Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,6,Mod(28,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.b (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: | \(4.65113077458\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 278x^{10} + 28285x^{8} + 1260472x^{6} + 22944832x^{4} + 140087936x^{2} + 966400 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{14}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 28.8 | ||
Root | \(3.61683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.28 |
Dual form | 29.6.b.a.28.5 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.61683i | 0.639372i | 0.947524 | + | 0.319686i | \(0.103577\pi\) | ||||
−0.947524 | + | 0.319686i | \(0.896423\pi\) | |||||||
\(3\) | − | 5.13082i | − | 0.329142i | −0.986365 | − | 0.164571i | \(-0.947376\pi\) | ||
0.986365 | − | 0.164571i | \(-0.0526240\pi\) | |||||||
\(4\) | 18.9185 | 0.591204 | ||||||||
\(5\) | 15.9022 | 0.284466 | 0.142233 | − | 0.989833i | \(-0.454572\pi\) | ||||
0.142233 | + | 0.989833i | \(0.454572\pi\) | |||||||
\(6\) | 18.5573 | 0.210444 | ||||||||
\(7\) | 69.7674 | 0.538155 | 0.269078 | − | 0.963118i | \(-0.413281\pi\) | ||||
0.269078 | + | 0.963118i | \(0.413281\pi\) | |||||||
\(8\) | 184.164i | 1.01737i | ||||||||
\(9\) | 216.675 | 0.891666 | ||||||||
\(10\) | 57.5154i | 0.181880i | ||||||||
\(11\) | 400.387i | 0.997697i | 0.866689 | + | 0.498848i | \(0.166244\pi\) | ||||
−0.866689 | + | 0.498848i | \(0.833756\pi\) | |||||||
\(12\) | − | 97.0675i | − | 0.194590i | ||||||
\(13\) | −178.686 | −0.293246 | −0.146623 | − | 0.989192i | \(-0.546840\pi\) | ||||
−0.146623 | + | 0.989192i | \(0.546840\pi\) | |||||||
\(14\) | 252.337i | 0.344081i | ||||||||
\(15\) | − | 81.5911i | − | 0.0936299i | ||||||
\(16\) | −60.6968 | −0.0592742 | ||||||||
\(17\) | − | 1410.99i | − | 1.18414i | −0.805888 | − | 0.592068i | \(-0.798312\pi\) | ||
0.805888 | − | 0.592068i | \(-0.201688\pi\) | |||||||
\(18\) | 783.676i | 0.570106i | ||||||||
\(19\) | − | 1727.73i | − | 1.09797i | −0.835832 | − | 0.548986i | \(-0.815014\pi\) | ||
0.835832 | − | 0.548986i | \(-0.184986\pi\) | |||||||
\(20\) | 300.845 | 0.168178 | ||||||||
\(21\) | − | 357.964i | − | 0.177130i | ||||||
\(22\) | −1448.13 | −0.637899 | ||||||||
\(23\) | −1109.14 | −0.437186 | −0.218593 | − | 0.975816i | \(-0.570147\pi\) | ||||
−0.218593 | + | 0.975816i | \(0.570147\pi\) | |||||||
\(24\) | 944.911 | 0.334859 | ||||||||
\(25\) | −2872.12 | −0.919079 | ||||||||
\(26\) | − | 646.278i | − | 0.187493i | ||||||
\(27\) | − | 2358.51i | − | 0.622627i | ||||||
\(28\) | 1319.90 | 0.318159 | ||||||||
\(29\) | −3442.35 | + | 2943.02i | −0.760081 | + | 0.649828i | ||||
\(30\) | 295.101 | 0.0598643 | ||||||||
\(31\) | 2033.09i | 0.379973i | 0.981787 | + | 0.189987i | \(0.0608445\pi\) | ||||
−0.981787 | + | 0.189987i | \(0.939156\pi\) | |||||||
\(32\) | 5673.71i | 0.979472i | ||||||||
\(33\) | 2054.31 | 0.328384 | ||||||||
\(34\) | 5103.31 | 0.757103 | ||||||||
\(35\) | 1109.45 | 0.153087 | ||||||||
\(36\) | 4099.17 | 0.527156 | ||||||||
\(37\) | − | 7214.27i | − | 0.866339i | −0.901312 | − | 0.433170i | \(-0.857395\pi\) | ||
0.901312 | − | 0.433170i | \(-0.142605\pi\) | |||||||
\(38\) | 6248.90 | 0.702012 | ||||||||
\(39\) | 916.806i | 0.0965197i | ||||||||
\(40\) | 2928.60i | 0.289408i | ||||||||
\(41\) | 7337.02i | 0.681648i | 0.940127 | + | 0.340824i | \(0.110706\pi\) | ||||
−0.940127 | + | 0.340824i | \(0.889294\pi\) | |||||||
\(42\) | 1294.70 | 0.113252 | ||||||||
\(43\) | − | 4978.67i | − | 0.410622i | −0.978697 | − | 0.205311i | \(-0.934179\pi\) | ||
0.978697 | − | 0.205311i | \(-0.0658206\pi\) | |||||||
\(44\) | 7574.73i | 0.589842i | ||||||||
\(45\) | 3445.60 | 0.253649 | ||||||||
\(46\) | − | 4011.57i | − | 0.279525i | ||||||
\(47\) | − | 493.299i | − | 0.0325736i | −0.999867 | − | 0.0162868i | \(-0.994816\pi\) | ||
0.999867 | − | 0.0162868i | \(-0.00518447\pi\) | |||||||
\(48\) | 311.424i | 0.0195096i | ||||||||
\(49\) | −11939.5 | −0.710389 | ||||||||
\(50\) | − | 10388.0i | − | 0.587633i | ||||||
\(51\) | −7239.53 | −0.389749 | ||||||||
\(52\) | −3380.48 | −0.173368 | ||||||||
\(53\) | −10825.6 | −0.529373 | −0.264686 | − | 0.964335i | \(-0.585268\pi\) | ||||
−0.264686 | + | 0.964335i | \(0.585268\pi\) | |||||||
\(54\) | 8530.32 | 0.398090 | ||||||||
\(55\) | 6367.02i | 0.283811i | ||||||||
\(56\) | 12848.6i | 0.547503i | ||||||||
\(57\) | −8864.65 | −0.361389 | ||||||||
\(58\) | −10644.4 | − | 12450.4i | −0.415482 | − | 0.485974i | ||||
\(59\) | −4332.32 | −0.162028 | −0.0810141 | − | 0.996713i | \(-0.525816\pi\) | ||||
−0.0810141 | + | 0.996713i | \(0.525816\pi\) | |||||||
\(60\) | − | 1543.58i | − | 0.0553543i | ||||||
\(61\) | − | 46481.5i | − | 1.59939i | −0.600404 | − | 0.799697i | \(-0.704994\pi\) | ||
0.600404 | − | 0.799697i | \(-0.295006\pi\) | |||||||
\(62\) | −7353.36 | −0.242944 | ||||||||
\(63\) | 15116.8 | 0.479855 | ||||||||
\(64\) | −22463.2 | −0.685521 | ||||||||
\(65\) | −2841.50 | −0.0834187 | ||||||||
\(66\) | 7430.11i | 0.209959i | ||||||||
\(67\) | −4487.33 | −0.122124 | −0.0610620 | − | 0.998134i | \(-0.519449\pi\) | ||||
−0.0610620 | + | 0.998134i | \(0.519449\pi\) | |||||||
\(68\) | − | 26693.8i | − | 0.700065i | ||||||
\(69\) | 5690.79i | 0.143896i | ||||||||
\(70\) | 4012.70i | 0.0978796i | ||||||||
\(71\) | 58697.7 | 1.38189 | 0.690947 | − | 0.722905i | \(-0.257194\pi\) | ||||
0.690947 | + | 0.722905i | \(0.257194\pi\) | |||||||
\(72\) | 39903.6i | 0.907154i | ||||||||
\(73\) | 15317.2i | 0.336414i | 0.985752 | + | 0.168207i | \(0.0537976\pi\) | ||||
−0.985752 | + | 0.168207i | \(0.946202\pi\) | |||||||
\(74\) | 26092.8 | 0.553913 | ||||||||
\(75\) | 14736.3i | 0.302507i | ||||||||
\(76\) | − | 32686.0i | − | 0.649125i | ||||||
\(77\) | 27934.0i | 0.536916i | ||||||||
\(78\) | −3315.93 | −0.0617120 | ||||||||
\(79\) | 33868.5i | 0.610559i | 0.952263 | + | 0.305279i | \(0.0987499\pi\) | ||||
−0.952263 | + | 0.305279i | \(0.901250\pi\) | |||||||
\(80\) | −965.210 | −0.0168615 | ||||||||
\(81\) | 40550.9 | 0.686733 | ||||||||
\(82\) | −26536.8 | −0.435826 | ||||||||
\(83\) | 45749.9 | 0.728945 | 0.364473 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364473 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(84\) | − | 6772.15i | − | 0.104720i | ||||||
\(85\) | − | 22437.8i | − | 0.336847i | ||||||
\(86\) | 18007.0 | 0.262540 | ||||||||
\(87\) | 15100.1 | + | 17662.1i | 0.213886 | + | 0.250175i | ||||
\(88\) | −73736.8 | −1.01503 | ||||||||
\(89\) | 104566.i | 1.39932i | 0.714478 | + | 0.699658i | \(0.246664\pi\) | ||||
−0.714478 | + | 0.699658i | \(0.753336\pi\) | |||||||
\(90\) | 12462.1i | 0.162176i | ||||||||
\(91\) | −12466.5 | −0.157812 | ||||||||
\(92\) | −20983.3 | −0.258466 | ||||||||
\(93\) | 10431.4 | 0.125065 | ||||||||
\(94\) | 1784.18 | 0.0208266 | ||||||||
\(95\) | − | 27474.6i | − | 0.312336i | ||||||
\(96\) | 29110.8 | 0.322386 | ||||||||
\(97\) | − | 151708.i | − | 1.63711i | −0.574428 | − | 0.818555i | \(-0.694776\pi\) | ||
0.574428 | − | 0.818555i | \(-0.305224\pi\) | |||||||
\(98\) | − | 43183.2i | − | 0.454203i | ||||||
\(99\) | 86753.8i | 0.889612i | ||||||||
\(100\) | −54336.3 | −0.543363 | ||||||||
\(101\) | 24654.4i | 0.240487i | 0.992744 | + | 0.120243i | \(0.0383675\pi\) | ||||
−0.992744 | + | 0.120243i | \(0.961633\pi\) | |||||||
\(102\) | − | 26184.2i | − | 0.249194i | ||||||
\(103\) | −24585.9 | −0.228346 | −0.114173 | − | 0.993461i | \(-0.536422\pi\) | ||||
−0.114173 | + | 0.993461i | \(0.536422\pi\) | |||||||
\(104\) | − | 32907.5i | − | 0.298340i | ||||||
\(105\) | − | 5692.40i | − | 0.0503874i | ||||||
\(106\) | − | 39154.3i | − | 0.338466i | ||||||
\(107\) | 100568. | 0.849183 | 0.424591 | − | 0.905385i | \(-0.360418\pi\) | ||||
0.424591 | + | 0.905385i | \(0.360418\pi\) | |||||||
\(108\) | − | 44619.5i | − | 0.368099i | ||||||
\(109\) | −147299. | −1.18750 | −0.593748 | − | 0.804651i | \(-0.702352\pi\) | ||||
−0.593748 | + | 0.804651i | \(0.702352\pi\) | |||||||
\(110\) | −23028.4 | −0.181461 | ||||||||
\(111\) | −37015.1 | −0.285149 | ||||||||
\(112\) | −4234.66 | −0.0318987 | ||||||||
\(113\) | − | 129508.i | − | 0.954117i | −0.878871 | − | 0.477059i | \(-0.841703\pi\) | ||
0.878871 | − | 0.477059i | \(-0.158297\pi\) | |||||||
\(114\) | − | 32062.0i | − | 0.231062i | ||||||
\(115\) | −17637.7 | −0.124365 | ||||||||
\(116\) | −65124.2 | + | 55677.6i | −0.449363 | + | 0.384181i | ||||
\(117\) | −38716.8 | −0.261478 | ||||||||
\(118\) | − | 15669.3i | − | 0.103596i | ||||||
\(119\) | − | 98441.1i | − | 0.637249i | ||||||
\(120\) | 15026.1 | 0.0952563 | ||||||||
\(121\) | 741.050 | 0.00460134 | ||||||||
\(122\) | 168116. | 1.02261 | ||||||||
\(123\) | 37644.9 | 0.224359 | ||||||||
\(124\) | 38463.1i | 0.224642i | ||||||||
\(125\) | −95367.2 | −0.545914 | ||||||||
\(126\) | 54675.1i | 0.306805i | ||||||||
\(127\) | 327753.i | 1.80317i | 0.432601 | + | 0.901586i | \(0.357596\pi\) | ||||
−0.432601 | + | 0.901586i | \(0.642404\pi\) | |||||||
\(128\) | 100313.i | 0.541170i | ||||||||
\(129\) | −25544.7 | −0.135153 | ||||||||
\(130\) | − | 10277.2i | − | 0.0533356i | ||||||
\(131\) | 307291.i | 1.56449i | 0.622972 | + | 0.782244i | \(0.285925\pi\) | ||||
−0.622972 | + | 0.782244i | \(0.714075\pi\) | |||||||
\(132\) | 38864.6 | 0.194142 | ||||||||
\(133\) | − | 120539.i | − | 0.590879i | ||||||
\(134\) | − | 16229.9i | − | 0.0780826i | ||||||
\(135\) | − | 37505.3i | − | 0.177116i | ||||||
\(136\) | 259853. | 1.20470 | ||||||||
\(137\) | − | 220879.i | − | 1.00543i | −0.864451 | − | 0.502717i | \(-0.832334\pi\) | ||
0.864451 | − | 0.502717i | \(-0.167666\pi\) | |||||||
\(138\) | −20582.6 | −0.0920033 | ||||||||
\(139\) | 228651. | 1.00378 | 0.501888 | − | 0.864932i | \(-0.332639\pi\) | ||||
0.501888 | + | 0.864932i | \(0.332639\pi\) | |||||||
\(140\) | 20989.2 | 0.0905057 | ||||||||
\(141\) | −2531.02 | −0.0107213 | ||||||||
\(142\) | 212300.i | 0.883544i | ||||||||
\(143\) | − | 71543.7i | − | 0.292571i | ||||||
\(144\) | −13151.5 | −0.0528528 | ||||||||
\(145\) | −54740.8 | + | 46800.4i | −0.216218 | + | 0.184854i | ||||
\(146\) | −55399.9 | −0.215093 | ||||||||
\(147\) | 61259.4i | 0.233819i | ||||||||
\(148\) | − | 136483.i | − | 0.512183i | ||||||
\(149\) | −276764. | −1.02128 | −0.510640 | − | 0.859795i | \(-0.670591\pi\) | ||||
−0.510640 | + | 0.859795i | \(0.670591\pi\) | |||||||
\(150\) | −53298.8 | −0.193415 | ||||||||
\(151\) | 401630. | 1.43345 | 0.716727 | − | 0.697354i | \(-0.245639\pi\) | ||||
0.716727 | + | 0.697354i | \(0.245639\pi\) | |||||||
\(152\) | 318185. | 1.11704 | ||||||||
\(153\) | − | 305726.i | − | 1.05585i | ||||||
\(154\) | −101033. | −0.343289 | ||||||||
\(155\) | 32330.6i | 0.108090i | ||||||||
\(156\) | 17344.6i | 0.0570628i | ||||||||
\(157\) | 10880.1i | 0.0352277i | 0.999845 | + | 0.0176138i | \(0.00560695\pi\) | ||||
−0.999845 | + | 0.0176138i | \(0.994393\pi\) | |||||||
\(158\) | −122497. | −0.390374 | ||||||||
\(159\) | 55544.1i | 0.174239i | ||||||||
\(160\) | 90224.2i | 0.278627i | ||||||||
\(161\) | −77381.8 | −0.235274 | ||||||||
\(162\) | 146666.i | 0.439078i | ||||||||
\(163\) | − | 391732.i | − | 1.15484i | −0.816449 | − | 0.577418i | \(-0.804061\pi\) | ||
0.816449 | − | 0.577418i | \(-0.195939\pi\) | |||||||
\(164\) | 138806.i | 0.402993i | ||||||||
\(165\) | 32668.0 | 0.0934142 | ||||||||
\(166\) | 165470.i | 0.466067i | ||||||||
\(167\) | −220260. | −0.611144 | −0.305572 | − | 0.952169i | \(-0.598848\pi\) | ||||
−0.305572 | + | 0.952169i | \(0.598848\pi\) | |||||||
\(168\) | 65924.0 | 0.180206 | ||||||||
\(169\) | −339364. | −0.914007 | ||||||||
\(170\) | 81153.7 | 0.215370 | ||||||||
\(171\) | − | 374355.i | − | 0.979023i | ||||||
\(172\) | − | 94189.2i | − | 0.242762i | ||||||
\(173\) | −660949. | −1.67901 | −0.839504 | − | 0.543353i | \(-0.817154\pi\) | ||||
−0.839504 | + | 0.543353i | \(0.817154\pi\) | |||||||
\(174\) | −63880.7 | + | 54614.6i | −0.159955 | + | 0.136753i | ||||
\(175\) | −200381. | −0.494607 | ||||||||
\(176\) | − | 24302.2i | − | 0.0591377i | ||||||
\(177\) | 22228.3i | 0.0533303i | ||||||||
\(178\) | −378198. | −0.894682 | ||||||||
\(179\) | −230503. | −0.537706 | −0.268853 | − | 0.963181i | \(-0.586645\pi\) | ||||
−0.268853 | + | 0.963181i | \(0.586645\pi\) | |||||||
\(180\) | 65185.6 | 0.149958 | ||||||||
\(181\) | 576366. | 1.30768 | 0.653841 | − | 0.756632i | \(-0.273157\pi\) | ||||
0.653841 | + | 0.756632i | \(0.273157\pi\) | |||||||
\(182\) | − | 45089.2i | − | 0.100901i | ||||||
\(183\) | −238488. | −0.526428 | ||||||||
\(184\) | − | 204263.i | − | 0.444781i | ||||||
\(185\) | − | 114722.i | − | 0.246444i | ||||||
\(186\) | 37728.7i | 0.0799632i | ||||||||
\(187\) | 564942. | 1.18141 | ||||||||
\(188\) | − | 9332.48i | − | 0.0192576i | ||||||
\(189\) | − | 164547.i | − | 0.335070i | ||||||
\(190\) | 99371.0 | 0.199699 | ||||||||
\(191\) | 254400.i | 0.504584i | 0.967651 | + | 0.252292i | \(0.0811844\pi\) | ||||
−0.967651 | + | 0.252292i | \(0.918816\pi\) | |||||||
\(192\) | 115254.i | 0.225634i | ||||||||
\(193\) | 263088.i | 0.508402i | 0.967151 | + | 0.254201i | \(0.0818125\pi\) | ||||
−0.967151 | + | 0.254201i | \(0.918188\pi\) | |||||||
\(194\) | 548701. | 1.04672 | ||||||||
\(195\) | 14579.2i | 0.0274566i | ||||||||
\(196\) | −225878. | −0.419985 | ||||||||
\(197\) | 515004. | 0.945465 | 0.472732 | − | 0.881206i | \(-0.343268\pi\) | ||||
0.472732 | + | 0.881206i | \(0.343268\pi\) | |||||||
\(198\) | −313774. | −0.568793 | ||||||||
\(199\) | 733536. | 1.31307 | 0.656536 | − | 0.754295i | \(-0.272021\pi\) | ||||
0.656536 | + | 0.754295i | \(0.272021\pi\) | |||||||
\(200\) | − | 528941.i | − | 0.935044i | ||||||
\(201\) | 23023.7i | 0.0401961i | ||||||||
\(202\) | −89170.8 | −0.153760 | ||||||||
\(203\) | −240164. | + | 205327.i | −0.409042 | + | 0.349708i | ||||
\(204\) | −136961. | −0.230421 | ||||||||
\(205\) | 116674.i | 0.193906i | ||||||||
\(206\) | − | 88923.0i | − | 0.145998i | ||||||
\(207\) | −240322. | −0.389824 | ||||||||
\(208\) | 10845.7 | 0.0173820 | ||||||||
\(209\) | 691760. | 1.09544 | ||||||||
\(210\) | 20588.4 | 0.0322163 | ||||||||
\(211\) | 1.27615e6i | 1.97331i | 0.162814 | + | 0.986657i | \(0.447943\pi\) | ||||
−0.162814 | + | 0.986657i | \(0.552057\pi\) | |||||||
\(212\) | −204804. | −0.312967 | ||||||||
\(213\) | − | 301167.i | − | 0.454840i | ||||||
\(214\) | 363738.i | 0.542943i | ||||||||
\(215\) | − | 79171.7i | − | 0.116808i | ||||||
\(216\) | 434351. | 0.633442 | ||||||||
\(217\) | 141844.i | 0.204485i | ||||||||
\(218\) | − | 532754.i | − | 0.759251i | ||||||
\(219\) | 78590.0 | 0.110728 | ||||||||
\(220\) | 120455.i | 0.167790i | ||||||||
\(221\) | 252124.i | 0.347243i | ||||||||
\(222\) | − | 133877.i | − | 0.182316i | ||||||
\(223\) | 920981. | 1.24019 | 0.620095 | − | 0.784526i | \(-0.287094\pi\) | ||||
0.620095 | + | 0.784526i | \(0.287094\pi\) | |||||||
\(224\) | 395840.i | 0.527108i | ||||||||
\(225\) | −622316. | −0.819511 | ||||||||
\(226\) | 468410. | 0.610036 | ||||||||
\(227\) | −829617. | −1.06859 | −0.534297 | − | 0.845297i | \(-0.679424\pi\) | ||||
−0.534297 | + | 0.845297i | \(0.679424\pi\) | |||||||
\(228\) | −167706. | −0.213654 | ||||||||
\(229\) | 763360.i | 0.961924i | 0.876741 | + | 0.480962i | \(0.159713\pi\) | ||||
−0.876741 | + | 0.480962i | \(0.840287\pi\) | |||||||
\(230\) | − | 63792.6i | − | 0.0795154i | ||||||
\(231\) | 143324. | 0.176722 | ||||||||
\(232\) | −541998. | − | 633956.i | −0.661116 | − | 0.773284i | ||||
\(233\) | −1.56800e6 | −1.89216 | −0.946078 | − | 0.323939i | \(-0.894993\pi\) | ||||
−0.946078 | + | 0.323939i | \(0.894993\pi\) | |||||||
\(234\) | − | 140032.i | − | 0.167181i | ||||||
\(235\) | − | 7844.51i | − | 0.00926608i | ||||||
\(236\) | −81961.1 | −0.0957916 | ||||||||
\(237\) | 173773. | 0.200961 | ||||||||
\(238\) | 356045. | 0.407439 | ||||||||
\(239\) | 1.00736e6 | 1.14075 | 0.570375 | − | 0.821384i | \(-0.306798\pi\) | ||||
0.570375 | + | 0.821384i | \(0.306798\pi\) | |||||||
\(240\) | 4952.32i | 0.00554984i | ||||||||
\(241\) | 264093. | 0.292896 | 0.146448 | − | 0.989218i | \(-0.453216\pi\) | ||||
0.146448 | + | 0.989218i | \(0.453216\pi\) | |||||||
\(242\) | 2680.25i | 0.00294197i | ||||||||
\(243\) | − | 781176.i | − | 0.848659i | ||||||
\(244\) | − | 879361.i | − | 0.945567i | ||||||
\(245\) | −189864. | −0.202082 | ||||||||
\(246\) | 136155.i | 0.143449i | ||||||||
\(247\) | 308721.i | 0.321976i | ||||||||
\(248\) | −374422. | −0.386574 | ||||||||
\(249\) | − | 234734.i | − | 0.239927i | ||||||
\(250\) | − | 344927.i | − | 0.349042i | ||||||
\(251\) | − | 359549.i | − | 0.360225i | −0.983646 | − | 0.180112i | \(-0.942354\pi\) | ||
0.983646 | − | 0.180112i | \(-0.0576461\pi\) | |||||||
\(252\) | 285988. | 0.283692 | ||||||||
\(253\) | − | 444085.i | − | 0.436179i | ||||||
\(254\) | −1.18543e6 | −1.15290 | ||||||||
\(255\) | −115124. | −0.110870 | ||||||||
\(256\) | −1.08164e6 | −1.03153 | ||||||||
\(257\) | 1.10353e6 | 1.04220 | 0.521101 | − | 0.853495i | \(-0.325521\pi\) | ||||
0.521101 | + | 0.853495i | \(0.325521\pi\) | |||||||
\(258\) | − | 92390.8i | − | 0.0864131i | ||||||
\(259\) | − | 503321.i | − | 0.466225i | ||||||
\(260\) | −53756.9 | −0.0493175 | ||||||||
\(261\) | −745870. | + | 637678.i | −0.677738 | + | 0.579429i | ||||
\(262\) | −1.11142e6 | −1.00029 | ||||||||
\(263\) | − | 980576.i | − | 0.874162i | −0.899422 | − | 0.437081i | \(-0.856012\pi\) | ||
0.899422 | − | 0.437081i | \(-0.143988\pi\) | |||||||
\(264\) | 378330.i | 0.334088i | ||||||||
\(265\) | −172150. | −0.150589 | ||||||||
\(266\) | 435970. | 0.377791 | ||||||||
\(267\) | 536509. | 0.460573 | ||||||||
\(268\) | −84893.6 | −0.0722002 | ||||||||
\(269\) | − | 1.34518e6i | − | 1.13344i | −0.823910 | − | 0.566721i | \(-0.808212\pi\) | ||
0.823910 | − | 0.566721i | \(-0.191788\pi\) | |||||||
\(270\) | 135651. | 0.113243 | ||||||||
\(271\) | 2.27613e6i | 1.88267i | 0.337476 | + | 0.941334i | \(0.390427\pi\) | ||||
−0.337476 | + | 0.941334i | \(0.609573\pi\) | |||||||
\(272\) | 85642.6i | 0.0701887i | ||||||||
\(273\) | 63963.2i | 0.0519426i | ||||||||
\(274\) | 798884. | 0.642846 | ||||||||
\(275\) | − | 1.14996e6i | − | 0.916962i | ||||||
\(276\) | 107661.i | 0.0850721i | ||||||||
\(277\) | 1.03963e6 | 0.814104 | 0.407052 | − | 0.913405i | \(-0.366557\pi\) | ||||
0.407052 | + | 0.913405i | \(0.366557\pi\) | |||||||
\(278\) | 826994.i | 0.641786i | ||||||||
\(279\) | 440520.i | 0.338809i | ||||||||
\(280\) | 204321.i | 0.155746i | ||||||||
\(281\) | 1.94505e6 | 1.46948 | 0.734741 | − | 0.678348i | \(-0.237304\pi\) | ||||
0.734741 | + | 0.678348i | \(0.237304\pi\) | |||||||
\(282\) | − | 9154.29i | − | 0.00685491i | ||||||
\(283\) | −2.37742e6 | −1.76458 | −0.882288 | − | 0.470710i | \(-0.843998\pi\) | ||||
−0.882288 | + | 0.470710i | \(0.843998\pi\) | |||||||
\(284\) | 1.11047e6 | 0.816981 | ||||||||
\(285\) | −140967. | −0.102803 | ||||||||
\(286\) | 258761. | 0.187062 | ||||||||
\(287\) | 511885.i | 0.366832i | ||||||||
\(288\) | 1.22935e6i | 0.873362i | ||||||||
\(289\) | −571034. | −0.402177 | ||||||||
\(290\) | −169269. | − | 197988.i | −0.118191 | − | 0.138243i | ||||
\(291\) | −778383. | −0.538842 | ||||||||
\(292\) | 289780.i | 0.198889i | ||||||||
\(293\) | 1.68298e6i | 1.14528i | 0.819808 | + | 0.572639i | \(0.194080\pi\) | ||||
−0.819808 | + | 0.572639i | \(0.805920\pi\) | |||||||
\(294\) | −221565. | −0.149497 | ||||||||
\(295\) | −68893.2 | −0.0460916 | ||||||||
\(296\) | 1.32861e6 | 0.881388 | ||||||||
\(297\) | 944316. | 0.621193 | ||||||||
\(298\) | − | 1.00101e6i | − | 0.652977i | ||||||
\(299\) | 198188. | 0.128203 | ||||||||
\(300\) | 278790.i | 0.178844i | ||||||||
\(301\) | − | 347349.i | − | 0.220979i | ||||||
\(302\) | 1.45263e6i | 0.916510i | ||||||||
\(303\) | 126497. | 0.0791542 | ||||||||
\(304\) | 104868.i | 0.0650814i | ||||||||
\(305\) | − | 739156.i | − | 0.454974i | ||||||
\(306\) | 1.10576e6 | 0.675082 | ||||||||
\(307\) | − | 2.20020e6i | − | 1.33234i | −0.745799 | − | 0.666171i | \(-0.767932\pi\) | ||
0.745799 | − | 0.666171i | \(-0.232068\pi\) | |||||||
\(308\) | 528470.i | 0.317427i | ||||||||
\(309\) | 126146.i | 0.0751582i | ||||||||
\(310\) | −116934. | −0.0691095 | ||||||||
\(311\) | 258930.i | 0.151803i | 0.997115 | + | 0.0759017i | \(0.0241835\pi\) | ||||
−0.997115 | + | 0.0759017i | \(0.975816\pi\) | |||||||
\(312\) | −168842. | −0.0981963 | ||||||||
\(313\) | 1.48259e6 | 0.855384 | 0.427692 | − | 0.903924i | \(-0.359327\pi\) | ||||
0.427692 | + | 0.903924i | \(0.359327\pi\) | |||||||
\(314\) | −39351.5 | −0.0225236 | ||||||||
\(315\) | 240390. | 0.136503 | ||||||||
\(316\) | 640741.i | 0.360965i | ||||||||
\(317\) | 1.94232e6i | 1.08561i | 0.839859 | + | 0.542804i | \(0.182637\pi\) | ||||
−0.839859 | + | 0.542804i | \(0.817363\pi\) | |||||||
\(318\) | −200894. | −0.111403 | ||||||||
\(319\) | −1.17835e6 | − | 1.37827e6i | −0.648331 | − | 0.758330i | ||||
\(320\) | −357213. | −0.195008 | ||||||||
\(321\) | − | 515997.i | − | 0.279502i | ||||||
\(322\) | − | 279877.i | − | 0.150428i | ||||||
\(323\) | −2.43780e6 | −1.30015 | ||||||||
\(324\) | 767163. | 0.405999 | ||||||||
\(325\) | 513208. | 0.269517 | ||||||||
\(326\) | 1.41683e6 | 0.738369 | ||||||||
\(327\) | 755762.i | 0.390855i | ||||||||
\(328\) | −1.35121e6 | −0.693488 | ||||||||
\(329\) | − | 34416.2i | − | 0.0175296i | ||||||
\(330\) | 118155.i | 0.0597264i | ||||||||
\(331\) | − | 2.96478e6i | − | 1.48738i | −0.668523 | − | 0.743691i | \(-0.733073\pi\) | ||
0.668523 | − | 0.743691i | \(-0.266927\pi\) | |||||||
\(332\) | 865520. | 0.430955 | ||||||||
\(333\) | − | 1.56315e6i | − | 0.772485i | ||||||
\(334\) | − | 796642.i | − | 0.390748i | ||||||
\(335\) | −71358.2 | −0.0347402 | ||||||||
\(336\) | 21727.3i | 0.0104992i | ||||||||
\(337\) | 2.71471e6i | 1.30211i | 0.759029 | + | 0.651057i | \(0.225674\pi\) | ||||
−0.759029 | + | 0.651057i | \(0.774326\pi\) | |||||||
\(338\) | − | 1.22742e6i | − | 0.584390i | ||||||
\(339\) | −664484. | −0.314040 | ||||||||
\(340\) | − | 424490.i | − | 0.199145i | ||||||
\(341\) | −814025. | −0.379098 | ||||||||
\(342\) | 1.35398e6 | 0.625960 | ||||||||
\(343\) | −2.00557e6 | −0.920455 | ||||||||
\(344\) | 916892. | 0.417755 | ||||||||
\(345\) | 90495.8i | 0.0409337i | ||||||||
\(346\) | − | 2.39054e6i | − | 1.07351i | ||||||
\(347\) | −2.39738e6 | −1.06884 | −0.534420 | − | 0.845219i | \(-0.679470\pi\) | ||||
−0.534420 | + | 0.845219i | \(0.679470\pi\) | |||||||
\(348\) | 285672. | + | 334140.i | 0.126450 | + | 0.147904i | ||||
\(349\) | −1.29162e6 | −0.567639 | −0.283820 | − | 0.958878i | \(-0.591602\pi\) | ||||
−0.283820 | + | 0.958878i | \(0.591602\pi\) | |||||||
\(350\) | − | 724743.i | − | 0.316238i | ||||||
\(351\) | 421433.i | 0.182583i | ||||||||
\(352\) | −2.27168e6 | −0.977216 | ||||||||
\(353\) | −827351. | −0.353389 | −0.176695 | − | 0.984266i | \(-0.556540\pi\) | ||||
−0.176695 | + | 0.984266i | \(0.556540\pi\) | |||||||
\(354\) | −80396.2 | −0.0340979 | ||||||||
\(355\) | 933420. | 0.393103 | ||||||||
\(356\) | 1.97823e6i | 0.827280i | ||||||||
\(357\) | −505083. | −0.209745 | ||||||||
\(358\) | − | 833692.i | − | 0.343794i | ||||||
\(359\) | − | 1.63510e6i | − | 0.669590i | −0.942291 | − | 0.334795i | \(-0.891333\pi\) | ||
0.942291 | − | 0.334795i | \(-0.108667\pi\) | |||||||
\(360\) | 634554.i | 0.258055i | ||||||||
\(361\) | −508941. | −0.205542 | ||||||||
\(362\) | 2.08462e6i | 0.836094i | ||||||||
\(363\) | − | 3802.19i | − | 0.00151449i | ||||||
\(364\) | −235847. | −0.0932991 | ||||||||
\(365\) | 243577.i | 0.0956984i | ||||||||
\(366\) | − | 862571.i | − | 0.336583i | ||||||
\(367\) | − | 1.76417e6i | − | 0.683715i | −0.939752 | − | 0.341858i | \(-0.888944\pi\) | ||
0.939752 | − | 0.341858i | \(-0.111056\pi\) | |||||||
\(368\) | 67321.2 | 0.0259139 | ||||||||
\(369\) | 1.58975e6i | 0.607802i | ||||||||
\(370\) | 414932. | 0.157570 | ||||||||
\(371\) | −755273. | −0.284885 | ||||||||
\(372\) | 197347. | 0.0739390 | ||||||||
\(373\) | 1.23465e6 | 0.459487 | 0.229744 | − | 0.973251i | \(-0.426211\pi\) | ||||
0.229744 | + | 0.973251i | \(0.426211\pi\) | |||||||
\(374\) | 2.04330e6i | 0.755359i | ||||||||
\(375\) | 489311.i | 0.179683i | ||||||||
\(376\) | 90847.7 | 0.0331394 | ||||||||
\(377\) | 615100. | − | 525877.i | 0.222891 | − | 0.190560i | ||||
\(378\) | 595139. | 0.214234 | ||||||||
\(379\) | 3.06325e6i | 1.09543i | 0.836665 | + | 0.547715i | \(0.184502\pi\) | ||||
−0.836665 | + | 0.547715i | \(0.815498\pi\) | |||||||
\(380\) | − | 519779.i | − | 0.184654i | ||||||
\(381\) | 1.68164e6 | 0.593499 | ||||||||
\(382\) | −920122. | −0.322617 | ||||||||
\(383\) | 4.47059e6 | 1.55728 | 0.778642 | − | 0.627469i | \(-0.215909\pi\) | ||||
0.778642 | + | 0.627469i | \(0.215909\pi\) | |||||||
\(384\) | 514689. | 0.178122 | ||||||||
\(385\) | 444211.i | 0.152735i | ||||||||
\(386\) | −951544. | −0.325058 | ||||||||
\(387\) | − | 1.07875e6i | − | 0.366138i | ||||||
\(388\) | − | 2.87008e6i | − | 0.967865i | ||||||
\(389\) | − | 863569.i | − | 0.289350i | −0.989479 | − | 0.144675i | \(-0.953786\pi\) | ||
0.989479 | − | 0.144675i | \(-0.0462136\pi\) | |||||||
\(390\) | −52730.5 | −0.0175550 | ||||||||
\(391\) | 1.56498e6i | 0.517688i | ||||||||
\(392\) | − | 2.19882e6i | − | 0.722729i | ||||||
\(393\) | 1.57666e6 | 0.514939 | ||||||||
\(394\) | 1.86268e6i | 0.604503i | ||||||||
\(395\) | 538581.i | 0.173684i | ||||||||
\(396\) | 1.64125e6i | 0.525942i | ||||||||
\(397\) | 3.83756e6 | 1.22202 | 0.611011 | − | 0.791622i | \(-0.290763\pi\) | ||||
0.611011 | + | 0.791622i | \(0.290763\pi\) | |||||||
\(398\) | 2.65308e6i | 0.839541i | ||||||||
\(399\) | −618464. | −0.194483 | ||||||||
\(400\) | 174329. | 0.0544777 | ||||||||
\(401\) | 354668. | 0.110144 | 0.0550721 | − | 0.998482i | \(-0.482461\pi\) | ||||
0.0550721 | + | 0.998482i | \(0.482461\pi\) | |||||||
\(402\) | −83272.7 | −0.0257003 | ||||||||
\(403\) | − | 363286.i | − | 0.111426i | ||||||
\(404\) | 466425.i | 0.142177i | ||||||||
\(405\) | 644847. | 0.195352 | ||||||||
\(406\) | −742634. | − | 868633.i | −0.223594 | − | 0.261530i | ||||
\(407\) | 2.88850e6 | 0.864344 | ||||||||
\(408\) | − | 1.33326e6i | − | 0.396519i | ||||||
\(409\) | 511145.i | 0.151090i | 0.997142 | + | 0.0755449i | \(0.0240696\pi\) | ||||
−0.997142 | + | 0.0755449i | \(0.975930\pi\) | |||||||
\(410\) | −421992. | −0.123978 | ||||||||
\(411\) | −1.13329e6 | −0.330931 | ||||||||
\(412\) | −465129. | −0.134999 | ||||||||
\(413\) | −302255. | −0.0871963 | ||||||||
\(414\) | − | 869206.i | − | 0.249242i | ||||||
\(415\) | 727522. | 0.207360 | ||||||||
\(416\) | − | 1.01381e6i | − | 0.287227i | ||||||
\(417\) | − | 1.17317e6i | − | 0.330385i | ||||||
\(418\) | 2.50198e6i | 0.700395i | ||||||||
\(419\) | 335901. | 0.0934708 | 0.0467354 | − | 0.998907i | \(-0.485118\pi\) | ||||
0.0467354 | + | 0.998907i | \(0.485118\pi\) | |||||||
\(420\) | − | 107692.i | − | 0.0297892i | ||||||
\(421\) | 1.22224e6i | 0.336085i | 0.985780 | + | 0.168043i | \(0.0537447\pi\) | ||||
−0.985780 | + | 0.168043i | \(0.946255\pi\) | |||||||
\(422\) | −4.61563e6 | −1.26168 | ||||||||
\(423\) | − | 106885.i | − | 0.0290447i | ||||||
\(424\) | − | 1.99368e6i | − | 0.538568i | ||||||
\(425\) | 4.05253e6i | 1.08831i | ||||||||
\(426\) | 1.08927e6 | 0.290812 | ||||||||
\(427\) | − | 3.24289e6i | − | 0.860722i | ||||||
\(428\) | 1.90260e6 | 0.502040 | ||||||||
\(429\) | −367077. | −0.0962974 | ||||||||
\(430\) | 286351. | 0.0746839 | ||||||||
\(431\) | −3.09666e6 | −0.802973 | −0.401486 | − | 0.915865i | \(-0.631506\pi\) | ||||
−0.401486 | + | 0.915865i | \(0.631506\pi\) | |||||||
\(432\) | 143154.i | 0.0369057i | ||||||||
\(433\) | 3.64328e6i | 0.933841i | 0.884299 | + | 0.466920i | \(0.154636\pi\) | ||||
−0.884299 | + | 0.466920i | \(0.845364\pi\) | |||||||
\(434\) | −513025. | −0.130742 | ||||||||
\(435\) | 240124. | + | 280865.i | 0.0608433 | + | 0.0711663i | ||||
\(436\) | −2.78667e6 | −0.702052 | ||||||||
\(437\) | 1.91629e6i | 0.480018i | ||||||||
\(438\) | 284247.i | 0.0707963i | ||||||||
\(439\) | 2.94312e6 | 0.728865 | 0.364432 | − | 0.931230i | \(-0.381263\pi\) | ||||
0.364432 | + | 0.931230i | \(0.381263\pi\) | |||||||
\(440\) | −1.17257e6 | −0.288741 | ||||||||
\(441\) | −2.58699e6 | −0.633429 | ||||||||
\(442\) | −911891. | −0.222018 | ||||||||
\(443\) | − | 2.50646e6i | − | 0.606809i | −0.952862 | − | 0.303405i | \(-0.901877\pi\) | ||
0.952862 | − | 0.303405i | \(-0.0981234\pi\) | |||||||
\(444\) | −700271. | −0.168581 | ||||||||
\(445\) | 1.66283e6i | 0.398058i | ||||||||
\(446\) | 3.33103e6i | 0.792943i | ||||||||
\(447\) | 1.42003e6i | 0.336146i | ||||||||
\(448\) | −1.56720e6 | −0.368917 | ||||||||
\(449\) | − | 5.06356e6i | − | 1.18533i | −0.805448 | − | 0.592666i | \(-0.798075\pi\) | ||
0.805448 | − | 0.592666i | \(-0.201925\pi\) | |||||||
\(450\) | − | 2.25081e6i | − | 0.523972i | ||||||
\(451\) | −2.93765e6 | −0.680078 | ||||||||
\(452\) | − | 2.45011e6i | − | 0.564078i | ||||||
\(453\) | − | 2.06069e6i | − | 0.471810i | ||||||
\(454\) | − | 3.00059e6i | − | 0.683229i | ||||||
\(455\) | −198244. | −0.0448922 | ||||||||
\(456\) | − | 1.63255e6i | − | 0.367666i | ||||||
\(457\) | 1.05399e6 | 0.236073 | 0.118037 | − | 0.993009i | \(-0.462340\pi\) | ||||
0.118037 | + | 0.993009i | \(0.462340\pi\) | |||||||
\(458\) | −2.76095e6 | −0.615027 | ||||||||
\(459\) | −3.32783e6 | −0.737274 | ||||||||
\(460\) | −333679. | −0.0735250 | ||||||||
\(461\) | − | 3.14678e6i | − | 0.689627i | −0.938671 | − | 0.344813i | \(-0.887942\pi\) | ||
0.938671 | − | 0.344813i | \(-0.112058\pi\) | |||||||
\(462\) | 518380.i | 0.112991i | ||||||||
\(463\) | 5.03811e6 | 1.09223 | 0.546116 | − | 0.837709i | \(-0.316106\pi\) | ||||
0.546116 | + | 0.837709i | \(0.316106\pi\) | |||||||
\(464\) | 208940. | − | 178632.i | 0.0450532 | − | 0.0385181i | ||||
\(465\) | 165882. | 0.0355769 | ||||||||
\(466\) | − | 5.67120e6i | − | 1.20979i | ||||||
\(467\) | − | 4.52631e6i | − | 0.960400i | −0.877159 | − | 0.480200i | \(-0.840564\pi\) | ||
0.877159 | − | 0.480200i | \(-0.159436\pi\) | |||||||
\(468\) | −732464. | −0.154587 | ||||||||
\(469\) | −313069. | −0.0657217 | ||||||||
\(470\) | 28372.3 | 0.00592447 | ||||||||
\(471\) | 55823.8 | 0.0115949 | ||||||||
\(472\) | − | 797856.i | − | 0.164843i | ||||||
\(473\) | 1.99340e6 | 0.409677 | ||||||||
\(474\) | 628507.i | 0.128489i | ||||||||
\(475\) | 4.96224e6i | 1.00912i | ||||||||
\(476\) | − | 1.86236e6i | − | 0.376744i | ||||||
\(477\) | −2.34563e6 | −0.472023 | ||||||||
\(478\) | 3.64346e6i | 0.729363i | ||||||||
\(479\) | 6.73376e6i | 1.34097i | 0.741924 | + | 0.670484i | \(0.233914\pi\) | ||||
−0.741924 | + | 0.670484i | \(0.766086\pi\) | |||||||
\(480\) | 462924. | 0.0917079 | ||||||||
\(481\) | 1.28909e6i | 0.254051i | ||||||||
\(482\) | 955179.i | 0.187270i | ||||||||
\(483\) | 397032.i | 0.0774386i | ||||||||
\(484\) | 14019.6 | 0.00272033 | ||||||||
\(485\) | − | 2.41248e6i | − | 0.465703i | ||||||
\(486\) | 2.82538e6 | 0.542609 | ||||||||
\(487\) | −1.18719e6 | −0.226829 | −0.113414 | − | 0.993548i | \(-0.536179\pi\) | ||||
−0.113414 | + | 0.993548i | \(0.536179\pi\) | |||||||
\(488\) | 8.56020e6 | 1.62718 | ||||||||
\(489\) | −2.00990e6 | −0.380105 | ||||||||
\(490\) | − | 686706.i | − | 0.129205i | ||||||
\(491\) | − | 6.54103e6i | − | 1.22445i | −0.790682 | − | 0.612227i | \(-0.790274\pi\) | ||
0.790682 | − | 0.612227i | \(-0.209726\pi\) | |||||||
\(492\) | 712186. | 0.132642 | ||||||||
\(493\) | 4.15257e6 | + | 4.85712e6i | 0.769485 | + | 0.900039i | ||||
\(494\) | −1.11659e6 | −0.205862 | ||||||||
\(495\) | 1.37957e6i | 0.253065i | ||||||||
\(496\) | − | 123402.i | − | 0.0225226i | ||||||
\(497\) | 4.09519e6 | 0.743674 | ||||||||
\(498\) | 848995. | 0.153402 | ||||||||
\(499\) | −4.90073e6 | −0.881067 | −0.440534 | − | 0.897736i | \(-0.645211\pi\) | ||||
−0.440534 | + | 0.897736i | \(0.645211\pi\) | |||||||
\(500\) | −1.80421e6 | −0.322746 | ||||||||
\(501\) | 1.13011e6i | 0.201153i | ||||||||
\(502\) | 1.30043e6 | 0.230317 | ||||||||
\(503\) | 400862.i | 0.0706439i | 0.999376 | + | 0.0353219i | \(0.0112457\pi\) | ||||
−0.999376 | + | 0.0353219i | \(0.988754\pi\) | |||||||
\(504\) | 2.78397e6i | 0.488190i | ||||||||
\(505\) | 392058.i | 0.0684104i | ||||||||
\(506\) | 1.60618e6 | 0.278881 | ||||||||
\(507\) | 1.74122e6i | 0.300838i | ||||||||
\(508\) | 6.20060e6i | 1.06604i | ||||||||
\(509\) | 653951. | 0.111880 | 0.0559398 | − | 0.998434i | \(-0.482185\pi\) | ||||
0.0559398 | + | 0.998434i | \(0.482185\pi\) | |||||||
\(510\) | − | 416385.i | − | 0.0708874i | ||||||
\(511\) | 1.06865e6i | 0.181043i | ||||||||
\(512\) | − | 702077.i | − | 0.118361i | ||||||
\(513\) | −4.07486e6 | −0.683626 | ||||||||
\(514\) | 3.99129e6i | 0.666355i | ||||||||
\(515\) | −390969. | −0.0649567 | ||||||||
\(516\) | −483267. | −0.0799030 | ||||||||
\(517\) | 197510. | 0.0324985 | ||||||||
\(518\) | 1.82043e6 | 0.298091 | ||||||||
\(519\) | 3.39121e6i | 0.552632i | ||||||||
\(520\) | − | 523301.i | − | 0.0848678i | ||||||
\(521\) | −7.46746e6 | −1.20525 | −0.602627 | − | 0.798023i | \(-0.705879\pi\) | ||||
−0.602627 | + | 0.798023i | \(0.705879\pi\) | |||||||
\(522\) | −2.30638e6 | − | 2.69769e6i | −0.370471 | − | 0.433327i | ||||
\(523\) | 1.19250e7 | 1.90636 | 0.953182 | − | 0.302398i | \(-0.0977872\pi\) | ||||
0.953182 | + | 0.302398i | \(0.0977872\pi\) | |||||||
\(524\) | 5.81350e6i | 0.924931i | ||||||||
\(525\) | 1.02812e6i | 0.162796i | ||||||||
\(526\) | 3.54658e6 | 0.558914 | ||||||||
\(527\) | 2.86867e6 | 0.449940 | ||||||||
\(528\) | −124690. | −0.0194647 | ||||||||
\(529\) | −5.20615e6 | −0.808868 | ||||||||
\(530\) | − | 622638.i | − | 0.0962822i | ||||||
\(531\) | −938704. | −0.144475 | ||||||||
\(532\) | − | 2.28042e6i | − | 0.349330i | ||||||
\(533\) | − | 1.31102e6i | − | 0.199891i | ||||||
\(534\) | 1.94046e6i | 0.294478i | ||||||||
\(535\) | 1.59925e6 | 0.241564 | ||||||||
\(536\) | − | 826404.i | − | 0.124245i | ||||||
\(537\) | 1.18267e6i | 0.176982i | ||||||||
\(538\) | 4.86529e6 | 0.724691 | ||||||||
\(539\) | − | 4.78043e6i | − | 0.708753i | ||||||
\(540\) | − | 709546.i | − | 0.104712i | ||||||
\(541\) | − | 3.10008e6i | − | 0.455386i | −0.973733 | − | 0.227693i | \(-0.926882\pi\) | ||
0.973733 | − | 0.227693i | \(-0.0731182\pi\) | |||||||
\(542\) | −8.23238e6 | −1.20373 | ||||||||
\(543\) | − | 2.95723e6i | − | 0.430413i | ||||||
\(544\) | 8.00555e6 | 1.15983 | ||||||||
\(545\) | −2.34236e6 | −0.337803 | ||||||||
\(546\) | −231344. | −0.0332106 | ||||||||
\(547\) | −1.00371e6 | −0.143430 | −0.0717149 | − | 0.997425i | \(-0.522847\pi\) | ||||
−0.0717149 | + | 0.997425i | \(0.522847\pi\) | |||||||
\(548\) | − | 4.17871e6i | − | 0.594417i | ||||||
\(549\) | − | 1.00714e7i | − | 1.42612i | ||||||
\(550\) | 4.15922e6 | 0.586280 | ||||||||
\(551\) | 5.08474e6 | + | 5.94744e6i | 0.713493 | + | 0.834548i | ||||
\(552\) | −1.04804e6 | −0.146396 | ||||||||
\(553\) | 2.36291e6i | 0.328576i | ||||||||
\(554\) | 3.76017e6i | 0.520515i | ||||||||
\(555\) | −588620. | −0.0811152 | ||||||||
\(556\) | 4.32575e6 | 0.593437 | ||||||||
\(557\) | −1.19484e7 | −1.63181 | −0.815906 | − | 0.578184i | \(-0.803762\pi\) | ||||
−0.815906 | + | 0.578184i | \(0.803762\pi\) | |||||||
\(558\) | −1.59329e6 | −0.216625 | ||||||||
\(559\) | 889620.i | 0.120414i | ||||||||
\(560\) | −67340.3 | −0.00907412 | ||||||||
\(561\) | − | 2.89861e6i | − | 0.388851i | ||||||
\(562\) | 7.03491e6i | 0.939545i | ||||||||
\(563\) | 1.50352e6i | 0.199912i | 0.994992 | + | 0.0999558i | \(0.0318701\pi\) | ||||
−0.994992 | + | 0.0999558i | \(0.968130\pi\) | |||||||
\(564\) | −47883.2 | −0.00633849 | ||||||||
\(565\) | − | 2.05946e6i | − | 0.271414i | ||||||
\(566\) | − | 8.59874e6i | − | 1.12822i | ||||||
\(567\) | 2.82913e6 | 0.369569 | ||||||||
\(568\) | 1.08100e7i | 1.40590i | ||||||||
\(569\) | − | 8.47841e6i | − | 1.09783i | −0.835879 | − | 0.548913i | \(-0.815042\pi\) | ||
0.835879 | − | 0.548913i | \(-0.184958\pi\) | |||||||
\(570\) | − | 509854.i | − | 0.0657293i | ||||||
\(571\) | −1.37549e7 | −1.76549 | −0.882747 | − | 0.469848i | \(-0.844309\pi\) | ||||
−0.882747 | + | 0.469848i | \(0.844309\pi\) | |||||||
\(572\) | − | 1.35350e6i | − | 0.172969i | ||||||
\(573\) | 1.30528e6 | 0.166080 | ||||||||
\(574\) | −1.85140e6 | −0.234542 | ||||||||
\(575\) | 3.18558e6 | 0.401809 | ||||||||
\(576\) | −4.86720e6 | −0.611256 | ||||||||
\(577\) | − | 1.43166e7i | − | 1.79019i | −0.445875 | − | 0.895095i | \(-0.647107\pi\) | ||
0.445875 | − | 0.895095i | \(-0.352893\pi\) | |||||||
\(578\) | − | 2.06533e6i | − | 0.257141i | ||||||
\(579\) | 1.34985e6 | 0.167336 | ||||||||
\(580\) | −1.03561e6 | + | 885394.i | −0.127829 | + | 0.109287i | ||||
\(581\) | 3.19185e6 | 0.392286 | ||||||||
\(582\) | − | 2.81528e6i | − | 0.344520i | ||||||
\(583\) | − | 4.33442e6i | − | 0.528153i | ||||||
\(584\) | −2.82088e6 | −0.342257 | ||||||||
\(585\) | −615680. | −0.0743816 | ||||||||
\(586\) | −6.08707e6 | −0.732258 | ||||||||
\(587\) | −7.54078e6 | −0.903277 | −0.451638 | − | 0.892201i | \(-0.649160\pi\) | ||||
−0.451638 | + | 0.892201i | \(0.649160\pi\) | |||||||
\(588\) | 1.15894e6i | 0.138235i | ||||||||
\(589\) | 3.51263e6 | 0.417200 | ||||||||
\(590\) | − | 249175.i | − | 0.0294696i | ||||||
\(591\) | − | 2.64239e6i | − | 0.311192i | ||||||
\(592\) | 437883.i | 0.0513516i | ||||||||
\(593\) | −7.99284e6 | −0.933392 | −0.466696 | − | 0.884418i | \(-0.654556\pi\) | ||||
−0.466696 | + | 0.884418i | \(0.654556\pi\) | |||||||
\(594\) | 3.41543e6i | 0.397173i | ||||||||
\(595\) | − | 1.56543e6i | − | 0.181276i | ||||||
\(596\) | −5.23597e6 | −0.603784 | ||||||||
\(597\) | − | 3.76364e6i | − | 0.432187i | ||||||
\(598\) | 716812.i | 0.0819695i | ||||||||
\(599\) | 1.22235e7i | 1.39196i | 0.718060 | + | 0.695981i | \(0.245030\pi\) | ||||
−0.718060 | + | 0.695981i | \(0.754970\pi\) | |||||||
\(600\) | −2.71390e6 | −0.307762 | ||||||||
\(601\) | 1.34301e6i | 0.151667i | 0.997120 | + | 0.0758337i | \(0.0241618\pi\) | ||||
−0.997120 | + | 0.0758337i | \(0.975838\pi\) | |||||||
\(602\) | 1.25630e6 | 0.141287 | ||||||||
\(603\) | −972291. | −0.108894 | ||||||||
\(604\) | 7.59825e6 | 0.847464 | ||||||||
\(605\) | 11784.3 | 0.00130893 | ||||||||
\(606\) | 457519.i | 0.0506090i | ||||||||
\(607\) | 1.50883e7i | 1.66215i | 0.556163 | + | 0.831073i | \(0.312273\pi\) | ||||
−0.556163 | + | 0.831073i | \(0.687727\pi\) | |||||||
\(608\) | 9.80262e6 | 1.07543 | ||||||||
\(609\) | 1.05350e6 | + | 1.23224e6i | 0.115104 | + | 0.134633i | ||||
\(610\) | 2.67340e6 | 0.290897 | ||||||||
\(611\) | 88145.6i | 0.00955208i | ||||||||
\(612\) | − | 5.78388e6i | − | 0.624224i | ||||||
\(613\) | 4.95968e6 | 0.533092 | 0.266546 | − | 0.963822i | \(-0.414118\pi\) | ||||
0.266546 | + | 0.963822i | \(0.414118\pi\) | |||||||
\(614\) | 7.95774e6 | 0.851862 | ||||||||
\(615\) | 598635. | 0.0638226 | ||||||||
\(616\) | −5.14443e6 | −0.546242 | ||||||||
\(617\) | 9.82407e6i | 1.03891i | 0.854497 | + | 0.519456i | \(0.173865\pi\) | ||||
−0.854497 | + | 0.519456i | \(0.826135\pi\) | |||||||
\(618\) | −456248. | −0.0480540 | ||||||||
\(619\) | − | 1.35526e7i | − | 1.42166i | −0.703364 | − | 0.710830i | \(-0.748320\pi\) | ||
0.703364 | − | 0.710830i | \(-0.251680\pi\) | |||||||
\(620\) | 611647.i | 0.0639030i | ||||||||
\(621\) | 2.61591e6i | 0.272204i | ||||||||
\(622\) | −936507. | −0.0970588 | ||||||||
\(623\) | 7.29530e6i | 0.753049i | ||||||||
\(624\) | − | 55647.2i | − | 0.00572113i | ||||||
\(625\) | 7.45884e6 | 0.763785 | ||||||||
\(626\) | 5.36229e6i | 0.546909i | ||||||||
\(627\) | − | 3.54929e6i | − | 0.360556i | ||||||
\(628\) | 205836.i | 0.0208267i | ||||||||
\(629\) | −1.01793e7 | −1.02586 | ||||||||
\(630\) | 869452.i | 0.0872758i | ||||||||
\(631\) | 7.34343e6 | 0.734219 | 0.367109 | − | 0.930178i | \(-0.380347\pi\) | ||||
0.367109 | + | 0.930178i | \(0.380347\pi\) | |||||||
\(632\) | −6.23734e6 | −0.621165 | ||||||||
\(633\) | 6.54770e6 | 0.649500 | ||||||||
\(634\) | −7.02505e6 | −0.694107 | ||||||||
\(635\) | 5.21197e6i | 0.512942i | ||||||||
\(636\) | 1.05081e6i | 0.103011i | ||||||||
\(637\) | 2.13342e6 | 0.208319 | ||||||||
\(638\) | 4.98498e6 | − | 4.26189e6i | 0.484855 | − | 0.414525i | ||||
\(639\) | 1.27183e7 | 1.23219 | ||||||||
\(640\) | 1.59520e6i | 0.153945i | ||||||||
\(641\) | − | 8.79727e6i | − | 0.845674i | −0.906206 | − | 0.422837i | \(-0.861034\pi\) | ||
0.906206 | − | 0.422837i | \(-0.138966\pi\) | |||||||
\(642\) | 1.86627e6 | 0.178705 | ||||||||
\(643\) | −8.56541e6 | −0.816998 | −0.408499 | − | 0.912759i | \(-0.633948\pi\) | ||||
−0.408499 | + | 0.912759i | \(0.633948\pi\) | |||||||
\(644\) | −1.46395e6 | −0.139095 | ||||||||
\(645\) | −406215. | −0.0384465 | ||||||||
\(646\) | − | 8.81713e6i | − | 0.831277i | ||||||
\(647\) | 1.67135e7 | 1.56967 | 0.784833 | − | 0.619707i | \(-0.212749\pi\) | ||||
0.784833 | + | 0.619707i | \(0.212749\pi\) | |||||||
\(648\) | 7.46801e6i | 0.698662i | ||||||||
\(649\) | − | 1.73461e6i | − | 0.161655i | ||||||
\(650\) | 1.85619e6i | 0.172321i | ||||||||
\(651\) | 727774. | 0.0673045 | ||||||||
\(652\) | − | 7.41099e6i | − | 0.682743i | ||||||
\(653\) | 1.18888e7i | 1.09108i | 0.838085 | + | 0.545540i | \(0.183675\pi\) | ||||
−0.838085 | + | 0.545540i | \(0.816325\pi\) | |||||||
\(654\) | −2.73346e6 | −0.249901 | ||||||||
\(655\) | 4.88660e6i | 0.445044i | ||||||||
\(656\) | − | 445334.i | − | 0.0404042i | ||||||
\(657\) | 3.31886e6i | 0.299968i | ||||||||
\(658\) | 124478. | 0.0112080 | ||||||||
\(659\) | 1.75331e6i | 0.157269i | 0.996903 | + | 0.0786347i | \(0.0250561\pi\) | ||||
−0.996903 | + | 0.0786347i | \(0.974944\pi\) | |||||||
\(660\) | 618031. | 0.0552268 | ||||||||
\(661\) | −1.32255e7 | −1.17736 | −0.588678 | − | 0.808367i | \(-0.700352\pi\) | ||||
−0.588678 | + | 0.808367i | \(0.700352\pi\) | |||||||
\(662\) | 1.07231e7 | 0.950990 | ||||||||
\(663\) | 1.29360e6 | 0.114292 | ||||||||
\(664\) | 8.42547e6i | 0.741608i | ||||||||
\(665\) | − | 1.91683e6i | − | 0.168085i | ||||||
\(666\) | 5.65365e6 | 0.493905 | ||||||||
\(667\) | 3.81805e6 | − | 3.26422e6i | 0.332297 | − | 0.284096i | ||||
\(668\) | −4.16698e6 | −0.361311 | ||||||||
\(669\) | − | 4.72538e6i | − | 0.408199i | ||||||
\(670\) | − | 258091.i | − | 0.0222119i | ||||||
\(671\) | 1.86106e7 | 1.59571 | ||||||||
\(672\) | 2.03098e6 | 0.173493 | ||||||||
\(673\) | −1.00137e7 | −0.852229 | −0.426114 | − | 0.904669i | \(-0.640118\pi\) | ||||
−0.426114 | + | 0.904669i | \(0.640118\pi\) | |||||||
\(674\) | −9.81866e6 | −0.832535 | ||||||||
\(675\) | 6.77392e6i | 0.572243i | ||||||||
\(676\) | −6.42027e6 | −0.540364 | ||||||||
\(677\) | 7.97980e6i | 0.669145i | 0.942370 | + | 0.334573i | \(0.108592\pi\) | ||||
−0.942370 | + | 0.334573i | \(0.891408\pi\) | |||||||
\(678\) | − | 2.40333e6i | − | 0.200788i | ||||||
\(679\) | − | 1.05842e7i | − | 0.881019i | ||||||
\(680\) | 4.13223e6 | 0.342698 | ||||||||
\(681\) | 4.25661e6i | 0.351719i | ||||||||
\(682\) | − | 2.94419e6i | − | 0.242385i | ||||||
\(683\) | 754224. | 0.0618655 | 0.0309328 | − | 0.999521i | \(-0.490152\pi\) | ||||
0.0309328 | + | 0.999521i | \(0.490152\pi\) | |||||||
\(684\) | − | 7.08224e6i | − | 0.578802i | ||||||
\(685\) | − | 3.51246e6i | − | 0.286012i | ||||||
\(686\) | − | 7.25381e6i | − | 0.588513i | ||||||
\(687\) | 3.91666e6 | 0.316610 | ||||||||
\(688\) | 302190.i | 0.0243393i | ||||||||
\(689\) | 1.93438e6 | 0.155237 | ||||||||
\(690\) | −327308. | −0.0261718 | ||||||||
\(691\) | −5.62347e6 | −0.448032 | −0.224016 | − | 0.974585i | \(-0.571917\pi\) | ||||
−0.224016 | + | 0.974585i | \(0.571917\pi\) | |||||||
\(692\) | −1.25042e7 | −0.992636 | ||||||||
\(693\) | 6.05259e6i | 0.478749i | ||||||||
\(694\) | − | 8.67092e6i | − | 0.683387i | ||||||
\(695\) | 3.63605e6 | 0.285541 | ||||||||
\(696\) | −3.25271e6 | + | 2.78089e6i | −0.254520 | + | 0.217601i | ||||
\(697\) | 1.03525e7 | 0.807163 | ||||||||
\(698\) | − | 4.67159e6i | − | 0.362933i | ||||||
\(699\) | 8.04513e6i | 0.622788i | ||||||||
\(700\) | −3.79090e6 | −0.292414 | ||||||||
\(701\) | −9.45506e6 | −0.726723 | −0.363362 | − | 0.931648i | \(-0.618371\pi\) | ||||
−0.363362 | + | 0.931648i | \(0.618371\pi\) | |||||||
\(702\) | −1.52425e6 | −0.116738 | ||||||||
\(703\) | −1.24643e7 | −0.951216 | ||||||||
\(704\) | − | 8.99396e6i | − | 0.683942i | ||||||
\(705\) | −40248.8 | −0.00304986 | ||||||||
\(706\) | − | 2.99239e6i | − | 0.225947i | ||||||
\(707\) | 1.72007e6i | 0.129419i | ||||||||
\(708\) | 420527.i | 0.0315291i | ||||||||
\(709\) | −1.39260e7 | −1.04043 | −0.520213 | − | 0.854037i | \(-0.674147\pi\) | ||||
−0.520213 | + | 0.854037i | \(0.674147\pi\) | |||||||
\(710\) | 3.37602e6i | 0.251339i | ||||||||
\(711\) | 7.33844e6i | 0.544414i | ||||||||
\(712\) | −1.92573e7 | −1.42362 | ||||||||
\(713\) | − | 2.25498e6i | − | 0.166119i | ||||||
\(714\) | − | 1.82680e6i | − | 0.134105i | ||||||
\(715\) | − | 1.13770e6i | − | 0.0832266i | ||||||
\(716\) | −4.36078e6 | −0.317894 | ||||||||
\(717\) | − | 5.16859e6i | − | 0.375469i | ||||||
\(718\) | 5.91390e6 | 0.428117 | ||||||||
\(719\) | −1.22839e7 | −0.886167 | −0.443083 | − | 0.896480i | \(-0.646115\pi\) | ||||
−0.443083 | + | 0.896480i | \(0.646115\pi\) | |||||||
\(720\) | −209137. | −0.0150348 | ||||||||
\(721\) | −1.71529e6 | −0.122885 | ||||||||
\(722\) | − | 1.84076e6i | − | 0.131417i | ||||||
\(723\) | − | 1.35501e6i | − | 0.0964044i | ||||||
\(724\) | 1.09040e7 | 0.773106 | ||||||||
\(725\) | 9.88685e6 | − | 8.45272e6i | 0.698575 | − | 0.597243i | ||||
\(726\) | 13751.9 | 0.000968325 | ||||||||
\(727\) | 1.04182e7i | 0.731068i | 0.930798 | + | 0.365534i | \(0.119114\pi\) | ||||
−0.930798 | + | 0.365534i | \(0.880886\pi\) | |||||||
\(728\) | − | 2.29587e6i | − | 0.160553i | ||||||
\(729\) | 5.84579e6 | 0.407403 | ||||||||
\(730\) | −880978. | −0.0611868 | ||||||||
\(731\) | −7.02486e6 | −0.486233 | ||||||||
\(732\) | −4.51184e6 | −0.311226 | ||||||||
\(733\) | − | 9.07566e6i | − | 0.623905i | −0.950098 | − | 0.311952i | \(-0.899017\pi\) | ||
0.950098 | − | 0.311952i | \(-0.100983\pi\) | |||||||
\(734\) | 6.38071e6 | 0.437148 | ||||||||
\(735\) | 974157.i | 0.0665136i | ||||||||
\(736\) | − | 6.29294e6i | − | 0.428212i | ||||||
\(737\) | − | 1.79667e6i | − | 0.121843i | ||||||
\(738\) | −5.74985e6 | −0.388611 | ||||||||
\(739\) | − | 1.74982e7i | − | 1.17864i | −0.807899 | − | 0.589321i | \(-0.799396\pi\) | ||
0.807899 | − | 0.589321i | \(-0.200604\pi\) | |||||||
\(740\) | − | 2.17038e6i | − | 0.145699i | ||||||
\(741\) | 1.58399e6 | 0.105976 | ||||||||
\(742\) | − | 2.73170e6i | − | 0.182147i | ||||||
\(743\) | 2.26818e7i | 1.50732i | 0.657266 | + | 0.753658i | \(0.271713\pi\) | ||||
−0.657266 | + | 0.753658i | \(0.728287\pi\) | |||||||
\(744\) | 1.92109e6i | 0.127238i | ||||||||
\(745\) | −4.40115e6 | −0.290520 | ||||||||
\(746\) | 4.46554e6i | 0.293783i | ||||||||
\(747\) | 9.91285e6 | 0.649975 | ||||||||
\(748\) | 1.06879e7 | 0.698453 | ||||||||
\(749\) | 7.01638e6 | 0.456992 | ||||||||
\(750\) | −1.76976e6 | −0.114884 | ||||||||
\(751\) | − | 1.25596e7i | − | 0.812598i | −0.913740 | − | 0.406299i | \(-0.866819\pi\) | ||
0.913740 | − | 0.406299i | \(-0.133181\pi\) | |||||||
\(752\) | 29941.7i | 0.00193077i | ||||||||
\(753\) | −1.84478e6 | −0.118565 | ||||||||
\(754\) | 1.90201e6 | + | 2.22471e6i | 0.121838 | + | 0.142510i | ||||
\(755\) | 6.38679e6 | 0.407770 | ||||||||
\(756\) | − | 3.11298e6i | − | 0.198095i | ||||||
\(757\) | 2.40929e7i | 1.52809i | 0.645163 | + | 0.764045i | \(0.276789\pi\) | ||||
−0.645163 | + | 0.764045i | \(0.723211\pi\) | |||||||
\(758\) | −1.10793e7 | −0.700387 | ||||||||
\(759\) | −2.27852e6 | −0.143565 | ||||||||
\(760\) | 5.05982e6 | 0.317762 | ||||||||
\(761\) | 1.54198e7 | 0.965198 | 0.482599 | − | 0.875841i | \(-0.339693\pi\) | ||||
0.482599 | + | 0.875841i | \(0.339693\pi\) | |||||||
\(762\) | 6.08221e6i | 0.379467i | ||||||||
\(763\) | −1.02766e7 | −0.639057 | ||||||||
\(764\) | 4.81287e6i | 0.298312i | ||||||||
\(765\) | − | 4.86170e6i | − | 0.300355i | ||||||
\(766\) | 1.61694e7i | 0.995683i | ||||||||
\(767\) | 774125. | 0.0475141 | ||||||||
\(768\) | 5.54968e6i | 0.339520i | ||||||||
\(769\) | − | 2.13698e7i | − | 1.30312i | −0.758597 | − | 0.651560i | \(-0.774115\pi\) | ||
0.758597 | − | 0.651560i | \(-0.225885\pi\) | |||||||
\(770\) | −1.60664e6 | −0.0976541 | ||||||||
\(771\) | − | 5.66202e6i | − | 0.343033i | ||||||
\(772\) | 4.97723e6i | 0.300569i | ||||||||
\(773\) | − | 2.07154e7i | − | 1.24694i | −0.781849 | − | 0.623468i | \(-0.785723\pi\) | ||
0.781849 | − | 0.623468i | \(-0.214277\pi\) | |||||||
\(774\) | 3.90167e6 | 0.234098 | ||||||||
\(775\) | − | 5.83929e6i | − | 0.349226i | ||||||
\(776\) | 2.79390e7 | 1.66555 | ||||||||
\(777\) | −2.58245e6 | −0.153454 | ||||||||
\(778\) | 3.12338e6 | 0.185002 | ||||||||
\(779\) | 1.26764e7 | 0.748430 | ||||||||
\(780\) | 275817.i | 0.0162325i | ||||||||
\(781\) | 2.35018e7i | 1.37871i | ||||||||
\(782\) | −5.66028e6 | −0.330995 | ||||||||
\(783\) | 6.94114e6 | + | 8.11880e6i | 0.404600 | + | 0.473247i | ||||
\(784\) | 724690. | 0.0421078 | ||||||||
\(785\) | 173017.i | 0.0100211i | ||||||||
\(786\) | 5.70250e6i | 0.329237i | ||||||||
\(787\) | 1.34403e7 | 0.773523 | 0.386761 | − | 0.922180i | \(-0.373594\pi\) | ||||
0.386761 | + | 0.922180i | \(0.373594\pi\) | |||||||
\(788\) | 9.74312e6 | 0.558962 | ||||||||
\(789\) | −5.03116e6 | −0.287723 | ||||||||
\(790\) | −1.94796e6 | −0.111048 | ||||||||
\(791\) | − | 9.03547e6i | − | 0.513463i | ||||||
\(792\) | −1.59769e7 | −0.905065 | ||||||||
\(793\) | 8.30560e6i | 0.469016i | ||||||||
\(794\) | 1.38798e7i | 0.781326i | ||||||||
\(795\) | 883270.i | 0.0495651i | ||||||||
\(796\) | 1.38774e7 | 0.776293 | ||||||||
\(797\) | − | 3.46238e6i | − | 0.193076i | −0.995329 | − | 0.0965381i | \(-0.969223\pi\) | ||
0.995329 | − | 0.0965381i | \(-0.0307770\pi\) | |||||||
\(798\) | − | 2.23688e6i | − | 0.124347i | ||||||
\(799\) | −696039. | −0.0385715 | ||||||||
\(800\) | − | 1.62956e7i | − | 0.900212i | ||||||
\(801\) | 2.26568e7i | 1.24772i | ||||||||
\(802\) | 1.28278e6i | 0.0704230i | ||||||||
\(803\) | −6.13283e6 | −0.335639 | ||||||||
\(804\) | 435574.i | 0.0237641i | ||||||||
\(805\) | −1.23054e6 | −0.0669276 | ||||||||
\(806\) | 1.31394e6 | 0.0712425 | ||||||||
\(807\) | −6.90187e6 | −0.373063 | ||||||||
\(808\) | −4.54045e6 | −0.244664 | ||||||||
\(809\) | 2.78688e7i | 1.49709i | 0.663086 | + | 0.748543i | \(0.269246\pi\) | ||||
−0.663086 | + | 0.748543i | \(0.730754\pi\) | |||||||
\(810\) | 2.33230e6i | 0.124903i | ||||||||
\(811\) | −2.87983e7 | −1.53750 | −0.768750 | − | 0.639549i | \(-0.779121\pi\) | ||||
−0.768750 | + | 0.639549i | \(0.779121\pi\) | |||||||
\(812\) | −4.54355e6 | + | 3.88448e6i | −0.241827 | + | 0.206749i | ||||
\(813\) | 1.16784e7 | 0.619665 | ||||||||
\(814\) | 1.04472e7i | 0.552637i | ||||||||
\(815\) | − | 6.22938e6i | − | 0.328512i | ||||||
\(816\) | 439416. | 0.0231021 | ||||||||
\(817\) | −8.60179e6 | −0.450852 | ||||||||
\(818\) | −1.84872e6 | −0.0966026 | ||||||||
\(819\) | −2.70117e6 | −0.140716 | ||||||||
\(820\) | 2.20731e6i | 0.114638i | ||||||||
\(821\) | 1.21782e7 | 0.630560 | 0.315280 | − | 0.948999i | \(-0.397902\pi\) | ||||
0.315280 | + | 0.948999i | \(0.397902\pi\) | |||||||
\(822\) | − | 4.09893e6i | − | 0.211588i | ||||||
\(823\) | − | 1.29219e7i | − | 0.665009i | −0.943102 | − | 0.332504i | \(-0.892106\pi\) | ||
0.943102 | − | 0.332504i | \(-0.107894\pi\) | |||||||
\(824\) | − | 4.52783e6i | − | 0.232312i | ||||||
\(825\) | −5.90024e6 | −0.301811 | ||||||||
\(826\) | − | 1.09320e6i | − | 0.0557508i | ||||||
\(827\) | − | 1.94679e7i | − | 0.989816i | −0.868945 | − | 0.494908i | \(-0.835202\pi\) | ||
0.868945 | − | 0.494908i | \(-0.164798\pi\) | |||||||
\(828\) | −4.54655e6 | −0.230465 | ||||||||
\(829\) | 941471.i | 0.0475796i | 0.999717 | + | 0.0237898i | \(0.00757324\pi\) | ||||
−0.999717 | + | 0.0237898i | \(0.992427\pi\) | |||||||
\(830\) | 2.63133e6i | 0.132580i | ||||||||
\(831\) | − | 5.33416e6i | − | 0.267956i | ||||||
\(832\) | 4.01386e6 | 0.201027 | ||||||||
\(833\) | 1.68465e7i | 0.841197i | ||||||||
\(834\) | 4.24316e6 | 0.211239 | ||||||||
\(835\) | −3.50260e6 | −0.173850 | ||||||||
\(836\) | 1.30871e7 | 0.647630 | ||||||||
\(837\) | 4.79507e6 | 0.236582 | ||||||||
\(838\) | 1.21490e6i | 0.0597626i | ||||||||
\(839\) | − | 8.91326e6i | − | 0.437151i | −0.975820 | − | 0.218576i | \(-0.929859\pi\) | ||
0.975820 | − | 0.218576i | \(-0.0701410\pi\) | |||||||
\(840\) | 1.04833e6 | 0.0512627 | ||||||||
\(841\) | 3.18839e6 | − | 2.02618e7i | 0.155447 | − | 0.987844i | ||||
\(842\) | −4.42062e6 | −0.214884 | ||||||||
\(843\) | − | 9.97967e6i | − | 0.483668i | ||||||
\(844\) | 2.41429e7i | 1.16663i | ||||||||
\(845\) | −5.39662e6 | −0.260004 | ||||||||
\(846\) | 386586. | 0.0185704 | ||||||||
\(847\) | 51701.2 | 0.00247623 | ||||||||
\(848\) | 657078. | 0.0313782 | ||||||||
\(849\) | 1.21981e7i | 0.580796i | ||||||||
\(850\) | −1.46573e7 | −0.695837 | ||||||||
\(851\) | 8.00163e6i | 0.378752i | ||||||||
\(852\) | − | 5.69763e6i | − | 0.268903i | ||||||
\(853\) | − | 3.30610e7i | − | 1.55576i | −0.628410 | − | 0.777882i | \(-0.716294\pi\) | ||
0.628410 | − | 0.777882i | \(-0.283706\pi\) | |||||||
\(854\) | 1.17290e7 | 0.550321 | ||||||||
\(855\) | − | 5.95305e6i | − | 0.278499i | ||||||
\(856\) | 1.85210e7i | 0.863934i | ||||||||
\(857\) | 6.63537e6 | 0.308612 | 0.154306 | − | 0.988023i | \(-0.450686\pi\) | ||||
0.154306 | + | 0.988023i | \(0.450686\pi\) | |||||||
\(858\) | − | 1.32766e6i | − | 0.0615698i | ||||||
\(859\) | − | 3.34962e7i | − | 1.54886i | −0.632659 | − | 0.774430i | \(-0.718037\pi\) | ||
0.632659 | − | 0.774430i | \(-0.281963\pi\) | |||||||
\(860\) | − | 1.49781e6i | − | 0.0690575i | ||||||
\(861\) | 2.62639e6 | 0.120740 | ||||||||
\(862\) | − | 1.12001e7i | − | 0.513398i | ||||||
\(863\) | −4.22267e7 | −1.93001 | −0.965006 | − | 0.262226i | \(-0.915543\pi\) | ||||
−0.965006 | + | 0.262226i | \(0.915543\pi\) | |||||||
\(864\) | 1.33815e7 | 0.609846 | ||||||||
\(865\) | −1.05105e7 | −0.477622 | ||||||||
\(866\) | −1.31771e7 | −0.597071 | ||||||||
\(867\) | 2.92987e6i | 0.132373i | ||||||||
\(868\) | 2.68347e6i | 0.120892i | ||||||||
\(869\) | −1.35605e7 | −0.609153 | ||||||||
\(870\) | −1.01584e6 | + | 868489.i | −0.0455017 | + | 0.0389015i | ||||
\(871\) | 801824. | 0.0358124 | ||||||||
\(872\) | − | 2.71270e7i | − | 1.20812i | ||||||
\(873\) | − | 3.28712e7i | − | 1.45975i | ||||||
\(874\) | −6.93090e6 | −0.306910 | ||||||||
\(875\) | −6.65352e6 | −0.293786 | ||||||||
\(876\) | 1.48681e6 | 0.0654627 | ||||||||
\(877\) | 1.96044e7 | 0.860707 | 0.430354 | − | 0.902660i | \(-0.358389\pi\) | ||||
0.430354 | + | 0.902660i | \(0.358389\pi\) | |||||||
\(878\) | 1.06448e7i | 0.466016i | ||||||||
\(879\) | 8.63508e6 | 0.376959 | ||||||||
\(880\) | − | 386458.i | − | 0.0168227i | ||||||
\(881\) | − | 3.24692e7i | − | 1.40939i | −0.709509 | − | 0.704697i | \(-0.751083\pi\) | ||
0.709509 | − | 0.704697i | \(-0.248917\pi\) | |||||||
\(882\) | − | 9.35671e6i | − | 0.404997i | ||||||
\(883\) | −3.02499e7 | −1.30564 | −0.652819 | − | 0.757514i | \(-0.726414\pi\) | ||||
−0.652819 | + | 0.757514i | \(0.726414\pi\) | |||||||
\(884\) | 4.76982e6i | 0.205292i | ||||||||
\(885\) | 353478.i | 0.0151707i | ||||||||
\(886\) | 9.06546e6 | 0.387977 | ||||||||
\(887\) | 2.46024e7i | 1.04995i | 0.851117 | + | 0.524976i | \(0.175926\pi\) | ||||
−0.851117 | + | 0.524976i | \(0.824074\pi\) | |||||||
\(888\) | − | 6.81684e6i | − | 0.290102i | ||||||
\(889\) | 2.28665e7i | 0.970386i | ||||||||
\(890\) | −6.01416e6 | −0.254507 | ||||||||
\(891\) | 1.62361e7i | 0.685151i | ||||||||
\(892\) | 1.74236e7 | 0.733205 | ||||||||
\(893\) | −852285. | −0.0357648 | ||||||||
\(894\) | −5.13600e6 | −0.214922 | ||||||||
\(895\) | −3.66550e6 | −0.152959 | ||||||||
\(896\) | 6.99860e6i | 0.291233i | ||||||||
\(897\) | − | 1.01687e6i | − | 0.0421971i | ||||||
\(898\) | 1.83140e7 | 0.757868 | ||||||||
\(899\) | −5.98344e6 | − | 6.99862e6i | −0.246917 | − | 0.288811i | ||||
\(900\) | −1.17733e7 | −0.484498 | ||||||||
\(901\) | 1.52748e7i | 0.626849i | ||||||||
\(902\) | − | 1.06250e7i | − | 0.434822i | ||||||
\(903\) | −1.78219e6 | −0.0727333 | ||||||||
\(904\) | 2.38508e7 | 0.970691 | ||||||||
\(905\) | 9.16546e6 | 0.371991 | ||||||||
\(906\) | 7.45317e6 | 0.301662 | ||||||||
\(907\) | − | 7.64741e6i | − | 0.308671i | −0.988018 | − | 0.154336i | \(-0.950676\pi\) | ||
0.988018 | − | 0.154336i | \(-0.0493237\pi\) | |||||||
\(908\) | −1.56951e7 | −0.631757 | ||||||||
\(909\) | 5.34198e6i | 0.214434i | ||||||||
\(910\) | − | 717015.i | − | 0.0287028i | ||||||
\(911\) | 1.93872e7i | 0.773960i | 0.922088 | + | 0.386980i | \(0.126482\pi\) | ||||
−0.922088 | + | 0.386980i | \(0.873518\pi\) | |||||||
\(912\) | 538056. | 0.0214210 | ||||||||
\(913\) | 1.83177e7i | 0.727266i | ||||||||
\(914\) | 3.81211e6i | 0.150939i | ||||||||
\(915\) | −3.79247e6 | −0.149751 | ||||||||
\(916\) | 1.44417e7i | 0.568693i | ||||||||
\(917\) | 2.14389e7i | 0.841937i | ||||||||
\(918\) | − | 1.20362e7i | − | 0.471392i | ||||||
\(919\) | 2.02240e7 | 0.789912 | 0.394956 | − | 0.918700i | \(-0.370760\pi\) | ||||
0.394956 | + | 0.918700i | \(0.370760\pi\) | |||||||
\(920\) | − | 3.24823e6i | − | 0.126525i | ||||||
\(921\) | −1.12888e7 | −0.438530 | ||||||||
\(922\) | 1.13814e7 | 0.440928 | ||||||||
\(923\) | −1.04885e7 | −0.405236 | ||||||||
\(924\) | 2.71148e6 | 0.104478 | ||||||||
\(925\) | 2.07203e7i | 0.796234i | ||||||||
\(926\) | 1.82220e7i | 0.698342i | ||||||||
\(927\) | −5.32714e6 | −0.203608 | ||||||||
\(928\) | −1.66979e7 | − | 1.95309e7i | −0.636489 | − | 0.744479i | ||||
\(929\) | −1.04574e7 | −0.397544 | −0.198772 | − | 0.980046i | \(-0.563695\pi\) | ||||
−0.198772 | + | 0.980046i | \(0.563695\pi\) | |||||||
\(930\) | 599968.i | 0.0227468i | ||||||||
\(931\) | 2.06282e7i | 0.779987i | ||||||||
\(932\) | −2.96643e7 | −1.11865 | ||||||||
\(933\) | 1.32852e6 | 0.0499649 | ||||||||
\(934\) | 1.63709e7 | 0.614052 | ||||||||
\(935\) | 8.98380e6 | 0.336071 | ||||||||
\(936\) | − | 7.13023e6i | − | 0.266020i | ||||||
\(937\) | 3.57506e7 | 1.33025 | 0.665127 | − | 0.746730i | \(-0.268377\pi\) | ||||
0.665127 | + | 0.746730i | \(0.268377\pi\) | |||||||
\(938\) | − | 1.13232e6i | − | 0.0420206i | ||||||
\(939\) | − | 7.60692e6i | − | 0.281543i | ||||||
\(940\) | − | 148407.i | − | 0.00547814i | ||||||
\(941\) | 2.85407e7 | 1.05073 | 0.525364 | − | 0.850878i | \(-0.323929\pi\) | ||||
0.525364 | + | 0.850878i | \(0.323929\pi\) | |||||||
\(942\) | 201905.i | 0.00741346i | ||||||||
\(943\) | − | 8.13778e6i | − | 0.298007i | ||||||
\(944\) | 262958. | 0.00960409 | ||||||||
\(945\) | − | 2.61665e6i | − | 0.0953161i | ||||||
\(946\) | 7.20979e6i | 0.261936i | ||||||||
\(947\) | 2.87524e7i | 1.04184i | 0.853606 | + | 0.520918i | \(0.174410\pi\) | ||||
−0.853606 | + | 0.520918i | \(0.825590\pi\) | |||||||
\(948\) | 3.28752e6 | 0.118809 | ||||||||
\(949\) | − | 2.73698e6i | − | 0.0986521i | ||||||
\(950\) | −1.79476e7 | −0.645204 | ||||||||
\(951\) | 9.96570e6 | 0.357319 | ||||||||
\(952\) | 1.81293e7 | 0.648318 | ||||||||
\(953\) | 8.91965e6 | 0.318138 | 0.159069 | − | 0.987267i | \(-0.449151\pi\) | ||||
0.159069 | + | 0.987267i | \(0.449151\pi\) | |||||||
\(954\) | − | 8.48375e6i | − | 0.301798i | ||||||
\(955\) | 4.04551e6i | 0.143537i | ||||||||
\(956\) | 1.90578e7 | 0.674416 | ||||||||
\(957\) | −7.07167e6 | + | 6.04589e6i | −0.249598 | + | 0.213393i | ||||
\(958\) | −2.43549e7 | −0.857377 | ||||||||
\(959\) | − | 1.54102e7i | − | 0.541080i | ||||||
\(960\) | 1.83279e6i | 0.0641853i | ||||||||
\(961\) | 2.44957e7 | 0.855620 | ||||||||
\(962\) | −4.66242e6 | −0.162433 | ||||||||
\(963\) | 2.17906e7 | 0.757187 | ||||||||
\(964\) | 4.99624e6 | 0.173161 | ||||||||
\(965\) | 4.18366e6i | 0.144623i | ||||||||
\(966\) | −1.43600e6 | −0.0495120 | ||||||||
\(967\) | 7.00946e6i | 0.241056i | 0.992710 | + | 0.120528i | \(0.0384588\pi\) | ||||
−0.992710 | + | 0.120528i | \(0.961541\pi\) | |||||||
\(968\) | 136475.i | 0.00468127i | ||||||||
\(969\) | 1.25079e7i | 0.427933i | ||||||||
\(970\) | 8.72552e6 | 0.297757 | ||||||||
\(971\) | − | 2.10516e7i | − | 0.716535i | −0.933619 | − | 0.358268i | \(-0.883368\pi\) | ||
0.933619 | − | 0.358268i | \(-0.116632\pi\) | |||||||
\(972\) | − | 1.47787e7i | − | 0.501731i | ||||||
\(973\) | 1.59524e7 | 0.540188 | ||||||||
\(974\) | − | 4.29387e6i | − | 0.145028i | ||||||
\(975\) | − | 2.63318e6i | − | 0.0887092i | ||||||
\(976\) | 2.82128e6i | 0.0948028i | ||||||||
\(977\) | 3.48891e7 | 1.16937 | 0.584687 | − | 0.811259i | \(-0.301217\pi\) | ||||
0.584687 | + | 0.811259i | \(0.301217\pi\) | |||||||
\(978\) | − | 7.26949e6i | − | 0.243028i | ||||||
\(979\) | −4.18669e7 | −1.39609 | ||||||||
\(980\) | −3.59194e6 | −0.119472 | ||||||||
\(981\) | −3.19159e7 | −1.05885 | ||||||||
\(982\) | 2.36578e7 | 0.782881 | ||||||||
\(983\) | − | 5.47844e7i | − | 1.80831i | −0.427204 | − | 0.904155i | \(-0.640501\pi\) | ||
0.427204 | − | 0.904155i | \(-0.359499\pi\) | |||||||
\(984\) | 6.93283e6i | 0.228256i | ||||||||
\(985\) | 8.18968e6 | 0.268953 | ||||||||
\(986\) | −1.75674e7 | + | 1.50192e7i | −0.575460 | + | 0.491987i | ||||
\(987\) | −176583. | −0.00576974 | ||||||||
\(988\) | 5.84054e6i | 0.190354i | ||||||||
\(989\) | 5.52204e6i | 0.179518i | ||||||||
\(990\) | −4.98968e6 | −0.161802 | ||||||||
\(991\) | 8.43462e6 | 0.272823 | 0.136412 | − | 0.990652i | \(-0.456443\pi\) | ||||
0.136412 | + | 0.990652i | \(0.456443\pi\) | |||||||
\(992\) | −1.15352e7 | −0.372173 | ||||||||
\(993\) | −1.52117e7 | −0.489560 | ||||||||
\(994\) | 1.48116e7i | 0.475484i | ||||||||
\(995\) | 1.16648e7 | 0.373525 | ||||||||
\(996\) | − | 4.44083e6i | − | 0.141845i | ||||||
\(997\) | 4.84695e7i | 1.54430i | 0.635443 | + | 0.772148i | \(0.280817\pi\) | ||||
−0.635443 | + | 0.772148i | \(0.719183\pi\) | |||||||
\(998\) | − | 1.77251e7i | − | 0.563329i | ||||||
\(999\) | −1.70149e7 | −0.539406 |
(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 | 29.6.b.a.28.8 | yes | 12 | |
3.2 | odd | 2 | 261.6.c.b.28.5 | 12 | |||
4.3 | odd | 2 | 464.6.e.c.289.8 | 12 | |||
29.12 | odd | 4 | 841.6.a.d.1.5 | 12 | |||
29.17 | odd | 4 | 841.6.a.d.1.8 | 12 | |||
29.28 | even | 2 | inner | 29.6.b.a.28.5 | ✓ | 12 | |
87.86 | odd | 2 | 261.6.c.b.28.8 | 12 | |||
116.115 | odd | 2 | 464.6.e.c.289.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.b.a.28.5 | ✓ | 12 | 29.28 | even | 2 | inner | |
29.6.b.a.28.8 | yes | 12 | 1.1 | even | 1 | trivial | |
261.6.c.b.28.5 | 12 | 3.2 | odd | 2 | |||
261.6.c.b.28.8 | 12 | 87.86 | odd | 2 | |||
464.6.e.c.289.5 | 12 | 116.115 | odd | 2 | |||
464.6.e.c.289.8 | 12 | 4.3 | odd | 2 | |||
841.6.a.d.1.5 | 12 | 29.12 | odd | 4 | |||
841.6.a.d.1.8 | 12 | 29.17 | odd | 4 |