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: | \(0\) |
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 | 1.1 | ||
Root | \(4.10376\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.51797 | −1.95090 | −0.975449 | − | 0.220225i | \(-0.929321\pi\) | ||||
−0.975449 | + | 0.220225i | \(0.929321\pi\) | |||||||
\(3\) | 3.86039 | 0.742933 | 0.371466 | − | 0.928446i | \(-0.378855\pi\) | ||||
0.371466 | + | 0.928446i | \(0.378855\pi\) | |||||||
\(4\) | 22.4480 | 2.80600 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −21.3015 | −1.44939 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −79.7239 | −3.52333 | ||||||||
\(9\) | −12.0974 | −0.448051 | ||||||||
\(10\) | 27.5899 | 0.872468 | ||||||||
\(11\) | 34.5211 | 0.946227 | 0.473113 | − | 0.881002i | \(-0.343130\pi\) | ||||
0.473113 | + | 0.881002i | \(0.343130\pi\) | |||||||
\(12\) | 86.6582 | 2.08467 | ||||||||
\(13\) | 68.8935 | 1.46982 | 0.734908 | − | 0.678167i | \(-0.237225\pi\) | ||||
0.734908 | + | 0.678167i | \(0.237225\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −19.3020 | −0.332250 | ||||||||
\(16\) | 260.330 | 4.06766 | ||||||||
\(17\) | −91.4346 | −1.30448 | −0.652239 | − | 0.758013i | \(-0.726170\pi\) | ||||
−0.652239 | + | 0.758013i | \(0.726170\pi\) | |||||||
\(18\) | 66.7530 | 0.874102 | ||||||||
\(19\) | 11.8278 | 0.142815 | 0.0714077 | − | 0.997447i | \(-0.477251\pi\) | ||||
0.0714077 | + | 0.997447i | \(0.477251\pi\) | |||||||
\(20\) | −112.240 | −1.25488 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −190.486 | −1.84599 | ||||||||
\(23\) | −0.104165 | −0.000944348 0 | −0.000472174 | − | 1.00000i | \(-0.500150\pi\) | ||||
−0.000472174 | 1.00000i | \(0.500150\pi\) | ||||||||
\(24\) | −307.765 | −2.61760 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −380.152 | −2.86746 | ||||||||
\(27\) | −150.931 | −1.07580 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 190.863 | 1.22215 | 0.611076 | − | 0.791572i | \(-0.290737\pi\) | ||||
0.611076 | + | 0.791572i | \(0.290737\pi\) | |||||||
\(30\) | 106.508 | 0.648185 | ||||||||
\(31\) | 159.802 | 0.925847 | 0.462924 | − | 0.886398i | \(-0.346800\pi\) | ||||
0.462924 | + | 0.886398i | \(0.346800\pi\) | |||||||
\(32\) | −798.703 | −4.41225 | ||||||||
\(33\) | 133.265 | 0.702983 | ||||||||
\(34\) | 504.534 | 2.54491 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −271.562 | −1.25723 | ||||||||
\(37\) | −177.908 | −0.790482 | −0.395241 | − | 0.918577i | \(-0.629339\pi\) | ||||
−0.395241 | + | 0.918577i | \(0.629339\pi\) | |||||||
\(38\) | −65.2657 | −0.278618 | ||||||||
\(39\) | 265.956 | 1.09197 | ||||||||
\(40\) | 398.619 | 1.57568 | ||||||||
\(41\) | 145.247 | 0.553264 | 0.276632 | − | 0.960976i | \(-0.410782\pi\) | ||||
0.276632 | + | 0.960976i | \(0.410782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.25729 | 0.0292843 | 0.0146421 | − | 0.999893i | \(-0.495339\pi\) | ||||
0.0146421 | + | 0.999893i | \(0.495339\pi\) | |||||||
\(44\) | 774.930 | 2.65512 | ||||||||
\(45\) | 60.4869 | 0.200375 | ||||||||
\(46\) | 0.574782 | 0.00184233 | ||||||||
\(47\) | 260.529 | 0.808553 | 0.404277 | − | 0.914637i | \(-0.367523\pi\) | ||||
0.404277 | + | 0.914637i | \(0.367523\pi\) | |||||||
\(48\) | 1004.98 | 3.02199 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −137.949 | −0.390180 | ||||||||
\(51\) | −352.973 | −0.969140 | ||||||||
\(52\) | 1546.52 | 4.12431 | ||||||||
\(53\) | 353.107 | 0.915151 | 0.457576 | − | 0.889171i | \(-0.348718\pi\) | ||||
0.457576 | + | 0.889171i | \(0.348718\pi\) | |||||||
\(54\) | 832.834 | 2.09879 | ||||||||
\(55\) | −172.605 | −0.423165 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 45.6601 | 0.106102 | ||||||||
\(58\) | −1053.18 | −2.38429 | ||||||||
\(59\) | 240.495 | 0.530673 | 0.265337 | − | 0.964156i | \(-0.414517\pi\) | ||||
0.265337 | + | 0.964156i | \(0.414517\pi\) | |||||||
\(60\) | −433.291 | −0.932294 | ||||||||
\(61\) | 778.188 | 1.63339 | 0.816695 | − | 0.577069i | \(-0.195804\pi\) | ||||
0.816695 | + | 0.577069i | \(0.195804\pi\) | |||||||
\(62\) | −881.783 | −1.80623 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2324.58 | 4.54020 | ||||||||
\(65\) | −344.467 | −0.657322 | ||||||||
\(66\) | −735.352 | −1.37145 | ||||||||
\(67\) | 151.945 | 0.277059 | 0.138530 | − | 0.990358i | \(-0.455762\pi\) | ||||
0.138530 | + | 0.990358i | \(0.455762\pi\) | |||||||
\(68\) | −2052.53 | −3.66037 | ||||||||
\(69\) | −0.402119 | −0.000701587 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −311.449 | −0.520594 | −0.260297 | − | 0.965529i | \(-0.583820\pi\) | ||||
−0.260297 | + | 0.965529i | \(0.583820\pi\) | |||||||
\(72\) | 964.450 | 1.57863 | ||||||||
\(73\) | 639.888 | 1.02593 | 0.512967 | − | 0.858408i | \(-0.328546\pi\) | ||||
0.512967 | + | 0.858408i | \(0.328546\pi\) | |||||||
\(74\) | 981.690 | 1.54215 | ||||||||
\(75\) | 96.5098 | 0.148587 | ||||||||
\(76\) | 265.512 | 0.400740 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1467.54 | −2.13033 | ||||||||
\(79\) | 391.186 | 0.557112 | 0.278556 | − | 0.960420i | \(-0.410144\pi\) | ||||
0.278556 | + | 0.960420i | \(0.410144\pi\) | |||||||
\(80\) | −1301.65 | −1.81911 | ||||||||
\(81\) | −256.024 | −0.351199 | ||||||||
\(82\) | −801.472 | −1.07936 | ||||||||
\(83\) | 493.205 | 0.652245 | 0.326122 | − | 0.945328i | \(-0.394258\pi\) | ||||
0.326122 | + | 0.945328i | \(0.394258\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 457.173 | 0.583381 | ||||||||
\(86\) | −45.5635 | −0.0571307 | ||||||||
\(87\) | 736.807 | 0.907977 | ||||||||
\(88\) | −2752.15 | −3.33387 | ||||||||
\(89\) | 473.850 | 0.564359 | 0.282180 | − | 0.959362i | \(-0.408943\pi\) | ||||
0.282180 | + | 0.959362i | \(0.408943\pi\) | |||||||
\(90\) | −333.765 | −0.390910 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.33831 | −0.00264984 | ||||||||
\(93\) | 616.898 | 0.687842 | ||||||||
\(94\) | −1437.59 | −1.57741 | ||||||||
\(95\) | −59.1392 | −0.0638690 | ||||||||
\(96\) | −3083.31 | −3.27801 | ||||||||
\(97\) | 839.005 | 0.878227 | 0.439114 | − | 0.898431i | \(-0.355293\pi\) | ||||
0.439114 | + | 0.898431i | \(0.355293\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −417.615 | −0.423958 | ||||||||
\(100\) | 561.201 | 0.561201 | ||||||||
\(101\) | 887.440 | 0.874293 | 0.437146 | − | 0.899390i | \(-0.355989\pi\) | ||||
0.437146 | + | 0.899390i | \(0.355989\pi\) | |||||||
\(102\) | 1947.70 | 1.89069 | ||||||||
\(103\) | 619.087 | 0.592238 | 0.296119 | − | 0.955151i | \(-0.404308\pi\) | ||||
0.296119 | + | 0.955151i | \(0.404308\pi\) | |||||||
\(104\) | −5492.46 | −5.17865 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1948.44 | −1.78537 | ||||||||
\(107\) | −2151.30 | −1.94368 | −0.971841 | − | 0.235639i | \(-0.924282\pi\) | ||||
−0.971841 | + | 0.235639i | \(0.924282\pi\) | |||||||
\(108\) | −3388.11 | −3.01871 | ||||||||
\(109\) | −407.076 | −0.357714 | −0.178857 | − | 0.983875i | \(-0.557240\pi\) | ||||
−0.178857 | + | 0.983875i | \(0.557240\pi\) | |||||||
\(110\) | 952.432 | 0.825553 | ||||||||
\(111\) | −686.793 | −0.587275 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −349.581 | −0.291025 | −0.145513 | − | 0.989356i | \(-0.546483\pi\) | ||||
−0.145513 | + | 0.989356i | \(0.546483\pi\) | |||||||
\(114\) | −251.951 | −0.206995 | ||||||||
\(115\) | 0.520827 | 0.000422325 0 | ||||||||
\(116\) | 4284.50 | 3.42936 | ||||||||
\(117\) | −833.431 | −0.658553 | ||||||||
\(118\) | −1327.04 | −1.03529 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1538.83 | 1.17063 | ||||||||
\(121\) | −139.296 | −0.104655 | ||||||||
\(122\) | −4294.02 | −3.18658 | ||||||||
\(123\) | 560.712 | 0.411038 | ||||||||
\(124\) | 3587.24 | 2.59793 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1183.78 | 0.827114 | 0.413557 | − | 0.910478i | \(-0.364286\pi\) | ||||
0.413557 | + | 0.910478i | \(0.364286\pi\) | |||||||
\(128\) | −6437.36 | −4.44522 | ||||||||
\(129\) | 31.8764 | 0.0217563 | ||||||||
\(130\) | 1900.76 | 1.28237 | ||||||||
\(131\) | 223.357 | 0.148968 | 0.0744840 | − | 0.997222i | \(-0.476269\pi\) | ||||
0.0744840 | + | 0.997222i | \(0.476269\pi\) | |||||||
\(132\) | 2991.53 | 1.97257 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −838.426 | −0.540515 | ||||||||
\(135\) | 754.656 | 0.481114 | ||||||||
\(136\) | 7289.52 | 4.59611 | ||||||||
\(137\) | 2036.66 | 1.27010 | 0.635050 | − | 0.772471i | \(-0.280979\pi\) | ||||
0.635050 | + | 0.772471i | \(0.280979\pi\) | |||||||
\(138\) | 2.21888 | 0.00136872 | ||||||||
\(139\) | 2687.00 | 1.63963 | 0.819815 | − | 0.572629i | \(-0.194076\pi\) | ||||
0.819815 | + | 0.572629i | \(0.194076\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1005.74 | 0.600701 | ||||||||
\(142\) | 1718.57 | 1.01563 | ||||||||
\(143\) | 2378.28 | 1.39078 | ||||||||
\(144\) | −3149.31 | −1.82252 | ||||||||
\(145\) | −954.316 | −0.546563 | ||||||||
\(146\) | −3530.88 | −2.00149 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3993.68 | −2.21810 | ||||||||
\(149\) | 673.500 | 0.370304 | 0.185152 | − | 0.982710i | \(-0.440722\pi\) | ||||
0.185152 | + | 0.982710i | \(0.440722\pi\) | |||||||
\(150\) | −532.538 | −0.289877 | ||||||||
\(151\) | −2125.18 | −1.14533 | −0.572664 | − | 0.819790i | \(-0.694090\pi\) | ||||
−0.572664 | + | 0.819790i | \(0.694090\pi\) | |||||||
\(152\) | −942.961 | −0.503186 | ||||||||
\(153\) | 1106.12 | 0.584473 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −799.010 | −0.414052 | ||||||||
\(156\) | 5970.18 | 3.06409 | ||||||||
\(157\) | −2813.03 | −1.42997 | −0.714983 | − | 0.699142i | \(-0.753565\pi\) | ||||
−0.714983 | + | 0.699142i | \(0.753565\pi\) | |||||||
\(158\) | −2158.55 | −1.08687 | ||||||||
\(159\) | 1363.13 | 0.679896 | ||||||||
\(160\) | 3993.52 | 1.97322 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1412.73 | 0.685153 | ||||||||
\(163\) | −1344.42 | −0.646032 | −0.323016 | − | 0.946394i | \(-0.604697\pi\) | ||||
−0.323016 | + | 0.946394i | \(0.604697\pi\) | |||||||
\(164\) | 3260.52 | 1.55246 | ||||||||
\(165\) | −666.324 | −0.314383 | ||||||||
\(166\) | −2721.49 | −1.27246 | ||||||||
\(167\) | 1451.24 | 0.672456 | 0.336228 | − | 0.941781i | \(-0.390849\pi\) | ||||
0.336228 | + | 0.941781i | \(0.390849\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2549.31 | 1.16036 | ||||||||
\(170\) | −2522.67 | −1.13812 | ||||||||
\(171\) | −143.086 | −0.0639886 | ||||||||
\(172\) | 185.360 | 0.0821718 | ||||||||
\(173\) | −1979.16 | −0.869784 | −0.434892 | − | 0.900483i | \(-0.643213\pi\) | ||||
−0.434892 | + | 0.900483i | \(0.643213\pi\) | |||||||
\(174\) | −4065.68 | −1.77137 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8986.87 | 3.84893 | ||||||||
\(177\) | 928.403 | 0.394254 | ||||||||
\(178\) | −2614.69 | −1.10101 | ||||||||
\(179\) | −4358.66 | −1.82001 | −0.910005 | − | 0.414598i | \(-0.863922\pi\) | ||||
−0.910005 | + | 0.414598i | \(0.863922\pi\) | |||||||
\(180\) | 1357.81 | 0.562252 | ||||||||
\(181\) | −377.923 | −0.155198 | −0.0775988 | − | 0.996985i | \(-0.524725\pi\) | ||||
−0.0775988 | + | 0.996985i | \(0.524725\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3004.11 | 1.21350 | ||||||||
\(184\) | 8.30447 | 0.00332725 | ||||||||
\(185\) | 889.538 | 0.353514 | ||||||||
\(186\) | −3404.03 | −1.34191 | ||||||||
\(187\) | −3156.42 | −1.23433 | ||||||||
\(188\) | 5848.36 | 2.26880 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 326.328 | 0.124602 | ||||||||
\(191\) | −2425.95 | −0.919033 | −0.459517 | − | 0.888169i | \(-0.651977\pi\) | ||||
−0.459517 | + | 0.888169i | \(0.651977\pi\) | |||||||
\(192\) | 8973.80 | 3.37306 | ||||||||
\(193\) | −622.923 | −0.232326 | −0.116163 | − | 0.993230i | \(-0.537060\pi\) | ||||
−0.116163 | + | 0.993230i | \(0.537060\pi\) | |||||||
\(194\) | −4629.61 | −1.71333 | ||||||||
\(195\) | −1329.78 | −0.488346 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2842.29 | 1.02794 | 0.513971 | − | 0.857807i | \(-0.328174\pi\) | ||||
0.513971 | + | 0.857807i | \(0.328174\pi\) | |||||||
\(198\) | 2304.39 | 0.827099 | ||||||||
\(199\) | −867.364 | −0.308974 | −0.154487 | − | 0.987995i | \(-0.549372\pi\) | ||||
−0.154487 | + | 0.987995i | \(0.549372\pi\) | |||||||
\(200\) | −1993.10 | −0.704666 | ||||||||
\(201\) | 586.565 | 0.205836 | ||||||||
\(202\) | −4896.87 | −1.70566 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7923.55 | −2.71941 | ||||||||
\(205\) | −726.237 | −0.247427 | ||||||||
\(206\) | −3416.11 | −1.15540 | ||||||||
\(207\) | 1.26013 | 0.000423116 0 | ||||||||
\(208\) | 17935.0 | 5.97871 | ||||||||
\(209\) | 408.309 | 0.135136 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5975.92 | −1.94976 | −0.974880 | − | 0.222730i | \(-0.928503\pi\) | ||||
−0.974880 | + | 0.222730i | \(0.928503\pi\) | |||||||
\(212\) | 7926.57 | 2.56792 | ||||||||
\(213\) | −1202.31 | −0.386766 | ||||||||
\(214\) | 11870.8 | 3.79192 | ||||||||
\(215\) | −41.2864 | −0.0130963 | ||||||||
\(216\) | 12032.8 | 3.79042 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2246.24 | 0.697864 | ||||||||
\(219\) | 2470.22 | 0.762200 | ||||||||
\(220\) | −3874.65 | −1.18740 | ||||||||
\(221\) | −6299.25 | −1.91734 | ||||||||
\(222\) | 3789.71 | 1.14571 | ||||||||
\(223\) | −5181.58 | −1.55598 | −0.777992 | − | 0.628274i | \(-0.783762\pi\) | ||||
−0.777992 | + | 0.628274i | \(0.783762\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −302.435 | −0.0896102 | ||||||||
\(226\) | 1928.98 | 0.567761 | ||||||||
\(227\) | 3753.06 | 1.09735 | 0.548677 | − | 0.836035i | \(-0.315132\pi\) | ||||
0.548677 | + | 0.836035i | \(0.315132\pi\) | |||||||
\(228\) | 1024.98 | 0.297723 | ||||||||
\(229\) | −6258.14 | −1.80589 | −0.902947 | − | 0.429752i | \(-0.858601\pi\) | ||||
−0.902947 | + | 0.429752i | \(0.858601\pi\) | |||||||
\(230\) | −2.87391 | −0.000823913 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15216.4 | −4.30605 | ||||||||
\(233\) | 1779.96 | 0.500469 | 0.250234 | − | 0.968185i | \(-0.419492\pi\) | ||||
0.250234 | + | 0.968185i | \(0.419492\pi\) | |||||||
\(234\) | 4598.85 | 1.28477 | ||||||||
\(235\) | −1302.64 | −0.361596 | ||||||||
\(236\) | 5398.63 | 1.48907 | ||||||||
\(237\) | 1510.13 | 0.413897 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3519.46 | 0.952532 | 0.476266 | − | 0.879301i | \(-0.341990\pi\) | ||||
0.476266 | + | 0.879301i | \(0.341990\pi\) | |||||||
\(240\) | −5024.88 | −1.35148 | ||||||||
\(241\) | 362.930 | 0.0970058 | 0.0485029 | − | 0.998823i | \(-0.484555\pi\) | ||||
0.0485029 | + | 0.998823i | \(0.484555\pi\) | |||||||
\(242\) | 768.629 | 0.204171 | ||||||||
\(243\) | 3086.79 | 0.814887 | ||||||||
\(244\) | 17468.8 | 4.58330 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3093.99 | −0.801894 | ||||||||
\(247\) | 814.861 | 0.209912 | ||||||||
\(248\) | −12740.0 | −3.26207 | ||||||||
\(249\) | 1903.97 | 0.484574 | ||||||||
\(250\) | 689.747 | 0.174494 | ||||||||
\(251\) | −5333.85 | −1.34131 | −0.670656 | − | 0.741768i | \(-0.733988\pi\) | ||||
−0.670656 | + | 0.741768i | \(0.733988\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.59590 | −0.000893567 0 | ||||||||
\(254\) | −6532.06 | −1.61361 | ||||||||
\(255\) | 1764.87 | 0.433412 | ||||||||
\(256\) | 16924.5 | 4.13197 | ||||||||
\(257\) | −2438.78 | −0.591933 | −0.295966 | − | 0.955198i | \(-0.595642\pi\) | ||||
−0.295966 | + | 0.955198i | \(0.595642\pi\) | |||||||
\(258\) | −175.893 | −0.0424442 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7732.62 | −1.84445 | ||||||||
\(261\) | −2308.95 | −0.547587 | ||||||||
\(262\) | −1232.48 | −0.290621 | ||||||||
\(263\) | 1526.25 | 0.357843 | 0.178921 | − | 0.983863i | \(-0.442739\pi\) | ||||
0.178921 | + | 0.983863i | \(0.442739\pi\) | |||||||
\(264\) | −10624.4 | −2.47684 | ||||||||
\(265\) | −1765.54 | −0.409268 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1829.25 | 0.419281 | ||||||||
\(268\) | 3410.86 | 0.777430 | ||||||||
\(269\) | −7564.12 | −1.71447 | −0.857235 | − | 0.514925i | \(-0.827820\pi\) | ||||
−0.857235 | + | 0.514925i | \(0.827820\pi\) | |||||||
\(270\) | −4164.17 | −0.938605 | ||||||||
\(271\) | 4282.68 | 0.959980 | 0.479990 | − | 0.877274i | \(-0.340640\pi\) | ||||
0.479990 | + | 0.877274i | \(0.340640\pi\) | |||||||
\(272\) | −23803.2 | −5.30617 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11238.2 | −2.47784 | ||||||||
\(275\) | 863.027 | 0.189245 | ||||||||
\(276\) | −9.02679 | −0.00196866 | ||||||||
\(277\) | −4008.41 | −0.869465 | −0.434732 | − | 0.900560i | \(-0.643157\pi\) | ||||
−0.434732 | + | 0.900560i | \(0.643157\pi\) | |||||||
\(278\) | −14826.8 | −3.19875 | ||||||||
\(279\) | −1933.18 | −0.414827 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6935.44 | 1.47236 | 0.736181 | − | 0.676785i | \(-0.236627\pi\) | ||||
0.736181 | + | 0.676785i | \(0.236627\pi\) | |||||||
\(282\) | −5549.66 | −1.17191 | ||||||||
\(283\) | −2666.64 | −0.560124 | −0.280062 | − | 0.959982i | \(-0.590355\pi\) | ||||
−0.280062 | + | 0.959982i | \(0.590355\pi\) | |||||||
\(284\) | −6991.41 | −1.46079 | ||||||||
\(285\) | −228.300 | −0.0474503 | ||||||||
\(286\) | −13123.3 | −2.71327 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9662.22 | 1.97692 | ||||||||
\(289\) | 3447.28 | 0.701665 | ||||||||
\(290\) | 5265.89 | 1.06629 | ||||||||
\(291\) | 3238.89 | 0.652464 | ||||||||
\(292\) | 14364.2 | 2.87878 | ||||||||
\(293\) | 5939.10 | 1.18418 | 0.592092 | − | 0.805870i | \(-0.298302\pi\) | ||||
0.592092 | + | 0.805870i | \(0.298302\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1202.47 | −0.237324 | ||||||||
\(296\) | 14183.5 | 2.78513 | ||||||||
\(297\) | −5210.31 | −1.01795 | ||||||||
\(298\) | −3716.36 | −0.722425 | ||||||||
\(299\) | −7.17632 | −0.00138802 | ||||||||
\(300\) | 2166.45 | 0.416934 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11726.7 | 2.23442 | ||||||||
\(303\) | 3425.87 | 0.649541 | ||||||||
\(304\) | 3079.14 | 0.580924 | ||||||||
\(305\) | −3890.94 | −0.730474 | ||||||||
\(306\) | −6103.53 | −1.14025 | ||||||||
\(307\) | 10381.5 | 1.92998 | 0.964992 | − | 0.262278i | \(-0.0844737\pi\) | ||||
0.964992 | + | 0.262278i | \(0.0844737\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2389.92 | 0.439993 | ||||||||
\(310\) | 4408.91 | 0.807772 | ||||||||
\(311\) | 4240.54 | 0.773181 | 0.386590 | − | 0.922252i | \(-0.373653\pi\) | ||||
0.386590 | + | 0.922252i | \(0.373653\pi\) | |||||||
\(312\) | −21203.0 | −3.84739 | ||||||||
\(313\) | −283.903 | −0.0512688 | −0.0256344 | − | 0.999671i | \(-0.508161\pi\) | ||||
−0.0256344 | + | 0.999671i | \(0.508161\pi\) | |||||||
\(314\) | 15522.2 | 2.78972 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8781.36 | 1.56326 | ||||||||
\(317\) | 1739.49 | 0.308201 | 0.154100 | − | 0.988055i | \(-0.450752\pi\) | ||||
0.154100 | + | 0.988055i | \(0.450752\pi\) | |||||||
\(318\) | −7521.73 | −1.32641 | ||||||||
\(319\) | 6588.80 | 1.15643 | ||||||||
\(320\) | −11622.9 | −2.03044 | ||||||||
\(321\) | −8304.85 | −1.44402 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1081.47 | −0.186300 | ||||||||
\(324\) | −5747.24 | −0.985466 | ||||||||
\(325\) | 1722.34 | 0.293963 | ||||||||
\(326\) | 7418.48 | 1.26034 | ||||||||
\(327\) | −1571.47 | −0.265758 | ||||||||
\(328\) | −11579.7 | −1.94933 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3676.76 | 0.613330 | ||||||||
\(331\) | 5606.96 | 0.931077 | 0.465538 | − | 0.885028i | \(-0.345861\pi\) | ||||
0.465538 | + | 0.885028i | \(0.345861\pi\) | |||||||
\(332\) | 11071.5 | 1.83020 | ||||||||
\(333\) | 2152.22 | 0.354176 | ||||||||
\(334\) | −8007.89 | −1.31189 | ||||||||
\(335\) | −759.723 | −0.123905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9427.44 | −1.52387 | −0.761937 | − | 0.647652i | \(-0.775751\pi\) | ||||
−0.761937 | + | 0.647652i | \(0.775751\pi\) | |||||||
\(338\) | −14067.0 | −2.26375 | ||||||||
\(339\) | −1349.52 | −0.216212 | ||||||||
\(340\) | 10262.6 | 1.63697 | ||||||||
\(341\) | 5516.53 | 0.876062 | ||||||||
\(342\) | 789.544 | 0.124835 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −658.303 | −0.103178 | ||||||||
\(345\) | 2.01060 | 0.000313759 0 | ||||||||
\(346\) | 10920.9 | 1.69686 | ||||||||
\(347\) | 11634.2 | 1.79988 | 0.899939 | − | 0.436017i | \(-0.143611\pi\) | ||||
0.899939 | + | 0.436017i | \(0.143611\pi\) | |||||||
\(348\) | 16539.9 | 2.54779 | ||||||||
\(349\) | −1317.10 | −0.202013 | −0.101006 | − | 0.994886i | \(-0.532206\pi\) | ||||
−0.101006 | + | 0.994886i | \(0.532206\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10398.2 | −1.58124 | ||||||||
\(352\) | −27572.1 | −4.17499 | ||||||||
\(353\) | 5848.82 | 0.881874 | 0.440937 | − | 0.897538i | \(-0.354646\pi\) | ||||
0.440937 | + | 0.897538i | \(0.354646\pi\) | |||||||
\(354\) | −5122.90 | −0.769150 | ||||||||
\(355\) | 1557.24 | 0.232817 | ||||||||
\(356\) | 10637.0 | 1.58359 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24051.0 | 3.55065 | ||||||||
\(359\) | −12422.0 | −1.82621 | −0.913104 | − | 0.407727i | \(-0.866321\pi\) | ||||
−0.913104 | + | 0.407727i | \(0.866321\pi\) | |||||||
\(360\) | −4822.25 | −0.705986 | ||||||||
\(361\) | −6719.10 | −0.979604 | ||||||||
\(362\) | 2085.37 | 0.302775 | ||||||||
\(363\) | −537.735 | −0.0777515 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3199.44 | −0.458812 | ||||||||
\(366\) | −16576.6 | −2.36741 | ||||||||
\(367\) | −6590.78 | −0.937427 | −0.468713 | − | 0.883350i | \(-0.655282\pi\) | ||||
−0.468713 | + | 0.883350i | \(0.655282\pi\) | |||||||
\(368\) | −27.1174 | −0.00384128 | ||||||||
\(369\) | −1757.11 | −0.247891 | ||||||||
\(370\) | −4908.45 | −0.689670 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 13848.1 | 1.93009 | ||||||||
\(373\) | 344.278 | 0.0477910 | 0.0238955 | − | 0.999714i | \(-0.492393\pi\) | ||||
0.0238955 | + | 0.999714i | \(0.492393\pi\) | |||||||
\(374\) | 17417.0 | 2.40806 | ||||||||
\(375\) | −482.549 | −0.0664499 | ||||||||
\(376\) | −20770.4 | −2.84880 | ||||||||
\(377\) | 13149.2 | 1.79634 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5241.23 | 0.710353 | 0.355177 | − | 0.934799i | \(-0.384421\pi\) | ||||
0.355177 | + | 0.934799i | \(0.384421\pi\) | |||||||
\(380\) | −1327.56 | −0.179217 | ||||||||
\(381\) | 4569.85 | 0.614490 | ||||||||
\(382\) | 13386.3 | 1.79294 | ||||||||
\(383\) | 7597.37 | 1.01360 | 0.506798 | − | 0.862065i | \(-0.330829\pi\) | ||||
0.506798 | + | 0.862065i | \(0.330829\pi\) | |||||||
\(384\) | −24850.7 | −3.30250 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3437.27 | 0.453245 | ||||||||
\(387\) | −99.8916 | −0.0131209 | ||||||||
\(388\) | 18834.0 | 2.46431 | ||||||||
\(389\) | 3101.84 | 0.404291 | 0.202146 | − | 0.979355i | \(-0.435209\pi\) | ||||
0.202146 | + | 0.979355i | \(0.435209\pi\) | |||||||
\(390\) | 7337.69 | 0.952713 | ||||||||
\(391\) | 9.52432 | 0.00123188 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 862.246 | 0.110673 | ||||||||
\(394\) | −15683.7 | −2.00541 | ||||||||
\(395\) | −1955.93 | −0.249148 | ||||||||
\(396\) | −9374.63 | −1.18963 | ||||||||
\(397\) | −2932.06 | −0.370669 | −0.185335 | − | 0.982675i | \(-0.559337\pi\) | ||||
−0.185335 | + | 0.982675i | \(0.559337\pi\) | |||||||
\(398\) | 4786.09 | 0.602777 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6508.25 | 0.813531 | ||||||||
\(401\) | 89.2375 | 0.0111130 | 0.00555649 | − | 0.999985i | \(-0.498231\pi\) | ||||
0.00555649 | + | 0.999985i | \(0.498231\pi\) | |||||||
\(402\) | −3236.65 | −0.401566 | ||||||||
\(403\) | 11009.3 | 1.36083 | ||||||||
\(404\) | 19921.3 | 2.45327 | ||||||||
\(405\) | 1280.12 | 0.157061 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6141.56 | −0.747975 | ||||||||
\(408\) | 28140.4 | 3.41460 | ||||||||
\(409\) | 147.388 | 0.0178188 | 0.00890940 | − | 0.999960i | \(-0.497164\pi\) | ||||
0.00890940 | + | 0.999960i | \(0.497164\pi\) | |||||||
\(410\) | 4007.36 | 0.482706 | ||||||||
\(411\) | 7862.31 | 0.943599 | ||||||||
\(412\) | 13897.3 | 1.66182 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.95336 | −0.000825457 0 | ||||||||
\(415\) | −2466.03 | −0.291693 | ||||||||
\(416\) | −55025.4 | −6.48520 | ||||||||
\(417\) | 10372.9 | 1.21813 | ||||||||
\(418\) | −2253.04 | −0.263636 | ||||||||
\(419\) | −3781.67 | −0.440923 | −0.220462 | − | 0.975396i | \(-0.570756\pi\) | ||||
−0.220462 | + | 0.975396i | \(0.570756\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10899.2 | −1.26175 | −0.630874 | − | 0.775885i | \(-0.717304\pi\) | ||||
−0.630874 | + | 0.775885i | \(0.717304\pi\) | |||||||
\(422\) | 32975.0 | 3.80378 | ||||||||
\(423\) | −3151.71 | −0.362273 | ||||||||
\(424\) | −28151.1 | −3.22438 | ||||||||
\(425\) | −2285.86 | −0.260896 | ||||||||
\(426\) | 6634.33 | 0.754541 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −48292.4 | −5.45398 | ||||||||
\(429\) | 9181.08 | 1.03326 | ||||||||
\(430\) | 227.817 | 0.0255496 | ||||||||
\(431\) | −11283.4 | −1.26102 | −0.630512 | − | 0.776180i | \(-0.717155\pi\) | ||||
−0.630512 | + | 0.776180i | \(0.717155\pi\) | |||||||
\(432\) | −39291.9 | −4.37600 | ||||||||
\(433\) | −8906.19 | −0.988462 | −0.494231 | − | 0.869331i | \(-0.664550\pi\) | ||||
−0.494231 | + | 0.869331i | \(0.664550\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3684.03 | −0.406059 | ||||||||
\(436\) | −9138.07 | −1.00375 | ||||||||
\(437\) | −1.23205 | −0.000134867 0 | ||||||||
\(438\) | −13630.6 | −1.48697 | ||||||||
\(439\) | 8149.49 | 0.886000 | 0.443000 | − | 0.896522i | \(-0.353914\pi\) | ||||
0.443000 | + | 0.896522i | \(0.353914\pi\) | |||||||
\(440\) | 13760.8 | 1.49095 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 34759.1 | 3.74054 | ||||||||
\(443\) | −11472.8 | −1.23045 | −0.615223 | − | 0.788353i | \(-0.710934\pi\) | ||||
−0.615223 | + | 0.788353i | \(0.710934\pi\) | |||||||
\(444\) | −15417.2 | −1.64790 | ||||||||
\(445\) | −2369.25 | −0.252389 | ||||||||
\(446\) | 28591.8 | 3.03557 | ||||||||
\(447\) | 2599.97 | 0.275111 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1963.80 | 0.206409 | 0.103204 | − | 0.994660i | \(-0.467090\pi\) | ||||
0.103204 | + | 0.994660i | \(0.467090\pi\) | |||||||
\(450\) | 1668.83 | 0.174820 | ||||||||
\(451\) | 5014.10 | 0.523514 | ||||||||
\(452\) | −7847.42 | −0.816618 | ||||||||
\(453\) | −8204.02 | −0.850902 | ||||||||
\(454\) | −20709.3 | −2.14083 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3640.20 | −0.373833 | ||||||||
\(457\) | 5589.85 | 0.572171 | 0.286086 | − | 0.958204i | \(-0.407646\pi\) | ||||
0.286086 | + | 0.958204i | \(0.407646\pi\) | |||||||
\(458\) | 34532.3 | 3.52311 | ||||||||
\(459\) | 13800.3 | 1.40336 | ||||||||
\(460\) | 11.6915 | 0.00118505 | ||||||||
\(461\) | −18790.9 | −1.89844 | −0.949219 | − | 0.314618i | \(-0.898124\pi\) | ||||
−0.949219 | + | 0.314618i | \(0.898124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7892.22 | −0.792187 | −0.396094 | − | 0.918210i | \(-0.629634\pi\) | ||||
−0.396094 | + | 0.918210i | \(0.629634\pi\) | |||||||
\(464\) | 49687.4 | 4.97130 | ||||||||
\(465\) | −3084.49 | −0.307612 | ||||||||
\(466\) | −9821.78 | −0.976363 | ||||||||
\(467\) | 385.511 | 0.0381998 | 0.0190999 | − | 0.999818i | \(-0.493920\pi\) | ||||
0.0190999 | + | 0.999818i | \(0.493920\pi\) | |||||||
\(468\) | −18708.9 | −1.84790 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7187.95 | 0.705437 | ||||||||
\(471\) | −10859.4 | −1.06237 | ||||||||
\(472\) | −19173.2 | −1.86974 | ||||||||
\(473\) | 285.050 | 0.0277096 | ||||||||
\(474\) | −8332.86 | −0.807471 | ||||||||
\(475\) | 295.696 | 0.0285631 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4271.67 | −0.410035 | ||||||||
\(478\) | −19420.3 | −1.85829 | ||||||||
\(479\) | 1694.46 | 0.161632 | 0.0808160 | − | 0.996729i | \(-0.474247\pi\) | ||||
0.0808160 | + | 0.996729i | \(0.474247\pi\) | |||||||
\(480\) | 15416.5 | 1.46597 | ||||||||
\(481\) | −12256.7 | −1.16186 | ||||||||
\(482\) | −2002.64 | −0.189248 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3126.91 | −0.293662 | ||||||||
\(485\) | −4195.03 | −0.392755 | ||||||||
\(486\) | −17032.8 | −1.58976 | ||||||||
\(487\) | 15711.2 | 1.46189 | 0.730945 | − | 0.682436i | \(-0.239079\pi\) | ||||
0.730945 | + | 0.682436i | \(0.239079\pi\) | |||||||
\(488\) | −62040.2 | −5.75498 | ||||||||
\(489\) | −5189.99 | −0.479958 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2716.34 | −0.249667 | −0.124834 | − | 0.992178i | \(-0.539840\pi\) | ||||
−0.124834 | + | 0.992178i | \(0.539840\pi\) | |||||||
\(492\) | 12586.9 | 1.15337 | ||||||||
\(493\) | −17451.5 | −1.59427 | ||||||||
\(494\) | −4496.38 | −0.409518 | ||||||||
\(495\) | 2088.07 | 0.189600 | ||||||||
\(496\) | 41601.2 | 3.76603 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10506.0 | −0.945355 | ||||||||
\(499\) | 4295.34 | 0.385342 | 0.192671 | − | 0.981263i | \(-0.438285\pi\) | ||||
0.192671 | + | 0.981263i | \(0.438285\pi\) | |||||||
\(500\) | −2806.00 | −0.250977 | ||||||||
\(501\) | 5602.34 | 0.499589 | ||||||||
\(502\) | 29432.0 | 2.61677 | ||||||||
\(503\) | 6515.26 | 0.577537 | 0.288769 | − | 0.957399i | \(-0.406754\pi\) | ||||
0.288769 | + | 0.957399i | \(0.406754\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4437.20 | −0.390996 | ||||||||
\(506\) | 19.8421 | 0.00174326 | ||||||||
\(507\) | 9841.34 | 0.862070 | ||||||||
\(508\) | 26573.5 | 2.32088 | ||||||||
\(509\) | 14391.8 | 1.25325 | 0.626624 | − | 0.779321i | \(-0.284436\pi\) | ||||
0.626624 | + | 0.779321i | \(0.284436\pi\) | |||||||
\(510\) | −9738.48 | −0.845544 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −41890.2 | −3.61583 | ||||||||
\(513\) | −1785.19 | −0.153641 | ||||||||
\(514\) | 13457.1 | 1.15480 | ||||||||
\(515\) | −3095.44 | −0.264857 | ||||||||
\(516\) | 715.562 | 0.0610481 | ||||||||
\(517\) | 8993.73 | 0.765075 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7640.32 | −0.646191 | ||||||||
\(520\) | 27462.3 | 2.31596 | ||||||||
\(521\) | 2913.36 | 0.244984 | 0.122492 | − | 0.992469i | \(-0.460911\pi\) | ||||
0.122492 | + | 0.992469i | \(0.460911\pi\) | |||||||
\(522\) | 12740.7 | 1.06829 | ||||||||
\(523\) | 16870.2 | 1.41048 | 0.705242 | − | 0.708967i | \(-0.250838\pi\) | ||||
0.705242 | + | 0.708967i | \(0.250838\pi\) | |||||||
\(524\) | 5013.93 | 0.418005 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8421.82 | −0.698115 | ||||||||
\(527\) | −14611.4 | −1.20775 | ||||||||
\(528\) | 34692.8 | 2.85949 | ||||||||
\(529\) | −12167.0 | −0.999999 | ||||||||
\(530\) | 9742.18 | 0.798441 | ||||||||
\(531\) | −2909.35 | −0.237769 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10006.6 | 0.813197 | ||||||||
\(534\) | −10093.7 | −0.817974 | ||||||||
\(535\) | 10756.5 | 0.869241 | ||||||||
\(536\) | −12113.6 | −0.976172 | ||||||||
\(537\) | −16826.1 | −1.35214 | ||||||||
\(538\) | 41738.6 | 3.34476 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16940.5 | 1.35001 | ||||||||
\(541\) | −2229.59 | −0.177186 | −0.0885929 | − | 0.996068i | \(-0.528237\pi\) | ||||
−0.0885929 | + | 0.996068i | \(0.528237\pi\) | |||||||
\(542\) | −23631.7 | −1.87282 | ||||||||
\(543\) | −1458.93 | −0.115301 | ||||||||
\(544\) | 73029.1 | 5.75569 | ||||||||
\(545\) | 2035.38 | 0.159975 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1218.73 | −0.0952639 | −0.0476319 | − | 0.998865i | \(-0.515167\pi\) | ||||
−0.0476319 | + | 0.998865i | \(0.515167\pi\) | |||||||
\(548\) | 45719.1 | 3.56391 | ||||||||
\(549\) | −9414.04 | −0.731843 | ||||||||
\(550\) | −4762.16 | −0.369198 | ||||||||
\(551\) | 2257.50 | 0.174542 | ||||||||
\(552\) | 32.0585 | 0.00247192 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22118.3 | 1.69624 | ||||||||
\(555\) | 3433.96 | 0.262637 | ||||||||
\(556\) | 60317.9 | 4.60081 | ||||||||
\(557\) | −22734.5 | −1.72943 | −0.864714 | − | 0.502264i | \(-0.832501\pi\) | ||||
−0.864714 | + | 0.502264i | \(0.832501\pi\) | |||||||
\(558\) | 10667.3 | 0.809285 | ||||||||
\(559\) | 568.873 | 0.0430425 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12185.0 | −0.917026 | ||||||||
\(562\) | −38269.6 | −2.87243 | ||||||||
\(563\) | 4302.11 | 0.322047 | 0.161023 | − | 0.986951i | \(-0.448521\pi\) | ||||
0.161023 | + | 0.986951i | \(0.448521\pi\) | |||||||
\(564\) | 22576.9 | 1.68557 | ||||||||
\(565\) | 1747.91 | 0.130150 | ||||||||
\(566\) | 14714.4 | 1.09275 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24829.9 | 1.83422 | ||||||||
\(569\) | 14866.9 | 1.09535 | 0.547675 | − | 0.836691i | \(-0.315513\pi\) | ||||
0.547675 | + | 0.836691i | \(0.315513\pi\) | |||||||
\(570\) | 1259.76 | 0.0925708 | ||||||||
\(571\) | 16514.5 | 1.21035 | 0.605174 | − | 0.796093i | \(-0.293103\pi\) | ||||
0.605174 | + | 0.796093i | \(0.293103\pi\) | |||||||
\(572\) | 53387.6 | 3.90253 | ||||||||
\(573\) | −9365.10 | −0.682780 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.60414 | −0.000188870 0 | ||||||||
\(576\) | −28121.4 | −2.03424 | ||||||||
\(577\) | 1867.97 | 0.134774 | 0.0673870 | − | 0.997727i | \(-0.478534\pi\) | ||||
0.0673870 | + | 0.997727i | \(0.478534\pi\) | |||||||
\(578\) | −19022.0 | −1.36888 | ||||||||
\(579\) | −2404.73 | −0.172603 | ||||||||
\(580\) | −21422.5 | −1.53366 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −17872.1 | −1.27289 | ||||||||
\(583\) | 12189.6 | 0.865941 | ||||||||
\(584\) | −51014.3 | −3.61471 | ||||||||
\(585\) | 4167.15 | 0.294514 | ||||||||
\(586\) | −32771.8 | −2.31022 | ||||||||
\(587\) | 3926.15 | 0.276064 | 0.138032 | − | 0.990428i | \(-0.455922\pi\) | ||||
0.138032 | + | 0.990428i | \(0.455922\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1890.11 | 0.132225 | ||||||||
\(590\) | 6635.21 | 0.462996 | ||||||||
\(591\) | 10972.3 | 0.763692 | ||||||||
\(592\) | −46314.7 | −3.21541 | ||||||||
\(593\) | −7554.18 | −0.523125 | −0.261562 | − | 0.965187i | \(-0.584238\pi\) | ||||
−0.261562 | + | 0.965187i | \(0.584238\pi\) | |||||||
\(594\) | 28750.3 | 1.98593 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15118.8 | 1.03907 | ||||||||
\(597\) | −3348.36 | −0.229547 | ||||||||
\(598\) | 39.5988 | 0.00270788 | ||||||||
\(599\) | 28210.9 | 1.92432 | 0.962160 | − | 0.272487i | \(-0.0878461\pi\) | ||||
0.962160 | + | 0.272487i | \(0.0878461\pi\) | |||||||
\(600\) | −7694.13 | −0.523519 | ||||||||
\(601\) | −23181.4 | −1.57336 | −0.786679 | − | 0.617363i | \(-0.788201\pi\) | ||||
−0.786679 | + | 0.617363i | \(0.788201\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1838.13 | −0.124137 | ||||||||
\(604\) | −47706.1 | −3.21380 | ||||||||
\(605\) | 696.478 | 0.0468031 | ||||||||
\(606\) | −18903.8 | −1.26719 | ||||||||
\(607\) | −24863.6 | −1.66257 | −0.831287 | − | 0.555844i | \(-0.812395\pi\) | ||||
−0.831287 | + | 0.555844i | \(0.812395\pi\) | |||||||
\(608\) | −9446.93 | −0.630137 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21470.1 | 1.42508 | ||||||||
\(611\) | 17948.7 | 1.18843 | ||||||||
\(612\) | 24830.2 | 1.64003 | ||||||||
\(613\) | −12792.7 | −0.842893 | −0.421446 | − | 0.906853i | \(-0.638477\pi\) | ||||
−0.421446 | + | 0.906853i | \(0.638477\pi\) | |||||||
\(614\) | −57285.0 | −3.76520 | ||||||||
\(615\) | −2803.56 | −0.183822 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19793.3 | 1.29149 | 0.645744 | − | 0.763554i | \(-0.276547\pi\) | ||||
0.645744 | + | 0.763554i | \(0.276547\pi\) | |||||||
\(618\) | −13187.5 | −0.858381 | ||||||||
\(619\) | −20951.7 | −1.36045 | −0.680226 | − | 0.733002i | \(-0.738118\pi\) | ||||
−0.680226 | + | 0.733002i | \(0.738118\pi\) | |||||||
\(620\) | −17936.2 | −1.16183 | ||||||||
\(621\) | 15.7218 | 0.00101593 | ||||||||
\(622\) | −23399.2 | −1.50840 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 69236.3 | 4.44178 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 1566.57 | 0.100020 | ||||||||
\(627\) | 1576.23 | 0.100397 | ||||||||
\(628\) | −63147.1 | −4.01249 | ||||||||
\(629\) | 16266.9 | 1.03117 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23273.5 | 1.46831 | 0.734156 | − | 0.678981i | \(-0.237578\pi\) | ||||
0.734156 | + | 0.678981i | \(0.237578\pi\) | |||||||
\(632\) | −31186.9 | −1.96289 | ||||||||
\(633\) | −23069.4 | −1.44854 | ||||||||
\(634\) | −9598.47 | −0.601268 | ||||||||
\(635\) | −5918.90 | −0.369896 | ||||||||
\(636\) | 30599.6 | 1.90779 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −36356.8 | −2.25608 | ||||||||
\(639\) | 3767.71 | 0.233253 | ||||||||
\(640\) | 32186.8 | 1.98796 | ||||||||
\(641\) | −22117.7 | −1.36287 | −0.681434 | − | 0.731880i | \(-0.738643\pi\) | ||||
−0.681434 | + | 0.731880i | \(0.738643\pi\) | |||||||
\(642\) | 45826.0 | 2.81714 | ||||||||
\(643\) | 20269.9 | 1.24318 | 0.621591 | − | 0.783342i | \(-0.286487\pi\) | ||||
0.621591 | + | 0.783342i | \(0.286487\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −159.382 | −0.00972969 | ||||||||
\(646\) | 5967.54 | 0.363451 | ||||||||
\(647\) | −3145.25 | −0.191117 | −0.0955583 | − | 0.995424i | \(-0.530464\pi\) | ||||
−0.0955583 | + | 0.995424i | \(0.530464\pi\) | |||||||
\(648\) | 20411.2 | 1.23739 | ||||||||
\(649\) | 8302.13 | 0.502137 | ||||||||
\(650\) | −9503.81 | −0.573493 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30179.6 | −1.81277 | ||||||||
\(653\) | −5953.35 | −0.356773 | −0.178386 | − | 0.983961i | \(-0.557088\pi\) | ||||
−0.178386 | + | 0.983961i | \(0.557088\pi\) | |||||||
\(654\) | 8671.35 | 0.518466 | ||||||||
\(655\) | −1116.79 | −0.0666205 | ||||||||
\(656\) | 37812.3 | 2.25049 | ||||||||
\(657\) | −7740.96 | −0.459671 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26277.5 | 1.55330 | 0.776652 | − | 0.629930i | \(-0.216916\pi\) | ||||
0.776652 | + | 0.629930i | \(0.216916\pi\) | |||||||
\(660\) | −14957.7 | −0.882161 | ||||||||
\(661\) | −24004.3 | −1.41250 | −0.706248 | − | 0.707964i | \(-0.749614\pi\) | ||||
−0.706248 | + | 0.707964i | \(0.749614\pi\) | |||||||
\(662\) | −30939.1 | −1.81644 | ||||||||
\(663\) | −24317.6 | −1.42446 | ||||||||
\(664\) | −39320.3 | −2.29808 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11875.9 | −0.690962 | ||||||||
\(667\) | −19.8814 | −0.00115414 | ||||||||
\(668\) | 32577.4 | 1.88691 | ||||||||
\(669\) | −20002.9 | −1.15599 | ||||||||
\(670\) | 4192.13 | 0.241725 | ||||||||
\(671\) | 26863.9 | 1.54556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9205.36 | 0.527252 | 0.263626 | − | 0.964625i | \(-0.415082\pi\) | ||||
0.263626 | + | 0.964625i | \(0.415082\pi\) | |||||||
\(674\) | 52020.4 | 2.97292 | ||||||||
\(675\) | −3773.28 | −0.215161 | ||||||||
\(676\) | 57227.1 | 3.25598 | ||||||||
\(677\) | −18773.1 | −1.06575 | −0.532873 | − | 0.846195i | \(-0.678888\pi\) | ||||
−0.532873 | + | 0.846195i | \(0.678888\pi\) | |||||||
\(678\) | 7446.62 | 0.421808 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −36447.6 | −2.05544 | ||||||||
\(681\) | 14488.3 | 0.815260 | ||||||||
\(682\) | −30440.1 | −1.70911 | ||||||||
\(683\) | −10222.2 | −0.572684 | −0.286342 | − | 0.958127i | \(-0.592439\pi\) | ||||
−0.286342 | + | 0.958127i | \(0.592439\pi\) | |||||||
\(684\) | −3212.00 | −0.179552 | ||||||||
\(685\) | −10183.3 | −0.568006 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24158.9 | −1.34166 | ||||||||
\(688\) | 2149.62 | 0.119118 | ||||||||
\(689\) | 24326.8 | 1.34510 | ||||||||
\(690\) | −11.0944 | −0.000612112 0 | ||||||||
\(691\) | 22355.1 | 1.23072 | 0.615361 | − | 0.788246i | \(-0.289010\pi\) | ||||
0.615361 | + | 0.788246i | \(0.289010\pi\) | |||||||
\(692\) | −44428.2 | −2.44062 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −64197.3 | −3.51138 | ||||||||
\(695\) | −13435.0 | −0.733264 | ||||||||
\(696\) | −58741.1 | −3.19910 | ||||||||
\(697\) | −13280.6 | −0.721722 | ||||||||
\(698\) | 7267.70 | 0.394107 | ||||||||
\(699\) | 6871.35 | 0.371814 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16217.3 | 0.873779 | 0.436890 | − | 0.899515i | \(-0.356080\pi\) | ||||
0.436890 | + | 0.899515i | \(0.356080\pi\) | |||||||
\(702\) | 57376.9 | 3.08483 | ||||||||
\(703\) | −2104.26 | −0.112893 | ||||||||
\(704\) | 80247.1 | 4.29606 | ||||||||
\(705\) | −5028.71 | −0.268642 | ||||||||
\(706\) | −32273.7 | −1.72045 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 20840.8 | 1.10628 | ||||||||
\(709\) | 3922.92 | 0.207798 | 0.103899 | − | 0.994588i | \(-0.466868\pi\) | ||||
0.103899 | + | 0.994588i | \(0.466868\pi\) | |||||||
\(710\) | −8592.83 | −0.454202 | ||||||||
\(711\) | −4732.33 | −0.249615 | ||||||||
\(712\) | −37777.1 | −1.98842 | ||||||||
\(713\) | −16.6458 | −0.000874322 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11891.4 | −0.621976 | ||||||||
\(716\) | −97843.4 | −5.10695 | ||||||||
\(717\) | 13586.5 | 0.707667 | ||||||||
\(718\) | 68544.3 | 3.56275 | ||||||||
\(719\) | 23908.6 | 1.24011 | 0.620055 | − | 0.784558i | \(-0.287110\pi\) | ||||
0.620055 | + | 0.784558i | \(0.287110\pi\) | |||||||
\(720\) | 15746.6 | 0.815055 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37075.8 | 1.91111 | ||||||||
\(723\) | 1401.05 | 0.0720688 | ||||||||
\(724\) | −8483.62 | −0.435485 | ||||||||
\(725\) | 4771.58 | 0.244430 | ||||||||
\(726\) | 2967.21 | 0.151685 | ||||||||
\(727\) | −26906.4 | −1.37263 | −0.686315 | − | 0.727305i | \(-0.740773\pi\) | ||||
−0.686315 | + | 0.727305i | \(0.740773\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18828.9 | 0.956605 | ||||||||
\(730\) | 17654.4 | 0.895095 | ||||||||
\(731\) | −755.001 | −0.0382007 | ||||||||
\(732\) | 67436.4 | 3.40508 | ||||||||
\(733\) | 27637.5 | 1.39265 | 0.696325 | − | 0.717726i | \(-0.254817\pi\) | ||||
0.696325 | + | 0.717726i | \(0.254817\pi\) | |||||||
\(734\) | 36367.7 | 1.82882 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 83.1973 | 0.00416670 | ||||||||
\(737\) | 5245.29 | 0.262161 | ||||||||
\(738\) | 9695.71 | 0.483610 | ||||||||
\(739\) | −14038.9 | −0.698821 | −0.349410 | − | 0.936970i | \(-0.613618\pi\) | ||||
−0.349410 | + | 0.936970i | \(0.613618\pi\) | |||||||
\(740\) | 19968.4 | 0.991963 | ||||||||
\(741\) | 3145.68 | 0.155951 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17698.7 | 0.873893 | 0.436946 | − | 0.899488i | \(-0.356060\pi\) | ||||
0.436946 | + | 0.899488i | \(0.356060\pi\) | |||||||
\(744\) | −49181.5 | −2.42350 | ||||||||
\(745\) | −3367.50 | −0.165605 | ||||||||
\(746\) | −1899.72 | −0.0932354 | ||||||||
\(747\) | −5966.50 | −0.292239 | ||||||||
\(748\) | −70855.4 | −3.46354 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2662.69 | 0.129637 | ||||||||
\(751\) | 17199.7 | 0.835719 | 0.417859 | − | 0.908512i | \(-0.362780\pi\) | ||||
0.417859 | + | 0.908512i | \(0.362780\pi\) | |||||||
\(752\) | 67823.4 | 3.28892 | ||||||||
\(753\) | −20590.7 | −0.996505 | ||||||||
\(754\) | −72557.1 | −3.50448 | ||||||||
\(755\) | 10625.9 | 0.512206 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19200.7 | −0.921879 | −0.460939 | − | 0.887432i | \(-0.652487\pi\) | ||||
−0.460939 | + | 0.887432i | \(0.652487\pi\) | |||||||
\(758\) | −28921.0 | −1.38583 | ||||||||
\(759\) | −13.8816 | −0.000663860 0 | ||||||||
\(760\) | 4714.80 | 0.225031 | ||||||||
\(761\) | −27918.7 | −1.32990 | −0.664949 | − | 0.746889i | \(-0.731547\pi\) | ||||
−0.664949 | + | 0.746889i | \(0.731547\pi\) | |||||||
\(762\) | −25216.3 | −1.19881 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −54457.7 | −2.57881 | ||||||||
\(765\) | −5530.59 | −0.261384 | ||||||||
\(766\) | −41922.1 | −1.97742 | ||||||||
\(767\) | 16568.5 | 0.779992 | ||||||||
\(768\) | 65335.3 | 3.06977 | ||||||||
\(769\) | −7436.29 | −0.348712 | −0.174356 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174356 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9414.64 | −0.439766 | ||||||||
\(772\) | −13983.4 | −0.651908 | ||||||||
\(773\) | 4989.84 | 0.232176 | 0.116088 | − | 0.993239i | \(-0.462965\pi\) | ||||
0.116088 | + | 0.993239i | \(0.462965\pi\) | |||||||
\(774\) | 551.199 | 0.0255975 | ||||||||
\(775\) | 3995.05 | 0.185169 | ||||||||
\(776\) | −66888.7 | −3.09429 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17115.9 | −0.788731 | ||||||||
\(779\) | 1717.96 | 0.0790146 | ||||||||
\(780\) | −29850.9 | −1.37030 | ||||||||
\(781\) | −10751.5 | −0.492600 | ||||||||
\(782\) | −52.5550 | −0.00240328 | ||||||||
\(783\) | −28807.2 | −1.31480 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14065.2 | 0.639500 | ||||||||
\(786\) | −4757.85 | −0.215912 | ||||||||
\(787\) | −2870.69 | −0.130024 | −0.0650122 | − | 0.997884i | \(-0.520709\pi\) | ||||
−0.0650122 | + | 0.997884i | \(0.520709\pi\) | |||||||
\(788\) | 63803.8 | 2.88441 | ||||||||
\(789\) | 5891.93 | 0.265853 | ||||||||
\(790\) | 10792.8 | 0.486063 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 33293.9 | 1.49374 | ||||||||
\(793\) | 53612.1 | 2.40078 | ||||||||
\(794\) | 16179.0 | 0.723138 | ||||||||
\(795\) | −6815.66 | −0.304059 | ||||||||
\(796\) | −19470.6 | −0.866982 | ||||||||
\(797\) | 4676.61 | 0.207847 | 0.103923 | − | 0.994585i | \(-0.466860\pi\) | ||||
0.103923 | + | 0.994585i | \(0.466860\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23821.3 | −1.05474 | ||||||||
\(800\) | −19967.6 | −0.882451 | ||||||||
\(801\) | −5732.34 | −0.252862 | ||||||||
\(802\) | −492.410 | −0.0216803 | ||||||||
\(803\) | 22089.6 | 0.970766 | ||||||||
\(804\) | 13167.2 | 0.577578 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −60749.1 | −2.65483 | ||||||||
\(807\) | −29200.5 | −1.27374 | ||||||||
\(808\) | −70750.2 | −3.08042 | ||||||||
\(809\) | −15376.9 | −0.668261 | −0.334131 | − | 0.942527i | \(-0.608443\pi\) | ||||
−0.334131 | + | 0.942527i | \(0.608443\pi\) | |||||||
\(810\) | −7063.67 | −0.306410 | ||||||||
\(811\) | 36422.9 | 1.57704 | 0.788522 | − | 0.615007i | \(-0.210847\pi\) | ||||
0.788522 | + | 0.615007i | \(0.210847\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16532.8 | 0.713200 | ||||||||
\(814\) | 33889.0 | 1.45922 | ||||||||
\(815\) | 6722.10 | 0.288914 | ||||||||
\(816\) | −91889.5 | −3.94213 | ||||||||
\(817\) | 97.6658 | 0.00418225 | ||||||||
\(818\) | −813.285 | −0.0347627 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16302.6 | −0.694282 | ||||||||
\(821\) | −25479.0 | −1.08310 | −0.541550 | − | 0.840669i | \(-0.682162\pi\) | ||||
−0.541550 | + | 0.840669i | \(0.682162\pi\) | |||||||
\(822\) | −43384.0 | −1.84087 | ||||||||
\(823\) | −17933.3 | −0.759557 | −0.379779 | − | 0.925077i | \(-0.624000\pi\) | ||||
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(824\) | −49356.1 | −2.08665 | ||||||||
\(825\) | 3331.62 | 0.140597 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13021.6 | 0.547529 | 0.273764 | − | 0.961797i | \(-0.411731\pi\) | ||||
0.273764 | + | 0.961797i | \(0.411731\pi\) | |||||||
\(828\) | 28.2874 | 0.00118727 | ||||||||
\(829\) | −11397.6 | −0.477509 | −0.238754 | − | 0.971080i | \(-0.576739\pi\) | ||||
−0.238754 | + | 0.971080i | \(0.576739\pi\) | |||||||
\(830\) | 13607.5 | 0.569063 | ||||||||
\(831\) | −15474.0 | −0.645954 | ||||||||
\(832\) | 160149. | 6.67326 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −57237.2 | −2.37646 | ||||||||
\(835\) | −7256.19 | −0.300731 | ||||||||
\(836\) | 9165.75 | 0.379191 | ||||||||
\(837\) | −24119.1 | −0.996031 | ||||||||
\(838\) | 20867.2 | 0.860196 | ||||||||
\(839\) | −37681.2 | −1.55053 | −0.775267 | − | 0.631633i | \(-0.782385\pi\) | ||||
−0.775267 | + | 0.631633i | \(0.782385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12039.8 | 0.493656 | ||||||||
\(842\) | 60141.7 | 2.46154 | ||||||||
\(843\) | 26773.5 | 1.09386 | ||||||||
\(844\) | −134148. | −5.47104 | ||||||||
\(845\) | −12746.6 | −0.518929 | ||||||||
\(846\) | 17391.1 | 0.706758 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 91924.4 | 3.72252 | ||||||||
\(849\) | −10294.3 | −0.416135 | ||||||||
\(850\) | 12613.3 | 0.508981 | ||||||||
\(851\) | 18.5318 | 0.000746490 0 | ||||||||
\(852\) | −26989.6 | −1.08527 | ||||||||
\(853\) | 21771.6 | 0.873911 | 0.436956 | − | 0.899483i | \(-0.356057\pi\) | ||||
0.436956 | + | 0.899483i | \(0.356057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 715.429 | 0.0286166 | ||||||||
\(856\) | 171510. | 6.84823 | ||||||||
\(857\) | 29860.2 | 1.19021 | 0.595103 | − | 0.803649i | \(-0.297111\pi\) | ||||
0.595103 | + | 0.803649i | \(0.297111\pi\) | |||||||
\(858\) | −50661.0 | −2.01578 | ||||||||
\(859\) | 18530.6 | 0.736039 | 0.368019 | − | 0.929818i | \(-0.380036\pi\) | ||||
0.368019 | + | 0.929818i | \(0.380036\pi\) | |||||||
\(860\) | −926.799 | −0.0367484 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 62261.4 | 2.46013 | ||||||||
\(863\) | −21296.5 | −0.840024 | −0.420012 | − | 0.907519i | \(-0.637974\pi\) | ||||
−0.420012 | + | 0.907519i | \(0.637974\pi\) | |||||||
\(864\) | 120549. | 4.74672 | ||||||||
\(865\) | 9895.79 | 0.388979 | ||||||||
\(866\) | 49144.1 | 1.92839 | ||||||||
\(867\) | 13307.8 | 0.521290 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13504.2 | 0.527155 | ||||||||
\(870\) | 20328.4 | 0.792181 | ||||||||
\(871\) | 10468.0 | 0.407226 | ||||||||
\(872\) | 32453.7 | 1.26035 | ||||||||
\(873\) | −10149.8 | −0.393491 | ||||||||
\(874\) | 6.79843 | 0.000263112 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 55451.5 | 2.13874 | ||||||||
\(877\) | −18793.4 | −0.723614 | −0.361807 | − | 0.932253i | \(-0.617840\pi\) | ||||
−0.361807 | + | 0.932253i | \(0.617840\pi\) | |||||||
\(878\) | −44968.7 | −1.72850 | ||||||||
\(879\) | 22927.3 | 0.879769 | ||||||||
\(880\) | −44934.4 | −1.72129 | ||||||||
\(881\) | 1638.62 | 0.0626634 | 0.0313317 | − | 0.999509i | \(-0.490025\pi\) | ||||
0.0313317 | + | 0.999509i | \(0.490025\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35424.1 | −1.35008 | −0.675038 | − | 0.737783i | \(-0.735873\pi\) | ||||
−0.675038 | + | 0.737783i | \(0.735873\pi\) | |||||||
\(884\) | −141406. | −5.38008 | ||||||||
\(885\) | −4642.01 | −0.176316 | ||||||||
\(886\) | 63306.5 | 2.40048 | ||||||||
\(887\) | −5131.41 | −0.194246 | −0.0971229 | − | 0.995272i | \(-0.530964\pi\) | ||||
−0.0971229 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(888\) | 54753.8 | 2.06916 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13073.5 | 0.492386 | ||||||||
\(891\) | −8838.22 | −0.332314 | ||||||||
\(892\) | −116316. | −4.36610 | ||||||||
\(893\) | 3081.49 | 0.115474 | ||||||||
\(894\) | −14346.6 | −0.536713 | ||||||||
\(895\) | 21793.3 | 0.813933 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.7034 | −0.00103120 | ||||||||
\(898\) | −10836.2 | −0.402682 | ||||||||
\(899\) | 30500.3 | 1.13153 | ||||||||
\(900\) | −6789.06 | −0.251447 | ||||||||
\(901\) | −32286.2 | −1.19380 | ||||||||
\(902\) | −27667.7 | −1.02132 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27870.0 | 1.02538 | ||||||||
\(905\) | 1889.61 | 0.0694065 | ||||||||
\(906\) | 45269.6 | 1.66002 | ||||||||
\(907\) | −19934.6 | −0.729787 | −0.364893 | − | 0.931049i | \(-0.618895\pi\) | ||||
−0.364893 | + | 0.931049i | \(0.618895\pi\) | |||||||
\(908\) | 84248.8 | 3.07918 | ||||||||
\(909\) | −10735.7 | −0.391728 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48387.4 | 1.75976 | 0.879882 | − | 0.475193i | \(-0.157622\pi\) | ||||
0.879882 | + | 0.475193i | \(0.157622\pi\) | |||||||
\(912\) | 11886.7 | 0.431587 | ||||||||
\(913\) | 17026.0 | 0.617172 | ||||||||
\(914\) | −30844.7 | −1.11625 | ||||||||
\(915\) | −15020.6 | −0.542693 | ||||||||
\(916\) | −140483. | −5.06735 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −76149.8 | −2.73782 | ||||||||
\(919\) | −14431.7 | −0.518019 | −0.259009 | − | 0.965875i | \(-0.583396\pi\) | ||||
−0.259009 | + | 0.965875i | \(0.583396\pi\) | |||||||
\(920\) | −41.5224 | −0.00148799 | ||||||||
\(921\) | 40076.8 | 1.43385 | ||||||||
\(922\) | 103688. | 3.70366 | ||||||||
\(923\) | −21456.8 | −0.765177 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4447.69 | −0.158096 | ||||||||
\(926\) | 43549.1 | 1.54548 | ||||||||
\(927\) | −7489.34 | −0.265353 | ||||||||
\(928\) | −152443. | −5.39244 | ||||||||
\(929\) | 5549.82 | 0.196000 | 0.0979998 | − | 0.995186i | \(-0.468756\pi\) | ||||
0.0979998 | + | 0.995186i | \(0.468756\pi\) | |||||||
\(930\) | 17020.1 | 0.600120 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 39956.7 | 1.40432 | ||||||||
\(933\) | 16370.2 | 0.574421 | ||||||||
\(934\) | −2127.24 | −0.0745239 | ||||||||
\(935\) | 15782.1 | 0.552010 | ||||||||
\(936\) | 66444.3 | 2.32030 | ||||||||
\(937\) | 26231.9 | 0.914576 | 0.457288 | − | 0.889319i | \(-0.348821\pi\) | ||||
0.457288 | + | 0.889319i | \(0.348821\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1095.98 | −0.0380893 | ||||||||
\(940\) | −29241.8 | −1.01464 | ||||||||
\(941\) | 2836.80 | 0.0982753 | 0.0491376 | − | 0.998792i | \(-0.484353\pi\) | ||||
0.0491376 | + | 0.998792i | \(0.484353\pi\) | |||||||
\(942\) | 59921.9 | 2.07257 | ||||||||
\(943\) | −15.1298 | −0.000522474 0 | ||||||||
\(944\) | 62607.9 | 2.15860 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1572.90 | −0.0540586 | ||||||||
\(947\) | −40272.9 | −1.38193 | −0.690967 | − | 0.722886i | \(-0.742815\pi\) | ||||
−0.690967 | + | 0.722886i | \(0.742815\pi\) | |||||||
\(948\) | 33899.5 | 1.16140 | ||||||||
\(949\) | 44084.1 | 1.50793 | ||||||||
\(950\) | −1631.64 | −0.0557236 | ||||||||
\(951\) | 6715.12 | 0.228972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17770.1 | 0.604019 | 0.302010 | − | 0.953305i | \(-0.402343\pi\) | ||||
0.302010 | + | 0.953305i | \(0.402343\pi\) | |||||||
\(954\) | 23571.0 | 0.799936 | ||||||||
\(955\) | 12129.7 | 0.411004 | ||||||||
\(956\) | 79005.0 | 2.67281 | ||||||||
\(957\) | 25435.4 | 0.859152 | ||||||||
\(958\) | −9349.97 | −0.315328 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −44869.0 | −1.50848 | ||||||||
\(961\) | −4254.35 | −0.142807 | ||||||||
\(962\) | 67632.0 | 2.26668 | ||||||||
\(963\) | 26025.1 | 0.870869 | ||||||||
\(964\) | 8147.07 | 0.272199 | ||||||||
\(965\) | 3114.61 | 0.103899 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3530.14 | −0.117396 | −0.0586978 | − | 0.998276i | \(-0.518695\pi\) | ||||
−0.0586978 | + | 0.998276i | \(0.518695\pi\) | |||||||
\(968\) | 11105.2 | 0.368734 | ||||||||
\(969\) | −4174.91 | −0.138408 | ||||||||
\(970\) | 23148.0 | 0.766226 | ||||||||
\(971\) | 17650.7 | 0.583356 | 0.291678 | − | 0.956517i | \(-0.405786\pi\) | ||||
0.291678 | + | 0.956517i | \(0.405786\pi\) | |||||||
\(972\) | 69292.3 | 2.28658 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −86693.8 | −2.85200 | ||||||||
\(975\) | 6648.89 | 0.218395 | ||||||||
\(976\) | 202586. | 6.64407 | ||||||||
\(977\) | −14477.6 | −0.474085 | −0.237042 | − | 0.971499i | \(-0.576178\pi\) | ||||
−0.237042 | + | 0.971499i | \(0.576178\pi\) | |||||||
\(978\) | 28638.2 | 0.936349 | ||||||||
\(979\) | 16357.8 | 0.534012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4924.56 | 0.160274 | ||||||||
\(982\) | 14988.7 | 0.487075 | ||||||||
\(983\) | −8764.09 | −0.284365 | −0.142183 | − | 0.989840i | \(-0.545412\pi\) | ||||
−0.142183 | + | 0.989840i | \(0.545412\pi\) | |||||||
\(984\) | −44702.1 | −1.44822 | ||||||||
\(985\) | −14211.4 | −0.459710 | ||||||||
\(986\) | 96296.9 | 3.11026 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18292.0 | 0.589015 | ||||||||
\(989\) | −0.860124 | −2.76546e−5 0 | ||||||||
\(990\) | −11521.9 | −0.369890 | ||||||||
\(991\) | 33624.1 | 1.07781 | 0.538903 | − | 0.842368i | \(-0.318839\pi\) | ||||
0.538903 | + | 0.842368i | \(0.318839\pi\) | |||||||
\(992\) | −127634. | −4.08507 | ||||||||
\(993\) | 21645.1 | 0.691727 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4336.82 | 0.138177 | ||||||||
\(996\) | 42740.3 | 1.35972 | ||||||||
\(997\) | 16631.3 | 0.528302 | 0.264151 | − | 0.964481i | \(-0.414908\pi\) | ||||
0.264151 | + | 0.964481i | \(0.414908\pi\) | |||||||
\(998\) | −23701.6 | −0.751764 | ||||||||
\(999\) | 26851.8 | 0.850404 |
(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.p.1.1 | yes | 6 | |
3.2 | odd | 2 | 2205.4.a.ca.1.6 | 6 | |||
5.4 | even | 2 | 1225.4.a.bi.1.6 | 6 | |||
7.2 | even | 3 | 245.4.e.p.116.6 | 12 | |||
7.3 | odd | 6 | 245.4.e.q.226.6 | 12 | |||
7.4 | even | 3 | 245.4.e.p.226.6 | 12 | |||
7.5 | odd | 6 | 245.4.e.q.116.6 | 12 | |||
7.6 | odd | 2 | 245.4.a.o.1.1 | ✓ | 6 | ||
21.20 | even | 2 | 2205.4.a.bz.1.6 | 6 | |||
35.34 | odd | 2 | 1225.4.a.bj.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.1 | ✓ | 6 | 7.6 | odd | 2 | ||
245.4.a.p.1.1 | yes | 6 | 1.1 | even | 1 | trivial | |
245.4.e.p.116.6 | 12 | 7.2 | even | 3 | |||
245.4.e.p.226.6 | 12 | 7.4 | even | 3 | |||
245.4.e.q.116.6 | 12 | 7.5 | odd | 6 | |||
245.4.e.q.226.6 | 12 | 7.3 | odd | 6 | |||
1225.4.a.bi.1.6 | 6 | 5.4 | even | 2 | |||
1225.4.a.bj.1.6 | 6 | 35.34 | odd | 2 | |||
2205.4.a.bz.1.6 | 6 | 21.20 | even | 2 | |||
2205.4.a.ca.1.6 | 6 | 3.2 | odd | 2 |