Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 33.6 | ||
Character | \(\chi\) | \(=\) | 76.33 |
Dual form | 76.5.j.a.53.6 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{7}{18}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 7.48759 | + | 1.32026i | 0.831955 | + | 0.146696i | 0.573374 | − | 0.819294i | \(-0.305634\pi\) |
0.258581 | + | 0.965990i | \(0.416745\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −18.9121 | − | 15.8691i | −0.756484 | − | 0.634765i | 0.180725 | − | 0.983534i | \(-0.442156\pi\) |
−0.937209 | + | 0.348768i | \(0.886600\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −39.3870 | − | 68.2202i | −0.803816 | − | 1.39225i | −0.917088 | − | 0.398686i | \(-0.869466\pi\) |
0.113272 | − | 0.993564i | \(-0.463867\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −21.7942 | − | 7.93242i | −0.269064 | − | 0.0979312i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.6645 | − | 35.7920i | 0.170781 | − | 0.295802i | −0.767912 | − | 0.640555i | \(-0.778704\pi\) |
0.938693 | + | 0.344753i | \(0.112037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 132.868 | − | 23.4283i | 0.786203 | − | 0.138629i | 0.233887 | − | 0.972264i | \(-0.424855\pi\) |
0.552316 | + | 0.833635i | \(0.313744\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −120.655 | − | 143.791i | −0.536243 | − | 0.639069i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 120.095 | − | 43.7109i | 0.415553 | − | 0.151249i | −0.125778 | − | 0.992058i | \(-0.540143\pi\) |
0.541331 | + | 0.840809i | \(0.317921\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −321.938 | + | 163.330i | −0.891795 | + | 0.452439i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −204.845 | − | 562.806i | −0.464501 | − | 1.27621i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 360.226 | − | 302.265i | 0.680956 | − | 0.571390i | −0.235330 | − | 0.971916i | \(-0.575617\pi\) |
0.916285 | + | 0.400526i | \(0.131173\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.69215 | − | 15.2679i | −0.00430744 | − | 0.0244287i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −686.056 | − | 396.094i | −0.941091 | − | 0.543339i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.3762 | − | 42.2458i | 0.0182833 | − | 0.0502328i | −0.930215 | − | 0.367014i | \(-0.880380\pi\) |
0.948499 | + | 0.316782i | \(0.102602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 469.811 | − | 271.246i | 0.488877 | − | 0.282254i | −0.235231 | − | 0.971939i | \(-0.575585\pi\) |
0.724109 | + | 0.689686i | \(0.242251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 201.983 | − | 240.714i | 0.185475 | − | 0.221041i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −337.706 | + | 1915.22i | −0.275678 | + | 1.56345i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1450.25i | 1.05935i | 0.848201 | + | 0.529675i | \(0.177686\pi\) | ||||
−0.848201 | + | 0.529675i | \(0.822314\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1025.80 | 0.674422 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1484.76 | − | 261.803i | −0.883258 | − | 0.155742i | −0.286420 | − | 0.958104i | \(-0.592465\pi\) |
−0.596838 | + | 0.802362i | \(0.703576\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2135.35 | + | 1791.77i | 1.15487 | + | 0.969051i | 0.999822 | − | 0.0188565i | \(-0.00600256\pi\) |
0.155047 | + | 0.987907i | \(0.450447\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 286.292 | + | 495.873i | 0.141379 | + | 0.244876i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3369.92 | + | 1226.55i | 1.52554 | + | 0.555251i | 0.962524 | − | 0.271195i | \(-0.0874189\pi\) |
0.563016 | + | 0.826446i | \(0.309641\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1902.17 | + | 3294.65i | −0.792239 | + | 1.37220i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 956.931 | − | 168.733i | 0.367909 | − | 0.0648723i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3048.52 | − | 3633.09i | −1.08527 | − | 1.29337i | −0.953268 | − | 0.302126i | \(-0.902304\pi\) |
−0.132002 | − | 0.991249i | \(-0.542141\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −958.798 | + | 348.974i | −0.316958 | + | 0.115363i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2626.18 | + | 797.908i | −0.808304 | + | 0.245586i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −165.867 | − | 455.717i | −0.0476494 | − | 0.130916i | 0.913585 | − | 0.406647i | \(-0.133302\pi\) |
−0.961235 | + | 0.275732i | \(0.911080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4390.65 | − | 3684.20i | 1.17997 | − | 0.990109i | 0.179987 | − | 0.983669i | \(-0.442395\pi\) |
0.999979 | − | 0.00643989i | \(-0.00204990\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 317.254 | + | 1799.24i | 0.0799330 | + | 0.453322i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2884.61 | − | 1665.43i | −0.682747 | − | 0.394184i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1803.52 | + | 4955.13i | −0.401764 | + | 1.10384i | 0.559649 | + | 0.828730i | \(0.310936\pi\) |
−0.961413 | + | 0.275109i | \(0.911286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3096.29 | − | 1787.65i | 0.650345 | − | 0.375477i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4213.11 | − | 5020.99i | 0.835769 | − | 0.996031i | −0.164185 | − | 0.986430i | \(-0.552499\pi\) |
0.999954 | − | 0.00960122i | \(-0.00305621\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 746.251 | − | 4232.20i | 0.140036 | − | 0.794182i | −0.831184 | − | 0.555997i | \(-0.812336\pi\) |
0.971220 | − | 0.238185i | \(-0.0765524\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 117.875i | − | 0.0209555i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3255.66 | −0.549107 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2534.46 | − | 446.894i | −0.406099 | − | 0.0716062i | −0.0331324 | − | 0.999451i | \(-0.510548\pi\) |
−0.372967 | + | 0.927845i | \(0.621659\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3174.85 | − | 2664.01i | −0.483897 | − | 0.406038i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 424.803 | + | 735.780i | 0.0616640 | + | 0.106805i | 0.895209 | − | 0.445646i | \(-0.147026\pi\) |
−0.833545 | + | 0.552451i | \(0.813693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2964.90 | − | 1079.13i | −0.410367 | − | 0.149361i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 170.906 | − | 296.019i | 0.0225798 | − | 0.0391094i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2584.79 | + | 455.768i | −0.326321 | + | 0.0575393i | −0.334409 | − | 0.942428i | \(-0.608537\pi\) |
0.00808769 | + | 0.999967i | \(0.497426\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6831.56 | − | 8141.54i | −0.824969 | − | 0.983159i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3875.87 | − | 1410.70i | 0.448129 | − | 0.163106i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8680.44 | + | 2019.96i | 0.961821 | + | 0.223818i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1831.36 | − | 5031.61i | −0.194639 | − | 0.534766i | 0.803529 | − | 0.595265i | \(-0.202953\pi\) |
−0.998168 | + | 0.0604994i | \(0.980731\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −734.284 | + | 616.138i | −0.0749193 | + | 0.0628648i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −520.903 | − | 2954.19i | −0.0510639 | − | 0.289598i | 0.948573 | − | 0.316560i | \(-0.102528\pi\) |
−0.999636 | + | 0.0269621i | \(0.991417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10090.0 | + | 5825.48i | 0.951081 | + | 0.549107i | 0.893417 | − | 0.449229i | \(-0.148301\pi\) |
0.0576645 | + | 0.998336i | \(0.481635\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5057.21 | + | 13894.6i | −0.458703 | + | 1.26028i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17390.7 | − | 10040.5i | 1.51897 | − | 0.876977i | 0.519218 | − | 0.854642i | \(-0.326223\pi\) |
0.999751 | − | 0.0223345i | \(-0.00710988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5451.03 | + | 6496.28i | −0.458802 | + | 0.546779i | −0.945000 | − | 0.327070i | \(-0.893939\pi\) |
0.486198 | + | 0.873849i | \(0.338383\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1914.71 | + | 10858.9i | −0.155403 | + | 0.881331i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 17452.2i | − | 1.36677i | −0.730060 | − | 0.683383i | \(-0.760508\pi\) | ||
0.730060 | − | 0.683383i | \(-0.239492\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11609.3 | −0.877830 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3081.60 | − | 543.369i | −0.225115 | − | 0.0396938i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7712.14 | − | 6471.25i | −0.544604 | − | 0.456977i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6466.45 | + | 11200.2i | 0.441667 | + | 0.764990i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10771.6 | − | 3920.54i | −0.711984 | − | 0.259141i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7906.37 | + | 13694.2i | −0.506008 | + | 0.876431i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9694.89 | + | 1709.47i | −0.601084 | + | 0.105987i | −0.465906 | − | 0.884834i | \(-0.654272\pi\) |
−0.135178 | + | 0.990821i | \(0.543161\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13623.0 | + | 16235.3i | 0.818643 | + | 0.975621i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6197.68 | − | 2255.77i | 0.361149 | − | 0.131448i | −0.155071 | − | 0.987903i | \(-0.549561\pi\) |
0.516221 | + | 0.856456i | \(0.327338\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 23822.6 | + | 15529.6i | 1.34675 | + | 0.877924i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6689.07 | + | 18378.1i | 0.367027 | + | 1.00840i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8187.49 | − | 6870.12i | 0.436224 | − | 0.366035i | −0.398070 | − | 0.917355i | \(-0.630320\pi\) |
0.834294 | + | 0.551320i | \(0.185875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3216.04 | + | 18239.1i | 0.166453 | + | 0.944002i | 0.947554 | + | 0.319597i | \(0.103547\pi\) |
−0.781101 | + | 0.624405i | \(0.785341\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23613.2 | + | 13633.1i | 1.18773 | + | 0.685735i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1907.12 | − | 5239.77i | 0.0932622 | − | 0.256236i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −961.200 | + | 554.949i | −0.0457170 | + | 0.0263947i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −18592.5 | + | 22157.6i | −0.860403 | + | 1.02539i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6952.63 | − | 39430.3i | 0.313167 | − | 1.77606i | −0.269150 | − | 0.963098i | \(-0.586743\pi\) |
0.582317 | − | 0.812962i | \(-0.302146\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13836.8i | 0.606853i | 0.952855 | + | 0.303426i | \(0.0981306\pi\) | ||||
−0.952855 | + | 0.303426i | \(0.901869\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2964.10 | −0.126622 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13189.5 | − | 2325.67i | −0.548993 | − | 0.0968022i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17234.5 | + | 14461.4i | 0.699196 | + | 0.586695i | 0.921545 | − | 0.388272i | \(-0.126928\pi\) |
−0.222349 | + | 0.974967i | \(0.571372\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18029.5 | − | 31228.0i | −0.713163 | − | 1.23523i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −34808.8 | − | 12669.4i | −1.34288 | − | 0.488768i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13640.6 | − | 23626.2i | 0.513403 | − | 0.889240i | −0.486476 | − | 0.873694i | \(-0.661718\pi\) |
0.999879 | − | 0.0155464i | \(-0.00494877\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7639.83 | + | 1347.11i | −0.280618 | + | 0.0494806i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −34444.7 | − | 41049.6i | −1.23506 | − | 1.47189i | −0.830154 | − | 0.557535i | \(-0.811747\pi\) |
−0.404910 | − | 0.914357i | \(-0.632697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9733.44 | + | 3542.68i | −0.340795 | + | 0.124039i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8311.98 | − | 1005.90i | 0.284258 | − | 0.0344003i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2130.96 | − | 5854.77i | −0.0712006 | − | 0.195622i | 0.898988 | − | 0.437973i | \(-0.144304\pi\) |
−0.970189 | + | 0.242351i | \(0.922081\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −935.547 | + | 785.017i | −0.0305485 | + | 0.0256332i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −640.281 | − | 3631.21i | −0.0204373 | − | 0.115906i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5998.31 | − | 3463.13i | −0.187207 | − | 0.108084i | 0.403467 | − | 0.914994i | \(-0.367805\pi\) |
−0.590675 | + | 0.806910i | \(0.701138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8398.82 | − | 23075.6i | 0.256367 | − | 0.704361i | −0.743018 | − | 0.669272i | \(-0.766606\pi\) |
0.999384 | − | 0.0350894i | \(-0.0111716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 37739.5 | − | 21788.9i | 1.12692 | − | 0.650629i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23014.2 | − | 27427.3i | 0.672439 | − | 0.801381i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 917.201 | − | 5201.71i | 0.0262290 | − | 0.148752i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 62403.8i | 1.74698i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 45795.4 | 1.25532 | 0.627661 | − | 0.778487i | \(-0.284012\pi\) | ||||
0.627661 | + | 0.778487i | \(0.284012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −38103.8 | − | 6718.72i | −1.02295 | − | 0.180373i | −0.363082 | − | 0.931757i | \(-0.618275\pi\) |
−0.659865 | + | 0.751384i | \(0.729387\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19399.9 | − | 16278.5i | −0.510189 | − | 0.428100i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14114.3 | − | 24446.7i | −0.363687 | − | 0.629924i | 0.624878 | − | 0.780722i | \(-0.285149\pi\) |
−0.988564 | + | 0.150799i | \(0.951815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21991.3 | − | 8004.19i | −0.555322 | − | 0.202121i | 0.0490873 | − | 0.998794i | \(-0.484369\pi\) |
−0.604410 | + | 0.796674i | \(0.706591\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20046.1 | + | 34720.9i | −0.496179 | + | 0.859407i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3487.64 | + | 614.965i | −0.0846330 | + | 0.0149231i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23925.3 | + | 28513.0i | 0.569310 | + | 0.678478i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10248.5 | + | 3730.15i | −0.239177 | + | 0.0870534i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −806.775 | + | 14898.0i | −0.0184697 | + | 0.341063i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15192.6 | + | 41741.4i | 0.341246 | + | 0.937566i | 0.985034 | + | 0.172362i | \(0.0551398\pi\) |
−0.643788 | + | 0.765204i | \(0.722638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 38175.1 | − | 32032.7i | 0.841436 | − | 0.706049i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11950.1 | − | 67772.4i | −0.258520 | − | 1.46614i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37008.9 | − | 21367.1i | −0.785935 | − | 0.453760i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11175.2 | − | 30703.7i | 0.233007 | − | 0.640181i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14932.7 | − | 8621.42i | 0.305742 | − | 0.176520i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −41501.0 | + | 49459.0i | −0.834544 | + | 0.994570i | 0.165422 | + | 0.986223i | \(0.447102\pi\) |
−0.999965 | + | 0.00834740i | \(0.997343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −62.4387 | + | 354.107i | −0.00123336 | + | 0.00699471i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 89792.7i | 1.74257i | 0.490780 | + | 0.871284i | \(0.336712\pi\) | ||||
−0.490780 | + | 0.871284i | \(0.663288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 77612.5 | 1.48000 | 0.739999 | − | 0.672608i | \(-0.234826\pi\) | ||||
0.739999 | + | 0.672608i | \(0.234826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24377.0 | − | 4298.33i | −0.456832 | − | 0.0805518i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 73056.6 | + | 61301.8i | 1.34570 | + | 1.12918i | 0.980122 | + | 0.198394i | \(0.0635724\pi\) |
0.365576 | + | 0.930781i | \(0.380872\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −44267.9 | − | 76674.3i | −0.801592 | − | 1.38840i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18387.0 | − | 6692.33i | −0.327352 | − | 0.119146i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13947.0 | + | 24156.9i | −0.244166 | + | 0.422907i | −0.961897 | − | 0.273413i | \(-0.911847\pi\) |
0.717731 | + | 0.696320i | \(0.245181\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −55198.3 | + | 9732.94i | −0.950367 | + | 0.167575i | −0.627280 | − | 0.778794i | \(-0.715832\pi\) |
−0.323087 | + | 0.946369i | \(0.604721\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20991.2 | + | 25016.3i | 0.355487 | + | 0.423653i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 88257.2 | − | 32123.0i | 1.47034 | − | 0.535160i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −38948.8 | + | 29243.9i | −0.638411 | + | 0.479338i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2209.33 | + | 6070.08i | 0.0356337 | + | 0.0979029i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28520.0 | + | 23931.1i | −0.452691 | + | 0.379852i | −0.840433 | − | 0.541915i | \(-0.817699\pi\) |
0.387743 | + | 0.921768i | \(0.373255\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3374.79 | − | 19139.4i | −0.0527237 | − | 0.299011i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −20775.2 | − | 11994.6i | −0.319496 | − | 0.184461i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24905.4 | + | 68427.0i | −0.377074 | + | 1.03600i | 0.595489 | + | 0.803364i | \(0.296958\pi\) |
−0.972563 | + | 0.232639i | \(0.925264\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 98936.4 | − | 57121.0i | 1.47488 | − | 0.851522i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −670.223 | + | 798.741i | −0.00983872 | + | 0.0117253i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13676.0 | + | 77560.4i | −0.197718 | + | 1.12132i | 0.710775 | + | 0.703419i | \(0.248344\pi\) |
−0.908494 | + | 0.417898i | \(0.862767\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 117087.i | 1.66731i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19955.6 | −0.279925 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 102925. | + | 18148.5i | 1.42239 | + | 0.250805i | 0.831310 | − | 0.555809i | \(-0.187592\pi\) |
0.591078 | + | 0.806615i | \(0.298703\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31987.2 | + | 26840.5i | 0.435550 | + | 0.365470i | 0.834041 | − | 0.551702i | \(-0.186022\pi\) |
−0.398491 | + | 0.917172i | \(0.630466\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −40403.0 | − | 69980.0i | −0.542111 | − | 0.938964i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −602.103 | − | 219.148i | −0.00796169 | − | 0.00289782i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −38102.9 | + | 65996.2i | −0.496591 | + | 0.860121i | −0.999992 | − | 0.00393174i | \(-0.998748\pi\) |
0.503401 | + | 0.864053i | \(0.332082\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12390.8 | + | 2184.83i | −0.159181 | + | 0.0280678i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −80364.3 | − | 95774.4i | −1.01777 | − | 1.21293i | −0.976884 | − | 0.213769i | \(-0.931426\pi\) |
−0.0408877 | − | 0.999164i | \(-0.513019\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 118315. | − | 43063.3i | 1.47730 | − | 0.537693i | 0.527228 | − | 0.849724i | \(-0.323231\pi\) |
0.950072 | + | 0.312031i | \(0.101009\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 62328.7 | + | 26585.1i | 0.767358 | + | 0.327302i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40619.8 | + | 111602.i | 0.493145 | + | 1.35490i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −51468.7 | + | 43187.3i | −0.616236 | + | 0.517084i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7069.39 | − | 40092.5i | −0.0834826 | − | 0.473453i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −72370.8 | − | 41783.3i | −0.843001 | − | 0.486707i | 0.0152825 | − | 0.999883i | \(-0.495135\pi\) |
−0.858283 | + | 0.513177i | \(0.828469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4094.93 | + | 11250.7i | −0.0470547 | + | 0.129282i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −28354.1 | + | 16370.2i | −0.321442 | + | 0.185584i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 40781.0 | − | 48600.9i | 0.456159 | − | 0.543629i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38130.2 | − | 216247.i | 0.420858 | − | 2.38680i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 22807.5i | − | 0.248423i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −141501. | −1.52111 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13430.9 | + | 2368.23i | 0.142504 | + | 0.0251274i | 0.244445 | − | 0.969663i | \(-0.421394\pi\) |
−0.101941 | + | 0.994790i | \(0.532505\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 67858.8 | + | 56940.3i | 0.710705 | + | 0.596352i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8649.51 | − | 14981.4i | −0.0894274 | − | 0.154893i | 0.817842 | − | 0.575443i | \(-0.195170\pi\) |
−0.907269 | + | 0.420550i | \(0.861837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −154613. | − | 56274.6i | −1.57818 | − | 0.574412i | −0.603376 | − | 0.797457i | \(-0.706178\pi\) |
−0.974808 | + | 0.223045i | \(0.928400\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 22552.4 | − | 39061.9i | 0.227285 | − | 0.393670i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −105079. | + | 18528.2i | −1.04567 | + | 0.184380i | −0.669991 | − | 0.742369i | \(-0.733702\pi\) |
−0.375681 | + | 0.926749i | \(0.622591\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1194.32 | − | 1423.34i | −0.0117365 | − | 0.0139871i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 143470. | − | 52218.9i | 1.39236 | − | 0.506778i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31523.8 | + | 33687.4i | −0.302157 | + | 0.322895i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −715.403 | − | 1965.55i | −0.00677305 | − | 0.0186088i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −49391.9 | + | 41444.7i | −0.461913 | + | 0.387591i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −49055.3 | − | 278207.i | −0.453205 | − | 2.57025i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 130677. | + | 75446.6i | 1.19274 | + | 0.688626i | 0.958926 | − | 0.283656i | \(-0.0915474\pi\) |
0.233810 | + | 0.972282i | \(0.424881\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11504.0 | − | 31607.0i | 0.103743 | − | 0.285033i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 112742. | − | 65091.6i | 1.00461 | − | 0.580010i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −47743.1 | + | 56898.0i | −0.420388 | + | 0.500999i | −0.934124 | − | 0.356949i | \(-0.883817\pi\) |
0.513735 | + | 0.857949i | \(0.328261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23041.6 | − | 130675.i | 0.200499 | − | 1.13709i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 22420.7i | − | 0.192815i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 110546. | 0.939626 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −86925.7 | − | 15327.4i | −0.730315 | − | 0.128774i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19642.1 | − | 16481.7i | −0.163128 | − | 0.136881i | 0.557569 | − | 0.830130i | \(-0.311734\pi\) |
−0.720698 | + | 0.693249i | \(0.756178\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2917.56 | − | 5053.35i | −0.0239535 | − | 0.0414886i | 0.853800 | − | 0.520601i | \(-0.174292\pi\) |
−0.877754 | + | 0.479112i | \(0.840959\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −100435. | − | 36555.3i | −0.815212 | − | 0.296713i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −104577. | + | 181132.i | −0.839238 | + | 1.45360i | 0.0512945 | + | 0.998684i | \(0.483665\pi\) |
−0.890533 | + | 0.454919i | \(0.849668\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −159358. | + | 28099.0i | −1.26449 | + | 0.222964i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −49201.6 | − | 58636.2i | −0.386049 | − | 0.460076i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 187053. | − | 68081.7i | 1.45136 | − | 0.528253i | 0.508391 | − | 0.861127i | \(-0.330241\pi\) |
0.942971 | + | 0.332874i | \(0.108018\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 76967.3 | − | 105165.i | 0.590598 | − | 0.806966i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 33630.9 | + | 92400.2i | 0.255226 | + | 0.701228i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −81274.5 | + | 68197.4i | −0.610054 | + | 0.511896i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13863.0 | − | 78620.8i | −0.102926 | − | 0.583721i | −0.992029 | − | 0.126013i | \(-0.959782\pi\) |
0.889103 | − | 0.457707i | \(-0.151329\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 30282.3 | + | 17483.5i | 0.222401 | + | 0.128403i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −127778. | + | 351067.i | −0.928343 | + | 2.55060i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 178067. | − | 102807.i | 1.27987 | − | 0.738932i | 0.303044 | − | 0.952976i | \(-0.401997\pi\) |
0.976824 | + | 0.214044i | \(0.0686637\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −77279.7 | + | 92098.3i | −0.549544 | + | 0.654922i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1053.27 | − | 5973.37i | 0.00741063 | − | 0.0420278i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 55178.6i | 0.384143i | 0.981381 | + | 0.192071i | \(0.0615205\pi\) | ||||
−0.981381 | + | 0.192071i | \(0.938480\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −74848.3 | −0.515623 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 73791.5 | + | 13011.4i | 0.503047 | + | 0.0887008i | 0.419413 | − | 0.907796i | \(-0.362236\pi\) |
0.0836346 | + | 0.996496i | \(0.473347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 61571.3 | + | 51664.4i | 0.415390 | + | 0.348554i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32325.1 | − | 55988.7i | −0.215833 | − | 0.373834i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 175467. | + | 63864.7i | 1.15957 | + | 0.422048i | 0.848942 | − | 0.528485i | \(-0.177240\pi\) |
0.310624 | + | 0.950533i | \(0.399462\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30048.9 | − | 52046.3i | 0.196551 | − | 0.340437i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 49383.9 | − | 8707.72i | 0.319743 | − | 0.0563793i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 40840.2 | + | 48671.4i | 0.261754 | + | 0.311946i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −184423. | + | 67124.6i | −1.17013 | + | 0.425893i | −0.852706 | − | 0.522391i | \(-0.825040\pi\) |
−0.317425 | + | 0.948283i | \(0.602818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 157871. | + | 147731.i | 0.991644 | + | 0.927956i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 63372.6 | + | 174115.i | 0.394106 | + | 1.08280i | 0.965109 | + | 0.261849i | \(0.0843321\pi\) |
−0.571003 | + | 0.820948i | \(0.693446\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 56068.2 | − | 47046.8i | 0.345229 | − | 0.289681i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17767.4 | + | 100764.i | 0.108322 | + | 0.614322i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 51907.4 | + | 29968.8i | 0.313358 | + | 0.180917i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25696.6 | − | 70600.7i | 0.153613 | − | 0.422049i | −0.838885 | − | 0.544309i | \(-0.816792\pi\) |
0.992498 | + | 0.122260i | \(0.0390142\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 70375.0 | − | 40631.0i | 0.416615 | − | 0.240533i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24556.1 | + | 29264.8i | −0.143966 | + | 0.171572i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3642.28 | − | 20656.4i | 0.0211484 | − | 0.119938i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 140813.i | 0.809785i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 124576. | 0.709588 | 0.354794 | − | 0.934945i | \(-0.384551\pi\) | ||||
0.354794 | + | 0.934945i | \(0.384551\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1648.98 | + | 290.759i | 0.00930359 | + | 0.00164047i | 0.178298 | − | 0.983977i | \(-0.442941\pi\) |
−0.168994 | + | 0.985617i | \(0.554052\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −63715.0 | − | 53463.2i | −0.356091 | − | 0.298796i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −990.690 | − | 1715.92i | −0.00548479 | − | 0.00949993i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −424271. | − | 154422.i | −2.32695 | − | 0.846942i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 21197.6 | − | 36715.3i | 0.115179 | − | 0.199495i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −261976. | + | 46193.4i | −1.41028 | + | 0.248671i | −0.826362 | − | 0.563139i | \(-0.809594\pi\) |
−0.583922 | + | 0.811810i | \(0.698482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −77709.0 | − | 92610.0i | −0.414472 | − | 0.493949i | 0.517904 | − | 0.855439i | \(-0.326713\pi\) |
−0.932376 | + | 0.361490i | \(0.882268\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7929.76 | + | 2886.20i | −0.0419065 | + | 0.0152527i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −66601.2 | + | 156146.i | −0.348754 | + | 0.817654i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −74737.9 | − | 205341.i | −0.387804 | − | 1.06548i | −0.967988 | − | 0.250997i | \(-0.919242\pi\) |
0.580184 | − | 0.814485i | \(-0.302981\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 67590.7 | − | 56715.3i | 0.347544 | − | 0.291624i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35869.4 | + | 203426.i | 0.182775 | + | 1.03657i | 0.928781 | + | 0.370629i | \(0.120858\pi\) |
−0.746006 | + | 0.665939i | \(0.768031\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 56116.5 | + | 32398.9i | 0.283381 | + | 0.163610i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 104117. | − | 286059.i | 0.521082 | − | 1.43166i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 140035. | − | 80849.4i | 0.694616 | − | 0.401037i | −0.110723 | − | 0.993851i | \(-0.535317\pi\) |
0.805339 | + | 0.592815i | \(0.201983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40052.3 | + | 47732.4i | −0.196913 | + | 0.234672i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −18268.3 | + | 103605.i | −0.0890229 | + | 0.504874i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 262385.i | 1.26741i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 102385. | 0.490234 | 0.245117 | − | 0.969493i | \(-0.421174\pi\) | ||||
0.245117 | + | 0.969493i | \(0.421174\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −99705.4 | − | 17580.7i | −0.473253 | − | 0.0834472i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 98923.7 | + | 83006.9i | 0.465477 | + | 0.390582i | 0.845142 | − | 0.534542i | \(-0.179516\pi\) |
−0.379664 | + | 0.925124i | \(0.623960\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −89167.8 | − | 154443.i | −0.415955 | − | 0.720454i | 0.579574 | − | 0.814920i | \(-0.303219\pi\) |
−0.995528 | + | 0.0944655i | \(0.969886\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −95687.4 | − | 34827.4i | −0.442536 | − | 0.161070i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −88798.3 | + | 153803.i | −0.407165 | + | 0.705231i | −0.994571 | − | 0.104062i | \(-0.966816\pi\) |
0.587405 | + | 0.809293i | \(0.300149\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 409075. | − | 72131.0i | 1.85976 | − | 0.327926i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 109952. | + | 131036.i | 0.495634 | + | 0.590673i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 108257. | − | 39402.5i | 0.483877 | − | 0.176117i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3360.43 | + | 4475.62i | 0.0148939 | + | 0.0198366i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 37620.8 | + | 103362.i | 0.165345 | + | 0.454282i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 347713. | − | 291766.i | 1.51548 | − | 1.27164i | 0.663340 | − | 0.748318i | \(-0.269138\pi\) |
0.852137 | − | 0.523318i | \(-0.175306\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 33976.9 | + | 192692.i | 0.146857 | + | 0.832865i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −243907. | − | 140820.i | −1.04551 | − | 0.603628i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −45212.5 | + | 124220.i | −0.192210 | + | 0.528091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21316.0 | − | 12306.8i | 0.0898767 | − | 0.0518904i | −0.454388 | − | 0.890804i | \(-0.650142\pi\) |
0.544265 | + | 0.838914i | \(0.316809\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 133328. | − | 158894.i | 0.557576 | − | 0.664493i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 217.503 | − | 1233.52i | 0.000902200 | − | 0.00511663i | −0.984353 | − | 0.176206i | \(-0.943618\pi\) |
0.985256 | + | 0.171089i | \(0.0547287\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5745.61i | − | 0.0236397i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23664.4 | 0.0965796 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −508475. | − | 89657.8i | −2.05853 | − | 0.362974i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −104194. | − | 87429.0i | −0.418447 | − | 0.351119i | 0.409125 | − | 0.912478i | \(-0.365834\pi\) |
−0.827572 | + | 0.561360i | \(0.810278\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −203711. | − | 352839.i | −0.811596 | − | 1.40573i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 60501.9 | + | 22020.9i | 0.239129 | + | 0.0870360i | 0.458805 | − | 0.888537i | \(-0.348278\pi\) |
−0.219676 | + | 0.975573i | \(0.570500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37029.0 | + | 64136.1i | −0.145198 | + | 0.251489i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −77557.3 | + | 13675.5i | −0.301722 | + | 0.0532017i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −262556. | − | 312902.i | −1.01341 | − | 1.20774i | −0.978052 | − | 0.208362i | \(-0.933187\pi\) |
−0.0353598 | − | 0.999375i | \(-0.511258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −318114. | + | 115784.i | −1.21826 | + | 0.443411i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 285562. | + | 15464.1i | 1.08509 | + | 0.0587612i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −98378.1 | − | 270292.i | −0.370923 | − | 1.01910i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 113539. | − | 95270.2i | 0.424778 | − | 0.356431i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8225.93 | − | 46651.6i | −0.0305387 | − | 0.173193i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −60388.8 | − | 34865.5i | −0.222475 | − | 0.128446i | 0.384621 | − | 0.923075i | \(-0.374332\pi\) |
−0.607096 | + | 0.794629i | \(0.707666\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 166145. | − | 456479.i | 0.607411 | − | 1.66885i | −0.128449 | − | 0.991716i | \(-0.541000\pi\) |
0.735861 | − | 0.677133i | \(-0.236778\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8041.43 | + | 4642.72i | −0.0291752 | + | 0.0168443i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 44565.5 | − | 53111.1i | 0.160464 | − | 0.191233i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10195.6 | + | 57822.3i | −0.0364337 | + | 0.206626i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11247.7i | 0.0398910i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −203411. | −0.716011 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −488228. | − | 86087.8i | −1.70575 | − | 0.300770i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −40340.7 | − | 33849.8i | −0.139893 | − | 0.117384i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 78614.8 | + | 136165.i | 0.270599 | + | 0.468692i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 381671. | + | 138917.i | 1.30405 | + | 0.474636i | 0.898314 | − | 0.439354i | \(-0.144793\pi\) |
0.405737 | + | 0.913990i | \(0.367015\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 93352.8 | − | 161692.i | 0.316612 | − | 0.548389i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 206181. | − | 36355.2i | 0.694152 | − | 0.122398i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 46267.0 | + | 55138.9i | 0.154631 | + | 0.184282i | 0.837798 | − | 0.545980i | \(-0.183842\pi\) |
−0.683167 | + | 0.730262i | \(0.739398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −124915. | + | 45465.4i | −0.414448 | + | 0.150847i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1949.84 | + | 16111.9i | 0.00642236 | + | 0.0530695i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 69337.6 | + | 190504.i | 0.226735 | + | 0.622949i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 208532. | − | 174979.i | 0.676998 | − | 0.568069i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23478.0 | − | 133150.i | −0.0756746 | − | 0.429172i | −0.998982 | − | 0.0451101i | \(-0.985636\pi\) |
0.923307 | − | 0.384062i | \(-0.125475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 325699. | + | 188042.i | 1.04230 | + | 0.601773i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13735.3 | − | 37737.3i | 0.0436426 | − | 0.119907i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35448.6 | + | 20466.2i | −0.111836 | + | 0.0645686i | −0.554875 | − | 0.831934i | \(-0.687234\pi\) |
0.443039 | + | 0.896503i | \(0.353900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −276952. | + | 330058.i | −0.867575 | + | 1.03394i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −56692.0 | + | 321516.i | −0.176342 | + | 1.00008i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 103071.i | 0.318355i | 0.987250 | + | 0.159178i | \(0.0508842\pi\) | ||||
−0.987250 | + | 0.159178i | \(0.949116\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 425127. | 1.30391 | 0.651954 | − | 0.758259i | \(-0.273950\pi\) | ||||
0.651954 | + | 0.758259i | \(0.273950\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 342897. | + | 60462.1i | 1.04437 | + | 0.184151i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5584.75 | − | 4686.16i | −0.0168915 | − | 0.0141736i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 222629. | + | 385604.i | 0.668697 | + | 1.15822i | 0.978269 | + | 0.207341i | \(0.0664811\pi\) |
−0.309571 | + | 0.950876i | \(0.600186\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −276435. | − | 100614.i | −0.824586 | − | 0.300125i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33463.4 | − | 57960.3i | 0.0991329 | − | 0.171703i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −193032. | + | 34036.8i | −0.567927 | + | 0.100141i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 49656.7 | + | 59178.5i | 0.145099 | + | 0.172923i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −397261. | + | 144591.i | −1.15292 | + | 0.419630i | −0.846564 | − | 0.532287i | \(-0.821333\pi\) |
−0.306359 | + | 0.951916i | \(0.599111\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −106947. | + | 164059.i | −0.308276 | + | 0.472900i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −73406.1 | − | 201682.i | −0.210163 | − | 0.577419i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −100063. | + | 83962.7i | −0.284553 | + | 0.238768i | −0.773880 | − | 0.633332i | \(-0.781687\pi\) |
0.489327 | + | 0.872100i | \(0.337242\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 43159.5 | + | 244770.i | 0.121911 | + | 0.691392i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −154094. | − | 88966.5i | −0.432353 | − | 0.249619i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −216612. | + | 595136.i | −0.603710 | + | 1.65868i | 0.139979 | + | 0.990154i | \(0.455296\pi\) |
−0.743689 | + | 0.668526i | \(0.766926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31516.2 | + | 18195.9i | −0.0872540 | + | 0.0503761i | −0.542992 | − | 0.839738i | \(-0.682709\pi\) |
0.455738 | + | 0.890114i | \(0.349375\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 78612.4 | − | 93686.6i | 0.216200 | − | 0.257658i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 55443.7 | − | 314437.i | 0.151475 | − | 0.859058i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 176712.i | − | 0.479610i | −0.970821 | − | 0.239805i | \(-0.922916\pi\) | ||
0.970821 | − | 0.239805i | \(-0.0770835\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −26925.9 | −0.0726000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 476491. | + | 84018.3i | 1.27636 | + | 0.225056i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 122043. | + | 102407.i | 0.324783 | + | 0.272525i | 0.790570 | − | 0.612371i | \(-0.209784\pi\) |
−0.465787 | + | 0.884897i | \(0.654229\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 141498. | + | 245082.i | 0.374111 | + | 0.647978i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 398569. | + | 145067.i | 1.04697 | + | 0.381065i | 0.807518 | − | 0.589843i | \(-0.200810\pi\) |
0.239451 | + | 0.970909i | \(0.423033\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25384.7 | + | 43967.7i | −0.0662509 | + | 0.114750i | −0.897248 | − | 0.441527i | \(-0.854437\pi\) |
0.830997 | + | 0.556276i | \(0.187770\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −366860. | + | 64687.4i | −0.951300 | + | 0.167740i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 132900. | + | 158384.i | 0.342411 | + | 0.408070i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 357736. | − | 130205.i | 0.915805 | − | 0.333326i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25710.1 | + | 110485.i | −0.0653986 | + | 0.281040i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 63391.8 | + | 174168.i | 0.160226 | + | 0.440216i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −118259. | + | 99230.9i | −0.297012 | + | 0.249223i | −0.779099 | − | 0.626900i | \(-0.784323\pi\) |
0.482087 | + | 0.876123i | \(0.339879\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 58646.5 | + | 332601.i | 0.146364 | + | 0.830072i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 210478. | + | 121520.i | 0.521988 | + | 0.301370i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −175550. | + | 482319.i | −0.432635 | + | 1.18865i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −131650. | + | 76008.1i | −0.322418 | + | 0.186148i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 485190. | − | 578226.i | 1.18085 | − | 1.40728i | 0.287587 | − | 0.957755i | \(-0.407147\pi\) |
0.893265 | − | 0.449530i | \(-0.148409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36966.7 | − | 209648.i | 0.0894105 | − | 0.507072i | −0.906907 | − | 0.421331i | \(-0.861563\pi\) |
0.996317 | − | 0.0857411i | \(-0.0273258\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 523229.i | − | 1.25769i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −700532. | −1.67348 | −0.836738 | − | 0.547603i | \(-0.815540\pi\) | ||||
−0.836738 | + | 0.547603i | \(0.815540\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19738.6 | − | 3480.45i | −0.0468627 | − | 0.00826316i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −248897. | − | 208850.i | −0.587297 | − | 0.492801i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 93437.4 | + | 161838.i | 0.219126 | + | 0.379538i | 0.954541 | − | 0.298079i | \(-0.0963460\pi\) |
−0.735415 | + | 0.677617i | \(0.763013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −153008. | − | 55690.5i | −0.356642 | − | 0.129807i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −49835.5 | + | 86317.6i | −0.115454 | + | 0.199972i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 632273. | − | 111487.i | 1.45591 | − | 0.256716i | 0.611002 | − | 0.791629i | \(-0.290767\pi\) |
0.844907 | + | 0.534913i | \(0.179656\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −453466. | − | 540420.i | −1.03787 | − | 1.23688i | −0.970990 | − | 0.239122i | \(-0.923141\pi\) |
−0.0668781 | − | 0.997761i | \(-0.521304\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 123193. | − | 44838.5i | 0.280258 | − | 0.102006i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −204094. | − | 671741.i | −0.461516 | − | 1.51900i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7230.53 | − | 19865.7i | −0.0162524 | − | 0.0446532i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −376042. | + | 315536.i | −0.840202 | + | 0.705013i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41134.0 | − | 233283.i | −0.0913600 | − | 0.518128i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 485127. | + | 280088.i | 1.07109 | + | 0.618393i | 0.928479 | − | 0.371386i | \(-0.121117\pi\) |
0.142610 | + | 0.989779i | \(0.454451\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4200.58 | + | 11541.0i | −0.00921939 | + | 0.0253301i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −149773. | + | 86471.5i | −0.326781 | + | 0.188667i | −0.654411 | − | 0.756139i | \(-0.727083\pi\) |
0.327630 | + | 0.944806i | \(0.393750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −271126. | + | 323115.i | −0.588073 | + | 0.700839i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −118550. | + | 672331.i | −0.255628 | + | 1.44974i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 561963.i | − | 1.20466i | −0.798245 | − | 0.602332i | \(-0.794238\pi\) | ||
0.798245 | − | 0.602332i | \(-0.205762\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −263865. | −0.562343 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 581131. | + | 102469.i | 1.23129 | + | 0.217110i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −490170. | − | 411301.i | −1.03254 | − | 0.866406i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27777.4 | + | 48111.9i | 0.0581750 | + | 0.100762i | 0.893646 | − | 0.448772i | \(-0.148139\pi\) |
−0.835471 | + | 0.549534i | \(0.814805\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 70954.3 | + | 25825.2i | 0.147745 | + | 0.0537747i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 228616. | − | 395975.i | 0.473301 | − | 0.819781i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −189755. | + | 33459.0i | −0.390596 | + | 0.0688727i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 466084. | + | 555457.i | 0.953915 | + | 1.13683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 444283. | − | 161706.i | 0.904115 | − | 0.329071i | 0.152215 | − | 0.988347i | \(-0.451359\pi\) |
0.751901 | + | 0.659276i | \(0.229137\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −236870. | − | 466891.i | −0.479291 | − | 0.944724i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −230230. | − | 632551.i | −0.463216 | − | 1.27267i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −181018. | + | 151893.i | −0.362146 | + | 0.303877i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37158.9 | − | 210739.i | −0.0739214 | − | 0.419229i | −0.999202 | − | 0.0399456i | \(-0.987282\pi\) |
0.925280 | − | 0.379284i | \(-0.123830\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 51691.5 | + | 29844.1i | 0.102254 | + | 0.0590364i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 87249.9 | − | 239717.i | 0.171627 | − | 0.471542i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −119218. | + | 68830.6i | −0.233201 | + | 0.134639i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −136323. | + | 162463.i | −0.265174 | + | 0.316022i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 74521.0 | − | 422629.i | 0.144152 | − | 0.817527i | −0.823892 | − | 0.566747i | \(-0.808202\pi\) |
0.968044 | − | 0.250780i | \(-0.0806871\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 917791.i | − | 1.76552i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −426152. | −0.815245 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −686.402 | − | 121.031i | −0.00130588 | − | 0.000230261i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 400152. | + | 335767.i | 0.757104 | + | 0.635286i | 0.937371 | − | 0.348332i | \(-0.113252\pi\) |
−0.180267 | + | 0.983618i | \(0.557696\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 291996. | + | 505752.i | 0.549442 | + | 0.951662i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 334765. | + | 121845.i | 0.626477 | + | 0.228019i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4773.63 | − | 8268.18i | 0.00888467 | − | 0.0153887i | −0.861549 | − | 0.507675i | \(-0.830505\pi\) |
0.870434 | + | 0.492286i | \(0.163839\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 703244. | − | 124001.i | 1.30176 | − | 0.229536i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 140085. | + | 166947.i | 0.257904 | + | 0.307358i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −610485. | + | 222198.i | −1.11786 | + | 0.406867i | −0.833870 | − | 0.551961i | \(-0.813880\pi\) |
−0.283987 | + | 0.958828i | \(0.591657\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −330243. | + | 167544.i | −0.601446 | + | 0.305135i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20420.2 | + | 56103.9i | 0.0369898 | + | 0.101629i | 0.956813 | − | 0.290705i | \(-0.0938900\pi\) |
−0.919823 | + | 0.392334i | \(0.871668\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −757214. | + | 635378.i | −1.36429 | + | 1.14477i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3421.70 | − | 19405.4i | −0.00613198 | − | 0.0347762i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.36993e6 | − | 790930.i | −2.44194 | − | 1.40986i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 211038. | − | 579823.i | 0.374181 | − | 1.02805i | −0.599547 | − | 0.800339i | \(-0.704653\pi\) |
0.973728 | − | 0.227714i | \(-0.0731251\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −245141. | + | 141532.i | −0.432341 | + | 0.249612i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 219579. | − | 261684.i | 0.385209 | − | 0.459074i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 83191.5 | − | 471802.i | 0.145173 | − | 0.823319i | −0.822054 | − | 0.569409i | \(-0.807172\pi\) |
0.967228 | − | 0.253910i | \(-0.0817168\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 147764.i | − | 0.256498i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 351157. | 0.606362 | 0.303181 | − | 0.952933i | \(-0.401951\pi\) | ||||
0.303181 | + | 0.952933i | \(0.401951\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 657877. | + | 116001.i | 1.13004 | + | 0.199257i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 56057.3 | + | 47037.7i | 0.0957876 | + | 0.0803754i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32715.2 | − | 56664.4i | −0.0556108 | − | 0.0963207i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 629039. | + | 228952.i | 1.06371 | + | 0.387160i | 0.813823 | − | 0.581113i | \(-0.197383\pi\) |
0.249892 | + | 0.968274i | \(0.419605\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −276823. | + | 479471.i | −0.465686 | + | 0.806592i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −717414. | + | 126499.i | −1.20064 | + | 0.211704i | −0.737973 | − | 0.674830i | \(-0.764217\pi\) |
−0.462662 | + | 0.886535i | \(0.653106\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5406.17 | − | 6442.82i | −0.00900090 | − | 0.0107269i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 816210. | − | 297076.i | 1.35195 | − | 0.492069i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 520760. | − | 158222.i | 0.858149 | − | 0.260730i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −92649.5 | − | 254552.i | −0.151894 | − | 0.417326i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −27282.3 | + | 22892.5i | −0.0444997 | + | 0.0373397i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −96449.5 | − | 546993.i | −0.156517 | − | 0.887651i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −359227. | − | 207400.i | −0.579988 | − | 0.334856i | 0.181140 | − | 0.983457i | \(-0.442021\pi\) |
−0.761129 | + | 0.648601i | \(0.775354\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −204800. | + | 562685.i | −0.328986 | + | 0.903881i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.19059e6 | + | 687390.i | −1.90288 | + | 1.09863i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 497065. | − | 592378.i | 0.790435 | − | 0.942004i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −154586. | + | 876698.i | −0.244588 | + | 1.38713i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 448699.i | − | 0.706380i | −0.935552 | − | 0.353190i | \(-0.885097\pi\) | ||
0.935552 | − | 0.353190i | \(-0.114903\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 458323. | 0.717924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 59948.7 | + | 10570.6i | 0.0934361 | + | 0.0164753i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −136058. | − | 114166.i | −0.211005 | − | 0.177054i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 457255. | + | 791989.i | 0.705614 | + | 1.22216i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 746703. | + | 271777.i | 1.14657 | + | 0.417317i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 412674. | − | 714773.i | 0.630537 | − | 1.09212i | −0.356906 | − | 0.934140i | \(-0.616168\pi\) |
0.987442 | − | 0.157981i | \(-0.0504984\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 422824. | − | 74555.3i | 0.642862 | − | 0.113354i | 0.157293 | − | 0.987552i | \(-0.449723\pi\) |
0.485570 | + | 0.874198i | \(0.338612\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 204071. | + | 243202.i | 0.308745 | + | 0.367948i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −632900. | + | 230357.i | −0.952840 | + | 0.346805i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −980103. | − | 228072.i | −1.46834 | − | 0.341687i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 84306.0 | + | 231629.i | 0.125687 | + | 0.345323i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 450369. | − | 377905.i | 0.668163 | − | 0.560656i | −0.244358 | − | 0.969685i | \(-0.578577\pi\) |
0.912521 | + | 0.409030i | \(0.134133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 85194.2 | + | 483160.i | 0.125780 | + | 0.713331i | 0.980842 | + | 0.194806i | \(0.0624077\pi\) |
−0.855062 | + | 0.518525i | \(0.826481\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4218.97 | − | 2435.82i | −0.00619867 | − | 0.00357880i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 268227. | − | 736947.i | 0.392185 | − | 1.07752i | −0.573816 | − | 0.818984i | \(-0.694538\pi\) |
0.966002 | − | 0.258536i | \(-0.0832401\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −860067. | + | 496560.i | −1.25148 | + | 0.722541i | −0.971403 | − | 0.237437i | \(-0.923693\pi\) |
−0.280075 | + | 0.959978i | \(0.590359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −372432. | + | 443847.i | −0.539318 | + | 0.642734i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −84428.1 | + | 478816.i | −0.121674 | + | 0.690047i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.32294e6i | 1.89744i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −429756. | −0.613438 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −435208. | − | 76738.9i | −0.618262 | − | 0.109016i | −0.144260 | − | 0.989540i | \(-0.546080\pi\) |
−0.474002 | + | 0.880524i | \(0.657191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 540260. | + | 453332.i | 0.763855 | + | 0.640951i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −475287. | − | 823222.i | −0.668808 | − | 1.15841i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 240299. | + | 87461.7i | 0.336542 | + | 0.122491i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 509388. | − | 882286.i | 0.710038 | − | 1.22982i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 942753. | − | 166233.i | 1.30792 | − | 0.230622i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 438360. | + | 522417.i | 0.605302 | + | 0.721371i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.29584e6 | + | 471646.i | −1.78095 | + | 0.648213i | −0.781238 | + | 0.624233i | \(0.785412\pi\) |
−0.999712 | + | 0.0239804i | \(0.992366\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −173160. | − | 112880.i | −0.236872 | − | 0.154414i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −58971.8 | − | 162024.i | −0.0802939 | − | 0.220606i | 0.893049 | − | 0.449959i | \(-0.148561\pi\) |
−0.973343 | + | 0.229353i | \(0.926339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −375604. | + | 315169.i | −0.509030 | + | 0.427127i | −0.860788 | − | 0.508964i | \(-0.830029\pi\) |
0.351758 | + | 0.936091i | \(0.385584\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 156800. | + | 889260.i | 0.211515 | + | 1.19956i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.19144e6 | + | 687878.i | 1.59974 | + | 0.923613i | 0.991535 | + | 0.129836i | \(0.0414451\pi\) |
0.608209 | + | 0.793777i | \(0.291888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −52609.2 | + | 144542.i | −0.0703120 | + | 0.193181i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −442395. | + | 255417.i | −0.588535 | + | 0.339791i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −68368.8 | + | 81478.8i | −0.0905354 | + | 0.107896i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −123541. | + | 700634.i | −0.162845 | + | 0.923538i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 124187.i | 0.162947i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.24563e6 | 1.62695 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.47452e6 | + | 259998.i | 1.91713 | + | 0.338042i | 0.998385 | − | 0.0568051i | \(-0.0180914\pi\) |
0.918747 | + | 0.394847i | \(0.129202\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −486718. | − | 408405.i | −0.629940 | − | 0.528583i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 117779. | + | 203999.i | 0.151746 | + | 0.262831i | 0.931869 | − | 0.362794i | \(-0.118177\pi\) |
−0.780124 | + | 0.625625i | \(0.784844\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 422773. | + | 153877.i | 0.542233 | + | 0.197357i | 0.598592 | − | 0.801054i | \(-0.295727\pi\) |
−0.0563591 | + | 0.998411i | \(0.517949\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45515.1 | + | 78834.5i | −0.0581125 | + | 0.100654i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 724708. | − | 127786.i | 0.921120 | − | 0.162418i | 0.307071 | − | 0.951687i | \(-0.400651\pi\) |
0.614048 | + | 0.789268i | \(0.289540\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 498473. | + | 594057.i | 0.630722 | + | 0.751665i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −160957. | + | 58583.7i | −0.202747 | + | 0.0737940i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.28524e6 | + | 155537.i | −1.61169 | + | 0.195043i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 58483.8 | + | 160683.i | 0.0730112 | + | 0.200597i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 369518. | − | 310062.i | 0.459251 | − | 0.385358i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4235.07 | − | 24018.3i | −0.00524012 | − | 0.0297182i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −524918. | − | 303061.i | −0.646609 | − | 0.373320i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 571006. | − | 1.56883e6i | 0.700270 | − | 1.92398i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −525029. | + | 303125.i | −0.641041 | + | 0.370105i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 228210. | − | 271970.i | 0.277409 | − | 0.330603i | −0.609293 | − | 0.792945i | \(-0.708547\pi\) |
0.886701 | + | 0.462343i | \(0.152991\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12081.2 | + | 68516.0i | −0.0146212 | + | 0.0829210i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 831035.i | 1.00134i | 0.865637 | + | 0.500671i | \(0.166913\pi\) | ||||
−0.865637 | + | 0.500671i | \(0.833087\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 35113.4 | 0.0421242 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.05950e6 | − | 186819.i | −1.26550 | − | 0.223141i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −397997. | − | 333959.i | −0.473305 | − | 0.397150i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −67362.5 | − | 116675.i | −0.0797603 | − | 0.138149i | 0.823386 | − | 0.567481i | \(-0.192082\pi\) |
−0.903146 | + | 0.429333i | \(0.858749\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 97438.4 | + | 35464.7i | 0.114871 | + | 0.0418097i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 442156. | − | 765837.i | 0.519006 | − | 0.898944i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22142.3 | − | 3904.29i | 0.0258786 | − | 0.00456309i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −173693. | − | 207000.i | −0.202127 | − | 0.240885i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −600073. | + | 218409.i | −0.695300 | + | 0.253069i | −0.665403 | − | 0.746484i | \(-0.731740\pi\) |
−0.0298973 | + | 0.999553i | \(0.509518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 74263.5 | − | 1.37135e6i | 0.0856793 | − | 1.58216i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −44984.6 | − | 123594.i | −0.0516774 | − | 0.141982i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −99892.7 | + | 83820.0i | −0.114264 | + | 0.0958792i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51925.6 | − | 294485.i | −0.0591429 | − | 0.335416i | 0.940851 | − | 0.338820i | \(-0.110028\pi\) |
−0.999994 | + | 0.00340378i | \(0.998917\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.08338e6 | − | 625491.i | −1.22871 | − | 0.709398i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 322134. | − | 885055.i | 0.363795 | − | 0.999518i | −0.613881 | − | 0.789399i | \(-0.710392\pi\) |
0.977676 | − | 0.210120i | \(-0.0673854\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −613981. | + | 354482.i | −0.690449 | + | 0.398631i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 990294. | − | 1.18019e6i | 1.10892 | − | 1.32156i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20729.8 | − | 117564.i | 0.0231151 | − | 0.131092i | −0.971067 | − | 0.238809i | \(-0.923243\pi\) |
0.994182 | + | 0.107717i | \(0.0343541\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 579809.i | − | 0.643802i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −811247. | −0.896999 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −262828. | − | 46343.7i | −0.289392 | − | 0.0510276i | 0.0270676 | − | 0.999634i | \(-0.491383\pi\) |
−0.316460 | + | 0.948606i | \(0.602494\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −866087. | − | 726733.i | −0.949631 | − | 0.796835i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7063.41 | − | 12234.2i | −0.00771242 | − | 0.0133583i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −791161. | − | 287959.i | −0.860256 | − | 0.313108i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −314612. | + | 544924.i | −0.340666 | + | 0.590051i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −458660. | + | 80874.2i | −0.494582 | + | 0.0872082i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 614001. | + | 731738.i | 0.659348 | + | 0.785780i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −651323. | + | 237062.i | −0.696536 | + | 0.253518i | −0.665931 | − | 0.746013i | \(-0.731966\pi\) |
−0.0306049 | + | 0.999532i | \(0.509743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −280513. | + | 210617.i | −0.298749 | + | 0.224309i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −200968. | − | 552156.i | −0.213152 | − | 0.585630i | 0.786330 | − | 0.617806i | \(-0.211978\pi\) |
−0.999482 | + | 0.0321764i | \(0.989756\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.11760e6 | − | 937780.i | 1.18049 | − | 0.990548i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2761.60 | − | 15661.8i | −0.00290503 | − | 0.0164753i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 825474. | + | 476587.i | 0.864797 | + | 0.499291i | 0.865616 | − | 0.500709i | \(-0.166927\pi\) |
−0.000818797 | 1.00000i | \(0.500261\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37100.7 | + | 101933.i | −0.0387094 | + | 0.106353i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 170332. | − | 98341.1i | 0.176994 | − | 0.102187i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −568150. | + | 677095.i | −0.587971 | + | 0.700717i | −0.975215 | − | 0.221260i | \(-0.928983\pi\) |
0.387243 | + | 0.921978i | \(0.373427\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −121017. | + | 686320.i | −0.124731 | + | 0.707383i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2.14786e6i | − | 2.20482i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.31080e6 | 1.34012 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −173201. | − | 30540.0i | −0.176361 | − | 0.0310972i | 0.0847700 | − | 0.996401i | \(-0.472984\pi\) |
−0.261131 | + | 0.965303i | \(0.584096\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 878849. | + | 737442.i | 0.891283 | + | 0.747876i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 288882. | + | 500359.i | 0.291793 | + | 0.505400i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 614047. | + | 223495.i | 0.617748 | + | 0.224842i | 0.631890 | − | 0.775058i | \(-0.282279\pi\) |
−0.0141420 | + | 0.999900i | \(0.504502\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 574436. | − | 994953.i | 0.575587 | − | 0.996945i |
(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 | 76.5.j.a.33.6 | ✓ | 42 | |
19.15 | odd | 18 | inner | 76.5.j.a.53.6 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.33.6 | ✓ | 42 | 1.1 | even | 1 | trivial | |
76.5.j.a.53.6 | yes | 42 | 19.15 | odd | 18 | inner |