534219i | \(0.820606\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.2165 | −1.64283 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.4643 | −1.30351 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −37.2131 | −2.15209 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.52513 | −0.145546 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.94769 | −0.169340 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.2441 | 1.15918 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.5836 | 0.661110 | 0.330555 | − | 0.943787i | \(-0.392764\pi\) | ||||
0.330555 | + | 0.943787i | \(0.392764\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.5291 | −0.655867 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.7999 | 0.895932 | 0.447966 | − | 0.894051i | \(-0.352149\pi\) | ||||
0.447966 | + | 0.894051i | \(0.352149\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.2658 | 1.14549 | 0.572745 | − | 0.819733i | \(-0.305878\pi\) | ||||
0.572745 | + | 0.819733i | \(0.305878\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.61200 | −0.372544 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.36537 | 0.357515 | 0.178757 | − | 0.983893i | \(-0.442792\pi\) | ||||
0.178757 | + | 0.983893i | \(0.442792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −33.6780 | −1.88561 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.55235 | 0.198273 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.64366 | 0.147097 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.6115 | −1.03238 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.23421 | 0.178852 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.57082 | 0.307130 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.5910 | −1.35165 | −0.675823 | − | 0.737064i | \(-0.736212\pi\) | ||||
−0.675823 | + | 0.737064i | \(0.736212\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21.0443 | −1.15322 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.0492 | −0.876863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.11956 | 0.387827 | 0.193913 | − | 0.981019i | \(-0.437882\pi\) | ||||
0.193913 | + | 0.981019i | \(0.437882\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.877285 | −0.0476476 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.3567 | −0.885766 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.3242 | −1.25573 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.51477 | −0.0813173 | −0.0406586 | − | 0.999173i | \(-0.512946\pi\) | ||||
−0.0406586 | + | 0.999173i | \(0.512946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.7937 | 1.32717 | 0.663587 | − | 0.748099i | \(-0.269033\pi\) | ||||
0.663587 | + | 0.748099i | \(0.269033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −20.6676 | −1.10315 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.8416 | −0.630267 | −0.315133 | − | 0.949047i | \(-0.602049\pi\) | ||||
−0.315133 | + | 0.949047i | \(0.602049\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.2485 | 1.92387 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.907578 | −0.0480341 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.6743 | 1.40781 | 0.703907 | − | 0.710292i | \(-0.251437\pi\) | ||||
0.703907 | + | 0.710292i | \(0.251437\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.0111 | −0.632162 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.7688 | −0.565215 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 38.6319 | 2.02209 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.6897 | 1.49759 | 0.748796 | − | 0.662801i | \(-0.230632\pi\) | ||||
0.748796 | + | 0.662801i | \(0.230632\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.90918 | −0.151446 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.17630 | 0.268740 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.8946 | −1.39255 | −0.696275 | − | 0.717775i | \(-0.745161\pi\) | ||||
−0.696275 | + | 0.717775i | \(0.745161\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.12169 | 0.109564 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.9844 | −1.59578 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.960453 | −0.0493351 | −0.0246676 | − | 0.999696i | \(-0.507853\pi\) | ||||
−0.0246676 | + | 0.999696i | \(0.507853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.04500 | −0.258463 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9913 | 0.561627 | 0.280814 | − | 0.959762i | \(-0.409396\pi\) | ||||
0.280814 | + | 0.959762i | \(0.409396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.5279 | −0.740411 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.49544 | 0.279349 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.4239 | −1.28904 | −0.644520 | − | 0.764587i | \(-0.722943\pi\) | ||||
−0.644520 | + | 0.764587i | \(0.722943\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.45881 | 0.427781 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.18681 | −0.160753 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.89563 | −0.296641 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.0140 | −0.753533 | −0.376767 | − | 0.926308i | \(-0.622964\pi\) | ||||
−0.376767 | + | 0.926308i | \(0.622964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.39933 | −0.120117 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.0656 | −0.552588 | −0.276294 | − | 0.961073i | \(-0.589106\pi\) | ||||
−0.276294 | + | 0.961073i | \(0.589106\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.0485 | −0.749618 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.88207 | 0.341973 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −46.2387 | −2.29197 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.5650 | 1.41245 | 0.706225 | − | 0.707988i | \(-0.250397\pi\) | ||||
0.706225 | + | 0.707988i | \(0.250397\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.75870 | 0.0867504 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.28732 | −0.456999 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.9275 | 0.683676 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.26411 | 0.208815 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.98566 | 0.0970057 | 0.0485029 | − | 0.998823i | \(-0.484555\pi\) | ||||
0.0485029 | + | 0.998823i | \(0.484555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.1984 | 1.22810 | 0.614048 | − | 0.789269i | \(-0.289540\pi\) | ||||
0.614048 | + | 0.789269i | \(0.289540\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.1238 | −0.589479 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.23054 | 0.205211 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.66325 | 0.322457 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.0924 | −0.921788 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.4984 | 1.32455 | 0.662275 | − | 0.749261i | \(-0.269591\pi\) | ||||
0.662275 | + | 0.749261i | \(0.269591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.1977 | 1.35509 | 0.677547 | − | 0.735480i | \(-0.263043\pi\) | ||||
0.677547 | + | 0.735480i | \(0.263043\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.4202 | −0.931129 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.3622 | 1.06973 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.31298 | −0.301302 | −0.150651 | − | 0.988587i | \(-0.548137\pi\) | ||||
−0.150651 | + | 0.988587i | \(0.548137\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.17630 | −0.103633 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −26.4557 | −1.25695 | −0.628473 | − | 0.777831i | \(-0.716320\pi\) | ||||
−0.628473 | + | 0.777831i | \(0.716320\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.6982 | −1.92928 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.84960 | −0.182080 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.5555 | −1.63077 | −0.815387 | − | 0.578916i | \(-0.803476\pi\) | ||||
−0.815387 | + | 0.578916i | \(0.803476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.39206 | −0.300990 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3069 | 0.531247 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.3659 | −0.626605 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.5922 | 1.24393 | 0.621965 | − | 0.783045i | \(-0.286334\pi\) | ||||
0.621965 | + | 0.783045i | \(0.286334\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.69790 | 0.219279 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.310199 | −0.0144474 | −0.00722371 | − | 0.999974i | \(-0.502299\pi\) | ||||
−0.00722371 | + | 0.999974i | \(0.502299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.4654 | −1.04406 | −0.522028 | − | 0.852928i | \(-0.674825\pi\) | ||||
−0.522028 | + | 0.852928i | \(0.674825\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.43201 | −0.437399 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.6126 | 0.537365 | 0.268682 | − | 0.963229i | \(-0.413412\pi\) | ||||
0.268682 | + | 0.963229i | \(0.413412\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.28251 | −0.243924 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.0162 | 0.737988 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.0746 | 0.555190 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.1841 | 0.513162 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.2652 | −0.515798 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.7976 | −1.45287 | −0.726435 | − | 0.687235i | \(-0.758824\pi\) | ||||
−0.726435 | + | 0.687235i | \(0.758824\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.5405 | −1.93968 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.67704 | −0.349317 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −46.0794 | −2.09236 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.0166 | 1.04298 | 0.521490 | − | 0.853257i | \(-0.325376\pi\) | ||||
0.521490 | + | 0.853257i | \(0.325376\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.42829 | −0.109811 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.3176 | 1.50360 | 0.751802 | − | 0.659389i | \(-0.229185\pi\) | ||||
0.751802 | + | 0.659389i | \(0.229185\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.04298 | 0.317200 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 31.6171 | 1.42108 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.9310 | 0.535177 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.0236 | −1.65741 | −0.828703 | − | 0.559689i | \(-0.810921\pi\) | ||||
−0.828703 | + | 0.559689i | \(0.810921\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.77688 | −0.0793853 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.4172 | 0.553654 | 0.276827 | − | 0.960920i | \(-0.410717\pi\) | ||||
0.276827 | + | 0.960920i | \(0.410717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.86759 | 0.439102 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.76682 | −0.256113 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.9257 | 0.528597 | 0.264299 | − | 0.964441i | \(-0.414860\pi\) | ||||
0.264299 | + | 0.964441i | \(0.414860\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.7155 | 0.562499 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.4196 | 0.548340 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 38.5945 | 1.70067 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.6385 | −1.17156 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.46119 | −0.239719 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.3980 | 1.15652 | 0.578259 | − | 0.815853i | \(-0.303732\pi\) | ||||
0.578259 | + | 0.815853i | \(0.303732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.6272 | −0.595874 | −0.297937 | − | 0.954586i | \(-0.596299\pi\) | ||||
−0.297937 | + | 0.954586i | \(0.596299\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.83955 | −0.167572 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.42063 | 0.149005 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.5515 | 2.11094 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.2120 | 0.877126 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.88081 | −0.254726 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.8917 | −0.514125 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.58927 | 0.0685823 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.78178 | −0.205966 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3358 | 1.13226 | 0.566132 | − | 0.824314i | \(-0.308439\pi\) | ||||
0.566132 | + | 0.824314i | \(0.308439\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.50937 | −0.107687 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.8267 | −0.463766 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.25139 | 0.0962624 | 0.0481312 | − | 0.998841i | \(-0.484673\pi\) | ||||
0.0481312 | + | 0.998841i | \(0.484673\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.5012 | −0.618898 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.6192 | 0.793206 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.94051 | −0.0825190 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.6633 | −1.13179 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.3355 | 1.28536 | 0.642679 | − | 0.766136i | \(-0.277823\pi\) | ||||
0.642679 | + | 0.766136i | \(0.277823\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.1089 | 0.469854 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.33984 | 0.183228 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.9867 | −0.463035 | −0.231518 | − | 0.972831i | \(-0.574369\pi\) | ||||
−0.231518 | + | 0.972831i | \(0.574369\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.93677 | 0.123551 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.26519 | 0.0951292 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.8479 | −1.20937 | −0.604684 | − | 0.796465i | \(-0.706701\pi\) | ||||
−0.604684 | + | 0.796465i | \(0.706701\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.5165 | 0.440100 | 0.220050 | − | 0.975489i | \(-0.429378\pi\) | ||||
0.220050 | + | 0.975489i | \(0.429378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.1043 | 0.714542 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 35.7854 | 1.49235 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.8288 | −1.53320 | −0.766601 | − | 0.642123i | \(-0.778054\pi\) | ||||
−0.766601 | + | 0.642123i | \(0.778054\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −10.8099 | −0.449242 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.58417 | 0.190183 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.7519 | −1.02512 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29.0883 | 1.20265 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.1420 | −1.24409 | −0.622047 | − | 0.782980i | \(-0.713699\pi\) | ||||
−0.622047 | + | 0.782980i | \(0.713699\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.04298 | 0.372610 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.6722 | 0.644669 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.88925 | −0.323973 | −0.161986 | − | 0.986793i | \(-0.551790\pi\) | ||||
−0.161986 | + | 0.986793i | \(0.551790\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.03818 | 0.124553 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8362 | −0.566276 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.8059 | −1.21783 | −0.608917 | − | 0.793234i | \(-0.708396\pi\) | ||||
−0.608917 | + | 0.793234i | \(0.708396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.9432 | 0.487175 | 0.243587 | − | 0.969879i | \(-0.421676\pi\) | ||||
0.243587 | + | 0.969879i | \(0.421676\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.4963 | 0.468167 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.0493 | 1.46561 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.67281 | 0.189664 | 0.0948318 | − | 0.995493i | \(-0.469769\pi\) | ||||
0.0948318 | + | 0.995493i | \(0.469769\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.39206 | −0.259019 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.5079 | −0.991483 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.3894 | 1.71209 | 0.856046 | − | 0.516900i | \(-0.172914\pi\) | ||||
0.856046 | + | 0.516900i | \(0.172914\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.68595 | −0.148632 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2809 | −0.937255 | −0.468628 | − | 0.883396i | \(-0.655251\pi\) | ||||
−0.468628 | + | 0.883396i | \(0.655251\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.2201 | 1.73716 | 0.868582 | − | 0.495545i | \(-0.165032\pi\) | ||||
0.868582 | + | 0.495545i | \(0.165032\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.7387 | 1.59466 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.3956 | −0.536683 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.2552 | −1.13021 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.4730 | 0.458189 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.66977 | 0.385559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.6825 | −1.22145 | −0.610725 | − | 0.791843i | \(-0.709122\pi\) | ||||
−0.610725 | + | 0.791843i | \(0.709122\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.72649 | 0.307100 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.8885 | 0.670200 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.39933 | −0.174308 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.9654 | −1.02718 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.3561 | −0.843517 | −0.421758 | − | 0.906708i | \(-0.638587\pi\) | ||||
−0.421758 | + | 0.906708i | \(0.638587\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.7013 | −0.895253 | −0.447626 | − | 0.894221i | \(-0.647731\pi\) | ||||
−0.447626 | + | 0.894221i | \(0.647731\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.96275 | 0.274158 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −35.2630 | −1.38633 | −0.693165 | − | 0.720779i | \(-0.743784\pi\) | ||||
−0.693165 | + | 0.720779i | \(0.743784\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.4099 | 1.74324 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.10449 | −0.121675 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.0593 | −1.17631 | −0.588155 | − | 0.808748i | \(-0.700146\pi\) | ||||
−0.588155 | + | 0.808748i | \(0.700146\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.6681 | 0.416836 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.6727 | −1.07961 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.9747 | 0.739148 | 0.369574 | − | 0.929201i | \(-0.379504\pi\) | ||||
0.369574 | + | 0.929201i | \(0.379504\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.8038 | 1.00365 | 0.501825 | − | 0.864969i | \(-0.332662\pi\) | ||||
0.501825 | + | 0.864969i | \(0.332662\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.99273 | 0.155065 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.03191 | 0.311464 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 59.5753 | 2.30676 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.26072 | −0.0874044 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −31.8622 | −1.23003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.38401 | 0.168991 | 0.0844956 | − | 0.996424i | \(-0.473072\pi\) | ||||
0.0844956 | + | 0.996424i | \(0.473072\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 19.8747 | 0.764976 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.1115 | −1.23415 | −0.617073 | − | 0.786906i | \(-0.711682\pi\) | ||||
−0.617073 | + | 0.786906i | \(0.711682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.1668 | −0.582047 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.4145 | −0.590684 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.7093 | 0.715892 | 0.357946 | − | 0.933742i | \(-0.383477\pi\) | ||||
0.357946 | + | 0.933742i | \(0.383477\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.88738 | −0.224945 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.8210 | 0.565457 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.7722 | −0.867553 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.9131 | 1.55641 | 0.778205 | − | 0.628011i | \(-0.216131\pi\) | ||||
0.778205 | + | 0.628011i | \(0.216131\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.4066 | 0.395314 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.2744 | −0.541459 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.33675 | 0.0506331 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.24421 | 0.198354 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.6240 | −0.665649 | −0.332825 | − | 0.942989i | \(-0.608002\pi\) | ||||
−0.332825 | + | 0.942989i | \(0.608002\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.5636 | 0.964148 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.3609 | −0.578526 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.24786 | 0.122148 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.18690 | −0.307466 | −0.153733 | − | 0.988112i | \(-0.549130\pi\) | ||||
−0.153733 | + | 0.988112i | \(0.549130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.22314 | 0.158380 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.9345 | 1.08361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 63.9130 | 2.39021 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.75488 | 0.252266 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.6093 | −1.58906 | −0.794530 | − | 0.607225i | \(-0.792283\pi\) | ||||
−0.794530 | + | 0.607225i | \(0.792283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.7031 | 0.473090 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.8792 | −0.739316 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 29.7956 | 1.10658 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.5470 | 0.391166 | 0.195583 | − | 0.980687i | \(-0.437340\pi\) | ||||
0.195583 | + | 0.980687i | \(0.437340\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.86138 | 0.291162 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.52513 | −0.0933951 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.61491 | 0.244327 | 0.122164 | − | 0.992510i | \(-0.461017\pi\) | ||||
0.122164 | + | 0.992510i | \(0.461017\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.75739 | −0.101708 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.2598 | 0.930457 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.834376 | 0.0306930 | 0.0153465 | − | 0.999882i | \(-0.495115\pi\) | ||||
0.0153465 | + | 0.999882i | \(0.495115\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.5554 | 0.387763 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.9082 | −1.94101 | −0.970506 | − | 0.241077i | \(-0.922499\pi\) | ||||
−0.970506 | + | 0.241077i | \(0.922499\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.8868 | 0.472136 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.97654 | −0.365022 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.91410 | −0.143018 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.3681 | −1.29060 | −0.645300 | − | 0.763929i | \(-0.723268\pi\) | ||||
−0.645300 | + | 0.763929i | \(0.723268\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.0448 | 0.548264 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.8508 | −1.37753 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.6550 | −0.714372 | −0.357186 | − | 0.934033i | \(-0.616264\pi\) | ||||
−0.357186 | + | 0.934033i | \(0.616264\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.7099 | 1.33248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.80776 | −0.246781 | −0.123390 | − | 0.992358i | \(-0.539377\pi\) | ||||
−0.123390 | + | 0.992358i | \(0.539377\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.56356 | −0.129009 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.61200 | −0.239057 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.8579 | 1.47529 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.3645 | 1.59983 | 0.799913 | − | 0.600116i | \(-0.204879\pi\) | ||||
0.799913 | + | 0.600116i | \(0.204879\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.9961 | −0.396013 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −25.6974 | −0.924270 | −0.462135 | − | 0.886810i | \(-0.652916\pi\) | ||||
−0.462135 | + | 0.886810i | \(0.652916\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.4711 | 0.519819 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.77607 | −0.314840 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.53392 | 0.126616 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57.0513 | −2.04146 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.0872 | 1.18244 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −53.6153 | −1.91361 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.6566 | −0.914558 | −0.457279 | − | 0.889323i | \(-0.651176\pi\) | ||||
−0.457279 | + | 0.889323i | \(0.651176\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.90547 | 0.103438 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.966622 | 0.0343691 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.3138 | −1.04096 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.2731 | −0.506213 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.3683 | 0.721483 | 0.360741 | − | 0.932666i | \(-0.382524\pi\) | ||||
0.360741 | + | 0.932666i | \(0.382524\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.57082 | 0.197082 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.1528 | 1.03006 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −60.8026 | −2.14568 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.6994 | 0.905785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.0130 | −0.493282 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.5480 | −1.28496 | −0.642480 | − | 0.766303i | \(-0.722094\pi\) | ||||
−0.642480 | + | 0.766303i | \(0.722094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.33037 | −0.257404 | −0.128702 | − | 0.991683i | \(-0.541081\pi\) | ||||
−0.128702 | + | 0.991683i | \(0.541081\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −22.5876 | −0.792182 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.12886 | 0.284742 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.67557 | −0.233549 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.57426 | 0.334552 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.76321 | 0.0615366 | 0.0307683 | − | 0.999527i | \(-0.490205\pi\) | ||||
0.0307683 | + | 0.999527i | \(0.490205\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.636323 | −0.0221808 | −0.0110904 | − | 0.999938i | \(-0.503530\pi\) | ||||
−0.0110904 | + | 0.999938i | \(0.503530\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.3599 | 0.639209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.81869 | 0.237109 | 0.118554 | − | 0.992948i | \(-0.462174\pi\) | ||||
0.118554 | + | 0.992948i | \(0.462174\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.9480 | 1.76950 | 0.884749 | − | 0.466068i | \(-0.154330\pi\) | ||||
0.884749 | + | 0.466068i | \(0.154330\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.2439 | 0.355356 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.00000 | 0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.94824 | 0.205847 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0698 | 0.555453 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.95064 | −0.101867 | −0.0509336 | − | 0.998702i | \(-0.516220\pi\) | ||||
−0.0509336 | + | 0.998702i | \(0.516220\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.6036 | 0.710470 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.8286 | −0.407400 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 19.3048 | 0.664106 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.8654 | 0.407700 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.7117 | 0.676504 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 81.7948 | 2.80389 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.8764 | −0.988709 | −0.494355 | − | 0.869260i | \(-0.664596\pi\) | ||||
−0.494355 | + | 0.869260i | \(0.664596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.4799 | −0.597799 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.83977 | −0.336120 | −0.168060 | − | 0.985777i | \(-0.553750\pi\) | ||||
−0.168060 | + | 0.985777i | \(0.553750\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.1344 | 0.379900 | 0.189950 | − | 0.981794i | \(-0.439167\pi\) | ||||
0.189950 | + | 0.981794i | \(0.439167\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.21321 | −0.0413460 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.7030 | −0.772818 | −0.386409 | − | 0.922328i | \(-0.626285\pi\) | ||||
−0.386409 | + | 0.922328i | \(0.626285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.2817 | 0.621596 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.907578 | −0.0308230 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.27910 | 0.314772 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.2395 | 0.787440 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33.0075 | 1.11713 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.33775 | −0.0790304 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.55717 | 0.0525819 | 0.0262910 | − | 0.999654i | \(-0.491630\pi\) | ||||
0.0262910 | + | 0.999654i | \(0.491630\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.2653 | 0.885907 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.3326 | −0.348113 | −0.174056 | − | 0.984736i | \(-0.555687\pi\) | ||||
−0.174056 | + | 0.984736i | \(0.555687\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.6160 | −0.794743 | −0.397371 | − | 0.917658i | \(-0.630078\pi\) | ||||
−0.397371 | + | 0.917658i | \(0.630078\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.6087 | 0.860828 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.9260 | −0.467588 | −0.233794 | − | 0.972286i | \(-0.575114\pi\) | ||||
−0.233794 | + | 0.972286i | \(0.575114\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.55875 | 0.186435 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.8317 | −0.362874 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.7274 | 0.492832 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.32021 | −0.177835 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.7738 | 1.12767 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.0915 | 0.803495 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.17630 | 0.172448 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.29175 | 0.0762646 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.40028 | 0.279235 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.3628 | −0.377295 | −0.188648 | − | 0.982045i | \(-0.560410\pi\) | ||||
−0.188648 | + | 0.982045i | \(0.560410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.06832 | −0.234442 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.75507 | −0.157543 | −0.0787713 | − | 0.996893i | \(-0.525100\pi\) | ||||
−0.0787713 | + | 0.996893i | \(0.525100\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.9205 | −0.725462 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.3731 | −0.607398 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.51134 | 0.115955 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.6303 | 1.07637 | 0.538187 | − | 0.842825i | \(-0.319109\pi\) | ||||
0.538187 | + | 0.842825i | \(0.319109\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.5130 | −0.346416 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −52.4882 | −1.72767 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.9084 | 1.34506 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.6459 | −0.908010 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.3546 | −1.55365 | −0.776827 | − | 0.629714i | \(-0.783172\pi\) | ||||
−0.776827 | + | 0.629714i | \(0.783172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.64366 | 0.0866424 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.3397 | −0.469460 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.5279 | −0.475113 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.6525 | −1.68741 | −0.843707 | − | 0.536803i | \(-0.819632\pi\) | ||||
−0.843707 | + | 0.536803i | \(0.819632\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18.3928 | −0.600226 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.7240 | −1.78395 | −0.891975 | − | 0.452084i | \(-0.850681\pi\) | ||||
−0.891975 | + | 0.452084i | \(0.850681\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.3073 | 0.368218 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14.2731 | 0.464303 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.9728 | 1.20145 | 0.600727 | − | 0.799454i | \(-0.294878\pi\) | ||||
0.600727 | + | 0.799454i | \(0.294878\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −55.9395 | −1.81587 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.77707 | −0.187334 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.91313 | −0.256331 | −0.128166 | − | 0.991753i | \(-0.540909\pi\) | ||||
−0.128166 | + | 0.991753i | \(0.540909\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −57.2578 | −1.85282 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.5654 | 0.988039 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.93780 | −0.0625747 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.2993 | −0.622557 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.51826 | 0.274497 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 36.1867 | 1.16489 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.05906 | −0.259162 | −0.129581 | − | 0.991569i | \(-0.541363\pi\) | ||||
−0.129581 | + | 0.991569i | \(0.541363\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.39933 | −0.0770775 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.81193 | 0.0581476 | 0.0290738 | − | 0.999577i | \(-0.490744\pi\) | ||||
0.0290738 | + | 0.999577i | \(0.490744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.69834 | −0.150622 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.8914 | 0.540959 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.1934 | 0.486079 | 0.243040 | − | 0.970016i | \(-0.421855\pi\) | ||||
0.243040 | + | 0.970016i | \(0.421855\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 64.0547 | 2.04720 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.75538 | 0.247610 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.6472 | −0.371488 | −0.185744 | − | 0.982598i | \(-0.559470\pi\) | ||||
−0.185744 | + | 0.982598i | \(0.559470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.4638 | −1.67164 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.05596 | −0.160933 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.3596 | −0.679195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.1759 | 1.49859 | 0.749296 | − | 0.662235i | \(-0.230392\pi\) | ||||
0.749296 | + | 0.662235i | \(0.230392\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.3183 | 0.708249 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.3175 | 1.46836 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.7574 | 1.25913 | 0.629564 | − | 0.776949i | \(-0.283234\pi\) | ||||
0.629564 | + | 0.776949i | \(0.283234\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.4276 | 1.43727 |
(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 | 1904.2.a.t.1.2 | 5 | ||
4.3 | odd | 2 | 119.2.a.b.1.3 | ✓ | 5 | ||
8.3 | odd | 2 | 7616.2.a.bt.1.2 | 5 | |||
8.5 | even | 2 | 7616.2.a.bq.1.4 | 5 | |||
12.11 | even | 2 | 1071.2.a.m.1.3 | 5 | |||
20.19 | odd | 2 | 2975.2.a.m.1.3 | 5 | |||
28.3 | even | 6 | 833.2.e.h.324.3 | 10 | |||
28.11 | odd | 6 | 833.2.e.i.324.3 | 10 | |||
28.19 | even | 6 | 833.2.e.h.18.3 | 10 | |||
28.23 | odd | 6 | 833.2.e.i.18.3 | 10 | |||
28.27 | even | 2 | 833.2.a.g.1.3 | 5 | |||
68.67 | odd | 2 | 2023.2.a.j.1.3 | 5 | |||
84.83 | odd | 2 | 7497.2.a.br.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
119.2.a.b.1.3 | ✓ | 5 | 4.3 | odd | 2 | ||
833.2.a.g.1.3 | 5 | 28.27 | even | 2 | |||
833.2.e.h.18.3 | 10 | 28.19 | even | 6 | |||
833.2.e.h.324.3 | 10 | 28.3 | even | 6 | |||
833.2.e.i.18.3 | 10 | 28.23 | odd | 6 | |||
833.2.e.i.324.3 | 10 | 28.11 | odd | 6 | |||
1071.2.a.m.1.3 | 5 | 12.11 | even | 2 | |||
1904.2.a.t.1.2 | 5 | 1.1 | even | 1 | trivial | ||
2023.2.a.j.1.3 | 5 | 68.67 | odd | 2 | |||
2975.2.a.m.1.3 | 5 | 20.19 | odd | 2 | |||
7497.2.a.br.1.3 | 5 | 84.83 | odd | 2 | |||
7616.2.a.bq.1.4 | 5 | 8.5 | even | 2 | |||
7616.2.a.bt.1.2 | 5 | 8.3 | odd | 2 |