Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 49x^{6} + 31x^{5} + 750x^{4} + 249x^{3} - 2892x^{2} - 620x + 2400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 115) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.85207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | ||||||||
\(3\) | −8.45088 | −1.62637 | −0.813186 | − | 0.582003i | \(-0.802269\pi\) | ||||
−0.813186 | + | 0.582003i | \(0.802269\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.9190 | −0.913539 | −0.456770 | − | 0.889585i | \(-0.650994\pi\) | ||||
−0.456770 | + | 0.889585i | \(0.650994\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 44.4174 | 1.64509 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.9363 | 0.436815 | 0.218408 | − | 0.975858i | \(-0.429914\pi\) | ||||
0.218408 | + | 0.975858i | \(0.429914\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −47.2304 | −1.00764 | −0.503821 | − | 0.863808i | \(-0.668073\pi\) | ||||
−0.503821 | + | 0.863808i | \(0.668073\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −42.2544 | −0.727336 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 88.4553 | 1.26197 | 0.630987 | − | 0.775794i | \(-0.282650\pi\) | ||||
0.630987 | + | 0.775794i | \(0.282650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0686 | −0.230244 | −0.115122 | − | 0.993351i | \(-0.536726\pi\) | ||||
−0.115122 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 142.980 | 1.48576 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −147.192 | −1.04915 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 178.581 | 1.14350 | 0.571752 | − | 0.820426i | \(-0.306264\pi\) | ||||
0.571752 | + | 0.820426i | \(0.306264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −249.161 | −1.44357 | −0.721785 | − | 0.692117i | \(-0.756678\pi\) | ||||
−0.721785 | + | 0.692117i | \(0.756678\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −134.676 | −0.710424 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −84.5949 | −0.408547 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −206.047 | −0.915513 | −0.457756 | − | 0.889078i | \(-0.651347\pi\) | ||||
−0.457756 | + | 0.889078i | \(0.651347\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 399.138 | 1.63880 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −83.5198 | −0.318137 | −0.159068 | − | 0.987268i | \(-0.550849\pi\) | ||||
−0.159068 | + | 0.987268i | \(0.550849\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 436.295 | 1.54731 | 0.773655 | − | 0.633607i | \(-0.218426\pi\) | ||||
0.773655 | + | 0.633607i | \(0.218426\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 222.087 | 0.735706 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −158.379 | −0.491531 | −0.245765 | − | 0.969329i | \(-0.579039\pi\) | ||||
−0.245765 | + | 0.969329i | \(0.579039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −56.7479 | −0.165446 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −747.525 | −2.05244 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −373.971 | −0.969224 | −0.484612 | − | 0.874729i | \(-0.661039\pi\) | ||||
−0.484612 | + | 0.874729i | \(0.661039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 79.6813 | 0.195350 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 161.146 | 0.374462 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −586.887 | −1.29502 | −0.647510 | − | 0.762057i | \(-0.724190\pi\) | ||||
−0.647510 | + | 0.762057i | \(0.724190\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 338.828 | 0.711188 | 0.355594 | − | 0.934640i | \(-0.384279\pi\) | ||||
0.355594 | + | 0.934640i | \(0.384279\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −751.497 | −1.50285 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −236.152 | −0.450631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 462.384 | 0.843123 | 0.421562 | − | 0.906800i | \(-0.361482\pi\) | ||||
0.421562 | + | 0.906800i | \(0.361482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 194.370 | 0.339122 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1148.86 | 1.92034 | 0.960170 | − | 0.279415i | \(-0.0901405\pi\) | ||||
0.960170 | + | 0.279415i | \(0.0901405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −887.052 | −1.42221 | −0.711106 | − | 0.703084i | \(-0.751806\pi\) | ||||
−0.711106 | + | 0.703084i | \(0.751806\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −211.272 | −0.325275 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −269.626 | −0.399048 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 460.823 | 0.656287 | 0.328144 | − | 0.944628i | \(-0.393577\pi\) | ||||
0.328144 | + | 0.944628i | \(0.393577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 44.6341 | 0.0612264 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −940.362 | −1.24359 | −0.621796 | − | 0.783179i | \(-0.713597\pi\) | ||||
−0.621796 | + | 0.783179i | \(0.713597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 442.276 | 0.564372 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1509.16 | −1.85976 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 309.068 | 0.368103 | 0.184051 | − | 0.982917i | \(-0.441079\pi\) | ||||
0.184051 | + | 0.982917i | \(0.441079\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 799.090 | 0.920521 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2105.63 | 2.34778 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −95.3428 | −0.102968 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1660.47 | −1.73809 | −0.869046 | − | 0.494731i | \(-0.835267\pi\) | ||||
−0.869046 | + | 0.494731i | \(0.835267\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 707.847 | 0.718599 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1555.86 | −1.53281 | −0.766404 | − | 0.642359i | \(-0.777956\pi\) | ||||
−0.766404 | + | 0.642359i | \(0.777956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 324.009 | 0.309957 | 0.154978 | − | 0.987918i | \(-0.450469\pi\) | ||||
0.154978 | + | 0.987918i | \(0.450469\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 714.902 | 0.664450 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1639.25 | −1.48105 | −0.740524 | − | 0.672030i | \(-0.765422\pi\) | ||||
−0.740524 | + | 0.672030i | \(0.765422\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1626.63 | 1.42938 | 0.714692 | − | 0.699439i | \(-0.246567\pi\) | ||||
0.714692 | + | 0.699439i | \(0.246567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1741.28 | 1.48897 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −768.913 | −0.640117 | −0.320059 | − | 0.947398i | \(-0.603703\pi\) | ||||
−0.320059 | + | 0.947398i | \(0.603703\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2097.85 | −1.65766 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1496.57 | −1.15286 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1077.04 | −0.809193 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 705.816 | 0.517409 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −825.661 | −0.576894 | −0.288447 | − | 0.957496i | \(-0.593139\pi\) | ||||
−0.288447 | + | 0.957496i | \(0.593139\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3687.07 | −2.51650 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1456.43 | −0.971364 | −0.485682 | − | 0.874136i | \(-0.661429\pi\) | ||||
−0.485682 | + | 0.874136i | \(0.661429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 322.621 | 0.210337 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −735.961 | −0.469196 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1303.26 | −0.812740 | −0.406370 | − | 0.913709i | \(-0.633206\pi\) | ||||
−0.406370 | + | 0.913709i | \(0.633206\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1196.28 | 0.729981 | 0.364990 | − | 0.931011i | \(-0.381072\pi\) | ||||
0.364990 | + | 0.931011i | \(0.381072\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1338.44 | 0.799412 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −752.676 | −0.440153 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 892.904 | 0.511391 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 479.570 | 0.269077 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2620.96 | 1.44106 | 0.720529 | − | 0.693425i | \(-0.243899\pi\) | ||||
0.720529 | + | 0.693425i | \(0.243899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 696.513 | 0.375374 | 0.187687 | − | 0.982229i | \(-0.439901\pi\) | ||||
0.187687 | + | 0.982229i | \(0.439901\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3928.95 | 2.07606 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1245.81 | −0.645584 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1778.37 | 0.904010 | 0.452005 | − | 0.892015i | \(-0.350709\pi\) | ||||
0.452005 | + | 0.892015i | \(0.350709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3160.39 | 1.57632 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 389.137 | 0.190486 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1569.03 | 0.753964 | 0.376982 | − | 0.926221i | \(-0.376962\pi\) | ||||
0.376982 | + | 0.926221i | \(0.376962\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −673.378 | −0.317711 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1823.00 | 0.844720 | 0.422360 | − | 0.906428i | \(-0.361202\pi\) | ||||
0.422360 | + | 0.906428i | \(0.361202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.7080 | 0.0153427 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −846.975 | −0.378771 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2950.88 | −1.29683 | −0.648414 | − | 0.761287i | \(-0.724568\pi\) | ||||
−0.648414 | + | 0.761287i | \(0.724568\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −422.975 | −0.182708 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4959.71 | 2.10619 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4148.62 | 1.73230 | 0.866152 | − | 0.499781i | \(-0.166586\pi\) | ||||
0.866152 | + | 0.499781i | \(0.166586\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3585.90 | 1.47258 | 0.736292 | − | 0.676664i | \(-0.236575\pi\) | ||||
0.736292 | + | 0.676664i | \(0.236575\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2863.40 | −1.15666 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1030.24 | −0.409430 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1409.65 | 0.551249 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2490.34 | 0.958443 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2626.76 | 0.995108 | 0.497554 | − | 0.867433i | \(-0.334232\pi\) | ||||
0.497554 | + | 0.867433i | \(0.334232\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2034.69 | 0.758862 | 0.379431 | − | 0.925220i | \(-0.376120\pi\) | ||||
0.379431 | + | 0.925220i | \(0.376120\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1995.69 | 0.732894 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3099.27 | 1.12088 | 0.560442 | − | 0.828194i | \(-0.310631\pi\) | ||||
0.560442 | + | 0.828194i | \(0.310631\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1118.39 | 0.398396 | 0.199198 | − | 0.979959i | \(-0.436166\pi\) | ||||
0.199198 | + | 0.979959i | \(0.436166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3907.56 | −1.37123 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3021.41 | −1.04464 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −417.599 | −0.142275 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1021.60 | −0.343025 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −303.882 | −0.100574 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1560.32 | 0.509086 | 0.254543 | − | 0.967062i | \(-0.418075\pi\) | ||||
0.254543 | + | 0.967062i | \(0.418075\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9708.85 | −3.12319 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2181.47 | 0.691978 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4215.55 | 1.31876 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7496.37 | 2.31305 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4177.77 | −1.27162 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −410.575 | −0.123292 | −0.0616461 | − | 0.998098i | \(-0.519635\pi\) | ||||
−0.0616461 | + | 0.998098i | \(0.519635\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1110.43 | 0.329018 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 286.544 | 0.0837822 | 0.0418911 | − | 0.999122i | \(-0.486662\pi\) | ||||
0.0418911 | + | 0.999122i | \(0.486662\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1449.53 | 0.418286 | 0.209143 | − | 0.977885i | \(-0.432933\pi\) | ||||
0.209143 | + | 0.977885i | \(0.432933\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2278.57 | 0.649000 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2733.70 | −0.768629 | −0.384314 | − | 0.923202i | \(-0.625562\pi\) | ||||
−0.384314 | + | 0.923202i | \(0.625562\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −791.895 | −0.219819 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3894.36 | −1.06737 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1198.55 | −0.324385 | −0.162192 | − | 0.986759i | \(-0.551857\pi\) | ||||
−0.162192 | + | 0.986759i | \(0.551857\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6709.37 | 1.79331 | 0.896656 | − | 0.442727i | \(-0.145989\pi\) | ||||
0.896656 | + | 0.442727i | \(0.145989\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3596.99 | 0.949576 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −283.740 | −0.0739896 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 900.615 | 0.232003 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7946.89 | 2.02255 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2033.02 | 0.511246 | 0.255623 | − | 0.966777i | \(-0.417719\pi\) | ||||
0.255623 | + | 0.966777i | \(0.417719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −366.534 | −0.0910822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3737.62 | −0.917879 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −281.707 | −0.0683751 | −0.0341875 | − | 0.999415i | \(-0.510884\pi\) | ||||
−0.0341875 | + | 0.999415i | \(0.510884\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3486.11 | 0.836357 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7932.09 | 1.88116 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4527.19 | 1.06144 | 0.530720 | − | 0.847547i | \(-0.321922\pi\) | ||||
0.530720 | + | 0.847547i | \(0.321922\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1869.86 | −0.433450 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2611.90 | −0.598672 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7346.53 | 1.66515 | 0.832575 | − | 0.553912i | \(-0.186866\pi\) | ||||
0.832575 | + | 0.553912i | \(0.186866\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7522.91 | −1.68629 | −0.843144 | − | 0.537687i | \(-0.819298\pi\) | ||||
−0.843144 | + | 0.537687i | \(0.819298\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6753.01 | −1.49711 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 398.407 | 0.0873630 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5255.63 | −1.14000 | −0.570000 | − | 0.821645i | \(-0.693057\pi\) | ||||
−0.570000 | + | 0.821645i | \(0.693057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11067.1 | −2.37480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 995.675 | 0.211377 | 0.105689 | − | 0.994399i | \(-0.466295\pi\) | ||||
0.105689 | + | 0.994399i | \(0.466295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1218.36 | 0.255916 | 0.127958 | − | 0.991780i | \(-0.459158\pi\) | ||||
0.127958 | + | 0.991780i | \(0.459158\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 805.731 | 0.167464 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1413.07 | 0.290630 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2911.33 | 0.592578 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14032.4 | 2.82679 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8475.85 | 1.68998 | 0.844991 | − | 0.534781i | \(-0.179606\pi\) | ||||
0.844991 | + | 0.534781i | \(0.179606\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2934.44 | −0.579151 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2345.69 | −0.458286 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1086.30 | 0.210108 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7381.67 | −1.41353 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13148.4 | 2.49292 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1694.14 | 0.318053 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6540.93 | −1.21600 | −0.607998 | − | 0.793938i | \(-0.708027\pi\) | ||||
−0.607998 | + | 0.793938i | \(0.708027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2738.16 | −0.504105 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3060.38 | −0.558001 | −0.279000 | − | 0.960291i | \(-0.590003\pi\) | ||||
−0.279000 | + | 0.960291i | \(0.590003\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3426.33 | 0.618747 | 0.309374 | − | 0.950941i | \(-0.399881\pi\) | ||||
0.309374 | + | 0.950941i | \(0.399881\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3757.48 | −0.672096 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1072.78 | −0.190073 | −0.0950365 | − | 0.995474i | \(-0.530297\pi\) | ||||
−0.0950365 | + | 0.995474i | \(0.530297\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2845.91 | 0.499500 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13853.1 | 2.40873 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1686.71 | −0.290561 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1180.76 | −0.201528 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13746.4 | −2.32471 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2679.61 | 0.449033 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3988.82 | 0.662374 | 0.331187 | − | 0.943565i | \(-0.392551\pi\) | ||||
0.331187 | + | 0.943565i | \(0.392551\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9152.08 | −1.50610 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2311.92 | 0.377056 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7537.14 | 1.21832 | 0.609161 | − | 0.793047i | \(-0.291506\pi\) | ||||
0.609161 | + | 0.793047i | \(0.291506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6497.99 | 1.04107 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3970.70 | −0.630573 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6763.33 | 1.06468 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 971.851 | 0.151660 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4451.78 | 0.688715 | 0.344358 | − | 0.938839i | \(-0.388097\pi\) | ||||
0.344358 | + | 0.938839i | \(0.388097\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7628.90 | 1.17010 | 0.585051 | − | 0.810996i | \(-0.301074\pi\) | ||||
0.585051 | + | 0.810996i | \(0.301074\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6951.94 | 1.05717 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6548.34 | −0.987346 | −0.493673 | − | 0.869648i | \(-0.664346\pi\) | ||||
−0.493673 | + | 0.869648i | \(0.664346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5744.28 | 0.858803 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12647.4 | 1.87498 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5823.20 | −0.856091 | −0.428045 | − | 0.903757i | \(-0.640798\pi\) | ||||
−0.428045 | + | 0.903757i | \(0.640798\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6495.39 | −0.946988 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9101.90 | 1.31605 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4435.26 | −0.636033 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4942.79 | 0.703028 | 0.351514 | − | 0.936183i | \(-0.385667\pi\) | ||||
0.351514 | + | 0.936183i | \(0.385667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3709.73 | −0.523363 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6327.21 | 0.885425 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8053.14 | 1.11790 | 0.558949 | − | 0.829202i | \(-0.311205\pi\) | ||||
0.558949 | + | 0.829202i | \(0.311205\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1056.36 | −0.145467 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8434.44 | −1.15224 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10795.6 | −1.46315 | −0.731574 | − | 0.681762i | \(-0.761214\pi\) | ||||
−0.731574 | + | 0.681762i | \(0.761214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6977.56 | 0.938245 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5073.32 | 0.676853 | 0.338426 | − | 0.940993i | \(-0.390105\pi\) | ||||
0.338426 | + | 0.940993i | \(0.390105\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1348.13 | −0.178460 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19379.1 | 2.54546 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7917.35 | 1.03194 | 0.515971 | − | 0.856606i | \(-0.327431\pi\) | ||||
0.515971 | + | 0.856606i | \(0.327431\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2034.47 | −0.263140 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12308.1 | 1.57980 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2304.12 | 0.293501 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3714.37 | 0.469570 | 0.234785 | − | 0.972047i | \(-0.424561\pi\) | ||||
0.234785 | + | 0.972047i | \(0.424561\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2726.43 | −0.342086 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12452.8 | 1.55078 | 0.775392 | − | 0.631480i | \(-0.217552\pi\) | ||||
0.775392 | + | 0.631480i | \(0.217552\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11768.0 | 1.45460 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 223.170 | 0.0273813 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3283.63 | −0.399910 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6780.15 | 0.819699 | 0.409850 | − | 0.912153i | \(-0.365581\pi\) | ||||
0.409850 | + | 0.912153i | \(0.365581\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11013.7 | 1.32182 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9929.53 | 1.18305 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4701.81 | −0.556152 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10109.6 | −1.18722 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4233.55 | −0.493610 | −0.246805 | − | 0.969065i | \(-0.579381\pi\) | ||||
−0.246805 | + | 0.969065i | \(0.579381\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4801.63 | −0.555860 | −0.277930 | − | 0.960601i | \(-0.589648\pi\) | ||||
−0.277930 | + | 0.960601i | \(0.589648\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7034.78 | −0.808611 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2211.38 | 0.252395 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5732.63 | −0.649699 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6360.77 | 0.715853 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5221.81 | −0.583586 | −0.291793 | − | 0.956481i | \(-0.594252\pi\) | ||||
−0.291793 | + | 0.956481i | \(0.594252\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8441.99 | 0.936943 | 0.468471 | − | 0.883479i | \(-0.344805\pi\) | ||||
0.468471 | + | 0.883479i | \(0.344805\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7545.82 | −0.831712 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 438.577 | 0.0480091 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4179.48 | 0.454386 | 0.227193 | − | 0.973850i | \(-0.427045\pi\) | ||||
0.227193 | + | 0.973850i | \(0.427045\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2520.59 | −0.272173 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14990.7 | −1.60774 | −0.803871 | − | 0.594804i | \(-0.797230\pi\) | ||||
−0.803871 | + | 0.594804i | \(0.797230\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1545.34 | 0.164621 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22149.4 | −2.34370 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12698.3 | −1.33468 | −0.667339 | − | 0.744754i | \(-0.732567\pi\) | ||||
−0.667339 | + | 0.744754i | \(0.732567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1330.99 | −0.138967 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5886.15 | −0.610497 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3995.45 | 0.411669 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16157.1 | −1.65382 | −0.826909 | − | 0.562335i | \(-0.809903\pi\) | ||||
−0.826909 | + | 0.562335i | \(0.809903\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13019.9 | −1.32400 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17397.1 | 1.75762 | 0.878812 | − | 0.477168i | \(-0.158337\pi\) | ||||
0.878812 | + | 0.477168i | \(0.158337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14721.3 | 1.47766 | 0.738832 | − | 0.673889i | \(-0.235378\pi\) | ||||
0.738832 | + | 0.673889i | \(0.235378\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10528.2 | 1.04996 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4696.10 | 0.465331 | 0.232666 | − | 0.972557i | \(-0.425255\pi\) | ||||
0.232666 | + | 0.972557i | \(0.425255\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7823.08 | −0.770226 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15028.8 | −1.47026 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6952.91 | 0.675888 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −476.714 | −0.0460487 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16610.8 | −1.59446 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12626.5 | −1.20443 | −0.602213 | − | 0.798336i | \(-0.705714\pi\) | ||||
−0.602213 | + | 0.798336i | \(0.705714\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9731.69 | 0.922509 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3288.55 | −0.309801 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8302.34 | −0.777299 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −597.241 | −0.0555720 | −0.0277860 | − | 0.999614i | \(-0.508846\pi\) | ||||
−0.0277860 | + | 0.999614i | \(0.508846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13259.7 | −1.22623 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5444.13 | −0.500387 | −0.250194 | − | 0.968196i | \(-0.580494\pi\) | ||||
−0.250194 | + | 0.968196i | \(0.580494\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15796.4 | 1.44307 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3539.24 | 0.321367 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19437.5 | −1.75431 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9840.24 | 0.882785 | 0.441392 | − | 0.897314i | \(-0.354485\pi\) | ||||
0.441392 | + | 0.897314i | \(0.354485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15406.0 | −1.37383 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2022.77 | 0.179306 | 0.0896528 | − | 0.995973i | \(-0.471424\pi\) | ||||
0.0896528 | + | 0.995973i | \(0.471424\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7779.28 | −0.685492 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −284.862 | −0.0249530 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12171.6 | 1.05991 | 0.529956 | − | 0.848025i | \(-0.322208\pi\) | ||||
0.529956 | + | 0.848025i | \(0.322208\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15008.0 | 1.29925 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2806.74 | 0.241561 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1620.04 | 0.138617 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2523.97 | −0.214708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24937.6 | 2.10913 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8718.74 | −0.733157 | −0.366579 | − | 0.930387i | \(-0.619471\pi\) | ||||
−0.366579 | + | 0.930387i | \(0.619471\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4412.10 | 0.368886 | 0.184443 | − | 0.982843i | \(-0.440952\pi\) | ||||
0.184443 | + | 0.982843i | \(0.440952\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3574.51 | 0.297151 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22039.6 | −1.82175 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26068.0 | −2.13042 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3944.67 | 0.320568 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8196.24 | −0.662344 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −35059.5 | −2.81737 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −904.350 | −0.0722692 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6786.56 | −0.539329 | −0.269665 | − | 0.962954i | \(-0.586913\pi\) | ||||
−0.269665 | + | 0.962954i | \(0.586913\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30304.0 | −2.39497 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8133.15 | 0.639240 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2847.33 | −0.222565 | −0.111282 | − | 0.993789i | \(-0.535496\pi\) | ||||
−0.111282 | + | 0.993789i | \(0.535496\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15049.9 | 1.16997 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3405.28 | −0.263284 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7796.67 | −0.599544 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8706.41 | 0.665885 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −951.795 | −0.0724037 | −0.0362018 | − | 0.999344i | \(-0.511526\pi\) | ||||
−0.0362018 | + | 0.999344i | \(0.511526\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20606.4 | −1.55913 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11912.8 | −0.896537 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15851.1 | 1.18658 | 0.593288 | − | 0.804990i | \(-0.297829\pi\) | ||||
0.593288 | + | 0.804990i | \(0.297829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3844.56 | −0.286269 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −755.163 | −0.0559328 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24461.5 | −1.80225 | −0.901125 | − | 0.433560i | \(-0.857257\pi\) | ||||
−0.901125 | + | 0.433560i | \(0.857257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21116.1 | 1.54760 | 0.773801 | − | 0.633429i | \(-0.218353\pi\) | ||||
0.773801 | + | 0.633429i | \(0.218353\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22198.4 | −1.61842 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14543.0 | −1.04928 | −0.524640 | − | 0.851324i | \(-0.675800\pi\) | ||||
−0.524640 | + | 0.851324i | \(0.675800\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17194.9 | −1.23419 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15910.0 | 1.13607 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5959.70 | −0.423372 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10489.2 | −0.741328 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −817.198 | −0.0574606 | −0.0287303 | − | 0.999587i | \(-0.509146\pi\) | ||||
−0.0287303 | + | 0.999587i | \(0.509146\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4751.15 | 0.332373 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26191.6 | −1.82297 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18784.4 | 1.30081 | 0.650406 | − | 0.759586i | \(-0.274599\pi\) | ||||
0.650406 | + | 0.759586i | \(0.274599\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7482.87 | −0.515576 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9451.41 | −0.647940 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5703.48 | −0.389045 | −0.194522 | − | 0.980898i | \(-0.562316\pi\) | ||||
−0.194522 | + | 0.980898i | \(0.562316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12055.2 | −0.818206 | −0.409103 | − | 0.912488i | \(-0.634158\pi\) | ||||
−0.409103 | + | 0.912488i | \(0.634158\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20537.9 | 1.38701 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5385.18 | −0.361882 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24047.6 | −1.60801 | −0.804005 | − | 0.594622i | \(-0.797302\pi\) | ||||
−0.804005 | + | 0.594622i | \(0.797302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25533.5 | 1.69897 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7480.30 | 0.495287 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7229.82 | 0.476362 | 0.238181 | − | 0.971221i | \(-0.423449\pi\) | ||||
0.238181 | + | 0.971221i | \(0.423449\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3529.08 | 0.231392 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13799.4 | 0.900397 | 0.450198 | − | 0.892929i | \(-0.351353\pi\) | ||||
0.450198 | + | 0.892929i | \(0.351353\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29923.6 | −1.94302 | −0.971510 | − | 0.237000i | \(-0.923836\pi\) | ||||
−0.971510 | + | 0.237000i | \(0.923836\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3385.42 | 0.218764 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5229.12 | −0.336276 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2568.07 | 0.163571 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18226.0 | −1.15535 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15319.2 | −0.966479 | −0.483240 | − | 0.875488i | \(-0.660540\pi\) | ||||
−0.483240 | + | 0.875488i | \(0.660540\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13186.1 | −0.827963 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4128.31 | −0.257995 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2680.22 | 0.166710 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 51029.2 | 3.15913 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4845.99 | 0.298604 | 0.149302 | − | 0.988792i | \(-0.452297\pi\) | ||||
0.149302 | + | 0.988792i | \(0.452297\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3001.58 | −0.184091 | −0.0920457 | − | 0.995755i | \(-0.529341\pi\) | ||||
−0.0920457 | + | 0.995755i | \(0.529341\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18435.4 | −1.12541 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13518.7 | 0.821445 | 0.410723 | − | 0.911760i | \(-0.365276\pi\) | ||||
0.410723 | + | 0.911760i | \(0.365276\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9352.79 | −0.565684 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35625.1 | −2.14479 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16824.5 | 1.00826 | 0.504129 | − | 0.863628i | \(-0.331814\pi\) | ||||
0.504129 | + | 0.863628i | \(0.331814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7282.14 | −0.434407 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −39400.5 | −2.33967 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −990.892 | −0.0585731 | −0.0292865 | − | 0.999571i | \(-0.509324\pi\) | ||||
−0.0292865 | + | 0.999571i | \(0.509324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16013.5 | 0.942287 | 0.471144 | − | 0.882056i | \(-0.343841\pi\) | ||||
0.471144 | + | 0.882056i | \(0.343841\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35305.9 | 2.06812 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1613.10 | 0.0940654 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4107.36 | −0.238437 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3469.72 | 0.200519 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5399.66 | 0.310658 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15026.3 | −0.860653 | −0.430327 | − | 0.902673i | \(-0.641602\pi\) | ||||
−0.430327 | + | 0.902673i | \(0.641602\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3679.80 | −0.209831 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1662.23 | −0.0943645 | −0.0471822 | − | 0.998886i | \(-0.515024\pi\) | ||||
−0.0471822 | + | 0.998886i | \(0.515024\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28093.4 | 1.58782 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2421.54 | −0.136261 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8169.66 | 0.457692 | 0.228846 | − | 0.973463i | \(-0.426505\pi\) | ||||
0.228846 | + | 0.973463i | \(0.426505\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6516.32 | −0.363468 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12249.8 | −0.680288 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 17662.8 | 0.976631 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31434.8 | 1.73059 | 0.865294 | − | 0.501265i | \(-0.167132\pi\) | ||||
0.865294 | + | 0.501265i | \(0.167132\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11976.1 | −0.656469 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5981.41 | 0.326457 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7387.76 | −0.401480 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23102.2 | 1.25008 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27244.8 | −1.46793 | −0.733967 | − | 0.679185i | \(-0.762333\pi\) | ||||
−0.733967 | + | 0.679185i | \(0.762333\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3929.03 | 0.210791 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6692.21 | 0.357508 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26323.5 | 1.40028 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8420.90 | 0.446056 | 0.223028 | − | 0.974812i | \(-0.428406\pi\) | ||||
0.223028 | + | 0.974812i | \(0.428406\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20468.6 | 1.07965 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5730.71 | 0.301005 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3763.38 | −0.196843 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10128.8 | 0.527570 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14850.3 | −0.770269 | −0.385134 | − | 0.922860i | \(-0.625845\pi\) | ||||
−0.385134 | + | 0.922860i | \(0.625845\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5481.90 | −0.283158 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −56700.1 | −2.91659 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4464.52 | 0.228701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14777.2 | −0.753857 | −0.376929 | − | 0.926242i | \(-0.623020\pi\) | ||||
−0.376929 | + | 0.926242i | \(0.623020\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31602.9 | −1.60559 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38592.6 | 1.95266 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2071.41 | 0.104378 | 0.0521891 | − | 0.998637i | \(-0.483380\pi\) | ||||
0.0521891 | + | 0.998637i | \(0.483380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2397.85 | 0.120335 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7368.68 | 0.368289 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30447.9 | 1.51562 | 0.757810 | − | 0.652475i | \(-0.226269\pi\) | ||||
0.757810 | + | 0.652475i | \(0.226269\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7610.99 | −0.377324 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3975.35 | 0.196287 | 0.0981436 | − | 0.995172i | \(-0.468710\pi\) | ||||
0.0981436 | + | 0.995172i | \(0.468710\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13104.8 | 0.644461 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −41768.4 | −2.04582 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27734.4 | 1.35299 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22811.5 | 1.10839 | 0.554196 | − | 0.832386i | \(-0.313026\pi\) | ||||
0.554196 | + | 0.832386i | \(0.313026\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17180.8 | −0.831477 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3482.56 | 0.167872 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22835.0 | 1.09637 | 0.548185 | − | 0.836357i | \(-0.315319\pi\) | ||||
0.548185 | + | 0.836357i | \(0.315319\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3097.54 | 0.148134 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15837.9 | −0.754432 | −0.377216 | − | 0.926125i | \(-0.623119\pi\) | ||||
−0.377216 | + | 0.926125i | \(0.623119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27520.9 | −1.30580 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19644.8 | 0.928441 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27718.9 | 1.30492 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7610.08 | 0.356861 | 0.178431 | − | 0.983952i | \(-0.442898\pi\) | ||||
0.178431 | + | 0.983952i | \(0.442898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2380.67 | 0.111203 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18824.4 | 0.875895 | 0.437948 | − | 0.899001i | \(-0.355706\pi\) | ||||
0.437948 | + | 0.899001i | \(0.355706\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6229.03 | −0.288714 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −29460.7 | −1.36023 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1592.60 | 0.0732489 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18308.5 | 0.838834 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26285.7 | −1.19971 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8891.86 | 0.404286 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5468.65 | 0.247696 | 0.123848 | − | 0.992301i | \(-0.460477\pi\) | ||||
0.123848 | + | 0.992301i | \(0.460477\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38258.8 | −1.72630 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13009.2 | 0.584772 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16003.0 | −0.716624 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15801.9 | 0.704952 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17054.5 | 0.757968 | 0.378984 | − | 0.925403i | \(-0.376273\pi\) | ||||
0.378984 | + | 0.925403i | \(0.376273\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14009.5 | −0.620299 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13728.0 | 0.605562 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14136.3 | −0.621244 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1945.68 | 0.0851880 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −62084.6 | −2.70816 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16137.0 | 0.701296 | 0.350648 | − | 0.936507i | \(-0.385961\pi\) | ||||
0.350648 | + | 0.936507i | \(0.385961\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27672.2 | 1.19816 | 0.599078 | − | 0.800691i | \(-0.295534\pi\) | ||||
0.599078 | + | 0.800691i | \(0.295534\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 63575.2 | 2.74253 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7845.17 | 0.337183 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8319.51 | −0.356258 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35493.5 | 1.51434 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 817.964 | 0.0347712 | 0.0173856 | − | 0.999849i | \(-0.494466\pi\) | ||||
0.0173856 | + | 0.999849i | \(0.494466\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29069.7 | 1.23123 | 0.615617 | − | 0.788045i | \(-0.288907\pi\) | ||||
0.615617 | + | 0.788045i | \(0.288907\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3366.89 | −0.142085 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3394.17 | 0.142717 | 0.0713584 | − | 0.997451i | \(-0.477267\pi\) | ||||
0.0713584 | + | 0.997451i | \(0.477267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12569.4 | 0.526602 | 0.263301 | − | 0.964714i | \(-0.415189\pi\) | ||||
0.263301 | + | 0.964714i | \(0.415189\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 44414.7 | 1.85406 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5019.65 | −0.208788 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9115.02 | 0.377770 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36674.6 | 1.51453 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8644.40 | 0.355706 | 0.177853 | − | 0.984057i | \(-0.443085\pi\) | ||||
0.177853 | + | 0.984057i | \(0.443085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7502.10 | 0.307602 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8414.33 | −0.343778 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 168.540 | 0.00686148 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18222.3 | 0.739229 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10296.2 | −0.416214 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4739.09 | 0.190898 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24763.3 | −0.993996 | −0.496998 | − | 0.867752i | \(-0.665564\pi\) | ||||
−0.496998 | + | 0.867752i | \(0.665564\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4234.88 | −0.169392 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10811.6 | −0.430942 | −0.215471 | − | 0.976510i | \(-0.569129\pi\) | ||||
−0.215471 | + | 0.976510i | \(0.569129\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40250.6 | −1.59876 | −0.799379 | − | 0.600828i | \(-0.794838\pi\) | ||||
−0.799379 | + | 0.600828i | \(0.794838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11941.7 | −0.472673 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37822.0 | −1.49186 | −0.745931 | − | 0.666023i | \(-0.767995\pi\) | ||||
−0.745931 | + | 0.666023i | \(0.767995\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14754.4 | −0.579960 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24603.3 | −0.963752 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7343.81 | 0.286676 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21838.6 | −0.849566 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −73753.6 | −2.85931 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2114.87 | −0.0817094 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4369.24 | −0.168231 | −0.0841157 | − | 0.996456i | \(-0.526807\pi\) | ||||
−0.0841157 | + | 0.996456i | \(0.526807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −71628.4 | −2.74854 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6206.68 | 0.237353 | 0.118677 | − | 0.992933i | \(-0.462135\pi\) | ||||
0.118677 | + | 0.992933i | \(0.462135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13024.5 | −0.496385 | −0.248192 | − | 0.968711i | \(-0.579837\pi\) | ||||
−0.248192 | + | 0.968711i | \(0.579837\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24798.6 | 0.941915 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44532.0 | −1.68573 | −0.842863 | − | 0.538128i | \(-0.819132\pi\) | ||||
−0.842863 | + | 0.538128i | \(0.819132\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13969.3 | 0.527016 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 711.301 | 0.0267446 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3020.06 | 0.113172 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20743.1 | 0.774710 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9180.18 | −0.341714 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −44495.4 | −1.65073 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33079.7 | −1.22314 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 62381.6 | 2.29892 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17929.5 | 0.658560 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36618.2 | 1.34056 | 0.670279 | − | 0.742109i | \(-0.266174\pi\) | ||||
0.670279 | + | 0.742109i | \(0.266174\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −69107.1 | −2.52160 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31521.0 | 1.14636 | 0.573182 | − | 0.819428i | \(-0.305709\pi\) | ||||
0.573182 | + | 0.819428i | \(0.305709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14985.9 | −0.543220 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14317.0 | −0.517273 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24641.3 | 0.887379 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7870.23 | 0.282497 | 0.141249 | − | 0.989974i | \(-0.454888\pi\) | ||||
0.141249 | + | 0.989974i | \(0.454888\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 55276.7 | 1.97766 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54260.9 | −1.93502 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5151.18 | −0.183103 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14391.6 | 0.509906 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5845.33 | −0.206436 | −0.103218 | − | 0.994659i | \(-0.532914\pi\) | ||||
−0.103218 | + | 0.994659i | \(0.532914\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1082.10 | 0.0380928 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25862.9 | 0.907517 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7048.23 | 0.246526 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2361.81 | −0.0823448 | −0.0411724 | − | 0.999152i | \(-0.513109\pi\) | ||||
−0.0411724 | + | 0.999152i | \(0.513109\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28955.5 | −1.00631 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29730.7 | 1.02996 | 0.514981 | − | 0.857202i | \(-0.327799\pi\) | ||||
0.514981 | + | 0.857202i | \(0.327799\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1920.96 | 0.0663361 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12451.7 | 0.428629 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8584.79 | −0.294581 | −0.147290 | − | 0.989093i | \(-0.547055\pi\) | ||||
−0.147290 | + | 0.989093i | \(0.547055\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41895.8 | 1.43308 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9065.90 | 0.309129 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51072.2 | 1.73598 | 0.867992 | − | 0.496579i | \(-0.165411\pi\) | ||||
0.867992 | + | 0.496579i | \(0.165411\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13133.8 | 0.445026 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24050.5 | −0.812373 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22049.9 | 0.742470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 32290.3 | 1.08389 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −72811.1 | −2.43645 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10173.5 | 0.339374 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2670.23 | 0.0887992 | 0.0443996 | − | 0.999014i | \(-0.485863\pi\) | ||||
0.0443996 | + | 0.999014i | \(0.485863\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14254.2 | 0.472561 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40190.1 | −1.32828 | −0.664141 | − | 0.747607i | \(-0.731203\pi\) | ||||
−0.664141 | + | 0.747607i | \(0.731203\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20239.9 | −0.666866 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9978.46 | 0.327760 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6199.68 | −0.203015 | −0.101507 | − | 0.994835i | \(-0.532367\pi\) | ||||
−0.101507 | + | 0.994835i | \(0.532367\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4925.39 | 0.160793 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 72250.6 | 2.35146 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42606.5 | 1.38244 | 0.691219 | − | 0.722645i | \(-0.257074\pi\) | ||||
0.691219 | + | 0.722645i | \(0.257074\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15496.4 | 0.501274 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22645.1 | −0.730295 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10034.8 | −0.322636 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6898.57 | 0.221131 | 0.110565 | − | 0.993869i | \(-0.464734\pi\) | ||||
0.110565 | + | 0.993869i | \(0.464734\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33709.1 | −1.07727 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5591.97 | 0.178168 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −49114.1 | −1.56014 | −0.780070 | − | 0.625693i | \(-0.784816\pi\) | ||||
−0.780070 | + | 0.625693i | \(0.784816\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30328.6 | 0.960513 |
(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 | 1840.4.a.v.1.2 | 8 | ||
4.3 | odd | 2 | 115.4.a.f.1.2 | ✓ | 8 | ||
12.11 | even | 2 | 1035.4.a.r.1.7 | 8 | |||
20.3 | even | 4 | 575.4.b.k.24.12 | 16 | |||
20.7 | even | 4 | 575.4.b.k.24.5 | 16 | |||
20.19 | odd | 2 | 575.4.a.n.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.4.a.f.1.2 | ✓ | 8 | 4.3 | odd | 2 | ||
575.4.a.n.1.7 | 8 | 20.19 | odd | 2 | |||
575.4.b.k.24.5 | 16 | 20.7 | even | 4 | |||
575.4.b.k.24.12 | 16 | 20.3 | even | 4 | |||
1035.4.a.r.1.7 | 8 | 12.11 | even | 2 | |||
1840.4.a.v.1.2 | 8 | 1.1 | even | 1 | trivial |