Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2500,4,Mod(1,2500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2500, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2500.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2500 = 2^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2500.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: | \(147.504775014\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 100) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.24 | ||
Character | \(\chi\) | \(=\) | 2500.1 |
$q$-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 | ||||||||
\(3\) | 4.95605 | 0.953793 | 0.476896 | − | 0.878959i | \(-0.341762\pi\) | ||||
0.476896 | + | 0.878959i | \(0.341762\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.8592 | 0.910309 | 0.455155 | − | 0.890412i | \(-0.349584\pi\) | ||||
0.455155 | + | 0.890412i | \(0.349584\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.43753 | −0.0902790 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 59.1321 | 1.62082 | 0.810409 | − | 0.585865i | \(-0.199245\pi\) | ||||
0.810409 | + | 0.585865i | \(0.199245\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.31508 | 0.134730 | 0.0673649 | − | 0.997728i | \(-0.478541\pi\) | ||||
0.0673649 | + | 0.997728i | \(0.478541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 131.580 | 1.87723 | 0.938616 | − | 0.344963i | \(-0.112109\pi\) | ||||
0.938616 | + | 0.344963i | \(0.112109\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 82.1717 | 0.992184 | 0.496092 | − | 0.868270i | \(-0.334768\pi\) | ||||
0.496092 | + | 0.868270i | \(0.334768\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 83.5549 | 0.868247 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 159.450 | 1.44555 | 0.722775 | − | 0.691084i | \(-0.242866\pi\) | ||||
0.722775 | + | 0.691084i | \(0.242866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −145.894 | −1.03990 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −50.0444 | −0.320448 | −0.160224 | − | 0.987081i | \(-0.551222\pi\) | ||||
−0.160224 | + | 0.987081i | \(0.551222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −44.6792 | −0.258859 | −0.129429 | − | 0.991589i | \(-0.541315\pi\) | ||||
−0.129429 | + | 0.991589i | \(0.541315\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 293.062 | 1.54592 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 75.0473 | 0.333451 | 0.166726 | − | 0.986003i | \(-0.446681\pi\) | ||||
0.166726 | + | 0.986003i | \(0.446681\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 31.2979 | 0.128504 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 353.628 | 1.34701 | 0.673504 | − | 0.739183i | \(-0.264788\pi\) | ||||
0.673504 | + | 0.739183i | \(0.264788\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 79.3703 | 0.281485 | 0.140743 | − | 0.990046i | \(-0.455051\pi\) | ||||
0.140743 | + | 0.990046i | \(0.455051\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −304.791 | −0.945923 | −0.472961 | − | 0.881083i | \(-0.656815\pi\) | ||||
−0.472961 | + | 0.881083i | \(0.656815\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −58.7686 | −0.171337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 652.120 | 1.79049 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −339.282 | −0.879319 | −0.439660 | − | 0.898164i | \(-0.644901\pi\) | ||||
−0.439660 | + | 0.898164i | \(0.644901\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 407.248 | 0.946338 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −786.798 | −1.73614 | −0.868070 | − | 0.496441i | \(-0.834640\pi\) | ||||
−0.868070 | + | 0.496441i | \(0.834640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −834.413 | −1.75140 | −0.875702 | − | 0.482851i | \(-0.839601\pi\) | ||||
−0.875702 | + | 0.482851i | \(0.839601\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −41.0948 | −0.0821818 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 607.900 | 1.10846 | 0.554229 | − | 0.832364i | \(-0.313013\pi\) | ||||
0.554229 | + | 0.832364i | \(0.313013\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 790.243 | 1.37875 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61.4511 | −0.102717 | −0.0513585 | − | 0.998680i | \(-0.516355\pi\) | ||||
−0.0513585 | + | 0.998680i | \(0.516355\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39.5735 | −0.0634483 | −0.0317241 | − | 0.999497i | \(-0.510100\pi\) | ||||
−0.0317241 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 996.917 | 1.47545 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 577.934 | 0.823072 | 0.411536 | − | 0.911394i | \(-0.364992\pi\) | ||||
0.411536 | + | 0.911394i | \(0.364992\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −657.245 | −0.901571 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 53.3674 | 0.0705763 | 0.0352881 | − | 0.999377i | \(-0.488765\pi\) | ||||
0.0352881 | + | 0.999377i | \(0.488765\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −248.023 | −0.305642 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1447.22 | −1.72365 | −0.861827 | − | 0.507202i | \(-0.830680\pi\) | ||||
−0.861827 | + | 0.507202i | \(0.830680\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 106.467 | 0.122646 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −221.432 | −0.246898 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 53.5327 | 0.0560353 | 0.0280177 | − | 0.999607i | \(-0.491081\pi\) | ||||
0.0280177 | + | 0.999607i | \(0.491081\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −144.136 | −0.146326 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −47.2102 | −0.0465108 | −0.0232554 | − | 0.999730i | \(-0.507403\pi\) | ||||
−0.0232554 | + | 0.999730i | \(0.507403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −147.154 | −0.140772 | −0.0703860 | − | 0.997520i | \(-0.522423\pi\) | ||||
−0.0703860 | + | 0.997520i | \(0.522423\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1350.74 | 1.22038 | 0.610192 | − | 0.792254i | \(-0.291092\pi\) | ||||
0.610192 | + | 0.792254i | \(0.291092\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 272.793 | 0.239714 | 0.119857 | − | 0.992791i | \(-0.461756\pi\) | ||||
0.119857 | + | 0.992791i | \(0.461756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 371.938 | 0.318043 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −632.450 | −0.526512 | −0.263256 | − | 0.964726i | \(-0.584796\pi\) | ||||
−0.263256 | + | 0.964726i | \(0.584796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.3932 | −0.0121633 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2218.34 | 1.70886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2165.60 | 1.62705 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1752.60 | 1.28477 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 916.288 | 0.640216 | 0.320108 | − | 0.947381i | \(-0.396281\pi\) | ||||
0.320108 | + | 0.947381i | \(0.396281\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 393.363 | 0.268478 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 654.768 | 0.436698 | 0.218349 | − | 0.975871i | \(-0.429933\pi\) | ||||
0.218349 | + | 0.975871i | \(0.429933\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1385.35 | 0.903194 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 568.184 | 0.354330 | 0.177165 | − | 0.984181i | \(-0.443307\pi\) | ||||
0.177165 | + | 0.984181i | \(0.443307\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2570.64 | 1.56862 | 0.784312 | − | 0.620367i | \(-0.213016\pi\) | ||||
0.784312 | + | 0.620367i | \(0.213016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1510.56 | −0.902215 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 373.424 | 0.218373 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −291.260 | −0.163420 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3146.97 | −1.73027 | −0.865134 | − | 0.501541i | \(-0.832767\pi\) | ||||
−0.865134 | + | 0.501541i | \(0.832767\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1560.39 | −0.840946 | −0.420473 | − | 0.907305i | \(-0.638136\pi\) | ||||
−0.420473 | + | 0.907305i | \(0.638136\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −320.732 | −0.169475 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2777.66 | 1.41198 | 0.705992 | − | 0.708219i | \(-0.250501\pi\) | ||||
0.705992 | + | 0.708219i | \(0.250501\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1681.50 | −0.838688 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2688.19 | 1.31590 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 543.340 | 0.261090 | 0.130545 | − | 0.991442i | \(-0.458327\pi\) | ||||
0.130545 | + | 0.991442i | \(0.458327\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −482.073 | −0.223377 | −0.111688 | − | 0.993743i | \(-0.535626\pi\) | ||||
−0.111688 | + | 0.993743i | \(0.535626\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2157.12 | −0.981848 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −200.296 | −0.0895734 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3520.67 | −1.54724 | −0.773618 | − | 0.633653i | \(-0.781555\pi\) | ||||
−0.773618 | + | 0.633653i | \(0.781555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3899.41 | −1.65592 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1517.69 | 0.633728 | 0.316864 | − | 0.948471i | \(-0.397370\pi\) | ||||
0.316864 | + | 0.948471i | \(0.397370\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3292.51 | 1.35210 | 0.676051 | − | 0.736855i | \(-0.263690\pi\) | ||||
0.676051 | + | 0.736855i | \(0.263690\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4135.40 | −1.67048 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7780.63 | 3.04265 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2459.65 | −0.946631 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4207.60 | 1.59399 | 0.796993 | − | 0.603988i | \(-0.206423\pi\) | ||||
0.796993 | + | 0.603988i | \(0.206423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1843.42 | −0.687524 | −0.343762 | − | 0.939057i | \(-0.611701\pi\) | ||||
−0.343762 | + | 0.939057i | \(0.611701\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3724.29 | −1.34693 | −0.673465 | − | 0.739220i | \(-0.735195\pi\) | ||||
−0.673465 | + | 0.739220i | \(0.735195\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −324.095 | −0.115450 | −0.0577248 | − | 0.998333i | \(-0.518385\pi\) | ||||
−0.0577248 | + | 0.998333i | \(0.518385\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3012.78 | 1.05724 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −843.706 | −0.291707 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −388.665 | −0.130503 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4858.99 | 1.60815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3761.42 | 1.22724 | 0.613618 | − | 0.789603i | \(-0.289713\pi\) | ||||
0.613618 | + | 0.789603i | \(0.289713\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −304.555 | −0.0979708 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −753.254 | −0.235641 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −196.128 | −0.0605165 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 830.941 | 0.252919 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2769.86 | −0.831763 | −0.415882 | − | 0.909419i | \(-0.636527\pi\) | ||||
−0.415882 | + | 0.909419i | \(0.636527\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1766.29 | 0.516445 | 0.258222 | − | 0.966086i | \(-0.416863\pi\) | ||||
0.258222 | + | 0.966086i | \(0.416863\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1076.11 | 0.310529 | 0.155265 | − | 0.987873i | \(-0.450377\pi\) | ||||
0.155265 | + | 0.987873i | \(0.450377\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4940.78 | 1.40727 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3391.67 | −0.953629 | −0.476814 | − | 0.879004i | \(-0.658209\pi\) | ||||
−0.476814 | + | 0.879004i | \(0.658209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2864.27 | 0.785040 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4277.50 | −1.15769 | −0.578847 | − | 0.815436i | \(-0.696497\pi\) | ||||
−0.578847 | + | 0.815436i | \(0.696497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2177.82 | 0.582098 | 0.291049 | − | 0.956708i | \(-0.405996\pi\) | ||||
0.291049 | + | 0.956708i | \(0.405996\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 681.796 | 0.179989 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 518.921 | 0.133677 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 264.492 | 0.0673152 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3829.18 | 0.962931 | 0.481465 | − | 0.876465i | \(-0.340105\pi\) | ||||
0.481465 | + | 0.876465i | \(0.340105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9428.61 | 2.34297 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1052.72 | 0.255513 | 0.127757 | − | 0.991806i | \(-0.459222\pi\) | ||||
0.127757 | + | 0.991806i | \(0.459222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1265.23 | 0.303544 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 121.985 | 0.0289298 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4044.38 | 0.948240 | 0.474120 | − | 0.880460i | \(-0.342766\pi\) | ||||
0.474120 | + | 0.880460i | \(0.342766\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7172.51 | −1.64401 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3642.86 | −0.825684 | −0.412842 | − | 0.910803i | \(-0.635464\pi\) | ||||
−0.412842 | + | 0.910803i | \(0.635464\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2890.83 | −0.647990 | −0.323995 | − | 0.946059i | \(-0.605026\pi\) | ||||
−0.323995 | + | 0.946059i | \(0.605026\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 527.656 | 0.116979 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4528.23 | −0.982220 | −0.491110 | − | 0.871098i | \(-0.663409\pi\) | ||||
−0.491110 | + | 0.871098i | \(0.663409\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 108.907 | 0.0233695 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3025.28 | 0.642254 | 0.321127 | − | 0.947036i | \(-0.395938\pi\) | ||||
0.321127 | + | 0.947036i | \(0.395938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5704.24 | 1.19817 | 0.599085 | − | 0.800686i | \(-0.295531\pi\) | ||||
0.599085 | + | 0.800686i | \(0.295531\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5961.86 | 1.22619 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12400.4 | 2.52400 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 265.311 | 0.0534461 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6874.37 | 1.37067 | 0.685333 | − | 0.728230i | \(-0.259657\pi\) | ||||
0.685333 | + | 0.728230i | \(0.259657\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8627.02 | −1.68549 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1006.94 | 0.194759 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1338.12 | 0.256238 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −233.976 | −0.0443616 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4653.22 | 0.865060 | 0.432530 | − | 0.901620i | \(-0.357621\pi\) | ||||
0.432530 | + | 0.901620i | \(0.357621\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −729.303 | −0.134267 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5194.35 | 0.947088 | 0.473544 | − | 0.880770i | \(-0.342975\pi\) | ||||
0.473544 | + | 0.880770i | \(0.342975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4763.02 | −0.860134 | −0.430067 | − | 0.902797i | \(-0.641510\pi\) | ||||
−0.430067 | + | 0.902797i | \(0.641510\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6267.40 | −1.11045 | −0.555225 | − | 0.831700i | \(-0.687368\pi\) | ||||
−0.555225 | + | 0.831700i | \(0.687368\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2959.23 | −0.519389 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6694.35 | 1.16399 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10812.2 | 1.86256 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1351.98 | 0.228637 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5138.53 | −0.861082 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9445.88 | −1.56856 | −0.784279 | − | 0.620409i | \(-0.786967\pi\) | ||||
−0.784279 | + | 0.620409i | \(0.786967\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −182.930 | −0.0301036 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11024.7 | −1.78205 | −0.891027 | − | 0.453951i | \(-0.850014\pi\) | ||||
−0.891027 | + | 0.453951i | \(0.850014\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3134.45 | −0.502183 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2641.97 | −0.419563 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6773.48 | −1.06628 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10088.3 | −1.56072 | −0.780359 | − | 0.625332i | \(-0.784964\pi\) | ||||
−0.780359 | + | 0.625332i | \(0.784964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7071.09 | 1.08455 | 0.542273 | − | 0.840202i | \(-0.317564\pi\) | ||||
0.542273 | + | 0.840202i | \(0.317564\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −921.332 | −0.140106 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10178.8 | −1.53474 | −0.767372 | − | 0.641203i | \(-0.778436\pi\) | ||||
−0.767372 | + | 0.641203i | \(0.778436\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10994.2 | 1.62990 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3407.04 | −0.500883 | −0.250441 | − | 0.968132i | \(-0.580576\pi\) | ||||
−0.250441 | + | 0.968132i | \(0.580576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −106.806 | −0.0155717 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10732.8 | 1.55187 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6663.08 | −0.947711 | −0.473855 | − | 0.880603i | \(-0.657138\pi\) | ||||
−0.473855 | + | 0.880603i | \(0.657138\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −861.979 | −0.121607 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5720.00 | −0.800452 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6128.85 | −0.850777 | −0.425389 | − | 0.905011i | \(-0.639863\pi\) | ||||
−0.425389 | + | 0.905011i | \(0.639863\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −316.034 | −0.0431740 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11685.1 | −1.58371 | −0.791854 | − | 0.610711i | \(-0.790884\pi\) | ||||
−0.791854 | + | 0.610711i | \(0.790884\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4541.17 | 0.610634 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10245.3 | 1.36686 | 0.683432 | − | 0.730015i | \(-0.260487\pi\) | ||||
0.683432 | + | 0.730015i | \(0.260487\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −193.468 | −0.0254122 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4513.74 | −0.588318 | −0.294159 | − | 0.955756i | \(-0.595040\pi\) | ||||
−0.294159 | + | 0.955756i | \(0.595040\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20980.5 | 2.71363 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3245.07 | 0.416519 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11765.6 | −1.48740 | −0.743698 | − | 0.668516i | \(-0.766930\pi\) | ||||
−0.743698 | + | 0.668516i | \(0.766930\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6865.85 | 0.861460 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6156.96 | 0.766743 | 0.383371 | − | 0.923594i | \(-0.374763\pi\) | ||||
0.383371 | + | 0.923594i | \(0.374763\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −282.153 | −0.0348760 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4437.70 | 0.540463 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5731.19 | 0.692882 | 0.346441 | − | 0.938072i | \(-0.387390\pi\) | ||||
0.346441 | + | 0.938072i | \(0.387390\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2815.95 | 0.337958 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13264.7 | −1.58043 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12740.2 | 1.49614 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1566.31 | 0.182624 | 0.0913120 | − | 0.995822i | \(-0.470894\pi\) | ||||
0.0913120 | + | 0.995822i | \(0.470894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15872.2 | 1.83744 | 0.918721 | − | 0.394907i | \(-0.129223\pi\) | ||||
0.918721 | + | 0.394907i | \(0.129223\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 742.939 | 0.0853970 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14067.5 | −1.59432 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1850.71 | 0.208282 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12464.3 | 1.39300 | 0.696501 | − | 0.717556i | \(-0.254739\pi\) | ||||
0.696501 | + | 0.717556i | \(0.254739\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14661.0 | −1.62717 | −0.813583 | − | 0.581448i | \(-0.802486\pi\) | ||||
−0.813583 | + | 0.581448i | \(0.802486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13102.3 | 1.43425 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3884.90 | 0.422360 | 0.211180 | − | 0.977447i | \(-0.432269\pi\) | ||||
0.211180 | + | 0.977447i | \(0.432269\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 143.250 | 0.0154681 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4840.23 | −0.519111 | −0.259556 | − | 0.965728i | \(-0.583576\pi\) | ||||
−0.259556 | + | 0.965728i | \(0.583576\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15596.6 | −1.65032 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9780.24 | 1.02797 | 0.513985 | − | 0.857799i | \(-0.328169\pi\) | ||||
0.513985 | + | 0.857799i | \(0.328169\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20910.7 | 2.18325 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7733.38 | −0.802088 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3537.61 | 0.362106 | 0.181053 | − | 0.983473i | \(-0.442050\pi\) | ||||
0.181053 | + | 0.983473i | \(0.442050\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19196.8 | −1.95213 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11295.6 | −1.14119 | −0.570596 | − | 0.821231i | \(-0.693288\pi\) | ||||
−0.570596 | + | 0.821231i | \(0.693288\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1997.51 | −0.200502 | −0.100251 | − | 0.994962i | \(-0.531965\pi\) | ||||
−0.100251 | + | 0.994962i | \(0.531965\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11446.6 | 1.13423 | 0.567115 | − | 0.823639i | \(-0.308059\pi\) | ||||
0.567115 | + | 0.823639i | \(0.308059\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10248.7 | 1.00904 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13766.2 | 1.34674 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4693.33 | 0.456236 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 827.010 | 0.0793841 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4392.43 | −0.418988 | −0.209494 | − | 0.977810i | \(-0.567182\pi\) | ||||
−0.209494 | + | 0.977810i | \(0.567182\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 473.930 | 0.0449258 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13322.8 | 1.25509 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7498.81 | 0.697749 | 0.348874 | − | 0.937169i | \(-0.386564\pi\) | ||||
0.348874 | + | 0.937169i | \(0.386564\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2692.82 | 0.249026 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 430.358 | 0.0395556 | 0.0197778 | − | 0.999804i | \(-0.493704\pi\) | ||||
0.0197778 | + | 0.999804i | \(0.493704\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6584.86 | −0.601556 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1036.01 | −0.0935043 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1063.14 | −0.0953765 | −0.0476883 | − | 0.998862i | \(-0.515185\pi\) | ||||
−0.0476883 | + | 0.998862i | \(0.515185\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2389.18 | −0.213055 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2735.01 | −0.242441 | −0.121221 | − | 0.992626i | \(-0.538681\pi\) | ||||
−0.121221 | + | 0.992626i | \(0.538681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10690.8 | −0.936480 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9333.33 | 0.812756 | 0.406378 | − | 0.913705i | \(-0.366792\pi\) | ||||
0.406378 | + | 0.913705i | \(0.366792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −667.176 | −0.0577576 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −11988.4 | −1.03177 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18022.9 | −1.53317 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17448.6 | −1.47574 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21936.7 | 1.84465 | 0.922325 | − | 0.386415i | \(-0.126287\pi\) | ||||
0.922325 | + | 0.386415i | \(0.126287\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10089.8 | −0.843588 | −0.421794 | − | 0.906692i | \(-0.638599\pi\) | ||||
−0.421794 | + | 0.906692i | \(0.638599\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5878.91 | −0.485938 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13257.3 | 1.08961 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1917.85 | 0.156737 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2233.19 | 0.181482 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7521.74 | 0.604445 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3475.11 | −0.277706 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4929.86 | −0.391777 | −0.195889 | − | 0.980626i | \(-0.562759\pi\) | ||||
−0.195889 | + | 0.980626i | \(0.562759\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16317.9 | 1.28963 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16651.7 | −1.30160 | −0.650801 | − | 0.759248i | \(-0.725567\pi\) | ||||
−0.650801 | + | 0.759248i | \(0.725567\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2033.91 | 0.158115 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4112.23 | −0.317944 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9743.49 | 0.749250 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13982.7 | 1.06367 | 0.531836 | − | 0.846847i | \(-0.321502\pi\) | ||||
0.531836 | + | 0.846847i | \(0.321502\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 501.230 | 0.0379244 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38561.2 | 2.90206 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9916.61 | 0.742336 | 0.371168 | − | 0.928566i | \(-0.378957\pi\) | ||||
0.371168 | + | 0.928566i | \(0.378957\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11080.6 | −0.820708 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8291.19 | 0.610870 | 0.305435 | − | 0.952213i | \(-0.401198\pi\) | ||||
0.305435 | + | 0.952213i | \(0.401198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5903.95 | 0.432702 | 0.216351 | − | 0.976316i | \(-0.430585\pi\) | ||||
0.216351 | + | 0.976316i | \(0.430585\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20853.1 | 1.52033 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6014.90 | −0.433975 | −0.216987 | − | 0.976174i | \(-0.569623\pi\) | ||||
−0.216987 | + | 0.976174i | \(0.569623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9136.07 | −0.655755 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 899.729 | 0.0642462 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20062.4 | −1.42522 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8567.35 | −0.602406 | −0.301203 | − | 0.953560i | \(-0.597388\pi\) | ||||
−0.301203 | + | 0.953560i | \(0.597388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3671.37 | −0.256835 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18457.8 | −1.28469 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19704.6 | −1.36453 | −0.682267 | − | 0.731103i | \(-0.739006\pi\) | ||||
−0.682267 | + | 0.731103i | \(0.739006\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1606.23 | −0.110115 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2540.05 | −0.173262 | −0.0866308 | − | 0.996240i | \(-0.527610\pi\) | ||||
−0.0866308 | + | 0.996240i | \(0.527610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18593.4 | −1.26197 | −0.630983 | − | 0.775797i | \(-0.717348\pi\) | ||||
−0.630983 | + | 0.775797i | \(0.717348\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1481.78 | −0.100071 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22878.6 | 1.52984 | 0.764922 | − | 0.644123i | \(-0.222778\pi\) | ||||
0.764922 | + | 0.644123i | \(0.222778\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4181.45 | −0.278228 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1924.78 | −0.127444 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14458.6 | 0.952654 | 0.476327 | − | 0.879268i | \(-0.341968\pi\) | ||||
0.476327 | + | 0.879268i | \(0.341968\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19540.3 | 1.27498 | 0.637489 | − | 0.770459i | \(-0.279973\pi\) | ||||
0.637489 | + | 0.770459i | \(0.279973\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18567.0 | 1.20561 | 0.602804 | − | 0.797889i | \(-0.294050\pi\) | ||||
0.602804 | + | 0.797889i | \(0.294050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23262.8 | −1.50323 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24399.0 | −1.56906 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24081.4 | 1.53384 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9874.75 | 0.625965 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6274.48 | −0.395853 | −0.197927 | − | 0.980217i | \(-0.563421\pi\) | ||||
−0.197927 | + | 0.980217i | \(0.563421\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18641.8 | 1.17053 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −371.128 | −0.0230842 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 149.789 | 0.00927319 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6631.88 | 0.408648 | 0.204324 | − | 0.978903i | \(-0.434500\pi\) | ||||
0.204324 | + | 0.978903i | \(0.434500\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12509.7 | 0.767240 | 0.383620 | − | 0.923491i | \(-0.374677\pi\) | ||||
0.383620 | + | 0.923491i | \(0.374677\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25315.1 | 1.53824 | 0.769120 | − | 0.639105i | \(-0.220695\pi\) | ||||
0.769120 | + | 0.639105i | \(0.220695\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46525.0 | −2.81397 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3733.17 | −0.224753 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 907.343 | 0.0543753 | 0.0271876 | − | 0.999630i | \(-0.491345\pi\) | ||||
0.0271876 | + | 0.999630i | \(0.491345\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 96.4617 | 0.00572805 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11641.2 | 0.688130 | 0.344065 | − | 0.938946i | \(-0.388196\pi\) | ||||
0.344065 | + | 0.938946i | \(0.388196\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19804.3 | −1.16535 | −0.582677 | − | 0.812704i | \(-0.697995\pi\) | ||||
−0.582677 | + | 0.812704i | \(0.697995\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4118.19 | 0.241233 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7979.58 | −0.463224 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13727.6 | −0.793330 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −49340.6 | −2.83871 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3948.28 | −0.226144 | −0.113072 | − | 0.993587i | \(-0.536069\pi\) | ||||
−0.113072 | + | 0.993587i | \(0.536069\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 25081.6 | 1.42388 | 0.711939 | − | 0.702241i | \(-0.247817\pi\) | ||||
0.711939 | + | 0.702241i | \(0.247817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 902.517 | 0.0510095 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8753.84 | 0.492581 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7372.10 | −0.413010 | −0.206505 | − | 0.978446i | \(-0.566209\pi\) | ||||
−0.206505 | + | 0.978446i | \(0.566209\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5333.25 | 0.296181 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2142.59 | −0.118471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30127.0 | 1.65859 | 0.829294 | − | 0.558812i | \(-0.188743\pi\) | ||||
0.829294 | + | 0.558812i | \(0.188743\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2430.02 | −0.133202 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46530.5 | 2.52865 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16809.3 | −0.909564 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 275.799 | 0.0148599 | 0.00742994 | − | 0.999972i | \(-0.497635\pi\) | ||||
0.00742994 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6166.76 | 0.330845 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −795.924 | −0.0423392 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4467.14 | −0.236625 | −0.118313 | − | 0.992976i | \(-0.537748\pi\) | ||||
−0.118313 | + | 0.992976i | \(0.537748\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1408.73 | −0.0743061 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7124.10 | −0.374193 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21199.5 | −1.10420 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4761.45 | 0.246971 | 0.123486 | − | 0.992346i | \(-0.460593\pi\) | ||||
0.123486 | + | 0.992346i | \(0.460593\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2480.89 | −0.128146 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10793.4 | 0.555201 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19899.2 | −1.01516 | −0.507578 | − | 0.861606i | \(-0.669459\pi\) | ||||
−0.507578 | + | 0.861606i | \(0.669459\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21124.6 | 1.07324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10443.6 | 0.528413 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23020.4 | −1.15999 | −0.579997 | − | 0.814618i | \(-0.696946\pi\) | ||||
−0.579997 | + | 0.814618i | \(0.696946\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35946.4 | 1.79661 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4820.32 | −0.239944 | −0.119972 | − | 0.992777i | \(-0.538280\pi\) | ||||
−0.119972 | + | 0.992777i | \(0.538280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2571.80 | 0.127500 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11267.6 | 0.556348 | 0.278174 | − | 0.960531i | \(-0.410271\pi\) | ||||
0.278174 | + | 0.960531i | \(0.410271\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −130.085 | −0.00637156 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22772.4 | 1.11093 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21124.7 | 1.02643 | 0.513216 | − | 0.858259i | \(-0.328454\pi\) | ||||
0.513216 | + | 0.858259i | \(0.328454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18977.6 | 0.918437 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25198.7 | −1.20986 | −0.604929 | − | 0.796279i | \(-0.706799\pi\) | ||||
−0.604929 | + | 0.796279i | \(0.706799\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 46728.7 | 2.23471 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9269.83 | 0.441565 | 0.220783 | − | 0.975323i | \(-0.429139\pi\) | ||||
0.220783 | + | 0.975323i | \(0.429139\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4599.06 | 0.218214 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4968.69 | −0.233910 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7084.96 | −0.332237 | −0.166119 | − | 0.986106i | \(-0.553123\pi\) | ||||
−0.166119 | + | 0.986106i | \(0.553123\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5217.34 | 0.243707 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13432.8 | −0.625024 | −0.312512 | − | 0.949914i | \(-0.601170\pi\) | ||||
−0.312512 | + | 0.949914i | \(0.601170\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6270.57 | 0.289518 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29058.2 | 1.33648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3633.73 | −0.166486 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7301.17 | 0.333235 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12623.8 | −0.571780 | −0.285890 | − | 0.958263i | \(-0.592289\pi\) | ||||
−0.285890 | + | 0.958263i | \(0.592289\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20044.2 | 0.904424 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10662.6 | −0.479289 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5269.39 | −0.235967 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20294.5 | −0.901967 | −0.450983 | − | 0.892532i | \(-0.648927\pi\) | ||||
−0.450983 | + | 0.892532i | \(0.648927\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40104.6 | −1.77572 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3527.65 | 0.155610 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2340.06 | −0.102838 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18054.2 | −0.787531 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42388.8 | −1.84217 | −0.921083 | − | 0.389366i | \(-0.872694\pi\) | ||||
−0.921083 | + | 0.389366i | \(0.872694\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23265.0 | −1.00733 | −0.503666 | − | 0.863898i | \(-0.668016\pi\) | ||||
−0.503666 | + | 0.863898i | \(0.668016\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14327.1 | −0.618048 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6522.00 | 0.279285 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −259.517 | −0.0110723 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20775.3 | −0.883145 | −0.441573 | − | 0.897225i | \(-0.645579\pi\) | ||||
−0.441573 | + | 0.897225i | \(0.645579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2474.84 | 0.104821 | 0.0524103 | − | 0.998626i | \(-0.483310\pi\) | ||||
0.0524103 | + | 0.998626i | \(0.483310\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10643.9 | 0.447552 | 0.223776 | − | 0.974641i | \(-0.428162\pi\) | ||||
0.223776 | + | 0.974641i | \(0.428162\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22637.2 | −0.948400 | −0.474200 | − | 0.880417i | \(-0.657263\pi\) | ||||
−0.474200 | + | 0.880417i | \(0.657263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22442.1 | −0.936834 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7732.80 | −0.321639 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6518.42 | 0.269187 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33780.2 | −1.39001 | −0.695007 | − | 0.719003i | \(-0.744599\pi\) | ||||
−0.695007 | + | 0.719003i | \(0.744599\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21884.6 | −0.897313 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14993.5 | 0.612577 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36510.3 | 1.48112 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28270.5 | 1.14281 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11966.3 | 0.482020 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37542.1 | 1.50694 | 0.753468 | − | 0.657485i | \(-0.228380\pi\) | ||||
0.753468 | + | 0.657485i | \(0.228380\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24120.1 | −0.961408 | −0.480704 | − | 0.876883i | \(-0.659619\pi\) | ||||
−0.480704 | + | 0.876883i | \(0.659619\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6703.01 | −0.266244 | −0.133122 | − | 0.991100i | \(-0.542500\pi\) | ||||
−0.133122 | + | 0.991100i | \(0.542500\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29547.3 | 1.16954 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31235.7 | 1.23207 | 0.616035 | − | 0.787719i | \(-0.288738\pi\) | ||||
0.616035 | + | 0.787719i | \(0.288738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 61457.1 | 2.40737 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34174.5 | 1.33405 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3838.93 | 0.149343 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −130.488 | −0.00505881 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24268.0 | −0.934403 | −0.467201 | − | 0.884151i | \(-0.654738\pi\) | ||||
−0.467201 | + | 0.884151i | \(0.654738\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34069.8 | 1.30733 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3250.81 | 0.124316 | 0.0621582 | − | 0.998066i | \(-0.480202\pi\) | ||||
0.0621582 | + | 0.998066i | \(0.480202\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12164.4 | −0.463607 | −0.231803 | − | 0.972763i | \(-0.574463\pi\) | ||||
−0.231803 | + | 0.972763i | \(0.574463\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12983.4 | −0.491476 | −0.245738 | − | 0.969336i | \(-0.579030\pi\) | ||||
−0.245738 | + | 0.969336i | \(0.579030\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15447.9 | 0.582795 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38864.3 | −1.46128 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25045.2 | −0.938529 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4990.45 | 0.185759 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2235.94 | 0.0829509 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44642.8 | −1.65069 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6631.78 | 0.244398 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34569.1 | 1.26554 | 0.632771 | − | 0.774339i | \(-0.281917\pi\) | ||||
0.632771 | + | 0.774339i | \(0.281917\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 115.076 | 0.00419895 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9403.56 | 0.341991 | 0.170995 | − | 0.985272i | \(-0.445302\pi\) | ||||
0.170995 | + | 0.985272i | \(0.445302\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3155.72 | 0.114391 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11038.8 | 0.397530 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40220.5 | −1.44369 | −0.721845 | − | 0.692055i | \(-0.756705\pi\) | ||||
−0.721845 | + | 0.692055i | \(0.756705\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23061.6 | 0.825088 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −388.069 | −0.0138391 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 358.693 | 0.0127088 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13218.6 | 0.466834 | 0.233417 | − | 0.972377i | \(-0.425009\pi\) | ||||
0.233417 | + | 0.972377i | \(0.425009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4829.12 | −0.169998 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25743.5 | 0.903326 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6749.65 | −0.235327 | −0.117664 | − | 0.993054i | \(-0.537540\pi\) | ||||
−0.117664 | + | 0.993054i | \(0.537540\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23605.8 | −0.820390 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24163.3 | 0.837089 | 0.418544 | − | 0.908196i | \(-0.362540\pi\) | ||||
0.418544 | + | 0.908196i | \(0.362540\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56385.9 | 1.94717 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2701.58 | −0.0927028 | −0.0463514 | − | 0.998925i | \(-0.514759\pi\) | ||||
−0.0463514 | + | 0.998925i | \(0.514759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −249.910 | −0.00854838 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31061.6 | −1.05914 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35584.4 | −1.20954 | −0.604770 | − | 0.796400i | \(-0.706735\pi\) | ||||
−0.604770 | + | 0.796400i | \(0.706735\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14666.1 | −0.495389 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9579.11 | 0.322550 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27794.8 | −0.932992 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3292.48 | −0.110175 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5885.66 | 0.195729 | 0.0978645 | − | 0.995200i | \(-0.468799\pi\) | ||||
0.0978645 | + | 0.995200i | \(0.468799\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 53585.8 | 1.77650 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41347.7 | 1.36654 | 0.683271 | − | 0.730165i | \(-0.260557\pi\) | ||||
0.683271 | + | 0.730165i | \(0.260557\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43338.8 | 1.42793 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27595.1 | 0.903630 | 0.451815 | − | 0.892112i | \(-0.350777\pi\) | ||||
0.451815 | + | 0.892112i | \(0.350777\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −85577.3 | −2.79373 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −664.941 | −0.0216411 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56743.0 | 1.84112 | 0.920559 | − | 0.390603i | \(-0.127733\pi\) | ||||
0.920559 | + | 0.390603i | \(0.127733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25466.8 | −0.821294 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12655.6 | 0.406901 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17553.2 | 0.562659 | 0.281329 | − | 0.959611i | \(-0.409225\pi\) | ||||
0.281329 | + | 0.959611i | \(0.409225\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −46814.3 | −1.49608 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21257.8 | 0.675269 | 0.337634 | − | 0.941277i | \(-0.390373\pi\) | ||||
0.337634 | + | 0.941277i | \(0.390373\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10948.9 | −0.346756 |
(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 | 2500.4.a.g.1.24 | 32 | ||
5.4 | even | 2 | inner | 2500.4.a.g.1.9 | 32 | ||
25.3 | odd | 20 | 100.4.i.a.9.3 | ✓ | 32 | ||
25.4 | even | 10 | 500.4.g.b.201.5 | 64 | |||
25.6 | even | 5 | 500.4.g.b.301.12 | 64 | |||
25.8 | odd | 20 | 500.4.i.a.449.6 | 32 | |||
25.17 | odd | 20 | 100.4.i.a.89.3 | yes | 32 | ||
25.19 | even | 10 | 500.4.g.b.301.5 | 64 | |||
25.21 | even | 5 | 500.4.g.b.201.12 | 64 | |||
25.22 | odd | 20 | 500.4.i.a.49.6 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
100.4.i.a.9.3 | ✓ | 32 | 25.3 | odd | 20 | ||
100.4.i.a.89.3 | yes | 32 | 25.17 | odd | 20 | ||
500.4.g.b.201.5 | 64 | 25.4 | even | 10 | |||
500.4.g.b.201.12 | 64 | 25.21 | even | 5 | |||
500.4.g.b.301.5 | 64 | 25.19 | even | 10 | |||
500.4.g.b.301.12 | 64 | 25.6 | even | 5 | |||
500.4.i.a.49.6 | 32 | 25.22 | odd | 20 | |||
500.4.i.a.449.6 | 32 | 25.8 | odd | 20 | |||
2500.4.a.g.1.9 | 32 | 5.4 | even | 2 | inner | ||
2500.4.a.g.1.24 | 32 | 1.1 | even | 1 | trivial |