Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), not 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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.15 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.6.h.a.71.15 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0499164 | − | 5.65663i | 0.00882405 | − | 0.999961i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −31.9950 | − | 0.564717i | −0.999844 | − | 0.0176474i | ||||
\(5\) | −70.1957 | + | 40.5275i | −1.25570 | + | 0.724978i | −0.972235 | − | 0.234005i | \(-0.924817\pi\) |
−0.283463 | + | 0.958983i | \(0.591483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 89.9985 | + | 51.9607i | 0.694209 | + | 0.400802i | 0.805187 | − | 0.593021i | \(-0.202065\pi\) |
−0.110978 | + | 0.993823i | \(0.535398\pi\) | |||||||
\(8\) | −4.79147 | + | 180.956i | −0.0264694 | + | 0.999650i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 225.745 | + | 399.094i | 0.713869 | + | 1.26205i | ||||
\(11\) | 214.271 | − | 371.129i | 0.533927 | − | 0.924789i | −0.465287 | − | 0.885160i | \(-0.654049\pi\) |
0.999214 | − | 0.0396293i | \(-0.0126177\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 42.9574 | + | 74.4044i | 0.0704985 | + | 0.122107i | 0.899120 | − | 0.437702i | \(-0.144208\pi\) |
−0.828621 | + | 0.559809i | \(0.810874\pi\) | |||||||
\(14\) | 298.415 | − | 506.495i | 0.406912 | − | 0.690645i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1023.36 | + | 36.1363i | 0.999377 | + | 0.0352893i | ||||
\(17\) | − | 1509.75i | − | 1.26701i | −0.773737 | − | 0.633507i | \(-0.781615\pi\) | ||
0.773737 | − | 0.633507i | \(-0.218385\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1224.53i | − | 0.778189i | −0.921198 | − | 0.389094i | \(-0.872788\pi\) | ||
0.921198 | − | 0.389094i | \(-0.127212\pi\) | |||||||
\(20\) | 2268.80 | − | 1257.04i | 1.26830 | − | 0.702705i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2088.64 | − | 1230.58i | −0.920042 | − | 0.542067i | ||||
\(23\) | 1530.14 | + | 2650.27i | 0.603129 | + | 1.04465i | 0.992344 | + | 0.123503i | \(0.0394130\pi\) |
−0.389215 | + | 0.921147i | \(0.627254\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1722.45 | − | 2983.38i | 0.551186 | − | 0.954681i | ||||
\(26\) | 423.023 | − | 239.280i | 0.122724 | − | 0.0694183i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2850.16 | − | 1713.31i | −0.687028 | − | 0.412990i | ||||
\(29\) | 4347.44 | + | 2510.00i | 0.959929 | + | 0.554215i | 0.896151 | − | 0.443749i | \(-0.146352\pi\) |
0.0637776 | + | 0.997964i | \(0.479685\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3400.78 | + | 1963.44i | −0.635587 | + | 0.366956i | −0.782913 | − | 0.622132i | \(-0.786267\pi\) |
0.147326 | + | 0.989088i | \(0.452933\pi\) | |||||||
\(32\) | 255.492 | − | 5786.98i | 0.0441065 | − | 0.999027i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8540.08 | − | 75.3610i | −1.26696 | − | 0.0111802i | ||||
\(35\) | −8423.34 | −1.16229 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13035.3 | 1.56537 | 0.782684 | − | 0.622419i | \(-0.213850\pi\) | ||||
0.782684 | + | 0.622419i | \(0.213850\pi\) | |||||||
\(38\) | −6926.71 | − | 61.1240i | −0.778158 | − | 0.00686677i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6997.35 | − | 12896.5i | −0.691486 | − | 1.27445i | ||||
\(41\) | 15071.6 | − | 8701.62i | 1.40024 | − | 0.808426i | 0.405819 | − | 0.913954i | \(-0.366986\pi\) |
0.994416 | + | 0.105527i | \(0.0336531\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5754.33 | − | 3322.27i | −0.474596 | − | 0.274008i | 0.243566 | − | 0.969884i | \(-0.421683\pi\) |
−0.718162 | + | 0.695876i | \(0.755016\pi\) | |||||||
\(44\) | −7065.19 | + | 11753.3i | −0.550164 | + | 0.915223i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15068.0 | − | 8523.13i | 1.04993 | − | 0.593888i | ||||
\(47\) | 10068.4 | − | 17438.9i | 0.664836 | − | 1.15153i | −0.314494 | − | 0.949260i | \(-0.601835\pi\) |
0.979330 | − | 0.202270i | \(-0.0648319\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3003.68 | − | 5202.52i | −0.178716 | − | 0.309545i | ||||
\(50\) | −16789.9 | − | 9892.22i | −0.949781 | − | 0.559588i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1332.41 | − | 2404.83i | −0.0683326 | − | 0.123332i | ||||
\(53\) | − | 18043.0i | − | 0.882304i | −0.897432 | − | 0.441152i | \(-0.854570\pi\) | ||
0.897432 | − | 0.441152i | \(-0.145430\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 34735.5i | 1.54834i | ||||||||
\(56\) | −9833.82 | + | 16036.8i | −0.419037 | + | 0.683357i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14415.1 | − | 24466.6i | 0.562664 | − | 0.955001i | ||||
\(59\) | 14736.4 | + | 25524.2i | 0.551140 | + | 0.954602i | 0.998193 | + | 0.0600943i | \(0.0191401\pi\) |
−0.447053 | + | 0.894507i | \(0.647527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11989.0 | + | 20765.6i | −0.412533 | + | 0.714528i | −0.995166 | − | 0.0982073i | \(-0.968689\pi\) |
0.582633 | + | 0.812735i | \(0.302023\pi\) | |||||||
\(62\) | 10936.7 | + | 19335.0i | 0.361334 | + | 0.638800i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32722.1 | − | 1734.09i | −0.998599 | − | 0.0529203i | ||||
\(65\) | −6030.85 | − | 3481.91i | −0.177050 | − | 0.102220i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −348.663 | + | 201.301i | −0.00948897 | + | 0.00547846i | −0.504737 | − | 0.863273i | \(-0.668411\pi\) |
0.495248 | + | 0.868752i | \(0.335077\pi\) | |||||||
\(68\) | −852.579 | + | 48304.3i | −0.0223595 | + | 1.26682i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −420.463 | + | 47647.8i | −0.0102561 | + | 1.16224i | ||||
\(71\) | 36645.5 | 0.862730 | 0.431365 | − | 0.902178i | \(-0.358032\pi\) | ||||
0.431365 | + | 0.902178i | \(0.358032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 58635.9 | 1.28782 | 0.643911 | − | 0.765100i | \(-0.277311\pi\) | ||||
0.643911 | + | 0.765100i | \(0.277311\pi\) | |||||||
\(74\) | 650.675 | − | 73735.9i | 0.0138129 | − | 1.56531i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −691.512 | + | 39178.8i | −0.0137330 | + | 0.778067i | ||||
\(77\) | 38568.2 | − | 22267.4i | 0.741314 | − | 0.427998i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39354.5 | + | 22721.3i | 0.709457 | + | 0.409605i | 0.810860 | − | 0.585240i | \(-0.199000\pi\) |
−0.101403 | + | 0.994845i | \(0.532333\pi\) | |||||||
\(80\) | −73300.1 | + | 38937.7i | −1.28050 | + | 0.680213i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −48469.5 | − | 85689.1i | −0.796039 | − | 1.40731i | ||||
\(83\) | −27253.7 | + | 47204.9i | −0.434241 | + | 0.752128i | −0.997233 | − | 0.0743344i | \(-0.976317\pi\) |
0.562992 | + | 0.826462i | \(0.309650\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 61186.2 | + | 105978.i | 0.918557 | + | 1.59099i | ||||
\(86\) | −19080.1 | + | 32384.3i | −0.278185 | + | 0.472160i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 66131.2 | + | 40551.9i | 0.910332 | + | 0.558219i | ||||
\(89\) | 45338.5i | 0.606726i | 0.952875 | + | 0.303363i | \(0.0981094\pi\) | ||||
−0.952875 | + | 0.303363i | \(0.901891\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8928.39i | 0.113024i | ||||||||
\(92\) | −47460.1 | − | 85659.6i | −0.584600 | − | 1.05513i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −98143.1 | − | 57823.6i | −1.14562 | − | 0.674971i | ||||
\(95\) | 49627.1 | + | 85956.6i | 0.564169 | + | 0.977170i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 41820.0 | − | 72434.3i | 0.451289 | − | 0.781655i | −0.547178 | − | 0.837016i | \(-0.684298\pi\) |
0.998466 | + | 0.0553615i | \(0.0176311\pi\) | |||||||
\(98\) | −29578.7 | + | 16731.0i | −0.311110 | + | 0.175977i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −56794.7 | + | 94480.6i | −0.567947 | + | 0.944806i | ||||
\(101\) | −107672. | − | 62164.7i | −1.05027 | − | 0.606374i | −0.127545 | − | 0.991833i | \(-0.540710\pi\) |
−0.922725 | + | 0.385459i | \(0.874043\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 57893.0 | − | 33424.5i | 0.537691 | − | 0.310436i | −0.206452 | − | 0.978457i | \(-0.566192\pi\) |
0.744143 | + | 0.668021i | \(0.232858\pi\) | |||||||
\(104\) | −13669.8 | + | 7416.89i | −0.123930 | + | 0.0672417i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −102062. | − | 900.639i | −0.882270 | − | 0.00778550i | ||||
\(107\) | −144038. | −1.21624 | −0.608119 | − | 0.793846i | \(-0.708076\pi\) | ||||
−0.608119 | + | 0.793846i | \(0.708076\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −137855. | −1.11136 | −0.555680 | − | 0.831396i | \(-0.687542\pi\) | ||||
−0.555680 | + | 0.831396i | \(0.687542\pi\) | |||||||
\(110\) | 196486. | + | 1733.87i | 1.54828 | + | 0.0136626i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 90223.4 | + | 56426.8i | 0.679633 | + | 0.425050i | ||||
\(113\) | 24697.0 | − | 14258.8i | 0.181948 | − | 0.105048i | −0.406259 | − | 0.913758i | \(-0.633167\pi\) |
0.588208 | + | 0.808710i | \(0.299834\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −214818. | − | 124025.i | −1.51470 | − | 0.874511i | ||||
\(116\) | −137679. | − | 82762.5i | −0.949999 | − | 0.571069i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 145117. | − | 82084.4i | 0.959428 | − | 0.542695i | ||||
\(119\) | 78447.4 | − | 135875.i | 0.507821 | − | 0.879573i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11298.8 | − | 19570.0i | −0.0701565 | − | 0.121515i | ||||
\(122\) | 116865. | + | 68854.0i | 0.710860 | + | 0.418822i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 109917. | − | 60899.9i | 0.641964 | − | 0.355683i | ||||
\(125\) | 25930.3i | 0.148434i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 74540.3i | 0.410093i | 0.978752 | + | 0.205046i | \(0.0657345\pi\) | ||||
−0.978752 | + | 0.205046i | \(0.934266\pi\) | |||||||
\(128\) | −11442.5 | + | 185010.i | −0.0617299 | + | 0.998093i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19996.9 | + | 33940.5i | −0.103778 | + | 0.176141i | ||||
\(131\) | −66965.9 | − | 115988.i | −0.340938 | − | 0.590522i | 0.643669 | − | 0.765304i | \(-0.277411\pi\) |
−0.984607 | + | 0.174782i | \(0.944078\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 63627.3 | − | 110206.i | 0.311899 | − | 0.540226i | ||||
\(134\) | 1121.28 | + | 1982.31i | 0.00539451 | + | 0.00953694i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 273197. | + | 7233.90i | 1.26657 | + | 0.0335371i | ||||
\(137\) | 143212. | + | 82683.3i | 0.651894 | + | 0.376371i | 0.789182 | − | 0.614160i | \(-0.210505\pi\) |
−0.137287 | + | 0.990531i | \(0.543838\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 105373. | − | 60837.0i | 0.462585 | − | 0.267074i | −0.250546 | − | 0.968105i | \(-0.580610\pi\) |
0.713131 | + | 0.701031i | \(0.247277\pi\) | |||||||
\(140\) | 269505. | + | 4756.81i | 1.16211 | + | 0.0205114i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1829.21 | − | 207290.i | 0.00761277 | − | 0.862696i | ||||
\(143\) | 36818.2 | 0.150564 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −406896. | −1.60717 | ||||||||
\(146\) | 2926.89 | − | 331682.i | 0.0113638 | − | 1.28777i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −417065. | − | 7361.26i | −1.56512 | − | 0.0276247i | ||||
\(149\) | 60786.2 | − | 35094.9i | 0.224305 | − | 0.129503i | −0.383637 | − | 0.923484i | \(-0.625329\pi\) |
0.607942 | + | 0.793981i | \(0.291995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 31118.1 | + | 17966.1i | 0.111064 | + | 0.0641225i | 0.554503 | − | 0.832182i | \(-0.312908\pi\) |
−0.443439 | + | 0.896304i | \(0.646242\pi\) | |||||||
\(152\) | 221586. | + | 5867.29i | 0.777916 | + | 0.0205982i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −124033. | − | 219278.i | −0.421440 | − | 0.745062i | ||||
\(155\) | 159147. | − | 275651.i | 0.532070 | − | 0.921573i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −84404.3 | − | 146193.i | −0.273285 | − | 0.473343i | 0.696416 | − | 0.717638i | \(-0.254777\pi\) |
−0.969701 | + | 0.244295i | \(0.921443\pi\) | |||||||
\(158\) | 130491. | − | 221480.i | 0.415850 | − | 0.705815i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 216597. | + | 416576.i | 0.668888 | + | 1.28645i | ||||
\(161\) | 318028.i | 0.966941i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 325623.i | 0.959943i | 0.877284 | + | 0.479972i | \(0.159353\pi\) | ||||
−0.877284 | + | 0.479972i | \(0.840647\pi\) | |||||||
\(164\) | −487131. | + | 269897.i | −1.41428 | + | 0.783590i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 265660. | + | 156521.i | 0.748267 | + | 0.440861i | ||||
\(167\) | −106712. | − | 184831.i | −0.296090 | − | 0.512843i | 0.679148 | − | 0.734002i | \(-0.262350\pi\) |
−0.975238 | + | 0.221158i | \(0.929016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 181956. | − | 315157.i | 0.490060 | − | 0.848809i | ||||
\(170\) | 602531. | − | 340818.i | 1.59903 | − | 0.904482i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 182234. | + | 109546.i | 0.469686 | + | 0.282341i | ||||
\(173\) | 27550.4 | + | 15906.2i | 0.0699862 | + | 0.0404066i | 0.534585 | − | 0.845115i | \(-0.320468\pi\) |
−0.464599 | + | 0.885521i | \(0.653801\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 310037. | − | 179000.i | 0.765276 | − | 0.441832i | ||||
\(176\) | 232688. | − | 372056.i | 0.566230 | − | 0.905371i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 256463. | + | 2263.13i | 0.606702 | + | 0.00535378i | ||||
\(179\) | −475398. | −1.10898 | −0.554491 | − | 0.832189i | \(-0.687087\pi\) | ||||
−0.554491 | + | 0.832189i | \(0.687087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4695.48 | 0.0106533 | 0.00532664 | − | 0.999986i | \(-0.498304\pi\) | ||||
0.00532664 | + | 0.999986i | \(0.498304\pi\) | |||||||
\(182\) | 50504.6 | + | 445.673i | 0.113019 | + | 0.000997327i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −486914. | + | 264188.i | −1.06025 | + | 0.575267i | ||||
\(185\) | −915021. | + | 528288.i | −1.96563 | + | 1.13486i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −560310. | − | 323495.i | −1.17172 | − | 0.676493i | ||||
\(188\) | −331986. | + | 552273.i | −0.685054 | + | 1.13962i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 488702. | − | 276431.i | 0.982110 | − | 0.555525i | ||||
\(191\) | −302770. | + | 524412.i | −0.600522 | + | 1.04013i | 0.392220 | + | 0.919871i | \(0.371707\pi\) |
−0.992742 | + | 0.120263i | \(0.961626\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 46694.6 | + | 80877.5i | 0.0902347 | + | 0.156291i | 0.907610 | − | 0.419815i | \(-0.137905\pi\) |
−0.817375 | + | 0.576106i | \(0.804572\pi\) | |||||||
\(194\) | −407647. | − | 240176.i | −0.777642 | − | 0.458168i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 93164.7 | + | 168151.i | 0.173225 | + | 0.312650i | ||||
\(197\) | − | 466419.i | − | 0.856270i | −0.903715 | − | 0.428135i | \(-0.859171\pi\) | ||
0.903715 | − | 0.428135i | \(-0.140829\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 625885.i | − | 1.12037i | −0.828367 | − | 0.560185i | \(-0.810730\pi\) | ||
0.828367 | − | 0.560185i | \(-0.189270\pi\) | |||||||
\(200\) | 531607. | + | 325983.i | 0.939757 | + | 0.576262i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −357018. | + | 605960.i | −0.615618 | + | 1.04488i | ||||
\(203\) | 260842. | + | 451792.i | 0.444261 | + | 0.769482i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −705309. | + | 1.22163e6i | −1.17218 | + | 2.03028i | ||||
\(206\) | −186181. | − | 329148.i | −0.305679 | − | 0.540409i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 41272.3 | + | 77695.0i | 0.0661455 | + | 0.124519i | ||||
\(209\) | −454457. | − | 262381.i | −0.719660 | − | 0.415496i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 756200. | − | 436592.i | 1.16931 | − | 0.675103i | 0.215794 | − | 0.976439i | \(-0.430766\pi\) |
0.953518 | + | 0.301336i | \(0.0974326\pi\) | |||||||
\(212\) | −10189.2 | + | 577285.i | −0.0155704 | + | 0.882167i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7189.87 | + | 814772.i | −0.0107321 | + | 1.21619i | ||||
\(215\) | 538572. | 0.794599 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −408088. | −0.588307 | ||||||||
\(218\) | −6881.20 | + | 779793.i | −0.00980670 | + | 1.11132i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 19615.7 | − | 1.11136e6i | 0.0273242 | − | 1.54810i | ||||
\(221\) | 112332. | − | 64854.8i | 0.154711 | − | 0.0893226i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −419169. | − | 242007.i | −0.564452 | − | 0.325886i | 0.190479 | − | 0.981691i | \(-0.438996\pi\) |
−0.754930 | + | 0.655805i | \(0.772329\pi\) | |||||||
\(224\) | 323689. | − | 507544.i | 0.431031 | − | 0.675856i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −79424.2 | − | 140414.i | −0.103438 | − | 0.182868i | ||||
\(227\) | −117910. | + | 204225.i | −0.151874 | + | 0.263054i | −0.931917 | − | 0.362673i | \(-0.881864\pi\) |
0.780042 | + | 0.625727i | \(0.215198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 124091. | + | 214932.i | 0.156369 | + | 0.270840i | 0.933557 | − | 0.358429i | \(-0.116688\pi\) |
−0.777187 | + | 0.629269i | \(0.783354\pi\) | |||||||
\(230\) | −712288. | + | 1.20895e6i | −0.887842 | + | 1.50692i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −475030. | + | 774669.i | −0.579430 | + | 0.944923i | ||||
\(233\) | 340275.i | 0.410620i | 0.978697 | + | 0.205310i | \(0.0658202\pi\) | ||||
−0.978697 | + | 0.205310i | \(0.934180\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.63218e6i | 1.92797i | ||||||||
\(236\) | −457078. | − | 824969.i | −0.534207 | − | 0.964179i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −764679. | − | 450531.i | −0.875057 | − | 0.515563i | ||||
\(239\) | −303908. | − | 526384.i | −0.344149 | − | 0.596084i | 0.641049 | − | 0.767500i | \(-0.278499\pi\) |
−0.985199 | + | 0.171415i | \(0.945166\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 756653. | − | 1.31056e6i | 0.839179 | − | 1.45350i | −0.0514039 | − | 0.998678i | \(-0.516370\pi\) |
0.890582 | − | 0.454822i | \(-0.150297\pi\) | |||||||
\(242\) | −111265. | + | 62936.1i | −0.122129 | + | 0.0690815i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 395315. | − | 657624.i | 0.425078 | − | 0.707137i | ||||
\(245\) | 421690. | + | 243463.i | 0.448826 | + | 0.259130i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 91110.3 | − | 52602.6i | 0.0950223 | − | 0.0548611i | ||||
\(248\) | −339002. | − | 624800.i | −0.350004 | − | 0.645077i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 146678. | + | 1294.34i | 0.148428 | + | 0.00130978i | ||||
\(251\) | 1.13311e6 | 1.13524 | 0.567622 | − | 0.823289i | \(-0.307864\pi\) | ||||
0.567622 | + | 0.823289i | \(0.307864\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.31146e6 | 1.28811 | ||||||||
\(254\) | 421647. | + | 3720.78i | 0.410077 | + | 0.00361868i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04596e6 | + | 73961.0i | 0.997509 | + | 0.0705347i | ||||
\(257\) | 928992. | − | 536354.i | 0.877362 | − | 0.506545i | 0.00757446 | − | 0.999971i | \(-0.497589\pi\) |
0.869788 | + | 0.493426i | \(0.164256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.17316e6 | + | 677323.i | 1.08669 | + | 0.627403i | ||||
\(260\) | 190991. | + | 114810.i | 0.175218 | + | 0.105328i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −659446. | + | 373012.i | −0.593507 | + | 0.335714i | ||||
\(263\) | −341490. | + | 591477.i | −0.304430 | + | 0.527289i | −0.977134 | − | 0.212623i | \(-0.931799\pi\) |
0.672704 | + | 0.739912i | \(0.265133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 731236. | + | 1.26654e6i | 0.639651 | + | 1.10791i | ||||
\(266\) | −620218. | − | 365418.i | −0.537452 | − | 0.316654i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 11269.2 | − | 6243.72i | 0.00958417 | − | 0.00531015i | ||||
\(269\) | − | 931829.i | − | 0.785155i | −0.919719 | − | 0.392577i | \(-0.871583\pi\) | ||
0.919719 | − | 0.392577i | \(-0.128417\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.76382e6i | 1.45892i | 0.684023 | + | 0.729460i | \(0.260229\pi\) | ||||
−0.684023 | + | 0.729460i | \(0.739771\pi\) | |||||||
\(272\) | 54556.6 | − | 1.54502e6i | 0.0447121 | − | 1.26622i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 474858. | − | 805969.i | 0.382109 | − | 0.648548i | ||||
\(275\) | −738145. | − | 1.27850e6i | −0.588586 | − | 1.01946i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 309348. | − | 535806.i | 0.242241 | − | 0.419573i | −0.719111 | − | 0.694895i | \(-0.755451\pi\) |
0.961352 | + | 0.275321i | \(0.0887843\pi\) | |||||||
\(278\) | −338873. | − | 599092.i | −0.262981 | − | 0.464924i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 40360.2 | − | 1.52425e6i | 0.0307651 | − | 1.16188i | ||||
\(281\) | 1.58185e6 | + | 913279.i | 1.19508 | + | 0.689982i | 0.959455 | − | 0.281861i | \(-0.0909518\pi\) |
0.235628 | + | 0.971843i | \(0.424285\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.63561e6 | + | 944320.i | −1.21399 | + | 0.700895i | −0.963625 | − | 0.267258i | \(-0.913883\pi\) |
−0.250361 | + | 0.968153i | \(0.580549\pi\) | |||||||
\(284\) | −1.17247e6 | − | 20694.3i | −0.862596 | − | 0.0152249i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1837.83 | − | 208267.i | 0.00132859 | − | 0.150558i | ||||
\(287\) | 1.80857e6 | 1.29607 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −859473. | −0.605324 | ||||||||
\(290\) | −20310.7 | + | 2.30166e6i | −0.0141818 | + | 1.60711i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.87606e6 | − | 33112.7i | −1.28762 | − | 0.0227267i | ||||
\(293\) | 965146. | − | 557227.i | 0.656786 | − | 0.379196i | −0.134265 | − | 0.990945i | \(-0.542867\pi\) |
0.791051 | + | 0.611750i | \(0.209534\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.06886e6 | − | 1.19446e6i | −1.38413 | − | 0.799128i | ||||
\(296\) | −62458.3 | + | 2.35881e6i | −0.0414344 | + | 1.56482i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −195485. | − | 345597.i | −0.127518 | − | 0.225439i | ||||
\(299\) | −131461. | + | 227698.i | −0.0850394 | + | 0.147293i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −345254. | − | 597998.i | −0.219646 | − | 0.380438i | ||||
\(302\) | 103181. | − | 175127.i | 0.0651001 | − | 0.110493i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 44249.9 | − | 1.25314e6i | 0.0274618 | − | 0.777704i | ||||
\(305\) | − | 1.94354e6i | − | 1.19631i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.64394e6i | − | 0.995497i | −0.867321 | − | 0.497749i | \(-0.834160\pi\) | ||
0.867321 | − | 0.497749i | \(-0.165840\pi\) | |||||||
\(308\) | −1.24656e6 | + | 690664.i | −0.748752 | + | 0.414849i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.55131e6 | − | 913995.i | −0.916842 | − | 0.540182i | ||||
\(311\) | 363235. | + | 629141.i | 0.212954 | + | 0.368848i | 0.952638 | − | 0.304107i | \(-0.0983581\pi\) |
−0.739683 | + | 0.672955i | \(0.765025\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 702457. | − | 1.21669e6i | 0.405284 | − | 0.701972i | −0.589071 | − | 0.808081i | \(-0.700506\pi\) |
0.994354 | + | 0.106110i | \(0.0338394\pi\) | |||||||
\(314\) | −831171. | + | 470147.i | −0.475736 | + | 0.269097i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.24632e6 | − | 749193.i | −0.702118 | − | 0.422062i | ||||
\(317\) | −1.21701e6 | − | 702639.i | −0.680213 | − | 0.392721i | 0.119722 | − | 0.992807i | \(-0.461800\pi\) |
−0.799935 | + | 0.600086i | \(0.795133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.86306e6 | − | 1.07564e6i | 1.02506 | − | 0.591821i | ||||
\(320\) | 2.36723e6 | − | 1.20442e6i | 1.29230 | − | 0.657510i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.79897e6 | + | 15874.8i | 0.966904 | + | 0.00853234i | ||||
\(323\) | −1.84873e6 | −0.985976 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 295969. | 0.155431 | ||||||||
\(326\) | 1.84193e6 | + | 16253.9i | 0.959906 | + | 0.00847059i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.50239e6 | + | 2.76900e6i | 0.771080 | + | 1.42114i | ||||
\(329\) | 1.81228e6 | − | 1.04632e6i | 0.923071 | − | 0.532935i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −214028. | − | 123569.i | −0.107374 | − | 0.0619926i | 0.445351 | − | 0.895356i | \(-0.353079\pi\) |
−0.552725 | + | 0.833363i | \(0.686412\pi\) | |||||||
\(332\) | 898642. | − | 1.49493e6i | 0.447447 | − | 0.744347i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.05085e6 | + | 594407.i | −0.515436 | + | 0.291553i | ||||
\(335\) | 16316.4 | − | 28260.9i | 0.00794352 | − | 0.0137586i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.07901e6 | + | 1.86890e6i | 0.517549 | + | 0.896421i | 0.999792 | + | 0.0203835i | \(0.00648871\pi\) |
−0.482244 | + | 0.876037i | \(0.660178\pi\) | |||||||
\(338\) | −1.77364e6 | − | 1.04499e6i | −0.844451 | − | 0.497531i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.89781e6 | − | 3.42531e6i | −0.890337 | − | 1.60695i | ||||
\(341\) | 1.68284e6i | 0.783712i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.37090e6i | − | 1.08812i | ||||||
\(344\) | 628755. | − | 1.02536e6i | 0.286474 | − | 0.467177i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 91350.9 | − | 155048.i | 0.0410225 | − | 0.0696269i | ||||
\(347\) | 804114. | + | 1.39277e6i | 0.358504 | + | 0.620947i | 0.987711 | − | 0.156291i | \(-0.0499537\pi\) |
−0.629207 | + | 0.777237i | \(0.716620\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 233867. | − | 405070.i | 0.102779 | − | 0.178019i | −0.810049 | − | 0.586362i | \(-0.800560\pi\) |
0.912829 | + | 0.408343i | \(0.133893\pi\) | |||||||
\(350\) | −997061. | − | 1.76270e6i | −0.435062 | − | 0.769145i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.09297e6 | − | 1.33480e6i | −0.900339 | − | 0.574197i | ||||
\(353\) | −397710. | − | 229618.i | −0.169875 | − | 0.0980773i | 0.412652 | − | 0.910889i | \(-0.364603\pi\) |
−0.582527 | + | 0.812811i | \(0.697936\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.57236e6 | + | 1.48515e6i | −1.08333 | + | 0.625460i | ||||
\(356\) | 25603.4 | − | 1.45061e6i | 0.0107071 | − | 0.606631i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −23730.1 | + | 2.68915e6i | −0.00978572 | + | 1.10894i | ||||
\(359\) | −2.21493e6 | −0.907037 | −0.453518 | − | 0.891247i | \(-0.649831\pi\) | ||||
−0.453518 | + | 0.891247i | \(0.649831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 976629. | 0.394423 | ||||||||
\(362\) | 234.381 | − | 26560.6i | 9.40050e−5 | − | 0.0106529i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5042.01 | − | 285664.i | 0.00199458 | − | 0.113006i | ||||
\(365\) | −4.11598e6 | + | 2.37636e6i | −1.61712 | + | 0.933643i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.54558e6 | + | 1.46969e6i | 0.986555 | + | 0.569588i | 0.904243 | − | 0.427019i | \(-0.140436\pi\) |
0.0823124 | + | 0.996607i | \(0.473769\pi\) | |||||||
\(368\) | 1.47011e6 | + | 2.76748e6i | 0.565889 | + | 1.06528i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.94266e6 | + | 5.20231e6i | 1.11747 | + | 1.97557i | ||||
\(371\) | 937525. | − | 1.62384e6i | 0.353629 | − | 0.612504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −830424. | − | 1.43834e6i | −0.309049 | − | 0.535289i | 0.669105 | − | 0.743168i | \(-0.266678\pi\) |
−0.978155 | + | 0.207878i | \(0.933344\pi\) | |||||||
\(374\) | −1.85786e6 | + | 3.15332e6i | −0.686806 | + | 1.16571i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.10744e6 | + | 1.90549e6i | 1.13353 | + | 0.695083i | ||||
\(377\) | 431292.i | 0.156285i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.69152e6i | 1.67770i | 0.544360 | + | 0.838852i | \(0.316773\pi\) | ||||
−0.544360 | + | 0.838852i | \(0.683227\pi\) | |||||||
\(380\) | −1.53928e6 | − | 2.77821e6i | −0.546837 | − | 0.986974i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.95129e6 | + | 1.73883e6i | 1.03479 | + | 0.609677i | ||||
\(383\) | 2.64821e6 | + | 4.58683e6i | 0.922476 | + | 1.59777i | 0.795571 | + | 0.605860i | \(0.207171\pi\) |
0.126904 | + | 0.991915i | \(0.459496\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.80488e6 | + | 3.12614e6i | −0.620578 | + | 1.07487i | ||||
\(386\) | 459825. | − | 260097.i | 0.157081 | − | 0.0888521i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.37894e6 | + | 2.29392e6i | −0.465013 | + | 0.773569i | ||||
\(389\) | 1.59537e6 | + | 921088.i | 0.534549 | + | 0.308622i | 0.742867 | − | 0.669439i | \(-0.233465\pi\) |
−0.208318 | + | 0.978061i | \(0.566799\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00124e6 | − | 2.31011e6i | 1.32359 | − | 0.764173i | ||||
\(392\) | 955818. | − | 518605.i | 0.314167 | − | 0.170460i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.63836e6 | − | 23281.9i | −0.856236 | − | 0.00755576i | ||||
\(395\) | −3.68335e6 | −1.18782 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 75711.5 | 0.0241094 | 0.0120547 | − | 0.999927i | \(-0.496163\pi\) | ||||
0.0120547 | + | 0.999927i | \(0.496163\pi\) | |||||||
\(398\) | −3.54040e6 | − | 31241.9i | −1.12033 | − | 0.00988620i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.87050e6 | − | 2.99083e6i | 0.584532 | − | 0.934636i | ||||
\(401\) | −2.92456e6 | + | 1.68849e6i | −0.908237 | + | 0.524371i | −0.879863 | − | 0.475227i | \(-0.842366\pi\) |
−0.0283735 | + | 0.999597i | \(0.509033\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −292178. | − | 168689.i | −0.0896158 | − | 0.0517397i | ||||
\(404\) | 3.40988e6 | + | 2.04977e6i | 1.03941 | + | 0.624814i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.56864e6 | − | 1.45294e6i | 0.773373 | − | 0.437454i | ||||
\(407\) | 2.79309e6 | − | 4.83777e6i | 0.835793 | − | 1.44764i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.75008e6 | − | 3.03123e6i | −0.517310 | − | 0.896007i | −0.999798 | − | 0.0201041i | \(-0.993600\pi\) |
0.482488 | − | 0.875902i | \(-0.339733\pi\) | |||||||
\(410\) | 6.87512e6 | + | 4.05066e6i | 2.01986 | + | 1.19005i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.87116e6 | + | 1.03673e6i | −0.543086 | + | 0.300899i | ||||
\(413\) | 3.06285e6i | 0.883591i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.41810e6i | − | 1.25926i | ||||||
\(416\) | 441552. | − | 229584.i | 0.125098 | − | 0.0650442i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.50688e6 | + | 2.55760e6i | −0.421830 | + | 0.715966i | ||||
\(419\) | −2.65830e6 | − | 4.60430e6i | −0.739721 | − | 1.28123i | −0.952621 | − | 0.304161i | \(-0.901624\pi\) |
0.212899 | − | 0.977074i | \(-0.431709\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.59023e6 | + | 4.48640e6i | −0.712250 | + | 1.23365i | 0.251761 | + | 0.967790i | \(0.418990\pi\) |
−0.964011 | + | 0.265864i | \(0.914343\pi\) | |||||||
\(422\) | −2.43190e6 | − | 4.29934e6i | −0.664758 | − | 1.17522i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.26498e6 | + | 86452.4i | 0.881995 | + | 0.0233541i | ||||
\(425\) | −4.50414e6 | − | 2.60047e6i | −1.20959 | − | 0.698360i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.15799e6 | + | 1.24591e6i | −0.572768 | + | 0.330688i | ||||
\(428\) | 4.60851e6 | + | 81340.9i | 1.21605 | + | 0.0214635i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 26883.6 | − | 3.04651e6i | 0.00701158 | − | 0.794568i | ||||
\(431\) | 5.72244e6 | 1.48384 | 0.741922 | − | 0.670486i | \(-0.233914\pi\) | ||||
0.741922 | + | 0.670486i | \(0.233914\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.17405e6 | −1.58252 | −0.791262 | − | 0.611478i | \(-0.790575\pi\) | ||||
−0.791262 | + | 0.611478i | \(0.790575\pi\) | |||||||
\(434\) | −20370.2 | + | 2.30840e6i | −0.00519125 | + | 0.588284i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.41066e6 | + | 77848.8i | 1.11119 | + | 0.0196126i | ||||
\(437\) | 3.24533e6 | − | 1.87369e6i | 0.812935 | − | 0.469348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.02340e6 | + | 2.90026e6i | 1.24405 | + | 0.718251i | 0.969915 | − | 0.243442i | \(-0.0782765\pi\) |
0.274131 | + | 0.961692i | \(0.411610\pi\) | |||||||
\(440\) | −6.28559e6 | − | 166434.i | −1.54780 | − | 0.0409837i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −361252. | − | 638657.i | −0.0879539 | − | 0.155493i | ||||
\(443\) | −2.08981e6 | + | 3.61966e6i | −0.505939 | + | 0.876312i | 0.494037 | + | 0.869441i | \(0.335521\pi\) |
−0.999976 | + | 0.00687158i | \(0.997813\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.83746e6 | − | 3.18257e6i | −0.439863 | − | 0.761864i | ||||
\(446\) | −1.38987e6 | + | 2.35900e6i | −0.330854 | + | 0.561554i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.85484e6 | − | 1.85633e6i | −0.672026 | − | 0.436978i | ||||
\(449\) | 970936.i | 0.227287i | 0.993522 | + | 0.113644i | \(0.0362522\pi\) | ||||
−0.993522 | + | 0.113644i | \(0.963748\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.45802e6i | − | 1.72656i | ||||||
\(452\) | −798233. | + | 442265.i | −0.183774 | + | 0.101821i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.14934e6 | + | 677166.i | 0.261704 | + | 0.154190i | ||||
\(455\) | −361845. | − | 626734.i | −0.0819397 | − | 0.141924i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.03810e6 | + | 1.79803e6i | −0.232513 | + | 0.402724i | −0.958547 | − | 0.284935i | \(-0.908028\pi\) |
0.726034 | + | 0.687659i | \(0.241361\pi\) | |||||||
\(458\) | 1.22199e6 | − | 691209.i | 0.272209 | − | 0.153973i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.80306e6 | + | 4.08950e6i | 1.49903 | + | 0.901105i | ||||
\(461\) | −2.52767e6 | − | 1.45935e6i | −0.553947 | − | 0.319821i | 0.196766 | − | 0.980451i | \(-0.436956\pi\) |
−0.750712 | + | 0.660629i | \(0.770290\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.02987e6 | + | 2.90400e6i | −1.09045 | + | 0.629569i | −0.933695 | − | 0.358069i | \(-0.883435\pi\) |
−0.156751 | + | 0.987638i | \(0.550102\pi\) | |||||||
\(464\) | 4.35831e6 | + | 2.72574e6i | 0.939773 | + | 0.587745i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.92481e6 | + | 16985.3i | 0.410604 | + | 0.00362333i | ||||
\(467\) | −8.31962e6 | −1.76527 | −0.882636 | − | 0.470058i | \(-0.844233\pi\) | ||||
−0.882636 | + | 0.470058i | \(0.844233\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −41838.9 | −0.00878311 | ||||||||
\(470\) | 9.23266e6 | + | 81472.6i | 1.92789 | + | 0.0170125i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.68936e6 | + | 2.54434e6i | −0.968856 | + | 0.525679i | ||||
\(473\) | −2.46598e6 | + | 1.42373e6i | −0.506799 | + | 0.292601i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.65323e6 | − | 2.10919e6i | −0.742922 | − | 0.428926i | ||||
\(476\) | −2.58666e6 | + | 4.30302e6i | −0.523265 | + | 0.870474i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.99273e6 | + | 1.69282e6i | −0.599098 | + | 0.338876i | ||||
\(479\) | 57304.6 | − | 99254.5i | 0.0114117 | − | 0.0197657i | −0.860263 | − | 0.509850i | \(-0.829701\pi\) |
0.871675 | + | 0.490085i | \(0.163034\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 559963. | + | 969884.i | 0.110356 | + | 0.191142i | ||||
\(482\) | −7.37560e6 | − | 4.34553e6i | −1.44604 | − | 0.851972i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 350453. | + | 632524.i | 0.0680011 | + | 0.122734i | ||||
\(485\) | 6.77943e6i | 1.30870i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.72517e6i | − | 0.520681i | −0.965517 | − | 0.260340i | \(-0.916165\pi\) | ||
0.965517 | − | 0.260340i | \(-0.0838348\pi\) | |||||||
\(488\) | −3.70021e6 | − | 2.26898e6i | −0.703358 | − | 0.431302i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.39823e6 | − | 2.37319e6i | 0.263080 | − | 0.446522i | ||||
\(491\) | −2.94851e6 | − | 5.10696e6i | −0.551948 | − | 0.956002i | −0.998134 | − | 0.0610621i | \(-0.980551\pi\) |
0.446186 | − | 0.894940i | \(-0.352782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.78946e6 | − | 6.56353e6i | 0.702198 | − | 1.21624i | ||||
\(494\) | −293006. | − | 518004.i | −0.0540205 | − | 0.0955027i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.55119e6 | + | 1.88642e6i | −0.648141 | + | 0.344298i | ||||
\(497\) | 3.29804e6 | + | 1.90413e6i | 0.598915 | + | 0.345784i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.34312e6 | + | 3.66220e6i | −1.14039 | + | 0.658402i | −0.946526 | − | 0.322627i | \(-0.895434\pi\) |
−0.193860 | + | 0.981029i | \(0.562101\pi\) | |||||||
\(500\) | 14643.3 | − | 829640.i | 0.00261947 | − | 0.148410i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 56560.9 | − | 6.40961e6i | 0.0100174 | − | 1.13520i | ||||
\(503\) | 5.80816e6 | 1.02357 | 0.511786 | − | 0.859113i | \(-0.328984\pi\) | ||||
0.511786 | + | 0.859113i | \(0.328984\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.00775e7 | 1.75843 | ||||||||
\(506\) | 65463.1 | − | 7.41843e6i | 0.0113663 | − | 1.28806i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 42094.2 | − | 2.38492e6i | 0.00723707 | − | 0.410029i | ||||
\(509\) | 3.70500e6 | − | 2.13908e6i | 0.633861 | − | 0.365960i | −0.148385 | − | 0.988930i | \(-0.547407\pi\) |
0.782246 | + | 0.622970i | \(0.214074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.27714e6 | + | 3.04676e6i | 0.894018 | + | 0.516162i | ||||
\(512\) | 470581. | − | 5.91295e6i | 0.0793340 | − | 0.996848i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.98758e6 | − | 5.28174e6i | −0.498784 | − | 0.881798i | ||||
\(515\) | −2.70922e6 | + | 4.69251e6i | −0.450119 | + | 0.779628i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.31472e6 | − | 7.47332e6i | −0.709948 | − | 1.22967i | ||||
\(518\) | 3.88993e6 | − | 6.60231e6i | 0.636967 | − | 1.08111i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 658969. | − | 1.07463e6i | 0.106870 | − | 0.174282i | ||||
\(521\) | − | 6.07298e6i | − | 0.980184i | −0.871671 | − | 0.490092i | \(-0.836963\pi\) | ||
0.871671 | − | 0.490092i | \(-0.163037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 525817.i | 0.0840583i | 0.999116 | + | 0.0420291i | \(0.0133822\pi\) | ||||
−0.999116 | + | 0.0420291i | \(0.986618\pi\) | |||||||
\(524\) | 2.07707e6 | + | 3.74886e6i | 0.330464 | + | 0.596446i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.32872e6 | + | 1.96121e6i | 0.524582 | + | 0.309071i | ||||
\(527\) | 2.96430e6 | + | 5.13432e6i | 0.464939 | + | 0.805297i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.46446e6 | + | 2.53652e6i | −0.227530 | + | 0.394093i | ||||
\(530\) | 7.20085e6 | − | 4.07312e6i | 1.11351 | − | 0.629850i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.09799e6 | + | 3.49010e6i | −0.321384 | + | 0.534637i | ||||
\(533\) | 1.29488e6 | + | 747598.i | 0.197429 | + | 0.113986i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.01109e7 | − | 5.83751e6i | 1.52723 | − | 0.881746i | ||||
\(536\) | −34756.0 | − | 64057.2i | −0.00522537 | − | 0.00963066i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.27101e6 | − | 46513.5i | −0.785124 | − | 0.00692825i | ||||
\(539\) | −2.57440e6 | −0.381685 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.11917e7 | 1.64400 | 0.822000 | − | 0.569488i | \(-0.192858\pi\) | ||||
0.822000 | + | 0.569488i | \(0.192858\pi\) | |||||||
\(542\) | 9.97730e6 | + | 88043.6i | 1.45886 | + | 0.0128736i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.73687e6 | − | 385728.i | −1.26578 | − | 0.0558836i | ||||
\(545\) | 9.67679e6 | − | 5.58690e6i | 1.39553 | − | 0.805711i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 776917. | + | 448553.i | 0.111021 | + | 0.0640982i | 0.554482 | − | 0.832195i | \(-0.312916\pi\) |
−0.443461 | + | 0.896294i | \(0.646250\pi\) | |||||||
\(548\) | −4.53537e6 | − | 2.72633e6i | −0.645151 | − | 0.387817i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.26888e6 | + | 4.11160e6i | −1.02461 | + | 0.579567i | ||||
\(551\) | 3.07356e6 | − | 5.32357e6i | 0.431284 | − | 0.747006i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.36123e6 | + | 4.08977e6i | 0.328341 | + | 0.568704i | ||||
\(554\) | −3.01542e6 | − | 1.77661e6i | −0.417420 | − | 0.245934i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.40576e6 | + | 1.88698e6i | −0.467226 | + | 0.258869i | ||||
\(557\) | − | 2.91603e6i | − | 0.398249i | −0.979974 | − | 0.199124i | \(-0.936190\pi\) | ||
0.979974 | − | 0.199124i | \(-0.0638098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 570864.i | − | 0.0772686i | ||||||
\(560\) | −8.62013e6 | − | 304388.i | −1.16157 | − | 0.0410164i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.24504e6 | − | 8.90233e6i | 0.700500 | − | 1.18895i | ||||
\(563\) | 1.88482e6 | + | 3.26460e6i | 0.250610 | + | 0.434070i | 0.963694 | − | 0.267009i | \(-0.0860354\pi\) |
−0.713084 | + | 0.701079i | \(0.752702\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.15575e6 | + | 2.00182e6i | −0.152315 | + | 0.263817i | ||||
\(566\) | 5.26003e6 | + | 9.29918e6i | 0.690156 | + | 1.22012i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −175586. | + | 6.63122e6i | −0.0228359 | + | 0.862428i | ||||
\(569\) | 578222. | + | 333836.i | 0.0748710 | + | 0.0432268i | 0.536968 | − | 0.843603i | \(-0.319570\pi\) |
−0.462097 | + | 0.886829i | \(0.652903\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.54218e6 | + | 3.19978e6i | −0.711361 | + | 0.410704i | −0.811565 | − | 0.584262i | \(-0.801384\pi\) |
0.100204 | + | 0.994967i | \(0.468051\pi\) | |||||||
\(572\) | −1.17800e6 | − | 20791.8i | −0.150541 | − | 0.00265707i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 90277.1 | − | 1.02304e7i | 0.0114366 | − | 1.29602i | ||||
\(575\) | 1.05424e7 | 1.32974 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.64788e6 | −1.08136 | −0.540680 | − | 0.841229i | \(-0.681833\pi\) | ||||
−0.540680 | + | 0.841229i | \(0.681833\pi\) | |||||||
\(578\) | −42901.8 | + | 4.86173e6i | −0.00534141 | + | 0.605300i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.30186e7 | + | 229781.i | 1.60692 | + | 0.0283625i | ||||
\(581\) | −4.90560e6 | + | 2.83225e6i | −0.602908 | + | 0.348089i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.69626e6 | − | 3.86609e6i | −0.815945 | − | 0.471086i | ||||
\(584\) | −280952. | + | 1.06105e7i | −0.0340879 | + | 1.28737i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.10385e6 | − | 5.48729e6i | −0.373385 | − | 0.660107i | ||||
\(587\) | 358200. | − | 620420.i | 0.0429072 | − | 0.0743175i | −0.843774 | − | 0.536698i | \(-0.819671\pi\) |
0.886681 | + | 0.462381i | \(0.153005\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.40429e6 | + | 4.16436e6i | 0.285561 | + | 0.494606i | ||||
\(590\) | −6.85989e6 | + | 1.16432e7i | −0.811310 | + | 1.37702i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.33398e7 | + | 471047.i | 1.56439 | + | 0.0552408i | ||||
\(593\) | − | 6.55369e6i | − | 0.765331i | −0.923887 | − | 0.382665i | \(-0.875006\pi\) | ||
0.923887 | − | 0.382665i | \(-0.124994\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.27171e7i | 1.47264i | ||||||||
\(596\) | −1.96467e6 | + | 1.08854e6i | −0.226556 | + | 0.125524i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.28144e6 | + | 754995.i | 0.146536 | + | 0.0863358i | ||||
\(599\) | 1.04139e6 | + | 1.80373e6i | 0.118589 | + | 0.205402i | 0.919209 | − | 0.393771i | \(-0.128830\pi\) |
−0.800620 | + | 0.599173i | \(0.795496\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 392578. | − | 679965.i | 0.0443343 | − | 0.0767893i | −0.843007 | − | 0.537903i | \(-0.819217\pi\) |
0.887341 | + | 0.461114i | \(0.152550\pi\) | |||||||
\(602\) | −3.39989e6 | + | 1.92313e6i | −0.382361 | + | 0.216280i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −985480. | − | 592398.i | −0.109915 | − | 0.0660725i | ||||
\(605\) | 1.58625e6 | + | 915822.i | 0.176191 | + | 0.101724i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.67650e6 | + | 5.00938e6i | −0.955812 | + | 0.551838i | −0.894882 | − | 0.446304i | \(-0.852740\pi\) |
−0.0609306 | + | 0.998142i | \(0.519407\pi\) | |||||||
\(608\) | −7.08632e6 | − | 312857.i | −0.777431 | − | 0.0343232i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.09939e7 | − | 97014.3i | −1.19626 | − | 0.0105563i | ||||
\(611\) | 1.73005e6 | 0.187480 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.81550e6 | −0.517595 | −0.258797 | − | 0.965932i | \(-0.583326\pi\) | ||||
−0.258797 | + | 0.965932i | \(0.583326\pi\) | |||||||
\(614\) | −9.29917e6 | − | 82059.5i | −0.995458 | − | 0.00878432i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.84461e6 | + | 7.08583e6i | 0.408226 | + | 0.752383i | ||||
\(617\) | −8.76037e6 | + | 5.05780e6i | −0.926423 | + | 0.534871i | −0.885678 | − | 0.464299i | \(-0.846306\pi\) |
−0.0407445 | + | 0.999170i | \(0.512973\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.10769e7 | + | 6.39527e6i | 1.16196 | + | 0.670860i | 0.951774 | − | 0.306800i | \(-0.0992584\pi\) |
0.210190 | + | 0.977661i | \(0.432592\pi\) | |||||||
\(620\) | −5.24757e6 | + | 8.72957e6i | −0.548251 | + | 0.912040i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.57695e6 | − | 2.02328e6i | 0.370712 | − | 0.209691i | ||||
\(623\) | −2.35582e6 | + | 4.08040e6i | −0.243177 | + | 0.421195i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.33178e6 | + | 7.50287e6i | 0.443575 | + | 0.768294i | ||||
\(626\) | −6.84731e6 | − | 4.03428e6i | −0.698368 | − | 0.411462i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.61796e6 | + | 4.72510e6i | 0.264889 | + | 0.478092i | ||||
\(629\) | − | 1.96800e7i | − | 1.98334i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.13313e7i | − | 1.13294i | −0.824082 | − | 0.566471i | \(-0.808308\pi\) | ||
0.824082 | − | 0.566471i | \(-0.191692\pi\) | |||||||
\(632\) | −4.30012e6 | + | 7.01256e6i | −0.428241 | + | 0.698367i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.03532e6 | + | 6.84909e6i | −0.398708 | + | 0.676721i | ||||
\(635\) | −3.02093e6 | − | 5.23241e6i | −0.297308 | − | 0.514953i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 258060. | − | 446974.i | 0.0251984 | − | 0.0436449i | ||||
\(638\) | −5.99151e6 | − | 1.05924e7i | −0.582753 | − | 1.03025i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6.69479e6 | − | 1.34507e7i | −0.646081 | − | 1.29806i | ||||
\(641\) | 1.30074e7 | + | 7.50980e6i | 1.25039 | + | 0.721910i | 0.971186 | − | 0.238323i | \(-0.0765976\pi\) |
0.279200 | + | 0.960233i | \(0.409931\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.31540e6 | + | 1.33680e6i | −0.220851 | + | 0.127508i | −0.606344 | − | 0.795202i | \(-0.707365\pi\) |
0.385493 | + | 0.922711i | \(0.374031\pi\) | |||||||
\(644\) | 179596. | − | 1.01753e7i | 0.0170640 | − | 0.966791i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −92281.7 | + | 1.04576e7i | −0.00870030 | + | 0.985937i | ||||
\(647\) | −1.55764e7 | −1.46288 | −0.731438 | − | 0.681908i | \(-0.761150\pi\) | ||||
−0.731438 | + | 0.681908i | \(0.761150\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.26303e7 | 1.17707 | ||||||||
\(650\) | 14773.7 | − | 1.67419e6i | 0.00137153 | − | 0.155425i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 183885. | − | 1.04183e7i | 0.0169405 | − | 0.959794i | ||||
\(653\) | −415132. | + | 239677.i | −0.0380981 | + | 0.0219959i | −0.518928 | − | 0.854818i | \(-0.673669\pi\) |
0.480830 | + | 0.876814i | \(0.340335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.40143e6 | + | 5.42792e6i | 0.856230 | + | 0.494345i | ||||
\(656\) | 1.57382e7 | − | 8.36027e6i | 1.42789 | − | 0.758509i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.82818e6 | − | 1.03036e7i | −0.524769 | − | 0.927737i | ||||
\(659\) | −155358. | + | 269087.i | −0.0139354 | + | 0.0241368i | −0.872909 | − | 0.487883i | \(-0.837769\pi\) |
0.858974 | + | 0.512020i | \(0.171103\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.04750e7 | + | 1.81433e7i | 0.932505 | + | 1.61515i | 0.779023 | + | 0.626995i | \(0.215715\pi\) |
0.153482 | + | 0.988151i | \(0.450951\pi\) | |||||||
\(662\) | −709668. | + | 1.20451e6i | −0.0629376 | + | 0.106823i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.41142e6 | − | 5.15791e6i | −0.740370 | − | 0.453997i | ||||
\(665\) | 1.03146e7i | 0.904481i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.53625e7i | 1.33705i | ||||||||
\(668\) | 3.30989e6 | + | 5.97395e6i | 0.286994 | + | 0.517989i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −159047. | − | 93706.7i | −0.0136880 | − | 0.00806462i | ||||
\(671\) | 5.13780e6 | + | 8.89893e6i | 0.440525 | + | 0.763012i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.73764e6 | − | 1.16699e7i | 0.573417 | − | 0.993187i | −0.422795 | − | 0.906225i | \(-0.638951\pi\) |
0.996212 | − | 0.0869616i | \(-0.0277157\pi\) | |||||||
\(674\) | 1.06256e7 | − | 6.01028e6i | 0.900953 | − | 0.509619i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.99965e6 | + | 9.98069e6i | −0.504963 | + | 0.840028i | ||||
\(677\) | −3.38026e6 | − | 1.95159e6i | −0.283451 | − | 0.163650i | 0.351534 | − | 0.936175i | \(-0.385660\pi\) |
−0.634985 | + | 0.772525i | \(0.718994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.52747e6 | − | 4.34599e6i | 0.626577 | − | 0.361755i | ||||
\(680\) | −1.94704e7 | + | 1.05642e7i | −1.61474 | + | 0.876123i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.51920e6 | + | 84001.1i | 0.783681 | + | 0.00691551i | ||||
\(683\) | 1.55558e7 | 1.27597 | 0.637985 | − | 0.770048i | \(-0.279768\pi\) | ||||
0.637985 | + | 0.770048i | \(0.279768\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.34038e7 | −1.09144 | ||||||||
\(686\) | −1.34113e7 | − | 118347.i | −1.08808 | − | 0.00960164i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.76871e6 | − | 3.60782e6i | −0.464631 | − | 0.290586i | ||||
\(689\) | 1.34248e6 | − | 775080.i | 0.107736 | − | 0.0622011i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.52435e6 | − | 5.49889e6i | −0.758823 | − | 0.438107i | 0.0700501 | − | 0.997543i | \(-0.477684\pi\) |
−0.828873 | + | 0.559437i | \(0.811017\pi\) | |||||||
\(692\) | −872493. | − | 524478.i | −0.0692622 | − | 0.0416353i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.91850e6 | − | 4.47905e6i | 0.624086 | − | 0.353010i | ||||
\(695\) | −4.93114e6 | + | 8.54099e6i | −0.387245 | + | 0.670728i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.31372e7 | − | 2.27543e7i | −1.02429 | − | 1.77412i | ||||
\(698\) | −2.27966e6 | − | 1.34312e6i | −0.177105 | − | 0.104346i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.00207e7 | + | 5.55202e6i | −0.772954 | + | 0.428258i | ||||
\(701\) | 1.51787e7i | 1.16665i | 0.812239 | + | 0.583324i | \(0.198248\pi\) | ||||
−0.812239 | + | 0.583324i | \(0.801752\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.59621e7i | − | 1.21815i | ||||||
\(704\) | −7.65497e6 | + | 1.17725e7i | −0.582119 | + | 0.895238i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.31872e6 | + | 2.23824e6i | −0.0995725 | + | 0.169003i | ||||
\(707\) | −6.46024e6 | − | 1.11895e7i | −0.486071 | − | 0.841900i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.34771e6 | + | 1.09946e7i | −0.474244 | + | 0.821414i | −0.999565 | − | 0.0294896i | \(-0.990612\pi\) |
0.525321 | + | 0.850904i | \(0.323945\pi\) | |||||||
\(710\) | 8.27255e6 | + | 1.46250e7i | 0.615876 | + | 1.08881i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.20427e6 | − | 217238.i | −0.606513 | − | 0.0160597i | ||||
\(713\) | −1.04073e7 | − | 6.00867e6i | −0.766682 | − | 0.442644i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.58447e6 | + | 1.49215e6i | −0.189063 | + | 0.109156i | ||||
\(716\) | 1.52104e7 | + | 268465.i | 1.10881 | + | 0.0195707i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −110561. | + | 1.25291e7i | −0.00800374 | + | 0.907001i | ||||
\(719\) | 1.30901e7 | 0.944324 | 0.472162 | − | 0.881512i | \(-0.343474\pi\) | ||||
0.472162 | + | 0.881512i | \(0.343474\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.94705e6 | 0.497693 | ||||||||
\(722\) | 48749.8 | − | 5.52443e6i | 0.00348040 | − | 0.394407i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −150232. | − | 2651.62i | −0.0106516 | − | 0.000188003i | ||||
\(725\) | 1.49766e7 | − | 8.64672e6i | 1.05820 | − | 0.610951i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.63075e6 | − | 3.82826e6i | −0.465293 | − | 0.268637i | 0.248974 | − | 0.968510i | \(-0.419907\pi\) |
−0.714267 | + | 0.699873i | \(0.753240\pi\) | |||||||
\(728\) | −1.61564e6 | − | 42780.1i | −0.112984 | − | 0.00299167i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.32368e7 | + | 2.34012e7i | 0.919337 | + | 1.62529i | ||||
\(731\) | −5.01578e6 | + | 8.68758e6i | −0.347172 | + | 0.601319i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.24808e6 | + | 1.60181e7i | 0.635757 | + | 1.10116i | 0.986354 | + | 0.164638i | \(0.0526455\pi\) |
−0.350597 | + | 0.936527i | \(0.614021\pi\) | |||||||
\(734\) | 8.44057e6 | − | 1.43260e7i | 0.578271 | − | 0.981491i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.57280e7 | − | 8.17774e6i | 1.07024 | − | 0.556466i | ||||
\(737\) | 172532.i | 0.0117004i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.75594e6i | 0.252992i | 0.991967 | + | 0.126496i | \(0.0403732\pi\) | ||||
−0.991967 | + | 0.126496i | \(0.959627\pi\) | |||||||
\(740\) | 2.95745e7 | − | 1.63859e7i | 1.98535 | − | 1.09999i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.13868e6 | − | 5.38429e6i | −0.609359 | − | 0.359020i | ||||
\(743\) | −22492.7 | − | 38958.6i | −0.00149476 | − | 0.00258899i | 0.865277 | − | 0.501294i | \(-0.167142\pi\) |
−0.866772 | + | 0.498705i | \(0.833809\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.84462e6 | + | 4.92702e6i | −0.187773 | + | 0.325232i | ||||
\(746\) | −8.17760e6 | + | 4.62561e6i | −0.537996 | + | 0.304314i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.77444e7 | + | 1.06666e7i | 1.15960 | + | 0.697066i | ||||
\(749\) | −1.29632e7 | − | 7.48433e6i | −0.844324 | − | 0.487471i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.26479e7 | − | 1.30757e7i | 1.46530 | − | 0.845993i | 0.466054 | − | 0.884756i | \(-0.345675\pi\) |
0.999248 | + | 0.0387633i | \(0.0123418\pi\) | |||||||
\(752\) | 1.09338e7 | − | 1.74825e7i | 0.705059 | − | 1.12735i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.43966e6 | + | 21528.5i | 0.156279 | + | 0.00137907i | ||||
\(755\) | −2.91248e6 | −0.185950 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.60555e6 | −0.545807 | −0.272903 | − | 0.962041i | \(-0.587984\pi\) | ||||
−0.272903 | + | 0.962041i | \(0.587984\pi\) | |||||||
\(758\) | 2.65382e7 | + | 234183.i | 1.67764 | + | 0.0148041i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.57921e7 | + | 8.56845e6i | −0.991761 | + | 0.538107i | ||||
\(761\) | −2.15910e7 | + | 1.24656e7i | −1.35148 | + | 0.780280i | −0.988458 | − | 0.151498i | \(-0.951590\pi\) |
−0.363027 | + | 0.931779i | \(0.618257\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.24067e7 | − | 7.16302e6i | −0.771516 | − | 0.445435i | ||||
\(764\) | 9.98326e6 | − | 1.66076e7i | 0.618784 | − | 1.02937i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.60782e7 | − | 1.47510e7i | 1.60585 | − | 0.908341i | ||||
\(767\) | −1.26608e6 | + | 2.19291e6i | −0.0777090 | + | 0.134596i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.62777e7 | − | 2.81939e7i | −0.992610 | − | 1.71925i | −0.601398 | − | 0.798950i | \(-0.705389\pi\) |
−0.391212 | − | 0.920300i | \(-0.627944\pi\) | |||||||
\(770\) | 1.75934e7 | + | 1.03656e7i | 1.06935 | + | 0.630039i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.44832e6 | − | 2.61405e6i | −0.0874625 | − | 0.157859i | ||||
\(773\) | − | 1.64551e6i | − | 0.0990493i | −0.998773 | − | 0.0495246i | \(-0.984229\pi\) | ||
0.998773 | − | 0.0495246i | \(-0.0157706\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.35278e7i | 0.809044i | ||||||||
\(776\) | 1.29070e7 | + | 7.91464e6i | 0.769436 | + | 0.471820i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.28989e6 | − | 8.97845e6i | 0.313327 | − | 0.531805i | ||||
\(779\) | −1.06554e7 | − | 1.84557e7i | −0.629108 | − | 1.08965i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.85208e6 | − | 1.36002e7i | 0.460635 | − | 0.797843i | ||||
\(782\) | −1.28677e7 | − | 2.27488e7i | −0.752464 | − | 1.33028i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.88585e6 | − | 5.43260e6i | −0.167681 | − | 0.315659i | ||||
\(785\) | 1.18496e7 | + | 6.84139e6i | 0.686326 | + | 0.396251i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.68858e7 | − | 9.74900e6i | 0.971816 | − | 0.561078i | 0.0720264 | − | 0.997403i | \(-0.477053\pi\) |
0.899789 | + | 0.436325i | \(0.143720\pi\) | |||||||
\(788\) | −263395. | + | 1.49231e7i | −0.0151109 | + | 0.856136i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −183859. | + | 2.08354e7i | −0.0104814 | + | 1.18777i | ||||
\(791\) | 2.96359e6 | 0.168414 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.06007e6 | −0.116332 | ||||||||
\(794\) | 3779.24 | − | 428272.i | 0.000212742 | − | 0.0241084i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −353448. | + | 2.00252e7i | −0.0197716 | + | 1.12020i | ||||
\(797\) | 318483. | − | 183876.i | 0.0177599 | − | 0.0102537i | −0.491094 | − | 0.871107i | \(-0.663403\pi\) |
0.508854 | + | 0.860853i | \(0.330069\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.63283e7 | − | 1.52007e7i | −1.45900 | − | 0.842356i | ||||
\(800\) | −1.68247e7 | − | 1.07300e7i | −0.929441 | − | 0.592757i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.40521e6 | + | 1.66274e7i | 0.516336 | + | 0.912829i | ||||
\(803\) | 1.25640e7 | − | 2.17614e7i | 0.687604 | − | 1.19096i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.28889e7 | − | 2.23242e7i | −0.701011 | − | 1.21419i | ||||
\(806\) | −968796. | + | 1.64432e6i | −0.0525285 | + | 0.0891558i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.17650e7 | − | 1.91861e7i | 0.633961 | − | 1.03385i | ||||
\(809\) | − | 5.76347e6i | − | 0.309609i | −0.987945 | − | 0.154804i | \(-0.950525\pi\) | ||
0.987945 | − | 0.154804i | \(-0.0494747\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 819789.i | − | 0.0437673i | −0.999761 | − | 0.0218837i | \(-0.993034\pi\) | ||
0.999761 | − | 0.0218837i | \(-0.00696634\pi\) | |||||||
\(812\) | −8.09052e6 | − | 1.46024e7i | −0.430612 | − | 0.777203i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.72261e7 | − | 1.60410e7i | −1.44020 | − | 0.848534i | ||||
\(815\) | −1.31967e7 | − | 2.28573e7i | −0.695938 | − | 1.20540i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.06821e6 | + | 7.04635e6i | −0.213230 | + | 0.369325i | ||||
\(818\) | −1.72339e7 | + | 9.74827e6i | −0.900536 | + | 0.509383i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.32563e7 | − | 3.86878e7i | 1.20783 | − | 2.00928i | ||||
\(821\) | 631565. | + | 364634.i | 0.0327009 | + | 0.0188799i | 0.516261 | − | 0.856431i | \(-0.327323\pi\) |
−0.483560 | + | 0.875311i | \(0.660657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.52844e7 | + | 8.82447e6i | −0.786592 | + | 0.454139i | −0.838762 | − | 0.544499i | \(-0.816720\pi\) |
0.0521692 | + | 0.998638i | \(0.483386\pi\) | |||||||
\(824\) | 5.77097e6 | + | 1.06362e7i | 0.296095 | + | 0.545720i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.73254e7 | + | 152887.i | 0.883557 | + | 0.00779685i | ||||
\(827\) | −2.90788e7 | −1.47847 | −0.739236 | − | 0.673447i | \(-0.764813\pi\) | ||||
−0.739236 | + | 0.673447i | \(0.764813\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.37334e7 | −0.694051 | −0.347026 | − | 0.937856i | \(-0.612808\pi\) | ||||
−0.347026 | + | 0.937856i | \(0.612808\pi\) | |||||||
\(830\) | −2.49916e7 | − | 220536.i | −1.25921 | − | 0.0111118i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.27663e6 | − | 2.50916e6i | −0.0639378 | − | 0.125667i | ||||
\(833\) | −7.85448e6 | + | 4.53478e6i | −0.392197 | + | 0.226435i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.49815e7 | + | 8.64958e6i | 0.743600 | + | 0.429318i | ||||
\(836\) | 1.43922e7 | + | 8.65153e6i | 0.712216 | + | 0.428131i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.61775e7 | + | 1.48072e7i | −1.28771 | + | 0.728387i | ||||
\(839\) | 5.44148e6 | − | 9.42491e6i | 0.266877 | − | 0.462245i | −0.701176 | − | 0.712988i | \(-0.747341\pi\) |
0.968054 | + | 0.250743i | \(0.0806748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.34460e6 | + | 4.06097e6i | 0.114309 | + | 0.197989i | ||||
\(842\) | 2.52487e7 | + | 1.48759e7i | 1.22732 | + | 0.723108i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.44412e7 | + | 1.35417e7i | −1.18104 | + | 0.654362i | ||||
\(845\) | 2.94969e7i | 1.42113i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.34837e6i | − | 0.112475i | ||||||
\(848\) | 652006. | − | 1.84645e7i | 0.0311359 | − | 0.881755i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.49347e7 | + | 2.53485e7i | −0.709006 | + | 1.20339i | ||||
\(851\) | 1.99458e7 | + | 3.45471e7i | 0.944119 | + | 1.63526i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.39626e6 | − | 2.41839e6i | 0.0657043 | − | 0.113803i | −0.831302 | − | 0.555821i | \(-0.812404\pi\) |
0.897006 | + | 0.442018i | \(0.145737\pi\) | |||||||
\(854\) | 6.93996e6 | + | 1.22691e7i | 0.325621 | + | 0.575664i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 690156. | − | 2.60646e7i | 0.0321931 | − | 1.21581i | ||||
\(857\) | 2.22286e7 | + | 1.28337e7i | 1.03386 | + | 0.596898i | 0.918087 | − | 0.396378i | \(-0.129733\pi\) |
0.115770 | + | 0.993276i | \(0.463066\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.15701e6 | + | 2.40005e6i | −0.192220 | + | 0.110978i | −0.593021 | − | 0.805187i | \(-0.702065\pi\) |
0.400802 | + | 0.916165i | \(0.368732\pi\) | |||||||
\(860\) | −1.72316e7 | − | 304141.i | −0.794475 | − | 0.0140226i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 285644. | − | 3.23698e7i | 0.0130935 | − | 1.48379i | ||||
\(863\) | −2.59610e7 | −1.18658 | −0.593288 | − | 0.804991i | \(-0.702170\pi\) | ||||
−0.593288 | + | 0.804991i | \(0.702170\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.57856e6 | −0.117175 | ||||||||
\(866\) | −308186. | + | 3.49243e7i | −0.0139643 | + | 1.58246i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.30568e7 | + | 230454.i | 0.588215 | + | 0.0103821i | ||||
\(869\) | 1.68651e7 | − | 9.73705e6i | 0.757597 | − | 0.437399i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29955.3 | − | 17294.7i | −0.00133792 | − | 0.000772446i | ||||
\(872\) | 660526. | − | 2.49456e7i | 0.0294170 | − | 1.11097i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.04368e7 | − | 1.84512e7i | −0.462157 | − | 0.817045i | ||||
\(875\) | −1.34735e6 | + | 2.33369e6i | −0.0594924 | + | 0.103044i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.75890e7 | + | 3.04651e7i | 0.772222 | + | 1.33753i | 0.936343 | + | 0.351088i | \(0.114188\pi\) |
−0.164120 | + | 0.986440i | \(0.552478\pi\) | |||||||
\(878\) | 1.66565e7 | − | 2.82708e7i | 0.729200 | − | 1.23766i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.25521e6 | + | 3.55470e7i | −0.0546399 | + | 1.54738i | ||||
\(881\) | 1.34812e7i | 0.585177i | 0.956238 | + | 0.292588i | \(0.0945166\pi\) | ||||
−0.956238 | + | 0.292588i | \(0.905483\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.27557e7i | 0.550557i | 0.961364 | + | 0.275279i | \(0.0887701\pi\) | ||||
−0.961364 | + | 0.275279i | \(0.911230\pi\) | |||||||
\(884\) | −3.63068e6 | + | 2.01159e6i | −0.156263 | + | 0.0865784i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.03708e7 | + | 1.20020e7i | 0.871814 | + | 0.513652i | ||||
\(887\) | 9.47111e6 | + | 1.64044e7i | 0.404196 | + | 0.700088i | 0.994228 | − | 0.107292i | \(-0.0342180\pi\) |
−0.590032 | + | 0.807380i | \(0.700885\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.87317e6 | + | 6.70852e6i | −0.164366 | + | 0.284690i | ||||
\(890\) | −1.80943e7 | + | 1.02350e7i | −0.765716 | + | 0.433123i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.32746e7 | + | 7.97973e6i | 0.558613 | + | 0.335797i | ||||
\(893\) | −2.13545e7 | − | 1.23290e7i | −0.896107 | − | 0.517368i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.33709e7 | − | 1.92667e7i | 1.39255 | − | 0.803988i | ||||
\(896\) | −1.06431e7 | + | 1.60561e7i | −0.442891 | + | 0.668144i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.49223e6 | + | 48465.6i | 0.227278 | + | 0.00200559i | ||||
\(899\) | −1.97130e7 | −0.813491 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.72403e7 | −1.11789 | ||||||||
\(902\) | −4.21873e7 | − | 372277.i | −1.72650 | − | 0.0152353i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.46188e6 | + | 4.53739e6i | 0.100195 | + | 0.184665i | ||||
\(905\) | −329602. | + | 190296.i | −0.0133773 | + | 0.00772339i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.65444e7 | − | 2.10989e7i | −1.47504 | − | 0.851613i | −0.475434 | − | 0.879752i | \(-0.657709\pi\) |
−0.999604 | + | 0.0281382i | \(0.991042\pi\) | |||||||
\(908\) | 3.88785e6 | − | 6.46761e6i | 0.156493 | − | 0.260333i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.56327e6 | + | 2.01554e6i | −0.142641 | + | 0.0806841i | ||||
\(911\) | 1.29463e7 | − | 2.24236e7i | 0.516831 | − | 0.895177i | −0.482978 | − | 0.875632i | \(-0.660445\pi\) |
0.999809 | − | 0.0195449i | \(-0.00622174\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.16794e7 | + | 2.02293e7i | 0.463706 | + | 0.803163i | ||||
\(914\) | 1.01190e7 | + | 5.96188e6i | 0.400657 | + | 0.236057i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.84892e6 | − | 6.94683e6i | −0.151565 | − | 0.273557i | ||||
\(917\) | − | 1.39184e7i | − | 0.546594i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.59722e7i | 1.40501i | 0.711681 | + | 0.702503i | \(0.247934\pi\) | ||||
−0.711681 | + | 0.702503i | \(0.752066\pi\) | |||||||
\(920\) | 2.34724e7 | − | 3.82783e7i | 0.914297 | − | 1.49102i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.38118e6 | + | 1.42253e7i | −0.324697 | + | 0.551103i | ||||
\(923\) | 1.57420e6 | + | 2.72659e6i | 0.0608212 | + | 0.105345i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.24527e7 | − | 3.88892e7i | 0.862809 | − | 1.49443i | ||||
\(926\) | 1.61758e7 | + | 2.85971e7i | 0.619923 | + | 1.09596i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.56360e7 | − | 2.45173e7i | 0.596015 | − | 0.934550i | ||||
\(929\) | −3.28939e7 | − | 1.89913e7i | −1.25048 | − | 0.721964i | −0.279273 | − | 0.960212i | \(-0.590094\pi\) |
−0.971204 | + | 0.238248i | \(0.923427\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.37063e6 | + | 3.67809e6i | −0.240884 | + | 0.139075i | ||||
\(932\) | 192159. | − | 1.08871e7i | 0.00724637 | − | 0.410556i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −415285. | + | 4.70611e7i | −0.0155768 | + | 1.76520i | ||||
\(935\) | 5.24417e7 | 1.96177 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.87349e7 | −0.697111 | −0.348555 | − | 0.937288i | \(-0.613328\pi\) | ||||
−0.348555 | + | 0.937288i | \(0.613328\pi\) | |||||||
\(938\) | −2088.45 | + | 236667.i | −7.75026e−5 | + | 0.00878276i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 921722. | − | 5.22217e7i | 0.0340236 | − | 1.92767i | ||||
\(941\) | −1.73547e7 | + | 1.00197e7i | −0.638915 | + | 0.368878i | −0.784196 | − | 0.620513i | \(-0.786925\pi\) |
0.145281 | + | 0.989390i | \(0.453591\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.61233e7 | + | 2.66293e7i | 1.68905 | + | 0.975171i | ||||
\(944\) | 1.41583e7 | + | 2.66530e7i | 0.517109 | + | 0.973456i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.93044e6 | + | 1.40202e7i | 0.288117 | + | 0.509361i | ||||
\(947\) | −1.05215e7 | + | 1.82237e7i | −0.381243 | + | 0.660332i | −0.991240 | − | 0.132071i | \(-0.957837\pi\) |
0.609997 | + | 0.792404i | \(0.291171\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.51885e6 | + | 4.36277e6i | 0.0907896 | + | 0.157252i | ||||
\(950\) | −1.21133e7 | + | 2.05597e7i | −0.435465 | + | 0.739108i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.42115e7 | + | 1.48466e7i | 0.865823 | + | 0.530925i | ||||
\(953\) | 3.31281e6i | 0.118158i | 0.998253 | + | 0.0590792i | \(0.0188164\pi\) | ||||
−0.998253 | + | 0.0590792i | \(0.981184\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.90820e7i | − | 1.74146i | ||||||
\(956\) | 9.42628e6 | + | 1.70133e7i | 0.333577 | + | 0.602065i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −558586. | − | 329106.i | −0.0196642 | − | 0.0115857i | ||||
\(959\) | 8.59256e6 | + | 1.48828e7i | 0.301701 | + | 0.522561i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.60435e6 | + | 1.14391e7i | −0.230686 | + | 0.399560i | ||||
\(962\) | 5.51423e6 | − | 3.11909e6i | 0.192109 | − | 0.108665i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.49492e7 | + | 4.15042e7i | −0.864698 | + | 1.43846i | ||||
\(965\) | −6.55552e6 | − | 3.78483e6i | −0.226615 | − | 0.130836i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.14131e7 | + | 6.58936e6i | −0.392498 | + | 0.226609i | −0.683242 | − | 0.730192i | \(-0.739431\pi\) |
0.290744 | + | 0.956801i | \(0.406097\pi\) | |||||||
\(968\) | 3.59545e6 | − | 1.95081e6i | 0.123329 | − | 0.0669155i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.83488e7 | + | 338405.i | 1.30865 | + | 0.0115480i | ||||
\(971\) | −5.16587e6 | −0.175831 | −0.0879155 | − | 0.996128i | \(-0.528021\pi\) | ||||
−0.0879155 | + | 0.996128i | \(0.528021\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.26445e7 | 0.428174 | ||||||||
\(974\) | −1.54153e7 | − | 136031.i | −0.520660 | − | 0.00459451i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.30195e7 | + | 2.08175e7i | −0.437491 | + | 0.699525i | ||||
\(977\) | −1.37911e6 | + | 796228.i | −0.0462234 | + | 0.0266871i | −0.522934 | − | 0.852373i | \(-0.675162\pi\) |
0.476710 | + | 0.879060i | \(0.341829\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.68264e7 | + | 9.71474e6i | 0.561093 | + | 0.323947i | ||||
\(980\) | −1.33545e7 | − | 8.02773e6i | −0.444183 | − | 0.267010i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.90354e7 | + | 1.64237e7i | −0.960836 | + | 0.543491i | ||||
\(983\) | 7.65007e6 | − | 1.32503e7i | 0.252512 | − | 0.437363i | −0.711705 | − | 0.702478i | \(-0.752077\pi\) |
0.964217 | + | 0.265115i | \(0.0854101\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.89028e7 | + | 3.27406e7i | 0.620776 | + | 1.07522i | ||||
\(986\) | −3.69383e7 | − | 2.17632e7i | −1.21000 | − | 0.712903i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.94478e6 | + | 1.63157e6i | −0.0959756 | + | 0.0531757i | ||||
\(989\) | − | 2.03341e7i | − | 0.661049i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.54893e7i | 1.47138i | 0.677317 | + | 0.735691i | \(0.263142\pi\) | ||||
−0.677317 | + | 0.735691i | \(0.736858\pi\) | |||||||
\(992\) | 1.04935e7 | + | 2.01819e7i | 0.338566 | + | 0.651153i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.09356e7 | − | 1.85608e7i | 0.351055 | − | 0.595840i | ||||
\(995\) | 2.53655e7 | + | 4.39344e7i | 0.812244 | + | 1.40685i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.16700e7 | + | 2.02131e7i | −0.371821 | + | 0.644013i | −0.989846 | − | 0.142146i | \(-0.954600\pi\) |
0.618025 | + | 0.786159i | \(0.287933\pi\) | |||||||
\(998\) | 2.03991e7 | + | 3.60635e7i | 0.648314 | + | 1.14615i | ||||
\(999\) | 0 | 0 |
(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 | 108.6.h.a.35.15 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.11.14 | ✓ | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.35.5 | 56 | ||
9.4 | even | 3 | 36.6.h.a.23.24 | yes | 56 | ||
9.5 | odd | 6 | inner | 108.6.h.a.71.5 | 56 | ||
12.11 | even | 2 | 36.6.h.a.11.24 | yes | 56 | ||
36.23 | even | 6 | inner | 108.6.h.a.71.15 | 56 | ||
36.31 | odd | 6 | 36.6.h.a.23.14 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.14 | ✓ | 56 | 3.2 | odd | 2 | ||
36.6.h.a.11.24 | yes | 56 | 12.11 | even | 2 | ||
36.6.h.a.23.14 | yes | 56 | 36.31 | odd | 6 | ||
36.6.h.a.23.24 | yes | 56 | 9.4 | even | 3 | ||
108.6.h.a.35.5 | 56 | 4.3 | odd | 2 | inner | ||
108.6.h.a.35.15 | 56 | 1.1 | even | 1 | trivial | ||
108.6.h.a.71.5 | 56 | 9.5 | odd | 6 | inner | ||
108.6.h.a.71.15 | 56 | 36.23 | even | 6 | inner |