Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(1,165)]
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, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.4633302691\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 143x^{3} + 71x^{2} + 4216x - 3740 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(5.93734\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.93734 | −1.04958 | −0.524792 | − | 0.851230i | \(-0.675857\pi\) | ||||
−0.524792 | + | 0.851230i | \(0.675857\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 3.25206 | 0.101627 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 53.4361 | 0.605978 | ||||||||
\(7\) | −105.553 | −0.814191 | −0.407096 | − | 0.913386i | \(-0.633458\pi\) | ||||
−0.407096 | + | 0.913386i | \(0.633458\pi\) | |||||||
\(8\) | 170.686 | 0.942918 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 148.434 | 0.469388 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −29.2685 | −0.0586742 | ||||||||
\(13\) | 124.247 | 0.203906 | 0.101953 | − | 0.994789i | \(-0.467491\pi\) | ||||
0.101953 | + | 0.994789i | \(0.467491\pi\) | |||||||
\(14\) | 626.706 | 0.854562 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | −1117.49 | −1.09130 | ||||||||
\(17\) | 1766.45 | 1.48245 | 0.741224 | − | 0.671257i | \(-0.234245\pi\) | ||||
0.741224 | + | 0.671257i | \(0.234245\pi\) | |||||||
\(18\) | −480.925 | −0.349861 | ||||||||
\(19\) | 1998.70 | 1.27017 | 0.635087 | − | 0.772441i | \(-0.280964\pi\) | ||||
0.635087 | + | 0.772441i | \(0.280964\pi\) | |||||||
\(20\) | −81.3014 | −0.0454489 | ||||||||
\(21\) | 949.979 | 0.470073 | ||||||||
\(22\) | 718.419 | 0.316462 | ||||||||
\(23\) | −2546.65 | −1.00381 | −0.501903 | − | 0.864924i | \(-0.667367\pi\) | ||||
−0.501903 | + | 0.864924i | \(0.667367\pi\) | |||||||
\(24\) | −1536.18 | −0.544394 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −737.700 | −0.214016 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −343.265 | −0.0827436 | ||||||||
\(29\) | −320.493 | −0.0707659 | −0.0353829 | − | 0.999374i | \(-0.511265\pi\) | ||||
−0.0353829 | + | 0.999374i | \(0.511265\pi\) | |||||||
\(30\) | −1335.90 | −0.271001 | ||||||||
\(31\) | 8554.39 | 1.59876 | 0.799382 | − | 0.600823i | \(-0.205160\pi\) | ||||
0.799382 | + | 0.600823i | \(0.205160\pi\) | |||||||
\(32\) | 1172.96 | 0.202492 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | −10488.0 | −1.55595 | ||||||||
\(35\) | 2638.83 | 0.364117 | ||||||||
\(36\) | 263.417 | 0.0338756 | ||||||||
\(37\) | 4126.28 | 0.495513 | 0.247756 | − | 0.968822i | \(-0.420307\pi\) | ||||
0.247756 | + | 0.968822i | \(0.420307\pi\) | |||||||
\(38\) | −11867.0 | −1.33315 | ||||||||
\(39\) | −1118.23 | −0.117725 | ||||||||
\(40\) | −4267.16 | −0.421686 | ||||||||
\(41\) | 4531.80 | 0.421028 | 0.210514 | − | 0.977591i | \(-0.432486\pi\) | ||||
0.210514 | + | 0.977591i | \(0.432486\pi\) | |||||||
\(42\) | −5640.35 | −0.493382 | ||||||||
\(43\) | −13412.4 | −1.10620 | −0.553100 | − | 0.833115i | \(-0.686555\pi\) | ||||
−0.553100 | + | 0.833115i | \(0.686555\pi\) | |||||||
\(44\) | −393.499 | −0.0306416 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | 15120.3 | 1.05358 | ||||||||
\(47\) | −24103.2 | −1.59159 | −0.795793 | − | 0.605569i | \(-0.792945\pi\) | ||||
−0.795793 | + | 0.605569i | \(0.792945\pi\) | |||||||
\(48\) | 10057.4 | 0.630062 | ||||||||
\(49\) | −5665.52 | −0.337093 | ||||||||
\(50\) | −3710.84 | −0.209917 | ||||||||
\(51\) | −15898.1 | −0.855892 | ||||||||
\(52\) | 404.060 | 0.0207223 | ||||||||
\(53\) | −28493.8 | −1.39335 | −0.696675 | − | 0.717387i | \(-0.745338\pi\) | ||||
−0.696675 | + | 0.717387i | \(0.745338\pi\) | |||||||
\(54\) | 4328.32 | 0.201993 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | −18016.5 | −0.767716 | ||||||||
\(57\) | −17988.3 | −0.733335 | ||||||||
\(58\) | 1902.88 | 0.0742747 | ||||||||
\(59\) | −18203.6 | −0.680813 | −0.340407 | − | 0.940278i | \(-0.610565\pi\) | ||||
−0.340407 | + | 0.940278i | \(0.610565\pi\) | |||||||
\(60\) | 731.713 | 0.0262399 | ||||||||
\(61\) | 4696.58 | 0.161606 | 0.0808030 | − | 0.996730i | \(-0.474252\pi\) | ||||
0.0808030 | + | 0.996730i | \(0.474252\pi\) | |||||||
\(62\) | −50790.3 | −1.67804 | ||||||||
\(63\) | −8549.81 | −0.271397 | ||||||||
\(64\) | 28795.4 | 0.878767 | ||||||||
\(65\) | −3106.19 | −0.0911893 | ||||||||
\(66\) | −6465.77 | −0.182709 | ||||||||
\(67\) | 5374.30 | 0.146263 | 0.0731315 | − | 0.997322i | \(-0.476701\pi\) | ||||
0.0731315 | + | 0.997322i | \(0.476701\pi\) | |||||||
\(68\) | 5744.60 | 0.150656 | ||||||||
\(69\) | 22919.9 | 0.579548 | ||||||||
\(70\) | −15667.6 | −0.382172 | ||||||||
\(71\) | −16054.9 | −0.377974 | −0.188987 | − | 0.981980i | \(-0.560520\pi\) | ||||
−0.188987 | + | 0.981980i | \(0.560520\pi\) | |||||||
\(72\) | 13825.6 | 0.314306 | ||||||||
\(73\) | 26176.0 | 0.574904 | 0.287452 | − | 0.957795i | \(-0.407192\pi\) | ||||
0.287452 | + | 0.957795i | \(0.407192\pi\) | |||||||
\(74\) | −24499.2 | −0.520082 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | 6499.88 | 0.129084 | ||||||||
\(77\) | 12771.9 | 0.245488 | ||||||||
\(78\) | 6639.30 | 0.123562 | ||||||||
\(79\) | −21818.8 | −0.393336 | −0.196668 | − | 0.980470i | \(-0.563012\pi\) | ||||
−0.196668 | + | 0.980470i | \(0.563012\pi\) | |||||||
\(80\) | 27937.2 | 0.488044 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −26906.8 | −0.441904 | ||||||||
\(83\) | −65176.7 | −1.03848 | −0.519239 | − | 0.854629i | \(-0.673784\pi\) | ||||
−0.519239 | + | 0.854629i | \(0.673784\pi\) | |||||||
\(84\) | 3089.39 | 0.0477720 | ||||||||
\(85\) | −44161.3 | −0.662971 | ||||||||
\(86\) | 79633.8 | 1.16105 | ||||||||
\(87\) | 2884.44 | 0.0408567 | ||||||||
\(88\) | −20653.1 | −0.284301 | ||||||||
\(89\) | 28370.0 | 0.379651 | 0.189826 | − | 0.981818i | \(-0.439208\pi\) | ||||
0.189826 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(90\) | 12023.1 | 0.156463 | ||||||||
\(91\) | −13114.7 | −0.166018 | ||||||||
\(92\) | −8281.86 | −0.102014 | ||||||||
\(93\) | −76989.5 | −0.923047 | ||||||||
\(94\) | 143109. | 1.67050 | ||||||||
\(95\) | −49967.5 | −0.568039 | ||||||||
\(96\) | −10556.6 | −0.116909 | ||||||||
\(97\) | −51795.2 | −0.558934 | −0.279467 | − | 0.960155i | \(-0.590158\pi\) | ||||
−0.279467 | + | 0.960155i | \(0.590158\pi\) | |||||||
\(98\) | 33638.1 | 0.353807 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 2032.54 | 0.0203254 | ||||||||
\(101\) | 152512. | 1.48765 | 0.743823 | − | 0.668376i | \(-0.233010\pi\) | ||||
0.743823 | + | 0.668376i | \(0.233010\pi\) | |||||||
\(102\) | 94392.3 | 0.898331 | ||||||||
\(103\) | 190367. | 1.76807 | 0.884035 | − | 0.467420i | \(-0.154816\pi\) | ||||
0.884035 | + | 0.467420i | \(0.154816\pi\) | |||||||
\(104\) | 21207.4 | 0.192266 | ||||||||
\(105\) | −23749.5 | −0.210223 | ||||||||
\(106\) | 169177. | 1.46244 | ||||||||
\(107\) | −68674.3 | −0.579875 | −0.289938 | − | 0.957046i | \(-0.593635\pi\) | ||||
−0.289938 | + | 0.957046i | \(0.593635\pi\) | |||||||
\(108\) | −2370.75 | −0.0195581 | ||||||||
\(109\) | 29463.1 | 0.237526 | 0.118763 | − | 0.992923i | \(-0.462107\pi\) | ||||
0.118763 | + | 0.992923i | \(0.462107\pi\) | |||||||
\(110\) | −17960.5 | −0.141526 | ||||||||
\(111\) | −37136.6 | −0.286084 | ||||||||
\(112\) | 117955. | 0.888526 | ||||||||
\(113\) | −99307.3 | −0.731619 | −0.365810 | − | 0.930690i | \(-0.619208\pi\) | ||||
−0.365810 | + | 0.930690i | \(0.619208\pi\) | |||||||
\(114\) | 106803. | 0.769697 | ||||||||
\(115\) | 63666.3 | 0.448916 | ||||||||
\(116\) | −1042.26 | −0.00719170 | ||||||||
\(117\) | 10064.0 | 0.0679685 | ||||||||
\(118\) | 108081. | 0.714571 | ||||||||
\(119\) | −186455. | −1.20700 | ||||||||
\(120\) | 38404.4 | 0.243460 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −27885.2 | −0.169619 | ||||||||
\(123\) | −40786.2 | −0.243080 | ||||||||
\(124\) | 27819.3 | 0.162477 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 50763.2 | 0.284854 | ||||||||
\(127\) | 192783. | 1.06062 | 0.530308 | − | 0.847805i | \(-0.322076\pi\) | ||||
0.530308 | + | 0.847805i | \(0.322076\pi\) | |||||||
\(128\) | −208503. | −1.12483 | ||||||||
\(129\) | 120711. | 0.638665 | ||||||||
\(130\) | 18442.5 | 0.0957109 | ||||||||
\(131\) | 194663. | 0.991074 | 0.495537 | − | 0.868587i | \(-0.334971\pi\) | ||||
0.495537 | + | 0.868587i | \(0.334971\pi\) | |||||||
\(132\) | 3541.49 | 0.0176909 | ||||||||
\(133\) | −210969. | −1.03416 | ||||||||
\(134\) | −31909.1 | −0.153515 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | 301509. | 1.39783 | ||||||||
\(137\) | −219837. | −1.00069 | −0.500345 | − | 0.865826i | \(-0.666793\pi\) | ||||
−0.500345 | + | 0.865826i | \(0.666793\pi\) | |||||||
\(138\) | −136083. | −0.608284 | ||||||||
\(139\) | −60583.0 | −0.265959 | −0.132979 | − | 0.991119i | \(-0.542454\pi\) | ||||
−0.132979 | + | 0.991119i | \(0.542454\pi\) | |||||||
\(140\) | 8581.63 | 0.0370041 | ||||||||
\(141\) | 216929. | 0.918902 | ||||||||
\(142\) | 95323.4 | 0.396715 | ||||||||
\(143\) | −15033.9 | −0.0614798 | ||||||||
\(144\) | −90516.7 | −0.363766 | ||||||||
\(145\) | 8012.33 | 0.0316475 | ||||||||
\(146\) | −155416. | −0.603410 | ||||||||
\(147\) | 50989.7 | 0.194621 | ||||||||
\(148\) | 13418.9 | 0.0503573 | ||||||||
\(149\) | 61572.6 | 0.227207 | 0.113604 | − | 0.993526i | \(-0.463761\pi\) | ||||
0.113604 | + | 0.993526i | \(0.463761\pi\) | |||||||
\(150\) | 33397.6 | 0.121196 | ||||||||
\(151\) | −194637. | −0.694676 | −0.347338 | − | 0.937740i | \(-0.612914\pi\) | ||||
−0.347338 | + | 0.937740i | \(0.612914\pi\) | |||||||
\(152\) | 341151. | 1.19767 | ||||||||
\(153\) | 143083. | 0.494150 | ||||||||
\(154\) | −75831.4 | −0.257660 | ||||||||
\(155\) | −213860. | −0.714989 | ||||||||
\(156\) | −3636.54 | −0.0119640 | ||||||||
\(157\) | 76011.6 | 0.246111 | 0.123055 | − | 0.992400i | \(-0.460731\pi\) | ||||
0.123055 | + | 0.992400i | \(0.460731\pi\) | |||||||
\(158\) | 129546. | 0.412839 | ||||||||
\(159\) | 256444. | 0.804451 | ||||||||
\(160\) | −29323.9 | −0.0905570 | ||||||||
\(161\) | 268807. | 0.817290 | ||||||||
\(162\) | −38954.9 | −0.116620 | ||||||||
\(163\) | −498250. | −1.46885 | −0.734426 | − | 0.678689i | \(-0.762548\pi\) | ||||
−0.734426 | + | 0.678689i | \(0.762548\pi\) | |||||||
\(164\) | 14737.7 | 0.0427877 | ||||||||
\(165\) | −27225.0 | −0.0778499 | ||||||||
\(166\) | 386976. | 1.08997 | ||||||||
\(167\) | −650928. | −1.80610 | −0.903050 | − | 0.429536i | \(-0.858677\pi\) | ||||
−0.903050 | + | 0.429536i | \(0.858677\pi\) | |||||||
\(168\) | 162149. | 0.443241 | ||||||||
\(169\) | −355856. | −0.958423 | ||||||||
\(170\) | 262201. | 0.695844 | ||||||||
\(171\) | 161895. | 0.423391 | ||||||||
\(172\) | −43617.7 | −0.112420 | ||||||||
\(173\) | −400605. | −1.01766 | −0.508828 | − | 0.860868i | \(-0.669921\pi\) | ||||
−0.508828 | + | 0.860868i | \(0.669921\pi\) | |||||||
\(174\) | −17125.9 | −0.0428825 | ||||||||
\(175\) | −65970.8 | −0.162838 | ||||||||
\(176\) | 135216. | 0.329039 | ||||||||
\(177\) | 163833. | 0.393068 | ||||||||
\(178\) | −168443. | −0.398476 | ||||||||
\(179\) | −820215. | −1.91335 | −0.956677 | − | 0.291151i | \(-0.905962\pi\) | ||||
−0.956677 | + | 0.291151i | \(0.905962\pi\) | |||||||
\(180\) | −6585.41 | −0.0151496 | ||||||||
\(181\) | 639863. | 1.45175 | 0.725873 | − | 0.687828i | \(-0.241436\pi\) | ||||
0.725873 | + | 0.687828i | \(0.241436\pi\) | |||||||
\(182\) | 77866.6 | 0.174250 | ||||||||
\(183\) | −42269.2 | −0.0933033 | ||||||||
\(184\) | −434679. | −0.946507 | ||||||||
\(185\) | −103157. | −0.221600 | ||||||||
\(186\) | 457113. | 0.968816 | ||||||||
\(187\) | −213741. | −0.446975 | ||||||||
\(188\) | −78384.9 | −0.161748 | ||||||||
\(189\) | 76948.3 | 0.156691 | ||||||||
\(190\) | 296674. | 0.596205 | ||||||||
\(191\) | 707635. | 1.40354 | 0.701772 | − | 0.712402i | \(-0.252393\pi\) | ||||
0.701772 | + | 0.712402i | \(0.252393\pi\) | |||||||
\(192\) | −259159. | −0.507356 | ||||||||
\(193\) | −993614. | −1.92010 | −0.960051 | − | 0.279825i | \(-0.909724\pi\) | ||||
−0.960051 | + | 0.279825i | \(0.909724\pi\) | |||||||
\(194\) | 307526. | 0.586648 | ||||||||
\(195\) | 27955.7 | 0.0526482 | ||||||||
\(196\) | −18424.6 | −0.0342576 | ||||||||
\(197\) | −661275. | −1.21399 | −0.606997 | − | 0.794704i | \(-0.707626\pi\) | ||||
−0.606997 | + | 0.794704i | \(0.707626\pi\) | |||||||
\(198\) | 58191.9 | 0.105487 | ||||||||
\(199\) | −414819. | −0.742551 | −0.371276 | − | 0.928523i | \(-0.621080\pi\) | ||||
−0.371276 | + | 0.928523i | \(0.621080\pi\) | |||||||
\(200\) | 106679. | 0.188584 | ||||||||
\(201\) | −48368.7 | −0.0844450 | ||||||||
\(202\) | −905514. | −1.56141 | ||||||||
\(203\) | 33829.1 | 0.0576169 | ||||||||
\(204\) | −51701.4 | −0.0869815 | ||||||||
\(205\) | −113295. | −0.188289 | ||||||||
\(206\) | −1.13028e6 | −1.85574 | ||||||||
\(207\) | −206279. | −0.334602 | ||||||||
\(208\) | −138845. | −0.222522 | ||||||||
\(209\) | −241842. | −0.382972 | ||||||||
\(210\) | 141009. | 0.220647 | ||||||||
\(211\) | −519315. | −0.803017 | −0.401509 | − | 0.915855i | \(-0.631514\pi\) | ||||
−0.401509 | + | 0.915855i | \(0.631514\pi\) | |||||||
\(212\) | −92663.3 | −0.141602 | ||||||||
\(213\) | 144494. | 0.218223 | ||||||||
\(214\) | 407743. | 0.608628 | ||||||||
\(215\) | 335309. | 0.494708 | ||||||||
\(216\) | −124430. | −0.181465 | ||||||||
\(217\) | −902943. | −1.30170 | ||||||||
\(218\) | −174933. | −0.249304 | ||||||||
\(219\) | −235584. | −0.331921 | ||||||||
\(220\) | 9837.47 | 0.0137033 | ||||||||
\(221\) | 219477. | 0.302279 | ||||||||
\(222\) | 220492. | 0.300270 | ||||||||
\(223\) | 1.10323e6 | 1.48561 | 0.742804 | − | 0.669509i | \(-0.233495\pi\) | ||||
0.742804 | + | 0.669509i | \(0.233495\pi\) | |||||||
\(224\) | −123809. | −0.164867 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 589622. | 0.767896 | ||||||||
\(227\) | 1.07714e6 | 1.38742 | 0.693712 | − | 0.720253i | \(-0.255974\pi\) | ||||
0.693712 | + | 0.720253i | \(0.255974\pi\) | |||||||
\(228\) | −58498.9 | −0.0745265 | ||||||||
\(229\) | 669513. | 0.843666 | 0.421833 | − | 0.906674i | \(-0.361387\pi\) | ||||
0.421833 | + | 0.906674i | \(0.361387\pi\) | |||||||
\(230\) | −378009. | −0.471175 | ||||||||
\(231\) | −114947. | −0.141732 | ||||||||
\(232\) | −54703.8 | −0.0667264 | ||||||||
\(233\) | 100605. | 0.121403 | 0.0607016 | − | 0.998156i | \(-0.480666\pi\) | ||||
0.0607016 | + | 0.998156i | \(0.480666\pi\) | |||||||
\(234\) | −59753.7 | −0.0713387 | ||||||||
\(235\) | 602580. | 0.711779 | ||||||||
\(236\) | −59199.2 | −0.0691889 | ||||||||
\(237\) | 196370. | 0.227093 | ||||||||
\(238\) | 1.10705e6 | 1.26684 | ||||||||
\(239\) | −867105. | −0.981921 | −0.490961 | − | 0.871182i | \(-0.663354\pi\) | ||||
−0.490961 | + | 0.871182i | \(0.663354\pi\) | |||||||
\(240\) | −251435. | −0.281772 | ||||||||
\(241\) | −618174. | −0.685595 | −0.342798 | − | 0.939409i | \(-0.611375\pi\) | ||||
−0.342798 | + | 0.939409i | \(0.611375\pi\) | |||||||
\(242\) | −86928.7 | −0.0954167 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 15273.6 | 0.0164235 | ||||||||
\(245\) | 141638. | 0.150752 | ||||||||
\(246\) | 242161. | 0.255133 | ||||||||
\(247\) | 248333. | 0.258995 | ||||||||
\(248\) | 1.46012e6 | 1.50750 | ||||||||
\(249\) | 586590. | 0.599565 | ||||||||
\(250\) | 92771.0 | 0.0938777 | ||||||||
\(251\) | 630505. | 0.631691 | 0.315845 | − | 0.948811i | \(-0.397712\pi\) | ||||
0.315845 | + | 0.948811i | \(0.397712\pi\) | |||||||
\(252\) | −27804.5 | −0.0275812 | ||||||||
\(253\) | 308145. | 0.302659 | ||||||||
\(254\) | −1.14462e6 | −1.11321 | ||||||||
\(255\) | 397452. | 0.382767 | ||||||||
\(256\) | 316500. | 0.301838 | ||||||||
\(257\) | 475889. | 0.449441 | 0.224720 | − | 0.974423i | \(-0.427853\pi\) | ||||
0.224720 | + | 0.974423i | \(0.427853\pi\) | |||||||
\(258\) | −716704. | −0.670333 | ||||||||
\(259\) | −435543. | −0.403442 | ||||||||
\(260\) | −10101.5 | −0.00926728 | ||||||||
\(261\) | −25959.9 | −0.0235886 | ||||||||
\(262\) | −1.15578e6 | −1.04022 | ||||||||
\(263\) | 415568. | 0.370470 | 0.185235 | − | 0.982694i | \(-0.440695\pi\) | ||||
0.185235 | + | 0.982694i | \(0.440695\pi\) | |||||||
\(264\) | 185878. | 0.164141 | ||||||||
\(265\) | 712344. | 0.623125 | ||||||||
\(266\) | 1.25260e6 | 1.08544 | ||||||||
\(267\) | −255330. | −0.219192 | ||||||||
\(268\) | 17477.5 | 0.0148642 | ||||||||
\(269\) | −1.86987e6 | −1.57554 | −0.787772 | − | 0.615967i | \(-0.788765\pi\) | ||||
−0.787772 | + | 0.615967i | \(0.788765\pi\) | |||||||
\(270\) | −108208. | −0.0903338 | ||||||||
\(271\) | −1.23898e6 | −1.02481 | −0.512404 | − | 0.858744i | \(-0.671245\pi\) | ||||
−0.512404 | + | 0.858744i | \(0.671245\pi\) | |||||||
\(272\) | −1.97399e6 | −1.61779 | ||||||||
\(273\) | 118032. | 0.0958506 | ||||||||
\(274\) | 1.30525e6 | 1.05031 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | 74536.7 | 0.0588976 | ||||||||
\(277\) | 846334. | 0.662739 | 0.331370 | − | 0.943501i | \(-0.392489\pi\) | ||||
0.331370 | + | 0.943501i | \(0.392489\pi\) | |||||||
\(278\) | 359702. | 0.279146 | ||||||||
\(279\) | 692905. | 0.532922 | ||||||||
\(280\) | 450413. | 0.343333 | ||||||||
\(281\) | −1.07789e6 | −0.814347 | −0.407174 | − | 0.913351i | \(-0.633486\pi\) | ||||
−0.407174 | + | 0.913351i | \(0.633486\pi\) | |||||||
\(282\) | −1.28798e6 | −0.964465 | ||||||||
\(283\) | −2.59466e6 | −1.92581 | −0.962906 | − | 0.269836i | \(-0.913031\pi\) | ||||
−0.962906 | + | 0.269836i | \(0.913031\pi\) | |||||||
\(284\) | −52211.4 | −0.0384122 | ||||||||
\(285\) | 449707. | 0.327957 | ||||||||
\(286\) | 89261.7 | 0.0645283 | ||||||||
\(287\) | −478346. | −0.342797 | ||||||||
\(288\) | 95009.5 | 0.0674972 | ||||||||
\(289\) | 1.70050e6 | 1.19765 | ||||||||
\(290\) | −47572.0 | −0.0332167 | ||||||||
\(291\) | 466157. | 0.322700 | ||||||||
\(292\) | 85125.7 | 0.0584256 | ||||||||
\(293\) | −155161. | −0.105588 | −0.0527939 | − | 0.998605i | \(-0.516813\pi\) | ||||
−0.0527939 | + | 0.998605i | \(0.516813\pi\) | |||||||
\(294\) | −302743. | −0.204271 | ||||||||
\(295\) | 455091. | 0.304469 | ||||||||
\(296\) | 704301. | 0.467228 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | −365578. | −0.238473 | ||||||||
\(299\) | −316415. | −0.204682 | ||||||||
\(300\) | −18292.8 | −0.0117348 | ||||||||
\(301\) | 1.41572e6 | 0.900659 | ||||||||
\(302\) | 1.15562e6 | 0.729121 | ||||||||
\(303\) | −1.37261e6 | −0.858893 | ||||||||
\(304\) | −2.23352e6 | −1.38614 | ||||||||
\(305\) | −117415. | −0.0722724 | ||||||||
\(306\) | −849531. | −0.518652 | ||||||||
\(307\) | −1.94896e6 | −1.18020 | −0.590102 | − | 0.807329i | \(-0.700912\pi\) | ||||
−0.590102 | + | 0.807329i | \(0.700912\pi\) | |||||||
\(308\) | 41535.1 | 0.0249481 | ||||||||
\(309\) | −1.71331e6 | −1.02080 | ||||||||
\(310\) | 1.26976e6 | 0.750441 | ||||||||
\(311\) | 853359. | 0.500300 | 0.250150 | − | 0.968207i | \(-0.419520\pi\) | ||||
0.250150 | + | 0.968207i | \(0.419520\pi\) | |||||||
\(312\) | −190866. | −0.111005 | ||||||||
\(313\) | 594619. | 0.343066 | 0.171533 | − | 0.985178i | \(-0.445128\pi\) | ||||
0.171533 | + | 0.985178i | \(0.445128\pi\) | |||||||
\(314\) | −451307. | −0.258314 | ||||||||
\(315\) | 213745. | 0.121372 | ||||||||
\(316\) | −70956.1 | −0.0399735 | ||||||||
\(317\) | 3.25318e6 | 1.81827 | 0.909137 | − | 0.416497i | \(-0.136743\pi\) | ||||
0.909137 | + | 0.416497i | \(0.136743\pi\) | |||||||
\(318\) | −1.52260e6 | −0.844339 | ||||||||
\(319\) | 38779.7 | 0.0213367 | ||||||||
\(320\) | −719886. | −0.392996 | ||||||||
\(321\) | 618069. | 0.334791 | ||||||||
\(322\) | −1.59600e6 | −0.857815 | ||||||||
\(323\) | 3.53061e6 | 1.88297 | ||||||||
\(324\) | 21336.7 | 0.0112919 | ||||||||
\(325\) | 77654.6 | 0.0407811 | ||||||||
\(326\) | 2.95828e6 | 1.54168 | ||||||||
\(327\) | −265168. | −0.137136 | ||||||||
\(328\) | 773516. | 0.396995 | ||||||||
\(329\) | 2.54417e6 | 1.29585 | ||||||||
\(330\) | 161644. | 0.0817100 | ||||||||
\(331\) | −2.05862e6 | −1.03278 | −0.516389 | − | 0.856354i | \(-0.672724\pi\) | ||||
−0.516389 | + | 0.856354i | \(0.672724\pi\) | |||||||
\(332\) | −211958. | −0.105537 | ||||||||
\(333\) | 334229. | 0.165171 | ||||||||
\(334\) | 3.86478e6 | 1.89565 | ||||||||
\(335\) | −134357. | −0.0654108 | ||||||||
\(336\) | −1.06159e6 | −0.512991 | ||||||||
\(337\) | 87610.8 | 0.0420226 | 0.0210113 | − | 0.999779i | \(-0.493311\pi\) | ||||
0.0210113 | + | 0.999779i | \(0.493311\pi\) | |||||||
\(338\) | 2.11284e6 | 1.00595 | ||||||||
\(339\) | 893766. | 0.422400 | ||||||||
\(340\) | −143615. | −0.0673756 | ||||||||
\(341\) | −1.03508e6 | −0.482046 | ||||||||
\(342\) | −961224. | −0.444385 | ||||||||
\(343\) | 2.37205e6 | 1.08865 | ||||||||
\(344\) | −2.28931e6 | −1.04306 | ||||||||
\(345\) | −572997. | −0.259182 | ||||||||
\(346\) | 2.37853e6 | 1.06812 | ||||||||
\(347\) | −3.19161e6 | −1.42294 | −0.711470 | − | 0.702716i | \(-0.751970\pi\) | ||||
−0.711470 | + | 0.702716i | \(0.751970\pi\) | |||||||
\(348\) | 9380.36 | 0.00415213 | ||||||||
\(349\) | −1.36137e6 | −0.598293 | −0.299146 | − | 0.954207i | \(-0.596702\pi\) | ||||
−0.299146 | + | 0.954207i | \(0.596702\pi\) | |||||||
\(350\) | 391691. | 0.170912 | ||||||||
\(351\) | −90576.4 | −0.0392416 | ||||||||
\(352\) | −141928. | −0.0610535 | ||||||||
\(353\) | −1.84373e6 | −0.787517 | −0.393758 | − | 0.919214i | \(-0.628825\pi\) | ||||
−0.393758 | + | 0.919214i | \(0.628825\pi\) | |||||||
\(354\) | −972731. | −0.412558 | ||||||||
\(355\) | 401372. | 0.169035 | ||||||||
\(356\) | 92261.0 | 0.0385827 | ||||||||
\(357\) | 1.67809e6 | 0.696860 | ||||||||
\(358\) | 4.86990e6 | 2.00823 | ||||||||
\(359\) | −345148. | −0.141341 | −0.0706707 | − | 0.997500i | \(-0.522514\pi\) | ||||
−0.0706707 | + | 0.997500i | \(0.522514\pi\) | |||||||
\(360\) | −345640. | −0.140562 | ||||||||
\(361\) | 1.51869e6 | 0.613342 | ||||||||
\(362\) | −3.79909e6 | −1.52373 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −42649.8 | −0.0168719 | ||||||||
\(365\) | −654399. | −0.257105 | ||||||||
\(366\) | 250967. | 0.0979296 | ||||||||
\(367\) | 810586. | 0.314148 | 0.157074 | − | 0.987587i | \(-0.449794\pi\) | ||||
0.157074 | + | 0.987587i | \(0.449794\pi\) | |||||||
\(368\) | 2.84586e6 | 1.09545 | ||||||||
\(369\) | 367075. | 0.140343 | ||||||||
\(370\) | 612479. | 0.232588 | ||||||||
\(371\) | 3.00761e6 | 1.13445 | ||||||||
\(372\) | −250374. | −0.0938063 | ||||||||
\(373\) | −637008. | −0.237068 | −0.118534 | − | 0.992950i | \(-0.537819\pi\) | ||||
−0.118534 | + | 0.992950i | \(0.537819\pi\) | |||||||
\(374\) | 1.26905e6 | 0.469138 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | −4.11409e6 | −1.50073 | ||||||||
\(377\) | −39820.4 | −0.0144295 | ||||||||
\(378\) | −456869. | −0.164461 | ||||||||
\(379\) | −3.62357e6 | −1.29580 | −0.647901 | − | 0.761725i | \(-0.724353\pi\) | ||||
−0.647901 | + | 0.761725i | \(0.724353\pi\) | |||||||
\(380\) | −162497. | −0.0577280 | ||||||||
\(381\) | −1.73504e6 | −0.612347 | ||||||||
\(382\) | −4.20147e6 | −1.47314 | ||||||||
\(383\) | 419232. | 0.146035 | 0.0730175 | − | 0.997331i | \(-0.476737\pi\) | ||||
0.0730175 | + | 0.997331i | \(0.476737\pi\) | |||||||
\(384\) | 1.87653e6 | 0.649422 | ||||||||
\(385\) | −319298. | −0.109786 | ||||||||
\(386\) | 5.89943e6 | 2.01531 | ||||||||
\(387\) | −1.08640e6 | −0.368734 | ||||||||
\(388\) | −168441. | −0.0568026 | ||||||||
\(389\) | −662976. | −0.222139 | −0.111069 | − | 0.993813i | \(-0.535428\pi\) | ||||
−0.111069 | + | 0.993813i | \(0.535428\pi\) | |||||||
\(390\) | −165982. | −0.0552587 | ||||||||
\(391\) | −4.49854e6 | −1.48809 | ||||||||
\(392\) | −967027. | −0.317851 | ||||||||
\(393\) | −1.75197e6 | −0.572197 | ||||||||
\(394\) | 3.92622e6 | 1.27419 | ||||||||
\(395\) | 545471. | 0.175905 | ||||||||
\(396\) | −31873.4 | −0.0102139 | ||||||||
\(397\) | 3.68928e6 | 1.17480 | 0.587402 | − | 0.809295i | \(-0.300151\pi\) | ||||
0.587402 | + | 0.809295i | \(0.300151\pi\) | |||||||
\(398\) | 2.46293e6 | 0.779370 | ||||||||
\(399\) | 1.89872e6 | 0.597075 | ||||||||
\(400\) | −698431. | −0.218260 | ||||||||
\(401\) | 4.03113e6 | 1.25189 | 0.625945 | − | 0.779867i | \(-0.284713\pi\) | ||||
0.625945 | + | 0.779867i | \(0.284713\pi\) | |||||||
\(402\) | 287181. | 0.0886322 | ||||||||
\(403\) | 1.06286e6 | 0.325997 | ||||||||
\(404\) | 495977. | 0.151185 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | −200855. | −0.0604738 | ||||||||
\(407\) | −499280. | −0.149403 | ||||||||
\(408\) | −2.71359e6 | −0.807036 | ||||||||
\(409\) | 4.07904e6 | 1.20573 | 0.602864 | − | 0.797844i | \(-0.294026\pi\) | ||||
0.602864 | + | 0.797844i | \(0.294026\pi\) | |||||||
\(410\) | 672671. | 0.197625 | ||||||||
\(411\) | 1.97853e6 | 0.577748 | ||||||||
\(412\) | 619086. | 0.179683 | ||||||||
\(413\) | 1.92145e6 | 0.554312 | ||||||||
\(414\) | 1.22475e6 | 0.351193 | ||||||||
\(415\) | 1.62942e6 | 0.464421 | ||||||||
\(416\) | 145737. | 0.0412891 | ||||||||
\(417\) | 545247. | 0.153551 | ||||||||
\(418\) | 1.43590e6 | 0.401961 | ||||||||
\(419\) | −1.22736e6 | −0.341537 | −0.170769 | − | 0.985311i | \(-0.554625\pi\) | ||||
−0.170769 | + | 0.985311i | \(0.554625\pi\) | |||||||
\(420\) | −77234.6 | −0.0213643 | ||||||||
\(421\) | −16159.8 | −0.00444357 | −0.00222178 | − | 0.999998i | \(-0.500707\pi\) | ||||
−0.00222178 | + | 0.999998i | \(0.500707\pi\) | |||||||
\(422\) | 3.08335e6 | 0.842834 | ||||||||
\(423\) | −1.95236e6 | −0.530528 | ||||||||
\(424\) | −4.86350e6 | −1.31381 | ||||||||
\(425\) | 1.10403e6 | 0.296490 | ||||||||
\(426\) | −857911. | −0.229044 | ||||||||
\(427\) | −495739. | −0.131578 | ||||||||
\(428\) | −223333. | −0.0589309 | ||||||||
\(429\) | 135305. | 0.0354954 | ||||||||
\(430\) | −1.99084e6 | −0.519238 | ||||||||
\(431\) | 185090. | 0.0479944 | 0.0239972 | − | 0.999712i | \(-0.492361\pi\) | ||||
0.0239972 | + | 0.999712i | \(0.492361\pi\) | |||||||
\(432\) | 814650. | 0.210021 | ||||||||
\(433\) | −2.83808e6 | −0.727453 | −0.363727 | − | 0.931506i | \(-0.618496\pi\) | ||||
−0.363727 | + | 0.931506i | \(0.618496\pi\) | |||||||
\(434\) | 5.36108e6 | 1.36624 | ||||||||
\(435\) | −72111.0 | −0.0182717 | ||||||||
\(436\) | 95815.6 | 0.0241390 | ||||||||
\(437\) | −5.08999e6 | −1.27501 | ||||||||
\(438\) | 1.39874e6 | 0.348379 | ||||||||
\(439\) | −1.17189e6 | −0.290218 | −0.145109 | − | 0.989416i | \(-0.546353\pi\) | ||||
−0.145109 | + | 0.989416i | \(0.546353\pi\) | |||||||
\(440\) | 516326. | 0.127143 | ||||||||
\(441\) | −458907. | −0.112364 | ||||||||
\(442\) | −1.30311e6 | −0.317268 | ||||||||
\(443\) | −6.32946e6 | −1.53235 | −0.766174 | − | 0.642634i | \(-0.777842\pi\) | ||||
−0.766174 | + | 0.642634i | \(0.777842\pi\) | |||||||
\(444\) | −120770. | −0.0290738 | ||||||||
\(445\) | −709251. | −0.169785 | ||||||||
\(446\) | −6.55026e6 | −1.55927 | ||||||||
\(447\) | −554153. | −0.131178 | ||||||||
\(448\) | −3.03945e6 | −0.715484 | ||||||||
\(449\) | −2.81992e6 | −0.660116 | −0.330058 | − | 0.943961i | \(-0.607068\pi\) | ||||
−0.330058 | + | 0.943961i | \(0.607068\pi\) | |||||||
\(450\) | −300578. | −0.0699723 | ||||||||
\(451\) | −548347. | −0.126945 | ||||||||
\(452\) | −322953. | −0.0743521 | ||||||||
\(453\) | 1.75173e6 | 0.401071 | ||||||||
\(454\) | −6.39537e6 | −1.45622 | ||||||||
\(455\) | 327868. | 0.0742455 | ||||||||
\(456\) | −3.07036e6 | −0.691475 | ||||||||
\(457\) | 624549. | 0.139887 | 0.0699433 | − | 0.997551i | \(-0.477718\pi\) | ||||
0.0699433 | + | 0.997551i | \(0.477718\pi\) | |||||||
\(458\) | −3.97513e6 | −0.885498 | ||||||||
\(459\) | −1.28774e6 | −0.285297 | ||||||||
\(460\) | 207046. | 0.0456219 | ||||||||
\(461\) | 3.84656e6 | 0.842985 | 0.421492 | − | 0.906832i | \(-0.361506\pi\) | ||||
0.421492 | + | 0.906832i | \(0.361506\pi\) | |||||||
\(462\) | 682483. | 0.148760 | ||||||||
\(463\) | −7.90622e6 | −1.71402 | −0.857011 | − | 0.515298i | \(-0.827681\pi\) | ||||
−0.857011 | + | 0.515298i | \(0.827681\pi\) | |||||||
\(464\) | 358148. | 0.0772267 | ||||||||
\(465\) | 1.92474e6 | 0.412799 | ||||||||
\(466\) | −597327. | −0.127423 | ||||||||
\(467\) | 7.13863e6 | 1.51469 | 0.757343 | − | 0.653017i | \(-0.226497\pi\) | ||||
0.757343 | + | 0.653017i | \(0.226497\pi\) | |||||||
\(468\) | 32728.8 | 0.00690742 | ||||||||
\(469\) | −567274. | −0.119086 | ||||||||
\(470\) | −3.57772e6 | −0.747071 | ||||||||
\(471\) | −684105. | −0.142092 | ||||||||
\(472\) | −3.10711e6 | −0.641951 | ||||||||
\(473\) | 1.62290e6 | 0.333532 | ||||||||
\(474\) | −1.16591e6 | −0.238353 | ||||||||
\(475\) | 1.24919e6 | 0.254035 | ||||||||
\(476\) | −606361. | −0.122663 | ||||||||
\(477\) | −2.30799e6 | −0.464450 | ||||||||
\(478\) | 5.14830e6 | 1.03061 | ||||||||
\(479\) | −6.55862e6 | −1.30609 | −0.653046 | − | 0.757319i | \(-0.726509\pi\) | ||||
−0.653046 | + | 0.757319i | \(0.726509\pi\) | |||||||
\(480\) | 263915. | 0.0522831 | ||||||||
\(481\) | 512680. | 0.101038 | ||||||||
\(482\) | 3.67031e6 | 0.719590 | ||||||||
\(483\) | −2.41927e6 | −0.471863 | ||||||||
\(484\) | 47613.4 | 0.00923880 | ||||||||
\(485\) | 1.29488e6 | 0.249963 | ||||||||
\(486\) | 350594. | 0.0673309 | ||||||||
\(487\) | −6.92845e6 | −1.32377 | −0.661887 | − | 0.749604i | \(-0.730244\pi\) | ||||
−0.661887 | + | 0.749604i | \(0.730244\pi\) | |||||||
\(488\) | 801643. | 0.152381 | ||||||||
\(489\) | 4.48425e6 | 0.848042 | ||||||||
\(490\) | −840953. | −0.158227 | ||||||||
\(491\) | −9.60498e6 | −1.79801 | −0.899006 | − | 0.437936i | \(-0.855710\pi\) | ||||
−0.899006 | + | 0.437936i | \(0.855710\pi\) | |||||||
\(492\) | −132639. | −0.0247035 | ||||||||
\(493\) | −566136. | −0.104907 | ||||||||
\(494\) | −1.47444e6 | −0.271838 | ||||||||
\(495\) | 245025. | 0.0449467 | ||||||||
\(496\) | −9.55944e6 | −1.74473 | ||||||||
\(497\) | 1.69465e6 | 0.307743 | ||||||||
\(498\) | −3.48279e6 | −0.629294 | ||||||||
\(499\) | 6.72389e6 | 1.20884 | 0.604421 | − | 0.796665i | \(-0.293405\pi\) | ||||
0.604421 | + | 0.796665i | \(0.293405\pi\) | |||||||
\(500\) | −50813.4 | −0.00908977 | ||||||||
\(501\) | 5.85835e6 | 1.04275 | ||||||||
\(502\) | −3.74353e6 | −0.663012 | ||||||||
\(503\) | −142175. | −0.0250555 | −0.0125277 | − | 0.999922i | \(-0.503988\pi\) | ||||
−0.0125277 | + | 0.999922i | \(0.503988\pi\) | |||||||
\(504\) | −1.45934e6 | −0.255905 | ||||||||
\(505\) | −3.81279e6 | −0.665296 | ||||||||
\(506\) | −1.82956e6 | −0.317666 | ||||||||
\(507\) | 3.20270e6 | 0.553346 | ||||||||
\(508\) | 626940. | 0.107787 | ||||||||
\(509\) | −1.05255e7 | −1.80072 | −0.900362 | − | 0.435143i | \(-0.856698\pi\) | ||||
−0.900362 | + | 0.435143i | \(0.856698\pi\) | |||||||
\(510\) | −2.35981e6 | −0.401746 | ||||||||
\(511\) | −2.76296e6 | −0.468082 | ||||||||
\(512\) | 4.79293e6 | 0.808027 | ||||||||
\(513\) | −1.45705e6 | −0.244445 | ||||||||
\(514\) | −2.82552e6 | −0.471726 | ||||||||
\(515\) | −4.75919e6 | −0.790705 | ||||||||
\(516\) | 392560. | 0.0649055 | ||||||||
\(517\) | 2.91649e6 | 0.479881 | ||||||||
\(518\) | 2.58597e6 | 0.423446 | ||||||||
\(519\) | 3.60544e6 | 0.587544 | ||||||||
\(520\) | −530184. | −0.0859841 | ||||||||
\(521\) | 2.99141e6 | 0.482816 | 0.241408 | − | 0.970424i | \(-0.422391\pi\) | ||||
0.241408 | + | 0.970424i | \(0.422391\pi\) | |||||||
\(522\) | 154133. | 0.0247582 | ||||||||
\(523\) | −5.44567e6 | −0.870557 | −0.435279 | − | 0.900296i | \(-0.643350\pi\) | ||||
−0.435279 | + | 0.900296i | \(0.643350\pi\) | |||||||
\(524\) | 633057. | 0.100720 | ||||||||
\(525\) | 593737. | 0.0940147 | ||||||||
\(526\) | −2.46737e6 | −0.388839 | ||||||||
\(527\) | 1.51109e7 | 2.37009 | ||||||||
\(528\) | −1.21695e6 | −0.189971 | ||||||||
\(529\) | 49092.3 | 0.00762736 | ||||||||
\(530\) | −4.22943e6 | −0.654022 | ||||||||
\(531\) | −1.47449e6 | −0.226938 | ||||||||
\(532\) | −686083. | −0.105099 | ||||||||
\(533\) | 563064. | 0.0858499 | ||||||||
\(534\) | 1.51598e6 | 0.230060 | ||||||||
\(535\) | 1.71686e6 | 0.259328 | ||||||||
\(536\) | 917320. | 0.137914 | ||||||||
\(537\) | 7.38194e6 | 1.10468 | ||||||||
\(538\) | 1.11021e7 | 1.65367 | ||||||||
\(539\) | 685528. | 0.101637 | ||||||||
\(540\) | 59268.7 | 0.00874664 | ||||||||
\(541\) | −340079. | −0.0499559 | −0.0249780 | − | 0.999688i | \(-0.507952\pi\) | ||||
−0.0249780 | + | 0.999688i | \(0.507952\pi\) | |||||||
\(542\) | 7.35628e6 | 1.07562 | ||||||||
\(543\) | −5.75877e6 | −0.838166 | ||||||||
\(544\) | 2.07197e6 | 0.300183 | ||||||||
\(545\) | −736577. | −0.106225 | ||||||||
\(546\) | −700799. | −0.100603 | ||||||||
\(547\) | 8.20219e6 | 1.17209 | 0.586046 | − | 0.810278i | \(-0.300684\pi\) | ||||
0.586046 | + | 0.810278i | \(0.300684\pi\) | |||||||
\(548\) | −714922. | −0.101697 | ||||||||
\(549\) | 380423. | 0.0538687 | ||||||||
\(550\) | 449012. | 0.0632923 | ||||||||
\(551\) | −640569. | −0.0898849 | ||||||||
\(552\) | 3.91211e6 | 0.546466 | ||||||||
\(553\) | 2.30305e6 | 0.320251 | ||||||||
\(554\) | −5.02498e6 | −0.695600 | ||||||||
\(555\) | 928414. | 0.127941 | ||||||||
\(556\) | −197019. | −0.0270285 | ||||||||
\(557\) | 6.21617e6 | 0.848956 | 0.424478 | − | 0.905438i | \(-0.360458\pi\) | ||||
0.424478 | + | 0.905438i | \(0.360458\pi\) | |||||||
\(558\) | −4.11402e6 | −0.559346 | ||||||||
\(559\) | −1.66645e6 | −0.225560 | ||||||||
\(560\) | −2.94887e6 | −0.397361 | ||||||||
\(561\) | 1.92367e6 | 0.258061 | ||||||||
\(562\) | 6.39982e6 | 0.854726 | ||||||||
\(563\) | −7.83265e6 | −1.04145 | −0.520724 | − | 0.853725i | \(-0.674338\pi\) | ||||
−0.520724 | + | 0.853725i | \(0.674338\pi\) | |||||||
\(564\) | 705464. | 0.0933850 | ||||||||
\(565\) | 2.48268e6 | 0.327190 | ||||||||
\(566\) | 1.54054e7 | 2.02130 | ||||||||
\(567\) | −692535. | −0.0904657 | ||||||||
\(568\) | −2.74035e6 | −0.356398 | ||||||||
\(569\) | −479265. | −0.0620576 | −0.0310288 | − | 0.999518i | \(-0.509878\pi\) | ||||
−0.0310288 | + | 0.999518i | \(0.509878\pi\) | |||||||
\(570\) | −2.67007e6 | −0.344219 | ||||||||
\(571\) | −5.13344e6 | −0.658898 | −0.329449 | − | 0.944173i | \(-0.606863\pi\) | ||||
−0.329449 | + | 0.944173i | \(0.606863\pi\) | |||||||
\(572\) | −48891.2 | −0.00624800 | ||||||||
\(573\) | −6.36871e6 | −0.810336 | ||||||||
\(574\) | 2.84010e6 | 0.359794 | ||||||||
\(575\) | −1.59166e6 | −0.200761 | ||||||||
\(576\) | 2.33243e6 | 0.292922 | ||||||||
\(577\) | 7.94103e6 | 0.992973 | 0.496486 | − | 0.868045i | \(-0.334623\pi\) | ||||
0.496486 | + | 0.868045i | \(0.334623\pi\) | |||||||
\(578\) | −1.00964e7 | −1.25704 | ||||||||
\(579\) | 8.94252e6 | 1.10857 | ||||||||
\(580\) | 26056.5 | 0.00321623 | ||||||||
\(581\) | 6.87961e6 | 0.845519 | ||||||||
\(582\) | −2.76773e6 | −0.338701 | ||||||||
\(583\) | 3.44774e6 | 0.420111 | ||||||||
\(584\) | 4.46788e6 | 0.542088 | ||||||||
\(585\) | −251601. | −0.0303964 | ||||||||
\(586\) | 921244. | 0.110823 | ||||||||
\(587\) | −1.01573e7 | −1.21669 | −0.608347 | − | 0.793671i | \(-0.708167\pi\) | ||||
−0.608347 | + | 0.793671i | \(0.708167\pi\) | |||||||
\(588\) | 165821. | 0.0197787 | ||||||||
\(589\) | 1.70976e7 | 2.03071 | ||||||||
\(590\) | −2.70203e6 | −0.319566 | ||||||||
\(591\) | 5.95147e6 | 0.700900 | ||||||||
\(592\) | −4.61108e6 | −0.540752 | ||||||||
\(593\) | −9.94917e6 | −1.16185 | −0.580925 | − | 0.813957i | \(-0.697309\pi\) | ||||
−0.580925 | + | 0.813957i | \(0.697309\pi\) | |||||||
\(594\) | −523727. | −0.0609030 | ||||||||
\(595\) | 4.66137e6 | 0.539785 | ||||||||
\(596\) | 200238. | 0.0230903 | ||||||||
\(597\) | 3.73338e6 | 0.428712 | ||||||||
\(598\) | 1.87866e6 | 0.214831 | ||||||||
\(599\) | 1.18037e7 | 1.34416 | 0.672080 | − | 0.740478i | \(-0.265401\pi\) | ||||
0.672080 | + | 0.740478i | \(0.265401\pi\) | |||||||
\(600\) | −960111. | −0.108879 | ||||||||
\(601\) | −8.52084e6 | −0.962268 | −0.481134 | − | 0.876647i | \(-0.659775\pi\) | ||||
−0.481134 | + | 0.876647i | \(0.659775\pi\) | |||||||
\(602\) | −8.40560e6 | −0.945317 | ||||||||
\(603\) | 435318. | 0.0487544 | ||||||||
\(604\) | −632969. | −0.0705977 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | 8.14963e6 | 0.901480 | ||||||||
\(607\) | 1.48363e7 | 1.63438 | 0.817191 | − | 0.576368i | \(-0.195530\pi\) | ||||
0.817191 | + | 0.576368i | \(0.195530\pi\) | |||||||
\(608\) | 2.34439e6 | 0.257199 | ||||||||
\(609\) | −304462. | −0.0332652 | ||||||||
\(610\) | 697131. | 0.0758559 | ||||||||
\(611\) | −2.99476e6 | −0.324533 | ||||||||
\(612\) | 465313. | 0.0502188 | ||||||||
\(613\) | 1.31231e7 | 1.41054 | 0.705272 | − | 0.708936i | \(-0.250825\pi\) | ||||
0.705272 | + | 0.708936i | \(0.250825\pi\) | |||||||
\(614\) | 1.15716e7 | 1.23872 | ||||||||
\(615\) | 1.01965e6 | 0.108709 | ||||||||
\(616\) | 2.18000e6 | 0.231475 | ||||||||
\(617\) | 4.62938e6 | 0.489564 | 0.244782 | − | 0.969578i | \(-0.421284\pi\) | ||||
0.244782 | + | 0.969578i | \(0.421284\pi\) | |||||||
\(618\) | 1.01725e7 | 1.07141 | ||||||||
\(619\) | 9.49235e6 | 0.995743 | 0.497872 | − | 0.867251i | \(-0.334115\pi\) | ||||
0.497872 | + | 0.867251i | \(0.334115\pi\) | |||||||
\(620\) | −695484. | −0.0726621 | ||||||||
\(621\) | 1.85651e6 | 0.193183 | ||||||||
\(622\) | −5.06669e6 | −0.525107 | ||||||||
\(623\) | −2.99455e6 | −0.309109 | ||||||||
\(624\) | 1.24961e6 | 0.128473 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −3.53045e6 | −0.360077 | ||||||||
\(627\) | 2.17658e6 | 0.221109 | ||||||||
\(628\) | 247194. | 0.0250115 | ||||||||
\(629\) | 7.28888e6 | 0.734572 | ||||||||
\(630\) | −1.26908e6 | −0.127391 | ||||||||
\(631\) | 1.14798e7 | 1.14779 | 0.573893 | − | 0.818930i | \(-0.305432\pi\) | ||||
0.573893 | + | 0.818930i | \(0.305432\pi\) | |||||||
\(632\) | −3.72418e6 | −0.370884 | ||||||||
\(633\) | 4.67384e6 | 0.463622 | ||||||||
\(634\) | −1.93152e7 | −1.90843 | ||||||||
\(635\) | −4.81957e6 | −0.474322 | ||||||||
\(636\) | 833970. | 0.0817537 | ||||||||
\(637\) | −703926. | −0.0687351 | ||||||||
\(638\) | −230248. | −0.0223947 | ||||||||
\(639\) | −1.30045e6 | −0.125991 | ||||||||
\(640\) | 5.21257e6 | 0.503040 | ||||||||
\(641\) | −1.85269e7 | −1.78097 | −0.890486 | − | 0.455010i | \(-0.849636\pi\) | ||||
−0.890486 | + | 0.455010i | \(0.849636\pi\) | |||||||
\(642\) | −3.66969e6 | −0.351392 | ||||||||
\(643\) | 1.34056e7 | 1.27867 | 0.639337 | − | 0.768927i | \(-0.279209\pi\) | ||||
0.639337 | + | 0.768927i | \(0.279209\pi\) | |||||||
\(644\) | 874176. | 0.0830586 | ||||||||
\(645\) | −3.01778e6 | −0.285620 | ||||||||
\(646\) | −2.09624e7 | −1.97633 | ||||||||
\(647\) | 8.21634e6 | 0.771645 | 0.385823 | − | 0.922573i | \(-0.373918\pi\) | ||||
0.385823 | + | 0.922573i | \(0.373918\pi\) | |||||||
\(648\) | 1.11987e6 | 0.104769 | ||||||||
\(649\) | 2.20264e6 | 0.205273 | ||||||||
\(650\) | −461062. | −0.0428032 | ||||||||
\(651\) | 8.12649e6 | 0.751537 | ||||||||
\(652\) | −1.62034e6 | −0.149275 | ||||||||
\(653\) | 4.81154e6 | 0.441571 | 0.220786 | − | 0.975322i | \(-0.429138\pi\) | ||||
0.220786 | + | 0.975322i | \(0.429138\pi\) | |||||||
\(654\) | 1.57439e6 | 0.143936 | ||||||||
\(655\) | −4.86659e6 | −0.443222 | ||||||||
\(656\) | −5.06424e6 | −0.459467 | ||||||||
\(657\) | 2.12025e6 | 0.191635 | ||||||||
\(658\) | −1.51056e7 | −1.36011 | ||||||||
\(659\) | −6.57414e6 | −0.589693 | −0.294846 | − | 0.955545i | \(-0.595268\pi\) | ||||
−0.294846 | + | 0.955545i | \(0.595268\pi\) | |||||||
\(660\) | −88537.2 | −0.00791163 | ||||||||
\(661\) | 1.07312e7 | 0.955315 | 0.477657 | − | 0.878546i | \(-0.341486\pi\) | ||||
0.477657 | + | 0.878546i | \(0.341486\pi\) | |||||||
\(662\) | 1.22228e7 | 1.08399 | ||||||||
\(663\) | −1.97529e6 | −0.174521 | ||||||||
\(664\) | −1.11248e7 | −0.979199 | ||||||||
\(665\) | 5.27423e6 | 0.462492 | ||||||||
\(666\) | −1.98443e6 | −0.173361 | ||||||||
\(667\) | 816184. | 0.0710352 | ||||||||
\(668\) | −2.11685e6 | −0.183548 | ||||||||
\(669\) | −9.92908e6 | −0.857716 | ||||||||
\(670\) | 797726. | 0.0686542 | ||||||||
\(671\) | −568287. | −0.0487260 | ||||||||
\(672\) | 1.11428e6 | 0.0951859 | ||||||||
\(673\) | 7.52813e6 | 0.640693 | 0.320346 | − | 0.947301i | \(-0.396201\pi\) | ||||
0.320346 | + | 0.947301i | \(0.396201\pi\) | |||||||
\(674\) | −520176. | −0.0441063 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | −1.15726e6 | −0.0974014 | ||||||||
\(677\) | −1.63689e7 | −1.37262 | −0.686308 | − | 0.727311i | \(-0.740770\pi\) | ||||
−0.686308 | + | 0.727311i | \(0.740770\pi\) | |||||||
\(678\) | −5.30659e6 | −0.443345 | ||||||||
\(679\) | 5.46715e6 | 0.455079 | ||||||||
\(680\) | −7.53774e6 | −0.625128 | ||||||||
\(681\) | −9.69429e6 | −0.801029 | ||||||||
\(682\) | 6.14563e6 | 0.505948 | ||||||||
\(683\) | 2.56590e6 | 0.210469 | 0.105234 | − | 0.994447i | \(-0.466441\pi\) | ||||
0.105234 | + | 0.994447i | \(0.466441\pi\) | |||||||
\(684\) | 526490. | 0.0430279 | ||||||||
\(685\) | 5.49592e6 | 0.447522 | ||||||||
\(686\) | −1.40837e7 | −1.14263 | ||||||||
\(687\) | −6.02562e6 | −0.487091 | ||||||||
\(688\) | 1.49882e7 | 1.20720 | ||||||||
\(689\) | −3.54028e6 | −0.284112 | ||||||||
\(690\) | 3.40208e6 | 0.272033 | ||||||||
\(691\) | −8.83595e6 | −0.703977 | −0.351988 | − | 0.936004i | \(-0.614494\pi\) | ||||
−0.351988 | + | 0.936004i | \(0.614494\pi\) | |||||||
\(692\) | −1.30279e6 | −0.103421 | ||||||||
\(693\) | 1.03453e6 | 0.0818293 | ||||||||
\(694\) | 1.89497e7 | 1.49350 | ||||||||
\(695\) | 1.51458e6 | 0.118940 | ||||||||
\(696\) | 492334. | 0.0385245 | ||||||||
\(697\) | 8.00520e6 | 0.624152 | ||||||||
\(698\) | 8.08294e6 | 0.627959 | ||||||||
\(699\) | −905446. | −0.0700922 | ||||||||
\(700\) | −214541. | −0.0165487 | ||||||||
\(701\) | 43232.3 | 0.00332287 | 0.00166143 | − | 0.999999i | \(-0.499471\pi\) | ||||
0.00166143 | + | 0.999999i | \(0.499471\pi\) | |||||||
\(702\) | 537783. | 0.0411874 | ||||||||
\(703\) | 8.24719e6 | 0.629387 | ||||||||
\(704\) | −3.48425e6 | −0.264958 | ||||||||
\(705\) | −5.42322e6 | −0.410946 | ||||||||
\(706\) | 1.09468e7 | 0.826565 | ||||||||
\(707\) | −1.60981e7 | −1.21123 | ||||||||
\(708\) | 532793. | 0.0399462 | ||||||||
\(709\) | −5.33741e6 | −0.398763 | −0.199382 | − | 0.979922i | \(-0.563893\pi\) | ||||
−0.199382 | + | 0.979922i | \(0.563893\pi\) | |||||||
\(710\) | −2.38309e6 | −0.177416 | ||||||||
\(711\) | −1.76733e6 | −0.131112 | ||||||||
\(712\) | 4.84238e6 | 0.357980 | ||||||||
\(713\) | −2.17850e7 | −1.60485 | ||||||||
\(714\) | −9.96341e6 | −0.731413 | ||||||||
\(715\) | 375848. | 0.0274946 | ||||||||
\(716\) | −2.66739e6 | −0.194448 | ||||||||
\(717\) | 7.80394e6 | 0.566913 | ||||||||
\(718\) | 2.04926e6 | 0.148350 | ||||||||
\(719\) | −9.14720e6 | −0.659881 | −0.329941 | − | 0.944002i | \(-0.607029\pi\) | ||||
−0.329941 | + | 0.944002i | \(0.607029\pi\) | |||||||
\(720\) | 2.26292e6 | 0.162681 | ||||||||
\(721\) | −2.00939e7 | −1.43955 | ||||||||
\(722\) | −9.01701e6 | −0.643754 | ||||||||
\(723\) | 5.56356e6 | 0.395829 | ||||||||
\(724\) | 2.08087e6 | 0.147536 | ||||||||
\(725\) | −200308. | −0.0141532 | ||||||||
\(726\) | 782358. | 0.0550889 | ||||||||
\(727\) | −1.61992e6 | −0.113673 | −0.0568367 | − | 0.998383i | \(-0.518101\pi\) | ||||
−0.0568367 | + | 0.998383i | \(0.518101\pi\) | |||||||
\(728\) | −2.23850e6 | −0.156541 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 3.88539e6 | 0.269853 | ||||||||
\(731\) | −2.36923e7 | −1.63989 | ||||||||
\(732\) | −137462. | −0.00948211 | ||||||||
\(733\) | 2.29112e7 | 1.57503 | 0.787515 | − | 0.616296i | \(-0.211367\pi\) | ||||
0.787515 | + | 0.616296i | \(0.211367\pi\) | |||||||
\(734\) | −4.81273e6 | −0.329724 | ||||||||
\(735\) | −1.27474e6 | −0.0870370 | ||||||||
\(736\) | −2.98711e6 | −0.203262 | ||||||||
\(737\) | −650290. | −0.0441000 | ||||||||
\(738\) | −2.17945e6 | −0.147301 | ||||||||
\(739\) | 5.61873e6 | 0.378466 | 0.189233 | − | 0.981932i | \(-0.439400\pi\) | ||||
0.189233 | + | 0.981932i | \(0.439400\pi\) | |||||||
\(740\) | −335473. | −0.0225205 | ||||||||
\(741\) | −2.23500e6 | −0.149531 | ||||||||
\(742\) | −1.78572e7 | −1.19070 | ||||||||
\(743\) | −2.58649e7 | −1.71885 | −0.859426 | − | 0.511261i | \(-0.829179\pi\) | ||||
−0.859426 | + | 0.511261i | \(0.829179\pi\) | |||||||
\(744\) | −1.31411e7 | −0.870358 | ||||||||
\(745\) | −1.53931e6 | −0.101610 | ||||||||
\(746\) | 3.78214e6 | 0.248823 | ||||||||
\(747\) | −5.27931e6 | −0.346159 | ||||||||
\(748\) | −695097. | −0.0454246 | ||||||||
\(749\) | 7.24879e6 | 0.472129 | ||||||||
\(750\) | −834939. | −0.0542003 | ||||||||
\(751\) | −2.70229e7 | −1.74837 | −0.874183 | − | 0.485596i | \(-0.838603\pi\) | ||||
−0.874183 | + | 0.485596i | \(0.838603\pi\) | |||||||
\(752\) | 2.69351e7 | 1.73689 | ||||||||
\(753\) | −5.67455e6 | −0.364707 | ||||||||
\(754\) | 236428. | 0.0151450 | ||||||||
\(755\) | 4.86592e6 | 0.310669 | ||||||||
\(756\) | 250240. | 0.0159240 | ||||||||
\(757\) | −1.63080e6 | −0.103433 | −0.0517166 | − | 0.998662i | \(-0.516469\pi\) | ||||
−0.0517166 | + | 0.998662i | \(0.516469\pi\) | |||||||
\(758\) | 2.15144e7 | 1.36005 | ||||||||
\(759\) | −2.77330e6 | −0.174740 | ||||||||
\(760\) | −8.52877e6 | −0.535614 | ||||||||
\(761\) | 1.46228e7 | 0.915311 | 0.457656 | − | 0.889130i | \(-0.348689\pi\) | ||||
0.457656 | + | 0.889130i | \(0.348689\pi\) | |||||||
\(762\) | 1.03016e7 | 0.642710 | ||||||||
\(763\) | −3.10992e6 | −0.193392 | ||||||||
\(764\) | 2.30127e6 | 0.142638 | ||||||||
\(765\) | −3.57707e6 | −0.220990 | ||||||||
\(766\) | −2.48912e6 | −0.153276 | ||||||||
\(767\) | −2.26175e6 | −0.138822 | ||||||||
\(768\) | −2.84850e6 | −0.174266 | ||||||||
\(769\) | 2.12198e7 | 1.29398 | 0.646988 | − | 0.762500i | \(-0.276028\pi\) | ||||
0.646988 | + | 0.762500i | \(0.276028\pi\) | |||||||
\(770\) | 1.89579e6 | 0.115229 | ||||||||
\(771\) | −4.28300e6 | −0.259485 | ||||||||
\(772\) | −3.23129e6 | −0.195134 | ||||||||
\(773\) | −7.33809e6 | −0.441707 | −0.220853 | − | 0.975307i | \(-0.570884\pi\) | ||||
−0.220853 | + | 0.975307i | \(0.570884\pi\) | |||||||
\(774\) | 6.45034e6 | 0.387017 | ||||||||
\(775\) | 5.34649e6 | 0.319753 | ||||||||
\(776\) | −8.84074e6 | −0.527029 | ||||||||
\(777\) | 3.91988e6 | 0.232927 | ||||||||
\(778\) | 3.93632e6 | 0.233153 | ||||||||
\(779\) | 9.05769e6 | 0.534778 | ||||||||
\(780\) | 90913.4 | 0.00535046 | ||||||||
\(781\) | 1.94264e6 | 0.113963 | ||||||||
\(782\) | 2.67094e7 | 1.56188 | ||||||||
\(783\) | 233640. | 0.0136189 | ||||||||
\(784\) | 6.33116e6 | 0.367869 | ||||||||
\(785\) | −1.90029e6 | −0.110064 | ||||||||
\(786\) | 1.04021e7 | 0.600569 | ||||||||
\(787\) | 6.32394e6 | 0.363958 | 0.181979 | − | 0.983302i | \(-0.441750\pi\) | ||||
0.181979 | + | 0.983302i | \(0.441750\pi\) | |||||||
\(788\) | −2.15050e6 | −0.123374 | ||||||||
\(789\) | −3.74011e6 | −0.213891 | ||||||||
\(790\) | −3.23865e6 | −0.184627 | ||||||||
\(791\) | 1.04822e7 | 0.595678 | ||||||||
\(792\) | −1.67290e6 | −0.0947669 | ||||||||
\(793\) | 583538. | 0.0329524 | ||||||||
\(794\) | −2.19045e7 | −1.23306 | ||||||||
\(795\) | −6.41109e6 | −0.359761 | ||||||||
\(796\) | −1.34902e6 | −0.0754631 | ||||||||
\(797\) | −2.37699e7 | −1.32551 | −0.662754 | − | 0.748837i | \(-0.730613\pi\) | ||||
−0.662754 | + | 0.748837i | \(0.730613\pi\) | |||||||
\(798\) | −1.12734e7 | −0.626680 | ||||||||
\(799\) | −4.25771e7 | −2.35944 | ||||||||
\(800\) | 733098. | 0.0404983 | ||||||||
\(801\) | 2.29797e6 | 0.126550 | ||||||||
\(802\) | −2.39342e7 | −1.31396 | ||||||||
\(803\) | −3.16729e6 | −0.173340 | ||||||||
\(804\) | −157298. | −0.00858187 | ||||||||
\(805\) | −6.72018e6 | −0.365503 | ||||||||
\(806\) | −6.31057e6 | −0.342161 | ||||||||
\(807\) | 1.68288e7 | 0.909641 | ||||||||
\(808\) | 2.60317e7 | 1.40273 | ||||||||
\(809\) | 3.06904e7 | 1.64866 | 0.824331 | − | 0.566108i | \(-0.191551\pi\) | ||||
0.824331 | + | 0.566108i | \(0.191551\pi\) | |||||||
\(810\) | 973873. | 0.0521543 | ||||||||
\(811\) | −1.80033e7 | −0.961172 | −0.480586 | − | 0.876948i | \(-0.659576\pi\) | ||||
−0.480586 | + | 0.876948i | \(0.659576\pi\) | |||||||
\(812\) | 110014. | 0.00585542 | ||||||||
\(813\) | 1.11509e7 | 0.591673 | ||||||||
\(814\) | 2.96440e6 | 0.156811 | ||||||||
\(815\) | 1.24562e7 | 0.656890 | ||||||||
\(816\) | 1.77659e7 | 0.934034 | ||||||||
\(817\) | −2.68073e7 | −1.40507 | ||||||||
\(818\) | −2.42187e7 | −1.26551 | ||||||||
\(819\) | −1.06229e6 | −0.0553394 | ||||||||
\(820\) | −368441. | −0.0191352 | ||||||||
\(821\) | −1.63239e7 | −0.845213 | −0.422607 | − | 0.906313i | \(-0.638885\pi\) | ||||
−0.422607 | + | 0.906313i | \(0.638885\pi\) | |||||||
\(822\) | −1.17472e7 | −0.606396 | ||||||||
\(823\) | 1.82069e7 | 0.936992 | 0.468496 | − | 0.883466i | \(-0.344796\pi\) | ||||
0.468496 | + | 0.883466i | \(0.344796\pi\) | |||||||
\(824\) | 3.24931e7 | 1.66715 | ||||||||
\(825\) | 680625. | 0.0348155 | ||||||||
\(826\) | −1.14083e7 | −0.581797 | ||||||||
\(827\) | −3.78345e7 | −1.92364 | −0.961820 | − | 0.273683i | \(-0.911758\pi\) | ||||
−0.961820 | + | 0.273683i | \(0.911758\pi\) | |||||||
\(828\) | −670830. | −0.0340045 | ||||||||
\(829\) | 5.02252e6 | 0.253826 | 0.126913 | − | 0.991914i | \(-0.459493\pi\) | ||||
0.126913 | + | 0.991914i | \(0.459493\pi\) | |||||||
\(830\) | −9.67441e6 | −0.487449 | ||||||||
\(831\) | −7.61701e6 | −0.382633 | ||||||||
\(832\) | 3.57776e6 | 0.179185 | ||||||||
\(833\) | −1.00079e7 | −0.499723 | ||||||||
\(834\) | −3.23732e6 | −0.161165 | ||||||||
\(835\) | 1.62732e7 | 0.807712 | ||||||||
\(836\) | −786485. | −0.0389202 | ||||||||
\(837\) | −6.23615e6 | −0.307682 | ||||||||
\(838\) | 7.28728e6 | 0.358472 | ||||||||
\(839\) | −2.82732e7 | −1.38666 | −0.693331 | − | 0.720619i | \(-0.743858\pi\) | ||||
−0.693331 | + | 0.720619i | \(0.743858\pi\) | |||||||
\(840\) | −4.05371e6 | −0.198223 | ||||||||
\(841\) | −2.04084e7 | −0.994992 | ||||||||
\(842\) | 95946.5 | 0.00466390 | ||||||||
\(843\) | 9.70103e6 | 0.470164 | ||||||||
\(844\) | −1.68884e6 | −0.0816080 | ||||||||
\(845\) | 8.89639e6 | 0.428620 | ||||||||
\(846\) | 1.15918e7 | 0.556834 | ||||||||
\(847\) | −1.54540e6 | −0.0740174 | ||||||||
\(848\) | 3.18415e7 | 1.52056 | ||||||||
\(849\) | 2.33519e7 | 1.11187 | ||||||||
\(850\) | −6.55502e6 | −0.311191 | ||||||||
\(851\) | −1.05082e7 | −0.497399 | ||||||||
\(852\) | 469903. | 0.0221773 | ||||||||
\(853\) | 7.27728e6 | 0.342449 | 0.171225 | − | 0.985232i | \(-0.445228\pi\) | ||||
0.171225 | + | 0.985232i | \(0.445228\pi\) | |||||||
\(854\) | 2.94338e6 | 0.138102 | ||||||||
\(855\) | −4.04736e6 | −0.189346 | ||||||||
\(856\) | −1.17218e7 | −0.546775 | ||||||||
\(857\) | 2.49180e7 | 1.15894 | 0.579469 | − | 0.814994i | \(-0.303260\pi\) | ||||
0.579469 | + | 0.814994i | \(0.303260\pi\) | |||||||
\(858\) | −803355. | −0.0372554 | ||||||||
\(859\) | −3.01693e7 | −1.39502 | −0.697512 | − | 0.716573i | \(-0.745710\pi\) | ||||
−0.697512 | + | 0.716573i | \(0.745710\pi\) | |||||||
\(860\) | 1.09044e6 | 0.0502756 | ||||||||
\(861\) | 4.30511e6 | 0.197914 | ||||||||
\(862\) | −1.09894e6 | −0.0503742 | ||||||||
\(863\) | 3.86426e7 | 1.76620 | 0.883099 | − | 0.469187i | \(-0.155453\pi\) | ||||
0.883099 | + | 0.469187i | \(0.155453\pi\) | |||||||
\(864\) | −855085. | −0.0389695 | ||||||||
\(865\) | 1.00151e7 | 0.455110 | ||||||||
\(866\) | 1.68507e7 | 0.763524 | ||||||||
\(867\) | −1.53045e7 | −0.691466 | ||||||||
\(868\) | −2.93642e6 | −0.132288 | ||||||||
\(869\) | 2.64008e6 | 0.118595 | ||||||||
\(870\) | 428148. | 0.0191776 | ||||||||
\(871\) | 667743. | 0.0298239 | ||||||||
\(872\) | 5.02895e6 | 0.223968 | ||||||||
\(873\) | −4.19541e6 | −0.186311 | ||||||||
\(874\) | 3.02210e7 | 1.33823 | ||||||||
\(875\) | 1.64927e6 | 0.0728235 | ||||||||
\(876\) | −766131. | −0.0337321 | ||||||||
\(877\) | 1.35160e7 | 0.593404 | 0.296702 | − | 0.954970i | \(-0.404113\pi\) | ||||
0.296702 | + | 0.954970i | \(0.404113\pi\) | |||||||
\(878\) | 6.95790e6 | 0.304608 | ||||||||
\(879\) | 1.39645e6 | 0.0609611 | ||||||||
\(880\) | −3.38041e6 | −0.147151 | ||||||||
\(881\) | 1.56537e7 | 0.679479 | 0.339739 | − | 0.940520i | \(-0.389661\pi\) | ||||
0.339739 | + | 0.940520i | \(0.389661\pi\) | |||||||
\(882\) | 2.72469e6 | 0.117936 | ||||||||
\(883\) | −7.31854e6 | −0.315880 | −0.157940 | − | 0.987449i | \(-0.550485\pi\) | ||||
−0.157940 | + | 0.987449i | \(0.550485\pi\) | |||||||
\(884\) | 713752. | 0.0307197 | ||||||||
\(885\) | −4.09582e6 | −0.175785 | ||||||||
\(886\) | 3.75802e7 | 1.60833 | ||||||||
\(887\) | 3.94393e6 | 0.168314 | 0.0841570 | − | 0.996453i | \(-0.473180\pi\) | ||||
0.0841570 | + | 0.996453i | \(0.473180\pi\) | |||||||
\(888\) | −6.33871e6 | −0.269754 | ||||||||
\(889\) | −2.03488e7 | −0.863545 | ||||||||
\(890\) | 4.21107e6 | 0.178204 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | 3.58777e6 | 0.150978 | ||||||||
\(893\) | −4.81750e7 | −2.02159 | ||||||||
\(894\) | 3.29020e6 | 0.137682 | ||||||||
\(895\) | 2.05054e7 | 0.855678 | ||||||||
\(896\) | 2.20082e7 | 0.915828 | ||||||||
\(897\) | 2.84773e6 | 0.118173 | ||||||||
\(898\) | 1.67428e7 | 0.692847 | ||||||||
\(899\) | −2.74162e6 | −0.113138 | ||||||||
\(900\) | 164635. | 0.00677512 | ||||||||
\(901\) | −5.03329e7 | −2.06557 | ||||||||
\(902\) | 3.25573e6 | 0.133239 | ||||||||
\(903\) | −1.27415e7 | −0.519996 | ||||||||
\(904\) | −1.69504e7 | −0.689857 | ||||||||
\(905\) | −1.59966e7 | −0.649241 | ||||||||
\(906\) | −1.04006e7 | −0.420958 | ||||||||
\(907\) | −2.09119e7 | −0.844064 | −0.422032 | − | 0.906581i | \(-0.638683\pi\) | ||||
−0.422032 | + | 0.906581i | \(0.638683\pi\) | |||||||
\(908\) | 3.50293e6 | 0.140999 | ||||||||
\(909\) | 1.23534e7 | 0.495882 | ||||||||
\(910\) | −1.94666e6 | −0.0779269 | ||||||||
\(911\) | 2.63760e7 | 1.05296 | 0.526481 | − | 0.850187i | \(-0.323511\pi\) | ||||
0.526481 | + | 0.850187i | \(0.323511\pi\) | |||||||
\(912\) | 2.01017e7 | 0.800288 | ||||||||
\(913\) | 7.88638e6 | 0.313113 | ||||||||
\(914\) | −3.70816e6 | −0.146823 | ||||||||
\(915\) | 1.05673e6 | 0.0417265 | ||||||||
\(916\) | 2.17729e6 | 0.0857390 | ||||||||
\(917\) | −2.05474e7 | −0.806924 | ||||||||
\(918\) | 7.64578e6 | 0.299444 | ||||||||
\(919\) | −1.74127e7 | −0.680109 | −0.340054 | − | 0.940406i | \(-0.610445\pi\) | ||||
−0.340054 | + | 0.940406i | \(0.610445\pi\) | |||||||
\(920\) | 1.08670e7 | 0.423291 | ||||||||
\(921\) | 1.75406e7 | 0.681391 | ||||||||
\(922\) | −2.28383e7 | −0.884783 | ||||||||
\(923\) | −1.99478e6 | −0.0770709 | ||||||||
\(924\) | −373816. | −0.0144038 | ||||||||
\(925\) | 2.57893e6 | 0.0991025 | ||||||||
\(926\) | 4.69419e7 | 1.79901 | ||||||||
\(927\) | 1.54198e7 | 0.589357 | ||||||||
\(928\) | −375924. | −0.0143295 | ||||||||
\(929\) | 1.23992e7 | 0.471360 | 0.235680 | − | 0.971831i | \(-0.424268\pi\) | ||||
0.235680 | + | 0.971831i | \(0.424268\pi\) | |||||||
\(930\) | −1.14278e7 | −0.433268 | ||||||||
\(931\) | −1.13237e7 | −0.428166 | ||||||||
\(932\) | 327174. | 0.0123378 | ||||||||
\(933\) | −7.68023e6 | −0.288848 | ||||||||
\(934\) | −4.23845e7 | −1.58979 | ||||||||
\(935\) | 5.34352e6 | 0.199893 | ||||||||
\(936\) | 1.71780e6 | 0.0640888 | ||||||||
\(937\) | 6.45952e6 | 0.240354 | 0.120177 | − | 0.992752i | \(-0.461654\pi\) | ||||
0.120177 | + | 0.992752i | \(0.461654\pi\) | |||||||
\(938\) | 3.36810e6 | 0.124991 | ||||||||
\(939\) | −5.35157e6 | −0.198069 | ||||||||
\(940\) | 1.95962e6 | 0.0723357 | ||||||||
\(941\) | −4.98442e6 | −0.183502 | −0.0917510 | − | 0.995782i | \(-0.529246\pi\) | ||||
−0.0917510 | + | 0.995782i | \(0.529246\pi\) | |||||||
\(942\) | 4.06176e6 | 0.149138 | ||||||||
\(943\) | −1.15409e7 | −0.422630 | ||||||||
\(944\) | 2.03424e7 | 0.742971 | ||||||||
\(945\) | −1.92371e6 | −0.0700744 | ||||||||
\(946\) | −9.63569e6 | −0.350070 | ||||||||
\(947\) | 8.49575e6 | 0.307841 | 0.153921 | − | 0.988083i | \(-0.450810\pi\) | ||||
0.153921 | + | 0.988083i | \(0.450810\pi\) | |||||||
\(948\) | 638605. | 0.0230787 | ||||||||
\(949\) | 3.25230e6 | 0.117226 | ||||||||
\(950\) | −7.41685e6 | −0.266631 | ||||||||
\(951\) | −2.92786e7 | −1.04978 | ||||||||
\(952\) | −3.18253e7 | −1.13810 | ||||||||
\(953\) | 3.18137e7 | 1.13470 | 0.567351 | − | 0.823476i | \(-0.307968\pi\) | ||||
0.567351 | + | 0.823476i | \(0.307968\pi\) | |||||||
\(954\) | 1.37034e7 | 0.487479 | ||||||||
\(955\) | −1.76909e7 | −0.627684 | ||||||||
\(956\) | −2.81987e6 | −0.0997895 | ||||||||
\(957\) | −349017. | −0.0123188 | ||||||||
\(958\) | 3.89408e7 | 1.37085 | ||||||||
\(959\) | 2.32045e7 | 0.814753 | ||||||||
\(960\) | 6.47897e6 | 0.226897 | ||||||||
\(961\) | 4.45484e7 | 1.55605 | ||||||||
\(962\) | −3.04396e6 | −0.106048 | ||||||||
\(963\) | −5.56262e6 | −0.193292 | ||||||||
\(964\) | −2.01034e6 | −0.0696748 | ||||||||
\(965\) | 2.48403e7 | 0.858696 | ||||||||
\(966\) | 1.43640e7 | 0.495260 | ||||||||
\(967\) | −4.98824e6 | −0.171546 | −0.0857732 | − | 0.996315i | \(-0.527336\pi\) | ||||
−0.0857732 | + | 0.996315i | \(0.527336\pi\) | |||||||
\(968\) | 2.49902e6 | 0.0857198 | ||||||||
\(969\) | −3.17754e7 | −1.08713 | ||||||||
\(970\) | −7.68815e6 | −0.262357 | ||||||||
\(971\) | 1.81815e7 | 0.618845 | 0.309422 | − | 0.950925i | \(-0.399864\pi\) | ||||
0.309422 | + | 0.950925i | \(0.399864\pi\) | |||||||
\(972\) | −192031. | −0.00651936 | ||||||||
\(973\) | 6.39473e6 | 0.216541 | ||||||||
\(974\) | 4.11366e7 | 1.38941 | ||||||||
\(975\) | −698892. | −0.0235450 | ||||||||
\(976\) | −5.24838e6 | −0.176360 | ||||||||
\(977\) | 1.72113e7 | 0.576870 | 0.288435 | − | 0.957499i | \(-0.406865\pi\) | ||||
0.288435 | + | 0.957499i | \(0.406865\pi\) | |||||||
\(978\) | −2.66245e7 | −0.890091 | ||||||||
\(979\) | −3.43277e6 | −0.114469 | ||||||||
\(980\) | 460615. | 0.0153205 | ||||||||
\(981\) | 2.38651e6 | 0.0791755 | ||||||||
\(982\) | 5.70281e7 | 1.88717 | ||||||||
\(983\) | −4.14848e7 | −1.36932 | −0.684661 | − | 0.728861i | \(-0.740050\pi\) | ||||
−0.684661 | + | 0.728861i | \(0.740050\pi\) | |||||||
\(984\) | −6.96164e6 | −0.229205 | ||||||||
\(985\) | 1.65319e7 | 0.542915 | ||||||||
\(986\) | 3.36134e6 | 0.110108 | ||||||||
\(987\) | −2.28975e7 | −0.748162 | ||||||||
\(988\) | 807593. | 0.0263209 | ||||||||
\(989\) | 3.41566e7 | 1.11041 | ||||||||
\(990\) | −1.45480e6 | −0.0471753 | ||||||||
\(991\) | −1.58584e7 | −0.512951 | −0.256475 | − | 0.966551i | \(-0.582561\pi\) | ||||
−0.256475 | + | 0.966551i | \(0.582561\pi\) | |||||||
\(992\) | 1.00339e7 | 0.323736 | ||||||||
\(993\) | 1.85276e7 | 0.596274 | ||||||||
\(994\) | −1.00617e7 | −0.323002 | ||||||||
\(995\) | 1.03705e7 | 0.332079 | ||||||||
\(996\) | 1.90762e6 | 0.0609319 | ||||||||
\(997\) | −4.08647e7 | −1.30200 | −0.651000 | − | 0.759078i | \(-0.725650\pi\) | ||||
−0.651000 | + | 0.759078i | \(0.725650\pi\) | |||||||
\(998\) | −3.99221e7 | −1.26878 | ||||||||
\(999\) | −3.00806e6 | −0.0953615 |
(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.a.g.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 495.6.a.i.1.4 | 5 | |||
5.4 | even | 2 | 825.6.a.k.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.g.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
495.6.a.i.1.4 | 5 | 3.2 | odd | 2 | |||
825.6.a.k.1.4 | 5 | 5.4 | even | 2 |