Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1163891200.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-3.05323\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.46745 | 1.57948 | 0.789740 | − | 0.613441i | \(-0.210215\pi\) | ||||
0.789740 | + | 0.613441i | \(0.210215\pi\) | |||||||
\(3\) | −9.80920 | −1.88778 | −0.943890 | − | 0.330259i | \(-0.892864\pi\) | ||||
−0.943890 | + | 0.330259i | \(0.892864\pi\) | |||||||
\(4\) | 11.9581 | 1.49476 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −43.8221 | −2.98171 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 17.6824 | 0.781461 | ||||||||
\(9\) | 69.2204 | 2.56372 | ||||||||
\(10\) | 22.3372 | 0.706365 | ||||||||
\(11\) | −56.5404 | −1.54978 | −0.774890 | − | 0.632096i | \(-0.782195\pi\) | ||||
−0.774890 | + | 0.632096i | \(0.782195\pi\) | |||||||
\(12\) | −117.299 | −2.82178 | ||||||||
\(13\) | −40.9643 | −0.873958 | −0.436979 | − | 0.899472i | \(-0.643952\pi\) | ||||
−0.436979 | + | 0.899472i | \(0.643952\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −49.0460 | −0.844241 | ||||||||
\(16\) | −16.6692 | −0.260456 | ||||||||
\(17\) | −2.18896 | −0.0312295 | −0.0156148 | − | 0.999878i | \(-0.504971\pi\) | ||||
−0.0156148 | + | 0.999878i | \(0.504971\pi\) | |||||||
\(18\) | 309.238 | 4.04934 | ||||||||
\(19\) | −16.4735 | −0.198910 | −0.0994549 | − | 0.995042i | \(-0.531710\pi\) | ||||
−0.0994549 | + | 0.995042i | \(0.531710\pi\) | |||||||
\(20\) | 59.7903 | 0.668476 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −252.591 | −2.44785 | ||||||||
\(23\) | −155.272 | −1.40767 | −0.703837 | − | 0.710361i | \(-0.748532\pi\) | ||||
−0.703837 | + | 0.710361i | \(0.748532\pi\) | |||||||
\(24\) | −173.451 | −1.47523 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −183.006 | −1.38040 | ||||||||
\(27\) | −414.148 | −2.95195 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.26048 | −0.0400876 | −0.0200438 | − | 0.999799i | \(-0.506381\pi\) | ||||
−0.0200438 | + | 0.999799i | \(0.506381\pi\) | |||||||
\(30\) | −219.110 | −1.33346 | ||||||||
\(31\) | −168.680 | −0.977286 | −0.488643 | − | 0.872484i | \(-0.662508\pi\) | ||||
−0.488643 | + | 0.872484i | \(0.662508\pi\) | |||||||
\(32\) | −215.928 | −1.19285 | ||||||||
\(33\) | 554.616 | 2.92564 | ||||||||
\(34\) | −9.77908 | −0.0493264 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 827.742 | 3.83214 | ||||||||
\(37\) | −37.1738 | −0.165171 | −0.0825856 | − | 0.996584i | \(-0.526318\pi\) | ||||
−0.0825856 | + | 0.996584i | \(0.526318\pi\) | |||||||
\(38\) | −73.5946 | −0.314174 | ||||||||
\(39\) | 401.827 | 1.64984 | ||||||||
\(40\) | 88.4122 | 0.349480 | ||||||||
\(41\) | 266.804 | 1.01629 | 0.508143 | − | 0.861273i | \(-0.330332\pi\) | ||||
0.508143 | + | 0.861273i | \(0.330332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14.6549 | −0.0519735 | −0.0259867 | − | 0.999662i | \(-0.508273\pi\) | ||||
−0.0259867 | + | 0.999662i | \(0.508273\pi\) | |||||||
\(44\) | −676.114 | −2.31655 | ||||||||
\(45\) | 346.102 | 1.14653 | ||||||||
\(46\) | −693.670 | −2.22339 | ||||||||
\(47\) | 169.840 | 0.527102 | 0.263551 | − | 0.964646i | \(-0.415106\pi\) | ||||
0.263551 | + | 0.964646i | \(0.415106\pi\) | |||||||
\(48\) | 163.511 | 0.491684 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 111.686 | 0.315896 | ||||||||
\(51\) | 21.4720 | 0.0589545 | ||||||||
\(52\) | −489.854 | −1.30636 | ||||||||
\(53\) | −151.391 | −0.392361 | −0.196180 | − | 0.980568i | \(-0.562854\pi\) | ||||
−0.196180 | + | 0.980568i | \(0.562854\pi\) | |||||||
\(54\) | −1850.18 | −4.66255 | ||||||||
\(55\) | −282.702 | −0.693083 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 161.592 | 0.375498 | ||||||||
\(58\) | −27.9683 | −0.0633176 | ||||||||
\(59\) | 234.076 | 0.516510 | 0.258255 | − | 0.966077i | \(-0.416853\pi\) | ||||
0.258255 | + | 0.966077i | \(0.416853\pi\) | |||||||
\(60\) | −586.495 | −1.26194 | ||||||||
\(61\) | 242.411 | 0.508813 | 0.254407 | − | 0.967097i | \(-0.418120\pi\) | ||||
0.254407 | + | 0.967097i | \(0.418120\pi\) | |||||||
\(62\) | −753.569 | −1.54360 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −831.294 | −1.62362 | ||||||||
\(65\) | −204.822 | −0.390846 | ||||||||
\(66\) | 2477.72 | 4.62100 | ||||||||
\(67\) | 820.771 | 1.49661 | 0.748307 | − | 0.663353i | \(-0.230867\pi\) | ||||
0.748307 | + | 0.663353i | \(0.230867\pi\) | |||||||
\(68\) | −26.1758 | −0.0466806 | ||||||||
\(69\) | 1523.10 | 2.65738 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 961.611 | 1.60736 | 0.803678 | − | 0.595065i | \(-0.202874\pi\) | ||||
0.803678 | + | 0.595065i | \(0.202874\pi\) | |||||||
\(72\) | 1223.98 | 2.00344 | ||||||||
\(73\) | −934.026 | −1.49753 | −0.748763 | − | 0.662837i | \(-0.769352\pi\) | ||||
−0.748763 | + | 0.662837i | \(0.769352\pi\) | |||||||
\(74\) | −166.072 | −0.260885 | ||||||||
\(75\) | −245.230 | −0.377556 | ||||||||
\(76\) | −196.992 | −0.297322 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1795.14 | 2.60589 | ||||||||
\(79\) | 300.236 | 0.427584 | 0.213792 | − | 0.976879i | \(-0.431419\pi\) | ||||
0.213792 | + | 0.976879i | \(0.431419\pi\) | |||||||
\(80\) | −83.3460 | −0.116480 | ||||||||
\(81\) | 2193.51 | 3.00893 | ||||||||
\(82\) | 1191.93 | 1.60520 | ||||||||
\(83\) | −1087.60 | −1.43830 | −0.719151 | − | 0.694854i | \(-0.755469\pi\) | ||||
−0.719151 | + | 0.694854i | \(0.755469\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9448 | −0.0139663 | ||||||||
\(86\) | −65.4702 | −0.0820910 | ||||||||
\(87\) | 61.4103 | 0.0756767 | ||||||||
\(88\) | −999.773 | −1.21109 | ||||||||
\(89\) | 1124.05 | 1.33875 | 0.669375 | − | 0.742925i | \(-0.266562\pi\) | ||||
0.669375 | + | 0.742925i | \(0.266562\pi\) | |||||||
\(90\) | 1546.19 | 1.81092 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1856.76 | −2.10413 | ||||||||
\(93\) | 1654.62 | 1.84490 | ||||||||
\(94\) | 758.753 | 0.832547 | ||||||||
\(95\) | −82.3676 | −0.0889552 | ||||||||
\(96\) | 2118.08 | 2.25183 | ||||||||
\(97\) | −752.168 | −0.787330 | −0.393665 | − | 0.919254i | \(-0.628793\pi\) | ||||
−0.393665 | + | 0.919254i | \(0.628793\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3913.75 | −3.97320 | ||||||||
\(100\) | 298.952 | 0.298952 | ||||||||
\(101\) | −559.226 | −0.550941 | −0.275471 | − | 0.961310i | \(-0.588834\pi\) | ||||
−0.275471 | + | 0.961310i | \(0.588834\pi\) | |||||||
\(102\) | 95.9249 | 0.0931175 | ||||||||
\(103\) | 205.331 | 0.196426 | 0.0982128 | − | 0.995165i | \(-0.468687\pi\) | ||||
0.0982128 | + | 0.995165i | \(0.468687\pi\) | |||||||
\(104\) | −724.349 | −0.682964 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −676.330 | −0.619726 | ||||||||
\(107\) | −1470.17 | −1.32829 | −0.664145 | − | 0.747604i | \(-0.731204\pi\) | ||||
−0.664145 | + | 0.747604i | \(0.731204\pi\) | |||||||
\(108\) | −4952.41 | −4.41246 | ||||||||
\(109\) | −774.193 | −0.680314 | −0.340157 | − | 0.940369i | \(-0.610480\pi\) | ||||
−0.340157 | + | 0.940369i | \(0.610480\pi\) | |||||||
\(110\) | −1262.96 | −1.09471 | ||||||||
\(111\) | 364.645 | 0.311807 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −406.121 | −0.338094 | −0.169047 | − | 0.985608i | \(-0.554069\pi\) | ||||
−0.169047 | + | 0.985608i | \(0.554069\pi\) | |||||||
\(114\) | 721.904 | 0.593092 | ||||||||
\(115\) | −776.361 | −0.629531 | ||||||||
\(116\) | −74.8632 | −0.0599213 | ||||||||
\(117\) | −2835.56 | −2.24058 | ||||||||
\(118\) | 1045.72 | 0.815817 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −867.253 | −0.659742 | ||||||||
\(121\) | 1865.82 | 1.40182 | ||||||||
\(122\) | 1082.96 | 0.803660 | ||||||||
\(123\) | −2617.13 | −1.91853 | ||||||||
\(124\) | −2017.09 | −1.46081 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −451.639 | −0.315563 | −0.157781 | − | 0.987474i | \(-0.550434\pi\) | ||||
−0.157781 | + | 0.987474i | \(0.550434\pi\) | |||||||
\(128\) | −1986.33 | −1.37163 | ||||||||
\(129\) | 143.753 | 0.0981145 | ||||||||
\(130\) | −915.029 | −0.617334 | ||||||||
\(131\) | −361.932 | −0.241390 | −0.120695 | − | 0.992690i | \(-0.538512\pi\) | ||||
−0.120695 | + | 0.992690i | \(0.538512\pi\) | |||||||
\(132\) | 6632.14 | 4.37313 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3666.75 | 2.36387 | ||||||||
\(135\) | −2070.74 | −1.32015 | ||||||||
\(136\) | −38.7062 | −0.0244047 | ||||||||
\(137\) | 2512.72 | 1.56698 | 0.783490 | − | 0.621404i | \(-0.213437\pi\) | ||||
0.783490 | + | 0.621404i | \(0.213437\pi\) | |||||||
\(138\) | 6804.35 | 4.19728 | ||||||||
\(139\) | −1165.71 | −0.711324 | −0.355662 | − | 0.934615i | \(-0.615745\pi\) | ||||
−0.355662 | + | 0.934615i | \(0.615745\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1666.00 | −0.995052 | ||||||||
\(142\) | 4295.94 | 2.53879 | ||||||||
\(143\) | 2316.14 | 1.35444 | ||||||||
\(144\) | −1153.85 | −0.667736 | ||||||||
\(145\) | −31.3024 | −0.0179277 | ||||||||
\(146\) | −4172.71 | −2.36531 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −444.526 | −0.246891 | ||||||||
\(149\) | −2637.49 | −1.45014 | −0.725072 | − | 0.688673i | \(-0.758194\pi\) | ||||
−0.725072 | + | 0.688673i | \(0.758194\pi\) | |||||||
\(150\) | −1095.55 | −0.596343 | ||||||||
\(151\) | −2582.32 | −1.39170 | −0.695849 | − | 0.718188i | \(-0.744972\pi\) | ||||
−0.695849 | + | 0.718188i | \(0.744972\pi\) | |||||||
\(152\) | −291.292 | −0.155440 | ||||||||
\(153\) | −151.521 | −0.0800637 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −843.401 | −0.437055 | ||||||||
\(156\) | 4805.07 | 2.46611 | ||||||||
\(157\) | −225.788 | −0.114776 | −0.0573880 | − | 0.998352i | \(-0.518277\pi\) | ||||
−0.0573880 | + | 0.998352i | \(0.518277\pi\) | |||||||
\(158\) | 1341.29 | 0.675361 | ||||||||
\(159\) | 1485.02 | 0.740691 | ||||||||
\(160\) | −1079.64 | −0.533457 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9799.38 | 4.75254 | ||||||||
\(163\) | 1489.01 | 0.715509 | 0.357755 | − | 0.933816i | \(-0.383542\pi\) | ||||
0.357755 | + | 0.933816i | \(0.383542\pi\) | |||||||
\(164\) | 3190.46 | 1.51910 | ||||||||
\(165\) | 2773.08 | 1.30839 | ||||||||
\(166\) | −4858.77 | −2.27177 | ||||||||
\(167\) | −2858.73 | −1.32464 | −0.662322 | − | 0.749220i | \(-0.730429\pi\) | ||||
−0.662322 | + | 0.749220i | \(0.730429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −518.925 | −0.236197 | ||||||||
\(170\) | −48.8954 | −0.0220594 | ||||||||
\(171\) | −1140.30 | −0.509948 | ||||||||
\(172\) | −175.245 | −0.0776877 | ||||||||
\(173\) | 32.0040 | 0.0140648 | 0.00703242 | − | 0.999975i | \(-0.497761\pi\) | ||||
0.00703242 | + | 0.999975i | \(0.497761\pi\) | |||||||
\(174\) | 274.347 | 0.119530 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 942.483 | 0.403650 | ||||||||
\(177\) | −2296.10 | −0.975057 | ||||||||
\(178\) | 5021.62 | 2.11453 | ||||||||
\(179\) | 738.444 | 0.308346 | 0.154173 | − | 0.988044i | \(-0.450729\pi\) | ||||
0.154173 | + | 0.988044i | \(0.450729\pi\) | |||||||
\(180\) | 4138.71 | 1.71378 | ||||||||
\(181\) | 1991.91 | 0.817997 | 0.408998 | − | 0.912535i | \(-0.365878\pi\) | ||||
0.408998 | + | 0.912535i | \(0.365878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2377.86 | −0.960528 | ||||||||
\(184\) | −2745.59 | −1.10004 | ||||||||
\(185\) | −185.869 | −0.0738668 | ||||||||
\(186\) | 7391.91 | 2.91399 | ||||||||
\(187\) | 123.765 | 0.0483989 | ||||||||
\(188\) | 2030.96 | 0.787890 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −367.973 | −0.140503 | ||||||||
\(191\) | 2153.68 | 0.815890 | 0.407945 | − | 0.913006i | \(-0.366245\pi\) | ||||
0.407945 | + | 0.913006i | \(0.366245\pi\) | |||||||
\(192\) | 8154.33 | 3.06504 | ||||||||
\(193\) | 1003.94 | 0.374431 | 0.187215 | − | 0.982319i | \(-0.440054\pi\) | ||||
0.187215 | + | 0.982319i | \(0.440054\pi\) | |||||||
\(194\) | −3360.27 | −1.24357 | ||||||||
\(195\) | 2009.14 | 0.737832 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1716.80 | 0.620899 | 0.310449 | − | 0.950590i | \(-0.399521\pi\) | ||||
0.310449 | + | 0.950590i | \(0.399521\pi\) | |||||||
\(198\) | −17484.5 | −6.27559 | ||||||||
\(199\) | 5337.86 | 1.90146 | 0.950730 | − | 0.310019i | \(-0.100335\pi\) | ||||
0.950730 | + | 0.310019i | \(0.100335\pi\) | |||||||
\(200\) | 442.061 | 0.156292 | ||||||||
\(201\) | −8051.10 | −2.82528 | ||||||||
\(202\) | −2498.31 | −0.870201 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 256.763 | 0.0881227 | ||||||||
\(205\) | 1334.02 | 0.454497 | ||||||||
\(206\) | 917.304 | 0.310250 | ||||||||
\(207\) | −10748.0 | −3.60888 | ||||||||
\(208\) | 682.842 | 0.227628 | ||||||||
\(209\) | 931.420 | 0.308266 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 860.589 | 0.280784 | 0.140392 | − | 0.990096i | \(-0.455164\pi\) | ||||
0.140392 | + | 0.990096i | \(0.455164\pi\) | |||||||
\(212\) | −1810.34 | −0.586485 | ||||||||
\(213\) | −9432.63 | −3.03433 | ||||||||
\(214\) | −6567.92 | −2.09801 | ||||||||
\(215\) | −73.2747 | −0.0232432 | ||||||||
\(216\) | −7323.14 | −2.30684 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3458.66 | −1.07454 | ||||||||
\(219\) | 9162.04 | 2.82700 | ||||||||
\(220\) | −3380.57 | −1.03599 | ||||||||
\(221\) | 89.6695 | 0.0272933 | ||||||||
\(222\) | 1629.03 | 0.492493 | ||||||||
\(223\) | 3661.12 | 1.09940 | 0.549701 | − | 0.835361i | \(-0.314741\pi\) | ||||
0.549701 | + | 0.835361i | \(0.314741\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1730.51 | 0.512743 | ||||||||
\(226\) | −1814.32 | −0.534013 | ||||||||
\(227\) | −6032.38 | −1.76380 | −0.881902 | − | 0.471434i | \(-0.843737\pi\) | ||||
−0.881902 | + | 0.471434i | \(0.843737\pi\) | |||||||
\(228\) | 1932.33 | 0.561279 | ||||||||
\(229\) | 3849.64 | 1.11088 | 0.555439 | − | 0.831557i | \(-0.312550\pi\) | ||||
0.555439 | + | 0.831557i | \(0.312550\pi\) | |||||||
\(230\) | −3468.35 | −0.994332 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −110.701 | −0.0313269 | ||||||||
\(233\) | −1705.20 | −0.479448 | −0.239724 | − | 0.970841i | \(-0.577057\pi\) | ||||
−0.239724 | + | 0.970841i | \(0.577057\pi\) | |||||||
\(234\) | −12667.7 | −3.53895 | ||||||||
\(235\) | 849.202 | 0.235727 | ||||||||
\(236\) | 2799.09 | 0.772057 | ||||||||
\(237\) | −2945.07 | −0.807185 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6804.54 | 1.84163 | 0.920814 | − | 0.390001i | \(-0.127525\pi\) | ||||
0.920814 | + | 0.390001i | \(0.127525\pi\) | |||||||
\(240\) | 817.557 | 0.219888 | ||||||||
\(241\) | −4642.98 | −1.24100 | −0.620499 | − | 0.784207i | \(-0.713070\pi\) | ||||
−0.620499 | + | 0.784207i | \(0.713070\pi\) | |||||||
\(242\) | 8335.44 | 2.21414 | ||||||||
\(243\) | −10334.6 | −2.72824 | ||||||||
\(244\) | 2898.77 | 0.760553 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11691.9 | −3.03027 | ||||||||
\(247\) | 674.827 | 0.173839 | ||||||||
\(248\) | −2982.68 | −0.763711 | ||||||||
\(249\) | 10668.4 | 2.71520 | ||||||||
\(250\) | 558.431 | 0.141273 | ||||||||
\(251\) | −5912.64 | −1.48686 | −0.743431 | − | 0.668813i | \(-0.766803\pi\) | ||||
−0.743431 | + | 0.668813i | \(0.766803\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8779.16 | 2.18159 | ||||||||
\(254\) | −2017.67 | −0.498425 | ||||||||
\(255\) | 107.360 | 0.0263653 | ||||||||
\(256\) | −2223.49 | −0.542844 | ||||||||
\(257\) | 1697.83 | 0.412093 | 0.206047 | − | 0.978542i | \(-0.433940\pi\) | ||||
0.206047 | + | 0.978542i | \(0.433940\pi\) | |||||||
\(258\) | 642.210 | 0.154970 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2449.27 | −0.584220 | ||||||||
\(261\) | −433.352 | −0.102773 | ||||||||
\(262\) | −1616.91 | −0.381271 | ||||||||
\(263\) | −5661.78 | −1.32745 | −0.663727 | − | 0.747975i | \(-0.731026\pi\) | ||||
−0.663727 | + | 0.747975i | \(0.731026\pi\) | |||||||
\(264\) | 9806.97 | 2.28628 | ||||||||
\(265\) | −756.954 | −0.175469 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11026.0 | −2.52727 | ||||||||
\(268\) | 9814.83 | 2.23708 | ||||||||
\(269\) | −5330.01 | −1.20809 | −0.604046 | − | 0.796950i | \(-0.706446\pi\) | ||||
−0.604046 | + | 0.796950i | \(0.706446\pi\) | |||||||
\(270\) | −9250.91 | −2.08516 | ||||||||
\(271\) | 2034.94 | 0.456139 | 0.228069 | − | 0.973645i | \(-0.426759\pi\) | ||||
0.228069 | + | 0.973645i | \(0.426759\pi\) | |||||||
\(272\) | 36.4883 | 0.00813392 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11225.5 | 2.47502 | ||||||||
\(275\) | −1413.51 | −0.309956 | ||||||||
\(276\) | 18213.3 | 3.97214 | ||||||||
\(277\) | −867.657 | −0.188204 | −0.0941019 | − | 0.995563i | \(-0.529998\pi\) | ||||
−0.0941019 | + | 0.995563i | \(0.529998\pi\) | |||||||
\(278\) | −5207.73 | −1.12352 | ||||||||
\(279\) | −11676.1 | −2.50548 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2049.70 | 0.435142 | 0.217571 | − | 0.976045i | \(-0.430187\pi\) | ||||
0.217571 | + | 0.976045i | \(0.430187\pi\) | |||||||
\(282\) | −7442.76 | −1.57167 | ||||||||
\(283\) | −6625.11 | −1.39160 | −0.695799 | − | 0.718237i | \(-0.744949\pi\) | ||||
−0.695799 | + | 0.718237i | \(0.744949\pi\) | |||||||
\(284\) | 11499.0 | 2.40261 | ||||||||
\(285\) | 807.960 | 0.167928 | ||||||||
\(286\) | 10347.2 | 2.13932 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −14946.6 | −3.05812 | ||||||||
\(289\) | −4908.21 | −0.999025 | ||||||||
\(290\) | −139.842 | −0.0283165 | ||||||||
\(291\) | 7378.16 | 1.48631 | ||||||||
\(292\) | −11169.1 | −2.23844 | ||||||||
\(293\) | 5670.84 | 1.13070 | 0.565348 | − | 0.824852i | \(-0.308742\pi\) | ||||
0.565348 | + | 0.824852i | \(0.308742\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1170.38 | 0.230990 | ||||||||
\(296\) | −657.323 | −0.129075 | ||||||||
\(297\) | 23416.1 | 4.57488 | ||||||||
\(298\) | −11782.8 | −2.29048 | ||||||||
\(299\) | 6360.62 | 1.23025 | ||||||||
\(300\) | −2932.48 | −0.564355 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11536.4 | −2.19816 | ||||||||
\(303\) | 5485.56 | 1.04006 | ||||||||
\(304\) | 274.600 | 0.0518073 | ||||||||
\(305\) | 1212.06 | 0.227548 | ||||||||
\(306\) | −676.911 | −0.126459 | ||||||||
\(307\) | 272.638 | 0.0506849 | 0.0253424 | − | 0.999679i | \(-0.491932\pi\) | ||||
0.0253424 | + | 0.999679i | \(0.491932\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2014.13 | −0.370808 | ||||||||
\(310\) | −3767.85 | −0.690321 | ||||||||
\(311\) | 1220.83 | 0.222595 | 0.111298 | − | 0.993787i | \(-0.464499\pi\) | ||||
0.111298 | + | 0.993787i | \(0.464499\pi\) | |||||||
\(312\) | 7105.28 | 1.28929 | ||||||||
\(313\) | −775.195 | −0.139989 | −0.0699946 | − | 0.997547i | \(-0.522298\pi\) | ||||
−0.0699946 | + | 0.997547i | \(0.522298\pi\) | |||||||
\(314\) | −1008.69 | −0.181286 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3590.24 | 0.639135 | ||||||||
\(317\) | 7393.24 | 1.30992 | 0.654962 | − | 0.755662i | \(-0.272685\pi\) | ||||
0.654962 | + | 0.755662i | \(0.272685\pi\) | |||||||
\(318\) | 6634.25 | 1.16991 | ||||||||
\(319\) | 353.970 | 0.0621270 | ||||||||
\(320\) | −4156.47 | −0.726105 | ||||||||
\(321\) | 14421.2 | 2.50752 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.0600 | 0.00621186 | ||||||||
\(324\) | 26230.1 | 4.49762 | ||||||||
\(325\) | −1024.11 | −0.174792 | ||||||||
\(326\) | 6652.06 | 1.13013 | ||||||||
\(327\) | 7594.21 | 1.28428 | ||||||||
\(328\) | 4717.74 | 0.794188 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 12388.6 | 2.06657 | ||||||||
\(331\) | −3736.95 | −0.620548 | −0.310274 | − | 0.950647i | \(-0.600421\pi\) | ||||
−0.310274 | + | 0.950647i | \(0.600421\pi\) | |||||||
\(332\) | −13005.5 | −2.14991 | ||||||||
\(333\) | −2573.18 | −0.423452 | ||||||||
\(334\) | −12771.2 | −2.09225 | ||||||||
\(335\) | 4103.85 | 0.669306 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8230.24 | −1.33036 | −0.665178 | − | 0.746685i | \(-0.731644\pi\) | ||||
−0.665178 | + | 0.746685i | \(0.731644\pi\) | |||||||
\(338\) | −2318.27 | −0.373068 | ||||||||
\(339\) | 3983.72 | 0.638247 | ||||||||
\(340\) | −130.879 | −0.0208762 | ||||||||
\(341\) | 9537.25 | 1.51458 | ||||||||
\(342\) | −5094.24 | −0.805453 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −259.135 | −0.0406152 | ||||||||
\(345\) | 7615.48 | 1.18842 | ||||||||
\(346\) | 142.976 | 0.0222151 | ||||||||
\(347\) | −12730.5 | −1.96948 | −0.984739 | − | 0.174036i | \(-0.944319\pi\) | ||||
−0.984739 | + | 0.174036i | \(0.944319\pi\) | |||||||
\(348\) | 734.348 | 0.113118 | ||||||||
\(349\) | −4487.30 | −0.688252 | −0.344126 | − | 0.938924i | \(-0.611825\pi\) | ||||
−0.344126 | + | 0.938924i | \(0.611825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16965.3 | 2.57989 | ||||||||
\(352\) | 12208.7 | 1.84865 | ||||||||
\(353\) | 12263.5 | 1.84906 | 0.924532 | − | 0.381106i | \(-0.124457\pi\) | ||||
0.924532 | + | 0.381106i | \(0.124457\pi\) | |||||||
\(354\) | −10257.7 | −1.54008 | ||||||||
\(355\) | 4808.05 | 0.718831 | ||||||||
\(356\) | 13441.4 | 2.00111 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3298.96 | 0.487026 | ||||||||
\(359\) | −11073.2 | −1.62791 | −0.813957 | − | 0.580925i | \(-0.802691\pi\) | ||||
−0.813957 | + | 0.580925i | \(0.802691\pi\) | |||||||
\(360\) | 6119.92 | 0.895968 | ||||||||
\(361\) | −6587.62 | −0.960435 | ||||||||
\(362\) | 8898.74 | 1.29201 | ||||||||
\(363\) | −18302.2 | −2.64632 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4670.13 | −0.669714 | ||||||||
\(366\) | −10623.0 | −1.51713 | ||||||||
\(367\) | −5864.72 | −0.834157 | −0.417079 | − | 0.908870i | \(-0.636946\pi\) | ||||
−0.417079 | + | 0.908870i | \(0.636946\pi\) | |||||||
\(368\) | 2588.26 | 0.366637 | ||||||||
\(369\) | 18468.3 | 2.60547 | ||||||||
\(370\) | −830.359 | −0.116671 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 19786.0 | 2.75768 | ||||||||
\(373\) | −9368.17 | −1.30044 | −0.650222 | − | 0.759744i | \(-0.725324\pi\) | ||||
−0.650222 | + | 0.759744i | \(0.725324\pi\) | |||||||
\(374\) | 552.913 | 0.0764451 | ||||||||
\(375\) | −1226.15 | −0.168848 | ||||||||
\(376\) | 3003.19 | 0.411909 | ||||||||
\(377\) | 256.456 | 0.0350349 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5537.81 | 0.750549 | 0.375275 | − | 0.926914i | \(-0.377548\pi\) | ||||
0.375275 | + | 0.926914i | \(0.377548\pi\) | |||||||
\(380\) | −984.958 | −0.132966 | ||||||||
\(381\) | 4430.21 | 0.595713 | ||||||||
\(382\) | 9621.46 | 1.28868 | ||||||||
\(383\) | −5243.17 | −0.699513 | −0.349756 | − | 0.936841i | \(-0.613736\pi\) | ||||
−0.349756 | + | 0.936841i | \(0.613736\pi\) | |||||||
\(384\) | 19484.3 | 2.58934 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4485.05 | 0.591406 | ||||||||
\(387\) | −1014.42 | −0.133245 | ||||||||
\(388\) | −8994.47 | −1.17687 | ||||||||
\(389\) | −10890.5 | −1.41947 | −0.709733 | − | 0.704471i | \(-0.751184\pi\) | ||||
−0.709733 | + | 0.704471i | \(0.751184\pi\) | |||||||
\(390\) | 8975.70 | 1.16539 | ||||||||
\(391\) | 339.886 | 0.0439610 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3550.26 | 0.455692 | ||||||||
\(394\) | 7669.71 | 0.980697 | ||||||||
\(395\) | 1501.18 | 0.191221 | ||||||||
\(396\) | −46800.8 | −5.93897 | ||||||||
\(397\) | −13307.0 | −1.68227 | −0.841135 | − | 0.540826i | \(-0.818112\pi\) | ||||
−0.841135 | + | 0.540826i | \(0.818112\pi\) | |||||||
\(398\) | 23846.6 | 3.00332 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −416.730 | −0.0520912 | ||||||||
\(401\) | 7227.02 | 0.900001 | 0.450000 | − | 0.893028i | \(-0.351424\pi\) | ||||
0.450000 | + | 0.893028i | \(0.351424\pi\) | |||||||
\(402\) | −35967.9 | −4.46247 | ||||||||
\(403\) | 6909.87 | 0.854107 | ||||||||
\(404\) | −6687.26 | −0.823524 | ||||||||
\(405\) | 10967.5 | 1.34563 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2101.82 | 0.255979 | ||||||||
\(408\) | 379.677 | 0.0460706 | ||||||||
\(409\) | −5852.64 | −0.707565 | −0.353783 | − | 0.935328i | \(-0.615105\pi\) | ||||
−0.353783 | + | 0.935328i | \(0.615105\pi\) | |||||||
\(410\) | 5959.66 | 0.717869 | ||||||||
\(411\) | −24647.8 | −2.95812 | ||||||||
\(412\) | 2455.36 | 0.293609 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −48016.1 | −5.70015 | ||||||||
\(415\) | −5437.98 | −0.643228 | ||||||||
\(416\) | 8845.35 | 1.04250 | ||||||||
\(417\) | 11434.7 | 1.34282 | ||||||||
\(418\) | 4161.07 | 0.486901 | ||||||||
\(419\) | 8344.19 | 0.972889 | 0.486444 | − | 0.873712i | \(-0.338294\pi\) | ||||
0.486444 | + | 0.873712i | \(0.338294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10955.3 | −1.26824 | −0.634122 | − | 0.773233i | \(-0.718638\pi\) | ||||
−0.634122 | + | 0.773233i | \(0.718638\pi\) | |||||||
\(422\) | 3844.63 | 0.443493 | ||||||||
\(423\) | 11756.4 | 1.35134 | ||||||||
\(424\) | −2676.96 | −0.306615 | ||||||||
\(425\) | −54.7241 | −0.00624591 | ||||||||
\(426\) | −42139.8 | −4.79267 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −17580.4 | −1.98547 | ||||||||
\(429\) | −22719.5 | −2.55689 | ||||||||
\(430\) | −327.351 | −0.0367122 | ||||||||
\(431\) | 9417.43 | 1.05249 | 0.526243 | − | 0.850334i | \(-0.323600\pi\) | ||||
0.526243 | + | 0.850334i | \(0.323600\pi\) | |||||||
\(432\) | 6903.51 | 0.768855 | ||||||||
\(433\) | −8783.79 | −0.974878 | −0.487439 | − | 0.873157i | \(-0.662069\pi\) | ||||
−0.487439 | + | 0.873157i | \(0.662069\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 307.051 | 0.0338436 | ||||||||
\(436\) | −9257.85 | −1.01690 | ||||||||
\(437\) | 2557.88 | 0.280000 | ||||||||
\(438\) | 40930.9 | 4.46519 | ||||||||
\(439\) | −10559.6 | −1.14802 | −0.574011 | − | 0.818847i | \(-0.694614\pi\) | ||||
−0.574011 | + | 0.818847i | \(0.694614\pi\) | |||||||
\(440\) | −4998.86 | −0.541617 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 400.593 | 0.0431092 | ||||||||
\(443\) | −4878.14 | −0.523177 | −0.261589 | − | 0.965179i | \(-0.584246\pi\) | ||||
−0.261589 | + | 0.965179i | \(0.584246\pi\) | |||||||
\(444\) | 4360.45 | 0.466076 | ||||||||
\(445\) | 5620.23 | 0.598707 | ||||||||
\(446\) | 16355.9 | 1.73649 | ||||||||
\(447\) | 25871.7 | 2.73756 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 43.7917 | 0.00460280 | 0.00230140 | − | 0.999997i | \(-0.499267\pi\) | ||||
0.00230140 | + | 0.999997i | \(0.499267\pi\) | |||||||
\(450\) | 7730.95 | 0.809868 | ||||||||
\(451\) | −15085.2 | −1.57502 | ||||||||
\(452\) | −4856.42 | −0.505369 | ||||||||
\(453\) | 25330.5 | 2.62722 | ||||||||
\(454\) | −26949.3 | −2.78589 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2857.34 | 0.293437 | ||||||||
\(457\) | 2869.76 | 0.293745 | 0.146873 | − | 0.989155i | \(-0.453079\pi\) | ||||
0.146873 | + | 0.989155i | \(0.453079\pi\) | |||||||
\(458\) | 17198.0 | 1.75461 | ||||||||
\(459\) | 906.555 | 0.0921882 | ||||||||
\(460\) | −9283.78 | −0.940997 | ||||||||
\(461\) | 17910.1 | 1.80945 | 0.904723 | − | 0.426001i | \(-0.140078\pi\) | ||||
0.904723 | + | 0.426001i | \(0.140078\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7630.72 | −0.765938 | −0.382969 | − | 0.923761i | \(-0.625098\pi\) | ||||
−0.382969 | + | 0.923761i | \(0.625098\pi\) | |||||||
\(464\) | 104.357 | 0.0104411 | ||||||||
\(465\) | 8273.09 | 0.825065 | ||||||||
\(466\) | −7617.89 | −0.757279 | ||||||||
\(467\) | 6246.30 | 0.618939 | 0.309469 | − | 0.950909i | \(-0.399849\pi\) | ||||
0.309469 | + | 0.950909i | \(0.399849\pi\) | |||||||
\(468\) | −33907.9 | −3.34913 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3793.76 | 0.372326 | ||||||||
\(471\) | 2214.80 | 0.216672 | ||||||||
\(472\) | 4139.03 | 0.403632 | ||||||||
\(473\) | 828.597 | 0.0805474 | ||||||||
\(474\) | −13156.9 | −1.27493 | ||||||||
\(475\) | −411.838 | −0.0397820 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10479.3 | −1.00590 | ||||||||
\(478\) | 30398.9 | 2.90882 | ||||||||
\(479\) | 4119.58 | 0.392961 | 0.196480 | − | 0.980508i | \(-0.437049\pi\) | ||||
0.196480 | + | 0.980508i | \(0.437049\pi\) | |||||||
\(480\) | 10590.4 | 1.00705 | ||||||||
\(481\) | 1522.80 | 0.144353 | ||||||||
\(482\) | −20742.2 | −1.96013 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 22311.6 | 2.09538 | ||||||||
\(485\) | −3760.84 | −0.352105 | ||||||||
\(486\) | −46169.1 | −4.30920 | ||||||||
\(487\) | −1421.46 | −0.132264 | −0.0661320 | − | 0.997811i | \(-0.521066\pi\) | ||||
−0.0661320 | + | 0.997811i | \(0.521066\pi\) | |||||||
\(488\) | 4286.43 | 0.397618 | ||||||||
\(489\) | −14606.0 | −1.35073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19241.1 | 1.76851 | 0.884253 | − | 0.467007i | \(-0.154668\pi\) | ||||
0.884253 | + | 0.467007i | \(0.154668\pi\) | |||||||
\(492\) | −31295.8 | −2.86773 | ||||||||
\(493\) | 13.7040 | 0.00125192 | ||||||||
\(494\) | 3014.75 | 0.274575 | ||||||||
\(495\) | −19568.7 | −1.77687 | ||||||||
\(496\) | 2811.76 | 0.254540 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 47660.6 | 4.28860 | ||||||||
\(499\) | 9576.48 | 0.859123 | 0.429561 | − | 0.903038i | \(-0.358668\pi\) | ||||
0.429561 | + | 0.903038i | \(0.358668\pi\) | |||||||
\(500\) | 1494.76 | 0.133695 | ||||||||
\(501\) | 28041.9 | 2.50064 | ||||||||
\(502\) | −26414.4 | −2.34847 | ||||||||
\(503\) | 10581.9 | 0.938019 | 0.469009 | − | 0.883193i | \(-0.344611\pi\) | ||||
0.469009 | + | 0.883193i | \(0.344611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2796.13 | −0.246388 | ||||||||
\(506\) | 39220.4 | 3.44577 | ||||||||
\(507\) | 5090.24 | 0.445888 | ||||||||
\(508\) | −5400.72 | −0.471690 | ||||||||
\(509\) | −7082.86 | −0.616782 | −0.308391 | − | 0.951260i | \(-0.599791\pi\) | ||||
−0.308391 | + | 0.951260i | \(0.599791\pi\) | |||||||
\(510\) | 479.625 | 0.0416434 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5957.37 | 0.514220 | ||||||||
\(513\) | 6822.47 | 0.587173 | ||||||||
\(514\) | 7584.98 | 0.650893 | ||||||||
\(515\) | 1026.65 | 0.0878442 | ||||||||
\(516\) | 1719.01 | 0.146657 | ||||||||
\(517\) | −9602.85 | −0.816891 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −313.933 | −0.0265513 | ||||||||
\(520\) | −3621.75 | −0.305431 | ||||||||
\(521\) | 7153.92 | 0.601572 | 0.300786 | − | 0.953692i | \(-0.402751\pi\) | ||||
0.300786 | + | 0.953692i | \(0.402751\pi\) | |||||||
\(522\) | −1935.98 | −0.162328 | ||||||||
\(523\) | 15781.3 | 1.31944 | 0.659721 | − | 0.751511i | \(-0.270674\pi\) | ||||
0.659721 | + | 0.751511i | \(0.270674\pi\) | |||||||
\(524\) | −4328.00 | −0.360820 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −25293.7 | −2.09669 | ||||||||
\(527\) | 369.235 | 0.0305202 | ||||||||
\(528\) | −9245.00 | −0.762002 | ||||||||
\(529\) | 11942.5 | 0.981547 | ||||||||
\(530\) | −3381.65 | −0.277150 | ||||||||
\(531\) | 16202.8 | 1.32418 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10929.4 | −0.888192 | ||||||||
\(534\) | −49258.0 | −3.99177 | ||||||||
\(535\) | −7350.86 | −0.594029 | ||||||||
\(536\) | 14513.2 | 1.16955 | ||||||||
\(537\) | −7243.54 | −0.582089 | ||||||||
\(538\) | −23811.5 | −1.90816 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −24762.0 | −1.97331 | ||||||||
\(541\) | −24277.2 | −1.92931 | −0.964656 | − | 0.263511i | \(-0.915119\pi\) | ||||
−0.964656 | + | 0.263511i | \(0.915119\pi\) | |||||||
\(542\) | 9090.97 | 0.720463 | ||||||||
\(543\) | −19539.0 | −1.54420 | ||||||||
\(544\) | 472.659 | 0.0372520 | ||||||||
\(545\) | −3870.96 | −0.304246 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −191.079 | −0.0149359 | −0.00746796 | − | 0.999972i | \(-0.502377\pi\) | ||||
−0.00746796 | + | 0.999972i | \(0.502377\pi\) | |||||||
\(548\) | 30047.3 | 2.34226 | ||||||||
\(549\) | 16779.8 | 1.30445 | ||||||||
\(550\) | −6314.78 | −0.489569 | ||||||||
\(551\) | 103.132 | 0.00797382 | ||||||||
\(552\) | 26932.1 | 2.07664 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3876.21 | −0.297264 | ||||||||
\(555\) | 1823.22 | 0.139444 | ||||||||
\(556\) | −13939.6 | −1.06326 | ||||||||
\(557\) | −15721.6 | −1.19595 | −0.597974 | − | 0.801515i | \(-0.704028\pi\) | ||||
−0.597974 | + | 0.801515i | \(0.704028\pi\) | |||||||
\(558\) | −52162.3 | −3.95736 | ||||||||
\(559\) | 600.330 | 0.0454226 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1214.04 | −0.0913665 | ||||||||
\(562\) | 9156.92 | 0.687298 | ||||||||
\(563\) | −3044.50 | −0.227905 | −0.113952 | − | 0.993486i | \(-0.536351\pi\) | ||||
−0.113952 | + | 0.993486i | \(0.536351\pi\) | |||||||
\(564\) | −19922.1 | −1.48736 | ||||||||
\(565\) | −2030.60 | −0.151200 | ||||||||
\(566\) | −29597.3 | −2.19800 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 17003.6 | 1.25609 | ||||||||
\(569\) | 13052.2 | 0.961647 | 0.480823 | − | 0.876817i | \(-0.340338\pi\) | ||||
0.480823 | + | 0.876817i | \(0.340338\pi\) | |||||||
\(570\) | 3609.52 | 0.265239 | ||||||||
\(571\) | −5811.05 | −0.425893 | −0.212946 | − | 0.977064i | \(-0.568306\pi\) | ||||
−0.212946 | + | 0.977064i | \(0.568306\pi\) | |||||||
\(572\) | 27696.5 | 2.02456 | ||||||||
\(573\) | −21125.9 | −1.54022 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3881.81 | −0.281535 | ||||||||
\(576\) | −57542.5 | −4.16250 | ||||||||
\(577\) | 22790.3 | 1.64432 | 0.822162 | − | 0.569254i | \(-0.192768\pi\) | ||||
0.822162 | + | 0.569254i | \(0.192768\pi\) | |||||||
\(578\) | −21927.2 | −1.57794 | ||||||||
\(579\) | −9847.84 | −0.706844 | ||||||||
\(580\) | −374.316 | −0.0267976 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 32961.5 | 2.34759 | ||||||||
\(583\) | 8559.70 | 0.608073 | ||||||||
\(584\) | −16515.9 | −1.17026 | ||||||||
\(585\) | −14177.8 | −1.00202 | ||||||||
\(586\) | 25334.2 | 1.78591 | ||||||||
\(587\) | 20600.3 | 1.44850 | 0.724248 | − | 0.689540i | \(-0.242187\pi\) | ||||
0.724248 | + | 0.689540i | \(0.242187\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2778.76 | 0.194392 | ||||||||
\(590\) | 5228.61 | 0.364845 | ||||||||
\(591\) | −16840.4 | −1.17212 | ||||||||
\(592\) | 619.657 | 0.0430198 | ||||||||
\(593\) | −773.830 | −0.0535875 | −0.0267938 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267938 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(594\) | 104610. | 7.22593 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31539.3 | −2.16762 | ||||||||
\(597\) | −52360.1 | −3.58954 | ||||||||
\(598\) | 28415.7 | 1.94315 | ||||||||
\(599\) | −13641.0 | −0.930479 | −0.465239 | − | 0.885185i | \(-0.654032\pi\) | ||||
−0.465239 | + | 0.885185i | \(0.654032\pi\) | |||||||
\(600\) | −4336.26 | −0.295045 | ||||||||
\(601\) | −14271.8 | −0.968650 | −0.484325 | − | 0.874888i | \(-0.660935\pi\) | ||||
−0.484325 | + | 0.874888i | \(0.660935\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 56814.1 | 3.83689 | ||||||||
\(604\) | −30879.6 | −2.08025 | ||||||||
\(605\) | 9329.09 | 0.626912 | ||||||||
\(606\) | 24506.4 | 1.64275 | ||||||||
\(607\) | −3234.90 | −0.216311 | −0.108155 | − | 0.994134i | \(-0.534494\pi\) | ||||
−0.108155 | + | 0.994134i | \(0.534494\pi\) | |||||||
\(608\) | 3557.10 | 0.237269 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5414.80 | 0.359408 | ||||||||
\(611\) | −6957.40 | −0.460665 | ||||||||
\(612\) | −1811.90 | −0.119676 | ||||||||
\(613\) | 8413.52 | 0.554354 | 0.277177 | − | 0.960819i | \(-0.410601\pi\) | ||||
0.277177 | + | 0.960819i | \(0.410601\pi\) | |||||||
\(614\) | 1217.99 | 0.0800558 | ||||||||
\(615\) | −13085.7 | −0.857991 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7077.93 | 0.461826 | 0.230913 | − | 0.972974i | \(-0.425829\pi\) | ||||
0.230913 | + | 0.972974i | \(0.425829\pi\) | |||||||
\(618\) | −8998.01 | −0.585685 | ||||||||
\(619\) | −5464.74 | −0.354841 | −0.177420 | − | 0.984135i | \(-0.556775\pi\) | ||||
−0.177420 | + | 0.984135i | \(0.556775\pi\) | |||||||
\(620\) | −10085.4 | −0.653292 | ||||||||
\(621\) | 64305.7 | 4.15539 | ||||||||
\(622\) | 5454.01 | 0.351585 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6698.13 | −0.429711 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −3463.14 | −0.221110 | ||||||||
\(627\) | −9136.48 | −0.581939 | ||||||||
\(628\) | −2699.98 | −0.171562 | ||||||||
\(629\) | 81.3721 | 0.00515822 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1569.98 | −0.0990492 | −0.0495246 | − | 0.998773i | \(-0.515771\pi\) | ||||
−0.0495246 | + | 0.998773i | \(0.515771\pi\) | |||||||
\(632\) | 5308.90 | 0.334140 | ||||||||
\(633\) | −8441.69 | −0.530058 | ||||||||
\(634\) | 33028.9 | 2.06900 | ||||||||
\(635\) | −2258.19 | −0.141124 | ||||||||
\(636\) | 17758.0 | 1.10715 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1581.34 | 0.0981284 | ||||||||
\(639\) | 66563.0 | 4.12080 | ||||||||
\(640\) | −9931.67 | −0.613412 | ||||||||
\(641\) | −14578.3 | −0.898298 | −0.449149 | − | 0.893457i | \(-0.648273\pi\) | ||||
−0.449149 | + | 0.893457i | \(0.648273\pi\) | |||||||
\(642\) | 64426.0 | 3.96058 | ||||||||
\(643\) | 11980.0 | 0.734750 | 0.367375 | − | 0.930073i | \(-0.380256\pi\) | ||||
0.367375 | + | 0.930073i | \(0.380256\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 718.766 | 0.0438781 | ||||||||
\(646\) | 161.096 | 0.00981151 | ||||||||
\(647\) | 5651.81 | 0.343424 | 0.171712 | − | 0.985147i | \(-0.445070\pi\) | ||||
0.171712 | + | 0.985147i | \(0.445070\pi\) | |||||||
\(648\) | 38786.6 | 2.35136 | ||||||||
\(649\) | −13234.7 | −0.800476 | ||||||||
\(650\) | −4575.15 | −0.276080 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17805.6 | 1.06951 | ||||||||
\(653\) | −2370.86 | −0.142081 | −0.0710405 | − | 0.997473i | \(-0.522632\pi\) | ||||
−0.0710405 | + | 0.997473i | \(0.522632\pi\) | |||||||
\(654\) | 33926.7 | 2.02850 | ||||||||
\(655\) | −1809.66 | −0.107953 | ||||||||
\(656\) | −4447.40 | −0.264698 | ||||||||
\(657\) | −64653.6 | −3.83923 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5233.92 | 0.309385 | 0.154692 | − | 0.987963i | \(-0.450561\pi\) | ||||
0.154692 | + | 0.987963i | \(0.450561\pi\) | |||||||
\(660\) | 33160.7 | 1.95572 | ||||||||
\(661\) | −10456.0 | −0.615265 | −0.307633 | − | 0.951505i | \(-0.599537\pi\) | ||||
−0.307633 | + | 0.951505i | \(0.599537\pi\) | |||||||
\(662\) | −16694.6 | −0.980144 | ||||||||
\(663\) | −879.585 | −0.0515238 | ||||||||
\(664\) | −19231.3 | −1.12398 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11495.5 | −0.668834 | ||||||||
\(667\) | 972.079 | 0.0564303 | ||||||||
\(668\) | −34184.9 | −1.98002 | ||||||||
\(669\) | −35912.7 | −2.07543 | ||||||||
\(670\) | 18333.7 | 1.05716 | ||||||||
\(671\) | −13706.0 | −0.788548 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17658.6 | −1.01143 | −0.505714 | − | 0.862701i | \(-0.668771\pi\) | ||||
−0.505714 | + | 0.862701i | \(0.668771\pi\) | |||||||
\(674\) | −36768.1 | −2.10127 | ||||||||
\(675\) | −10353.7 | −0.590391 | ||||||||
\(676\) | −6205.34 | −0.353057 | ||||||||
\(677\) | 9124.03 | 0.517969 | 0.258984 | − | 0.965881i | \(-0.416612\pi\) | ||||
0.258984 | + | 0.965881i | \(0.416612\pi\) | |||||||
\(678\) | 17797.0 | 1.00810 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −193.531 | −0.0109141 | ||||||||
\(681\) | 59172.8 | 3.32967 | ||||||||
\(682\) | 42607.1 | 2.39225 | ||||||||
\(683\) | 10523.7 | 0.589570 | 0.294785 | − | 0.955564i | \(-0.404752\pi\) | ||||
0.294785 | + | 0.955564i | \(0.404752\pi\) | |||||||
\(684\) | −13635.8 | −0.762250 | ||||||||
\(685\) | 12563.6 | 0.700775 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37761.9 | −2.09710 | ||||||||
\(688\) | 244.286 | 0.0135368 | ||||||||
\(689\) | 6201.62 | 0.342907 | ||||||||
\(690\) | 34021.8 | 1.87708 | ||||||||
\(691\) | −32928.1 | −1.81280 | −0.906400 | − | 0.422420i | \(-0.861181\pi\) | ||||
−0.906400 | + | 0.422420i | \(0.861181\pi\) | |||||||
\(692\) | 382.706 | 0.0210235 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −56872.8 | −3.11075 | ||||||||
\(695\) | −5828.54 | −0.318114 | ||||||||
\(696\) | 1085.88 | 0.0591384 | ||||||||
\(697\) | −584.024 | −0.0317381 | ||||||||
\(698\) | −20046.8 | −1.08708 | ||||||||
\(699\) | 16726.7 | 0.905093 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2582.50 | −0.139144 | −0.0695719 | − | 0.997577i | \(-0.522163\pi\) | ||||
−0.0695719 | + | 0.997577i | \(0.522163\pi\) | |||||||
\(702\) | 75791.5 | 4.07488 | ||||||||
\(703\) | 612.383 | 0.0328542 | ||||||||
\(704\) | 47001.7 | 2.51625 | ||||||||
\(705\) | −8329.99 | −0.445001 | ||||||||
\(706\) | 54786.4 | 2.92056 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −27456.9 | −1.45748 | ||||||||
\(709\) | −6866.00 | −0.363693 | −0.181846 | − | 0.983327i | \(-0.558207\pi\) | ||||
−0.181846 | + | 0.983327i | \(0.558207\pi\) | |||||||
\(710\) | 21479.7 | 1.13538 | ||||||||
\(711\) | 20782.4 | 1.09620 | ||||||||
\(712\) | 19875.9 | 1.04618 | ||||||||
\(713\) | 26191.4 | 1.37570 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11580.7 | 0.605725 | ||||||||
\(716\) | 8830.36 | 0.460902 | ||||||||
\(717\) | −66747.1 | −3.47659 | ||||||||
\(718\) | −49468.9 | −2.57126 | ||||||||
\(719\) | 6581.85 | 0.341393 | 0.170696 | − | 0.985324i | \(-0.445398\pi\) | ||||
0.170696 | + | 0.985324i | \(0.445398\pi\) | |||||||
\(720\) | −5769.24 | −0.298621 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −29429.8 | −1.51699 | ||||||||
\(723\) | 45543.9 | 2.34273 | ||||||||
\(724\) | 23819.4 | 1.22271 | ||||||||
\(725\) | −156.512 | −0.00801753 | ||||||||
\(726\) | −81764.0 | −4.17982 | ||||||||
\(727\) | −15527.2 | −0.792119 | −0.396060 | − | 0.918225i | \(-0.629623\pi\) | ||||
−0.396060 | + | 0.918225i | \(0.629623\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 42149.0 | 2.14139 | ||||||||
\(730\) | −20863.5 | −1.05780 | ||||||||
\(731\) | 32.0792 | 0.00162311 | ||||||||
\(732\) | −28434.6 | −1.43576 | ||||||||
\(733\) | 3391.32 | 0.170889 | 0.0854443 | − | 0.996343i | \(-0.472769\pi\) | ||||
0.0854443 | + | 0.996343i | \(0.472769\pi\) | |||||||
\(734\) | −26200.3 | −1.31754 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 33527.7 | 1.67914 | ||||||||
\(737\) | −46406.7 | −2.31942 | ||||||||
\(738\) | 82505.9 | 4.11529 | ||||||||
\(739\) | −14335.0 | −0.713562 | −0.356781 | − | 0.934188i | \(-0.616126\pi\) | ||||
−0.356781 | + | 0.934188i | \(0.616126\pi\) | |||||||
\(740\) | −2222.63 | −0.110413 | ||||||||
\(741\) | −6619.51 | −0.328170 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27668.2 | −1.36615 | −0.683073 | − | 0.730350i | \(-0.739357\pi\) | ||||
−0.683073 | + | 0.730350i | \(0.739357\pi\) | |||||||
\(744\) | 29257.7 | 1.44172 | ||||||||
\(745\) | −13187.4 | −0.648524 | ||||||||
\(746\) | −41851.8 | −2.05403 | ||||||||
\(747\) | −75283.7 | −3.68740 | ||||||||
\(748\) | 1479.99 | 0.0723446 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5477.76 | −0.266693 | ||||||||
\(751\) | −16929.9 | −0.822609 | −0.411305 | − | 0.911498i | \(-0.634927\pi\) | ||||
−0.411305 | + | 0.911498i | \(0.634927\pi\) | |||||||
\(752\) | −2831.10 | −0.137287 | ||||||||
\(753\) | 57998.2 | 2.80687 | ||||||||
\(754\) | 1145.70 | 0.0553370 | ||||||||
\(755\) | −12911.6 | −0.622386 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19445.3 | 0.933622 | 0.466811 | − | 0.884357i | \(-0.345403\pi\) | ||||
0.466811 | + | 0.884357i | \(0.345403\pi\) | |||||||
\(758\) | 24739.9 | 1.18548 | ||||||||
\(759\) | −86116.5 | −4.11836 | ||||||||
\(760\) | −1456.46 | −0.0695150 | ||||||||
\(761\) | −9996.97 | −0.476202 | −0.238101 | − | 0.971240i | \(-0.576525\pi\) | ||||
−0.238101 | + | 0.971240i | \(0.576525\pi\) | |||||||
\(762\) | 19791.7 | 0.940917 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 25753.9 | 1.21956 | ||||||||
\(765\) | −757.605 | −0.0358056 | ||||||||
\(766\) | −23423.6 | −1.10487 | ||||||||
\(767\) | −9588.76 | −0.451408 | ||||||||
\(768\) | 21810.6 | 1.02477 | ||||||||
\(769\) | −8382.34 | −0.393075 | −0.196538 | − | 0.980496i | \(-0.562970\pi\) | ||||
−0.196538 | + | 0.980496i | \(0.562970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16654.4 | −0.777942 | ||||||||
\(772\) | 12005.2 | 0.559684 | ||||||||
\(773\) | 11297.5 | 0.525668 | 0.262834 | − | 0.964841i | \(-0.415343\pi\) | ||||
0.262834 | + | 0.964841i | \(0.415343\pi\) | |||||||
\(774\) | −4531.87 | −0.210458 | ||||||||
\(775\) | −4217.00 | −0.195457 | ||||||||
\(776\) | −13300.2 | −0.615268 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −48652.9 | −2.24202 | ||||||||
\(779\) | −4395.20 | −0.202149 | ||||||||
\(780\) | 24025.4 | 1.10288 | ||||||||
\(781\) | −54369.9 | −2.49105 | ||||||||
\(782\) | 1518.42 | 0.0694356 | ||||||||
\(783\) | 2592.76 | 0.118337 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1128.94 | −0.0513294 | ||||||||
\(786\) | 15860.6 | 0.719756 | ||||||||
\(787\) | 25174.4 | 1.14024 | 0.570120 | − | 0.821561i | \(-0.306897\pi\) | ||||
0.570120 | + | 0.821561i | \(0.306897\pi\) | |||||||
\(788\) | 20529.6 | 0.928093 | ||||||||
\(789\) | 55537.5 | 2.50594 | ||||||||
\(790\) | 6706.43 | 0.302030 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −69204.6 | −3.10490 | ||||||||
\(793\) | −9930.22 | −0.444681 | ||||||||
\(794\) | −59448.4 | −2.65711 | ||||||||
\(795\) | 7425.11 | 0.331247 | ||||||||
\(796\) | 63830.5 | 2.84222 | ||||||||
\(797\) | 26277.4 | 1.16787 | 0.583936 | − | 0.811800i | \(-0.301512\pi\) | ||||
0.583936 | + | 0.811800i | \(0.301512\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −371.775 | −0.0164611 | ||||||||
\(800\) | −5398.21 | −0.238569 | ||||||||
\(801\) | 77806.9 | 3.43217 | ||||||||
\(802\) | 32286.3 | 1.42153 | ||||||||
\(803\) | 52810.2 | 2.32084 | ||||||||
\(804\) | −96275.6 | −4.22311 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30869.5 | 1.34905 | ||||||||
\(807\) | 52283.1 | 2.28061 | ||||||||
\(808\) | −9888.48 | −0.430539 | ||||||||
\(809\) | 15676.9 | 0.681298 | 0.340649 | − | 0.940191i | \(-0.389353\pi\) | ||||
0.340649 | + | 0.940191i | \(0.389353\pi\) | |||||||
\(810\) | 48996.9 | 2.12540 | ||||||||
\(811\) | −26600.5 | −1.15175 | −0.575876 | − | 0.817537i | \(-0.695339\pi\) | ||||
−0.575876 | + | 0.817537i | \(0.695339\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19961.1 | −0.861090 | ||||||||
\(814\) | 9389.77 | 0.404314 | ||||||||
\(815\) | 7445.04 | 0.319986 | ||||||||
\(816\) | −357.921 | −0.0153551 | ||||||||
\(817\) | 241.419 | 0.0103380 | ||||||||
\(818\) | −26146.3 | −1.11759 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15952.3 | 0.679363 | ||||||||
\(821\) | 35601.3 | 1.51339 | 0.756696 | − | 0.653767i | \(-0.226812\pi\) | ||||
0.756696 | + | 0.653767i | \(0.226812\pi\) | |||||||
\(822\) | −110113. | −4.67229 | ||||||||
\(823\) | 41975.0 | 1.77783 | 0.888916 | − | 0.458071i | \(-0.151459\pi\) | ||||
0.888916 | + | 0.458071i | \(0.151459\pi\) | |||||||
\(824\) | 3630.75 | 0.153499 | ||||||||
\(825\) | 13865.4 | 0.585129 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27719.4 | 1.16554 | 0.582768 | − | 0.812639i | \(-0.301970\pi\) | ||||
0.582768 | + | 0.812639i | \(0.301970\pi\) | |||||||
\(828\) | −128525. | −5.39440 | ||||||||
\(829\) | −27222.3 | −1.14049 | −0.570246 | − | 0.821474i | \(-0.693152\pi\) | ||||
−0.570246 | + | 0.821474i | \(0.693152\pi\) | |||||||
\(830\) | −24293.9 | −1.01597 | ||||||||
\(831\) | 8511.01 | 0.355287 | ||||||||
\(832\) | 34053.4 | 1.41898 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 51083.7 | 2.12096 | ||||||||
\(835\) | −14293.7 | −0.592399 | ||||||||
\(836\) | 11138.0 | 0.460784 | ||||||||
\(837\) | 69858.5 | 2.88490 | ||||||||
\(838\) | 37277.2 | 1.53666 | ||||||||
\(839\) | 24081.1 | 0.990909 | 0.495454 | − | 0.868634i | \(-0.335002\pi\) | ||||
0.495454 | + | 0.868634i | \(0.335002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24349.8 | −0.998393 | ||||||||
\(842\) | −48942.4 | −2.00317 | ||||||||
\(843\) | −20105.9 | −0.821452 | ||||||||
\(844\) | 10291.0 | 0.419704 | ||||||||
\(845\) | −2594.62 | −0.105631 | ||||||||
\(846\) | 52521.1 | 2.13441 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2523.56 | 0.102193 | ||||||||
\(849\) | 64987.0 | 2.62703 | ||||||||
\(850\) | −244.477 | −0.00986529 | ||||||||
\(851\) | 5772.06 | 0.232507 | ||||||||
\(852\) | −112796. | −4.53560 | ||||||||
\(853\) | 18493.0 | 0.742309 | 0.371155 | − | 0.928571i | \(-0.378962\pi\) | ||||
0.371155 | + | 0.928571i | \(0.378962\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5701.52 | −0.228056 | ||||||||
\(856\) | −25996.2 | −1.03801 | ||||||||
\(857\) | 3499.25 | 0.139477 | 0.0697387 | − | 0.997565i | \(-0.477783\pi\) | ||||
0.0697387 | + | 0.997565i | \(0.477783\pi\) | |||||||
\(858\) | −101498. | −4.03856 | ||||||||
\(859\) | 32158.0 | 1.27732 | 0.638660 | − | 0.769489i | \(-0.279489\pi\) | ||||
0.638660 | + | 0.769489i | \(0.279489\pi\) | |||||||
\(860\) | −876.224 | −0.0347430 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42071.9 | 1.66238 | ||||||||
\(863\) | −47704.7 | −1.88168 | −0.940838 | − | 0.338857i | \(-0.889960\pi\) | ||||
−0.940838 | + | 0.338857i | \(0.889960\pi\) | |||||||
\(864\) | 89426.2 | 3.52123 | ||||||||
\(865\) | 160.020 | 0.00628999 | ||||||||
\(866\) | −39241.1 | −1.53980 | ||||||||
\(867\) | 48145.6 | 1.88594 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16975.4 | −0.662661 | ||||||||
\(870\) | 1371.73 | 0.0534554 | ||||||||
\(871\) | −33622.3 | −1.30798 | ||||||||
\(872\) | −13689.6 | −0.531639 | ||||||||
\(873\) | −52065.3 | −2.01849 | ||||||||
\(874\) | 11427.2 | 0.442255 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 109560. | 4.22569 | ||||||||
\(877\) | −24437.3 | −0.940923 | −0.470461 | − | 0.882421i | \(-0.655913\pi\) | ||||
−0.470461 | + | 0.882421i | \(0.655913\pi\) | |||||||
\(878\) | −47174.4 | −1.81328 | ||||||||
\(879\) | −55626.4 | −2.13451 | ||||||||
\(880\) | 4712.42 | 0.180518 | ||||||||
\(881\) | 13975.8 | 0.534458 | 0.267229 | − | 0.963633i | \(-0.413892\pi\) | ||||
0.267229 | + | 0.963633i | \(0.413892\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3193.55 | 0.121712 | 0.0608558 | − | 0.998147i | \(-0.480617\pi\) | ||||
0.0608558 | + | 0.998147i | \(0.480617\pi\) | |||||||
\(884\) | 1072.27 | 0.0407969 | ||||||||
\(885\) | −11480.5 | −0.436059 | ||||||||
\(886\) | −21792.8 | −0.826348 | ||||||||
\(887\) | −20099.3 | −0.760843 | −0.380422 | − | 0.924813i | \(-0.624221\pi\) | ||||
−0.380422 | + | 0.924813i | \(0.624221\pi\) | |||||||
\(888\) | 6447.81 | 0.243665 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 25108.1 | 0.945646 | ||||||||
\(891\) | −124022. | −4.66317 | ||||||||
\(892\) | 43779.9 | 1.64334 | ||||||||
\(893\) | −2797.87 | −0.104846 | ||||||||
\(894\) | 115580. | 4.32392 | ||||||||
\(895\) | 3692.22 | 0.137896 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −62392.6 | −2.32244 | ||||||||
\(898\) | 195.637 | 0.00727004 | ||||||||
\(899\) | 1056.02 | 0.0391771 | ||||||||
\(900\) | 20693.5 | 0.766427 | ||||||||
\(901\) | 331.389 | 0.0122532 | ||||||||
\(902\) | −67392.3 | −2.48771 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7181.20 | −0.264207 | ||||||||
\(905\) | 9959.55 | 0.365819 | ||||||||
\(906\) | 113163. | 4.14965 | ||||||||
\(907\) | 23212.6 | 0.849792 | 0.424896 | − | 0.905242i | \(-0.360311\pi\) | ||||
0.424896 | + | 0.905242i | \(0.360311\pi\) | |||||||
\(908\) | −72135.6 | −2.63646 | ||||||||
\(909\) | −38709.8 | −1.41246 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2754.63 | 0.100181 | 0.0500905 | − | 0.998745i | \(-0.484049\pi\) | ||||
0.0500905 | + | 0.998745i | \(0.484049\pi\) | |||||||
\(912\) | −2693.61 | −0.0978008 | ||||||||
\(913\) | 61493.1 | 2.22905 | ||||||||
\(914\) | 12820.5 | 0.463965 | ||||||||
\(915\) | −11889.3 | −0.429561 | ||||||||
\(916\) | 46034.2 | 1.66049 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4049.98 | 0.145609 | ||||||||
\(919\) | 16218.0 | 0.582137 | 0.291068 | − | 0.956702i | \(-0.405989\pi\) | ||||
0.291068 | + | 0.956702i | \(0.405989\pi\) | |||||||
\(920\) | −13728.0 | −0.491954 | ||||||||
\(921\) | −2674.36 | −0.0956819 | ||||||||
\(922\) | 80012.2 | 2.85798 | ||||||||
\(923\) | −39391.7 | −1.40476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −929.344 | −0.0330342 | ||||||||
\(926\) | −34089.8 | −1.20978 | ||||||||
\(927\) | 14213.1 | 0.503580 | ||||||||
\(928\) | 1351.81 | 0.0478184 | ||||||||
\(929\) | −42592.6 | −1.50422 | −0.752109 | − | 0.659038i | \(-0.770964\pi\) | ||||
−0.752109 | + | 0.659038i | \(0.770964\pi\) | |||||||
\(930\) | 36959.6 | 1.30317 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −20390.9 | −0.716659 | ||||||||
\(933\) | −11975.4 | −0.420211 | ||||||||
\(934\) | 27905.0 | 0.977602 | ||||||||
\(935\) | 618.825 | 0.0216446 | ||||||||
\(936\) | −50139.7 | −1.75093 | ||||||||
\(937\) | 4670.79 | 0.162848 | 0.0814238 | − | 0.996680i | \(-0.474053\pi\) | ||||
0.0814238 | + | 0.996680i | \(0.474053\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7604.04 | 0.264269 | ||||||||
\(940\) | 10154.8 | 0.352355 | ||||||||
\(941\) | −11036.5 | −0.382338 | −0.191169 | − | 0.981557i | \(-0.561228\pi\) | ||||
−0.191169 | + | 0.981557i | \(0.561228\pi\) | |||||||
\(942\) | 9894.48 | 0.342229 | ||||||||
\(943\) | −41427.2 | −1.43060 | ||||||||
\(944\) | −3901.86 | −0.134528 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3701.71 | 0.127223 | ||||||||
\(947\) | 28219.0 | 0.968314 | 0.484157 | − | 0.874981i | \(-0.339126\pi\) | ||||
0.484157 | + | 0.874981i | \(0.339126\pi\) | |||||||
\(948\) | −35217.3 | −1.20655 | ||||||||
\(949\) | 38261.7 | 1.30878 | ||||||||
\(950\) | −1839.86 | −0.0628348 | ||||||||
\(951\) | −72521.7 | −2.47285 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42209.7 | 1.43474 | 0.717370 | − | 0.696693i | \(-0.245346\pi\) | ||||
0.717370 | + | 0.696693i | \(0.245346\pi\) | |||||||
\(954\) | −46815.8 | −1.58880 | ||||||||
\(955\) | 10768.4 | 0.364877 | ||||||||
\(956\) | 81369.2 | 2.75279 | ||||||||
\(957\) | −3472.16 | −0.117282 | ||||||||
\(958\) | 18404.0 | 0.620674 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 40771.6 | 1.37073 | ||||||||
\(961\) | −1337.99 | −0.0449126 | ||||||||
\(962\) | 6803.02 | 0.228002 | ||||||||
\(963\) | −101766. | −3.40536 | ||||||||
\(964\) | −55521.0 | −1.85499 | ||||||||
\(965\) | 5019.70 | 0.167451 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11522.8 | 0.383193 | 0.191596 | − | 0.981474i | \(-0.438634\pi\) | ||||
0.191596 | + | 0.981474i | \(0.438634\pi\) | |||||||
\(968\) | 32992.2 | 1.09547 | ||||||||
\(969\) | −353.719 | −0.0117266 | ||||||||
\(970\) | −16801.3 | −0.556143 | ||||||||
\(971\) | −42660.3 | −1.40992 | −0.704961 | − | 0.709246i | \(-0.749035\pi\) | ||||
−0.704961 | + | 0.709246i | \(0.749035\pi\) | |||||||
\(972\) | −123581. | −4.07806 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6350.30 | −0.208908 | ||||||||
\(975\) | 10045.7 | 0.329968 | ||||||||
\(976\) | −4040.80 | −0.132524 | ||||||||
\(977\) | −13991.7 | −0.458171 | −0.229085 | − | 0.973406i | \(-0.573573\pi\) | ||||
−0.229085 | + | 0.973406i | \(0.573573\pi\) | |||||||
\(978\) | −65251.3 | −2.13344 | ||||||||
\(979\) | −63554.1 | −2.07477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −53589.9 | −1.74413 | ||||||||
\(982\) | 85958.4 | 2.79332 | ||||||||
\(983\) | −25963.2 | −0.842420 | −0.421210 | − | 0.906963i | \(-0.638394\pi\) | ||||
−0.421210 | + | 0.906963i | \(0.638394\pi\) | |||||||
\(984\) | −46277.3 | −1.49925 | ||||||||
\(985\) | 8584.01 | 0.277674 | ||||||||
\(986\) | 61.2217 | 0.00197738 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8069.62 | 0.259847 | ||||||||
\(989\) | 2275.51 | 0.0731617 | ||||||||
\(990\) | −87422.3 | −2.80653 | ||||||||
\(991\) | 14482.3 | 0.464224 | 0.232112 | − | 0.972689i | \(-0.425436\pi\) | ||||
0.232112 | + | 0.972689i | \(0.425436\pi\) | |||||||
\(992\) | 36422.8 | 1.16575 | ||||||||
\(993\) | 36656.5 | 1.17146 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26689.3 | 0.850359 | ||||||||
\(996\) | 127574. | 4.05857 | ||||||||
\(997\) | 4184.45 | 0.132922 | 0.0664609 | − | 0.997789i | \(-0.478829\pi\) | ||||
0.0664609 | + | 0.997789i | \(0.478829\pi\) | |||||||
\(998\) | 42782.4 | 1.35697 | ||||||||
\(999\) | 15395.4 | 0.487578 |
(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 | 245.4.a.o.1.6 | ✓ | 6 | |
3.2 | odd | 2 | 2205.4.a.bz.1.1 | 6 | |||
5.4 | even | 2 | 1225.4.a.bj.1.1 | 6 | |||
7.2 | even | 3 | 245.4.e.q.116.1 | 12 | |||
7.3 | odd | 6 | 245.4.e.p.226.1 | 12 | |||
7.4 | even | 3 | 245.4.e.q.226.1 | 12 | |||
7.5 | odd | 6 | 245.4.e.p.116.1 | 12 | |||
7.6 | odd | 2 | 245.4.a.p.1.6 | yes | 6 | ||
21.20 | even | 2 | 2205.4.a.ca.1.1 | 6 | |||
35.34 | odd | 2 | 1225.4.a.bi.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
245.4.a.p.1.6 | yes | 6 | 7.6 | odd | 2 | ||
245.4.e.p.116.1 | 12 | 7.5 | odd | 6 | |||
245.4.e.p.226.1 | 12 | 7.3 | odd | 6 | |||
245.4.e.q.116.1 | 12 | 7.2 | even | 3 | |||
245.4.e.q.226.1 | 12 | 7.4 | even | 3 | |||
1225.4.a.bi.1.1 | 6 | 35.34 | odd | 2 | |||
1225.4.a.bj.1.1 | 6 | 5.4 | even | 2 | |||
2205.4.a.bz.1.1 | 6 | 3.2 | odd | 2 | |||
2205.4.a.ca.1.1 | 6 | 21.20 | even | 2 |