Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(23,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.23");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.g (of order \(12\), degree \(4\), 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: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 29.2 | ||
Character | \(\chi\) | \(=\) | 74.29 |
Dual form | 74.5.g.a.23.2 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.732051 | − | 2.73205i | 0.183013 | − | 0.683013i | ||||
\(3\) | −12.4198 | − | 7.17059i | −1.37998 | − | 0.796732i | −0.387824 | − | 0.921733i | \(-0.626773\pi\) |
−0.992157 | + | 0.125001i | \(0.960107\pi\) | |||||||
\(4\) | −6.92820 | − | 4.00000i | −0.433013 | − | 0.250000i | ||||
\(5\) | 11.3964 | + | 42.5318i | 0.455854 | + | 1.70127i | 0.685565 | + | 0.728011i | \(0.259555\pi\) |
−0.229711 | + | 0.973259i | \(0.573778\pi\) | |||||||
\(6\) | −28.6824 | + | 28.6824i | −0.796732 | + | 0.796732i | ||||
\(7\) | 6.42196 | − | 11.1232i | 0.131061 | − | 0.227003i | −0.793025 | − | 0.609189i | \(-0.791495\pi\) |
0.924086 | + | 0.382185i | \(0.124828\pi\) | |||||||
\(8\) | −16.0000 | + | 16.0000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 62.3348 | + | 107.967i | 0.769565 | + | 1.33293i | ||||
\(10\) | 124.542 | 1.24542 | ||||||||
\(11\) | − | 116.105i | − | 0.959547i | −0.877392 | − | 0.479774i | \(-0.840719\pi\) | ||
0.877392 | − | 0.479774i | \(-0.159281\pi\) | |||||||
\(12\) | 57.3647 | + | 99.3586i | 0.398366 | + | 0.689991i | ||||
\(13\) | 28.9334 | + | 107.981i | 0.171203 | + | 0.638940i | 0.997167 | + | 0.0752168i | \(0.0239649\pi\) |
−0.825964 | + | 0.563723i | \(0.809368\pi\) | |||||||
\(14\) | −25.6879 | − | 25.6879i | −0.131061 | − | 0.131061i | ||||
\(15\) | 163.437 | − | 609.956i | 0.726387 | − | 2.71091i | ||||
\(16\) | 32.0000 | + | 55.4256i | 0.125000 | + | 0.216506i | ||||
\(17\) | 501.141 | + | 134.280i | 1.73405 | + | 0.464637i | 0.981110 | − | 0.193451i | \(-0.0619682\pi\) |
0.752940 | + | 0.658089i | \(0.228635\pi\) | |||||||
\(18\) | 340.604 | − | 91.2644i | 1.05125 | − | 0.281680i | ||||
\(19\) | 76.0134 | + | 283.686i | 0.210564 | + | 0.785834i | 0.987681 | + | 0.156479i | \(0.0500143\pi\) |
−0.777118 | + | 0.629355i | \(0.783319\pi\) | |||||||
\(20\) | 91.1708 | − | 340.254i | 0.227927 | − | 0.850635i | ||||
\(21\) | −159.519 | + | 92.0986i | −0.361722 | + | 0.208840i | ||||
\(22\) | −317.205 | − | 84.9949i | −0.655383 | − | 0.175609i | ||||
\(23\) | −416.700 | + | 416.700i | −0.787713 | + | 0.787713i | −0.981119 | − | 0.193406i | \(-0.938047\pi\) |
0.193406 | + | 0.981119i | \(0.438047\pi\) | |||||||
\(24\) | 313.447 | − | 83.9878i | 0.544178 | − | 0.145812i | ||||
\(25\) | −1137.81 | + | 656.914i | −1.82049 | + | 1.05106i | ||||
\(26\) | 316.190 | 0.467737 | ||||||||
\(27\) | − | 626.273i | − | 0.859085i | ||||||
\(28\) | −88.9854 | + | 51.3757i | −0.113502 | + | 0.0655303i | ||||
\(29\) | 629.268 | + | 629.268i | 0.748238 | + | 0.748238i | 0.974148 | − | 0.225911i | \(-0.0725357\pi\) |
−0.225911 | + | 0.974148i | \(0.572536\pi\) | |||||||
\(30\) | −1546.79 | − | 893.037i | −1.71865 | − | 0.992264i | ||||
\(31\) | 556.172 | + | 556.172i | 0.578743 | + | 0.578743i | 0.934557 | − | 0.355814i | \(-0.115796\pi\) |
−0.355814 | + | 0.934557i | \(0.615796\pi\) | |||||||
\(32\) | 174.851 | − | 46.8513i | 0.170753 | − | 0.0457532i | ||||
\(33\) | −832.543 | + | 1442.01i | −0.764502 | + | 1.32416i | ||||
\(34\) | 733.721 | − | 1270.84i | 0.634706 | − | 1.09934i | ||||
\(35\) | 546.275 | + | 146.374i | 0.445939 | + | 0.119489i | ||||
\(36\) | − | 997.356i | − | 0.769565i | ||||||
\(37\) | −530.192 | − | 1262.16i | −0.387285 | − | 0.921960i | ||||
\(38\) | 830.690 | 0.575270 | ||||||||
\(39\) | 414.939 | − | 1548.57i | 0.272807 | − | 1.01813i | ||||
\(40\) | −862.850 | − | 498.167i | −0.539281 | − | 0.311354i | ||||
\(41\) | 1372.33 | + | 792.313i | 0.816375 | + | 0.471334i | 0.849165 | − | 0.528128i | \(-0.177106\pi\) |
−0.0327899 | + | 0.999462i | \(0.510439\pi\) | |||||||
\(42\) | 134.842 | + | 503.236i | 0.0764409 | + | 0.285281i | ||||
\(43\) | −753.477 | + | 753.477i | −0.407505 | + | 0.407505i | −0.880868 | − | 0.473363i | \(-0.843040\pi\) |
0.473363 | + | 0.880868i | \(0.343040\pi\) | |||||||
\(44\) | −464.421 | + | 804.401i | −0.239887 | + | 0.415496i | ||||
\(45\) | −3881.64 | + | 3881.64i | −1.91686 | + | 1.91686i | ||||
\(46\) | 833.400 | + | 1443.49i | 0.393857 | + | 0.682180i | ||||
\(47\) | −58.2936 | −0.0263891 | −0.0131946 | − | 0.999913i | \(-0.504200\pi\) | ||||
−0.0131946 | + | 0.999913i | \(0.504200\pi\) | |||||||
\(48\) | − | 917.836i | − | 0.398366i | ||||||
\(49\) | 1118.02 | + | 1936.46i | 0.465646 | + | 0.806523i | ||||
\(50\) | 961.788 | + | 3589.44i | 0.384715 | + | 1.43578i | ||||
\(51\) | −5261.21 | − | 5261.21i | −2.02276 | − | 2.02276i | ||||
\(52\) | 231.467 | − | 863.847i | 0.0856017 | − | 0.319470i | ||||
\(53\) | −1894.64 | − | 3281.62i | −0.674490 | − | 1.16825i | −0.976618 | − | 0.214984i | \(-0.931030\pi\) |
0.302127 | − | 0.953268i | \(-0.402303\pi\) | |||||||
\(54\) | −1711.01 | − | 458.464i | −0.586766 | − | 0.157223i | ||||
\(55\) | 4938.16 | − | 1323.18i | 1.63245 | − | 0.437413i | ||||
\(56\) | 75.2193 | + | 280.722i | 0.0239857 | + | 0.0895160i | ||||
\(57\) | 1090.12 | − | 4068.39i | 0.335526 | − | 1.25220i | ||||
\(58\) | 2179.85 | − | 1258.54i | 0.647993 | − | 0.374119i | ||||
\(59\) | −3913.81 | − | 1048.70i | −1.12433 | − | 0.301265i | −0.351698 | − | 0.936113i | \(-0.614396\pi\) |
−0.772636 | + | 0.634849i | \(0.781062\pi\) | |||||||
\(60\) | −3572.15 | + | 3572.15i | −0.992264 | + | 0.992264i | ||||
\(61\) | −5014.41 | + | 1343.61i | −1.34760 | + | 0.361088i | −0.859248 | − | 0.511560i | \(-0.829068\pi\) |
−0.488350 | + | 0.872648i | \(0.662401\pi\) | |||||||
\(62\) | 1926.64 | − | 1112.34i | 0.501206 | − | 0.289372i | ||||
\(63\) | 1601.25 | 0.403438 | ||||||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | −4262.88 | + | 2461.18i | −1.00897 | + | 0.582527i | ||||
\(66\) | 3330.17 | + | 3330.17i | 0.764502 | + | 0.764502i | ||||
\(67\) | 7024.07 | + | 4055.35i | 1.56473 | + | 0.903397i | 0.996767 | + | 0.0803431i | \(0.0256016\pi\) |
0.567963 | + | 0.823054i | \(0.307732\pi\) | |||||||
\(68\) | −2934.88 | − | 2934.88i | −0.634706 | − | 0.634706i | ||||
\(69\) | 8163.33 | − | 2187.36i | 1.71463 | − | 0.459433i | ||||
\(70\) | 799.802 | − | 1385.30i | 0.163225 | − | 0.282714i | ||||
\(71\) | −849.084 | + | 1470.66i | −0.168436 | + | 0.291739i | −0.937870 | − | 0.346987i | \(-0.887205\pi\) |
0.769434 | + | 0.638726i | \(0.220538\pi\) | |||||||
\(72\) | −2724.83 | − | 730.116i | −0.525623 | − | 0.140840i | ||||
\(73\) | − | 4435.14i | − | 0.832265i | −0.909304 | − | 0.416133i | \(-0.863385\pi\) | ||
0.909304 | − | 0.416133i | \(-0.136615\pi\) | |||||||
\(74\) | −3836.42 | + | 524.545i | −0.700589 | + | 0.0957898i | ||||
\(75\) | 18841.8 | 3.34966 | ||||||||
\(76\) | 608.108 | − | 2269.49i | 0.105282 | − | 0.392917i | ||||
\(77\) | −1291.46 | − | 745.624i | −0.217821 | − | 0.125759i | ||||
\(78\) | −3927.03 | − | 2267.27i | −0.645468 | − | 0.372661i | ||||
\(79\) | 2480.61 | + | 9257.76i | 0.397470 | + | 1.48338i | 0.817533 | + | 0.575882i | \(0.195341\pi\) |
−0.420063 | + | 0.907495i | \(0.637992\pi\) | |||||||
\(80\) | −1992.67 | + | 1992.67i | −0.311354 | + | 0.311354i | ||||
\(81\) | 558.369 | − | 967.124i | 0.0851043 | − | 0.147405i | ||||
\(82\) | 3169.25 | − | 3169.25i | 0.471334 | − | 0.471334i | ||||
\(83\) | −2498.63 | − | 4327.76i | −0.362699 | − | 0.628213i | 0.625705 | − | 0.780060i | \(-0.284811\pi\) |
−0.988404 | + | 0.151847i | \(0.951478\pi\) | |||||||
\(84\) | 1473.58 | 0.208840 | ||||||||
\(85\) | 22844.7i | 3.16189i | ||||||||
\(86\) | 1506.95 | + | 2610.12i | 0.203753 | + | 0.352910i | ||||
\(87\) | −3303.18 | − | 12327.6i | −0.436409 | − | 1.62870i | ||||
\(88\) | 1857.68 | + | 1857.68i | 0.239887 | + | 0.239887i | ||||
\(89\) | 1361.09 | − | 5079.66i | 0.171833 | − | 0.641291i | −0.825236 | − | 0.564788i | \(-0.808958\pi\) |
0.997069 | − | 0.0765027i | \(-0.0243754\pi\) | |||||||
\(90\) | 7763.27 | + | 13446.4i | 0.958429 | + | 1.66005i | ||||
\(91\) | 1386.90 | + | 371.618i | 0.167480 | + | 0.0448760i | ||||
\(92\) | 4553.78 | − | 1220.18i | 0.538018 | − | 0.144162i | ||||
\(93\) | −2919.48 | − | 10895.6i | −0.337551 | − | 1.25976i | ||||
\(94\) | −42.6739 | + | 159.261i | −0.00482955 | + | 0.0180241i | ||||
\(95\) | −11199.4 | + | 6465.97i | −1.24093 | + | 0.716451i | ||||
\(96\) | −2507.57 | − | 671.902i | −0.272089 | − | 0.0729061i | ||||
\(97\) | 10038.9 | − | 10038.9i | 1.06695 | − | 1.06695i | 0.0693574 | − | 0.997592i | \(-0.477905\pi\) |
0.997592 | − | 0.0693574i | \(-0.0220949\pi\) | |||||||
\(98\) | 6108.96 | − | 1636.89i | 0.636085 | − | 0.170438i | ||||
\(99\) | 12535.5 | − | 7237.39i | 1.27901 | − | 0.738434i | ||||
\(100\) | 10510.6 | 1.05106 | ||||||||
\(101\) | 11990.1i | 1.17538i | 0.809084 | + | 0.587692i | \(0.199963\pi\) | ||||
−0.809084 | + | 0.587692i | \(0.800037\pi\) | |||||||
\(102\) | −18225.4 | + | 10522.4i | −1.75177 | + | 1.01138i | ||||
\(103\) | −1487.26 | − | 1487.26i | −0.140189 | − | 0.140189i | 0.633530 | − | 0.773718i | \(-0.281606\pi\) |
−0.773718 | + | 0.633530i | \(0.781606\pi\) | |||||||
\(104\) | −2190.63 | − | 1264.76i | −0.202536 | − | 0.116934i | ||||
\(105\) | −5735.05 | − | 5735.05i | −0.520186 | − | 0.520186i | ||||
\(106\) | −10352.5 | + | 2773.95i | −0.921371 | + | 0.246881i | ||||
\(107\) | −1311.64 | + | 2271.83i | −0.114564 | + | 0.198430i | −0.917605 | − | 0.397493i | \(-0.869880\pi\) |
0.803041 | + | 0.595923i | \(0.203214\pi\) | |||||||
\(108\) | −2505.09 | + | 4338.95i | −0.214771 | + | 0.371995i | ||||
\(109\) | −4767.40 | − | 1277.42i | −0.401263 | − | 0.107518i | 0.0525429 | − | 0.998619i | \(-0.483267\pi\) |
−0.453806 | + | 0.891101i | \(0.649934\pi\) | |||||||
\(110\) | − | 14459.9i | − | 1.19504i | ||||||
\(111\) | −2465.56 | + | 19477.7i | −0.200110 | + | 1.58085i | ||||
\(112\) | 822.011 | 0.0655303 | ||||||||
\(113\) | 2578.19 | − | 9621.93i | 0.201910 | − | 0.753538i | −0.788459 | − | 0.615087i | \(-0.789121\pi\) |
0.990369 | − | 0.138451i | \(-0.0442124\pi\) | |||||||
\(114\) | −10317.0 | − | 5956.54i | −0.793862 | − | 0.458337i | ||||
\(115\) | −22471.9 | − | 12974.1i | −1.69920 | − | 0.981031i | ||||
\(116\) | −1842.62 | − | 6876.77i | −0.136937 | − | 0.511056i | ||||
\(117\) | −9854.81 | + | 9854.81i | −0.719908 | + | 0.719908i | ||||
\(118\) | −5730.21 | + | 9925.02i | −0.411535 | + | 0.712799i | ||||
\(119\) | 4711.93 | − | 4711.93i | 0.332740 | − | 0.332740i | ||||
\(120\) | 7144.30 | + | 12374.3i | 0.496132 | + | 0.859325i | ||||
\(121\) | 1160.58 | 0.0792691 | ||||||||
\(122\) | 14683.2i | 0.986510i | ||||||||
\(123\) | −11362.7 | − | 19680.8i | −0.751055 | − | 1.30086i | ||||
\(124\) | −1628.59 | − | 6077.96i | −0.105917 | − | 0.395289i | ||||
\(125\) | −21446.9 | − | 21446.9i | −1.37260 | − | 1.37260i | ||||
\(126\) | 1172.19 | − | 4374.69i | 0.0738343 | − | 0.275554i | ||||
\(127\) | 9036.76 | + | 15652.1i | 0.560280 | + | 0.970434i | 0.997472 | + | 0.0710656i | \(0.0226400\pi\) |
−0.437191 | + | 0.899369i | \(0.644027\pi\) | |||||||
\(128\) | −1398.81 | − | 374.810i | −0.0853766 | − | 0.0228766i | ||||
\(129\) | 14760.9 | − | 3955.18i | 0.887022 | − | 0.237677i | ||||
\(130\) | 3603.41 | + | 13448.1i | 0.213220 | + | 0.795746i | ||||
\(131\) | −2676.97 | + | 9990.59i | −0.155991 | + | 0.582168i | 0.843027 | + | 0.537871i | \(0.180771\pi\) |
−0.999018 | + | 0.0442968i | \(0.985895\pi\) | |||||||
\(132\) | 11536.1 | − | 6660.34i | 0.662078 | − | 0.382251i | ||||
\(133\) | 3643.64 | + | 976.311i | 0.205984 | + | 0.0551931i | ||||
\(134\) | 16221.4 | − | 16221.4i | 0.903397 | − | 0.903397i | ||||
\(135\) | 26636.5 | − | 7137.23i | 1.46154 | − | 0.391617i | ||||
\(136\) | −10166.7 | + | 5869.76i | −0.549672 | + | 0.317353i | ||||
\(137\) | −20258.4 | −1.07935 | −0.539677 | − | 0.841872i | \(-0.681454\pi\) | ||||
−0.539677 | + | 0.841872i | \(0.681454\pi\) | |||||||
\(138\) | − | 23903.9i | − | 1.25519i | ||||||
\(139\) | 17822.2 | − | 10289.6i | 0.922426 | − | 0.532563i | 0.0380175 | − | 0.999277i | \(-0.487896\pi\) |
0.884408 | + | 0.466714i | \(0.154562\pi\) | |||||||
\(140\) | −3199.21 | − | 3199.21i | −0.163225 | − | 0.163225i | ||||
\(141\) | 723.997 | + | 418.000i | 0.0364165 | + | 0.0210251i | ||||
\(142\) | 3396.34 | + | 3396.34i | 0.168436 | + | 0.168436i | ||||
\(143\) | 12537.1 | − | 3359.32i | 0.613093 | − | 0.164278i | ||||
\(144\) | −3989.43 | + | 6909.89i | −0.192391 | + | 0.333231i | ||||
\(145\) | −19592.5 | + | 33935.2i | −0.931867 | + | 1.61404i | ||||
\(146\) | −12117.0 | − | 3246.75i | −0.568448 | − | 0.152315i | ||||
\(147\) | − | 32067.4i | − | 1.48398i | ||||||
\(148\) | −1375.37 | + | 10865.3i | −0.0627910 | + | 0.496042i | ||||
\(149\) | 8415.51 | 0.379060 | 0.189530 | − | 0.981875i | \(-0.439304\pi\) | ||||
0.189530 | + | 0.981875i | \(0.439304\pi\) | |||||||
\(150\) | 13793.2 | − | 51476.9i | 0.613030 | − | 2.28786i | ||||
\(151\) | −23646.4 | − | 13652.3i | −1.03708 | − | 0.598758i | −0.118074 | − | 0.993005i | \(-0.537672\pi\) |
−0.919005 | + | 0.394247i | \(0.871005\pi\) | |||||||
\(152\) | −5755.19 | − | 3322.76i | −0.249099 | − | 0.143818i | ||||
\(153\) | 16740.7 | + | 62477.0i | 0.715137 | + | 2.66893i | ||||
\(154\) | −2982.49 | + | 2982.49i | −0.125759 | + | 0.125759i | ||||
\(155\) | −17316.6 | + | 29993.3i | −0.720776 | + | 1.24842i | ||||
\(156\) | −9069.08 | + | 9069.08i | −0.372661 | + | 0.372661i | ||||
\(157\) | 8379.29 | + | 14513.4i | 0.339944 | + | 0.588801i | 0.984422 | − | 0.175822i | \(-0.0562584\pi\) |
−0.644478 | + | 0.764623i | \(0.722925\pi\) | |||||||
\(158\) | 27108.6 | 1.08591 | ||||||||
\(159\) | 54342.9i | 2.14955i | ||||||||
\(160\) | 3985.33 | + | 6902.80i | 0.155677 | + | 0.269641i | ||||
\(161\) | 1958.99 | + | 7311.06i | 0.0755755 | + | 0.282052i | ||||
\(162\) | −2233.48 | − | 2233.48i | −0.0851043 | − | 0.0851043i | ||||
\(163\) | 5333.68 | − | 19905.6i | 0.200748 | − | 0.749203i | −0.789955 | − | 0.613165i | \(-0.789896\pi\) |
0.990704 | − | 0.136039i | \(-0.0434371\pi\) | |||||||
\(164\) | −6338.50 | − | 10978.6i | −0.235667 | − | 0.408187i | ||||
\(165\) | −70819.0 | − | 18975.9i | −2.60125 | − | 0.697003i | ||||
\(166\) | −13652.8 | + | 3658.25i | −0.495456 | + | 0.132757i | ||||
\(167\) | −9491.45 | − | 35422.6i | −0.340329 | − | 1.27013i | −0.897975 | − | 0.440047i | \(-0.854962\pi\) |
0.557645 | − | 0.830079i | \(-0.311705\pi\) | |||||||
\(168\) | 1078.73 | − | 4025.89i | 0.0382204 | − | 0.142641i | ||||
\(169\) | 13911.8 | − | 8032.00i | 0.487092 | − | 0.281222i | ||||
\(170\) | 62412.9 | + | 16723.5i | 2.15961 | + | 0.578667i | ||||
\(171\) | −25890.4 | + | 25890.4i | −0.885416 | + | 0.885416i | ||||
\(172\) | 8234.15 | − | 2206.33i | 0.278331 | − | 0.0745786i | ||||
\(173\) | −6878.00 | + | 3971.01i | −0.229811 | + | 0.132681i | −0.610485 | − | 0.792028i | \(-0.709025\pi\) |
0.380674 | + | 0.924709i | \(0.375692\pi\) | |||||||
\(174\) | −36097.8 | −1.19229 | ||||||||
\(175\) | 16874.7i | 0.551011i | ||||||||
\(176\) | 6435.20 | − | 3715.37i | 0.207748 | − | 0.119943i | ||||
\(177\) | 41089.0 | + | 41089.0i | 1.31153 | + | 1.31153i | ||||
\(178\) | −12881.5 | − | 7437.14i | −0.406562 | − | 0.234729i | ||||
\(179\) | 8973.82 | + | 8973.82i | 0.280073 | + | 0.280073i | 0.833138 | − | 0.553065i | \(-0.186542\pi\) |
−0.553065 | + | 0.833138i | \(0.686542\pi\) | |||||||
\(180\) | 42419.3 | − | 11366.2i | 1.30924 | − | 0.350809i | ||||
\(181\) | −31151.0 | + | 53955.1i | −0.950857 | + | 1.64693i | −0.207280 | + | 0.978282i | \(0.566461\pi\) |
−0.743577 | + | 0.668650i | \(0.766872\pi\) | |||||||
\(182\) | 2030.56 | − | 3517.03i | 0.0613018 | − | 0.106178i | ||||
\(183\) | 71912.6 | + | 19268.9i | 2.14735 | + | 0.575381i | ||||
\(184\) | − | 13334.4i | − | 0.393857i | ||||||
\(185\) | 47639.8 | − | 36934.1i | 1.39196 | − | 1.07915i | ||||
\(186\) | −31904.7 | −0.922207 | ||||||||
\(187\) | 15590.6 | − | 58185.0i | 0.445841 | − | 1.66390i | ||||
\(188\) | 403.870 | + | 233.174i | 0.0114268 | + | 0.00659729i | ||||
\(189\) | −6966.14 | − | 4021.90i | −0.195015 | − | 0.112592i | ||||
\(190\) | 9466.84 | + | 35330.7i | 0.262239 | + | 0.978690i | ||||
\(191\) | 22712.1 | − | 22712.1i | 0.622575 | − | 0.622575i | −0.323614 | − | 0.946189i | \(-0.604898\pi\) |
0.946189 | + | 0.323614i | \(0.104898\pi\) | |||||||
\(192\) | −3671.34 | + | 6358.95i | −0.0995916 | + | 0.172498i | ||||
\(193\) | 32518.0 | − | 32518.0i | 0.872991 | − | 0.872991i | −0.119806 | − | 0.992797i | \(-0.538227\pi\) |
0.992797 | + | 0.119806i | \(0.0382274\pi\) | |||||||
\(194\) | −20077.9 | − | 34775.9i | −0.533475 | − | 0.924005i | ||||
\(195\) | 70592.3 | 1.85647 | ||||||||
\(196\) | − | 17888.3i | − | 0.465646i | ||||||
\(197\) | −16739.0 | − | 28992.9i | −0.431318 | − | 0.747065i | 0.565669 | − | 0.824632i | \(-0.308618\pi\) |
−0.996987 | + | 0.0775674i | \(0.975285\pi\) | |||||||
\(198\) | −10596.3 | − | 39545.8i | −0.270286 | − | 1.00872i | ||||
\(199\) | 26054.4 | + | 26054.4i | 0.657923 | + | 0.657923i | 0.954888 | − | 0.296965i | \(-0.0959745\pi\) |
−0.296965 | + | 0.954888i | \(0.595974\pi\) | |||||||
\(200\) | 7694.31 | − | 28715.5i | 0.192358 | − | 0.717889i | ||||
\(201\) | −58158.5 | − | 100734.i | −1.43953 | − | 2.49334i | ||||
\(202\) | 32757.6 | + | 8777.36i | 0.802803 | + | 0.215110i | ||||
\(203\) | 11040.6 | − | 2958.32i | 0.267917 | − | 0.0717881i | ||||
\(204\) | 15405.9 | + | 57495.6i | 0.370192 | + | 1.38157i | ||||
\(205\) | −18059.0 | + | 67396.9i | −0.429719 | + | 1.60373i | ||||
\(206\) | −5152.03 | + | 2974.53i | −0.121407 | + | 0.0700945i | ||||
\(207\) | −70964.8 | − | 19015.0i | −1.65616 | − | 0.443767i | ||||
\(208\) | −5059.04 | + | 5059.04i | −0.116934 | + | 0.116934i | ||||
\(209\) | 32937.4 | − | 8825.56i | 0.754045 | − | 0.202046i | ||||
\(210\) | −19866.8 | + | 11470.1i | −0.450494 | + | 0.260093i | ||||
\(211\) | 31308.2 | 0.703222 | 0.351611 | − | 0.936146i | \(-0.385634\pi\) | ||||
0.351611 | + | 0.936146i | \(0.385634\pi\) | |||||||
\(212\) | 30314.3i | 0.674490i | ||||||||
\(213\) | 21091.0 | − | 12176.9i | 0.464876 | − | 0.268396i | ||||
\(214\) | 5246.57 | + | 5246.57i | 0.114564 | + | 0.114564i | ||||
\(215\) | −40633.6 | − | 23459.8i | −0.879039 | − | 0.507514i | ||||
\(216\) | 10020.4 | + | 10020.4i | 0.214771 | + | 0.214771i | ||||
\(217\) | 9758.12 | − | 2614.68i | 0.207227 | − | 0.0555263i | ||||
\(218\) | −6979.96 | + | 12089.7i | −0.146872 | + | 0.254390i | ||||
\(219\) | −31802.6 | + | 55083.7i | −0.663093 | + | 1.14851i | ||||
\(220\) | −39505.3 | − | 10585.4i | −0.816225 | − | 0.218707i | ||||
\(221\) | 57998.8i | 1.18750i | ||||||||
\(222\) | 51409.0 | + | 20994.7i | 1.04312 | + | 0.425994i | ||||
\(223\) | 52715.7 | 1.06006 | 0.530030 | − | 0.847979i | \(-0.322181\pi\) | ||||
0.530030 | + | 0.847979i | \(0.322181\pi\) | |||||||
\(224\) | 601.754 | − | 2245.78i | 0.0119929 | − | 0.0447580i | ||||
\(225\) | −141850. | − | 81897.1i | −2.80197 | − | 1.61772i | ||||
\(226\) | −24400.2 | − | 14087.5i | −0.477724 | − | 0.275814i | ||||
\(227\) | −8511.26 | − | 31764.5i | −0.165174 | − | 0.616438i | −0.998018 | − | 0.0629303i | \(-0.979955\pi\) |
0.832844 | − | 0.553508i | \(-0.186711\pi\) | |||||||
\(228\) | −23826.2 | + | 23826.2i | −0.458337 | + | 0.458337i | ||||
\(229\) | −20946.4 | + | 36280.3i | −0.399428 | + | 0.691830i | −0.993655 | − | 0.112467i | \(-0.964125\pi\) |
0.594227 | + | 0.804297i | \(0.297458\pi\) | |||||||
\(230\) | −51896.5 | + | 51896.5i | −0.981031 | + | 0.981031i | ||||
\(231\) | 10693.1 | + | 18521.0i | 0.200392 | + | 0.347089i | ||||
\(232\) | −20136.6 | −0.374119 | ||||||||
\(233\) | 54089.5i | 0.996326i | 0.867083 | + | 0.498163i | \(0.165992\pi\) | ||||
−0.867083 | + | 0.498163i | \(0.834008\pi\) | |||||||
\(234\) | 19709.6 | + | 34138.1i | 0.359954 | + | 0.623458i | ||||
\(235\) | −664.334 | − | 2479.33i | −0.0120296 | − | 0.0448951i | ||||
\(236\) | 22920.9 | + | 22920.9i | 0.411535 | + | 0.411535i | ||||
\(237\) | 35574.9 | − | 132767.i | 0.633354 | − | 2.36371i | ||||
\(238\) | −9423.86 | − | 16322.6i | −0.166370 | − | 0.288161i | ||||
\(239\) | −77889.4 | − | 20870.4i | −1.36359 | − | 0.365372i | −0.498454 | − | 0.866916i | \(-0.666099\pi\) |
−0.865132 | + | 0.501544i | \(0.832765\pi\) | |||||||
\(240\) | 39037.2 | − | 10460.0i | 0.677729 | − | 0.181597i | ||||
\(241\) | −4223.66 | − | 15762.9i | −0.0727202 | − | 0.271396i | 0.919986 | − | 0.391950i | \(-0.128199\pi\) |
−0.992707 | + | 0.120554i | \(0.961533\pi\) | |||||||
\(242\) | 849.602 | − | 3170.76i | 0.0145072 | − | 0.0541418i | ||||
\(243\) | −57801.5 | + | 33371.7i | −0.978874 | + | 0.565153i | ||||
\(244\) | 40115.3 | + | 10748.9i | 0.673799 | + | 0.180544i | ||||
\(245\) | −69619.8 | + | 69619.8i | −1.15985 | + | 1.15985i | ||||
\(246\) | −62087.0 | + | 16636.2i | −1.02596 | + | 0.274905i | ||||
\(247\) | −28433.3 | + | 16416.0i | −0.466052 | + | 0.269075i | ||||
\(248\) | −17797.5 | −0.289372 | ||||||||
\(249\) | 71666.7i | 1.15590i | ||||||||
\(250\) | −74294.3 | + | 42893.8i | −1.18871 | + | 0.686301i | ||||
\(251\) | −46328.6 | − | 46328.6i | −0.735363 | − | 0.735363i | 0.236314 | − | 0.971677i | \(-0.424061\pi\) |
−0.971677 | + | 0.236314i | \(0.924061\pi\) | |||||||
\(252\) | −11093.8 | − | 6404.99i | −0.174694 | − | 0.100860i | ||||
\(253\) | 48381.1 | + | 48381.1i | 0.755848 | + | 0.755848i | ||||
\(254\) | 49377.8 | − | 13230.7i | 0.765357 | − | 0.205077i | ||||
\(255\) | 163810. | − | 283727.i | 2.51918 | − | 4.36336i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −28401.7 | − | 7610.22i | −0.430010 | − | 0.115221i | 0.0373210 | − | 0.999303i | \(-0.488118\pi\) |
−0.467331 | + | 0.884083i | \(0.654784\pi\) | |||||||
\(258\) | − | 43223.0i | − | 0.649345i | ||||||
\(259\) | −17444.1 | − | 2208.15i | −0.260046 | − | 0.0329177i | ||||
\(260\) | 39378.8 | 0.582527 | ||||||||
\(261\) | −28714.9 | + | 107165.i | −0.421528 | + | 1.57316i | ||||
\(262\) | 25335.1 | + | 14627.2i | 0.369080 | + | 0.213088i | ||||
\(263\) | −41108.1 | − | 23733.8i | −0.594313 | − | 0.343127i | 0.172488 | − | 0.985012i | \(-0.444819\pi\) |
−0.766801 | + | 0.641885i | \(0.778153\pi\) | |||||||
\(264\) | −9751.42 | − | 36392.8i | −0.139914 | − | 0.522165i | ||||
\(265\) | 117981. | − | 117981.i | 1.68004 | − | 1.68004i | ||||
\(266\) | 5334.66 | − | 9239.91i | 0.0753952 | − | 0.130588i | ||||
\(267\) | −53328.7 | + | 53328.7i | −0.748064 | + | 0.748064i | ||||
\(268\) | −32442.8 | − | 56192.6i | −0.451699 | − | 0.782365i | ||||
\(269\) | 48197.1 | 0.666065 | 0.333033 | − | 0.942915i | \(-0.391928\pi\) | ||||
0.333033 | + | 0.942915i | \(0.391928\pi\) | |||||||
\(270\) | − | 77997.1i | − | 1.06992i | ||||||
\(271\) | 43985.7 | + | 76185.5i | 0.598926 | + | 1.03737i | 0.992980 | + | 0.118283i | \(0.0377389\pi\) |
−0.394054 | + | 0.919087i | \(0.628928\pi\) | |||||||
\(272\) | 8593.93 | + | 32073.0i | 0.116159 | + | 0.433513i | ||||
\(273\) | −14560.3 | − | 14560.3i | −0.195365 | − | 0.195365i | ||||
\(274\) | −14830.2 | + | 55347.0i | −0.197536 | + | 0.737213i | ||||
\(275\) | 76271.1 | + | 132105.i | 1.00854 | + | 1.74685i | ||||
\(276\) | −65306.7 | − | 17498.9i | −0.857313 | − | 0.229716i | ||||
\(277\) | −72840.7 | + | 19517.6i | −0.949324 | + | 0.254371i | −0.700075 | − | 0.714069i | \(-0.746850\pi\) |
−0.249249 | + | 0.968440i | \(0.580184\pi\) | |||||||
\(278\) | −15065.1 | − | 56223.7i | −0.194931 | − | 0.727494i | ||||
\(279\) | −25379.4 | + | 94717.1i | −0.326041 | + | 1.21680i | ||||
\(280\) | −11082.4 | + | 6398.42i | −0.141357 | + | 0.0816124i | ||||
\(281\) | 119831. | + | 32108.7i | 1.51760 | + | 0.406640i | 0.918951 | − | 0.394372i | \(-0.129038\pi\) |
0.598649 | + | 0.801012i | \(0.295705\pi\) | |||||||
\(282\) | 1672.00 | − | 1672.00i | 0.0210251 | − | 0.0210251i | ||||
\(283\) | −22714.6 | + | 6086.35i | −0.283617 | + | 0.0759948i | −0.397823 | − | 0.917462i | \(-0.630234\pi\) |
0.114206 | + | 0.993457i | \(0.463567\pi\) | |||||||
\(284\) | 11765.3 | − | 6792.67i | 0.145870 | − | 0.0842178i | ||||
\(285\) | 185459. | 2.28328 | ||||||||
\(286\) | − | 36711.3i | − | 0.448815i | ||||||
\(287\) | 17626.1 | − | 10176.4i | 0.213989 | − | 0.123547i | ||||
\(288\) | 15957.7 | + | 15957.7i | 0.192391 | + | 0.192391i | ||||
\(289\) | 160779. | + | 92826.0i | 1.92502 | + | 1.11141i | ||||
\(290\) | 78370.0 | + | 78370.0i | 0.931867 | + | 0.931867i | ||||
\(291\) | −196667. | + | 52696.7i | −2.32244 | + | 0.622297i | ||||
\(292\) | −17740.6 | + | 30727.6i | −0.208066 | + | 0.360381i | ||||
\(293\) | 47090.0 | − | 81562.2i | 0.548521 | − | 0.950066i | −0.449855 | − | 0.893102i | \(-0.648524\pi\) |
0.998376 | − | 0.0569647i | \(-0.0181423\pi\) | |||||||
\(294\) | −87609.7 | − | 23474.9i | −1.01358 | − | 0.271588i | ||||
\(295\) | − | 178413.i | − | 2.05013i | ||||||
\(296\) | 28677.7 | + | 11711.5i | 0.327311 | + | 0.133669i | ||||
\(297\) | −72713.6 | −0.824333 | ||||||||
\(298\) | 6160.58 | − | 22991.6i | 0.0693728 | − | 0.258903i | ||||
\(299\) | −57052.2 | − | 32939.1i | −0.638161 | − | 0.368442i | ||||
\(300\) | −130540. | − | 75367.4i | −1.45045 | − | 0.837415i | ||||
\(301\) | 3542.25 | + | 13219.9i | 0.0390972 | + | 0.145913i | ||||
\(302\) | −54609.1 | + | 54609.1i | −0.598758 | + | 0.598758i | ||||
\(303\) | 85976.1 | − | 148915.i | 0.936467 | − | 1.62201i | ||||
\(304\) | −13291.0 | + | 13291.0i | −0.143818 | + | 0.143818i | ||||
\(305\) | −114292. | − | 197960.i | −1.22862 | − | 2.12803i | ||||
\(306\) | 182945. | 1.95379 | ||||||||
\(307\) | 133438.i | 1.41580i | 0.706313 | + | 0.707899i | \(0.250357\pi\) | ||||
−0.706313 | + | 0.707899i | \(0.749643\pi\) | |||||||
\(308\) | 5964.99 | + | 10331.7i | 0.0628794 | + | 0.108910i | ||||
\(309\) | 7807.00 | + | 29136.1i | 0.0817650 | + | 0.305151i | ||||
\(310\) | 69266.6 | + | 69266.6i | 0.720776 | + | 0.720776i | ||||
\(311\) | 22407.9 | − | 83627.3i | 0.231675 | − | 0.864624i | −0.747944 | − | 0.663762i | \(-0.768959\pi\) |
0.979619 | − | 0.200862i | \(-0.0643744\pi\) | |||||||
\(312\) | 18138.2 | + | 31416.2i | 0.186330 | + | 0.322734i | ||||
\(313\) | −129678. | − | 34747.2i | −1.32367 | − | 0.354675i | −0.473317 | − | 0.880892i | \(-0.656943\pi\) |
−0.850350 | + | 0.526217i | \(0.823610\pi\) | |||||||
\(314\) | 45785.3 | − | 12268.1i | 0.464373 | − | 0.124428i | ||||
\(315\) | 18248.4 | + | 68103.8i | 0.183909 | + | 0.686358i | ||||
\(316\) | 19844.9 | − | 74062.1i | 0.198735 | − | 0.741689i | ||||
\(317\) | −208.710 | + | 120.499i | −0.00207695 | + | 0.00119913i | −0.501038 | − | 0.865425i | \(-0.667048\pi\) |
0.498961 | + | 0.866624i | \(0.333715\pi\) | |||||||
\(318\) | 148467. | + | 39781.7i | 1.46817 | + | 0.393396i | ||||
\(319\) | 73061.3 | − | 73061.3i | 0.717969 | − | 0.717969i | ||||
\(320\) | 21776.3 | − | 5834.93i | 0.212659 | − | 0.0569818i | ||||
\(321\) | 32580.7 | − | 18810.5i | 0.316192 | − | 0.182553i | ||||
\(322\) | 21408.3 | 0.206476 | ||||||||
\(323\) | 152374.i | 1.46051i | ||||||||
\(324\) | −7736.99 | + | 4466.95i | −0.0737025 | + | 0.0425521i | ||||
\(325\) | −103855. | − | 103855.i | −0.983240 | − | 0.983240i | ||||
\(326\) | −50478.5 | − | 29143.8i | −0.474976 | − | 0.274227i | ||||
\(327\) | 50050.5 | + | 50050.5i | 0.468072 | + | 0.468072i | ||||
\(328\) | −34634.2 | + | 9280.21i | −0.321927 | + | 0.0862602i | ||||
\(329\) | −374.360 | + | 648.410i | −0.00345857 | + | 0.00599043i | ||||
\(330\) | −103686. | + | 179590.i | −0.952124 | + | 1.64913i | ||||
\(331\) | −125081. | − | 33515.4i | −1.14166 | − | 0.305906i | −0.362041 | − | 0.932162i | \(-0.617920\pi\) |
−0.779618 | + | 0.626256i | \(0.784587\pi\) | |||||||
\(332\) | 39978.1i | 0.362699i | ||||||||
\(333\) | 103223. | − | 135920.i | 0.930864 | − | 1.22573i | ||||
\(334\) | −103724. | −0.929797 | ||||||||
\(335\) | −92432.4 | + | 344962.i | −0.823635 | + | 3.07385i | ||||
\(336\) | −10209.2 | − | 5894.31i | −0.0904305 | − | 0.0522101i | ||||
\(337\) | 54667.4 | + | 31562.3i | 0.481359 | + | 0.277913i | 0.720983 | − | 0.692953i | \(-0.243691\pi\) |
−0.239624 | + | 0.970866i | \(0.577024\pi\) | |||||||
\(338\) | −11759.7 | − | 43887.6i | −0.102935 | − | 0.384157i | ||||
\(339\) | −101016. | + | 101016.i | −0.879000 | + | 0.879000i | ||||
\(340\) | 91378.8 | − | 158273.i | 0.790474 | − | 1.36914i | ||||
\(341\) | 64574.5 | − | 64574.5i | 0.555331 | − | 0.555331i | ||||
\(342\) | 51780.9 | + | 89687.1i | 0.442708 | + | 0.766793i | ||||
\(343\) | 59557.7 | 0.506232 | ||||||||
\(344\) | − | 24111.3i | − | 0.203753i | ||||||
\(345\) | 186064. | + | 322273.i | 1.56324 | + | 2.70761i | ||||
\(346\) | 5813.97 | + | 21698.0i | 0.0485647 | + | 0.181246i | ||||
\(347\) | 24526.3 | + | 24526.3i | 0.203692 | + | 0.203692i | 0.801580 | − | 0.597888i | \(-0.203993\pi\) |
−0.597888 | + | 0.801580i | \(0.703993\pi\) | |||||||
\(348\) | −26425.4 | + | 98621.0i | −0.218204 | + | 0.814349i | ||||
\(349\) | −86628.5 | − | 150045.i | −0.711230 | − | 1.23189i | −0.964396 | − | 0.264463i | \(-0.914805\pi\) |
0.253166 | − | 0.967423i | \(-0.418528\pi\) | |||||||
\(350\) | 46102.6 | + | 12353.1i | 0.376347 | + | 0.100842i | ||||
\(351\) | 67625.5 | − | 18120.2i | 0.548904 | − | 0.147078i | ||||
\(352\) | −5439.67 | − | 20301.1i | −0.0439023 | − | 0.163846i | ||||
\(353\) | 33574.0 | − | 125300.i | 0.269435 | − | 1.00554i | −0.690045 | − | 0.723766i | \(-0.742409\pi\) |
0.959480 | − | 0.281777i | \(-0.0909239\pi\) | |||||||
\(354\) | 142337. | − | 82178.0i | 1.13582 | − | 0.655766i | ||||
\(355\) | −72226.1 | − | 19352.9i | −0.573109 | − | 0.153564i | ||||
\(356\) | −29748.6 | + | 29748.6i | −0.234729 | + | 0.234729i | ||||
\(357\) | −92308.6 | + | 24734.0i | −0.724279 | + | 0.194070i | ||||
\(358\) | 31086.2 | − | 17947.6i | 0.242550 | − | 0.140036i | ||||
\(359\) | −24962.2 | −0.193684 | −0.0968421 | − | 0.995300i | \(-0.530874\pi\) | ||||
−0.0968421 | + | 0.995300i | \(0.530874\pi\) | |||||||
\(360\) | − | 124212.i | − | 0.958429i | ||||||
\(361\) | 38161.6 | − | 22032.6i | 0.292828 | − | 0.169064i | ||||
\(362\) | 124604. | + | 124604.i | 0.950857 | + | 0.950857i | ||||
\(363\) | −14414.2 | − | 8322.03i | −0.109390 | − | 0.0631562i | ||||
\(364\) | −8122.24 | − | 8122.24i | −0.0613018 | − | 0.0613018i | ||||
\(365\) | 188634. | − | 50544.4i | 1.41591 | − | 0.379391i | ||||
\(366\) | 105287. | − | 182363.i | 0.785985 | − | 1.36137i | ||||
\(367\) | 13470.9 | − | 23332.3i | 0.100015 | − | 0.173231i | −0.811676 | − | 0.584108i | \(-0.801444\pi\) |
0.911691 | + | 0.410878i | \(0.134778\pi\) | |||||||
\(368\) | −36430.3 | − | 9761.46i | −0.269009 | − | 0.0720808i | ||||
\(369\) | 197555.i | 1.45089i | ||||||||
\(370\) | −66031.0 | − | 157192.i | −0.482330 | − | 1.14822i | ||||
\(371\) | −48669.3 | −0.353596 | ||||||||
\(372\) | −23355.8 | + | 87165.2i | −0.168776 | + | 0.629879i | ||||
\(373\) | 63125.0 | + | 36445.2i | 0.453716 | + | 0.261953i | 0.709398 | − | 0.704808i | \(-0.248967\pi\) |
−0.255683 | + | 0.966761i | \(0.582300\pi\) | |||||||
\(374\) | −147551. | − | 85188.8i | −1.05487 | − | 0.609031i | ||||
\(375\) | 112580. | + | 420154.i | 0.800569 | + | 2.98776i | ||||
\(376\) | 932.698 | − | 932.698i | 0.00659729 | − | 0.00659729i | ||||
\(377\) | −49742.0 | + | 86155.7i | −0.349978 | + | 0.606180i | ||||
\(378\) | −16087.6 | + | 16087.6i | −0.112592 | + | 0.112592i | ||||
\(379\) | −90490.4 | − | 156734.i | −0.629976 | − | 1.09115i | −0.987556 | − | 0.157268i | \(-0.949731\pi\) |
0.357579 | − | 0.933883i | \(-0.383602\pi\) | |||||||
\(380\) | 103456. | 0.716451 | ||||||||
\(381\) | − | 259196.i | − | 1.78557i | ||||||
\(382\) | −45424.3 | − | 78677.2i | −0.311287 | − | 0.539165i | ||||
\(383\) | −8815.07 | − | 32898.3i | −0.0600936 | − | 0.224272i | 0.929348 | − | 0.369205i | \(-0.120370\pi\) |
−0.989441 | + | 0.144933i | \(0.953703\pi\) | |||||||
\(384\) | 14685.4 | + | 14685.4i | 0.0995916 | + | 0.0995916i | ||||
\(385\) | 16994.8 | − | 63425.4i | 0.114655 | − | 0.427899i | ||||
\(386\) | −65036.1 | − | 112646.i | −0.436495 | − | 0.756032i | ||||
\(387\) | −128318. | − | 34382.8i | −0.856776 | − | 0.229572i | ||||
\(388\) | −109707. | + | 29396.0i | −0.728740 | + | 0.195265i | ||||
\(389\) | −10372.0 | − | 38708.8i | −0.0685430 | − | 0.255806i | 0.923149 | − | 0.384443i | \(-0.125606\pi\) |
−0.991692 | + | 0.128637i | \(0.958940\pi\) | |||||||
\(390\) | 51677.2 | − | 192862.i | 0.339758 | − | 1.26799i | ||||
\(391\) | −264780. | + | 152871.i | −1.73193 | + | 0.999933i | ||||
\(392\) | −48871.7 | − | 13095.1i | −0.318042 | − | 0.0852192i | ||||
\(393\) | 104886. | − | 104886.i | 0.679098 | − | 0.679098i | ||||
\(394\) | −91463.8 | + | 24507.6i | −0.589192 | + | 0.157873i | ||||
\(395\) | −365479. | + | 211009.i | −2.34244 | + | 1.35241i | ||||
\(396\) | −115798. | −0.738434 | ||||||||
\(397\) | − | 200596.i | − | 1.27274i | −0.771382 | − | 0.636372i | \(-0.780434\pi\) | ||
0.771382 | − | 0.636372i | \(-0.219566\pi\) | |||||||
\(398\) | 90255.2 | − | 52108.8i | 0.569778 | − | 0.328962i | ||||
\(399\) | −38252.7 | − | 38252.7i | −0.240279 | − | 0.240279i | ||||
\(400\) | −72819.7 | − | 42042.5i | −0.455123 | − | 0.262765i | ||||
\(401\) | 57086.9 | + | 57086.9i | 0.355016 | + | 0.355016i | 0.861972 | − | 0.506956i | \(-0.169229\pi\) |
−0.506956 | + | 0.861972i | \(0.669229\pi\) | |||||||
\(402\) | −317784. | + | 85150.0i | −1.96644 | + | 0.526905i | ||||
\(403\) | −43964.0 | + | 76147.9i | −0.270699 | + | 0.468865i | ||||
\(404\) | 47960.4 | − | 83069.9i | 0.293846 | − | 0.508957i | ||||
\(405\) | 47496.8 | + | 12726.7i | 0.289571 | + | 0.0775902i | ||||
\(406\) | − | 32329.1i | − | 0.196129i | ||||||
\(407\) | −146544. | + | 61558.1i | −0.884664 | + | 0.371618i | ||||
\(408\) | 168359. | 1.01138 | ||||||||
\(409\) | 27545.1 | − | 102800.i | 0.164664 | − | 0.614533i | −0.833419 | − | 0.552641i | \(-0.813620\pi\) |
0.998083 | − | 0.0618916i | \(-0.0197133\pi\) | |||||||
\(410\) | 170912. | + | 98675.9i | 1.01673 | + | 0.587007i | ||||
\(411\) | 251606. | + | 145265.i | 1.48949 | + | 0.859957i | ||||
\(412\) | 4355.01 | + | 16253.1i | 0.0256564 | + | 0.0957508i | ||||
\(413\) | −36799.2 | + | 36799.2i | −0.215744 | + | 0.215744i | ||||
\(414\) | −103900. | + | 179959.i | −0.606196 | + | 1.04996i | ||||
\(415\) | 155592. | − | 155592.i | 0.903423 | − | 0.903423i | ||||
\(416\) | 10118.1 | + | 17525.0i | 0.0584671 | + | 0.101268i | ||||
\(417\) | −295131. | −1.69724 | ||||||||
\(418\) | − | 96447.5i | − | 0.551999i | ||||||
\(419\) | 31934.2 | + | 55311.6i | 0.181898 | + | 0.315056i | 0.942527 | − | 0.334131i | \(-0.108443\pi\) |
−0.760629 | + | 0.649187i | \(0.775109\pi\) | |||||||
\(420\) | 16793.4 | + | 62673.8i | 0.0952007 | + | 0.355294i | ||||
\(421\) | 27945.5 | + | 27945.5i | 0.157669 | + | 0.157669i | 0.781533 | − | 0.623864i | \(-0.214438\pi\) |
−0.623864 | + | 0.781533i | \(0.714438\pi\) | |||||||
\(422\) | 22919.2 | − | 85535.5i | 0.128699 | − | 0.480310i | ||||
\(423\) | −3633.72 | − | 6293.79i | −0.0203082 | − | 0.0351748i | ||||
\(424\) | 82820.2 | + | 22191.6i | 0.460685 | + | 0.123440i | ||||
\(425\) | −658412. | + | 176421.i | −3.64519 | + | 0.976725i | ||||
\(426\) | −17828.2 | − | 66535.7i | −0.0982398 | − | 0.366636i | ||||
\(427\) | −17257.2 | + | 64404.8i | −0.0946487 | + | 0.353234i | ||||
\(428\) | 18174.6 | − | 10493.1i | 0.0992152 | − | 0.0572819i | ||||
\(429\) | −179797. | − | 48176.6i | −0.976942 | − | 0.261771i | ||||
\(430\) | −93839.3 | + | 93839.3i | −0.507514 | + | 0.507514i | ||||
\(431\) | 41795.3 | − | 11199.0i | 0.224995 | − | 0.0602873i | −0.144560 | − | 0.989496i | \(-0.546177\pi\) |
0.369555 | + | 0.929209i | \(0.379510\pi\) | |||||||
\(432\) | 34711.6 | − | 20040.7i | 0.185997 | − | 0.107386i | ||||
\(433\) | 79871.2 | 0.426005 | 0.213002 | − | 0.977052i | \(-0.431676\pi\) | ||||
0.213002 | + | 0.977052i | \(0.431676\pi\) | |||||||
\(434\) | − | 28573.7i | − | 0.151701i | ||||||
\(435\) | 486671. | − | 280980.i | 2.57192 | − | 1.48490i | ||||
\(436\) | 27919.9 | + | 27919.9i | 0.146872 | + | 0.146872i | ||||
\(437\) | −149887. | − | 86537.2i | −0.784875 | − | 0.453148i | ||||
\(438\) | 127210. | + | 127210.i | 0.663093 | + | 0.663093i | ||||
\(439\) | 96535.4 | − | 25866.6i | 0.500908 | − | 0.134218i | 0.000486404 | − | 1.00000i | \(-0.499845\pi\) |
0.500421 | + | 0.865782i | \(0.333179\pi\) | |||||||
\(440\) | −57839.7 | + | 100181.i | −0.298759 | + | 0.517466i | ||||
\(441\) | −139383. | + | 241418.i | −0.716690 | + | 1.24134i | ||||
\(442\) | 158456. | + | 42458.0i | 0.811079 | + | 0.217328i | ||||
\(443\) | − | 240502.i | − | 1.22550i | −0.790278 | − | 0.612748i | \(-0.790064\pi\) | ||
0.790278 | − | 0.612748i | \(-0.209936\pi\) | |||||||
\(444\) | 94992.5 | − | 125083.i | 0.481863 | − | 0.634500i | ||||
\(445\) | 231559. | 1.16934 | ||||||||
\(446\) | 38590.6 | − | 144022.i | 0.194004 | − | 0.724034i | ||||
\(447\) | −104519. | − | 60344.2i | −0.523095 | − | 0.302009i | ||||
\(448\) | −5695.06 | − | 3288.05i | −0.0283754 | − | 0.0163826i | ||||
\(449\) | 32901.3 | + | 122789.i | 0.163200 | + | 0.609071i | 0.998263 | + | 0.0589167i | \(0.0187646\pi\) |
−0.835063 | + | 0.550155i | \(0.814569\pi\) | |||||||
\(450\) | −327589. | + | 327589.i | −1.61772 | + | 1.61772i | ||||
\(451\) | 91991.7 | − | 159334.i | 0.452268 | − | 0.783350i | ||||
\(452\) | −56349.9 | + | 56349.9i | −0.275814 | + | 0.275814i | ||||
\(453\) | 195790. | + | 339118.i | 0.954099 | + | 1.65255i | ||||
\(454\) | −93012.8 | −0.451264 | ||||||||
\(455\) | 63222.3i | 0.305385i | ||||||||
\(456\) | 47652.3 | + | 82536.3i | 0.229168 | + | 0.396931i | ||||
\(457\) | −42900.7 | − | 160108.i | −0.205415 | − | 0.766619i | −0.989323 | − | 0.145742i | \(-0.953443\pi\) |
0.783908 | − | 0.620877i | \(-0.213224\pi\) | |||||||
\(458\) | 83785.7 | + | 83785.7i | 0.399428 | + | 0.399428i | ||||
\(459\) | 84096.0 | − | 313851.i | 0.399163 | − | 1.48970i | ||||
\(460\) | 103793. | + | 179775.i | 0.490515 | + | 0.849598i | ||||
\(461\) | −171527. | − | 45960.4i | −0.807105 | − | 0.216263i | −0.168404 | − | 0.985718i | \(-0.553861\pi\) |
−0.638701 | + | 0.769455i | \(0.720528\pi\) | |||||||
\(462\) | 58428.3 | − | 15655.8i | 0.273741 | − | 0.0733486i | ||||
\(463\) | −27205.5 | − | 101532.i | −0.126910 | − | 0.473634i | 0.872991 | − | 0.487737i | \(-0.162177\pi\) |
−0.999901 | + | 0.0141029i | \(0.995511\pi\) | |||||||
\(464\) | −14741.0 | + | 55014.1i | −0.0684685 | + | 0.255528i | ||||
\(465\) | 430140. | − | 248341.i | 1.98931 | − | 1.14853i | ||||
\(466\) | 147775. | + | 39596.3i | 0.680503 | + | 0.182340i | ||||
\(467\) | 206813. | − | 206813.i | 0.948295 | − | 0.948295i | −0.0504321 | − | 0.998727i | \(-0.516060\pi\) |
0.998727 | + | 0.0504321i | \(0.0160599\pi\) | |||||||
\(468\) | 107695. | − | 28856.9i | 0.491706 | − | 0.131752i | ||||
\(469\) | 90216.7 | − | 52086.6i | 0.410149 | − | 0.236799i | ||||
\(470\) | −7259.98 | −0.0328655 | ||||||||
\(471\) | − | 240338.i | − | 1.08338i | ||||||
\(472\) | 79400.2 | − | 45841.7i | 0.356400 | − | 0.205767i | ||||
\(473\) | 87482.6 | + | 87482.6i | 0.391020 | + | 0.391020i | ||||
\(474\) | −336684. | − | 194385.i | −1.49853 | − | 0.865178i | ||||
\(475\) | −272846. | − | 272846.i | −1.20929 | − | 1.20929i | ||||
\(476\) | −51492.9 | + | 13797.5i | −0.227265 | + | 0.0608956i | ||||
\(477\) | 236204. | − | 409118.i | 1.03813 | − | 1.79809i | ||||
\(478\) | −114038. | + | 197520.i | −0.499107 | + | 0.864479i | ||||
\(479\) | 398538. | + | 106788.i | 1.73700 | + | 0.465427i | 0.981776 | − | 0.190042i | \(-0.0608625\pi\) |
0.755222 | + | 0.655469i | \(0.227529\pi\) | |||||||
\(480\) | − | 114309.i | − | 0.496132i | ||||||
\(481\) | 120949. | − | 93769.3i | 0.522773 | − | 0.405294i | ||||
\(482\) | −46157.1 | −0.198675 | ||||||||
\(483\) | 28094.3 | − | 104849.i | 0.120427 | − | 0.449439i | ||||
\(484\) | −8040.72 | − | 4642.31i | −0.0343245 | − | 0.0198173i | ||||
\(485\) | 541380. | + | 312566.i | 2.30154 | + | 1.32880i | ||||
\(486\) | 48859.6 | + | 182347.i | 0.206860 | + | 0.772014i | ||||
\(487\) | −248814. | + | 248814.i | −1.04910 | + | 1.04910i | −0.0503711 | + | 0.998731i | \(0.516040\pi\) |
−0.998731 | + | 0.0503711i | \(0.983960\pi\) | |||||||
\(488\) | 58732.9 | − | 101728.i | 0.246628 | − | 0.427171i | ||||
\(489\) | −208978. | + | 208978.i | −0.873943 | + | 0.873943i | ||||
\(490\) | 139240. | + | 241170.i | 0.579923 | + | 1.00446i | ||||
\(491\) | −421783. | −1.74955 | −0.874774 | − | 0.484532i | \(-0.838990\pi\) | ||||
−0.874774 | + | 0.484532i | \(0.838990\pi\) | |||||||
\(492\) | 181803.i | 0.751055i | ||||||||
\(493\) | 230853. | + | 399850.i | 0.949822 | + | 1.64514i | ||||
\(494\) | 24034.7 | + | 89698.7i | 0.0984883 | + | 0.367563i | ||||
\(495\) | 450678. | + | 450678.i | 1.83932 | + | 1.83932i | ||||
\(496\) | −13028.7 | + | 48623.7i | −0.0529587 | + | 0.197644i | ||||
\(497\) | 10905.6 | + | 18889.0i | 0.0441505 | + | 0.0764709i | ||||
\(498\) | 195797. | + | 52463.7i | 0.789492 | + | 0.211544i | ||||
\(499\) | −63426.3 | + | 16995.0i | −0.254723 | + | 0.0682528i | −0.383921 | − | 0.923366i | \(-0.625426\pi\) |
0.129198 | + | 0.991619i | \(0.458760\pi\) | |||||||
\(500\) | 62800.9 | + | 234376.i | 0.251204 | + | 0.937505i | ||||
\(501\) | −136119. | + | 508001.i | −0.542303 | + | 2.02390i | ||||
\(502\) | −160487. | + | 92657.2i | −0.636843 | + | 0.367681i | ||||
\(503\) | 27387.4 | + | 7338.43i | 0.108247 | + | 0.0290046i | 0.312536 | − | 0.949906i | \(-0.398822\pi\) |
−0.204289 | + | 0.978911i | \(0.565488\pi\) | |||||||
\(504\) | −25619.9 | + | 25619.9i | −0.100860 | + | 0.100860i | ||||
\(505\) | −509960. | + | 136643.i | −1.99965 | + | 0.535804i | ||||
\(506\) | 167597. | − | 96762.1i | 0.654584 | − | 0.377924i | ||||
\(507\) | −230377. | −0.896236 | ||||||||
\(508\) | − | 144588.i | − | 0.560280i | ||||||
\(509\) | 30456.8 | − | 17584.2i | 0.117557 | − | 0.0678715i | −0.440069 | − | 0.897964i | \(-0.645046\pi\) |
0.557626 | + | 0.830093i | \(0.311713\pi\) | |||||||
\(510\) | −655240. | − | 655240.i | −2.51918 | − | 2.51918i | ||||
\(511\) | −49332.8 | − | 28482.3i | −0.188927 | − | 0.109077i | ||||
\(512\) | 8192.00 | + | 8192.00i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 177665. | − | 47605.2i | 0.675098 | − | 0.180892i | ||||
\(514\) | −41583.0 | + | 72023.9i | −0.157394 | + | 0.272615i | ||||
\(515\) | 46306.6 | − | 80205.4i | 0.174594 | − | 0.302405i | ||||
\(516\) | −118087. | − | 31641.4i | −0.443511 | − | 0.118838i | ||||
\(517\) | 6768.19i | 0.0253216i | ||||||||
\(518\) | −18802.8 | + | 46041.8i | −0.0700749 | + | 0.171590i | ||||
\(519\) | 113898. | 0.422846 | ||||||||
\(520\) | 28827.3 | − | 107585.i | 0.106610 | − | 0.397873i | ||||
\(521\) | −67431.0 | − | 38931.3i | −0.248418 | − | 0.143424i | 0.370621 | − | 0.928784i | \(-0.379145\pi\) |
−0.619040 | + | 0.785360i | \(0.712478\pi\) | |||||||
\(522\) | 271761. | + | 156901.i | 0.997345 | + | 0.575817i | ||||
\(523\) | −94518.2 | − | 352747.i | −0.345551 | − | 1.28961i | −0.891967 | − | 0.452100i | \(-0.850675\pi\) |
0.546416 | − | 0.837514i | \(-0.315992\pi\) | |||||||
\(524\) | 58508.9 | − | 58508.9i | 0.213088 | − | 0.213088i | ||||
\(525\) | 121002. | − | 209581.i | 0.439008 | − | 0.760384i | ||||
\(526\) | −94935.0 | + | 94935.0i | −0.343127 | + | 0.343127i | ||||
\(527\) | 204038. | + | 353403.i | 0.734664 | + | 1.27248i | ||||
\(528\) | −106566. | −0.382251 | ||||||||
\(529\) | − | 67437.2i | − | 0.240984i | ||||||
\(530\) | −235962. | − | 408698.i | −0.840021 | − | 1.45496i | ||||
\(531\) | −130741. | − | 487933.i | −0.463685 | − | 1.73050i | ||||
\(532\) | −21338.7 | − | 21338.7i | −0.0753952 | − | 0.0753952i | ||||
\(533\) | −45848.6 | + | 171109.i | −0.161388 | + | 0.602309i | ||||
\(534\) | 106657. | + | 184736.i | 0.374032 | + | 0.647842i | ||||
\(535\) | −111573. | − | 29895.9i | −0.389808 | − | 0.104449i | ||||
\(536\) | −177271. | + | 47499.6i | −0.617032 | + | 0.165333i | ||||
\(537\) | −47105.7 | − | 175801.i | −0.163352 | − | 0.609639i | ||||
\(538\) | 35282.7 | − | 131677.i | 0.121898 | − | 0.454931i | ||||
\(539\) | 224833. | − | 129808.i | 0.773897 | − | 0.446810i | ||||
\(540\) | −213092. | − | 57097.8i | −0.730768 | − | 0.195809i | ||||
\(541\) | −16081.3 | + | 16081.3i | −0.0549448 | + | 0.0549448i | −0.734045 | − | 0.679101i | \(-0.762370\pi\) |
0.679101 | + | 0.734045i | \(0.262370\pi\) | |||||||
\(542\) | 240342. | − | 64399.6i | 0.818148 | − | 0.219222i | ||||
\(543\) | 773781. | − | 446742.i | 2.62433 | − | 1.51516i | ||||
\(544\) | 93916.2 | 0.317353 | ||||||||
\(545\) | − | 217324.i | − | 0.731669i | ||||||
\(546\) | −50438.4 | + | 29120.6i | −0.169191 | + | 0.0976823i | ||||
\(547\) | 167720. | + | 167720.i | 0.560544 | + | 0.560544i | 0.929462 | − | 0.368918i | \(-0.120272\pi\) |
−0.368918 | + | 0.929462i | \(0.620272\pi\) | |||||||
\(548\) | 140354. | + | 81033.6i | 0.467374 | + | 0.269839i | ||||
\(549\) | −457638. | − | 457638.i | −1.51837 | − | 1.51837i | ||||
\(550\) | 416753. | − | 111669.i | 1.37770 | − | 0.369153i | ||||
\(551\) | −130682. | + | 226347.i | −0.430439 | + | 0.745542i | ||||
\(552\) | −95615.6 | + | 165611.i | −0.313798 | + | 0.543515i | ||||
\(553\) | 118906. | + | 31860.8i | 0.388824 | + | 0.104185i | ||||
\(554\) | 213292.i | 0.694953i | ||||||||
\(555\) | −856517. | + | 117110.i | −2.78067 | + | 0.380195i | ||||
\(556\) | −164634. | −0.532563 | ||||||||
\(557\) | −43645.3 | + | 162887.i | −0.140678 | + | 0.525019i | 0.859231 | + | 0.511587i | \(0.170942\pi\) |
−0.999910 | + | 0.0134319i | \(0.995724\pi\) | |||||||
\(558\) | 240193. | + | 138675.i | 0.771422 | + | 0.445381i | ||||
\(559\) | −103162. | − | 59560.5i | −0.330138 | − | 0.190605i | ||||
\(560\) | 9367.93 | + | 34961.6i | 0.0298722 | + | 0.111485i | ||||
\(561\) | −610854. | + | 610854.i | −1.94094 | + | 1.94094i | ||||
\(562\) | 175445. | − | 303880.i | 0.555480 | − | 0.962120i | ||||
\(563\) | 284102. | − | 284102.i | 0.896310 | − | 0.896310i | −0.0987978 | − | 0.995108i | \(-0.531500\pi\) |
0.995108 | + | 0.0987978i | \(0.0314997\pi\) | |||||||
\(564\) | −3344.00 | − | 5791.97i | −0.0105125 | − | 0.0182083i | ||||
\(565\) | 438620. | 1.37401 | ||||||||
\(566\) | 66512.9i | 0.207622i | ||||||||
\(567\) | −7171.65 | − | 12421.7i | −0.0223076 | − | 0.0386379i | ||||
\(568\) | −9945.16 | − | 37115.9i | −0.0308259 | − | 0.115044i | ||||
\(569\) | 24828.2 | + | 24828.2i | 0.0766867 | + | 0.0766867i | 0.744410 | − | 0.667723i | \(-0.232731\pi\) |
−0.667723 | + | 0.744410i | \(0.732731\pi\) | |||||||
\(570\) | 135766. | − | 506684.i | 0.417869 | − | 1.55951i | ||||
\(571\) | 251600. | + | 435783.i | 0.771681 | + | 1.33659i | 0.936641 | + | 0.350291i | \(0.113917\pi\) |
−0.164960 | + | 0.986300i | \(0.552749\pi\) | |||||||
\(572\) | −100297. | − | 26874.5i | −0.306547 | − | 0.0821389i | ||||
\(573\) | −444940. | + | 119221.i | −1.35517 | + | 0.363116i | ||||
\(574\) | −14899.3 | − | 55604.9i | −0.0452212 | − | 0.168768i | ||||
\(575\) | 200389. | − | 747861.i | 0.606091 | − | 2.26196i | ||||
\(576\) | 55279.1 | − | 31915.4i | 0.166616 | − | 0.0961956i | ||||
\(577\) | 80446.3 | + | 21555.5i | 0.241632 | + | 0.0647451i | 0.377602 | − | 0.925968i | \(-0.376749\pi\) |
−0.135971 | + | 0.990713i | \(0.543415\pi\) | |||||||
\(578\) | 371304. | − | 371304.i | 1.11141 | − | 1.11141i | ||||
\(579\) | −637042. | + | 170695.i | −1.90025 | + | 0.509171i | ||||
\(580\) | 271482. | − | 156740.i | 0.807021 | − | 0.465934i | ||||
\(581\) | −64184.6 | −0.190142 | ||||||||
\(582\) | 575880.i | 1.70015i | ||||||||
\(583\) | −381013. | + | 219978.i | −1.12099 | + | 0.647205i | ||||
\(584\) | 70962.3 | + | 70962.3i | 0.208066 | + | 0.208066i | ||||
\(585\) | −531451. | − | 306834.i | −1.55293 | − | 0.896585i | ||||
\(586\) | −188360. | − | 188360.i | −0.548521 | − | 0.548521i | ||||
\(587\) | 417363. | − | 111832.i | 1.21126 | − | 0.324556i | 0.404004 | − | 0.914757i | \(-0.367618\pi\) |
0.807256 | + | 0.590201i | \(0.200952\pi\) | |||||||
\(588\) | −128269. | + | 222169.i | −0.370995 | + | 0.642583i | ||||
\(589\) | −115502. | + | 200055.i | −0.332934 | + | 0.576658i | ||||
\(590\) | −487432. | − | 130607.i | −1.40026 | − | 0.375200i | ||||
\(591\) | 480115.i | 1.37458i | ||||||||
\(592\) | 52990.0 | − | 69775.5i | 0.151200 | − | 0.199095i | ||||
\(593\) | 488787. | 1.38999 | 0.694993 | − | 0.719016i | \(-0.255407\pi\) | ||||
0.694993 | + | 0.719016i | \(0.255407\pi\) | |||||||
\(594\) | −53230.0 | + | 198657.i | −0.150863 | + | 0.563030i | ||||
\(595\) | 254105. | + | 146708.i | 0.717761 | + | 0.414400i | ||||
\(596\) | −58304.3 | − | 33662.0i | −0.164138 | − | 0.0947650i | ||||
\(597\) | −136766. | − | 510417.i | −0.383733 | − | 1.43211i | ||||
\(598\) | −131756. | + | 131756.i | −0.368442 | + | 0.368442i | ||||
\(599\) | 218664. | − | 378737.i | 0.609429 | − | 1.05556i | −0.381905 | − | 0.924202i | \(-0.624732\pi\) |
0.991335 | − | 0.131361i | \(-0.0419348\pi\) | |||||||
\(600\) | −301469. | + | 301469.i | −0.837415 | + | 0.837415i | ||||
\(601\) | 141041. | + | 244291.i | 0.390479 | + | 0.676330i | 0.992513 | − | 0.122141i | \(-0.0389761\pi\) |
−0.602034 | + | 0.798471i | \(0.705643\pi\) | |||||||
\(602\) | 38710.4 | 0.106816 | ||||||||
\(603\) | 1.01116e6i | 2.78089i | ||||||||
\(604\) | 109218. | + | 189171.i | 0.299379 | + | 0.518539i | ||||
\(605\) | 13226.4 | + | 49361.4i | 0.0361351 | + | 0.134858i | ||||
\(606\) | −343904. | − | 343904.i | −0.936467 | − | 0.936467i | ||||
\(607\) | −108246. | + | 403979.i | −0.293788 | + | 1.09643i | 0.648387 | + | 0.761311i | \(0.275444\pi\) |
−0.942175 | + | 0.335121i | \(0.891223\pi\) | |||||||
\(608\) | 26582.1 | + | 46041.5i | 0.0719088 | + | 0.124550i | ||||
\(609\) | −158335. | − | 42425.8i | −0.426916 | − | 0.114392i | ||||
\(610\) | −624503. | + | 167335.i | −1.67832 | + | 0.449705i | ||||
\(611\) | −1686.63 | − | 6294.60i | −0.00451791 | − | 0.0168611i | ||||
\(612\) | 133925. | − | 499816.i | 0.357569 | − | 1.33446i | ||||
\(613\) | −304350. | + | 175717.i | −0.809939 | + | 0.467619i | −0.846935 | − | 0.531697i | \(-0.821555\pi\) |
0.0369954 | + | 0.999315i | \(0.488221\pi\) | |||||||
\(614\) | 364558. | + | 97683.1i | 0.967008 | + | 0.259109i | ||||
\(615\) | 707565. | − | 707565.i | 1.87075 | − | 1.87075i | ||||
\(616\) | 32593.3 | − | 8733.35i | 0.0858948 | − | 0.0230154i | ||||
\(617\) | −413405. | + | 238680.i | −1.08594 | + | 0.626967i | −0.932492 | − | 0.361189i | \(-0.882371\pi\) |
−0.153447 | + | 0.988157i | \(0.549037\pi\) | |||||||
\(618\) | 85316.5 | 0.223386 | ||||||||
\(619\) | 316130.i | 0.825059i | 0.910944 | + | 0.412529i | \(0.135355\pi\) | ||||
−0.910944 | + | 0.412529i | \(0.864645\pi\) | |||||||
\(620\) | 239947. | − | 138533.i | 0.624211 | − | 0.360388i | ||||
\(621\) | 260968. | + | 260968.i | 0.676712 | + | 0.676712i | ||||
\(622\) | −212070. | − | 122439.i | −0.548150 | − | 0.316474i | ||||
\(623\) | −47761.1 | − | 47761.1i | −0.123055 | − | 0.123055i | ||||
\(624\) | 99108.7 | − | 26556.1i | 0.254532 | − | 0.0682017i | ||||
\(625\) | 257188. | − | 445462.i | 0.658400 | − | 1.14038i | ||||
\(626\) | −189862. | + | 328851.i | −0.484496 | + | 0.839171i | ||||
\(627\) | −472362. | − | 126569.i | −1.20154 | − | 0.321953i | ||||
\(628\) | − | 134069.i | − | 0.339944i | ||||||
\(629\) | −96217.4 | − | 703716.i | −0.243194 | − | 1.77867i | ||||
\(630\) | 199422. | 0.502449 | ||||||||
\(631\) | −36745.7 | + | 137137.i | −0.0922887 | + | 0.344426i | −0.996594 | − | 0.0824594i | \(-0.973723\pi\) |
0.904306 | + | 0.426885i | \(0.140389\pi\) | |||||||
\(632\) | −187814. | − | 108434.i | −0.470212 | − | 0.271477i | ||||
\(633\) | −388842. | − | 224498.i | −0.970433 | − | 0.560280i | ||||
\(634\) | 176.423 | + | 658.418i | 0.000438910 | + | 0.00163804i | ||||
\(635\) | −562727. | + | 562727.i | −1.39556 | + | 1.39556i | ||||
\(636\) | 217371. | − | 376498.i | 0.537388 | − | 0.930784i | ||||
\(637\) | −176753. | + | 176753.i | −0.435600 | + | 0.435600i | ||||
\(638\) | −146123. | − | 253092.i | −0.358985 | − | 0.621780i | ||||
\(639\) | −211710. | −0.518489 | ||||||||
\(640\) | − | 63765.3i | − | 0.155677i | ||||||
\(641\) | −159617. | − | 276465.i | −0.388475 | − | 0.672859i | 0.603769 | − | 0.797159i | \(-0.293665\pi\) |
−0.992245 | + | 0.124300i | \(0.960331\pi\) | |||||||
\(642\) | −27540.5 | − | 102782.i | −0.0668192 | − | 0.249373i | ||||
\(643\) | −323.568 | − | 323.568i | −0.000782607 | − | 0.000782607i | 0.706715 | − | 0.707498i | \(-0.250176\pi\) |
−0.707498 | + | 0.706715i | \(0.750176\pi\) | |||||||
\(644\) | 15671.9 | − | 58488.5i | 0.0377878 | − | 0.141026i | ||||
\(645\) | 336442. | + | 582734.i | 0.808705 | + | 1.40072i | ||||
\(646\) | 416293. | + | 111545.i | 0.997548 | + | 0.267292i | ||||
\(647\) | 497884. | − | 133408.i | 1.18938 | − | 0.318693i | 0.390737 | − | 0.920502i | \(-0.372220\pi\) |
0.798640 | + | 0.601810i | \(0.205553\pi\) | |||||||
\(648\) | 6540.07 | + | 24407.9i | 0.0155752 | + | 0.0581273i | ||||
\(649\) | −121760. | + | 454414.i | −0.289078 | + | 1.07885i | ||||
\(650\) | −359763. | + | 207709.i | −0.851511 | + | 0.491620i | ||||
\(651\) | −139943. | − | 37497.6i | −0.330209 | − | 0.0884792i | ||||
\(652\) | −116575. | + | 116575.i | −0.274227 | + | 0.274227i | ||||
\(653\) | 296061. | − | 79329.3i | 0.694312 | − | 0.186040i | 0.105630 | − | 0.994405i | \(-0.466314\pi\) |
0.588681 | + | 0.808365i | \(0.299647\pi\) | |||||||
\(654\) | 173380. | − | 100101.i | 0.405362 | − | 0.234036i | ||||
\(655\) | −455425. | −1.06153 | ||||||||
\(656\) | 101416.i | 0.235667i | ||||||||
\(657\) | 478849. | − | 276464.i | 1.10935 | − | 0.640482i | ||||
\(658\) | 1497.44 | + | 1497.44i | 0.00345857 | + | 0.00345857i | ||||
\(659\) | −157427. | − | 90890.4i | −0.362500 | − | 0.209289i | 0.307677 | − | 0.951491i | \(-0.400448\pi\) |
−0.670177 | + | 0.742201i | \(0.733782\pi\) | |||||||
\(660\) | 414745. | + | 414745.i | 0.952124 | + | 0.952124i | ||||
\(661\) | 418602. | − | 112164.i | 0.958072 | − | 0.256715i | 0.254288 | − | 0.967128i | \(-0.418159\pi\) |
0.703784 | + | 0.710414i | \(0.251492\pi\) | |||||||
\(662\) | −183132. | + | 317193.i | −0.417876 | + | 0.723783i | ||||
\(663\) | 415885. | − | 720335.i | 0.946121 | − | 1.63873i | ||||
\(664\) | 109222. | + | 29266.0i | 0.247728 | + | 0.0663785i | ||||
\(665\) | 166097.i | 0.375594i | ||||||||
\(666\) | −295776. | − | 381510.i | −0.666829 | − | 0.860116i | ||||
\(667\) | −524432. | −1.17879 | ||||||||
\(668\) | −75931.6 | + | 283381.i | −0.170165 | + | 0.635063i | ||||
\(669\) | −654720. | − | 378003.i | −1.46286 | − | 0.844584i | ||||
\(670\) | 874790. | + | 505060.i | 1.94874 | + | 1.12511i | ||||
\(671\) | 156000. | + | 582199.i | 0.346481 | + | 1.29308i | ||||
\(672\) | −23577.2 | + | 23577.2i | −0.0522101 | + | 0.0522101i | ||||
\(673\) | −152927. | + | 264877.i | −0.337640 | + | 0.584809i | −0.983988 | − | 0.178233i | \(-0.942962\pi\) |
0.646349 | + | 0.763042i | \(0.276295\pi\) | |||||||
\(674\) | 126249. | − | 126249.i | 0.277913 | − | 0.277913i | ||||
\(675\) | 411407. | + | 712578.i | 0.902951 | + | 1.56396i | ||||
\(676\) | −128512. | −0.281222 | ||||||||
\(677\) | − | 98874.0i | − | 0.215727i | −0.994166 | − | 0.107864i | \(-0.965599\pi\) | ||
0.994166 | − | 0.107864i | \(-0.0344010\pi\) | |||||||
\(678\) | 202031. | + | 349928.i | 0.439500 | + | 0.761237i | ||||
\(679\) | −47195.0 | − | 176134.i | −0.102366 | − | 0.382036i | ||||
\(680\) | −365515. | − | 365515.i | −0.790474 | − | 0.790474i | ||||
\(681\) | −122062. | + | 455540.i | −0.263199 | + | 0.982273i | ||||
\(682\) | −129149. | − | 223693.i | −0.277666 | − | 0.480931i | ||||
\(683\) | −57625.8 | − | 15440.8i | −0.123531 | − | 0.0331000i | 0.196524 | − | 0.980499i | \(-0.437035\pi\) |
−0.320055 | + | 0.947399i | \(0.603701\pi\) | |||||||
\(684\) | 282936. | − | 75812.5i | 0.604750 | − | 0.162042i | ||||
\(685\) | −230872. | − | 861626.i | −0.492028 | − | 1.83627i | ||||
\(686\) | 43599.3 | − | 162715.i | 0.0926469 | − | 0.345763i | ||||
\(687\) | 520302. | − | 300396.i | 1.10241 | − | 0.636475i | ||||
\(688\) | −65873.2 | − | 17650.7i | −0.139166 | − | 0.0372893i | ||||
\(689\) | 299534. | − | 299534.i | 0.630968 | − | 0.630968i | ||||
\(690\) | 1.01667e6 | − | 272417.i | 2.13542 | − | 0.572185i | ||||
\(691\) | 293430. | − | 169412.i | 0.614537 | − | 0.354803i | −0.160202 | − | 0.987084i | \(-0.551214\pi\) |
0.774739 | + | 0.632281i | \(0.217881\pi\) | |||||||
\(692\) | 63536.2 | 0.132681 | ||||||||
\(693\) | − | 185913.i | − | 0.387118i | ||||||
\(694\) | 84961.6 | − | 49052.6i | 0.176402 | − | 0.101846i | ||||
\(695\) | 640745. | + | 640745.i | 1.32652 | + | 1.32652i | ||||
\(696\) | 250093. | + | 144391.i | 0.516277 | + | 0.298073i | ||||
\(697\) | 581336. | + | 581336.i | 1.19664 | + | 1.19664i | ||||
\(698\) | −473347. | + | 126833.i | −0.971558 | + | 0.260328i | ||||
\(699\) | 387854. | − | 671783.i | 0.793805 | − | 1.37491i | ||||
\(700\) | 67498.8 | − | 116911.i | 0.137753 | − | 0.238595i | ||||
\(701\) | −546293. | − | 146379.i | −1.11170 | − | 0.297880i | −0.344183 | − | 0.938903i | \(-0.611844\pi\) |
−0.767522 | + | 0.641022i | \(0.778511\pi\) | |||||||
\(702\) | − | 198021.i | − | 0.401825i | ||||||
\(703\) | 317756. | − | 246350.i | 0.642960 | − | 0.498473i | ||||
\(704\) | −59445.9 | −0.119943 | ||||||||
\(705\) | −9527.34 | + | 35556.5i | −0.0191687 | + | 0.0715387i | ||||
\(706\) | −317747. | − | 183452.i | −0.637489 | − | 0.368054i | ||||
\(707\) | 133368. | + | 77000.0i | 0.266816 | + | 0.154047i | ||||
\(708\) | −120317. | − | 449029.i | −0.240027 | − | 0.895794i | ||||
\(709\) | 305093. | − | 305093.i | 0.606933 | − | 0.606933i | −0.335211 | − | 0.942143i | \(-0.608807\pi\) |
0.942143 | + | 0.335211i | \(0.108807\pi\) | |||||||
\(710\) | −105746. | + | 183158.i | −0.209772 | + | 0.363337i | ||||
\(711\) | −844904. | + | 844904.i | −1.67135 | + | 1.67135i | ||||
\(712\) | 59497.2 | + | 103052.i | 0.117364 | + | 0.203281i | ||||
\(713\) | −463514. | −0.911767 | ||||||||
\(714\) | 270298.i | 0.530209i | ||||||||
\(715\) | 285755. | + | 494943.i | 0.558962 | + | 0.968151i | ||||
\(716\) | −26277.2 | − | 98067.7i | −0.0512569 | − | 0.191293i | ||||
\(717\) | 817720. | + | 817720.i | 1.59062 | + | 1.59062i | ||||
\(718\) | −18273.6 | + | 68198.0i | −0.0354467 | + | 0.132289i | ||||
\(719\) | −189202. | − | 327707.i | −0.365988 | − | 0.633910i | 0.622946 | − | 0.782265i | \(-0.285936\pi\) |
−0.988934 | + | 0.148355i | \(0.952602\pi\) | |||||||
\(720\) | −339355. | − | 90929.8i | −0.654619 | − | 0.175405i | ||||
\(721\) | −26094.3 | + | 6991.93i | −0.0501966 | + | 0.0134501i | ||||
\(722\) | −32258.0 | − | 120388.i | −0.0618817 | − | 0.230946i | ||||
\(723\) | −60572.3 | + | 226059.i | −0.115877 | + | 0.432459i | ||||
\(724\) | 431641. | − | 249208.i | 0.823466 | − | 0.475428i | ||||
\(725\) | −1.12936e6 | − | 302611.i | −2.14860 | − | 0.575717i | ||||
\(726\) | −33288.1 | + | 33288.1i | −0.0631562 | + | 0.0631562i | ||||
\(727\) | −284060. | + | 76113.6i | −0.537453 | + | 0.144010i | −0.517328 | − | 0.855787i | \(-0.673073\pi\) |
−0.0201254 | + | 0.999797i | \(0.506407\pi\) | |||||||
\(728\) | −28136.3 | + | 16244.5i | −0.0530889 | + | 0.0306509i | ||||
\(729\) | 866724. | 1.63089 | ||||||||
\(730\) | − | 552360.i | − | 1.03652i | ||||||
\(731\) | −478775. | + | 276421.i | −0.895977 | + | 0.517292i | ||||
\(732\) | −421149. | − | 421149.i | −0.785985 | − | 0.785985i | ||||
\(733\) | −376903. | − | 217605.i | −0.701491 | − | 0.405006i | 0.106411 | − | 0.994322i | \(-0.466064\pi\) |
−0.807903 | + | 0.589316i | \(0.799397\pi\) | |||||||
\(734\) | −53883.6 | − | 53883.6i | −0.100015 | − | 0.100015i | ||||
\(735\) | 1.36388e6 | − | 365451.i | 2.52465 | − | 0.676479i | ||||
\(736\) | −53337.6 | + | 92383.5i | −0.0984641 | + | 0.170545i | ||||
\(737\) | 470847. | − | 815532.i | 0.866852 | − | 1.50143i | ||||
\(738\) | 539729. | + | 144620.i | 0.990976 | + | 0.265531i | ||||
\(739\) | − | 52403.6i | − | 0.0959561i | −0.998848 | − | 0.0479780i | \(-0.984722\pi\) | ||
0.998848 | − | 0.0479780i | \(-0.0152778\pi\) | |||||||
\(740\) | −477794. | + | 65327.7i | −0.872524 | + | 0.119298i | ||||
\(741\) | 470850. | 0.857523 | ||||||||
\(742\) | −35628.4 | + | 132967.i | −0.0647126 | + | 0.241511i | ||||
\(743\) | 188619. | + | 108899.i | 0.341671 | + | 0.197264i | 0.661011 | − | 0.750376i | \(-0.270128\pi\) |
−0.319340 | + | 0.947640i | \(0.603461\pi\) | |||||||
\(744\) | 221042. | + | 127619.i | 0.399327 | + | 0.230552i | ||||
\(745\) | 95906.1 | + | 357926.i | 0.172796 | + | 0.644883i | ||||
\(746\) | 145781. | − | 145781.i | 0.261953 | − | 0.261953i | ||||
\(747\) | 311504. | − | 539540.i | 0.558241 | − | 0.966902i | ||||
\(748\) | −340755. | + | 340755.i | −0.609031 | + | 0.609031i | ||||
\(749\) | 16846.6 | + | 29179.2i | 0.0300296 | + | 0.0520128i | ||||
\(750\) | 1.23030e6 | 2.18719 | ||||||||
\(751\) | 743989.i | 1.31913i | 0.751649 | + | 0.659563i | \(0.229259\pi\) | ||||
−0.751649 | + | 0.659563i | \(0.770741\pi\) | |||||||
\(752\) | −1865.40 | − | 3230.96i | −0.00329864 | − | 0.00571342i | ||||
\(753\) | 243190. | + | 907597.i | 0.428899 | + | 1.60067i | ||||
\(754\) | 198968. | + | 198968.i | 0.349978 | + | 0.349978i | ||||
\(755\) | 311172. | − | 1.16131e6i | 0.545892 | − | 2.03730i | ||||
\(756\) | 32175.2 | + | 55729.1i | 0.0562961 | + | 0.0975076i | ||||
\(757\) | 881800. | + | 236278.i | 1.53879 | + | 0.412317i | 0.925874 | − | 0.377834i | \(-0.123331\pi\) |
0.612913 | + | 0.790150i | \(0.289998\pi\) | |||||||
\(758\) | −494449. | + | 132487.i | −0.860564 | + | 0.230587i | ||||
\(759\) | −253964. | − | 947806.i | −0.440847 | − | 1.64526i | ||||
\(760\) | 75734.7 | − | 282646.i | 0.131120 | − | 0.489345i | ||||
\(761\) | 595874. | − | 344028.i | 1.02893 | − | 0.594052i | 0.112251 | − | 0.993680i | \(-0.464194\pi\) |
0.916678 | + | 0.399628i | \(0.130861\pi\) | |||||||
\(762\) | −708136. | − | 189744.i | −1.21957 | − | 0.326783i | ||||
\(763\) | −44825.1 | + | 44825.1i | −0.0769967 | + | 0.0769967i | ||||
\(764\) | −248203. | + | 66505.8i | −0.425226 | + | 0.113939i | ||||
\(765\) | −2.46647e6 | + | 1.42402e6i | −4.21457 | + | 2.43328i | ||||
\(766\) | −96332.9 | −0.164179 | ||||||||
\(767\) | − | 452959.i | − | 0.769960i | ||||||
\(768\) | 50871.6 | − | 29370.7i | 0.0862488 | − | 0.0497958i | ||||
\(769\) | −452328. | − | 452328.i | −0.764894 | − | 0.764894i | 0.212309 | − | 0.977203i | \(-0.431902\pi\) |
−0.977203 | + | 0.212309i | \(0.931902\pi\) | |||||||
\(770\) | −160840. | − | 92861.2i | −0.271277 | − | 0.156622i | ||||
\(771\) | 298175. | + | 298175.i | 0.501605 | + | 0.501605i | ||||
\(772\) | −355364. | + | 95219.4i | −0.596264 | + | 0.159768i | ||||
\(773\) | −156741. | + | 271483.i | −0.262315 | + | 0.454343i | −0.966857 | − | 0.255320i | \(-0.917819\pi\) |
0.704542 | + | 0.709663i | \(0.251153\pi\) | |||||||
\(774\) | −187871. | + | 325403.i | −0.313602 | + | 0.543174i | ||||
\(775\) | −998174. | − | 267460.i | −1.66189 | − | 0.445303i | ||||
\(776\) | 321246.i | 0.533475i | ||||||||
\(777\) | 200819. | + | 152510.i | 0.332632 | + | 0.252613i | ||||
\(778\) | −113347. | −0.187263 | ||||||||
\(779\) | −120453. | + | 449536.i | −0.198492 | + | 0.740781i | ||||
\(780\) | −489078. | − | 282369.i | −0.803876 | − | 0.464118i | ||||
\(781\) | 170751. | + | 98583.1i | 0.279937 | + | 0.161622i | ||||
\(782\) | 223818. | + | 835301.i | 0.366001 | + | 1.36593i | ||||
\(783\) | 394093. | − | 394093.i | 0.642800 | − | 0.642800i | ||||
\(784\) | −71553.1 | + | 123934.i | −0.116412 | + | 0.201631i | ||||
\(785\) | −521785. | + | 521785.i | −0.846745 | + | 0.846745i | ||||
\(786\) | −209772. | − | 363336.i | −0.339549 | − | 0.588116i | ||||
\(787\) | 903858. | 1.45932 | 0.729661 | − | 0.683810i | \(-0.239678\pi\) | ||||
0.729661 | + | 0.683810i | \(0.239678\pi\) | |||||||
\(788\) | 267824.i | 0.431318i | ||||||||
\(789\) | 340370. | + | 589538.i | 0.546761 | + | 0.947017i | ||||
\(790\) | 308939. | + | 1.15298e6i | 0.495015 | + | 1.84742i | ||||
\(791\) | −90469.3 | − | 90469.3i | −0.144593 | − | 0.144593i | ||||
\(792\) | −84770.2 | + | 316367.i | −0.135143 | + | 0.504360i | ||||
\(793\) | −290168. | − | 502585.i | −0.461427 | − | 0.799215i | ||||
\(794\) | −548038. | − | 146846.i | −0.869300 | − | 0.232928i | ||||
\(795\) | −2.31130e6 | + | 619310.i | −3.65697 | + | 0.979883i | ||||
\(796\) | −76292.6 | − | 284728.i | −0.120408 | − | 0.449370i | ||||
\(797\) | −40570.1 | + | 151410.i | −0.0638690 | + | 0.238362i | −0.990480 | − | 0.137660i | \(-0.956042\pi\) |
0.926611 | + | 0.376022i | \(0.122708\pi\) | |||||||
\(798\) | −132511. | + | 76505.4i | −0.208088 | + | 0.120140i | ||||
\(799\) | −29213.3 | − | 7827.68i | −0.0457601 | − | 0.0122614i | ||||
\(800\) | −168170. | + | 168170.i | −0.262765 | + | 0.262765i | ||||
\(801\) | 633279. | − | 169687.i | 0.987030 | − | 0.264474i | ||||
\(802\) | 197755. | − | 114174.i | 0.307453 | − | 0.177508i | ||||
\(803\) | −514943. | −0.798598 | ||||||||
\(804\) | 930536.i | 1.43953i | ||||||||
\(805\) | −288627. | + | 166639.i | −0.445395 | + | 0.257149i | ||||
\(806\) | 175856. | + | 175856.i | 0.270699 | + | 0.270699i | ||||
\(807\) | −598600. | − | 345602.i | −0.919157 | − | 0.530676i | ||||
\(808\) | −191842. | − | 191842.i | −0.293846 | − | 0.293846i | ||||
\(809\) | −939846. | + | 251831.i | −1.43602 | + | 0.384780i | −0.891137 | − | 0.453734i | \(-0.850092\pi\) |
−0.544880 | + | 0.838514i | \(0.683425\pi\) | |||||||
\(810\) | 69540.2 | − | 120447.i | 0.105990 | − | 0.183580i | ||||
\(811\) | −21948.9 | + | 38016.7i | −0.0333712 | + | 0.0578006i | −0.882229 | − | 0.470821i | \(-0.843958\pi\) |
0.848857 | + | 0.528622i | \(0.177291\pi\) | |||||||
\(812\) | −88324.7 | − | 23666.5i | −0.133958 | − | 0.0358941i | ||||
\(813\) | − | 1.26161e6i | − | 1.90873i | ||||||
\(814\) | 60902.4 | + | 445429.i | 0.0919148 | + | 0.672248i | ||||
\(815\) | 907404. | 1.36611 | ||||||||
\(816\) | 123247. | − | 459965.i | 0.185096 | − | 0.690787i | ||||
\(817\) | −271025. | − | 156477.i | −0.406037 | − | 0.234426i | ||||
\(818\) | −260689. | − | 150509.i | −0.389598 | − | 0.224935i | ||||
\(819\) | 46329.5 | + | 172904.i | 0.0690700 | + | 0.257773i | ||||
\(820\) | 394704. | − | 394704.i | 0.587007 | − | 0.587007i | ||||
\(821\) | 43145.0 | − | 74729.4i | 0.0640095 | − | 0.110868i | −0.832245 | − | 0.554409i | \(-0.812945\pi\) |
0.896254 | + | 0.443541i | \(0.146278\pi\) | |||||||
\(822\) | 581059. | − | 581059.i | 0.859957 | − | 0.859957i | ||||
\(823\) | −557966. | − | 966426.i | −0.823774 | − | 1.42682i | −0.902852 | − | 0.429950i | \(-0.858531\pi\) |
0.0790782 | − | 0.996868i | \(-0.474802\pi\) | |||||||
\(824\) | 47592.5 | 0.0700945 | ||||||||
\(825\) | − | 2.18764e6i | − | 3.21416i | ||||||
\(826\) | 73598.4 | + | 127476.i | 0.107872 | + | 0.186840i | ||||
\(827\) | −141929. | − | 529687.i | −0.207520 | − | 0.774477i | −0.988666 | − | 0.150128i | \(-0.952031\pi\) |
0.781146 | − | 0.624348i | \(-0.214635\pi\) | |||||||
\(828\) | 415599. | + | 415599.i | 0.606196 | + | 0.606196i | ||||
\(829\) | −296689. | + | 1.10726e6i | −0.431710 | + | 1.61116i | 0.317109 | + | 0.948389i | \(0.397288\pi\) |
−0.748819 | + | 0.662774i | \(0.769379\pi\) | |||||||
\(830\) | −311184. | − | 538986.i | −0.451711 | − | 0.782387i | ||||
\(831\) | 1.04462e6 | + | 279905.i | 1.51271 | + | 0.405331i | ||||
\(832\) | 55286.2 | − | 14813.9i | 0.0798675 | − | 0.0214004i | ||||
\(833\) | 300255. | + | 1.12057e6i | 0.432713 | + | 1.61491i | ||||
\(834\) | −216051. | + | 806314.i | −0.310616 | + | 1.15924i | ||||
\(835\) | 1.39842e6 | − | 807376.i | 2.00569 | − | 1.15798i | ||||
\(836\) | −263499. | − | 70604.5i | −0.377022 | − | 0.101023i | ||||
\(837\) | 348316. | − | 348316.i | 0.497190 | − | 0.497190i | ||||
\(838\) | 174492. | − | 46754.9i | 0.248477 | − | 0.0665792i | ||||
\(839\) | 735951. | − | 424901.i | 1.04550 | − | 0.603621i | 0.124115 | − | 0.992268i | \(-0.460391\pi\) |
0.921387 | + | 0.388647i | \(0.127057\pi\) | |||||||
\(840\) | 183522. | 0.260093 | ||||||||
\(841\) | 84674.9i | 0.119719i | ||||||||
\(842\) | 96806.0 | − | 55891.0i | 0.136546 | − | 0.0788347i | ||||
\(843\) | −1.25804e6 | − | 1.25804e6i | −1.77028 | − | 1.77028i | ||||
\(844\) | −216909. | − | 125233.i | −0.304504 | − | 0.175806i | ||||
\(845\) | 500159. | + | 500159.i | 0.700478 | + | 0.700478i | ||||
\(846\) | −19855.0 | + | 5320.13i | −0.0277415 | + | 0.00743330i | ||||
\(847\) | 7453.19 | − | 12909.3i | 0.0103890 | − | 0.0179944i | ||||
\(848\) | 121257. | − | 210024.i | 0.168623 | − | 0.292063i | ||||
\(849\) | 325754. | + | 87285.5i | 0.451933 | + | 0.121095i | ||||
\(850\) | 1.92796e6i | 2.66846i | ||||||||
\(851\) | 746875. | + | 305013.i | 1.03131 | + | 0.421171i | ||||
\(852\) | −194830. | −0.268396 | ||||||||
\(853\) | −41509.5 | + | 154916.i | −0.0570492 | + | 0.212911i | −0.988566 | − | 0.150787i | \(-0.951819\pi\) |
0.931517 | + | 0.363698i | \(0.118486\pi\) | |||||||
\(854\) | 163324. | + | 94295.1i | 0.223941 | + | 0.129293i | ||||
\(855\) | −1.39622e6 | − | 806110.i | −1.90995 | − | 1.10271i | ||||
\(856\) | −15363.0 | − | 57335.5i | −0.0209666 | − | 0.0782486i | ||||
\(857\) | 574043. | − | 574043.i | 0.781597 | − | 0.781597i | −0.198503 | − | 0.980100i | \(-0.563608\pi\) |
0.980100 | + | 0.198503i | \(0.0636081\pi\) | |||||||
\(858\) | −263242. | + | 455948.i | −0.357586 | + | 0.619357i | ||||
\(859\) | 791961. | − | 791961.i | 1.07329 | − | 1.07329i | 0.0761977 | − | 0.997093i | \(-0.475722\pi\) |
0.997093 | − | 0.0761977i | \(-0.0242780\pi\) | |||||||
\(860\) | 187679. | + | 325069.i | 0.253757 | + | 0.439520i | ||||
\(861\) | −291884. | −0.393734 | ||||||||
\(862\) | − | 122385.i | − | 0.164708i | ||||||
\(863\) | −63820.2 | − | 110540.i | −0.0856913 | − | 0.148422i | 0.819994 | − | 0.572372i | \(-0.193977\pi\) |
−0.905686 | + | 0.423950i | \(0.860643\pi\) | |||||||
\(864\) | −29341.7 | − | 109505.i | −0.0393059 | − | 0.146691i | ||||
\(865\) | −247278. | − | 247278.i | −0.330487 | − | 0.330487i | ||||
\(866\) | 58469.8 | − | 218212.i | 0.0779642 | − | 0.290967i | ||||
\(867\) | −1.33123e6 | − | 2.30577e6i | −1.77099 | − | 3.06745i | ||||
\(868\) | −78064.9 | − | 20917.4i | −0.103614 | − | 0.0277632i | ||||
\(869\) | 1.07487e6 | − | 288012.i | 1.42337 | − | 0.381391i | ||||
\(870\) | −411383. | − | 1.53530e6i | −0.543510 | − | 2.02841i | ||||
\(871\) | −234670. | + | 875801.i | −0.309330 | + | 1.15443i | ||||
\(872\) | 96717.2 | − | 55839.7i | 0.127195 | − | 0.0734362i | ||||
\(873\) | 1.70965e6 | + | 458098.i | 2.24325 | + | 0.601077i | ||||
\(874\) | −346149. | + | 346149.i | −0.453148 | + | 0.453148i | ||||
\(875\) | −376289. | + | 100826.i | −0.491480 | + | 0.131692i | ||||
\(876\) | 440670. | − | 254421.i | 0.574255 | − | 0.331546i | ||||
\(877\) | 390802. | 0.508109 | 0.254055 | − | 0.967190i | \(-0.418236\pi\) | ||||
0.254055 | + | 0.967190i | \(0.418236\pi\) | |||||||
\(878\) | − | 282675.i | − | 0.366690i | ||||||
\(879\) | −1.16970e6 | + | 675326.i | −1.51390 | + | 0.874049i | ||||
\(880\) | 231359. | + | 231359.i | 0.298759 | + | 0.298759i | ||||
\(881\) | −194891. | − | 112521.i | −0.251097 | − | 0.144971i | 0.369170 | − | 0.929362i | \(-0.379642\pi\) |
−0.620266 | + | 0.784391i | \(0.712975\pi\) | |||||||
\(882\) | 557531. | + | 557531.i | 0.716690 | + | 0.716690i | ||||
\(883\) | 551829. | − | 147862.i | 0.707755 | − | 0.189642i | 0.113053 | − | 0.993589i | \(-0.463937\pi\) |
0.594702 | + | 0.803946i | \(0.297270\pi\) | |||||||
\(884\) | 231995. | − | 401827.i | 0.296875 | − | 0.514203i | ||||
\(885\) | −1.27932e6 | + | 2.21585e6i | −1.63340 | + | 2.82914i | ||||
\(886\) | −657065. | − | 176060.i | −0.837029 | − | 0.224281i | ||||
\(887\) | 423925.i | 0.538817i | 0.963026 | + | 0.269409i | \(0.0868282\pi\) | ||||
−0.963026 | + | 0.269409i | \(0.913172\pi\) | |||||||
\(888\) | −272193. | − | 351091.i | −0.345185 | − | 0.445240i | ||||
\(889\) | 232135. | 0.293723 | ||||||||
\(890\) | 169513. | − | 632630.i | 0.214004 | − | 0.798674i | ||||
\(891\) | −112288. | − | 64829.6i | −0.141442 | − | 0.0816616i | ||||
\(892\) | −365225. | − | 210863.i | −0.459019 | − | 0.265015i | ||||
\(893\) | −4431.10 | − | 16537.1i | −0.00555659 | − | 0.0207375i | ||||
\(894\) | −241377. | + | 241377.i | −0.302009 | + | 0.302009i | ||||
\(895\) | −279404. | + | 483941.i | −0.348807 | + | 0.604152i | ||||
\(896\) | −13152.2 | + | 13152.2i | −0.0163826 | + | 0.0163826i | ||||
\(897\) | 472386. | + | 818196.i | 0.587100 | + | 1.01689i | ||||
\(898\) | 359552. | 0.445871 | ||||||||
\(899\) | 699962.i | 0.866075i | ||||||||
\(900\) | 655177. | + | 1.13480e6i | 0.808860 | + | 1.40099i | ||||
\(901\) | −508826. | − | 1.89897e6i | −0.626787 | − | 2.33920i | ||||
\(902\) | −367967. | − | 367967.i | −0.452268 | − | 0.452268i | ||||
\(903\) | 50800.1 | − | 189588.i | 0.0623001 | − | 0.232507i | ||||
\(904\) | 112700. | + | 195202.i | 0.137907 | + | 0.238862i | ||||
\(905\) | −2.64981e6 | − | 710016.i | −3.23533 | − | 0.866904i | ||||
\(906\) | 1.06982e6 | − | 286656.i | 1.30332 | − | 0.349225i | ||||
\(907\) | 401027. | + | 1.49665e6i | 0.487482 | + | 1.81931i | 0.568613 | + | 0.822605i | \(0.307480\pi\) |
−0.0811309 | + | 0.996703i | \(0.525853\pi\) | |||||||
\(908\) | −68090.1 | + | 254116.i | −0.0825871 | + | 0.308219i | ||||
\(909\) | −1.29454e6 | + | 747400.i | −1.56670 | + | 0.904535i | ||||
\(910\) | 172727. | + | 46282.0i | 0.208582 | + | 0.0558893i | ||||
\(911\) | 704696. | − | 704696.i | 0.849112 | − | 0.849112i | −0.140911 | − | 0.990022i | \(-0.545003\pi\) |
0.990022 | + | 0.140911i | \(0.0450030\pi\) | |||||||
\(912\) | 260377. | − | 69767.9i | 0.313050 | − | 0.0838814i | ||||
\(913\) | −502476. | + | 290104.i | −0.602800 | + | 0.348027i | ||||
\(914\) | −468828. | −0.561204 | ||||||||
\(915\) | 3.27816e6i | 3.91551i | ||||||||
\(916\) | 290242. | − | 167571.i | 0.345915 | − | 0.199714i | ||||
\(917\) | 93935.6 | + | 93935.6i | 0.111710 | + | 0.111710i | ||||
\(918\) | −795894. | − | 459509.i | −0.944430 | − | 0.545267i | ||||
\(919\) | −256802. | − | 256802.i | −0.304065 | − | 0.304065i | 0.538537 | − | 0.842602i | \(-0.318977\pi\) |
−0.842602 | + | 0.538537i | \(0.818977\pi\) | |||||||
\(920\) | 567136. | − | 151964.i | 0.670056 | − | 0.179541i | ||||
\(921\) | 956827. | − | 1.65727e6i | 1.12801 | − | 1.95378i | ||||
\(922\) | −251132. | + | 434974.i | −0.295421 | + | 0.511684i | ||||
\(923\) | −183370. | − | 49133.8i | −0.215241 | − | 0.0576735i | ||||
\(924\) | − | 171090.i | − | 0.200392i | ||||||
\(925\) | 1.43239e6 | + | 1.08781e6i | 1.67409 | + | 1.27136i | ||||
\(926\) | −297308. | −0.346724 | ||||||||
\(927\) | 67867.2 | − | 253284.i | 0.0789769 | − | 0.294746i | ||||
\(928\) | 139510. | + | 80546.3i | 0.161998 | + | 0.0935297i | ||||
\(929\) | 909376. | + | 525028.i | 1.05369 | + | 0.608347i | 0.923679 | − | 0.383166i | \(-0.125166\pi\) |
0.130008 | + | 0.991513i | \(0.458500\pi\) | |||||||
\(930\) | −363597. | − | 1.35696e6i | −0.420392 | − | 1.56892i | ||||
\(931\) | −464363. | + | 464363.i | −0.535745 | + | 0.535745i | ||||
\(932\) | 216358. | − | 374743.i | 0.249082 | − | 0.431422i | ||||
\(933\) | −877959. | + | 877959.i | −1.00858 | + | 1.00858i | ||||
\(934\) | −413626. | − | 716421.i | −0.474148 | − | 0.821248i | ||||
\(935\) | 2.65239e6 | 3.03399 | ||||||||
\(936\) | − | 315354.i | − | 0.359954i | ||||||
\(937\) | −435065. | − | 753554.i | −0.495535 | − | 0.858292i | 0.504451 | − | 0.863440i | \(-0.331695\pi\) |
−0.999987 | + | 0.00514776i | \(0.998361\pi\) | |||||||
\(938\) | −76260.1 | − | 284607.i | −0.0866746 | − | 0.323474i | ||||
\(939\) | 1.36142e6 | + | 1.36142e6i | 1.54405 | + | 1.54405i | ||||
\(940\) | −5314.68 | + | 19834.6i | −0.00601480 | + | 0.0224475i | ||||
\(941\) | −180851. | − | 313244.i | −0.204241 | − | 0.353755i | 0.745650 | − | 0.666338i | \(-0.232139\pi\) |
−0.949891 | + | 0.312583i | \(0.898806\pi\) | |||||||
\(942\) | −656615. | − | 175940.i | −0.739962 | − | 0.198272i | ||||
\(943\) | −902006. | + | 241692.i | −1.01435 | + | 0.271793i | ||||
\(944\) | −67116.9 | − | 250484.i | −0.0753161 | − | 0.281084i | ||||
\(945\) | 91670.0 | − | 342117.i | 0.102651 | − | 0.383099i | ||||
\(946\) | 303049. | − | 174965.i | 0.338634 | − | 0.195510i | ||||
\(947\) | 378542. | + | 101430.i | 0.422098 | + | 0.113101i | 0.463615 | − | 0.886037i | \(-0.346552\pi\) |
−0.0415164 | + | 0.999138i | \(0.513219\pi\) | |||||||
\(948\) | −777539. | + | 777539.i | −0.865178 | + | 0.865178i | ||||
\(949\) | 478910. | − | 128324.i | 0.531768 | − | 0.142487i | ||||
\(950\) | −945166. | + | 545692.i | −1.04728 | + | 0.604645i | ||||
\(951\) | 3456.19 | 0.00382153 | ||||||||
\(952\) | 150782.i | 0.166370i | ||||||||
\(953\) | 10801.1 | − | 6236.04i | 0.0118928 | − | 0.00686630i | −0.494042 | − | 0.869438i | \(-0.664481\pi\) |
0.505935 | + | 0.862572i | \(0.331148\pi\) | |||||||
\(954\) | −944817. | − | 944817.i | −1.03813 | − | 1.03813i | ||||
\(955\) | 1.22482e6 | + | 707152.i | 1.34297 | + | 0.775365i | ||||
\(956\) | 456152. | + | 456152.i | 0.499107 | + | 0.499107i | ||||
\(957\) | −1.43130e6 | + | 383516.i | −1.56281 | + | 0.418755i | ||||
\(958\) | 583501. | − | 1.01065e6i | 0.635785 | − | 1.10121i | ||||
\(959\) | −130099. | + | 225338.i | −0.141461 | + | 0.245017i | ||||
\(960\) | −312297. | − | 83679.8i | −0.338864 | − | 0.0907984i | ||||
\(961\) | − | 304866.i | − | 0.330113i | ||||||
\(962\) | −167642. | − | 399083.i | −0.181147 | − | 0.431235i | ||||
\(963\) | −327043. | −0.352657 | ||||||||
\(964\) | −33789.3 | + | 126103.i | −0.0363601 | + | 0.135698i | ||||
\(965\) | 1.75364e6 | + | 1.01246e6i | 1.88315 | + | 1.08724i | ||||
\(966\) | −265887. | − | 153510.i | −0.284933 | − | 0.164506i | ||||
\(967\) | 116414. | + | 434465.i | 0.124496 | + | 0.464624i | 0.999821 | − | 0.0189101i | \(-0.00601963\pi\) |
−0.875326 | + | 0.483534i | \(0.839353\pi\) | |||||||
\(968\) | −18569.3 | + | 18569.3i | −0.0198173 | + | 0.0198173i | ||||
\(969\) | 1.09261e6 | − | 1.89245e6i | 1.16364 | − | 2.01548i | ||||
\(970\) | 1.25026e6 | − | 1.25026e6i | 1.32880 | − | 1.32880i | ||||
\(971\) | 888811. | + | 1.53947e6i | 0.942695 | + | 1.63280i | 0.760302 | + | 0.649570i | \(0.225051\pi\) |
0.182393 | + | 0.983226i | \(0.441616\pi\) | |||||||
\(972\) | 533948. | 0.565153 | ||||||||
\(973\) | − | 264319.i | − | 0.279192i | ||||||
\(974\) | 497629. | + | 861918.i | 0.524551 | + | 0.908549i | ||||
\(975\) | 545158. | + | 2.03456e6i | 0.573473 | + | 2.14023i | ||||
\(976\) | −234931. | − | 234931.i | −0.246628 | − | 0.246628i | ||||
\(977\) | −91322.1 | + | 340819.i | −0.0956724 | + | 0.357054i | −0.997121 | − | 0.0758329i | \(-0.975838\pi\) |
0.901448 | + | 0.432887i | \(0.142505\pi\) | |||||||
\(978\) | 417956. | + | 723922.i | 0.436972 | + | 0.756857i | ||||
\(979\) | −589775. | − | 158030.i | −0.615349 | − | 0.164882i | ||||
\(980\) | 760819. | − | 203861.i | 0.792190 | − | 0.212267i | ||||
\(981\) | −159256. | − | 594350.i | −0.165484 | − | 0.617596i | ||||
\(982\) | −308766. | + | 1.15233e6i | −0.320189 | + | 1.19496i | ||||
\(983\) | −704183. | + | 406560.i | −0.728749 | + | 0.420744i | −0.817964 | − | 0.575269i | \(-0.804897\pi\) |
0.0892151 | + | 0.996012i | \(0.471564\pi\) | |||||||
\(984\) | 496696. | + | 133089.i | 0.512980 | + | 0.137453i | ||||
\(985\) | 1.04235e6 | − | 1.04235e6i | 1.07434 | − | 1.07434i | ||||
\(986\) | 1.26141e6 | − | 337993.i | 1.29748 | − | 0.347659i | ||||
\(987\) | 9298.96 | − | 5368.76i | 0.00954553 | − | 0.00551112i | ||||
\(988\) | 262656. | 0.269075 | ||||||||
\(989\) | − | 627948.i | − | 0.641994i | ||||||
\(990\) | 1.56120e6 | − | 901357.i | 1.59289 | − | 0.919658i | ||||
\(991\) | −923115. | − | 923115.i | −0.939958 | − | 0.939958i | 0.0583386 | − | 0.998297i | \(-0.481420\pi\) |
−0.998297 | + | 0.0583386i | \(0.981420\pi\) | |||||||
\(992\) | 123305. | + | 71190.0i | 0.125302 | + | 0.0723429i | ||||
\(993\) | 1.31316e6 | + | 1.31316e6i | 1.33174 | + | 1.33174i | ||||
\(994\) | 59589.2 | − | 15966.9i | 0.0603107 | − | 0.0161602i | ||||
\(995\) | −811215. | + | 1.40507e6i | −0.819388 | + | 1.41922i | ||||
\(996\) | 286667. | − | 496522.i | 0.288974 | − | 0.500518i | ||||
\(997\) | −1.33469e6 | − | 357630.i | −1.34274 | − | 0.359786i | −0.485289 | − | 0.874354i | \(-0.661286\pi\) |
−0.857450 | + | 0.514568i | \(0.827952\pi\) | |||||||
\(998\) | 185725.i | 0.186470i | ||||||||
\(999\) | −790459. | + | 332045.i | −0.792042 | + | 0.332710i |
(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 | 74.5.g.a.29.2 | yes | 28 | |
37.23 | odd | 12 | inner | 74.5.g.a.23.2 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.g.a.23.2 | ✓ | 28 | 37.23 | odd | 12 | inner | |
74.5.g.a.29.2 | yes | 28 | 1.1 | even | 1 | trivial |