Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [40,6,Mod(21,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("40.21");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.41535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{42}\cdot 3^{4}\cdot 5^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.15 | ||
Root | \(0.236693 - 3.99299i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 40.21 |
Dual form | 40.6.d.a.21.16 |
$q$-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 \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.22968 | − | 3.75630i | 0.747709 | − | 0.664026i | ||||
\(3\) | − | 25.0521i | − | 1.60709i | −0.595243 | − | 0.803546i | \(-0.702944\pi\) | ||
0.595243 | − | 0.803546i | \(-0.297056\pi\) | |||||||
\(4\) | 3.78045 | − | 31.7759i | 0.118139 | − | 0.992997i | ||||
\(5\) | 25.0000i | 0.447214i | ||||||||
\(6\) | −94.1031 | − | 105.962i | −1.06715 | − | 1.20164i | ||||
\(7\) | 103.624 | 0.799310 | 0.399655 | − | 0.916666i | \(-0.369130\pi\) | ||||
0.399655 | + | 0.916666i | \(0.369130\pi\) | |||||||
\(8\) | −103.370 | − | 148.603i | −0.571042 | − | 0.820921i | ||||
\(9\) | −384.607 | −1.58274 | ||||||||
\(10\) | 93.9075 | + | 105.742i | 0.296961 | + | 0.334386i | ||||
\(11\) | 740.776i | 1.84589i | 0.384935 | + | 0.922944i | \(0.374224\pi\) | ||||
−0.384935 | + | 0.922944i | \(0.625776\pi\) | |||||||
\(12\) | −796.053 | − | 94.7080i | −1.59584 | − | 0.189860i | ||||
\(13\) | − | 892.067i | − | 1.46399i | −0.681309 | − | 0.731996i | \(-0.738589\pi\) | ||
0.681309 | − | 0.731996i | \(-0.261411\pi\) | |||||||
\(14\) | 438.297 | − | 389.243i | 0.597652 | − | 0.530763i | ||||
\(15\) | 626.302 | 0.718713 | ||||||||
\(16\) | −995.416 | − | 240.254i | −0.972086 | − | 0.234623i | ||||
\(17\) | 1138.81 | 0.955717 | 0.477859 | − | 0.878437i | \(-0.341413\pi\) | ||||
0.477859 | + | 0.878437i | \(0.341413\pi\) | |||||||
\(18\) | −1626.77 | + | 1444.70i | −1.18343 | + | 1.05098i | ||||
\(19\) | − | 1155.46i | − | 0.734294i | −0.930163 | − | 0.367147i | \(-0.880335\pi\) | ||
0.930163 | − | 0.367147i | \(-0.119665\pi\) | |||||||
\(20\) | 794.398 | + | 94.5111i | 0.444082 | + | 0.0528333i | ||||
\(21\) | − | 2596.00i | − | 1.28457i | ||||||
\(22\) | 2782.58 | + | 3133.25i | 1.22572 | + | 1.38019i | ||||
\(23\) | 1602.57 | 0.631682 | 0.315841 | − | 0.948812i | \(-0.397713\pi\) | ||||
0.315841 | + | 0.948812i | \(0.397713\pi\) | |||||||
\(24\) | −3722.80 | + | 2589.63i | −1.31929 | + | 0.917717i | ||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | −3350.87 | − | 3773.16i | −0.972129 | − | 1.09464i | ||||
\(27\) | 3547.55i | 0.936524i | ||||||||
\(28\) | 391.745 | − | 3292.75i | 0.0944297 | − | 0.793713i | ||||
\(29\) | 2158.47i | 0.476596i | 0.971192 | + | 0.238298i | \(0.0765896\pi\) | ||||
−0.971192 | + | 0.238298i | \(0.923410\pi\) | |||||||
\(30\) | 2649.06 | − | 2352.58i | 0.537389 | − | 0.477244i | ||||
\(31\) | 4955.24 | 0.926106 | 0.463053 | − | 0.886331i | \(-0.346754\pi\) | ||||
0.463053 | + | 0.886331i | \(0.346754\pi\) | |||||||
\(32\) | −5112.76 | + | 2722.88i | −0.882634 | + | 0.470061i | ||||
\(33\) | 18558.0 | 2.96651 | ||||||||
\(34\) | 4816.81 | − | 4277.71i | 0.714599 | − | 0.634621i | ||||
\(35\) | 2590.60i | 0.357462i | ||||||||
\(36\) | −1453.99 | + | 12221.2i | −0.186984 | + | 1.57166i | ||||
\(37\) | 4403.89i | 0.528850i | 0.964406 | + | 0.264425i | \(0.0851821\pi\) | ||||
−0.964406 | + | 0.264425i | \(0.914818\pi\) | |||||||
\(38\) | −4340.24 | − | 4887.22i | −0.487590 | − | 0.549039i | ||||
\(39\) | −22348.1 | −2.35277 | ||||||||
\(40\) | 3715.06 | − | 2584.24i | 0.367127 | − | 0.255378i | ||||
\(41\) | 3780.62 | 0.351240 | 0.175620 | − | 0.984458i | \(-0.443807\pi\) | ||||
0.175620 | + | 0.984458i | \(0.443807\pi\) | |||||||
\(42\) | −9751.34 | − | 10980.3i | −0.852985 | − | 0.960482i | ||||
\(43\) | 13068.3i | 1.07783i | 0.842361 | + | 0.538913i | \(0.181165\pi\) | ||||
−0.842361 | + | 0.538913i | \(0.818835\pi\) | |||||||
\(44\) | 23538.8 | + | 2800.46i | 1.83296 | + | 0.218071i | ||||
\(45\) | − | 9615.17i | − | 0.707825i | ||||||
\(46\) | 6778.38 | − | 6019.75i | 0.472315 | − | 0.419453i | ||||
\(47\) | −8000.58 | −0.528296 | −0.264148 | − | 0.964482i | \(-0.585091\pi\) | ||||
−0.264148 | + | 0.964482i | \(0.585091\pi\) | |||||||
\(48\) | −6018.87 | + | 24937.3i | −0.377061 | + | 1.56223i | ||||
\(49\) | −6069.06 | −0.361103 | ||||||||
\(50\) | −2643.55 | + | 2347.69i | −0.149542 | + | 0.132805i | ||||
\(51\) | − | 28529.6i | − | 1.53593i | ||||||
\(52\) | −28346.2 | − | 3372.41i | −1.45374 | − | 0.172955i | ||||
\(53\) | − | 34313.6i | − | 1.67794i | −0.544175 | − | 0.838971i | \(-0.683157\pi\) | ||
0.544175 | − | 0.838971i | \(-0.316843\pi\) | |||||||
\(54\) | 13325.6 | + | 15005.0i | 0.621876 | + | 0.700248i | ||||
\(55\) | −18519.4 | −0.825506 | ||||||||
\(56\) | −10711.6 | − | 15398.8i | −0.456440 | − | 0.656170i | ||||
\(57\) | −28946.6 | −1.18008 | ||||||||
\(58\) | 8107.85 | + | 9129.64i | 0.316472 | + | 0.356356i | ||||
\(59\) | 22065.0i | 0.825227i | 0.910906 | + | 0.412613i | \(0.135384\pi\) | ||||
−0.910906 | + | 0.412613i | \(0.864616\pi\) | |||||||
\(60\) | 2367.70 | − | 19901.3i | 0.0849080 | − | 0.713680i | ||||
\(61\) | 2822.53i | 0.0971212i | 0.998820 | + | 0.0485606i | \(0.0154634\pi\) | ||||
−0.998820 | + | 0.0485606i | \(0.984537\pi\) | |||||||
\(62\) | 20959.1 | − | 18613.4i | 0.692458 | − | 0.614959i | ||||
\(63\) | −39854.5 | −1.26510 | ||||||||
\(64\) | −11397.4 | + | 30722.0i | −0.347821 | + | 0.937561i | ||||
\(65\) | 22301.7 | 0.654717 | ||||||||
\(66\) | 78494.4 | − | 69709.3i | 2.21809 | − | 1.96984i | ||||
\(67\) | 54981.5i | 1.49634i | 0.663509 | + | 0.748168i | \(0.269066\pi\) | ||||
−0.663509 | + | 0.748168i | \(0.730934\pi\) | |||||||
\(68\) | 4305.21 | − | 36186.7i | 0.112907 | − | 0.949024i | ||||
\(69\) | − | 40147.8i | − | 1.01517i | ||||||
\(70\) | 9731.07 | + | 10957.4i | 0.237364 | + | 0.267278i | ||||
\(71\) | 42879.2 | 1.00949 | 0.504744 | − | 0.863269i | \(-0.331587\pi\) | ||||
0.504744 | + | 0.863269i | \(0.331587\pi\) | |||||||
\(72\) | 39756.7 | + | 57153.5i | 0.903814 | + | 1.29931i | ||||
\(73\) | −20893.2 | −0.458879 | −0.229440 | − | 0.973323i | \(-0.573689\pi\) | ||||
−0.229440 | + | 0.973323i | \(0.573689\pi\) | |||||||
\(74\) | 16542.3 | + | 18627.1i | 0.351170 | + | 0.395426i | ||||
\(75\) | 15657.6i | 0.321418i | ||||||||
\(76\) | −36715.7 | − | 4368.14i | −0.729152 | − | 0.0867487i | ||||
\(77\) | 76762.2i | 1.47544i | ||||||||
\(78\) | −94525.5 | + | 83946.2i | −1.75919 | + | 1.56230i | ||||
\(79\) | 30227.6 | 0.544925 | 0.272462 | − | 0.962166i | \(-0.412162\pi\) | ||||
0.272462 | + | 0.962166i | \(0.412162\pi\) | |||||||
\(80\) | 6006.35 | − | 24885.4i | 0.104927 | − | 0.434730i | ||||
\(81\) | −4586.03 | −0.0776648 | ||||||||
\(82\) | 15990.8 | − | 14201.1i | 0.262625 | − | 0.233232i | ||||
\(83\) | 93949.9i | 1.49693i | 0.663175 | + | 0.748465i | \(0.269209\pi\) | ||||
−0.663175 | + | 0.748465i | \(0.730791\pi\) | |||||||
\(84\) | −82490.2 | − | 9814.03i | −1.27557 | − | 0.151757i | ||||
\(85\) | 28470.3i | 0.427410i | ||||||||
\(86\) | 49088.5 | + | 55274.9i | 0.715704 | + | 0.805901i | ||||
\(87\) | 54074.1 | 0.765934 | ||||||||
\(88\) | 110081. | − | 76573.8i | 1.51533 | − | 1.05408i | ||||
\(89\) | 1178.06 | 0.0157650 | 0.00788248 | − | 0.999969i | \(-0.497491\pi\) | ||||
0.00788248 | + | 0.999969i | \(0.497491\pi\) | |||||||
\(90\) | −36117.5 | − | 40669.1i | −0.470014 | − | 0.529247i | ||||
\(91\) | − | 92439.5i | − | 1.17018i | ||||||
\(92\) | 6058.44 | − | 50923.2i | 0.0746262 | − | 0.627258i | ||||
\(93\) | − | 124139.i | − | 1.48834i | ||||||
\(94\) | −33839.9 | + | 30052.6i | −0.395012 | + | 0.350802i | ||||
\(95\) | 28886.4 | 0.328386 | ||||||||
\(96\) | 68213.9 | + | 128085.i | 0.755431 | + | 1.41847i | ||||
\(97\) | 74100.8 | 0.799638 | 0.399819 | − | 0.916594i | \(-0.369073\pi\) | ||||
0.399819 | + | 0.916594i | \(0.369073\pi\) | |||||||
\(98\) | −25670.2 | + | 22797.2i | −0.270000 | + | 0.239782i | ||||
\(99\) | − | 284908.i | − | 2.92157i | ||||||
\(100\) | −2362.78 | + | 19859.9i | −0.0236278 | + | 0.198599i | ||||
\(101\) | 31104.3i | 0.303401i | 0.988427 | + | 0.151700i | \(0.0484749\pi\) | ||||
−0.988427 | + | 0.151700i | \(0.951525\pi\) | |||||||
\(102\) | −107166. | − | 120671.i | −1.01989 | − | 1.14843i | ||||
\(103\) | −140298. | −1.30305 | −0.651523 | − | 0.758629i | \(-0.725870\pi\) | ||||
−0.651523 | + | 0.758629i | \(0.725870\pi\) | |||||||
\(104\) | −132563. | + | 92212.7i | −1.20182 | + | 0.836002i | ||||
\(105\) | 64900.0 | 0.574475 | ||||||||
\(106\) | −128892. | − | 145136.i | −1.11420 | − | 1.25461i | ||||
\(107\) | − | 34792.6i | − | 0.293784i | −0.989153 | − | 0.146892i | \(-0.953073\pi\) | ||
0.989153 | − | 0.146892i | \(-0.0469269\pi\) | |||||||
\(108\) | 112727. | + | 13411.3i | 0.929965 | + | 0.110640i | ||||
\(109\) | 83759.2i | 0.675252i | 0.941280 | + | 0.337626i | \(0.109624\pi\) | ||||
−0.941280 | + | 0.337626i | \(0.890376\pi\) | |||||||
\(110\) | −78331.2 | + | 69564.4i | −0.617239 | + | 0.548157i | ||||
\(111\) | 110327. | 0.849910 | ||||||||
\(112\) | −103149. | − | 24896.1i | −0.776999 | − | 0.187537i | ||||
\(113\) | 57262.1 | 0.421863 | 0.210931 | − | 0.977501i | \(-0.432350\pi\) | ||||
0.210931 | + | 0.977501i | \(0.432350\pi\) | |||||||
\(114\) | −122435. | + | 108732.i | −0.882355 | + | 0.783602i | ||||
\(115\) | 40064.3i | 0.282497i | ||||||||
\(116\) | 68587.3 | + | 8159.97i | 0.473259 | + | 0.0563046i | ||||
\(117\) | 343095.i | 2.31713i | ||||||||
\(118\) | 82882.6 | + | 93327.9i | 0.547972 | + | 0.617030i | ||||
\(119\) | 118008. | 0.763914 | ||||||||
\(120\) | −64740.7 | − | 93070.1i | −0.410416 | − | 0.590007i | ||||
\(121\) | −387698. | −2.40730 | ||||||||
\(122\) | 10602.3 | + | 11938.4i | 0.0644910 | + | 0.0726184i | ||||
\(123\) | − | 94712.5i | − | 0.564475i | ||||||
\(124\) | 18733.0 | − | 157457.i | 0.109409 | − | 0.919621i | ||||
\(125\) | − | 15625.0i | − | 0.0894427i | ||||||
\(126\) | −168572. | + | 149705.i | −0.945930 | + | 0.840062i | ||||
\(127\) | −8848.12 | −0.0486790 | −0.0243395 | − | 0.999704i | \(-0.507748\pi\) | ||||
−0.0243395 | + | 0.999704i | \(0.507748\pi\) | |||||||
\(128\) | 67193.5 | + | 172756.i | 0.362495 | + | 0.931986i | ||||
\(129\) | 327389. | 1.73217 | ||||||||
\(130\) | 94329.0 | − | 83771.7i | 0.489538 | − | 0.434749i | ||||
\(131\) | 110458.i | 0.562365i | 0.959654 | + | 0.281183i | \(0.0907267\pi\) | ||||
−0.959654 | + | 0.281183i | \(0.909273\pi\) | |||||||
\(132\) | 70157.4 | − | 589697.i | 0.350460 | − | 2.94574i | ||||
\(133\) | − | 119733.i | − | 0.586929i | ||||||
\(134\) | 206527. | + | 232554.i | 0.993606 | + | 1.11882i | ||||
\(135\) | −88688.7 | −0.418826 | ||||||||
\(136\) | −117719. | − | 169230.i | −0.545755 | − | 0.784568i | ||||
\(137\) | −304365. | −1.38546 | −0.692728 | − | 0.721199i | \(-0.743591\pi\) | ||||
−0.692728 | + | 0.721199i | \(0.743591\pi\) | |||||||
\(138\) | −150807. | − | 169813.i | −0.674100 | − | 0.759053i | ||||
\(139\) | − | 59379.5i | − | 0.260675i | −0.991470 | − | 0.130338i | \(-0.958394\pi\) | ||
0.991470 | − | 0.130338i | \(-0.0416061\pi\) | |||||||
\(140\) | 82318.7 | + | 9793.63i | 0.354959 | + | 0.0422302i | ||||
\(141\) | 200431.i | 0.849020i | ||||||||
\(142\) | 181366. | − | 161067.i | 0.754804 | − | 0.670326i | ||||
\(143\) | 660822. | 2.70237 | ||||||||
\(144\) | 382844. | + | 92403.4i | 1.53856 | + | 0.371349i | ||||
\(145\) | −53961.7 | −0.213140 | ||||||||
\(146\) | −88371.8 | + | 78481.2i | −0.343108 | + | 0.304708i | ||||
\(147\) | 152043.i | 0.580326i | ||||||||
\(148\) | 139938. | + | 16648.7i | 0.525146 | + | 0.0624777i | ||||
\(149\) | − | 233744.i | − | 0.862529i | −0.902225 | − | 0.431265i | \(-0.858068\pi\) | ||
0.902225 | − | 0.431265i | \(-0.141932\pi\) | |||||||
\(150\) | 58814.4 | + | 66226.5i | 0.213430 | + | 0.240328i | ||||
\(151\) | −89068.4 | −0.317893 | −0.158947 | − | 0.987287i | \(-0.550810\pi\) | ||||
−0.158947 | + | 0.987287i | \(0.550810\pi\) | |||||||
\(152\) | −171704. | + | 119439.i | −0.602797 | + | 0.419313i | ||||
\(153\) | −437994. | −1.51266 | ||||||||
\(154\) | 288342. | + | 324680.i | 0.979728 | + | 1.10320i | ||||
\(155\) | 123881.i | 0.414167i | ||||||||
\(156\) | −84485.9 | + | 710132.i | −0.277954 | + | 2.33629i | ||||
\(157\) | − | 608909.i | − | 1.97153i | −0.168132 | − | 0.985764i | \(-0.553773\pi\) | ||
0.168132 | − | 0.985764i | \(-0.446227\pi\) | |||||||
\(158\) | 127853. | − | 113544.i | 0.407445 | − | 0.361844i | ||||
\(159\) | −859628. | −2.69661 | ||||||||
\(160\) | −68072.1 | − | 127819.i | −0.210218 | − | 0.394726i | ||||
\(161\) | 166065. | 0.504910 | ||||||||
\(162\) | −19397.4 | + | 17226.5i | −0.0580707 | + | 0.0515714i | ||||
\(163\) | − | 172801.i | − | 0.509421i | −0.967017 | − | 0.254711i | \(-0.918020\pi\) | ||
0.967017 | − | 0.254711i | \(-0.0819802\pi\) | |||||||
\(164\) | 14292.4 | − | 120133.i | 0.0414951 | − | 0.348780i | ||||
\(165\) | 463950.i | 1.32666i | ||||||||
\(166\) | 352904. | + | 397378.i | 0.994000 | + | 1.11927i | ||||
\(167\) | 441506. | 1.22503 | 0.612513 | − | 0.790461i | \(-0.290159\pi\) | ||||
0.612513 | + | 0.790461i | \(0.290159\pi\) | |||||||
\(168\) | −385772. | + | 268348.i | −1.05453 | + | 0.733541i | ||||
\(169\) | −424490. | −1.14327 | ||||||||
\(170\) | 106943. | + | 120420.i | 0.283811 | + | 0.319578i | ||||
\(171\) | 444397.i | 1.16220i | ||||||||
\(172\) | 415258. | + | 49404.1i | 1.07028 | + | 0.127333i | ||||
\(173\) | 281414.i | 0.714874i | 0.933937 | + | 0.357437i | \(0.116349\pi\) | ||||
−0.933937 | + | 0.357437i | \(0.883651\pi\) | |||||||
\(174\) | 228717. | − | 203119.i | 0.572696 | − | 0.508600i | ||||
\(175\) | −64765.0 | −0.159862 | ||||||||
\(176\) | 177975. | − | 737381.i | 0.433088 | − | 1.79436i | ||||
\(177\) | 552774. | 1.32622 | ||||||||
\(178\) | 4982.83 | − | 4425.15i | 0.0117876 | − | 0.0104683i | ||||
\(179\) | − | 805768.i | − | 1.87965i | −0.341655 | − | 0.939825i | \(-0.610987\pi\) | ||
0.341655 | − | 0.939825i | \(-0.389013\pi\) | |||||||
\(180\) | −305531. | − | 36349.6i | −0.702868 | − | 0.0836217i | ||||
\(181\) | − | 610344.i | − | 1.38477i | −0.721528 | − | 0.692385i | \(-0.756560\pi\) | ||
0.721528 | − | 0.692385i | \(-0.243440\pi\) | |||||||
\(182\) | −347231. | − | 390990.i | −0.777033 | − | 0.874958i | ||||
\(183\) | 70710.3 | 0.156083 | ||||||||
\(184\) | −165658. | − | 238147.i | −0.360717 | − | 0.518561i | ||||
\(185\) | −110097. | −0.236509 | ||||||||
\(186\) | −466304. | − | 525070.i | −0.988295 | − | 1.11284i | ||||
\(187\) | 843604.i | 1.76415i | ||||||||
\(188\) | −30245.8 | + | 254226.i | −0.0624123 | + | 0.524596i | ||||
\(189\) | 367611.i | 0.748573i | ||||||||
\(190\) | 122180. | − | 108506.i | 0.245538 | − | 0.218057i | ||||
\(191\) | −845737. | −1.67746 | −0.838729 | − | 0.544549i | \(-0.816701\pi\) | ||||
−0.838729 | + | 0.544549i | \(0.816701\pi\) | |||||||
\(192\) | 769650. | + | 285529.i | 1.50675 | + | 0.558981i | ||||
\(193\) | −184089. | −0.355742 | −0.177871 | − | 0.984054i | \(-0.556921\pi\) | ||||
−0.177871 | + | 0.984054i | \(0.556921\pi\) | |||||||
\(194\) | 313423. | − | 278345.i | 0.597897 | − | 0.530981i | ||||
\(195\) | − | 558703.i | − | 1.05219i | ||||||
\(196\) | −22943.7 | + | 192850.i | −0.0426603 | + | 0.358574i | ||||
\(197\) | 390522.i | 0.716935i | 0.933542 | + | 0.358468i | \(0.116701\pi\) | ||||
−0.933542 | + | 0.358468i | \(0.883299\pi\) | |||||||
\(198\) | −1.07020e6 | − | 1.20507e6i | −1.94000 | − | 2.18448i | ||||
\(199\) | −584263. | −1.04587 | −0.522933 | − | 0.852374i | \(-0.675162\pi\) | ||||
−0.522933 | + | 0.852374i | \(0.675162\pi\) | |||||||
\(200\) | 64606.1 | + | 92876.6i | 0.114208 | + | 0.164184i | ||||
\(201\) | 1.37740e6 | 2.40475 | ||||||||
\(202\) | 116837. | + | 131561.i | 0.201466 | + | 0.226856i | ||||
\(203\) | 223669.i | 0.380948i | ||||||||
\(204\) | −906553. | − | 107855.i | −1.52517 | − | 0.181453i | ||||
\(205\) | 94515.6i | 0.157079i | ||||||||
\(206\) | −593418. | + | 527003.i | −0.974300 | + | 0.865256i | ||||
\(207\) | −616361. | −0.999791 | ||||||||
\(208\) | −214323. | + | 887978.i | −0.343487 | + | 1.42313i | ||||
\(209\) | 855935. | 1.35542 | ||||||||
\(210\) | 274506. | − | 243784.i | 0.429540 | − | 0.381466i | ||||
\(211\) | 428258.i | 0.662215i | 0.943593 | + | 0.331107i | \(0.107422\pi\) | ||||
−0.943593 | + | 0.331107i | \(0.892578\pi\) | |||||||
\(212\) | −1.09035e6 | − | 129721.i | −1.66619 | − | 0.198230i | ||||
\(213\) | − | 1.07421e6i | − | 1.62234i | ||||||
\(214\) | −130691. | − | 147162.i | −0.195080 | − | 0.219665i | ||||
\(215\) | −326708. | −0.482018 | ||||||||
\(216\) | 527174. | − | 366709.i | 0.768812 | − | 0.534795i | ||||
\(217\) | 513482. | 0.740246 | ||||||||
\(218\) | 314624. | + | 354275.i | 0.448385 | + | 0.504893i | ||||
\(219\) | 523419.i | 0.737461i | ||||||||
\(220\) | −70011.6 | + | 588471.i | −0.0975244 | + | 0.819725i | ||||
\(221\) | − | 1.01590e6i | − | 1.39916i | ||||||
\(222\) | 466647. | − | 414420.i | 0.635486 | − | 0.564362i | ||||
\(223\) | 955618. | 1.28683 | 0.643416 | − | 0.765517i | \(-0.277516\pi\) | ||||
0.643416 | + | 0.765517i | \(0.277516\pi\) | |||||||
\(224\) | −529805. | + | 282156.i | −0.705499 | + | 0.375724i | ||||
\(225\) | 240379. | 0.316549 | ||||||||
\(226\) | 242201. | − | 215094.i | 0.315431 | − | 0.280128i | ||||
\(227\) | − | 866233.i | − | 1.11576i | −0.829922 | − | 0.557879i | \(-0.811615\pi\) | ||
0.829922 | − | 0.557879i | \(-0.188385\pi\) | |||||||
\(228\) | −109431. | + | 919805.i | −0.139413 | + | 1.17181i | ||||
\(229\) | 654035.i | 0.824161i | 0.911147 | + | 0.412080i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412080i | \(0.864802\pi\) | |||||||
\(230\) | 150494. | + | 169460.i | 0.187585 | + | 0.211226i | ||||
\(231\) | 1.92305e6 | 2.37116 | ||||||||
\(232\) | 320754. | − | 223120.i | 0.391248 | − | 0.272157i | ||||
\(233\) | −820513. | −0.990138 | −0.495069 | − | 0.868854i | \(-0.664857\pi\) | ||||
−0.495069 | + | 0.868854i | \(0.664857\pi\) | |||||||
\(234\) | 1.28877e6 | + | 1.45118e6i | 1.53863 | + | 1.73254i | ||||
\(235\) | − | 200015.i | − | 0.236261i | ||||||
\(236\) | 701135. | + | 83415.4i | 0.819448 | + | 0.0974914i | ||||
\(237\) | − | 757265.i | − | 0.875744i | ||||||
\(238\) | 499137. | − | 443274.i | 0.571186 | − | 0.507259i | ||||
\(239\) | 867314. | 0.982159 | 0.491079 | − | 0.871115i | \(-0.336603\pi\) | ||||
0.491079 | + | 0.871115i | \(0.336603\pi\) | |||||||
\(240\) | −623431. | − | 150472.i | −0.698651 | − | 0.168627i | ||||
\(241\) | −1.65377e6 | −1.83414 | −0.917072 | − | 0.398722i | \(-0.869454\pi\) | ||||
−0.917072 | + | 0.398722i | \(0.869454\pi\) | |||||||
\(242\) | −1.63984e6 | + | 1.45631e6i | −1.79996 | + | 1.59851i | ||||
\(243\) | 976943.i | 1.06134i | ||||||||
\(244\) | 89688.5 | + | 10670.4i | 0.0964411 | + | 0.0114738i | ||||
\(245\) | − | 151726.i | − | 0.161490i | ||||||
\(246\) | −355768. | − | 400604.i | −0.374826 | − | 0.422063i | ||||
\(247\) | −1.03075e6 | −1.07500 | ||||||||
\(248\) | −512222. | − | 736362.i | −0.528846 | − | 0.760260i | ||||
\(249\) | 2.35364e6 | 2.40570 | ||||||||
\(250\) | −58692.2 | − | 66088.8i | −0.0593923 | − | 0.0668772i | ||||
\(251\) | 860879.i | 0.862497i | 0.902233 | + | 0.431249i | \(0.141927\pi\) | ||||
−0.902233 | + | 0.431249i | \(0.858073\pi\) | |||||||
\(252\) | −150668. | + | 1.26641e6i | −0.149458 | + | 1.25624i | ||||
\(253\) | 1.18715e6i | 1.16601i | ||||||||
\(254\) | −37424.7 | + | 33236.2i | −0.0363978 | + | 0.0323241i | ||||
\(255\) | 713240. | 0.686887 | ||||||||
\(256\) | 933132. | + | 478306.i | 0.889904 | + | 0.456148i | ||||
\(257\) | −765335. | −0.722801 | −0.361401 | − | 0.932411i | \(-0.617701\pi\) | ||||
−0.361401 | + | 0.932411i | \(0.617701\pi\) | |||||||
\(258\) | 1.38475e6 | − | 1.22977e6i | 1.29516 | − | 1.15020i | ||||
\(259\) | 456349.i | 0.422715i | ||||||||
\(260\) | 84310.2 | − | 708656.i | 0.0773476 | − | 0.650133i | ||||
\(261\) | − | 830162.i | − | 0.754330i | ||||||
\(262\) | 414913. | + | 467202.i | 0.373425 | + | 0.420486i | ||||
\(263\) | 260746. | 0.232449 | 0.116225 | − | 0.993223i | \(-0.462921\pi\) | ||||
0.116225 | + | 0.993223i | \(0.462921\pi\) | |||||||
\(264\) | −1.91833e6 | − | 2.75776e6i | −1.69400 | − | 2.43527i | ||||
\(265\) | 857841. | 0.750399 | ||||||||
\(266\) | −449754. | − | 506433.i | −0.389736 | − | 0.438852i | ||||
\(267\) | − | 29512.9i | − | 0.0253357i | ||||||
\(268\) | 1.74709e6 | + | 207854.i | 1.48586 | + | 0.176776i | ||||
\(269\) | 1.12412e6i | 0.947175i | 0.880747 | + | 0.473587i | \(0.157041\pi\) | ||||
−0.880747 | + | 0.473587i | \(0.842959\pi\) | |||||||
\(270\) | −375125. | + | 333141.i | −0.313160 | + | 0.278111i | ||||
\(271\) | −1.07277e6 | −0.887330 | −0.443665 | − | 0.896193i | \(-0.646322\pi\) | ||||
−0.443665 | + | 0.896193i | \(0.646322\pi\) | |||||||
\(272\) | −1.13359e6 | − | 273604.i | −0.929039 | − | 0.224233i | ||||
\(273\) | −2.31580e6 | −1.88059 | ||||||||
\(274\) | −1.28737e6 | + | 1.14328e6i | −1.03592 | + | 0.919979i | ||||
\(275\) | − | 462985.i | − | 0.369177i | ||||||
\(276\) | −1.27573e6 | − | 151777.i | −1.00806 | − | 0.119931i | ||||
\(277\) | − | 615080.i | − | 0.481651i | −0.970568 | − | 0.240825i | \(-0.922582\pi\) | ||
0.970568 | − | 0.240825i | \(-0.0774181\pi\) | |||||||
\(278\) | −223047. | − | 251157.i | −0.173095 | − | 0.194909i | ||||
\(279\) | −1.90582e6 | −1.46579 | ||||||||
\(280\) | 384970. | − | 267790.i | 0.293448 | − | 0.204126i | ||||
\(281\) | −652198. | −0.492736 | −0.246368 | − | 0.969176i | \(-0.579237\pi\) | ||||
−0.246368 | + | 0.969176i | \(0.579237\pi\) | |||||||
\(282\) | 752880. | + | 847761.i | 0.563771 | + | 0.634820i | ||||
\(283\) | 908596.i | 0.674380i | 0.941437 | + | 0.337190i | \(0.109476\pi\) | ||||
−0.941437 | + | 0.337190i | \(0.890524\pi\) | |||||||
\(284\) | 162103. | − | 1.36253e6i | 0.119260 | − | 1.00242i | ||||
\(285\) | − | 723665.i | − | 0.527747i | ||||||
\(286\) | 2.79507e6 | − | 2.48224e6i | 2.02058 | − | 1.79444i | ||||
\(287\) | 391763. | 0.280750 | ||||||||
\(288\) | 1.96640e6 | − | 1.04724e6i | 1.39698 | − | 0.743986i | ||||
\(289\) | −122967. | −0.0866050 | ||||||||
\(290\) | −228241. | + | 202696.i | −0.159367 | + | 0.141531i | ||||
\(291\) | − | 1.85638e6i | − | 1.28509i | ||||||
\(292\) | −78985.7 | + | 663901.i | −0.0542115 | + | 0.455666i | ||||
\(293\) | − | 514047.i | − | 0.349811i | −0.984585 | − | 0.174906i | \(-0.944038\pi\) | ||
0.984585 | − | 0.174906i | \(-0.0559621\pi\) | |||||||
\(294\) | 571117. | + | 643092.i | 0.385351 | + | 0.433915i | ||||
\(295\) | −551624. | −0.369053 | ||||||||
\(296\) | 654429. | − | 455229.i | 0.434144 | − | 0.301996i | ||||
\(297\) | −2.62794e6 | −1.72872 | ||||||||
\(298\) | −878010. | − | 988661.i | −0.572742 | − | 0.644921i | ||||
\(299\) | − | 1.42960e6i | − | 0.924778i | ||||||
\(300\) | 497533. | + | 59192.5i | 0.319168 | + | 0.0379720i | ||||
\(301\) | 1.35419e6i | 0.861517i | ||||||||
\(302\) | −376731. | + | 334568.i | −0.237692 | + | 0.211089i | ||||
\(303\) | 779227. | 0.487593 | ||||||||
\(304\) | −277604. | + | 1.15016e6i | −0.172282 | + | 0.713797i | ||||
\(305\) | −70563.3 | −0.0434339 | ||||||||
\(306\) | −1.85258e6 | + | 1.64524e6i | −1.13103 | + | 1.00444i | ||||
\(307\) | − | 1.46693e6i | − | 0.888309i | −0.895950 | − | 0.444155i | \(-0.853504\pi\) | ||
0.895950 | − | 0.444155i | \(-0.146496\pi\) | |||||||
\(308\) | 2.43919e6 | + | 290195.i | 1.46510 | + | 0.174307i | ||||
\(309\) | 3.51477e6i | 2.09411i | ||||||||
\(310\) | 465334. | + | 523978.i | 0.275018 | + | 0.309677i | ||||
\(311\) | 547919. | 0.321229 | 0.160615 | − | 0.987017i | \(-0.448652\pi\) | ||||
0.160615 | + | 0.987017i | \(0.448652\pi\) | |||||||
\(312\) | 2.31012e6 | + | 3.32099e6i | 1.34353 | + | 1.93144i | ||||
\(313\) | 1.70857e6 | 0.985762 | 0.492881 | − | 0.870097i | \(-0.335944\pi\) | ||||
0.492881 | + | 0.870097i | \(0.335944\pi\) | |||||||
\(314\) | −2.28724e6 | − | 2.57549e6i | −1.30915 | − | 1.47413i | ||||
\(315\) | − | 996363.i | − | 0.565772i | ||||||
\(316\) | 114274. | − | 960510.i | 0.0643768 | − | 0.541109i | ||||
\(317\) | 978608.i | 0.546966i | 0.961877 | + | 0.273483i | \(0.0881758\pi\) | ||||
−0.961877 | + | 0.273483i | \(0.911824\pi\) | |||||||
\(318\) | −3.63596e6 | + | 3.22902e6i | −2.01628 | + | 1.79062i | ||||
\(319\) | −1.59894e6 | −0.879743 | ||||||||
\(320\) | −768050. | − | 284935.i | −0.419290 | − | 0.155550i | ||||
\(321\) | −871627. | −0.472137 | ||||||||
\(322\) | 702403. | − | 623790.i | 0.377526 | − | 0.335273i | ||||
\(323\) | − | 1.31585e6i | − | 0.701777i | ||||||
\(324\) | −17337.2 | + | 145725.i | −0.00917523 | + | 0.0771209i | ||||
\(325\) | 557542.i | 0.292799i | ||||||||
\(326\) | −649092. | − | 730893.i | −0.338269 | − | 0.380899i | ||||
\(327\) | 2.09834e6 | 1.08519 | ||||||||
\(328\) | −390802. | − | 561810.i | −0.200573 | − | 0.288340i | ||||
\(329\) | −829053. | −0.422272 | ||||||||
\(330\) | 1.74273e6 | + | 1.96236e6i | 0.880939 | + | 0.991959i | ||||
\(331\) | − | 345907.i | − | 0.173536i | −0.996229 | − | 0.0867679i | \(-0.972346\pi\) | ||
0.996229 | − | 0.0867679i | \(-0.0276539\pi\) | |||||||
\(332\) | 2.98534e6 | + | 355173.i | 1.48645 | + | 0.176846i | ||||
\(333\) | − | 1.69377e6i | − | 0.837034i | ||||||
\(334\) | 1.86743e6 | − | 1.65843e6i | 0.915963 | − | 0.813449i | ||||
\(335\) | −1.37454e6 | −0.669182 | ||||||||
\(336\) | −623699. | + | 2.58410e6i | −0.301389 | + | 1.24871i | ||||
\(337\) | 376513. | 0.180595 | 0.0902975 | − | 0.995915i | \(-0.471218\pi\) | ||||
0.0902975 | + | 0.995915i | \(0.471218\pi\) | |||||||
\(338\) | −1.79546e6 | + | 1.59451e6i | −0.854837 | + | 0.759164i | ||||
\(339\) | − | 1.43454e6i | − | 0.677972i | ||||||
\(340\) | 904669. | + | 107630.i | 0.424417 | + | 0.0504937i | ||||
\(341\) | 3.67073e6i | 1.70949i | ||||||||
\(342\) | 1.66929e6 | + | 1.87966e6i | 0.771731 | + | 0.868988i | ||||
\(343\) | −2.37051e6 | −1.08794 | ||||||||
\(344\) | 1.94199e6 | − | 1.35087e6i | 0.884810 | − | 0.615484i | ||||
\(345\) | 1.00370e6 | 0.453998 | ||||||||
\(346\) | 1.05707e6 | + | 1.19029e6i | 0.474695 | + | 0.534518i | ||||
\(347\) | − | 164656.i | − | 0.0734099i | −0.999326 | − | 0.0367049i | \(-0.988314\pi\) | ||
0.999326 | − | 0.0367049i | \(-0.0116862\pi\) | |||||||
\(348\) | 204424. | − | 1.71825e6i | 0.0904867 | − | 0.760571i | ||||
\(349\) | 35942.6i | 0.0157959i | 0.999969 | + | 0.00789797i | \(0.00251403\pi\) | ||||
−0.999969 | + | 0.00789797i | \(0.997486\pi\) | |||||||
\(350\) | −273936. | + | 243277.i | −0.119530 | + | 0.106153i | ||||
\(351\) | 3.16465e6 | 1.37106 | ||||||||
\(352\) | −2.01705e6 | − | 3.78741e6i | −0.867679 | − | 1.62924i | ||||
\(353\) | 1.39430e6 | 0.595550 | 0.297775 | − | 0.954636i | \(-0.403756\pi\) | ||||
0.297775 | + | 0.954636i | \(0.403756\pi\) | |||||||
\(354\) | 2.33806e6 | − | 2.07638e6i | 0.991624 | − | 0.880642i | ||||
\(355\) | 1.07198e6i | 0.451457i | ||||||||
\(356\) | 4453.60 | − | 37434.0i | 0.00186246 | − | 0.0156546i | ||||
\(357\) | − | 2.95635e6i | − | 1.22768i | ||||||
\(358\) | −3.02670e6 | − | 3.40814e6i | −1.24814 | − | 1.40543i | ||||
\(359\) | 3.50589e6 | 1.43569 | 0.717847 | − | 0.696201i | \(-0.245128\pi\) | ||||
0.717847 | + | 0.696201i | \(0.245128\pi\) | |||||||
\(360\) | −1.42884e6 | + | 993917.i | −0.581068 | + | 0.404198i | ||||
\(361\) | 1.14102e6 | 0.460812 | ||||||||
\(362\) | −2.29263e6 | − | 2.58156e6i | −0.919524 | − | 1.03541i | ||||
\(363\) | 9.71265e6i | 3.86875i | ||||||||
\(364\) | −2.93735e6 | − | 349463.i | −1.16199 | − | 0.138244i | ||||
\(365\) | − | 522331.i | − | 0.205217i | ||||||
\(366\) | 299082. | − | 265609.i | 0.116705 | − | 0.103643i | ||||
\(367\) | 3.64440e6 | 1.41241 | 0.706206 | − | 0.708007i | \(-0.250405\pi\) | ||||
0.706206 | + | 0.708007i | \(0.250405\pi\) | |||||||
\(368\) | −1.59523e6 | − | 385025.i | −0.614049 | − | 0.148207i | ||||
\(369\) | −1.45405e6 | −0.555923 | ||||||||
\(370\) | −465677. | + | 413558.i | −0.176840 | + | 0.157048i | ||||
\(371\) | − | 3.55572e6i | − | 1.34120i | ||||||
\(372\) | −3.94464e6 | − | 469302.i | −1.47792 | − | 0.175831i | ||||
\(373\) | − | 4.19252e6i | − | 1.56028i | −0.625603 | − | 0.780142i | \(-0.715147\pi\) | ||
0.625603 | − | 0.780142i | \(-0.284853\pi\) | |||||||
\(374\) | 3.16883e6 | + | 3.56818e6i | 1.17144 | + | 1.31907i | ||||
\(375\) | −391439. | −0.143743 | ||||||||
\(376\) | 827018. | + | 1.18891e6i | 0.301679 | + | 0.433689i | ||||
\(377\) | 1.92550e6 | 0.697734 | ||||||||
\(378\) | 1.38086e6 | + | 1.55488e6i | 0.497072 | + | 0.559715i | ||||
\(379\) | 2.31089e6i | 0.826384i | 0.910644 | + | 0.413192i | \(0.135586\pi\) | ||||
−0.910644 | + | 0.413192i | \(0.864414\pi\) | |||||||
\(380\) | 109204. | − | 917893.i | 0.0387952 | − | 0.326087i | ||||
\(381\) | 221664.i | 0.0782316i | ||||||||
\(382\) | −3.57720e6 | + | 3.17684e6i | −1.25425 | + | 1.11388i | ||||
\(383\) | 1.18240e6 | 0.411876 | 0.205938 | − | 0.978565i | \(-0.433976\pi\) | ||||
0.205938 | + | 0.978565i | \(0.433976\pi\) | |||||||
\(384\) | 4.32791e6 | − | 1.68334e6i | 1.49779 | − | 0.582563i | ||||
\(385\) | −1.91906e6 | −0.659835 | ||||||||
\(386\) | −778639. | + | 691494.i | −0.265992 | + | 0.236222i | ||||
\(387\) | − | 5.02617e6i | − | 1.70592i | ||||||
\(388\) | 280134. | − | 2.35462e6i | 0.0944684 | − | 0.794038i | ||||
\(389\) | 5.09219e6i | 1.70620i | 0.521745 | + | 0.853102i | \(0.325281\pi\) | ||||
−0.521745 | + | 0.853102i | \(0.674719\pi\) | |||||||
\(390\) | −2.09866e6 | − | 2.36314e6i | −0.698682 | − | 0.786733i | ||||
\(391\) | 1.82503e6 | 0.603709 | ||||||||
\(392\) | 627357. | + | 901877.i | 0.206205 | + | 0.296437i | ||||
\(393\) | 2.76720e6 | 0.903773 | ||||||||
\(394\) | 1.46692e6 | + | 1.65178e6i | 0.476064 | + | 0.536059i | ||||
\(395\) | 755691.i | 0.243698i | ||||||||
\(396\) | −9.05320e6 | − | 1.07708e6i | −2.90111 | − | 0.345151i | ||||
\(397\) | 63006.9i | 0.0200637i | 0.999950 | + | 0.0100319i | \(0.00319330\pi\) | ||||
−0.999950 | + | 0.0100319i | \(0.996807\pi\) | |||||||
\(398\) | −2.47125e6 | + | 2.19467e6i | −0.782004 | + | 0.694482i | ||||
\(399\) | −2.99957e6 | −0.943248 | ||||||||
\(400\) | 622135. | + | 150159.i | 0.194417 | + | 0.0469246i | ||||
\(401\) | −4.48960e6 | −1.39427 | −0.697135 | − | 0.716940i | \(-0.745542\pi\) | ||||
−0.697135 | + | 0.716940i | \(0.745542\pi\) | |||||||
\(402\) | 5.82597e6 | − | 5.17392e6i | 1.79805 | − | 1.59682i | ||||
\(403\) | − | 4.42041e6i | − | 1.35581i | ||||||
\(404\) | 988367. | + | 117588.i | 0.301276 | + | 0.0358434i | ||||
\(405\) | − | 114651.i | − | 0.0347327i | ||||||
\(406\) | 840169. | + | 946050.i | 0.252960 | + | 0.284839i | ||||
\(407\) | −3.26230e6 | −0.976197 | ||||||||
\(408\) | −4.23957e6 | + | 2.94909e6i | −1.26087 | + | 0.877078i | ||||
\(409\) | 2.03416e6 | 0.601281 | 0.300641 | − | 0.953738i | \(-0.402800\pi\) | ||||
0.300641 | + | 0.953738i | \(0.402800\pi\) | |||||||
\(410\) | 355029. | + | 399771.i | 0.104305 | + | 0.117450i | ||||
\(411\) | 7.62497e6i | 2.22656i | ||||||||
\(412\) | −530391. | + | 4.45811e6i | −0.153940 | + | 1.29392i | ||||
\(413\) | 2.28646e6i | 0.659612i | ||||||||
\(414\) | −2.60701e6 | + | 2.31524e6i | −0.747553 | + | 0.663887i | ||||
\(415\) | −2.34875e6 | −0.669447 | ||||||||
\(416\) | 2.42899e6 | + | 4.56093e6i | 0.688165 | + | 1.29217i | ||||
\(417\) | −1.48758e6 | −0.418929 | ||||||||
\(418\) | 3.62034e6 | − | 3.21515e6i | 1.01346 | − | 0.900037i | ||||
\(419\) | − | 1.53143e6i | − | 0.426150i | −0.977036 | − | 0.213075i | \(-0.931652\pi\) | ||
0.977036 | − | 0.213075i | \(-0.0683479\pi\) | |||||||
\(420\) | 245351. | − | 2.06225e6i | 0.0678679 | − | 0.570452i | ||||
\(421\) | − | 4.86857e6i | − | 1.33874i | −0.742929 | − | 0.669370i | \(-0.766564\pi\) | ||
0.742929 | − | 0.669370i | \(-0.233436\pi\) | |||||||
\(422\) | 1.60866e6 | + | 1.81139e6i | 0.439728 | + | 0.495144i | ||||
\(423\) | 3.07708e6 | 0.836157 | ||||||||
\(424\) | −5.09909e6 | + | 3.54699e6i | −1.37746 | + | 0.958176i | ||||
\(425\) | −711757. | −0.191143 | ||||||||
\(426\) | −4.03507e6 | − | 4.54359e6i | −1.07728 | − | 1.21304i | ||||
\(427\) | 292482.i | 0.0776300i | ||||||||
\(428\) | −1.10557e6 | − | 131532.i | −0.291726 | − | 0.0347073i | ||||
\(429\) | − | 1.65550e7i | − | 4.34295i | ||||||
\(430\) | −1.38187e6 | + | 1.22721e6i | −0.360410 | + | 0.320073i | ||||
\(431\) | 537754. | 0.139441 | 0.0697204 | − | 0.997567i | \(-0.477789\pi\) | ||||
0.0697204 | + | 0.997567i | \(0.477789\pi\) | |||||||
\(432\) | 852313. | − | 3.53129e6i | 0.219730 | − | 0.910382i | ||||
\(433\) | 1.48235e6 | 0.379954 | 0.189977 | − | 0.981789i | \(-0.439159\pi\) | ||||
0.189977 | + | 0.981789i | \(0.439159\pi\) | |||||||
\(434\) | 2.17187e6 | − | 1.92879e6i | 0.553489 | − | 0.491543i | ||||
\(435\) | 1.35185e6i | 0.342536i | ||||||||
\(436\) | 2.66152e6 | + | 316647.i | 0.670524 | + | 0.0797736i | ||||
\(437\) | − | 1.85171e6i | − | 0.463840i | ||||||
\(438\) | 1.96612e6 | + | 2.21390e6i | 0.489693 | + | 0.551407i | ||||
\(439\) | −2.49966e6 | −0.619041 | −0.309520 | − | 0.950893i | \(-0.600168\pi\) | ||||
−0.309520 | + | 0.950893i | \(0.600168\pi\) | |||||||
\(440\) | 1.91434e6 | + | 2.75203e6i | 0.471399 | + | 0.677675i | ||||
\(441\) | 2.33420e6 | 0.571534 | ||||||||
\(442\) | −3.81601e6 | − | 4.29692e6i | −0.929080 | − | 1.04617i | ||||
\(443\) | − | 5.00804e6i | − | 1.21244i | −0.795299 | − | 0.606218i | \(-0.792686\pi\) | ||
0.795299 | − | 0.606218i | \(-0.207314\pi\) | |||||||
\(444\) | 417084. | − | 3.50573e6i | 0.100407 | − | 0.843958i | ||||
\(445\) | 29451.5i | 0.00705030i | ||||||||
\(446\) | 4.04196e6 | − | 3.58959e6i | 0.962177 | − | 0.854490i | ||||
\(447\) | −5.85576e6 | −1.38616 | ||||||||
\(448\) | −1.18105e6 | + | 3.18354e6i | −0.278017 | + | 0.749402i | ||||
\(449\) | 3.04025e6 | 0.711694 | 0.355847 | − | 0.934544i | \(-0.384192\pi\) | ||||
0.355847 | + | 0.934544i | \(0.384192\pi\) | |||||||
\(450\) | 1.01673e6 | − | 902936.i | 0.236687 | − | 0.210197i | ||||
\(451\) | 2.80059e6i | 0.648349i | ||||||||
\(452\) | 216476. | − | 1.81956e6i | 0.0498384 | − | 0.418909i | ||||
\(453\) | 2.23135e6i | 0.510884i | ||||||||
\(454\) | −3.25383e6 | − | 3.66389e6i | −0.740892 | − | 0.834263i | ||||
\(455\) | 2.31099e6 | 0.523322 | ||||||||
\(456\) | 2.99220e6 | + | 4.30154e6i | 0.673874 | + | 0.968750i | ||||
\(457\) | 7.20014e6 | 1.61269 | 0.806345 | − | 0.591446i | \(-0.201443\pi\) | ||||
0.806345 | + | 0.591446i | \(0.201443\pi\) | |||||||
\(458\) | 2.45675e6 | + | 2.76636e6i | 0.547264 | + | 0.616233i | ||||
\(459\) | 4.03999e6i | 0.895052i | ||||||||
\(460\) | 1.27308e6 | + | 151461.i | 0.280518 | + | 0.0333739i | ||||
\(461\) | 7.87732e6i | 1.72634i | 0.504914 | + | 0.863170i | \(0.331524\pi\) | ||||
−0.504914 | + | 0.863170i | \(0.668476\pi\) | |||||||
\(462\) | 8.13391e6 | − | 7.22356e6i | 1.77294 | − | 1.57451i | ||||
\(463\) | −6.18812e6 | −1.34155 | −0.670774 | − | 0.741662i | \(-0.734038\pi\) | ||||
−0.670774 | + | 0.741662i | \(0.734038\pi\) | |||||||
\(464\) | 518581. | − | 2.14858e6i | 0.111821 | − | 0.463293i | ||||
\(465\) | 3.10348e6 | 0.665605 | ||||||||
\(466\) | −3.47051e6 | + | 3.08209e6i | −0.740336 | + | 0.657477i | ||||
\(467\) | 7.21143e6i | 1.53013i | 0.643952 | + | 0.765066i | \(0.277294\pi\) | ||||
−0.643952 | + | 0.765066i | \(0.722706\pi\) | |||||||
\(468\) | 1.09022e7 | + | 1.29705e6i | 2.30090 | + | 0.273743i | ||||
\(469\) | 5.69740e6i | 1.19604i | ||||||||
\(470\) | −751315. | − | 845999.i | −0.156883 | − | 0.176655i | ||||
\(471\) | −1.52544e7 | −3.16843 | ||||||||
\(472\) | 3.27891e6 | − | 2.28085e6i | 0.677446 | − | 0.471239i | ||||
\(473\) | −9.68070e6 | −1.98955 | ||||||||
\(474\) | −2.84451e6 | − | 3.20299e6i | −0.581517 | − | 0.654802i | ||||
\(475\) | 722161.i | 0.146859i | ||||||||
\(476\) | 446124. | − | 3.74982e6i | 0.0902480 | − | 0.758565i | ||||
\(477\) | 1.31973e7i | 2.65575i | ||||||||
\(478\) | 3.66846e6 | − | 3.25789e6i | 0.734369 | − | 0.652179i | ||||
\(479\) | 4.05783e6 | 0.808081 | 0.404040 | − | 0.914741i | \(-0.367605\pi\) | ||||
0.404040 | + | 0.914741i | \(0.367605\pi\) | |||||||
\(480\) | −3.20213e6 | + | 1.70535e6i | −0.634361 | + | 0.337839i | ||||
\(481\) | 3.92856e6 | 0.774232 | ||||||||
\(482\) | −6.99494e6 | + | 6.21206e6i | −1.37141 | + | 1.21792i | ||||
\(483\) | − | 4.16028e6i | − | 0.811437i | ||||||
\(484\) | −1.46567e6 | + | 1.23195e7i | −0.284396 | + | 2.39044i | ||||
\(485\) | 1.85252e6i | 0.357609i | ||||||||
\(486\) | 3.66969e6 | + | 4.13216e6i | 0.704756 | + | 0.793573i | ||||
\(487\) | 121792. | 0.0232700 | 0.0116350 | − | 0.999932i | \(-0.496296\pi\) | ||||
0.0116350 | + | 0.999932i | \(0.496296\pi\) | |||||||
\(488\) | 419435. | − | 291764.i | 0.0797288 | − | 0.0554603i | ||||
\(489\) | −4.32902e6 | −0.818687 | ||||||||
\(490\) | −569930. | − | 641755.i | −0.107234 | − | 0.120748i | ||||
\(491\) | − | 2.80649e6i | − | 0.525363i | −0.964883 | − | 0.262682i | \(-0.915393\pi\) | ||
0.964883 | − | 0.262682i | \(-0.0846069\pi\) | |||||||
\(492\) | −3.00957e6 | − | 358055.i | −0.560522 | − | 0.0666864i | ||||
\(493\) | 2.45809e6i | 0.455491i | ||||||||
\(494\) | −4.35973e6 | + | 3.87179e6i | −0.803789 | + | 0.713829i | ||||
\(495\) | 7.12269e6 | 1.30656 | ||||||||
\(496\) | −4.93253e6 | − | 1.19052e6i | −0.900255 | − | 0.217286i | ||||
\(497\) | 4.44332e6 | 0.806894 | ||||||||
\(498\) | 9.95516e6 | − | 8.84098e6i | 1.79877 | − | 1.59745i | ||||
\(499\) | − | 2.59476e6i | − | 0.466494i | −0.972418 | − | 0.233247i | \(-0.925065\pi\) | ||
0.972418 | − | 0.233247i | \(-0.0749351\pi\) | |||||||
\(500\) | −496499. | − | 59069.5i | −0.0888164 | − | 0.0105667i | ||||
\(501\) | − | 1.10606e7i | − | 1.96873i | ||||||
\(502\) | 3.23372e6 | + | 3.64125e6i | 0.572721 | + | 0.644897i | ||||
\(503\) | 1.04638e6 | 0.184404 | 0.0922021 | − | 0.995740i | \(-0.470609\pi\) | ||||
0.0922021 | + | 0.995740i | \(0.470609\pi\) | |||||||
\(504\) | 4.11975e6 | + | 5.92248e6i | 0.722428 | + | 1.03855i | ||||
\(505\) | −777607. | −0.135685 | ||||||||
\(506\) | 4.45928e6 | + | 5.02126e6i | 0.774264 | + | 0.871840i | ||||
\(507\) | 1.06344e7i | 1.83735i | ||||||||
\(508\) | −33449.8 | + | 281157.i | −0.00575089 | + | 0.0483381i | ||||
\(509\) | − | 8.38369e6i | − | 1.43430i | −0.696918 | − | 0.717151i | \(-0.745446\pi\) | ||
0.696918 | − | 0.717151i | \(-0.254554\pi\) | |||||||
\(510\) | 3.01678e6 | − | 2.67914e6i | 0.513592 | − | 0.456111i | ||||
\(511\) | −2.16504e6 | −0.366787 | ||||||||
\(512\) | 5.74351e6 | − | 1.48204e6i | 0.968284 | − | 0.249853i | ||||
\(513\) | 4.09904e6 | 0.687684 | ||||||||
\(514\) | −3.23713e6 | + | 2.87483e6i | −0.540445 | + | 0.479959i | ||||
\(515\) | − | 3.50746e6i | − | 0.582740i | ||||||
\(516\) | 1.23767e6 | − | 1.04031e7i | 0.204636 | − | 1.72004i | ||||
\(517\) | − | 5.92664e6i | − | 0.975174i | ||||||
\(518\) | 1.71418e6 | + | 1.93021e6i | 0.280694 | + | 0.316068i | ||||
\(519\) | 7.05000e6 | 1.14887 | ||||||||
\(520\) | −2.30532e6 | − | 3.31408e6i | −0.373871 | − | 0.537471i | ||||
\(521\) | −4.38397e6 | −0.707577 | −0.353788 | − | 0.935325i | \(-0.615107\pi\) | ||||
−0.353788 | + | 0.935325i | \(0.615107\pi\) | |||||||
\(522\) | −3.11834e6 | − | 3.51132e6i | −0.500895 | − | 0.564020i | ||||
\(523\) | − | 915789.i | − | 0.146400i | −0.997317 | − | 0.0732000i | \(-0.976679\pi\) | ||
0.997317 | − | 0.0732000i | \(-0.0233211\pi\) | |||||||
\(524\) | 3.50990e6 | + | 417580.i | 0.558427 | + | 0.0664372i | ||||
\(525\) | 1.62250e6i | 0.256913i | ||||||||
\(526\) | 1.10287e6 | − | 979439.i | 0.173804 | − | 0.154352i | ||||
\(527\) | 5.64309e6 | 0.885096 | ||||||||
\(528\) | −1.84729e7 | − | 4.45863e6i | −2.88370 | − | 0.696012i | ||||
\(529\) | −3.86810e6 | −0.600978 | ||||||||
\(530\) | 3.62840e6 | − | 3.22231e6i | 0.561080 | − | 0.498284i | ||||
\(531\) | − | 8.48634e6i | − | 1.30612i | ||||||
\(532\) | −3.80463e6 | − | 452645.i | −0.582819 | − | 0.0693391i | ||||
\(533\) | − | 3.37257e6i | − | 0.514212i | ||||||
\(534\) | −110859. | − | 124830.i | −0.0168236 | − | 0.0189438i | ||||
\(535\) | 869815. | 0.131384 | ||||||||
\(536\) | 8.17038e6 | − | 5.68342e6i | 1.22837 | − | 0.854471i | ||||
\(537\) | −2.01862e7 | −3.02077 | ||||||||
\(538\) | 4.22251e6 | + | 4.75465e6i | 0.628949 | + | 0.708212i | ||||
\(539\) | − | 4.49581e6i | − | 0.666556i | ||||||
\(540\) | −335283. | + | 2.81816e6i | −0.0494797 | + | 0.415893i | ||||
\(541\) | − | 6.98594e6i | − | 1.02620i | −0.858329 | − | 0.513100i | \(-0.828497\pi\) | ||
0.858329 | − | 0.513100i | \(-0.171503\pi\) | |||||||
\(542\) | −4.53750e6 | + | 4.02966e6i | −0.663465 | + | 0.589210i | ||||
\(543\) | −1.52904e7 | −2.22545 | ||||||||
\(544\) | −5.82247e6 | + | 3.10085e6i | −0.843548 | + | 0.449245i | ||||
\(545\) | −2.09398e6 | −0.301982 | ||||||||
\(546\) | −9.79511e6 | + | 8.69885e6i | −1.40614 | + | 1.24876i | ||||
\(547\) | 4.72947e6i | 0.675841i | 0.941175 | + | 0.337920i | \(0.109723\pi\) | ||||
−0.941175 | + | 0.337920i | \(0.890277\pi\) | |||||||
\(548\) | −1.15063e6 | + | 9.67146e6i | −0.163676 | + | 1.37575i | ||||
\(549\) | − | 1.08556e6i | − | 0.153718i | ||||||
\(550\) | −1.73911e6 | − | 1.95828e6i | −0.245143 | − | 0.276038i | ||||
\(551\) | 2.49402e6 | 0.349962 | ||||||||
\(552\) | −5.96607e6 | + | 4.15007e6i | −0.833375 | + | 0.579706i | ||||
\(553\) | 3.13231e6 | 0.435564 | ||||||||
\(554\) | −2.31042e6 | − | 2.60159e6i | −0.319829 | − | 0.360135i | ||||
\(555\) | 2.75817e6i | 0.380091i | ||||||||
\(556\) | −1.88684e6 | − | 224481.i | −0.258850 | − | 0.0307959i | ||||
\(557\) | − | 3.26312e6i | − | 0.445651i | −0.974858 | − | 0.222825i | \(-0.928472\pi\) | ||
0.974858 | − | 0.222825i | \(-0.0715280\pi\) | |||||||
\(558\) | −8.06102e6 | + | 7.15883e6i | −1.09598 | + | 0.973322i | ||||
\(559\) | 1.16578e7 | 1.57793 | ||||||||
\(560\) | 622403. | − | 2.57873e6i | 0.0838690 | − | 0.347484i | ||||
\(561\) | 2.11340e7 | 2.83514 | ||||||||
\(562\) | −2.75859e6 | + | 2.44985e6i | −0.368423 | + | 0.327189i | ||||
\(563\) | − | 5.81898e6i | − | 0.773706i | −0.922141 | − | 0.386853i | \(-0.873562\pi\) | ||
0.922141 | − | 0.386853i | \(-0.126438\pi\) | |||||||
\(564\) | 6.36889e6 | + | 757720.i | 0.843074 | + | 0.100302i | ||||
\(565\) | 1.43155e6i | 0.188663i | ||||||||
\(566\) | 3.41296e6 | + | 3.84307e6i | 0.447806 | + | 0.504240i | ||||
\(567\) | −475223. | −0.0620782 | ||||||||
\(568\) | −4.43241e6 | − | 6.37196e6i | −0.576461 | − | 0.828710i | ||||
\(569\) | −9.08770e6 | −1.17672 | −0.588360 | − | 0.808599i | \(-0.700226\pi\) | ||||
−0.588360 | + | 0.808599i | \(0.700226\pi\) | |||||||
\(570\) | −2.71830e6 | − | 3.06088e6i | −0.350438 | − | 0.394601i | ||||
\(571\) | − | 258870.i | − | 0.0332270i | −0.999862 | − | 0.0166135i | \(-0.994712\pi\) | ||
0.999862 | − | 0.0166135i | \(-0.00528849\pi\) | |||||||
\(572\) | 2.49820e6 | − | 2.09982e7i | 0.319255 | − | 2.68344i | ||||
\(573\) | 2.11875e7i | 2.69583i | ||||||||
\(574\) | 1.65704e6 | − | 1.47158e6i | 0.209919 | − | 0.186425i | ||||
\(575\) | −1.00161e6 | −0.126336 | ||||||||
\(576\) | 4.38352e6 | − | 1.18159e7i | 0.550512 | − | 1.48392i | ||||
\(577\) | 2.45070e6 | 0.306444 | 0.153222 | − | 0.988192i | \(-0.451035\pi\) | ||||
0.153222 | + | 0.988192i | \(0.451035\pi\) | |||||||
\(578\) | −520110. | + | 461900.i | −0.0647554 | + | 0.0575080i | ||||
\(579\) | 4.61182e6i | 0.571710i | ||||||||
\(580\) | −203999. | + | 1.71468e6i | −0.0251802 | + | 0.211648i | ||||
\(581\) | 9.73547e6i | 1.19651i | ||||||||
\(582\) | −6.97311e6 | − | 7.85190e6i | −0.853334 | − | 0.960875i | ||||
\(583\) | 2.54187e7 | 3.09729 | ||||||||
\(584\) | 2.15973e6 | + | 3.10479e6i | 0.262039 | + | 0.376703i | ||||
\(585\) | −8.57737e6 | −1.03625 | ||||||||
\(586\) | −1.93091e6 | − | 2.17426e6i | −0.232284 | − | 0.261557i | ||||
\(587\) | 3.61982e6i | 0.433602i | 0.976216 | + | 0.216801i | \(0.0695623\pi\) | ||||
−0.976216 | + | 0.216801i | \(0.930438\pi\) | |||||||
\(588\) | 4.83129e6 | + | 574789.i | 0.576262 | + | 0.0685591i | ||||
\(589\) | − | 5.72557e6i | − | 0.680034i | ||||||
\(590\) | −2.33320e6 | + | 2.07207e6i | −0.275944 | + | 0.245061i | ||||
\(591\) | 9.78339e6 | 1.15218 | ||||||||
\(592\) | 1.05805e6 | − | 4.38371e6i | 0.124080 | − | 0.514088i | ||||
\(593\) | −7.07347e6 | −0.826030 | −0.413015 | − | 0.910724i | \(-0.635524\pi\) | ||||
−0.413015 | + | 0.910724i | \(0.635524\pi\) | |||||||
\(594\) | −1.11153e7 | + | 9.87132e6i | −1.29258 | + | 1.14791i | ||||
\(595\) | 2.95020e6i | 0.341633i | ||||||||
\(596\) | −7.42741e6 | − | 883655.i | −0.856489 | − | 0.101898i | ||||
\(597\) | 1.46370e7i | 1.68080i | ||||||||
\(598\) | −5.37001e6 | − | 6.04677e6i | −0.614077 | − | 0.691465i | ||||
\(599\) | −2.71813e6 | −0.309530 | −0.154765 | − | 0.987951i | \(-0.549462\pi\) | ||||
−0.154765 | + | 0.987951i | \(0.549462\pi\) | |||||||
\(600\) | 2.32675e6 | − | 1.61852e6i | 0.263859 | − | 0.183543i | ||||
\(601\) | 1.67171e6 | 0.188788 | 0.0943942 | − | 0.995535i | \(-0.469909\pi\) | ||||
0.0943942 | + | 0.995535i | \(0.469909\pi\) | |||||||
\(602\) | 5.08675e6 | + | 5.72780e6i | 0.572070 | + | 0.644165i | ||||
\(603\) | − | 2.11462e7i | − | 2.36832i | ||||||
\(604\) | −336718. | + | 2.83023e6i | −0.0375556 | + | 0.315667i | ||||
\(605\) | − | 9.69245e6i | − | 1.07658i | ||||||
\(606\) | 3.29588e6 | − | 2.92701e6i | 0.364578 | − | 0.323774i | ||||
\(607\) | −2.35562e6 | −0.259498 | −0.129749 | − | 0.991547i | \(-0.541417\pi\) | ||||
−0.129749 | + | 0.991547i | \(0.541417\pi\) | |||||||
\(608\) | 3.14617e6 | + | 5.90758e6i | 0.345163 | + | 0.648113i | ||||
\(609\) | 5.60338e6 | 0.612219 | ||||||||
\(610\) | −298460. | + | 265057.i | −0.0324760 | + | 0.0288413i | ||||
\(611\) | 7.13705e6i | 0.773421i | ||||||||
\(612\) | −1.65581e6 | + | 1.39177e7i | −0.178704 | + | 1.50206i | ||||
\(613\) | − | 1.88749e6i | − | 0.202877i | −0.994842 | − | 0.101439i | \(-0.967655\pi\) | ||
0.994842 | − | 0.101439i | \(-0.0323445\pi\) | |||||||
\(614\) | −5.51024e6 | − | 6.20466e6i | −0.589860 | − | 0.664197i | ||||
\(615\) | 2.36781e6 | 0.252441 | ||||||||
\(616\) | 1.14071e7 | − | 7.93489e6i | 1.21122 | − | 0.842537i | ||||
\(617\) | 1.45446e7 | 1.53812 | 0.769058 | − | 0.639178i | \(-0.220725\pi\) | ||||
0.769058 | + | 0.639178i | \(0.220725\pi\) | |||||||
\(618\) | 1.32025e7 | + | 1.48664e7i | 1.39055 | + | 1.56579i | ||||
\(619\) | 1.08497e7i | 1.13813i | 0.822292 | + | 0.569066i | \(0.192695\pi\) | ||||
−0.822292 | + | 0.569066i | \(0.807305\pi\) | |||||||
\(620\) | 3.93643e6 | + | 468326.i | 0.411267 | + | 0.0489293i | ||||
\(621\) | 5.68521e6i | 0.591585i | ||||||||
\(622\) | 2.31752e6 | − | 2.05815e6i | 0.240186 | − | 0.213305i | ||||
\(623\) | 122075. | 0.0126011 | ||||||||
\(624\) | 2.22457e7 | + | 5.36923e6i | 2.28710 | + | 0.552015i | ||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 7.22671e6 | − | 6.41790e6i | 0.737063 | − | 0.654571i | ||||
\(627\) | − | 2.14430e7i | − | 2.17829i | ||||||
\(628\) | −1.93486e7 | − | 2.30195e6i | −1.95772 | − | 0.232914i | ||||
\(629\) | 5.01520e6i | 0.505431i | ||||||||
\(630\) | −3.74264e6 | − | 4.21430e6i | −0.375687 | − | 0.423033i | ||||
\(631\) | 3.76561e6 | 0.376497 | 0.188249 | − | 0.982121i | \(-0.439719\pi\) | ||||
0.188249 | + | 0.982121i | \(0.439719\pi\) | |||||||
\(632\) | −3.12462e6 | − | 4.49190e6i | −0.311175 | − | 0.447340i | ||||
\(633\) | 1.07287e7 | 1.06424 | ||||||||
\(634\) | 3.67594e6 | + | 4.13920e6i | 0.363200 | + | 0.408972i | ||||
\(635\) | − | 221203.i | − | 0.0217699i | ||||||
\(636\) | −3.24978e6 | + | 2.73155e7i | −0.318574 | + | 2.67772i | ||||
\(637\) | 5.41400e6i | 0.528652i | ||||||||
\(638\) | −6.76302e6 | + | 6.00610e6i | −0.657792 | + | 0.584173i | ||||
\(639\) | −1.64917e7 | −1.59776 | ||||||||
\(640\) | −4.31891e6 | + | 1.67984e6i | −0.416797 | + | 0.162113i | ||||
\(641\) | −223711. | −0.0215052 | −0.0107526 | − | 0.999942i | \(-0.503423\pi\) | ||||
−0.0107526 | + | 0.999942i | \(0.503423\pi\) | |||||||
\(642\) | −3.68671e6 | + | 3.27409e6i | −0.353021 | + | 0.313511i | ||||
\(643\) | − | 2.53011e6i | − | 0.241330i | −0.992693 | − | 0.120665i | \(-0.961497\pi\) | ||
0.992693 | − | 0.120665i | \(-0.0385028\pi\) | |||||||
\(644\) | 627800. | − | 5.27687e6i | 0.0596495 | − | 0.501374i | ||||
\(645\) | 8.18472e6i | 0.774648i | ||||||||
\(646\) | −4.94272e6 | − | 5.56562e6i | −0.465998 | − | 0.524726i | ||||
\(647\) | −8.44825e6 | −0.793425 | −0.396713 | − | 0.917943i | \(-0.629849\pi\) | ||||
−0.396713 | + | 0.917943i | \(0.629849\pi\) | |||||||
\(648\) | 474056. | + | 681495.i | 0.0443499 | + | 0.0637566i | ||||
\(649\) | −1.63452e7 | −1.52328 | ||||||||
\(650\) | 2.09429e6 | + | 2.35822e6i | 0.194426 | + | 0.218928i | ||||
\(651\) | − | 1.28638e7i | − | 1.18964i | ||||||
\(652\) | −5.49091e6 | − | 653265.i | −0.505854 | − | 0.0601825i | ||||
\(653\) | 1.72303e7i | 1.58128i | 0.612280 | + | 0.790641i | \(0.290253\pi\) | ||||
−0.612280 | + | 0.790641i | \(0.709747\pi\) | |||||||
\(654\) | 8.87532e6 | − | 7.88200e6i | 0.811409 | − | 0.720596i | ||||
\(655\) | −2.76145e6 | −0.251497 | ||||||||
\(656\) | −3.76329e6 | − | 908310.i | −0.341435 | − | 0.0824090i | ||||
\(657\) | 8.03568e6 | 0.726289 | ||||||||
\(658\) | −3.50663e6 | + | 3.11417e6i | −0.315737 | + | 0.280400i | ||||
\(659\) | − | 5.43243e6i | − | 0.487282i | −0.969865 | − | 0.243641i | \(-0.921658\pi\) | ||
0.969865 | − | 0.243641i | \(-0.0783419\pi\) | |||||||
\(660\) | 1.47424e7 | + | 1.75394e6i | 1.31737 | + | 0.156731i | ||||
\(661\) | − | 1.12770e7i | − | 1.00390i | −0.864897 | − | 0.501949i | \(-0.832616\pi\) | ||
0.864897 | − | 0.501949i | \(-0.167384\pi\) | |||||||
\(662\) | −1.29933e6 | − | 1.46308e6i | −0.115232 | − | 0.129754i | ||||
\(663\) | −2.54503e7 | −2.24858 | ||||||||
\(664\) | 1.39612e7 | − | 9.71158e6i | 1.22886 | − | 0.854810i | ||||
\(665\) | 2.99333e6 | 0.262483 | ||||||||
\(666\) | −6.36229e6 | − | 7.16410e6i | −0.555812 | − | 0.625858i | ||||
\(667\) | 3.45911e6i | 0.301057i | ||||||||
\(668\) | 1.66909e6 | − | 1.40292e7i | 0.144723 | − | 1.21645i | ||||
\(669\) | − | 2.39402e7i | − | 2.06806i | ||||||
\(670\) | −5.81385e6 | + | 5.16317e6i | −0.500354 | + | 0.444354i | ||||
\(671\) | −2.09086e6 | −0.179275 | ||||||||
\(672\) | 7.06860e6 | + | 1.32727e7i | 0.603823 | + | 1.13380i | ||||
\(673\) | 1.15475e7 | 0.982769 | 0.491384 | − | 0.870943i | \(-0.336491\pi\) | ||||
0.491384 | + | 0.870943i | \(0.336491\pi\) | |||||||
\(674\) | 1.59253e6 | − | 1.41430e6i | 0.135033 | − | 0.119920i | ||||
\(675\) | − | 2.21722e6i | − | 0.187305i | ||||||
\(676\) | −1.60476e6 | + | 1.34886e7i | −0.135065 | + | 1.13527i | ||||
\(677\) | 8.72804e6i | 0.731889i | 0.930637 | + | 0.365944i | \(0.119254\pi\) | ||||
−0.930637 | + | 0.365944i | \(0.880746\pi\) | |||||||
\(678\) | −5.38854e6 | − | 6.06763e6i | −0.450191 | − | 0.506926i | ||||
\(679\) | 7.67862e6 | 0.639159 | ||||||||
\(680\) | 4.23075e6 | − | 2.94296e6i | 0.350869 | − | 0.244069i | ||||
\(681\) | −2.17009e7 | −1.79313 | ||||||||
\(682\) | 1.37883e7 | + | 1.55260e7i | 1.13514 | + | 1.27820i | ||||
\(683\) | 5.37492e6i | 0.440880i | 0.975401 | + | 0.220440i | \(0.0707493\pi\) | ||||
−0.975401 | + | 0.220440i | \(0.929251\pi\) | |||||||
\(684\) | 1.41211e7 | + | 1.68002e6i | 1.15406 | + | 0.137301i | ||||
\(685\) | − | 7.60912e6i | − | 0.619595i | ||||||
\(686\) | −1.00265e7 | + | 8.90434e6i | −0.813466 | + | 0.722423i | ||||
\(687\) | 1.63849e7 | 1.32450 | ||||||||
\(688\) | 3.13972e6 | − | 1.30084e7i | 0.252883 | − | 1.04774i | ||||
\(689\) | −3.06101e7 | −2.45650 | ||||||||
\(690\) | 4.24531e6 | − | 3.77018e6i | 0.339459 | − | 0.301467i | ||||
\(691\) | − | 1.03106e7i | − | 0.821467i | −0.911756 | − | 0.410733i | \(-0.865273\pi\) | ||
0.911756 | − | 0.410733i | \(-0.134727\pi\) | |||||||
\(692\) | 8.94217e6 | + | 1.06387e6i | 0.709868 | + | 0.0844545i | ||||
\(693\) | − | 2.95233e7i | − | 2.33524i | ||||||
\(694\) | −618498. | − | 696444.i | −0.0487461 | − | 0.0548893i | ||||
\(695\) | 1.48449e6 | 0.116577 | ||||||||
\(696\) | −5.58963e6 | − | 8.03555e6i | −0.437381 | − | 0.628771i | ||||
\(697\) | 4.30541e6 | 0.335686 | ||||||||
\(698\) | 135011. | + | 152026.i | 0.0104889 | + | 0.0118108i | ||||
\(699\) | 2.05556e7i | 1.59124i | ||||||||
\(700\) | −244841. | + | 2.05797e6i | −0.0188859 | + | 0.158743i | ||||
\(701\) | 7.87993e6i | 0.605658i | 0.953045 | + | 0.302829i | \(0.0979311\pi\) | ||||
−0.953045 | + | 0.302829i | \(0.902069\pi\) | |||||||
\(702\) | 1.33855e7 | − | 1.18874e7i | 1.02516 | − | 0.910422i | ||||
\(703\) | 5.08851e6 | 0.388331 | ||||||||
\(704\) | −2.27581e7 | − | 8.44293e6i | −1.73063 | − | 0.642039i | ||||
\(705\) | −5.01078e6 | −0.379693 | ||||||||
\(706\) | 5.89743e6 | − | 5.23739e6i | 0.445298 | − | 0.395460i | ||||
\(707\) | 3.22315e6i | 0.242511i | ||||||||
\(708\) | 2.08973e6 | − | 1.75649e7i | 0.156678 | − | 1.31693i | ||||
\(709\) | 2.06172e7i | 1.54033i | 0.637846 | + | 0.770164i | \(0.279826\pi\) | ||||
−0.637846 | + | 0.770164i | \(0.720174\pi\) | |||||||
\(710\) | 4.02668e6 | + | 4.53414e6i | 0.299779 | + | 0.337559i | ||||
\(711\) | −1.16258e7 | −0.862476 | ||||||||
\(712\) | −121776. | − | 175063.i | −0.00900246 | − | 0.0129418i | ||||
\(713\) | 7.94115e6 | 0.585005 | ||||||||
\(714\) | −1.11049e7 | − | 1.25044e7i | −0.815212 | − | 0.917949i | ||||
\(715\) | 1.65205e7i | 1.20853i | ||||||||
\(716\) | −2.56040e7 | − | 3.04616e6i | −1.86649 | − | 0.222060i | ||||
\(717\) | − | 2.17280e7i | − | 1.57842i | ||||||
\(718\) | 1.48288e7 | − | 1.31692e7i | 1.07348 | − | 0.953338i | ||||
\(719\) | 1.37162e7 | 0.989490 | 0.494745 | − | 0.869038i | \(-0.335262\pi\) | ||||
0.494745 | + | 0.869038i | \(0.335262\pi\) | |||||||
\(720\) | −2.31009e6 | + | 9.57110e6i | −0.166072 | + | 0.688067i | ||||
\(721\) | −1.45383e7 | −1.04154 | ||||||||
\(722\) | 4.82614e6 | − | 4.28600e6i | 0.344554 | − | 0.305991i | ||||
\(723\) | 4.14305e7i | 2.94764i | ||||||||
\(724\) | −1.93942e7 | − | 2.30737e6i | −1.37507 | − | 0.163595i | ||||
\(725\) | − | 1.34904e6i | − | 0.0953193i | ||||||
\(726\) | 3.64836e7 | + | 4.10814e7i | 2.56895 | + | 2.89270i | ||||
\(727\) | −2.33681e7 | −1.63979 | −0.819895 | − | 0.572514i | \(-0.805968\pi\) | ||||
−0.819895 | + | 0.572514i | \(0.805968\pi\) | |||||||
\(728\) | −1.37367e7 | + | 9.55545e6i | −0.960629 | + | 0.668225i | ||||
\(729\) | 2.33601e7 | 1.62800 | ||||||||
\(730\) | −1.96203e6 | − | 2.20929e6i | −0.136269 | − | 0.153443i | ||||
\(731\) | 1.48823e7i | 1.03010i | ||||||||
\(732\) | 267316. | − | 2.24688e6i | 0.0184394 | − | 0.154990i | ||||
\(733\) | − | 2.94411e6i | − | 0.202392i | −0.994866 | − | 0.101196i | \(-0.967733\pi\) | ||
0.994866 | − | 0.101196i | \(-0.0322670\pi\) | |||||||
\(734\) | 1.54147e7 | − | 1.36895e7i | 1.05607 | − | 0.937878i | ||||
\(735\) | −3.80106e6 | −0.259530 | ||||||||
\(736\) | −8.19358e6 | + | 4.36362e6i | −0.557544 | + | 0.296929i | ||||
\(737\) | −4.07289e7 | −2.76207 | ||||||||
\(738\) | −6.15019e6 | + | 5.46186e6i | −0.415669 | + | 0.369147i | ||||
\(739\) | − | 3.66027e6i | − | 0.246548i | −0.992373 | − | 0.123274i | \(-0.960661\pi\) | ||
0.992373 | − | 0.123274i | \(-0.0393395\pi\) | |||||||
\(740\) | −416217. | + | 3.49844e6i | −0.0279409 | + | 0.234853i | ||||
\(741\) | 2.58223e7i | 1.72763i | ||||||||
\(742\) | −1.33563e7 | − | 1.50396e7i | −0.890590 | − | 1.00283i | ||||
\(743\) | −2.60824e7 | −1.73331 | −0.866653 | − | 0.498912i | \(-0.833733\pi\) | ||||
−0.866653 | + | 0.498912i | \(0.833733\pi\) | |||||||
\(744\) | −1.84474e7 | + | 1.28322e7i | −1.22181 | + | 0.849904i | ||||
\(745\) | 5.84359e6 | 0.385735 | ||||||||
\(746\) | −1.57484e7 | − | 1.77331e7i | −1.03607 | − | 1.16664i | ||||
\(747\) | − | 3.61338e7i | − | 2.36926i | ||||||
\(748\) | 2.68063e7 | + | 3.18920e6i | 1.75179 | + | 0.208414i | ||||
\(749\) | − | 3.60535e6i | − | 0.234824i | ||||||
\(750\) | −1.65566e6 | + | 1.47036e6i | −0.107478 | + | 0.0954489i | ||||
\(751\) | −1.03196e7 | −0.667673 | −0.333836 | − | 0.942631i | \(-0.608343\pi\) | ||||
−0.333836 | + | 0.942631i | \(0.608343\pi\) | |||||||
\(752\) | 7.96391e6 | + | 1.92217e6i | 0.513549 | + | 0.123950i | ||||
\(753\) | 2.15668e7 | 1.38611 | ||||||||
\(754\) | 8.14425e6 | − | 7.23275e6i | 0.521702 | − | 0.463313i | ||||
\(755\) | − | 2.22671e6i | − | 0.142166i | ||||||
\(756\) | 1.16812e7 | + | 1.38973e6i | 0.743331 | + | 0.0884356i | ||||
\(757\) | − | 2.70313e7i | − | 1.71446i | −0.514936 | − | 0.857228i | \(-0.672184\pi\) | ||
0.514936 | − | 0.857228i | \(-0.327816\pi\) | |||||||
\(758\) | 8.68040e6 | + | 9.77434e6i | 0.548740 | + | 0.617895i | ||||
\(759\) | 2.97405e7 | 1.87389 | ||||||||
\(760\) | −2.98598e6 | − | 4.29260e6i | −0.187522 | − | 0.269579i | ||||
\(761\) | 1.29548e7 | 0.810905 | 0.405452 | − | 0.914116i | \(-0.367114\pi\) | ||||
0.405452 | + | 0.914116i | \(0.367114\pi\) | |||||||
\(762\) | 832635. | + | 937568.i | 0.0519478 | + | 0.0584945i | ||||
\(763\) | 8.67946e6i | 0.539736i | ||||||||
\(764\) | −3.19726e6 | + | 2.68741e7i | −0.198173 | + | 1.66571i | ||||
\(765\) | − | 1.09499e7i | − | 0.676480i | ||||||
\(766\) | 5.00116e6 | − | 4.44143e6i | 0.307963 | − | 0.273496i | ||||
\(767\) | 1.96834e7 | 1.20813 | ||||||||
\(768\) | 1.19826e7 | − | 2.33769e7i | 0.733072 | − | 1.43016i | ||||
\(769\) | 8.35551e6 | 0.509515 | 0.254757 | − | 0.967005i | \(-0.418004\pi\) | ||||
0.254757 | + | 0.967005i | \(0.418004\pi\) | |||||||
\(770\) | −8.11700e6 | + | 7.20854e6i | −0.493365 | + | 0.438148i | ||||
\(771\) | 1.91732e7i | 1.16161i | ||||||||
\(772\) | −695939. | + | 5.84960e6i | −0.0420270 | + | 0.353251i | ||||
\(773\) | − | 3.12215e7i | − | 1.87934i | −0.342087 | − | 0.939668i | \(-0.611134\pi\) | ||
0.342087 | − | 0.939668i | \(-0.388866\pi\) | |||||||
\(774\) | −1.88798e7 | − | 2.12591e7i | −1.13278 | − | 1.27553i | ||||
\(775\) | −3.09703e6 | −0.185221 | ||||||||
\(776\) | −7.65978e6 | − | 1.10116e7i | −0.456627 | − | 0.656439i | ||||
\(777\) | 1.14325e7 | 0.679342 | ||||||||
\(778\) | 1.91278e7 | + | 2.15384e7i | 1.13296 | + | 1.27574i | ||||
\(779\) | − | 4.36835e6i | − | 0.257913i | ||||||
\(780\) | −1.77533e7 | − | 2.11215e6i | −1.04482 | − | 0.124305i | ||||
\(781\) | 3.17639e7i | 1.86340i | ||||||||
\(782\) | 7.71929e6 | − | 6.85535e6i | 0.451399 | − | 0.400879i | ||||
\(783\) | −7.65727e6 | −0.446344 | ||||||||
\(784\) | 6.04124e6 | + | 1.45812e6i | 0.351023 | + | 0.0847232i | ||||
\(785\) | 1.52227e7 | 0.881695 | ||||||||
\(786\) | 1.17044e7 | − | 1.03944e7i | 0.675760 | − | 0.600129i | ||||
\(787\) | 1.14664e7i | 0.659920i | 0.943995 | + | 0.329960i | \(0.107035\pi\) | ||||
−0.943995 | + | 0.329960i | \(0.892965\pi\) | |||||||
\(788\) | 1.24092e7 | + | 1.47635e6i | 0.711915 | + | 0.0846980i | ||||
\(789\) | − | 6.53222e6i | − | 0.373567i | ||||||
\(790\) | 2.83860e6 | + | 3.19633e6i | 0.161822 | + | 0.182215i | ||||
\(791\) | 5.93373e6 | 0.337199 | ||||||||
\(792\) | −4.23380e7 | + | 2.94508e7i | −2.39838 | + | 1.66834i | ||||
\(793\) | 2.51789e6 | 0.142185 | ||||||||
\(794\) | 236673. | + | 266499.i | 0.0133228 | + | 0.0150018i | ||||
\(795\) | − | 2.14907e7i | − | 1.20596i | ||||||
\(796\) | −2.20878e6 | + | 1.85655e7i | −0.123557 | + | 1.03854i | ||||
\(797\) | − | 2.28998e7i | − | 1.27699i | −0.769628 | − | 0.638493i | \(-0.779558\pi\) | ||
0.769628 | − | 0.638493i | \(-0.220442\pi\) | |||||||
\(798\) | −1.26872e7 | + | 1.12673e7i | −0.705276 | + | 0.626342i | ||||
\(799\) | −9.11115e6 | −0.504901 | ||||||||
\(800\) | 3.19548e6 | − | 1.70180e6i | 0.176527 | − | 0.0940121i | ||||
\(801\) | −453090. | −0.0249519 | ||||||||
\(802\) | −1.89896e7 | + | 1.68643e7i | −1.04251 | + | 0.925831i | ||||
\(803\) | − | 1.54772e7i | − | 0.847040i | ||||||
\(804\) | 5.20719e6 | − | 4.37681e7i | 0.284095 | − | 2.38791i | ||||
\(805\) | 4.15163e6i | 0.225803i | ||||||||
\(806\) | −1.66044e7 | − | 1.86969e7i | −0.900295 | − | 1.01375i | ||||
\(807\) | 2.81614e7 | 1.52220 | ||||||||
\(808\) | 4.62217e6 | − | 3.21524e6i | 0.249068 | − | 0.173255i | ||||
\(809\) | 2.82761e7 | 1.51896 | 0.759482 | − | 0.650528i | \(-0.225452\pi\) | ||||
0.759482 | + | 0.650528i | \(0.225452\pi\) | |||||||
\(810\) | −430662. | − | 484936.i | −0.0230634 | − | 0.0259700i | ||||
\(811\) | − | 2.97657e7i | − | 1.58915i | −0.607167 | − | 0.794574i | \(-0.707694\pi\) | ||
0.607167 | − | 0.794574i | \(-0.292306\pi\) | |||||||
\(812\) | 7.10729e6 | + | 845570.i | 0.378281 | + | 0.0450048i | ||||
\(813\) | 2.68752e7i | 1.42602i | ||||||||
\(814\) | −1.37985e7 | + | 1.22542e7i | −0.729912 | + | 0.648220i | ||||
\(815\) | 4.32002e6 | 0.227820 | ||||||||
\(816\) | −6.85435e6 | + | 2.83988e7i | −0.360364 | + | 1.49305i | ||||
\(817\) | 1.50999e7 | 0.791441 | ||||||||
\(818\) | 8.60387e6 | − | 7.64092e6i | 0.449584 | − | 0.399266i | ||||
\(819\) | 3.55529e7i | 1.85210i | ||||||||
\(820\) | 3.00332e6 | + | 357311.i | 0.155979 | + | 0.0185572i | ||||
\(821\) | − | 2.33663e7i | − | 1.20985i | −0.796282 | − | 0.604926i | \(-0.793203\pi\) | ||
0.796282 | − | 0.604926i | \(-0.206797\pi\) | |||||||
\(822\) | 2.86417e7 | + | 3.22512e7i | 1.47849 | + | 1.66482i | ||||
\(823\) | −3.90864e6 | −0.201153 | −0.100576 | − | 0.994929i | \(-0.532069\pi\) | ||||
−0.100576 | + | 0.994929i | \(0.532069\pi\) | |||||||
\(824\) | 1.45026e7 | + | 2.08487e7i | 0.744094 | + | 1.06970i | ||||
\(825\) | −1.15987e7 | −0.593302 | ||||||||
\(826\) | 8.58863e6 | + | 9.67101e6i | 0.438000 | + | 0.493198i | ||||
\(827\) | − | 1.34407e7i | − | 0.683371i | −0.939814 | − | 0.341686i | \(-0.889002\pi\) | ||
0.939814 | − | 0.341686i | \(-0.110998\pi\) | |||||||
\(828\) | −2.33012e6 | + | 1.95854e7i | −0.118114 | + | 0.992790i | ||||
\(829\) | 2.39273e7i | 1.20923i | 0.796519 | + | 0.604613i | \(0.206672\pi\) | ||||
−0.796519 | + | 0.604613i | \(0.793328\pi\) | |||||||
\(830\) | −9.93446e6 | + | 8.82260e6i | −0.500552 | + | 0.444530i | ||||
\(831\) | −1.54090e7 | −0.774057 | ||||||||
\(832\) | 2.74061e7 | + | 1.01673e7i | 1.37258 | + | 0.509208i | ||||
\(833\) | −6.91151e6 | −0.345112 | ||||||||
\(834\) | −6.29200e6 | + | 5.58780e6i | −0.313237 | + | 0.278180i | ||||
\(835\) | 1.10376e7i | 0.547848i | ||||||||
\(836\) | 3.23582e6 | − | 2.71981e7i | 0.160128 | − | 1.34593i | ||||
\(837\) | 1.75790e7i | 0.867320i | ||||||||
\(838\) | −5.75251e6 | − | 6.47747e6i | −0.282975 | − | 0.318636i | ||||
\(839\) | −4.44572e6 | −0.218041 | −0.109020 | − | 0.994040i | \(-0.534771\pi\) | ||||
−0.109020 | + | 0.994040i | \(0.534771\pi\) | |||||||
\(840\) | −6.70869e6 | − | 9.64430e6i | −0.328050 | − | 0.471598i | ||||
\(841\) | 1.58522e7 | 0.772856 | ||||||||
\(842\) | −1.82878e7 | − | 2.05925e7i | −0.888958 | − | 1.00099i | ||||
\(843\) | 1.63389e7i | 0.791871i | ||||||||
\(844\) | 1.36083e7 | + | 1.61900e6i | 0.657577 | + | 0.0782334i | ||||
\(845\) | − | 1.06122e7i | − | 0.511288i | ||||||
\(846\) | 1.30151e7 | − | 1.15584e7i | 0.625203 | − | 0.555230i | ||||
\(847\) | −4.01748e7 | −1.92418 | ||||||||
\(848\) | −8.24400e6 | + | 3.41564e7i | −0.393684 | + | 1.63111i | ||||
\(849\) | 2.27622e7 | 1.08379 | ||||||||
\(850\) | −3.01051e6 | + | 2.67357e6i | −0.142920 | + | 0.126924i | ||||
\(851\) | 7.05756e6i | 0.334065i | ||||||||
\(852\) | −3.41341e7 | − | 4.06101e6i | −1.61098 | − | 0.191662i | ||||
\(853\) | 2.57954e7i | 1.21386i | 0.794754 | + | 0.606931i | \(0.207600\pi\) | ||||
−0.794754 | + | 0.606931i | \(0.792400\pi\) | |||||||
\(854\) | 1.09865e6 | + | 1.23711e6i | 0.0515483 | + | 0.0580447i | ||||
\(855\) | −1.11099e7 | −0.519752 | ||||||||
\(856\) | −5.17027e6 | + | 3.59650e6i | −0.241173 | + | 0.167763i | ||||
\(857\) | 1.79012e7 | 0.832590 | 0.416295 | − | 0.909230i | \(-0.363328\pi\) | ||||
0.416295 | + | 0.909230i | \(0.363328\pi\) | |||||||
\(858\) | −6.21854e7 | − | 7.00222e7i | −2.88383 | − | 3.24727i | ||||
\(859\) | − | 2.50747e7i | − | 1.15945i | −0.814811 | − | 0.579727i | \(-0.803159\pi\) | ||
0.814811 | − | 0.579727i | \(-0.196841\pi\) | |||||||
\(860\) | −1.23510e6 | + | 1.03814e7i | −0.0569451 | + | 0.478643i | ||||
\(861\) | − | 9.81449e6i | − | 0.451190i | ||||||
\(862\) | 2.27453e6 | − | 2.01996e6i | 0.104261 | − | 0.0925924i | ||||
\(863\) | 8.98511e6 | 0.410673 | 0.205337 | − | 0.978691i | \(-0.434171\pi\) | ||||
0.205337 | + | 0.978691i | \(0.434171\pi\) | |||||||
\(864\) | −9.65955e6 | − | 1.81378e7i | −0.440223 | − | 0.826608i | ||||
\(865\) | −7.03534e6 | −0.319702 | ||||||||
\(866\) | 6.26988e6 | − | 5.56815e6i | 0.284095 | − | 0.252300i | ||||
\(867\) | 3.08057e6i | 0.139182i | ||||||||
\(868\) | 1.94119e6 | − | 1.63164e7i | 0.0874519 | − | 0.735062i | ||||
\(869\) | 2.23919e7i | 1.00587i | ||||||||
\(870\) | 5.07797e6 | + | 5.71791e6i | 0.227453 | + | 0.256118i | ||||
\(871\) | 4.90471e7 | 2.19063 | ||||||||
\(872\) | 1.24468e7 | − | 8.65816e6i | 0.554329 | − | 0.385598i | ||||
\(873\) | −2.84997e7 | −1.26562 | ||||||||
\(874\) | −6.95556e6 | − | 7.83213e6i | −0.308002 | − | 0.346818i | ||||
\(875\) | − | 1.61913e6i | − | 0.0714925i | ||||||
\(876\) | 1.66321e7 | + | 1.97876e6i | 0.732297 | + | 0.0871229i | ||||
\(877\) | − | 1.08381e7i | − | 0.475834i | −0.971286 | − | 0.237917i | \(-0.923535\pi\) | ||
0.971286 | − | 0.237917i | \(-0.0764646\pi\) | |||||||
\(878\) | −1.05728e7 | + | 9.38946e6i | −0.462863 | + | 0.411059i | ||||
\(879\) | −1.28780e7 | −0.562179 | ||||||||
\(880\) | 1.84345e7 | + | 4.44936e6i | 0.802463 | + | 0.193683i | ||||
\(881\) | −816876. | −0.0354582 | −0.0177291 | − | 0.999843i | \(-0.505644\pi\) | ||||
−0.0177291 | + | 0.999843i | \(0.505644\pi\) | |||||||
\(882\) | 9.87293e6 | − | 8.76796e6i | 0.427341 | − | 0.379513i | ||||
\(883\) | − | 2.50842e6i | − | 0.108268i | −0.998534 | − | 0.0541339i | \(-0.982760\pi\) | ||
0.998534 | − | 0.0541339i | \(-0.0172398\pi\) | |||||||
\(884\) | −3.22810e7 | − | 3.84054e6i | −1.38936 | − | 0.165296i | ||||
\(885\) | 1.38193e7i | 0.593102i | ||||||||
\(886\) | −1.88117e7 | − | 2.11824e7i | −0.805089 | − | 0.906550i | ||||
\(887\) | −1.58294e7 | −0.675545 | −0.337773 | − | 0.941228i | \(-0.609673\pi\) | ||||
−0.337773 | + | 0.941228i | \(0.609673\pi\) | |||||||
\(888\) | −1.14044e7 | − | 1.63948e7i | −0.485335 | − | 0.697709i | ||||
\(889\) | −916878. | −0.0389096 | ||||||||
\(890\) | 110629. | + | 124571.i | 0.00468158 | + | 0.00527158i | ||||
\(891\) | − | 3.39722e6i | − | 0.143360i | ||||||
\(892\) | 3.61266e6 | − | 3.03656e7i | 0.152025 | − | 1.27782i | ||||
\(893\) | 9.24434e6i | 0.387924i | ||||||||
\(894\) | −2.47680e7 | + | 2.19960e7i | −1.03645 | + | 0.920449i | ||||
\(895\) | 2.01442e7 | 0.840605 | ||||||||
\(896\) | 6.96286e6 | + | 1.79017e7i | 0.289746 | + | 0.744946i | ||||
\(897\) | −3.58145e7 | −1.48620 | ||||||||
\(898\) | 1.28593e7 | − | 1.14201e7i | 0.532140 | − | 0.472583i | ||||
\(899\) | 1.06957e7i | 0.441379i | ||||||||
\(900\) | 908741. | − | 7.63827e6i | 0.0373967 | − | 0.314332i | ||||
\(901\) | − | 3.90768e7i | − | 1.60364i | ||||||
\(902\) | 1.05199e7 | + | 1.18456e7i | 0.430521 | + | 0.484777i | ||||
\(903\) | 3.39253e7 | 1.38454 | ||||||||
\(904\) | −5.91917e6 | − | 8.50929e6i | −0.240902 | − | 0.346316i | ||||
\(905\) | 1.52586e7 | 0.619288 | ||||||||
\(906\) | 8.38162e6 | + | 9.43790e6i | 0.339240 | + | 0.381993i | ||||
\(907\) | − | 2.36328e7i | − | 0.953887i | −0.878934 | − | 0.476944i | \(-0.841745\pi\) | ||
0.878934 | − | 0.476944i | \(-0.158255\pi\) | |||||||
\(908\) | −2.75253e7 | − | 3.27475e6i | −1.10794 | − | 0.131814i | ||||
\(909\) | − | 1.19629e7i | − | 0.480206i | ||||||
\(910\) | 9.77475e6 | − | 8.68076e6i | 0.391293 | − | 0.347500i | ||||
\(911\) | −9.17484e6 | −0.366271 | −0.183136 | − | 0.983088i | \(-0.558625\pi\) | ||||
−0.183136 | + | 0.983088i | \(0.558625\pi\) | |||||||
\(912\) | 2.88139e7 | + | 6.95455e6i | 1.14714 | + | 0.276874i | ||||
\(913\) | −6.95959e7 | −2.76316 | ||||||||
\(914\) | 3.04543e7 | − | 2.70459e7i | 1.20582 | − | 1.07087i | ||||
\(915\) | 1.76776e6i | 0.0698023i | ||||||||
\(916\) | 2.07825e7 | + | 2.47254e6i | 0.818389 | + | 0.0973655i | ||||
\(917\) | 1.14461e7i | 0.449504i | ||||||||
\(918\) | 1.51754e7 | + | 1.70879e7i | 0.594338 | + | 0.669239i | ||||
\(919\) | −3.58059e7 | −1.39851 | −0.699255 | − | 0.714872i | \(-0.746485\pi\) | ||||
−0.699255 | + | 0.714872i | \(0.746485\pi\) | |||||||
\(920\) | 5.95366e6 | − | 4.14144e6i | 0.231907 | − | 0.161318i | ||||
\(921\) | −3.67497e7 | −1.42759 | ||||||||
\(922\) | 2.95896e7 | + | 3.33186e7i | 1.14633 | + | 1.29080i | ||||
\(923\) | − | 3.82511e7i | − | 1.47788i | ||||||
\(924\) | 7.27000e6 | − | 6.11068e7i | 0.280127 | − | 2.35456i | ||||
\(925\) | − | 2.75243e6i | − | 0.105770i | ||||||
\(926\) | −2.61738e7 | + | 2.32444e7i | −1.00309 | + | 0.890823i | ||||
\(927\) | 5.39597e7 | 2.06239 | ||||||||
\(928\) | −5.87726e6 | − | 1.10357e7i | −0.224029 | − | 0.420660i | ||||
\(929\) | −2.41031e7 | −0.916291 | −0.458146 | − | 0.888877i | \(-0.651486\pi\) | ||||
−0.458146 | + | 0.888877i | \(0.651486\pi\) | |||||||
\(930\) | 1.31267e7 | − | 1.16576e7i | 0.497679 | − | 0.441979i | ||||
\(931\) | 7.01254e6i | 0.265156i | ||||||||
\(932\) | −3.10191e6 | + | 2.60726e7i | −0.116974 | + | 0.983204i | ||||
\(933\) | − | 1.37265e7i | − | 0.516245i | ||||||
\(934\) | 2.70883e7 | + | 3.05021e7i | 1.01605 | + | 1.14409i | ||||
\(935\) | −2.10901e7 | −0.788950 | ||||||||
\(936\) | 5.09848e7 | − | 3.54656e7i | 1.90218 | − | 1.32318i | ||||
\(937\) | −1.84615e7 | −0.686938 | −0.343469 | − | 0.939164i | \(-0.611602\pi\) | ||||
−0.343469 | + | 0.939164i | \(0.611602\pi\) | |||||||
\(938\) | 2.14011e7 | + | 2.40982e7i | 0.794200 | + | 0.894288i | ||||
\(939\) | − | 4.28032e7i | − | 1.58421i | ||||||
\(940\) | −6.35565e6 | − | 756144.i | −0.234607 | − | 0.0279116i | ||||
\(941\) | − | 3.10319e6i | − | 0.114244i | −0.998367 | − | 0.0571220i | \(-0.981808\pi\) | ||
0.998367 | − | 0.0571220i | \(-0.0181924\pi\) | |||||||
\(942\) | −6.45214e7 | + | 5.73002e7i | −2.36906 | + | 2.10392i | ||||
\(943\) | 6.05873e6 | 0.221872 | ||||||||
\(944\) | 5.30120e6 | − | 2.19638e7i | 0.193617 | − | 0.802192i | ||||
\(945\) | −9.19028e6 | −0.334772 | ||||||||
\(946\) | −4.09463e7 | + | 3.63636e7i | −1.48760 | + | 1.32111i | ||||
\(947\) | 4.89572e7i | 1.77395i | 0.461817 | + | 0.886975i | \(0.347198\pi\) | ||||
−0.461817 | + | 0.886975i | \(0.652802\pi\) | |||||||
\(948\) | −2.40628e7 | − | 2.86280e6i | −0.869611 | − | 0.103459i | ||||
\(949\) | 1.86382e7i | 0.671796i | ||||||||
\(950\) | 2.71265e6 | + | 3.05451e6i | 0.0975181 | + | 0.109808i | ||||
\(951\) | 2.45162e7 | 0.879025 | ||||||||
\(952\) | −1.21985e7 | − | 1.75363e7i | −0.436227 | − | 0.627113i | ||||
\(953\) | 3.94753e7 | 1.40797 | 0.703984 | − | 0.710216i | \(-0.251403\pi\) | ||||
0.703984 | + | 0.710216i | \(0.251403\pi\) | |||||||
\(954\) | 4.95729e7 | + | 5.58203e7i | 1.76349 | + | 1.98573i | ||||
\(955\) | − | 2.11434e7i | − | 0.750182i | ||||||
\(956\) | 3.27883e6 | − | 2.75597e7i | 0.116031 | − | 0.975281i | ||||
\(957\) | 4.00568e7i | 1.41383i | ||||||||
\(958\) | 1.71633e7 | − | 1.52424e7i | 0.604210 | − | 0.536587i | ||||
\(959\) | −3.15395e7 | −1.10741 | ||||||||
\(960\) | −7.13822e6 | + | 1.92412e7i | −0.249984 | + | 0.673837i | ||||
\(961\) | −4.07470e6 | −0.142327 | ||||||||
\(962\) | 1.66166e7 | − | 1.47569e7i | 0.578901 | − | 0.514110i | ||||
\(963\) | 1.33815e7i | 0.464984i | ||||||||
\(964\) | −6.25200e6 | + | 5.25501e7i | −0.216684 | + | 1.82130i | ||||
\(965\) | − | 4.60223e6i | − | 0.159093i | ||||||
\(966\) | −1.56272e7 | − | 1.75967e7i | −0.538815 | − | 0.606719i | ||||
\(967\) | −2.23447e7 | −0.768438 | −0.384219 | − | 0.923242i | \(-0.625529\pi\) | ||||
−0.384219 | + | 0.923242i | \(0.625529\pi\) | |||||||
\(968\) | 4.00762e7 | + | 5.76129e7i | 1.37467 | + | 1.97620i | ||||
\(969\) | −3.29647e7 | −1.12782 | ||||||||
\(970\) | 6.95862e6 | + | 7.83557e6i | 0.237462 | + | 0.267388i | ||||
\(971\) | 2.63033e7i | 0.895288i | 0.894212 | + | 0.447644i | \(0.147737\pi\) | ||||
−0.894212 | + | 0.447644i | \(0.852263\pi\) | |||||||
\(972\) | 3.10433e7 | + | 3.69328e6i | 1.05391 | + | 0.125385i | ||||
\(973\) | − | 6.15315e6i | − | 0.208360i | ||||||
\(974\) | 515141. | − | 457486.i | 0.0173992 | − | 0.0154519i | ||||
\(975\) | 1.39676e7 | 0.470554 | ||||||||
\(976\) | 678125. | − | 2.80959e6i | 0.0227869 | − | 0.0944102i | ||||
\(977\) | 4.78338e7 | 1.60324 | 0.801619 | − | 0.597835i | \(-0.203972\pi\) | ||||
0.801619 | + | 0.597835i | \(0.203972\pi\) | |||||||
\(978\) | −1.83104e7 | + | 1.62611e7i | −0.612140 | + | 0.543629i | ||||
\(979\) | 872679.i | 0.0291003i | ||||||||
\(980\) | −4.82125e6 | − | 573594.i | −0.160359 | − | 0.0190783i | ||||
\(981\) | − | 3.22144e7i | − | 1.06875i | ||||||
\(982\) | −1.05420e7 | − | 1.18706e7i | −0.348855 | − | 0.392819i | ||||
\(983\) | 4.88361e7 | 1.61197 | 0.805986 | − | 0.591935i | \(-0.201636\pi\) | ||||
0.805986 | + | 0.591935i | \(0.201636\pi\) | |||||||
\(984\) | −1.40745e7 | + | 9.79040e6i | −0.463389 | + | 0.322339i | ||||
\(985\) | −9.76305e6 | −0.320623 | ||||||||
\(986\) | 9.23331e6 | + | 1.03969e7i | 0.302458 | + | 0.340575i | ||||
\(987\) | 2.07695e7i | 0.678630i | ||||||||
\(988\) | −3.89668e6 | + | 3.27529e7i | −0.126999 | + | 1.06747i | ||||
\(989\) | 2.09429e7i | 0.680843i | ||||||||
\(990\) | 3.01267e7 | − | 2.67549e7i | 0.976931 | − | 0.867593i | ||||
\(991\) | 7.49231e6 | 0.242344 | 0.121172 | − | 0.992632i | \(-0.461335\pi\) | ||||
0.121172 | + | 0.992632i | \(0.461335\pi\) | |||||||
\(992\) | −2.53350e7 | + | 1.34925e7i | −0.817413 | + | 0.435326i | ||||
\(993\) | −8.66569e6 | −0.278888 | ||||||||
\(994\) | 1.87938e7 | − | 1.66904e7i | 0.603323 | − | 0.535799i | ||||
\(995\) | − | 1.46066e7i | − | 0.467725i | ||||||
\(996\) | 8.89781e6 | − | 7.47891e7i | 0.284207 | − | 2.38886i | ||||
\(997\) | 1.46209e7i | 0.465841i | 0.972496 | + | 0.232920i | \(0.0748281\pi\) | ||||
−0.972496 | + | 0.232920i | \(0.925172\pi\) | |||||||
\(998\) | −9.74670e6 | − | 1.09750e7i | −0.309764 | − | 0.348802i | ||||
\(999\) | −1.56230e7 | −0.495280 |
(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 | 40.6.d.a.21.15 | ✓ | 20 | |
3.2 | odd | 2 | 360.6.k.b.181.6 | 20 | |||
4.3 | odd | 2 | 160.6.d.a.81.18 | 20 | |||
5.2 | odd | 4 | 200.6.f.b.149.16 | 20 | |||
5.3 | odd | 4 | 200.6.f.c.149.5 | 20 | |||
5.4 | even | 2 | 200.6.d.b.101.6 | 20 | |||
8.3 | odd | 2 | 160.6.d.a.81.3 | 20 | |||
8.5 | even | 2 | inner | 40.6.d.a.21.16 | yes | 20 | |
20.3 | even | 4 | 800.6.f.b.49.4 | 20 | |||
20.7 | even | 4 | 800.6.f.c.49.17 | 20 | |||
20.19 | odd | 2 | 800.6.d.c.401.3 | 20 | |||
24.5 | odd | 2 | 360.6.k.b.181.5 | 20 | |||
40.3 | even | 4 | 800.6.f.c.49.18 | 20 | |||
40.13 | odd | 4 | 200.6.f.b.149.15 | 20 | |||
40.19 | odd | 2 | 800.6.d.c.401.18 | 20 | |||
40.27 | even | 4 | 800.6.f.b.49.3 | 20 | |||
40.29 | even | 2 | 200.6.d.b.101.5 | 20 | |||
40.37 | odd | 4 | 200.6.f.c.149.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.d.a.21.15 | ✓ | 20 | 1.1 | even | 1 | trivial | |
40.6.d.a.21.16 | yes | 20 | 8.5 | even | 2 | inner | |
160.6.d.a.81.3 | 20 | 8.3 | odd | 2 | |||
160.6.d.a.81.18 | 20 | 4.3 | odd | 2 | |||
200.6.d.b.101.5 | 20 | 40.29 | even | 2 | |||
200.6.d.b.101.6 | 20 | 5.4 | even | 2 | |||
200.6.f.b.149.15 | 20 | 40.13 | odd | 4 | |||
200.6.f.b.149.16 | 20 | 5.2 | odd | 4 | |||
200.6.f.c.149.5 | 20 | 5.3 | odd | 4 | |||
200.6.f.c.149.6 | 20 | 40.37 | odd | 4 | |||
360.6.k.b.181.5 | 20 | 24.5 | odd | 2 | |||
360.6.k.b.181.6 | 20 | 3.2 | odd | 2 | |||
800.6.d.c.401.3 | 20 | 20.19 | odd | 2 | |||
800.6.d.c.401.18 | 20 | 40.19 | odd | 2 | |||
800.6.f.b.49.3 | 20 | 40.27 | even | 4 | |||
800.6.f.b.49.4 | 20 | 20.3 | even | 4 | |||
800.6.f.c.49.17 | 20 | 20.7 | even | 4 | |||
800.6.f.c.49.18 | 20 | 40.3 | even | 4 |