Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,4,Mod(99,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.99");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(28.9109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 185x^{10} + 12748x^{8} + 405460x^{6} + 5908496x^{4} + 33016000x^{2} + 60840000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.4 | ||
Root | \(2.06759i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.99 |
Dual form | 490.4.c.f.99.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | 3.06759i | 0.590358i | 0.955442 | + | 0.295179i | \(0.0953793\pi\) | ||||
−0.955442 | + | 0.295179i | \(0.904621\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −9.26709 | − | 6.25468i | −0.828874 | − | 0.559435i | ||||
\(6\) | 6.13518 | 0.417446 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 17.5899 | 0.651478 | ||||||||
\(10\) | −12.5094 | + | 18.5342i | −0.395581 | + | 0.586102i | ||||
\(11\) | −49.5016 | −1.35685 | −0.678423 | − | 0.734672i | \(-0.737336\pi\) | ||||
−0.678423 | + | 0.734672i | \(0.737336\pi\) | |||||||
\(12\) | − | 12.2704i | − | 0.295179i | ||||||
\(13\) | − | 44.6154i | − | 0.951852i | −0.879485 | − | 0.475926i | \(-0.842113\pi\) | ||
0.879485 | − | 0.475926i | \(-0.157887\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 19.1868 | − | 28.4276i | 0.330267 | − | 0.489332i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 39.2912i | − | 0.560560i | −0.959918 | − | 0.280280i | \(-0.909573\pi\) | ||
0.959918 | − | 0.280280i | \(-0.0904273\pi\) | |||||||
\(18\) | − | 35.1798i | − | 0.460664i | ||||||
\(19\) | 56.3157 | 0.679984 | 0.339992 | − | 0.940428i | \(-0.389576\pi\) | ||||
0.339992 | + | 0.940428i | \(0.389576\pi\) | |||||||
\(20\) | 37.0684 | + | 25.0187i | 0.414437 | + | 0.279718i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 99.0033i | 0.959435i | ||||||||
\(23\) | 91.6603i | 0.830978i | 0.909598 | + | 0.415489i | \(0.136390\pi\) | ||||
−0.909598 | + | 0.415489i | \(0.863610\pi\) | |||||||
\(24\) | −24.5407 | −0.208723 | ||||||||
\(25\) | 46.7580 | + | 115.925i | 0.374064 | + | 0.927403i | ||||
\(26\) | −89.2307 | −0.673061 | ||||||||
\(27\) | 136.783i | 0.974963i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −281.845 | −1.80473 | −0.902367 | − | 0.430969i | \(-0.858172\pi\) | ||||
−0.902367 | + | 0.430969i | \(0.858172\pi\) | |||||||
\(30\) | −56.8553 | − | 38.3736i | −0.346010 | − | 0.233534i | ||||
\(31\) | 70.5654 | 0.408836 | 0.204418 | − | 0.978884i | \(-0.434470\pi\) | ||||
0.204418 | + | 0.978884i | \(0.434470\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | − | 151.851i | − | 0.801025i | ||||||
\(34\) | −78.5824 | −0.396376 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −70.3596 | −0.325739 | ||||||||
\(37\) | 197.089i | 0.875710i | 0.899046 | + | 0.437855i | \(0.144262\pi\) | ||||
−0.899046 | + | 0.437855i | \(0.855738\pi\) | |||||||
\(38\) | − | 112.631i | − | 0.480822i | ||||||
\(39\) | 136.862 | 0.561933 | ||||||||
\(40\) | 50.0374 | − | 74.1367i | 0.197790 | − | 0.293051i | ||||
\(41\) | 399.021 | 1.51992 | 0.759959 | − | 0.649971i | \(-0.225219\pi\) | ||||
0.759959 | + | 0.649971i | \(0.225219\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 203.567i | 0.721946i | 0.932576 | + | 0.360973i | \(0.117555\pi\) | ||||
−0.932576 | + | 0.360973i | \(0.882445\pi\) | |||||||
\(44\) | 198.007 | 0.678423 | ||||||||
\(45\) | −163.007 | − | 110.019i | −0.539993 | − | 0.364460i | ||||
\(46\) | 183.321 | 0.587590 | ||||||||
\(47\) | 68.4988i | 0.212587i | 0.994335 | + | 0.106293i | \(0.0338983\pi\) | ||||
−0.994335 | + | 0.106293i | \(0.966102\pi\) | |||||||
\(48\) | 49.0814i | 0.147589i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 231.851 | − | 93.5161i | 0.655773 | − | 0.264503i | ||||
\(51\) | 120.529 | 0.330931 | ||||||||
\(52\) | 178.461i | 0.475926i | ||||||||
\(53\) | 617.486i | 1.60034i | 0.599771 | + | 0.800172i | \(0.295258\pi\) | ||||
−0.599771 | + | 0.800172i | \(0.704742\pi\) | |||||||
\(54\) | 273.567 | 0.689403 | ||||||||
\(55\) | 458.736 | + | 309.617i | 1.12465 | + | 0.759068i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 172.753i | 0.401434i | ||||||||
\(58\) | 563.690i | 1.27614i | ||||||||
\(59\) | −480.513 | −1.06029 | −0.530147 | − | 0.847905i | \(-0.677863\pi\) | ||||
−0.530147 | + | 0.847905i | \(0.677863\pi\) | |||||||
\(60\) | −76.7471 | + | 113.711i | −0.165134 | + | 0.244666i | ||||
\(61\) | −23.4974 | −0.0493202 | −0.0246601 | − | 0.999696i | \(-0.507850\pi\) | ||||
−0.0246601 | + | 0.999696i | \(0.507850\pi\) | |||||||
\(62\) | − | 141.131i | − | 0.289091i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −279.055 | + | 413.455i | −0.532500 | + | 0.788965i | ||||
\(66\) | −303.701 | −0.566410 | ||||||||
\(67\) | 252.124i | 0.459729i | 0.973223 | + | 0.229865i | \(0.0738283\pi\) | ||||
−0.973223 | + | 0.229865i | \(0.926172\pi\) | |||||||
\(68\) | 157.165i | 0.280280i | ||||||||
\(69\) | −281.176 | −0.490574 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 835.640 | 1.39679 | 0.698396 | − | 0.715711i | \(-0.253897\pi\) | ||||
0.698396 | + | 0.715711i | \(0.253897\pi\) | |||||||
\(72\) | 140.719i | 0.230332i | ||||||||
\(73\) | 257.786i | 0.413309i | 0.978414 | + | 0.206654i | \(0.0662576\pi\) | ||||
−0.978414 | + | 0.206654i | \(0.933742\pi\) | |||||||
\(74\) | 394.179 | 0.619221 | ||||||||
\(75\) | −355.611 | + | 143.434i | −0.547500 | + | 0.220832i | ||||
\(76\) | −225.263 | −0.339992 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 273.723i | − | 0.397347i | ||||||
\(79\) | 773.700 | 1.10187 | 0.550937 | − | 0.834547i | \(-0.314270\pi\) | ||||
0.550937 | + | 0.834547i | \(0.314270\pi\) | |||||||
\(80\) | −148.273 | − | 100.075i | −0.207218 | − | 0.139859i | ||||
\(81\) | 55.3315 | 0.0759006 | ||||||||
\(82\) | − | 798.043i | − | 1.07474i | ||||||
\(83\) | 1341.21i | 1.77369i | 0.462065 | + | 0.886846i | \(0.347109\pi\) | ||||
−0.462065 | + | 0.886846i | \(0.652891\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −245.754 | + | 364.115i | −0.313597 | + | 0.464633i | ||||
\(86\) | 407.134 | 0.510493 | ||||||||
\(87\) | − | 864.584i | − | 1.06544i | ||||||
\(88\) | − | 396.013i | − | 0.479717i | ||||||
\(89\) | −1301.12 | −1.54964 | −0.774821 | − | 0.632181i | \(-0.782160\pi\) | ||||
−0.774821 | + | 0.632181i | \(0.782160\pi\) | |||||||
\(90\) | −220.038 | + | 326.014i | −0.257712 | + | 0.381833i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 366.641i | − | 0.415489i | ||||||
\(93\) | 216.466i | 0.241360i | ||||||||
\(94\) | 136.998 | 0.150322 | ||||||||
\(95\) | −521.883 | − | 352.236i | −0.563621 | − | 0.380407i | ||||
\(96\) | 98.1629 | 0.104362 | ||||||||
\(97\) | − | 323.729i | − | 0.338862i | −0.985542 | − | 0.169431i | \(-0.945807\pi\) | ||
0.985542 | − | 0.169431i | \(-0.0541931\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −870.729 | −0.883955 | ||||||||
\(100\) | −187.032 | − | 463.701i | −0.187032 | − | 0.463701i | ||||
\(101\) | 1181.02 | 1.16352 | 0.581761 | − | 0.813360i | \(-0.302364\pi\) | ||||
0.581761 | + | 0.813360i | \(0.302364\pi\) | |||||||
\(102\) | − | 241.059i | − | 0.234003i | ||||||
\(103\) | 732.042i | 0.700294i | 0.936695 | + | 0.350147i | \(0.113868\pi\) | ||||
−0.936695 | + | 0.350147i | \(0.886132\pi\) | |||||||
\(104\) | 356.923 | 0.336530 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1234.97 | 1.13161 | ||||||||
\(107\) | 1338.04i | 1.20891i | 0.796639 | + | 0.604455i | \(0.206609\pi\) | ||||
−0.796639 | + | 0.604455i | \(0.793391\pi\) | |||||||
\(108\) | − | 547.134i | − | 0.487481i | ||||||
\(109\) | 51.7571 | 0.0454810 | 0.0227405 | − | 0.999741i | \(-0.492761\pi\) | ||||
0.0227405 | + | 0.999741i | \(0.492761\pi\) | |||||||
\(110\) | 619.233 | − | 917.473i | 0.536742 | − | 0.795251i | ||||
\(111\) | −604.589 | −0.516982 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 471.803i | − | 0.392774i | −0.980526 | − | 0.196387i | \(-0.937079\pi\) | ||
0.980526 | − | 0.196387i | \(-0.0629209\pi\) | |||||||
\(114\) | 345.507 | 0.283857 | ||||||||
\(115\) | 573.306 | − | 849.424i | 0.464878 | − | 0.688776i | ||||
\(116\) | 1127.38 | 0.902367 | ||||||||
\(117\) | − | 784.780i | − | 0.620110i | ||||||
\(118\) | 961.025i | 0.749742i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 227.421 | + | 153.494i | 0.173005 | + | 0.116767i | ||||
\(121\) | 1119.41 | 0.841031 | ||||||||
\(122\) | 46.9948i | 0.0348746i | ||||||||
\(123\) | 1224.03i | 0.897296i | ||||||||
\(124\) | −282.262 | −0.204418 | ||||||||
\(125\) | 291.765 | − | 1366.75i | 0.208770 | − | 0.977965i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 202.294i | 0.141344i | 0.997500 | + | 0.0706721i | \(0.0225144\pi\) | ||||
−0.997500 | + | 0.0706721i | \(0.977486\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | −624.460 | −0.426206 | ||||||||
\(130\) | 826.909 | + | 558.109i | 0.557883 | + | 0.376534i | ||||
\(131\) | −1168.96 | −0.779635 | −0.389817 | − | 0.920892i | \(-0.627462\pi\) | ||||
−0.389817 | + | 0.920892i | \(0.627462\pi\) | |||||||
\(132\) | 607.403i | 0.400512i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 504.248 | 0.325078 | ||||||||
\(135\) | 855.537 | − | 1267.59i | 0.545429 | − | 0.808121i | ||||
\(136\) | 314.330 | 0.198188 | ||||||||
\(137\) | 146.718i | 0.0914958i | 0.998953 | + | 0.0457479i | \(0.0145671\pi\) | ||||
−0.998953 | + | 0.0457479i | \(0.985433\pi\) | |||||||
\(138\) | 562.352i | 0.346888i | ||||||||
\(139\) | 2505.64 | 1.52896 | 0.764479 | − | 0.644648i | \(-0.222996\pi\) | ||||
0.764479 | + | 0.644648i | \(0.222996\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −210.126 | −0.125502 | ||||||||
\(142\) | − | 1671.28i | − | 0.987681i | ||||||
\(143\) | 2208.53i | 1.29152i | ||||||||
\(144\) | 281.438 | 0.162869 | ||||||||
\(145\) | 2611.88 | + | 1762.85i | 1.49590 | + | 1.00963i | ||||
\(146\) | 515.571 | 0.292253 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 788.357i | − | 0.437855i | ||||||
\(149\) | −2108.18 | −1.15912 | −0.579559 | − | 0.814930i | \(-0.696775\pi\) | ||||
−0.579559 | + | 0.814930i | \(0.696775\pi\) | |||||||
\(150\) | 286.869 | + | 711.223i | 0.156152 | + | 0.387141i | ||||
\(151\) | −2215.51 | −1.19401 | −0.597004 | − | 0.802238i | \(-0.703642\pi\) | ||||
−0.597004 | + | 0.802238i | \(0.703642\pi\) | |||||||
\(152\) | 450.525i | 0.240411i | ||||||||
\(153\) | − | 691.128i | − | 0.365192i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −653.936 | − | 441.364i | −0.338874 | − | 0.228717i | ||||
\(156\) | −547.446 | −0.280967 | ||||||||
\(157\) | − | 2262.03i | − | 1.14987i | −0.818199 | − | 0.574935i | \(-0.805028\pi\) | ||
0.818199 | − | 0.574935i | \(-0.194972\pi\) | |||||||
\(158\) | − | 1547.40i | − | 0.779143i | ||||||
\(159\) | −1894.19 | −0.944775 | ||||||||
\(160\) | −200.150 | + | 296.547i | −0.0988951 | + | 0.146526i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 110.663i | − | 0.0536698i | ||||||
\(163\) | − | 87.7158i | − | 0.0421499i | −0.999778 | − | 0.0210750i | \(-0.993291\pi\) | ||
0.999778 | − | 0.0210750i | \(-0.00670886\pi\) | |||||||
\(164\) | −1596.09 | −0.759959 | ||||||||
\(165\) | −949.777 | + | 1407.21i | −0.448122 | + | 0.663949i | ||||
\(166\) | 2682.41 | 1.25419 | ||||||||
\(167\) | − | 1851.38i | − | 0.857868i | −0.903336 | − | 0.428934i | \(-0.858889\pi\) | ||
0.903336 | − | 0.428934i | \(-0.141111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 206.469 | 0.0939779 | ||||||||
\(170\) | 728.230 | + | 491.508i | 0.328545 | + | 0.221747i | ||||
\(171\) | 990.587 | 0.442995 | ||||||||
\(172\) | − | 814.268i | − | 0.360973i | ||||||
\(173\) | − | 1842.08i | − | 0.809541i | −0.914418 | − | 0.404771i | \(-0.867351\pi\) | ||
0.914418 | − | 0.404771i | \(-0.132649\pi\) | |||||||
\(174\) | −1729.17 | −0.753379 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −792.026 | −0.339211 | ||||||||
\(177\) | − | 1474.02i | − | 0.625953i | ||||||
\(178\) | 2602.23i | 1.09576i | ||||||||
\(179\) | −748.532 | −0.312558 | −0.156279 | − | 0.987713i | \(-0.549950\pi\) | ||||
−0.156279 | + | 0.987713i | \(0.549950\pi\) | |||||||
\(180\) | 652.029 | + | 440.076i | 0.269996 | + | 0.182230i | ||||
\(181\) | −1393.90 | −0.572418 | −0.286209 | − | 0.958167i | \(-0.592395\pi\) | ||||
−0.286209 | + | 0.958167i | \(0.592395\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 72.0803i | − | 0.0291166i | ||||||
\(184\) | −733.282 | −0.293795 | ||||||||
\(185\) | 1232.73 | − | 1826.44i | 0.489903 | − | 0.725853i | ||||
\(186\) | 432.931 | 0.170667 | ||||||||
\(187\) | 1944.98i | 0.760593i | ||||||||
\(188\) | − | 273.995i | − | 0.106293i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −704.473 | + | 1043.77i | −0.268989 | + | 0.398541i | ||||
\(191\) | −958.174 | −0.362990 | −0.181495 | − | 0.983392i | \(-0.558094\pi\) | ||||
−0.181495 | + | 0.983392i | \(0.558094\pi\) | |||||||
\(192\) | − | 196.326i | − | 0.0737947i | ||||||
\(193\) | − | 4577.04i | − | 1.70706i | −0.521044 | − | 0.853530i | \(-0.674457\pi\) | ||
0.521044 | − | 0.853530i | \(-0.325543\pi\) | |||||||
\(194\) | −647.457 | −0.239612 | ||||||||
\(195\) | −1268.31 | − | 856.025i | −0.465772 | − | 0.314365i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3429.27i | 1.24023i | 0.784511 | + | 0.620115i | \(0.212914\pi\) | ||||
−0.784511 | + | 0.620115i | \(0.787086\pi\) | |||||||
\(198\) | 1741.46i | 0.625050i | ||||||||
\(199\) | 146.016 | 0.0520140 | 0.0260070 | − | 0.999662i | \(-0.491721\pi\) | ||||
0.0260070 | + | 0.999662i | \(0.491721\pi\) | |||||||
\(200\) | −927.403 | + | 374.064i | −0.327886 | + | 0.132252i | ||||
\(201\) | −773.413 | −0.271405 | ||||||||
\(202\) | − | 2362.04i | − | 0.822734i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −482.117 | −0.165465 | ||||||||
\(205\) | −3697.77 | − | 2495.75i | −1.25982 | − | 0.850296i | ||||
\(206\) | 1464.08 | 0.495182 | ||||||||
\(207\) | 1612.29i | 0.541363i | ||||||||
\(208\) | − | 713.846i | − | 0.237963i | ||||||
\(209\) | −2787.72 | −0.922634 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −705.410 | −0.230154 | −0.115077 | − | 0.993357i | \(-0.536711\pi\) | ||||
−0.115077 | + | 0.993357i | \(0.536711\pi\) | |||||||
\(212\) | − | 2469.94i | − | 0.800172i | ||||||
\(213\) | 2563.40i | 0.824607i | ||||||||
\(214\) | 2676.08 | 0.854829 | ||||||||
\(215\) | 1273.25 | − | 1886.47i | 0.403882 | − | 0.598402i | ||||
\(216\) | −1094.27 | −0.344701 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 103.514i | − | 0.0321600i | ||||||
\(219\) | −790.781 | −0.244000 | ||||||||
\(220\) | −1834.95 | − | 1238.47i | −0.562327 | − | 0.379534i | ||||
\(221\) | −1752.99 | −0.533570 | ||||||||
\(222\) | 1209.18i | 0.365562i | ||||||||
\(223\) | − | 2232.07i | − | 0.670271i | −0.942170 | − | 0.335135i | \(-0.891218\pi\) | ||
0.942170 | − | 0.335135i | \(-0.108782\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 822.469 | + | 2039.11i | 0.243694 | + | 0.604182i | ||||
\(226\) | −943.606 | −0.277733 | ||||||||
\(227\) | 5464.96i | 1.59789i | 0.601401 | + | 0.798947i | \(0.294609\pi\) | ||||
−0.601401 | + | 0.798947i | \(0.705391\pi\) | |||||||
\(228\) | − | 691.014i | − | 0.200717i | ||||||
\(229\) | −1943.89 | −0.560942 | −0.280471 | − | 0.959862i | \(-0.590491\pi\) | ||||
−0.280471 | + | 0.959862i | \(0.590491\pi\) | |||||||
\(230\) | −1698.85 | − | 1146.61i | −0.487038 | − | 0.328719i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 2254.76i | − | 0.638070i | ||||||
\(233\) | 3307.25i | 0.929893i | 0.885339 | + | 0.464946i | \(0.153926\pi\) | ||||
−0.885339 | + | 0.464946i | \(0.846074\pi\) | |||||||
\(234\) | −1569.56 | −0.438484 | ||||||||
\(235\) | 428.438 | − | 634.785i | 0.118929 | − | 0.176208i | ||||
\(236\) | 1922.05 | 0.530147 | ||||||||
\(237\) | 2373.39i | 0.650500i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6107.99 | −1.65311 | −0.826554 | − | 0.562857i | \(-0.809702\pi\) | ||||
−0.826554 | + | 0.562857i | \(0.809702\pi\) | |||||||
\(240\) | 306.989 | − | 454.842i | 0.0825668 | − | 0.122333i | ||||
\(241\) | −3962.60 | −1.05914 | −0.529571 | − | 0.848265i | \(-0.677647\pi\) | ||||
−0.529571 | + | 0.848265i | \(0.677647\pi\) | |||||||
\(242\) | − | 2238.82i | − | 0.594699i | ||||||
\(243\) | 3862.89i | 1.01977i | ||||||||
\(244\) | 93.9895 | 0.0246601 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2448.07 | 0.634484 | ||||||||
\(247\) | − | 2512.54i | − | 0.647244i | ||||||
\(248\) | 564.523i | 0.144545i | ||||||||
\(249\) | −4114.27 | −1.04711 | ||||||||
\(250\) | −2733.49 | − | 583.529i | −0.691526 | − | 0.147623i | ||||
\(251\) | −3.92299 | −0.000986522 | −0.000493261 | − | 1.00000i | \(-0.500157\pi\) | ||||
−0.000493261 | 1.00000i | \(0.500157\pi\) | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4537.33i | − | 1.12751i | ||||||
\(254\) | 404.589 | 0.0999455 | ||||||||
\(255\) | −1116.96 | − | 753.872i | −0.274300 | − | 0.185134i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 219.595i | 0.0532994i | 0.999645 | + | 0.0266497i | \(0.00848386\pi\) | ||||
−0.999645 | + | 0.0266497i | \(0.991516\pi\) | |||||||
\(258\) | 1248.92i | 0.301373i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1116.22 | − | 1653.82i | 0.266250 | − | 0.394483i | ||||
\(261\) | −4957.62 | −1.17574 | ||||||||
\(262\) | 2337.91i | 0.551285i | ||||||||
\(263\) | − | 5467.72i | − | 1.28195i | −0.767560 | − | 0.640977i | \(-0.778529\pi\) | ||
0.767560 | − | 0.640977i | \(-0.221471\pi\) | |||||||
\(264\) | 1214.81 | 0.283205 | ||||||||
\(265\) | 3862.17 | − | 5722.30i | 0.895289 | − | 1.32648i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3991.29i | − | 0.914843i | ||||||
\(268\) | − | 1008.50i | − | 0.229865i | ||||||
\(269\) | 291.731 | 0.0661233 | 0.0330616 | − | 0.999453i | \(-0.489474\pi\) | ||||
0.0330616 | + | 0.999453i | \(0.489474\pi\) | |||||||
\(270\) | −2535.17 | − | 1711.07i | −0.571428 | − | 0.385676i | ||||
\(271\) | 2661.02 | 0.596478 | 0.298239 | − | 0.954491i | \(-0.403601\pi\) | ||||
0.298239 | + | 0.954491i | \(0.403601\pi\) | |||||||
\(272\) | − | 628.659i | − | 0.140140i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 293.435 | 0.0646973 | ||||||||
\(275\) | −2314.60 | − | 5738.49i | −0.507547 | − | 1.25834i | ||||
\(276\) | 1124.70 | 0.245287 | ||||||||
\(277\) | 4502.66i | 0.976673i | 0.872655 | + | 0.488336i | \(0.162396\pi\) | ||||
−0.872655 | + | 0.488336i | \(0.837604\pi\) | |||||||
\(278\) | − | 5011.27i | − | 1.08114i | ||||||
\(279\) | 1241.24 | 0.266348 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −462.388 | −0.0981628 | −0.0490814 | − | 0.998795i | \(-0.515629\pi\) | ||||
−0.0490814 | + | 0.998795i | \(0.515629\pi\) | |||||||
\(282\) | 420.253i | 0.0887435i | ||||||||
\(283\) | 7145.71i | 1.50095i | 0.660899 | + | 0.750474i | \(0.270175\pi\) | ||||
−0.660899 | + | 0.750474i | \(0.729825\pi\) | |||||||
\(284\) | −3342.56 | −0.698396 | ||||||||
\(285\) | 1080.52 | − | 1600.92i | 0.224576 | − | 0.332738i | ||||
\(286\) | 4417.07 | 0.913240 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 562.877i | − | 0.115166i | ||||||
\(289\) | 3369.20 | 0.685773 | ||||||||
\(290\) | 3525.70 | − | 5223.76i | 0.713917 | − | 1.05776i | ||||
\(291\) | 993.066 | 0.200050 | ||||||||
\(292\) | − | 1031.14i | − | 0.206654i | ||||||
\(293\) | 8656.21i | 1.72594i | 0.505254 | + | 0.862971i | \(0.331399\pi\) | ||||
−0.505254 | + | 0.862971i | \(0.668601\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4452.95 | + | 3005.45i | 0.878851 | + | 0.593166i | ||||
\(296\) | −1576.71 | −0.309610 | ||||||||
\(297\) | − | 6771.01i | − | 1.32287i | ||||||
\(298\) | 4216.36i | 0.819621i | ||||||||
\(299\) | 4089.46 | 0.790968 | ||||||||
\(300\) | 1422.45 | − | 573.738i | 0.273750 | − | 0.110416i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4431.01i | 0.844291i | ||||||||
\(303\) | 3622.88i | 0.686894i | ||||||||
\(304\) | 901.051 | 0.169996 | ||||||||
\(305\) | 217.752 | + | 146.969i | 0.0408802 | + | 0.0275915i | ||||
\(306\) | −1382.26 | −0.258230 | ||||||||
\(307\) | − | 4296.26i | − | 0.798699i | −0.916799 | − | 0.399349i | \(-0.869236\pi\) | ||
0.916799 | − | 0.399349i | \(-0.130764\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2245.60 | −0.413424 | ||||||||
\(310\) | −882.728 | + | 1307.87i | −0.161728 | + | 0.239620i | ||||
\(311\) | 3935.13 | 0.717494 | 0.358747 | − | 0.933435i | \(-0.383204\pi\) | ||||
0.358747 | + | 0.933435i | \(0.383204\pi\) | |||||||
\(312\) | 1094.89i | 0.198673i | ||||||||
\(313\) | 10498.9i | 1.89596i | 0.318334 | + | 0.947979i | \(0.396877\pi\) | ||||
−0.318334 | + | 0.947979i | \(0.603123\pi\) | |||||||
\(314\) | −4524.05 | −0.813080 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3094.80 | −0.550937 | ||||||||
\(317\) | − | 5747.17i | − | 1.01828i | −0.860685 | − | 0.509138i | \(-0.829964\pi\) | ||
0.860685 | − | 0.509138i | \(-0.170036\pi\) | |||||||
\(318\) | 3788.39i | 0.668057i | ||||||||
\(319\) | 13951.8 | 2.44874 | ||||||||
\(320\) | 593.094 | + | 400.299i | 0.103609 | + | 0.0699294i | ||||
\(321\) | −4104.56 | −0.713690 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2212.71i | − | 0.381172i | ||||||
\(324\) | −221.326 | −0.0379503 | ||||||||
\(325\) | 5172.05 | − | 2086.13i | 0.882750 | − | 0.356054i | ||||
\(326\) | −175.432 | −0.0298045 | ||||||||
\(327\) | 158.770i | 0.0268501i | ||||||||
\(328\) | 3192.17i | 0.537372i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2814.43 | + | 1899.55i | 0.469483 | + | 0.316870i | ||||
\(331\) | 9408.09 | 1.56228 | 0.781141 | − | 0.624355i | \(-0.214638\pi\) | ||||
0.781141 | + | 0.624355i | \(0.214638\pi\) | |||||||
\(332\) | − | 5364.82i | − | 0.886846i | ||||||
\(333\) | 3466.78i | 0.570506i | ||||||||
\(334\) | −3702.76 | −0.606605 | ||||||||
\(335\) | 1576.95 | − | 2336.46i | 0.257189 | − | 0.381058i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4501.95i | 0.727706i | 0.931456 | + | 0.363853i | \(0.118539\pi\) | ||||
−0.931456 | + | 0.363853i | \(0.881461\pi\) | |||||||
\(338\) | − | 412.939i | − | 0.0664524i | ||||||
\(339\) | 1447.30 | 0.231877 | ||||||||
\(340\) | 983.015 | − | 1456.46i | 0.156798 | − | 0.232317i | ||||
\(341\) | −3493.10 | −0.554728 | ||||||||
\(342\) | − | 1981.17i | − | 0.313244i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1628.54 | −0.255246 | ||||||||
\(345\) | 2605.69 | + | 1758.67i | 0.406624 | + | 0.274445i | ||||
\(346\) | −3684.16 | −0.572432 | ||||||||
\(347\) | − | 4993.36i | − | 0.772500i | −0.922394 | − | 0.386250i | \(-0.873770\pi\) | ||
0.922394 | − | 0.386250i | \(-0.126230\pi\) | |||||||
\(348\) | 3458.34i | 0.532719i | ||||||||
\(349\) | −6675.06 | −1.02381 | −0.511903 | − | 0.859044i | \(-0.671059\pi\) | ||||
−0.511903 | + | 0.859044i | \(0.671059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6102.65 | 0.928020 | ||||||||
\(352\) | 1584.05i | 0.239859i | ||||||||
\(353\) | 2839.32i | 0.428107i | 0.976822 | + | 0.214054i | \(0.0686667\pi\) | ||||
−0.976822 | + | 0.214054i | \(0.931333\pi\) | |||||||
\(354\) | −2948.03 | −0.442616 | ||||||||
\(355\) | −7743.96 | − | 5226.66i | −1.15776 | − | 0.781415i | ||||
\(356\) | 5204.47 | 0.774821 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1497.06i | 0.221012i | ||||||||
\(359\) | 8484.41 | 1.24733 | 0.623663 | − | 0.781693i | \(-0.285644\pi\) | ||||
0.623663 | + | 0.781693i | \(0.285644\pi\) | |||||||
\(360\) | 880.153 | − | 1304.06i | 0.128856 | − | 0.190916i | ||||
\(361\) | −3687.54 | −0.537621 | ||||||||
\(362\) | 2787.80i | 0.404761i | ||||||||
\(363\) | 3433.90i | 0.496509i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1612.37 | − | 2388.92i | 0.231220 | − | 0.342581i | ||||
\(366\) | −144.161 | −0.0205885 | ||||||||
\(367\) | − | 11319.7i | − | 1.61004i | −0.593247 | − | 0.805020i | \(-0.702154\pi\) | ||
0.593247 | − | 0.805020i | \(-0.297846\pi\) | |||||||
\(368\) | 1466.56i | 0.207744i | ||||||||
\(369\) | 7018.74 | 0.990193 | ||||||||
\(370\) | −3652.89 | − | 2465.46i | −0.513256 | − | 0.346414i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 865.863i | − | 0.120680i | ||||||
\(373\) | 11306.2i | 1.56947i | 0.619832 | + | 0.784735i | \(0.287201\pi\) | ||||
−0.619832 | + | 0.784735i | \(0.712799\pi\) | |||||||
\(374\) | 3889.96 | 0.537821 | ||||||||
\(375\) | 4192.62 | + | 895.014i | 0.577349 | + | 0.123249i | ||||
\(376\) | −547.991 | −0.0751608 | ||||||||
\(377\) | 12574.6i | 1.71784i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10626.4 | 1.44022 | 0.720109 | − | 0.693861i | \(-0.244092\pi\) | ||||
0.720109 | + | 0.693861i | \(0.244092\pi\) | |||||||
\(380\) | 2087.53 | + | 1408.95i | 0.281811 | + | 0.190204i | ||||
\(381\) | −620.556 | −0.0834437 | ||||||||
\(382\) | 1916.35i | 0.256672i | ||||||||
\(383\) | − | 7582.88i | − | 1.01166i | −0.862632 | − | 0.505832i | \(-0.831186\pi\) | ||
0.862632 | − | 0.505832i | \(-0.168814\pi\) | |||||||
\(384\) | −392.651 | −0.0521808 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9154.08 | −1.20707 | ||||||||
\(387\) | 3580.72i | 0.470332i | ||||||||
\(388\) | 1294.91i | 0.169431i | ||||||||
\(389\) | −3212.83 | −0.418758 | −0.209379 | − | 0.977835i | \(-0.567144\pi\) | ||||
−0.209379 | + | 0.977835i | \(0.567144\pi\) | |||||||
\(390\) | −1712.05 | + | 2536.62i | −0.222290 | + | 0.329350i | ||||
\(391\) | 3601.44 | 0.465813 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3585.88i | − | 0.460264i | ||||||
\(394\) | 6858.54 | 0.876976 | ||||||||
\(395\) | −7169.95 | − | 4839.24i | −0.913315 | − | 0.616427i | ||||
\(396\) | 3482.91 | 0.441977 | ||||||||
\(397\) | − | 13180.8i | − | 1.66631i | −0.553039 | − | 0.833155i | \(-0.686532\pi\) | ||
0.553039 | − | 0.833155i | \(-0.313468\pi\) | |||||||
\(398\) | − | 292.031i | − | 0.0367794i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 748.128 | + | 1854.81i | 0.0935161 | + | 0.231851i | ||||
\(401\) | −7194.23 | −0.895917 | −0.447959 | − | 0.894054i | \(-0.647849\pi\) | ||||
−0.447959 | + | 0.894054i | \(0.647849\pi\) | |||||||
\(402\) | 1546.83i | 0.191912i | ||||||||
\(403\) | − | 3148.30i | − | 0.389152i | ||||||
\(404\) | −4724.07 | −0.581761 | ||||||||
\(405\) | −512.762 | − | 346.081i | −0.0629120 | − | 0.0424615i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9756.24i | − | 1.18820i | ||||||
\(408\) | 964.234i | 0.117002i | ||||||||
\(409\) | 1089.15 | 0.131675 | 0.0658376 | − | 0.997830i | \(-0.479028\pi\) | ||||
0.0658376 | + | 0.997830i | \(0.479028\pi\) | |||||||
\(410\) | −4991.50 | + | 7395.53i | −0.601250 | + | 0.890828i | ||||
\(411\) | −450.069 | −0.0540153 | ||||||||
\(412\) | − | 2928.17i | − | 0.350147i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3224.59 | 0.382802 | ||||||||
\(415\) | 8388.81 | − | 12429.1i | 0.992266 | − | 1.47017i | ||||
\(416\) | −1427.69 | −0.168265 | ||||||||
\(417\) | 7686.26i | 0.902633i | ||||||||
\(418\) | 5575.44i | 0.652401i | ||||||||
\(419\) | 12514.5 | 1.45913 | 0.729563 | − | 0.683914i | \(-0.239724\pi\) | ||||
0.729563 | + | 0.683914i | \(0.239724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −827.022 | −0.0957401 | −0.0478701 | − | 0.998854i | \(-0.515243\pi\) | ||||
−0.0478701 | + | 0.998854i | \(0.515243\pi\) | |||||||
\(422\) | 1410.82i | 0.162743i | ||||||||
\(423\) | 1204.89i | 0.138496i | ||||||||
\(424\) | −4939.89 | −0.565807 | ||||||||
\(425\) | 4554.85 | − | 1837.18i | 0.519865 | − | 0.209685i | ||||
\(426\) | 5126.80 | 0.583085 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 5352.17i | − | 0.604455i | ||||||
\(429\) | −6774.87 | −0.762457 | ||||||||
\(430\) | −3772.95 | − | 2546.49i | −0.423134 | − | 0.285588i | ||||
\(431\) | −1680.44 | −0.187805 | −0.0939025 | − | 0.995581i | \(-0.529934\pi\) | ||||
−0.0939025 | + | 0.995581i | \(0.529934\pi\) | |||||||
\(432\) | 2188.54i | 0.243741i | ||||||||
\(433\) | 7421.56i | 0.823689i | 0.911254 | + | 0.411845i | \(0.135115\pi\) | ||||
−0.911254 | + | 0.411845i | \(0.864885\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5407.69 | + | 8012.18i | −0.596044 | + | 0.883114i | ||||
\(436\) | −207.028 | −0.0227405 | ||||||||
\(437\) | 5161.91i | 0.565052i | ||||||||
\(438\) | 1581.56i | 0.172534i | ||||||||
\(439\) | −4798.23 | −0.521656 | −0.260828 | − | 0.965385i | \(-0.583996\pi\) | ||||
−0.260828 | + | 0.965385i | \(0.583996\pi\) | |||||||
\(440\) | −2476.93 | + | 3669.89i | −0.268371 | + | 0.397625i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3505.98i | 0.377291i | ||||||||
\(443\) | 15935.6i | 1.70908i | 0.519384 | + | 0.854541i | \(0.326161\pi\) | ||||
−0.519384 | + | 0.854541i | \(0.673839\pi\) | |||||||
\(444\) | 2418.36 | 0.258491 | ||||||||
\(445\) | 12057.6 | + | 8138.06i | 1.28446 | + | 0.866924i | ||||
\(446\) | −4464.14 | −0.473953 | ||||||||
\(447\) | − | 6467.03i | − | 0.684295i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9352.06 | 0.982964 | 0.491482 | − | 0.870888i | \(-0.336455\pi\) | ||||
0.491482 | + | 0.870888i | \(0.336455\pi\) | |||||||
\(450\) | 4078.23 | − | 1644.94i | 0.427221 | − | 0.172318i | ||||
\(451\) | −19752.2 | −2.06230 | ||||||||
\(452\) | 1887.21i | 0.196387i | ||||||||
\(453\) | − | 6796.26i | − | 0.704892i | ||||||
\(454\) | 10929.9 | 1.12988 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1382.03 | −0.141928 | ||||||||
\(457\) | 8577.22i | 0.877955i | 0.898498 | + | 0.438977i | \(0.144659\pi\) | ||||
−0.898498 | + | 0.438977i | \(0.855341\pi\) | |||||||
\(458\) | 3887.78i | 0.396646i | ||||||||
\(459\) | 5374.39 | 0.546525 | ||||||||
\(460\) | −2293.22 | + | 3397.70i | −0.232439 | + | 0.344388i | ||||
\(461\) | −8463.98 | −0.855113 | −0.427556 | − | 0.903989i | \(-0.640625\pi\) | ||||
−0.427556 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4297.74i | 0.431388i | 0.976461 | + | 0.215694i | \(0.0692014\pi\) | ||||
−0.976461 | + | 0.215694i | \(0.930799\pi\) | |||||||
\(464\) | −4509.52 | −0.451183 | ||||||||
\(465\) | 1353.92 | − | 2006.01i | 0.135025 | − | 0.200057i | ||||
\(466\) | 6614.50 | 0.657533 | ||||||||
\(467\) | − | 1030.13i | − | 0.102074i | −0.998697 | − | 0.0510371i | \(-0.983747\pi\) | ||
0.998697 | − | 0.0510371i | \(-0.0162527\pi\) | |||||||
\(468\) | 3139.12i | 0.310055i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1269.57 | − | 856.876i | −0.124598 | − | 0.0840952i | ||||
\(471\) | 6938.97 | 0.678834 | ||||||||
\(472\) | − | 3844.10i | − | 0.374871i | ||||||
\(473\) | − | 10076.9i | − | 0.979569i | ||||||
\(474\) | 4746.79 | 0.459973 | ||||||||
\(475\) | 2633.21 | + | 6528.42i | 0.254358 | + | 0.630619i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10861.5i | 1.04259i | ||||||||
\(478\) | 12216.0i | 1.16892i | ||||||||
\(479\) | −5137.48 | −0.490058 | −0.245029 | − | 0.969516i | \(-0.578797\pi\) | ||||
−0.245029 | + | 0.969516i | \(0.578797\pi\) | |||||||
\(480\) | −909.684 | − | 613.977i | −0.0865025 | − | 0.0583835i | ||||
\(481\) | 8793.21 | 0.833546 | ||||||||
\(482\) | 7925.20i | 0.748927i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4477.65 | −0.420515 | ||||||||
\(485\) | −2024.82 | + | 3000.02i | −0.189572 | + | 0.280874i | ||||
\(486\) | 7725.78 | 0.721087 | ||||||||
\(487\) | 526.537i | 0.0489932i | 0.999700 | + | 0.0244966i | \(0.00779829\pi\) | ||||
−0.999700 | + | 0.0244966i | \(0.992202\pi\) | |||||||
\(488\) | − | 187.979i | − | 0.0174373i | ||||||
\(489\) | 269.076 | 0.0248835 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1546.87 | −0.142178 | −0.0710889 | − | 0.997470i | \(-0.522647\pi\) | ||||
−0.0710889 | + | 0.997470i | \(0.522647\pi\) | |||||||
\(492\) | − | 4896.13i | − | 0.448648i | ||||||
\(493\) | 11074.0i | 1.01166i | ||||||||
\(494\) | −5025.09 | −0.457671 | ||||||||
\(495\) | 8069.12 | + | 5446.13i | 0.732687 | + | 0.494515i | ||||
\(496\) | 1129.05 | 0.102209 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8228.54i | 0.740421i | ||||||||
\(499\) | −9492.84 | −0.851619 | −0.425809 | − | 0.904813i | \(-0.640011\pi\) | ||||
−0.425809 | + | 0.904813i | \(0.640011\pi\) | |||||||
\(500\) | −1167.06 | + | 5466.99i | −0.104385 | + | 0.488982i | ||||
\(501\) | 5679.27 | 0.506449 | ||||||||
\(502\) | 7.84599i | 0.000697577i | ||||||||
\(503\) | 9819.97i | 0.870479i | 0.900315 | + | 0.435239i | \(0.143336\pi\) | ||||
−0.900315 | + | 0.435239i | \(0.856664\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10944.6 | − | 7386.89i | −0.964413 | − | 0.650915i | ||||
\(506\) | −9074.67 | −0.797269 | ||||||||
\(507\) | 633.363i | 0.0554806i | ||||||||
\(508\) | − | 809.177i | − | 0.0706721i | ||||||
\(509\) | 2638.05 | 0.229724 | 0.114862 | − | 0.993381i | \(-0.463357\pi\) | ||||
0.114862 | + | 0.993381i | \(0.463357\pi\) | |||||||
\(510\) | −1507.74 | + | 2233.91i | −0.130910 | + | 0.193959i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | 7703.06i | 0.662960i | ||||||||
\(514\) | 439.189 | 0.0376884 | ||||||||
\(515\) | 4578.69 | − | 6783.90i | 0.391769 | − | 0.580455i | ||||
\(516\) | 2497.84 | 0.213103 | ||||||||
\(517\) | − | 3390.80i | − | 0.288448i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5650.74 | 0.477919 | ||||||||
\(520\) | −3307.64 | − | 2232.44i | −0.278941 | − | 0.188267i | ||||
\(521\) | 4426.35 | 0.372211 | 0.186106 | − | 0.982530i | \(-0.440413\pi\) | ||||
0.186106 | + | 0.982530i | \(0.440413\pi\) | |||||||
\(522\) | 9915.24i | 0.831376i | ||||||||
\(523\) | − | 905.764i | − | 0.0757291i | −0.999283 | − | 0.0378645i | \(-0.987944\pi\) | ||
0.999283 | − | 0.0378645i | \(-0.0120555\pi\) | |||||||
\(524\) | 4675.82 | 0.389817 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10935.4 | −0.906478 | ||||||||
\(527\) | − | 2772.60i | − | 0.229177i | ||||||
\(528\) | − | 2429.61i | − | 0.200256i | ||||||
\(529\) | 3765.39 | 0.309476 | ||||||||
\(530\) | −11444.6 | − | 7724.35i | −0.937965 | − | 0.633065i | ||||
\(531\) | −8452.16 | −0.690758 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 17802.5i | − | 1.44674i | ||||||
\(534\) | −7982.58 | −0.646892 | ||||||||
\(535\) | 8369.02 | − | 12399.8i | 0.676307 | − | 1.00203i | ||||
\(536\) | −2016.99 | −0.162539 | ||||||||
\(537\) | − | 2296.19i | − | 0.184521i | ||||||
\(538\) | − | 583.462i | − | 0.0467562i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3422.15 | + | 5070.34i | −0.272714 | + | 0.404061i | ||||
\(541\) | 19620.6 | 1.55926 | 0.779628 | − | 0.626243i | \(-0.215408\pi\) | ||||
0.779628 | + | 0.626243i | \(0.215408\pi\) | |||||||
\(542\) | − | 5322.04i | − | 0.421774i | ||||||
\(543\) | − | 4275.91i | − | 0.337932i | ||||||
\(544\) | −1257.32 | −0.0990939 | ||||||||
\(545\) | −479.638 | − | 323.724i | −0.0376980 | − | 0.0254437i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6717.26i | 0.525062i | 0.964923 | + | 0.262531i | \(0.0845573\pi\) | ||||
−0.964923 | + | 0.262531i | \(0.915443\pi\) | |||||||
\(548\) | − | 586.870i | − | 0.0457479i | ||||||
\(549\) | −413.316 | −0.0321310 | ||||||||
\(550\) | −11477.0 | + | 4629.20i | −0.889783 | + | 0.358890i | ||||
\(551\) | −15872.3 | −1.22719 | ||||||||
\(552\) | − | 2249.41i | − | 0.173444i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9005.31 | 0.690612 | ||||||||
\(555\) | 5602.78 | + | 3781.51i | 0.428513 | + | 0.289218i | ||||
\(556\) | −10022.5 | −0.764479 | ||||||||
\(557\) | − | 13104.0i | − | 0.996827i | −0.866940 | − | 0.498413i | \(-0.833916\pi\) | ||
0.866940 | − | 0.498413i | \(-0.166084\pi\) | |||||||
\(558\) | − | 2482.48i | − | 0.188336i | ||||||
\(559\) | 9082.21 | 0.687186 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5966.40 | −0.449022 | ||||||||
\(562\) | 924.776i | 0.0694116i | ||||||||
\(563\) | 16648.7i | 1.24629i | 0.782108 | + | 0.623143i | \(0.214145\pi\) | ||||
−0.782108 | + | 0.623143i | \(0.785855\pi\) | |||||||
\(564\) | 840.505 | 0.0627512 | ||||||||
\(565\) | −2950.97 | + | 4372.24i | −0.219732 | + | 0.325560i | ||||
\(566\) | 14291.4 | 1.06133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6685.12i | 0.493841i | ||||||||
\(569\) | −14697.7 | −1.08288 | −0.541441 | − | 0.840739i | \(-0.682121\pi\) | ||||
−0.541441 | + | 0.840739i | \(0.682121\pi\) | |||||||
\(570\) | −3201.84 | − | 2161.03i | −0.235282 | − | 0.158800i | ||||
\(571\) | 2997.78 | 0.219708 | 0.109854 | − | 0.993948i | \(-0.464962\pi\) | ||||
0.109854 | + | 0.993948i | \(0.464962\pi\) | |||||||
\(572\) | − | 8834.13i | − | 0.645758i | ||||||
\(573\) | − | 2939.28i | − | 0.214294i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10625.8 | + | 4285.85i | −0.770651 | + | 0.310839i | ||||
\(576\) | −1125.75 | −0.0814347 | ||||||||
\(577\) | 4873.27i | 0.351607i | 0.984425 | + | 0.175803i | \(0.0562523\pi\) | ||||
−0.984425 | + | 0.175803i | \(0.943748\pi\) | |||||||
\(578\) | − | 6738.40i | − | 0.484915i | ||||||
\(579\) | 14040.5 | 1.00778 | ||||||||
\(580\) | −10447.5 | − | 7051.39i | −0.747948 | − | 0.504816i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 1986.13i | − | 0.141457i | ||||||
\(583\) | − | 30566.6i | − | 2.17142i | ||||||
\(584\) | −2062.29 | −0.146127 | ||||||||
\(585\) | −4908.54 | + | 7272.62i | −0.346912 | + | 0.513993i | ||||
\(586\) | 17312.4 | 1.22043 | ||||||||
\(587\) | − | 23971.4i | − | 1.68553i | −0.538283 | − | 0.842764i | \(-0.680927\pi\) | ||
0.538283 | − | 0.842764i | \(-0.319073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3973.94 | 0.278002 | ||||||||
\(590\) | 6010.90 | − | 8905.91i | 0.419432 | − | 0.621441i | ||||
\(591\) | −10519.6 | −0.732180 | ||||||||
\(592\) | 3153.43i | 0.218928i | ||||||||
\(593\) | 1561.67i | 0.108145i | 0.998537 | + | 0.0540726i | \(0.0172202\pi\) | ||||
−0.998537 | + | 0.0540726i | \(0.982780\pi\) | |||||||
\(594\) | −13542.0 | −0.935413 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8432.71 | 0.579559 | ||||||||
\(597\) | 447.916i | 0.0307069i | ||||||||
\(598\) | − | 8178.91i | − | 0.559299i | ||||||
\(599\) | −17401.4 | −1.18698 | −0.593491 | − | 0.804841i | \(-0.702251\pi\) | ||||
−0.593491 | + | 0.804841i | \(0.702251\pi\) | |||||||
\(600\) | −1147.48 | − | 2844.89i | −0.0780758 | − | 0.193570i | ||||
\(601\) | −26823.7 | −1.82057 | −0.910283 | − | 0.413987i | \(-0.864136\pi\) | ||||
−0.910283 | + | 0.413987i | \(0.864136\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4434.84i | 0.299503i | ||||||||
\(604\) | 8862.02 | 0.597004 | ||||||||
\(605\) | −10373.7 | − | 7001.56i | −0.697109 | − | 0.470502i | ||||
\(606\) | 7245.76 | 0.485707 | ||||||||
\(607\) | 22721.4i | 1.51933i | 0.650315 | + | 0.759665i | \(0.274637\pi\) | ||||
−0.650315 | + | 0.759665i | \(0.725363\pi\) | |||||||
\(608\) | − | 1802.10i | − | 0.120205i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 293.937 | − | 435.505i | 0.0195101 | − | 0.0289067i | ||||
\(611\) | 3056.10 | 0.202351 | ||||||||
\(612\) | 2764.51i | 0.182596i | ||||||||
\(613\) | 22931.6i | 1.51092i | 0.655192 | + | 0.755462i | \(0.272588\pi\) | ||||
−0.655192 | + | 0.755462i | \(0.727412\pi\) | |||||||
\(614\) | −8592.52 | −0.564765 | ||||||||
\(615\) | 7655.93 | − | 11343.2i | 0.501979 | − | 0.743745i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4299.04i | 0.280507i | 0.990116 | + | 0.140253i | \(0.0447918\pi\) | ||||
−0.990116 | + | 0.140253i | \(0.955208\pi\) | |||||||
\(618\) | 4491.21i | 0.292335i | ||||||||
\(619\) | 5321.89 | 0.345565 | 0.172783 | − | 0.984960i | \(-0.444724\pi\) | ||||
0.172783 | + | 0.984960i | \(0.444724\pi\) | |||||||
\(620\) | 2615.75 | + | 1765.46i | 0.169437 | + | 0.114359i | ||||
\(621\) | −12537.6 | −0.810173 | ||||||||
\(622\) | − | 7870.25i | − | 0.507345i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2189.79 | 0.140483 | ||||||||
\(625\) | −11252.4 | + | 10840.9i | −0.720152 | + | 0.693816i | ||||
\(626\) | 20997.9 | 1.34064 | ||||||||
\(627\) | − | 8551.58i | − | 0.544684i | ||||||
\(628\) | 9048.11i | 0.574935i | ||||||||
\(629\) | 7743.87 | 0.490888 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19486.3 | 1.22938 | 0.614688 | − | 0.788771i | \(-0.289282\pi\) | ||||
0.614688 | + | 0.788771i | \(0.289282\pi\) | |||||||
\(632\) | 6189.60i | 0.389571i | ||||||||
\(633\) | − | 2163.91i | − | 0.135873i | ||||||
\(634\) | −11494.3 | −0.720030 | ||||||||
\(635\) | 1265.29 | − | 1874.68i | 0.0790730 | − | 0.117157i | ||||
\(636\) | 7576.77 | 0.472388 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 27903.6i | − | 1.73152i | ||||||
\(639\) | 14698.8 | 0.909979 | ||||||||
\(640\) | 800.599 | − | 1186.19i | 0.0494476 | − | 0.0732628i | ||||
\(641\) | −28574.7 | −1.76074 | −0.880368 | − | 0.474290i | \(-0.842705\pi\) | ||||
−0.880368 | + | 0.474290i | \(0.842705\pi\) | |||||||
\(642\) | 8209.13i | 0.504655i | ||||||||
\(643\) | 6347.10i | 0.389277i | 0.980875 | + | 0.194639i | \(0.0623534\pi\) | ||||
−0.980875 | + | 0.194639i | \(0.937647\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5786.93 | + | 3905.80i | 0.353271 | + | 0.238435i | ||||
\(646\) | −4425.42 | −0.269529 | ||||||||
\(647\) | − | 2649.69i | − | 0.161005i | −0.996754 | − | 0.0805024i | \(-0.974348\pi\) | ||
0.996754 | − | 0.0805024i | \(-0.0256525\pi\) | |||||||
\(648\) | 442.652i | 0.0268349i | ||||||||
\(649\) | 23786.2 | 1.43866 | ||||||||
\(650\) | −4172.25 | − | 10344.1i | −0.251768 | − | 0.624199i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 350.863i | 0.0210750i | ||||||||
\(653\) | − | 7061.62i | − | 0.423189i | −0.977358 | − | 0.211595i | \(-0.932134\pi\) | ||
0.977358 | − | 0.211595i | \(-0.0678657\pi\) | |||||||
\(654\) | 317.539 | 0.0189859 | ||||||||
\(655\) | 10832.8 | + | 7311.44i | 0.646219 | + | 0.436155i | ||||
\(656\) | 6384.34 | 0.379980 | ||||||||
\(657\) | 4534.42i | 0.269261i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11227.0 | −0.663646 | −0.331823 | − | 0.943342i | \(-0.607664\pi\) | ||||
−0.331823 | + | 0.943342i | \(0.607664\pi\) | |||||||
\(660\) | 3799.11 | − | 5628.86i | 0.224061 | − | 0.331974i | ||||
\(661\) | 28750.0 | 1.69175 | 0.845873 | − | 0.533385i | \(-0.179080\pi\) | ||||
0.845873 | + | 0.533385i | \(0.179080\pi\) | |||||||
\(662\) | − | 18816.2i | − | 1.10470i | ||||||
\(663\) | − | 5377.46i | − | 0.314997i | ||||||
\(664\) | −10729.6 | −0.627095 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6933.56 | 0.403408 | ||||||||
\(667\) | − | 25834.0i | − | 1.49969i | ||||||
\(668\) | 7405.52i | 0.428934i | ||||||||
\(669\) | 6847.07 | 0.395700 | ||||||||
\(670\) | −4672.91 | − | 3153.91i | −0.269448 | − | 0.181860i | ||||
\(671\) | 1163.16 | 0.0669199 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4440.57i | 0.254341i | 0.991881 | + | 0.127170i | \(0.0405895\pi\) | ||||
−0.991881 | + | 0.127170i | \(0.959411\pi\) | |||||||
\(674\) | 9003.90 | 0.514566 | ||||||||
\(675\) | −15856.7 | + | 6395.73i | −0.904183 | + | 0.364699i | ||||
\(676\) | −825.878 | −0.0469889 | ||||||||
\(677\) | − | 16309.8i | − | 0.925905i | −0.886383 | − | 0.462953i | \(-0.846790\pi\) | ||
0.886383 | − | 0.462953i | \(-0.153210\pi\) | |||||||
\(678\) | − | 2894.59i | − | 0.163962i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2912.92 | − | 1966.03i | −0.164273 | − | 0.110873i | ||||
\(681\) | −16764.3 | −0.943330 | ||||||||
\(682\) | 6986.21i | 0.392252i | ||||||||
\(683\) | − | 4866.44i | − | 0.272634i | −0.990665 | − | 0.136317i | \(-0.956473\pi\) | ||
0.990665 | − | 0.136317i | \(-0.0435266\pi\) | |||||||
\(684\) | −3962.35 | −0.221497 | ||||||||
\(685\) | 917.671 | − | 1359.65i | 0.0511860 | − | 0.0758385i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 5963.05i | − | 0.331157i | ||||||
\(688\) | 3257.07i | 0.180486i | ||||||||
\(689\) | 27549.4 | 1.52329 | ||||||||
\(690\) | 3517.33 | − | 5211.37i | 0.194062 | − | 0.287527i | ||||
\(691\) | −15027.1 | −0.827291 | −0.413646 | − | 0.910438i | \(-0.635745\pi\) | ||||
−0.413646 | + | 0.910438i | \(0.635745\pi\) | |||||||
\(692\) | 7368.31i | 0.404771i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9986.72 | −0.546240 | ||||||||
\(695\) | −23220.0 | − | 15671.9i | −1.26731 | − | 0.855353i | ||||
\(696\) | 6916.67 | 0.376689 | ||||||||
\(697\) | − | 15678.0i | − | 0.852005i | ||||||
\(698\) | 13350.1i | 0.723939i | ||||||||
\(699\) | −10145.3 | −0.548970 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10821.8 | −0.583073 | −0.291536 | − | 0.956560i | \(-0.594166\pi\) | ||||
−0.291536 | + | 0.956560i | \(0.594166\pi\) | |||||||
\(702\) | − | 12205.3i | − | 0.656209i | ||||||
\(703\) | 11099.2i | 0.595469i | ||||||||
\(704\) | 3168.10 | 0.169606 | ||||||||
\(705\) | 1947.26 | + | 1314.27i | 0.104026 | + | 0.0702104i | ||||
\(706\) | 5678.64 | 0.302718 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5896.06i | 0.312977i | ||||||||
\(709\) | −20502.7 | −1.08603 | −0.543016 | − | 0.839722i | \(-0.682718\pi\) | ||||
−0.543016 | + | 0.839722i | \(0.682718\pi\) | |||||||
\(710\) | −10453.3 | + | 15487.9i | −0.552544 | + | 0.818663i | ||||
\(711\) | 13609.3 | 0.717846 | ||||||||
\(712\) | − | 10408.9i | − | 0.547881i | ||||||
\(713\) | 6468.05i | 0.339734i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13813.7 | − | 20466.7i | 0.722520 | − | 1.07050i | ||||
\(716\) | 2994.13 | 0.156279 | ||||||||
\(717\) | − | 18736.8i | − | 0.975926i | ||||||
\(718\) | − | 16968.8i | − | 0.881993i | ||||||
\(719\) | −273.658 | −0.0141943 | −0.00709717 | − | 0.999975i | \(-0.502259\pi\) | ||||
−0.00709717 | + | 0.999975i | \(0.502259\pi\) | |||||||
\(720\) | −2608.11 | − | 1760.31i | −0.134998 | − | 0.0911149i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 7375.09i | 0.380156i | ||||||||
\(723\) | − | 12155.6i | − | 0.625273i | ||||||
\(724\) | 5575.60 | 0.286209 | ||||||||
\(725\) | −13178.5 | − | 32673.0i | −0.675086 | − | 1.67371i | ||||
\(726\) | 6867.79 | 0.351085 | ||||||||
\(727\) | 1244.59i | 0.0634931i | 0.999496 | + | 0.0317465i | \(0.0101069\pi\) | ||||
−0.999496 | + | 0.0317465i | \(0.989893\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10355.8 | −0.526129 | ||||||||
\(730\) | −4777.85 | − | 3224.73i | −0.242241 | − | 0.163497i | ||||
\(731\) | 7998.39 | 0.404694 | ||||||||
\(732\) | 288.321i | 0.0145583i | ||||||||
\(733\) | 15653.2i | 0.788765i | 0.918946 | + | 0.394383i | \(0.129042\pi\) | ||||
−0.918946 | + | 0.394383i | \(0.870958\pi\) | |||||||
\(734\) | −22639.5 | −1.13847 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2933.13 | 0.146898 | ||||||||
\(737\) | − | 12480.6i | − | 0.623782i | ||||||
\(738\) | − | 14037.5i | − | 0.700172i | ||||||
\(739\) | 5366.29 | 0.267121 | 0.133560 | − | 0.991041i | \(-0.457359\pi\) | ||||
0.133560 | + | 0.991041i | \(0.457359\pi\) | |||||||
\(740\) | −4930.92 | + | 7305.78i | −0.244952 | + | 0.362927i | ||||
\(741\) | 7707.46 | 0.382106 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 7927.48i | − | 0.391428i | −0.980661 | − | 0.195714i | \(-0.937298\pi\) | ||
0.980661 | − | 0.195714i | \(-0.0627024\pi\) | |||||||
\(744\) | −1731.73 | −0.0853335 | ||||||||
\(745\) | 19536.7 | + | 13186.0i | 0.960763 | + | 0.648452i | ||||
\(746\) | 22612.4 | 1.10978 | ||||||||
\(747\) | 23591.7i | 1.15552i | ||||||||
\(748\) | − | 7779.91i | − | 0.380297i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1790.03 | − | 8385.24i | 0.0871501 | − | 0.408248i | ||||
\(751\) | 7386.52 | 0.358906 | 0.179453 | − | 0.983767i | \(-0.442567\pi\) | ||||
0.179453 | + | 0.983767i | \(0.442567\pi\) | |||||||
\(752\) | 1095.98i | 0.0531467i | ||||||||
\(753\) | − | 12.0341i | − | 0.000582401i | ||||||
\(754\) | 25149.2 | 1.21470 | ||||||||
\(755\) | 20531.3 | + | 13857.3i | 0.989683 | + | 0.667970i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 13406.0i | − | 0.643659i | −0.946798 | − | 0.321829i | \(-0.895702\pi\) | ||
0.946798 | − | 0.321829i | \(-0.104298\pi\) | |||||||
\(758\) | − | 21252.8i | − | 1.01839i | ||||||
\(759\) | 13918.7 | 0.665634 | ||||||||
\(760\) | 2817.89 | − | 4175.06i | 0.134494 | − | 0.199270i | ||||
\(761\) | −25885.0 | −1.23302 | −0.616510 | − | 0.787347i | \(-0.711454\pi\) | ||||
−0.616510 | + | 0.787347i | \(0.711454\pi\) | |||||||
\(762\) | 1241.11i | 0.0590036i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3832.69 | 0.181495 | ||||||||
\(765\) | −4322.78 | + | 6404.75i | −0.204301 | + | 0.302698i | ||||
\(766\) | −15165.8 | −0.715354 | ||||||||
\(767\) | 21438.2i | 1.00924i | ||||||||
\(768\) | 785.303i | 0.0368974i | ||||||||
\(769\) | −11600.6 | −0.543991 | −0.271996 | − | 0.962299i | \(-0.587684\pi\) | ||||
−0.271996 | + | 0.962299i | \(0.587684\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −673.626 | −0.0314657 | ||||||||
\(772\) | 18308.2i | 0.853530i | ||||||||
\(773\) | − | 28247.3i | − | 1.31434i | −0.753742 | − | 0.657170i | \(-0.771753\pi\) | ||
0.753742 | − | 0.657170i | \(-0.228247\pi\) | |||||||
\(774\) | 7161.44 | 0.332575 | ||||||||
\(775\) | 3299.50 | + | 8180.32i | 0.152931 | + | 0.379156i | ||||
\(776\) | 2589.83 | 0.119806 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6425.65i | 0.296106i | ||||||||
\(779\) | 22471.2 | 1.03352 | ||||||||
\(780\) | 5073.24 | + | 3424.10i | 0.232886 | + | 0.157183i | ||||
\(781\) | −41365.6 | −1.89523 | ||||||||
\(782\) | − | 7202.89i | − | 0.329379i | ||||||
\(783\) | − | 38551.7i | − | 1.75955i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14148.3 | + | 20962.4i | −0.643277 | + | 0.953097i | ||||
\(786\) | −7171.75 | −0.325456 | ||||||||
\(787\) | 10505.3i | 0.475822i | 0.971287 | + | 0.237911i | \(0.0764627\pi\) | ||||
−0.971287 | + | 0.237911i | \(0.923537\pi\) | |||||||
\(788\) | − | 13717.1i | − | 0.620115i | ||||||
\(789\) | 16772.7 | 0.756812 | ||||||||
\(790\) | −9678.49 | + | 14339.9i | −0.435880 | + | 0.645811i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 6965.83i | − | 0.312525i | ||||||
\(793\) | 1048.34i | 0.0469455i | ||||||||
\(794\) | −26361.6 | −1.17826 | ||||||||
\(795\) | 17553.7 | + | 11847.6i | 0.783100 | + | 0.528541i | ||||
\(796\) | −584.063 | −0.0260070 | ||||||||
\(797\) | − | 2165.99i | − | 0.0962651i | −0.998841 | − | 0.0481325i | \(-0.984673\pi\) | ||
0.998841 | − | 0.0481325i | \(-0.0153270\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2691.40 | 0.119168 | ||||||||
\(800\) | 3709.61 | − | 1496.26i | 0.163943 | − | 0.0661258i | ||||
\(801\) | −22886.5 | −1.00956 | ||||||||
\(802\) | 14388.5i | 0.633509i | ||||||||
\(803\) | − | 12760.8i | − | 0.560796i | ||||||
\(804\) | 3093.65 | 0.135702 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6296.60 | −0.275172 | ||||||||
\(807\) | 894.911i | 0.0390364i | ||||||||
\(808\) | 9448.14i | 0.411367i | ||||||||
\(809\) | −5348.67 | −0.232446 | −0.116223 | − | 0.993223i | \(-0.537079\pi\) | ||||
−0.116223 | + | 0.993223i | \(0.537079\pi\) | |||||||
\(810\) | −692.162 | + | 1025.52i | −0.0300248 | + | 0.0444855i | ||||
\(811\) | −33841.2 | −1.46526 | −0.732629 | − | 0.680628i | \(-0.761707\pi\) | ||||
−0.732629 | + | 0.680628i | \(0.761707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8162.92i | 0.352135i | ||||||||
\(814\) | −19512.5 | −0.840187 | ||||||||
\(815\) | −548.634 | + | 812.871i | −0.0235801 | + | 0.0349370i | ||||
\(816\) | 1928.47 | 0.0827327 | ||||||||
\(817\) | 11464.0i | 0.490912i | ||||||||
\(818\) | − | 2178.31i | − | 0.0931084i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14791.1 | + | 9983.00i | 0.629910 | + | 0.425148i | ||||
\(821\) | 14581.5 | 0.619850 | 0.309925 | − | 0.950761i | \(-0.399696\pi\) | ||||
0.309925 | + | 0.950761i | \(0.399696\pi\) | |||||||
\(822\) | 900.138i | 0.0381946i | ||||||||
\(823\) | 3078.27i | 0.130379i | 0.997873 | + | 0.0651894i | \(0.0207651\pi\) | ||||
−0.997873 | + | 0.0651894i | \(0.979235\pi\) | |||||||
\(824\) | −5856.34 | −0.247591 | ||||||||
\(825\) | 17603.3 | − | 7100.24i | 0.742873 | − | 0.299635i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 40275.0i | − | 1.69347i | −0.532017 | − | 0.846734i | \(-0.678566\pi\) | ||
0.532017 | − | 0.846734i | \(-0.321434\pi\) | |||||||
\(828\) | − | 6449.18i | − | 0.270682i | ||||||
\(829\) | −29186.9 | −1.22280 | −0.611402 | − | 0.791320i | \(-0.709394\pi\) | ||||
−0.611402 | + | 0.791320i | \(0.709394\pi\) | |||||||
\(830\) | −24858.2 | − | 16777.6i | −1.03957 | − | 0.701638i | ||||
\(831\) | −13812.3 | −0.576587 | ||||||||
\(832\) | 2855.38i | 0.118981i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 15372.5 | 0.638258 | ||||||||
\(835\) | −11579.8 | + | 17156.9i | −0.479922 | + | 0.711065i | ||||
\(836\) | 11150.9 | 0.461317 | ||||||||
\(837\) | 9652.18i | 0.398600i | ||||||||
\(838\) | − | 25029.0i | − | 1.03176i | ||||||
\(839\) | −9396.07 | −0.386637 | −0.193318 | − | 0.981136i | \(-0.561925\pi\) | ||||
−0.193318 | + | 0.981136i | \(0.561925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55047.5 | 2.25706 | ||||||||
\(842\) | 1654.04i | 0.0676985i | ||||||||
\(843\) | − | 1418.42i | − | 0.0579512i | ||||||
\(844\) | 2821.64 | 0.115077 | ||||||||
\(845\) | −1913.37 | − | 1291.40i | −0.0778958 | − | 0.0525745i | ||||
\(846\) | 2409.77 | 0.0979312 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9879.77i | 0.400086i | ||||||||
\(849\) | −21920.1 | −0.886097 | ||||||||
\(850\) | −3674.36 | − | 9109.69i | −0.148270 | − | 0.367600i | ||||
\(851\) | −18065.3 | −0.727696 | ||||||||
\(852\) | − | 10253.6i | − | 0.412304i | ||||||
\(853\) | − | 20167.0i | − | 0.809502i | −0.914427 | − | 0.404751i | \(-0.867358\pi\) | ||
0.914427 | − | 0.404751i | \(-0.132642\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9179.86 | − | 6195.80i | −0.367187 | − | 0.247827i | ||||
\(856\) | −10704.3 | −0.427414 | ||||||||
\(857\) | 42479.4i | 1.69320i | 0.532232 | + | 0.846599i | \(0.321353\pi\) | ||||
−0.532232 | + | 0.846599i | \(0.678647\pi\) | |||||||
\(858\) | 13549.7i | 0.539138i | ||||||||
\(859\) | −21043.7 | −0.835857 | −0.417929 | − | 0.908480i | \(-0.637244\pi\) | ||||
−0.417929 | + | 0.908480i | \(0.637244\pi\) | |||||||
\(860\) | −5092.98 | + | 7545.90i | −0.201941 | + | 0.299201i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3360.88i | 0.132798i | ||||||||
\(863\) | 8451.15i | 0.333349i | 0.986012 | + | 0.166675i | \(0.0533029\pi\) | ||||
−0.986012 | + | 0.166675i | \(0.946697\pi\) | |||||||
\(864\) | 4377.07 | 0.172351 | ||||||||
\(865\) | −11521.6 | + | 17070.7i | −0.452886 | + | 0.671008i | ||||
\(866\) | 14843.1 | 0.582436 | ||||||||
\(867\) | 10335.3i | 0.404851i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38299.4 | −1.49507 | ||||||||
\(870\) | 16024.4 | + | 10815.4i | 0.624456 | + | 0.421467i | ||||
\(871\) | 11248.6 | 0.437594 | ||||||||
\(872\) | 414.057i | 0.0160800i | ||||||||
\(873\) | − | 5694.35i | − | 0.220761i | ||||||
\(874\) | 10323.8 | 0.399552 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3163.12 | 0.122000 | ||||||||
\(877\) | 34430.9i | 1.32571i | 0.748747 | + | 0.662856i | \(0.230656\pi\) | ||||
−0.748747 | + | 0.662856i | \(0.769344\pi\) | |||||||
\(878\) | 9596.46i | 0.368867i | ||||||||
\(879\) | −26553.7 | −1.01892 | ||||||||
\(880\) | 7339.78 | + | 4953.87i | 0.281164 | + | 0.189767i | ||||
\(881\) | −11602.4 | −0.443695 | −0.221848 | − | 0.975081i | \(-0.571209\pi\) | ||||
−0.221848 | + | 0.975081i | \(0.571209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37934.8i | 1.44576i | 0.690974 | + | 0.722880i | \(0.257182\pi\) | ||||
−0.690974 | + | 0.722880i | \(0.742818\pi\) | |||||||
\(884\) | 7011.96 | 0.266785 | ||||||||
\(885\) | −9219.49 | + | 13659.8i | −0.350181 | + | 0.518837i | ||||
\(886\) | 31871.2 | 1.20850 | ||||||||
\(887\) | − | 25436.3i | − | 0.962871i | −0.876481 | − | 0.481436i | \(-0.840115\pi\) | ||
0.876481 | − | 0.481436i | \(-0.159885\pi\) | |||||||
\(888\) | − | 4836.71i | − | 0.182781i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16276.1 | − | 24115.1i | 0.613008 | − | 0.908249i | ||||
\(891\) | −2739.00 | −0.102985 | ||||||||
\(892\) | 8928.28i | 0.335135i | ||||||||
\(893\) | 3857.56i | 0.144556i | ||||||||
\(894\) | −12934.1 | −0.483870 | ||||||||
\(895\) | 6936.72 | + | 4681.83i | 0.259071 | + | 0.174856i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12544.8i | 0.466954i | ||||||||
\(898\) | − | 18704.1i | − | 0.695061i | ||||||
\(899\) | −19888.5 | −0.737840 | ||||||||
\(900\) | −3289.87 | − | 8156.46i | −0.121847 | − | 0.302091i | ||||
\(901\) | 24261.8 | 0.897088 | ||||||||
\(902\) | 39504.4i | 1.45826i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3774.42 | 0.138867 | ||||||||
\(905\) | 12917.4 | + | 8718.39i | 0.474463 | + | 0.320231i | ||||
\(906\) | −13592.5 | −0.498434 | ||||||||
\(907\) | − | 6031.85i | − | 0.220821i | −0.993886 | − | 0.110410i | \(-0.964783\pi\) | ||
0.993886 | − | 0.110410i | \(-0.0352165\pi\) | |||||||
\(908\) | − | 21859.8i | − | 0.798947i | ||||||
\(909\) | 20774.0 | 0.758008 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21631.5 | −0.786699 | −0.393349 | − | 0.919389i | \(-0.628684\pi\) | ||||
−0.393349 | + | 0.919389i | \(0.628684\pi\) | |||||||
\(912\) | 2764.05i | 0.100359i | ||||||||
\(913\) | − | 66391.9i | − | 2.40663i | ||||||
\(914\) | 17154.4 | 0.620808 | ||||||||
\(915\) | −450.839 | + | 667.975i | −0.0162888 | + | 0.0241340i | ||||
\(916\) | 7775.56 | 0.280471 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 10748.8i | − | 0.386451i | ||||||
\(919\) | 28244.7 | 1.01383 | 0.506913 | − | 0.861997i | \(-0.330786\pi\) | ||||
0.506913 | + | 0.861997i | \(0.330786\pi\) | |||||||
\(920\) | 6795.40 | + | 4586.44i | 0.243519 | + | 0.164359i | ||||
\(921\) | 13179.2 | 0.471518 | ||||||||
\(922\) | 16928.0i | 0.604656i | ||||||||
\(923\) | − | 37282.4i | − | 1.32954i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22847.6 | + | 9215.50i | −0.812136 | + | 0.327572i | ||||
\(926\) | 8595.47 | 0.305038 | ||||||||
\(927\) | 12876.5i | 0.456226i | ||||||||
\(928\) | 9019.03i | 0.319035i | ||||||||
\(929\) | −44944.2 | −1.58727 | −0.793633 | − | 0.608396i | \(-0.791813\pi\) | ||||
−0.793633 | + | 0.608396i | \(0.791813\pi\) | |||||||
\(930\) | −4012.02 | − | 2707.85i | −0.141462 | − | 0.0954772i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 13229.0i | − | 0.464946i | ||||||
\(933\) | 12071.4i | 0.423578i | ||||||||
\(934\) | −2060.25 | −0.0721773 | ||||||||
\(935\) | 12165.2 | − | 18024.3i | 0.425503 | − | 0.630436i | ||||
\(936\) | 6278.24 | 0.219242 | ||||||||
\(937\) | − | 3777.71i | − | 0.131710i | −0.997829 | − | 0.0658551i | \(-0.979022\pi\) | ||
0.997829 | − | 0.0658551i | \(-0.0209775\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32206.4 | −1.11929 | ||||||||
\(940\) | −1713.75 | + | 2539.14i | −0.0594643 | + | 0.0881039i | ||||
\(941\) | −352.846 | −0.0122236 | −0.00611182 | − | 0.999981i | \(-0.501945\pi\) | ||||
−0.00611182 | + | 0.999981i | \(0.501945\pi\) | |||||||
\(942\) | − | 13877.9i | − | 0.480008i | ||||||
\(943\) | 36574.4i | 1.26302i | ||||||||
\(944\) | −7688.20 | −0.265074 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −20153.8 | −0.692660 | ||||||||
\(947\) | − | 13534.8i | − | 0.464438i | −0.972664 | − | 0.232219i | \(-0.925401\pi\) | ||
0.972664 | − | 0.232219i | \(-0.0745986\pi\) | |||||||
\(948\) | − | 9493.58i | − | 0.325250i | ||||||
\(949\) | 11501.2 | 0.393409 | ||||||||
\(950\) | 13056.8 | − | 5266.42i | 0.445915 | − | 0.179858i | ||||
\(951\) | 17630.0 | 0.601147 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 51886.1i | 1.76365i | 0.471579 | + | 0.881824i | \(0.343684\pi\) | ||||
−0.471579 | + | 0.881824i | \(0.656316\pi\) | |||||||
\(954\) | 21723.0 | 0.737221 | ||||||||
\(955\) | 8879.48 | + | 5993.07i | 0.300873 | + | 0.203069i | ||||
\(956\) | 24432.0 | 0.826554 | ||||||||
\(957\) | 42798.3i | 1.44564i | ||||||||
\(958\) | 10275.0i | 0.346523i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1227.95 | + | 1819.37i | −0.0412834 | + | 0.0611665i | ||||
\(961\) | −24811.5 | −0.832853 | ||||||||
\(962\) | − | 17586.4i | − | 0.589406i | ||||||
\(963\) | 23536.0i | 0.787578i | ||||||||
\(964\) | 15850.4 | 0.529571 | ||||||||
\(965\) | −28627.9 | + | 42415.8i | −0.954989 | + | 1.41494i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45517.8i | 1.51371i | 0.653585 | + | 0.756853i | \(0.273264\pi\) | ||||
−0.653585 | + | 0.756853i | \(0.726736\pi\) | |||||||
\(968\) | 8955.30i | 0.297349i | ||||||||
\(969\) | 6787.69 | 0.225028 | ||||||||
\(970\) | 6000.05 | + | 4049.64i | 0.198608 | + | 0.134047i | ||||
\(971\) | 23398.3 | 0.773313 | 0.386656 | − | 0.922224i | \(-0.373630\pi\) | ||||
0.386656 | + | 0.922224i | \(0.373630\pi\) | |||||||
\(972\) | − | 15451.6i | − | 0.509886i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1053.07 | 0.0346434 | ||||||||
\(975\) | 6399.38 | + | 15865.7i | 0.210199 | + | 0.521139i | ||||
\(976\) | −375.958 | −0.0123300 | ||||||||
\(977\) | 34323.9i | 1.12397i | 0.827148 | + | 0.561985i | \(0.189962\pi\) | ||||
−0.827148 | + | 0.561985i | \(0.810038\pi\) | |||||||
\(978\) | − | 538.152i | − | 0.0175953i | ||||||
\(979\) | 64407.4 | 2.10262 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 910.402 | 0.0296299 | ||||||||
\(982\) | 3093.74i | 0.100535i | ||||||||
\(983\) | − | 37157.0i | − | 1.20562i | −0.797885 | − | 0.602809i | \(-0.794048\pi\) | ||
0.797885 | − | 0.602809i | \(-0.205952\pi\) | |||||||
\(984\) | −9792.27 | −0.317242 | ||||||||
\(985\) | 21449.0 | − | 31779.4i | 0.693829 | − | 1.02800i | ||||
\(986\) | 22148.0 | 0.715352 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10050.2i | 0.323622i | ||||||||
\(989\) | −18659.0 | −0.599921 | ||||||||
\(990\) | 10892.3 | − | 16138.2i | 0.349675 | − | 0.518088i | ||||
\(991\) | −10542.5 | −0.337935 | −0.168968 | − | 0.985622i | \(-0.554043\pi\) | ||||
−0.168968 | + | 0.985622i | \(0.554043\pi\) | |||||||
\(992\) | − | 2258.09i | − | 0.0722727i | ||||||
\(993\) | 28860.2i | 0.922306i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1353.14 | − | 913.281i | −0.0431130 | − | 0.0290985i | ||||
\(996\) | 16457.1 | 0.523556 | ||||||||
\(997\) | − | 36255.9i | − | 1.15169i | −0.817558 | − | 0.575846i | \(-0.804673\pi\) | ||
0.817558 | − | 0.575846i | \(-0.195327\pi\) | |||||||
\(998\) | 18985.7i | 0.602185i | ||||||||
\(999\) | −26958.6 | −0.853785 |
(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 | 490.4.c.f.99.4 | 12 | ||
5.2 | odd | 4 | 2450.4.a.cy.1.4 | 6 | |||
5.3 | odd | 4 | 2450.4.a.cv.1.3 | 6 | |||
5.4 | even | 2 | inner | 490.4.c.f.99.9 | 12 | ||
7.2 | even | 3 | 70.4.i.a.39.3 | yes | 24 | ||
7.4 | even | 3 | 70.4.i.a.9.10 | yes | 24 | ||
7.6 | odd | 2 | 490.4.c.e.99.3 | 12 | |||
35.2 | odd | 12 | 350.4.e.n.151.3 | 12 | |||
35.4 | even | 6 | 70.4.i.a.9.3 | ✓ | 24 | ||
35.9 | even | 6 | 70.4.i.a.39.10 | yes | 24 | ||
35.13 | even | 4 | 2450.4.a.cw.1.4 | 6 | |||
35.18 | odd | 12 | 350.4.e.o.51.4 | 12 | |||
35.23 | odd | 12 | 350.4.e.o.151.4 | 12 | |||
35.27 | even | 4 | 2450.4.a.cx.1.3 | 6 | |||
35.32 | odd | 12 | 350.4.e.n.51.3 | 12 | |||
35.34 | odd | 2 | 490.4.c.e.99.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.i.a.9.3 | ✓ | 24 | 35.4 | even | 6 | ||
70.4.i.a.9.10 | yes | 24 | 7.4 | even | 3 | ||
70.4.i.a.39.3 | yes | 24 | 7.2 | even | 3 | ||
70.4.i.a.39.10 | yes | 24 | 35.9 | even | 6 | ||
350.4.e.n.51.3 | 12 | 35.32 | odd | 12 | |||
350.4.e.n.151.3 | 12 | 35.2 | odd | 12 | |||
350.4.e.o.51.4 | 12 | 35.18 | odd | 12 | |||
350.4.e.o.151.4 | 12 | 35.23 | odd | 12 | |||
490.4.c.e.99.3 | 12 | 7.6 | odd | 2 | |||
490.4.c.e.99.10 | 12 | 35.34 | odd | 2 | |||
490.4.c.f.99.4 | 12 | 1.1 | even | 1 | trivial | ||
490.4.c.f.99.9 | 12 | 5.4 | even | 2 | inner | ||
2450.4.a.cv.1.3 | 6 | 5.3 | odd | 4 | |||
2450.4.a.cw.1.4 | 6 | 35.13 | even | 4 | |||
2450.4.a.cx.1.3 | 6 | 35.27 | even | 4 | |||
2450.4.a.cy.1.4 | 6 | 5.2 | odd | 4 |