Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,4,Mod(1,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.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: | \(4.36614134042\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.15629.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 26x - 45 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(5.80916\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 6.12805 | 1.17934 | 0.589672 | − | 0.807643i | \(-0.299257\pi\) | ||||
0.589672 | + | 0.807643i | \(0.299257\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 18.7464 | 1.67673 | 0.838364 | − | 0.545111i | \(-0.183513\pi\) | ||||
0.838364 | + | 0.545111i | \(0.183513\pi\) | |||||||
\(6\) | −12.2561 | −0.833923 | ||||||||
\(7\) | −21.9178 | −1.18345 | −0.591724 | − | 0.806141i | \(-0.701552\pi\) | ||||
−0.591724 | + | 0.806141i | \(0.701552\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 10.5531 | 0.390854 | ||||||||
\(10\) | −37.4928 | −1.18563 | ||||||||
\(11\) | 57.7703 | 1.58349 | 0.791745 | − | 0.610852i | \(-0.209173\pi\) | ||||
0.791745 | + | 0.610852i | \(0.209173\pi\) | |||||||
\(12\) | 24.5122 | 0.589672 | ||||||||
\(13\) | −18.6447 | −0.397777 | −0.198889 | − | 0.980022i | \(-0.563733\pi\) | ||||
−0.198889 | + | 0.980022i | \(0.563733\pi\) | |||||||
\(14\) | 43.8355 | 0.836824 | ||||||||
\(15\) | 114.879 | 1.97744 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −44.5600 | −0.635728 | −0.317864 | − | 0.948136i | \(-0.602966\pi\) | ||||
−0.317864 | + | 0.948136i | \(0.602966\pi\) | |||||||
\(18\) | −21.1061 | −0.276375 | ||||||||
\(19\) | 128.560 | 1.55230 | 0.776149 | − | 0.630549i | \(-0.217170\pi\) | ||||
0.776149 | + | 0.630549i | \(0.217170\pi\) | |||||||
\(20\) | 74.9855 | 0.838364 | ||||||||
\(21\) | −134.313 | −1.39569 | ||||||||
\(22\) | −115.541 | −1.11970 | ||||||||
\(23\) | −112.094 | −1.01622 | −0.508111 | − | 0.861291i | \(-0.669656\pi\) | ||||
−0.508111 | + | 0.861291i | \(0.669656\pi\) | |||||||
\(24\) | −49.0244 | −0.416961 | ||||||||
\(25\) | 226.427 | 1.81141 | ||||||||
\(26\) | 37.2894 | 0.281271 | ||||||||
\(27\) | −100.788 | −0.718393 | ||||||||
\(28\) | −87.6711 | −0.591724 | ||||||||
\(29\) | −127.235 | −0.814721 | −0.407360 | − | 0.913268i | \(-0.633551\pi\) | ||||
−0.407360 | + | 0.913268i | \(0.633551\pi\) | |||||||
\(30\) | −229.758 | −1.39826 | ||||||||
\(31\) | 38.8369 | 0.225010 | 0.112505 | − | 0.993651i | \(-0.464113\pi\) | ||||
0.112505 | + | 0.993651i | \(0.464113\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 354.019 | 1.86748 | ||||||||
\(34\) | 89.1199 | 0.449528 | ||||||||
\(35\) | −410.879 | −1.98432 | ||||||||
\(36\) | 42.2122 | 0.195427 | ||||||||
\(37\) | −37.0000 | −0.164399 | ||||||||
\(38\) | −257.120 | −1.09764 | ||||||||
\(39\) | −114.256 | −0.469117 | ||||||||
\(40\) | −149.971 | −0.592813 | ||||||||
\(41\) | −438.665 | −1.67093 | −0.835463 | − | 0.549546i | \(-0.814801\pi\) | ||||
−0.835463 | + | 0.549546i | \(0.814801\pi\) | |||||||
\(42\) | 268.627 | 0.986904 | ||||||||
\(43\) | −256.005 | −0.907915 | −0.453958 | − | 0.891023i | \(-0.649988\pi\) | ||||
−0.453958 | + | 0.891023i | \(0.649988\pi\) | |||||||
\(44\) | 231.081 | 0.791745 | ||||||||
\(45\) | 197.832 | 0.655355 | ||||||||
\(46\) | 224.187 | 0.718578 | ||||||||
\(47\) | 275.094 | 0.853758 | 0.426879 | − | 0.904309i | \(-0.359613\pi\) | ||||
0.426879 | + | 0.904309i | \(0.359613\pi\) | |||||||
\(48\) | 98.0489 | 0.294836 | ||||||||
\(49\) | 137.388 | 0.400549 | ||||||||
\(50\) | −452.854 | −1.28086 | ||||||||
\(51\) | −273.066 | −0.749743 | ||||||||
\(52\) | −74.5788 | −0.198889 | ||||||||
\(53\) | 0.358276 | 0.000928548 0 | 0.000464274 | − | 1.00000i | \(-0.499852\pi\) | ||||
0.000464274 | 1.00000i | \(0.499852\pi\) | ||||||||
\(54\) | 201.576 | 0.507981 | ||||||||
\(55\) | 1082.98 | 2.65508 | ||||||||
\(56\) | 175.342 | 0.418412 | ||||||||
\(57\) | 787.822 | 1.83070 | ||||||||
\(58\) | 254.469 | 0.576094 | ||||||||
\(59\) | 698.000 | 1.54020 | 0.770101 | − | 0.637922i | \(-0.220206\pi\) | ||||
0.770101 | + | 0.637922i | \(0.220206\pi\) | |||||||
\(60\) | 459.515 | 0.988720 | ||||||||
\(61\) | −494.971 | −1.03893 | −0.519463 | − | 0.854493i | \(-0.673868\pi\) | ||||
−0.519463 | + | 0.854493i | \(0.673868\pi\) | |||||||
\(62\) | −77.6738 | −0.159106 | ||||||||
\(63\) | −231.299 | −0.462555 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −349.520 | −0.666964 | ||||||||
\(66\) | −708.039 | −1.32051 | ||||||||
\(67\) | −525.144 | −0.957561 | −0.478781 | − | 0.877935i | \(-0.658921\pi\) | ||||
−0.478781 | + | 0.877935i | \(0.658921\pi\) | |||||||
\(68\) | −178.240 | −0.317864 | ||||||||
\(69\) | −686.915 | −1.19848 | ||||||||
\(70\) | 821.758 | 1.40313 | ||||||||
\(71\) | −1014.99 | −1.69659 | −0.848294 | − | 0.529526i | \(-0.822370\pi\) | ||||
−0.848294 | + | 0.529526i | \(0.822370\pi\) | |||||||
\(72\) | −84.4244 | −0.138188 | ||||||||
\(73\) | −14.4727 | −0.0232041 | −0.0116021 | − | 0.999933i | \(-0.503693\pi\) | ||||
−0.0116021 | + | 0.999933i | \(0.503693\pi\) | |||||||
\(74\) | 74.0000 | 0.116248 | ||||||||
\(75\) | 1387.56 | 2.13628 | ||||||||
\(76\) | 514.240 | 0.776149 | ||||||||
\(77\) | −1266.19 | −1.87398 | ||||||||
\(78\) | 228.511 | 0.331716 | ||||||||
\(79\) | 980.168 | 1.39592 | 0.697959 | − | 0.716138i | \(-0.254092\pi\) | ||||
0.697959 | + | 0.716138i | \(0.254092\pi\) | |||||||
\(80\) | 299.942 | 0.419182 | ||||||||
\(81\) | −902.566 | −1.23809 | ||||||||
\(82\) | 877.330 | 1.18152 | ||||||||
\(83\) | −273.659 | −0.361904 | −0.180952 | − | 0.983492i | \(-0.557918\pi\) | ||||
−0.180952 | + | 0.983492i | \(0.557918\pi\) | |||||||
\(84\) | −537.253 | −0.697847 | ||||||||
\(85\) | −835.338 | −1.06594 | ||||||||
\(86\) | 512.010 | 0.641993 | ||||||||
\(87\) | −779.701 | −0.960836 | ||||||||
\(88\) | −462.162 | −0.559848 | ||||||||
\(89\) | 559.670 | 0.666572 | 0.333286 | − | 0.942826i | \(-0.391843\pi\) | ||||
0.333286 | + | 0.942826i | \(0.391843\pi\) | |||||||
\(90\) | −395.663 | −0.463406 | ||||||||
\(91\) | 408.650 | 0.470749 | ||||||||
\(92\) | −448.374 | −0.508111 | ||||||||
\(93\) | 237.995 | 0.265364 | ||||||||
\(94\) | −550.189 | −0.603698 | ||||||||
\(95\) | 2410.03 | 2.60278 | ||||||||
\(96\) | −196.098 | −0.208481 | ||||||||
\(97\) | 77.1825 | 0.0807907 | 0.0403953 | − | 0.999184i | \(-0.487138\pi\) | ||||
0.0403953 | + | 0.999184i | \(0.487138\pi\) | |||||||
\(98\) | −274.777 | −0.283231 | ||||||||
\(99\) | 609.653 | 0.618913 | ||||||||
\(100\) | 905.707 | 0.905707 | ||||||||
\(101\) | −1786.86 | −1.76038 | −0.880192 | − | 0.474617i | \(-0.842586\pi\) | ||||
−0.880192 | + | 0.474617i | \(0.842586\pi\) | |||||||
\(102\) | 546.132 | 0.530148 | ||||||||
\(103\) | 405.434 | 0.387850 | 0.193925 | − | 0.981016i | \(-0.437878\pi\) | ||||
0.193925 | + | 0.981016i | \(0.437878\pi\) | |||||||
\(104\) | 149.158 | 0.140636 | ||||||||
\(105\) | −2517.89 | −2.34020 | ||||||||
\(106\) | −0.716553 | −0.000656582 0 | ||||||||
\(107\) | 1283.22 | 1.15938 | 0.579691 | − | 0.814837i | \(-0.303173\pi\) | ||||
0.579691 | + | 0.814837i | \(0.303173\pi\) | |||||||
\(108\) | −403.151 | −0.359197 | ||||||||
\(109\) | 1054.88 | 0.926965 | 0.463483 | − | 0.886106i | \(-0.346600\pi\) | ||||
0.463483 | + | 0.886106i | \(0.346600\pi\) | |||||||
\(110\) | −2165.97 | −1.87743 | ||||||||
\(111\) | −226.738 | −0.193883 | ||||||||
\(112\) | −350.684 | −0.295862 | ||||||||
\(113\) | 1565.33 | 1.30314 | 0.651568 | − | 0.758591i | \(-0.274112\pi\) | ||||
0.651568 | + | 0.758591i | \(0.274112\pi\) | |||||||
\(114\) | −1575.64 | −1.29450 | ||||||||
\(115\) | −2101.35 | −1.70393 | ||||||||
\(116\) | −508.939 | −0.407360 | ||||||||
\(117\) | −196.758 | −0.155473 | ||||||||
\(118\) | −1396.00 | −1.08909 | ||||||||
\(119\) | 976.655 | 0.752351 | ||||||||
\(120\) | −919.031 | −0.699130 | ||||||||
\(121\) | 2006.40 | 1.50744 | ||||||||
\(122\) | 989.941 | 0.734632 | ||||||||
\(123\) | −2688.16 | −1.97060 | ||||||||
\(124\) | 155.348 | 0.112505 | ||||||||
\(125\) | 1901.39 | 1.36052 | ||||||||
\(126\) | 462.599 | 0.327076 | ||||||||
\(127\) | 1514.19 | 1.05797 | 0.528986 | − | 0.848631i | \(-0.322572\pi\) | ||||
0.528986 | + | 0.848631i | \(0.322572\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −1568.81 | −1.07075 | ||||||||
\(130\) | 699.041 | 0.471615 | ||||||||
\(131\) | 1487.35 | 0.991987 | 0.495993 | − | 0.868326i | \(-0.334804\pi\) | ||||
0.495993 | + | 0.868326i | \(0.334804\pi\) | |||||||
\(132\) | 1416.08 | 0.933740 | ||||||||
\(133\) | −2817.75 | −1.83706 | ||||||||
\(134\) | 1050.29 | 0.677098 | ||||||||
\(135\) | −1889.41 | −1.20455 | ||||||||
\(136\) | 356.480 | 0.224764 | ||||||||
\(137\) | 608.789 | 0.379652 | 0.189826 | − | 0.981818i | \(-0.439208\pi\) | ||||
0.189826 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(138\) | 1373.83 | 0.847451 | ||||||||
\(139\) | 1184.95 | 0.723067 | 0.361534 | − | 0.932359i | \(-0.382253\pi\) | ||||
0.361534 | + | 0.932359i | \(0.382253\pi\) | |||||||
\(140\) | −1643.52 | −0.992160 | ||||||||
\(141\) | 1685.79 | 1.00687 | ||||||||
\(142\) | 2029.99 | 1.19967 | ||||||||
\(143\) | −1077.11 | −0.629876 | ||||||||
\(144\) | 168.849 | 0.0977135 | ||||||||
\(145\) | −2385.19 | −1.36606 | ||||||||
\(146\) | 28.9454 | 0.0164078 | ||||||||
\(147\) | 841.923 | 0.472385 | ||||||||
\(148\) | −148.000 | −0.0821995 | ||||||||
\(149\) | −747.940 | −0.411233 | −0.205616 | − | 0.978633i | \(-0.565920\pi\) | ||||
−0.205616 | + | 0.978633i | \(0.565920\pi\) | |||||||
\(150\) | −2775.11 | −1.51058 | ||||||||
\(151\) | 1272.79 | 0.685946 | 0.342973 | − | 0.939345i | \(-0.388566\pi\) | ||||
0.342973 | + | 0.939345i | \(0.388566\pi\) | |||||||
\(152\) | −1028.48 | −0.548821 | ||||||||
\(153\) | −470.244 | −0.248477 | ||||||||
\(154\) | 2532.39 | 1.32510 | ||||||||
\(155\) | 728.051 | 0.377280 | ||||||||
\(156\) | −457.023 | −0.234558 | ||||||||
\(157\) | 1995.46 | 1.01436 | 0.507181 | − | 0.861839i | \(-0.330687\pi\) | ||||
0.507181 | + | 0.861839i | \(0.330687\pi\) | |||||||
\(158\) | −1960.34 | −0.987063 | ||||||||
\(159\) | 2.19554 | 0.00109508 | ||||||||
\(160\) | −599.884 | −0.296406 | ||||||||
\(161\) | 2456.84 | 1.20265 | ||||||||
\(162\) | 1805.13 | 0.875460 | ||||||||
\(163\) | 3323.18 | 1.59688 | 0.798440 | − | 0.602075i | \(-0.205659\pi\) | ||||
0.798440 | + | 0.602075i | \(0.205659\pi\) | |||||||
\(164\) | −1754.66 | −0.835463 | ||||||||
\(165\) | 6636.58 | 3.13126 | ||||||||
\(166\) | 547.319 | 0.255905 | ||||||||
\(167\) | −3663.64 | −1.69761 | −0.848804 | − | 0.528707i | \(-0.822677\pi\) | ||||
−0.848804 | + | 0.528707i | \(0.822677\pi\) | |||||||
\(168\) | 1074.51 | 0.493452 | ||||||||
\(169\) | −1849.38 | −0.841773 | ||||||||
\(170\) | 1670.68 | 0.753735 | ||||||||
\(171\) | 1356.70 | 0.606722 | ||||||||
\(172\) | −1024.02 | −0.453958 | ||||||||
\(173\) | −3094.32 | −1.35987 | −0.679933 | − | 0.733274i | \(-0.737991\pi\) | ||||
−0.679933 | + | 0.733274i | \(0.737991\pi\) | |||||||
\(174\) | 1559.40 | 0.679414 | ||||||||
\(175\) | −4962.77 | −2.14372 | ||||||||
\(176\) | 924.324 | 0.395872 | ||||||||
\(177\) | 4277.38 | 1.81643 | ||||||||
\(178\) | −1119.34 | −0.471338 | ||||||||
\(179\) | 1247.66 | 0.520977 | 0.260488 | − | 0.965477i | \(-0.416116\pi\) | ||||
0.260488 | + | 0.965477i | \(0.416116\pi\) | |||||||
\(180\) | 791.326 | 0.327678 | ||||||||
\(181\) | 2860.98 | 1.17489 | 0.587445 | − | 0.809264i | \(-0.300134\pi\) | ||||
0.587445 | + | 0.809264i | \(0.300134\pi\) | |||||||
\(182\) | −817.300 | −0.332870 | ||||||||
\(183\) | −3033.21 | −1.22525 | ||||||||
\(184\) | 896.748 | 0.359289 | ||||||||
\(185\) | −693.616 | −0.275652 | ||||||||
\(186\) | −475.989 | −0.187641 | ||||||||
\(187\) | −2574.24 | −1.00667 | ||||||||
\(188\) | 1100.38 | 0.426879 | ||||||||
\(189\) | 2209.04 | 0.850181 | ||||||||
\(190\) | −4820.07 | −1.84044 | ||||||||
\(191\) | −1176.94 | −0.445865 | −0.222932 | − | 0.974834i | \(-0.571563\pi\) | ||||
−0.222932 | + | 0.974834i | \(0.571563\pi\) | |||||||
\(192\) | 392.195 | 0.147418 | ||||||||
\(193\) | 1983.29 | 0.739690 | 0.369845 | − | 0.929094i | \(-0.379411\pi\) | ||||
0.369845 | + | 0.929094i | \(0.379411\pi\) | |||||||
\(194\) | −154.365 | −0.0571276 | ||||||||
\(195\) | −2141.88 | −0.786581 | ||||||||
\(196\) | 549.553 | 0.200275 | ||||||||
\(197\) | −2747.71 | −0.993737 | −0.496869 | − | 0.867826i | \(-0.665517\pi\) | ||||
−0.496869 | + | 0.867826i | \(0.665517\pi\) | |||||||
\(198\) | −1219.31 | −0.437638 | ||||||||
\(199\) | 1669.49 | 0.594707 | 0.297354 | − | 0.954767i | \(-0.403896\pi\) | ||||
0.297354 | + | 0.954767i | \(0.403896\pi\) | |||||||
\(200\) | −1811.41 | −0.640432 | ||||||||
\(201\) | −3218.11 | −1.12929 | ||||||||
\(202\) | 3573.71 | 1.24478 | ||||||||
\(203\) | 2788.70 | 0.964179 | ||||||||
\(204\) | −1092.26 | −0.374871 | ||||||||
\(205\) | −8223.39 | −2.80169 | ||||||||
\(206\) | −810.867 | −0.274251 | ||||||||
\(207\) | −1182.93 | −0.397195 | ||||||||
\(208\) | −298.315 | −0.0994444 | ||||||||
\(209\) | 7426.94 | 2.45805 | ||||||||
\(210\) | 5035.78 | 1.65477 | ||||||||
\(211\) | 1864.44 | 0.608308 | 0.304154 | − | 0.952623i | \(-0.401626\pi\) | ||||
0.304154 | + | 0.952623i | \(0.401626\pi\) | |||||||
\(212\) | 1.43311 | 0.000464274 0 | ||||||||
\(213\) | −6219.94 | −2.00086 | ||||||||
\(214\) | −2566.45 | −0.819806 | ||||||||
\(215\) | −4799.16 | −1.52233 | ||||||||
\(216\) | 806.302 | 0.253990 | ||||||||
\(217\) | −851.218 | −0.266288 | ||||||||
\(218\) | −2109.76 | −0.655463 | ||||||||
\(219\) | −88.6896 | −0.0273657 | ||||||||
\(220\) | 4331.93 | 1.32754 | ||||||||
\(221\) | 830.807 | 0.252878 | ||||||||
\(222\) | 453.476 | 0.137096 | ||||||||
\(223\) | −2200.54 | −0.660803 | −0.330401 | − | 0.943841i | \(-0.607184\pi\) | ||||
−0.330401 | + | 0.943841i | \(0.607184\pi\) | |||||||
\(224\) | 701.368 | 0.209206 | ||||||||
\(225\) | 2389.49 | 0.707998 | ||||||||
\(226\) | −3130.67 | −0.921456 | ||||||||
\(227\) | −2020.06 | −0.590643 | −0.295321 | − | 0.955398i | \(-0.595427\pi\) | ||||
−0.295321 | + | 0.955398i | \(0.595427\pi\) | |||||||
\(228\) | 3151.29 | 0.915348 | ||||||||
\(229\) | −1993.14 | −0.575154 | −0.287577 | − | 0.957758i | \(-0.592850\pi\) | ||||
−0.287577 | + | 0.957758i | \(0.592850\pi\) | |||||||
\(230\) | 4202.70 | 1.20486 | ||||||||
\(231\) | −7759.31 | −2.21007 | ||||||||
\(232\) | 1017.88 | 0.288047 | ||||||||
\(233\) | −2822.20 | −0.793512 | −0.396756 | − | 0.917924i | \(-0.629864\pi\) | ||||
−0.396756 | + | 0.917924i | \(0.629864\pi\) | |||||||
\(234\) | 393.517 | 0.109936 | ||||||||
\(235\) | 5157.02 | 1.43152 | ||||||||
\(236\) | 2792.00 | 0.770101 | ||||||||
\(237\) | 6006.52 | 1.64627 | ||||||||
\(238\) | −1953.31 | −0.531993 | ||||||||
\(239\) | 3010.33 | 0.814735 | 0.407368 | − | 0.913264i | \(-0.366447\pi\) | ||||
0.407368 | + | 0.913264i | \(0.366447\pi\) | |||||||
\(240\) | 1838.06 | 0.494360 | ||||||||
\(241\) | 2988.16 | 0.798689 | 0.399344 | − | 0.916801i | \(-0.369238\pi\) | ||||
0.399344 | + | 0.916801i | \(0.369238\pi\) | |||||||
\(242\) | −4012.80 | −1.06592 | ||||||||
\(243\) | −2809.70 | −0.741738 | ||||||||
\(244\) | −1979.88 | −0.519463 | ||||||||
\(245\) | 2575.53 | 0.671612 | ||||||||
\(246\) | 5376.33 | 1.39342 | ||||||||
\(247\) | −2396.96 | −0.617469 | ||||||||
\(248\) | −310.695 | −0.0795531 | ||||||||
\(249\) | −1677.00 | −0.426809 | ||||||||
\(250\) | −3802.77 | −0.962034 | ||||||||
\(251\) | 687.024 | 0.172767 | 0.0863836 | − | 0.996262i | \(-0.472469\pi\) | ||||
0.0863836 | + | 0.996262i | \(0.472469\pi\) | |||||||
\(252\) | −925.197 | −0.231278 | ||||||||
\(253\) | −6475.67 | −1.60918 | ||||||||
\(254\) | −3028.38 | −0.748099 | ||||||||
\(255\) | −5119.00 | −1.25711 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2247.34 | −0.545468 | −0.272734 | − | 0.962089i | \(-0.587928\pi\) | ||||
−0.272734 | + | 0.962089i | \(0.587928\pi\) | |||||||
\(258\) | 3137.62 | 0.757131 | ||||||||
\(259\) | 810.957 | 0.194558 | ||||||||
\(260\) | −1398.08 | −0.333482 | ||||||||
\(261\) | −1342.71 | −0.318437 | ||||||||
\(262\) | −2974.70 | −0.701441 | ||||||||
\(263\) | 582.840 | 0.136652 | 0.0683259 | − | 0.997663i | \(-0.478234\pi\) | ||||
0.0683259 | + | 0.997663i | \(0.478234\pi\) | |||||||
\(264\) | −2832.15 | −0.660254 | ||||||||
\(265\) | 6.71638 | 0.00155692 | ||||||||
\(266\) | 5635.49 | 1.29900 | ||||||||
\(267\) | 3429.69 | 0.786118 | ||||||||
\(268\) | −2100.58 | −0.478781 | ||||||||
\(269\) | −1121.78 | −0.254260 | −0.127130 | − | 0.991886i | \(-0.540577\pi\) | ||||
−0.127130 | + | 0.991886i | \(0.540577\pi\) | |||||||
\(270\) | 3778.81 | 0.851745 | ||||||||
\(271\) | −52.7185 | −0.0118171 | −0.00590853 | − | 0.999983i | \(-0.501881\pi\) | ||||
−0.00590853 | + | 0.999983i | \(0.501881\pi\) | |||||||
\(272\) | −712.959 | −0.158932 | ||||||||
\(273\) | 2504.23 | 0.555175 | ||||||||
\(274\) | −1217.58 | −0.268454 | ||||||||
\(275\) | 13080.7 | 2.86836 | ||||||||
\(276\) | −2747.66 | −0.599238 | ||||||||
\(277\) | −3642.45 | −0.790084 | −0.395042 | − | 0.918663i | \(-0.629270\pi\) | ||||
−0.395042 | + | 0.918663i | \(0.629270\pi\) | |||||||
\(278\) | −2369.90 | −0.511286 | ||||||||
\(279\) | 409.848 | 0.0879460 | ||||||||
\(280\) | 3287.03 | 0.701563 | ||||||||
\(281\) | 6839.66 | 1.45203 | 0.726014 | − | 0.687680i | \(-0.241371\pi\) | ||||
0.726014 | + | 0.687680i | \(0.241371\pi\) | |||||||
\(282\) | −3371.59 | −0.711968 | ||||||||
\(283\) | 5729.18 | 1.20341 | 0.601704 | − | 0.798719i | \(-0.294489\pi\) | ||||
0.601704 | + | 0.798719i | \(0.294489\pi\) | |||||||
\(284\) | −4059.98 | −0.848294 | ||||||||
\(285\) | 14768.8 | 3.06958 | ||||||||
\(286\) | 2154.22 | 0.445390 | ||||||||
\(287\) | 9614.56 | 1.97745 | ||||||||
\(288\) | −337.698 | −0.0690939 | ||||||||
\(289\) | −2927.41 | −0.595850 | ||||||||
\(290\) | 4770.38 | 0.965953 | ||||||||
\(291\) | 472.979 | 0.0952801 | ||||||||
\(292\) | −57.8909 | −0.0116021 | ||||||||
\(293\) | 4372.85 | 0.871894 | 0.435947 | − | 0.899972i | \(-0.356414\pi\) | ||||
0.435947 | + | 0.899972i | \(0.356414\pi\) | |||||||
\(294\) | −1683.85 | −0.334027 | ||||||||
\(295\) | 13085.0 | 2.58250 | ||||||||
\(296\) | 296.000 | 0.0581238 | ||||||||
\(297\) | −5822.54 | −1.13757 | ||||||||
\(298\) | 1495.88 | 0.290785 | ||||||||
\(299\) | 2089.95 | 0.404230 | ||||||||
\(300\) | 5550.22 | 1.06814 | ||||||||
\(301\) | 5611.05 | 1.07447 | ||||||||
\(302\) | −2545.57 | −0.485037 | ||||||||
\(303\) | −10950.0 | −2.07610 | ||||||||
\(304\) | 2056.96 | 0.388075 | ||||||||
\(305\) | −9278.91 | −1.74200 | ||||||||
\(306\) | 940.487 | 0.175700 | ||||||||
\(307\) | −5480.70 | −1.01889 | −0.509446 | − | 0.860502i | \(-0.670150\pi\) | ||||
−0.509446 | + | 0.860502i | \(0.670150\pi\) | |||||||
\(308\) | −5064.78 | −0.936989 | ||||||||
\(309\) | 2484.52 | 0.457409 | ||||||||
\(310\) | −1456.10 | −0.266778 | ||||||||
\(311\) | −4414.78 | −0.804949 | −0.402475 | − | 0.915431i | \(-0.631850\pi\) | ||||
−0.402475 | + | 0.915431i | \(0.631850\pi\) | |||||||
\(312\) | 914.045 | 0.165858 | ||||||||
\(313\) | −2574.12 | −0.464849 | −0.232424 | − | 0.972614i | \(-0.574666\pi\) | ||||
−0.232424 | + | 0.972614i | \(0.574666\pi\) | |||||||
\(314\) | −3990.92 | −0.717263 | ||||||||
\(315\) | −4336.03 | −0.775579 | ||||||||
\(316\) | 3920.67 | 0.697959 | ||||||||
\(317\) | 8967.38 | 1.58883 | 0.794414 | − | 0.607377i | \(-0.207778\pi\) | ||||
0.794414 | + | 0.607377i | \(0.207778\pi\) | |||||||
\(318\) | −4.39107 | −0.000774337 0 | ||||||||
\(319\) | −7350.38 | −1.29010 | ||||||||
\(320\) | 1199.77 | 0.209591 | ||||||||
\(321\) | 7863.66 | 1.36731 | ||||||||
\(322\) | −4913.68 | −0.850400 | ||||||||
\(323\) | −5728.63 | −0.986840 | ||||||||
\(324\) | −3610.26 | −0.619044 | ||||||||
\(325\) | −4221.66 | −0.720540 | ||||||||
\(326\) | −6646.36 | −1.12916 | ||||||||
\(327\) | 6464.37 | 1.09321 | ||||||||
\(328\) | 3509.32 | 0.590762 | ||||||||
\(329\) | −6029.45 | −1.01038 | ||||||||
\(330\) | −13273.2 | −2.21413 | ||||||||
\(331\) | −9429.00 | −1.56575 | −0.782877 | − | 0.622177i | \(-0.786249\pi\) | ||||
−0.782877 | + | 0.622177i | \(0.786249\pi\) | |||||||
\(332\) | −1094.64 | −0.180952 | ||||||||
\(333\) | −390.463 | −0.0642560 | ||||||||
\(334\) | 7327.27 | 1.20039 | ||||||||
\(335\) | −9844.56 | −1.60557 | ||||||||
\(336\) | −2149.01 | −0.348923 | ||||||||
\(337\) | 7683.47 | 1.24197 | 0.620987 | − | 0.783821i | \(-0.286732\pi\) | ||||
0.620987 | + | 0.783821i | \(0.286732\pi\) | |||||||
\(338\) | 3698.75 | 0.595223 | ||||||||
\(339\) | 9592.46 | 1.53685 | ||||||||
\(340\) | −3341.35 | −0.532971 | ||||||||
\(341\) | 2243.62 | 0.356301 | ||||||||
\(342\) | −2713.40 | −0.429017 | ||||||||
\(343\) | 4506.55 | 0.709419 | ||||||||
\(344\) | 2048.04 | 0.320997 | ||||||||
\(345\) | −12877.2 | −2.00952 | ||||||||
\(346\) | 6188.64 | 0.961570 | ||||||||
\(347\) | −3186.70 | −0.493000 | −0.246500 | − | 0.969143i | \(-0.579281\pi\) | ||||
−0.246500 | + | 0.969143i | \(0.579281\pi\) | |||||||
\(348\) | −3118.81 | −0.480418 | ||||||||
\(349\) | −1658.03 | −0.254304 | −0.127152 | − | 0.991883i | \(-0.540584\pi\) | ||||
−0.127152 | + | 0.991883i | \(0.540584\pi\) | |||||||
\(350\) | 9925.54 | 1.51584 | ||||||||
\(351\) | 1879.16 | 0.285761 | ||||||||
\(352\) | −1848.65 | −0.279924 | ||||||||
\(353\) | 2121.24 | 0.319837 | 0.159918 | − | 0.987130i | \(-0.448877\pi\) | ||||
0.159918 | + | 0.987130i | \(0.448877\pi\) | |||||||
\(354\) | −8554.77 | −1.28441 | ||||||||
\(355\) | −19027.5 | −2.84471 | ||||||||
\(356\) | 2238.68 | 0.333286 | ||||||||
\(357\) | 5984.99 | 0.887281 | ||||||||
\(358\) | −2495.33 | −0.368386 | ||||||||
\(359\) | −6278.89 | −0.923084 | −0.461542 | − | 0.887118i | \(-0.652704\pi\) | ||||
−0.461542 | + | 0.887118i | \(0.652704\pi\) | |||||||
\(360\) | −1582.65 | −0.231703 | ||||||||
\(361\) | 9668.66 | 1.40963 | ||||||||
\(362\) | −5721.96 | −0.830773 | ||||||||
\(363\) | 12295.3 | 1.77779 | ||||||||
\(364\) | 1634.60 | 0.235374 | ||||||||
\(365\) | −271.311 | −0.0389070 | ||||||||
\(366\) | 6066.41 | 0.866384 | ||||||||
\(367\) | −9201.10 | −1.30870 | −0.654351 | − | 0.756191i | \(-0.727058\pi\) | ||||
−0.654351 | + | 0.756191i | \(0.727058\pi\) | |||||||
\(368\) | −1793.50 | −0.254056 | ||||||||
\(369\) | −4629.26 | −0.653088 | ||||||||
\(370\) | 1387.23 | 0.194916 | ||||||||
\(371\) | −7.85262 | −0.00109889 | ||||||||
\(372\) | 951.978 | 0.132682 | ||||||||
\(373\) | 528.312 | 0.0733377 | 0.0366688 | − | 0.999327i | \(-0.488325\pi\) | ||||
0.0366688 | + | 0.999327i | \(0.488325\pi\) | |||||||
\(374\) | 5148.48 | 0.711822 | ||||||||
\(375\) | 11651.8 | 1.60452 | ||||||||
\(376\) | −2200.75 | −0.301849 | ||||||||
\(377\) | 2372.25 | 0.324077 | ||||||||
\(378\) | −4418.09 | −0.601169 | ||||||||
\(379\) | −2504.25 | −0.339406 | −0.169703 | − | 0.985495i | \(-0.554281\pi\) | ||||
−0.169703 | + | 0.985495i | \(0.554281\pi\) | |||||||
\(380\) | 9640.14 | 1.30139 | ||||||||
\(381\) | 9279.03 | 1.24771 | ||||||||
\(382\) | 2353.87 | 0.315274 | ||||||||
\(383\) | −5155.87 | −0.687866 | −0.343933 | − | 0.938994i | \(-0.611759\pi\) | ||||
−0.343933 | + | 0.938994i | \(0.611759\pi\) | |||||||
\(384\) | −784.391 | −0.104240 | ||||||||
\(385\) | −23736.6 | −3.14215 | ||||||||
\(386\) | −3966.57 | −0.523040 | ||||||||
\(387\) | −2701.63 | −0.354862 | ||||||||
\(388\) | 308.730 | 0.0403953 | ||||||||
\(389\) | 10222.9 | 1.33245 | 0.666224 | − | 0.745752i | \(-0.267910\pi\) | ||||
0.666224 | + | 0.745752i | \(0.267910\pi\) | |||||||
\(390\) | 4283.76 | 0.556197 | ||||||||
\(391\) | 4994.88 | 0.646041 | ||||||||
\(392\) | −1099.11 | −0.141616 | ||||||||
\(393\) | 9114.55 | 1.16989 | ||||||||
\(394\) | 5495.42 | 0.702678 | ||||||||
\(395\) | 18374.6 | 2.34057 | ||||||||
\(396\) | 2438.61 | 0.309457 | ||||||||
\(397\) | 6440.88 | 0.814254 | 0.407127 | − | 0.913372i | \(-0.366531\pi\) | ||||
0.407127 | + | 0.913372i | \(0.366531\pi\) | |||||||
\(398\) | −3338.97 | −0.420522 | ||||||||
\(399\) | −17267.3 | −2.16653 | ||||||||
\(400\) | 3622.83 | 0.452854 | ||||||||
\(401\) | −9165.65 | −1.14142 | −0.570712 | − | 0.821150i | \(-0.693333\pi\) | ||||
−0.570712 | + | 0.821150i | \(0.693333\pi\) | |||||||
\(402\) | 6436.23 | 0.798532 | ||||||||
\(403\) | −724.102 | −0.0895039 | ||||||||
\(404\) | −7147.42 | −0.880192 | ||||||||
\(405\) | −16919.8 | −2.07593 | ||||||||
\(406\) | −5577.40 | −0.681778 | ||||||||
\(407\) | −2137.50 | −0.260324 | ||||||||
\(408\) | 2184.53 | 0.265074 | ||||||||
\(409\) | 5305.56 | 0.641426 | 0.320713 | − | 0.947176i | \(-0.396078\pi\) | ||||
0.320713 | + | 0.947176i | \(0.396078\pi\) | |||||||
\(410\) | 16446.8 | 1.98109 | ||||||||
\(411\) | 3730.69 | 0.447741 | ||||||||
\(412\) | 1621.73 | 0.193925 | ||||||||
\(413\) | −15298.6 | −1.82275 | ||||||||
\(414\) | 2365.86 | 0.280859 | ||||||||
\(415\) | −5130.12 | −0.606814 | ||||||||
\(416\) | 596.630 | 0.0703178 | ||||||||
\(417\) | 7261.45 | 0.852745 | ||||||||
\(418\) | −14853.9 | −1.73810 | ||||||||
\(419\) | −1097.10 | −0.127916 | −0.0639582 | − | 0.997953i | \(-0.520372\pi\) | ||||
−0.0639582 | + | 0.997953i | \(0.520372\pi\) | |||||||
\(420\) | −10071.6 | −1.17010 | ||||||||
\(421\) | 6390.76 | 0.739826 | 0.369913 | − | 0.929066i | \(-0.379387\pi\) | ||||
0.369913 | + | 0.929066i | \(0.379387\pi\) | |||||||
\(422\) | −3728.87 | −0.430139 | ||||||||
\(423\) | 2903.08 | 0.333695 | ||||||||
\(424\) | −2.86621 | −0.000328291 0 | ||||||||
\(425\) | −10089.6 | −1.15157 | ||||||||
\(426\) | 12439.9 | 1.41482 | ||||||||
\(427\) | 10848.6 | 1.22952 | ||||||||
\(428\) | 5132.89 | 0.579691 | ||||||||
\(429\) | −6600.58 | −0.742841 | ||||||||
\(430\) | 9598.33 | 1.07645 | ||||||||
\(431\) | 14874.6 | 1.66238 | 0.831190 | − | 0.555989i | \(-0.187660\pi\) | ||||
0.831190 | + | 0.555989i | \(0.187660\pi\) | |||||||
\(432\) | −1612.60 | −0.179598 | ||||||||
\(433\) | 9227.03 | 1.02407 | 0.512036 | − | 0.858964i | \(-0.328892\pi\) | ||||
0.512036 | + | 0.858964i | \(0.328892\pi\) | |||||||
\(434\) | 1702.44 | 0.188294 | ||||||||
\(435\) | −14616.6 | −1.61106 | ||||||||
\(436\) | 4219.52 | 0.463483 | ||||||||
\(437\) | −14410.7 | −1.57748 | ||||||||
\(438\) | 177.379 | 0.0193505 | ||||||||
\(439\) | 2282.58 | 0.248159 | 0.124079 | − | 0.992272i | \(-0.460402\pi\) | ||||
0.124079 | + | 0.992272i | \(0.460402\pi\) | |||||||
\(440\) | −8663.87 | −0.938713 | ||||||||
\(441\) | 1449.87 | 0.156556 | ||||||||
\(442\) | −1661.61 | −0.178812 | ||||||||
\(443\) | 7122.03 | 0.763833 | 0.381916 | − | 0.924197i | \(-0.375264\pi\) | ||||
0.381916 | + | 0.924197i | \(0.375264\pi\) | |||||||
\(444\) | −906.952 | −0.0969415 | ||||||||
\(445\) | 10491.8 | 1.11766 | ||||||||
\(446\) | 4401.08 | 0.467258 | ||||||||
\(447\) | −4583.42 | −0.484985 | ||||||||
\(448\) | −1402.74 | −0.147931 | ||||||||
\(449\) | 2321.34 | 0.243988 | 0.121994 | − | 0.992531i | \(-0.461071\pi\) | ||||
0.121994 | + | 0.992531i | \(0.461071\pi\) | |||||||
\(450\) | −4778.99 | −0.500630 | ||||||||
\(451\) | −25341.8 | −2.64590 | ||||||||
\(452\) | 6261.34 | 0.651568 | ||||||||
\(453\) | 7799.70 | 0.808966 | ||||||||
\(454\) | 4040.11 | 0.417647 | ||||||||
\(455\) | 7660.71 | 0.789318 | ||||||||
\(456\) | −6302.58 | −0.647249 | ||||||||
\(457\) | 7882.87 | 0.806882 | 0.403441 | − | 0.915006i | \(-0.367814\pi\) | ||||
0.403441 | + | 0.915006i | \(0.367814\pi\) | |||||||
\(458\) | 3986.27 | 0.406695 | ||||||||
\(459\) | 4491.10 | 0.456703 | ||||||||
\(460\) | −8405.39 | −0.851964 | ||||||||
\(461\) | −17965.7 | −1.81507 | −0.907534 | − | 0.419979i | \(-0.862038\pi\) | ||||
−0.907534 | + | 0.419979i | \(0.862038\pi\) | |||||||
\(462\) | 15518.6 | 1.56275 | ||||||||
\(463\) | −15536.2 | −1.55946 | −0.779729 | − | 0.626118i | \(-0.784643\pi\) | ||||
−0.779729 | + | 0.626118i | \(0.784643\pi\) | |||||||
\(464\) | −2035.76 | −0.203680 | ||||||||
\(465\) | 4461.54 | 0.444944 | ||||||||
\(466\) | 5644.40 | 0.561098 | ||||||||
\(467\) | 8320.10 | 0.824428 | 0.412214 | − | 0.911087i | \(-0.364756\pi\) | ||||
0.412214 | + | 0.911087i | \(0.364756\pi\) | |||||||
\(468\) | −787.034 | −0.0777364 | ||||||||
\(469\) | 11510.0 | 1.13322 | ||||||||
\(470\) | −10314.0 | −1.01224 | ||||||||
\(471\) | 12228.3 | 1.19628 | ||||||||
\(472\) | −5584.00 | −0.544544 | ||||||||
\(473\) | −14789.5 | −1.43767 | ||||||||
\(474\) | −12013.0 | −1.16409 | ||||||||
\(475\) | 29109.4 | 2.81186 | ||||||||
\(476\) | 3906.62 | 0.376176 | ||||||||
\(477\) | 3.78091 | 0.000362927 0 | ||||||||
\(478\) | −6020.65 | −0.576105 | ||||||||
\(479\) | 12756.6 | 1.21684 | 0.608418 | − | 0.793616i | \(-0.291804\pi\) | ||||
0.608418 | + | 0.793616i | \(0.291804\pi\) | |||||||
\(480\) | −3676.12 | −0.349565 | ||||||||
\(481\) | 689.854 | 0.0653942 | ||||||||
\(482\) | −5976.31 | −0.564758 | ||||||||
\(483\) | 15055.7 | 1.41834 | ||||||||
\(484\) | 8025.61 | 0.753720 | ||||||||
\(485\) | 1446.89 | 0.135464 | ||||||||
\(486\) | 5619.40 | 0.524488 | ||||||||
\(487\) | −10017.3 | −0.932087 | −0.466044 | − | 0.884762i | \(-0.654321\pi\) | ||||
−0.466044 | + | 0.884762i | \(0.654321\pi\) | |||||||
\(488\) | 3959.77 | 0.367316 | ||||||||
\(489\) | 20364.6 | 1.88327 | ||||||||
\(490\) | −5151.07 | −0.474901 | ||||||||
\(491\) | −15622.5 | −1.43591 | −0.717957 | − | 0.696088i | \(-0.754923\pi\) | ||||
−0.717957 | + | 0.696088i | \(0.754923\pi\) | |||||||
\(492\) | −10752.7 | −0.985299 | ||||||||
\(493\) | 5669.57 | 0.517941 | ||||||||
\(494\) | 4793.92 | 0.436617 | ||||||||
\(495\) | 11428.8 | 1.03775 | ||||||||
\(496\) | 621.390 | 0.0562525 | ||||||||
\(497\) | 22246.4 | 2.00782 | ||||||||
\(498\) | 3354.00 | 0.301800 | ||||||||
\(499\) | −13165.1 | −1.18107 | −0.590534 | − | 0.807013i | \(-0.701083\pi\) | ||||
−0.590534 | + | 0.807013i | \(0.701083\pi\) | |||||||
\(500\) | 7605.54 | 0.680261 | ||||||||
\(501\) | −22451.0 | −2.00207 | ||||||||
\(502\) | −1374.05 | −0.122165 | ||||||||
\(503\) | 7491.62 | 0.664085 | 0.332042 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332042 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(504\) | 1850.39 | 0.163538 | ||||||||
\(505\) | −33497.1 | −2.95168 | ||||||||
\(506\) | 12951.3 | 1.13786 | ||||||||
\(507\) | −11333.1 | −0.992741 | ||||||||
\(508\) | 6056.75 | 0.528986 | ||||||||
\(509\) | −19209.6 | −1.67279 | −0.836397 | − | 0.548124i | \(-0.815342\pi\) | ||||
−0.836397 | + | 0.548124i | \(0.815342\pi\) | |||||||
\(510\) | 10238.0 | 0.888914 | ||||||||
\(511\) | 317.209 | 0.0274609 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −12957.3 | −1.11516 | ||||||||
\(514\) | 4494.69 | 0.385704 | ||||||||
\(515\) | 7600.41 | 0.650319 | ||||||||
\(516\) | −6275.25 | −0.535373 | ||||||||
\(517\) | 15892.3 | 1.35192 | ||||||||
\(518\) | −1621.91 | −0.137573 | ||||||||
\(519\) | −18962.2 | −1.60375 | ||||||||
\(520\) | 2796.16 | 0.235807 | ||||||||
\(521\) | −22521.1 | −1.89380 | −0.946899 | − | 0.321530i | \(-0.895803\pi\) | ||||
−0.946899 | + | 0.321530i | \(0.895803\pi\) | |||||||
\(522\) | 2685.43 | 0.225169 | ||||||||
\(523\) | 6652.48 | 0.556200 | 0.278100 | − | 0.960552i | \(-0.410295\pi\) | ||||
0.278100 | + | 0.960552i | \(0.410295\pi\) | |||||||
\(524\) | 5949.40 | 0.495993 | ||||||||
\(525\) | −30412.1 | −2.52818 | ||||||||
\(526\) | −1165.68 | −0.0966275 | ||||||||
\(527\) | −1730.57 | −0.143045 | ||||||||
\(528\) | 5664.31 | 0.466870 | ||||||||
\(529\) | 397.967 | 0.0327087 | ||||||||
\(530\) | −13.4328 | −0.00110091 | ||||||||
\(531\) | 7366.03 | 0.601994 | ||||||||
\(532\) | −11271.0 | −0.918532 | ||||||||
\(533\) | 8178.78 | 0.664657 | ||||||||
\(534\) | −6859.38 | −0.555870 | ||||||||
\(535\) | 24055.8 | 1.94397 | ||||||||
\(536\) | 4201.16 | 0.338549 | ||||||||
\(537\) | 7645.76 | 0.614411 | ||||||||
\(538\) | 2243.56 | 0.179789 | ||||||||
\(539\) | 7936.96 | 0.634265 | ||||||||
\(540\) | −7557.63 | −0.602275 | ||||||||
\(541\) | 2547.01 | 0.202411 | 0.101205 | − | 0.994866i | \(-0.467730\pi\) | ||||
0.101205 | + | 0.994866i | \(0.467730\pi\) | |||||||
\(542\) | 105.437 | 0.00835592 | ||||||||
\(543\) | 17532.3 | 1.38560 | ||||||||
\(544\) | 1425.92 | 0.112382 | ||||||||
\(545\) | 19775.2 | 1.55427 | ||||||||
\(546\) | −5008.46 | −0.392568 | ||||||||
\(547\) | −12621.3 | −0.986556 | −0.493278 | − | 0.869872i | \(-0.664201\pi\) | ||||
−0.493278 | + | 0.869872i | \(0.664201\pi\) | |||||||
\(548\) | 2435.15 | 0.189826 | ||||||||
\(549\) | −5223.45 | −0.406068 | ||||||||
\(550\) | −26161.5 | −2.02823 | ||||||||
\(551\) | −16357.3 | −1.26469 | ||||||||
\(552\) | 5495.32 | 0.423726 | ||||||||
\(553\) | −21483.1 | −1.65200 | ||||||||
\(554\) | 7284.89 | 0.558674 | ||||||||
\(555\) | −4250.52 | −0.325089 | ||||||||
\(556\) | 4739.81 | 0.361534 | ||||||||
\(557\) | −7719.22 | −0.587206 | −0.293603 | − | 0.955927i | \(-0.594854\pi\) | ||||
−0.293603 | + | 0.955927i | \(0.594854\pi\) | |||||||
\(558\) | −819.696 | −0.0621872 | ||||||||
\(559\) | 4773.13 | 0.361148 | ||||||||
\(560\) | −6574.06 | −0.496080 | ||||||||
\(561\) | −15775.1 | −1.18721 | ||||||||
\(562\) | −13679.3 | −1.02674 | ||||||||
\(563\) | 16041.0 | 1.20080 | 0.600399 | − | 0.799701i | \(-0.295008\pi\) | ||||
0.600399 | + | 0.799701i | \(0.295008\pi\) | |||||||
\(564\) | 6743.17 | 0.503437 | ||||||||
\(565\) | 29344.4 | 2.18500 | ||||||||
\(566\) | −11458.4 | −0.850938 | ||||||||
\(567\) | 19782.2 | 1.46521 | ||||||||
\(568\) | 8119.96 | 0.599834 | ||||||||
\(569\) | −22137.9 | −1.63105 | −0.815527 | − | 0.578719i | \(-0.803553\pi\) | ||||
−0.815527 | + | 0.578719i | \(0.803553\pi\) | |||||||
\(570\) | −29537.6 | −2.17052 | ||||||||
\(571\) | 2259.08 | 0.165569 | 0.0827843 | − | 0.996567i | \(-0.473619\pi\) | ||||
0.0827843 | + | 0.996567i | \(0.473619\pi\) | |||||||
\(572\) | −4308.43 | −0.314938 | ||||||||
\(573\) | −7212.33 | −0.525828 | ||||||||
\(574\) | −19229.1 | −1.39827 | ||||||||
\(575\) | −25381.0 | −1.84080 | ||||||||
\(576\) | 675.395 | 0.0488567 | ||||||||
\(577\) | −3558.04 | −0.256713 | −0.128356 | − | 0.991728i | \(-0.540970\pi\) | ||||
−0.128356 | + | 0.991728i | \(0.540970\pi\) | |||||||
\(578\) | 5854.82 | 0.421329 | ||||||||
\(579\) | 12153.7 | 0.872349 | ||||||||
\(580\) | −9540.76 | −0.683032 | ||||||||
\(581\) | 5998.00 | 0.428294 | ||||||||
\(582\) | −945.957 | −0.0673732 | ||||||||
\(583\) | 20.6977 | 0.00147035 | ||||||||
\(584\) | 115.782 | 0.00820391 | ||||||||
\(585\) | −3688.51 | −0.260686 | ||||||||
\(586\) | −8745.71 | −0.616522 | ||||||||
\(587\) | −3589.31 | −0.252379 | −0.126190 | − | 0.992006i | \(-0.540275\pi\) | ||||
−0.126190 | + | 0.992006i | \(0.540275\pi\) | |||||||
\(588\) | 3367.69 | 0.236193 | ||||||||
\(589\) | 4992.87 | 0.349283 | ||||||||
\(590\) | −26170.0 | −1.82610 | ||||||||
\(591\) | −16838.1 | −1.17196 | ||||||||
\(592\) | −592.000 | −0.0410997 | ||||||||
\(593\) | −13372.9 | −0.926069 | −0.463035 | − | 0.886340i | \(-0.653239\pi\) | ||||
−0.463035 | + | 0.886340i | \(0.653239\pi\) | |||||||
\(594\) | 11645.1 | 0.804382 | ||||||||
\(595\) | 18308.7 | 1.26149 | ||||||||
\(596\) | −2991.76 | −0.205616 | ||||||||
\(597\) | 10230.7 | 0.701365 | ||||||||
\(598\) | −4179.90 | −0.285834 | ||||||||
\(599\) | 18874.1 | 1.28743 | 0.643717 | − | 0.765264i | \(-0.277391\pi\) | ||||
0.643717 | + | 0.765264i | \(0.277391\pi\) | |||||||
\(600\) | −11100.4 | −0.755290 | ||||||||
\(601\) | 9262.10 | 0.628634 | 0.314317 | − | 0.949318i | \(-0.398225\pi\) | ||||
0.314317 | + | 0.949318i | \(0.398225\pi\) | |||||||
\(602\) | −11222.1 | −0.759766 | ||||||||
\(603\) | −5541.88 | −0.374266 | ||||||||
\(604\) | 5091.14 | 0.342973 | ||||||||
\(605\) | 37612.8 | 2.52757 | ||||||||
\(606\) | 21899.9 | 1.46802 | ||||||||
\(607\) | 14170.9 | 0.947580 | 0.473790 | − | 0.880638i | \(-0.342886\pi\) | ||||
0.473790 | + | 0.880638i | \(0.342886\pi\) | |||||||
\(608\) | −4113.92 | −0.274410 | ||||||||
\(609\) | 17089.3 | 1.13710 | ||||||||
\(610\) | 18557.8 | 1.23178 | ||||||||
\(611\) | −5129.05 | −0.339606 | ||||||||
\(612\) | −1880.97 | −0.124238 | ||||||||
\(613\) | −5229.34 | −0.344553 | −0.172277 | − | 0.985049i | \(-0.555112\pi\) | ||||
−0.172277 | + | 0.985049i | \(0.555112\pi\) | |||||||
\(614\) | 10961.4 | 0.720466 | ||||||||
\(615\) | −50393.4 | −3.30416 | ||||||||
\(616\) | 10129.6 | 0.662551 | ||||||||
\(617\) | 22237.1 | 1.45094 | 0.725470 | − | 0.688253i | \(-0.241622\pi\) | ||||
0.725470 | + | 0.688253i | \(0.241622\pi\) | |||||||
\(618\) | −4969.04 | −0.323437 | ||||||||
\(619\) | −7885.16 | −0.512005 | −0.256003 | − | 0.966676i | \(-0.582406\pi\) | ||||
−0.256003 | + | 0.966676i | \(0.582406\pi\) | |||||||
\(620\) | 2912.20 | 0.188640 | ||||||||
\(621\) | 11297.7 | 0.730048 | ||||||||
\(622\) | 8829.56 | 0.569185 | ||||||||
\(623\) | −12266.7 | −0.788853 | ||||||||
\(624\) | −1828.09 | −0.117279 | ||||||||
\(625\) | 7340.76 | 0.469808 | ||||||||
\(626\) | 5148.24 | 0.328698 | ||||||||
\(627\) | 45512.7 | 2.89889 | ||||||||
\(628\) | 7981.83 | 0.507181 | ||||||||
\(629\) | 1648.72 | 0.104513 | ||||||||
\(630\) | 8672.05 | 0.548417 | ||||||||
\(631\) | 3424.85 | 0.216072 | 0.108036 | − | 0.994147i | \(-0.465544\pi\) | ||||
0.108036 | + | 0.994147i | \(0.465544\pi\) | |||||||
\(632\) | −7841.35 | −0.493532 | ||||||||
\(633\) | 11425.4 | 0.717405 | ||||||||
\(634\) | −17934.8 | −1.12347 | ||||||||
\(635\) | 28385.5 | 1.77393 | ||||||||
\(636\) | 8.78215 | 0.000547539 0 | ||||||||
\(637\) | −2561.56 | −0.159329 | ||||||||
\(638\) | 14700.8 | 0.912240 | ||||||||
\(639\) | −10711.3 | −0.663118 | ||||||||
\(640\) | −2399.54 | −0.148203 | ||||||||
\(641\) | −9634.06 | −0.593639 | −0.296819 | − | 0.954934i | \(-0.595926\pi\) | ||||
−0.296819 | + | 0.954934i | \(0.595926\pi\) | |||||||
\(642\) | −15727.3 | −0.966834 | ||||||||
\(643\) | 12056.9 | 0.739470 | 0.369735 | − | 0.929137i | \(-0.379449\pi\) | ||||
0.369735 | + | 0.929137i | \(0.379449\pi\) | |||||||
\(644\) | 9827.36 | 0.601323 | ||||||||
\(645\) | −29409.5 | −1.79535 | ||||||||
\(646\) | 11457.3 | 0.697801 | ||||||||
\(647\) | −16899.0 | −1.02684 | −0.513422 | − | 0.858137i | \(-0.671622\pi\) | ||||
−0.513422 | + | 0.858137i | \(0.671622\pi\) | |||||||
\(648\) | 7220.52 | 0.437730 | ||||||||
\(649\) | 40323.7 | 2.43889 | ||||||||
\(650\) | 8443.32 | 0.509499 | ||||||||
\(651\) | −5216.31 | −0.314045 | ||||||||
\(652\) | 13292.7 | 0.798440 | ||||||||
\(653\) | −15988.9 | −0.958182 | −0.479091 | − | 0.877765i | \(-0.659034\pi\) | ||||
−0.479091 | + | 0.877765i | \(0.659034\pi\) | |||||||
\(654\) | −12928.7 | −0.773017 | ||||||||
\(655\) | 27882.4 | 1.66329 | ||||||||
\(656\) | −7018.64 | −0.417732 | ||||||||
\(657\) | −152.731 | −0.00906943 | ||||||||
\(658\) | 12058.9 | 0.714445 | ||||||||
\(659\) | −22424.5 | −1.32554 | −0.662772 | − | 0.748822i | \(-0.730620\pi\) | ||||
−0.662772 | + | 0.748822i | \(0.730620\pi\) | |||||||
\(660\) | 26546.3 | 1.56563 | ||||||||
\(661\) | 5630.87 | 0.331339 | 0.165670 | − | 0.986181i | \(-0.447021\pi\) | ||||
0.165670 | + | 0.986181i | \(0.447021\pi\) | |||||||
\(662\) | 18858.0 | 1.10716 | ||||||||
\(663\) | 5091.23 | 0.298231 | ||||||||
\(664\) | 2189.28 | 0.127952 | ||||||||
\(665\) | −52822.6 | −3.08026 | ||||||||
\(666\) | 780.926 | 0.0454358 | ||||||||
\(667\) | 14262.2 | 0.827938 | ||||||||
\(668\) | −14654.5 | −0.848804 | ||||||||
\(669\) | −13485.0 | −0.779314 | ||||||||
\(670\) | 19689.1 | 1.13531 | ||||||||
\(671\) | −28594.6 | −1.64513 | ||||||||
\(672\) | 4298.02 | 0.246726 | ||||||||
\(673\) | 29088.7 | 1.66610 | 0.833050 | − | 0.553197i | \(-0.186592\pi\) | ||||
0.833050 | + | 0.553197i | \(0.186592\pi\) | |||||||
\(674\) | −15366.9 | −0.878209 | ||||||||
\(675\) | −22821.1 | −1.30131 | ||||||||
\(676\) | −7397.50 | −0.420887 | ||||||||
\(677\) | −12811.2 | −0.727291 | −0.363646 | − | 0.931537i | \(-0.618468\pi\) | ||||
−0.363646 | + | 0.931537i | \(0.618468\pi\) | |||||||
\(678\) | −19184.9 | −1.08671 | ||||||||
\(679\) | −1691.67 | −0.0956116 | ||||||||
\(680\) | 6682.70 | 0.376868 | ||||||||
\(681\) | −12379.0 | −0.696571 | ||||||||
\(682\) | −4487.23 | −0.251943 | ||||||||
\(683\) | −14164.5 | −0.793544 | −0.396772 | − | 0.917917i | \(-0.629870\pi\) | ||||
−0.396772 | + | 0.917917i | \(0.629870\pi\) | |||||||
\(684\) | 5426.80 | 0.303361 | ||||||||
\(685\) | 11412.6 | 0.636573 | ||||||||
\(686\) | −9013.09 | −0.501635 | ||||||||
\(687\) | −12214.1 | −0.678304 | ||||||||
\(688\) | −4096.08 | −0.226979 | ||||||||
\(689\) | −6.67995 | −0.000369355 0 | ||||||||
\(690\) | 25754.4 | 1.42094 | ||||||||
\(691\) | −13318.1 | −0.733204 | −0.366602 | − | 0.930378i | \(-0.619479\pi\) | ||||
−0.366602 | + | 0.930378i | \(0.619479\pi\) | |||||||
\(692\) | −12377.3 | −0.679933 | ||||||||
\(693\) | −13362.2 | −0.732451 | ||||||||
\(694\) | 6373.40 | 0.348604 | ||||||||
\(695\) | 22213.6 | 1.21239 | ||||||||
\(696\) | 6237.61 | 0.339707 | ||||||||
\(697\) | 19546.9 | 1.06226 | ||||||||
\(698\) | 3316.05 | 0.179820 | ||||||||
\(699\) | −17294.6 | −0.935824 | ||||||||
\(700\) | −19851.1 | −1.07186 | ||||||||
\(701\) | −20777.7 | −1.11949 | −0.559745 | − | 0.828665i | \(-0.689101\pi\) | ||||
−0.559745 | + | 0.828665i | \(0.689101\pi\) | |||||||
\(702\) | −3758.31 | −0.202063 | ||||||||
\(703\) | −4756.72 | −0.255196 | ||||||||
\(704\) | 3697.30 | 0.197936 | ||||||||
\(705\) | 31602.5 | 1.68825 | ||||||||
\(706\) | −4242.48 | −0.226159 | ||||||||
\(707\) | 39163.9 | 2.08332 | ||||||||
\(708\) | 17109.5 | 0.908214 | ||||||||
\(709\) | 16081.4 | 0.851833 | 0.425917 | − | 0.904762i | \(-0.359952\pi\) | ||||
0.425917 | + | 0.904762i | \(0.359952\pi\) | |||||||
\(710\) | 38055.0 | 2.01152 | ||||||||
\(711\) | 10343.8 | 0.545600 | ||||||||
\(712\) | −4477.36 | −0.235669 | ||||||||
\(713\) | −4353.36 | −0.228660 | ||||||||
\(714\) | −11970.0 | −0.627403 | ||||||||
\(715\) | −20191.9 | −1.05613 | ||||||||
\(716\) | 4990.66 | 0.260488 | ||||||||
\(717\) | 18447.4 | 0.960854 | ||||||||
\(718\) | 12557.8 | 0.652719 | ||||||||
\(719\) | −2335.59 | −0.121145 | −0.0605723 | − | 0.998164i | \(-0.519293\pi\) | ||||
−0.0605723 | + | 0.998164i | \(0.519293\pi\) | |||||||
\(720\) | 3165.31 | 0.163839 | ||||||||
\(721\) | −8886.20 | −0.459000 | ||||||||
\(722\) | −19337.3 | −0.996760 | ||||||||
\(723\) | 18311.6 | 0.941929 | ||||||||
\(724\) | 11443.9 | 0.587445 | ||||||||
\(725\) | −28809.4 | −1.47580 | ||||||||
\(726\) | −24590.7 | −1.25709 | ||||||||
\(727\) | −14356.4 | −0.732392 | −0.366196 | − | 0.930538i | \(-0.619340\pi\) | ||||
−0.366196 | + | 0.930538i | \(0.619340\pi\) | |||||||
\(728\) | −3269.20 | −0.166435 | ||||||||
\(729\) | 7151.27 | 0.363322 | ||||||||
\(730\) | 542.622 | 0.0275114 | ||||||||
\(731\) | 11407.6 | 0.577187 | ||||||||
\(732\) | −12132.8 | −0.612626 | ||||||||
\(733\) | −17167.8 | −0.865087 | −0.432544 | − | 0.901613i | \(-0.642384\pi\) | ||||
−0.432544 | + | 0.901613i | \(0.642384\pi\) | |||||||
\(734\) | 18402.2 | 0.925392 | ||||||||
\(735\) | 15783.0 | 0.792062 | ||||||||
\(736\) | 3586.99 | 0.179645 | ||||||||
\(737\) | −30337.7 | −1.51629 | ||||||||
\(738\) | 9258.52 | 0.461803 | ||||||||
\(739\) | 4163.21 | 0.207234 | 0.103617 | − | 0.994617i | \(-0.466958\pi\) | ||||
0.103617 | + | 0.994617i | \(0.466958\pi\) | |||||||
\(740\) | −2774.46 | −0.137826 | ||||||||
\(741\) | −14688.7 | −0.728209 | ||||||||
\(742\) | 15.7052 | 0.000777031 0 | ||||||||
\(743\) | 28806.1 | 1.42233 | 0.711166 | − | 0.703024i | \(-0.248167\pi\) | ||||
0.711166 | + | 0.703024i | \(0.248167\pi\) | |||||||
\(744\) | −1903.96 | −0.0938205 | ||||||||
\(745\) | −14021.2 | −0.689525 | ||||||||
\(746\) | −1056.62 | −0.0518576 | ||||||||
\(747\) | −2887.94 | −0.141452 | ||||||||
\(748\) | −10297.0 | −0.503334 | ||||||||
\(749\) | −28125.4 | −1.37207 | ||||||||
\(750\) | −23303.6 | −1.13457 | ||||||||
\(751\) | −3865.88 | −0.187840 | −0.0939200 | − | 0.995580i | \(-0.529940\pi\) | ||||
−0.0939200 | + | 0.995580i | \(0.529940\pi\) | |||||||
\(752\) | 4401.51 | 0.213439 | ||||||||
\(753\) | 4210.12 | 0.203752 | ||||||||
\(754\) | −4744.50 | −0.229157 | ||||||||
\(755\) | 23860.1 | 1.15014 | ||||||||
\(756\) | 8836.17 | 0.425091 | ||||||||
\(757\) | −22540.5 | −1.08223 | −0.541114 | − | 0.840949i | \(-0.681997\pi\) | ||||
−0.541114 | + | 0.840949i | \(0.681997\pi\) | |||||||
\(758\) | 5008.50 | 0.239996 | ||||||||
\(759\) | −39683.3 | −1.89778 | ||||||||
\(760\) | −19280.3 | −0.920222 | ||||||||
\(761\) | 40558.8 | 1.93200 | 0.966001 | − | 0.258538i | \(-0.0832408\pi\) | ||||
0.966001 | + | 0.258538i | \(0.0832408\pi\) | |||||||
\(762\) | −18558.1 | −0.882267 | ||||||||
\(763\) | −23120.6 | −1.09702 | ||||||||
\(764\) | −4707.75 | −0.222932 | ||||||||
\(765\) | −8815.37 | −0.416628 | ||||||||
\(766\) | 10311.7 | 0.486395 | ||||||||
\(767\) | −13014.0 | −0.612657 | ||||||||
\(768\) | 1568.78 | 0.0737090 | ||||||||
\(769\) | 38115.1 | 1.78734 | 0.893671 | − | 0.448722i | \(-0.148121\pi\) | ||||
0.893671 | + | 0.448722i | \(0.148121\pi\) | |||||||
\(770\) | 47473.1 | 2.22184 | ||||||||
\(771\) | −13771.8 | −0.643295 | ||||||||
\(772\) | 7933.15 | 0.369845 | ||||||||
\(773\) | 19667.0 | 0.915099 | 0.457549 | − | 0.889184i | \(-0.348727\pi\) | ||||
0.457549 | + | 0.889184i | \(0.348727\pi\) | |||||||
\(774\) | 5403.27 | 0.250926 | ||||||||
\(775\) | 8793.71 | 0.407586 | ||||||||
\(776\) | −617.460 | −0.0285638 | ||||||||
\(777\) | 4969.59 | 0.229451 | ||||||||
\(778\) | −20445.8 | −0.942183 | ||||||||
\(779\) | −56394.8 | −2.59378 | ||||||||
\(780\) | −8567.52 | −0.393290 | ||||||||
\(781\) | −58636.5 | −2.68653 | ||||||||
\(782\) | −9989.77 | −0.456820 | ||||||||
\(783\) | 12823.7 | 0.585290 | ||||||||
\(784\) | 2198.21 | 0.100137 | ||||||||
\(785\) | 37407.6 | 1.70081 | ||||||||
\(786\) | −18229.1 | −0.827240 | ||||||||
\(787\) | −42414.0 | −1.92109 | −0.960543 | − | 0.278132i | \(-0.910285\pi\) | ||||
−0.960543 | + | 0.278132i | \(0.910285\pi\) | |||||||
\(788\) | −10990.8 | −0.496869 | ||||||||
\(789\) | 3571.67 | 0.161160 | ||||||||
\(790\) | −36749.2 | −1.65504 | ||||||||
\(791\) | −34308.6 | −1.54219 | ||||||||
\(792\) | −4877.22 | −0.218819 | ||||||||
\(793\) | 9228.57 | 0.413261 | ||||||||
\(794\) | −12881.8 | −0.575764 | ||||||||
\(795\) | 41.1584 | 0.00183615 | ||||||||
\(796\) | 6677.95 | 0.297354 | ||||||||
\(797\) | −20257.9 | −0.900343 | −0.450171 | − | 0.892942i | \(-0.648637\pi\) | ||||
−0.450171 | + | 0.892942i | \(0.648637\pi\) | |||||||
\(798\) | 34534.6 | 1.53197 | ||||||||
\(799\) | −12258.2 | −0.542758 | ||||||||
\(800\) | −7245.66 | −0.320216 | ||||||||
\(801\) | 5906.23 | 0.260532 | ||||||||
\(802\) | 18331.3 | 0.807108 | ||||||||
\(803\) | −836.092 | −0.0367435 | ||||||||
\(804\) | −12872.5 | −0.564647 | ||||||||
\(805\) | 46056.9 | 2.01651 | ||||||||
\(806\) | 1448.20 | 0.0632888 | ||||||||
\(807\) | −6874.32 | −0.299861 | ||||||||
\(808\) | 14294.8 | 0.622390 | ||||||||
\(809\) | 22120.5 | 0.961327 | 0.480664 | − | 0.876905i | \(-0.340396\pi\) | ||||
0.480664 | + | 0.876905i | \(0.340396\pi\) | |||||||
\(810\) | 33839.7 | 1.46791 | ||||||||
\(811\) | −325.141 | −0.0140780 | −0.00703898 | − | 0.999975i | \(-0.502241\pi\) | ||||
−0.00703898 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(812\) | 11154.8 | 0.482090 | ||||||||
\(813\) | −323.062 | −0.0139364 | ||||||||
\(814\) | 4275.00 | 0.184077 | ||||||||
\(815\) | 62297.6 | 2.67753 | ||||||||
\(816\) | −4369.05 | −0.187436 | ||||||||
\(817\) | −32912.0 | −1.40936 | ||||||||
\(818\) | −10611.1 | −0.453557 | ||||||||
\(819\) | 4312.50 | 0.183994 | ||||||||
\(820\) | −32893.5 | −1.40084 | ||||||||
\(821\) | 28457.1 | 1.20969 | 0.604847 | − | 0.796341i | \(-0.293234\pi\) | ||||
0.604847 | + | 0.796341i | \(0.293234\pi\) | |||||||
\(822\) | −7461.38 | −0.316600 | ||||||||
\(823\) | −3812.08 | −0.161459 | −0.0807295 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807295 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(824\) | −3243.47 | −0.137126 | ||||||||
\(825\) | 80159.5 | 3.38278 | ||||||||
\(826\) | 30597.2 | 1.28888 | ||||||||
\(827\) | 27739.8 | 1.16639 | 0.583197 | − | 0.812330i | \(-0.301801\pi\) | ||||
0.583197 | + | 0.812330i | \(0.301801\pi\) | |||||||
\(828\) | −4731.72 | −0.198597 | ||||||||
\(829\) | 3649.24 | 0.152887 | 0.0764434 | − | 0.997074i | \(-0.475644\pi\) | ||||
0.0764434 | + | 0.997074i | \(0.475644\pi\) | |||||||
\(830\) | 10260.2 | 0.429082 | ||||||||
\(831\) | −22321.1 | −0.931782 | ||||||||
\(832\) | −1193.26 | −0.0497222 | ||||||||
\(833\) | −6122.02 | −0.254640 | ||||||||
\(834\) | −14522.9 | −0.602982 | ||||||||
\(835\) | −68679.9 | −2.84643 | ||||||||
\(836\) | 29707.8 | 1.22902 | ||||||||
\(837\) | −3914.28 | −0.161646 | ||||||||
\(838\) | 2194.21 | 0.0904506 | ||||||||
\(839\) | −10275.5 | −0.422826 | −0.211413 | − | 0.977397i | \(-0.567807\pi\) | ||||
−0.211413 | + | 0.977397i | \(0.567807\pi\) | |||||||
\(840\) | 20143.1 | 0.827385 | ||||||||
\(841\) | −8200.32 | −0.336230 | ||||||||
\(842\) | −12781.5 | −0.523136 | ||||||||
\(843\) | 41913.8 | 1.71244 | ||||||||
\(844\) | 7457.74 | 0.304154 | ||||||||
\(845\) | −34669.1 | −1.41142 | ||||||||
\(846\) | −5806.17 | −0.235958 | ||||||||
\(847\) | −43975.8 | −1.78398 | ||||||||
\(848\) | 5.73242 | 0.000232137 0 | ||||||||
\(849\) | 35108.7 | 1.41923 | ||||||||
\(850\) | 20179.1 | 0.814281 | ||||||||
\(851\) | 4147.46 | 0.167066 | ||||||||
\(852\) | −24879.8 | −1.00043 | ||||||||
\(853\) | 13200.6 | 0.529870 | 0.264935 | − | 0.964266i | \(-0.414649\pi\) | ||||
0.264935 | + | 0.964266i | \(0.414649\pi\) | |||||||
\(854\) | −21697.3 | −0.869398 | ||||||||
\(855\) | 25433.2 | 1.01731 | ||||||||
\(856\) | −10265.8 | −0.409903 | ||||||||
\(857\) | −11275.5 | −0.449431 | −0.224716 | − | 0.974424i | \(-0.572145\pi\) | ||||
−0.224716 | + | 0.974424i | \(0.572145\pi\) | |||||||
\(858\) | 13201.2 | 0.525268 | ||||||||
\(859\) | 35615.6 | 1.41465 | 0.707327 | − | 0.706886i | \(-0.249901\pi\) | ||||
0.707327 | + | 0.706886i | \(0.249901\pi\) | |||||||
\(860\) | −19196.7 | −0.761163 | ||||||||
\(861\) | 58918.5 | 2.33210 | ||||||||
\(862\) | −29749.3 | −1.17548 | ||||||||
\(863\) | −16687.2 | −0.658216 | −0.329108 | − | 0.944292i | \(-0.606748\pi\) | ||||
−0.329108 | + | 0.944292i | \(0.606748\pi\) | |||||||
\(864\) | 3225.21 | 0.126995 | ||||||||
\(865\) | −58007.3 | −2.28012 | ||||||||
\(866\) | −18454.1 | −0.724128 | ||||||||
\(867\) | −17939.3 | −0.702712 | ||||||||
\(868\) | −3404.87 | −0.133144 | ||||||||
\(869\) | 56624.6 | 2.21042 | ||||||||
\(870\) | 29233.2 | 1.13919 | ||||||||
\(871\) | 9791.15 | 0.380896 | ||||||||
\(872\) | −8439.04 | −0.327732 | ||||||||
\(873\) | 814.511 | 0.0315774 | ||||||||
\(874\) | 28821.5 | 1.11545 | ||||||||
\(875\) | −41674.1 | −1.61011 | ||||||||
\(876\) | −354.758 | −0.0136828 | ||||||||
\(877\) | 4058.29 | 0.156258 | 0.0781292 | − | 0.996943i | \(-0.475105\pi\) | ||||
0.0781292 | + | 0.996943i | \(0.475105\pi\) | |||||||
\(878\) | −4565.16 | −0.175475 | ||||||||
\(879\) | 26797.1 | 1.02826 | ||||||||
\(880\) | 17327.7 | 0.663770 | ||||||||
\(881\) | 7089.26 | 0.271105 | 0.135552 | − | 0.990770i | \(-0.456719\pi\) | ||||
0.135552 | + | 0.990770i | \(0.456719\pi\) | |||||||
\(882\) | −2899.73 | −0.110702 | ||||||||
\(883\) | −13613.9 | −0.518851 | −0.259425 | − | 0.965763i | \(-0.583533\pi\) | ||||
−0.259425 | + | 0.965763i | \(0.583533\pi\) | |||||||
\(884\) | 3323.23 | 0.126439 | ||||||||
\(885\) | 80185.5 | 3.04566 | ||||||||
\(886\) | −14244.1 | −0.540111 | ||||||||
\(887\) | 34658.8 | 1.31198 | 0.655991 | − | 0.754768i | \(-0.272251\pi\) | ||||
0.655991 | + | 0.754768i | \(0.272251\pi\) | |||||||
\(888\) | 1813.90 | 0.0685480 | ||||||||
\(889\) | −33187.6 | −1.25205 | ||||||||
\(890\) | −20983.6 | −0.790305 | ||||||||
\(891\) | −52141.4 | −1.96050 | ||||||||
\(892\) | −8802.16 | −0.330401 | ||||||||
\(893\) | 35366.1 | 1.32529 | ||||||||
\(894\) | 9166.84 | 0.342936 | ||||||||
\(895\) | 23389.2 | 0.873536 | ||||||||
\(896\) | 2805.47 | 0.104603 | ||||||||
\(897\) | 12807.3 | 0.476727 | ||||||||
\(898\) | −4642.68 | −0.172526 | ||||||||
\(899\) | −4941.40 | −0.183320 | ||||||||
\(900\) | 9557.98 | 0.353999 | ||||||||
\(901\) | −15.9648 | −0.000590304 0 | ||||||||
\(902\) | 50683.6 | 1.87093 | ||||||||
\(903\) | 34384.8 | 1.26717 | ||||||||
\(904\) | −12522.7 | −0.460728 | ||||||||
\(905\) | 53633.1 | 1.96997 | ||||||||
\(906\) | −15599.4 | −0.572026 | ||||||||
\(907\) | −28527.3 | −1.04436 | −0.522180 | − | 0.852836i | \(-0.674881\pi\) | ||||
−0.522180 | + | 0.852836i | \(0.674881\pi\) | |||||||
\(908\) | −8080.23 | −0.295321 | ||||||||
\(909\) | −18856.8 | −0.688053 | ||||||||
\(910\) | −15321.4 | −0.558132 | ||||||||
\(911\) | 25045.5 | 0.910862 | 0.455431 | − | 0.890271i | \(-0.349485\pi\) | ||||
0.455431 | + | 0.890271i | \(0.349485\pi\) | |||||||
\(912\) | 12605.2 | 0.457674 | ||||||||
\(913\) | −15809.4 | −0.573071 | ||||||||
\(914\) | −15765.7 | −0.570552 | ||||||||
\(915\) | −56861.7 | −2.05441 | ||||||||
\(916\) | −7972.55 | −0.287577 | ||||||||
\(917\) | −32599.4 | −1.17396 | ||||||||
\(918\) | −8982.20 | −0.322938 | ||||||||
\(919\) | 26149.1 | 0.938608 | 0.469304 | − | 0.883037i | \(-0.344505\pi\) | ||||
0.469304 | + | 0.883037i | \(0.344505\pi\) | |||||||
\(920\) | 16810.8 | 0.602430 | ||||||||
\(921\) | −33586.0 | −1.20163 | ||||||||
\(922\) | 35931.4 | 1.28345 | ||||||||
\(923\) | 18924.3 | 0.674864 | ||||||||
\(924\) | −31037.2 | −1.10503 | ||||||||
\(925\) | −8377.79 | −0.297795 | ||||||||
\(926\) | 31072.4 | 1.10270 | ||||||||
\(927\) | 4278.56 | 0.151593 | ||||||||
\(928\) | 4071.51 | 0.144024 | ||||||||
\(929\) | −31005.3 | −1.09499 | −0.547497 | − | 0.836807i | \(-0.684419\pi\) | ||||
−0.547497 | + | 0.836807i | \(0.684419\pi\) | |||||||
\(930\) | −8923.07 | −0.314623 | ||||||||
\(931\) | 17662.6 | 0.621772 | ||||||||
\(932\) | −11288.8 | −0.396756 | ||||||||
\(933\) | −27054.0 | −0.949313 | ||||||||
\(934\) | −16640.2 | −0.582959 | ||||||||
\(935\) | −48257.7 | −1.68791 | ||||||||
\(936\) | 1574.07 | 0.0549680 | ||||||||
\(937\) | 39648.0 | 1.38233 | 0.691166 | − | 0.722696i | \(-0.257098\pi\) | ||||
0.691166 | + | 0.722696i | \(0.257098\pi\) | |||||||
\(938\) | −23020.0 | −0.801310 | ||||||||
\(939\) | −15774.3 | −0.548217 | ||||||||
\(940\) | 20628.1 | 0.715760 | ||||||||
\(941\) | 19549.2 | 0.677242 | 0.338621 | − | 0.940923i | \(-0.390040\pi\) | ||||
0.338621 | + | 0.940923i | \(0.390040\pi\) | |||||||
\(942\) | −24456.6 | −0.845900 | ||||||||
\(943\) | 49171.5 | 1.69803 | ||||||||
\(944\) | 11168.0 | 0.385050 | ||||||||
\(945\) | 41411.6 | 1.42552 | ||||||||
\(946\) | 29578.9 | 1.01659 | ||||||||
\(947\) | 15025.4 | 0.515587 | 0.257793 | − | 0.966200i | \(-0.417005\pi\) | ||||
0.257793 | + | 0.966200i | \(0.417005\pi\) | |||||||
\(948\) | 24026.1 | 0.823134 | ||||||||
\(949\) | 269.839 | 0.00923009 | ||||||||
\(950\) | −58218.9 | −1.98828 | ||||||||
\(951\) | 54952.6 | 1.87377 | ||||||||
\(952\) | −7813.24 | −0.265996 | ||||||||
\(953\) | 1441.58 | 0.0490003 | 0.0245002 | − | 0.999700i | \(-0.492201\pi\) | ||||
0.0245002 | + | 0.999700i | \(0.492201\pi\) | |||||||
\(954\) | −7.56182 | −0.000256628 0 | ||||||||
\(955\) | −22063.3 | −0.747594 | ||||||||
\(956\) | 12041.3 | 0.407368 | ||||||||
\(957\) | −45043.5 | −1.52147 | ||||||||
\(958\) | −25513.2 | −0.860433 | ||||||||
\(959\) | −13343.3 | −0.449298 | ||||||||
\(960\) | 7352.25 | 0.247180 | ||||||||
\(961\) | −28282.7 | −0.949370 | ||||||||
\(962\) | −1379.71 | −0.0462407 | ||||||||
\(963\) | 13541.9 | 0.453149 | ||||||||
\(964\) | 11952.6 | 0.399344 | ||||||||
\(965\) | 37179.5 | 1.24026 | ||||||||
\(966\) | −30111.3 | −1.00291 | ||||||||
\(967\) | 15366.4 | 0.511012 | 0.255506 | − | 0.966807i | \(-0.417758\pi\) | ||||
0.255506 | + | 0.966807i | \(0.417758\pi\) | |||||||
\(968\) | −16051.2 | −0.532960 | ||||||||
\(969\) | −35105.3 | −1.16382 | ||||||||
\(970\) | −2893.79 | −0.0957875 | ||||||||
\(971\) | 22937.8 | 0.758094 | 0.379047 | − | 0.925377i | \(-0.376252\pi\) | ||||
0.379047 | + | 0.925377i | \(0.376252\pi\) | |||||||
\(972\) | −11238.8 | −0.370869 | ||||||||
\(973\) | −25971.5 | −0.855712 | ||||||||
\(974\) | 20034.6 | 0.659085 | ||||||||
\(975\) | −25870.6 | −0.849765 | ||||||||
\(976\) | −7919.53 | −0.259732 | ||||||||
\(977\) | −6065.55 | −0.198623 | −0.0993113 | − | 0.995056i | \(-0.531664\pi\) | ||||
−0.0993113 | + | 0.995056i | \(0.531664\pi\) | |||||||
\(978\) | −40729.2 | −1.33167 | ||||||||
\(979\) | 32332.3 | 1.05551 | ||||||||
\(980\) | 10302.1 | 0.335806 | ||||||||
\(981\) | 11132.2 | 0.362308 | ||||||||
\(982\) | 31245.0 | 1.01534 | ||||||||
\(983\) | −50064.8 | −1.62443 | −0.812216 | − | 0.583356i | \(-0.801739\pi\) | ||||
−0.812216 | + | 0.583356i | \(0.801739\pi\) | |||||||
\(984\) | 21505.3 | 0.696712 | ||||||||
\(985\) | −51509.6 | −1.66623 | ||||||||
\(986\) | −11339.1 | −0.366239 | ||||||||
\(987\) | −36948.8 | −1.19158 | ||||||||
\(988\) | −9587.84 | −0.308735 | ||||||||
\(989\) | 28696.5 | 0.922644 | ||||||||
\(990\) | −22857.6 | −0.733799 | ||||||||
\(991\) | −839.793 | −0.0269192 | −0.0134596 | − | 0.999909i | \(-0.504284\pi\) | ||||
−0.0134596 | + | 0.999909i | \(0.504284\pi\) | |||||||
\(992\) | −1242.78 | −0.0397765 | ||||||||
\(993\) | −57781.4 | −1.84656 | ||||||||
\(994\) | −44492.8 | −1.41975 | ||||||||
\(995\) | 31296.8 | 0.997162 | ||||||||
\(996\) | −6708.00 | −0.213405 | ||||||||
\(997\) | 22126.0 | 0.702847 | 0.351423 | − | 0.936217i | \(-0.385698\pi\) | ||||
0.351423 | + | 0.936217i | \(0.385698\pi\) | |||||||
\(998\) | 26330.3 | 0.835141 | ||||||||
\(999\) | 3729.15 | 0.118103 |
(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 | 74.4.a.c.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 666.4.a.n.1.1 | 3 | |||
4.3 | odd | 2 | 592.4.a.c.1.1 | 3 | |||
5.4 | even | 2 | 1850.4.a.i.1.1 | 3 | |||
8.3 | odd | 2 | 2368.4.a.f.1.3 | 3 | |||
8.5 | even | 2 | 2368.4.a.e.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.4.a.c.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
592.4.a.c.1.1 | 3 | 4.3 | odd | 2 | |||
666.4.a.n.1.1 | 3 | 3.2 | odd | 2 | |||
1850.4.a.i.1.1 | 3 | 5.4 | even | 2 | |||
2368.4.a.e.1.1 | 3 | 8.5 | even | 2 | |||
2368.4.a.f.1.3 | 3 | 8.3 | odd | 2 |