Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.1 | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.6.c.b.34.26 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 10.7531i | − | 1.90089i | −0.310892 | − | 0.950445i | \(-0.600628\pi\) | ||
0.310892 | − | 0.950445i | \(-0.399372\pi\) | |||||||
\(3\) | 9.00000i | 0.577350i | ||||||||
\(4\) | −83.6283 | −2.61338 | ||||||||
\(5\) | 8.68170 | + | 55.2234i | 0.155303 | + | 0.987867i | ||||
\(6\) | 96.7775 | 1.09748 | ||||||||
\(7\) | − | 41.3813i | − | 0.319197i | −0.987182 | − | 0.159599i | \(-0.948980\pi\) | ||
0.987182 | − | 0.159599i | \(-0.0510200\pi\) | |||||||
\(8\) | 555.162i | 3.06687i | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 593.821 | − | 93.3549i | 1.87783 | − | 0.295214i | ||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | − | 752.654i | − | 1.50884i | ||||||
\(13\) | − | 13.6514i | − | 0.0224037i | −0.999937 | − | 0.0112019i | \(-0.996434\pi\) | ||
0.999937 | − | 0.0112019i | \(-0.00356574\pi\) | |||||||
\(14\) | −444.975 | −0.606759 | ||||||||
\(15\) | −497.011 | + | 78.1353i | −0.570345 | + | 0.0896643i | ||||
\(16\) | 3293.58 | 3.21639 | ||||||||
\(17\) | − | 1143.92i | − | 0.960005i | −0.877267 | − | 0.480002i | \(-0.840636\pi\) | ||
0.877267 | − | 0.480002i | \(-0.159364\pi\) | |||||||
\(18\) | 870.998i | 0.633630i | ||||||||
\(19\) | 1425.16 | 0.905689 | 0.452844 | − | 0.891590i | \(-0.350409\pi\) | ||||
0.452844 | + | 0.891590i | \(0.350409\pi\) | |||||||
\(20\) | −726.036 | − | 4618.24i | −0.405866 | − | 2.58168i | ||||
\(21\) | 372.432 | 0.184289 | ||||||||
\(22\) | − | 1301.12i | − | 0.573140i | ||||||
\(23\) | − | 2533.88i | − | 0.998770i | −0.866380 | − | 0.499385i | \(-0.833559\pi\) | ||
0.866380 | − | 0.499385i | \(-0.166441\pi\) | |||||||
\(24\) | −4996.46 | −1.77066 | ||||||||
\(25\) | −2974.26 | + | 958.867i | −0.951762 | + | 0.306837i | ||||
\(26\) | −146.795 | −0.0425870 | ||||||||
\(27\) | − | 729.000i | − | 0.192450i | ||||||
\(28\) | 3460.65i | 0.834185i | ||||||||
\(29\) | −8594.21 | −1.89763 | −0.948814 | − | 0.315837i | \(-0.897715\pi\) | ||||
−0.948814 | + | 0.315837i | \(0.897715\pi\) | |||||||
\(30\) | 840.194 | + | 5344.39i | 0.170442 | + | 1.08416i | ||||
\(31\) | 434.427 | 0.0811918 | 0.0405959 | − | 0.999176i | \(-0.487074\pi\) | ||||
0.0405959 | + | 0.999176i | \(0.487074\pi\) | |||||||
\(32\) | − | 17650.9i | − | 3.04714i | ||||||
\(33\) | 1089.00i | 0.174078i | ||||||||
\(34\) | −12300.6 | −1.82486 | ||||||||
\(35\) | 2285.22 | − | 359.260i | 0.315324 | − | 0.0495723i | ||||
\(36\) | 6773.89 | 0.871128 | ||||||||
\(37\) | − | 14403.2i | − | 1.72963i | −0.502090 | − | 0.864815i | \(-0.667436\pi\) | ||
0.502090 | − | 0.864815i | \(-0.332564\pi\) | |||||||
\(38\) | − | 15324.8i | − | 1.72162i | ||||||
\(39\) | 122.863 | 0.0129348 | ||||||||
\(40\) | −30657.9 | + | 4819.75i | −3.02965 | + | 0.476293i | ||||
\(41\) | 12386.5 | 1.15077 | 0.575387 | − | 0.817881i | \(-0.304851\pi\) | ||||
0.575387 | + | 0.817881i | \(0.304851\pi\) | |||||||
\(42\) | − | 4004.78i | − | 0.350312i | ||||||
\(43\) | − | 2699.39i | − | 0.222635i | −0.993785 | − | 0.111318i | \(-0.964493\pi\) | ||
0.993785 | − | 0.111318i | \(-0.0355071\pi\) | |||||||
\(44\) | −10119.0 | −0.787965 | ||||||||
\(45\) | −703.218 | − | 4473.10i | −0.0517677 | − | 0.329289i | ||||
\(46\) | −27246.9 | −1.89855 | ||||||||
\(47\) | 1691.93i | 0.111722i | 0.998439 | + | 0.0558608i | \(0.0177903\pi\) | ||||
−0.998439 | + | 0.0558608i | \(0.982210\pi\) | |||||||
\(48\) | 29642.3i | 1.85698i | ||||||||
\(49\) | 15094.6 | 0.898113 | ||||||||
\(50\) | 10310.8 | + | 31982.4i | 0.583264 | + | 1.80919i | ||||
\(51\) | 10295.3 | 0.554259 | ||||||||
\(52\) | 1141.65i | 0.0585495i | ||||||||
\(53\) | − | 9465.19i | − | 0.462850i | −0.972853 | − | 0.231425i | \(-0.925661\pi\) | ||
0.972853 | − | 0.231425i | \(-0.0743387\pi\) | |||||||
\(54\) | −7838.98 | −0.365826 | ||||||||
\(55\) | 1050.49 | + | 6682.04i | 0.0468256 | + | 0.297853i | ||||
\(56\) | 22973.3 | 0.978935 | ||||||||
\(57\) | 12826.4i | 0.522900i | ||||||||
\(58\) | 92414.0i | 3.60718i | ||||||||
\(59\) | 41470.4 | 1.55099 | 0.775493 | − | 0.631356i | \(-0.217501\pi\) | ||||
0.775493 | + | 0.631356i | \(0.217501\pi\) | |||||||
\(60\) | 41564.2 | − | 6534.32i | 1.49053 | − | 0.234327i | ||||
\(61\) | −17867.3 | −0.614802 | −0.307401 | − | 0.951580i | \(-0.599459\pi\) | ||||
−0.307401 | + | 0.951580i | \(0.599459\pi\) | |||||||
\(62\) | − | 4671.41i | − | 0.154337i | ||||||
\(63\) | 3351.88i | 0.106399i | ||||||||
\(64\) | −84406.7 | −2.57589 | ||||||||
\(65\) | 753.880 | − | 118.518i | 0.0221319 | − | 0.00347937i | ||||
\(66\) | 11710.1 | 0.330903 | ||||||||
\(67\) | − | 51700.6i | − | 1.40705i | −0.710672 | − | 0.703523i | \(-0.751609\pi\) | ||
0.710672 | − | 0.703523i | \(-0.248391\pi\) | |||||||
\(68\) | 95664.1i | 2.50886i | ||||||||
\(69\) | 22804.9 | 0.576640 | ||||||||
\(70\) | −3863.15 | − | 24573.1i | −0.0942315 | − | 0.599397i | ||||
\(71\) | −16645.8 | −0.391885 | −0.195943 | − | 0.980615i | \(-0.562777\pi\) | ||||
−0.195943 | + | 0.980615i | \(0.562777\pi\) | |||||||
\(72\) | − | 44968.1i | − | 1.02229i | ||||||
\(73\) | − | 49707.4i | − | 1.09173i | −0.837874 | − | 0.545863i | \(-0.816202\pi\) | ||
0.837874 | − | 0.545863i | \(-0.183798\pi\) | |||||||
\(74\) | −154878. | −3.28784 | ||||||||
\(75\) | −8629.80 | − | 26768.3i | −0.177153 | − | 0.549500i | ||||
\(76\) | −119184. | −2.36691 | ||||||||
\(77\) | − | 5007.14i | − | 0.0962416i | ||||||
\(78\) | − | 1321.15i | − | 0.0245876i | ||||||
\(79\) | −71497.6 | −1.28891 | −0.644456 | − | 0.764641i | \(-0.722916\pi\) | ||||
−0.644456 | + | 0.764641i | \(0.722916\pi\) | |||||||
\(80\) | 28593.9 | + | 181883.i | 0.499515 | + | 3.17737i | ||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | − | 133193.i | − | 2.18750i | ||||||
\(83\) | − | 33539.3i | − | 0.534390i | −0.963642 | − | 0.267195i | \(-0.913903\pi\) | ||
0.963642 | − | 0.267195i | \(-0.0860969\pi\) | |||||||
\(84\) | −31145.8 | −0.481617 | ||||||||
\(85\) | 63171.2 | − | 9931.17i | 0.948357 | − | 0.149092i | ||||
\(86\) | −29026.7 | −0.423205 | ||||||||
\(87\) | − | 77347.9i | − | 1.09560i | ||||||
\(88\) | 67174.6i | 0.924695i | ||||||||
\(89\) | 76978.3 | 1.03013 | 0.515066 | − | 0.857150i | \(-0.327767\pi\) | ||||
0.515066 | + | 0.857150i | \(0.327767\pi\) | |||||||
\(90\) | −48099.5 | + | 7561.74i | −0.625942 | + | 0.0984047i | ||||
\(91\) | −564.914 | −0.00715120 | ||||||||
\(92\) | 211904.i | 2.61017i | ||||||||
\(93\) | 3909.84i | 0.0468761i | ||||||||
\(94\) | 18193.4 | 0.212371 | ||||||||
\(95\) | 12372.8 | + | 78702.1i | 0.140656 | + | 0.894700i | ||||
\(96\) | 158858. | 1.75927 | ||||||||
\(97\) | − | 17713.7i | − | 0.191152i | −0.995422 | − | 0.0955761i | \(-0.969531\pi\) | ||
0.995422 | − | 0.0955761i | \(-0.0304693\pi\) | |||||||
\(98\) | − | 162313.i | − | 1.70721i | ||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 248732. | − | 80188.4i | 2.48732 | − | 0.801884i | ||||
\(101\) | −2788.38 | −0.0271987 | −0.0135994 | − | 0.999908i | \(-0.504329\pi\) | ||||
−0.0135994 | + | 0.999908i | \(0.504329\pi\) | |||||||
\(102\) | − | 110706.i | − | 1.05359i | ||||||
\(103\) | 3106.69i | 0.0288539i | 0.999896 | + | 0.0144269i | \(0.00459240\pi\) | ||||
−0.999896 | + | 0.0144269i | \(0.995408\pi\) | |||||||
\(104\) | 7578.76 | 0.0687092 | ||||||||
\(105\) | 3233.34 | + | 20567.0i | 0.0286206 | + | 0.182053i | ||||
\(106\) | −101780. | −0.879826 | ||||||||
\(107\) | 21599.2i | 0.182381i | 0.995833 | + | 0.0911904i | \(0.0290672\pi\) | ||||
−0.995833 | + | 0.0911904i | \(0.970933\pi\) | |||||||
\(108\) | 60965.0i | 0.502946i | ||||||||
\(109\) | −190632. | −1.53684 | −0.768421 | − | 0.639945i | \(-0.778957\pi\) | ||||
−0.768421 | + | 0.639945i | \(0.778957\pi\) | |||||||
\(110\) | 71852.3 | − | 11295.9i | 0.566186 | − | 0.0890104i | ||||
\(111\) | 129628. | 0.998603 | ||||||||
\(112\) | − | 136293.i | − | 1.02666i | ||||||
\(113\) | − | 239503.i | − | 1.76447i | −0.470808 | − | 0.882236i | \(-0.656038\pi\) | ||
0.470808 | − | 0.882236i | \(-0.343962\pi\) | |||||||
\(114\) | 137923. | 0.993975 | ||||||||
\(115\) | 139929. | − | 21998.4i | 0.986652 | − | 0.155112i | ||||
\(116\) | 718719. | 4.95923 | ||||||||
\(117\) | 1105.77i | 0.00746791i | ||||||||
\(118\) | − | 445934.i | − | 2.94826i | ||||||
\(119\) | −47336.9 | −0.306431 | ||||||||
\(120\) | −43377.8 | − | 275922.i | −0.274988 | − | 1.74917i | ||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 192129.i | 1.16867i | ||||||||
\(123\) | 111479.i | 0.664400i | ||||||||
\(124\) | −36330.3 | −0.212185 | ||||||||
\(125\) | −78773.5 | − | 155924.i | −0.450926 | − | 0.892561i | ||||
\(126\) | 36043.0 | 0.202253 | ||||||||
\(127\) | 112217.i | 0.617373i | 0.951164 | + | 0.308687i | \(0.0998894\pi\) | ||||
−0.951164 | + | 0.308687i | \(0.900111\pi\) | |||||||
\(128\) | 342801.i | 1.84934i | ||||||||
\(129\) | 24294.5 | 0.128539 | ||||||||
\(130\) | −1274.43 | − | 8106.51i | −0.00661389 | − | 0.0420703i | ||||
\(131\) | 334801. | 1.70455 | 0.852273 | − | 0.523097i | \(-0.175224\pi\) | ||||
0.852273 | + | 0.523097i | \(0.175224\pi\) | |||||||
\(132\) | − | 91071.2i | − | 0.454932i | ||||||
\(133\) | − | 58974.9i | − | 0.289093i | ||||||
\(134\) | −555939. | −2.67464 | ||||||||
\(135\) | 40257.9 | − | 6328.96i | 0.190115 | − | 0.0298881i | ||||
\(136\) | 635061. | 2.94420 | ||||||||
\(137\) | − | 913.914i | − | 0.00416010i | −0.999998 | − | 0.00208005i | \(-0.999338\pi\) | ||
0.999998 | − | 0.00208005i | \(-0.000662101\pi\) | |||||||
\(138\) | − | 245222.i | − | 1.09613i | ||||||
\(139\) | −270355. | −1.18685 | −0.593427 | − | 0.804888i | \(-0.702226\pi\) | ||||
−0.593427 | + | 0.804888i | \(0.702226\pi\) | |||||||
\(140\) | −191109. | + | 30044.3i | −0.824063 | + | 0.129551i | ||||
\(141\) | −15227.4 | −0.0645025 | ||||||||
\(142\) | 178993.i | 0.744931i | ||||||||
\(143\) | − | 1651.82i | − | 0.00675498i | ||||||
\(144\) | −266780. | −1.07213 | ||||||||
\(145\) | −74612.4 | − | 474602.i | −0.294707 | − | 1.87460i | ||||
\(146\) | −534507. | −2.07525 | ||||||||
\(147\) | 135851.i | 0.518526i | ||||||||
\(148\) | 1.20451e6i | 4.52019i | ||||||||
\(149\) | 533592. | 1.96899 | 0.984496 | − | 0.175407i | \(-0.0561242\pi\) | ||||
0.984496 | + | 0.175407i | \(0.0561242\pi\) | |||||||
\(150\) | −287841. | + | 92796.8i | −1.04454 | + | 0.336748i | ||||
\(151\) | −109266. | −0.389980 | −0.194990 | − | 0.980805i | \(-0.562467\pi\) | ||||
−0.194990 | + | 0.980805i | \(0.562467\pi\) | |||||||
\(152\) | 791193.i | 2.77763i | ||||||||
\(153\) | 92657.5i | 0.320002i | ||||||||
\(154\) | −53842.0 | −0.182945 | ||||||||
\(155\) | 3771.56 | + | 23990.5i | 0.0126093 | + | 0.0802067i | ||||
\(156\) | −10274.8 | −0.0338036 | ||||||||
\(157\) | 362759.i | 1.17454i | 0.809390 | + | 0.587272i | \(0.199798\pi\) | ||||
−0.809390 | + | 0.587272i | \(0.800202\pi\) | |||||||
\(158\) | 768818.i | 2.45008i | ||||||||
\(159\) | 85186.7 | 0.267226 | ||||||||
\(160\) | 974744. | − | 153240.i | 3.01017 | − | 0.473230i | ||||
\(161\) | −104855. | −0.318805 | ||||||||
\(162\) | − | 70550.8i | − | 0.211210i | ||||||
\(163\) | 339033.i | 0.999478i | 0.866176 | + | 0.499739i | \(0.166571\pi\) | ||||
−0.866176 | + | 0.499739i | \(0.833429\pi\) | |||||||
\(164\) | −1.03586e6 | −3.00742 | ||||||||
\(165\) | −60138.3 | + | 9454.38i | −0.171966 | + | 0.0270348i | ||||
\(166\) | −360650. | −1.01582 | ||||||||
\(167\) | − | 459806.i | − | 1.27580i | −0.770118 | − | 0.637901i | \(-0.779803\pi\) | ||
0.770118 | − | 0.637901i | \(-0.220197\pi\) | |||||||
\(168\) | 206760.i | 0.565188i | ||||||||
\(169\) | 371107. | 0.999498 | ||||||||
\(170\) | −106791. | − | 679284.i | −0.283407 | − | 1.80272i | ||||
\(171\) | −115438. | −0.301896 | ||||||||
\(172\) | 225745.i | 0.581831i | ||||||||
\(173\) | − | 527699.i | − | 1.34051i | −0.742130 | − | 0.670256i | \(-0.766184\pi\) | ||
0.742130 | − | 0.670256i | \(-0.233816\pi\) | |||||||
\(174\) | −831726. | −2.08261 | ||||||||
\(175\) | 39679.2 | + | 123079.i | 0.0979416 | + | 0.303800i | ||||
\(176\) | 398524. | 0.969778 | ||||||||
\(177\) | 373234.i | 0.895463i | ||||||||
\(178\) | − | 827752.i | − | 1.95817i | ||||||
\(179\) | −789810. | −1.84243 | −0.921213 | − | 0.389059i | \(-0.872800\pi\) | ||||
−0.921213 | + | 0.389059i | \(0.872800\pi\) | |||||||
\(180\) | 58808.9 | + | 374078.i | 0.135289 | + | 0.860558i | ||||
\(181\) | −375428. | −0.851786 | −0.425893 | − | 0.904773i | \(-0.640040\pi\) | ||||
−0.425893 | + | 0.904773i | \(0.640040\pi\) | |||||||
\(182\) | 6074.56i | 0.0135937i | ||||||||
\(183\) | − | 160806.i | − | 0.354956i | ||||||
\(184\) | 1.40671e6 | 3.06309 | ||||||||
\(185\) | 795392. | − | 125044.i | 1.70864 | − | 0.268617i | ||||
\(186\) | 42042.7 | 0.0891063 | ||||||||
\(187\) | − | 138414.i | − | 0.289452i | ||||||
\(188\) | − | 141493.i | − | 0.291972i | ||||||
\(189\) | −30167.0 | −0.0614295 | ||||||||
\(190\) | 846289. | − | 133045.i | 1.70073 | − | 0.267372i | ||||
\(191\) | 339151. | 0.672681 | 0.336341 | − | 0.941740i | \(-0.390811\pi\) | ||||
0.336341 | + | 0.941740i | \(0.390811\pi\) | |||||||
\(192\) | − | 759660.i | − | 1.48719i | ||||||
\(193\) | 359337.i | 0.694398i | 0.937792 | + | 0.347199i | \(0.112867\pi\) | ||||
−0.937792 | + | 0.347199i | \(0.887133\pi\) | |||||||
\(194\) | −190476. | −0.363359 | ||||||||
\(195\) | 1066.66 | + | 6784.92i | 0.00200881 | + | 0.0127779i | ||||
\(196\) | −1.26233e6 | −2.34711 | ||||||||
\(197\) | 604048.i | 1.10893i | 0.832206 | + | 0.554467i | \(0.187078\pi\) | ||||
−0.832206 | + | 0.554467i | \(0.812922\pi\) | |||||||
\(198\) | 105391.i | 0.191047i | ||||||||
\(199\) | 1.03446e6 | 1.85174 | 0.925868 | − | 0.377846i | \(-0.123335\pi\) | ||||
0.925868 | + | 0.377846i | \(0.123335\pi\) | |||||||
\(200\) | −532326. | − | 1.65119e6i | −0.941029 | − | 2.91893i | ||||
\(201\) | 465305. | 0.812358 | ||||||||
\(202\) | 29983.6i | 0.0517018i | ||||||||
\(203\) | 355639.i | 0.605717i | ||||||||
\(204\) | −860976. | −1.44849 | ||||||||
\(205\) | 107536. | + | 684027.i | 0.178719 | + | 1.13681i | ||||
\(206\) | 33406.4 | 0.0548481 | ||||||||
\(207\) | 205244.i | 0.332923i | ||||||||
\(208\) | − | 44962.2i | − | 0.0720591i | ||||||
\(209\) | 172444. | 0.273075 | ||||||||
\(210\) | 221158. | − | 34768.3i | 0.346062 | − | 0.0544046i | ||||
\(211\) | −758371. | −1.17267 | −0.586335 | − | 0.810069i | \(-0.699430\pi\) | ||||
−0.586335 | + | 0.810069i | \(0.699430\pi\) | |||||||
\(212\) | 791558.i | 1.20960i | ||||||||
\(213\) | − | 149812.i | − | 0.226255i | ||||||
\(214\) | 232258. | 0.346686 | ||||||||
\(215\) | 149069. | − | 23435.3i | 0.219934 | − | 0.0345759i | ||||
\(216\) | 404713. | 0.590218 | ||||||||
\(217\) | − | 17977.1i | − | 0.0259162i | ||||||
\(218\) | 2.04988e6i | 2.92137i | ||||||||
\(219\) | 447367. | 0.630309 | ||||||||
\(220\) | −87850.3 | − | 558807.i | −0.122373 | − | 0.778404i | ||||
\(221\) | −15616.2 | −0.0215077 | ||||||||
\(222\) | − | 1.39390e6i | − | 1.89823i | ||||||
\(223\) | − | 1.08373e6i | − | 1.45935i | −0.683792 | − | 0.729677i | \(-0.739671\pi\) | ||
0.683792 | − | 0.729677i | \(-0.260329\pi\) | |||||||
\(224\) | −730418. | −0.972638 | ||||||||
\(225\) | 240915. | − | 77668.2i | 0.317254 | − | 0.102279i | ||||
\(226\) | −2.57539e6 | −3.35407 | ||||||||
\(227\) | 635159.i | 0.818122i | 0.912507 | + | 0.409061i | \(0.134144\pi\) | ||||
−0.912507 | + | 0.409061i | \(0.865856\pi\) | |||||||
\(228\) | − | 1.07265e6i | − | 1.36654i | ||||||
\(229\) | −622829. | −0.784838 | −0.392419 | − | 0.919787i | \(-0.628362\pi\) | ||||
−0.392419 | + | 0.919787i | \(0.628362\pi\) | |||||||
\(230\) | −236550. | − | 1.50467e6i | −0.294851 | − | 1.87552i | ||||
\(231\) | 45064.2 | 0.0555651 | ||||||||
\(232\) | − | 4.77118e6i | − | 5.81977i | ||||||
\(233\) | 1.31801e6i | 1.59048i | 0.606296 | + | 0.795239i | \(0.292655\pi\) | ||||
−0.606296 | + | 0.795239i | \(0.707345\pi\) | |||||||
\(234\) | 11890.4 | 0.0141957 | ||||||||
\(235\) | −93434.1 | + | 14688.8i | −0.110366 | + | 0.0173507i | ||||
\(236\) | −3.46810e6 | −4.05332 | ||||||||
\(237\) | − | 643478.i | − | 0.744154i | ||||||
\(238\) | 509016.i | 0.582491i | ||||||||
\(239\) | 240029. | 0.271812 | 0.135906 | − | 0.990722i | \(-0.456605\pi\) | ||||
0.135906 | + | 0.990722i | \(0.456605\pi\) | |||||||
\(240\) | −1.63695e6 | + | 257345.i | −1.83445 | + | 0.288395i | ||||
\(241\) | 659027. | 0.730904 | 0.365452 | − | 0.930830i | \(-0.380914\pi\) | ||||
0.365452 | + | 0.930830i | \(0.380914\pi\) | |||||||
\(242\) | − | 157436.i | − | 0.172808i | ||||||
\(243\) | 59049.0i | 0.0641500i | ||||||||
\(244\) | 1.49422e6 | 1.60671 | ||||||||
\(245\) | 131047. | + | 833575.i | 0.139480 | + | 0.887216i | ||||
\(246\) | 1.19874e6 | 1.26295 | ||||||||
\(247\) | − | 19455.5i | − | 0.0202908i | ||||||
\(248\) | 241177.i | 0.249004i | ||||||||
\(249\) | 301854. | 0.308530 | ||||||||
\(250\) | −1.67666e6 | + | 847057.i | −1.69666 | + | 0.857161i | ||||
\(251\) | 1.72716e6 | 1.73040 | 0.865202 | − | 0.501424i | \(-0.167190\pi\) | ||||
0.865202 | + | 0.501424i | \(0.167190\pi\) | |||||||
\(252\) | − | 280312.i | − | 0.278062i | ||||||
\(253\) | − | 306599.i | − | 0.301141i | ||||||
\(254\) | 1.20667e6 | 1.17356 | ||||||||
\(255\) | 89380.6 | + | 568541.i | 0.0860781 | + | 0.547534i | ||||
\(256\) | 985142. | 0.939505 | ||||||||
\(257\) | 889184.i | 0.839767i | 0.907578 | + | 0.419883i | \(0.137929\pi\) | ||||
−0.907578 | + | 0.419883i | \(0.862071\pi\) | |||||||
\(258\) | − | 261240.i | − | 0.244338i | ||||||
\(259\) | −596021. | −0.552093 | ||||||||
\(260\) | −63045.7 | + | 9911.44i | −0.0578391 | + | 0.00909292i | ||||
\(261\) | 696131. | 0.632542 | ||||||||
\(262\) | − | 3.60014e6i | − | 3.24015i | ||||||
\(263\) | − | 352666.i | − | 0.314394i | −0.987567 | − | 0.157197i | \(-0.949754\pi\) | ||
0.987567 | − | 0.157197i | \(-0.0502458\pi\) | |||||||
\(264\) | −604571. | −0.533873 | ||||||||
\(265\) | 522701. | − | 82174.0i | 0.457234 | − | 0.0718819i | ||||
\(266\) | −634160. | −0.549535 | ||||||||
\(267\) | 692804.i | 0.594747i | ||||||||
\(268\) | 4.32363e6i | 3.67715i | ||||||||
\(269\) | 506736. | 0.426973 | 0.213487 | − | 0.976946i | \(-0.431518\pi\) | ||||
0.213487 | + | 0.976946i | \(0.431518\pi\) | |||||||
\(270\) | −68055.7 | − | 432895.i | −0.0568140 | − | 0.361388i | ||||
\(271\) | −1.33528e6 | −1.10446 | −0.552230 | − | 0.833691i | \(-0.686223\pi\) | ||||
−0.552230 | + | 0.833691i | \(0.686223\pi\) | |||||||
\(272\) | − | 3.76760e6i | − | 3.08775i | ||||||
\(273\) | − | 5084.23i | − | 0.00412875i | ||||||
\(274\) | −9827.37 | −0.00790790 | ||||||||
\(275\) | −359885. | + | 116023.i | −0.286967 | + | 0.0925150i | ||||
\(276\) | −1.90713e6 | −1.50698 | ||||||||
\(277\) | 1.72199e6i | 1.34844i | 0.738532 | + | 0.674218i | \(0.235519\pi\) | ||||
−0.738532 | + | 0.674218i | \(0.764481\pi\) | |||||||
\(278\) | 2.90714e6i | 2.25608i | ||||||||
\(279\) | −35188.5 | −0.0270639 | ||||||||
\(280\) | 199448. | + | 1.26867e6i | 0.152032 | + | 0.967057i | ||||
\(281\) | −1.20590e6 | −0.911061 | −0.455530 | − | 0.890220i | \(-0.650550\pi\) | ||||
−0.455530 | + | 0.890220i | \(0.650550\pi\) | |||||||
\(282\) | 163741.i | 0.122612i | ||||||||
\(283\) | 920183.i | 0.682980i | 0.939885 | + | 0.341490i | \(0.110932\pi\) | ||||
−0.939885 | + | 0.341490i | \(0.889068\pi\) | |||||||
\(284\) | 1.39206e6 | 1.02415 | ||||||||
\(285\) | −708319. | + | 111355.i | −0.516555 | + | 0.0812079i | ||||
\(286\) | −17762.2 | −0.0128405 | ||||||||
\(287\) | − | 512571.i | − | 0.367324i | ||||||
\(288\) | 1.42972e6i | 1.01571i | ||||||||
\(289\) | 111304. | 0.0783911 | ||||||||
\(290\) | −5.10342e6 | + | 802311.i | −3.56341 | + | 0.560206i | ||||
\(291\) | 159423. | 0.110362 | ||||||||
\(292\) | 4.15694e6i | 2.85310i | ||||||||
\(293\) | − | 125447.i | − | 0.0853674i | −0.999089 | − | 0.0426837i | \(-0.986409\pi\) | ||
0.999089 | − | 0.0426837i | \(-0.0135908\pi\) | |||||||
\(294\) | 1.46082e6 | 0.985661 | ||||||||
\(295\) | 360034. | + | 2.29014e6i | 0.240873 | + | 1.53217i | ||||
\(296\) | 7.99608e6 | 5.30454 | ||||||||
\(297\) | − | 88209.0i | − | 0.0580259i | ||||||
\(298\) | − | 5.73775e6i | − | 3.74284i | ||||||
\(299\) | −34591.1 | −0.0223762 | ||||||||
\(300\) | 721696. | + | 2.23859e6i | 0.462968 | + | 1.43605i | ||||
\(301\) | −111704. | −0.0710646 | ||||||||
\(302\) | 1.17494e6i | 0.741310i | ||||||||
\(303\) | − | 25095.4i | − | 0.0157032i | ||||||
\(304\) | 4.69388e6 | 2.91305 | ||||||||
\(305\) | −155119. | − | 986696.i | −0.0954807 | − | 0.607343i | ||||
\(306\) | 996352. | 0.608288 | ||||||||
\(307\) | − | 922678.i | − | 0.558733i | −0.960185 | − | 0.279366i | \(-0.909876\pi\) | ||
0.960185 | − | 0.279366i | \(-0.0901244\pi\) | |||||||
\(308\) | 418738.i | 0.251516i | ||||||||
\(309\) | −27960.2 | −0.0166588 | ||||||||
\(310\) | 257972. | − | 40555.8i | 0.152464 | − | 0.0239690i | ||||
\(311\) | −1.60136e6 | −0.938831 | −0.469416 | − | 0.882977i | \(-0.655535\pi\) | ||||
−0.469416 | + | 0.882977i | \(0.655535\pi\) | |||||||
\(312\) | 68208.9i | 0.0396693i | ||||||||
\(313\) | 177127.i | 0.102193i | 0.998694 | + | 0.0510967i | \(0.0162717\pi\) | ||||
−0.998694 | + | 0.0510967i | \(0.983728\pi\) | |||||||
\(314\) | 3.90077e6 | 2.23268 | ||||||||
\(315\) | −185103. | + | 29100.1i | −0.105108 | + | 0.0165241i | ||||
\(316\) | 5.97922e6 | 3.36842 | ||||||||
\(317\) | − | 578254.i | − | 0.323199i | −0.986856 | − | 0.161600i | \(-0.948335\pi\) | ||
0.986856 | − | 0.161600i | \(-0.0516653\pi\) | |||||||
\(318\) | − | 916018.i | − | 0.507968i | ||||||
\(319\) | −1.03990e6 | −0.572156 | ||||||||
\(320\) | −732794. | − | 4.66123e6i | −0.400043 | − | 2.54463i | ||||
\(321\) | −194393. | −0.105298 | ||||||||
\(322\) | 1.12751e6i | 0.606013i | ||||||||
\(323\) | − | 1.63027e6i | − | 0.869466i | ||||||
\(324\) | −548685. | −0.290376 | ||||||||
\(325\) | 13089.9 | + | 40602.9i | 0.00687430 | + | 0.0213230i | ||||
\(326\) | 3.64565e6 | 1.89990 | ||||||||
\(327\) | − | 1.71569e6i | − | 0.887296i | ||||||
\(328\) | 6.87653e6i | 3.52927i | ||||||||
\(329\) | 70014.2 | 0.0356612 | ||||||||
\(330\) | 101663. | + | 646671.i | 0.0513902 | + | 0.326888i | ||||
\(331\) | −3.23768e6 | −1.62429 | −0.812145 | − | 0.583456i | \(-0.801700\pi\) | ||||
−0.812145 | + | 0.583456i | \(0.801700\pi\) | |||||||
\(332\) | 2.80483e6i | 1.39657i | ||||||||
\(333\) | 1.16666e6i | 0.576543i | ||||||||
\(334\) | −4.94432e6 | −2.42516 | ||||||||
\(335\) | 2.85508e6 | − | 448849.i | 1.38997 | − | 0.218519i | ||||
\(336\) | 1.22663e6 | 0.592744 | ||||||||
\(337\) | − | 1.82330e6i | − | 0.874546i | −0.899329 | − | 0.437273i | \(-0.855944\pi\) | ||
0.899329 | − | 0.437273i | \(-0.144056\pi\) | |||||||
\(338\) | − | 3.99053e6i | − | 1.89994i | ||||||
\(339\) | 2.15553e6 | 1.01872 | ||||||||
\(340\) | −5.28290e6 | + | 830527.i | −2.47842 | + | 0.389634i | ||||
\(341\) | 52565.6 | 0.0244802 | ||||||||
\(342\) | 1.24131e6i | 0.573872i | ||||||||
\(343\) | − | 1.32013e6i | − | 0.605872i | ||||||
\(344\) | 1.49860e6 | 0.682792 | ||||||||
\(345\) | 197985. | + | 1.25936e6i | 0.0895540 | + | 0.569644i | ||||
\(346\) | −5.67438e6 | −2.54817 | ||||||||
\(347\) | − | 564150.i | − | 0.251519i | −0.992061 | − | 0.125759i | \(-0.959863\pi\) | ||
0.992061 | − | 0.125759i | \(-0.0401368\pi\) | |||||||
\(348\) | 6.46847e6i | 2.86321i | ||||||||
\(349\) | −2.72653e6 | −1.19825 | −0.599124 | − | 0.800657i | \(-0.704484\pi\) | ||||
−0.599124 | + | 0.800657i | \(0.704484\pi\) | |||||||
\(350\) | 1.32347e6 | − | 426672.i | 0.577490 | − | 0.186176i | ||||
\(351\) | −9951.90 | −0.00431160 | ||||||||
\(352\) | − | 2.13576e6i | − | 0.918747i | ||||||
\(353\) | 694975.i | 0.296847i | 0.988924 | + | 0.148423i | \(0.0474198\pi\) | ||||
−0.988924 | + | 0.148423i | \(0.952580\pi\) | |||||||
\(354\) | 4.01340e6 | 1.70218 | ||||||||
\(355\) | −144514. | − | 919239.i | −0.0608610 | − | 0.387130i | ||||
\(356\) | −6.43756e6 | −2.69213 | ||||||||
\(357\) | − | 426032.i | − | 0.176918i | ||||||
\(358\) | 8.49287e6i | 3.50225i | ||||||||
\(359\) | 306112. | 0.125356 | 0.0626779 | − | 0.998034i | \(-0.480036\pi\) | ||||
0.0626779 | + | 0.998034i | \(0.480036\pi\) | |||||||
\(360\) | 2.48329e6 | − | 390400.i | 1.00988 | − | 0.158764i | ||||
\(361\) | −445023. | −0.179728 | ||||||||
\(362\) | 4.03700e6i | 1.61915i | ||||||||
\(363\) | 131769.i | 0.0524864i | ||||||||
\(364\) | 47242.8 | 0.0186888 | ||||||||
\(365\) | 2.74501e6 | − | 431545.i | 1.07848 | − | 0.169548i | ||||
\(366\) | −1.72916e6 | −0.674733 | ||||||||
\(367\) | − | 1.51571e6i | − | 0.587423i | −0.955894 | − | 0.293712i | \(-0.905109\pi\) | ||
0.955894 | − | 0.293712i | \(-0.0948906\pi\) | |||||||
\(368\) | − | 8.34553e6i | − | 3.21244i | ||||||
\(369\) | −1.00331e6 | −0.383592 | ||||||||
\(370\) | −1.34460e6 | − | 8.55289e6i | −0.510611 | − | 3.24795i | ||||
\(371\) | −391682. | −0.147740 | ||||||||
\(372\) | − | 326973.i | − | 0.122505i | ||||||
\(373\) | 1.05811e6i | 0.393783i | 0.980425 | + | 0.196892i | \(0.0630847\pi\) | ||||
−0.980425 | + | 0.196892i | \(0.936915\pi\) | |||||||
\(374\) | −1.48838e6 | −0.550217 | ||||||||
\(375\) | 1.40332e6 | − | 708962.i | 0.515321 | − | 0.260342i | ||||
\(376\) | −939294. | −0.342635 | ||||||||
\(377\) | 117323.i | 0.0425139i | ||||||||
\(378\) | 324387.i | 0.116771i | ||||||||
\(379\) | −812383. | −0.290511 | −0.145256 | − | 0.989394i | \(-0.546400\pi\) | ||||
−0.145256 | + | 0.989394i | \(0.546400\pi\) | |||||||
\(380\) | −1.03472e6 | − | 6.58172e6i | −0.367589 | − | 2.33819i | ||||
\(381\) | −1.00995e6 | −0.356441 | ||||||||
\(382\) | − | 3.64691e6i | − | 1.27869i | ||||||
\(383\) | − | 1.22178e6i | − | 0.425593i | −0.977096 | − | 0.212797i | \(-0.931743\pi\) | ||
0.977096 | − | 0.212797i | \(-0.0682572\pi\) | |||||||
\(384\) | −3.08521e6 | −1.06772 | ||||||||
\(385\) | 276511. | − | 43470.5i | 0.0950738 | − | 0.0149466i | ||||
\(386\) | 3.86397e6 | 1.31997 | ||||||||
\(387\) | 218650.i | 0.0742118i | ||||||||
\(388\) | 1.48136e6i | 0.499554i | ||||||||
\(389\) | 4.08811e6 | 1.36977 | 0.684887 | − | 0.728649i | \(-0.259852\pi\) | ||||
0.684887 | + | 0.728649i | \(0.259852\pi\) | |||||||
\(390\) | 72958.6 | − | 11469.9i | 0.0242893 | − | 0.00381853i | ||||
\(391\) | −2.89855e6 | −0.958824 | ||||||||
\(392\) | 8.37994e6i | 2.75439i | ||||||||
\(393\) | 3.01321e6i | 0.984120i | ||||||||
\(394\) | 6.49536e6 | 2.10796 | ||||||||
\(395\) | −620721. | − | 3.94834e6i | −0.200172 | − | 1.27327i | ||||
\(396\) | 819641. | 0.262655 | ||||||||
\(397\) | − | 15256.4i | − | 0.00485822i | −0.999997 | − | 0.00242911i | \(-0.999227\pi\) | ||
0.999997 | − | 0.00242911i | \(-0.000773210\pi\) | |||||||
\(398\) | − | 1.11236e7i | − | 3.51995i | ||||||
\(399\) | 530774. | 0.166908 | ||||||||
\(400\) | −9.79596e6 | + | 3.15811e6i | −3.06124 | + | 0.986909i | ||||
\(401\) | −4.75411e6 | −1.47642 | −0.738208 | − | 0.674574i | \(-0.764328\pi\) | ||||
−0.738208 | + | 0.674574i | \(0.764328\pi\) | |||||||
\(402\) | − | 5.00345e6i | − | 1.54420i | ||||||
\(403\) | − | 5930.55i | − | 0.00181900i | ||||||
\(404\) | 233188. | 0.0710807 | ||||||||
\(405\) | 56960.7 | + | 362321.i | 0.0172559 | + | 0.109763i | ||||
\(406\) | 3.82421e6 | 1.15140 | ||||||||
\(407\) | − | 1.74278e6i | − | 0.521503i | ||||||
\(408\) | 5.71555e6i | 1.69984i | ||||||||
\(409\) | 6.12814e6 | 1.81143 | 0.905713 | − | 0.423891i | \(-0.139336\pi\) | ||||
0.905713 | + | 0.423891i | \(0.139336\pi\) | |||||||
\(410\) | 7.35538e6 | − | 1.15634e6i | 2.16095 | − | 0.339725i | ||||
\(411\) | 8225.23 | 0.00240184 | ||||||||
\(412\) | − | 259807.i | − | 0.0754063i | ||||||
\(413\) | − | 1.71610e6i | − | 0.495071i | ||||||
\(414\) | 2.20700e6 | 0.632851 | ||||||||
\(415\) | 1.85215e6 | − | 291178.i | 0.527907 | − | 0.0829925i | ||||
\(416\) | −240961. | −0.0682673 | ||||||||
\(417\) | − | 2.43320e6i | − | 0.685231i | ||||||
\(418\) | − | 1.85430e6i | − | 0.519086i | ||||||
\(419\) | 3.61815e6 | 1.00682 | 0.503410 | − | 0.864048i | \(-0.332079\pi\) | ||||
0.503410 | + | 0.864048i | \(0.332079\pi\) | |||||||
\(420\) | −270399. | − | 1.71998e6i | −0.0747965 | − | 0.475773i | ||||
\(421\) | −1.49527e6 | −0.411164 | −0.205582 | − | 0.978640i | \(-0.565909\pi\) | ||||
−0.205582 | + | 0.978640i | \(0.565909\pi\) | |||||||
\(422\) | 8.15481e6i | 2.22912i | ||||||||
\(423\) | − | 137046.i | − | 0.0372406i | ||||||
\(424\) | 5.25471e6 | 1.41950 | ||||||||
\(425\) | 1.09687e6 | + | 3.40231e6i | 0.294565 | + | 0.913696i | ||||
\(426\) | −1.61094e6 | −0.430086 | ||||||||
\(427\) | 739374.i | 0.196243i | ||||||||
\(428\) | − | 1.80631e6i | − | 0.476631i | ||||||
\(429\) | 14866.4 | 0.00389999 | ||||||||
\(430\) | −252001. | − | 1.60295e6i | −0.0657251 | − | 0.418070i | ||||
\(431\) | 538580. | 0.139655 | 0.0698276 | − | 0.997559i | \(-0.477755\pi\) | ||||
0.0698276 | + | 0.997559i | \(0.477755\pi\) | |||||||
\(432\) | − | 2.40102e6i | − | 0.618995i | ||||||
\(433\) | − | 5.50572e6i | − | 1.41122i | −0.708600 | − | 0.705610i | \(-0.750673\pi\) | ||
0.708600 | − | 0.705610i | \(-0.249327\pi\) | |||||||
\(434\) | −193309. | −0.0492638 | ||||||||
\(435\) | 4.27142e6 | − | 671511.i | 1.08230 | − | 0.170149i | ||||
\(436\) | 1.59422e7 | 4.01636 | ||||||||
\(437\) | − | 3.61117e6i | − | 0.904575i | ||||||
\(438\) | − | 4.81056e6i | − | 1.19815i | ||||||
\(439\) | −4.55179e6 | −1.12725 | −0.563626 | − | 0.826030i | \(-0.690594\pi\) | ||||
−0.563626 | + | 0.826030i | \(0.690594\pi\) | |||||||
\(440\) | −3.70961e6 | + | 583190.i | −0.913475 | + | 0.143608i | ||||
\(441\) | −1.22266e6 | −0.299371 | ||||||||
\(442\) | 167921.i | 0.0408837i | ||||||||
\(443\) | − | 1.92800e6i | − | 0.466764i | −0.972385 | − | 0.233382i | \(-0.925021\pi\) | ||
0.972385 | − | 0.233382i | \(-0.0749793\pi\) | |||||||
\(444\) | −1.08406e7 | −2.60973 | ||||||||
\(445\) | 668303. | + | 4.25100e6i | 0.159983 | + | 1.01763i | ||||
\(446\) | −1.16535e7 | −2.77407 | ||||||||
\(447\) | 4.80233e6i | 1.13680i | ||||||||
\(448\) | 3.49286e6i | 0.822216i | ||||||||
\(449\) | −2.25763e6 | −0.528491 | −0.264246 | − | 0.964455i | \(-0.585123\pi\) | ||||
−0.264246 | + | 0.964455i | \(0.585123\pi\) | |||||||
\(450\) | −835171. | − | 2.59057e6i | −0.194421 | − | 0.603065i | ||||
\(451\) | 1.49877e6 | 0.346972 | ||||||||
\(452\) | 2.00292e7i | 4.61124i | ||||||||
\(453\) | − | 983394.i | − | 0.225155i | ||||||
\(454\) | 6.82991e6 | 1.55516 | ||||||||
\(455\) | −4904.42 | − | 31196.5i | −0.00111060 | − | 0.00706444i | ||||
\(456\) | −7.12074e6 | −1.60366 | ||||||||
\(457\) | 1.40364e6i | 0.314388i | 0.987568 | + | 0.157194i | \(0.0502448\pi\) | ||||
−0.987568 | + | 0.157194i | \(0.949755\pi\) | |||||||
\(458\) | 6.69732e6i | 1.49189i | ||||||||
\(459\) | −833918. | −0.184753 | ||||||||
\(460\) | −1.17020e7 | + | 1.83968e6i | −2.57850 | + | 0.405367i | ||||
\(461\) | 1.28230e6 | 0.281021 | 0.140510 | − | 0.990079i | \(-0.455126\pi\) | ||||
0.140510 | + | 0.990079i | \(0.455126\pi\) | |||||||
\(462\) | − | 484578.i | − | 0.105623i | ||||||
\(463\) | − | 5.16733e6i | − | 1.12025i | −0.828409 | − | 0.560124i | \(-0.810754\pi\) | ||
0.828409 | − | 0.560124i | \(-0.189246\pi\) | |||||||
\(464\) | −2.83057e7 | −6.10351 | ||||||||
\(465\) | −215915. | + | 33944.1i | −0.0463073 | + | 0.00728000i | ||||
\(466\) | 1.41726e7 | 3.02332 | ||||||||
\(467\) | − | 1.85528e6i | − | 0.393657i | −0.980438 | − | 0.196828i | \(-0.936936\pi\) | ||
0.980438 | − | 0.196828i | \(-0.0630642\pi\) | |||||||
\(468\) | − | 92473.4i | − | 0.0195165i | ||||||
\(469\) | −2.13944e6 | −0.449125 | ||||||||
\(470\) | 157950. | + | 1.00470e6i | 0.0329818 | + | 0.209794i | ||||
\(471\) | −3.26483e6 | −0.678123 | ||||||||
\(472\) | 2.30228e7i | 4.75667i | ||||||||
\(473\) | − | 326626.i | − | 0.0671271i | ||||||
\(474\) | −6.91936e6 | −1.41456 | ||||||||
\(475\) | −4.23879e6 | + | 1.36654e6i | −0.862000 | + | 0.277899i | ||||
\(476\) | 3.95870e6 | 0.800821 | ||||||||
\(477\) | 766681.i | 0.154283i | ||||||||
\(478\) | − | 2.58104e6i | − | 0.516685i | ||||||
\(479\) | −2.77689e6 | −0.552993 | −0.276497 | − | 0.961015i | \(-0.589173\pi\) | ||||
−0.276497 | + | 0.961015i | \(0.589173\pi\) | |||||||
\(480\) | 1.37916e6 | + | 8.77270e6i | 0.273220 | + | 1.73792i | ||||
\(481\) | −196624. | −0.0387502 | ||||||||
\(482\) | − | 7.08655e6i | − | 1.38937i | ||||||
\(483\) | − | 943695.i | − | 0.184062i | ||||||
\(484\) | −1.22440e6 | −0.237580 | ||||||||
\(485\) | 978210. | − | 153785.i | 0.188833 | − | 0.0296865i | ||||
\(486\) | 634957. | 0.121942 | ||||||||
\(487\) | − | 8.55421e6i | − | 1.63440i | −0.576356 | − | 0.817198i | \(-0.695526\pi\) | ||
0.576356 | − | 0.817198i | \(-0.304474\pi\) | |||||||
\(488\) | − | 9.91927e6i | − | 1.88552i | ||||||
\(489\) | −3.05130e6 | −0.577049 | ||||||||
\(490\) | 8.96348e6 | − | 1.40915e6i | 1.68650 | − | 0.265136i | ||||
\(491\) | −9.34368e6 | −1.74910 | −0.874550 | − | 0.484936i | \(-0.838843\pi\) | ||||
−0.874550 | + | 0.484936i | \(0.838843\pi\) | |||||||
\(492\) | − | 9.32278e6i | − | 1.73633i | ||||||
\(493\) | 9.83109e6i | 1.82173i | ||||||||
\(494\) | −209206. | −0.0385706 | ||||||||
\(495\) | −85089.4 | − | 541245.i | −0.0156085 | − | 0.0992844i | ||||
\(496\) | 1.43082e6 | 0.261144 | ||||||||
\(497\) | 688825.i | 0.125089i | ||||||||
\(498\) | − | 3.24585e6i | − | 0.586483i | ||||||
\(499\) | −1.03633e7 | −1.86314 | −0.931569 | − | 0.363564i | \(-0.881560\pi\) | ||||
−0.931569 | + | 0.363564i | \(0.881560\pi\) | |||||||
\(500\) | 6.58770e6 | + | 1.30397e7i | 1.17844 | + | 2.33261i | ||||
\(501\) | 4.13825e6 | 0.736585 | ||||||||
\(502\) | − | 1.85722e7i | − | 3.28931i | ||||||
\(503\) | 5.19173e6i | 0.914938i | 0.889225 | + | 0.457469i | \(0.151244\pi\) | ||||
−0.889225 | + | 0.457469i | \(0.848756\pi\) | |||||||
\(504\) | −1.86084e6 | −0.326312 | ||||||||
\(505\) | −24207.9 | − | 153984.i | −0.00422405 | − | 0.0268687i | ||||
\(506\) | −3.29688e6 | −0.572435 | ||||||||
\(507\) | 3.33996e6i | 0.577060i | ||||||||
\(508\) | − | 9.38448e6i | − | 1.61343i | ||||||
\(509\) | −591024. | −0.101114 | −0.0505569 | − | 0.998721i | \(-0.516100\pi\) | ||||
−0.0505569 | + | 0.998721i | \(0.516100\pi\) | |||||||
\(510\) | 6.11355e6 | − | 961115.i | 1.04080 | − | 0.163625i | ||||
\(511\) | −2.05696e6 | −0.348476 | ||||||||
\(512\) | 376329.i | 0.0634444i | ||||||||
\(513\) | − | 1.03894e6i | − | 0.174300i | ||||||
\(514\) | 9.56145e6 | 1.59630 | ||||||||
\(515\) | −171562. | + | 26971.3i | −0.0285038 | + | 0.00448110i | ||||
\(516\) | −2.03171e6 | −0.335921 | ||||||||
\(517\) | 204723.i | 0.0336854i | ||||||||
\(518\) | 6.40905e6i | 1.04947i | ||||||||
\(519\) | 4.74929e6 | 0.773945 | ||||||||
\(520\) | 65796.6 | + | 418525.i | 0.0106707 | + | 0.0678755i | ||||
\(521\) | 4.41573e6 | 0.712702 | 0.356351 | − | 0.934352i | \(-0.384021\pi\) | ||||
0.356351 | + | 0.934352i | \(0.384021\pi\) | |||||||
\(522\) | − | 7.48554e6i | − | 1.20239i | ||||||
\(523\) | 7.91473e6i | 1.26527i | 0.774452 | + | 0.632633i | \(0.218026\pi\) | ||||
−0.774452 | + | 0.632633i | \(0.781974\pi\) | |||||||
\(524\) | −2.79988e7 | −4.45463 | ||||||||
\(525\) | −1.10771e6 | + | 357112.i | −0.175399 | + | 0.0565466i | ||||
\(526\) | −3.79224e6 | −0.597629 | ||||||||
\(527\) | − | 496949.i | − | 0.0779445i | ||||||
\(528\) | 3.58671e6i | 0.559902i | ||||||||
\(529\) | 15819.3 | 0.00245780 | ||||||||
\(530\) | −883622. | − | 5.62063e6i | −0.136640 | − | 0.869151i | ||||
\(531\) | −3.35910e6 | −0.516996 | ||||||||
\(532\) | 4.93197e6i | 0.755512i | ||||||||
\(533\) | − | 169094.i | − | 0.0257816i | ||||||
\(534\) | 7.44977e6 | 1.13055 | ||||||||
\(535\) | −1.19278e6 | + | 187518.i | −0.180168 | + | 0.0283243i | ||||
\(536\) | 2.87022e7 | 4.31522 | ||||||||
\(537\) | − | 7.10829e6i | − | 1.06372i | ||||||
\(538\) | − | 5.44896e6i | − | 0.811629i | ||||||
\(539\) | 1.82645e6 | 0.270791 | ||||||||
\(540\) | −3.36670e6 | + | 529280.i | −0.496844 | + | 0.0781090i | ||||
\(541\) | 1.37134e6 | 0.201443 | 0.100722 | − | 0.994915i | \(-0.467885\pi\) | ||||
0.100722 | + | 0.994915i | \(0.467885\pi\) | |||||||
\(542\) | 1.43584e7i | 2.09946i | ||||||||
\(543\) | − | 3.37886e6i | − | 0.491779i | ||||||
\(544\) | −2.01912e7 | −2.92527 | ||||||||
\(545\) | −1.65501e6 | − | 1.05273e7i | −0.238676 | − | 1.51820i | ||||
\(546\) | −54671.0 | −0.00784830 | ||||||||
\(547\) | − | 7.82390e6i | − | 1.11803i | −0.829156 | − | 0.559017i | \(-0.811179\pi\) | ||
0.829156 | − | 0.559017i | \(-0.188821\pi\) | |||||||
\(548\) | 76429.1i | 0.0108719i | ||||||||
\(549\) | 1.44726e6 | 0.204934 | ||||||||
\(550\) | 1.24760e6 | + | 3.86986e6i | 0.175861 | + | 0.545493i | ||||
\(551\) | −1.22481e7 | −1.71866 | ||||||||
\(552\) | 1.26604e7i | 1.76848i | ||||||||
\(553\) | 2.95866e6i | 0.411417i | ||||||||
\(554\) | 1.85166e7 | 2.56323 | ||||||||
\(555\) | 1.12540e6 | + | 7.15853e6i | 0.155086 | + | 0.986486i | ||||
\(556\) | 2.26093e7 | 3.10171 | ||||||||
\(557\) | − | 8.25549e6i | − | 1.12747i | −0.825956 | − | 0.563735i | \(-0.809364\pi\) | ||
0.825956 | − | 0.563735i | \(-0.190636\pi\) | |||||||
\(558\) | 378385.i | 0.0514456i | ||||||||
\(559\) | −36850.5 | −0.00498786 | ||||||||
\(560\) | 7.52655e6 | − | 1.18325e6i | 1.01421 | − | 0.159444i | ||||
\(561\) | 1.24573e6 | 0.167115 | ||||||||
\(562\) | 1.29672e7i | 1.73183i | ||||||||
\(563\) | 1.20969e7i | 1.60843i | 0.594340 | + | 0.804214i | \(0.297413\pi\) | ||||
−0.594340 | + | 0.804214i | \(0.702587\pi\) | |||||||
\(564\) | 1.27344e6 | 0.168570 | ||||||||
\(565\) | 1.32262e7 | − | 2.07929e6i | 1.74306 | − | 0.274028i | ||||
\(566\) | 9.89478e6 | 1.29827 | ||||||||
\(567\) | − | 271503.i | − | 0.0354663i | ||||||
\(568\) | − | 9.24112e6i | − | 1.20186i | ||||||
\(569\) | 7.97678e6 | 1.03287 | 0.516437 | − | 0.856325i | \(-0.327258\pi\) | ||||
0.516437 | + | 0.856325i | \(0.327258\pi\) | |||||||
\(570\) | 1.19741e6 | + | 7.61660e6i | 0.154367 | + | 0.981915i | ||||
\(571\) | −8.94027e6 | −1.14752 | −0.573760 | − | 0.819023i | \(-0.694516\pi\) | ||||
−0.573760 | + | 0.819023i | \(0.694516\pi\) | |||||||
\(572\) | 138139.i | 0.0176533i | ||||||||
\(573\) | 3.05236e6i | 0.388373i | ||||||||
\(574\) | −5.51171e6 | −0.698242 | ||||||||
\(575\) | 2.42965e6 | + | 7.53639e6i | 0.306460 | + | 0.950592i | ||||
\(576\) | 6.83694e6 | 0.858629 | ||||||||
\(577\) | 4.92430e6i | 0.615751i | 0.951427 | + | 0.307875i | \(0.0996180\pi\) | ||||
−0.951427 | + | 0.307875i | \(0.900382\pi\) | |||||||
\(578\) | − | 1.19686e6i | − | 0.149013i | ||||||
\(579\) | −3.23403e6 | −0.400911 | ||||||||
\(580\) | 6.23970e6 | + | 3.96901e7i | 0.770183 | + | 4.89906i | ||||
\(581\) | −1.38790e6 | −0.170576 | ||||||||
\(582\) | − | 1.71428e6i | − | 0.209786i | ||||||
\(583\) | − | 1.14529e6i | − | 0.139554i | ||||||
\(584\) | 2.75957e7 | 3.34818 | ||||||||
\(585\) | −61064.3 | + | 9599.94i | −0.00737730 | + | 0.00115979i | ||||
\(586\) | −1.34894e6 | −0.162274 | ||||||||
\(587\) | − | 1.22885e7i | − | 1.47199i | −0.676989 | − | 0.735993i | \(-0.736715\pi\) | ||
0.676989 | − | 0.735993i | \(-0.263285\pi\) | |||||||
\(588\) | − | 1.13610e7i | − | 1.35511i | ||||||
\(589\) | 619126. | 0.0735345 | ||||||||
\(590\) | 2.46260e7 | − | 3.87146e6i | 2.91248 | − | 0.457873i | ||||
\(591\) | −5.43643e6 | −0.640244 | ||||||||
\(592\) | − | 4.74380e7i | − | 5.56317i | ||||||
\(593\) | − | 8.20846e6i | − | 0.958572i | −0.877659 | − | 0.479286i | \(-0.840896\pi\) | ||
0.877659 | − | 0.479286i | \(-0.159104\pi\) | |||||||
\(594\) | −948517. | −0.110301 | ||||||||
\(595\) | −410965. | − | 2.61411e6i | −0.0475896 | − | 0.302713i | ||||
\(596\) | −4.46234e7 | −5.14573 | ||||||||
\(597\) | 9.31010e6i | 1.06910i | ||||||||
\(598\) | 371960.i | 0.0425347i | ||||||||
\(599\) | 2.00442e6 | 0.228256 | 0.114128 | − | 0.993466i | \(-0.463593\pi\) | ||||
0.114128 | + | 0.993466i | \(0.463593\pi\) | |||||||
\(600\) | 1.48607e7 | − | 4.79094e6i | 1.68524 | − | 0.543303i | ||||
\(601\) | −871399. | −0.0984081 | −0.0492041 | − | 0.998789i | \(-0.515668\pi\) | ||||
−0.0492041 | + | 0.998789i | \(0.515668\pi\) | |||||||
\(602\) | 1.20116e6i | 0.135086i | ||||||||
\(603\) | 4.18775e6i | 0.469015i | ||||||||
\(604\) | 9.13773e6 | 1.01917 | ||||||||
\(605\) | 127109. | + | 808526.i | 0.0141185 | + | 0.0898061i | ||||
\(606\) | −269853. | −0.0298501 | ||||||||
\(607\) | 1.04538e7i | 1.15160i | 0.817589 | + | 0.575802i | \(0.195310\pi\) | ||||
−0.817589 | + | 0.575802i | \(0.804690\pi\) | |||||||
\(608\) | − | 2.51554e7i | − | 2.75976i | ||||||
\(609\) | −3.20075e6 | −0.349711 | ||||||||
\(610\) | −1.06100e7 | + | 1.66800e6i | −1.15449 | + | 0.181498i | ||||
\(611\) | 23097.3 | 0.00250298 | ||||||||
\(612\) | − | 7.74879e6i | − | 0.836287i | ||||||
\(613\) | − | 5.79441e6i | − | 0.622814i | −0.950277 | − | 0.311407i | \(-0.899200\pi\) | ||
0.950277 | − | 0.311407i | \(-0.100800\pi\) | |||||||
\(614\) | −9.92161e6 | −1.06209 | ||||||||
\(615\) | −6.15624e6 | + | 967826.i | −0.656339 | + | 0.103183i | ||||
\(616\) | 2.77977e6 | 0.295160 | ||||||||
\(617\) | − | 7.10900e6i | − | 0.751788i | −0.926663 | − | 0.375894i | \(-0.877336\pi\) | ||
0.926663 | − | 0.375894i | \(-0.122664\pi\) | |||||||
\(618\) | 300657.i | 0.0316665i | ||||||||
\(619\) | 1.13332e7 | 1.18885 | 0.594424 | − | 0.804152i | \(-0.297380\pi\) | ||||
0.594424 | + | 0.804152i | \(0.297380\pi\) | |||||||
\(620\) | −315409. | − | 2.00629e6i | −0.0329530 | − | 0.209611i | ||||
\(621\) | −1.84720e6 | −0.192213 | ||||||||
\(622\) | 1.72195e7i | 1.78462i | ||||||||
\(623\) | − | 3.18546e6i | − | 0.328815i | ||||||
\(624\) | 404660. | 0.0416034 | ||||||||
\(625\) | 7.92677e6 | − | 5.70383e6i | 0.811702 | − | 0.584072i | ||||
\(626\) | 1.90465e6 | 0.194259 | ||||||||
\(627\) | 1.55200e6i | 0.157660i | ||||||||
\(628\) | − | 3.03369e7i | − | 3.06953i | ||||||
\(629\) | −1.64761e7 | −1.66045 | ||||||||
\(630\) | 312915. | + | 1.99042e6i | 0.0314105 | + | 0.199799i | ||||
\(631\) | 3.77282e6 | 0.377218 | 0.188609 | − | 0.982052i | \(-0.439602\pi\) | ||||
0.188609 | + | 0.982052i | \(0.439602\pi\) | |||||||
\(632\) | − | 3.96927e7i | − | 3.95292i | ||||||
\(633\) | − | 6.82534e6i | − | 0.677041i | ||||||
\(634\) | −6.21800e6 | −0.614366 | ||||||||
\(635\) | −6.19699e6 | + | 974231.i | −0.609882 | + | 0.0958799i | ||||
\(636\) | −7.12402e6 | −0.698365 | ||||||||
\(637\) | − | 206063.i | − | 0.0201211i | ||||||
\(638\) | 1.11821e7i | 1.08761i | ||||||||
\(639\) | 1.34831e6 | 0.130628 | ||||||||
\(640\) | −1.89306e7 | + | 2.97609e6i | −1.82690 | + | 0.287208i | ||||
\(641\) | 1.76552e6 | 0.169718 | 0.0848591 | − | 0.996393i | \(-0.472956\pi\) | ||||
0.0848591 | + | 0.996393i | \(0.472956\pi\) | |||||||
\(642\) | 2.09032e6i | 0.200159i | ||||||||
\(643\) | 3.29197e6i | 0.313999i | 0.987599 | + | 0.157000i | \(0.0501822\pi\) | ||||
−0.987599 | + | 0.157000i | \(0.949818\pi\) | |||||||
\(644\) | 8.76885e6 | 0.833159 | ||||||||
\(645\) | 210918. | + | 1.34162e6i | 0.0199624 | + | 0.126979i | ||||
\(646\) | −1.75304e7 | −1.65276 | ||||||||
\(647\) | − | 1.62220e7i | − | 1.52350i | −0.647868 | − | 0.761752i | \(-0.724339\pi\) | ||
0.647868 | − | 0.761752i | \(-0.275661\pi\) | |||||||
\(648\) | 3.64242e6i | 0.340763i | ||||||||
\(649\) | 5.01792e6 | 0.467640 | ||||||||
\(650\) | 436605. | − | 140757.i | 0.0405327 | − | 0.0130673i | ||||
\(651\) | 161794. | 0.0149627 | ||||||||
\(652\) | − | 2.83528e7i | − | 2.61202i | ||||||
\(653\) | 3.42354e6i | 0.314190i | 0.987583 | + | 0.157095i | \(0.0502129\pi\) | ||||
−0.987583 | + | 0.157095i | \(0.949787\pi\) | |||||||
\(654\) | −1.84489e7 | −1.68665 | ||||||||
\(655\) | 2.90664e6 | + | 1.84889e7i | 0.264721 | + | 1.68386i | ||||
\(656\) | 4.07961e7 | 3.70134 | ||||||||
\(657\) | 4.02630e6i | 0.363909i | ||||||||
\(658\) | − | 752867.i | − | 0.0677881i | ||||||
\(659\) | −5.40108e6 | −0.484470 | −0.242235 | − | 0.970218i | \(-0.577881\pi\) | ||||
−0.242235 | + | 0.970218i | \(0.577881\pi\) | |||||||
\(660\) | 5.02926e6 | − | 790653.i | 0.449412 | − | 0.0706523i | ||||
\(661\) | 4.42083e6 | 0.393550 | 0.196775 | − | 0.980449i | \(-0.436953\pi\) | ||||
0.196775 | + | 0.980449i | \(0.436953\pi\) | |||||||
\(662\) | 3.48149e7i | 3.08760i | ||||||||
\(663\) | − | 140545.i | − | 0.0124175i | ||||||
\(664\) | 1.86197e7 | 1.63890 | ||||||||
\(665\) | 3.25680e6 | − | 512003.i | 0.285586 | − | 0.0448971i | ||||
\(666\) | 1.25451e7 | 1.09595 | ||||||||
\(667\) | 2.17767e7i | 1.89529i | ||||||||
\(668\) | 3.84528e7i | 3.33416i | ||||||||
\(669\) | 9.75360e6 | 0.842558 | ||||||||
\(670\) | −4.82650e6 | − | 3.07009e7i | −0.415380 | − | 2.64219i | ||||
\(671\) | −2.16195e6 | −0.185370 | ||||||||
\(672\) | − | 6.57376e6i | − | 0.561553i | ||||||
\(673\) | 1.15029e7i | 0.978969i | 0.872012 | + | 0.489484i | \(0.162815\pi\) | ||||
−0.872012 | + | 0.489484i | \(0.837185\pi\) | |||||||
\(674\) | −1.96060e7 | −1.66242 | ||||||||
\(675\) | 699014. | + | 2.16823e6i | 0.0590509 | + | 0.183167i | ||||
\(676\) | −3.10350e7 | −2.61207 | ||||||||
\(677\) | 2.08105e7i | 1.74506i | 0.488560 | + | 0.872530i | \(0.337522\pi\) | ||||
−0.488560 | + | 0.872530i | \(0.662478\pi\) | |||||||
\(678\) | − | 2.31785e7i | − | 1.93647i | ||||||
\(679\) | −733014. | −0.0610152 | ||||||||
\(680\) | 5.51341e6 | + | 3.50702e7i | 0.457244 | + | 2.90848i | ||||
\(681\) | −5.71643e6 | −0.472343 | ||||||||
\(682\) | − | 565241.i | − | 0.0465343i | ||||||
\(683\) | 2.29333e7i | 1.88111i | 0.339638 | + | 0.940556i | \(0.389695\pi\) | ||||
−0.339638 | + | 0.940556i | \(0.610305\pi\) | |||||||
\(684\) | 9.65386e6 | 0.788971 | ||||||||
\(685\) | 50469.5 | − | 7934.33i | 0.00410963 | − | 0.000646077i | ||||
\(686\) | −1.41954e7 | −1.15170 | ||||||||
\(687\) | − | 5.60546e6i | − | 0.453126i | ||||||
\(688\) | − | 8.89066e6i | − | 0.716082i | ||||||
\(689\) | −129214. | −0.0103696 | ||||||||
\(690\) | 1.35420e7 | − | 2.12895e6i | 1.08283 | − | 0.170232i | ||||
\(691\) | −1.87802e7 | −1.49626 | −0.748128 | − | 0.663554i | \(-0.769047\pi\) | ||||
−0.748128 | + | 0.663554i | \(0.769047\pi\) | |||||||
\(692\) | 4.41306e7i | 3.50327i | ||||||||
\(693\) | 405578.i | 0.0320805i | ||||||||
\(694\) | −6.06634e6 | −0.478110 | ||||||||
\(695\) | −2.34714e6 | − | 1.49299e7i | −0.184322 | − | 1.17245i | ||||
\(696\) | 4.29406e7 | 3.36004 | ||||||||
\(697\) | − | 1.41692e7i | − | 1.10475i | ||||||
\(698\) | 2.93185e7i | 2.27774i | ||||||||
\(699\) | −1.18621e7 | −0.918263 | ||||||||
\(700\) | −3.31830e6 | − | 1.02928e7i | −0.255959 | − | 0.793945i | ||||
\(701\) | −4.01030e6 | −0.308235 | −0.154118 | − | 0.988053i | \(-0.549253\pi\) | ||||
−0.154118 | + | 0.988053i | \(0.549253\pi\) | |||||||
\(702\) | 107013.i | 0.00819588i | ||||||||
\(703\) | − | 2.05268e7i | − | 1.56651i | ||||||
\(704\) | −1.02132e7 | −0.776659 | ||||||||
\(705\) | −132199. | − | 840907.i | −0.0100174 | − | 0.0637199i | ||||
\(706\) | 7.47310e6 | 0.564273 | ||||||||
\(707\) | 115387.i | 0.00868176i | ||||||||
\(708\) | − | 3.12129e7i | − | 2.34019i | ||||||
\(709\) | 326851. | 0.0244193 | 0.0122097 | − | 0.999925i | \(-0.496113\pi\) | ||||
0.0122097 | + | 0.999925i | \(0.496113\pi\) | |||||||
\(710\) | −9.88463e6 | + | 1.55397e6i | −0.735892 | + | 0.115690i | ||||
\(711\) | 5.79130e6 | 0.429638 | ||||||||
\(712\) | 4.27354e7i | 3.15928i | ||||||||
\(713\) | − | 1.10078e6i | − | 0.0810919i | ||||||
\(714\) | −4.58115e6 | −0.336301 | ||||||||
\(715\) | 91219.4 | − | 14340.7i | 0.00667302 | − | 0.00104907i | ||||
\(716\) | 6.60504e7 | 4.81496 | ||||||||
\(717\) | 2.16026e6i | 0.156931i | ||||||||
\(718\) | − | 3.29164e6i | − | 0.238287i | ||||||
\(719\) | 1.34067e7 | 0.967161 | 0.483581 | − | 0.875300i | \(-0.339336\pi\) | ||||
0.483581 | + | 0.875300i | \(0.339336\pi\) | |||||||
\(720\) | −2.31611e6 | − | 1.47325e7i | −0.166505 | − | 1.05912i | ||||
\(721\) | 128559. | 0.00921008 | ||||||||
\(722\) | 4.78536e6i | 0.341643i | ||||||||
\(723\) | 5.93124e6i | 0.421988i | ||||||||
\(724\) | 3.13964e7 | 2.22604 | ||||||||
\(725\) | 2.55614e7 | − | 8.24070e6i | 1.80609 | − | 0.582263i | ||||
\(726\) | 1.41692e6 | 0.0997709 | ||||||||
\(727\) | 2.14838e7i | 1.50756i | 0.657127 | + | 0.753780i | \(0.271771\pi\) | ||||
−0.657127 | + | 0.753780i | \(0.728229\pi\) | |||||||
\(728\) | − | 313619.i | − | 0.0219318i | ||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | −4.64043e6 | − | 2.95173e7i | −0.322293 | − | 2.05007i | ||||
\(731\) | −3.08788e6 | −0.213731 | ||||||||
\(732\) | 1.34479e7i | 0.927637i | ||||||||
\(733\) | 8.60145e6i | 0.591305i | 0.955296 | + | 0.295653i | \(0.0955371\pi\) | ||||
−0.955296 | + | 0.295653i | \(0.904463\pi\) | |||||||
\(734\) | −1.62985e7 | −1.11663 | ||||||||
\(735\) | −7.50218e6 | + | 1.17942e6i | −0.512235 | + | 0.0805286i | ||||
\(736\) | −4.47252e7 | −3.04339 | ||||||||
\(737\) | − | 6.25577e6i | − | 0.424240i | ||||||
\(738\) | 1.07886e7i | 0.729165i | ||||||||
\(739\) | 4.69199e6 | 0.316043 | 0.158022 | − | 0.987436i | \(-0.449488\pi\) | ||||
0.158022 | + | 0.987436i | \(0.449488\pi\) | |||||||
\(740\) | −6.65172e7 | + | 1.04572e7i | −4.46534 | + | 0.701999i | ||||
\(741\) | 175099. | 0.0117149 | ||||||||
\(742\) | 4.21178e6i | 0.280838i | ||||||||
\(743\) | − | 1.84011e7i | − | 1.22284i | −0.791305 | − | 0.611422i | \(-0.790598\pi\) | ||
0.791305 | − | 0.611422i | \(-0.209402\pi\) | |||||||
\(744\) | −2.17059e6 | −0.143763 | ||||||||
\(745\) | 4.63249e6 | + | 2.94668e7i | 0.305790 | + | 1.94510i | ||||
\(746\) | 1.13779e7 | 0.748539 | ||||||||
\(747\) | 2.71668e6i | 0.178130i | ||||||||
\(748\) | 1.15754e7i | 0.756450i | ||||||||
\(749\) | 893804. | 0.0582154 | ||||||||
\(750\) | −7.62351e6 | − | 1.50899e7i | −0.494882 | − | 0.979568i | ||||
\(751\) | 4.90697e6 | 0.317478 | 0.158739 | − | 0.987321i | \(-0.449257\pi\) | ||||
0.158739 | + | 0.987321i | \(0.449257\pi\) | |||||||
\(752\) | 5.57251e6i | 0.359341i | ||||||||
\(753\) | 1.55444e7i | 0.999049i | ||||||||
\(754\) | 1.26158e6 | 0.0808143 | ||||||||
\(755\) | −948615. | − | 6.03404e6i | −0.0605651 | − | 0.385249i | ||||
\(756\) | 2.52281e6 | 0.160539 | ||||||||
\(757\) | − | 1.77340e7i | − | 1.12478i | −0.826872 | − | 0.562390i | \(-0.809882\pi\) | ||
0.826872 | − | 0.562390i | \(-0.190118\pi\) | |||||||
\(758\) | 8.73560e6i | 0.552230i | ||||||||
\(759\) | 2.75939e6 | 0.173864 | ||||||||
\(760\) | −4.36924e7 | + | 6.86891e6i | −2.74392 | + | 0.431374i | ||||
\(761\) | 7.16267e6 | 0.448346 | 0.224173 | − | 0.974549i | \(-0.428032\pi\) | ||||
0.224173 | + | 0.974549i | \(0.428032\pi\) | |||||||
\(762\) | 1.08600e7i | 0.677554i | ||||||||
\(763\) | 7.88859e6i | 0.490556i | ||||||||
\(764\) | −2.83626e7 | −1.75797 | ||||||||
\(765\) | −5.11687e6 | + | 804425.i | −0.316119 | + | 0.0496972i | ||||
\(766\) | −1.31378e7 | −0.809006 | ||||||||
\(767\) | − | 566131.i | − | 0.0347479i | ||||||
\(768\) | 8.86628e6i | 0.542423i | ||||||||
\(769\) | 1.90012e7 | 1.15869 | 0.579343 | − | 0.815084i | \(-0.303309\pi\) | ||||
0.579343 | + | 0.815084i | \(0.303309\pi\) | |||||||
\(770\) | −467441. | − | 2.97334e6i | −0.0284119 | − | 0.180725i | ||||
\(771\) | −8.00265e6 | −0.484840 | ||||||||
\(772\) | − | 3.00507e7i | − | 1.81473i | ||||||
\(773\) | − | 6.66234e6i | − | 0.401031i | −0.979690 | − | 0.200516i | \(-0.935738\pi\) | ||
0.979690 | − | 0.200516i | \(-0.0642618\pi\) | |||||||
\(774\) | 2.35116e6 | 0.141068 | ||||||||
\(775\) | −1.29210e6 | + | 416557.i | −0.0772753 | + | 0.0249127i | ||||
\(776\) | 9.83395e6 | 0.586238 | ||||||||
\(777\) | − | 5.36419e6i | − | 0.318751i | ||||||
\(778\) | − | 4.39597e7i | − | 2.60379i | ||||||
\(779\) | 1.76528e7 | 1.04224 | ||||||||
\(780\) | −89203.0 | − | 567411.i | −0.00524980 | − | 0.0333934i | ||||
\(781\) | −2.01414e6 | −0.118158 | ||||||||
\(782\) | 3.11683e7i | 1.82262i | ||||||||
\(783\) | 6.26518e6i | 0.365198i | ||||||||
\(784\) | 4.97153e7 | 2.88868 | ||||||||
\(785\) | −2.00328e7 | + | 3.14937e6i | −1.16029 | + | 0.182410i | ||||
\(786\) | 3.24012e7 | 1.87070 | ||||||||
\(787\) | 9.20508e6i | 0.529774i | 0.964279 | + | 0.264887i | \(0.0853347\pi\) | ||||
−0.964279 | + | 0.264887i | \(0.914665\pi\) | |||||||
\(788\) | − | 5.05155e7i | − | 2.89807i | ||||||
\(789\) | 3.17400e6 | 0.181516 | ||||||||
\(790\) | −4.24567e7 | + | 6.67465e6i | −2.42035 | + | 0.380505i | ||||
\(791\) | −9.91094e6 | −0.563214 | ||||||||
\(792\) | − | 5.44114e6i | − | 0.308232i | ||||||
\(793\) | 243915.i | 0.0137739i | ||||||||
\(794\) | −164053. | −0.00923494 | ||||||||
\(795\) | 739566. | + | 4.70430e6i | 0.0415011 | + | 0.263984i | ||||
\(796\) | −8.65098e7 | −4.83930 | ||||||||
\(797\) | 2.71663e7i | 1.51490i | 0.652893 | + | 0.757450i | \(0.273555\pi\) | ||||
−0.652893 | + | 0.757450i | \(0.726445\pi\) | |||||||
\(798\) | − | 5.70744e6i | − | 0.317274i | ||||||
\(799\) | 1.93543e6 | 0.107253 | ||||||||
\(800\) | 1.69249e7 | + | 5.24984e7i | 0.934977 | + | 2.90015i | ||||
\(801\) | −6.23524e6 | −0.343378 | ||||||||
\(802\) | 5.11213e7i | 2.80650i | ||||||||
\(803\) | − | 6.01460e6i | − | 0.329168i | ||||||
\(804\) | −3.89127e7 | −2.12300 | ||||||||
\(805\) | −910320. | − | 5.79046e6i | −0.0495113 | − | 0.314937i | ||||
\(806\) | −63771.6 | −0.00345772 | ||||||||
\(807\) | 4.56062e6i | 0.246513i | ||||||||
\(808\) | − | 1.54800e6i | − | 0.0834149i | ||||||
\(809\) | 2.31559e7 | 1.24392 | 0.621958 | − | 0.783051i | \(-0.286338\pi\) | ||||
0.621958 | + | 0.783051i | \(0.286338\pi\) | |||||||
\(810\) | 3.89606e6 | − | 612501.i | 0.208647 | − | 0.0328016i | ||||
\(811\) | 1.33212e6 | 0.0711200 | 0.0355600 | − | 0.999368i | \(-0.488679\pi\) | ||||
0.0355600 | + | 0.999368i | \(0.488679\pi\) | |||||||
\(812\) | − | 2.97415e7i | − | 1.58297i | ||||||
\(813\) | − | 1.20176e7i | − | 0.637661i | ||||||
\(814\) | −1.87402e7 | −0.991320 | ||||||||
\(815\) | −1.87226e7 | + | 2.94339e6i | −0.987352 | + | 0.155222i | ||||
\(816\) | 3.39084e7 | 1.78271 | ||||||||
\(817\) | − | 3.84705e6i | − | 0.201638i | ||||||
\(818\) | − | 6.58963e7i | − | 3.44332i | ||||||
\(819\) | 45758.1 | 0.00238373 | ||||||||
\(820\) | −8.99307e6 | − | 5.72040e7i | −0.467061 | − | 2.97093i | ||||
\(821\) | 1.06084e7 | 0.549277 | 0.274638 | − | 0.961548i | \(-0.411442\pi\) | ||||
0.274638 | + | 0.961548i | \(0.411442\pi\) | |||||||
\(822\) | − | 88446.4i | − | 0.00456563i | ||||||
\(823\) | 1.83916e7i | 0.946496i | 0.880929 | + | 0.473248i | \(0.156919\pi\) | ||||
−0.880929 | + | 0.473248i | \(0.843081\pi\) | |||||||
\(824\) | −1.72471e6 | −0.0884910 | ||||||||
\(825\) | −1.04421e6 | − | 3.23896e6i | −0.0534135 | − | 0.165680i | ||||
\(826\) | −1.84533e7 | −0.941075 | ||||||||
\(827\) | − | 1.95386e7i | − | 0.993414i | −0.867918 | − | 0.496707i | \(-0.834542\pi\) | ||
0.867918 | − | 0.496707i | \(-0.165458\pi\) | |||||||
\(828\) | − | 1.71642e7i | − | 0.870057i | ||||||
\(829\) | 3.37798e7 | 1.70714 | 0.853572 | − | 0.520974i | \(-0.174431\pi\) | ||||
0.853572 | + | 0.520974i | \(0.174431\pi\) | |||||||
\(830\) | −3.13106e6 | − | 1.99163e7i | −0.157760 | − | 1.00349i | ||||
\(831\) | −1.54979e7 | −0.778520 | ||||||||
\(832\) | 1.15227e6i | 0.0577095i | ||||||||
\(833\) | − | 1.72670e7i | − | 0.862193i | ||||||
\(834\) | −2.61643e7 | −1.30255 | ||||||||
\(835\) | 2.53921e7 | − | 3.99190e6i | 1.26032 | − | 0.198136i | ||||
\(836\) | −1.44212e7 | −0.713651 | ||||||||
\(837\) | − | 316697.i | − | 0.0156254i | ||||||
\(838\) | − | 3.89062e7i | − | 1.91385i | ||||||
\(839\) | −2.77050e7 | −1.35879 | −0.679396 | − | 0.733772i | \(-0.737758\pi\) | ||||
−0.679396 | + | 0.733772i | \(0.737758\pi\) | |||||||
\(840\) | −1.14180e7 | + | 1.79503e6i | −0.558331 | + | 0.0877754i | ||||
\(841\) | 5.33493e7 | 2.60099 | ||||||||
\(842\) | 1.60788e7i | 0.781578i | ||||||||
\(843\) | − | 1.08531e7i | − | 0.526001i | ||||||
\(844\) | 6.34213e7 | 3.06463 | ||||||||
\(845\) | 3.22184e6 | + | 2.04938e7i | 0.155225 | + | 0.987371i | ||||
\(846\) | −1.47367e6 | −0.0707902 | ||||||||
\(847\) | − | 605864.i | − | 0.0290179i | ||||||
\(848\) | − | 3.11744e7i | − | 1.48870i | ||||||
\(849\) | −8.28165e6 | −0.394319 | ||||||||
\(850\) | 3.65852e7 | − | 1.17947e7i | 1.73684 | − | 0.559936i | ||||
\(851\) | −3.64958e7 | −1.72750 | ||||||||
\(852\) | 1.25285e7i | 0.591291i | ||||||||
\(853\) | − | 1.04555e7i | − | 0.492007i | −0.969269 | − | 0.246003i | \(-0.920883\pi\) | ||
0.969269 | − | 0.246003i | \(-0.0791174\pi\) | |||||||
\(854\) | 7.95053e6 | 0.373037 | ||||||||
\(855\) | −1.00220e6 | − | 6.37487e6i | −0.0468854 | − | 0.298233i | ||||
\(856\) | −1.19911e7 | −0.559337 | ||||||||
\(857\) | − | 2.53866e7i | − | 1.18074i | −0.807134 | − | 0.590369i | \(-0.798982\pi\) | ||
0.807134 | − | 0.590369i | \(-0.201018\pi\) | |||||||
\(858\) | − | 159860.i | − | 0.00741345i | ||||||
\(859\) | −1.84775e6 | −0.0854396 | −0.0427198 | − | 0.999087i | \(-0.513602\pi\) | ||||
−0.0427198 | + | 0.999087i | \(0.513602\pi\) | |||||||
\(860\) | −1.24664e7 | + | 1.95985e6i | −0.574772 | + | 0.0903602i | ||||
\(861\) | 4.61314e6 | 0.212075 | ||||||||
\(862\) | − | 5.79138e6i | − | 0.265469i | ||||||
\(863\) | 2.89194e7i | 1.32179i | 0.750479 | + | 0.660894i | \(0.229823\pi\) | ||||
−0.750479 | + | 0.660894i | \(0.770177\pi\) | |||||||
\(864\) | −1.28675e7 | −0.586422 | ||||||||
\(865\) | 2.91413e7 | − | 4.58133e6i | 1.32425 | − | 0.208186i | ||||
\(866\) | −5.92034e7 | −2.68257 | ||||||||
\(867\) | 1.00174e6i | 0.0452591i | ||||||||
\(868\) | 1.50340e6i | 0.0677289i | ||||||||
\(869\) | −8.65121e6 | −0.388622 | ||||||||
\(870\) | −7.22080e6 | − | 4.59308e7i | −0.323435 | − | 2.05734i | ||||
\(871\) | −705788. | −0.0315231 | ||||||||
\(872\) | − | 1.05832e8i | − | 4.71329i | ||||||
\(873\) | 1.43481e6i | 0.0637174i | ||||||||
\(874\) | −3.88312e7 | −1.71950 | ||||||||
\(875\) | −6.45234e6 | + | 3.25975e6i | −0.284903 | + | 0.143934i | ||||
\(876\) | −3.74125e7 | −1.64724 | ||||||||
\(877\) | − | 2.63977e7i | − | 1.15896i | −0.814988 | − | 0.579478i | \(-0.803257\pi\) | ||
0.814988 | − | 0.579478i | \(-0.196743\pi\) | |||||||
\(878\) | 4.89457e7i | 2.14278i | ||||||||
\(879\) | 1.12903e6 | 0.0492869 | ||||||||
\(880\) | 3.45986e6 | + | 2.20078e7i | 0.150610 | + | 0.958012i | ||||
\(881\) | 1.08347e7 | 0.470304 | 0.235152 | − | 0.971959i | \(-0.424441\pi\) | ||||
0.235152 | + | 0.971959i | \(0.424441\pi\) | |||||||
\(882\) | 1.31474e7i | 0.569072i | ||||||||
\(883\) | 2.45316e7i | 1.05883i | 0.848364 | + | 0.529413i | \(0.177588\pi\) | ||||
−0.848364 | + | 0.529413i | \(0.822412\pi\) | |||||||
\(884\) | 1.30595e6 | 0.0562078 | ||||||||
\(885\) | −2.06112e7 | + | 3.24030e6i | −0.884598 | + | 0.139068i | ||||
\(886\) | −2.07319e7 | −0.887268 | ||||||||
\(887\) | − | 2.84619e7i | − | 1.21466i | −0.794450 | − | 0.607330i | \(-0.792241\pi\) | ||
0.794450 | − | 0.607330i | \(-0.207759\pi\) | |||||||
\(888\) | 7.19647e7i | 3.06258i | ||||||||
\(889\) | 4.64367e6 | 0.197064 | ||||||||
\(890\) | 4.57113e7 | − | 7.18630e6i | 1.93441 | − | 0.304110i | ||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 9.06308e7i | 3.81385i | ||||||||
\(893\) | 2.41127e6i | 0.101185i | ||||||||
\(894\) | 5.16398e7 | 2.16093 | ||||||||
\(895\) | −6.85689e6 | − | 4.36160e7i | −0.286134 | − | 1.82007i | ||||
\(896\) | 1.41855e7 | 0.590304 | ||||||||
\(897\) | − | 311320.i | − | 0.0129189i | ||||||
\(898\) | 2.42765e7i | 1.00460i | ||||||||
\(899\) | −3.73355e6 | −0.154072 | ||||||||
\(900\) | −2.01473e7 | + | 6.49526e6i | −0.829106 | + | 0.267295i | ||||
\(901\) | −1.08274e7 | −0.444338 | ||||||||
\(902\) | − | 1.61164e7i | − | 0.659555i | ||||||
\(903\) | − | 1.00534e6i | − | 0.0410291i | ||||||
\(904\) | 1.32963e8 | 5.41139 | ||||||||
\(905\) | −3.25936e6 | − | 2.07324e7i | −0.132285 | − | 0.841452i | ||||
\(906\) | −1.05745e7 | −0.427995 | ||||||||
\(907\) | − | 1.85629e7i | − | 0.749253i | −0.927176 | − | 0.374626i | \(-0.877771\pi\) | ||
0.927176 | − | 0.374626i | \(-0.122229\pi\) | |||||||
\(908\) | − | 5.31173e7i | − | 2.13807i | ||||||
\(909\) | 225859. | 0.00906625 | ||||||||
\(910\) | −335458. | + | 52737.5i | −0.0134287 | + | 0.00211114i | ||||
\(911\) | 3.93363e7 | 1.57035 | 0.785177 | − | 0.619271i | \(-0.212572\pi\) | ||||
0.785177 | + | 0.619271i | \(0.212572\pi\) | |||||||
\(912\) | 4.22449e7i | 1.68185i | ||||||||
\(913\) | − | 4.05825e6i | − | 0.161125i | ||||||
\(914\) | 1.50935e7 | 0.597617 | ||||||||
\(915\) | 8.88027e6 | − | 1.39607e6i | 0.350650 | − | 0.0551258i | ||||
\(916\) | 5.20861e7 | 2.05108 | ||||||||
\(917\) | − | 1.38545e7i | − | 0.544086i | ||||||
\(918\) | 8.96717e6i | 0.351195i | ||||||||
\(919\) | −2.72458e7 | −1.06417 | −0.532084 | − | 0.846691i | \(-0.678591\pi\) | ||||
−0.532084 | + | 0.846691i | \(0.678591\pi\) | |||||||
\(920\) | 1.22126e7 | + | 7.76834e7i | 0.475708 | + | 3.02593i | ||||
\(921\) | 8.30410e6 | 0.322584 | ||||||||
\(922\) | − | 1.37887e7i | − | 0.534190i | ||||||
\(923\) | 227239.i | 0.00877969i | ||||||||
\(924\) | −3.76864e6 | −0.145213 | ||||||||
\(925\) | 1.38107e7 | + | 4.28387e7i | 0.530715 | + | 1.64620i | ||||
\(926\) | −5.55646e7 | −2.12947 | ||||||||
\(927\) | − | 251642.i | − | 0.00961796i | ||||||
\(928\) | 1.51696e8i | 5.78233i | ||||||||
\(929\) | 2.98863e7 | 1.13614 | 0.568071 | − | 0.822980i | \(-0.307690\pi\) | ||||
0.568071 | + | 0.822980i | \(0.307690\pi\) | |||||||
\(930\) | 365003. | + | 2.32174e6i | 0.0138385 | + | 0.0880252i | ||||
\(931\) | 2.15122e7 | 0.813411 | ||||||||
\(932\) | − | 1.10223e8i | − | 4.15653i | ||||||
\(933\) | − | 1.44122e7i | − | 0.542035i | ||||||
\(934\) | −1.99500e7 | −0.748298 | ||||||||
\(935\) | 7.64371e6 | − | 1.20167e6i | 0.285940 | − | 0.0449528i | ||||
\(936\) | −613880. | −0.0229031 | ||||||||
\(937\) | 3.91979e7i | 1.45852i | 0.684234 | + | 0.729262i | \(0.260137\pi\) | ||||
−0.684234 | + | 0.729262i | \(0.739863\pi\) | |||||||
\(938\) | 2.30055e7i | 0.853737i | ||||||||
\(939\) | −1.59414e6 | −0.0590014 | ||||||||
\(940\) | 7.81373e6 | − | 1.22840e6i | 0.288429 | − | 0.0453441i | ||||
\(941\) | 2.33041e7 | 0.857941 | 0.428971 | − | 0.903318i | \(-0.358876\pi\) | ||||
0.428971 | + | 0.903318i | \(0.358876\pi\) | |||||||
\(942\) | 3.51069e7i | 1.28904i | ||||||||
\(943\) | − | 3.13859e7i | − | 1.14936i | ||||||
\(944\) | 1.36586e8 | 4.98858 | ||||||||
\(945\) | −261901. | − | 1.66592e6i | −0.00954019 | − | 0.0606842i | ||||
\(946\) | −3.51223e6 | −0.127601 | ||||||||
\(947\) | − | 2.41038e7i | − | 0.873394i | −0.899609 | − | 0.436697i | \(-0.856148\pi\) | ||
0.899609 | − | 0.436697i | \(-0.143852\pi\) | |||||||
\(948\) | 5.38130e7i | 1.94476i | ||||||||
\(949\) | −678578. | −0.0244587 | ||||||||
\(950\) | 1.46945e7 | + | 4.55799e7i | 0.528256 | + | 1.63857i | ||||
\(951\) | 5.20428e6 | 0.186599 | ||||||||
\(952\) | − | 2.62796e7i | − | 0.939782i | ||||||
\(953\) | 3.46893e7i | 1.23727i | 0.785680 | + | 0.618633i | \(0.212313\pi\) | ||||
−0.785680 | + | 0.618633i | \(0.787687\pi\) | |||||||
\(954\) | 8.24416e6 | 0.293275 | ||||||||
\(955\) | 2.94441e6 | + | 1.87291e7i | 0.104469 | + | 0.664520i | ||||
\(956\) | −2.00732e7 | −0.710349 | ||||||||
\(957\) | − | 9.35909e6i | − | 0.330334i | ||||||
\(958\) | 2.98601e7i | 1.05118i | ||||||||
\(959\) | −37819.0 | −0.00132789 | ||||||||
\(960\) | 4.19511e7 | − | 6.59515e6i | 1.46915 | − | 0.230965i | ||||
\(961\) | −2.84404e7 | −0.993408 | ||||||||
\(962\) | 2.11431e6i | 0.0736598i | ||||||||
\(963\) | − | 1.74954e6i | − | 0.0607936i | ||||||
\(964\) | −5.51133e7 | −1.91013 | ||||||||
\(965\) | −1.98438e7 | + | 3.11965e6i | −0.685973 | + | 0.107842i | ||||
\(966\) | −1.01476e7 | −0.349882 | ||||||||
\(967\) | − | 3.99380e7i | − | 1.37347i | −0.726906 | − | 0.686737i | \(-0.759042\pi\) | ||
0.726906 | − | 0.686737i | \(-0.240958\pi\) | |||||||
\(968\) | 8.12813e6i | 0.278806i | ||||||||
\(969\) | 1.46724e7 | 0.501986 | ||||||||
\(970\) | −1.65366e6 | − | 1.05187e7i | −0.0564308 | − | 0.358951i | ||||
\(971\) | −3.25227e6 | −0.110698 | −0.0553488 | − | 0.998467i | \(-0.517627\pi\) | ||||
−0.0553488 | + | 0.998467i | \(0.517627\pi\) | |||||||
\(972\) | − | 4.93817e6i | − | 0.167649i | ||||||
\(973\) | 1.11876e7i | 0.378841i | ||||||||
\(974\) | −9.19839e7 | −3.10681 | ||||||||
\(975\) | −365426. | + | 117809.i | −0.0123108 | + | 0.00396888i | ||||
\(976\) | −5.88476e7 | −1.97744 | ||||||||
\(977\) | − | 2.38653e7i | − | 0.799892i | −0.916539 | − | 0.399946i | \(-0.869029\pi\) | ||
0.916539 | − | 0.399946i | \(-0.130971\pi\) | |||||||
\(978\) | 3.28108e7i | 1.09691i | ||||||||
\(979\) | 9.31437e6 | 0.310597 | ||||||||
\(980\) | −1.09592e7 | − | 6.97104e7i | −0.364514 | − | 2.31864i | ||||
\(981\) | 1.54412e7 | 0.512281 | ||||||||
\(982\) | 1.00473e8i | 3.32485i | ||||||||
\(983\) | − | 2.22870e7i | − | 0.735645i | −0.929896 | − | 0.367823i | \(-0.880103\pi\) | ||
0.929896 | − | 0.367823i | \(-0.119897\pi\) | |||||||
\(984\) | −6.18888e7 | −2.03763 | ||||||||
\(985\) | −3.33576e7 | + | 5.24417e6i | −1.09548 | + | 0.172221i | ||||
\(986\) | 1.05714e8 | 3.46291 | ||||||||
\(987\) | 630128.i | 0.0205890i | ||||||||
\(988\) | 1.62703e6i | 0.0530277i | ||||||||
\(989\) | −6.83991e6 | −0.222362 | ||||||||
\(990\) | −5.82004e6 | + | 914971.i | −0.188729 | + | 0.0296701i | ||||
\(991\) | −1.74834e7 | −0.565513 | −0.282756 | − | 0.959192i | \(-0.591249\pi\) | ||||
−0.282756 | + | 0.959192i | \(0.591249\pi\) | |||||||
\(992\) | − | 7.66803e6i | − | 0.247403i | ||||||
\(993\) | − | 2.91391e7i | − | 0.937784i | ||||||
\(994\) | 7.40697e6 | 0.237780 | ||||||||
\(995\) | 8.98084e6 | + | 5.71262e7i | 0.287580 | + | 1.82927i | ||||
\(996\) | −2.52435e7 | −0.806308 | ||||||||
\(997\) | − | 4.50302e7i | − | 1.43472i | −0.696705 | − | 0.717358i | \(-0.745351\pi\) | ||
0.696705 | − | 0.717358i | \(-0.254649\pi\) | |||||||
\(998\) | 1.11437e8i | 3.54162i | ||||||||
\(999\) | −1.04999e7 | −0.332868 |
(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 | 165.6.c.b.34.1 | ✓ | 26 | |
5.2 | odd | 4 | 825.6.a.y.1.13 | 13 | |||
5.3 | odd | 4 | 825.6.a.v.1.1 | 13 | |||
5.4 | even | 2 | inner | 165.6.c.b.34.26 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.1 | ✓ | 26 | 1.1 | even | 1 | trivial | |
165.6.c.b.34.26 | yes | 26 | 5.4 | even | 2 | inner | |
825.6.a.v.1.1 | 13 | 5.3 | odd | 4 | |||
825.6.a.y.1.13 | 13 | 5.2 | odd | 4 |