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: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 438 x^{18} + 80439 x^{16} + 8097428 x^{14} + 488971671 x^{12} + 18162509334 x^{10} + \cdots + 9871083181584 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{23}\cdot 5^{2}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.8 | ||
Root | \(-7.79189i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.99 |
Dual form | 490.4.c.g.99.13 |
$q$-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 | ||||||
\(3\) | 6.79189i | 1.30710i | 0.756883 | + | 0.653550i | \(0.226721\pi\) | ||||
−0.756883 | + | 0.653550i | \(0.773279\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −10.7861 | − | 2.94297i | −0.964734 | − | 0.263228i | ||||
\(6\) | 13.5838 | 0.924259 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | −19.1298 | −0.708511 | ||||||||
\(10\) | −5.88595 | + | 21.5721i | −0.186130 | + | 0.682170i | ||||
\(11\) | 69.2093 | 1.89704 | 0.948518 | − | 0.316724i | \(-0.102583\pi\) | ||||
0.948518 | + | 0.316724i | \(0.102583\pi\) | |||||||
\(12\) | − | 27.1676i | − | 0.653550i | ||||||
\(13\) | − | 28.3716i | − | 0.605298i | −0.953102 | − | 0.302649i | \(-0.902129\pi\) | ||
0.953102 | − | 0.302649i | \(-0.0978710\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 19.9884 | − | 73.2577i | 0.344065 | − | 1.26100i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 11.3106i | − | 0.161366i | −0.996740 | − | 0.0806831i | \(-0.974290\pi\) | ||
0.996740 | − | 0.0806831i | \(-0.0257102\pi\) | |||||||
\(18\) | 38.2596i | 0.500993i | ||||||||
\(19\) | −74.2184 | −0.896151 | −0.448075 | − | 0.893996i | \(-0.647890\pi\) | ||||
−0.448075 | + | 0.893996i | \(0.647890\pi\) | |||||||
\(20\) | 43.1442 | + | 11.7719i | 0.482367 | + | 0.131614i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 138.419i | − | 1.34141i | ||||||
\(23\) | 66.6640i | 0.604365i | 0.953250 | + | 0.302183i | \(0.0977152\pi\) | ||||
−0.953250 | + | 0.302183i | \(0.902285\pi\) | |||||||
\(24\) | −54.3351 | −0.462130 | ||||||||
\(25\) | 107.678 | + | 63.4861i | 0.861422 | + | 0.507889i | ||||
\(26\) | −56.7433 | −0.428010 | ||||||||
\(27\) | 53.4536i | 0.381006i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 134.560 | 0.861624 | 0.430812 | − | 0.902442i | \(-0.358227\pi\) | ||||
0.430812 | + | 0.902442i | \(0.358227\pi\) | |||||||
\(30\) | −146.515 | − | 39.9767i | −0.891664 | − | 0.243291i | ||||
\(31\) | −160.637 | −0.930684 | −0.465342 | − | 0.885131i | \(-0.654069\pi\) | ||||
−0.465342 | + | 0.885131i | \(0.654069\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | 470.062i | 2.47962i | ||||||||
\(34\) | −22.6212 | −0.114103 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 76.5192 | 0.354255 | ||||||||
\(37\) | − | 284.750i | − | 1.26521i | −0.774476 | − | 0.632603i | \(-0.781986\pi\) | ||
0.774476 | − | 0.632603i | \(-0.218014\pi\) | |||||||
\(38\) | 148.437i | 0.633674i | ||||||||
\(39\) | 192.697 | 0.791185 | ||||||||
\(40\) | 23.5438 | − | 86.2884i | 0.0930650 | − | 0.341085i | ||||
\(41\) | 149.376 | 0.568990 | 0.284495 | − | 0.958678i | \(-0.408174\pi\) | ||||
0.284495 | + | 0.958678i | \(0.408174\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 513.925i | 1.82262i | 0.411717 | + | 0.911312i | \(0.364929\pi\) | ||||
−0.411717 | + | 0.911312i | \(0.635071\pi\) | |||||||
\(44\) | −276.837 | −0.948518 | ||||||||
\(45\) | 206.335 | + | 56.2985i | 0.683524 | + | 0.186500i | ||||
\(46\) | 133.328 | 0.427351 | ||||||||
\(47\) | 411.615i | 1.27745i | 0.769435 | + | 0.638726i | \(0.220538\pi\) | ||||
−0.769435 | + | 0.638726i | \(0.779462\pi\) | |||||||
\(48\) | 108.670i | 0.326775i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 126.972 | − | 215.356i | 0.359132 | − | 0.609118i | ||||
\(51\) | 76.8204 | 0.210922 | ||||||||
\(52\) | 113.487i | 0.302649i | ||||||||
\(53\) | 354.813i | 0.919571i | 0.888030 | + | 0.459785i | \(0.152074\pi\) | ||||
−0.888030 | + | 0.459785i | \(0.847926\pi\) | |||||||
\(54\) | 106.907 | 0.269412 | ||||||||
\(55\) | −746.495 | − | 203.681i | −1.83013 | − | 0.499352i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 504.083i | − | 1.17136i | ||||||
\(58\) | − | 269.119i | − | 0.609260i | ||||||
\(59\) | −210.828 | −0.465212 | −0.232606 | − | 0.972571i | \(-0.574725\pi\) | ||||
−0.232606 | + | 0.972571i | \(0.574725\pi\) | |||||||
\(60\) | −79.9534 | + | 293.031i | −0.172032 | + | 0.630502i | ||||
\(61\) | 587.114 | 1.23233 | 0.616166 | − | 0.787616i | \(-0.288685\pi\) | ||||
0.616166 | + | 0.787616i | \(0.288685\pi\) | |||||||
\(62\) | 321.273i | 0.658093i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | −83.4970 | + | 306.018i | −0.159331 | + | 0.583952i | ||||
\(66\) | 940.124 | 1.75335 | ||||||||
\(67\) | 1034.20i | 1.88578i | 0.333102 | + | 0.942891i | \(0.391905\pi\) | ||||
−0.333102 | + | 0.942891i | \(0.608095\pi\) | |||||||
\(68\) | 45.2424i | 0.0806831i | ||||||||
\(69\) | −452.774 | −0.789966 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1033.04 | −1.72675 | −0.863373 | − | 0.504566i | \(-0.831653\pi\) | ||||
−0.863373 | + | 0.504566i | \(0.831653\pi\) | |||||||
\(72\) | − | 153.038i | − | 0.250496i | ||||||
\(73\) | 743.489i | 1.19204i | 0.802970 | + | 0.596019i | \(0.203252\pi\) | ||||
−0.802970 | + | 0.596019i | \(0.796748\pi\) | |||||||
\(74\) | −569.500 | −0.894636 | ||||||||
\(75\) | −431.191 | + | 731.336i | −0.663862 | + | 1.12597i | ||||
\(76\) | 296.874 | 0.448075 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 385.394i | − | 0.559453i | ||||||
\(79\) | −609.837 | −0.868507 | −0.434254 | − | 0.900791i | \(-0.642988\pi\) | ||||
−0.434254 | + | 0.900791i | \(0.642988\pi\) | |||||||
\(80\) | −172.577 | − | 47.0876i | −0.241183 | − | 0.0658069i | ||||
\(81\) | −879.555 | −1.20652 | ||||||||
\(82\) | − | 298.752i | − | 0.402337i | ||||||
\(83\) | 1149.96i | 1.52078i | 0.649466 | + | 0.760391i | \(0.274993\pi\) | ||||
−0.649466 | + | 0.760391i | \(0.725007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −33.2868 | + | 121.997i | −0.0424760 | + | 0.155675i | ||||
\(86\) | 1027.85 | 1.28879 | ||||||||
\(87\) | 913.914i | 1.12623i | ||||||||
\(88\) | 553.675i | 0.670703i | ||||||||
\(89\) | 735.658 | 0.876175 | 0.438087 | − | 0.898932i | \(-0.355656\pi\) | ||||
0.438087 | + | 0.898932i | \(0.355656\pi\) | |||||||
\(90\) | 112.597 | − | 412.670i | 0.131875 | − | 0.483325i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 266.656i | − | 0.302183i | ||||||
\(93\) | − | 1091.03i | − | 1.21650i | ||||||
\(94\) | 823.230 | 0.903294 | ||||||||
\(95\) | 800.523 | + | 218.423i | 0.864547 | + | 0.235892i | ||||
\(96\) | 217.341 | 0.231065 | ||||||||
\(97\) | − | 333.373i | − | 0.348958i | −0.984661 | − | 0.174479i | \(-0.944176\pi\) | ||
0.984661 | − | 0.174479i | \(-0.0558241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1323.96 | −1.34407 | ||||||||
\(100\) | −430.711 | − | 253.945i | −0.430711 | − | 0.253945i | ||||
\(101\) | 3.00584 | 0.00296131 | 0.00148065 | − | 0.999999i | \(-0.499529\pi\) | ||||
0.00148065 | + | 0.999999i | \(0.499529\pi\) | |||||||
\(102\) | − | 153.641i | − | 0.149144i | ||||||
\(103\) | − | 746.724i | − | 0.714339i | −0.934040 | − | 0.357170i | \(-0.883742\pi\) | ||
0.934040 | − | 0.357170i | \(-0.116258\pi\) | |||||||
\(104\) | 226.973 | 0.214005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 709.625 | 0.650235 | ||||||||
\(107\) | − | 771.055i | − | 0.696642i | −0.937375 | − | 0.348321i | \(-0.886752\pi\) | ||
0.937375 | − | 0.348321i | \(-0.113248\pi\) | |||||||
\(108\) | − | 213.814i | − | 0.190503i | ||||||
\(109\) | 845.588 | 0.743052 | 0.371526 | − | 0.928423i | \(-0.378835\pi\) | ||||
0.371526 | + | 0.928423i | \(0.378835\pi\) | |||||||
\(110\) | −407.362 | + | 1492.99i | −0.353095 | + | 1.29410i | ||||
\(111\) | 1933.99 | 1.65375 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 881.711i | − | 0.734021i | −0.930217 | − | 0.367011i | \(-0.880381\pi\) | ||
0.930217 | − | 0.367011i | \(-0.119619\pi\) | |||||||
\(114\) | −1008.17 | −0.828276 | ||||||||
\(115\) | 196.190 | − | 719.041i | 0.159086 | − | 0.583051i | ||||
\(116\) | −538.238 | −0.430812 | ||||||||
\(117\) | 542.744i | 0.428860i | ||||||||
\(118\) | 421.657i | 0.328955i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 586.062 | + | 159.907i | 0.445832 | + | 0.121645i | ||||
\(121\) | 3458.93 | 2.59874 | ||||||||
\(122\) | − | 1174.23i | − | 0.871391i | ||||||
\(123\) | 1014.54i | 0.743727i | ||||||||
\(124\) | 642.547 | 0.465342 | ||||||||
\(125\) | −974.580 | − | 1001.66i | −0.697353 | − | 0.716728i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 486.055i | − | 0.339610i | −0.985478 | − | 0.169805i | \(-0.945686\pi\) | ||
0.985478 | − | 0.169805i | \(-0.0543137\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | −3490.52 | −2.38235 | ||||||||
\(130\) | 612.036 | + | 166.994i | 0.412916 | + | 0.112664i | ||||
\(131\) | 1171.60 | 0.781398 | 0.390699 | − | 0.920518i | \(-0.372233\pi\) | ||||
0.390699 | + | 0.920518i | \(0.372233\pi\) | |||||||
\(132\) | − | 1880.25i | − | 1.23981i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2068.40 | 1.33345 | ||||||||
\(135\) | 157.313 | − | 576.553i | 0.100291 | − | 0.367569i | ||||
\(136\) | 90.4849 | 0.0570516 | ||||||||
\(137\) | − | 663.078i | − | 0.413508i | −0.978393 | − | 0.206754i | \(-0.933710\pi\) | ||
0.978393 | − | 0.206754i | \(-0.0662899\pi\) | |||||||
\(138\) | 905.549i | 0.558590i | ||||||||
\(139\) | 1395.82 | 0.851741 | 0.425870 | − | 0.904784i | \(-0.359968\pi\) | ||||
0.425870 | + | 0.904784i | \(0.359968\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2795.64 | −1.66976 | ||||||||
\(142\) | 2066.08i | 1.22099i | ||||||||
\(143\) | − | 1963.58i | − | 1.14827i | ||||||
\(144\) | −306.077 | −0.177128 | ||||||||
\(145\) | −1451.37 | − | 396.005i | −0.831238 | − | 0.226803i | ||||
\(146\) | 1486.98 | 0.842898 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1139.00i | 0.632603i | ||||||||
\(149\) | −710.861 | −0.390845 | −0.195423 | − | 0.980719i | \(-0.562608\pi\) | ||||
−0.195423 | + | 0.980719i | \(0.562608\pi\) | |||||||
\(150\) | 1462.67 | + | 862.382i | 0.796178 | + | 0.469421i | ||||
\(151\) | 1739.00 | 0.937204 | 0.468602 | − | 0.883409i | \(-0.344758\pi\) | ||||
0.468602 | + | 0.883409i | \(0.344758\pi\) | |||||||
\(152\) | − | 593.747i | − | 0.316837i | ||||||
\(153\) | 216.370i | 0.114330i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1732.64 | + | 472.749i | 0.897862 | + | 0.244982i | ||||
\(156\) | −770.788 | −0.395593 | ||||||||
\(157\) | 3551.13i | 1.80517i | 0.430517 | + | 0.902583i | \(0.358331\pi\) | ||||
−0.430517 | + | 0.902583i | \(0.641669\pi\) | |||||||
\(158\) | 1219.67i | 0.614127i | ||||||||
\(159\) | −2409.85 | −1.20197 | ||||||||
\(160\) | −94.1752 | + | 345.154i | −0.0465325 | + | 0.170542i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1759.11i | 0.853141i | ||||||||
\(163\) | 2446.20i | 1.17547i | 0.809055 | + | 0.587733i | \(0.199979\pi\) | ||||
−0.809055 | + | 0.587733i | \(0.800021\pi\) | |||||||
\(164\) | −597.503 | −0.284495 | ||||||||
\(165\) | 1383.38 | − | 5070.11i | 0.652703 | − | 2.39217i | ||||
\(166\) | 2299.93 | 1.07536 | ||||||||
\(167\) | 2080.53i | 0.964049i | 0.876158 | + | 0.482025i | \(0.160098\pi\) | ||||
−0.876158 | + | 0.482025i | \(0.839902\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1392.05 | 0.633614 | ||||||||
\(170\) | 243.994 | + | 66.5736i | 0.110079 | + | 0.0300351i | ||||
\(171\) | 1419.78 | 0.634933 | ||||||||
\(172\) | − | 2055.70i | − | 0.911312i | ||||||
\(173\) | − | 2513.87i | − | 1.10477i | −0.833588 | − | 0.552387i | \(-0.813717\pi\) | ||
0.833588 | − | 0.552387i | \(-0.186283\pi\) | |||||||
\(174\) | 1827.83 | 0.796364 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1107.35 | 0.474259 | ||||||||
\(177\) | − | 1431.92i | − | 0.608079i | ||||||
\(178\) | − | 1471.32i | − | 0.619549i | ||||||
\(179\) | −990.726 | −0.413689 | −0.206844 | − | 0.978374i | \(-0.566319\pi\) | ||||
−0.206844 | + | 0.978374i | \(0.566319\pi\) | |||||||
\(180\) | −825.340 | − | 225.194i | −0.341762 | − | 0.0932498i | ||||
\(181\) | −1777.12 | −0.729792 | −0.364896 | − | 0.931048i | \(-0.618895\pi\) | ||||
−0.364896 | + | 0.931048i | \(0.618895\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3987.62i | 1.61078i | ||||||||
\(184\) | −533.312 | −0.213675 | ||||||||
\(185\) | −838.012 | + | 3071.33i | −0.333037 | + | 1.22059i | ||||
\(186\) | −2182.05 | −0.860193 | ||||||||
\(187\) | − | 782.800i | − | 0.306117i | ||||||
\(188\) | − | 1646.46i | − | 0.638726i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 436.846 | − | 1601.05i | 0.166801 | − | 0.611327i | ||||
\(191\) | 2336.71 | 0.885226 | 0.442613 | − | 0.896713i | \(-0.354051\pi\) | ||||
0.442613 | + | 0.896713i | \(0.354051\pi\) | |||||||
\(192\) | − | 434.681i | − | 0.163388i | ||||||
\(193\) | − | 800.791i | − | 0.298664i | −0.988787 | − | 0.149332i | \(-0.952288\pi\) | ||
0.988787 | − | 0.149332i | \(-0.0477124\pi\) | |||||||
\(194\) | −666.746 | −0.246750 | ||||||||
\(195\) | −2078.44 | − | 567.102i | −0.763283 | − | 0.208262i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2168.24i | − | 0.784167i | −0.919930 | − | 0.392083i | \(-0.871754\pi\) | ||
0.919930 | − | 0.392083i | \(-0.128246\pi\) | |||||||
\(198\) | 2647.92i | 0.950401i | ||||||||
\(199\) | −1625.98 | −0.579210 | −0.289605 | − | 0.957146i | \(-0.593524\pi\) | ||||
−0.289605 | + | 0.957146i | \(0.593524\pi\) | |||||||
\(200\) | −507.889 | + | 861.422i | −0.179566 | + | 0.304559i | ||||
\(201\) | −7024.16 | −2.46491 | ||||||||
\(202\) | − | 6.01168i | − | 0.00209396i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −307.282 | −0.105461 | ||||||||
\(205\) | −1611.18 | − | 439.609i | −0.548924 | − | 0.149774i | ||||
\(206\) | −1493.45 | −0.505114 | ||||||||
\(207\) | − | 1275.27i | − | 0.428199i | ||||||
\(208\) | − | 453.946i | − | 0.151325i | ||||||
\(209\) | −5136.60 | −1.70003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −818.927 | −0.267191 | −0.133595 | − | 0.991036i | \(-0.542652\pi\) | ||||
−0.133595 | + | 0.991036i | \(0.542652\pi\) | |||||||
\(212\) | − | 1419.25i | − | 0.459785i | ||||||
\(213\) | − | 7016.28i | − | 2.25703i | ||||||
\(214\) | −1542.11 | −0.492600 | ||||||||
\(215\) | 1512.47 | − | 5543.22i | 0.479765 | − | 1.75835i | ||||
\(216\) | −427.629 | −0.134706 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 1691.18i | − | 0.525417i | ||||||
\(219\) | −5049.69 | −1.55811 | ||||||||
\(220\) | 2985.98 | + | 814.725i | 0.915067 | + | 0.249676i | ||||
\(221\) | −320.901 | −0.0976747 | ||||||||
\(222\) | − | 3867.99i | − | 1.16938i | ||||||
\(223\) | 4820.46i | 1.44754i | 0.690040 | + | 0.723771i | \(0.257593\pi\) | ||||
−0.690040 | + | 0.723771i | \(0.742407\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2059.85 | − | 1214.48i | −0.610327 | − | 0.359845i | ||||
\(226\) | −1763.42 | −0.519031 | ||||||||
\(227\) | − | 5000.05i | − | 1.46196i | −0.682399 | − | 0.730980i | \(-0.739063\pi\) | ||
0.682399 | − | 0.730980i | \(-0.260937\pi\) | |||||||
\(228\) | 2016.33i | 0.585679i | ||||||||
\(229\) | 6313.04 | 1.82173 | 0.910867 | − | 0.412700i | \(-0.135414\pi\) | ||||
0.910867 | + | 0.412700i | \(0.135414\pi\) | |||||||
\(230\) | −1438.08 | − | 392.381i | −0.412280 | − | 0.112490i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1076.48i | 0.304630i | ||||||||
\(233\) | 4697.78i | 1.32087i | 0.750885 | + | 0.660433i | \(0.229627\pi\) | ||||
−0.750885 | + | 0.660433i | \(0.770373\pi\) | |||||||
\(234\) | 1085.49 | 0.303250 | ||||||||
\(235\) | 1211.37 | − | 4439.70i | 0.336260 | − | 1.23240i | ||||
\(236\) | 843.314 | 0.232606 | ||||||||
\(237\) | − | 4141.95i | − | 1.13523i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4151.19 | −1.12351 | −0.561753 | − | 0.827305i | \(-0.689873\pi\) | ||||
−0.561753 | + | 0.827305i | \(0.689873\pi\) | |||||||
\(240\) | 319.814 | − | 1172.12i | 0.0860162 | − | 0.315251i | ||||
\(241\) | 2451.44 | 0.655232 | 0.327616 | − | 0.944811i | \(-0.393755\pi\) | ||||
0.327616 | + | 0.944811i | \(0.393755\pi\) | |||||||
\(242\) | − | 6917.86i | − | 1.83759i | ||||||
\(243\) | − | 4530.60i | − | 1.19604i | ||||||
\(244\) | −2348.46 | −0.616166 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2029.09 | 0.525894 | ||||||||
\(247\) | 2105.70i | 0.542438i | ||||||||
\(248\) | − | 1285.09i | − | 0.329046i | ||||||
\(249\) | −7810.43 | −1.98781 | ||||||||
\(250\) | −2003.32 | + | 1949.16i | −0.506803 | + | 0.493103i | ||||
\(251\) | −3104.12 | −0.780598 | −0.390299 | − | 0.920688i | \(-0.627628\pi\) | ||||
−0.390299 | + | 0.920688i | \(0.627628\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4613.77i | 1.14650i | ||||||||
\(254\) | −972.111 | −0.240140 | ||||||||
\(255\) | −828.589 | − | 226.081i | −0.203483 | − | 0.0555204i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 7683.54i | 1.86493i | 0.361265 | + | 0.932463i | \(0.382345\pi\) | ||||
−0.361265 | + | 0.932463i | \(0.617655\pi\) | |||||||
\(258\) | 6981.05i | 1.68458i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 333.988 | − | 1224.07i | 0.0796656 | − | 0.291976i | ||||
\(261\) | −2574.10 | −0.610470 | ||||||||
\(262\) | − | 2343.20i | − | 0.552532i | ||||||
\(263\) | 3678.45i | 0.862445i | 0.902246 | + | 0.431222i | \(0.141918\pi\) | ||||
−0.902246 | + | 0.431222i | \(0.858082\pi\) | |||||||
\(264\) | −3760.50 | −0.876677 | ||||||||
\(265\) | 1044.20 | − | 3827.03i | 0.242056 | − | 0.887141i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4996.51i | 1.14525i | ||||||||
\(268\) | − | 4136.79i | − | 0.942891i | ||||||
\(269\) | −3612.17 | −0.818729 | −0.409364 | − | 0.912371i | \(-0.634249\pi\) | ||||
−0.409364 | + | 0.912371i | \(0.634249\pi\) | |||||||
\(270\) | −1153.11 | − | 314.625i | −0.259910 | − | 0.0709166i | ||||
\(271\) | 2374.98 | 0.532360 | 0.266180 | − | 0.963923i | \(-0.414238\pi\) | ||||
0.266180 | + | 0.963923i | \(0.414238\pi\) | |||||||
\(272\) | − | 180.970i | − | 0.0403416i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1326.16 | −0.292394 | ||||||||
\(275\) | 7452.31 | + | 4393.83i | 1.63415 | + | 0.963484i | ||||
\(276\) | 1811.10 | 0.394983 | ||||||||
\(277\) | − | 1964.57i | − | 0.426136i | −0.977037 | − | 0.213068i | \(-0.931654\pi\) | ||
0.977037 | − | 0.213068i | \(-0.0683455\pi\) | |||||||
\(278\) | − | 2791.64i | − | 0.602272i | ||||||
\(279\) | 3072.95 | 0.659400 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4525.40 | 0.960721 | 0.480360 | − | 0.877071i | \(-0.340506\pi\) | ||||
0.480360 | + | 0.877071i | \(0.340506\pi\) | |||||||
\(282\) | 5591.29i | 1.18070i | ||||||||
\(283\) | − | 167.067i | − | 0.0350922i | −0.999846 | − | 0.0175461i | \(-0.994415\pi\) | ||
0.999846 | − | 0.0175461i | \(-0.00558538\pi\) | |||||||
\(284\) | 4132.15 | 0.863373 | ||||||||
\(285\) | −1483.50 | + | 5437.07i | −0.308334 | + | 1.13005i | ||||
\(286\) | −3927.16 | −0.811951 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 612.153i | 0.125248i | ||||||||
\(289\) | 4785.07 | 0.973961 | ||||||||
\(290\) | −792.011 | + | 2902.73i | −0.160374 | + | 0.587774i | ||||
\(291\) | 2264.23 | 0.456123 | ||||||||
\(292\) | − | 2973.95i | − | 0.596019i | ||||||
\(293\) | 1220.67i | 0.243388i | 0.992568 | + | 0.121694i | \(0.0388326\pi\) | ||||
−0.992568 | + | 0.121694i | \(0.961167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2274.01 | + | 620.463i | 0.448806 | + | 0.122457i | ||||
\(296\) | 2278.00 | 0.447318 | ||||||||
\(297\) | 3699.49i | 0.722781i | ||||||||
\(298\) | 1421.72i | 0.276369i | ||||||||
\(299\) | 1891.37 | 0.365821 | ||||||||
\(300\) | 1724.76 | − | 2925.34i | 0.331931 | − | 0.562983i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 3478.00i | − | 0.662704i | ||||||
\(303\) | 20.4153i | 0.00387073i | ||||||||
\(304\) | −1187.49 | −0.224038 | ||||||||
\(305\) | −6332.65 | − | 1727.86i | −1.18887 | − | 0.324384i | ||||
\(306\) | 432.739 | 0.0808433 | ||||||||
\(307\) | − | 6193.89i | − | 1.15148i | −0.817633 | − | 0.575739i | \(-0.804714\pi\) | ||
0.817633 | − | 0.575739i | \(-0.195286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5071.67 | 0.933713 | ||||||||
\(310\) | 945.499 | − | 3465.27i | 0.173228 | − | 0.634884i | ||||
\(311\) | −5280.54 | −0.962803 | −0.481402 | − | 0.876500i | \(-0.659872\pi\) | ||||
−0.481402 | + | 0.876500i | \(0.659872\pi\) | |||||||
\(312\) | 1541.58i | 0.279726i | ||||||||
\(313\) | − | 7753.59i | − | 1.40019i | −0.714051 | − | 0.700094i | \(-0.753142\pi\) | ||
0.714051 | − | 0.700094i | \(-0.246858\pi\) | |||||||
\(314\) | 7102.26 | 1.27644 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2439.35 | 0.434254 | ||||||||
\(317\) | − | 212.730i | − | 0.0376912i | −0.999822 | − | 0.0188456i | \(-0.994001\pi\) | ||
0.999822 | − | 0.0188456i | \(-0.00599909\pi\) | |||||||
\(318\) | 4819.70i | 0.849922i | ||||||||
\(319\) | 9312.78 | 1.63453 | ||||||||
\(320\) | 690.307 | + | 188.350i | 0.120592 | + | 0.0329034i | ||||
\(321\) | 5236.92 | 0.910581 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 839.455i | 0.144608i | ||||||||
\(324\) | 3518.22 | 0.603262 | ||||||||
\(325\) | 1801.21 | − | 3055.00i | 0.307424 | − | 0.521417i | ||||
\(326\) | 4892.39 | 0.831180 | ||||||||
\(327\) | 5743.14i | 0.971243i | ||||||||
\(328\) | 1195.01i | 0.201168i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10140.2 | − | 2766.76i | −1.69152 | − | 0.461531i | ||||
\(331\) | −12028.8 | −1.99747 | −0.998736 | − | 0.0502714i | \(-0.983991\pi\) | ||||
−0.998736 | + | 0.0502714i | \(0.983991\pi\) | |||||||
\(332\) | − | 4599.85i | − | 0.760391i | ||||||
\(333\) | 5447.21i | 0.896413i | ||||||||
\(334\) | 4161.06 | 0.681686 | ||||||||
\(335\) | 3043.62 | − | 11154.9i | 0.496390 | − | 1.81928i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1044.91i | − | 0.168901i | −0.996428 | − | 0.0844507i | \(-0.973086\pi\) | ||
0.996428 | − | 0.0844507i | \(-0.0269135\pi\) | |||||||
\(338\) | − | 2784.10i | − | 0.448033i | ||||||
\(339\) | 5988.49 | 0.959439 | ||||||||
\(340\) | 133.147 | − | 487.987i | 0.0212380 | − | 0.0778377i | ||||
\(341\) | −11117.6 | −1.76554 | ||||||||
\(342\) | − | 2839.56i | − | 0.448965i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4111.40 | −0.644395 | ||||||||
\(345\) | 4883.65 | + | 1332.50i | 0.762107 | + | 0.207941i | ||||
\(346\) | −5027.74 | −0.781193 | ||||||||
\(347\) | 7390.86i | 1.14341i | 0.820460 | + | 0.571703i | \(0.193717\pi\) | ||||
−0.820460 | + | 0.571703i | \(0.806283\pi\) | |||||||
\(348\) | − | 3655.66i | − | 0.563114i | ||||||
\(349\) | 9299.14 | 1.42628 | 0.713140 | − | 0.701022i | \(-0.247272\pi\) | ||||
0.713140 | + | 0.701022i | \(0.247272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1516.57 | 0.230622 | ||||||||
\(352\) | − | 2214.70i | − | 0.335352i | ||||||
\(353\) | 1872.73i | 0.282367i | 0.989983 | + | 0.141183i | \(0.0450907\pi\) | ||||
−0.989983 | + | 0.141183i | \(0.954909\pi\) | |||||||
\(354\) | −2863.85 | −0.429977 | ||||||||
\(355\) | 11142.4 | + | 3040.20i | 1.66585 | + | 0.454527i | ||||
\(356\) | −2942.63 | −0.438087 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1981.45i | 0.292522i | ||||||||
\(359\) | 4300.48 | 0.632230 | 0.316115 | − | 0.948721i | \(-0.397621\pi\) | ||||
0.316115 | + | 0.948721i | \(0.397621\pi\) | |||||||
\(360\) | −450.388 | + | 1650.68i | −0.0659376 | + | 0.241662i | ||||
\(361\) | −1350.63 | −0.196914 | ||||||||
\(362\) | 3554.24i | 0.516041i | ||||||||
\(363\) | 23492.7i | 3.39682i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2188.07 | − | 8019.31i | 0.313777 | − | 1.15000i | ||||
\(366\) | 7975.24 | 1.13900 | ||||||||
\(367\) | 9618.48i | 1.36807i | 0.729451 | + | 0.684033i | \(0.239776\pi\) | ||||
−0.729451 | + | 0.684033i | \(0.760224\pi\) | |||||||
\(368\) | 1066.62i | 0.151091i | ||||||||
\(369\) | −2857.53 | −0.403136 | ||||||||
\(370\) | 6142.66 | + | 1676.02i | 0.863086 | + | 0.235493i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4364.11i | 0.608248i | ||||||||
\(373\) | − | 9483.14i | − | 1.31640i | −0.752842 | − | 0.658202i | \(-0.771317\pi\) | ||
0.752842 | − | 0.658202i | \(-0.228683\pi\) | |||||||
\(374\) | −1565.60 | −0.216458 | ||||||||
\(375\) | 6803.15 | − | 6619.24i | 0.936835 | − | 0.911510i | ||||
\(376\) | −3292.92 | −0.451647 | ||||||||
\(377\) | − | 3817.68i | − | 0.521539i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −558.846 | −0.0757414 | −0.0378707 | − | 0.999283i | \(-0.512057\pi\) | ||||
−0.0378707 | + | 0.999283i | \(0.512057\pi\) | |||||||
\(380\) | −3202.09 | − | 873.691i | −0.432274 | − | 0.117946i | ||||
\(381\) | 3301.24 | 0.443904 | ||||||||
\(382\) | − | 4673.42i | − | 0.625950i | ||||||
\(383\) | 2251.51i | 0.300383i | 0.988657 | + | 0.150191i | \(0.0479890\pi\) | ||||
−0.988657 | + | 0.150191i | \(0.952011\pi\) | |||||||
\(384\) | −869.362 | −0.115532 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1601.58 | −0.211188 | ||||||||
\(387\) | − | 9831.28i | − | 1.29135i | ||||||
\(388\) | 1333.49i | 0.174479i | ||||||||
\(389\) | −5246.70 | −0.683851 | −0.341926 | − | 0.939727i | \(-0.611079\pi\) | ||||
−0.341926 | + | 0.939727i | \(0.611079\pi\) | |||||||
\(390\) | −1134.20 | + | 4156.88i | −0.147263 | + | 0.539723i | ||||
\(391\) | 754.010 | 0.0975241 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7957.38i | 1.02137i | ||||||||
\(394\) | −4336.48 | −0.554490 | ||||||||
\(395\) | 6577.74 | + | 1794.74i | 0.837878 | + | 0.228615i | ||||
\(396\) | 5295.84 | 0.672035 | ||||||||
\(397\) | 4750.94i | 0.600612i | 0.953843 | + | 0.300306i | \(0.0970888\pi\) | ||||
−0.953843 | + | 0.300306i | \(0.902911\pi\) | |||||||
\(398\) | 3251.96i | 0.409563i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1722.84 | + | 1015.78i | 0.215356 | + | 0.126972i | ||||
\(401\) | −10598.9 | −1.31991 | −0.659956 | − | 0.751305i | \(-0.729425\pi\) | ||||
−0.659956 | + | 0.751305i | \(0.729425\pi\) | |||||||
\(402\) | 14048.3i | 1.74295i | ||||||||
\(403\) | 4557.53i | 0.563341i | ||||||||
\(404\) | −12.0234 | −0.00148065 | ||||||||
\(405\) | 9486.93 | + | 2588.51i | 1.16397 | + | 0.317590i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 19707.4i | − | 2.40014i | ||||||
\(408\) | 614.563i | 0.0745721i | ||||||||
\(409\) | 5914.26 | 0.715016 | 0.357508 | − | 0.933910i | \(-0.383627\pi\) | ||||
0.357508 | + | 0.933910i | \(0.383627\pi\) | |||||||
\(410\) | −879.218 | + | 3222.35i | −0.105906 | + | 0.388148i | ||||
\(411\) | 4503.55 | 0.540496 | ||||||||
\(412\) | 2986.90i | 0.357170i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2550.54 | −0.302783 | ||||||||
\(415\) | 3384.31 | − | 12403.6i | 0.400312 | − | 1.46715i | ||||
\(416\) | −907.892 | −0.107003 | ||||||||
\(417\) | 9480.26i | 1.11331i | ||||||||
\(418\) | 10273.2i | 1.20210i | ||||||||
\(419\) | −483.168 | −0.0563349 | −0.0281674 | − | 0.999603i | \(-0.508967\pi\) | ||||
−0.0281674 | + | 0.999603i | \(0.508967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5789.84 | −0.670260 | −0.335130 | − | 0.942172i | \(-0.608780\pi\) | ||||
−0.335130 | + | 0.942172i | \(0.608780\pi\) | |||||||
\(422\) | 1637.85i | 0.188932i | ||||||||
\(423\) | − | 7874.11i | − | 0.905088i | ||||||
\(424\) | −2838.50 | −0.325117 | ||||||||
\(425\) | 718.067 | − | 1217.90i | 0.0819561 | − | 0.139004i | ||||
\(426\) | −14032.6 | −1.59596 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3084.22i | 0.348321i | ||||||||
\(429\) | 13336.4 | 1.50091 | ||||||||
\(430\) | −11086.4 | − | 3024.94i | −1.24334 | − | 0.339245i | ||||
\(431\) | 642.154 | 0.0717668 | 0.0358834 | − | 0.999356i | \(-0.488576\pi\) | ||||
0.0358834 | + | 0.999356i | \(0.488576\pi\) | |||||||
\(432\) | 855.258i | 0.0952514i | ||||||||
\(433\) | 2336.33i | 0.259300i | 0.991560 | + | 0.129650i | \(0.0413853\pi\) | ||||
−0.991560 | + | 0.129650i | \(0.958615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2689.63 | − | 9857.53i | 0.296454 | − | 1.08651i | ||||
\(436\) | −3382.35 | −0.371526 | ||||||||
\(437\) | − | 4947.69i | − | 0.541602i | ||||||
\(438\) | 10099.4i | 1.10175i | ||||||||
\(439\) | 8930.85 | 0.970948 | 0.485474 | − | 0.874251i | \(-0.338647\pi\) | ||||
0.485474 | + | 0.874251i | \(0.338647\pi\) | |||||||
\(440\) | 1629.45 | − | 5971.96i | 0.176548 | − | 0.647050i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 641.801i | 0.0690664i | ||||||||
\(443\) | 7112.29i | 0.762788i | 0.924413 | + | 0.381394i | \(0.124556\pi\) | ||||
−0.924413 | + | 0.381394i | \(0.875444\pi\) | |||||||
\(444\) | −7735.97 | −0.826876 | ||||||||
\(445\) | −7934.84 | − | 2165.02i | −0.845275 | − | 0.230633i | ||||
\(446\) | 9640.92 | 1.02357 | ||||||||
\(447\) | − | 4828.09i | − | 0.510874i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4508.90 | 0.473916 | 0.236958 | − | 0.971520i | \(-0.423850\pi\) | ||||
0.236958 | + | 0.971520i | \(0.423850\pi\) | |||||||
\(450\) | −2428.95 | + | 4119.71i | −0.254449 | + | 0.431566i | ||||
\(451\) | 10338.2 | 1.07939 | ||||||||
\(452\) | 3526.84i | 0.367011i | ||||||||
\(453\) | 11811.1i | 1.22502i | ||||||||
\(454\) | −10000.1 | −1.03376 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4032.67 | 0.414138 | ||||||||
\(457\) | 2048.24i | 0.209656i | 0.994490 | + | 0.104828i | \(0.0334292\pi\) | ||||
−0.994490 | + | 0.104828i | \(0.966571\pi\) | |||||||
\(458\) | − | 12626.1i | − | 1.28816i | ||||||
\(459\) | 604.593 | 0.0614814 | ||||||||
\(460\) | −784.761 | + | 2876.16i | −0.0795428 | + | 0.291526i | ||||
\(461\) | −9007.55 | −0.910030 | −0.455015 | − | 0.890484i | \(-0.650366\pi\) | ||||
−0.455015 | + | 0.890484i | \(0.650366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3016.17i | 0.302750i | 0.988476 | + | 0.151375i | \(0.0483702\pi\) | ||||
−0.988476 | + | 0.151375i | \(0.951630\pi\) | |||||||
\(464\) | 2152.95 | 0.215406 | ||||||||
\(465\) | −3210.86 | + | 11767.9i | −0.320216 | + | 1.17360i | ||||
\(466\) | 9395.56 | 0.933993 | ||||||||
\(467\) | − | 9182.69i | − | 0.909902i | −0.890516 | − | 0.454951i | \(-0.849657\pi\) | ||
0.890516 | − | 0.454951i | \(-0.150343\pi\) | |||||||
\(468\) | − | 2170.97i | − | 0.214430i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8879.40 | − | 2422.74i | −0.871439 | − | 0.237772i | ||||
\(471\) | −24118.9 | −2.35953 | ||||||||
\(472\) | − | 1686.63i | − | 0.164477i | ||||||
\(473\) | 35568.4i | 3.45758i | ||||||||
\(474\) | −8283.90 | −0.802726 | ||||||||
\(475\) | −7991.67 | − | 4711.84i | −0.771965 | − | 0.455145i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6787.49i | − | 0.651526i | ||||||
\(478\) | 8302.38i | 0.794439i | ||||||||
\(479\) | 19335.2 | 1.84436 | 0.922181 | − | 0.386760i | \(-0.126406\pi\) | ||||
0.922181 | + | 0.386760i | \(0.126406\pi\) | |||||||
\(480\) | −2344.25 | − | 639.627i | −0.222916 | − | 0.0608226i | ||||
\(481\) | −8078.83 | −0.765827 | ||||||||
\(482\) | − | 4902.87i | − | 0.463319i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13835.7 | −1.29937 | ||||||||
\(485\) | −981.108 | + | 3595.78i | −0.0918553 | + | 0.336651i | ||||
\(486\) | −9061.20 | −0.845729 | ||||||||
\(487\) | − | 9704.88i | − | 0.903019i | −0.892266 | − | 0.451509i | \(-0.850886\pi\) | ||
0.892266 | − | 0.451509i | \(-0.149114\pi\) | |||||||
\(488\) | 4696.92i | 0.435695i | ||||||||
\(489\) | −16614.3 | −1.53645 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2284.05 | −0.209934 | −0.104967 | − | 0.994476i | \(-0.533474\pi\) | ||||
−0.104967 | + | 0.994476i | \(0.533474\pi\) | |||||||
\(492\) | − | 4058.18i | − | 0.371863i | ||||||
\(493\) | − | 1521.95i | − | 0.139037i | ||||||
\(494\) | 4211.39 | 0.383562 | ||||||||
\(495\) | 14280.3 | + | 3896.38i | 1.29667 | + | 0.353796i | ||||
\(496\) | −2570.19 | −0.232671 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 15620.9i | 1.40560i | ||||||||
\(499\) | −6801.94 | −0.610214 | −0.305107 | − | 0.952318i | \(-0.598692\pi\) | ||||
−0.305107 | + | 0.952318i | \(0.598692\pi\) | |||||||
\(500\) | 3898.32 | + | 4006.63i | 0.348676 | + | 0.358364i | ||||
\(501\) | −14130.7 | −1.26011 | ||||||||
\(502\) | 6208.23i | 0.551966i | ||||||||
\(503\) | − | 8820.72i | − | 0.781902i | −0.920412 | − | 0.390951i | \(-0.872146\pi\) | ||
0.920412 | − | 0.390951i | \(-0.127854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.4211 | − | 8.84610i | −0.00285687 | − | 0.000779498i | ||||
\(506\) | 9227.53 | 0.810700 | ||||||||
\(507\) | 9454.65i | 0.828197i | ||||||||
\(508\) | 1944.22i | 0.169805i | ||||||||
\(509\) | −11132.7 | −0.969449 | −0.484724 | − | 0.874667i | \(-0.661080\pi\) | ||||
−0.484724 | + | 0.874667i | \(0.661080\pi\) | |||||||
\(510\) | −452.161 | + | 1657.18i | −0.0392589 | + | 0.143884i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | − | 3967.24i | − | 0.341438i | ||||||
\(514\) | 15367.1 | 1.31870 | ||||||||
\(515\) | −2197.59 | + | 8054.21i | −0.188034 | + | 0.689147i | ||||
\(516\) | 13962.1 | 1.19118 | ||||||||
\(517\) | 28487.6i | 2.42337i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17073.9 | 1.44405 | ||||||||
\(520\) | −2448.14 | − | 667.976i | −0.206458 | − | 0.0563321i | ||||
\(521\) | −4640.75 | −0.390240 | −0.195120 | − | 0.980779i | \(-0.562510\pi\) | ||||
−0.195120 | + | 0.980779i | \(0.562510\pi\) | |||||||
\(522\) | 5148.19i | 0.431667i | ||||||||
\(523\) | − | 201.305i | − | 0.0168307i | −0.999965 | − | 0.00841534i | \(-0.997321\pi\) | ||
0.999965 | − | 0.00841534i | \(-0.00267872\pi\) | |||||||
\(524\) | −4686.40 | −0.390699 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7356.90 | 0.609840 | ||||||||
\(527\) | 1816.90i | 0.150181i | ||||||||
\(528\) | 7520.99i | 0.619904i | ||||||||
\(529\) | 7722.92 | 0.634743 | ||||||||
\(530\) | −7654.05 | − | 2088.41i | −0.627303 | − | 0.171160i | ||||
\(531\) | 4033.11 | 0.329608 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4238.04i | − | 0.344409i | ||||||
\(534\) | 9993.01 | 0.809813 | ||||||||
\(535\) | −2269.19 | + | 8316.64i | −0.183375 | + | 0.672074i | ||||
\(536\) | −8273.58 | −0.666725 | ||||||||
\(537\) | − | 6728.90i | − | 0.540733i | ||||||
\(538\) | 7224.34i | 0.578929i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −629.250 | + | 2306.21i | −0.0501456 | + | 0.183784i | ||||
\(541\) | 3721.35 | 0.295736 | 0.147868 | − | 0.989007i | \(-0.452759\pi\) | ||||
0.147868 | + | 0.989007i | \(0.452759\pi\) | |||||||
\(542\) | − | 4749.96i | − | 0.376436i | ||||||
\(543\) | − | 12070.0i | − | 0.953912i | ||||||
\(544\) | −361.939 | −0.0285258 | ||||||||
\(545\) | −9120.55 | − | 2488.54i | −0.716847 | − | 0.195592i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5900.64i | 0.461231i | 0.973045 | + | 0.230615i | \(0.0740739\pi\) | ||||
−0.973045 | + | 0.230615i | \(0.925926\pi\) | |||||||
\(548\) | 2652.31i | 0.206754i | ||||||||
\(549\) | −11231.4 | −0.873121 | ||||||||
\(550\) | 8787.66 | − | 14904.6i | 0.681286 | − | 1.15552i | ||||
\(551\) | −9986.80 | −0.772145 | ||||||||
\(552\) | − | 3622.20i | − | 0.279295i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3929.14 | −0.301323 | ||||||||
\(555\) | −20860.1 | − | 5691.69i | −1.59543 | − | 0.435313i | ||||
\(556\) | −5583.28 | −0.425870 | ||||||||
\(557\) | − | 11769.4i | − | 0.895309i | −0.894206 | − | 0.447655i | \(-0.852259\pi\) | ||
0.894206 | − | 0.447655i | \(-0.147741\pi\) | |||||||
\(558\) | − | 6145.89i | − | 0.466266i | ||||||
\(559\) | 14580.9 | 1.10323 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5316.69 | 0.400126 | ||||||||
\(562\) | − | 9050.79i | − | 0.679332i | ||||||
\(563\) | − | 11661.6i | − | 0.872965i | −0.899713 | − | 0.436482i | \(-0.856224\pi\) | ||
0.899713 | − | 0.436482i | \(-0.143776\pi\) | |||||||
\(564\) | 11182.6 | 0.834878 | ||||||||
\(565\) | −2594.85 | + | 9510.18i | −0.193215 | + | 0.708135i | ||||
\(566\) | −334.133 | −0.0248139 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 8264.30i | − | 0.610497i | ||||||
\(569\) | −10613.7 | −0.781986 | −0.390993 | − | 0.920394i | \(-0.627868\pi\) | ||||
−0.390993 | + | 0.920394i | \(0.627868\pi\) | |||||||
\(570\) | 10874.1 | + | 2967.01i | 0.799066 | + | 0.218025i | ||||
\(571\) | −5276.34 | −0.386704 | −0.193352 | − | 0.981129i | \(-0.561936\pi\) | ||||
−0.193352 | + | 0.981129i | \(0.561936\pi\) | |||||||
\(572\) | 7854.33i | 0.574136i | ||||||||
\(573\) | 15870.7i | 1.15708i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4232.24 | + | 7178.23i | −0.306950 | + | 0.520614i | ||||
\(576\) | 1224.31 | 0.0885639 | ||||||||
\(577\) | 5712.12i | 0.412129i | 0.978538 | + | 0.206065i | \(0.0660657\pi\) | ||||
−0.978538 | + | 0.206065i | \(0.933934\pi\) | |||||||
\(578\) | − | 9570.14i | − | 0.688694i | ||||||
\(579\) | 5438.89 | 0.390384 | ||||||||
\(580\) | 5805.47 | + | 1584.02i | 0.415619 | + | 0.113402i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 4528.47i | − | 0.322528i | ||||||
\(583\) | 24556.3i | 1.74446i | ||||||||
\(584\) | −5947.91 | −0.421449 | ||||||||
\(585\) | 1597.28 | − | 5854.06i | 0.112888 | − | 0.413736i | ||||
\(586\) | 2441.35 | 0.172101 | ||||||||
\(587\) | − | 18045.4i | − | 1.26885i | −0.772985 | − | 0.634424i | \(-0.781237\pi\) | ||
0.772985 | − | 0.634424i | \(-0.218763\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11922.2 | 0.834033 | ||||||||
\(590\) | 1240.93 | − | 4548.01i | 0.0865900 | − | 0.317354i | ||||
\(591\) | 14726.5 | 1.02498 | ||||||||
\(592\) | − | 4556.00i | − | 0.316302i | ||||||
\(593\) | − | 26700.2i | − | 1.84898i | −0.381204 | − | 0.924491i | \(-0.624490\pi\) | ||
0.381204 | − | 0.924491i | \(-0.375510\pi\) | |||||||
\(594\) | 7398.97 | 0.511083 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2843.44 | 0.195423 | ||||||||
\(597\) | − | 11043.5i | − | 0.757086i | ||||||
\(598\) | − | 3782.73i | − | 0.258675i | ||||||
\(599\) | 23229.1 | 1.58450 | 0.792249 | − | 0.610197i | \(-0.208910\pi\) | ||||
0.792249 | + | 0.610197i | \(0.208910\pi\) | |||||||
\(600\) | −5850.69 | − | 3449.53i | −0.398089 | − | 0.234711i | ||||
\(601\) | 28766.2 | 1.95241 | 0.976205 | − | 0.216850i | \(-0.0695781\pi\) | ||||
0.976205 | + | 0.216850i | \(0.0695781\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 19784.0i | − | 1.33610i | ||||||
\(604\) | −6956.00 | −0.468602 | ||||||||
\(605\) | −37308.2 | − | 10179.5i | −2.50710 | − | 0.684061i | ||||
\(606\) | 40.8307 | 0.00273702 | ||||||||
\(607\) | 1266.07i | 0.0846592i | 0.999104 | + | 0.0423296i | \(0.0134780\pi\) | ||||
−0.999104 | + | 0.0423296i | \(0.986522\pi\) | |||||||
\(608\) | 2374.99i | 0.158419i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3455.72 | + | 12665.3i | −0.229374 | + | 0.840660i | ||||
\(611\) | 11678.2 | 0.773239 | ||||||||
\(612\) | − | 865.478i | − | 0.0571649i | ||||||
\(613\) | 11761.1i | 0.774920i | 0.921887 | + | 0.387460i | \(0.126647\pi\) | ||||
−0.921887 | + | 0.387460i | \(0.873353\pi\) | |||||||
\(614\) | −12387.8 | −0.814218 | ||||||||
\(615\) | 2985.78 | − | 10942.9i | 0.195769 | − | 0.717498i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1282.04i | − | 0.0836518i | −0.999125 | − | 0.0418259i | \(-0.986683\pi\) | ||
0.999125 | − | 0.0418259i | \(-0.0133175\pi\) | |||||||
\(618\) | − | 10143.3i | − | 0.660235i | ||||||
\(619\) | 2004.70 | 0.130171 | 0.0650854 | − | 0.997880i | \(-0.479268\pi\) | ||||
0.0650854 | + | 0.997880i | \(0.479268\pi\) | |||||||
\(620\) | −6930.54 | − | 1891.00i | −0.448931 | − | 0.122491i | ||||
\(621\) | −3563.43 | −0.230266 | ||||||||
\(622\) | 10561.1i | 0.680805i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3083.15 | 0.197796 | ||||||||
\(625\) | 7564.02 | + | 13672.1i | 0.484097 | + | 0.875014i | ||||
\(626\) | −15507.2 | −0.990082 | ||||||||
\(627\) | − | 34887.3i | − | 2.22211i | ||||||
\(628\) | − | 14204.5i | − | 0.902583i | ||||||
\(629\) | −3220.70 | −0.204162 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28022.2 | −1.76790 | −0.883949 | − | 0.467582i | \(-0.845125\pi\) | ||||
−0.883949 | + | 0.467582i | \(0.845125\pi\) | |||||||
\(632\) | − | 4878.70i | − | 0.307064i | ||||||
\(633\) | − | 5562.06i | − | 0.349245i | ||||||
\(634\) | −425.460 | −0.0266517 | ||||||||
\(635\) | −1430.45 | + | 5242.62i | −0.0893946 | + | 0.327633i | ||||
\(636\) | 9639.39 | 0.600986 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 18625.6i | − | 1.15579i | ||||||
\(639\) | 19761.8 | 1.22342 | ||||||||
\(640\) | 376.701 | − | 1380.61i | 0.0232662 | − | 0.0852712i | ||||
\(641\) | 13405.5 | 0.826030 | 0.413015 | − | 0.910724i | \(-0.364476\pi\) | ||||
0.413015 | + | 0.910724i | \(0.364476\pi\) | |||||||
\(642\) | − | 10473.8i | − | 0.643878i | ||||||
\(643\) | − | 8670.90i | − | 0.531799i | −0.964001 | − | 0.265899i | \(-0.914331\pi\) | ||
0.964001 | − | 0.265899i | \(-0.0856689\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37649.0 | + | 10272.5i | 2.29834 | + | 0.627101i | ||||
\(646\) | 1678.91 | 0.102254 | ||||||||
\(647\) | − | 21187.8i | − | 1.28745i | −0.765259 | − | 0.643723i | \(-0.777389\pi\) | ||
0.765259 | − | 0.643723i | \(-0.222611\pi\) | |||||||
\(648\) | − | 7036.44i | − | 0.426570i | ||||||
\(649\) | −14591.3 | −0.882525 | ||||||||
\(650\) | −6109.99 | − | 3602.41i | −0.368698 | − | 0.217382i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 9784.79i | − | 0.587733i | ||||||
\(653\) | − | 22491.4i | − | 1.34787i | −0.738793 | − | 0.673933i | \(-0.764604\pi\) | ||
0.738793 | − | 0.673933i | \(-0.235396\pi\) | |||||||
\(654\) | 11486.3 | 0.686772 | ||||||||
\(655\) | −12636.9 | − | 3447.99i | −0.753841 | − | 0.205686i | ||||
\(656\) | 2390.01 | 0.142247 | ||||||||
\(657\) | − | 14222.8i | − | 0.844572i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16930.9 | −1.00081 | −0.500406 | − | 0.865791i | \(-0.666816\pi\) | ||||
−0.500406 | + | 0.865791i | \(0.666816\pi\) | |||||||
\(660\) | −5533.52 | + | 20280.5i | −0.326352 | + | 1.19608i | ||||
\(661\) | −510.961 | −0.0300667 | −0.0150333 | − | 0.999887i | \(-0.504785\pi\) | ||||
−0.0150333 | + | 0.999887i | \(0.504785\pi\) | |||||||
\(662\) | 24057.6i | 1.41243i | ||||||||
\(663\) | − | 2179.52i | − | 0.127671i | ||||||
\(664\) | −9199.71 | −0.537678 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10894.4 | 0.633859 | ||||||||
\(667\) | 8970.28i | 0.520735i | ||||||||
\(668\) | − | 8322.12i | − | 0.482025i | ||||||
\(669\) | −32740.0 | −1.89208 | ||||||||
\(670\) | −22309.8 | − | 6087.23i | −1.28642 | − | 0.351001i | ||||
\(671\) | 40633.8 | 2.33778 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33178.8i | 1.90037i | 0.311683 | + | 0.950186i | \(0.399107\pi\) | ||||
−0.311683 | + | 0.950186i | \(0.600893\pi\) | |||||||
\(674\) | −2089.82 | −0.119431 | ||||||||
\(675\) | −3393.56 | + | 5755.77i | −0.193509 | + | 0.328207i | ||||
\(676\) | −5568.20 | −0.316807 | ||||||||
\(677\) | − | 5258.20i | − | 0.298507i | −0.988799 | − | 0.149253i | \(-0.952313\pi\) | ||
0.988799 | − | 0.149253i | \(-0.0476870\pi\) | |||||||
\(678\) | − | 11977.0i | − | 0.678426i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −975.974 | − | 266.295i | −0.0550396 | − | 0.0150175i | ||||
\(681\) | 33959.8 | 1.91093 | ||||||||
\(682\) | 22235.1i | 1.24843i | ||||||||
\(683\) | − | 20819.9i | − | 1.16640i | −0.812328 | − | 0.583201i | \(-0.801800\pi\) | ||
0.812328 | − | 0.583201i | \(-0.198200\pi\) | |||||||
\(684\) | −5679.13 | −0.317466 | ||||||||
\(685\) | −1951.42 | + | 7151.99i | −0.108847 | + | 0.398925i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42877.5i | 2.38119i | ||||||||
\(688\) | 8222.80i | 0.455656i | ||||||||
\(689\) | 10066.6 | 0.556614 | ||||||||
\(690\) | 2665.01 | − | 9767.30i | 0.147036 | − | 0.538891i | ||||
\(691\) | −2113.50 | −0.116355 | −0.0581775 | − | 0.998306i | \(-0.518529\pi\) | ||||
−0.0581775 | + | 0.998306i | \(0.518529\pi\) | |||||||
\(692\) | 10055.5i | 0.552387i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14781.7 | 0.808511 | ||||||||
\(695\) | −15055.4 | − | 4107.86i | −0.821703 | − | 0.224202i | ||||
\(696\) | −7311.31 | −0.398182 | ||||||||
\(697\) | − | 1689.53i | − | 0.0918158i | ||||||
\(698\) | − | 18598.3i | − | 1.00853i | ||||||
\(699\) | −31906.8 | −1.72650 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7392.50 | −0.398304 | −0.199152 | − | 0.979969i | \(-0.563819\pi\) | ||||
−0.199152 | + | 0.979969i | \(0.563819\pi\) | |||||||
\(702\) | − | 3033.13i | − | 0.163074i | ||||||
\(703\) | 21133.7i | 1.13382i | ||||||||
\(704\) | −4429.40 | −0.237129 | ||||||||
\(705\) | 30154.0 | + | 8227.51i | 1.61087 | + | 0.439526i | ||||
\(706\) | 3745.46 | 0.199663 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5727.70i | 0.304040i | ||||||||
\(709\) | 16827.4 | 0.891351 | 0.445675 | − | 0.895195i | \(-0.352964\pi\) | ||||
0.445675 | + | 0.895195i | \(0.352964\pi\) | |||||||
\(710\) | 6080.41 | − | 22284.8i | 0.321399 | − | 1.17793i | ||||
\(711\) | 11666.1 | 0.615347 | ||||||||
\(712\) | 5885.26i | 0.309775i | ||||||||
\(713\) | − | 10708.7i | − | 0.562473i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5778.77 | + | 21179.3i | −0.302257 | + | 1.10778i | ||||
\(716\) | 3962.90 | 0.206844 | ||||||||
\(717\) | − | 28194.4i | − | 1.46854i | ||||||
\(718\) | − | 8600.96i | − | 0.447054i | ||||||
\(719\) | 31417.3 | 1.62958 | 0.814790 | − | 0.579757i | \(-0.196852\pi\) | ||||
0.814790 | + | 0.579757i | \(0.196852\pi\) | |||||||
\(720\) | 3301.36 | + | 900.776i | 0.170881 | + | 0.0466249i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2701.26i | 0.139239i | ||||||||
\(723\) | 16649.9i | 0.856454i | ||||||||
\(724\) | 7108.49 | 0.364896 | ||||||||
\(725\) | 14489.1 | + | 8542.67i | 0.742222 | + | 0.437609i | ||||
\(726\) | 46985.3 | 2.40191 | ||||||||
\(727\) | − | 12784.5i | − | 0.652201i | −0.945335 | − | 0.326101i | \(-0.894265\pi\) | ||
0.945335 | − | 0.326101i | \(-0.105735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7023.33 | 0.356822 | ||||||||
\(730\) | −16038.6 | − | 4376.13i | −0.813172 | − | 0.221874i | ||||
\(731\) | 5812.80 | 0.294110 | ||||||||
\(732\) | − | 15950.5i | − | 0.805391i | ||||||
\(733\) | − | 3569.49i | − | 0.179867i | −0.995948 | − | 0.0899333i | \(-0.971335\pi\) | ||
0.995948 | − | 0.0899333i | \(-0.0286654\pi\) | |||||||
\(734\) | 19237.0 | 0.967369 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2133.25 | 0.106838 | ||||||||
\(737\) | 71576.1i | 3.57740i | ||||||||
\(738\) | 5715.06i | 0.285060i | ||||||||
\(739\) | 20274.7 | 1.00922 | 0.504612 | − | 0.863346i | \(-0.331636\pi\) | ||||
0.504612 | + | 0.863346i | \(0.331636\pi\) | |||||||
\(740\) | 3352.05 | − | 12285.3i | 0.166519 | − | 0.610294i | ||||
\(741\) | −14301.7 | −0.709021 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 23416.6i | − | 1.15622i | −0.815959 | − | 0.578109i | \(-0.803791\pi\) | ||
0.815959 | − | 0.578109i | \(-0.196209\pi\) | |||||||
\(744\) | 8728.21 | 0.430097 | ||||||||
\(745\) | 7667.38 | + | 2092.04i | 0.377062 | + | 0.102881i | ||||
\(746\) | −18966.3 | −0.930838 | ||||||||
\(747\) | − | 21998.6i | − | 1.07749i | ||||||
\(748\) | 3131.20i | 0.153059i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13238.5 | − | 13606.3i | −0.644535 | − | 0.662442i | ||||
\(751\) | 27051.6 | 1.31442 | 0.657209 | − | 0.753708i | \(-0.271737\pi\) | ||||
0.657209 | + | 0.753708i | \(0.271737\pi\) | |||||||
\(752\) | 6585.84i | 0.319363i | ||||||||
\(753\) | − | 21082.8i | − | 1.02032i | ||||||
\(754\) | −7635.35 | −0.368784 | ||||||||
\(755\) | −18756.9 | − | 5117.83i | −0.904153 | − | 0.246698i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7695.13i | 0.369464i | 0.982789 | + | 0.184732i | \(0.0591417\pi\) | ||||
−0.982789 | + | 0.184732i | \(0.940858\pi\) | |||||||
\(758\) | 1117.69i | 0.0535572i | ||||||||
\(759\) | −31336.2 | −1.49859 | ||||||||
\(760\) | −1747.38 | + | 6404.19i | −0.0834003 | + | 0.305664i | ||||
\(761\) | −19601.5 | −0.933709 | −0.466854 | − | 0.884334i | \(-0.654613\pi\) | ||||
−0.466854 | + | 0.884334i | \(0.654613\pi\) | |||||||
\(762\) | − | 6602.47i | − | 0.313887i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −9346.83 | −0.442613 | ||||||||
\(765\) | 636.770 | − | 2333.77i | 0.0300947 | − | 0.110298i | ||||
\(766\) | 4503.01 | 0.212403 | ||||||||
\(767\) | 5981.55i | 0.281592i | ||||||||
\(768\) | 1738.72i | 0.0816938i | ||||||||
\(769\) | −9832.15 | −0.461062 | −0.230531 | − | 0.973065i | \(-0.574046\pi\) | ||||
−0.230531 | + | 0.973065i | \(0.574046\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −52185.8 | −2.43765 | ||||||||
\(772\) | 3203.16i | 0.149332i | ||||||||
\(773\) | − | 33561.5i | − | 1.56161i | −0.624776 | − | 0.780804i | \(-0.714810\pi\) | ||
0.624776 | − | 0.780804i | \(-0.285190\pi\) | |||||||
\(774\) | −19662.6 | −0.913121 | ||||||||
\(775\) | −17297.0 | − | 10198.2i | −0.801712 | − | 0.472684i | ||||
\(776\) | 2666.99 | 0.123375 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10493.4i | 0.483556i | ||||||||
\(779\) | −11086.4 | −0.509901 | ||||||||
\(780\) | 8313.76 | + | 2268.41i | 0.381642 | + | 0.104131i | ||||
\(781\) | −71495.8 | −3.27570 | ||||||||
\(782\) | − | 1508.02i | − | 0.0689600i | ||||||
\(783\) | 7192.70i | 0.328283i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10450.9 | − | 38302.7i | 0.475169 | − | 1.74150i | ||||
\(786\) | 15914.8 | 0.722215 | ||||||||
\(787\) | − | 19916.4i | − | 0.902087i | −0.892502 | − | 0.451044i | \(-0.851052\pi\) | ||
0.892502 | − | 0.451044i | \(-0.148948\pi\) | |||||||
\(788\) | 8672.97i | 0.392083i | ||||||||
\(789\) | −24983.6 | −1.12730 | ||||||||
\(790\) | 3589.47 | − | 13155.5i | 0.161655 | − | 0.592469i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 10591.7i | − | 0.475201i | ||||||
\(793\) | − | 16657.4i | − | 0.745929i | ||||||
\(794\) | 9501.88 | 0.424697 | ||||||||
\(795\) | 25992.7 | + | 7092.12i | 1.15958 | + | 0.316392i | ||||
\(796\) | 6503.93 | 0.289605 | ||||||||
\(797\) | 2485.71i | 0.110475i | 0.998473 | + | 0.0552373i | \(0.0175915\pi\) | ||||
−0.998473 | + | 0.0552373i | \(0.982408\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4655.62 | 0.206137 | ||||||||
\(800\) | 2031.56 | − | 3445.69i | 0.0897829 | − | 0.152279i | ||||
\(801\) | −14073.0 | −0.620779 | ||||||||
\(802\) | 21197.8i | 0.933318i | ||||||||
\(803\) | 51456.3i | 2.26134i | ||||||||
\(804\) | 28096.6 | 1.23245 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9115.05 | 0.398342 | ||||||||
\(807\) | − | 24533.5i | − | 1.07016i | ||||||
\(808\) | 24.0467i | 0.00104698i | ||||||||
\(809\) | −7580.66 | −0.329446 | −0.164723 | − | 0.986340i | \(-0.552673\pi\) | ||||
−0.164723 | + | 0.986340i | \(0.552673\pi\) | |||||||
\(810\) | 5177.02 | − | 18973.9i | 0.224570 | − | 0.823054i | ||||
\(811\) | −18439.3 | −0.798387 | −0.399193 | − | 0.916867i | \(-0.630710\pi\) | ||||
−0.399193 | + | 0.916867i | \(0.630710\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16130.6i | 0.695848i | ||||||||
\(814\) | −39414.7 | −1.69716 | ||||||||
\(815\) | 7199.09 | − | 26384.8i | 0.309415 | − | 1.13401i | ||||
\(816\) | 1229.13 | 0.0527305 | ||||||||
\(817\) | − | 38142.7i | − | 1.63335i | ||||||
\(818\) | − | 11828.5i | − | 0.505592i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6444.70 | + | 1758.44i | 0.274462 | + | 0.0748869i | ||||
\(821\) | −6651.55 | −0.282754 | −0.141377 | − | 0.989956i | \(-0.545153\pi\) | ||||
−0.141377 | + | 0.989956i | \(0.545153\pi\) | |||||||
\(822\) | − | 9007.11i | − | 0.382188i | ||||||
\(823\) | − | 7392.45i | − | 0.313104i | −0.987670 | − | 0.156552i | \(-0.949962\pi\) | ||
0.987670 | − | 0.156552i | \(-0.0500379\pi\) | |||||||
\(824\) | 5973.80 | 0.252557 | ||||||||
\(825\) | −29842.4 | + | 50615.3i | −1.25937 | + | 2.13600i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6122.78i | − | 0.257449i | −0.991680 | − | 0.128724i | \(-0.958912\pi\) | ||
0.991680 | − | 0.128724i | \(-0.0410882\pi\) | |||||||
\(828\) | 5101.07i | 0.214100i | ||||||||
\(829\) | −383.866 | −0.0160823 | −0.00804115 | − | 0.999968i | \(-0.502560\pi\) | ||||
−0.00804115 | + | 0.999968i | \(0.502560\pi\) | |||||||
\(830\) | −24807.1 | − | 6768.63i | −1.03743 | − | 0.283063i | ||||
\(831\) | 13343.1 | 0.557002 | ||||||||
\(832\) | 1815.78i | 0.0756623i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 18960.5 | 0.787229 | ||||||||
\(835\) | 6122.95 | − | 22440.7i | 0.253764 | − | 0.930051i | ||||
\(836\) | 20546.4 | 0.850015 | ||||||||
\(837\) | − | 8586.61i | − | 0.354596i | ||||||
\(838\) | 966.336i | 0.0398348i | ||||||||
\(839\) | −27506.6 | −1.13186 | −0.565932 | − | 0.824452i | \(-0.691484\pi\) | ||||
−0.565932 | + | 0.824452i | \(0.691484\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6282.71 | −0.257604 | ||||||||
\(842\) | 11579.7i | 0.473946i | ||||||||
\(843\) | 30736.0i | 1.25576i | ||||||||
\(844\) | 3275.71 | 0.133595 | ||||||||
\(845\) | −15014.7 | − | 4096.77i | −0.611269 | − | 0.166785i | ||||
\(846\) | −15748.2 | −0.639994 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5677.00i | 0.229893i | ||||||||
\(849\) | 1134.70 | 0.0458690 | ||||||||
\(850\) | −2435.80 | − | 1436.13i | −0.0982910 | − | 0.0579517i | ||||
\(851\) | 18982.6 | 0.764647 | ||||||||
\(852\) | 28065.1i | 1.12852i | ||||||||
\(853\) | − | 36571.5i | − | 1.46798i | −0.679162 | − | 0.733988i | \(-0.737657\pi\) | ||
0.679162 | − | 0.733988i | \(-0.262343\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15313.8 | − | 4178.38i | −0.612541 | − | 0.167132i | ||||
\(856\) | 6168.44 | 0.246300 | ||||||||
\(857\) | 29925.1i | 1.19279i | 0.802690 | + | 0.596396i | \(0.203401\pi\) | ||||
−0.802690 | + | 0.596396i | \(0.796599\pi\) | |||||||
\(858\) | − | 26672.9i | − | 1.06130i | ||||||
\(859\) | −1497.15 | −0.0594668 | −0.0297334 | − | 0.999558i | \(-0.509466\pi\) | ||||
−0.0297334 | + | 0.999558i | \(0.509466\pi\) | |||||||
\(860\) | −6049.87 | + | 22172.9i | −0.239882 | + | 0.879173i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 1284.31i | − | 0.0507468i | ||||||
\(863\) | 2753.12i | 0.108595i | 0.998525 | + | 0.0542975i | \(0.0172919\pi\) | ||||
−0.998525 | + | 0.0542975i | \(0.982708\pi\) | |||||||
\(864\) | 1710.52 | 0.0673529 | ||||||||
\(865\) | −7398.25 | + | 27114.7i | −0.290807 | + | 1.06581i | ||||
\(866\) | 4672.65 | 0.183352 | ||||||||
\(867\) | 32499.7i | 1.27306i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42206.4 | −1.64759 | ||||||||
\(870\) | −19715.1 | − | 5379.25i | −0.768279 | − | 0.209625i | ||||
\(871\) | 29341.9 | 1.14146 | ||||||||
\(872\) | 6764.70i | 0.262708i | ||||||||
\(873\) | 6377.36i | 0.247240i | ||||||||
\(874\) | −9895.38 | −0.382971 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20198.8 | 0.779056 | ||||||||
\(877\) | − | 45447.4i | − | 1.74989i | −0.484226 | − | 0.874943i | \(-0.660899\pi\) | ||
0.484226 | − | 0.874943i | \(-0.339101\pi\) | |||||||
\(878\) | − | 17861.7i | − | 0.686564i | ||||||
\(879\) | −8290.69 | −0.318132 | ||||||||
\(880\) | −11943.9 | − | 3258.90i | −0.457534 | − | 0.124838i | ||||
\(881\) | 41341.0 | 1.58095 | 0.790473 | − | 0.612497i | \(-0.209835\pi\) | ||||
0.790473 | + | 0.612497i | \(0.209835\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24941.7i | 0.950572i | 0.879831 | + | 0.475286i | \(0.157655\pi\) | ||||
−0.879831 | + | 0.475286i | \(0.842345\pi\) | |||||||
\(884\) | 1283.60 | 0.0488373 | ||||||||
\(885\) | −4214.12 | + | 15444.8i | −0.160063 | + | 0.586635i | ||||
\(886\) | 14224.6 | 0.539373 | ||||||||
\(887\) | − | 14450.7i | − | 0.547022i | −0.961869 | − | 0.273511i | \(-0.911815\pi\) | ||
0.961869 | − | 0.273511i | \(-0.0881850\pi\) | |||||||
\(888\) | 15471.9i | 0.584690i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4330.04 | + | 15869.7i | −0.163082 | + | 0.597700i | ||||
\(891\) | −60873.4 | −2.28882 | ||||||||
\(892\) | − | 19281.8i | − | 0.723771i | ||||||
\(893\) | − | 30549.4i | − | 1.14479i | ||||||
\(894\) | −9656.18 | −0.361243 | ||||||||
\(895\) | 10686.0 | + | 2915.68i | 0.399100 | + | 0.108894i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12846.0i | 0.478165i | ||||||||
\(898\) | − | 9017.81i | − | 0.335109i | ||||||
\(899\) | −21615.2 | −0.801899 | ||||||||
\(900\) | 8239.42 | + | 4857.91i | 0.305164 | + | 0.179922i | ||||
\(901\) | 4013.15 | 0.148388 | ||||||||
\(902\) | − | 20676.4i | − | 0.763247i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7053.69 | 0.259516 | ||||||||
\(905\) | 19168.1 | + | 5230.02i | 0.704055 | + | 0.192101i | ||||
\(906\) | 23622.2 | 0.866220 | ||||||||
\(907\) | − | 7808.12i | − | 0.285848i | −0.989734 | − | 0.142924i | \(-0.954350\pi\) | ||
0.989734 | − | 0.142924i | \(-0.0456505\pi\) | |||||||
\(908\) | 20000.2i | 0.730980i | ||||||||
\(909\) | −57.5011 | −0.00209812 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17340.9 | −0.630659 | −0.315330 | − | 0.948982i | \(-0.602115\pi\) | ||||
−0.315330 | + | 0.948982i | \(0.602115\pi\) | |||||||
\(912\) | − | 8065.33i | − | 0.292840i | ||||||
\(913\) | 79588.2i | 2.88498i | ||||||||
\(914\) | 4096.49 | 0.148249 | ||||||||
\(915\) | 11735.5 | − | 43010.7i | 0.424002 | − | 1.55398i | ||||
\(916\) | −25252.1 | −0.910867 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 1209.19i | − | 0.0434739i | ||||||
\(919\) | −3716.76 | −0.133411 | −0.0667055 | − | 0.997773i | \(-0.521249\pi\) | ||||
−0.0667055 | + | 0.997773i | \(0.521249\pi\) | |||||||
\(920\) | 5752.33 | + | 1569.52i | 0.206140 | + | 0.0562452i | ||||
\(921\) | 42068.2 | 1.50510 | ||||||||
\(922\) | 18015.1i | 0.643488i | ||||||||
\(923\) | 29309.0i | 1.04520i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18077.7 | − | 30661.3i | 0.642585 | − | 1.08988i | ||||
\(926\) | 6032.34 | 0.214077 | ||||||||
\(927\) | 14284.7i | 0.506117i | ||||||||
\(928\) | − | 4305.91i | − | 0.152315i | ||||||
\(929\) | 19318.5 | 0.682261 | 0.341131 | − | 0.940016i | \(-0.389190\pi\) | ||||
0.341131 | + | 0.940016i | \(0.389190\pi\) | |||||||
\(930\) | 23535.7 | + | 6421.73i | 0.829857 | + | 0.226427i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 18791.1i | − | 0.660433i | ||||||
\(933\) | − | 35864.8i | − | 1.25848i | ||||||
\(934\) | −18365.4 | −0.643398 | ||||||||
\(935\) | −2303.76 | + | 8443.32i | −0.0805786 | + | 0.295322i | ||||
\(936\) | −4341.95 | −0.151625 | ||||||||
\(937\) | 19563.7i | 0.682090i | 0.940047 | + | 0.341045i | \(0.110781\pi\) | ||||
−0.940047 | + | 0.341045i | \(0.889219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 52661.5 | 1.83019 | ||||||||
\(940\) | −4845.49 | + | 17758.8i | −0.168130 | + | 0.616200i | ||||
\(941\) | −44457.2 | −1.54013 | −0.770065 | − | 0.637966i | \(-0.779776\pi\) | ||||
−0.770065 | + | 0.637966i | \(0.779776\pi\) | |||||||
\(942\) | 48237.8i | 1.66844i | ||||||||
\(943\) | 9957.99i | 0.343878i | ||||||||
\(944\) | −3373.26 | −0.116303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 71136.8 | 2.44488 | ||||||||
\(947\) | 32366.4i | 1.11063i | 0.831640 | + | 0.555316i | \(0.187403\pi\) | ||||
−0.831640 | + | 0.555316i | \(0.812597\pi\) | |||||||
\(948\) | 16567.8i | 0.567613i | ||||||||
\(949\) | 21094.0 | 0.721538 | ||||||||
\(950\) | −9423.68 | + | 15983.3i | −0.321836 | + | 0.545861i | ||||
\(951\) | 1444.84 | 0.0492661 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 38984.4i | − | 1.32511i | −0.749013 | − | 0.662555i | \(-0.769472\pi\) | ||
0.749013 | − | 0.662555i | \(-0.230528\pi\) | |||||||
\(954\) | −13575.0 | −0.460698 | ||||||||
\(955\) | −25203.9 | − | 6876.87i | −0.854008 | − | 0.233016i | ||||
\(956\) | 16604.8 | 0.561753 | ||||||||
\(957\) | 63251.4i | 2.13650i | ||||||||
\(958\) | − | 38670.5i | − | 1.30416i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1279.25 | + | 4688.49i | −0.0430081 | + | 0.157625i | ||||
\(961\) | −3986.86 | −0.133828 | ||||||||
\(962\) | 16157.7i | 0.541522i | ||||||||
\(963\) | 14750.1i | 0.493578i | ||||||||
\(964\) | −9805.74 | −0.327616 | ||||||||
\(965\) | −2356.71 | + | 8637.37i | −0.0786167 | + | 0.288132i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9949.53i | − | 0.330874i | −0.986220 | − | 0.165437i | \(-0.947097\pi\) | ||
0.986220 | − | 0.165437i | \(-0.0529035\pi\) | |||||||
\(968\) | 27671.4i | 0.918795i | ||||||||
\(969\) | −5701.49 | −0.189018 | ||||||||
\(970\) | 7191.56 | + | 1962.22i | 0.238049 | + | 0.0649515i | ||||
\(971\) | −40427.1 | −1.33612 | −0.668058 | − | 0.744110i | \(-0.732874\pi\) | ||||
−0.668058 | + | 0.744110i | \(0.732874\pi\) | |||||||
\(972\) | 18122.4i | 0.598021i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −19409.8 | −0.638531 | ||||||||
\(975\) | 20749.2 | + | 12233.6i | 0.681545 | + | 0.401834i | ||||
\(976\) | 9393.83 | 0.308083 | ||||||||
\(977\) | 37619.1i | 1.23187i | 0.787796 | + | 0.615937i | \(0.211222\pi\) | ||||
−0.787796 | + | 0.615937i | \(0.788778\pi\) | |||||||
\(978\) | 33228.6i | 1.08644i | ||||||||
\(979\) | 50914.4 | 1.66213 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16175.9 | −0.526460 | ||||||||
\(982\) | 4568.10i | 0.148446i | ||||||||
\(983\) | 8270.45i | 0.268348i | 0.990958 | + | 0.134174i | \(0.0428381\pi\) | ||||
−0.990958 | + | 0.134174i | \(0.957162\pi\) | |||||||
\(984\) | −8116.36 | −0.262947 | ||||||||
\(985\) | −6381.08 | + | 23386.8i | −0.206414 | + | 0.756512i | ||||
\(986\) | −3043.90 | −0.0983140 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 8422.79i | − | 0.271219i | ||||||
\(989\) | −34260.3 | −1.10153 | ||||||||
\(990\) | 7792.76 | − | 28560.6i | 0.250172 | − | 0.916884i | ||||
\(991\) | −7181.21 | −0.230190 | −0.115095 | − | 0.993354i | \(-0.536717\pi\) | ||||
−0.115095 | + | 0.993354i | \(0.536717\pi\) | |||||||
\(992\) | 5140.37i | 0.164523i | ||||||||
\(993\) | − | 81698.3i | − | 2.61089i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17537.9 | + | 4785.22i | 0.558784 | + | 0.152464i | ||||
\(996\) | 31241.7 | 0.993907 | ||||||||
\(997\) | − | 11574.8i | − | 0.367680i | −0.982956 | − | 0.183840i | \(-0.941147\pi\) | ||
0.982956 | − | 0.183840i | \(-0.0588528\pi\) | |||||||
\(998\) | 13603.9i | 0.431486i | ||||||||
\(999\) | 15220.9 | 0.482051 |
(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.g.99.8 | yes | 20 | |
5.2 | odd | 4 | 2450.4.a.dc.1.8 | 10 | |||
5.3 | odd | 4 | 2450.4.a.db.1.3 | 10 | |||
5.4 | even | 2 | inner | 490.4.c.g.99.13 | yes | 20 | |
7.6 | odd | 2 | inner | 490.4.c.g.99.3 | ✓ | 20 | |
35.13 | even | 4 | 2450.4.a.db.1.8 | 10 | |||
35.27 | even | 4 | 2450.4.a.dc.1.3 | 10 | |||
35.34 | odd | 2 | inner | 490.4.c.g.99.18 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
490.4.c.g.99.3 | ✓ | 20 | 7.6 | odd | 2 | inner | |
490.4.c.g.99.8 | yes | 20 | 1.1 | even | 1 | trivial | |
490.4.c.g.99.13 | yes | 20 | 5.4 | even | 2 | inner | |
490.4.c.g.99.18 | yes | 20 | 35.34 | odd | 2 | inner | |
2450.4.a.db.1.3 | 10 | 5.3 | odd | 4 | |||
2450.4.a.db.1.8 | 10 | 35.13 | even | 4 | |||
2450.4.a.dc.1.3 | 10 | 35.27 | even | 4 | |||
2450.4.a.dc.1.8 | 10 | 5.2 | odd | 4 |