Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,4,Mod(1,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2205.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(130.099211563\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.1163891200.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2\cdot 7 \) |
Twist minimal: | no (minimal twist has level 245) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(4.10376\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1 |
$q$-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 | \(-0.0706790\pi\) | ||||
0.975449 | + | 0.220225i | \(0.0706790\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 22.4480 | 2.80600 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 79.7239 | 3.52333 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −27.5899 | −0.872468 | ||||||||
\(11\) | −34.5211 | −0.946227 | −0.473113 | − | 0.881002i | \(-0.656870\pi\) | ||||
−0.473113 | + | 0.881002i | \(0.656870\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −68.8935 | −1.46982 | −0.734908 | − | 0.678167i | \(-0.762775\pi\) | ||||
−0.734908 | + | 0.678167i | \(0.762775\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 260.330 | 4.06766 | ||||||||
\(17\) | −91.4346 | −1.30448 | −0.652239 | − | 0.758013i | \(-0.726170\pi\) | ||||
−0.652239 | + | 0.758013i | \(0.726170\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.8278 | −0.142815 | −0.0714077 | − | 0.997447i | \(-0.522749\pi\) | ||||
−0.0714077 | + | 0.997447i | \(0.522749\pi\) | |||||||
\(20\) | −112.240 | −1.25488 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −190.486 | −1.84599 | ||||||||
\(23\) | 0.104165 | 0.000944348 0 | 0.000472174 | − | 1.00000i | \(-0.499850\pi\) | ||||
0.000472174 | 1.00000i | \(0.499850\pi\) | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −380.152 | −2.86746 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −190.863 | −1.22215 | −0.611076 | − | 0.791572i | \(-0.709263\pi\) | ||||
−0.611076 | + | 0.791572i | \(0.709263\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −159.802 | −0.925847 | −0.462924 | − | 0.886398i | \(-0.653200\pi\) | ||||
−0.462924 | + | 0.886398i | \(0.653200\pi\) | |||||||
\(32\) | 798.703 | 4.41225 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −504.534 | −2.54491 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −177.908 | −0.790482 | −0.395241 | − | 0.918577i | \(-0.629339\pi\) | ||||
−0.395241 | + | 0.918577i | \(0.629339\pi\) | |||||||
\(38\) | −65.2657 | −0.278618 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −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 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.574782 | 0.00184233 | ||||||||
\(47\) | 260.529 | 0.808553 | 0.404277 | − | 0.914637i | \(-0.367523\pi\) | ||||
0.404277 | + | 0.914637i | \(0.367523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 137.949 | 0.390180 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1546.52 | −4.12431 | ||||||||
\(53\) | −353.107 | −0.915151 | −0.457576 | − | 0.889171i | \(-0.651282\pi\) | ||||
−0.457576 | + | 0.889171i | \(0.651282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 172.605 | 0.423165 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1053.18 | −2.38429 | ||||||||
\(59\) | 240.495 | 0.530673 | 0.265337 | − | 0.964156i | \(-0.414517\pi\) | ||||
0.265337 | + | 0.964156i | \(0.414517\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −778.188 | −1.63339 | −0.816695 | − | 0.577069i | \(-0.804196\pi\) | ||||
−0.816695 | + | 0.577069i | \(0.804196\pi\) | |||||||
\(62\) | −881.783 | −1.80623 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2324.58 | 4.54020 | ||||||||
\(65\) | 344.467 | 0.657322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 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 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 311.449 | 0.520594 | 0.260297 | − | 0.965529i | \(-0.416180\pi\) | ||||
0.260297 | + | 0.965529i | \(0.416180\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −639.888 | −1.02593 | −0.512967 | − | 0.858408i | \(-0.671454\pi\) | ||||
−0.512967 | + | 0.858408i | \(0.671454\pi\) | |||||||
\(74\) | −981.690 | −1.54215 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −265.512 | −0.400740 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 391.186 | 0.557112 | 0.278556 | − | 0.960420i | \(-0.410144\pi\) | ||||
0.278556 | + | 0.960420i | \(0.410144\pi\) | |||||||
\(80\) | −1301.65 | −1.81911 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2752.15 | −3.33387 | ||||||||
\(89\) | 473.850 | 0.564359 | 0.282180 | − | 0.959362i | \(-0.408943\pi\) | ||||
0.282180 | + | 0.959362i | \(0.408943\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.33831 | 0.00264984 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1437.59 | 1.57741 | ||||||||
\(95\) | 59.1392 | 0.0638690 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −839.005 | −0.878227 | −0.439114 | − | 0.898431i | \(-0.644707\pi\) | ||||
−0.439114 | + | 0.898431i | \(0.644707\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 561.201 | 0.561201 | ||||||||
\(101\) | 887.440 | 0.874293 | 0.437146 | − | 0.899390i | \(-0.355989\pi\) | ||||
0.437146 | + | 0.899390i | \(0.355989\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −619.087 | −0.592238 | −0.296119 | − | 0.955151i | \(-0.595692\pi\) | ||||
−0.296119 | + | 0.955151i | \(0.595692\pi\) | |||||||
\(104\) | −5492.46 | −5.17865 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1948.44 | −1.78537 | ||||||||
\(107\) | 2151.30 | 1.94368 | 0.971841 | − | 0.235639i | \(-0.0757183\pi\) | ||||
0.971841 | + | 0.235639i | \(0.0757183\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −407.076 | −0.357714 | −0.178857 | − | 0.983875i | \(-0.557240\pi\) | ||||
−0.178857 | + | 0.983875i | \(0.557240\pi\) | |||||||
\(110\) | 952.432 | 0.825553 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 349.581 | 0.291025 | 0.145513 | − | 0.989356i | \(-0.453517\pi\) | ||||
0.145513 | + | 0.989356i | \(0.453517\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.520827 | −0.000422325 0 | ||||||||
\(116\) | −4284.50 | −3.42936 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1327.04 | 1.03529 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139.296 | −0.104655 | ||||||||
\(122\) | −4294.02 | −3.18658 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1900.76 | 1.28237 | ||||||||
\(131\) | 223.357 | 0.148968 | 0.0744840 | − | 0.997222i | \(-0.476269\pi\) | ||||
0.0744840 | + | 0.997222i | \(0.476269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 838.426 | 0.540515 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7289.52 | −4.59611 | ||||||||
\(137\) | −2036.66 | −1.27010 | −0.635050 | − | 0.772471i | \(-0.719021\pi\) | ||||
−0.635050 | + | 0.772471i | \(0.719021\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2687.00 | −1.63963 | −0.819815 | − | 0.572629i | \(-0.805924\pi\) | ||||
−0.819815 | + | 0.572629i | \(0.805924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1718.57 | 1.01563 | ||||||||
\(143\) | 2378.28 | 1.39078 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 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 | \(-0.559278\pi\) | ||||
−0.185152 | + | 0.982710i | \(0.559278\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2125.18 | −1.14533 | −0.572664 | − | 0.819790i | \(-0.694090\pi\) | ||||
−0.572664 | + | 0.819790i | \(0.694090\pi\) | |||||||
\(152\) | −942.961 | −0.503186 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 799.010 | 0.414052 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2813.03 | 1.42997 | 0.714983 | − | 0.699142i | \(-0.246435\pi\) | ||||
0.714983 | + | 0.699142i | \(0.246435\pi\) | |||||||
\(158\) | 2158.55 | 1.08687 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3993.52 | −1.97322 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1344.42 | −0.646032 | −0.323016 | − | 0.946394i | \(-0.604697\pi\) | ||||
−0.323016 | + | 0.946394i | \(0.604697\pi\) | |||||||
\(164\) | 3260.52 | 1.55246 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 185.360 | 0.0821718 | ||||||||
\(173\) | −1979.16 | −0.869784 | −0.434892 | − | 0.900483i | \(-0.643213\pi\) | ||||
−0.434892 | + | 0.900483i | \(0.643213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8986.87 | −3.84893 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2614.69 | 1.10101 | ||||||||
\(179\) | 4358.66 | 1.82001 | 0.910005 | − | 0.414598i | \(-0.136078\pi\) | ||||
0.910005 | + | 0.414598i | \(0.136078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 377.923 | 0.155198 | 0.0775988 | − | 0.996985i | \(-0.475275\pi\) | ||||
0.0775988 | + | 0.996985i | \(0.475275\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.30447 | 0.00332725 | ||||||||
\(185\) | 889.538 | 0.353514 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 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 | \(-0.348023\pi\) | ||||
0.459517 | + | 0.888169i | \(0.348023\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −622.923 | −0.232326 | −0.116163 | − | 0.993230i | \(-0.537060\pi\) | ||||
−0.116163 | + | 0.993230i | \(0.537060\pi\) | |||||||
\(194\) | −4629.61 | −1.71333 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2842.29 | −1.02794 | −0.513971 | − | 0.857807i | \(-0.671826\pi\) | ||||
−0.513971 | + | 0.857807i | \(0.671826\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 867.364 | 0.308974 | 0.154487 | − | 0.987995i | \(-0.450628\pi\) | ||||
0.154487 | + | 0.987995i | \(0.450628\pi\) | |||||||
\(200\) | 1993.10 | 0.704666 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4896.87 | 1.70566 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −726.237 | −0.247427 | ||||||||
\(206\) | −3416.11 | −1.15540 | ||||||||
\(207\) | 0 | 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 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11870.8 | 3.79192 | ||||||||
\(215\) | −41.2864 | −0.0130963 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2246.24 | −0.697864 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3874.65 | 1.18740 | ||||||||
\(221\) | 6299.25 | 1.91734 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5181.58 | 1.55598 | 0.777992 | − | 0.628274i | \(-0.216238\pi\) | ||||
0.777992 | + | 0.628274i | \(0.216238\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1928.98 | 0.567761 | ||||||||
\(227\) | 3753.06 | 1.09735 | 0.548677 | − | 0.836035i | \(-0.315132\pi\) | ||||
0.548677 | + | 0.836035i | \(0.315132\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6258.14 | 1.80589 | 0.902947 | − | 0.429752i | \(-0.141399\pi\) | ||||
0.902947 | + | 0.429752i | \(0.141399\pi\) | |||||||
\(230\) | −2.87391 | −0.000823913 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15216.4 | −4.30605 | ||||||||
\(233\) | −1779.96 | −0.500469 | −0.250234 | − | 0.968185i | \(-0.580508\pi\) | ||||
−0.250234 | + | 0.968185i | \(0.580508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1302.64 | −0.361596 | ||||||||
\(236\) | 5398.63 | 1.48907 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3519.46 | −0.952532 | −0.476266 | − | 0.879301i | \(-0.658010\pi\) | ||||
−0.476266 | + | 0.879301i | \(0.658010\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −362.930 | −0.0970058 | −0.0485029 | − | 0.998823i | \(-0.515445\pi\) | ||||
−0.0485029 | + | 0.998823i | \(0.515445\pi\) | |||||||
\(242\) | −768.629 | −0.204171 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −17468.8 | −4.58330 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 814.861 | 0.209912 | ||||||||
\(248\) | −12740.0 | −3.26207 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16924.5 | 4.13197 | ||||||||
\(257\) | −2438.78 | −0.591933 | −0.295966 | − | 0.955198i | \(-0.595642\pi\) | ||||
−0.295966 | + | 0.955198i | \(0.595642\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7732.62 | 1.84445 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1232.48 | 0.290621 | ||||||||
\(263\) | −1526.25 | −0.357843 | −0.178921 | − | 0.983863i | \(-0.557261\pi\) | ||||
−0.178921 | + | 0.983863i | \(0.557261\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1765.54 | 0.409268 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3410.86 | 0.777430 | ||||||||
\(269\) | −7564.12 | −1.71447 | −0.857235 | − | 0.514925i | \(-0.827820\pi\) | ||||
−0.857235 | + | 0.514925i | \(0.827820\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4282.68 | −0.959980 | −0.479990 | − | 0.877274i | \(-0.659360\pi\) | ||||
−0.479990 | + | 0.877274i | \(0.659360\pi\) | |||||||
\(272\) | −23803.2 | −5.30617 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11238.2 | −2.47784 | ||||||||
\(275\) | −863.027 | −0.189245 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4008.41 | −0.869465 | −0.434732 | − | 0.900560i | \(-0.643157\pi\) | ||||
−0.434732 | + | 0.900560i | \(0.643157\pi\) | |||||||
\(278\) | −14826.8 | −3.19875 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6935.44 | −1.47236 | −0.736181 | − | 0.676785i | \(-0.763373\pi\) | ||||
−0.736181 | + | 0.676785i | \(0.763373\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2666.64 | 0.560124 | 0.280062 | − | 0.959982i | \(-0.409645\pi\) | ||||
0.280062 | + | 0.959982i | \(0.409645\pi\) | |||||||
\(284\) | 6991.41 | 1.46079 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13123.3 | 2.71327 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3447.28 | 0.701665 | ||||||||
\(290\) | 5265.89 | 1.06629 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −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 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3716.36 | −0.722425 | ||||||||
\(299\) | −7.17632 | −0.00138802 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −11726.7 | −2.23442 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3079.14 | −0.580924 | ||||||||
\(305\) | 3890.94 | 0.730474 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10381.5 | −1.92998 | −0.964992 | − | 0.262278i | \(-0.915526\pi\) | ||||
−0.964992 | + | 0.262278i | \(0.915526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4408.91 | 0.807772 | ||||||||
\(311\) | 4240.54 | 0.773181 | 0.386590 | − | 0.922252i | \(-0.373653\pi\) | ||||
0.386590 | + | 0.922252i | \(0.373653\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 283.903 | 0.0512688 | 0.0256344 | − | 0.999671i | \(-0.491839\pi\) | ||||
0.0256344 | + | 0.999671i | \(0.491839\pi\) | |||||||
\(314\) | 15522.2 | 2.78972 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8781.36 | 1.56326 | ||||||||
\(317\) | −1739.49 | −0.308201 | −0.154100 | − | 0.988055i | \(-0.549248\pi\) | ||||
−0.154100 | + | 0.988055i | \(0.549248\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6588.80 | 1.15643 | ||||||||
\(320\) | −11622.9 | −2.03044 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1081.47 | 0.186300 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1722.34 | −0.293963 | ||||||||
\(326\) | −7418.48 | −1.26034 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11579.7 | 1.94933 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5606.96 | 0.931077 | 0.465538 | − | 0.885028i | \(-0.345861\pi\) | ||||
0.465538 | + | 0.885028i | \(0.345861\pi\) | |||||||
\(332\) | 11071.5 | 1.83020 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10262.6 | 1.63697 | ||||||||
\(341\) | 5516.53 | 0.876062 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 658.303 | 0.103178 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10920.9 | −1.69686 | ||||||||
\(347\) | −11634.2 | −1.79988 | −0.899939 | − | 0.436017i | \(-0.856389\pi\) | ||||
−0.899939 | + | 0.436017i | \(0.856389\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1317.10 | 0.202013 | 0.101006 | − | 0.994886i | \(-0.467794\pi\) | ||||
0.101006 | + | 0.994886i | \(0.467794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27572.1 | −4.17499 | ||||||||
\(353\) | 5848.82 | 0.881874 | 0.440937 | − | 0.897538i | \(-0.354646\pi\) | ||||
0.440937 | + | 0.897538i | \(0.354646\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −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 | \(-0.133679\pi\) | ||||
0.913104 | + | 0.407727i | \(0.133679\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6719.10 | −0.979604 | ||||||||
\(362\) | 2085.37 | 0.302775 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3199.44 | 0.458812 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6590.78 | 0.937427 | 0.468713 | − | 0.883350i | \(-0.344718\pi\) | ||||
0.468713 | + | 0.883350i | \(0.344718\pi\) | |||||||
\(368\) | 27.1174 | 0.00384128 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4908.45 | 0.689670 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 344.278 | 0.0477910 | 0.0238955 | − | 0.999714i | \(-0.492393\pi\) | ||||
0.0238955 | + | 0.999714i | \(0.492393\pi\) | |||||||
\(374\) | 17417.0 | 2.40806 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13386.3 | 1.79294 | ||||||||
\(383\) | 7597.37 | 1.01360 | 0.506798 | − | 0.862065i | \(-0.330829\pi\) | ||||
0.506798 | + | 0.862065i | \(0.330829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3437.27 | −0.453245 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18834.0 | −2.46431 | ||||||||
\(389\) | −3101.84 | −0.404291 | −0.202146 | − | 0.979355i | \(-0.564791\pi\) | ||||
−0.202146 | + | 0.979355i | \(0.564791\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.52432 | −0.00123188 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15683.7 | −2.00541 | ||||||||
\(395\) | −1955.93 | −0.249148 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2932.06 | 0.370669 | 0.185335 | − | 0.982675i | \(-0.440663\pi\) | ||||
0.185335 | + | 0.982675i | \(0.440663\pi\) | |||||||
\(398\) | 4786.09 | 0.602777 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6508.25 | 0.813531 | ||||||||
\(401\) | −89.2375 | −0.0111130 | −0.00555649 | − | 0.999985i | \(-0.501769\pi\) | ||||
−0.00555649 | + | 0.999985i | \(0.501769\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11009.3 | 1.36083 | ||||||||
\(404\) | 19921.3 | 2.45327 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6141.56 | 0.747975 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −147.388 | −0.0178188 | −0.00890940 | − | 0.999960i | \(-0.502836\pi\) | ||||
−0.00890940 | + | 0.999960i | \(0.502836\pi\) | |||||||
\(410\) | −4007.36 | −0.482706 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13897.3 | −1.66182 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2466.03 | −0.291693 | ||||||||
\(416\) | −55025.4 | −6.48520 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −28151.1 | −3.22438 | ||||||||
\(425\) | −2285.86 | −0.260896 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 48292.4 | 5.45398 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −227.817 | −0.0255496 | ||||||||
\(431\) | 11283.4 | 1.26102 | 0.630512 | − | 0.776180i | \(-0.282845\pi\) | ||||
0.630512 | + | 0.776180i | \(0.282845\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8906.19 | 0.988462 | 0.494231 | − | 0.869331i | \(-0.335450\pi\) | ||||
0.494231 | + | 0.869331i | \(0.335450\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9138.07 | −1.00375 | ||||||||
\(437\) | −1.23205 | −0.000134867 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8149.49 | −0.886000 | −0.443000 | − | 0.896522i | \(-0.646086\pi\) | ||||
−0.443000 | + | 0.896522i | \(0.646086\pi\) | |||||||
\(440\) | 13760.8 | 1.49095 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 34759.1 | 3.74054 | ||||||||
\(443\) | 11472.8 | 1.23045 | 0.615223 | − | 0.788353i | \(-0.289066\pi\) | ||||
0.615223 | + | 0.788353i | \(0.289066\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2369.25 | −0.252389 | ||||||||
\(446\) | 28591.8 | 3.03557 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1963.80 | −0.206409 | −0.103204 | − | 0.994660i | \(-0.532910\pi\) | ||||
−0.103204 | + | 0.994660i | \(0.532910\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5014.10 | −0.523514 | ||||||||
\(452\) | 7847.42 | 0.816618 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20709.3 | 2.14083 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5589.85 | 0.572171 | 0.286086 | − | 0.958204i | \(-0.407646\pi\) | ||||
0.286086 | + | 0.958204i | \(0.407646\pi\) | |||||||
\(458\) | 34532.3 | 3.52311 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −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 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9821.78 | −0.976363 | ||||||||
\(467\) | 385.511 | 0.0381998 | 0.0190999 | − | 0.999818i | \(-0.493920\pi\) | ||||
0.0190999 | + | 0.999818i | \(0.493920\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7187.95 | −0.705437 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19173.2 | 1.86974 | ||||||||
\(473\) | −285.050 | −0.0277096 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −295.696 | −0.0285631 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −19420.3 | −1.85829 | ||||||||
\(479\) | 1694.46 | 0.161632 | 0.0808160 | − | 0.996729i | \(-0.474247\pi\) | ||||
0.0808160 | + | 0.996729i | \(0.474247\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12256.7 | 1.16186 | ||||||||
\(482\) | −2002.64 | −0.189248 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3126.91 | −0.293662 | ||||||||
\(485\) | 4195.03 | 0.392755 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15711.2 | 1.46189 | 0.730945 | − | 0.682436i | \(-0.239079\pi\) | ||||
0.730945 | + | 0.682436i | \(0.239079\pi\) | |||||||
\(488\) | −62040.2 | −5.75498 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2716.34 | 0.249667 | 0.124834 | − | 0.992178i | \(-0.460160\pi\) | ||||
0.124834 | + | 0.992178i | \(0.460160\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17451.5 | 1.59427 | ||||||||
\(494\) | 4496.38 | 0.409518 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −41601.2 | −3.76603 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4295.34 | 0.385342 | 0.192671 | − | 0.981263i | \(-0.438285\pi\) | ||||
0.192671 | + | 0.981263i | \(0.438285\pi\) | |||||||
\(500\) | −2806.00 | −0.250977 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26573.5 | 2.32088 | ||||||||
\(509\) | 14391.8 | 1.25325 | 0.626624 | − | 0.779321i | \(-0.284436\pi\) | ||||
0.626624 | + | 0.779321i | \(0.284436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 41890.2 | 3.61583 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13457.1 | −1.15480 | ||||||||
\(515\) | 3095.44 | 0.264857 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8993.73 | −0.765075 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 27462.3 | 2.31596 | ||||||||
\(521\) | 2913.36 | 0.244984 | 0.122492 | − | 0.992469i | \(-0.460911\pi\) | ||||
0.122492 | + | 0.992469i | \(0.460911\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16870.2 | −1.41048 | −0.705242 | − | 0.708967i | \(-0.749162\pi\) | ||||
−0.705242 | + | 0.708967i | \(0.749162\pi\) | |||||||
\(524\) | 5013.93 | 0.418005 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8421.82 | −0.698115 | ||||||||
\(527\) | 14611.4 | 1.20775 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12167.0 | −0.999999 | ||||||||
\(530\) | 9742.18 | 0.798441 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10006.6 | −0.813197 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10756.5 | −0.869241 | ||||||||
\(536\) | 12113.6 | 0.976172 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −41738.6 | −3.34476 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2229.59 | −0.177186 | −0.0885929 | − | 0.996068i | \(-0.528237\pi\) | ||||
−0.0885929 | + | 0.996068i | \(0.528237\pi\) | |||||||
\(542\) | −23631.7 | −1.87282 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −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 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4762.16 | −0.369198 | ||||||||
\(551\) | 2257.50 | 0.174542 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −22118.3 | −1.69624 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −60317.9 | −4.60081 | ||||||||
\(557\) | 22734.5 | 1.72943 | 0.864714 | − | 0.502264i | \(-0.167499\pi\) | ||||
0.864714 | + | 0.502264i | \(0.167499\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −568.873 | −0.0430425 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −38269.6 | −2.87243 | ||||||||
\(563\) | 4302.11 | 0.322047 | 0.161023 | − | 0.986951i | \(-0.448521\pi\) | ||||
0.161023 | + | 0.986951i | \(0.448521\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −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 | \(-0.684487\pi\) | ||||
−0.547675 | + | 0.836691i | \(0.684487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16514.5 | 1.21035 | 0.605174 | − | 0.796093i | \(-0.293103\pi\) | ||||
0.605174 | + | 0.796093i | \(0.293103\pi\) | |||||||
\(572\) | 53387.6 | 3.90253 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.60414 | 0.000188870 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1867.97 | −0.134774 | −0.0673870 | − | 0.997727i | \(-0.521466\pi\) | ||||
−0.0673870 | + | 0.997727i | \(0.521466\pi\) | |||||||
\(578\) | 19022.0 | 1.36888 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 21422.5 | 1.53366 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12189.6 | 0.865941 | ||||||||
\(584\) | −51014.3 | −3.61471 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −46314.7 | −3.21541 | ||||||||
\(593\) | −7554.18 | −0.523125 | −0.261562 | − | 0.965187i | \(-0.584238\pi\) | ||||
−0.261562 | + | 0.965187i | \(0.584238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15118.8 | −1.03907 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −39.5988 | −0.00270788 | ||||||||
\(599\) | −28210.9 | −1.92432 | −0.962160 | − | 0.272487i | \(-0.912154\pi\) | ||||
−0.962160 | + | 0.272487i | \(0.912154\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23181.4 | 1.57336 | 0.786679 | − | 0.617363i | \(-0.211799\pi\) | ||||
0.786679 | + | 0.617363i | \(0.211799\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −47706.1 | −3.21380 | ||||||||
\(605\) | 696.478 | 0.0468031 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24863.6 | 1.66257 | 0.831287 | − | 0.555844i | \(-0.187605\pi\) | ||||
0.831287 | + | 0.555844i | \(0.187605\pi\) | |||||||
\(608\) | −9446.93 | −0.630137 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21470.1 | 1.42508 | ||||||||
\(611\) | −17948.7 | −1.18843 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12792.7 | −0.842893 | −0.421446 | − | 0.906853i | \(-0.638477\pi\) | ||||
−0.421446 | + | 0.906853i | \(0.638477\pi\) | |||||||
\(614\) | −57285.0 | −3.76520 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19793.3 | −1.29149 | −0.645744 | − | 0.763554i | \(-0.723453\pi\) | ||||
−0.645744 | + | 0.763554i | \(0.723453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20951.7 | 1.36045 | 0.680226 | − | 0.733002i | \(-0.261882\pi\) | ||||
0.680226 | + | 0.733002i | \(0.261882\pi\) | |||||||
\(620\) | 17936.2 | 1.16183 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23399.2 | 1.50840 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 1566.57 | 0.100020 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9598.47 | −0.601268 | ||||||||
\(635\) | −5918.90 | −0.369896 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36356.8 | 2.25608 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −32186.8 | −1.98796 | ||||||||
\(641\) | 22117.7 | 1.36287 | 0.681434 | − | 0.731880i | \(-0.261357\pi\) | ||||
0.681434 | + | 0.731880i | \(0.261357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20269.9 | −1.24318 | −0.621591 | − | 0.783342i | \(-0.713513\pi\) | ||||
−0.621591 | + | 0.783342i | \(0.713513\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5967.54 | 0.363451 | ||||||||
\(647\) | −3145.25 | −0.191117 | −0.0955583 | − | 0.995424i | \(-0.530464\pi\) | ||||
−0.0955583 | + | 0.995424i | \(0.530464\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −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 | \(-0.442912\pi\) | ||||
0.178386 | + | 0.983961i | \(0.442912\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1116.79 | −0.0666205 | ||||||||
\(656\) | 37812.3 | 2.25049 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26277.5 | −1.55330 | −0.776652 | − | 0.629930i | \(-0.783084\pi\) | ||||
−0.776652 | + | 0.629930i | \(0.783084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24004.3 | 1.41250 | 0.706248 | − | 0.707964i | \(-0.250386\pi\) | ||||
0.706248 | + | 0.707964i | \(0.250386\pi\) | |||||||
\(662\) | 30939.1 | 1.81644 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 39320.3 | 2.29808 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.8814 | −0.00115414 | ||||||||
\(668\) | 32577.4 | 1.88691 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −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 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 57227.1 | 3.25598 | ||||||||
\(677\) | −18773.1 | −1.06575 | −0.532873 | − | 0.846195i | \(-0.678888\pi\) | ||||
−0.532873 | + | 0.846195i | \(0.678888\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 36447.6 | 2.05544 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 30440.1 | 1.70911 | ||||||||
\(683\) | 10222.2 | 0.572684 | 0.286342 | − | 0.958127i | \(-0.407561\pi\) | ||||
0.286342 | + | 0.958127i | \(0.407561\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10183.3 | 0.568006 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2149.62 | 0.119118 | ||||||||
\(689\) | 24326.8 | 1.34510 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22355.1 | −1.23072 | −0.615361 | − | 0.788246i | \(-0.710990\pi\) | ||||
−0.615361 | + | 0.788246i | \(0.710990\pi\) | |||||||
\(692\) | −44428.2 | −2.44062 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −64197.3 | −3.51138 | ||||||||
\(695\) | 13435.0 | 0.733264 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13280.6 | −0.721722 | ||||||||
\(698\) | 7267.70 | 0.394107 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16217.3 | −0.873779 | −0.436890 | − | 0.899515i | \(-0.643920\pi\) | ||||
−0.436890 | + | 0.899515i | \(0.643920\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2104.26 | 0.112893 | ||||||||
\(704\) | −80247.1 | −4.29606 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 32273.7 | 1.72045 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3922.92 | 0.207798 | 0.103899 | − | 0.994588i | \(-0.466868\pi\) | ||||
0.103899 | + | 0.994588i | \(0.466868\pi\) | |||||||
\(710\) | −8592.83 | −0.454202 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 37777.1 | 1.98842 | ||||||||
\(713\) | −16.6458 | −0.000874322 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11891.4 | −0.621976 | ||||||||
\(716\) | 97843.4 | 5.10695 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 68544.3 | 3.56275 | ||||||||
\(719\) | 23908.6 | 1.24011 | 0.620055 | − | 0.784558i | \(-0.287110\pi\) | ||||
0.620055 | + | 0.784558i | \(0.287110\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −37075.8 | −1.91111 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8483.62 | 0.435485 | ||||||||
\(725\) | −4771.58 | −0.244430 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26906.4 | 1.37263 | 0.686315 | − | 0.727305i | \(-0.259227\pi\) | ||||
0.686315 | + | 0.727305i | \(0.259227\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 17654.4 | 0.895095 | ||||||||
\(731\) | −755.001 | −0.0382007 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27637.5 | −1.39265 | −0.696325 | − | 0.717726i | \(-0.745183\pi\) | ||||
−0.696325 | + | 0.717726i | \(0.745183\pi\) | |||||||
\(734\) | 36367.7 | 1.82882 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 83.1973 | 0.00416670 | ||||||||
\(737\) | −5245.29 | −0.262161 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14038.9 | −0.698821 | −0.349410 | − | 0.936970i | \(-0.613618\pi\) | ||||
−0.349410 | + | 0.936970i | \(0.613618\pi\) | |||||||
\(740\) | 19968.4 | 0.991963 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17698.7 | −0.873893 | −0.436946 | − | 0.899488i | \(-0.643940\pi\) | ||||
−0.436946 | + | 0.899488i | \(0.643940\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3367.50 | 0.165605 | ||||||||
\(746\) | 1899.72 | 0.0932354 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 70855.4 | 3.46354 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17199.7 | 0.835719 | 0.417859 | − | 0.908512i | \(-0.362780\pi\) | ||||
0.417859 | + | 0.908512i | \(0.362780\pi\) | |||||||
\(752\) | 67823.4 | 3.28892 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4714.80 | 0.225031 | ||||||||
\(761\) | −27918.7 | −1.32990 | −0.664949 | − | 0.746889i | \(-0.731547\pi\) | ||||
−0.664949 | + | 0.746889i | \(0.731547\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 54457.7 | 2.57881 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 41922.1 | 1.97742 | ||||||||
\(767\) | −16568.5 | −0.779992 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7436.29 | 0.348712 | 0.174356 | − | 0.984683i | \(-0.444216\pi\) | ||||
0.174356 | + | 0.984683i | \(0.444216\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13983.4 | −0.651908 | ||||||||
\(773\) | 4989.84 | 0.232176 | 0.116088 | − | 0.993239i | \(-0.462965\pi\) | ||||
0.116088 | + | 0.993239i | \(0.462965\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3995.05 | −0.185169 | ||||||||
\(776\) | −66888.7 | −3.09429 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17115.9 | −0.788731 | ||||||||
\(779\) | −1717.96 | −0.0790146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10751.5 | −0.492600 | ||||||||
\(782\) | −52.5550 | −0.00240328 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14065.2 | −0.639500 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2870.69 | 0.130024 | 0.0650122 | − | 0.997884i | \(-0.479291\pi\) | ||||
0.0650122 | + | 0.997884i | \(0.479291\pi\) | |||||||
\(788\) | −63803.8 | −2.88441 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10792.8 | −0.486063 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53612.1 | 2.40078 | ||||||||
\(794\) | 16179.0 | 0.723138 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −492.410 | −0.0216803 | ||||||||
\(803\) | 22089.6 | 0.970766 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 60749.1 | 2.65483 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 70750.2 | 3.08042 | ||||||||
\(809\) | 15376.9 | 0.668261 | 0.334131 | − | 0.942527i | \(-0.391557\pi\) | ||||
0.334131 | + | 0.942527i | \(0.391557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36422.9 | −1.57704 | −0.788522 | − | 0.615007i | \(-0.789153\pi\) | ||||
−0.788522 | + | 0.615007i | \(0.789153\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 33889.0 | 1.45922 | ||||||||
\(815\) | 6722.10 | 0.288914 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −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 | \(-0.317838\pi\) | ||||
0.541550 | + | 0.840669i | \(0.317838\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17933.3 | −0.759557 | −0.379779 | − | 0.925077i | \(-0.624000\pi\) | ||||
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(824\) | −49356.1 | −2.08665 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13021.6 | −0.547529 | −0.273764 | − | 0.961797i | \(-0.588269\pi\) | ||||
−0.273764 | + | 0.961797i | \(0.588269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11397.6 | 0.477509 | 0.238754 | − | 0.971080i | \(-0.423261\pi\) | ||||
0.238754 | + | 0.971080i | \(0.423261\pi\) | |||||||
\(830\) | −13607.5 | −0.569063 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −160149. | −6.67326 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7256.19 | −0.300731 | ||||||||
\(836\) | 9165.75 | 0.379191 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −134148. | −5.47104 | ||||||||
\(845\) | −12746.6 | −0.518929 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −91924.4 | −3.72252 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12613.3 | −0.508981 | ||||||||
\(851\) | −18.5318 | −0.000746490 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21771.6 | −0.873911 | −0.436956 | − | 0.899483i | \(-0.643943\pi\) | ||||
−0.436956 | + | 0.899483i | \(0.643943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 171510. | 6.84823 | ||||||||
\(857\) | 29860.2 | 1.19021 | 0.595103 | − | 0.803649i | \(-0.297111\pi\) | ||||
0.595103 | + | 0.803649i | \(0.297111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18530.6 | −0.736039 | −0.368019 | − | 0.929818i | \(-0.619964\pi\) | ||||
−0.368019 | + | 0.929818i | \(0.619964\pi\) | |||||||
\(860\) | −926.799 | −0.0367484 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 62261.4 | 2.46013 | ||||||||
\(863\) | 21296.5 | 0.840024 | 0.420012 | − | 0.907519i | \(-0.362026\pi\) | ||||
0.420012 | + | 0.907519i | \(0.362026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9895.79 | 0.388979 | ||||||||
\(866\) | 49144.1 | 1.92839 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13504.2 | −0.527155 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10468.0 | −0.407226 | ||||||||
\(872\) | −32453.7 | −1.26035 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.79843 | −0.000263112 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18793.4 | −0.723614 | −0.361807 | − | 0.932253i | \(-0.617840\pi\) | ||||
−0.361807 | + | 0.932253i | \(0.617840\pi\) | |||||||
\(878\) | −44968.7 | −1.72850 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 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 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 63306.5 | 2.40048 | ||||||||
\(887\) | −5131.41 | −0.194246 | −0.0971229 | − | 0.995272i | \(-0.530964\pi\) | ||||
−0.0971229 | + | 0.995272i | \(0.530964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −13073.5 | −0.492386 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 116316. | 4.36610 | ||||||||
\(893\) | −3081.49 | −0.115474 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21793.3 | −0.813933 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10836.2 | −0.402682 | ||||||||
\(899\) | 30500.3 | 1.13153 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32286.2 | 1.19380 | ||||||||
\(902\) | −27667.7 | −1.02132 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27870.0 | 1.02538 | ||||||||
\(905\) | −1889.61 | −0.0694065 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19934.6 | −0.729787 | −0.364893 | − | 0.931049i | \(-0.618895\pi\) | ||||
−0.364893 | + | 0.931049i | \(0.618895\pi\) | |||||||
\(908\) | 84248.8 | 3.07918 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48387.4 | −1.75976 | −0.879882 | − | 0.475193i | \(-0.842378\pi\) | ||||
−0.879882 | + | 0.475193i | \(0.842378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17026.0 | −0.617172 | ||||||||
\(914\) | 30844.7 | 1.11625 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 140483. | 5.06735 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14431.7 | −0.518019 | −0.259009 | − | 0.965875i | \(-0.583396\pi\) | ||||
−0.259009 | + | 0.965875i | \(0.583396\pi\) | |||||||
\(920\) | −41.5224 | −0.00148799 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −103688. | −3.70366 | ||||||||
\(923\) | −21456.8 | −0.765177 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4447.69 | −0.158096 | ||||||||
\(926\) | −43549.1 | −1.54548 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −152443. | −5.39244 | ||||||||
\(929\) | 5549.82 | 0.196000 | 0.0979998 | − | 0.995186i | \(-0.468756\pi\) | ||||
0.0979998 | + | 0.995186i | \(0.468756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −39956.7 | −1.40432 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2127.24 | 0.0745239 | ||||||||
\(935\) | −15782.1 | −0.552010 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26231.9 | −0.914576 | −0.457288 | − | 0.889319i | \(-0.651179\pi\) | ||||
−0.457288 | + | 0.889319i | \(0.651179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −29241.8 | −1.01464 | ||||||||
\(941\) | 2836.80 | 0.0982753 | 0.0491376 | − | 0.998792i | \(-0.484353\pi\) | ||||
0.0491376 | + | 0.998792i | \(0.484353\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 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 | \(-0.257185\pi\) | ||||
0.690967 | + | 0.722886i | \(0.257185\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44084.1 | 1.50793 | ||||||||
\(950\) | −1631.64 | −0.0557236 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17770.1 | −0.604019 | −0.302010 | − | 0.953305i | \(-0.597657\pi\) | ||||
−0.302010 | + | 0.953305i | \(0.597657\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12129.7 | −0.411004 | ||||||||
\(956\) | −79005.0 | −2.67281 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9349.97 | 0.315328 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4254.35 | −0.142807 | ||||||||
\(962\) | 67632.0 | 2.26668 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −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 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23148.0 | 0.766226 | ||||||||
\(971\) | 17650.7 | 0.583356 | 0.291678 | − | 0.956517i | \(-0.405786\pi\) | ||||
0.291678 | + | 0.956517i | \(0.405786\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 86693.8 | 2.85200 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −202586. | −6.64407 | ||||||||
\(977\) | 14477.6 | 0.474085 | 0.237042 | − | 0.971499i | \(-0.423822\pi\) | ||||
0.237042 | + | 0.971499i | \(0.423822\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16357.8 | −0.534012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14988.7 | 0.487075 | ||||||||
\(983\) | −8764.09 | −0.284365 | −0.142183 | − | 0.989840i | \(-0.545412\pi\) | ||||
−0.142183 | + | 0.989840i | \(0.545412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14211.4 | 0.459710 | ||||||||
\(986\) | 96296.9 | 3.11026 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18292.0 | 0.589015 | ||||||||
\(989\) | 0.860124 | 2.76546e−5 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33624.1 | 1.07781 | 0.538903 | − | 0.842368i | \(-0.318839\pi\) | ||||
0.538903 | + | 0.842368i | \(0.318839\pi\) | |||||||
\(992\) | −127634. | −4.08507 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4336.82 | −0.138177 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16631.3 | −0.528302 | −0.264151 | − | 0.964481i | \(-0.585092\pi\) | ||||
−0.264151 | + | 0.964481i | \(0.585092\pi\) | |||||||
\(998\) | 23701.6 | 0.751764 | ||||||||
\(999\) | 0 | 0 |
(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 | 2205.4.a.bz.1.6 | 6 | ||
3.2 | odd | 2 | 245.4.a.o.1.1 | ✓ | 6 | ||
7.6 | odd | 2 | 2205.4.a.ca.1.6 | 6 | |||
15.14 | odd | 2 | 1225.4.a.bj.1.6 | 6 | |||
21.2 | odd | 6 | 245.4.e.q.116.6 | 12 | |||
21.5 | even | 6 | 245.4.e.p.116.6 | 12 | |||
21.11 | odd | 6 | 245.4.e.q.226.6 | 12 | |||
21.17 | even | 6 | 245.4.e.p.226.6 | 12 | |||
21.20 | even | 2 | 245.4.a.p.1.1 | yes | 6 | ||
105.104 | even | 2 | 1225.4.a.bi.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.1 | ✓ | 6 | 3.2 | odd | 2 | ||
245.4.a.p.1.1 | yes | 6 | 21.20 | even | 2 | ||
245.4.e.p.116.6 | 12 | 21.5 | even | 6 | |||
245.4.e.p.226.6 | 12 | 21.17 | even | 6 | |||
245.4.e.q.116.6 | 12 | 21.2 | odd | 6 | |||
245.4.e.q.226.6 | 12 | 21.11 | odd | 6 | |||
1225.4.a.bi.1.6 | 6 | 105.104 | even | 2 | |||
1225.4.a.bj.1.6 | 6 | 15.14 | odd | 2 | |||
2205.4.a.bz.1.6 | 6 | 1.1 | even | 1 | trivial | ||
2205.4.a.ca.1.6 | 6 | 7.6 | odd | 2 |