Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.04224\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.04224 | 0.722042 | 0.361021 | − | 0.932558i | \(-0.382428\pi\) | ||||
0.361021 | + | 0.932558i | \(0.382428\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −3.82924 | −0.478656 | ||||||||
\(5\) | 12.0825 | 1.08069 | 0.540344 | − | 0.841444i | \(-0.318294\pi\) | ||||
0.540344 | + | 0.841444i | \(0.318294\pi\) | |||||||
\(6\) | 6.12673 | 0.416871 | ||||||||
\(7\) | 29.7373 | 1.60566 | 0.802832 | − | 0.596206i | \(-0.203326\pi\) | ||||
0.802832 | + | 0.596206i | \(0.203326\pi\) | |||||||
\(8\) | −24.1582 | −1.06765 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 24.6753 | 0.780302 | ||||||||
\(11\) | 28.0636 | 0.769226 | 0.384613 | − | 0.923078i | \(-0.374335\pi\) | ||||
0.384613 | + | 0.923078i | \(0.374335\pi\) | |||||||
\(12\) | −11.4877 | −0.276352 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 60.7308 | 1.15936 | ||||||||
\(15\) | 36.2474 | 0.623935 | ||||||||
\(16\) | −18.7029 | −0.292233 | ||||||||
\(17\) | −50.6556 | −0.722693 | −0.361347 | − | 0.932432i | \(-0.617683\pi\) | ||||
−0.361347 | + | 0.932432i | \(0.617683\pi\) | |||||||
\(18\) | 18.3802 | 0.240681 | ||||||||
\(19\) | 105.148 | 1.26962 | 0.634808 | − | 0.772670i | \(-0.281079\pi\) | ||||
0.634808 | + | 0.772670i | \(0.281079\pi\) | |||||||
\(20\) | −46.2667 | −0.517277 | ||||||||
\(21\) | 89.2119 | 0.927030 | ||||||||
\(22\) | 57.3126 | 0.555413 | ||||||||
\(23\) | −160.592 | −1.45590 | −0.727951 | − | 0.685629i | \(-0.759527\pi\) | ||||
−0.727951 | + | 0.685629i | \(0.759527\pi\) | |||||||
\(24\) | −72.4746 | −0.616409 | ||||||||
\(25\) | 20.9857 | 0.167886 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −113.871 | −0.768560 | ||||||||
\(29\) | 140.105 | 0.897132 | 0.448566 | − | 0.893750i | \(-0.351935\pi\) | ||||
0.448566 | + | 0.893750i | \(0.351935\pi\) | |||||||
\(30\) | 74.0259 | 0.450507 | ||||||||
\(31\) | 223.593 | 1.29544 | 0.647718 | − | 0.761880i | \(-0.275724\pi\) | ||||
0.647718 | + | 0.761880i | \(0.275724\pi\) | |||||||
\(32\) | 155.070 | 0.856647 | ||||||||
\(33\) | 84.1907 | 0.444113 | ||||||||
\(34\) | −103.451 | −0.521815 | ||||||||
\(35\) | 359.300 | 1.73522 | ||||||||
\(36\) | −34.4632 | −0.159552 | ||||||||
\(37\) | −228.352 | −1.01462 | −0.507308 | − | 0.861765i | \(-0.669359\pi\) | ||||
−0.507308 | + | 0.861765i | \(0.669359\pi\) | |||||||
\(38\) | 214.739 | 0.916716 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −291.890 | −1.15380 | ||||||||
\(41\) | −295.902 | −1.12713 | −0.563563 | − | 0.826073i | \(-0.690570\pi\) | ||||
−0.563563 | + | 0.826073i | \(0.690570\pi\) | |||||||
\(42\) | 182.192 | 0.669354 | ||||||||
\(43\) | 192.103 | 0.681291 | 0.340645 | − | 0.940192i | \(-0.389354\pi\) | ||||
0.340645 | + | 0.940192i | \(0.389354\pi\) | |||||||
\(44\) | −107.462 | −0.368194 | ||||||||
\(45\) | 108.742 | 0.360229 | ||||||||
\(46\) | −327.968 | −1.05122 | ||||||||
\(47\) | 36.9300 | 0.114613 | 0.0573063 | − | 0.998357i | \(-0.481749\pi\) | ||||
0.0573063 | + | 0.998357i | \(0.481749\pi\) | |||||||
\(48\) | −56.1088 | −0.168721 | ||||||||
\(49\) | 541.307 | 1.57815 | ||||||||
\(50\) | 42.8579 | 0.121220 | ||||||||
\(51\) | −151.967 | −0.417247 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 149.102 | 0.386429 | 0.193214 | − | 0.981157i | \(-0.438109\pi\) | ||||
0.193214 | + | 0.981157i | \(0.438109\pi\) | |||||||
\(54\) | 55.1406 | 0.138957 | ||||||||
\(55\) | 339.077 | 0.831293 | ||||||||
\(56\) | −718.399 | −1.71429 | ||||||||
\(57\) | 315.445 | 0.733013 | ||||||||
\(58\) | 286.128 | 0.647767 | ||||||||
\(59\) | 438.867 | 0.968400 | 0.484200 | − | 0.874957i | \(-0.339111\pi\) | ||||
0.484200 | + | 0.874957i | \(0.339111\pi\) | |||||||
\(60\) | −138.800 | −0.298650 | ||||||||
\(61\) | 286.146 | 0.600610 | 0.300305 | − | 0.953843i | \(-0.402912\pi\) | ||||
0.300305 | + | 0.953843i | \(0.402912\pi\) | |||||||
\(62\) | 456.631 | 0.935358 | ||||||||
\(63\) | 267.636 | 0.535221 | ||||||||
\(64\) | 466.313 | 0.910768 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 171.938 | 0.320668 | ||||||||
\(67\) | −537.128 | −0.979412 | −0.489706 | − | 0.871888i | \(-0.662896\pi\) | ||||
−0.489706 | + | 0.871888i | \(0.662896\pi\) | |||||||
\(68\) | 193.973 | 0.345921 | ||||||||
\(69\) | −481.776 | −0.840566 | ||||||||
\(70\) | 733.777 | 1.25290 | ||||||||
\(71\) | 102.729 | 0.171713 | 0.0858567 | − | 0.996307i | \(-0.472637\pi\) | ||||
0.0858567 | + | 0.996307i | \(0.472637\pi\) | |||||||
\(72\) | −217.424 | −0.355884 | ||||||||
\(73\) | −75.5209 | −0.121083 | −0.0605414 | − | 0.998166i | \(-0.519283\pi\) | ||||
−0.0605414 | + | 0.998166i | \(0.519283\pi\) | |||||||
\(74\) | −466.350 | −0.732596 | ||||||||
\(75\) | 62.9571 | 0.0969288 | ||||||||
\(76\) | −402.639 | −0.607709 | ||||||||
\(77\) | 834.535 | 1.23512 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.5526 | 0.0249978 | 0.0124989 | − | 0.999922i | \(-0.496021\pi\) | ||||
0.0124989 | + | 0.999922i | \(0.496021\pi\) | |||||||
\(80\) | −225.977 | −0.315813 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −604.304 | −0.813831 | ||||||||
\(83\) | 1463.08 | 1.93487 | 0.967434 | − | 0.253122i | \(-0.0814573\pi\) | ||||
0.967434 | + | 0.253122i | \(0.0814573\pi\) | |||||||
\(84\) | −341.614 | −0.443728 | ||||||||
\(85\) | −612.044 | −0.781005 | ||||||||
\(86\) | 392.322 | 0.491920 | ||||||||
\(87\) | 420.315 | 0.517960 | ||||||||
\(88\) | −677.965 | −0.821265 | ||||||||
\(89\) | −334.905 | −0.398875 | −0.199438 | − | 0.979911i | \(-0.563911\pi\) | ||||
−0.199438 | + | 0.979911i | \(0.563911\pi\) | |||||||
\(90\) | 222.078 | 0.260101 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 614.946 | 0.696876 | ||||||||
\(93\) | 670.779 | 0.747920 | ||||||||
\(94\) | 75.4200 | 0.0827551 | ||||||||
\(95\) | 1270.45 | 1.37206 | ||||||||
\(96\) | 465.209 | 0.494585 | ||||||||
\(97\) | −748.756 | −0.783760 | −0.391880 | − | 0.920016i | \(-0.628175\pi\) | ||||
−0.391880 | + | 0.920016i | \(0.628175\pi\) | |||||||
\(98\) | 1105.48 | 1.13949 | ||||||||
\(99\) | 252.572 | 0.256409 | ||||||||
\(100\) | −80.3594 | −0.0803594 | ||||||||
\(101\) | −784.002 | −0.772387 | −0.386194 | − | 0.922418i | \(-0.626210\pi\) | ||||
−0.386194 | + | 0.922418i | \(0.626210\pi\) | |||||||
\(102\) | −310.353 | −0.301270 | ||||||||
\(103\) | 396.040 | 0.378864 | 0.189432 | − | 0.981894i | \(-0.439335\pi\) | ||||
0.189432 | + | 0.981894i | \(0.439335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1077.90 | 1.00183 | ||||||||
\(106\) | 304.502 | 0.279018 | ||||||||
\(107\) | −1436.59 | −1.29795 | −0.648974 | − | 0.760810i | \(-0.724802\pi\) | ||||
−0.648974 | + | 0.760810i | \(0.724802\pi\) | |||||||
\(108\) | −103.390 | −0.0921173 | ||||||||
\(109\) | −1977.92 | −1.73807 | −0.869037 | − | 0.494746i | \(-0.835261\pi\) | ||||
−0.869037 | + | 0.494746i | \(0.835261\pi\) | |||||||
\(110\) | 692.477 | 0.600228 | ||||||||
\(111\) | −685.056 | −0.585789 | ||||||||
\(112\) | −556.175 | −0.469228 | ||||||||
\(113\) | 122.405 | 0.101902 | 0.0509509 | − | 0.998701i | \(-0.483775\pi\) | ||||
0.0509509 | + | 0.998701i | \(0.483775\pi\) | |||||||
\(114\) | 644.216 | 0.529266 | ||||||||
\(115\) | −1940.35 | −1.57338 | ||||||||
\(116\) | −536.496 | −0.429417 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 896.273 | 0.699225 | ||||||||
\(119\) | −1506.36 | −1.16040 | ||||||||
\(120\) | −875.671 | −0.666145 | ||||||||
\(121\) | −543.436 | −0.408291 | ||||||||
\(122\) | 584.379 | 0.433665 | ||||||||
\(123\) | −887.706 | −0.650746 | ||||||||
\(124\) | −856.192 | −0.620067 | ||||||||
\(125\) | −1256.75 | −0.899256 | ||||||||
\(126\) | 546.577 | 0.386452 | ||||||||
\(127\) | 2309.61 | 1.61374 | 0.806868 | − | 0.590731i | \(-0.201161\pi\) | ||||
0.806868 | + | 0.590731i | \(0.201161\pi\) | |||||||
\(128\) | −288.232 | −0.199034 | ||||||||
\(129\) | 576.310 | 0.393343 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1444.26 | −0.963250 | −0.481625 | − | 0.876377i | \(-0.659953\pi\) | ||||
−0.481625 | + | 0.876377i | \(0.659953\pi\) | |||||||
\(132\) | −322.387 | −0.212577 | ||||||||
\(133\) | 3126.83 | 2.03858 | ||||||||
\(134\) | −1096.94 | −0.707176 | ||||||||
\(135\) | 326.226 | 0.207978 | ||||||||
\(136\) | 1223.75 | 0.771584 | ||||||||
\(137\) | −735.918 | −0.458932 | −0.229466 | − | 0.973317i | \(-0.573698\pi\) | ||||
−0.229466 | + | 0.973317i | \(0.573698\pi\) | |||||||
\(138\) | −983.904 | −0.606924 | ||||||||
\(139\) | −1505.14 | −0.918449 | −0.459225 | − | 0.888320i | \(-0.651873\pi\) | ||||
−0.459225 | + | 0.888320i | \(0.651873\pi\) | |||||||
\(140\) | −1375.85 | −0.830573 | ||||||||
\(141\) | 110.790 | 0.0661716 | ||||||||
\(142\) | 209.797 | 0.123984 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −168.326 | −0.0974111 | ||||||||
\(145\) | 1692.81 | 0.969520 | ||||||||
\(146\) | −154.232 | −0.0874269 | ||||||||
\(147\) | 1623.92 | 0.911148 | ||||||||
\(148\) | 874.415 | 0.485652 | ||||||||
\(149\) | 427.843 | 0.235237 | 0.117618 | − | 0.993059i | \(-0.462474\pi\) | ||||
0.117618 | + | 0.993059i | \(0.462474\pi\) | |||||||
\(150\) | 128.574 | 0.0699867 | ||||||||
\(151\) | −1601.83 | −0.863278 | −0.431639 | − | 0.902046i | \(-0.642065\pi\) | ||||
−0.431639 | + | 0.902046i | \(0.642065\pi\) | |||||||
\(152\) | −2540.20 | −1.35551 | ||||||||
\(153\) | −455.900 | −0.240898 | ||||||||
\(154\) | 1704.32 | 0.891807 | ||||||||
\(155\) | 2701.55 | 1.39996 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −730.346 | −0.371261 | −0.185631 | − | 0.982620i | \(-0.559433\pi\) | ||||
−0.185631 | + | 0.982620i | \(0.559433\pi\) | |||||||
\(158\) | 35.8467 | 0.0180495 | ||||||||
\(159\) | 447.306 | 0.223105 | ||||||||
\(160\) | 1873.62 | 0.925767 | ||||||||
\(161\) | −4775.58 | −2.33769 | ||||||||
\(162\) | 165.422 | 0.0802269 | ||||||||
\(163\) | 1898.36 | 0.912215 | 0.456107 | − | 0.889925i | \(-0.349243\pi\) | ||||
0.456107 | + | 0.889925i | \(0.349243\pi\) | |||||||
\(164\) | 1133.08 | 0.539505 | ||||||||
\(165\) | 1017.23 | 0.479947 | ||||||||
\(166\) | 2987.97 | 1.39706 | ||||||||
\(167\) | 1427.50 | 0.661457 | 0.330729 | − | 0.943726i | \(-0.392706\pi\) | ||||
0.330729 | + | 0.943726i | \(0.392706\pi\) | |||||||
\(168\) | −2155.20 | −0.989745 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1249.94 | −0.563919 | ||||||||
\(171\) | 946.336 | 0.423205 | ||||||||
\(172\) | −735.611 | −0.326104 | ||||||||
\(173\) | −2044.40 | −0.898454 | −0.449227 | − | 0.893418i | \(-0.648301\pi\) | ||||
−0.449227 | + | 0.893418i | \(0.648301\pi\) | |||||||
\(174\) | 858.385 | 0.373988 | ||||||||
\(175\) | 624.058 | 0.269568 | ||||||||
\(176\) | −524.871 | −0.224793 | ||||||||
\(177\) | 1316.60 | 0.559106 | ||||||||
\(178\) | −683.958 | −0.288004 | ||||||||
\(179\) | −3889.72 | −1.62420 | −0.812098 | − | 0.583521i | \(-0.801675\pi\) | ||||
−0.812098 | + | 0.583521i | \(0.801675\pi\) | |||||||
\(180\) | −416.400 | −0.172426 | ||||||||
\(181\) | −2477.02 | −1.01721 | −0.508606 | − | 0.861000i | \(-0.669839\pi\) | ||||
−0.508606 | + | 0.861000i | \(0.669839\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 858.437 | 0.346762 | ||||||||
\(184\) | 3879.61 | 1.55440 | ||||||||
\(185\) | −2759.05 | −1.09648 | ||||||||
\(186\) | 1369.89 | 0.540029 | ||||||||
\(187\) | −1421.58 | −0.555914 | ||||||||
\(188\) | −141.414 | −0.0548600 | ||||||||
\(189\) | 802.907 | 0.309010 | ||||||||
\(190\) | 2594.57 | 0.990683 | ||||||||
\(191\) | 2276.81 | 0.862535 | 0.431267 | − | 0.902224i | \(-0.358067\pi\) | ||||
0.431267 | + | 0.902224i | \(0.358067\pi\) | |||||||
\(192\) | 1398.94 | 0.525832 | ||||||||
\(193\) | 3922.42 | 1.46291 | 0.731456 | − | 0.681888i | \(-0.238841\pi\) | ||||
0.731456 | + | 0.681888i | \(0.238841\pi\) | |||||||
\(194\) | −1529.14 | −0.565907 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2072.80 | −0.755392 | ||||||||
\(197\) | −5063.23 | −1.83117 | −0.915584 | − | 0.402128i | \(-0.868271\pi\) | ||||
−0.915584 | + | 0.402128i | \(0.868271\pi\) | |||||||
\(198\) | 515.814 | 0.185138 | ||||||||
\(199\) | 3270.06 | 1.16487 | 0.582433 | − | 0.812879i | \(-0.302101\pi\) | ||||
0.582433 | + | 0.812879i | \(0.302101\pi\) | |||||||
\(200\) | −506.977 | −0.179243 | ||||||||
\(201\) | −1611.38 | −0.565464 | ||||||||
\(202\) | −1601.12 | −0.557696 | ||||||||
\(203\) | 4166.34 | 1.44049 | ||||||||
\(204\) | 581.918 | 0.199718 | ||||||||
\(205\) | −3575.22 | −1.21807 | ||||||||
\(206\) | 808.810 | 0.273555 | ||||||||
\(207\) | −1445.33 | −0.485301 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2950.84 | 0.976622 | ||||||||
\(210\) | 2201.33 | 0.723363 | ||||||||
\(211\) | −2812.18 | −0.917527 | −0.458764 | − | 0.888558i | \(-0.651708\pi\) | ||||
−0.458764 | + | 0.888558i | \(0.651708\pi\) | |||||||
\(212\) | −570.948 | −0.184966 | ||||||||
\(213\) | 308.186 | 0.0991388 | ||||||||
\(214\) | −2933.87 | −0.937173 | ||||||||
\(215\) | 2321.08 | 0.736262 | ||||||||
\(216\) | −652.271 | −0.205470 | ||||||||
\(217\) | 6649.05 | 2.08003 | ||||||||
\(218\) | −4039.39 | −1.25496 | ||||||||
\(219\) | −226.563 | −0.0699072 | ||||||||
\(220\) | −1298.41 | −0.397903 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1399.05 | −0.422964 | ||||||||
\(223\) | −917.736 | −0.275588 | −0.137794 | − | 0.990461i | \(-0.544001\pi\) | ||||
−0.137794 | + | 0.990461i | \(0.544001\pi\) | |||||||
\(224\) | 4611.35 | 1.37549 | ||||||||
\(225\) | 188.871 | 0.0559619 | ||||||||
\(226\) | 249.981 | 0.0735774 | ||||||||
\(227\) | −1336.39 | −0.390746 | −0.195373 | − | 0.980729i | \(-0.562592\pi\) | ||||
−0.195373 | + | 0.980729i | \(0.562592\pi\) | |||||||
\(228\) | −1207.92 | −0.350861 | ||||||||
\(229\) | 164.820 | 0.0475617 | 0.0237808 | − | 0.999717i | \(-0.492430\pi\) | ||||
0.0237808 | + | 0.999717i | \(0.492430\pi\) | |||||||
\(230\) | −3962.66 | −1.13604 | ||||||||
\(231\) | 2503.60 | 0.713096 | ||||||||
\(232\) | −3384.68 | −0.957824 | ||||||||
\(233\) | −4243.42 | −1.19312 | −0.596558 | − | 0.802570i | \(-0.703465\pi\) | ||||
−0.596558 | + | 0.802570i | \(0.703465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 446.205 | 0.123860 | ||||||||
\(236\) | −1680.53 | −0.463530 | ||||||||
\(237\) | 52.6579 | 0.0144325 | ||||||||
\(238\) | −3076.35 | −0.837859 | ||||||||
\(239\) | −2491.07 | −0.674200 | −0.337100 | − | 0.941469i | \(-0.609446\pi\) | ||||
−0.337100 | + | 0.941469i | \(0.609446\pi\) | |||||||
\(240\) | −677.932 | −0.182335 | ||||||||
\(241\) | 2917.40 | 0.779776 | 0.389888 | − | 0.920862i | \(-0.372514\pi\) | ||||
0.389888 | + | 0.920862i | \(0.372514\pi\) | |||||||
\(242\) | −1109.83 | −0.294803 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −1095.72 | −0.287485 | ||||||||
\(245\) | 6540.32 | 1.70549 | ||||||||
\(246\) | −1812.91 | −0.469866 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5401.60 | −1.38307 | ||||||||
\(249\) | 4389.25 | 1.11710 | ||||||||
\(250\) | −2566.58 | −0.649300 | ||||||||
\(251\) | −1313.88 | −0.330403 | −0.165202 | − | 0.986260i | \(-0.552827\pi\) | ||||
−0.165202 | + | 0.986260i | \(0.552827\pi\) | |||||||
\(252\) | −1024.84 | −0.256187 | ||||||||
\(253\) | −4506.79 | −1.11992 | ||||||||
\(254\) | 4716.78 | 1.16519 | ||||||||
\(255\) | −1836.13 | −0.450914 | ||||||||
\(256\) | −4319.15 | −1.05448 | ||||||||
\(257\) | −987.582 | −0.239703 | −0.119851 | − | 0.992792i | \(-0.538242\pi\) | ||||
−0.119851 | + | 0.992792i | \(0.538242\pi\) | |||||||
\(258\) | 1176.97 | 0.284010 | ||||||||
\(259\) | −6790.57 | −1.62913 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1260.94 | 0.299044 | ||||||||
\(262\) | −2949.53 | −0.695507 | ||||||||
\(263\) | −6986.45 | −1.63803 | −0.819017 | − | 0.573769i | \(-0.805481\pi\) | ||||
−0.819017 | + | 0.573769i | \(0.805481\pi\) | |||||||
\(264\) | −2033.90 | −0.474158 | ||||||||
\(265\) | 1801.52 | 0.417609 | ||||||||
\(266\) | 6385.74 | 1.47194 | ||||||||
\(267\) | −1004.72 | −0.230291 | ||||||||
\(268\) | 2056.79 | 0.468801 | ||||||||
\(269\) | −5904.34 | −1.33827 | −0.669134 | − | 0.743142i | \(-0.733335\pi\) | ||||
−0.669134 | + | 0.743142i | \(0.733335\pi\) | |||||||
\(270\) | 666.233 | 0.150169 | ||||||||
\(271\) | −2131.54 | −0.477793 | −0.238897 | − | 0.971045i | \(-0.576786\pi\) | ||||
−0.238897 | + | 0.971045i | \(0.576786\pi\) | |||||||
\(272\) | 947.408 | 0.211195 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1502.92 | −0.331368 | ||||||||
\(275\) | 588.934 | 0.129142 | ||||||||
\(276\) | 1844.84 | 0.402342 | ||||||||
\(277\) | 4032.41 | 0.874673 | 0.437336 | − | 0.899298i | \(-0.355922\pi\) | ||||
0.437336 | + | 0.899298i | \(0.355922\pi\) | |||||||
\(278\) | −3073.86 | −0.663159 | ||||||||
\(279\) | 2012.34 | 0.431812 | ||||||||
\(280\) | −8680.03 | −1.85261 | ||||||||
\(281\) | −2298.29 | −0.487916 | −0.243958 | − | 0.969786i | \(-0.578446\pi\) | ||||
−0.243958 | + | 0.969786i | \(0.578446\pi\) | |||||||
\(282\) | 226.260 | 0.0477787 | ||||||||
\(283\) | 6656.80 | 1.39825 | 0.699127 | − | 0.714998i | \(-0.253572\pi\) | ||||
0.699127 | + | 0.714998i | \(0.253572\pi\) | |||||||
\(284\) | −393.373 | −0.0821916 | ||||||||
\(285\) | 3811.35 | 0.792158 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8799.33 | −1.80978 | ||||||||
\(288\) | 1395.63 | 0.285549 | ||||||||
\(289\) | −2347.01 | −0.477715 | ||||||||
\(290\) | 3457.13 | 0.700034 | ||||||||
\(291\) | −2246.27 | −0.452504 | ||||||||
\(292\) | 289.188 | 0.0579570 | ||||||||
\(293\) | 7466.99 | 1.48883 | 0.744413 | − | 0.667719i | \(-0.232729\pi\) | ||||
0.744413 | + | 0.667719i | \(0.232729\pi\) | |||||||
\(294\) | 3316.44 | 0.657887 | ||||||||
\(295\) | 5302.59 | 1.04654 | ||||||||
\(296\) | 5516.57 | 1.08326 | ||||||||
\(297\) | 757.717 | 0.148038 | ||||||||
\(298\) | 873.759 | 0.169851 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −241.078 | −0.0463955 | ||||||||
\(301\) | 5712.64 | 1.09392 | ||||||||
\(302\) | −3271.32 | −0.623323 | ||||||||
\(303\) | −2352.01 | −0.445938 | ||||||||
\(304\) | −1966.58 | −0.371024 | ||||||||
\(305\) | 3457.34 | 0.649071 | ||||||||
\(306\) | −931.059 | −0.173938 | ||||||||
\(307\) | −3965.99 | −0.737299 | −0.368650 | − | 0.929568i | \(-0.620180\pi\) | ||||
−0.368650 | + | 0.929568i | \(0.620180\pi\) | |||||||
\(308\) | −3195.64 | −0.591196 | ||||||||
\(309\) | 1188.12 | 0.218737 | ||||||||
\(310\) | 5517.23 | 1.01083 | ||||||||
\(311\) | 7372.29 | 1.34419 | 0.672097 | − | 0.740463i | \(-0.265394\pi\) | ||||
0.672097 | + | 0.740463i | \(0.265394\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8249.55 | 1.48975 | 0.744875 | − | 0.667204i | \(-0.232509\pi\) | ||||
0.744875 | + | 0.667204i | \(0.232509\pi\) | |||||||
\(314\) | −1491.54 | −0.268066 | ||||||||
\(315\) | 3233.70 | 0.578407 | ||||||||
\(316\) | −67.2133 | −0.0119653 | ||||||||
\(317\) | −5575.26 | −0.987817 | −0.493909 | − | 0.869514i | \(-0.664432\pi\) | ||||
−0.493909 | + | 0.869514i | \(0.664432\pi\) | |||||||
\(318\) | 913.507 | 0.161091 | ||||||||
\(319\) | 3931.85 | 0.690098 | ||||||||
\(320\) | 5634.21 | 0.984256 | ||||||||
\(321\) | −4309.77 | −0.749371 | ||||||||
\(322\) | −9752.88 | −1.68791 | ||||||||
\(323\) | −5326.35 | −0.917543 | ||||||||
\(324\) | −310.169 | −0.0531840 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3876.91 | 0.658657 | ||||||||
\(327\) | −5933.75 | −1.00348 | ||||||||
\(328\) | 7148.46 | 1.20338 | ||||||||
\(329\) | 1098.20 | 0.184029 | ||||||||
\(330\) | 2077.43 | 0.346542 | ||||||||
\(331\) | −4157.36 | −0.690361 | −0.345180 | − | 0.938536i | \(-0.612182\pi\) | ||||
−0.345180 | + | 0.938536i | \(0.612182\pi\) | |||||||
\(332\) | −5602.50 | −0.926136 | ||||||||
\(333\) | −2055.17 | −0.338206 | ||||||||
\(334\) | 2915.30 | 0.477600 | ||||||||
\(335\) | −6489.82 | −1.05844 | ||||||||
\(336\) | −1668.52 | −0.270909 | ||||||||
\(337\) | 3225.18 | 0.521326 | 0.260663 | − | 0.965430i | \(-0.416059\pi\) | ||||
0.260663 | + | 0.965430i | \(0.416059\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 367.215 | 0.0588330 | ||||||||
\(340\) | 2343.67 | 0.373833 | ||||||||
\(341\) | 6274.82 | 0.996483 | ||||||||
\(342\) | 1932.65 | 0.305572 | ||||||||
\(343\) | 5897.11 | 0.928321 | ||||||||
\(344\) | −4640.87 | −0.727381 | ||||||||
\(345\) | −5821.04 | −0.908389 | ||||||||
\(346\) | −4175.15 | −0.648721 | ||||||||
\(347\) | 3290.49 | 0.509057 | 0.254529 | − | 0.967065i | \(-0.418080\pi\) | ||||
0.254529 | + | 0.967065i | \(0.418080\pi\) | |||||||
\(348\) | −1609.49 | −0.247924 | ||||||||
\(349\) | −4491.52 | −0.688899 | −0.344449 | − | 0.938805i | \(-0.611934\pi\) | ||||
−0.344449 | + | 0.938805i | \(0.611934\pi\) | |||||||
\(350\) | 1274.48 | 0.194639 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4351.81 | 0.658955 | ||||||||
\(353\) | 5897.88 | 0.889270 | 0.444635 | − | 0.895712i | \(-0.353333\pi\) | ||||
0.444635 | + | 0.895712i | \(0.353333\pi\) | |||||||
\(354\) | 2688.82 | 0.403698 | ||||||||
\(355\) | 1241.21 | 0.185569 | ||||||||
\(356\) | 1282.43 | 0.190924 | ||||||||
\(357\) | −4519.08 | −0.669958 | ||||||||
\(358\) | −7943.75 | −1.17274 | ||||||||
\(359\) | −9277.20 | −1.36388 | −0.681938 | − | 0.731410i | \(-0.738863\pi\) | ||||
−0.681938 | + | 0.731410i | \(0.738863\pi\) | |||||||
\(360\) | −2627.01 | −0.384599 | ||||||||
\(361\) | 4197.19 | 0.611924 | ||||||||
\(362\) | −5058.67 | −0.734469 | ||||||||
\(363\) | −1630.31 | −0.235727 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −912.477 | −0.130853 | ||||||||
\(366\) | 1753.14 | 0.250377 | ||||||||
\(367\) | −6574.36 | −0.935092 | −0.467546 | − | 0.883969i | \(-0.654862\pi\) | ||||
−0.467546 | + | 0.883969i | \(0.654862\pi\) | |||||||
\(368\) | 3003.54 | 0.425463 | ||||||||
\(369\) | −2663.12 | −0.375708 | ||||||||
\(370\) | −5634.65 | −0.791707 | ||||||||
\(371\) | 4433.89 | 0.620474 | ||||||||
\(372\) | −2568.58 | −0.357996 | ||||||||
\(373\) | −5345.55 | −0.742043 | −0.371021 | − | 0.928624i | \(-0.620992\pi\) | ||||
−0.371021 | + | 0.928624i | \(0.620992\pi\) | |||||||
\(374\) | −2903.20 | −0.401393 | ||||||||
\(375\) | −3770.24 | −0.519186 | ||||||||
\(376\) | −892.162 | −0.122366 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1639.73 | 0.223118 | ||||||||
\(379\) | −1038.51 | −0.140751 | −0.0703757 | − | 0.997521i | \(-0.522420\pi\) | ||||
−0.0703757 | + | 0.997521i | \(0.522420\pi\) | |||||||
\(380\) | −4864.87 | −0.656743 | ||||||||
\(381\) | 6928.82 | 0.931691 | ||||||||
\(382\) | 4649.80 | 0.622786 | ||||||||
\(383\) | 6749.19 | 0.900437 | 0.450219 | − | 0.892918i | \(-0.351346\pi\) | ||||
0.450219 | + | 0.892918i | \(0.351346\pi\) | |||||||
\(384\) | −864.696 | −0.114912 | ||||||||
\(385\) | 10083.2 | 1.33478 | ||||||||
\(386\) | 8010.54 | 1.05628 | ||||||||
\(387\) | 1728.93 | 0.227097 | ||||||||
\(388\) | 2867.17 | 0.375151 | ||||||||
\(389\) | −1246.11 | −0.162417 | −0.0812083 | − | 0.996697i | \(-0.525878\pi\) | ||||
−0.0812083 | + | 0.996697i | \(0.525878\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8134.89 | 1.05217 | ||||||||
\(392\) | −13077.0 | −1.68492 | ||||||||
\(393\) | −4332.78 | −0.556133 | ||||||||
\(394\) | −10340.3 | −1.32218 | ||||||||
\(395\) | 212.079 | 0.0270148 | ||||||||
\(396\) | −967.161 | −0.122731 | ||||||||
\(397\) | 8355.69 | 1.05632 | 0.528161 | − | 0.849144i | \(-0.322882\pi\) | ||||
0.528161 | + | 0.849144i | \(0.322882\pi\) | |||||||
\(398\) | 6678.25 | 0.841082 | ||||||||
\(399\) | 9380.49 | 1.17697 | ||||||||
\(400\) | −392.494 | −0.0490618 | ||||||||
\(401\) | 3283.66 | 0.408923 | 0.204461 | − | 0.978875i | \(-0.434456\pi\) | ||||
0.204461 | + | 0.978875i | \(0.434456\pi\) | |||||||
\(402\) | −3290.83 | −0.408288 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3002.14 | 0.369708 | ||||||||
\(405\) | 978.679 | 0.120076 | ||||||||
\(406\) | 8508.68 | 1.04010 | ||||||||
\(407\) | −6408.37 | −0.780470 | ||||||||
\(408\) | 3671.24 | 0.445474 | ||||||||
\(409\) | 10928.9 | 1.32127 | 0.660636 | − | 0.750706i | \(-0.270287\pi\) | ||||
0.660636 | + | 0.750706i | \(0.270287\pi\) | |||||||
\(410\) | −7301.47 | −0.879497 | ||||||||
\(411\) | −2207.75 | −0.264965 | ||||||||
\(412\) | −1516.53 | −0.181345 | ||||||||
\(413\) | 13050.7 | 1.55492 | ||||||||
\(414\) | −2951.71 | −0.350408 | ||||||||
\(415\) | 17677.6 | 2.09099 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4515.43 | −0.530267 | ||||||||
\(418\) | 6026.33 | 0.705162 | ||||||||
\(419\) | 7302.94 | 0.851485 | 0.425742 | − | 0.904844i | \(-0.360013\pi\) | ||||
0.425742 | + | 0.904844i | \(0.360013\pi\) | |||||||
\(420\) | −4127.54 | −0.479531 | ||||||||
\(421\) | 7580.99 | 0.877612 | 0.438806 | − | 0.898582i | \(-0.355401\pi\) | ||||
0.438806 | + | 0.898582i | \(0.355401\pi\) | |||||||
\(422\) | −5743.15 | −0.662493 | ||||||||
\(423\) | 332.370 | 0.0382042 | ||||||||
\(424\) | −3602.03 | −0.412571 | ||||||||
\(425\) | −1063.04 | −0.121330 | ||||||||
\(426\) | 629.391 | 0.0715823 | ||||||||
\(427\) | 8509.19 | 0.964377 | ||||||||
\(428\) | 5501.06 | 0.621270 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4740.21 | 0.531612 | ||||||||
\(431\) | −10056.7 | −1.12394 | −0.561968 | − | 0.827159i | \(-0.689956\pi\) | ||||
−0.561968 | + | 0.827159i | \(0.689956\pi\) | |||||||
\(432\) | −504.979 | −0.0562403 | ||||||||
\(433\) | 2733.38 | 0.303367 | 0.151683 | − | 0.988429i | \(-0.451531\pi\) | ||||
0.151683 | + | 0.988429i | \(0.451531\pi\) | |||||||
\(434\) | 13579.0 | 1.50187 | ||||||||
\(435\) | 5078.44 | 0.559752 | ||||||||
\(436\) | 7573.93 | 0.831939 | ||||||||
\(437\) | −16886.0 | −1.84844 | ||||||||
\(438\) | −462.696 | −0.0504759 | ||||||||
\(439\) | 6744.23 | 0.733223 | 0.366611 | − | 0.930374i | \(-0.380518\pi\) | ||||
0.366611 | + | 0.930374i | \(0.380518\pi\) | |||||||
\(440\) | −8191.48 | −0.887531 | ||||||||
\(441\) | 4871.76 | 0.526051 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8655.69 | 0.928317 | 0.464158 | − | 0.885752i | \(-0.346357\pi\) | ||||
0.464158 | + | 0.885752i | \(0.346357\pi\) | |||||||
\(444\) | 2623.25 | 0.280391 | ||||||||
\(445\) | −4046.48 | −0.431059 | ||||||||
\(446\) | −1874.24 | −0.198986 | ||||||||
\(447\) | 1283.53 | 0.135814 | ||||||||
\(448\) | 13866.9 | 1.46239 | ||||||||
\(449\) | −6522.46 | −0.685555 | −0.342777 | − | 0.939417i | \(-0.611368\pi\) | ||||
−0.342777 | + | 0.939417i | \(0.611368\pi\) | |||||||
\(450\) | 385.721 | 0.0404068 | ||||||||
\(451\) | −8304.07 | −0.867014 | ||||||||
\(452\) | −468.719 | −0.0487759 | ||||||||
\(453\) | −4805.49 | −0.498414 | ||||||||
\(454\) | −2729.23 | −0.282135 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7620.59 | −0.782602 | ||||||||
\(457\) | 1551.23 | 0.158782 | 0.0793909 | − | 0.996844i | \(-0.474702\pi\) | ||||
0.0793909 | + | 0.996844i | \(0.474702\pi\) | |||||||
\(458\) | 336.603 | 0.0343415 | ||||||||
\(459\) | −1367.70 | −0.139082 | ||||||||
\(460\) | 7430.06 | 0.753105 | ||||||||
\(461\) | −7766.25 | −0.784621 | −0.392310 | − | 0.919833i | \(-0.628324\pi\) | ||||
−0.392310 | + | 0.919833i | \(0.628324\pi\) | |||||||
\(462\) | 5112.97 | 0.514885 | ||||||||
\(463\) | 2004.52 | 0.201205 | 0.100603 | − | 0.994927i | \(-0.467923\pi\) | ||||
0.100603 | + | 0.994927i | \(0.467923\pi\) | |||||||
\(464\) | −2620.37 | −0.262172 | ||||||||
\(465\) | 8104.66 | 0.808268 | ||||||||
\(466\) | −8666.10 | −0.861479 | ||||||||
\(467\) | 18674.3 | 1.85042 | 0.925209 | − | 0.379458i | \(-0.123889\pi\) | ||||
0.925209 | + | 0.379458i | \(0.123889\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15972.7 | −1.57261 | ||||||||
\(470\) | 911.259 | 0.0894324 | ||||||||
\(471\) | −2191.04 | −0.214348 | ||||||||
\(472\) | −10602.2 | −1.03391 | ||||||||
\(473\) | 5391.11 | 0.524067 | ||||||||
\(474\) | 107.540 | 0.0104209 | ||||||||
\(475\) | 2206.61 | 0.213150 | ||||||||
\(476\) | 5768.22 | 0.555433 | ||||||||
\(477\) | 1341.92 | 0.128810 | ||||||||
\(478\) | −5087.36 | −0.486800 | ||||||||
\(479\) | 9313.02 | 0.888357 | 0.444178 | − | 0.895938i | \(-0.353496\pi\) | ||||
0.444178 | + | 0.895938i | \(0.353496\pi\) | |||||||
\(480\) | 5620.86 | 0.534492 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5958.03 | 0.563031 | ||||||||
\(483\) | −14326.7 | −1.34967 | ||||||||
\(484\) | 2080.95 | 0.195431 | ||||||||
\(485\) | −9046.81 | −0.846999 | ||||||||
\(486\) | 496.265 | 0.0463190 | ||||||||
\(487\) | 3536.80 | 0.329092 | 0.164546 | − | 0.986369i | \(-0.447384\pi\) | ||||
0.164546 | + | 0.986369i | \(0.447384\pi\) | |||||||
\(488\) | −6912.76 | −0.641241 | ||||||||
\(489\) | 5695.08 | 0.526667 | ||||||||
\(490\) | 13356.9 | 1.23144 | ||||||||
\(491\) | −3361.78 | −0.308992 | −0.154496 | − | 0.987993i | \(-0.549375\pi\) | ||||
−0.154496 | + | 0.987993i | \(0.549375\pi\) | |||||||
\(492\) | 3399.24 | 0.311483 | ||||||||
\(493\) | −7097.10 | −0.648351 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3051.69 | 0.277098 | ||||||||
\(496\) | −4181.84 | −0.378569 | ||||||||
\(497\) | 3054.87 | 0.275714 | ||||||||
\(498\) | 8963.91 | 0.806591 | ||||||||
\(499\) | −4027.43 | −0.361308 | −0.180654 | − | 0.983547i | \(-0.557821\pi\) | ||||
−0.180654 | + | 0.983547i | \(0.557821\pi\) | |||||||
\(500\) | 4812.40 | 0.430434 | ||||||||
\(501\) | 4282.50 | 0.381892 | ||||||||
\(502\) | −2683.26 | −0.238565 | ||||||||
\(503\) | 1766.67 | 0.156604 | 0.0783022 | − | 0.996930i | \(-0.475050\pi\) | ||||
0.0783022 | + | 0.996930i | \(0.475050\pi\) | |||||||
\(504\) | −6465.59 | −0.571429 | ||||||||
\(505\) | −9472.67 | −0.834709 | ||||||||
\(506\) | −9203.96 | −0.808628 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8844.05 | −0.772424 | ||||||||
\(509\) | 6816.27 | 0.593567 | 0.296784 | − | 0.954945i | \(-0.404086\pi\) | ||||
0.296784 | + | 0.954945i | \(0.404086\pi\) | |||||||
\(510\) | −3749.83 | −0.325579 | ||||||||
\(511\) | −2245.79 | −0.194418 | ||||||||
\(512\) | −6514.89 | −0.562344 | ||||||||
\(513\) | 2839.01 | 0.244338 | ||||||||
\(514\) | −2016.88 | −0.173076 | ||||||||
\(515\) | 4785.13 | 0.409433 | ||||||||
\(516\) | −2206.83 | −0.188276 | ||||||||
\(517\) | 1036.39 | 0.0881630 | ||||||||
\(518\) | −13868.0 | −1.17630 | ||||||||
\(519\) | −6133.19 | −0.518723 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5442.27 | −0.457640 | −0.228820 | − | 0.973469i | \(-0.573487\pi\) | ||||
−0.228820 | + | 0.973469i | \(0.573487\pi\) | |||||||
\(522\) | 2575.15 | 0.215922 | ||||||||
\(523\) | 20728.5 | 1.73307 | 0.866535 | − | 0.499117i | \(-0.166342\pi\) | ||||
0.866535 | + | 0.499117i | \(0.166342\pi\) | |||||||
\(524\) | 5530.43 | 0.461065 | ||||||||
\(525\) | 1872.17 | 0.155635 | ||||||||
\(526\) | −14268.0 | −1.18273 | ||||||||
\(527\) | −11326.2 | −0.936202 | ||||||||
\(528\) | −1574.61 | −0.129785 | ||||||||
\(529\) | 13622.8 | 1.11965 | ||||||||
\(530\) | 3679.13 | 0.301531 | ||||||||
\(531\) | 3949.80 | 0.322800 | ||||||||
\(532\) | −11973.4 | −0.975775 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2051.87 | −0.166279 | ||||||||
\(535\) | −17357.5 | −1.40268 | ||||||||
\(536\) | 12976.0 | 1.04567 | ||||||||
\(537\) | −11669.2 | −0.937730 | ||||||||
\(538\) | −12058.1 | −0.966285 | ||||||||
\(539\) | 15191.0 | 1.21396 | ||||||||
\(540\) | −1249.20 | −0.0995500 | ||||||||
\(541\) | 8577.44 | 0.681651 | 0.340825 | − | 0.940127i | \(-0.389294\pi\) | ||||
0.340825 | + | 0.940127i | \(0.389294\pi\) | |||||||
\(542\) | −4353.13 | −0.344987 | ||||||||
\(543\) | −7431.05 | −0.587287 | ||||||||
\(544\) | −7855.14 | −0.619093 | ||||||||
\(545\) | −23898.1 | −1.87832 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8723.99 | 0.681921 | 0.340961 | − | 0.940078i | \(-0.389248\pi\) | ||||
0.340961 | + | 0.940078i | \(0.389248\pi\) | |||||||
\(548\) | 2818.01 | 0.219671 | ||||||||
\(549\) | 2575.31 | 0.200203 | ||||||||
\(550\) | 1202.75 | 0.0932459 | ||||||||
\(551\) | 14731.8 | 1.13901 | ||||||||
\(552\) | 11638.8 | 0.897431 | ||||||||
\(553\) | 521.968 | 0.0401380 | ||||||||
\(554\) | 8235.17 | 0.631550 | ||||||||
\(555\) | −8277.15 | −0.633055 | ||||||||
\(556\) | 5763.56 | 0.439621 | ||||||||
\(557\) | −965.006 | −0.0734087 | −0.0367043 | − | 0.999326i | \(-0.511686\pi\) | ||||
−0.0367043 | + | 0.999326i | \(0.511686\pi\) | |||||||
\(558\) | 4109.68 | 0.311786 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6719.95 | −0.507089 | ||||||||
\(561\) | −4264.73 | −0.320957 | ||||||||
\(562\) | −4693.66 | −0.352296 | ||||||||
\(563\) | −14605.2 | −1.09331 | −0.546657 | − | 0.837357i | \(-0.684100\pi\) | ||||
−0.546657 | + | 0.837357i | \(0.684100\pi\) | |||||||
\(564\) | −424.242 | −0.0316734 | ||||||||
\(565\) | 1478.95 | 0.110124 | ||||||||
\(566\) | 13594.8 | 1.00960 | ||||||||
\(567\) | 2408.72 | 0.178407 | ||||||||
\(568\) | −2481.74 | −0.183330 | ||||||||
\(569\) | 7802.48 | 0.574863 | 0.287432 | − | 0.957801i | \(-0.407199\pi\) | ||||
0.287432 | + | 0.957801i | \(0.407199\pi\) | |||||||
\(570\) | 7783.71 | 0.571971 | ||||||||
\(571\) | 11988.2 | 0.878618 | 0.439309 | − | 0.898336i | \(-0.355223\pi\) | ||||
0.439309 | + | 0.898336i | \(0.355223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6830.43 | 0.497985 | ||||||||
\(574\) | −17970.4 | −1.30674 | ||||||||
\(575\) | −3370.14 | −0.244425 | ||||||||
\(576\) | 4196.82 | 0.303589 | ||||||||
\(577\) | 5576.90 | 0.402374 | 0.201187 | − | 0.979553i | \(-0.435520\pi\) | ||||
0.201187 | + | 0.979553i | \(0.435520\pi\) | |||||||
\(578\) | −4793.17 | −0.344930 | ||||||||
\(579\) | 11767.3 | 0.844613 | ||||||||
\(580\) | −6482.19 | −0.464066 | ||||||||
\(581\) | 43508.1 | 3.10675 | ||||||||
\(582\) | −4587.43 | −0.326727 | ||||||||
\(583\) | 4184.33 | 0.297251 | ||||||||
\(584\) | 1824.45 | 0.129274 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15249.4 | 1.07499 | ||||||||
\(587\) | 26754.0 | 1.88119 | 0.940593 | − | 0.339535i | \(-0.110270\pi\) | ||||
0.940593 | + | 0.339535i | \(0.110270\pi\) | |||||||
\(588\) | −6218.39 | −0.436126 | ||||||||
\(589\) | 23510.5 | 1.64471 | ||||||||
\(590\) | 10829.2 | 0.755644 | ||||||||
\(591\) | −15189.7 | −1.05722 | ||||||||
\(592\) | 4270.85 | 0.296505 | ||||||||
\(593\) | −3589.40 | −0.248565 | −0.124283 | − | 0.992247i | \(-0.539663\pi\) | ||||
−0.124283 | + | 0.992247i | \(0.539663\pi\) | |||||||
\(594\) | 1547.44 | 0.106889 | ||||||||
\(595\) | −18200.5 | −1.25403 | ||||||||
\(596\) | −1638.32 | −0.112597 | ||||||||
\(597\) | 9810.18 | 0.672536 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7462.78 | −0.509050 | −0.254525 | − | 0.967066i | \(-0.581919\pi\) | ||||
−0.254525 | + | 0.967066i | \(0.581919\pi\) | |||||||
\(600\) | −1520.93 | −0.103486 | ||||||||
\(601\) | −16511.0 | −1.12063 | −0.560316 | − | 0.828279i | \(-0.689320\pi\) | ||||
−0.560316 | + | 0.828279i | \(0.689320\pi\) | |||||||
\(602\) | 11666.6 | 0.789858 | ||||||||
\(603\) | −4834.15 | −0.326471 | ||||||||
\(604\) | 6133.80 | 0.413213 | ||||||||
\(605\) | −6566.04 | −0.441235 | ||||||||
\(606\) | −4803.37 | −0.321986 | ||||||||
\(607\) | −11953.6 | −0.799309 | −0.399654 | − | 0.916666i | \(-0.630870\pi\) | ||||
−0.399654 | + | 0.916666i | \(0.630870\pi\) | |||||||
\(608\) | 16305.3 | 1.08761 | ||||||||
\(609\) | 12499.0 | 0.831669 | ||||||||
\(610\) | 7060.73 | 0.468657 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1745.75 | 0.115307 | ||||||||
\(613\) | −4575.65 | −0.301482 | −0.150741 | − | 0.988573i | \(-0.548166\pi\) | ||||
−0.150741 | + | 0.988573i | \(0.548166\pi\) | |||||||
\(614\) | −8099.51 | −0.532361 | ||||||||
\(615\) | −10725.7 | −0.703253 | ||||||||
\(616\) | −20160.9 | −1.31868 | ||||||||
\(617\) | −19231.0 | −1.25480 | −0.627400 | − | 0.778697i | \(-0.715881\pi\) | ||||
−0.627400 | + | 0.778697i | \(0.715881\pi\) | |||||||
\(618\) | 2426.43 | 0.157937 | ||||||||
\(619\) | −11715.6 | −0.760727 | −0.380363 | − | 0.924837i | \(-0.624201\pi\) | ||||
−0.380363 | + | 0.924837i | \(0.624201\pi\) | |||||||
\(620\) | −10344.9 | −0.670099 | ||||||||
\(621\) | −4335.99 | −0.280189 | ||||||||
\(622\) | 15056.0 | 0.970564 | ||||||||
\(623\) | −9959.17 | −0.640459 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17807.8 | −1.13970 | ||||||||
\(626\) | 16847.6 | 1.07566 | ||||||||
\(627\) | 8852.52 | 0.563853 | ||||||||
\(628\) | 2796.68 | 0.177706 | ||||||||
\(629\) | 11567.3 | 0.733256 | ||||||||
\(630\) | 6603.99 | 0.417634 | ||||||||
\(631\) | −8780.09 | −0.553930 | −0.276965 | − | 0.960880i | \(-0.589329\pi\) | ||||
−0.276965 | + | 0.960880i | \(0.589329\pi\) | |||||||
\(632\) | −424.040 | −0.0266889 | ||||||||
\(633\) | −8436.53 | −0.529735 | ||||||||
\(634\) | −11386.0 | −0.713245 | ||||||||
\(635\) | 27905.7 | 1.74395 | ||||||||
\(636\) | −1712.84 | −0.106790 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8029.78 | 0.498279 | ||||||||
\(639\) | 924.558 | 0.0572378 | ||||||||
\(640\) | −3482.55 | −0.215094 | ||||||||
\(641\) | 24991.7 | 1.53996 | 0.769980 | − | 0.638068i | \(-0.220266\pi\) | ||||
0.769980 | + | 0.638068i | \(0.220266\pi\) | |||||||
\(642\) | −8801.60 | −0.541077 | ||||||||
\(643\) | −2353.86 | −0.144365 | −0.0721827 | − | 0.997391i | \(-0.522996\pi\) | ||||
−0.0721827 | + | 0.997391i | \(0.522996\pi\) | |||||||
\(644\) | 18286.8 | 1.11895 | ||||||||
\(645\) | 6963.24 | 0.425081 | ||||||||
\(646\) | −10877.7 | −0.662504 | ||||||||
\(647\) | −5910.80 | −0.359162 | −0.179581 | − | 0.983743i | \(-0.557474\pi\) | ||||
−0.179581 | + | 0.983743i | \(0.557474\pi\) | |||||||
\(648\) | −1956.81 | −0.118628 | ||||||||
\(649\) | 12316.2 | 0.744918 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19947.2 | 1.20091 | ||||||||
\(652\) | −7269.28 | −0.436637 | ||||||||
\(653\) | 5924.34 | 0.355034 | 0.177517 | − | 0.984118i | \(-0.443194\pi\) | ||||
0.177517 | + | 0.984118i | \(0.443194\pi\) | |||||||
\(654\) | −12118.2 | −0.724553 | ||||||||
\(655\) | −17450.2 | −1.04097 | ||||||||
\(656\) | 5534.23 | 0.329383 | ||||||||
\(657\) | −679.688 | −0.0403610 | ||||||||
\(658\) | 2242.79 | 0.132877 | ||||||||
\(659\) | −12839.5 | −0.758964 | −0.379482 | − | 0.925199i | \(-0.623898\pi\) | ||||
−0.379482 | + | 0.925199i | \(0.623898\pi\) | |||||||
\(660\) | −3895.22 | −0.229729 | ||||||||
\(661\) | 10265.5 | 0.604057 | 0.302028 | − | 0.953299i | \(-0.402336\pi\) | ||||
0.302028 | + | 0.953299i | \(0.402336\pi\) | |||||||
\(662\) | −8490.35 | −0.498469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −35345.4 | −2.06577 | ||||||||
\(665\) | 37779.8 | 2.20306 | ||||||||
\(666\) | −4197.15 | −0.244199 | ||||||||
\(667\) | −22499.7 | −1.30614 | ||||||||
\(668\) | −5466.25 | −0.316610 | ||||||||
\(669\) | −2753.21 | −0.159111 | ||||||||
\(670\) | −13253.8 | −0.764236 | ||||||||
\(671\) | 8030.27 | 0.462004 | ||||||||
\(672\) | 13834.1 | 0.794137 | ||||||||
\(673\) | 9862.82 | 0.564909 | 0.282454 | − | 0.959281i | \(-0.408851\pi\) | ||||
0.282454 | + | 0.959281i | \(0.408851\pi\) | |||||||
\(674\) | 6586.61 | 0.376419 | ||||||||
\(675\) | 566.614 | 0.0323096 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32615.5 | 1.85158 | 0.925788 | − | 0.378043i | \(-0.123403\pi\) | ||||
0.925788 | + | 0.378043i | \(0.123403\pi\) | |||||||
\(678\) | 749.943 | 0.0424799 | ||||||||
\(679\) | −22266.0 | −1.25845 | ||||||||
\(680\) | 14785.9 | 0.833841 | ||||||||
\(681\) | −4009.17 | −0.225597 | ||||||||
\(682\) | 12814.7 | 0.719502 | ||||||||
\(683\) | −21627.4 | −1.21164 | −0.605820 | − | 0.795602i | \(-0.707155\pi\) | ||||
−0.605820 | + | 0.795602i | \(0.707155\pi\) | |||||||
\(684\) | −3623.75 | −0.202570 | ||||||||
\(685\) | −8891.70 | −0.495962 | ||||||||
\(686\) | 12043.3 | 0.670286 | ||||||||
\(687\) | 494.461 | 0.0274598 | ||||||||
\(688\) | −3592.90 | −0.199096 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −11888.0 | −0.655895 | ||||||||
\(691\) | 14233.1 | 0.783580 | 0.391790 | − | 0.920055i | \(-0.371856\pi\) | ||||
0.391790 | + | 0.920055i | \(0.371856\pi\) | |||||||
\(692\) | 7828.49 | 0.430050 | ||||||||
\(693\) | 7510.81 | 0.411706 | ||||||||
\(694\) | 6719.98 | 0.367561 | ||||||||
\(695\) | −18185.8 | −0.992557 | ||||||||
\(696\) | −10154.0 | −0.553000 | ||||||||
\(697\) | 14989.1 | 0.814566 | ||||||||
\(698\) | −9172.78 | −0.497414 | ||||||||
\(699\) | −12730.3 | −0.688845 | ||||||||
\(700\) | −2389.67 | −0.129030 | ||||||||
\(701\) | −28747.0 | −1.54887 | −0.774437 | − | 0.632651i | \(-0.781967\pi\) | ||||
−0.774437 | + | 0.632651i | \(0.781967\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24010.8 | −1.28817 | ||||||||
\(704\) | 13086.4 | 0.700586 | ||||||||
\(705\) | 1338.61 | 0.0715109 | ||||||||
\(706\) | 12044.9 | 0.642090 | ||||||||
\(707\) | −23314.1 | −1.24019 | ||||||||
\(708\) | −5041.59 | −0.267619 | ||||||||
\(709\) | −1818.65 | −0.0963339 | −0.0481670 | − | 0.998839i | \(-0.515338\pi\) | ||||
−0.0481670 | + | 0.998839i | \(0.515338\pi\) | |||||||
\(710\) | 2534.86 | 0.133988 | ||||||||
\(711\) | 157.974 | 0.00833260 | ||||||||
\(712\) | 8090.70 | 0.425859 | ||||||||
\(713\) | −35907.3 | −1.88603 | ||||||||
\(714\) | −9229.06 | −0.483738 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14894.7 | 0.777431 | ||||||||
\(717\) | −7473.20 | −0.389249 | ||||||||
\(718\) | −18946.3 | −0.984776 | ||||||||
\(719\) | 26141.8 | 1.35595 | 0.677973 | − | 0.735087i | \(-0.262859\pi\) | ||||
0.677973 | + | 0.735087i | \(0.262859\pi\) | |||||||
\(720\) | −2033.80 | −0.105271 | ||||||||
\(721\) | 11777.2 | 0.608328 | ||||||||
\(722\) | 8571.68 | 0.441835 | ||||||||
\(723\) | 8752.19 | 0.450204 | ||||||||
\(724\) | 9485.10 | 0.486894 | ||||||||
\(725\) | 2940.20 | 0.150616 | ||||||||
\(726\) | −3329.48 | −0.170205 | ||||||||
\(727\) | −1340.10 | −0.0683652 | −0.0341826 | − | 0.999416i | \(-0.510883\pi\) | ||||
−0.0341826 | + | 0.999416i | \(0.510883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −1863.50 | −0.0944811 | ||||||||
\(731\) | −9731.11 | −0.492364 | ||||||||
\(732\) | −3287.16 | −0.165980 | ||||||||
\(733\) | −32517.1 | −1.63854 | −0.819269 | − | 0.573409i | \(-0.805620\pi\) | ||||
−0.819269 | + | 0.573409i | \(0.805620\pi\) | |||||||
\(734\) | −13426.4 | −0.675176 | ||||||||
\(735\) | 19620.9 | 0.984666 | ||||||||
\(736\) | −24903.0 | −1.24719 | ||||||||
\(737\) | −15073.7 | −0.753389 | ||||||||
\(738\) | −5438.73 | −0.271277 | ||||||||
\(739\) | −22170.5 | −1.10359 | −0.551797 | − | 0.833978i | \(-0.686058\pi\) | ||||
−0.551797 | + | 0.833978i | \(0.686058\pi\) | |||||||
\(740\) | 10565.1 | 0.524838 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9055.07 | 0.448008 | ||||||||
\(743\) | −30387.8 | −1.50043 | −0.750216 | − | 0.661193i | \(-0.770051\pi\) | ||||
−0.750216 | + | 0.661193i | \(0.770051\pi\) | |||||||
\(744\) | −16204.8 | −0.798518 | ||||||||
\(745\) | 5169.39 | 0.254217 | ||||||||
\(746\) | −10916.9 | −0.535786 | ||||||||
\(747\) | 13167.7 | 0.644956 | ||||||||
\(748\) | 5443.57 | 0.266092 | ||||||||
\(749\) | −42720.3 | −2.08407 | ||||||||
\(750\) | −7699.75 | −0.374874 | ||||||||
\(751\) | −16898.3 | −0.821077 | −0.410539 | − | 0.911843i | \(-0.634659\pi\) | ||||
−0.410539 | + | 0.911843i | \(0.634659\pi\) | |||||||
\(752\) | −690.699 | −0.0334936 | ||||||||
\(753\) | −3941.63 | −0.190758 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19354.0 | −0.932934 | ||||||||
\(756\) | −3074.53 | −0.147909 | ||||||||
\(757\) | 32925.8 | 1.58086 | 0.790428 | − | 0.612555i | \(-0.209858\pi\) | ||||
0.790428 | + | 0.612555i | \(0.209858\pi\) | |||||||
\(758\) | −2120.89 | −0.101628 | ||||||||
\(759\) | −13520.4 | −0.646585 | ||||||||
\(760\) | −30691.8 | −1.46488 | ||||||||
\(761\) | −16792.0 | −0.799882 | −0.399941 | − | 0.916541i | \(-0.630969\pi\) | ||||
−0.399941 | + | 0.916541i | \(0.630969\pi\) | |||||||
\(762\) | 14150.3 | 0.672720 | ||||||||
\(763\) | −58817.9 | −2.79076 | ||||||||
\(764\) | −8718.46 | −0.412857 | ||||||||
\(765\) | −5508.39 | −0.260335 | ||||||||
\(766\) | 13783.5 | 0.650153 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12957.4 | −0.608804 | ||||||||
\(769\) | −1541.57 | −0.0722891 | −0.0361445 | − | 0.999347i | \(-0.511508\pi\) | ||||
−0.0361445 | + | 0.999347i | \(0.511508\pi\) | |||||||
\(770\) | 20592.4 | 0.963765 | ||||||||
\(771\) | −2962.75 | −0.138393 | ||||||||
\(772\) | −15019.9 | −0.700231 | ||||||||
\(773\) | −38071.2 | −1.77144 | −0.885721 | − | 0.464218i | \(-0.846335\pi\) | ||||
−0.885721 | + | 0.464218i | \(0.846335\pi\) | |||||||
\(774\) | 3530.90 | 0.163973 | ||||||||
\(775\) | 4692.26 | 0.217485 | ||||||||
\(776\) | 18088.6 | 0.836782 | ||||||||
\(777\) | −20371.7 | −0.940580 | ||||||||
\(778\) | −2544.85 | −0.117272 | ||||||||
\(779\) | −31113.6 | −1.43102 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2882.93 | 0.132086 | ||||||||
\(782\) | 16613.4 | 0.759712 | ||||||||
\(783\) | 3782.83 | 0.172653 | ||||||||
\(784\) | −10124.0 | −0.461189 | ||||||||
\(785\) | −8824.38 | −0.401217 | ||||||||
\(786\) | −8848.60 | −0.401551 | ||||||||
\(787\) | 20049.8 | 0.908129 | 0.454065 | − | 0.890969i | \(-0.349973\pi\) | ||||
0.454065 | + | 0.890969i | \(0.349973\pi\) | |||||||
\(788\) | 19388.3 | 0.876498 | ||||||||
\(789\) | −20959.4 | −0.945720 | ||||||||
\(790\) | 433.117 | 0.0195058 | ||||||||
\(791\) | 3640.00 | 0.163620 | ||||||||
\(792\) | −6101.69 | −0.273755 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 17064.4 | 0.762709 | ||||||||
\(795\) | 5404.55 | 0.241106 | ||||||||
\(796\) | −12521.9 | −0.557570 | ||||||||
\(797\) | −22401.9 | −0.995627 | −0.497813 | − | 0.867284i | \(-0.665864\pi\) | ||||
−0.497813 | + | 0.867284i | \(0.665864\pi\) | |||||||
\(798\) | 19157.2 | 0.849823 | ||||||||
\(799\) | −1870.71 | −0.0828298 | ||||||||
\(800\) | 3254.24 | 0.143819 | ||||||||
\(801\) | −3014.15 | −0.132958 | ||||||||
\(802\) | 6706.02 | 0.295259 | ||||||||
\(803\) | −2119.39 | −0.0931401 | ||||||||
\(804\) | 6170.38 | 0.270662 | ||||||||
\(805\) | −57700.7 | −2.52631 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −17713.0 | −0.772649 | ||||||||
\(808\) | 18940.1 | 0.824640 | ||||||||
\(809\) | −41966.4 | −1.82381 | −0.911903 | − | 0.410406i | \(-0.865387\pi\) | ||||
−0.911903 | + | 0.410406i | \(0.865387\pi\) | |||||||
\(810\) | 1998.70 | 0.0867002 | ||||||||
\(811\) | −13029.1 | −0.564133 | −0.282067 | − | 0.959395i | \(-0.591020\pi\) | ||||
−0.282067 | + | 0.959395i | \(0.591020\pi\) | |||||||
\(812\) | −15953.9 | −0.689500 | ||||||||
\(813\) | −6394.63 | −0.275854 | ||||||||
\(814\) | −13087.4 | −0.563532 | ||||||||
\(815\) | 22936.8 | 0.985819 | ||||||||
\(816\) | 2842.22 | 0.121933 | ||||||||
\(817\) | 20199.4 | 0.864977 | ||||||||
\(818\) | 22319.5 | 0.954014 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13690.4 | 0.583036 | ||||||||
\(821\) | 8898.14 | 0.378255 | 0.189127 | − | 0.981953i | \(-0.439434\pi\) | ||||
0.189127 | + | 0.981953i | \(0.439434\pi\) | |||||||
\(822\) | −4508.77 | −0.191316 | ||||||||
\(823\) | 22723.6 | 0.962448 | 0.481224 | − | 0.876598i | \(-0.340192\pi\) | ||||
0.481224 | + | 0.876598i | \(0.340192\pi\) | |||||||
\(824\) | −9567.61 | −0.404494 | ||||||||
\(825\) | 1766.80 | 0.0745602 | ||||||||
\(826\) | 26652.7 | 1.12272 | ||||||||
\(827\) | 19073.3 | 0.801989 | 0.400994 | − | 0.916081i | \(-0.368665\pi\) | ||||
0.400994 | + | 0.916081i | \(0.368665\pi\) | |||||||
\(828\) | 5534.52 | 0.232292 | ||||||||
\(829\) | 42503.8 | 1.78072 | 0.890361 | − | 0.455255i | \(-0.150452\pi\) | ||||
0.890361 | + | 0.455255i | \(0.150452\pi\) | |||||||
\(830\) | 36102.0 | 1.50978 | ||||||||
\(831\) | 12097.2 | 0.504992 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27420.2 | −1.14052 | ||||||||
\(834\) | −9221.59 | −0.382875 | ||||||||
\(835\) | 17247.7 | 0.714829 | ||||||||
\(836\) | −11299.5 | −0.467465 | ||||||||
\(837\) | 6037.01 | 0.249307 | ||||||||
\(838\) | 14914.4 | 0.614808 | ||||||||
\(839\) | −19427.2 | −0.799408 | −0.399704 | − | 0.916644i | \(-0.630887\pi\) | ||||
−0.399704 | + | 0.916644i | \(0.630887\pi\) | |||||||
\(840\) | −26040.1 | −1.06960 | ||||||||
\(841\) | −4759.60 | −0.195154 | ||||||||
\(842\) | 15482.2 | 0.633673 | ||||||||
\(843\) | −6894.86 | −0.281698 | ||||||||
\(844\) | 10768.5 | 0.439180 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 678.780 | 0.0275850 | ||||||||
\(847\) | −16160.3 | −0.655578 | ||||||||
\(848\) | −2788.64 | −0.112927 | ||||||||
\(849\) | 19970.4 | 0.807282 | ||||||||
\(850\) | −2170.99 | −0.0876052 | ||||||||
\(851\) | 36671.5 | 1.47718 | ||||||||
\(852\) | −1180.12 | −0.0474533 | ||||||||
\(853\) | 26851.8 | 1.07783 | 0.538914 | − | 0.842361i | \(-0.318835\pi\) | ||||
0.538914 | + | 0.842361i | \(0.318835\pi\) | |||||||
\(854\) | 17377.8 | 0.696320 | ||||||||
\(855\) | 11434.1 | 0.457353 | ||||||||
\(856\) | 34705.4 | 1.38576 | ||||||||
\(857\) | 41539.4 | 1.65573 | 0.827864 | − | 0.560929i | \(-0.189556\pi\) | ||||
0.827864 | + | 0.560929i | \(0.189556\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11936.2 | −0.474107 | −0.237054 | − | 0.971497i | \(-0.576182\pi\) | ||||
−0.237054 | + | 0.971497i | \(0.576182\pi\) | |||||||
\(860\) | −8887.99 | −0.352416 | ||||||||
\(861\) | −26398.0 | −1.04488 | ||||||||
\(862\) | −20538.3 | −0.811529 | ||||||||
\(863\) | 41128.6 | 1.62229 | 0.811143 | − | 0.584848i | \(-0.198846\pi\) | ||||
0.811143 | + | 0.584848i | \(0.198846\pi\) | |||||||
\(864\) | 4186.88 | 0.164862 | ||||||||
\(865\) | −24701.3 | −0.970948 | ||||||||
\(866\) | 5582.22 | 0.219043 | ||||||||
\(867\) | −7041.04 | −0.275809 | ||||||||
\(868\) | −25460.8 | −0.995619 | ||||||||
\(869\) | 492.590 | 0.0192290 | ||||||||
\(870\) | 10371.4 | 0.404165 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 47782.9 | 1.85566 | ||||||||
\(873\) | −6738.81 | −0.261253 | ||||||||
\(874\) | −34485.3 | −1.33465 | ||||||||
\(875\) | −37372.3 | −1.44390 | ||||||||
\(876\) | 867.564 | 0.0334615 | ||||||||
\(877\) | −6406.86 | −0.246687 | −0.123343 | − | 0.992364i | \(-0.539362\pi\) | ||||
−0.123343 | + | 0.992364i | \(0.539362\pi\) | |||||||
\(878\) | 13773.4 | 0.529417 | ||||||||
\(879\) | 22401.0 | 0.859574 | ||||||||
\(880\) | −6341.73 | −0.242931 | ||||||||
\(881\) | −2938.07 | −0.112357 | −0.0561783 | − | 0.998421i | \(-0.517892\pi\) | ||||
−0.0561783 | + | 0.998421i | \(0.517892\pi\) | |||||||
\(882\) | 9949.32 | 0.379831 | ||||||||
\(883\) | 3022.06 | 0.115176 | 0.0575881 | − | 0.998340i | \(-0.481659\pi\) | ||||
0.0575881 | + | 0.998340i | \(0.481659\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15907.8 | 0.604219 | ||||||||
\(886\) | 17677.0 | 0.670284 | ||||||||
\(887\) | −10060.4 | −0.380830 | −0.190415 | − | 0.981704i | \(-0.560983\pi\) | ||||
−0.190415 | + | 0.981704i | \(0.560983\pi\) | |||||||
\(888\) | 16549.7 | 0.625419 | ||||||||
\(889\) | 68681.5 | 2.59112 | ||||||||
\(890\) | −8263.89 | −0.311243 | ||||||||
\(891\) | 2273.15 | 0.0854696 | ||||||||
\(892\) | 3514.24 | 0.131912 | ||||||||
\(893\) | 3883.13 | 0.145514 | ||||||||
\(894\) | 2621.28 | 0.0980634 | ||||||||
\(895\) | −46997.3 | −1.75525 | ||||||||
\(896\) | −8571.24 | −0.319582 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13320.5 | −0.494999 | ||||||||
\(899\) | 31326.5 | 1.16218 | ||||||||
\(900\) | −723.234 | −0.0267865 | ||||||||
\(901\) | −7552.84 | −0.279269 | ||||||||
\(902\) | −16958.9 | −0.626020 | ||||||||
\(903\) | 17137.9 | 0.631577 | ||||||||
\(904\) | −2957.09 | −0.108796 | ||||||||
\(905\) | −29928.4 | −1.09929 | ||||||||
\(906\) | −9813.97 | −0.359876 | ||||||||
\(907\) | −43158.6 | −1.58000 | −0.789999 | − | 0.613108i | \(-0.789919\pi\) | ||||
−0.789999 | + | 0.613108i | \(0.789919\pi\) | |||||||
\(908\) | 5117.36 | 0.187033 | ||||||||
\(909\) | −7056.02 | −0.257462 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32665.9 | −1.18800 | −0.594001 | − | 0.804464i | \(-0.702453\pi\) | ||||
−0.594001 | + | 0.804464i | \(0.702453\pi\) | |||||||
\(912\) | −5899.75 | −0.214211 | ||||||||
\(913\) | 41059.3 | 1.48835 | ||||||||
\(914\) | 3167.98 | 0.114647 | ||||||||
\(915\) | 10372.0 | 0.374741 | ||||||||
\(916\) | −631.137 | −0.0227657 | ||||||||
\(917\) | −42948.4 | −1.54665 | ||||||||
\(918\) | −2793.18 | −0.100423 | ||||||||
\(919\) | 18989.9 | 0.681633 | 0.340816 | − | 0.940130i | \(-0.389297\pi\) | ||||
0.340816 | + | 0.940130i | \(0.389297\pi\) | |||||||
\(920\) | 46875.3 | 1.67982 | ||||||||
\(921\) | −11898.0 | −0.425680 | ||||||||
\(922\) | −15860.6 | −0.566529 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −9586.91 | −0.341327 | ||||||||
\(925\) | −4792.12 | −0.170340 | ||||||||
\(926\) | 4093.72 | 0.145279 | ||||||||
\(927\) | 3564.36 | 0.126288 | ||||||||
\(928\) | 21726.0 | 0.768525 | ||||||||
\(929\) | −5596.81 | −0.197659 | −0.0988295 | − | 0.995104i | \(-0.531510\pi\) | ||||
−0.0988295 | + | 0.995104i | \(0.531510\pi\) | |||||||
\(930\) | 16551.7 | 0.583603 | ||||||||
\(931\) | 56917.6 | 2.00365 | ||||||||
\(932\) | 16249.1 | 0.571091 | ||||||||
\(933\) | 22116.9 | 0.776070 | ||||||||
\(934\) | 38137.5 | 1.33608 | ||||||||
\(935\) | −17176.1 | −0.600770 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40294.4 | 1.40487 | 0.702433 | − | 0.711750i | \(-0.252097\pi\) | ||||
0.702433 | + | 0.711750i | \(0.252097\pi\) | |||||||
\(938\) | −32620.2 | −1.13549 | ||||||||
\(939\) | 24748.6 | 0.860108 | ||||||||
\(940\) | −1708.63 | −0.0592865 | ||||||||
\(941\) | 43648.8 | 1.51213 | 0.756063 | − | 0.654499i | \(-0.227120\pi\) | ||||
0.756063 | + | 0.654499i | \(0.227120\pi\) | |||||||
\(942\) | −4474.63 | −0.154768 | ||||||||
\(943\) | 47519.5 | 1.64098 | ||||||||
\(944\) | −8208.10 | −0.282999 | ||||||||
\(945\) | 9701.09 | 0.333943 | ||||||||
\(946\) | 11010.0 | 0.378398 | ||||||||
\(947\) | −10486.6 | −0.359839 | −0.179919 | − | 0.983681i | \(-0.557584\pi\) | ||||
−0.179919 | + | 0.983681i | \(0.557584\pi\) | |||||||
\(948\) | −201.640 | −0.00690819 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4506.44 | 0.153903 | ||||||||
\(951\) | −16725.8 | −0.570317 | ||||||||
\(952\) | 36390.9 | 1.23890 | ||||||||
\(953\) | 33058.8 | 1.12369 | 0.561846 | − | 0.827242i | \(-0.310091\pi\) | ||||
0.561846 | + | 0.827242i | \(0.310091\pi\) | |||||||
\(954\) | 2740.52 | 0.0930059 | ||||||||
\(955\) | 27509.5 | 0.932131 | ||||||||
\(956\) | 9538.90 | 0.322709 | ||||||||
\(957\) | 11795.5 | 0.398428 | ||||||||
\(958\) | 19019.5 | 0.641431 | ||||||||
\(959\) | −21884.2 | −0.736891 | ||||||||
\(960\) | 16902.6 | 0.568260 | ||||||||
\(961\) | 20202.8 | 0.678152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12929.3 | −0.432650 | ||||||||
\(964\) | −11171.4 | −0.373244 | ||||||||
\(965\) | 47392.5 | 1.58095 | ||||||||
\(966\) | −29258.7 | −0.974515 | ||||||||
\(967\) | −53634.9 | −1.78364 | −0.891821 | − | 0.452389i | \(-0.850572\pi\) | ||||
−0.891821 | + | 0.452389i | \(0.850572\pi\) | |||||||
\(968\) | 13128.4 | 0.435913 | ||||||||
\(969\) | −15979.1 | −0.529743 | ||||||||
\(970\) | −18475.8 | −0.611569 | ||||||||
\(971\) | −4086.80 | −0.135069 | −0.0675344 | − | 0.997717i | \(-0.521513\pi\) | ||||
−0.0675344 | + | 0.997717i | \(0.521513\pi\) | |||||||
\(972\) | −930.506 | −0.0307058 | ||||||||
\(973\) | −44758.8 | −1.47472 | ||||||||
\(974\) | 7223.00 | 0.237618 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5351.76 | −0.175518 | ||||||||
\(977\) | 14381.0 | 0.470919 | 0.235459 | − | 0.971884i | \(-0.424341\pi\) | ||||
0.235459 | + | 0.971884i | \(0.424341\pi\) | |||||||
\(978\) | 11630.7 | 0.380276 | ||||||||
\(979\) | −9398.64 | −0.306825 | ||||||||
\(980\) | −25044.5 | −0.816343 | ||||||||
\(981\) | −17801.3 | −0.579358 | ||||||||
\(982\) | −6865.57 | −0.223105 | ||||||||
\(983\) | −12916.5 | −0.419099 | −0.209549 | − | 0.977798i | \(-0.567200\pi\) | ||||
−0.209549 | + | 0.977798i | \(0.567200\pi\) | |||||||
\(984\) | 21445.4 | 0.694770 | ||||||||
\(985\) | −61176.2 | −1.97892 | ||||||||
\(986\) | −14494.0 | −0.468137 | ||||||||
\(987\) | 3294.59 | 0.106249 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30850.3 | −0.991893 | ||||||||
\(990\) | 6232.30 | 0.200076 | ||||||||
\(991\) | −5838.98 | −0.187166 | −0.0935829 | − | 0.995611i | \(-0.529832\pi\) | ||||
−0.0935829 | + | 0.995611i | \(0.529832\pi\) | |||||||
\(992\) | 34672.5 | 1.10973 | ||||||||
\(993\) | −12472.1 | −0.398580 | ||||||||
\(994\) | 6238.79 | 0.199077 | ||||||||
\(995\) | 39510.3 | 1.25886 | ||||||||
\(996\) | −16807.5 | −0.534705 | ||||||||
\(997\) | 44290.1 | 1.40690 | 0.703452 | − | 0.710743i | \(-0.251641\pi\) | ||||
0.703452 | + | 0.710743i | \(0.251641\pi\) | |||||||
\(998\) | −8224.99 | −0.260879 | ||||||||
\(999\) | −6165.50 | −0.195263 |
(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 | 507.4.a.r.1.7 | 10 | ||
3.2 | odd | 2 | 1521.4.a.bk.1.4 | 10 | |||
13.5 | odd | 4 | 507.4.b.i.337.4 | 10 | |||
13.6 | odd | 12 | 39.4.j.c.10.2 | yes | 10 | ||
13.8 | odd | 4 | 507.4.b.i.337.7 | 10 | |||
13.11 | odd | 12 | 39.4.j.c.4.2 | ✓ | 10 | ||
13.12 | even | 2 | inner | 507.4.a.r.1.4 | 10 | ||
39.11 | even | 12 | 117.4.q.e.82.4 | 10 | |||
39.32 | even | 12 | 117.4.q.e.10.4 | 10 | |||
39.38 | odd | 2 | 1521.4.a.bk.1.7 | 10 | |||
52.11 | even | 12 | 624.4.bv.h.433.4 | 10 | |||
52.19 | even | 12 | 624.4.bv.h.49.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.2 | ✓ | 10 | 13.11 | odd | 12 | ||
39.4.j.c.10.2 | yes | 10 | 13.6 | odd | 12 | ||
117.4.q.e.10.4 | 10 | 39.32 | even | 12 | |||
117.4.q.e.82.4 | 10 | 39.11 | even | 12 | |||
507.4.a.r.1.4 | 10 | 13.12 | even | 2 | inner | ||
507.4.a.r.1.7 | 10 | 1.1 | even | 1 | trivial | ||
507.4.b.i.337.4 | 10 | 13.5 | odd | 4 | |||
507.4.b.i.337.7 | 10 | 13.8 | odd | 4 | |||
624.4.bv.h.49.2 | 10 | 52.19 | even | 12 | |||
624.4.bv.h.433.4 | 10 | 52.11 | even | 12 | |||
1521.4.a.bk.1.4 | 10 | 3.2 | odd | 2 | |||
1521.4.a.bk.1.7 | 10 | 39.38 | odd | 2 |