Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1540841.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 27x^{2} - 18x + 92 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.63835\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.63835 | −1.28635 | −0.643176 | − | 0.765718i | \(-0.722384\pi\) | ||||
−0.643176 | + | 0.765718i | \(0.722384\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 5.23763 | 0.654703 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 10.9151 | 0.742676 | ||||||||
\(7\) | −20.8444 | −1.12549 | −0.562747 | − | 0.826629i | \(-0.690255\pi\) | ||||
−0.562747 | + | 0.826629i | \(0.690255\pi\) | |||||||
\(8\) | 10.0505 | 0.444173 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −15.7129 | −0.377993 | ||||||||
\(13\) | −67.4988 | −1.44006 | −0.720031 | − | 0.693942i | \(-0.755872\pi\) | ||||
−0.720031 | + | 0.693942i | \(0.755872\pi\) | |||||||
\(14\) | 75.8394 | 1.44778 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −78.4683 | −1.22607 | ||||||||
\(17\) | 57.8120 | 0.824792 | 0.412396 | − | 0.911005i | \(-0.364692\pi\) | ||||
0.412396 | + | 0.911005i | \(0.364692\pi\) | |||||||
\(18\) | −32.7452 | −0.428784 | ||||||||
\(19\) | −7.98646 | −0.0964326 | −0.0482163 | − | 0.998837i | \(-0.515354\pi\) | ||||
−0.0482163 | + | 0.998837i | \(0.515354\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 62.5333 | 0.649804 | ||||||||
\(22\) | 40.0219 | 0.387850 | ||||||||
\(23\) | −67.5185 | −0.612112 | −0.306056 | − | 0.952013i | \(-0.599010\pi\) | ||||
−0.306056 | + | 0.952013i | \(0.599010\pi\) | |||||||
\(24\) | −30.1515 | −0.256444 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 245.585 | 1.85243 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −109.175 | −0.736864 | ||||||||
\(29\) | −56.1558 | −0.359582 | −0.179791 | − | 0.983705i | \(-0.557542\pi\) | ||||
−0.179791 | + | 0.983705i | \(0.557542\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −127.085 | −0.736296 | −0.368148 | − | 0.929767i | \(-0.620008\pi\) | ||||
−0.368148 | + | 0.929767i | \(0.620008\pi\) | |||||||
\(32\) | 205.091 | 1.13298 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | −210.341 | −1.06097 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 47.1386 | 0.218234 | ||||||||
\(37\) | 95.4222 | 0.423981 | 0.211991 | − | 0.977272i | \(-0.432005\pi\) | ||||
0.211991 | + | 0.977272i | \(0.432005\pi\) | |||||||
\(38\) | 29.0576 | 0.124046 | ||||||||
\(39\) | 202.497 | 0.831420 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −485.903 | −1.85086 | −0.925431 | − | 0.378917i | \(-0.876297\pi\) | ||||
−0.925431 | + | 0.378917i | \(0.876297\pi\) | |||||||
\(42\) | −227.518 | −0.835877 | ||||||||
\(43\) | 146.216 | 0.518552 | 0.259276 | − | 0.965803i | \(-0.416516\pi\) | ||||
0.259276 | + | 0.965803i | \(0.416516\pi\) | |||||||
\(44\) | −57.6139 | −0.197400 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 245.656 | 0.787392 | ||||||||
\(47\) | −164.296 | −0.509894 | −0.254947 | − | 0.966955i | \(-0.582058\pi\) | ||||
−0.254947 | + | 0.966955i | \(0.582058\pi\) | |||||||
\(48\) | 235.405 | 0.707870 | ||||||||
\(49\) | 91.4901 | 0.266735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −173.436 | −0.476194 | ||||||||
\(52\) | −353.534 | −0.942813 | ||||||||
\(53\) | −431.492 | −1.11830 | −0.559151 | − | 0.829066i | \(-0.688873\pi\) | ||||
−0.559151 | + | 0.829066i | \(0.688873\pi\) | |||||||
\(54\) | 98.2356 | 0.247559 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −209.497 | −0.499914 | ||||||||
\(57\) | 23.9594 | 0.0556754 | ||||||||
\(58\) | 204.315 | 0.462549 | ||||||||
\(59\) | −804.178 | −1.77449 | −0.887246 | − | 0.461296i | \(-0.847385\pi\) | ||||
−0.887246 | + | 0.461296i | \(0.847385\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −120.847 | −0.253653 | −0.126826 | − | 0.991925i | \(-0.540479\pi\) | ||||
−0.126826 | + | 0.991925i | \(0.540479\pi\) | |||||||
\(62\) | 462.381 | 0.947137 | ||||||||
\(63\) | −187.600 | −0.375164 | ||||||||
\(64\) | −118.449 | −0.231346 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −120.066 | −0.223925 | ||||||||
\(67\) | 371.469 | 0.677346 | 0.338673 | − | 0.940904i | \(-0.390022\pi\) | ||||
0.338673 | + | 0.940904i | \(0.390022\pi\) | |||||||
\(68\) | 302.798 | 0.539994 | ||||||||
\(69\) | 202.555 | 0.353403 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 529.835 | 0.885631 | 0.442816 | − | 0.896613i | \(-0.353980\pi\) | ||||
0.442816 | + | 0.896613i | \(0.353980\pi\) | |||||||
\(72\) | 90.4545 | 0.148058 | ||||||||
\(73\) | −1059.19 | −1.69820 | −0.849100 | − | 0.528232i | \(-0.822855\pi\) | ||||
−0.849100 | + | 0.528232i | \(0.822855\pi\) | |||||||
\(74\) | −347.180 | −0.545389 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −41.8301 | −0.0631348 | ||||||||
\(77\) | 229.289 | 0.339349 | ||||||||
\(78\) | −736.754 | −1.06950 | ||||||||
\(79\) | −168.663 | −0.240204 | −0.120102 | − | 0.992762i | \(-0.538322\pi\) | ||||
−0.120102 | + | 0.992762i | \(0.538322\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1767.89 | 2.38086 | ||||||||
\(83\) | 144.130 | 0.190606 | 0.0953032 | − | 0.995448i | \(-0.469618\pi\) | ||||
0.0953032 | + | 0.995448i | \(0.469618\pi\) | |||||||
\(84\) | 327.526 | 0.425429 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −531.986 | −0.667041 | ||||||||
\(87\) | 168.468 | 0.207605 | ||||||||
\(88\) | −110.555 | −0.133923 | ||||||||
\(89\) | −1400.20 | −1.66765 | −0.833823 | − | 0.552032i | \(-0.813853\pi\) | ||||
−0.833823 | + | 0.552032i | \(0.813853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1406.97 | 1.62078 | ||||||||
\(92\) | −353.637 | −0.400752 | ||||||||
\(93\) | 381.256 | 0.425101 | ||||||||
\(94\) | 597.767 | 0.655904 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −615.274 | −0.654127 | ||||||||
\(97\) | −29.6912 | −0.0310792 | −0.0155396 | − | 0.999879i | \(-0.504947\pi\) | ||||
−0.0155396 | + | 0.999879i | \(0.504947\pi\) | |||||||
\(98\) | −332.873 | −0.343115 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.5982 | −0.0173375 | −0.00866874 | − | 0.999962i | \(-0.502759\pi\) | ||||
−0.00866874 | + | 0.999962i | \(0.502759\pi\) | |||||||
\(102\) | 631.022 | 0.612553 | ||||||||
\(103\) | −1423.03 | −1.36131 | −0.680655 | − | 0.732604i | \(-0.738305\pi\) | ||||
−0.680655 | + | 0.732604i | \(0.738305\pi\) | |||||||
\(104\) | −678.397 | −0.639637 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1569.92 | 1.43853 | ||||||||
\(107\) | 1335.15 | 1.20629 | 0.603147 | − | 0.797630i | \(-0.293913\pi\) | ||||
0.603147 | + | 0.797630i | \(0.293913\pi\) | |||||||
\(108\) | −141.416 | −0.125998 | ||||||||
\(109\) | 1565.39 | 1.37557 | 0.687784 | − | 0.725916i | \(-0.258584\pi\) | ||||
0.687784 | + | 0.725916i | \(0.258584\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −286.266 | −0.244786 | ||||||||
\(112\) | 1635.63 | 1.37993 | ||||||||
\(113\) | −1176.83 | −0.979709 | −0.489854 | − | 0.871804i | \(-0.662950\pi\) | ||||
−0.489854 | + | 0.871804i | \(0.662950\pi\) | |||||||
\(114\) | −87.1728 | −0.0716182 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −294.123 | −0.235420 | ||||||||
\(117\) | −607.490 | −0.480021 | ||||||||
\(118\) | 2925.89 | 2.28262 | ||||||||
\(119\) | −1205.06 | −0.928298 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 439.683 | 0.326287 | ||||||||
\(123\) | 1457.71 | 1.06860 | ||||||||
\(124\) | −665.625 | −0.482056 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 682.555 | 0.482594 | ||||||||
\(127\) | −311.155 | −0.217406 | −0.108703 | − | 0.994074i | \(-0.534670\pi\) | ||||
−0.108703 | + | 0.994074i | \(0.534670\pi\) | |||||||
\(128\) | −1209.77 | −0.835388 | ||||||||
\(129\) | −438.648 | −0.299386 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 582.818 | 0.388711 | 0.194355 | − | 0.980931i | \(-0.437739\pi\) | ||||
0.194355 | + | 0.980931i | \(0.437739\pi\) | |||||||
\(132\) | 172.842 | 0.113969 | ||||||||
\(133\) | 166.473 | 0.108534 | ||||||||
\(134\) | −1351.54 | −0.871306 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 581.039 | 0.366351 | ||||||||
\(137\) | 2367.98 | 1.47672 | 0.738358 | − | 0.674410i | \(-0.235602\pi\) | ||||
0.738358 | + | 0.674410i | \(0.235602\pi\) | |||||||
\(138\) | −736.969 | −0.454601 | ||||||||
\(139\) | 2573.48 | 1.57036 | 0.785179 | − | 0.619269i | \(-0.212571\pi\) | ||||
0.785179 | + | 0.619269i | \(0.212571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 492.888 | 0.294388 | ||||||||
\(142\) | −1927.73 | −1.13923 | ||||||||
\(143\) | 742.487 | 0.434195 | ||||||||
\(144\) | −706.215 | −0.408689 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3853.70 | 2.18448 | ||||||||
\(147\) | −274.470 | −0.153999 | ||||||||
\(148\) | 499.786 | 0.277582 | ||||||||
\(149\) | 1992.38 | 1.09545 | 0.547724 | − | 0.836659i | \(-0.315494\pi\) | ||||
0.547724 | + | 0.836659i | \(0.315494\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2961.20 | 1.59589 | 0.797944 | − | 0.602731i | \(-0.205921\pi\) | ||||
0.797944 | + | 0.602731i | \(0.205921\pi\) | |||||||
\(152\) | −80.2679 | −0.0428328 | ||||||||
\(153\) | 520.308 | 0.274931 | ||||||||
\(154\) | −834.234 | −0.436522 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1060.60 | 0.544334 | ||||||||
\(157\) | −1302.56 | −0.662139 | −0.331070 | − | 0.943606i | \(-0.607409\pi\) | ||||
−0.331070 | + | 0.943606i | \(0.607409\pi\) | |||||||
\(158\) | 613.657 | 0.308987 | ||||||||
\(159\) | 1294.48 | 0.645652 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1407.38 | 0.688928 | ||||||||
\(162\) | −294.707 | −0.142928 | ||||||||
\(163\) | 563.163 | 0.270615 | 0.135308 | − | 0.990804i | \(-0.456798\pi\) | ||||
0.135308 | + | 0.990804i | \(0.456798\pi\) | |||||||
\(164\) | −2544.98 | −1.21176 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −524.396 | −0.245187 | ||||||||
\(167\) | −1128.96 | −0.523124 | −0.261562 | − | 0.965187i | \(-0.584238\pi\) | ||||
−0.261562 | + | 0.965187i | \(0.584238\pi\) | |||||||
\(168\) | 628.490 | 0.288626 | ||||||||
\(169\) | 2359.09 | 1.07378 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −71.8782 | −0.0321442 | ||||||||
\(172\) | 765.825 | 0.339498 | ||||||||
\(173\) | −3091.97 | −1.35883 | −0.679416 | − | 0.733754i | \(-0.737767\pi\) | ||||
−0.679416 | + | 0.733754i | \(0.737767\pi\) | |||||||
\(174\) | −612.945 | −0.267053 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 863.151 | 0.369673 | ||||||||
\(177\) | 2412.53 | 1.02450 | ||||||||
\(178\) | 5094.41 | 2.14518 | ||||||||
\(179\) | 2879.27 | 1.20227 | 0.601136 | − | 0.799147i | \(-0.294715\pi\) | ||||
0.601136 | + | 0.799147i | \(0.294715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −702.137 | −0.288339 | −0.144170 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144170 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(182\) | −5119.07 | −2.08489 | ||||||||
\(183\) | 362.540 | 0.146447 | ||||||||
\(184\) | −678.594 | −0.271884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1387.14 | −0.546830 | ||||||||
\(187\) | −635.932 | −0.248684 | ||||||||
\(188\) | −860.521 | −0.333829 | ||||||||
\(189\) | 562.799 | 0.216601 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4294.28 | 1.62682 | 0.813412 | − | 0.581688i | \(-0.197608\pi\) | ||||
0.813412 | + | 0.581688i | \(0.197608\pi\) | |||||||
\(192\) | 355.348 | 0.133568 | ||||||||
\(193\) | 3888.11 | 1.45012 | 0.725059 | − | 0.688687i | \(-0.241813\pi\) | ||||
0.725059 | + | 0.688687i | \(0.241813\pi\) | |||||||
\(194\) | 108.027 | 0.0399788 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 479.191 | 0.174632 | ||||||||
\(197\) | 3062.26 | 1.10750 | 0.553748 | − | 0.832684i | \(-0.313197\pi\) | ||||
0.553748 | + | 0.832684i | \(0.313197\pi\) | |||||||
\(198\) | 360.197 | 0.129283 | ||||||||
\(199\) | 4874.64 | 1.73645 | 0.868226 | − | 0.496168i | \(-0.165260\pi\) | ||||
0.868226 | + | 0.496168i | \(0.165260\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1114.41 | −0.391066 | ||||||||
\(202\) | 64.0285 | 0.0223021 | ||||||||
\(203\) | 1170.54 | 0.404707 | ||||||||
\(204\) | −908.393 | −0.311766 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5177.47 | 1.75112 | ||||||||
\(207\) | −607.666 | −0.204037 | ||||||||
\(208\) | 5296.52 | 1.76561 | ||||||||
\(209\) | 87.8511 | 0.0290755 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4324.02 | −1.41080 | −0.705398 | − | 0.708811i | \(-0.749232\pi\) | ||||
−0.705398 | + | 0.708811i | \(0.749232\pi\) | |||||||
\(212\) | −2259.99 | −0.732156 | ||||||||
\(213\) | −1589.50 | −0.511319 | ||||||||
\(214\) | −4857.74 | −1.55172 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −271.363 | −0.0854812 | ||||||||
\(217\) | 2649.02 | 0.828697 | ||||||||
\(218\) | −5695.43 | −1.76947 | ||||||||
\(219\) | 3177.56 | 0.980456 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3902.24 | −1.18775 | ||||||||
\(222\) | 1041.54 | 0.314881 | ||||||||
\(223\) | 6205.69 | 1.86351 | 0.931757 | − | 0.363084i | \(-0.118276\pi\) | ||||
0.931757 | + | 0.363084i | \(0.118276\pi\) | |||||||
\(224\) | −4275.01 | −1.27516 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4281.73 | 1.26025 | ||||||||
\(227\) | −1535.81 | −0.449055 | −0.224528 | − | 0.974468i | \(-0.572084\pi\) | ||||
−0.224528 | + | 0.974468i | \(0.572084\pi\) | |||||||
\(228\) | 125.490 | 0.0364509 | ||||||||
\(229\) | 94.7362 | 0.0273378 | 0.0136689 | − | 0.999907i | \(-0.495649\pi\) | ||||
0.0136689 | + | 0.999907i | \(0.495649\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −687.866 | −0.195923 | ||||||||
\(232\) | −564.394 | −0.159717 | ||||||||
\(233\) | −654.983 | −0.184160 | −0.0920801 | − | 0.995752i | \(-0.529352\pi\) | ||||
−0.0920801 | + | 0.995752i | \(0.529352\pi\) | |||||||
\(234\) | 2210.26 | 0.617476 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4211.98 | −1.16177 | ||||||||
\(237\) | 505.990 | 0.138682 | ||||||||
\(238\) | 4384.43 | 1.19412 | ||||||||
\(239\) | −5660.64 | −1.53204 | −0.766018 | − | 0.642819i | \(-0.777765\pi\) | ||||
−0.766018 | + | 0.642819i | \(0.777765\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4156.88 | −1.11107 | −0.555536 | − | 0.831493i | \(-0.687487\pi\) | ||||
−0.555536 | + | 0.831493i | \(0.687487\pi\) | |||||||
\(242\) | −440.241 | −0.116941 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −632.950 | −0.166067 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5303.66 | −1.37459 | ||||||||
\(247\) | 539.077 | 0.138869 | ||||||||
\(248\) | −1277.27 | −0.327043 | ||||||||
\(249\) | −432.390 | −0.110047 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7156.50 | −1.79966 | −0.899829 | − | 0.436243i | \(-0.856309\pi\) | ||||
−0.899829 | + | 0.436243i | \(0.856309\pi\) | |||||||
\(252\) | −982.578 | −0.245621 | ||||||||
\(253\) | 742.703 | 0.184559 | ||||||||
\(254\) | 1132.09 | 0.279660 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5349.17 | 1.30595 | ||||||||
\(257\) | 2188.36 | 0.531152 | 0.265576 | − | 0.964090i | \(-0.414438\pi\) | ||||
0.265576 | + | 0.964090i | \(0.414438\pi\) | |||||||
\(258\) | 1595.96 | 0.385116 | ||||||||
\(259\) | −1989.02 | −0.477188 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −505.403 | −0.119861 | ||||||||
\(262\) | −2120.50 | −0.500019 | ||||||||
\(263\) | −757.388 | −0.177576 | −0.0887881 | − | 0.996051i | \(-0.528299\pi\) | ||||
−0.0887881 | + | 0.996051i | \(0.528299\pi\) | |||||||
\(264\) | 331.666 | 0.0773207 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −605.689 | −0.139613 | ||||||||
\(267\) | 4200.59 | 0.962816 | ||||||||
\(268\) | 1945.62 | 0.443461 | ||||||||
\(269\) | −6782.64 | −1.53734 | −0.768671 | − | 0.639645i | \(-0.779081\pi\) | ||||
−0.768671 | + | 0.639645i | \(0.779081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7040.87 | 1.57824 | 0.789119 | − | 0.614241i | \(-0.210538\pi\) | ||||
0.789119 | + | 0.614241i | \(0.210538\pi\) | |||||||
\(272\) | −4536.41 | −1.01125 | ||||||||
\(273\) | −4220.92 | −0.935758 | ||||||||
\(274\) | −8615.54 | −1.89958 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1060.91 | 0.231374 | ||||||||
\(277\) | 3211.46 | 0.696599 | 0.348300 | − | 0.937383i | \(-0.386759\pi\) | ||||
0.348300 | + | 0.937383i | \(0.386759\pi\) | |||||||
\(278\) | −9363.24 | −2.02003 | ||||||||
\(279\) | −1143.77 | −0.245432 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3986.15 | 0.846241 | 0.423120 | − | 0.906073i | \(-0.360935\pi\) | ||||
0.423120 | + | 0.906073i | \(0.360935\pi\) | |||||||
\(282\) | −1793.30 | −0.378686 | ||||||||
\(283\) | −7838.75 | −1.64652 | −0.823260 | − | 0.567664i | \(-0.807847\pi\) | ||||
−0.823260 | + | 0.567664i | \(0.807847\pi\) | |||||||
\(284\) | 2775.08 | 0.579826 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2701.43 | −0.558528 | ||||||||
\(287\) | 10128.4 | 2.08313 | ||||||||
\(288\) | 1845.82 | 0.377660 | ||||||||
\(289\) | −1570.77 | −0.319718 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 89.0735 | 0.0179436 | ||||||||
\(292\) | −5547.63 | −1.11182 | ||||||||
\(293\) | 5430.65 | 1.08280 | 0.541402 | − | 0.840764i | \(-0.317894\pi\) | ||||
0.541402 | + | 0.840764i | \(0.317894\pi\) | |||||||
\(294\) | 998.620 | 0.198098 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 959.040 | 0.188321 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −7248.97 | −1.40913 | ||||||||
\(299\) | 4557.42 | 0.881480 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3047.79 | −0.583627 | ||||||||
\(302\) | −10773.9 | −2.05288 | ||||||||
\(303\) | 52.7946 | 0.0100098 | ||||||||
\(304\) | 626.684 | 0.118233 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1893.06 | −0.353658 | ||||||||
\(307\) | −8045.25 | −1.49566 | −0.747828 | − | 0.663892i | \(-0.768903\pi\) | ||||
−0.747828 | + | 0.663892i | \(0.768903\pi\) | |||||||
\(308\) | 1200.93 | 0.222173 | ||||||||
\(309\) | 4269.08 | 0.785952 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4712.06 | −0.859152 | −0.429576 | − | 0.903031i | \(-0.641337\pi\) | ||||
−0.429576 | + | 0.903031i | \(0.641337\pi\) | |||||||
\(312\) | 2035.19 | 0.369295 | ||||||||
\(313\) | 1425.19 | 0.257369 | 0.128684 | − | 0.991686i | \(-0.458925\pi\) | ||||
0.128684 | + | 0.991686i | \(0.458925\pi\) | |||||||
\(314\) | 4739.19 | 0.851744 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −883.395 | −0.157262 | ||||||||
\(317\) | 2031.54 | 0.359944 | 0.179972 | − | 0.983672i | \(-0.442399\pi\) | ||||
0.179972 | + | 0.983672i | \(0.442399\pi\) | |||||||
\(318\) | −4709.76 | −0.830536 | ||||||||
\(319\) | 617.714 | 0.108418 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4005.44 | −0.696454 | ||||||||
\(322\) | −5120.56 | −0.886204 | ||||||||
\(323\) | −461.713 | −0.0795369 | ||||||||
\(324\) | 424.248 | 0.0727448 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2048.99 | −0.348107 | ||||||||
\(327\) | −4696.16 | −0.794184 | ||||||||
\(328\) | −4883.57 | −0.822103 | ||||||||
\(329\) | 3424.65 | 0.573882 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 316.790 | 0.0526054 | 0.0263027 | − | 0.999654i | \(-0.491627\pi\) | ||||
0.0263027 | + | 0.999654i | \(0.491627\pi\) | |||||||
\(332\) | 754.899 | 0.124791 | ||||||||
\(333\) | 858.799 | 0.141327 | ||||||||
\(334\) | 4107.57 | 0.672922 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4906.88 | −0.796703 | ||||||||
\(337\) | −4441.65 | −0.717958 | −0.358979 | − | 0.933346i | \(-0.616875\pi\) | ||||
−0.358979 | + | 0.933346i | \(0.616875\pi\) | |||||||
\(338\) | −8583.22 | −1.38126 | ||||||||
\(339\) | 3530.50 | 0.565635 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1397.94 | 0.222002 | ||||||||
\(342\) | 261.518 | 0.0413488 | ||||||||
\(343\) | 5242.58 | 0.825285 | ||||||||
\(344\) | 1469.54 | 0.230327 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11249.7 | 1.74794 | ||||||||
\(347\) | −258.695 | −0.0400215 | −0.0200108 | − | 0.999800i | \(-0.506370\pi\) | ||||
−0.0200108 | + | 0.999800i | \(0.506370\pi\) | |||||||
\(348\) | 882.370 | 0.135920 | ||||||||
\(349\) | 9929.62 | 1.52298 | 0.761491 | − | 0.648176i | \(-0.224468\pi\) | ||||
0.761491 | + | 0.648176i | \(0.224468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1822.47 | 0.277140 | ||||||||
\(352\) | −2256.01 | −0.341607 | ||||||||
\(353\) | 1008.73 | 0.152095 | 0.0760474 | − | 0.997104i | \(-0.475770\pi\) | ||||
0.0760474 | + | 0.997104i | \(0.475770\pi\) | |||||||
\(354\) | −8777.66 | −1.31787 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7333.70 | −1.09181 | ||||||||
\(357\) | 3615.17 | 0.535953 | ||||||||
\(358\) | −10475.8 | −1.54655 | ||||||||
\(359\) | 5813.26 | 0.854630 | 0.427315 | − | 0.904103i | \(-0.359460\pi\) | ||||
0.427315 | + | 0.904103i | \(0.359460\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6795.22 | −0.990701 | ||||||||
\(362\) | 2554.62 | 0.370906 | ||||||||
\(363\) | −363.000 | −0.0524864 | ||||||||
\(364\) | 7369.21 | 1.06113 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1319.05 | −0.188382 | ||||||||
\(367\) | 10247.0 | 1.45747 | 0.728733 | − | 0.684798i | \(-0.240110\pi\) | ||||
0.728733 | + | 0.684798i | \(0.240110\pi\) | |||||||
\(368\) | 5298.06 | 0.750490 | ||||||||
\(369\) | −4373.13 | −0.616954 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8994.20 | 1.25864 | ||||||||
\(372\) | 1996.88 | 0.278315 | ||||||||
\(373\) | 2202.63 | 0.305759 | 0.152879 | − | 0.988245i | \(-0.451145\pi\) | ||||
0.152879 | + | 0.988245i | \(0.451145\pi\) | |||||||
\(374\) | 2313.75 | 0.319896 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1651.26 | −0.226481 | ||||||||
\(377\) | 3790.45 | 0.517821 | ||||||||
\(378\) | −2047.66 | −0.278626 | ||||||||
\(379\) | −1851.13 | −0.250887 | −0.125444 | − | 0.992101i | \(-0.540035\pi\) | ||||
−0.125444 | + | 0.992101i | \(0.540035\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 933.464 | 0.125519 | ||||||||
\(382\) | −15624.1 | −2.09267 | ||||||||
\(383\) | −5880.65 | −0.784562 | −0.392281 | − | 0.919846i | \(-0.628314\pi\) | ||||
−0.392281 | + | 0.919846i | \(0.628314\pi\) | |||||||
\(384\) | 3629.31 | 0.482311 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14146.3 | −1.86536 | ||||||||
\(387\) | 1315.95 | 0.172851 | ||||||||
\(388\) | −155.511 | −0.0203476 | ||||||||
\(389\) | −6963.66 | −0.907639 | −0.453820 | − | 0.891094i | \(-0.649939\pi\) | ||||
−0.453820 | + | 0.891094i | \(0.649939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3903.38 | −0.504865 | ||||||||
\(392\) | 919.520 | 0.118477 | ||||||||
\(393\) | −1748.46 | −0.224422 | ||||||||
\(394\) | −11141.6 | −1.42463 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −518.525 | −0.0658002 | ||||||||
\(397\) | −3024.31 | −0.382332 | −0.191166 | − | 0.981558i | \(-0.561227\pi\) | ||||
−0.191166 | + | 0.981558i | \(0.561227\pi\) | |||||||
\(398\) | −17735.7 | −2.23369 | ||||||||
\(399\) | −499.420 | −0.0626623 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13392.7 | −1.66783 | −0.833914 | − | 0.551895i | \(-0.813905\pi\) | ||||
−0.833914 | + | 0.551895i | \(0.813905\pi\) | |||||||
\(402\) | 4054.61 | 0.503049 | ||||||||
\(403\) | 8578.11 | 1.06031 | ||||||||
\(404\) | −92.1728 | −0.0113509 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4258.83 | −0.520596 | ||||||||
\(407\) | −1049.64 | −0.127835 | ||||||||
\(408\) | −1743.12 | −0.211513 | ||||||||
\(409\) | 7637.16 | 0.923308 | 0.461654 | − | 0.887060i | \(-0.347256\pi\) | ||||
0.461654 | + | 0.887060i | \(0.347256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7103.93 | −0.852582 | ||||||||
\(412\) | −7453.28 | −0.891254 | ||||||||
\(413\) | 16762.6 | 1.99718 | ||||||||
\(414\) | 2210.91 | 0.262464 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −13843.4 | −1.63156 | ||||||||
\(417\) | −7720.44 | −0.906647 | ||||||||
\(418\) | −319.633 | −0.0374014 | ||||||||
\(419\) | 12523.9 | 1.46022 | 0.730112 | − | 0.683328i | \(-0.239468\pi\) | ||||
0.730112 | + | 0.683328i | \(0.239468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11150.0 | −1.29078 | −0.645391 | − | 0.763852i | \(-0.723306\pi\) | ||||
−0.645391 | + | 0.763852i | \(0.723306\pi\) | |||||||
\(422\) | 15732.3 | 1.81478 | ||||||||
\(423\) | −1478.66 | −0.169965 | ||||||||
\(424\) | −4336.71 | −0.496720 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5783.18 | 0.657737 | ||||||||
\(427\) | 2518.98 | 0.285485 | ||||||||
\(428\) | 6993.00 | 0.789765 | ||||||||
\(429\) | −2227.46 | −0.250683 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2093.77 | −0.233998 | −0.116999 | − | 0.993132i | \(-0.537327\pi\) | ||||
−0.116999 | + | 0.993132i | \(0.537327\pi\) | |||||||
\(432\) | 2118.64 | 0.235957 | ||||||||
\(433\) | 4391.47 | 0.487392 | 0.243696 | − | 0.969852i | \(-0.421640\pi\) | ||||
0.243696 | + | 0.969852i | \(0.421640\pi\) | |||||||
\(434\) | −9638.07 | −1.06600 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8198.91 | 0.900589 | ||||||||
\(437\) | 539.234 | 0.0590276 | ||||||||
\(438\) | −11561.1 | −1.26121 | ||||||||
\(439\) | 15614.6 | 1.69759 | 0.848797 | − | 0.528719i | \(-0.177328\pi\) | ||||
0.848797 | + | 0.528719i | \(0.177328\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 823.411 | 0.0889116 | ||||||||
\(442\) | 14197.7 | 1.52787 | ||||||||
\(443\) | −7909.57 | −0.848296 | −0.424148 | − | 0.905593i | \(-0.639426\pi\) | ||||
−0.424148 | + | 0.905593i | \(0.639426\pi\) | |||||||
\(444\) | −1499.36 | −0.160262 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −22578.5 | −2.39714 | ||||||||
\(447\) | −5977.13 | −0.632458 | ||||||||
\(448\) | 2469.01 | 0.260379 | ||||||||
\(449\) | −14958.7 | −1.57226 | −0.786128 | − | 0.618064i | \(-0.787917\pi\) | ||||
−0.786128 | + | 0.618064i | \(0.787917\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5344.93 | 0.558056 | ||||||||
\(452\) | −6163.81 | −0.641419 | ||||||||
\(453\) | −8883.61 | −0.921387 | ||||||||
\(454\) | 5587.84 | 0.577644 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 240.804 | 0.0247295 | ||||||||
\(457\) | −14584.6 | −1.49286 | −0.746430 | − | 0.665464i | \(-0.768234\pi\) | ||||
−0.746430 | + | 0.665464i | \(0.768234\pi\) | |||||||
\(458\) | −344.684 | −0.0351660 | ||||||||
\(459\) | −1560.92 | −0.158731 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1802.35 | −0.182091 | −0.0910454 | − | 0.995847i | \(-0.529021\pi\) | ||||
−0.0910454 | + | 0.995847i | \(0.529021\pi\) | |||||||
\(462\) | 2502.70 | 0.252026 | ||||||||
\(463\) | −6753.79 | −0.677916 | −0.338958 | − | 0.940801i | \(-0.610074\pi\) | ||||
−0.338958 | + | 0.940801i | \(0.610074\pi\) | |||||||
\(464\) | 4406.45 | 0.440872 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2383.06 | 0.236895 | ||||||||
\(467\) | 1744.55 | 0.172866 | 0.0864329 | − | 0.996258i | \(-0.472453\pi\) | ||||
0.0864329 | + | 0.996258i | \(0.472453\pi\) | |||||||
\(468\) | −3181.80 | −0.314271 | ||||||||
\(469\) | −7743.06 | −0.762349 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3907.69 | 0.382286 | ||||||||
\(472\) | −8082.39 | −0.788182 | ||||||||
\(473\) | −1608.38 | −0.156349 | ||||||||
\(474\) | −1840.97 | −0.178394 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6311.64 | −0.607760 | ||||||||
\(477\) | −3883.43 | −0.372767 | ||||||||
\(478\) | 20595.4 | 1.97074 | ||||||||
\(479\) | 16930.6 | 1.61499 | 0.807495 | − | 0.589874i | \(-0.200823\pi\) | ||||
0.807495 | + | 0.589874i | \(0.200823\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6440.88 | −0.610559 | ||||||||
\(482\) | 15124.2 | 1.42923 | ||||||||
\(483\) | −4222.15 | −0.397753 | ||||||||
\(484\) | 633.753 | 0.0595185 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 884.120 | 0.0825196 | ||||||||
\(487\) | 3932.10 | 0.365874 | 0.182937 | − | 0.983125i | \(-0.441440\pi\) | ||||
0.182937 | + | 0.983125i | \(0.441440\pi\) | |||||||
\(488\) | −1214.57 | −0.112666 | ||||||||
\(489\) | −1689.49 | −0.156240 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11477.9 | 1.05497 | 0.527484 | − | 0.849565i | \(-0.323136\pi\) | ||||
0.527484 | + | 0.849565i | \(0.323136\pi\) | |||||||
\(492\) | 7634.94 | 0.699613 | ||||||||
\(493\) | −3246.48 | −0.296580 | ||||||||
\(494\) | −1961.35 | −0.178635 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9972.16 | 0.902749 | ||||||||
\(497\) | −11044.1 | −0.996772 | ||||||||
\(498\) | 1573.19 | 0.141559 | ||||||||
\(499\) | 12806.6 | 1.14890 | 0.574451 | − | 0.818539i | \(-0.305215\pi\) | ||||
0.574451 | + | 0.818539i | \(0.305215\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3386.89 | 0.302026 | ||||||||
\(502\) | 26037.9 | 2.31500 | ||||||||
\(503\) | −1319.41 | −0.116958 | −0.0584789 | − | 0.998289i | \(-0.518625\pi\) | ||||
−0.0584789 | + | 0.998289i | \(0.518625\pi\) | |||||||
\(504\) | −1885.47 | −0.166638 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2702.22 | −0.237408 | ||||||||
\(507\) | −7077.28 | −0.619947 | ||||||||
\(508\) | −1629.71 | −0.142336 | ||||||||
\(509\) | 1658.45 | 0.144419 | 0.0722097 | − | 0.997389i | \(-0.476995\pi\) | ||||
0.0722097 | + | 0.997389i | \(0.476995\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22078.2 | 1.91131 | ||||||||
\(512\) | −9784.02 | −0.844524 | ||||||||
\(513\) | 215.635 | 0.0185585 | ||||||||
\(514\) | −7962.02 | −0.683248 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2297.48 | −0.196009 | ||||||||
\(517\) | 1807.26 | 0.153739 | ||||||||
\(518\) | 7236.76 | 0.613832 | ||||||||
\(519\) | 9275.90 | 0.784522 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2790.40 | 0.234644 | 0.117322 | − | 0.993094i | \(-0.462569\pi\) | ||||
0.117322 | + | 0.993094i | \(0.462569\pi\) | |||||||
\(522\) | 1838.83 | 0.154183 | ||||||||
\(523\) | 2440.70 | 0.204062 | 0.102031 | − | 0.994781i | \(-0.467466\pi\) | ||||
0.102031 | + | 0.994781i | \(0.467466\pi\) | |||||||
\(524\) | 3052.59 | 0.254490 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2755.64 | 0.228426 | ||||||||
\(527\) | −7347.05 | −0.607292 | ||||||||
\(528\) | −2589.45 | −0.213431 | ||||||||
\(529\) | −7608.25 | −0.625319 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7237.60 | −0.591498 | ||||||||
\(532\) | 871.925 | 0.0710578 | ||||||||
\(533\) | 32797.9 | 2.66536 | ||||||||
\(534\) | −15283.2 | −1.23852 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3733.45 | 0.300859 | ||||||||
\(537\) | −8637.81 | −0.694132 | ||||||||
\(538\) | 24677.6 | 1.97756 | ||||||||
\(539\) | −1006.39 | −0.0804236 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7756.41 | −0.616403 | −0.308202 | − | 0.951321i | \(-0.599727\pi\) | ||||
−0.308202 | + | 0.951321i | \(0.599727\pi\) | |||||||
\(542\) | −25617.2 | −2.03017 | ||||||||
\(543\) | 2106.41 | 0.166473 | ||||||||
\(544\) | 11856.7 | 0.934474 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15357.2 | 1.20371 | ||||||||
\(547\) | 13056.6 | 1.02058 | 0.510290 | − | 0.860002i | \(-0.329538\pi\) | ||||
0.510290 | + | 0.860002i | \(0.329538\pi\) | |||||||
\(548\) | 12402.6 | 0.966810 | ||||||||
\(549\) | −1087.62 | −0.0845510 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 448.487 | 0.0346754 | ||||||||
\(552\) | 2035.78 | 0.156972 | ||||||||
\(553\) | 3515.69 | 0.270348 | ||||||||
\(554\) | −11684.4 | −0.896072 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13478.9 | 1.02812 | ||||||||
\(557\) | 1837.48 | 0.139778 | 0.0698892 | − | 0.997555i | \(-0.477735\pi\) | ||||
0.0698892 | + | 0.997555i | \(0.477735\pi\) | |||||||
\(558\) | 4161.43 | 0.315712 | ||||||||
\(559\) | −9869.42 | −0.746748 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1907.80 | 0.143578 | ||||||||
\(562\) | −14503.0 | −1.08856 | ||||||||
\(563\) | −11473.6 | −0.858890 | −0.429445 | − | 0.903093i | \(-0.641291\pi\) | ||||
−0.429445 | + | 0.903093i | \(0.641291\pi\) | |||||||
\(564\) | 2581.56 | 0.192736 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 28520.1 | 2.11801 | ||||||||
\(567\) | −1688.40 | −0.125055 | ||||||||
\(568\) | 5325.10 | 0.393374 | ||||||||
\(569\) | 9698.61 | 0.714564 | 0.357282 | − | 0.933997i | \(-0.383703\pi\) | ||||
0.357282 | + | 0.933997i | \(0.383703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14019.8 | 1.02752 | 0.513758 | − | 0.857935i | \(-0.328253\pi\) | ||||
0.513758 | + | 0.857935i | \(0.328253\pi\) | |||||||
\(572\) | 3888.87 | 0.284269 | ||||||||
\(573\) | −12882.8 | −0.939247 | ||||||||
\(574\) | −36850.6 | −2.67964 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1066.04 | −0.0771155 | ||||||||
\(577\) | −3912.25 | −0.282269 | −0.141134 | − | 0.989990i | \(-0.545075\pi\) | ||||
−0.141134 | + | 0.989990i | \(0.545075\pi\) | |||||||
\(578\) | 5715.03 | 0.411270 | ||||||||
\(579\) | −11664.3 | −0.837226 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3004.31 | −0.214526 | ||||||||
\(582\) | −324.081 | −0.0230818 | ||||||||
\(583\) | 4746.41 | 0.337181 | ||||||||
\(584\) | −10645.4 | −0.754295 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19758.6 | −1.39287 | ||||||||
\(587\) | −11148.5 | −0.783899 | −0.391949 | − | 0.919987i | \(-0.628199\pi\) | ||||
−0.391949 | + | 0.919987i | \(0.628199\pi\) | |||||||
\(588\) | −1437.57 | −0.100824 | ||||||||
\(589\) | 1014.96 | 0.0710030 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9186.77 | −0.639413 | ||||||||
\(592\) | −7487.61 | −0.519829 | ||||||||
\(593\) | 17155.0 | 1.18798 | 0.593989 | − | 0.804473i | \(-0.297552\pi\) | ||||
0.593989 | + | 0.804473i | \(0.297552\pi\) | |||||||
\(594\) | −1080.59 | −0.0746418 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10435.3 | 0.717194 | ||||||||
\(597\) | −14623.9 | −1.00254 | ||||||||
\(598\) | −16581.5 | −1.13389 | ||||||||
\(599\) | −2891.03 | −0.197203 | −0.0986014 | − | 0.995127i | \(-0.531437\pi\) | ||||
−0.0986014 | + | 0.995127i | \(0.531437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11439.4 | 0.776412 | 0.388206 | − | 0.921573i | \(-0.373095\pi\) | ||||
0.388206 | + | 0.921573i | \(0.373095\pi\) | |||||||
\(602\) | 11088.9 | 0.750750 | ||||||||
\(603\) | 3343.22 | 0.225782 | ||||||||
\(604\) | 15509.7 | 1.04483 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −192.085 | −0.0128761 | ||||||||
\(607\) | 7768.78 | 0.519481 | 0.259741 | − | 0.965678i | \(-0.416363\pi\) | ||||
0.259741 | + | 0.965678i | \(0.416363\pi\) | |||||||
\(608\) | −1637.96 | −0.109256 | ||||||||
\(609\) | −3511.61 | −0.233658 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11089.8 | 0.734279 | ||||||||
\(612\) | 2725.18 | 0.179998 | ||||||||
\(613\) | 6469.74 | 0.426281 | 0.213140 | − | 0.977022i | \(-0.431631\pi\) | ||||
0.213140 | + | 0.977022i | \(0.431631\pi\) | |||||||
\(614\) | 29271.5 | 1.92394 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2304.46 | 0.150730 | ||||||||
\(617\) | 18323.7 | 1.19560 | 0.597799 | − | 0.801646i | \(-0.296042\pi\) | ||||
0.597799 | + | 0.801646i | \(0.296042\pi\) | |||||||
\(618\) | −15532.4 | −1.01101 | ||||||||
\(619\) | −16697.1 | −1.08419 | −0.542096 | − | 0.840317i | \(-0.682369\pi\) | ||||
−0.542096 | + | 0.840317i | \(0.682369\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1823.00 | 0.117801 | ||||||||
\(622\) | 17144.1 | 1.10517 | ||||||||
\(623\) | 29186.3 | 1.87692 | ||||||||
\(624\) | −15889.6 | −1.01938 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5185.35 | −0.331067 | ||||||||
\(627\) | −263.553 | −0.0167868 | ||||||||
\(628\) | −6822.34 | −0.433505 | ||||||||
\(629\) | 5516.54 | 0.349696 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20458.8 | 1.29073 | 0.645367 | − | 0.763873i | \(-0.276705\pi\) | ||||
0.645367 | + | 0.763873i | \(0.276705\pi\) | |||||||
\(632\) | −1695.15 | −0.106692 | ||||||||
\(633\) | 12972.1 | 0.814524 | ||||||||
\(634\) | −7391.45 | −0.463016 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6779.98 | 0.422710 | ||||||||
\(637\) | −6175.47 | −0.384115 | ||||||||
\(638\) | −2247.46 | −0.139464 | ||||||||
\(639\) | 4768.51 | 0.295210 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4676.71 | 0.288173 | 0.144087 | − | 0.989565i | \(-0.453976\pi\) | ||||
0.144087 | + | 0.989565i | \(0.453976\pi\) | |||||||
\(642\) | 14573.2 | 0.895886 | ||||||||
\(643\) | 2321.97 | 0.142410 | 0.0712049 | − | 0.997462i | \(-0.477316\pi\) | ||||
0.0712049 | + | 0.997462i | \(0.477316\pi\) | |||||||
\(644\) | 7371.35 | 0.451043 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1679.88 | 0.102312 | ||||||||
\(647\) | −18149.3 | −1.10282 | −0.551408 | − | 0.834236i | \(-0.685909\pi\) | ||||
−0.551408 | + | 0.834236i | \(0.685909\pi\) | |||||||
\(648\) | 814.090 | 0.0493526 | ||||||||
\(649\) | 8845.96 | 0.535030 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7947.06 | −0.478448 | ||||||||
\(652\) | 2949.64 | 0.177173 | ||||||||
\(653\) | −23089.9 | −1.38374 | −0.691868 | − | 0.722024i | \(-0.743212\pi\) | ||||
−0.691868 | + | 0.722024i | \(0.743212\pi\) | |||||||
\(654\) | 17086.3 | 1.02160 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 38128.0 | 2.26928 | ||||||||
\(657\) | −9532.69 | −0.566067 | ||||||||
\(658\) | −12460.1 | −0.738215 | ||||||||
\(659\) | 415.639 | 0.0245690 | 0.0122845 | − | 0.999925i | \(-0.496090\pi\) | ||||
0.0122845 | + | 0.999925i | \(0.496090\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12044.0 | 0.708710 | 0.354355 | − | 0.935111i | \(-0.384700\pi\) | ||||
0.354355 | + | 0.935111i | \(0.384700\pi\) | |||||||
\(662\) | −1152.60 | −0.0676691 | ||||||||
\(663\) | 11706.7 | 0.685749 | ||||||||
\(664\) | 1448.58 | 0.0846622 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3124.62 | −0.181796 | ||||||||
\(667\) | 3791.56 | 0.220105 | ||||||||
\(668\) | −5913.09 | −0.342491 | ||||||||
\(669\) | −18617.1 | −1.07590 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1329.31 | 0.0764792 | ||||||||
\(672\) | 12825.0 | 0.736215 | ||||||||
\(673\) | −8699.88 | −0.498300 | −0.249150 | − | 0.968465i | \(-0.580151\pi\) | ||||
−0.249150 | + | 0.968465i | \(0.580151\pi\) | |||||||
\(674\) | 16160.3 | 0.923547 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12356.0 | 0.703007 | ||||||||
\(677\) | 29389.8 | 1.66845 | 0.834225 | − | 0.551424i | \(-0.185915\pi\) | ||||
0.834225 | + | 0.551424i | \(0.185915\pi\) | |||||||
\(678\) | −12845.2 | −0.727606 | ||||||||
\(679\) | 618.895 | 0.0349794 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4607.44 | 0.259262 | ||||||||
\(682\) | −5086.20 | −0.285573 | ||||||||
\(683\) | −12261.0 | −0.686905 | −0.343452 | − | 0.939170i | \(-0.611596\pi\) | ||||
−0.343452 | + | 0.939170i | \(0.611596\pi\) | |||||||
\(684\) | −376.471 | −0.0210449 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19074.4 | −1.06161 | ||||||||
\(687\) | −284.209 | −0.0157835 | ||||||||
\(688\) | −11473.3 | −0.635780 | ||||||||
\(689\) | 29125.2 | 1.61042 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22711.4 | −1.25034 | −0.625168 | − | 0.780490i | \(-0.714970\pi\) | ||||
−0.625168 | + | 0.780490i | \(0.714970\pi\) | |||||||
\(692\) | −16194.6 | −0.889631 | ||||||||
\(693\) | 2063.60 | 0.113116 | ||||||||
\(694\) | 941.224 | 0.0514818 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1693.18 | 0.0922125 | ||||||||
\(697\) | −28091.0 | −1.52658 | ||||||||
\(698\) | −36127.5 | −1.95909 | ||||||||
\(699\) | 1964.95 | 0.106325 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21070.9 | −1.13529 | −0.567643 | − | 0.823275i | \(-0.692145\pi\) | ||||
−0.567643 | + | 0.823275i | \(0.692145\pi\) | |||||||
\(702\) | −6630.79 | −0.356500 | ||||||||
\(703\) | −762.086 | −0.0408856 | ||||||||
\(704\) | 1302.94 | 0.0697536 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3670.13 | −0.195648 | ||||||||
\(707\) | 366.824 | 0.0195132 | ||||||||
\(708\) | 12636.0 | 0.670746 | ||||||||
\(709\) | 8521.30 | 0.451374 | 0.225687 | − | 0.974200i | \(-0.427537\pi\) | ||||
0.225687 | + | 0.974200i | \(0.427537\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1517.97 | −0.0800679 | ||||||||
\(712\) | −14072.7 | −0.740724 | ||||||||
\(713\) | 8580.61 | 0.450696 | ||||||||
\(714\) | −13153.3 | −0.689425 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15080.5 | 0.787132 | ||||||||
\(717\) | 16981.9 | 0.884521 | ||||||||
\(718\) | −21150.7 | −1.09936 | ||||||||
\(719\) | 8217.19 | 0.426216 | 0.213108 | − | 0.977029i | \(-0.431641\pi\) | ||||
0.213108 | + | 0.977029i | \(0.431641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29662.1 | 1.53214 | ||||||||
\(722\) | 24723.4 | 1.27439 | ||||||||
\(723\) | 12470.6 | 0.641478 | ||||||||
\(724\) | −3677.53 | −0.188777 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1320.72 | 0.0675160 | ||||||||
\(727\) | 20870.8 | 1.06473 | 0.532363 | − | 0.846516i | \(-0.321304\pi\) | ||||
0.532363 | + | 0.846516i | \(0.321304\pi\) | |||||||
\(728\) | 14140.8 | 0.719907 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8453.04 | 0.427698 | ||||||||
\(732\) | 1898.85 | 0.0958790 | ||||||||
\(733\) | 33776.4 | 1.70199 | 0.850997 | − | 0.525171i | \(-0.175998\pi\) | ||||
0.850997 | + | 0.525171i | \(0.175998\pi\) | |||||||
\(734\) | −37282.3 | −1.87482 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13847.5 | −0.693512 | ||||||||
\(737\) | −4086.16 | −0.204228 | ||||||||
\(738\) | 15911.0 | 0.793620 | ||||||||
\(739\) | −14342.3 | −0.713922 | −0.356961 | − | 0.934119i | \(-0.616187\pi\) | ||||
−0.356961 | + | 0.934119i | \(0.616187\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1617.23 | −0.0801761 | ||||||||
\(742\) | −32724.1 | −1.61906 | ||||||||
\(743\) | 19225.5 | 0.949279 | 0.474640 | − | 0.880180i | \(-0.342578\pi\) | ||||
0.474640 | + | 0.880180i | \(0.342578\pi\) | |||||||
\(744\) | 3831.81 | 0.188819 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8013.96 | −0.393313 | ||||||||
\(747\) | 1297.17 | 0.0635354 | ||||||||
\(748\) | −3330.77 | −0.162814 | ||||||||
\(749\) | −27830.4 | −1.35768 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19629.4 | −0.953776 | −0.476888 | − | 0.878964i | \(-0.658235\pi\) | ||||
−0.476888 | + | 0.878964i | \(0.658235\pi\) | |||||||
\(752\) | 12892.0 | 0.625164 | ||||||||
\(753\) | 21469.5 | 1.03903 | ||||||||
\(754\) | −13791.0 | −0.666100 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2947.73 | 0.141810 | ||||||||
\(757\) | 26801.5 | 1.28681 | 0.643406 | − | 0.765525i | \(-0.277521\pi\) | ||||
0.643406 | + | 0.765525i | \(0.277521\pi\) | |||||||
\(758\) | 6735.07 | 0.322729 | ||||||||
\(759\) | −2228.11 | −0.106555 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6490.31 | 0.309164 | 0.154582 | − | 0.987980i | \(-0.450597\pi\) | ||||
0.154582 | + | 0.987980i | \(0.450597\pi\) | |||||||
\(762\) | −3396.27 | −0.161462 | ||||||||
\(763\) | −32629.6 | −1.54819 | ||||||||
\(764\) | 22491.8 | 1.06509 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21395.9 | 1.00922 | ||||||||
\(767\) | 54281.1 | 2.55538 | ||||||||
\(768\) | −16047.5 | −0.753991 | ||||||||
\(769\) | 14356.1 | 0.673204 | 0.336602 | − | 0.941647i | \(-0.390722\pi\) | ||||
0.336602 | + | 0.941647i | \(0.390722\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6565.07 | −0.306661 | ||||||||
\(772\) | 20364.5 | 0.949397 | ||||||||
\(773\) | −19127.6 | −0.890004 | −0.445002 | − | 0.895529i | \(-0.646797\pi\) | ||||
−0.445002 | + | 0.895529i | \(0.646797\pi\) | |||||||
\(774\) | −4787.88 | −0.222347 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −298.411 | −0.0138045 | ||||||||
\(777\) | 5967.06 | 0.275505 | ||||||||
\(778\) | 25336.3 | 1.16754 | ||||||||
\(779\) | 3880.65 | 0.178483 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5828.18 | −0.267028 | ||||||||
\(782\) | 14201.9 | 0.649435 | ||||||||
\(783\) | 1516.21 | 0.0692016 | ||||||||
\(784\) | −7179.07 | −0.327035 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6361.50 | 0.288686 | ||||||||
\(787\) | −23509.7 | −1.06484 | −0.532420 | − | 0.846480i | \(-0.678717\pi\) | ||||
−0.532420 | + | 0.846480i | \(0.678717\pi\) | |||||||
\(788\) | 16039.0 | 0.725082 | ||||||||
\(789\) | 2272.16 | 0.102524 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24530.4 | 1.10266 | ||||||||
\(792\) | −994.999 | −0.0446411 | ||||||||
\(793\) | 8157.01 | 0.365276 | ||||||||
\(794\) | 11003.5 | 0.491814 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25531.5 | 1.13686 | ||||||||
\(797\) | −43145.1 | −1.91754 | −0.958769 | − | 0.284187i | \(-0.908276\pi\) | ||||
−0.958769 | + | 0.284187i | \(0.908276\pi\) | |||||||
\(798\) | 1817.07 | 0.0806058 | ||||||||
\(799\) | −9498.27 | −0.420557 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12601.8 | −0.555882 | ||||||||
\(802\) | 48727.3 | 2.14541 | ||||||||
\(803\) | 11651.1 | 0.512027 | ||||||||
\(804\) | −5836.85 | −0.256032 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −31210.2 | −1.36394 | ||||||||
\(807\) | 20347.9 | 0.887584 | ||||||||
\(808\) | −176.871 | −0.00770085 | ||||||||
\(809\) | −23470.4 | −1.02000 | −0.509998 | − | 0.860176i | \(-0.670354\pi\) | ||||
−0.509998 | + | 0.860176i | \(0.670354\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4906.52 | −0.212443 | −0.106221 | − | 0.994343i | \(-0.533875\pi\) | ||||
−0.106221 | + | 0.994343i | \(0.533875\pi\) | |||||||
\(812\) | 6130.83 | 0.264963 | ||||||||
\(813\) | −21122.6 | −0.911196 | ||||||||
\(814\) | 3818.98 | 0.164441 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13609.2 | 0.583846 | ||||||||
\(817\) | −1167.75 | −0.0500054 | ||||||||
\(818\) | −27786.7 | −1.18770 | ||||||||
\(819\) | 12662.8 | 0.540260 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45229.6 | 1.92268 | 0.961342 | − | 0.275356i | \(-0.0887958\pi\) | ||||
0.961342 | + | 0.275356i | \(0.0887958\pi\) | |||||||
\(822\) | 25846.6 | 1.09672 | ||||||||
\(823\) | −24192.1 | −1.02465 | −0.512323 | − | 0.858793i | \(-0.671215\pi\) | ||||
−0.512323 | + | 0.858793i | \(0.671215\pi\) | |||||||
\(824\) | −14302.1 | −0.604657 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −60988.4 | −2.56908 | ||||||||
\(827\) | −2031.70 | −0.0854282 | −0.0427141 | − | 0.999087i | \(-0.513600\pi\) | ||||
−0.0427141 | + | 0.999087i | \(0.513600\pi\) | |||||||
\(828\) | −3182.73 | −0.133584 | ||||||||
\(829\) | 17010.6 | 0.712671 | 0.356335 | − | 0.934358i | \(-0.384026\pi\) | ||||
0.356335 | + | 0.934358i | \(0.384026\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9634.38 | −0.402182 | ||||||||
\(832\) | 7995.20 | 0.333153 | ||||||||
\(833\) | 5289.22 | 0.220001 | ||||||||
\(834\) | 28089.7 | 1.16627 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 460.131 | 0.0190358 | ||||||||
\(837\) | 3431.30 | 0.141700 | ||||||||
\(838\) | −45566.5 | −1.87836 | ||||||||
\(839\) | 3184.10 | 0.131022 | 0.0655109 | − | 0.997852i | \(-0.479132\pi\) | ||||
0.0655109 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21235.5 | −0.870701 | ||||||||
\(842\) | 40567.8 | 1.66040 | ||||||||
\(843\) | −11958.4 | −0.488577 | ||||||||
\(844\) | −22647.6 | −0.923653 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5379.90 | 0.218635 | ||||||||
\(847\) | −2522.18 | −0.102318 | ||||||||
\(848\) | 33858.4 | 1.37111 | ||||||||
\(849\) | 23516.2 | 0.950619 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6442.76 | −0.259524 | ||||||||
\(852\) | −8325.23 | −0.334762 | ||||||||
\(853\) | −20566.8 | −0.825548 | −0.412774 | − | 0.910833i | \(-0.635440\pi\) | ||||
−0.412774 | + | 0.910833i | \(0.635440\pi\) | |||||||
\(854\) | −9164.94 | −0.367234 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13418.9 | 0.535804 | ||||||||
\(857\) | −48125.8 | −1.91826 | −0.959129 | − | 0.282971i | \(-0.908680\pi\) | ||||
−0.959129 | + | 0.282971i | \(0.908680\pi\) | |||||||
\(858\) | 8104.30 | 0.322466 | ||||||||
\(859\) | −22013.7 | −0.874387 | −0.437194 | − | 0.899367i | \(-0.644028\pi\) | ||||
−0.437194 | + | 0.899367i | \(0.644028\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30385.1 | −1.20270 | ||||||||
\(862\) | 7617.86 | 0.301004 | ||||||||
\(863\) | 23417.0 | 0.923667 | 0.461834 | − | 0.886967i | \(-0.347192\pi\) | ||||
0.461834 | + | 0.886967i | \(0.347192\pi\) | |||||||
\(864\) | −5537.47 | −0.218042 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −15977.7 | −0.626958 | ||||||||
\(867\) | 4712.32 | 0.184589 | ||||||||
\(868\) | 13874.6 | 0.542550 | ||||||||
\(869\) | 1855.30 | 0.0724241 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25073.7 | −0.975421 | ||||||||
\(872\) | 15732.9 | 0.610991 | ||||||||
\(873\) | −267.221 | −0.0103597 | ||||||||
\(874\) | −1961.92 | −0.0759303 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16642.9 | 0.641908 | ||||||||
\(877\) | 29017.9 | 1.11729 | 0.558645 | − | 0.829407i | \(-0.311321\pi\) | ||||
0.558645 | + | 0.829407i | \(0.311321\pi\) | |||||||
\(878\) | −56811.4 | −2.18370 | ||||||||
\(879\) | −16291.9 | −0.625158 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33241.1 | −1.27119 | −0.635597 | − | 0.772021i | \(-0.719246\pi\) | ||||
−0.635597 | + | 0.772021i | \(0.719246\pi\) | |||||||
\(882\) | −2995.86 | −0.114372 | ||||||||
\(883\) | 5618.39 | 0.214127 | 0.107063 | − | 0.994252i | \(-0.465855\pi\) | ||||
0.107063 | + | 0.994252i | \(0.465855\pi\) | |||||||
\(884\) | −20438.5 | −0.777625 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28777.8 | 1.09121 | ||||||||
\(887\) | 14334.2 | 0.542612 | 0.271306 | − | 0.962493i | \(-0.412545\pi\) | ||||
0.271306 | + | 0.962493i | \(0.412545\pi\) | |||||||
\(888\) | −2877.12 | −0.108727 | ||||||||
\(889\) | 6485.84 | 0.244688 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 32503.1 | 1.22005 | ||||||||
\(893\) | 1312.14 | 0.0491704 | ||||||||
\(894\) | 21746.9 | 0.813564 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 25217.0 | 0.940223 | ||||||||
\(897\) | −13672.3 | −0.508922 | ||||||||
\(898\) | 54424.9 | 2.02247 | ||||||||
\(899\) | 7136.58 | 0.264759 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24945.4 | −0.922367 | ||||||||
\(902\) | −19446.8 | −0.717856 | ||||||||
\(903\) | 9143.37 | 0.336957 | ||||||||
\(904\) | −11827.7 | −0.435161 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 32321.7 | 1.18523 | ||||||||
\(907\) | 36659.3 | 1.34207 | 0.671033 | − | 0.741428i | \(-0.265851\pi\) | ||||
0.671033 | + | 0.741428i | \(0.265851\pi\) | |||||||
\(908\) | −8044.02 | −0.293998 | ||||||||
\(909\) | −158.384 | −0.00577916 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9050.97 | −0.329168 | −0.164584 | − | 0.986363i | \(-0.552628\pi\) | ||||
−0.164584 | + | 0.986363i | \(0.552628\pi\) | |||||||
\(912\) | −1880.05 | −0.0682618 | ||||||||
\(913\) | −1585.43 | −0.0574700 | ||||||||
\(914\) | 53063.8 | 1.92035 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 496.193 | 0.0178981 | ||||||||
\(917\) | −12148.5 | −0.437491 | ||||||||
\(918\) | 5679.19 | 0.204184 | ||||||||
\(919\) | −46444.5 | −1.66710 | −0.833549 | − | 0.552445i | \(-0.813695\pi\) | ||||
−0.833549 | + | 0.552445i | \(0.813695\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24135.7 | 0.863518 | ||||||||
\(922\) | 6557.59 | 0.234233 | ||||||||
\(923\) | −35763.2 | −1.27536 | ||||||||
\(924\) | −3602.79 | −0.128272 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24572.7 | 0.872039 | ||||||||
\(927\) | −12807.2 | −0.453770 | ||||||||
\(928\) | −11517.1 | −0.407400 | ||||||||
\(929\) | −18695.8 | −0.660267 | −0.330133 | − | 0.943934i | \(-0.607094\pi\) | ||||
−0.330133 | + | 0.943934i | \(0.607094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −730.682 | −0.0257219 | ||||||||
\(932\) | −3430.55 | −0.120570 | ||||||||
\(933\) | 14136.2 | 0.496032 | ||||||||
\(934\) | −6347.30 | −0.222366 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6105.57 | −0.213212 | ||||||||
\(937\) | 13323.6 | 0.464530 | 0.232265 | − | 0.972653i | \(-0.425386\pi\) | ||||
0.232265 | + | 0.972653i | \(0.425386\pi\) | |||||||
\(938\) | 28172.0 | 0.980649 | ||||||||
\(939\) | −4275.57 | −0.148592 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9500.50 | −0.329126 | −0.164563 | − | 0.986367i | \(-0.552621\pi\) | ||||
−0.164563 | + | 0.986367i | \(0.552621\pi\) | |||||||
\(942\) | −14217.6 | −0.491755 | ||||||||
\(943\) | 32807.4 | 1.13293 | ||||||||
\(944\) | 63102.5 | 2.17565 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5851.85 | 0.201120 | ||||||||
\(947\) | −15179.4 | −0.520869 | −0.260435 | − | 0.965491i | \(-0.583866\pi\) | ||||
−0.260435 | + | 0.965491i | \(0.583866\pi\) | |||||||
\(948\) | 2650.18 | 0.0907953 | ||||||||
\(949\) | 71494.0 | 2.44551 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6094.61 | −0.207814 | ||||||||
\(952\) | −12111.4 | −0.412325 | ||||||||
\(953\) | −5051.55 | −0.171706 | −0.0858530 | − | 0.996308i | \(-0.527362\pi\) | ||||
−0.0858530 | + | 0.996308i | \(0.527362\pi\) | |||||||
\(954\) | 14129.3 | 0.479510 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −29648.3 | −1.00303 | ||||||||
\(957\) | −1853.14 | −0.0625952 | ||||||||
\(958\) | −61599.6 | −2.07745 | ||||||||
\(959\) | −49359.1 | −1.66203 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13640.3 | −0.457867 | ||||||||
\(962\) | 23434.2 | 0.785395 | ||||||||
\(963\) | 12016.3 | 0.402098 | ||||||||
\(964\) | −21772.2 | −0.727422 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 15361.7 | 0.511650 | ||||||||
\(967\) | −15341.1 | −0.510172 | −0.255086 | − | 0.966918i | \(-0.582104\pi\) | ||||
−0.255086 | + | 0.966918i | \(0.582104\pi\) | |||||||
\(968\) | 1216.11 | 0.0403794 | ||||||||
\(969\) | 1385.14 | 0.0459206 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5397.65 | −0.178392 | −0.0891961 | − | 0.996014i | \(-0.528430\pi\) | ||||
−0.0891961 | + | 0.996014i | \(0.528430\pi\) | |||||||
\(972\) | −1272.74 | −0.0419992 | ||||||||
\(973\) | −53642.7 | −1.76743 | ||||||||
\(974\) | −14306.4 | −0.470643 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9482.63 | 0.310995 | ||||||||
\(977\) | −24180.4 | −0.791812 | −0.395906 | − | 0.918291i | \(-0.629569\pi\) | ||||
−0.395906 | + | 0.918291i | \(0.629569\pi\) | |||||||
\(978\) | 6146.96 | 0.200980 | ||||||||
\(979\) | 15402.2 | 0.502814 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14088.5 | 0.458523 | ||||||||
\(982\) | −41760.5 | −1.35706 | ||||||||
\(983\) | −15159.6 | −0.491877 | −0.245938 | − | 0.969285i | \(-0.579096\pi\) | ||||
−0.245938 | + | 0.969285i | \(0.579096\pi\) | |||||||
\(984\) | 14650.7 | 0.474642 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11811.9 | 0.381507 | ||||||||
\(987\) | −10274.0 | −0.331331 | ||||||||
\(988\) | 2823.48 | 0.0909180 | ||||||||
\(989\) | −9872.29 | −0.317412 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3654.97 | −0.117158 | −0.0585792 | − | 0.998283i | \(-0.518657\pi\) | ||||
−0.0585792 | + | 0.998283i | \(0.518657\pi\) | |||||||
\(992\) | −26064.1 | −0.834210 | ||||||||
\(993\) | −950.371 | −0.0303717 | ||||||||
\(994\) | 40182.4 | 1.28220 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2264.70 | −0.0720479 | ||||||||
\(997\) | −46219.9 | −1.46820 | −0.734102 | − | 0.679040i | \(-0.762396\pi\) | ||||
−0.734102 | + | 0.679040i | \(0.762396\pi\) | |||||||
\(998\) | −46595.0 | −1.47789 | ||||||||
\(999\) | −2576.40 | −0.0815952 |
(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 | 825.4.a.t.1.2 | 4 | ||
3.2 | odd | 2 | 2475.4.a.be.1.3 | 4 | |||
5.2 | odd | 4 | 825.4.c.p.199.3 | 8 | |||
5.3 | odd | 4 | 825.4.c.p.199.6 | 8 | |||
5.4 | even | 2 | 165.4.a.h.1.3 | ✓ | 4 | ||
15.14 | odd | 2 | 495.4.a.m.1.2 | 4 | |||
55.54 | odd | 2 | 1815.4.a.t.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.h.1.3 | ✓ | 4 | 5.4 | even | 2 | ||
495.4.a.m.1.2 | 4 | 15.14 | odd | 2 | |||
825.4.a.t.1.2 | 4 | 1.1 | even | 1 | trivial | ||
825.4.c.p.199.3 | 8 | 5.2 | odd | 4 | |||
825.4.c.p.199.6 | 8 | 5.3 | odd | 4 | |||
1815.4.a.t.1.2 | 4 | 55.54 | odd | 2 | |||
2475.4.a.be.1.3 | 4 | 3.2 | odd | 2 |