Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,5,Mod(11,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.11");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.55054944626\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 73x^{4} + 1096x^{2} + 180 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.6 | ||
Root | \(7.20990i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.11 |
Dual form | 15.5.c.a.11.1 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.20990i | 1.80247i | 0.433325 | + | 0.901237i | \(0.357340\pi\) | ||||
−0.433325 | + | 0.901237i | \(0.642660\pi\) | |||||||
\(3\) | 8.77108 | − | 2.01697i | 0.974564 | − | 0.224108i | ||||
\(4\) | −35.9827 | −2.24892 | ||||||||
\(5\) | − | 11.1803i | − | 0.447214i | ||||||
\(6\) | 14.5422 | + | 63.2386i | 0.403949 | + | 1.75663i | ||||
\(7\) | 23.3388 | 0.476303 | 0.238151 | − | 0.971228i | \(-0.423459\pi\) | ||||
0.238151 | + | 0.971228i | \(0.423459\pi\) | |||||||
\(8\) | − | 144.073i | − | 2.25114i | ||||||
\(9\) | 72.8637 | − | 35.3820i | 0.899551 | − | 0.436815i | ||||
\(10\) | 80.6091 | 0.806091 | ||||||||
\(11\) | 33.9875i | 0.280888i | 0.990089 | + | 0.140444i | \(0.0448531\pi\) | ||||
−0.990089 | + | 0.140444i | \(0.955147\pi\) | |||||||
\(12\) | −315.607 | + | 72.5760i | −2.19171 | + | 0.504000i | ||||
\(13\) | −125.965 | −0.745357 | −0.372678 | − | 0.927961i | \(-0.621561\pi\) | ||||
−0.372678 | + | 0.927961i | \(0.621561\pi\) | |||||||
\(14\) | 168.271i | 0.858524i | ||||||||
\(15\) | −22.5504 | − | 98.0636i | −0.100224 | − | 0.435838i | ||||
\(16\) | 463.029 | 1.80871 | ||||||||
\(17\) | − | 308.095i | − | 1.06607i | −0.846093 | − | 0.533036i | \(-0.821051\pi\) | ||
0.846093 | − | 0.533036i | \(-0.178949\pi\) | |||||||
\(18\) | 255.101 | + | 525.340i | 0.787348 | + | 1.62142i | ||||
\(19\) | −363.724 | −1.00755 | −0.503773 | − | 0.863836i | \(-0.668055\pi\) | ||||
−0.503773 | + | 0.863836i | \(0.668055\pi\) | |||||||
\(20\) | 402.298i | 1.00575i | ||||||||
\(21\) | 204.707 | − | 47.0738i | 0.464188 | − | 0.106743i | ||||
\(22\) | −245.046 | −0.506294 | ||||||||
\(23\) | 102.256i | 0.193301i | 0.995318 | + | 0.0966506i | \(0.0308129\pi\) | ||||
−0.995318 | + | 0.0966506i | \(0.969187\pi\) | |||||||
\(24\) | −290.591 | − | 1263.68i | −0.504498 | − | 2.19388i | ||||
\(25\) | −125.000 | −0.200000 | ||||||||
\(26\) | − | 908.197i | − | 1.34349i | ||||||
\(27\) | 567.728 | − | 457.302i | 0.778777 | − | 0.627301i | ||||
\(28\) | −839.794 | −1.07117 | ||||||||
\(29\) | 1565.10i | 1.86100i | 0.366296 | + | 0.930498i | \(0.380626\pi\) | ||||
−0.366296 | + | 0.930498i | \(0.619374\pi\) | |||||||
\(30\) | 707.029 | − | 162.586i | 0.785588 | − | 0.180651i | ||||
\(31\) | 326.954 | 0.340222 | 0.170111 | − | 0.985425i | \(-0.445587\pi\) | ||||
0.170111 | + | 0.985425i | \(0.445587\pi\) | |||||||
\(32\) | 1033.23i | 1.00901i | ||||||||
\(33\) | 68.5518 | + | 298.107i | 0.0629493 | + | 0.273744i | ||||
\(34\) | 2221.33 | 1.92157 | ||||||||
\(35\) | − | 260.936i | − | 0.213009i | ||||||
\(36\) | −2621.83 | + | 1273.14i | −2.02302 | + | 0.982360i | ||||
\(37\) | 72.4778 | 0.0529421 | 0.0264711 | − | 0.999650i | \(-0.491573\pi\) | ||||
0.0264711 | + | 0.999650i | \(0.491573\pi\) | |||||||
\(38\) | − | 2622.41i | − | 1.81608i | ||||||
\(39\) | −1104.85 | + | 254.068i | −0.726398 | + | 0.167040i | ||||
\(40\) | −1610.78 | −1.00674 | ||||||||
\(41\) | 2149.01i | 1.27841i | 0.769036 | + | 0.639205i | \(0.220736\pi\) | ||||
−0.769036 | + | 0.639205i | \(0.779264\pi\) | |||||||
\(42\) | 339.397 | + | 1475.92i | 0.192402 | + | 0.836687i | ||||
\(43\) | 1501.27 | 0.811934 | 0.405967 | − | 0.913888i | \(-0.366935\pi\) | ||||
0.405967 | + | 0.913888i | \(0.366935\pi\) | |||||||
\(44\) | − | 1222.96i | − | 0.631695i | ||||||
\(45\) | −395.583 | − | 814.640i | −0.195350 | − | 0.402292i | ||||
\(46\) | −737.258 | −0.348420 | ||||||||
\(47\) | − | 1958.33i | − | 0.886522i | −0.896393 | − | 0.443261i | \(-0.853822\pi\) | ||
0.896393 | − | 0.443261i | \(-0.146178\pi\) | |||||||
\(48\) | 4061.27 | − | 933.916i | 1.76270 | − | 0.405346i | ||||
\(49\) | −1856.30 | −0.773136 | ||||||||
\(50\) | − | 901.237i | − | 0.360495i | ||||||
\(51\) | −621.418 | − | 2702.32i | −0.238915 | − | 1.03896i | ||||
\(52\) | 4532.57 | 1.67625 | ||||||||
\(53\) | 2965.17i | 1.05560i | 0.849370 | + | 0.527798i | \(0.176982\pi\) | ||||
−0.849370 | + | 0.527798i | \(0.823018\pi\) | |||||||
\(54\) | 3297.10 | + | 4093.26i | 1.13069 | + | 1.40373i | ||||
\(55\) | 379.992 | 0.125617 | ||||||||
\(56\) | − | 3362.50i | − | 1.07222i | ||||||
\(57\) | −3190.25 | + | 733.621i | −0.981919 | + | 0.225799i | ||||
\(58\) | −11284.2 | −3.35440 | ||||||||
\(59\) | − | 5045.29i | − | 1.44938i | −0.689075 | − | 0.724690i | \(-0.741983\pi\) | ||
0.689075 | − | 0.724690i | \(-0.258017\pi\) | |||||||
\(60\) | 811.424 | + | 3528.59i | 0.225396 | + | 0.980164i | ||||
\(61\) | 736.716 | 0.197989 | 0.0989944 | − | 0.995088i | \(-0.468437\pi\) | ||||
0.0989944 | + | 0.995088i | \(0.468437\pi\) | |||||||
\(62\) | 2357.30i | 0.613242i | ||||||||
\(63\) | 1700.55 | − | 825.775i | 0.428459 | − | 0.208056i | ||||
\(64\) | −40.9924 | −0.0100079 | ||||||||
\(65\) | 1408.34i | 0.333334i | ||||||||
\(66\) | −2149.32 | + | 494.252i | −0.493416 | + | 0.113465i | ||||
\(67\) | 4254.63 | 0.947791 | 0.473895 | − | 0.880581i | \(-0.342847\pi\) | ||||
0.473895 | + | 0.880581i | \(0.342847\pi\) | |||||||
\(68\) | 11086.1i | 2.39751i | ||||||||
\(69\) | 206.248 | + | 896.898i | 0.0433203 | + | 0.188384i | ||||
\(70\) | 1881.32 | 0.383944 | ||||||||
\(71\) | 1303.84i | 0.258647i | 0.991602 | + | 0.129323i | \(0.0412805\pi\) | ||||
−0.991602 | + | 0.129323i | \(0.958719\pi\) | |||||||
\(72\) | −5097.59 | − | 10497.7i | −0.983332 | − | 2.02502i | ||||
\(73\) | 6768.14 | 1.27006 | 0.635029 | − | 0.772488i | \(-0.280988\pi\) | ||||
0.635029 | + | 0.772488i | \(0.280988\pi\) | |||||||
\(74\) | 522.557i | 0.0954269i | ||||||||
\(75\) | −1096.38 | + | 252.121i | −0.194913 | + | 0.0448216i | ||||
\(76\) | 13087.8 | 2.26589 | ||||||||
\(77\) | 793.229i | 0.133788i | ||||||||
\(78\) | −1831.81 | − | 7965.87i | −0.301086 | − | 1.30931i | ||||
\(79\) | −6367.07 | −1.02020 | −0.510100 | − | 0.860115i | \(-0.670392\pi\) | ||||
−0.510100 | + | 0.860115i | \(0.670392\pi\) | |||||||
\(80\) | − | 5176.82i | − | 0.808879i | ||||||
\(81\) | 4057.23 | − | 5156.13i | 0.618385 | − | 0.785875i | ||||
\(82\) | −15494.1 | −2.30430 | ||||||||
\(83\) | − | 6892.17i | − | 1.00046i | −0.865893 | − | 0.500230i | \(-0.833249\pi\) | ||
0.865893 | − | 0.500230i | \(-0.166751\pi\) | |||||||
\(84\) | −7365.90 | + | 1693.84i | −1.04392 | + | 0.240057i | ||||
\(85\) | −3444.60 | −0.476762 | ||||||||
\(86\) | 10824.0i | 1.46349i | ||||||||
\(87\) | 3156.76 | + | 13727.6i | 0.417064 | + | 1.81366i | ||||
\(88\) | 4896.68 | 0.632319 | ||||||||
\(89\) | − | 6401.82i | − | 0.808208i | −0.914713 | − | 0.404104i | \(-0.867583\pi\) | ||
0.914713 | − | 0.404104i | \(-0.132417\pi\) | |||||||
\(90\) | 5873.48 | − | 2852.11i | 0.725121 | − | 0.352113i | ||||
\(91\) | −2939.88 | −0.355016 | ||||||||
\(92\) | − | 3679.45i | − | 0.434718i | ||||||
\(93\) | 2867.74 | − | 659.456i | 0.331568 | − | 0.0762465i | ||||
\(94\) | 14119.3 | 1.59793 | ||||||||
\(95\) | 4066.56i | 0.450588i | ||||||||
\(96\) | 2083.99 | + | 9062.51i | 0.226127 | + | 0.983345i | ||||
\(97\) | −9879.94 | −1.05005 | −0.525026 | − | 0.851086i | \(-0.675944\pi\) | ||||
−0.525026 | + | 0.851086i | \(0.675944\pi\) | |||||||
\(98\) | − | 13383.7i | − | 1.39356i | ||||||
\(99\) | 1202.55 | + | 2476.45i | 0.122696 | + | 0.252674i | ||||
\(100\) | 4497.83 | 0.449783 | ||||||||
\(101\) | 11119.7i | 1.09006i | 0.838415 | + | 0.545032i | \(0.183482\pi\) | ||||
−0.838415 | + | 0.545032i | \(0.816518\pi\) | |||||||
\(102\) | 19483.5 | − | 4480.36i | 1.87269 | − | 0.430638i | ||||
\(103\) | −12245.5 | −1.15426 | −0.577128 | − | 0.816653i | \(-0.695827\pi\) | ||||
−0.577128 | + | 0.816653i | \(0.695827\pi\) | |||||||
\(104\) | 18148.2i | 1.67790i | ||||||||
\(105\) | −526.301 | − | 2288.69i | −0.0477370 | − | 0.207591i | ||||
\(106\) | −21378.6 | −1.90269 | ||||||||
\(107\) | 708.790i | 0.0619085i | 0.999521 | + | 0.0309542i | \(0.00985462\pi\) | ||||
−0.999521 | + | 0.0309542i | \(0.990145\pi\) | |||||||
\(108\) | −20428.4 | + | 16455.0i | −1.75140 | + | 1.41075i | ||||
\(109\) | −908.407 | −0.0764588 | −0.0382294 | − | 0.999269i | \(-0.512172\pi\) | ||||
−0.0382294 | + | 0.999269i | \(0.512172\pi\) | |||||||
\(110\) | 2739.70i | 0.226422i | ||||||||
\(111\) | 635.708 | − | 146.186i | 0.0515955 | − | 0.0118647i | ||||
\(112\) | 10806.6 | 0.861493 | ||||||||
\(113\) | − | 3441.26i | − | 0.269501i | −0.990880 | − | 0.134751i | \(-0.956977\pi\) | ||
0.990880 | − | 0.134751i | \(-0.0430233\pi\) | |||||||
\(114\) | −5289.33 | − | 23001.4i | −0.406997 | − | 1.76988i | ||||
\(115\) | 1143.26 | 0.0864469 | ||||||||
\(116\) | − | 56316.4i | − | 4.18523i | ||||||
\(117\) | −9178.29 | + | 4456.91i | −0.670487 | + | 0.325583i | ||||
\(118\) | 36376.0 | 2.61247 | ||||||||
\(119\) | − | 7190.57i | − | 0.507773i | ||||||
\(120\) | −14128.3 | + | 3248.91i | −0.981133 | + | 0.225618i | ||||
\(121\) | 13485.8 | 0.921102 | ||||||||
\(122\) | 5311.65i | 0.356870i | ||||||||
\(123\) | 4334.48 | + | 18849.1i | 0.286502 | + | 1.24589i | ||||
\(124\) | −11764.7 | −0.765131 | ||||||||
\(125\) | 1397.54i | 0.0894427i | ||||||||
\(126\) | 5953.76 | + | 12260.8i | 0.375016 | + | 0.772286i | ||||
\(127\) | 28648.5 | 1.77621 | 0.888106 | − | 0.459638i | \(-0.152021\pi\) | ||||
0.888106 | + | 0.459638i | \(0.152021\pi\) | |||||||
\(128\) | 16236.1i | 0.990971i | ||||||||
\(129\) | 13167.7 | − | 3028.01i | 0.791282 | − | 0.181961i | ||||
\(130\) | −10154.0 | −0.600826 | ||||||||
\(131\) | 400.763i | 0.0233531i | 0.999932 | + | 0.0116766i | \(0.00371685\pi\) | ||||
−0.999932 | + | 0.0116766i | \(0.996283\pi\) | |||||||
\(132\) | −2466.68 | − | 10726.7i | −0.141568 | − | 0.615627i | ||||
\(133\) | −8488.90 | −0.479897 | ||||||||
\(134\) | 30675.5i | 1.70837i | ||||||||
\(135\) | −5112.80 | − | 6347.40i | −0.280538 | − | 0.348280i | ||||
\(136\) | −44388.1 | −2.39988 | ||||||||
\(137\) | − | 29277.7i | − | 1.55989i | −0.625845 | − | 0.779947i | \(-0.715246\pi\) | ||
0.625845 | − | 0.779947i | \(-0.284754\pi\) | |||||||
\(138\) | −6466.55 | + | 1487.03i | −0.339558 | + | 0.0780838i | ||||
\(139\) | 1852.04 | 0.0958565 | 0.0479282 | − | 0.998851i | \(-0.484738\pi\) | ||||
0.0479282 | + | 0.998851i | \(0.484738\pi\) | |||||||
\(140\) | 9389.18i | 0.479040i | ||||||||
\(141\) | −3949.89 | − | 17176.6i | −0.198677 | − | 0.863973i | ||||
\(142\) | −9400.54 | −0.466204 | ||||||||
\(143\) | − | 4281.25i | − | 0.209362i | ||||||
\(144\) | 33738.0 | − | 16382.9i | 1.62703 | − | 0.790071i | ||||
\(145\) | 17498.3 | 0.832263 | ||||||||
\(146\) | 48797.6i | 2.28925i | ||||||||
\(147\) | −16281.7 | + | 3744.10i | −0.753470 | + | 0.173266i | ||||
\(148\) | −2607.94 | −0.119062 | ||||||||
\(149\) | 19905.0i | 0.896582i | 0.893888 | + | 0.448291i | \(0.147967\pi\) | ||||
−0.893888 | + | 0.448291i | \(0.852033\pi\) | |||||||
\(150\) | −1817.77 | − | 7904.83i | −0.0807898 | − | 0.351326i | ||||
\(151\) | −24648.2 | −1.08101 | −0.540506 | − | 0.841340i | \(-0.681767\pi\) | ||||
−0.540506 | + | 0.841340i | \(0.681767\pi\) | |||||||
\(152\) | 52402.8i | 2.26813i | ||||||||
\(153\) | −10901.0 | − | 22448.9i | −0.465676 | − | 0.958986i | ||||
\(154\) | −5719.10 | −0.241149 | ||||||||
\(155\) | − | 3655.45i | − | 0.152152i | ||||||
\(156\) | 39755.5 | − | 9142.06i | 1.63361 | − | 0.375660i | ||||
\(157\) | 1399.18 | 0.0567642 | 0.0283821 | − | 0.999597i | \(-0.490964\pi\) | ||||
0.0283821 | + | 0.999597i | \(0.490964\pi\) | |||||||
\(158\) | − | 45905.9i | − | 1.83888i | ||||||
\(159\) | 5980.66 | + | 26007.8i | 0.236568 | + | 1.02875i | ||||
\(160\) | 11551.8 | 0.451243 | ||||||||
\(161\) | 2386.54i | 0.0920699i | ||||||||
\(162\) | 37175.2 | + | 29252.2i | 1.41652 | + | 1.11462i | ||||
\(163\) | 8023.34 | 0.301981 | 0.150991 | − | 0.988535i | \(-0.451754\pi\) | ||||
0.150991 | + | 0.988535i | \(0.451754\pi\) | |||||||
\(164\) | − | 77327.0i | − | 2.87504i | ||||||
\(165\) | 3332.94 | − | 766.432i | 0.122422 | − | 0.0281518i | ||||
\(166\) | 49691.8 | 1.80330 | ||||||||
\(167\) | − | 20948.5i | − | 0.751138i | −0.926794 | − | 0.375569i | \(-0.877447\pi\) | ||
0.926794 | − | 0.375569i | \(-0.122553\pi\) | |||||||
\(168\) | −6782.06 | − | 29492.7i | −0.240294 | − | 1.04495i | ||||
\(169\) | −12693.7 | −0.444443 | ||||||||
\(170\) | − | 24835.2i | − | 0.859351i | ||||||
\(171\) | −26502.3 | + | 12869.3i | −0.906339 | + | 0.440111i | ||||
\(172\) | −54019.5 | −1.82597 | ||||||||
\(173\) | 20564.6i | 0.687112i | 0.939132 | + | 0.343556i | \(0.111632\pi\) | ||||
−0.939132 | + | 0.343556i | \(0.888368\pi\) | |||||||
\(174\) | −98974.6 | + | 22759.9i | −3.26908 | + | 0.751747i | ||||
\(175\) | −2917.36 | −0.0952606 | ||||||||
\(176\) | 15737.2i | 0.508045i | ||||||||
\(177\) | −10176.2 | − | 44252.6i | −0.324817 | − | 1.41251i | ||||
\(178\) | 46156.5 | 1.45678 | ||||||||
\(179\) | 32395.6i | 1.01107i | 0.862807 | + | 0.505533i | \(0.168704\pi\) | ||||
−0.862807 | + | 0.505533i | \(0.831296\pi\) | |||||||
\(180\) | 14234.1 | + | 29312.9i | 0.439325 | + | 0.904720i | ||||
\(181\) | 18055.4 | 0.551125 | 0.275562 | − | 0.961283i | \(-0.411136\pi\) | ||||
0.275562 | + | 0.961283i | \(0.411136\pi\) | |||||||
\(182\) | − | 21196.3i | − | 0.639907i | ||||||
\(183\) | 6461.79 | − | 1485.93i | 0.192953 | − | 0.0443708i | ||||
\(184\) | 14732.4 | 0.435148 | ||||||||
\(185\) | − | 810.326i | − | 0.0236764i | ||||||
\(186\) | 4754.61 | + | 20676.1i | 0.137432 | + | 0.597644i | ||||
\(187\) | 10471.4 | 0.299447 | ||||||||
\(188\) | 70465.8i | 1.99371i | ||||||||
\(189\) | 13250.1 | − | 10672.9i | 0.370934 | − | 0.298785i | ||||
\(190\) | −29319.5 | −0.812174 | ||||||||
\(191\) | − | 11720.8i | − | 0.321285i | −0.987013 | − | 0.160642i | \(-0.948643\pi\) | ||
0.987013 | − | 0.160642i | \(-0.0513566\pi\) | |||||||
\(192\) | −359.548 | + | 82.6806i | −0.00975336 | + | 0.00224285i | ||||
\(193\) | −28253.2 | −0.758496 | −0.379248 | − | 0.925295i | \(-0.623817\pi\) | ||||
−0.379248 | + | 0.925295i | \(0.623817\pi\) | |||||||
\(194\) | − | 71233.4i | − | 1.89269i | ||||||
\(195\) | 2840.57 | + | 12352.6i | 0.0747027 | + | 0.324855i | ||||
\(196\) | 66794.6 | 1.73872 | ||||||||
\(197\) | 53312.1i | 1.37370i | 0.726797 | + | 0.686852i | \(0.241008\pi\) | ||||
−0.726797 | + | 0.686852i | \(0.758992\pi\) | |||||||
\(198\) | −17855.0 | + | 8670.24i | −0.455438 | + | 0.221157i | ||||
\(199\) | 50464.4 | 1.27432 | 0.637161 | − | 0.770731i | \(-0.280109\pi\) | ||||
0.637161 | + | 0.770731i | \(0.280109\pi\) | |||||||
\(200\) | 18009.1i | 0.450228i | ||||||||
\(201\) | 37317.7 | − | 8581.47i | 0.923683 | − | 0.212407i | ||||
\(202\) | −80172.2 | −1.96481 | ||||||||
\(203\) | 36527.6i | 0.886398i | ||||||||
\(204\) | 22360.3 | + | 97236.7i | 0.537300 | + | 2.33652i | ||||
\(205\) | 24026.6 | 0.571722 | ||||||||
\(206\) | − | 88288.9i | − | 2.08052i | ||||||
\(207\) | 3618.03 | + | 7450.77i | 0.0844368 | + | 0.173884i | ||||
\(208\) | −58325.6 | −1.34813 | ||||||||
\(209\) | − | 12362.1i | − | 0.283008i | ||||||
\(210\) | 16501.2 | − | 3794.58i | 0.374178 | − | 0.0860448i | ||||
\(211\) | −67329.0 | −1.51230 | −0.756148 | − | 0.654400i | \(-0.772921\pi\) | ||||
−0.756148 | + | 0.654400i | \(0.772921\pi\) | |||||||
\(212\) | − | 106695.i | − | 2.37395i | ||||||
\(213\) | 2629.80 | + | 11436.1i | 0.0579648 | + | 0.252068i | ||||
\(214\) | −5110.31 | −0.111589 | ||||||||
\(215\) | − | 16784.7i | − | 0.363108i | ||||||
\(216\) | −65884.9 | − | 81794.3i | −1.41214 | − | 1.75314i | ||||
\(217\) | 7630.72 | 0.162049 | ||||||||
\(218\) | − | 6549.52i | − | 0.137815i | ||||||
\(219\) | 59363.9 | − | 13651.1i | 1.23775 | − | 0.284630i | ||||
\(220\) | −13673.1 | −0.282502 | ||||||||
\(221\) | 38809.2i | 0.794604i | ||||||||
\(222\) | 1053.98 | + | 4583.39i | 0.0213859 | + | 0.0929996i | ||||
\(223\) | −56592.7 | −1.13802 | −0.569011 | − | 0.822330i | \(-0.692674\pi\) | ||||
−0.569011 | + | 0.822330i | \(0.692674\pi\) | |||||||
\(224\) | 24114.3i | 0.480594i | ||||||||
\(225\) | −9107.96 | + | 4422.75i | −0.179910 | + | 0.0873630i | ||||
\(226\) | 24811.1 | 0.485769 | ||||||||
\(227\) | 19015.9i | 0.369033i | 0.982829 | + | 0.184516i | \(0.0590719\pi\) | ||||
−0.982829 | + | 0.184516i | \(0.940928\pi\) | |||||||
\(228\) | 114794. | − | 26397.6i | 2.20825 | − | 0.507803i | ||||
\(229\) | −79079.9 | −1.50798 | −0.753989 | − | 0.656887i | \(-0.771873\pi\) | ||||
−0.753989 | + | 0.656887i | \(0.771873\pi\) | |||||||
\(230\) | 8242.79i | 0.155818i | ||||||||
\(231\) | 1599.92 | + | 6957.47i | 0.0299829 | + | 0.130385i | ||||
\(232\) | 225488. | 4.18936 | ||||||||
\(233\) | − | 36312.6i | − | 0.668876i | −0.942418 | − | 0.334438i | \(-0.891454\pi\) | ||
0.942418 | − | 0.334438i | \(-0.108546\pi\) | |||||||
\(234\) | −32133.9 | − | 66174.6i | −0.586855 | − | 1.20854i | ||||
\(235\) | −21894.8 | −0.396465 | ||||||||
\(236\) | 181543.i | 3.25953i | ||||||||
\(237\) | −55846.0 | + | 12842.2i | −0.994250 | + | 0.228635i | ||||
\(238\) | 51843.3 | 0.915248 | ||||||||
\(239\) | − | 46783.7i | − | 0.819028i | −0.912304 | − | 0.409514i | \(-0.865698\pi\) | ||
0.912304 | − | 0.409514i | \(-0.134302\pi\) | |||||||
\(240\) | −10441.5 | − | 45406.3i | −0.181276 | − | 0.788304i | ||||
\(241\) | 30646.4 | 0.527649 | 0.263824 | − | 0.964571i | \(-0.415016\pi\) | ||||
0.263824 | + | 0.964571i | \(0.415016\pi\) | |||||||
\(242\) | 97231.6i | 1.66026i | ||||||||
\(243\) | 25186.5 | − | 53408.1i | 0.426535 | − | 0.904471i | ||||
\(244\) | −26509.0 | −0.445260 | ||||||||
\(245\) | 20754.0i | 0.345757i | ||||||||
\(246\) | −135900. | + | 31251.2i | −2.24569 | + | 0.516412i | ||||
\(247\) | 45816.6 | 0.750981 | ||||||||
\(248\) | − | 47105.2i | − | 0.765888i | ||||||
\(249\) | −13901.3 | − | 60451.8i | −0.224211 | − | 0.975013i | ||||
\(250\) | −10076.1 | −0.161218 | ||||||||
\(251\) | − | 114804.i | − | 1.82226i | −0.412120 | − | 0.911130i | \(-0.635212\pi\) | ||
0.412120 | − | 0.911130i | \(-0.364788\pi\) | |||||||
\(252\) | −61190.4 | + | 29713.6i | −0.963568 | + | 0.467901i | ||||
\(253\) | −3475.44 | −0.0542960 | ||||||||
\(254\) | 206553.i | 3.20158i | ||||||||
\(255\) | −30212.9 | + | 6947.66i | −0.464635 | + | 0.106846i | ||||
\(256\) | −117716. | −1.79621 | ||||||||
\(257\) | 89602.7i | 1.35661i | 0.734780 | + | 0.678305i | \(0.237285\pi\) | ||||
−0.734780 | + | 0.678305i | \(0.762715\pi\) | |||||||
\(258\) | 21831.6 | + | 94938.0i | 0.327980 | + | 1.42627i | ||||
\(259\) | 1691.55 | 0.0252165 | ||||||||
\(260\) | − | 50675.6i | − | 0.749640i | ||||||
\(261\) | 55376.3 | + | 114039.i | 0.812911 | + | 1.67406i | ||||
\(262\) | −2889.46 | −0.0420935 | ||||||||
\(263\) | − | 113892.i | − | 1.64658i | −0.567620 | − | 0.823291i | \(-0.692136\pi\) | ||
0.567620 | − | 0.823291i | \(-0.307864\pi\) | |||||||
\(264\) | 42949.2 | − | 9876.46i | 0.616236 | − | 0.141708i | ||||
\(265\) | 33151.6 | 0.472077 | ||||||||
\(266\) | − | 61204.1i | − | 0.865003i | ||||||
\(267\) | −12912.3 | − | 56150.9i | −0.181126 | − | 0.787651i | ||||
\(268\) | −153093. | −2.13150 | ||||||||
\(269\) | 39232.3i | 0.542174i | 0.962555 | + | 0.271087i | \(0.0873832\pi\) | ||||
−0.962555 | + | 0.271087i | \(0.912617\pi\) | |||||||
\(270\) | 45764.1 | − | 36862.7i | 0.627765 | − | 0.505662i | ||||
\(271\) | 52549.5 | 0.715533 | 0.357767 | − | 0.933811i | \(-0.383538\pi\) | ||||
0.357767 | + | 0.933811i | \(0.383538\pi\) | |||||||
\(272\) | − | 142657.i | − | 1.92821i | ||||||
\(273\) | −25786.0 | + | 5929.66i | −0.345986 | + | 0.0795618i | ||||
\(274\) | 211089. | 2.81167 | ||||||||
\(275\) | − | 4248.44i | − | 0.0561777i | ||||||
\(276\) | −7421.35 | − | 32272.8i | −0.0974237 | − | 0.423661i | ||||
\(277\) | −28707.3 | −0.374139 | −0.187069 | − | 0.982347i | \(-0.559899\pi\) | ||||
−0.187069 | + | 0.982347i | \(0.559899\pi\) | |||||||
\(278\) | 13353.0i | 0.172779i | ||||||||
\(279\) | 23823.0 | − | 11568.3i | 0.306047 | − | 0.148614i | ||||
\(280\) | −37593.8 | −0.479513 | ||||||||
\(281\) | − | 83537.2i | − | 1.05796i | −0.848636 | − | 0.528978i | \(-0.822576\pi\) | ||
0.848636 | − | 0.528978i | \(-0.177424\pi\) | |||||||
\(282\) | 123842. | − | 28478.3i | 1.55729 | − | 0.358109i | ||||
\(283\) | 126719. | 1.58223 | 0.791115 | − | 0.611667i | \(-0.209501\pi\) | ||||
0.791115 | + | 0.611667i | \(0.209501\pi\) | |||||||
\(284\) | − | 46915.6i | − | 0.581675i | ||||||
\(285\) | 8202.13 | + | 35668.1i | 0.100980 | + | 0.439127i | ||||
\(286\) | 30867.4 | 0.377370 | ||||||||
\(287\) | 50155.3i | 0.608910i | ||||||||
\(288\) | 36557.6 | + | 75284.7i | 0.440751 | + | 0.907656i | ||||
\(289\) | −11401.3 | −0.136508 | ||||||||
\(290\) | 126161.i | 1.50013i | ||||||||
\(291\) | −86657.7 | + | 19927.5i | −1.02334 | + | 0.235325i | ||||
\(292\) | −243536. | −2.85626 | ||||||||
\(293\) | 69385.0i | 0.808222i | 0.914710 | + | 0.404111i | \(0.132419\pi\) | ||||
−0.914710 | + | 0.404111i | \(0.867581\pi\) | |||||||
\(294\) | −26994.6 | − | 117390.i | −0.312307 | − | 1.35811i | ||||
\(295\) | −56408.1 | −0.648182 | ||||||||
\(296\) | − | 10442.1i | − | 0.119180i | ||||||
\(297\) | 15542.6 | + | 19295.7i | 0.176202 | + | 0.218749i | ||||
\(298\) | −143513. | −1.61607 | ||||||||
\(299\) | − | 12880.7i | − | 0.144078i | ||||||
\(300\) | 39450.8 | − | 9072.00i | 0.438343 | − | 0.100800i | ||||
\(301\) | 35037.8 | 0.386727 | ||||||||
\(302\) | − | 177711.i | − | 1.94850i | ||||||
\(303\) | 22428.2 | + | 97532.1i | 0.244292 | + | 1.06234i | ||||
\(304\) | −168415. | −1.82236 | ||||||||
\(305\) | − | 8236.74i | − | 0.0885432i | ||||||
\(306\) | 161854. | − | 78595.2i | 1.72855 | − | 0.839369i | ||||
\(307\) | 63952.5 | 0.678549 | 0.339274 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339274 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(308\) | − | 28542.5i | − | 0.300878i | ||||||
\(309\) | −107406. | + | 24698.8i | −1.12490 | + | 0.258678i | ||||
\(310\) | 26355.4 | 0.274250 | ||||||||
\(311\) | 18806.5i | 0.194441i | 0.995263 | + | 0.0972203i | \(0.0309951\pi\) | ||||
−0.995263 | + | 0.0972203i | \(0.969005\pi\) | |||||||
\(312\) | 36604.4 | + | 159179.i | 0.376031 | + | 1.63522i | ||||
\(313\) | 62746.1 | 0.640469 | 0.320235 | − | 0.947338i | \(-0.396238\pi\) | ||||
0.320235 | + | 0.947338i | \(0.396238\pi\) | |||||||
\(314\) | 10088.0i | 0.102316i | ||||||||
\(315\) | −9232.45 | − | 19012.8i | −0.0930456 | − | 0.191613i | ||||
\(316\) | 229104. | 2.29434 | ||||||||
\(317\) | − | 93427.4i | − | 0.929728i | −0.885382 | − | 0.464864i | \(-0.846103\pi\) | ||
0.885382 | − | 0.464864i | \(-0.153897\pi\) | |||||||
\(318\) | −187513. | + | 43120.0i | −1.85429 | + | 0.426407i | ||||
\(319\) | −53193.8 | −0.522732 | ||||||||
\(320\) | 458.309i | 0.00447568i | ||||||||
\(321\) | 1429.61 | + | 6216.86i | 0.0138742 | + | 0.0603338i | ||||
\(322\) | −17206.7 | −0.165954 | ||||||||
\(323\) | 112061.i | 1.07412i | ||||||||
\(324\) | −145990. | + | 185531.i | −1.39070 | + | 1.76737i | ||||
\(325\) | 15745.7 | 0.149071 | ||||||||
\(326\) | 57847.5i | 0.544314i | ||||||||
\(327\) | −7967.71 | + | 1832.23i | −0.0745140 | + | 0.0171350i | ||||
\(328\) | 309614. | 2.87788 | ||||||||
\(329\) | − | 45705.1i | − | 0.422253i | ||||||
\(330\) | 5525.90 | + | 24030.2i | 0.0507429 | + | 0.220663i | ||||
\(331\) | −71675.0 | −0.654202 | −0.327101 | − | 0.944989i | \(-0.606072\pi\) | ||||
−0.327101 | + | 0.944989i | \(0.606072\pi\) | |||||||
\(332\) | 247999.i | 2.24995i | ||||||||
\(333\) | 5281.00 | − | 2564.41i | 0.0476242 | − | 0.0231259i | ||||
\(334\) | 151036. | 1.35391 | ||||||||
\(335\) | − | 47568.3i | − | 0.423865i | ||||||
\(336\) | 94785.2 | − | 21796.5i | 0.839580 | − | 0.193067i | ||||
\(337\) | −87920.2 | −0.774157 | −0.387078 | − | 0.922047i | \(-0.626516\pi\) | ||||
−0.387078 | + | 0.922047i | \(0.626516\pi\) | |||||||
\(338\) | − | 91520.6i | − | 0.801098i | ||||||
\(339\) | −6940.92 | − | 30183.6i | −0.0603973 | − | 0.262646i | ||||
\(340\) | 123946. | 1.07220 | ||||||||
\(341\) | 11112.3i | 0.0955645i | ||||||||
\(342\) | −92786.3 | − | 191079.i | −0.793290 | − | 1.63365i | ||||
\(343\) | −99360.4 | −0.844550 | ||||||||
\(344\) | − | 216292.i | − | 1.82778i | ||||||
\(345\) | 10027.6 | − | 2305.92i | 0.0842481 | − | 0.0193734i | ||||
\(346\) | −148269. | −1.23850 | ||||||||
\(347\) | 5941.38i | 0.0493433i | 0.999696 | + | 0.0246717i | \(0.00785403\pi\) | ||||
−0.999696 | + | 0.0246717i | \(0.992146\pi\) | |||||||
\(348\) | −113589. | − | 493955.i | −0.937942 | − | 4.07877i | ||||
\(349\) | −65214.3 | −0.535417 | −0.267709 | − | 0.963500i | \(-0.586266\pi\) | ||||
−0.267709 | + | 0.963500i | \(0.586266\pi\) | |||||||
\(350\) | − | 21033.8i | − | 0.171705i | ||||||
\(351\) | −71514.1 | + | 57604.2i | −0.580467 | + | 0.467563i | ||||
\(352\) | −35116.8 | −0.283419 | ||||||||
\(353\) | − | 36220.5i | − | 0.290673i | −0.989382 | − | 0.145337i | \(-0.953573\pi\) | ||
0.989382 | − | 0.145337i | \(-0.0464265\pi\) | |||||||
\(354\) | 319057. | − | 73369.4i | 2.54602 | − | 0.585475i | ||||
\(355\) | 14577.4 | 0.115670 | ||||||||
\(356\) | 230354.i | 1.81759i | ||||||||
\(357\) | −14503.2 | − | 63069.1i | −0.113796 | − | 0.494857i | ||||
\(358\) | −233569. | −1.82242 | ||||||||
\(359\) | 152925.i | 1.18656i | 0.804997 | + | 0.593279i | \(0.202167\pi\) | ||||
−0.804997 | + | 0.593279i | \(0.797833\pi\) | |||||||
\(360\) | −117368. | + | 56992.8i | −0.905615 | + | 0.439759i | ||||
\(361\) | 1974.27 | 0.0151493 | ||||||||
\(362\) | 130178.i | 0.993389i | ||||||||
\(363\) | 118285. | − | 27200.6i | 0.897673 | − | 0.206426i | ||||
\(364\) | 105785. | 0.798400 | ||||||||
\(365\) | − | 75670.1i | − | 0.567987i | ||||||
\(366\) | 10713.4 | + | 46588.9i | 0.0799773 | + | 0.347792i | ||||
\(367\) | 143778. | 1.06748 | 0.533740 | − | 0.845649i | \(-0.320786\pi\) | ||||
0.533740 | + | 0.845649i | \(0.320786\pi\) | |||||||
\(368\) | 47347.6i | 0.349625i | ||||||||
\(369\) | 76036.2 | + | 156584.i | 0.558429 | + | 1.15000i | ||||
\(370\) | 5842.37 | 0.0426762 | ||||||||
\(371\) | 69203.7i | 0.502784i | ||||||||
\(372\) | −103189. | + | 23729.0i | −0.745670 | + | 0.171472i | ||||
\(373\) | 102685. | 0.738056 | 0.369028 | − | 0.929418i | \(-0.379691\pi\) | ||||
0.369028 | + | 0.929418i | \(0.379691\pi\) | |||||||
\(374\) | 75497.5i | 0.539746i | ||||||||
\(375\) | 2818.80 | + | 12258.0i | 0.0200448 | + | 0.0871677i | ||||
\(376\) | −282142. | −1.99568 | ||||||||
\(377\) | − | 197148.i | − | 1.38711i | ||||||
\(378\) | 76950.6 | + | 95532.1i | 0.538553 | + | 0.668599i | ||||
\(379\) | −148649. | −1.03486 | −0.517432 | − | 0.855724i | \(-0.673112\pi\) | ||||
−0.517432 | + | 0.855724i | \(0.673112\pi\) | |||||||
\(380\) | − | 146326.i | − | 1.01334i | ||||||
\(381\) | 251279. | − | 57783.3i | 1.73103 | − | 0.398063i | ||||
\(382\) | 84505.7 | 0.579108 | ||||||||
\(383\) | 88390.0i | 0.602568i | 0.953535 | + | 0.301284i | \(0.0974152\pi\) | ||||
−0.953535 | + | 0.301284i | \(0.902585\pi\) | |||||||
\(384\) | 32747.7 | + | 142408.i | 0.222084 | + | 0.965765i | ||||
\(385\) | 8868.57 | 0.0598318 | ||||||||
\(386\) | − | 203703.i | − | 1.36717i | ||||||
\(387\) | 109388. | − | 53117.8i | 0.730376 | − | 0.354665i | ||||
\(388\) | 355506. | 2.36148 | ||||||||
\(389\) | − | 107542.i | − | 0.710687i | −0.934736 | − | 0.355344i | \(-0.884364\pi\) | ||
0.934736 | − | 0.355344i | \(-0.115636\pi\) | |||||||
\(390\) | −89061.1 | + | 20480.2i | −0.585543 | + | 0.134650i | ||||
\(391\) | 31504.6 | 0.206073 | ||||||||
\(392\) | 267442.i | 1.74044i | ||||||||
\(393\) | 808.328 | + | 3515.13i | 0.00523362 | + | 0.0227591i | ||||
\(394\) | −384375. | −2.47607 | ||||||||
\(395\) | 71186.0i | 0.456247i | ||||||||
\(396\) | −43270.8 | − | 89109.4i | −0.275934 | − | 0.568242i | ||||
\(397\) | −131243. | −0.832710 | −0.416355 | − | 0.909202i | \(-0.636693\pi\) | ||||
−0.416355 | + | 0.909202i | \(0.636693\pi\) | |||||||
\(398\) | 363844.i | 2.29693i | ||||||||
\(399\) | −74456.8 | + | 17121.9i | −0.467691 | + | 0.107549i | ||||
\(400\) | −57878.6 | −0.361742 | ||||||||
\(401\) | 21480.0i | 0.133581i | 0.997767 | + | 0.0667907i | \(0.0212760\pi\) | ||||
−0.997767 | + | 0.0667907i | \(0.978724\pi\) | |||||||
\(402\) | 61871.6 | + | 269057.i | 0.382859 | + | 1.66492i | ||||
\(403\) | −41184.8 | −0.253587 | ||||||||
\(404\) | − | 400118.i | − | 2.45146i | ||||||
\(405\) | −57647.3 | − | 45361.2i | −0.351454 | − | 0.276550i | ||||
\(406\) | −263360. | −1.59771 | ||||||||
\(407\) | 2463.34i | 0.0148708i | ||||||||
\(408\) | −389332. | + | 89529.5i | −2.33883 | + | 0.537831i | ||||
\(409\) | 118822. | 0.710313 | 0.355156 | − | 0.934807i | \(-0.384428\pi\) | ||||
0.355156 | + | 0.934807i | \(0.384428\pi\) | |||||||
\(410\) | 173230.i | 1.03052i | ||||||||
\(411\) | −59052.2 | − | 256797.i | −0.349585 | − | 1.52022i | ||||
\(412\) | 440626. | 2.59583 | ||||||||
\(413\) | − | 117751.i | − | 0.690344i | ||||||
\(414\) | −53719.3 | + | 26085.7i | −0.313422 | + | 0.152195i | ||||
\(415\) | −77056.8 | −0.447419 | ||||||||
\(416\) | − | 130151.i | − | 0.752073i | ||||||
\(417\) | 16244.4 | − | 3735.52i | 0.0934183 | − | 0.0214822i | ||||
\(418\) | 89129.3 | 0.510115 | ||||||||
\(419\) | 95945.4i | 0.546507i | 0.961942 | + | 0.273254i | \(0.0880998\pi\) | ||||
−0.961942 | + | 0.273254i | \(0.911900\pi\) | |||||||
\(420\) | 18937.7 | + | 82353.2i | 0.107357 | + | 0.466855i | ||||
\(421\) | 73818.2 | 0.416485 | 0.208242 | − | 0.978077i | \(-0.433226\pi\) | ||||
0.208242 | + | 0.978077i | \(0.433226\pi\) | |||||||
\(422\) | − | 485435.i | − | 2.72588i | ||||||
\(423\) | −69289.6 | − | 142691.i | −0.387246 | − | 0.797472i | ||||
\(424\) | 427201. | 2.37630 | ||||||||
\(425\) | 38511.8i | 0.213214i | ||||||||
\(426\) | −82452.9 | + | 18960.6i | −0.454346 | + | 0.104480i | ||||
\(427\) | 17194.1 | 0.0943026 | ||||||||
\(428\) | − | 25504.2i | − | 0.139227i | ||||||
\(429\) | −8635.15 | − | 37551.1i | −0.0469197 | − | 0.204037i | ||||
\(430\) | 121016. | 0.654493 | ||||||||
\(431\) | 107733.i | 0.579955i | 0.957033 | + | 0.289977i | \(0.0936478\pi\) | ||||
−0.957033 | + | 0.289977i | \(0.906352\pi\) | |||||||
\(432\) | 262875. | − | 211744.i | 1.40858 | − | 1.13460i | ||||
\(433\) | −114738. | −0.611974 | −0.305987 | − | 0.952036i | \(-0.598986\pi\) | ||||
−0.305987 | + | 0.952036i | \(0.598986\pi\) | |||||||
\(434\) | 55016.7i | 0.292089i | ||||||||
\(435\) | 153479. | − | 35293.6i | 0.811094 | − | 0.186517i | ||||
\(436\) | 32686.9 | 0.171949 | ||||||||
\(437\) | − | 37193.1i | − | 0.194760i | ||||||
\(438\) | 98423.4 | + | 428008.i | 0.513039 | + | 2.23102i | ||||
\(439\) | 257591. | 1.33660 | 0.668300 | − | 0.743892i | \(-0.267022\pi\) | ||||
0.668300 | + | 0.743892i | \(0.267022\pi\) | |||||||
\(440\) | − | 54746.5i | − | 0.282782i | ||||||
\(441\) | −135257. | + | 65679.6i | −0.695475 | + | 0.337717i | ||||
\(442\) | −279811. | −1.43225 | ||||||||
\(443\) | 35360.6i | 0.180182i | 0.995934 | + | 0.0900911i | \(0.0287158\pi\) | ||||
−0.995934 | + | 0.0900911i | \(0.971284\pi\) | |||||||
\(444\) | −22874.5 | + | 5260.14i | −0.116034 | + | 0.0266828i | ||||
\(445\) | −71574.5 | −0.361442 | ||||||||
\(446\) | − | 408028.i | − | 2.05126i | ||||||
\(447\) | 40147.8 | + | 174588.i | 0.200931 | + | 0.873777i | ||||
\(448\) | −956.716 | −0.00476680 | ||||||||
\(449\) | 8230.74i | 0.0408269i | 0.999792 | + | 0.0204134i | \(0.00649825\pi\) | ||||
−0.999792 | + | 0.0204134i | \(0.993502\pi\) | |||||||
\(450\) | −31887.6 | − | 65667.5i | −0.157470 | − | 0.324284i | ||||
\(451\) | −73039.4 | −0.359091 | ||||||||
\(452\) | 123826.i | 0.606086i | ||||||||
\(453\) | −216191. | + | 49714.6i | −1.05352 | + | 0.242263i | ||||
\(454\) | −137103. | −0.665172 | ||||||||
\(455\) | 32868.9i | 0.158768i | ||||||||
\(456\) | 105695. | + | 459629.i | 0.508305 | + | 2.21044i | ||||
\(457\) | −180660. | −0.865027 | −0.432514 | − | 0.901627i | \(-0.642373\pi\) | ||||
−0.432514 | + | 0.901627i | \(0.642373\pi\) | |||||||
\(458\) | − | 570158.i | − | 2.71809i | ||||||
\(459\) | −140892. | − | 174914.i | −0.668748 | − | 0.830232i | ||||
\(460\) | −41137.5 | −0.194412 | ||||||||
\(461\) | − | 34875.9i | − | 0.164106i | −0.996628 | − | 0.0820529i | \(-0.973852\pi\) | ||
0.996628 | − | 0.0820529i | \(-0.0261476\pi\) | |||||||
\(462\) | −50162.7 | + | 11535.3i | −0.235016 | + | 0.0540435i | ||||
\(463\) | −206020. | −0.961054 | −0.480527 | − | 0.876980i | \(-0.659555\pi\) | ||||
−0.480527 | + | 0.876980i | \(0.659555\pi\) | |||||||
\(464\) | 724686.i | 3.36600i | ||||||||
\(465\) | −7372.94 | − | 32062.3i | −0.0340985 | − | 0.148282i | ||||
\(466\) | 261810. | 1.20563 | ||||||||
\(467\) | 274766.i | 1.25988i | 0.776644 | + | 0.629940i | \(0.216921\pi\) | ||||
−0.776644 | + | 0.629940i | \(0.783079\pi\) | |||||||
\(468\) | 330259. | − | 160371.i | 1.50787 | − | 0.732209i | ||||
\(469\) | 99298.2 | 0.451436 | ||||||||
\(470\) | − | 157859.i | − | 0.714618i | ||||||
\(471\) | 12272.3 | − | 2822.11i | 0.0553204 | − | 0.0127213i | ||||
\(472\) | −726890. | −3.26276 | ||||||||
\(473\) | 51024.3i | 0.228063i | ||||||||
\(474\) | −92590.9 | − | 402644.i | −0.412108 | − | 1.79211i | ||||
\(475\) | 45465.5 | 0.201509 | ||||||||
\(476\) | 258736.i | 1.14194i | ||||||||
\(477\) | 104914. | + | 216053.i | 0.461101 | + | 0.949564i | ||||
\(478\) | 337306. | 1.47628 | ||||||||
\(479\) | − | 160960.i | − | 0.701533i | −0.936463 | − | 0.350766i | \(-0.885921\pi\) | ||
0.936463 | − | 0.350766i | \(-0.114079\pi\) | |||||||
\(480\) | 101322. | − | 23299.7i | 0.439765 | − | 0.101127i | ||||
\(481\) | −9129.68 | −0.0394608 | ||||||||
\(482\) | 220957.i | 0.951074i | ||||||||
\(483\) | 4813.59 | + | 20932.6i | 0.0206336 | + | 0.0897280i | ||||
\(484\) | −485257. | −2.07148 | ||||||||
\(485\) | 110461.i | 0.469597i | ||||||||
\(486\) | 385067. | + | 181592.i | 1.63029 | + | 0.768819i | ||||
\(487\) | −69827.5 | −0.294421 | −0.147210 | − | 0.989105i | \(-0.547029\pi\) | ||||
−0.147210 | + | 0.989105i | \(0.547029\pi\) | |||||||
\(488\) | − | 106141.i | − | 0.445700i | ||||||
\(489\) | 70373.4 | − | 16182.9i | 0.294300 | − | 0.0676764i | ||||
\(490\) | −149635. | −0.623218 | ||||||||
\(491\) | 430893.i | 1.78734i | 0.448727 | + | 0.893669i | \(0.351878\pi\) | ||||
−0.448727 | + | 0.893669i | \(0.648122\pi\) | |||||||
\(492\) | −155966. | − | 678241.i | −0.644318 | − | 2.80191i | ||||
\(493\) | 482198. | 1.98396 | ||||||||
\(494\) | 330333.i | 1.35363i | ||||||||
\(495\) | 27687.6 | − | 13444.9i | 0.112999 | − | 0.0548715i | ||||
\(496\) | 151389. | 0.615362 | ||||||||
\(497\) | 30430.1i | 0.123194i | ||||||||
\(498\) | 435851. | − | 100227.i | 1.75744 | − | 0.404135i | ||||
\(499\) | 282872. | 1.13603 | 0.568013 | − | 0.823019i | \(-0.307712\pi\) | ||||
0.568013 | + | 0.823019i | \(0.307712\pi\) | |||||||
\(500\) | − | 50287.3i | − | 0.201149i | ||||||
\(501\) | −42252.5 | − | 183741.i | −0.168336 | − | 0.732032i | ||||
\(502\) | 827726. | 3.28458 | ||||||||
\(503\) | − | 240734.i | − | 0.951483i | −0.879585 | − | 0.475742i | \(-0.842180\pi\) | ||
0.879585 | − | 0.475742i | \(-0.157820\pi\) | |||||||
\(504\) | −118972. | − | 245004.i | −0.468364 | − | 0.964521i | ||||
\(505\) | 124322. | 0.487491 | ||||||||
\(506\) | − | 25057.5i | − | 0.0978673i | ||||||
\(507\) | −111338. | + | 25602.9i | −0.433138 | + | 0.0996032i | ||||
\(508\) | −1.03085e6 | −3.99455 | ||||||||
\(509\) | − | 225427.i | − | 0.870102i | −0.900406 | − | 0.435051i | \(-0.856730\pi\) | ||
0.900406 | − | 0.435051i | \(-0.143270\pi\) | |||||||
\(510\) | −50092.0 | − | 217832.i | −0.192587 | − | 0.837493i | ||||
\(511\) | 157961. | 0.604933 | ||||||||
\(512\) | − | 588946.i | − | 2.24665i | ||||||
\(513\) | −206497. | + | 166332.i | −0.784654 | + | 0.632035i | ||||
\(514\) | −646027. | −2.44526 | ||||||||
\(515\) | 136909.i | 0.516199i | ||||||||
\(516\) | −473810. | + | 108956.i | −1.77953 | + | 0.409215i | ||||
\(517\) | 66558.6 | 0.249014 | ||||||||
\(518\) | 12195.9i | 0.0454521i | ||||||||
\(519\) | 41478.2 | + | 180374.i | 0.153987 | + | 0.669635i | ||||
\(520\) | 202903. | 0.750381 | ||||||||
\(521\) | 154960.i | 0.570880i | 0.958397 | + | 0.285440i | \(0.0921397\pi\) | ||||
−0.958397 | + | 0.285440i | \(0.907860\pi\) | |||||||
\(522\) | −822208. | + | 399258.i | −3.01745 | + | 1.46525i | ||||
\(523\) | −128163. | −0.468553 | −0.234277 | − | 0.972170i | \(-0.575272\pi\) | ||||
−0.234277 | + | 0.972170i | \(0.575272\pi\) | |||||||
\(524\) | − | 14420.5i | − | 0.0525193i | ||||||
\(525\) | −25588.4 | + | 5884.22i | −0.0928376 | + | 0.0213486i | ||||
\(526\) | 821153. | 2.96792 | ||||||||
\(527\) | − | 100733.i | − | 0.362701i | ||||||
\(528\) | 31741.5 | + | 138032.i | 0.113857 | + | 0.495123i | ||||
\(529\) | 269385. | 0.962635 | ||||||||
\(530\) | 239020.i | 0.850907i | ||||||||
\(531\) | −178513. | − | 367618.i | −0.633111 | − | 1.30379i | ||||
\(532\) | 305453. | 1.07925 | ||||||||
\(533\) | − | 270700.i | − | 0.952872i | ||||||
\(534\) | 404842. | − | 93096.3i | 1.41972 | − | 0.326475i | ||||
\(535\) | 7924.52 | 0.0276863 | ||||||||
\(536\) | − | 612978.i | − | 2.13361i | ||||||
\(537\) | 65340.9 | + | 284144.i | 0.226588 | + | 0.985349i | ||||
\(538\) | −282861. | −0.977256 | ||||||||
\(539\) | − | 63090.9i | − | 0.217165i | ||||||
\(540\) | 183972. | + | 228396.i | 0.630905 | + | 0.783252i | ||||
\(541\) | −499660. | −1.70718 | −0.853591 | − | 0.520943i | \(-0.825580\pi\) | ||||
−0.853591 | + | 0.520943i | \(0.825580\pi\) | |||||||
\(542\) | 378876.i | 1.28973i | ||||||||
\(543\) | 158365. | − | 36417.2i | 0.537107 | − | 0.123511i | ||||
\(544\) | 318332. | 1.07568 | ||||||||
\(545\) | 10156.3i | 0.0341934i | ||||||||
\(546\) | −42752.3 | − | 185914.i | −0.143408 | − | 0.623630i | ||||
\(547\) | −244301. | −0.816490 | −0.408245 | − | 0.912872i | \(-0.633859\pi\) | ||||
−0.408245 | + | 0.912872i | \(0.633859\pi\) | |||||||
\(548\) | 1.05349e6i | 3.50807i | ||||||||
\(549\) | 53679.8 | − | 26066.5i | 0.178101 | − | 0.0864845i | ||||
\(550\) | 30630.8 | 0.101259 | ||||||||
\(551\) | − | 569264.i | − | 1.87504i | ||||||
\(552\) | 129219. | − | 29714.8i | 0.424080 | − | 0.0975201i | ||||
\(553\) | −148600. | −0.485924 | ||||||||
\(554\) | − | 206977.i | − | 0.674376i | ||||||
\(555\) | −1634.40 | − | 7107.43i | −0.00530608 | − | 0.0230742i | ||||
\(556\) | −66641.4 | −0.215573 | ||||||||
\(557\) | − | 247875.i | − | 0.798954i | −0.916743 | − | 0.399477i | \(-0.869192\pi\) | ||
0.916743 | − | 0.399477i | \(-0.130808\pi\) | |||||||
\(558\) | 83406.1 | + | 171762.i | 0.267873 | + | 0.551643i | ||||
\(559\) | −189107. | −0.605181 | ||||||||
\(560\) | − | 120821.i | − | 0.385271i | ||||||
\(561\) | 91845.2 | − | 21120.4i | 0.291830 | − | 0.0671085i | ||||
\(562\) | 602295. | 1.90694 | ||||||||
\(563\) | 265392.i | 0.837279i | 0.908152 | + | 0.418640i | \(0.137493\pi\) | ||||
−0.908152 | + | 0.418640i | \(0.862507\pi\) | |||||||
\(564\) | 142127. | + | 618061.i | 0.446807 | + | 1.94300i | ||||
\(565\) | −38474.5 | −0.120525 | ||||||||
\(566\) | 913633.i | 2.85193i | ||||||||
\(567\) | 94690.9 | − | 120338.i | 0.294539 | − | 0.374315i | ||||
\(568\) | 187848. | 0.582250 | ||||||||
\(569\) | 551671.i | 1.70394i | 0.523587 | + | 0.851972i | \(0.324593\pi\) | ||||
−0.523587 | + | 0.851972i | \(0.675407\pi\) | |||||||
\(570\) | −257164. | + | 59136.6i | −0.791516 | + | 0.182015i | ||||
\(571\) | 325456. | 0.998205 | 0.499102 | − | 0.866543i | \(-0.333663\pi\) | ||||
0.499102 | + | 0.866543i | \(0.333663\pi\) | |||||||
\(572\) | 154051.i | 0.470838i | ||||||||
\(573\) | −23640.5 | − | 102804.i | −0.0720024 | − | 0.313113i | ||||
\(574\) | −361615. | −1.09755 | ||||||||
\(575\) | − | 12782.0i | − | 0.0386602i | ||||||
\(576\) | −2986.86 | + | 1450.40i | −0.00900264 | + | 0.00437161i | ||||
\(577\) | −262408. | −0.788181 | −0.394091 | − | 0.919072i | \(-0.628940\pi\) | ||||
−0.394091 | + | 0.919072i | \(0.628940\pi\) | |||||||
\(578\) | − | 82202.3i | − | 0.246053i | ||||||
\(579\) | −247811. | + | 56985.9i | −0.739203 | + | 0.169985i | ||||
\(580\) | −629636. | −1.87169 | ||||||||
\(581\) | − | 160855.i | − | 0.476522i | ||||||
\(582\) | −143676. | − | 624793.i | −0.424167 | − | 1.84455i | ||||
\(583\) | −100779. | −0.296505 | ||||||||
\(584\) | − | 975106.i | − | 2.85908i | ||||||
\(585\) | 49829.7 | + | 102616.i | 0.145605 | + | 0.299851i | ||||
\(586\) | −500259. | −1.45680 | ||||||||
\(587\) | − | 427538.i | − | 1.24079i | −0.784290 | − | 0.620395i | \(-0.786972\pi\) | ||
0.784290 | − | 0.620395i | \(-0.213028\pi\) | |||||||
\(588\) | 585860. | − | 134723.i | 1.69449 | − | 0.389660i | ||||
\(589\) | −118921. | −0.342790 | ||||||||
\(590\) | − | 406696.i | − | 1.16833i | ||||||
\(591\) | 107529. | + | 467605.i | 0.307858 | + | 1.33876i | ||||
\(592\) | 33559.3 | 0.0957568 | ||||||||
\(593\) | 63018.6i | 0.179209i | 0.995977 | + | 0.0896043i | \(0.0285603\pi\) | ||||
−0.995977 | + | 0.0896043i | \(0.971440\pi\) | |||||||
\(594\) | −139120. | + | 112060.i | −0.394290 | + | 0.317599i | ||||
\(595\) | −80393.0 | −0.227083 | ||||||||
\(596\) | − | 716235.i | − | 2.01634i | ||||||
\(597\) | 442628. | − | 101785.i | 1.24191 | − | 0.285586i | ||||
\(598\) | 92868.9 | 0.259698 | ||||||||
\(599\) | − | 634561.i | − | 1.76856i | −0.466959 | − | 0.884279i | \(-0.654650\pi\) | ||
0.466959 | − | 0.884279i | \(-0.345350\pi\) | |||||||
\(600\) | 36323.9 | + | 157959.i | 0.100900 | + | 0.438776i | ||||
\(601\) | −474806. | −1.31452 | −0.657260 | − | 0.753664i | \(-0.728285\pi\) | ||||
−0.657260 | + | 0.753664i | \(0.728285\pi\) | |||||||
\(602\) | 252619.i | 0.697065i | ||||||||
\(603\) | 310008. | − | 150538.i | 0.852587 | − | 0.414009i | ||||
\(604\) | 886906. | 2.43111 | ||||||||
\(605\) | − | 150776.i | − | 0.411929i | ||||||
\(606\) | −703197. | + | 161705.i | −1.91484 | + | 0.440330i | ||||
\(607\) | −163861. | −0.444731 | −0.222365 | − | 0.974963i | \(-0.571378\pi\) | ||||
−0.222365 | + | 0.974963i | \(0.571378\pi\) | |||||||
\(608\) | − | 375809.i | − | 1.01662i | ||||||
\(609\) | 73675.1 | + | 320386.i | 0.198649 | + | 0.863852i | ||||
\(610\) | 59386.0 | 0.159597 | ||||||||
\(611\) | 246681.i | 0.660775i | ||||||||
\(612\) | 392247. | + | 807771.i | 1.04727 | + | 2.15668i | ||||
\(613\) | 328099. | 0.873139 | 0.436570 | − | 0.899670i | \(-0.356193\pi\) | ||||
0.436570 | + | 0.899670i | \(0.356193\pi\) | |||||||
\(614\) | 461091.i | 1.22307i | ||||||||
\(615\) | 210739. | − | 48461.0i | 0.557180 | − | 0.128127i | ||||
\(616\) | 114283. | 0.301175 | ||||||||
\(617\) | 405778.i | 1.06590i | 0.846146 | + | 0.532952i | \(0.178917\pi\) | ||||
−0.846146 | + | 0.532952i | \(0.821083\pi\) | |||||||
\(618\) | −178076. | − | 774389.i | −0.466261 | − | 2.02760i | ||||
\(619\) | 184587. | 0.481747 | 0.240874 | − | 0.970557i | \(-0.422566\pi\) | ||||
0.240874 | + | 0.970557i | \(0.422566\pi\) | |||||||
\(620\) | 131533.i | 0.342177i | ||||||||
\(621\) | 46762.0 | + | 58053.8i | 0.121258 | + | 0.150538i | ||||
\(622\) | −135593. | −0.350474 | ||||||||
\(623\) | − | 149411.i | − | 0.384952i | ||||||
\(624\) | −511579. | + | 117641.i | −1.31384 | + | 0.302127i | ||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | 452393.i | 1.15443i | ||||||||
\(627\) | −24933.9 | − | 108429.i | −0.0634243 | − | 0.275810i | ||||
\(628\) | −50346.2 | −0.127658 | ||||||||
\(629\) | − | 22330.0i | − | 0.0564401i | ||||||
\(630\) | 137080. | − | 66565.0i | 0.345377 | − | 0.167712i | ||||
\(631\) | 712031. | 1.78830 | 0.894149 | − | 0.447769i | \(-0.147781\pi\) | ||||
0.894149 | + | 0.447769i | \(0.147781\pi\) | |||||||
\(632\) | 917322.i | 2.29661i | ||||||||
\(633\) | −590548. | + | 135801.i | −1.47383 | + | 0.338918i | ||||
\(634\) | 673602. | 1.67581 | ||||||||
\(635\) | − | 320300.i | − | 0.794346i | ||||||
\(636\) | −215200. | − | 935828.i | −0.532021 | − | 2.31357i | ||||
\(637\) | 233829. | 0.576262 | ||||||||
\(638\) | − | 383522.i | − | 0.942212i | ||||||
\(639\) | 46132.4 | + | 95002.4i | 0.112981 | + | 0.232666i | ||||
\(640\) | 181525. | 0.443176 | ||||||||
\(641\) | 388033.i | 0.944393i | 0.881493 | + | 0.472196i | \(0.156539\pi\) | ||||
−0.881493 | + | 0.472196i | \(0.843461\pi\) | |||||||
\(642\) | −44822.9 | + | 10307.3i | −0.108750 | + | 0.0250079i | ||||
\(643\) | −276131. | −0.667872 | −0.333936 | − | 0.942596i | \(-0.608377\pi\) | ||||
−0.333936 | + | 0.942596i | \(0.608377\pi\) | |||||||
\(644\) | − | 85874.2i | − | 0.207057i | ||||||
\(645\) | −33854.2 | − | 147220.i | −0.0813753 | − | 0.353872i | ||||
\(646\) | −807952. | −1.93607 | ||||||||
\(647\) | − | 603278.i | − | 1.44115i | −0.693378 | − | 0.720574i | \(-0.743878\pi\) | ||
0.693378 | − | 0.720574i | \(-0.256122\pi\) | |||||||
\(648\) | −742859. | − | 584536.i | −1.76912 | − | 1.39207i | ||||
\(649\) | 171477. | 0.407114 | ||||||||
\(650\) | 113525.i | 0.268697i | ||||||||
\(651\) | 66929.6 | − | 15390.9i | 0.157927 | − | 0.0363164i | ||||
\(652\) | −288701. | −0.679131 | ||||||||
\(653\) | 625614.i | 1.46717i | 0.679598 | + | 0.733584i | \(0.262154\pi\) | ||||
−0.679598 | + | 0.733584i | \(0.737846\pi\) | |||||||
\(654\) | −13210.2 | − | 57446.4i | −0.0308854 | − | 0.134310i | ||||
\(655\) | 4480.67 | 0.0104438 | ||||||||
\(656\) | 995053.i | 2.31227i | ||||||||
\(657\) | 493152. | − | 239471.i | 1.14248 | − | 0.554781i | ||||
\(658\) | 329529. | 0.761100 | ||||||||
\(659\) | 706201.i | 1.62614i | 0.582167 | + | 0.813069i | \(0.302205\pi\) | ||||
−0.582167 | + | 0.813069i | \(0.697795\pi\) | |||||||
\(660\) | −119928. | + | 27578.3i | −0.275317 | + | 0.0633110i | ||||
\(661\) | −296423. | −0.678437 | −0.339219 | − | 0.940708i | \(-0.610163\pi\) | ||||
−0.339219 | + | 0.940708i | \(0.610163\pi\) | |||||||
\(662\) | − | 516769.i | − | 1.17918i | ||||||
\(663\) | 78277.1 | + | 340399.i | 0.178077 | + | 0.774392i | ||||
\(664\) | −992975. | −2.25218 | ||||||||
\(665\) | 94908.8i | 0.214617i | ||||||||
\(666\) | 18489.1 | + | 38075.4i | 0.0416839 | + | 0.0858414i | ||||
\(667\) | −160041. | −0.359733 | ||||||||
\(668\) | 753782.i | 1.68925i | ||||||||
\(669\) | −496379. | + | 114146.i | −1.10908 | + | 0.255040i | ||||
\(670\) | 342962. | 0.764006 | ||||||||
\(671\) | 25039.1i | 0.0556127i | ||||||||
\(672\) | 48637.9 | + | 211508.i | 0.107705 | + | 0.468370i | ||||
\(673\) | 52622.9 | 0.116184 | 0.0580918 | − | 0.998311i | \(-0.481498\pi\) | ||||
0.0580918 | + | 0.998311i | \(0.481498\pi\) | |||||||
\(674\) | − | 633896.i | − | 1.39540i | ||||||
\(675\) | −70966.0 | + | 57162.8i | −0.155755 | + | 0.125460i | ||||
\(676\) | 456754. | 0.999515 | ||||||||
\(677\) | 341720.i | 0.745578i | 0.927916 | + | 0.372789i | \(0.121599\pi\) | ||||
−0.927916 | + | 0.372789i | \(0.878401\pi\) | |||||||
\(678\) | 217621. | − | 50043.4i | 0.473413 | − | 0.108865i | ||||
\(679\) | −230586. | −0.500143 | ||||||||
\(680\) | 496274.i | 1.07326i | ||||||||
\(681\) | 38354.5 | + | 166790.i | 0.0827032 | + | 0.359646i | ||||
\(682\) | −80118.8 | −0.172253 | ||||||||
\(683\) | − | 247237.i | − | 0.529996i | −0.964249 | − | 0.264998i | \(-0.914629\pi\) | ||
0.964249 | − | 0.264998i | \(-0.0853714\pi\) | |||||||
\(684\) | 953622. | − | 463071.i | 2.03828 | − | 0.989774i | ||||
\(685\) | −327334. | −0.697606 | ||||||||
\(686\) | − | 716379.i | − | 1.52228i | ||||||
\(687\) | −693616. | + | 159502.i | −1.46962 | + | 0.337950i | ||||
\(688\) | 695130. | 1.46855 | ||||||||
\(689\) | − | 373509.i | − | 0.786796i | ||||||
\(690\) | 16625.5 | + | 72298.2i | 0.0349201 | + | 0.151855i | ||||
\(691\) | 471510. | 0.987496 | 0.493748 | − | 0.869605i | \(-0.335627\pi\) | ||||
0.493748 | + | 0.869605i | \(0.335627\pi\) | |||||||
\(692\) | − | 739968.i | − | 1.54526i | ||||||
\(693\) | 28066.0 | + | 57797.6i | 0.0584406 | + | 0.120349i | ||||
\(694\) | −42836.8 | −0.0889401 | ||||||||
\(695\) | − | 20706.5i | − | 0.0428683i | ||||||
\(696\) | 1.97778e6 | − | 454803.i | 4.08280 | − | 0.938869i | ||||
\(697\) | 662097. | 1.36288 | ||||||||
\(698\) | − | 470189.i | − | 0.965076i | ||||||
\(699\) | −73241.5 | − | 318501.i | −0.149900 | − | 0.651863i | ||||
\(700\) | 104974. | 0.214233 | ||||||||
\(701\) | − | 530831.i | − | 1.08024i | −0.841588 | − | 0.540120i | \(-0.818379\pi\) | ||
0.841588 | − | 0.540120i | \(-0.181621\pi\) | |||||||
\(702\) | −415321. | − | 515609.i | −0.842771 | − | 1.04628i | ||||
\(703\) | −26361.9 | −0.0533416 | ||||||||
\(704\) | − | 1393.23i | − | 0.00281111i | ||||||
\(705\) | −192041. | + | 44161.1i | −0.386380 | + | 0.0888508i | ||||
\(706\) | 261146. | 0.523931 | ||||||||
\(707\) | 259522.i | 0.519200i | ||||||||
\(708\) | 366167. | + | 1.59233e6i | 0.730487 | + | 3.17662i | ||||
\(709\) | −938943. | −1.86787 | −0.933936 | − | 0.357441i | \(-0.883649\pi\) | ||||
−0.933936 | + | 0.357441i | \(0.883649\pi\) | |||||||
\(710\) | 105101.i | 0.208493i | ||||||||
\(711\) | −463928. | + | 225280.i | −0.917722 | + | 0.445639i | ||||
\(712\) | −922329. | −1.81939 | ||||||||
\(713\) | 33433.1i | 0.0657653i | ||||||||
\(714\) | 454722. | − | 104566.i | 0.891968 | − | 0.205114i | ||||
\(715\) | −47865.8 | −0.0936296 | ||||||||
\(716\) | − | 1.16568e6i | − | 2.27380i | ||||||
\(717\) | −94361.3 | − | 410343.i | −0.183551 | − | 0.798195i | ||||
\(718\) | −1.10257e6 | −2.13874 | ||||||||
\(719\) | 918433.i | 1.77660i | 0.459263 | + | 0.888300i | \(0.348114\pi\) | ||||
−0.459263 | + | 0.888300i | \(0.651886\pi\) | |||||||
\(720\) | −183166. | − | 377202.i | −0.353330 | − | 0.727628i | ||||
\(721\) | −285796. | −0.549776 | ||||||||
\(722\) | 14234.3i | 0.0273062i | ||||||||
\(723\) | 268802. | − | 61812.8i | 0.514228 | − | 0.118250i | ||||
\(724\) | −649681. | −1.23943 | ||||||||
\(725\) | − | 195637.i | − | 0.372199i | ||||||
\(726\) | 196113. | + | 852826.i | 0.372078 | + | 1.61803i | ||||
\(727\) | −314965. | −0.595928 | −0.297964 | − | 0.954577i | \(-0.596308\pi\) | ||||
−0.297964 | + | 0.954577i | \(0.596308\pi\) | |||||||
\(728\) | 423558.i | 0.799190i | ||||||||
\(729\) | 113190. | − | 519247.i | 0.212987 | − | 0.977055i | ||||
\(730\) | 545574. | 1.02378 | ||||||||
\(731\) | − | 462532.i | − | 0.865580i | ||||||
\(732\) | −232513. | + | 53467.9i | −0.433935 | + | 0.0997863i | ||||
\(733\) | 958567. | 1.78408 | 0.892040 | − | 0.451956i | \(-0.149274\pi\) | ||||
0.892040 | + | 0.451956i | \(0.149274\pi\) | |||||||
\(734\) | 1.03662e6i | 1.92411i | ||||||||
\(735\) | 41860.3 | + | 182035.i | 0.0774868 | + | 0.336962i | ||||
\(736\) | −105654. | −0.195043 | ||||||||
\(737\) | 144604.i | 0.266224i | ||||||||
\(738\) | −1.12896e6 | + | 548213.i | −2.07284 | + | 1.00655i | ||||
\(739\) | 197682. | 0.361976 | 0.180988 | − | 0.983485i | \(-0.442071\pi\) | ||||
0.180988 | + | 0.983485i | \(0.442071\pi\) | |||||||
\(740\) | 29157.7i | 0.0532463i | ||||||||
\(741\) | 401861. | − | 92410.8i | 0.731880 | − | 0.168301i | ||||
\(742\) | −498952. | −0.906255 | ||||||||
\(743\) | 81590.4i | 0.147796i | 0.997266 | + | 0.0738978i | \(0.0235439\pi\) | ||||
−0.997266 | + | 0.0738978i | \(0.976456\pi\) | |||||||
\(744\) | −95009.7 | − | 413163.i | −0.171641 | − | 0.746407i | ||||
\(745\) | 222545. | 0.400964 | ||||||||
\(746\) | 740349.i | 1.33033i | ||||||||
\(747\) | −243859. | − | 502189.i | −0.437016 | − | 0.899965i | ||||
\(748\) | −376788. | −0.673431 | ||||||||
\(749\) | 16542.3i | 0.0294872i | ||||||||
\(750\) | −88378.6 | + | 20323.3i | −0.157118 | + | 0.0361303i | ||||
\(751\) | 132505. | 0.234938 | 0.117469 | − | 0.993077i | \(-0.462522\pi\) | ||||
0.117469 | + | 0.993077i | \(0.462522\pi\) | |||||||
\(752\) | − | 906762.i | − | 1.60346i | ||||||
\(753\) | −231557. | − | 1.00696e6i | −0.408383 | − | 1.77591i | ||||
\(754\) | 1.42142e6 | 2.50022 | ||||||||
\(755\) | 275575.i | 0.483443i | ||||||||
\(756\) | −476775. | + | 384040.i | −0.834199 | + | 0.671943i | ||||
\(757\) | 997153. | 1.74008 | 0.870042 | − | 0.492978i | \(-0.164092\pi\) | ||||
0.870042 | + | 0.492978i | \(0.164092\pi\) | |||||||
\(758\) | − | 1.07174e6i | − | 1.86532i | ||||||
\(759\) | −30483.3 | + | 7009.85i | −0.0529150 | + | 0.0121682i | ||||
\(760\) | 585881. | 1.01434 | ||||||||
\(761\) | − | 316363.i | − | 0.546281i | −0.961974 | − | 0.273140i | \(-0.911938\pi\) | ||
0.961974 | − | 0.273140i | \(-0.0880623\pi\) | |||||||
\(762\) | 416612. | + | 1.81169e6i | 0.717499 | + | 3.12014i | ||||
\(763\) | −21201.2 | −0.0364175 | ||||||||
\(764\) | 421745.i | 0.722542i | ||||||||
\(765\) | −250986. | + | 121877.i | −0.428872 | + | 0.208257i | ||||
\(766\) | −637283. | −1.08611 | ||||||||
\(767\) | 635532.i | 1.08031i | ||||||||
\(768\) | −1.03250e6 | + | 237430.i | −1.75052 | + | 0.402544i | ||||
\(769\) | 584632. | 0.988621 | 0.494311 | − | 0.869285i | \(-0.335421\pi\) | ||||
0.494311 | + | 0.869285i | \(0.335421\pi\) | |||||||
\(770\) | 63941.5i | 0.107845i | ||||||||
\(771\) | 180726. | + | 785913.i | 0.304027 | + | 1.32210i | ||||
\(772\) | 1.01663e6 | 1.70579 | ||||||||
\(773\) | − | 662736.i | − | 1.10913i | −0.832141 | − | 0.554564i | \(-0.812885\pi\) | ||
0.832141 | − | 0.554564i | \(-0.187115\pi\) | |||||||
\(774\) | 382974. | + | 788675.i | 0.639275 | + | 1.31649i | ||||
\(775\) | −40869.2 | −0.0680444 | ||||||||
\(776\) | 1.42343e6i | 2.36381i | ||||||||
\(777\) | 14836.7 | − | 3411.80i | 0.0245751 | − | 0.00565121i | ||||
\(778\) | 775367. | 1.28100 | ||||||||
\(779\) | − | 781646.i | − | 1.28806i | ||||||
\(780\) | −102211. | − | 444480.i | −0.168000 | − | 0.730572i | ||||
\(781\) | −44314.2 | −0.0726509 | ||||||||
\(782\) | 227145.i | 0.371441i | ||||||||
\(783\) | 715723. | + | 888551.i | 1.16740 | + | 1.44930i | ||||
\(784\) | −859520. | −1.39838 | ||||||||
\(785\) | − | 15643.3i | − | 0.0253857i | ||||||
\(786\) | −25343.7 | + | 5827.96i | −0.0410228 | + | 0.00943348i | ||||
\(787\) | −773806. | −1.24935 | −0.624673 | − | 0.780886i | \(-0.714768\pi\) | ||||
−0.624673 | + | 0.780886i | \(0.714768\pi\) | |||||||
\(788\) | − | 1.91831e6i | − | 3.08935i | ||||||
\(789\) | −229718. | − | 998959.i | −0.369012 | − | 1.60470i | ||||
\(790\) | −513244. | −0.822374 | ||||||||
\(791\) | − | 80315.0i | − | 0.128364i | ||||||
\(792\) | 356790. | − | 173254.i | 0.568804 | − | 0.276207i | ||||
\(793\) | −92800.7 | −0.147572 | ||||||||
\(794\) | − | 946246.i | − | 1.50094i | ||||||
\(795\) | 290776. | − | 66865.9i | 0.460070 | − | 0.105796i | ||||
\(796\) | −1.81584e6 | −2.86584 | ||||||||
\(797\) | 481401.i | 0.757863i | 0.925425 | + | 0.378932i | \(0.123708\pi\) | ||||
−0.925425 | + | 0.378932i | \(0.876292\pi\) | |||||||
\(798\) | −123447. | − | 536826.i | −0.193854 | − | 0.843001i | ||||
\(799\) | −603350. | −0.945096 | ||||||||
\(800\) | − | 129153.i | − | 0.201802i | ||||||
\(801\) | −226509. | − | 466460.i | −0.353038 | − | 0.727025i | ||||
\(802\) | −154869. | −0.240777 | ||||||||
\(803\) | 230032.i | 0.356745i | ||||||||
\(804\) | −1.34279e6 | + | 308784.i | −2.07729 | + | 0.477686i | ||||
\(805\) | 26682.4 | 0.0411749 | ||||||||
\(806\) | − | 296938.i | − | 0.457084i | ||||||
\(807\) | 79130.4 | + | 344109.i | 0.121506 | + | 0.528384i | ||||
\(808\) | 1.60205e6 | 2.45389 | ||||||||
\(809\) | 391432.i | 0.598081i | 0.954240 | + | 0.299040i | \(0.0966665\pi\) | ||||
−0.954240 | + | 0.299040i | \(0.903333\pi\) | |||||||
\(810\) | 327049. | − | 415631.i | 0.498475 | − | 0.633487i | ||||
\(811\) | 1.15536e6 | 1.75661 | 0.878305 | − | 0.478101i | \(-0.158675\pi\) | ||||
0.878305 | + | 0.478101i | \(0.158675\pi\) | |||||||
\(812\) | − | 1.31436e6i | − | 1.99343i | ||||||
\(813\) | 460916. | − | 105991.i | 0.697333 | − | 0.160357i | ||||
\(814\) | −17760.4 | −0.0268043 | ||||||||
\(815\) | − | 89703.7i | − | 0.135050i | ||||||
\(816\) | −287735. | − | 1.25125e6i | −0.432127 | − | 1.87917i | ||||
\(817\) | −546047. | −0.818061 | ||||||||
\(818\) | 856694.i | 1.28032i | ||||||||
\(819\) | −214211. | + | 104019.i | −0.319355 | + | 0.155076i | ||||
\(820\) | −864542. | −1.28576 | ||||||||
\(821\) | 299979.i | 0.445045i | 0.974928 | + | 0.222522i | \(0.0714291\pi\) | ||||
−0.974928 | + | 0.222522i | \(0.928571\pi\) | |||||||
\(822\) | 1.85148e6 | − | 425760.i | 2.74015 | − | 0.630118i | ||||
\(823\) | 32530.4 | 0.0480275 | 0.0240138 | − | 0.999712i | \(-0.492355\pi\) | ||||
0.0240138 | + | 0.999712i | \(0.492355\pi\) | |||||||
\(824\) | 1.76425e6i | 2.59839i | ||||||||
\(825\) | −8568.97 | − | 37263.4i | −0.0125899 | − | 0.0547488i | ||||
\(826\) | 848975. | 1.24433 | ||||||||
\(827\) | 764819.i | 1.11827i | 0.829076 | + | 0.559136i | \(0.188867\pi\) | ||||
−0.829076 | + | 0.559136i | \(0.811133\pi\) | |||||||
\(828\) | −130186. | − | 268098.i | −0.189891 | − | 0.391051i | ||||
\(829\) | −137003. | −0.199352 | −0.0996758 | − | 0.995020i | \(-0.531781\pi\) | ||||
−0.0996758 | + | 0.995020i | \(0.531781\pi\) | |||||||
\(830\) | − | 555572.i | − | 0.806462i | ||||||
\(831\) | −251794. | + | 57901.8i | −0.364622 | + | 0.0838475i | ||||
\(832\) | 5163.63 | 0.00745947 | ||||||||
\(833\) | 571916.i | 0.824218i | ||||||||
\(834\) | 26932.7 | + | 117121.i | 0.0387211 | + | 0.168384i | ||||
\(835\) | −234211. | −0.335919 | ||||||||
\(836\) | 444820.i | 0.636461i | ||||||||
\(837\) | 185621. | − | 149517.i | 0.264957 | − | 0.213422i | ||||
\(838\) | −691757. | −0.985066 | ||||||||
\(839\) | − | 1.12228e6i | − | 1.59433i | −0.603759 | − | 0.797167i | \(-0.706331\pi\) | ||
0.603759 | − | 0.797167i | \(-0.293669\pi\) | |||||||
\(840\) | −329739. | + | 75825.7i | −0.467317 | + | 0.107463i | ||||
\(841\) | −1.74225e6 | −2.46331 | ||||||||
\(842\) | 532222.i | 0.750704i | ||||||||
\(843\) | −168492. | − | 732711.i | −0.237096 | − | 1.03105i | ||||
\(844\) | 2.42267e6 | 3.40103 | ||||||||
\(845\) | 141920.i | 0.198761i | ||||||||
\(846\) | 1.02879e6 | − | 499571.i | 1.43742 | − | 0.698001i | ||||
\(847\) | 314744. | 0.438723 | ||||||||
\(848\) | 1.37296e6i | 1.90927i | ||||||||
\(849\) | 1.11146e6 | − | 255589.i | 1.54199 | − | 0.354590i | ||||
\(850\) | −277666. | −0.384313 | ||||||||
\(851\) | 7411.31i | 0.0102338i | ||||||||
\(852\) | −94627.3 | − | 411500.i | −0.130358 | − | 0.566879i | ||||
\(853\) | 43550.6 | 0.0598544 | 0.0299272 | − | 0.999552i | \(-0.490472\pi\) | ||||
0.0299272 | + | 0.999552i | \(0.490472\pi\) | |||||||
\(854\) | 123968.i | 0.169978i | ||||||||
\(855\) | 143883. | + | 296304.i | 0.196824 | + | 0.405327i | ||||
\(856\) | 102118. | 0.139365 | ||||||||
\(857\) | 300075.i | 0.408572i | 0.978911 | + | 0.204286i | \(0.0654872\pi\) | ||||
−0.978911 | + | 0.204286i | \(0.934513\pi\) | |||||||
\(858\) | 270740. | − | 62258.6i | 0.367771 | − | 0.0845716i | ||||
\(859\) | −498647. | −0.675782 | −0.337891 | − | 0.941185i | \(-0.609713\pi\) | ||||
−0.337891 | + | 0.941185i | \(0.609713\pi\) | |||||||
\(860\) | 603957.i | 0.816599i | ||||||||
\(861\) | 101162. | + | 439916.i | 0.136462 | + | 0.593422i | ||||
\(862\) | −776744. | −1.04535 | ||||||||
\(863\) | − | 13487.9i | − | 0.0181102i | −0.999959 | − | 0.00905512i | \(-0.997118\pi\) | ||
0.999959 | − | 0.00905512i | \(-0.00288237\pi\) | |||||||
\(864\) | 472497. | + | 586592.i | 0.632953 | + | 0.785794i | ||||
\(865\) | 229919. | 0.307286 | ||||||||
\(866\) | − | 827252.i | − | 1.10307i | ||||||
\(867\) | −100002. | + | 22996.1i | −0.133036 | + | 0.0305926i | ||||
\(868\) | −274573. | −0.364434 | ||||||||
\(869\) | − | 216401.i | − | 0.286562i | ||||||
\(870\) | 254463. | + | 1.10657e6i | 0.336192 | + | 1.46198i | ||||
\(871\) | −535936. | −0.706443 | ||||||||
\(872\) | 130877.i | 0.172119i | ||||||||
\(873\) | −719888. | + | 349572.i | −0.944575 | + | 0.458678i | ||||
\(874\) | 268158. | 0.351050 | ||||||||
\(875\) | 32617.0i | 0.0426018i | ||||||||
\(876\) | −2.13607e6 | + | 491205.i | −2.78360 | + | 0.640109i | ||||
\(877\) | −944732. | −1.22831 | −0.614157 | − | 0.789184i | \(-0.710504\pi\) | ||||
−0.614157 | + | 0.789184i | \(0.710504\pi\) | |||||||
\(878\) | 1.85720e6i | 2.40919i | ||||||||
\(879\) | 139948. | + | 608582.i | 0.181129 | + | 0.787664i | ||||
\(880\) | 175947. | 0.227205 | ||||||||
\(881\) | − | 1.28495e6i | − | 1.65552i | −0.561082 | − | 0.827760i | \(-0.689615\pi\) | ||
0.561082 | − | 0.827760i | \(-0.310385\pi\) | |||||||
\(882\) | −473543. | − | 975187.i | −0.608727 | − | 1.25358i | ||||
\(883\) | −1.22382e6 | −1.56963 | −0.784815 | − | 0.619731i | \(-0.787242\pi\) | ||||
−0.784815 | + | 0.619731i | \(0.787242\pi\) | |||||||
\(884\) | − | 1.39646e6i | − | 1.78700i | ||||||
\(885\) | −494760. | + | 113773.i | −0.631695 | + | 0.145263i | ||||
\(886\) | −254946. | −0.324774 | ||||||||
\(887\) | − | 755435.i | − | 0.960173i | −0.877221 | − | 0.480087i | \(-0.840605\pi\) | ||
0.877221 | − | 0.480087i | \(-0.159395\pi\) | |||||||
\(888\) | −21061.4 | − | 91588.4i | −0.0267092 | − | 0.116149i | ||||
\(889\) | 668624. | 0.846015 | ||||||||
\(890\) | − | 516045.i | − | 0.651490i | ||||||
\(891\) | 175244. | + | 137895.i | 0.220743 | + | 0.173697i | ||||
\(892\) | 2.03636e6 | 2.55932 | ||||||||
\(893\) | 712291.i | 0.893212i | ||||||||
\(894\) | −1.25877e6 | + | 289462.i | −1.57496 | + | 0.362173i | ||||
\(895\) | 362193. | 0.452162 | ||||||||
\(896\) | 378931.i | 0.472002i | ||||||||
\(897\) | −25980.1 | − | 112978.i | −0.0322891 | − | 0.140414i | ||||
\(898\) | −59342.8 | −0.0735894 | ||||||||
\(899\) | 511714.i | 0.633152i | ||||||||
\(900\) | 327729. | − | 159142.i | 0.404603 | − | 0.196472i | ||||
\(901\) | 913553. | 1.12534 | ||||||||
\(902\) | − | 526607.i | − | 0.647252i | ||||||
\(903\) | 307319. | − | 70670.2i | 0.376890 | − | 0.0866685i | ||||
\(904\) | −495793. | −0.606685 | ||||||||
\(905\) | − | 201866.i | − | 0.246471i | ||||||
\(906\) | −358437. | − | 1.55871e6i | −0.436674 | − | 1.89894i | ||||
\(907\) | 1.28653e6 | 1.56389 | 0.781946 | − | 0.623346i | \(-0.214227\pi\) | ||||
0.781946 | + | 0.623346i | \(0.214227\pi\) | |||||||
\(908\) | − | 684242.i | − | 0.829924i | ||||||
\(909\) | 393439. | + | 810225.i | 0.476156 | + | 0.980568i | ||||
\(910\) | −236982. | −0.286175 | ||||||||
\(911\) | 501962.i | 0.604831i | 0.953176 | + | 0.302416i | \(0.0977931\pi\) | ||||
−0.953176 | + | 0.302416i | \(0.902207\pi\) | |||||||
\(912\) | −1.47718e6 | + | 339688.i | −1.77600 | + | 0.408404i | ||||
\(913\) | 234248. | 0.281018 | ||||||||
\(914\) | − | 1.30254e6i | − | 1.55919i | ||||||
\(915\) | −16613.3 | − | 72245.1i | −0.0198432 | − | 0.0862911i | ||||
\(916\) | 2.84551e6 | 3.39132 | ||||||||
\(917\) | 9353.35i | 0.0111232i | ||||||||
\(918\) | 1.26111e6 | − | 1.01582e6i | 1.49647 | − | 1.20540i | ||||
\(919\) | −252142. | −0.298548 | −0.149274 | − | 0.988796i | \(-0.547694\pi\) | ||||
−0.149274 | + | 0.988796i | \(0.547694\pi\) | |||||||
\(920\) | − | 164713.i | − | 0.194604i | ||||||
\(921\) | 560933. | − | 128990.i | 0.661289 | − | 0.152068i | ||||
\(922\) | 251452. | 0.295797 | ||||||||
\(923\) | − | 164238.i | − | 0.192784i | ||||||
\(924\) | −57569.4 | − | 250348.i | −0.0674291 | − | 0.293225i | ||||
\(925\) | −9059.72 | −0.0105884 | ||||||||
\(926\) | − | 1.48539e6i | − | 1.73228i | ||||||
\(927\) | −892253. | + | 433271.i | −1.03831 | + | 0.504197i | ||||
\(928\) | −1.61710e6 | −1.87776 | ||||||||
\(929\) | 1.28900e6i | 1.49356i | 0.665074 | + | 0.746778i | \(0.268400\pi\) | ||||
−0.665074 | + | 0.746778i | \(0.731600\pi\) | |||||||
\(930\) | 231166. | − | 53158.2i | 0.267274 | − | 0.0614616i | ||||
\(931\) | 675181. | 0.778970 | ||||||||
\(932\) | 1.30662e6i | 1.50425i | ||||||||
\(933\) | 37932.1 | + | 164953.i | 0.0435757 | + | 0.189495i | ||||
\(934\) | −1.98104e6 | −2.27090 | ||||||||
\(935\) | − | 117073.i | − | 0.133917i | ||||||
\(936\) | 642120. | + | 1.32234e6i | 0.732933 | + | 1.50936i | ||||
\(937\) | 596815. | 0.679768 | 0.339884 | − | 0.940467i | \(-0.389612\pi\) | ||||
0.339884 | + | 0.940467i | \(0.389612\pi\) | |||||||
\(938\) | 715930.i | 0.813701i | ||||||||
\(939\) | 550351. | − | 126557.i | 0.624178 | − | 0.143534i | ||||
\(940\) | 787832. | 0.891616 | ||||||||
\(941\) | 1.55891e6i | 1.76052i | 0.474493 | + | 0.880259i | \(0.342631\pi\) | ||||
−0.474493 | + | 0.880259i | \(0.657369\pi\) | |||||||
\(942\) | 20347.1 | + | 88482.2i | 0.0229298 | + | 0.0997136i | ||||
\(943\) | −219749. | −0.247118 | ||||||||
\(944\) | − | 2.33612e6i | − | 2.62150i | ||||||
\(945\) | −119327. | − | 148141.i | −0.133621 | − | 0.165887i | ||||
\(946\) | −367880. | −0.411078 | ||||||||
\(947\) | − | 226143.i | − | 0.252164i | −0.992020 | − | 0.126082i | \(-0.959760\pi\) | ||
0.992020 | − | 0.126082i | \(-0.0402402\pi\) | |||||||
\(948\) | 2.00949e6 | − | 462096.i | 2.23599 | − | 0.514180i | ||||
\(949\) | −852551. | −0.946647 | ||||||||
\(950\) | 327802.i | 0.363215i | ||||||||
\(951\) | −188440. | − | 819459.i | −0.208359 | − | 0.906080i | ||||
\(952\) | −1.03597e6 | −1.14307 | ||||||||
\(953\) | − | 1.71407e6i | − | 1.88731i | −0.330927 | − | 0.943656i | \(-0.607361\pi\) | ||
0.330927 | − | 0.943656i | \(-0.392639\pi\) | |||||||
\(954\) | −1.55772e6 | + | 756418.i | −1.71156 | + | 0.831122i | ||||
\(955\) | −131042. | −0.143683 | ||||||||
\(956\) | 1.68340e6i | 1.84192i | ||||||||
\(957\) | −466567. | + | 107290.i | −0.509436 | + | 0.117148i | ||||
\(958\) | 1.16051e6 | 1.26449 | ||||||||
\(959\) | − | 683307.i | − | 0.742982i | ||||||
\(960\) | 924.397 | + | 4019.87i | 0.00100303 | + | 0.00436184i | ||||
\(961\) | −816622. | −0.884249 | ||||||||
\(962\) | − | 65824.1i | − | 0.0711271i | ||||||
\(963\) | 25078.4 | + | 51645.1i | 0.0270426 | + | 0.0556899i | ||||
\(964\) | −1.10274e6 | −1.18664 | ||||||||
\(965\) | 315880.i | 0.339210i | ||||||||
\(966\) | −150922. | + | 34705.5i | −0.161733 | + | 0.0371915i | ||||
\(967\) | 1.48328e6 | 1.58625 | 0.793123 | − | 0.609061i | \(-0.208454\pi\) | ||||
0.793123 | + | 0.609061i | \(0.208454\pi\) | |||||||
\(968\) | − | 1.94295e6i | − | 2.07353i | ||||||
\(969\) | 226025. | + | 982900.i | 0.240718 | + | 1.04680i | ||||
\(970\) | −796413. | −0.846438 | ||||||||
\(971\) | 25773.5i | 0.0273360i | 0.999907 | + | 0.0136680i | \(0.00435080\pi\) | ||||
−0.999907 | + | 0.0136680i | \(0.995649\pi\) | |||||||
\(972\) | −906277. | + | 1.92177e6i | −0.959242 | + | 2.03408i | ||||
\(973\) | 43224.5 | 0.0456567 | ||||||||
\(974\) | − | 503449.i | − | 0.530686i | ||||||
\(975\) | 138106. | − | 31758.5i | 0.145280 | − | 0.0334081i | ||||
\(976\) | 341121. | 0.358104 | ||||||||
\(977\) | − | 1.63957e6i | − | 1.71767i | −0.512249 | − | 0.858837i | \(-0.671187\pi\) | ||
0.512249 | − | 0.858837i | \(-0.328813\pi\) | |||||||
\(978\) | 116677. | + | 507385.i | 0.121985 | + | 0.530469i | ||||
\(979\) | 217582. | 0.227016 | ||||||||
\(980\) | − | 746786.i | − | 0.777578i | ||||||
\(981\) | −66189.9 | + | 32141.3i | −0.0687786 | + | 0.0333984i | ||||
\(982\) | −3.10670e6 | −3.22163 | ||||||||
\(983\) | − | 1.02737e6i | − | 1.06322i | −0.846991 | − | 0.531608i | \(-0.821588\pi\) | ||
0.846991 | − | 0.531608i | \(-0.178412\pi\) | |||||||
\(984\) | 2.71565e6 | − | 624482.i | 2.80468 | − | 0.644955i | ||||
\(985\) | 596047. | 0.614339 | ||||||||
\(986\) | 3.47660e6i | 3.57603i | ||||||||
\(987\) | −92185.8 | − | 400883.i | −0.0946302 | − | 0.411513i | ||||
\(988\) | −1.64860e6 | −1.68889 | ||||||||
\(989\) | 153514.i | 0.156948i | ||||||||
\(990\) | 96936.2 | + | 199625.i | 0.0989044 | + | 0.203678i | ||||
\(991\) | 101778. | 0.103635 | 0.0518174 | − | 0.998657i | \(-0.483499\pi\) | ||||
0.0518174 | + | 0.998657i | \(0.483499\pi\) | |||||||
\(992\) | 337817.i | 0.343288i | ||||||||
\(993\) | −628667. | + | 144566.i | −0.637562 | + | 0.146612i | ||||
\(994\) | −219398. | −0.222054 | ||||||||
\(995\) | − | 564210.i | − | 0.569894i | ||||||
\(996\) | 500206. | + | 2.17521e6i | 0.504232 | + | 2.19272i | ||||
\(997\) | −466189. | −0.468999 | −0.234499 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234499 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(998\) | 2.03948e6i | 2.04766i | ||||||||
\(999\) | 41147.7 | − | 33144.3i | 0.0412301 | − | 0.0332106i |
(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 | 15.5.c.a.11.6 | yes | 6 | |
3.2 | odd | 2 | inner | 15.5.c.a.11.1 | ✓ | 6 | |
4.3 | odd | 2 | 240.5.l.d.161.2 | 6 | |||
5.2 | odd | 4 | 75.5.d.d.74.1 | 12 | |||
5.3 | odd | 4 | 75.5.d.d.74.12 | 12 | |||
5.4 | even | 2 | 75.5.c.i.26.1 | 6 | |||
12.11 | even | 2 | 240.5.l.d.161.1 | 6 | |||
15.2 | even | 4 | 75.5.d.d.74.11 | 12 | |||
15.8 | even | 4 | 75.5.d.d.74.2 | 12 | |||
15.14 | odd | 2 | 75.5.c.i.26.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.5.c.a.11.1 | ✓ | 6 | 3.2 | odd | 2 | inner | |
15.5.c.a.11.6 | yes | 6 | 1.1 | even | 1 | trivial | |
75.5.c.i.26.1 | 6 | 5.4 | even | 2 | |||
75.5.c.i.26.6 | 6 | 15.14 | odd | 2 | |||
75.5.d.d.74.1 | 12 | 5.2 | odd | 4 | |||
75.5.d.d.74.2 | 12 | 15.8 | even | 4 | |||
75.5.d.d.74.11 | 12 | 15.2 | even | 4 | |||
75.5.d.d.74.12 | 12 | 5.3 | odd | 4 | |||
240.5.l.d.161.1 | 6 | 12.11 | even | 2 | |||
240.5.l.d.161.2 | 6 | 4.3 | odd | 2 |