Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,5,Mod(37,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.37");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.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: | \(3.92805859719\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 450x^{6} + 68229x^{4} + 4001228x^{2} + 77475204 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(12.2418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.37 |
Dual form | 38.5.b.a.37.5 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.82843i | − | 0.707107i | ||||||
\(3\) | 10.8276i | 1.20306i | 0.798849 | + | 0.601532i | \(0.205443\pi\) | ||||
−0.798849 | + | 0.601532i | \(0.794557\pi\) | |||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | −26.2296 | −1.04918 | −0.524592 | − | 0.851353i | \(-0.675782\pi\) | ||||
−0.524592 | + | 0.851353i | \(0.675782\pi\) | |||||||
\(6\) | 30.6250 | 0.850695 | ||||||||
\(7\) | −86.0910 | −1.75696 | −0.878480 | − | 0.477779i | \(-0.841442\pi\) | ||||
−0.878480 | + | 0.477779i | \(0.841442\pi\) | |||||||
\(8\) | 22.6274i | 0.353553i | ||||||||
\(9\) | −36.2364 | −0.447363 | ||||||||
\(10\) | 74.1886i | 0.741886i | ||||||||
\(11\) | 114.743 | 0.948291 | 0.474145 | − | 0.880447i | \(-0.342757\pi\) | ||||
0.474145 | + | 0.880447i | \(0.342757\pi\) | |||||||
\(12\) | − | 86.6206i | − | 0.601532i | ||||||
\(13\) | 231.848i | 1.37188i | 0.727656 | + | 0.685942i | \(0.240610\pi\) | ||||
−0.727656 | + | 0.685942i | \(0.759390\pi\) | |||||||
\(14\) | 243.502i | 1.24236i | ||||||||
\(15\) | − | 284.003i | − | 1.26224i | ||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | −244.466 | −0.845903 | −0.422952 | − | 0.906152i | \(-0.639006\pi\) | ||||
−0.422952 | + | 0.906152i | \(0.639006\pi\) | |||||||
\(18\) | 102.492i | 0.316333i | ||||||||
\(19\) | 253.655 | − | 256.866i | 0.702645 | − | 0.711540i | ||||
\(20\) | 209.837 | 0.524592 | ||||||||
\(21\) | − | 932.157i | − | 2.11373i | ||||||
\(22\) | − | 324.543i | − | 0.670543i | ||||||
\(23\) | −269.052 | −0.508604 | −0.254302 | − | 0.967125i | \(-0.581846\pi\) | ||||
−0.254302 | + | 0.967125i | \(0.581846\pi\) | |||||||
\(24\) | −245.000 | −0.425347 | ||||||||
\(25\) | 62.9931 | 0.100789 | ||||||||
\(26\) | 655.766 | 0.970069 | ||||||||
\(27\) | 484.681i | 0.664858i | ||||||||
\(28\) | 688.728 | 0.878480 | ||||||||
\(29\) | 1131.05i | 1.34489i | 0.740148 | + | 0.672443i | \(0.234755\pi\) | ||||
−0.740148 | + | 0.672443i | \(0.765245\pi\) | |||||||
\(30\) | −803.282 | −0.892536 | ||||||||
\(31\) | − | 1037.59i | − | 1.07970i | −0.841762 | − | 0.539850i | \(-0.818481\pi\) | ||
0.841762 | − | 0.539850i | \(-0.181519\pi\) | |||||||
\(32\) | − | 181.019i | − | 0.176777i | ||||||
\(33\) | 1242.39i | 1.14085i | ||||||||
\(34\) | 691.455i | 0.598144i | ||||||||
\(35\) | 2258.14 | 1.84338 | ||||||||
\(36\) | 289.891 | 0.223681 | ||||||||
\(37\) | − | 302.815i | − | 0.221194i | −0.993865 | − | 0.110597i | \(-0.964724\pi\) | ||
0.993865 | − | 0.110597i | \(-0.0352763\pi\) | |||||||
\(38\) | −726.527 | − | 717.444i | −0.503135 | − | 0.496845i | ||||
\(39\) | −2510.36 | −1.65046 | ||||||||
\(40\) | − | 593.509i | − | 0.370943i | ||||||
\(41\) | 1769.82i | 1.05283i | 0.850226 | + | 0.526417i | \(0.176465\pi\) | ||||
−0.850226 | + | 0.526417i | \(0.823535\pi\) | |||||||
\(42\) | −2636.54 | −1.49464 | ||||||||
\(43\) | −2316.56 | −1.25287 | −0.626435 | − | 0.779474i | \(-0.715487\pi\) | ||||
−0.626435 | + | 0.779474i | \(0.715487\pi\) | |||||||
\(44\) | −917.946 | −0.474145 | ||||||||
\(45\) | 950.467 | 0.469366 | ||||||||
\(46\) | 760.993i | 0.359638i | ||||||||
\(47\) | −835.757 | −0.378342 | −0.189171 | − | 0.981944i | \(-0.560580\pi\) | ||||
−0.189171 | + | 0.981944i | \(0.560580\pi\) | |||||||
\(48\) | 692.965i | 0.300766i | ||||||||
\(49\) | 5010.66 | 2.08691 | ||||||||
\(50\) | − | 178.171i | − | 0.0712685i | ||||||
\(51\) | − | 2646.98i | − | 1.01768i | ||||||
\(52\) | − | 1854.79i | − | 0.685942i | ||||||
\(53\) | 656.208i | 0.233609i | 0.993155 | + | 0.116805i | \(0.0372651\pi\) | ||||
−0.993155 | + | 0.116805i | \(0.962735\pi\) | |||||||
\(54\) | 1370.89 | 0.470125 | ||||||||
\(55\) | −3009.67 | −0.994932 | ||||||||
\(56\) | − | 1948.02i | − | 0.621179i | ||||||
\(57\) | 2781.24 | + | 2746.47i | 0.856029 | + | 0.845327i | ||||
\(58\) | 3199.09 | 0.950979 | ||||||||
\(59\) | 4923.33i | 1.41434i | 0.707042 | + | 0.707171i | \(0.250029\pi\) | ||||
−0.707042 | + | 0.707171i | \(0.749971\pi\) | |||||||
\(60\) | 2272.03i | 0.631118i | ||||||||
\(61\) | −1576.71 | −0.423733 | −0.211866 | − | 0.977299i | \(-0.567954\pi\) | ||||
−0.211866 | + | 0.977299i | \(0.567954\pi\) | |||||||
\(62\) | −2934.75 | −0.763463 | ||||||||
\(63\) | 3119.63 | 0.785999 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − | 6081.30i | − | 1.43936i | ||||||
\(66\) | 3514.01 | 0.806706 | ||||||||
\(67\) | − | 7000.44i | − | 1.55946i | −0.626113 | − | 0.779732i | \(-0.715355\pi\) | ||
0.626113 | − | 0.779732i | \(-0.284645\pi\) | |||||||
\(68\) | 1955.73 | 0.422952 | ||||||||
\(69\) | − | 2913.18i | − | 0.611884i | ||||||
\(70\) | − | 6386.97i | − | 1.30346i | ||||||
\(71\) | 4101.26i | 0.813581i | 0.913521 | + | 0.406790i | \(0.133352\pi\) | ||||
−0.913521 | + | 0.406790i | \(0.866648\pi\) | |||||||
\(72\) | − | 819.936i | − | 0.158167i | ||||||
\(73\) | 7018.02 | 1.31695 | 0.658474 | − | 0.752603i | \(-0.271202\pi\) | ||||
0.658474 | + | 0.752603i | \(0.271202\pi\) | |||||||
\(74\) | −856.490 | −0.156408 | ||||||||
\(75\) | 682.062i | 0.121256i | ||||||||
\(76\) | −2029.24 | + | 2054.93i | −0.351323 | + | 0.355770i | ||||
\(77\) | −9878.36 | −1.66611 | ||||||||
\(78\) | 7100.36i | 1.16705i | ||||||||
\(79\) | − | 1264.00i | − | 0.202532i | −0.994859 | − | 0.101266i | \(-0.967711\pi\) | ||
0.994859 | − | 0.101266i | \(-0.0322893\pi\) | |||||||
\(80\) | −1678.70 | −0.262296 | ||||||||
\(81\) | −8183.07 | −1.24723 | ||||||||
\(82\) | 5005.79 | 0.744467 | ||||||||
\(83\) | 1020.09 | 0.148075 | 0.0740377 | − | 0.997255i | \(-0.476411\pi\) | ||||
0.0740377 | + | 0.997255i | \(0.476411\pi\) | |||||||
\(84\) | 7457.26i | 1.05687i | ||||||||
\(85\) | 6412.25 | 0.887509 | ||||||||
\(86\) | 6552.21i | 0.885913i | ||||||||
\(87\) | −12246.5 | −1.61799 | ||||||||
\(88\) | 2596.34i | 0.335271i | ||||||||
\(89\) | 3746.30i | 0.472958i | 0.971637 | + | 0.236479i | \(0.0759934\pi\) | ||||
−0.971637 | + | 0.236479i | \(0.924007\pi\) | |||||||
\(90\) | − | 2688.33i | − | 0.331892i | ||||||
\(91\) | − | 19960.1i | − | 2.41034i | ||||||
\(92\) | 2152.41 | 0.254302 | ||||||||
\(93\) | 11234.6 | 1.29895 | ||||||||
\(94\) | 2363.88i | 0.267528i | ||||||||
\(95\) | −6653.27 | + | 6737.50i | −0.737205 | + | 0.746537i | ||||
\(96\) | 1960.00 | 0.212674 | ||||||||
\(97\) | 13041.0i | 1.38601i | 0.720933 | + | 0.693005i | \(0.243713\pi\) | ||||
−0.720933 | + | 0.693005i | \(0.756287\pi\) | |||||||
\(98\) | − | 14172.3i | − | 1.47567i | ||||||
\(99\) | −4157.88 | −0.424230 | ||||||||
\(100\) | −503.945 | −0.0503945 | ||||||||
\(101\) | −4755.84 | −0.466213 | −0.233106 | − | 0.972451i | \(-0.574889\pi\) | ||||
−0.233106 | + | 0.972451i | \(0.574889\pi\) | |||||||
\(102\) | −7486.78 | −0.719606 | ||||||||
\(103\) | 8727.79i | 0.822678i | 0.911483 | + | 0.411339i | \(0.134939\pi\) | ||||
−0.911483 | + | 0.411339i | \(0.865061\pi\) | |||||||
\(104\) | −5246.13 | −0.485034 | ||||||||
\(105\) | 24450.1i | 2.21770i | ||||||||
\(106\) | 1856.04 | 0.165187 | ||||||||
\(107\) | − | 16884.9i | − | 1.47479i | −0.675462 | − | 0.737395i | \(-0.736056\pi\) | ||
0.675462 | − | 0.737395i | \(-0.263944\pi\) | |||||||
\(108\) | − | 3877.45i | − | 0.332429i | ||||||
\(109\) | − | 205.403i | − | 0.0172883i | −0.999963 | − | 0.00864416i | \(-0.997248\pi\) | ||
0.999963 | − | 0.00864416i | \(-0.00275156\pi\) | |||||||
\(110\) | 8512.63i | 0.703524i | ||||||||
\(111\) | 3278.75 | 0.266111 | ||||||||
\(112\) | −5509.83 | −0.439240 | ||||||||
\(113\) | − | 4276.02i | − | 0.334875i | −0.985883 | − | 0.167438i | \(-0.946451\pi\) | ||
0.985883 | − | 0.167438i | \(-0.0535492\pi\) | |||||||
\(114\) | 7768.18 | − | 7866.53i | 0.597737 | − | 0.605304i | ||||
\(115\) | 7057.13 | 0.533620 | ||||||||
\(116\) | − | 9048.40i | − | 0.672443i | ||||||
\(117\) | − | 8401.35i | − | 0.613730i | ||||||
\(118\) | 13925.3 | 1.00009 | ||||||||
\(119\) | 21046.3 | 1.48622 | ||||||||
\(120\) | 6426.26 | 0.446268 | ||||||||
\(121\) | −1475.00 | −0.100744 | ||||||||
\(122\) | 4459.61i | 0.299624i | ||||||||
\(123\) | −19162.8 | −1.26663 | ||||||||
\(124\) | 8300.73i | 0.539850i | ||||||||
\(125\) | 14741.2 | 0.943439 | ||||||||
\(126\) | − | 8823.64i | − | 0.555785i | ||||||
\(127\) | − | 4501.00i | − | 0.279063i | −0.990218 | − | 0.139531i | \(-0.955440\pi\) | ||
0.990218 | − | 0.139531i | \(-0.0445596\pi\) | |||||||
\(128\) | 1448.15i | 0.0883883i | ||||||||
\(129\) | − | 25082.7i | − | 1.50728i | ||||||
\(130\) | −17200.5 | −1.01778 | ||||||||
\(131\) | 27606.3 | 1.60866 | 0.804332 | − | 0.594180i | \(-0.202523\pi\) | ||||
0.804332 | + | 0.594180i | \(0.202523\pi\) | |||||||
\(132\) | − | 9939.13i | − | 0.570427i | ||||||
\(133\) | −21837.4 | + | 22113.9i | −1.23452 | + | 1.25015i | ||||
\(134\) | −19800.2 | −1.10271 | ||||||||
\(135\) | − | 12713.0i | − | 0.697559i | ||||||
\(136\) | − | 5531.64i | − | 0.299072i | ||||||
\(137\) | 8250.29 | 0.439570 | 0.219785 | − | 0.975548i | \(-0.429464\pi\) | ||||
0.219785 | + | 0.975548i | \(0.429464\pi\) | |||||||
\(138\) | −8239.71 | −0.432667 | ||||||||
\(139\) | 27435.0 | 1.41996 | 0.709978 | − | 0.704224i | \(-0.248705\pi\) | ||||
0.709978 | + | 0.704224i | \(0.248705\pi\) | |||||||
\(140\) | −18065.1 | −0.921688 | ||||||||
\(141\) | − | 9049.22i | − | 0.455169i | ||||||
\(142\) | 11600.1 | 0.575289 | ||||||||
\(143\) | 26603.0i | 1.30095i | ||||||||
\(144\) | −2319.13 | −0.111841 | ||||||||
\(145\) | − | 29667.0i | − | 1.41104i | ||||||
\(146\) | − | 19850.0i | − | 0.931223i | ||||||
\(147\) | 54253.3i | 2.51068i | ||||||||
\(148\) | 2422.52i | 0.110597i | ||||||||
\(149\) | −40247.3 | −1.81286 | −0.906430 | − | 0.422355i | \(-0.861204\pi\) | ||||
−0.906430 | + | 0.422355i | \(0.861204\pi\) | |||||||
\(150\) | 1929.16 | 0.0857406 | ||||||||
\(151\) | − | 16932.1i | − | 0.742605i | −0.928512 | − | 0.371303i | \(-0.878911\pi\) | ||
0.928512 | − | 0.371303i | \(-0.121089\pi\) | |||||||
\(152\) | 5812.22 | + | 5739.56i | 0.251568 | + | 0.248423i | ||||
\(153\) | 8858.57 | 0.378426 | ||||||||
\(154\) | 27940.2i | 1.17812i | ||||||||
\(155\) | 27215.6i | 1.13280i | ||||||||
\(156\) | 20082.8 | 0.825232 | ||||||||
\(157\) | 5684.97 | 0.230637 | 0.115319 | − | 0.993329i | \(-0.463211\pi\) | ||||
0.115319 | + | 0.993329i | \(0.463211\pi\) | |||||||
\(158\) | −3575.14 | −0.143212 | ||||||||
\(159\) | −7105.14 | −0.281047 | ||||||||
\(160\) | 4748.07i | 0.185471i | ||||||||
\(161\) | 23162.9 | 0.893597 | ||||||||
\(162\) | 23145.2i | 0.881924i | ||||||||
\(163\) | −30550.6 | −1.14986 | −0.574929 | − | 0.818203i | \(-0.694970\pi\) | ||||
−0.574929 | + | 0.818203i | \(0.694970\pi\) | |||||||
\(164\) | − | 14158.5i | − | 0.526417i | ||||||
\(165\) | − | 32587.4i | − | 1.19697i | ||||||
\(166\) | − | 2885.26i | − | 0.104705i | ||||||
\(167\) | 28241.5i | 1.01264i | 0.862345 | + | 0.506320i | \(0.168995\pi\) | ||||
−0.862345 | + | 0.506320i | \(0.831005\pi\) | |||||||
\(168\) | 21092.3 | 0.747318 | ||||||||
\(169\) | −25192.7 | −0.882066 | ||||||||
\(170\) | − | 18136.6i | − | 0.627564i | ||||||
\(171\) | −9191.54 | + | 9307.90i | −0.314337 | + | 0.318317i | ||||
\(172\) | 18532.4 | 0.626435 | ||||||||
\(173\) | 35673.0i | 1.19192i | 0.803013 | + | 0.595961i | \(0.203229\pi\) | ||||
−0.803013 | + | 0.595961i | \(0.796771\pi\) | |||||||
\(174\) | 34638.4i | 1.14409i | ||||||||
\(175\) | −5423.14 | −0.177082 | ||||||||
\(176\) | 7343.56 | 0.237073 | ||||||||
\(177\) | −53307.7 | −1.70154 | ||||||||
\(178\) | 10596.1 | 0.334432 | ||||||||
\(179\) | − | 34371.5i | − | 1.07273i | −0.843985 | − | 0.536367i | \(-0.819796\pi\) | ||
0.843985 | − | 0.536367i | \(-0.180204\pi\) | |||||||
\(180\) | −7603.74 | −0.234683 | ||||||||
\(181\) | − | 29195.1i | − | 0.891153i | −0.895244 | − | 0.445577i | \(-0.852999\pi\) | ||
0.895244 | − | 0.445577i | \(-0.147001\pi\) | |||||||
\(182\) | −56455.6 | −1.70437 | ||||||||
\(183\) | − | 17071.9i | − | 0.509777i | ||||||
\(184\) | − | 6087.95i | − | 0.179819i | ||||||
\(185\) | 7942.72i | 0.232074i | ||||||||
\(186\) | − | 31776.2i | − | 0.918494i | ||||||
\(187\) | −28050.8 | −0.802163 | ||||||||
\(188\) | 6686.05 | 0.189171 | ||||||||
\(189\) | − | 41726.7i | − | 1.16813i | ||||||
\(190\) | 19056.5 | + | 18818.3i | 0.527882 | + | 0.521282i | ||||
\(191\) | 13498.2 | 0.370008 | 0.185004 | − | 0.982738i | \(-0.440770\pi\) | ||||
0.185004 | + | 0.982738i | \(0.440770\pi\) | |||||||
\(192\) | − | 5543.72i | − | 0.150383i | ||||||
\(193\) | 20819.7i | 0.558933i | 0.960155 | + | 0.279467i | \(0.0901577\pi\) | ||||
−0.960155 | + | 0.279467i | \(0.909842\pi\) | |||||||
\(194\) | 36885.4 | 0.980056 | ||||||||
\(195\) | 65845.7 | 1.73164 | ||||||||
\(196\) | −40085.3 | −1.04345 | ||||||||
\(197\) | 34233.5 | 0.882101 | 0.441051 | − | 0.897482i | \(-0.354606\pi\) | ||||
0.441051 | + | 0.897482i | \(0.354606\pi\) | |||||||
\(198\) | 11760.3i | 0.299976i | ||||||||
\(199\) | −55504.1 | −1.40158 | −0.700792 | − | 0.713366i | \(-0.747170\pi\) | ||||
−0.700792 | + | 0.713366i | \(0.747170\pi\) | |||||||
\(200\) | 1425.37i | 0.0356343i | ||||||||
\(201\) | 75797.8 | 1.87614 | ||||||||
\(202\) | 13451.5i | 0.329662i | ||||||||
\(203\) | − | 97373.2i | − | 2.36291i | ||||||
\(204\) | 21175.8i | 0.508838i | ||||||||
\(205\) | − | 46421.6i | − | 1.10462i | ||||||
\(206\) | 24685.9 | 0.581721 | ||||||||
\(207\) | 9749.46 | 0.227531 | ||||||||
\(208\) | 14838.3i | 0.342971i | ||||||||
\(209\) | 29105.2 | − | 29473.6i | 0.666312 | − | 0.674747i | ||||
\(210\) | 69155.4 | 1.56815 | ||||||||
\(211\) | 77552.5i | 1.74193i | 0.491345 | + | 0.870965i | \(0.336505\pi\) | ||||
−0.491345 | + | 0.870965i | \(0.663495\pi\) | |||||||
\(212\) | − | 5249.66i | − | 0.116805i | ||||||
\(213\) | −44406.7 | −0.978790 | ||||||||
\(214\) | −47757.6 | −1.04283 | ||||||||
\(215\) | 60762.4 | 1.31449 | ||||||||
\(216\) | −10967.1 | −0.235063 | ||||||||
\(217\) | 89327.3i | 1.89699i | ||||||||
\(218\) | −580.966 | −0.0122247 | ||||||||
\(219\) | 75988.1i | 1.58437i | ||||||||
\(220\) | 24077.4 | 0.497466 | ||||||||
\(221\) | − | 56679.1i | − | 1.16048i | ||||||
\(222\) | − | 9273.71i | − | 0.188169i | ||||||
\(223\) | − | 30754.3i | − | 0.618438i | −0.950991 | − | 0.309219i | \(-0.899932\pi\) | ||
0.950991 | − | 0.309219i | \(-0.100068\pi\) | |||||||
\(224\) | 15584.1i | 0.310590i | ||||||||
\(225\) | −2282.64 | −0.0450892 | ||||||||
\(226\) | −12094.4 | −0.236792 | ||||||||
\(227\) | 81299.3i | 1.57774i | 0.614561 | + | 0.788869i | \(0.289333\pi\) | ||||
−0.614561 | + | 0.788869i | \(0.710667\pi\) | |||||||
\(228\) | −22249.9 | − | 21971.7i | −0.428014 | − | 0.422664i | ||||
\(229\) | −93187.0 | −1.77699 | −0.888494 | − | 0.458889i | \(-0.848248\pi\) | ||||
−0.888494 | + | 0.458889i | \(0.848248\pi\) | |||||||
\(230\) | − | 19960.6i | − | 0.377326i | ||||||
\(231\) | − | 106959.i | − | 2.00444i | ||||||
\(232\) | −25592.7 | −0.475489 | ||||||||
\(233\) | −3379.09 | −0.0622426 | −0.0311213 | − | 0.999516i | \(-0.509908\pi\) | ||||
−0.0311213 | + | 0.999516i | \(0.509908\pi\) | |||||||
\(234\) | −23762.6 | −0.433973 | ||||||||
\(235\) | 21921.6 | 0.396950 | ||||||||
\(236\) | − | 39386.6i | − | 0.707171i | ||||||
\(237\) | 13686.1 | 0.243659 | ||||||||
\(238\) | − | 59528.0i | − | 1.05091i | ||||||
\(239\) | 35917.8 | 0.628802 | 0.314401 | − | 0.949290i | \(-0.398196\pi\) | ||||
0.314401 | + | 0.949290i | \(0.398196\pi\) | |||||||
\(240\) | − | 18176.2i | − | 0.315559i | ||||||
\(241\) | 57352.1i | 0.987451i | 0.869618 | + | 0.493726i | \(0.164365\pi\) | ||||
−0.869618 | + | 0.493726i | \(0.835635\pi\) | |||||||
\(242\) | 4171.92i | 0.0712370i | ||||||||
\(243\) | − | 49343.6i | − | 0.835639i | ||||||
\(244\) | 12613.7 | 0.211866 | ||||||||
\(245\) | −131428. | −2.18955 | ||||||||
\(246\) | 54200.6i | 0.895641i | ||||||||
\(247\) | 59554.0 | + | 58809.5i | 0.976151 | + | 0.963948i | ||||
\(248\) | 23478.0 | 0.381731 | ||||||||
\(249\) | 11045.1i | 0.178144i | ||||||||
\(250\) | − | 41694.5i | − | 0.667112i | ||||||
\(251\) | −52486.8 | −0.833110 | −0.416555 | − | 0.909110i | \(-0.636763\pi\) | ||||
−0.416555 | + | 0.909110i | \(0.636763\pi\) | |||||||
\(252\) | −24957.0 | −0.392999 | ||||||||
\(253\) | −30871.9 | −0.482305 | ||||||||
\(254\) | −12730.8 | −0.197327 | ||||||||
\(255\) | 69429.2i | 1.06773i | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 85222.5i | 1.29029i | 0.764059 | + | 0.645146i | \(0.223204\pi\) | ||||
−0.764059 | + | 0.645146i | \(0.776796\pi\) | |||||||
\(258\) | −70944.5 | −1.06581 | ||||||||
\(259\) | 26069.6i | 0.388629i | ||||||||
\(260\) | 48650.4i | 0.719680i | ||||||||
\(261\) | − | 40985.2i | − | 0.601653i | ||||||
\(262\) | − | 78082.4i | − | 1.13750i | ||||||
\(263\) | −27539.5 | −0.398149 | −0.199074 | − | 0.979984i | \(-0.563794\pi\) | ||||
−0.199074 | + | 0.979984i | \(0.563794\pi\) | |||||||
\(264\) | −28112.1 | −0.403353 | ||||||||
\(265\) | − | 17212.1i | − | 0.245099i | ||||||
\(266\) | 62547.5 | + | 61765.5i | 0.883988 | + | 0.872937i | ||||
\(267\) | −40563.3 | −0.568999 | ||||||||
\(268\) | 56003.5i | 0.779732i | ||||||||
\(269\) | 58880.0i | 0.813697i | 0.913496 | + | 0.406849i | \(0.133372\pi\) | ||||
−0.913496 | + | 0.406849i | \(0.866628\pi\) | |||||||
\(270\) | −35957.8 | −0.493249 | ||||||||
\(271\) | 99955.1 | 1.36103 | 0.680513 | − | 0.732736i | \(-0.261757\pi\) | ||||
0.680513 | + | 0.732736i | \(0.261757\pi\) | |||||||
\(272\) | −15645.8 | −0.211476 | ||||||||
\(273\) | 216119. | 2.89980 | ||||||||
\(274\) | − | 23335.4i | − | 0.310823i | ||||||
\(275\) | 7228.03 | 0.0955772 | ||||||||
\(276\) | 23305.4i | 0.305942i | ||||||||
\(277\) | 66298.2 | 0.864056 | 0.432028 | − | 0.901860i | \(-0.357798\pi\) | ||||
0.432028 | + | 0.901860i | \(0.357798\pi\) | |||||||
\(278\) | − | 77597.8i | − | 1.00406i | ||||||
\(279\) | 37598.6i | 0.483017i | ||||||||
\(280\) | 51095.8i | 0.651732i | ||||||||
\(281\) | 55021.9i | 0.696824i | 0.937341 | + | 0.348412i | \(0.113279\pi\) | ||||
−0.937341 | + | 0.348412i | \(0.886721\pi\) | |||||||
\(282\) | −25595.1 | −0.321853 | ||||||||
\(283\) | 10575.2 | 0.132044 | 0.0660219 | − | 0.997818i | \(-0.478969\pi\) | ||||
0.0660219 | + | 0.997818i | \(0.478969\pi\) | |||||||
\(284\) | − | 32810.1i | − | 0.406790i | ||||||
\(285\) | −72950.8 | − | 72038.8i | −0.898132 | − | 0.886904i | ||||
\(286\) | 75244.7 | 0.919907 | ||||||||
\(287\) | − | 152365.i | − | 1.84979i | ||||||
\(288\) | 6559.49i | 0.0790833i | ||||||||
\(289\) | −23757.3 | −0.284447 | ||||||||
\(290\) | −83911.0 | −0.997752 | ||||||||
\(291\) | −141202. | −1.66746 | ||||||||
\(292\) | −56144.2 | −0.658474 | ||||||||
\(293\) | − | 9449.70i | − | 0.110074i | −0.998484 | − | 0.0550368i | \(-0.982472\pi\) | ||
0.998484 | − | 0.0550368i | \(-0.0175276\pi\) | |||||||
\(294\) | 153452. | 1.77532 | ||||||||
\(295\) | − | 129137.i | − | 1.48391i | ||||||
\(296\) | 6851.92 | 0.0782040 | ||||||||
\(297\) | 55613.9i | 0.630479i | ||||||||
\(298\) | 113837.i | 1.28189i | ||||||||
\(299\) | − | 62379.2i | − | 0.697746i | ||||||
\(300\) | − | 5456.50i | − | 0.0606278i | ||||||
\(301\) | 199435. | 2.20124 | ||||||||
\(302\) | −47891.3 | −0.525101 | ||||||||
\(303\) | − | 51494.2i | − | 0.560884i | ||||||
\(304\) | 16233.9 | − | 16439.4i | 0.175661 | − | 0.177885i | ||||
\(305\) | 41356.5 | 0.444574 | ||||||||
\(306\) | − | 25055.8i | − | 0.267587i | ||||||
\(307\) | − | 112622.i | − | 1.19494i | −0.801890 | − | 0.597472i | \(-0.796172\pi\) | ||
0.801890 | − | 0.597472i | \(-0.203828\pi\) | |||||||
\(308\) | 79026.9 | 0.833054 | ||||||||
\(309\) | −94500.8 | −0.989734 | ||||||||
\(310\) | 76977.4 | 0.801013 | ||||||||
\(311\) | −75878.9 | −0.784513 | −0.392257 | − | 0.919856i | \(-0.628305\pi\) | ||||
−0.392257 | + | 0.919856i | \(0.628305\pi\) | |||||||
\(312\) | − | 56802.9i | − | 0.583527i | ||||||
\(313\) | −110960. | −1.13260 | −0.566301 | − | 0.824199i | \(-0.691626\pi\) | ||||
−0.566301 | + | 0.824199i | \(0.691626\pi\) | |||||||
\(314\) | − | 16079.5i | − | 0.163085i | ||||||
\(315\) | −81826.7 | −0.824658 | ||||||||
\(316\) | 10112.0i | 0.101266i | ||||||||
\(317\) | − | 63970.1i | − | 0.636589i | −0.947992 | − | 0.318294i | \(-0.896890\pi\) | ||
0.947992 | − | 0.318294i | \(-0.103110\pi\) | |||||||
\(318\) | 20096.4i | 0.198730i | ||||||||
\(319\) | 129780.i | 1.27534i | ||||||||
\(320\) | 13429.6 | 0.131148 | ||||||||
\(321\) | 182822. | 1.77427 | ||||||||
\(322\) | − | 65514.7i | − | 0.631869i | ||||||
\(323\) | −62010.0 | + | 62795.0i | −0.594370 | + | 0.601894i | ||||
\(324\) | 65464.6 | 0.623615 | ||||||||
\(325\) | 14604.8i | 0.138271i | ||||||||
\(326\) | 86410.0i | 0.813072i | ||||||||
\(327\) | 2224.01 | 0.0207990 | ||||||||
\(328\) | −40046.4 | −0.372233 | ||||||||
\(329\) | 71951.1 | 0.664731 | ||||||||
\(330\) | −92171.2 | −0.846384 | ||||||||
\(331\) | − | 79462.6i | − | 0.725282i | −0.931929 | − | 0.362641i | \(-0.881875\pi\) | ||
0.931929 | − | 0.362641i | \(-0.118125\pi\) | |||||||
\(332\) | −8160.74 | −0.0740377 | ||||||||
\(333\) | 10972.9i | 0.0989541i | ||||||||
\(334\) | 79879.1 | 0.716045 | ||||||||
\(335\) | 183619.i | 1.63617i | ||||||||
\(336\) | − | 59658.1i | − | 0.528434i | ||||||
\(337\) | − | 2779.80i | − | 0.0244767i | −0.999925 | − | 0.0122384i | \(-0.996104\pi\) | ||
0.999925 | − | 0.0122384i | \(-0.00389569\pi\) | |||||||
\(338\) | 71255.7i | 0.623715i | ||||||||
\(339\) | 46298.9 | 0.402876 | ||||||||
\(340\) | −51298.0 | −0.443755 | ||||||||
\(341\) | − | 119057.i | − | 1.02387i | ||||||
\(342\) | 26326.7 | + | 25997.6i | 0.225084 | + | 0.222270i | ||||
\(343\) | −224669. | −1.90965 | ||||||||
\(344\) | − | 52417.7i | − | 0.442956i | ||||||
\(345\) | 76411.6i | 0.641979i | ||||||||
\(346\) | 100899. | 0.842816 | ||||||||
\(347\) | −15728.1 | −0.130622 | −0.0653110 | − | 0.997865i | \(-0.520804\pi\) | ||||
−0.0653110 | + | 0.997865i | \(0.520804\pi\) | |||||||
\(348\) | 97972.2 | 0.808993 | ||||||||
\(349\) | −41782.5 | −0.343039 | −0.171519 | − | 0.985181i | \(-0.554868\pi\) | ||||
−0.171519 | + | 0.985181i | \(0.554868\pi\) | |||||||
\(350\) | 15339.0i | 0.125216i | ||||||||
\(351\) | −112373. | −0.912108 | ||||||||
\(352\) | − | 20770.7i | − | 0.167636i | ||||||
\(353\) | 39292.1 | 0.315323 | 0.157661 | − | 0.987493i | \(-0.449605\pi\) | ||||
0.157661 | + | 0.987493i | \(0.449605\pi\) | |||||||
\(354\) | 150777.i | 1.20317i | ||||||||
\(355\) | − | 107575.i | − | 0.853597i | ||||||
\(356\) | − | 29970.4i | − | 0.236479i | ||||||
\(357\) | 227881.i | 1.78802i | ||||||||
\(358\) | −97217.2 | −0.758537 | ||||||||
\(359\) | 160964. | 1.24894 | 0.624468 | − | 0.781050i | \(-0.285316\pi\) | ||||
0.624468 | + | 0.781050i | \(0.285316\pi\) | |||||||
\(360\) | 21506.6i | 0.165946i | ||||||||
\(361\) | −1639.37 | − | 130311.i | −0.0125794 | − | 0.999921i | ||||
\(362\) | −82576.1 | −0.630141 | ||||||||
\(363\) | − | 15970.7i | − | 0.121202i | ||||||
\(364\) | 159681.i | 1.20517i | ||||||||
\(365\) | −184080. | −1.38172 | ||||||||
\(366\) | −48286.7 | −0.360467 | ||||||||
\(367\) | 19835.4 | 0.147268 | 0.0736340 | − | 0.997285i | \(-0.476540\pi\) | ||||
0.0736340 | + | 0.997285i | \(0.476540\pi\) | |||||||
\(368\) | −17219.3 | −0.127151 | ||||||||
\(369\) | − | 64131.7i | − | 0.470999i | ||||||
\(370\) | 22465.4 | 0.164101 | ||||||||
\(371\) | − | 56493.6i | − | 0.410442i | ||||||
\(372\) | −89876.8 | −0.649474 | ||||||||
\(373\) | 14463.5i | 0.103958i | 0.998648 | + | 0.0519788i | \(0.0165528\pi\) | ||||
−0.998648 | + | 0.0519788i | \(0.983447\pi\) | |||||||
\(374\) | 79339.7i | 0.567215i | ||||||||
\(375\) | 159612.i | 1.13502i | ||||||||
\(376\) | − | 18911.0i | − | 0.133764i | ||||||
\(377\) | −262232. | −1.84503 | ||||||||
\(378\) | −118021. | −0.825991 | ||||||||
\(379\) | 25932.7i | 0.180539i | 0.995917 | + | 0.0902693i | \(0.0287728\pi\) | ||||
−0.995917 | + | 0.0902693i | \(0.971227\pi\) | |||||||
\(380\) | 53226.2 | − | 53900.0i | 0.368602 | − | 0.373269i | ||||
\(381\) | 48734.9 | 0.335730 | ||||||||
\(382\) | − | 38178.8i | − | 0.261635i | ||||||
\(383\) | 9634.98i | 0.0656831i | 0.999461 | + | 0.0328415i | \(0.0104557\pi\) | ||||
−0.999461 | + | 0.0328415i | \(0.989544\pi\) | |||||||
\(384\) | −15680.0 | −0.106337 | ||||||||
\(385\) | 259106. | 1.74806 | ||||||||
\(386\) | 58887.0 | 0.395226 | ||||||||
\(387\) | 83943.6 | 0.560487 | ||||||||
\(388\) | − | 104328.i | − | 0.693005i | ||||||
\(389\) | 101890. | 0.673335 | 0.336668 | − | 0.941624i | \(-0.390700\pi\) | ||||
0.336668 | + | 0.941624i | \(0.390700\pi\) | |||||||
\(390\) | − | 186240.i | − | 1.22446i | ||||||
\(391\) | 65774.0 | 0.430230 | ||||||||
\(392\) | 113378.i | 0.737833i | ||||||||
\(393\) | 298909.i | 1.93533i | ||||||||
\(394\) | − | 96826.9i | − | 0.623740i | ||||||
\(395\) | 33154.3i | 0.212494i | ||||||||
\(396\) | 33263.0 | 0.212115 | ||||||||
\(397\) | 100161. | 0.635503 | 0.317752 | − | 0.948174i | \(-0.397072\pi\) | ||||
0.317752 | + | 0.948174i | \(0.397072\pi\) | |||||||
\(398\) | 156989.i | 0.991069i | ||||||||
\(399\) | −239440. | − | 236446.i | −1.50401 | − | 1.48521i | ||||
\(400\) | 4031.56 | 0.0251972 | ||||||||
\(401\) | − | 16696.5i | − | 0.103833i | −0.998651 | − | 0.0519165i | \(-0.983467\pi\) | ||
0.998651 | − | 0.0519165i | \(-0.0165330\pi\) | |||||||
\(402\) | − | 214388.i | − | 1.32663i | ||||||
\(403\) | 240564. | 1.48122 | ||||||||
\(404\) | 38046.7 | 0.233106 | ||||||||
\(405\) | 214639. | 1.30857 | ||||||||
\(406\) | −275413. | −1.67083 | ||||||||
\(407\) | − | 34745.9i | − | 0.209756i | ||||||
\(408\) | 59894.2 | 0.359803 | ||||||||
\(409\) | − | 1173.94i | − | 0.00701780i | −0.999994 | − | 0.00350890i | \(-0.998883\pi\) | ||
0.999994 | − | 0.00350890i | \(-0.00111692\pi\) | |||||||
\(410\) | −131300. | −0.781083 | ||||||||
\(411\) | 89330.7i | 0.528831i | ||||||||
\(412\) | − | 69822.3i | − | 0.411339i | ||||||
\(413\) | − | 423854.i | − | 2.48494i | ||||||
\(414\) | − | 27575.7i | − | 0.160889i | ||||||
\(415\) | −26756.6 | −0.155359 | ||||||||
\(416\) | 41969.0 | 0.242517 | ||||||||
\(417\) | 297054.i | 1.70830i | ||||||||
\(418\) | −83364.0 | − | 82321.9i | −0.477118 | − | 0.471154i | ||||
\(419\) | −209961. | −1.19595 | −0.597973 | − | 0.801517i | \(-0.704027\pi\) | ||||
−0.597973 | + | 0.801517i | \(0.704027\pi\) | |||||||
\(420\) | − | 195601.i | − | 1.10885i | ||||||
\(421\) | 249117.i | 1.40552i | 0.711425 | + | 0.702762i | \(0.248050\pi\) | ||||
−0.711425 | + | 0.702762i | \(0.751950\pi\) | |||||||
\(422\) | 219351. | 1.23173 | ||||||||
\(423\) | 30284.8 | 0.169256 | ||||||||
\(424\) | −14848.3 | −0.0825933 | ||||||||
\(425\) | −15399.7 | −0.0852577 | ||||||||
\(426\) | 125601.i | 0.692109i | ||||||||
\(427\) | 135741. | 0.744481 | ||||||||
\(428\) | 135079.i | 0.737395i | ||||||||
\(429\) | −288046. | −1.56512 | ||||||||
\(430\) | − | 171862.i | − | 0.929486i | ||||||
\(431\) | 126947.i | 0.683387i | 0.939811 | + | 0.341694i | \(0.111001\pi\) | ||||
−0.939811 | + | 0.341694i | \(0.888999\pi\) | |||||||
\(432\) | 31019.6i | 0.166214i | ||||||||
\(433\) | − | 327343.i | − | 1.74593i | −0.487783 | − | 0.872965i | \(-0.662194\pi\) | ||
0.487783 | − | 0.872965i | \(-0.337806\pi\) | |||||||
\(434\) | 252656. | 1.34137 | ||||||||
\(435\) | 321222. | 1.69757 | ||||||||
\(436\) | 1643.22i | 0.00864416i | ||||||||
\(437\) | −68246.3 | + | 69110.3i | −0.357368 | + | 0.361893i | ||||
\(438\) | 214927. | 1.12032 | ||||||||
\(439\) | − | 323562.i | − | 1.67891i | −0.543425 | − | 0.839457i | \(-0.682873\pi\) | ||
0.543425 | − | 0.839457i | \(-0.317127\pi\) | |||||||
\(440\) | − | 68101.1i | − | 0.351762i | ||||||
\(441\) | −181568. | −0.933605 | ||||||||
\(442\) | −160313. | −0.820584 | ||||||||
\(443\) | 188338. | 0.959689 | 0.479845 | − | 0.877354i | \(-0.340693\pi\) | ||||
0.479845 | + | 0.877354i | \(0.340693\pi\) | |||||||
\(444\) | −26230.0 | −0.133055 | ||||||||
\(445\) | − | 98264.0i | − | 0.496220i | ||||||
\(446\) | −86986.3 | −0.437302 | ||||||||
\(447\) | − | 435781.i | − | 2.18099i | ||||||
\(448\) | 44078.6 | 0.219620 | ||||||||
\(449\) | 31205.6i | 0.154789i | 0.997001 | + | 0.0773945i | \(0.0246601\pi\) | ||||
−0.997001 | + | 0.0773945i | \(0.975340\pi\) | |||||||
\(450\) | 6456.29i | 0.0318829i | ||||||||
\(451\) | 203074.i | 0.998394i | ||||||||
\(452\) | 34208.2i | 0.167438i | ||||||||
\(453\) | 183334. | 0.893402 | ||||||||
\(454\) | 229949. | 1.11563 | ||||||||
\(455\) | 523545.i | 2.52890i | ||||||||
\(456\) | −62145.5 | + | 62932.2i | −0.298868 | + | 0.302652i | ||||
\(457\) | 89688.2 | 0.429440 | 0.214720 | − | 0.976676i | \(-0.431116\pi\) | ||||
0.214720 | + | 0.976676i | \(0.431116\pi\) | |||||||
\(458\) | 263573.i | 1.25652i | ||||||||
\(459\) | − | 118488.i | − | 0.562405i | ||||||
\(460\) | −56457.0 | −0.266810 | ||||||||
\(461\) | −71209.7 | −0.335071 | −0.167536 | − | 0.985866i | \(-0.553581\pi\) | ||||
−0.167536 | + | 0.985866i | \(0.553581\pi\) | |||||||
\(462\) | −302525. | −1.41735 | ||||||||
\(463\) | −96472.6 | −0.450030 | −0.225015 | − | 0.974355i | \(-0.572243\pi\) | ||||
−0.225015 | + | 0.974355i | \(0.572243\pi\) | |||||||
\(464\) | 72387.2i | 0.336222i | ||||||||
\(465\) | −294679. | −1.36284 | ||||||||
\(466\) | 9557.51i | 0.0440122i | ||||||||
\(467\) | 337202. | 1.54617 | 0.773084 | − | 0.634304i | \(-0.218713\pi\) | ||||
0.773084 | + | 0.634304i | \(0.218713\pi\) | |||||||
\(468\) | 67210.8i | 0.306865i | ||||||||
\(469\) | 602675.i | 2.73992i | ||||||||
\(470\) | − | 62003.6i | − | 0.280686i | ||||||
\(471\) | 61554.5i | 0.277471i | ||||||||
\(472\) | −111402. | −0.500046 | ||||||||
\(473\) | −265809. | −1.18808 | ||||||||
\(474\) | − | 38710.1i | − | 0.172293i | ||||||
\(475\) | 15978.5 | − | 16180.8i | 0.0708189 | − | 0.0717154i | ||||
\(476\) | −168371. | −0.743109 | ||||||||
\(477\) | − | 23778.6i | − | 0.104508i | ||||||
\(478\) | − | 101591.i | − | 0.444630i | ||||||
\(479\) | 126684. | 0.552143 | 0.276071 | − | 0.961137i | \(-0.410967\pi\) | ||||
0.276071 | + | 0.961137i | \(0.410967\pi\) | |||||||
\(480\) | −51410.1 | −0.223134 | ||||||||
\(481\) | 70207.1 | 0.303453 | ||||||||
\(482\) | 162216. | 0.698233 | ||||||||
\(483\) | 250798.i | 1.07505i | ||||||||
\(484\) | 11800.0 | 0.0503722 | ||||||||
\(485\) | − | 342059.i | − | 1.45418i | ||||||
\(486\) | −139565. | −0.590886 | ||||||||
\(487\) | 233861.i | 0.986053i | 0.870014 | + | 0.493027i | \(0.164109\pi\) | ||||
−0.870014 | + | 0.493027i | \(0.835891\pi\) | |||||||
\(488\) | − | 35676.9i | − | 0.149812i | ||||||
\(489\) | − | 330789.i | − | 1.38335i | ||||||
\(490\) | 371734.i | 1.54825i | ||||||||
\(491\) | −423929. | −1.75845 | −0.879226 | − | 0.476406i | \(-0.841939\pi\) | ||||
−0.879226 | + | 0.476406i | \(0.841939\pi\) | |||||||
\(492\) | 153302. | 0.633314 | ||||||||
\(493\) | − | 276503.i | − | 1.13764i | ||||||
\(494\) | 166338. | − | 168444.i | 0.681614 | − | 0.690243i | ||||
\(495\) | 109060. | 0.445096 | ||||||||
\(496\) | − | 66405.8i | − | 0.269925i | ||||||
\(497\) | − | 353082.i | − | 1.42943i | ||||||
\(498\) | 31240.3 | 0.125967 | ||||||||
\(499\) | −175944. | −0.706600 | −0.353300 | − | 0.935510i | \(-0.614941\pi\) | ||||
−0.353300 | + | 0.935510i | \(0.614941\pi\) | |||||||
\(500\) | −117930. | −0.471719 | ||||||||
\(501\) | −305787. | −1.21827 | ||||||||
\(502\) | 148455.i | 0.589098i | ||||||||
\(503\) | 108798. | 0.430017 | 0.215009 | − | 0.976612i | \(-0.431022\pi\) | ||||
0.215009 | + | 0.976612i | \(0.431022\pi\) | |||||||
\(504\) | 70589.1i | 0.277892i | ||||||||
\(505\) | 124744. | 0.489143 | ||||||||
\(506\) | 87318.8i | 0.341041i | ||||||||
\(507\) | − | 272776.i | − | 1.06118i | ||||||
\(508\) | 36008.0i | 0.139531i | ||||||||
\(509\) | 72826.1i | 0.281094i | 0.990074 | + | 0.140547i | \(0.0448861\pi\) | ||||
−0.990074 | + | 0.140547i | \(0.955114\pi\) | |||||||
\(510\) | 196375. | 0.754999 | ||||||||
\(511\) | −604188. | −2.31383 | ||||||||
\(512\) | − | 11585.2i | − | 0.0441942i | ||||||
\(513\) | 124498. | + | 122942.i | 0.473073 | + | 0.467159i | ||||
\(514\) | 241046. | 0.912375 | ||||||||
\(515\) | − | 228927.i | − | 0.863141i | ||||||
\(516\) | 200661.i | 0.753641i | ||||||||
\(517\) | −95897.4 | −0.358778 | ||||||||
\(518\) | 73736.1 | 0.274802 | ||||||||
\(519\) | −386253. | −1.43396 | ||||||||
\(520\) | 137604. | 0.508891 | ||||||||
\(521\) | 93748.1i | 0.345372i | 0.984977 | + | 0.172686i | \(0.0552446\pi\) | ||||
−0.984977 | + | 0.172686i | \(0.944755\pi\) | |||||||
\(522\) | −115924. | −0.425433 | ||||||||
\(523\) | 87245.8i | 0.318964i | 0.987201 | + | 0.159482i | \(0.0509823\pi\) | ||||
−0.987201 | + | 0.159482i | \(0.949018\pi\) | |||||||
\(524\) | −220850. | −0.804332 | ||||||||
\(525\) | − | 58719.4i | − | 0.213041i | ||||||
\(526\) | 77893.6i | 0.281534i | ||||||||
\(527\) | 253656.i | 0.913321i | ||||||||
\(528\) | 79513.0i | 0.285214i | ||||||||
\(529\) | −207452. | −0.741322 | ||||||||
\(530\) | −48683.1 | −0.173311 | ||||||||
\(531\) | − | 178404.i | − | 0.632724i | ||||||
\(532\) | 174699. | − | 176911.i | 0.617260 | − | 0.625074i | ||||
\(533\) | −410329. | −1.44437 | ||||||||
\(534\) | 114730.i | 0.402343i | ||||||||
\(535\) | 442884.i | 1.54733i | ||||||||
\(536\) | 158402. | 0.551354 | ||||||||
\(537\) | 372160. | 1.29057 | ||||||||
\(538\) | 166538. | 0.575371 | ||||||||
\(539\) | 574940. | 1.97900 | ||||||||
\(540\) | 101704.i | 0.348779i | ||||||||
\(541\) | 374060. | 1.27805 | 0.639024 | − | 0.769187i | \(-0.279338\pi\) | ||||
0.639024 | + | 0.769187i | \(0.279338\pi\) | |||||||
\(542\) | − | 282716.i | − | 0.962391i | ||||||
\(543\) | 316112. | 1.07211 | ||||||||
\(544\) | 44253.1i | 0.149536i | ||||||||
\(545\) | 5387.63i | 0.0181386i | ||||||||
\(546\) | − | 611277.i | − | 2.05047i | ||||||
\(547\) | 160411.i | 0.536118i | 0.963402 | + | 0.268059i | \(0.0863823\pi\) | ||||
−0.963402 | + | 0.268059i | \(0.913618\pi\) | |||||||
\(548\) | −66002.3 | −0.219785 | ||||||||
\(549\) | 57134.3 | 0.189562 | ||||||||
\(550\) | − | 20443.9i | − | 0.0675833i | ||||||
\(551\) | 290528. | + | 286896.i | 0.956941 | + | 0.944978i | ||||
\(552\) | 65917.7 | 0.216334 | ||||||||
\(553\) | 108819.i | 0.355841i | ||||||||
\(554\) | − | 187520.i | − | 0.610980i | ||||||
\(555\) | −86000.4 | −0.279199 | ||||||||
\(556\) | −219480. | −0.709978 | ||||||||
\(557\) | 460605. | 1.48463 | 0.742314 | − | 0.670052i | \(-0.233728\pi\) | ||||
0.742314 | + | 0.670052i | \(0.233728\pi\) | |||||||
\(558\) | 106345. | 0.341545 | ||||||||
\(559\) | − | 537090.i | − | 1.71879i | ||||||
\(560\) | 144521. | 0.460844 | ||||||||
\(561\) | − | 303722.i | − | 0.965053i | ||||||
\(562\) | 155626. | 0.492729 | ||||||||
\(563\) | − | 73084.0i | − | 0.230571i | −0.993332 | − | 0.115286i | \(-0.963222\pi\) | ||
0.993332 | − | 0.115286i | \(-0.0367783\pi\) | |||||||
\(564\) | 72393.7i | 0.227585i | ||||||||
\(565\) | 112158.i | 0.351346i | ||||||||
\(566\) | − | 29911.3i | − | 0.0933690i | ||||||
\(567\) | 704489. | 2.19133 | ||||||||
\(568\) | −92801.0 | −0.287644 | ||||||||
\(569\) | − | 609592.i | − | 1.88285i | −0.337227 | − | 0.941424i | \(-0.609489\pi\) | ||
0.337227 | − | 0.941424i | \(-0.390511\pi\) | |||||||
\(570\) | −203757. | + | 206336.i | −0.627136 | + | 0.635075i | ||||
\(571\) | −11273.0 | −0.0345755 | −0.0172877 | − | 0.999851i | \(-0.505503\pi\) | ||||
−0.0172877 | + | 0.999851i | \(0.505503\pi\) | |||||||
\(572\) | − | 212824.i | − | 0.650473i | ||||||
\(573\) | 146153.i | 0.445143i | ||||||||
\(574\) | −430954. | −1.30800 | ||||||||
\(575\) | −16948.4 | −0.0512617 | ||||||||
\(576\) | 18553.0 | 0.0559204 | ||||||||
\(577\) | −186962. | −0.561567 | −0.280783 | − | 0.959771i | \(-0.590594\pi\) | ||||
−0.280783 | + | 0.959771i | \(0.590594\pi\) | |||||||
\(578\) | 67195.9i | 0.201135i | ||||||||
\(579\) | −225427. | −0.672433 | ||||||||
\(580\) | 237336.i | 0.705518i | ||||||||
\(581\) | −87820.8 | −0.260163 | ||||||||
\(582\) | 399379.i | 1.17907i | ||||||||
\(583\) | 75295.4i | 0.221529i | ||||||||
\(584\) | 158800.i | 0.465612i | ||||||||
\(585\) | 220364.i | 0.643916i | ||||||||
\(586\) | −26727.8 | −0.0778337 | ||||||||
\(587\) | −258778. | −0.751020 | −0.375510 | − | 0.926818i | \(-0.622532\pi\) | ||||
−0.375510 | + | 0.926818i | \(0.622532\pi\) | |||||||
\(588\) | − | 434027.i | − | 1.25534i | ||||||
\(589\) | −266522. | − | 263190.i | −0.768250 | − | 0.758645i | ||||
\(590\) | −365255. | −1.04928 | ||||||||
\(591\) | 370665.i | 1.06122i | ||||||||
\(592\) | − | 19380.2i | − | 0.0552986i | ||||||
\(593\) | −603214. | −1.71539 | −0.857693 | − | 0.514162i | \(-0.828103\pi\) | ||||
−0.857693 | + | 0.514162i | \(0.828103\pi\) | |||||||
\(594\) | 157300. | 0.445816 | ||||||||
\(595\) | −552037. | −1.55932 | ||||||||
\(596\) | 321979. | 0.906430 | ||||||||
\(597\) | − | 600975.i | − | 1.68619i | ||||||
\(598\) | −176435. | −0.493381 | ||||||||
\(599\) | 32971.2i | 0.0918927i | 0.998944 | + | 0.0459464i | \(0.0146303\pi\) | ||||
−0.998944 | + | 0.0459464i | \(0.985370\pi\) | |||||||
\(600\) | −15433.3 | −0.0428703 | ||||||||
\(601\) | 61000.3i | 0.168882i | 0.996428 | + | 0.0844410i | \(0.0269104\pi\) | ||||
−0.996428 | + | 0.0844410i | \(0.973090\pi\) | |||||||
\(602\) | − | 564086.i | − | 1.55651i | ||||||
\(603\) | 253671.i | 0.697647i | ||||||||
\(604\) | 135457.i | 0.371303i | ||||||||
\(605\) | 38688.6 | 0.105699 | ||||||||
\(606\) | −145648. | −0.396605 | ||||||||
\(607\) | 252238.i | 0.684594i | 0.939592 | + | 0.342297i | \(0.111205\pi\) | ||||
−0.939592 | + | 0.342297i | \(0.888795\pi\) | |||||||
\(608\) | −46497.7 | − | 45916.4i | −0.125784 | − | 0.124211i | ||||
\(609\) | 1.05432e6 | 2.84273 | ||||||||
\(610\) | − | 116974.i | − | 0.314361i | ||||||
\(611\) | − | 193769.i | − | 0.519041i | ||||||
\(612\) | −70868.6 | −0.189213 | ||||||||
\(613\) | 384604. | 1.02351 | 0.511757 | − | 0.859131i | \(-0.328995\pi\) | ||||
0.511757 | + | 0.859131i | \(0.328995\pi\) | |||||||
\(614\) | −318544. | −0.844953 | ||||||||
\(615\) | 502633. | 1.32893 | ||||||||
\(616\) | − | 223522.i | − | 0.589058i | ||||||
\(617\) | 89917.4 | 0.236197 | 0.118098 | − | 0.993002i | \(-0.462320\pi\) | ||||
0.118098 | + | 0.993002i | \(0.462320\pi\) | |||||||
\(618\) | 267289.i | 0.699847i | ||||||||
\(619\) | −133253. | −0.347772 | −0.173886 | − | 0.984766i | \(-0.555632\pi\) | ||||
−0.173886 | + | 0.984766i | \(0.555632\pi\) | |||||||
\(620\) | − | 217725.i | − | 0.566402i | ||||||
\(621\) | − | 130404.i | − | 0.338150i | ||||||
\(622\) | 214618.i | 0.554735i | ||||||||
\(623\) | − | 322523.i | − | 0.830968i | ||||||
\(624\) | −160663. | −0.412616 | ||||||||
\(625\) | −426028. | −1.09063 | ||||||||
\(626\) | 313842.i | 0.800870i | ||||||||
\(627\) | 319128. | + | 315139.i | 0.811764 | + | 0.801616i | ||||
\(628\) | −45479.8 | −0.115319 | ||||||||
\(629\) | 74028.0i | 0.187109i | ||||||||
\(630\) | 231441.i | 0.583121i | ||||||||
\(631\) | 250184. | 0.628348 | 0.314174 | − | 0.949365i | \(-0.398273\pi\) | ||||
0.314174 | + | 0.949365i | \(0.398273\pi\) | |||||||
\(632\) | 28601.1 | 0.0716059 | ||||||||
\(633\) | −839705. | −2.09565 | ||||||||
\(634\) | −180935. | −0.450136 | ||||||||
\(635\) | 118060.i | 0.292788i | ||||||||
\(636\) | 56841.1 | 0.140523 | ||||||||
\(637\) | 1.16171e6i | 2.86299i | ||||||||
\(638\) | 367074. | 0.901804 | ||||||||
\(639\) | − | 148615.i | − | 0.363966i | ||||||
\(640\) | − | 37984.6i | − | 0.0927357i | ||||||
\(641\) | 601164.i | 1.46311i | 0.681782 | + | 0.731555i | \(0.261205\pi\) | ||||
−0.681782 | + | 0.731555i | \(0.738795\pi\) | |||||||
\(642\) | − | 517099.i | − | 1.25460i | ||||||
\(643\) | 379057. | 0.916816 | 0.458408 | − | 0.888742i | \(-0.348420\pi\) | ||||
0.458408 | + | 0.888742i | \(0.348420\pi\) | |||||||
\(644\) | −185304. | −0.446799 | ||||||||
\(645\) | 657909.i | 1.58142i | ||||||||
\(646\) | 177611. | + | 175391.i | 0.425604 | + | 0.420283i | ||||
\(647\) | 245678. | 0.586892 | 0.293446 | − | 0.955976i | \(-0.405198\pi\) | ||||
0.293446 | + | 0.955976i | \(0.405198\pi\) | |||||||
\(648\) | − | 185162.i | − | 0.440962i | ||||||
\(649\) | 564918.i | 1.34121i | ||||||||
\(650\) | 41308.7 | 0.0977722 | ||||||||
\(651\) | −967198. | −2.28220 | ||||||||
\(652\) | 244405. | 0.574929 | ||||||||
\(653\) | −15905.7 | −0.0373016 | −0.0186508 | − | 0.999826i | \(-0.505937\pi\) | ||||
−0.0186508 | + | 0.999826i | \(0.505937\pi\) | |||||||
\(654\) | − | 6290.45i | − | 0.0147071i | ||||||
\(655\) | −724102. | −1.68779 | ||||||||
\(656\) | 113268.i | 0.263209i | ||||||||
\(657\) | −254308. | −0.589154 | ||||||||
\(658\) | − | 203509.i | − | 0.470036i | ||||||
\(659\) | 481053.i | 1.10770i | 0.832617 | + | 0.553850i | \(0.186842\pi\) | ||||
−0.832617 | + | 0.553850i | \(0.813158\pi\) | |||||||
\(660\) | 260700.i | 0.598484i | ||||||||
\(661\) | − | 468775.i | − | 1.07290i | −0.843931 | − | 0.536452i | \(-0.819764\pi\) | ||
0.843931 | − | 0.536452i | \(-0.180236\pi\) | |||||||
\(662\) | −224754. | −0.512852 | ||||||||
\(663\) | 613697. | 1.39613 | ||||||||
\(664\) | 23082.0i | 0.0523526i | ||||||||
\(665\) | 572787. | − | 580038.i | 1.29524 | − | 1.31164i | ||||
\(666\) | 31036.1 | 0.0699711 | ||||||||
\(667\) | − | 304311.i | − | 0.684015i | ||||||
\(668\) | − | 225932.i | − | 0.506320i | ||||||
\(669\) | 332994. | 0.744020 | ||||||||
\(670\) | 519352. | 1.15694 | ||||||||
\(671\) | −180917. | −0.401822 | ||||||||
\(672\) | −168738. | −0.373659 | ||||||||
\(673\) | 229158.i | 0.505947i | 0.967473 | + | 0.252973i | \(0.0814085\pi\) | ||||
−0.967473 | + | 0.252973i | \(0.918592\pi\) | |||||||
\(674\) | −7862.46 | −0.0173077 | ||||||||
\(675\) | 30531.6i | 0.0670103i | ||||||||
\(676\) | 201541. | 0.441033 | ||||||||
\(677\) | − | 38248.1i | − | 0.0834512i | −0.999129 | − | 0.0417256i | \(-0.986714\pi\) | ||
0.999129 | − | 0.0417256i | \(-0.0132855\pi\) | |||||||
\(678\) | − | 130953.i | − | 0.284876i | ||||||
\(679\) | − | 1.12271e6i | − | 2.43516i | ||||||
\(680\) | 145093.i | 0.313782i | ||||||||
\(681\) | −880274. | −1.89812 | ||||||||
\(682\) | −336743. | −0.723985 | ||||||||
\(683\) | 31694.5i | 0.0679426i | 0.999423 | + | 0.0339713i | \(0.0108155\pi\) | ||||
−0.999423 | + | 0.0339713i | \(0.989185\pi\) | |||||||
\(684\) | 73532.3 | − | 74463.2i | 0.157169 | − | 0.159158i | ||||
\(685\) | −216402. | −0.461190 | ||||||||
\(686\) | 635459.i | 1.35033i | ||||||||
\(687\) | − | 1.00899e6i | − | 2.13783i | ||||||
\(688\) | −148260. | −0.313217 | ||||||||
\(689\) | −152141. | −0.320484 | ||||||||
\(690\) | 216125. | 0.453948 | ||||||||
\(691\) | 140291. | 0.293815 | 0.146907 | − | 0.989150i | \(-0.453068\pi\) | ||||
0.146907 | + | 0.989150i | \(0.453068\pi\) | |||||||
\(692\) | − | 285384.i | − | 0.595961i | ||||||
\(693\) | 357956. | 0.745355 | ||||||||
\(694\) | 44485.7i | 0.0923637i | ||||||||
\(695\) | −719609. | −1.48980 | ||||||||
\(696\) | − | 277107.i | − | 0.572044i | ||||||
\(697\) | − | 432660.i | − | 0.890597i | ||||||
\(698\) | 118179.i | 0.242565i | ||||||||
\(699\) | − | 36587.3i | − | 0.0748818i | ||||||
\(700\) | 43385.1 | 0.0885410 | ||||||||
\(701\) | 550797. | 1.12087 | 0.560436 | − | 0.828198i | \(-0.310634\pi\) | ||||
0.560436 | + | 0.828198i | \(0.310634\pi\) | |||||||
\(702\) | 317838.i | 0.644958i | ||||||||
\(703\) | −77782.9 | − | 76810.5i | −0.157389 | − | 0.155421i | ||||
\(704\) | −58748.5 | −0.118536 | ||||||||
\(705\) | 237358.i | 0.477557i | ||||||||
\(706\) | − | 111135.i | − | 0.222967i | ||||||
\(707\) | 409435. | 0.819117 | ||||||||
\(708\) | 426461. | 0.850772 | ||||||||
\(709\) | 725719. | 1.44370 | 0.721848 | − | 0.692051i | \(-0.243293\pi\) | ||||
0.721848 | + | 0.692051i | \(0.243293\pi\) | |||||||
\(710\) | −304267. | −0.603584 | ||||||||
\(711\) | 45802.9i | 0.0906053i | ||||||||
\(712\) | −84769.1 | −0.167216 | ||||||||
\(713\) | 279166.i | 0.549140i | ||||||||
\(714\) | 644544. | 1.26432 | ||||||||
\(715\) | − | 697787.i | − | 1.36493i | ||||||
\(716\) | 274972.i | 0.536367i | ||||||||
\(717\) | 388903.i | 0.756489i | ||||||||
\(718\) | − | 455275.i | − | 0.883131i | ||||||
\(719\) | 184282. | 0.356472 | 0.178236 | − | 0.983988i | \(-0.442961\pi\) | ||||
0.178236 | + | 0.983988i | \(0.442961\pi\) | |||||||
\(720\) | 60829.9 | 0.117342 | ||||||||
\(721\) | − | 751384.i | − | 1.44541i | ||||||
\(722\) | −368574. | + | 4636.83i | −0.707051 | + | 0.00889501i | ||||
\(723\) | −620985. | −1.18797 | ||||||||
\(724\) | 233561.i | 0.445577i | ||||||||
\(725\) | 71248.3i | 0.135550i | ||||||||
\(726\) | −45171.8 | −0.0857027 | ||||||||
\(727\) | −30302.5 | −0.0573336 | −0.0286668 | − | 0.999589i | \(-0.509126\pi\) | ||||
−0.0286668 | + | 0.999589i | \(0.509126\pi\) | |||||||
\(728\) | 451645. | 0.852186 | ||||||||
\(729\) | −128557. | −0.241902 | ||||||||
\(730\) | 520657.i | 0.977025i | ||||||||
\(731\) | 566319. | 1.05981 | ||||||||
\(732\) | 136575.i | 0.254889i | ||||||||
\(733\) | 210592. | 0.391954 | 0.195977 | − | 0.980609i | \(-0.437212\pi\) | ||||
0.195977 | + | 0.980609i | \(0.437212\pi\) | |||||||
\(734\) | − | 56102.9i | − | 0.104134i | ||||||
\(735\) | − | 1.42304e6i | − | 2.63417i | ||||||
\(736\) | 48703.6i | 0.0899094i | ||||||||
\(737\) | − | 803252.i | − | 1.47883i | ||||||
\(738\) | −181392. | −0.333047 | ||||||||
\(739\) | −257029. | −0.470645 | −0.235323 | − | 0.971917i | \(-0.575615\pi\) | ||||
−0.235323 | + | 0.971917i | \(0.575615\pi\) | |||||||
\(740\) | − | 63541.8i | − | 0.116037i | ||||||
\(741\) | −636764. | + | 644825.i | −1.15969 | + | 1.17437i | ||||
\(742\) | −159788. | −0.290226 | ||||||||
\(743\) | 459249.i | 0.831899i | 0.909388 | + | 0.415949i | \(0.136551\pi\) | ||||
−0.909388 | + | 0.415949i | \(0.863449\pi\) | |||||||
\(744\) | 254210.i | 0.459247i | ||||||||
\(745\) | 1.05567e6 | 1.90203 | ||||||||
\(746\) | 40909.0 | 0.0735091 | ||||||||
\(747\) | −36964.5 | −0.0662435 | ||||||||
\(748\) | 224407. | 0.401081 | ||||||||
\(749\) | 1.45364e6i | 2.59115i | ||||||||
\(750\) | 451450. | 0.802578 | ||||||||
\(751\) | 705805.i | 1.25142i | 0.780054 | + | 0.625712i | \(0.215192\pi\) | ||||
−0.780054 | + | 0.625712i | \(0.784808\pi\) | |||||||
\(752\) | −53488.4 | −0.0945854 | ||||||||
\(753\) | − | 568305.i | − | 1.00228i | ||||||
\(754\) | 741704.i | 1.30463i | ||||||||
\(755\) | 444124.i | 0.779130i | ||||||||
\(756\) | 333814.i | 0.584064i | ||||||||
\(757\) | 128249. | 0.223801 | 0.111901 | − | 0.993719i | \(-0.464306\pi\) | ||||
0.111901 | + | 0.993719i | \(0.464306\pi\) | |||||||
\(758\) | 73348.8 | 0.127660 | ||||||||
\(759\) | − | 334267.i | − | 0.580244i | ||||||
\(760\) | −152452. | − | 150546.i | −0.263941 | − | 0.260641i | ||||
\(761\) | 779962. | 1.34680 | 0.673402 | − | 0.739277i | \(-0.264833\pi\) | ||||
0.673402 | + | 0.739277i | \(0.264833\pi\) | |||||||
\(762\) | − | 137843.i | − | 0.237397i | ||||||
\(763\) | 17683.3i | 0.0303749i | ||||||||
\(764\) | −107986. | −0.185004 | ||||||||
\(765\) | −232357. | −0.397039 | ||||||||
\(766\) | 27251.8 | 0.0464449 | ||||||||
\(767\) | −1.14147e6 | −1.94031 | ||||||||
\(768\) | 44349.7i | 0.0751915i | ||||||||
\(769\) | −50722.8 | −0.0857730 | −0.0428865 | − | 0.999080i | \(-0.513655\pi\) | ||||
−0.0428865 | + | 0.999080i | \(0.513655\pi\) | |||||||
\(770\) | − | 732861.i | − | 1.23606i | ||||||
\(771\) | −922754. | −1.55230 | ||||||||
\(772\) | − | 166558.i | − | 0.279467i | ||||||
\(773\) | − | 942086.i | − | 1.57664i | −0.615267 | − | 0.788318i | \(-0.710952\pi\) | ||
0.615267 | − | 0.788318i | \(-0.289048\pi\) | |||||||
\(774\) | − | 237428.i | − | 0.396324i | ||||||
\(775\) | − | 65361.0i | − | 0.108822i | ||||||
\(776\) | −295083. | −0.490028 | ||||||||
\(777\) | −282271. | −0.467546 | ||||||||
\(778\) | − | 288188.i | − | 0.476120i | ||||||
\(779\) | 454606. | + | 448922.i | 0.749135 | + | 0.739769i | ||||
\(780\) | −526766. | −0.865821 | ||||||||
\(781\) | 470592.i | 0.771511i | ||||||||
\(782\) | − | 186037.i | − | 0.304219i | ||||||
\(783\) | −548199. | −0.894159 | ||||||||
\(784\) | 320683. | 0.521727 | ||||||||
\(785\) | −149115. | −0.241981 | ||||||||
\(786\) | 845443. | 1.36848 | ||||||||
\(787\) | 764737.i | 1.23470i | 0.786687 | + | 0.617352i | \(0.211794\pi\) | ||||
−0.786687 | + | 0.617352i | \(0.788206\pi\) | |||||||
\(788\) | −273868. | −0.441051 | ||||||||
\(789\) | − | 298186.i | − | 0.478998i | ||||||
\(790\) | 93774.6 | 0.150256 | ||||||||
\(791\) | 368127.i | 0.588362i | ||||||||
\(792\) | − | 94082.1i | − | 0.149988i | ||||||
\(793\) | − | 365557.i | − | 0.581312i | ||||||
\(794\) | − | 283298.i | − | 0.449368i | ||||||
\(795\) | 186365. | 0.294870 | ||||||||
\(796\) | 444033. | 0.700792 | ||||||||
\(797\) | 555222.i | 0.874077i | 0.899443 | + | 0.437039i | \(0.143973\pi\) | ||||
−0.899443 | + | 0.437039i | \(0.856027\pi\) | |||||||
\(798\) | −668771. | + | 677237.i | −1.05020 | + | 1.06349i | ||||
\(799\) | 204314. | 0.320040 | ||||||||
\(800\) | − | 11403.0i | − | 0.0178171i | ||||||
\(801\) | − | 135752.i | − | 0.211584i | ||||||
\(802\) | −47224.7 | −0.0734211 | ||||||||
\(803\) | 805270. | 1.24885 | ||||||||
\(804\) | −606382. | −0.938068 | ||||||||
\(805\) | −607555. | −0.937549 | ||||||||
\(806\) | − | 680417.i | − | 1.04738i | ||||||
\(807\) | −637527. | −0.978930 | ||||||||
\(808\) | − | 107612.i | − | 0.164831i | ||||||
\(809\) | −94777.3 | −0.144813 | −0.0724065 | − | 0.997375i | \(-0.523068\pi\) | ||||
−0.0724065 | + | 0.997375i | \(0.523068\pi\) | |||||||
\(810\) | − | 607090.i | − | 0.925302i | ||||||
\(811\) | − | 68642.4i | − | 0.104364i | −0.998638 | − | 0.0521820i | \(-0.983382\pi\) | ||
0.998638 | − | 0.0521820i | \(-0.0166176\pi\) | |||||||
\(812\) | 778986.i | 1.18146i | ||||||||
\(813\) | 1.08227e6i | 1.63740i | ||||||||
\(814\) | −98276.4 | −0.148320 | ||||||||
\(815\) | 801330. | 1.20641 | ||||||||
\(816\) | − | 169406.i | − | 0.254419i | ||||||
\(817\) | −587606. | + | 595045.i | −0.880323 | + | 0.891467i | ||||
\(818\) | −3320.42 | −0.00496233 | ||||||||
\(819\) | 723281.i | 1.07830i | ||||||||
\(820\) | 371373.i | 0.552309i | ||||||||
\(821\) | 601916. | 0.892996 | 0.446498 | − | 0.894785i | \(-0.352671\pi\) | ||||
0.446498 | + | 0.894785i | \(0.352671\pi\) | |||||||
\(822\) | 252665. | 0.373940 | ||||||||
\(823\) | −307730. | −0.454329 | −0.227165 | − | 0.973856i | \(-0.572946\pi\) | ||||
−0.227165 | + | 0.973856i | \(0.572946\pi\) | |||||||
\(824\) | −197487. | −0.290860 | ||||||||
\(825\) | 78262.0i | 0.114986i | ||||||||
\(826\) | −1.19884e6 | −1.75712 | ||||||||
\(827\) | − | 194825.i | − | 0.284862i | −0.989805 | − | 0.142431i | \(-0.954508\pi\) | ||
0.989805 | − | 0.142431i | \(-0.0454919\pi\) | |||||||
\(828\) | −77995.7 | −0.113765 | ||||||||
\(829\) | − | 1.14738e6i | − | 1.66955i | −0.550592 | − | 0.834774i | \(-0.685598\pi\) | ||
0.550592 | − | 0.834774i | \(-0.314402\pi\) | |||||||
\(830\) | 75679.2i | 0.109855i | ||||||||
\(831\) | 717848.i | 1.03951i | ||||||||
\(832\) | − | 118706.i | − | 0.171486i | ||||||
\(833\) | −1.22494e6 | −1.76532 | ||||||||
\(834\) | 840196. | 1.20795 | ||||||||
\(835\) | − | 740765.i | − | 1.06245i | ||||||
\(836\) | −232841. | + | 235789.i | −0.333156 | + | 0.337374i | ||||
\(837\) | 502901. | 0.717846 | ||||||||
\(838\) | 593860.i | 0.845661i | ||||||||
\(839\) | 283733.i | 0.403075i | 0.979481 | + | 0.201538i | \(0.0645938\pi\) | ||||
−0.979481 | + | 0.201538i | \(0.935406\pi\) | |||||||
\(840\) | −553243. | −0.784075 | ||||||||
\(841\) | −571993. | −0.808721 | ||||||||
\(842\) | 704608. | 0.993856 | ||||||||
\(843\) | −595754. | −0.838324 | ||||||||
\(844\) | − | 620420.i | − | 0.870965i | ||||||
\(845\) | 660795. | 0.925450 | ||||||||
\(846\) | − | 85658.4i | − | 0.119682i | ||||||
\(847\) | 126984. | 0.177004 | ||||||||
\(848\) | 41997.3i | 0.0584023i | ||||||||
\(849\) | 114504.i | 0.158857i | ||||||||
\(850\) | 43556.8i | 0.0602863i | ||||||||
\(851\) | 81472.9i | 0.112500i | ||||||||
\(852\) | 355254. | 0.489395 | ||||||||
\(853\) | 975341. | 1.34047 | 0.670237 | − | 0.742147i | \(-0.266193\pi\) | ||||
0.670237 | + | 0.742147i | \(0.266193\pi\) | |||||||
\(854\) | − | 383932.i | − | 0.526428i | ||||||
\(855\) | 241091. | − | 244143.i | 0.329798 | − | 0.333973i | ||||
\(856\) | 382061. | 0.521417 | ||||||||
\(857\) | 5569.67i | 0.00758347i | 0.999993 | + | 0.00379173i | \(0.00120695\pi\) | ||||
−0.999993 | + | 0.00379173i | \(0.998793\pi\) | |||||||
\(858\) | 814718.i | 1.10671i | ||||||||
\(859\) | 312767. | 0.423871 | 0.211936 | − | 0.977284i | \(-0.432023\pi\) | ||||
0.211936 | + | 0.977284i | \(0.432023\pi\) | |||||||
\(860\) | −486099. | −0.657246 | ||||||||
\(861\) | 1.64975e6 | 2.22541 | ||||||||
\(862\) | 359060. | 0.483228 | ||||||||
\(863\) | − | 359441.i | − | 0.482621i | −0.970448 | − | 0.241311i | \(-0.922423\pi\) | ||
0.970448 | − | 0.241311i | \(-0.0775773\pi\) | |||||||
\(864\) | 87736.7 | 0.117531 | ||||||||
\(865\) | − | 935690.i | − | 1.25055i | ||||||
\(866\) | −925865. | −1.23456 | ||||||||
\(867\) | − | 257234.i | − | 0.342208i | ||||||
\(868\) | − | 714618.i | − | 0.948494i | ||||||
\(869\) | − | 145036.i | − | 0.192059i | ||||||
\(870\) | − | 908553.i | − | 1.20036i | ||||||
\(871\) | 1.62304e6 | 2.13940 | ||||||||
\(872\) | 4647.73 | 0.00611234 | ||||||||
\(873\) | − | 472557.i | − | 0.620049i | ||||||
\(874\) | 195473. | + | 193030.i | 0.255897 | + | 0.252698i | ||||
\(875\) | −1.26909e6 | −1.65758 | ||||||||
\(876\) | − | 607905.i | − | 0.792187i | ||||||
\(877\) | − | 415375.i | − | 0.540059i | −0.962852 | − | 0.270030i | \(-0.912967\pi\) | ||
0.962852 | − | 0.270030i | \(-0.0870335\pi\) | |||||||
\(878\) | −915172. | −1.18717 | ||||||||
\(879\) | 102317. | 0.132425 | ||||||||
\(880\) | −192619. | −0.248733 | ||||||||
\(881\) | −403508. | −0.519876 | −0.259938 | − | 0.965625i | \(-0.583702\pi\) | ||||
−0.259938 | + | 0.965625i | \(0.583702\pi\) | |||||||
\(882\) | 513553.i | 0.660158i | ||||||||
\(883\) | 265307. | 0.340273 | 0.170137 | − | 0.985420i | \(-0.445579\pi\) | ||||
0.170137 | + | 0.985420i | \(0.445579\pi\) | |||||||
\(884\) | 453433.i | 0.580241i | ||||||||
\(885\) | 1.39824e6 | 1.78523 | ||||||||
\(886\) | − | 532700.i | − | 0.678603i | ||||||
\(887\) | − | 264831.i | − | 0.336605i | −0.985735 | − | 0.168303i | \(-0.946171\pi\) | ||
0.985735 | − | 0.168303i | \(-0.0538286\pi\) | |||||||
\(888\) | 74189.7i | 0.0940844i | ||||||||
\(889\) | 387496.i | 0.490302i | ||||||||
\(890\) | −277933. | −0.350881 | ||||||||
\(891\) | −938952. | −1.18274 | ||||||||
\(892\) | 246034.i | 0.309219i | ||||||||
\(893\) | −211994. | + | 214678.i | −0.265840 | + | 0.269205i | ||||
\(894\) | −1.23257e6 | −1.54219 | ||||||||
\(895\) | 901551.i | 1.12550i | ||||||||
\(896\) | − | 124673.i | − | 0.155295i | ||||||
\(897\) | 675416. | 0.839433 | ||||||||
\(898\) | 88262.9 | 0.109452 | ||||||||
\(899\) | 1.17357e6 | 1.45207 | ||||||||
\(900\) | 18261.1 | 0.0225446 | ||||||||
\(901\) | − | 160421.i | − | 0.197611i | ||||||
\(902\) | 574381. | 0.705971 | ||||||||
\(903\) | 2.15939e6i | 2.64823i | ||||||||
\(904\) | 96755.3 | 0.118396 | ||||||||
\(905\) | 765776.i | 0.934985i | ||||||||
\(906\) | − | 518547.i | − | 0.631731i | ||||||
\(907\) | − | 1.43037e6i | − | 1.73874i | −0.494165 | − | 0.869368i | \(-0.664526\pi\) | ||
0.494165 | − | 0.869368i | \(-0.335474\pi\) | |||||||
\(908\) | − | 650394.i | − | 0.788869i | ||||||
\(909\) | 172334. | 0.208566 | ||||||||
\(910\) | 1.48081e6 | 1.78820 | ||||||||
\(911\) | − | 1.14296e6i | − | 1.37719i | −0.725148 | − | 0.688593i | \(-0.758229\pi\) | ||
0.725148 | − | 0.688593i | \(-0.241771\pi\) | |||||||
\(912\) | 177999. | + | 175774.i | 0.214007 | + | 0.211332i | ||||
\(913\) | 117049. | 0.140419 | ||||||||
\(914\) | − | 253676.i | − | 0.303660i | ||||||
\(915\) | 447790.i | 0.534851i | ||||||||
\(916\) | 745496. | 0.888494 | ||||||||
\(917\) | −2.37665e6 | −2.82636 | ||||||||
\(918\) | −335135. | −0.397681 | ||||||||
\(919\) | −627508. | −0.742999 | −0.371500 | − | 0.928433i | \(-0.621156\pi\) | ||||
−0.371500 | + | 0.928433i | \(0.621156\pi\) | |||||||
\(920\) | 159685.i | 0.188663i | ||||||||
\(921\) | 1.21943e6 | 1.43759 | ||||||||
\(922\) | 201411.i | 0.236931i | ||||||||
\(923\) | −950871. | −1.11614 | ||||||||
\(924\) | 855669.i | 1.00222i | ||||||||
\(925\) | − | 19075.2i | − | 0.0222939i | ||||||
\(926\) | 272866.i | 0.318220i | ||||||||
\(927\) | − | 316263.i | − | 0.368035i | ||||||
\(928\) | 204742. | 0.237745 | ||||||||
\(929\) | −1.63447e6 | −1.89385 | −0.946924 | − | 0.321458i | \(-0.895827\pi\) | ||||
−0.946924 | + | 0.321458i | \(0.895827\pi\) | |||||||
\(930\) | 833479.i | 0.963670i | ||||||||
\(931\) | 1.27098e6 | − | 1.28707e6i | 1.46636 | − | 1.48492i | ||||
\(932\) | 27032.7 | 0.0311213 | ||||||||
\(933\) | − | 821585.i | − | 0.943820i | ||||||
\(934\) | − | 953752.i | − | 1.09331i | ||||||
\(935\) | 735762. | 0.841617 | ||||||||
\(936\) | 190101. | 0.216986 | ||||||||
\(937\) | −55506.2 | −0.0632211 | −0.0316106 | − | 0.999500i | \(-0.510064\pi\) | ||||
−0.0316106 | + | 0.999500i | \(0.510064\pi\) | |||||||
\(938\) | 1.70462e6 | 1.93741 | ||||||||
\(939\) | − | 1.20143e6i | − | 1.36259i | ||||||
\(940\) | −175373. | −0.198475 | ||||||||
\(941\) | 1.60327e6i | 1.81062i | 0.424747 | + | 0.905312i | \(0.360363\pi\) | ||||
−0.424747 | + | 0.905312i | \(0.639637\pi\) | |||||||
\(942\) | 174102. | 0.196202 | ||||||||
\(943\) | − | 476172.i | − | 0.535476i | ||||||
\(944\) | 315093.i | 0.353586i | ||||||||
\(945\) | 1.09448e6i | 1.22558i | ||||||||
\(946\) | 751822.i | 0.840103i | ||||||||
\(947\) | 165986. | 0.185086 | 0.0925428 | − | 0.995709i | \(-0.470501\pi\) | ||||
0.0925428 | + | 0.995709i | \(0.470501\pi\) | |||||||
\(948\) | −109489. | −0.121830 | ||||||||
\(949\) | 1.62712e6i | 1.80670i | ||||||||
\(950\) | −45766.2 | − | 45194.0i | −0.0507104 | − | 0.0500765i | ||||
\(951\) | 692642. | 0.765857 | ||||||||
\(952\) | 476224.i | 0.525457i | ||||||||
\(953\) | − | 821794.i | − | 0.904851i | −0.891802 | − | 0.452426i | \(-0.850559\pi\) | ||
0.891802 | − | 0.452426i | \(-0.149441\pi\) | |||||||
\(954\) | −67256.0 | −0.0738983 | ||||||||
\(955\) | −354054. | −0.388206 | ||||||||
\(956\) | −287342. | −0.314401 | ||||||||
\(957\) | −1.40521e6 | −1.53432 | ||||||||
\(958\) | − | 358317.i | − | 0.390424i | ||||||
\(959\) | −710276. | −0.772307 | ||||||||
\(960\) | 145410.i | 0.157780i | ||||||||
\(961\) | −153074. | −0.165750 | ||||||||
\(962\) | − | 198576.i | − | 0.214574i | ||||||
\(963\) | 611847.i | 0.659766i | ||||||||
\(964\) | − | 458817.i | − | 0.493726i | ||||||
\(965\) | − | 546093.i | − | 0.586424i | ||||||
\(966\) | 709365. | 0.760179 | ||||||||
\(967\) | −859901. | −0.919593 | −0.459796 | − | 0.888024i | \(-0.652078\pi\) | ||||
−0.459796 | + | 0.888024i | \(0.652078\pi\) | |||||||
\(968\) | − | 33375.4i | − | 0.0356185i | ||||||
\(969\) | −679918. | − | 671418.i | −0.724118 | − | 0.715065i | ||||
\(970\) | −967490. | −1.02826 | ||||||||
\(971\) | − | 1.15671e6i | − | 1.22684i | −0.789759 | − | 0.613418i | \(-0.789794\pi\) | ||
0.789759 | − | 0.613418i | \(-0.210206\pi\) | |||||||
\(972\) | 394749.i | 0.417819i | ||||||||
\(973\) | −2.36191e6 | −2.49481 | ||||||||
\(974\) | 661459. | 0.697245 | ||||||||
\(975\) | −158135. | −0.166349 | ||||||||
\(976\) | −100909. | −0.105933 | ||||||||
\(977\) | − | 627667.i | − | 0.657567i | −0.944405 | − | 0.328784i | \(-0.893361\pi\) | ||
0.944405 | − | 0.328784i | \(-0.106639\pi\) | |||||||
\(978\) | −935611. | −0.978178 | ||||||||
\(979\) | 429862.i | 0.448502i | ||||||||
\(980\) | 1.05142e6 | 1.09478 | ||||||||
\(981\) | 7443.05i | 0.00773415i | ||||||||
\(982\) | 1.19905e6i | 1.24341i | ||||||||
\(983\) | 1.45983e6i | 1.51075i | 0.655290 | + | 0.755377i | \(0.272546\pi\) | ||||
−0.655290 | + | 0.755377i | \(0.727454\pi\) | |||||||
\(984\) | − | 433605.i | − | 0.447820i | ||||||
\(985\) | −897931. | −0.925487 | ||||||||
\(986\) | −782070. | −0.804436 | ||||||||
\(987\) | 779056.i | 0.799714i | ||||||||
\(988\) | −476432. | − | 470476.i | −0.488075 | − | 0.481974i | ||||
\(989\) | 623273. | 0.637215 | ||||||||
\(990\) | − | 308467.i | − | 0.314730i | ||||||
\(991\) | 977409.i | 0.995243i | 0.867394 | + | 0.497621i | \(0.165793\pi\) | ||||
−0.867394 | + | 0.497621i | \(0.834207\pi\) | |||||||
\(992\) | −187824. | −0.190866 | ||||||||
\(993\) | 860388. | 0.872561 | ||||||||
\(994\) | −998666. | −1.01076 | ||||||||
\(995\) | 1.45585e6 | 1.47052 | ||||||||
\(996\) | − | 88361.0i | − | 0.0890721i | ||||||
\(997\) | 1.39372e6 | 1.40212 | 0.701059 | − | 0.713104i | \(-0.252711\pi\) | ||||
0.701059 | + | 0.713104i | \(0.252711\pi\) | |||||||
\(998\) | 497645.i | 0.499642i | ||||||||
\(999\) | 146769. | 0.147063 |
(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 | 38.5.b.a.37.4 | ✓ | 8 | |
3.2 | odd | 2 | 342.5.d.a.37.7 | 8 | |||
4.3 | odd | 2 | 304.5.e.e.113.2 | 8 | |||
19.18 | odd | 2 | inner | 38.5.b.a.37.5 | yes | 8 | |
57.56 | even | 2 | 342.5.d.a.37.3 | 8 | |||
76.75 | even | 2 | 304.5.e.e.113.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.5.b.a.37.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
38.5.b.a.37.5 | yes | 8 | 19.18 | odd | 2 | inner | |
304.5.e.e.113.2 | 8 | 4.3 | odd | 2 | |||
304.5.e.e.113.7 | 8 | 76.75 | even | 2 | |||
342.5.d.a.37.3 | 8 | 57.56 | even | 2 | |||
342.5.d.a.37.7 | 8 | 3.2 | odd | 2 |