Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,6,Mod(47,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.47");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.n (of order \(4\), degree \(2\), 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: | \(12.8307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + \cdots + 57\!\cdots\!24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{65}\cdot 3^{4}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 63.4 | ||
Root | \(5.50401 + 11.9953i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.63 |
Dual form | 80.6.n.d.47.4 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −7.48311 | + | 7.48311i | −0.480042 | + | 0.480042i | −0.905145 | − | 0.425103i | \(-0.860238\pi\) |
0.425103 | + | 0.905145i | \(0.360238\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 34.7301 | + | 43.8043i | 0.621271 | + | 0.783595i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −19.2260 | − | 19.2260i | −0.148301 | − | 0.148301i | 0.629058 | − | 0.777359i | \(-0.283441\pi\) |
−0.777359 | + | 0.629058i | \(0.783441\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 131.006i | 0.539120i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 180.642i | − | 0.450130i | −0.974344 | − | 0.225065i | \(-0.927741\pi\) | ||
0.974344 | − | 0.225065i | \(-0.0722594\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 44.2050 | + | 44.2050i | 0.0725459 | + | 0.0725459i | 0.742449 | − | 0.669903i | \(-0.233664\pi\) |
−0.669903 | + | 0.742449i | \(0.733664\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −587.682 | − | 67.9032i | −0.674395 | − | 0.0779224i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −621.037 | + | 621.037i | −0.521189 | + | 0.521189i | −0.917930 | − | 0.396742i | \(-0.870141\pi\) |
0.396742 | + | 0.917930i | \(0.370141\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2674.30 | −1.69952 | −0.849759 | − | 0.527172i | \(-0.823253\pi\) | ||||
−0.849759 | + | 0.527172i | \(0.823253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 287.741 | 0.142381 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2233.28 | + | 2233.28i | −0.880285 | + | 0.880285i | −0.993563 | − | 0.113278i | \(-0.963865\pi\) |
0.113278 | + | 0.993563i | \(0.463865\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −712.637 | + | 3042.66i | −0.228044 | + | 0.973651i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2798.73 | − | 2798.73i | −0.738842 | − | 0.738842i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 705.810i | 0.155845i | 0.996959 | + | 0.0779225i | \(0.0248287\pi\) | ||||
−0.996959 | + | 0.0779225i | \(0.975171\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2761.15i | − | 0.516043i | −0.966139 | − | 0.258021i | \(-0.916930\pi\) | ||
0.966139 | − | 0.258021i | \(-0.0830705\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1351.77 | + | 1351.77i | 0.216081 | + | 0.216081i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 174.460 | − | 1509.90i | 0.0240728 | − | 0.208343i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3542.51 | + | 3542.51i | −0.425409 | + | 0.425409i | −0.887061 | − | 0.461652i | \(-0.847257\pi\) |
0.461652 | + | 0.887061i | \(0.347257\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −661.582 | −0.0696502 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10907.4 | 1.01336 | 0.506679 | − | 0.862135i | \(-0.330873\pi\) | ||||
0.506679 | + | 0.862135i | \(0.330873\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5349.56 | + | 5349.56i | −0.441212 | + | 0.441212i | −0.892419 | − | 0.451207i | \(-0.850993\pi\) |
0.451207 | + | 0.892419i | \(0.350993\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5738.63 | + | 4549.86i | −0.422452 | + | 0.334940i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13279.7 | + | 13279.7i | 0.876884 | + | 0.876884i | 0.993211 | − | 0.116327i | \(-0.0371121\pi\) |
−0.116327 | + | 0.993211i | \(0.537112\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 16067.7i | − | 0.956014i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 9294.57i | − | 0.500385i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −15680.4 | − | 15680.4i | −0.766774 | − | 0.766774i | 0.210763 | − | 0.977537i | \(-0.432405\pi\) |
−0.977537 | + | 0.210763i | \(0.932405\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7912.91 | − | 6273.73i | 0.352719 | − | 0.279653i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 20012.1 | − | 20012.1i | 0.815840 | − | 0.815840i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 45931.3 | 1.71783 | 0.858913 | − | 0.512122i | \(-0.171140\pi\) | ||||
0.858913 | + | 0.512122i | \(0.171140\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17547.9 | −0.603809 | −0.301904 | − | 0.953338i | \(-0.597622\pi\) | ||||
−0.301904 | + | 0.953338i | \(0.597622\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2518.72 | − | 2518.72i | 0.0799519 | − | 0.0799519i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −401.125 | + | 3471.62i | −0.0117760 | + | 0.101917i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31089.0 | + | 31089.0i | 0.846097 | + | 0.846097i | 0.989644 | − | 0.143547i | \(-0.0458508\pi\) |
−0.143547 | + | 0.989644i | \(0.545851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 33423.8i | − | 0.845148i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10610.1i | − | 0.249788i | −0.992170 | − | 0.124894i | \(-0.960141\pi\) | ||
0.992170 | − | 0.124894i | \(-0.0398592\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 50962.5 | + | 50962.5i | 1.11929 | + | 1.11929i | 0.991845 | + | 0.127447i | \(0.0406783\pi\) |
0.127447 | + | 0.991845i | \(0.459322\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17435.8 | − | 28101.3i | −0.357923 | − | 0.576864i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3473.03 | + | 3473.03i | −0.0667546 | + | 0.0667546i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24770.6 | 0.446548 | 0.223274 | − | 0.974756i | \(-0.428326\pi\) | ||||
0.223274 | + | 0.974756i | \(0.428326\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10051.9 | 0.170231 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −48930.7 | + | 48930.7i | −0.779626 | + | 0.779626i | −0.979767 | − | 0.200141i | \(-0.935860\pi\) |
0.200141 | + | 0.979767i | \(0.435860\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −48772.8 | − | 5635.40i | −0.732200 | − | 0.0846014i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5281.66 | − | 5281.66i | −0.0748122 | − | 0.0748122i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 26108.1i | 0.349382i | 0.984623 | + | 0.174691i | \(0.0558926\pi\) | ||||
−0.984623 | + | 0.174691i | \(0.944107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1699.77i | − | 0.0215173i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20662.0 | + | 20662.0i | 0.247722 | + | 0.247722i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −92878.7 | − | 117146.i | −1.05586 | − | 1.33173i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39967.8 | − | 39967.8i | 0.431301 | − | 0.431301i | −0.457770 | − | 0.889071i | \(-0.651352\pi\) |
0.889071 | + | 0.457770i | \(0.151352\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23665.2 | 0.242674 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −196040. | −1.91223 | −0.956115 | − | 0.292991i | \(-0.905350\pi\) | ||||
−0.956115 | + | 0.292991i | \(0.905350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −148017. | + | 148017.i | −1.37473 | + | 1.37473i | −0.521450 | + | 0.853282i | \(0.674609\pi\) |
−0.853282 | + | 0.521450i | \(0.825391\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9993.27 | + | 12604.3i | 0.0884575 | + | 0.111569i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −40600.5 | − | 40600.5i | −0.342824 | − | 0.342824i | 0.514604 | − | 0.857428i | \(-0.327939\pi\) |
−0.857428 | + | 0.514604i | \(0.827939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 50412.1i | 0.406414i | 0.979136 | + | 0.203207i | \(0.0651364\pi\) | ||||
−0.979136 | + | 0.203207i | \(0.934864\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 53018.0i | − | 0.408428i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 152938. | + | 152938.i | 1.12673 | + | 1.12673i | 0.990706 | + | 0.136024i | \(0.0434323\pi\) |
0.136024 | + | 0.990706i | \(0.456568\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −175389. | − | 20265.2i | −1.23668 | − | 0.142891i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5791.12 | + | 5791.12i | −0.0391109 | + | 0.0391109i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 23880.1 | 0.154586 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 128419. | 0.797383 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −81621.6 | + | 81621.6i | −0.486455 | + | 0.486455i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −158032. | + | 74455.4i | −0.904625 | + | 0.426207i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 190114. | + | 190114.i | 1.04593 | + | 1.04593i | 0.998893 | + | 0.0470414i | \(0.0149793\pi\) |
0.0470414 | + | 0.998893i | \(0.485021\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 80062.7i | − | 0.423600i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 225175.i | − | 1.14641i | −0.819411 | − | 0.573207i | \(-0.805699\pi\) | ||
0.819411 | − | 0.573207i | \(-0.194301\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 51416.1 | + | 51416.1i | 0.252040 | + | 0.252040i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 25396.2 | − | 219797.i | 0.119932 | − | 1.03797i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 120197. | − | 120197.i | 0.547133 | − | 0.547133i | −0.378477 | − | 0.925611i | \(-0.623552\pi\) |
0.925611 | + | 0.378477i | \(0.123552\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 336335. | 1.47651 | 0.738253 | − | 0.674524i | \(-0.235651\pi\) | ||||
0.738253 | + | 0.674524i | \(0.235651\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −198746. | −0.841882 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7985.29 | − | 7985.29i | 0.0326551 | − | 0.0326551i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30917.5 | + | 24512.9i | −0.122119 | + | 0.0968221i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 120237. | + | 120237.i | 0.458927 | + | 0.458927i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 339978.i | − | 1.25454i | −0.778802 | − | 0.627270i | \(-0.784172\pi\) | ||
0.778802 | − | 0.627270i | \(-0.215828\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 224030.i | 0.799582i | 0.916606 | + | 0.399791i | \(0.130917\pi\) | ||||
−0.916606 | + | 0.399791i | \(0.869083\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −81359.5 | − | 81359.5i | −0.280983 | − | 0.280983i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 120950. | − | 95895.0i | 0.404369 | − | 0.320602i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 168847. | − | 168847.i | 0.546694 | − | 0.546694i | −0.378789 | − | 0.925483i | \(-0.623660\pi\) |
0.925483 | + | 0.378789i | \(0.123660\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 234676. | 0.736168 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 85874.1 | 0.261094 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −343693. | + | 343693.i | −1.01322 | + | 1.01322i | −0.0133036 | + | 0.999912i | \(0.504235\pi\) |
−0.999912 | + | 0.0133036i | \(0.995765\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12266.2 | + | 106160.i | −0.0350752 | + | 0.303565i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 220038. | + | 220038.i | 0.610529 | + | 0.610529i | 0.943084 | − | 0.332555i | \(-0.107911\pi\) |
−0.332555 | + | 0.943084i | \(0.607911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 367385.i | − | 0.989474i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 350349.i | − | 0.916243i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −103453. | − | 103453.i | −0.262802 | − | 0.262802i | 0.563389 | − | 0.826192i | \(-0.309497\pi\) |
−0.826192 | + | 0.563389i | \(0.809497\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 72199.3 | − | 44797.0i | 0.178212 | − | 0.110574i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −343709. | + | 343709.i | −0.824628 | + | 0.824628i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 377900. | 0.881544 | 0.440772 | − | 0.897619i | \(-0.354705\pi\) | ||||
0.440772 | + | 0.897619i | \(0.354705\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 583576. | 1.32404 | 0.662020 | − | 0.749486i | \(-0.269699\pi\) | ||||
0.662020 | + | 0.749486i | \(0.269699\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 131313. | − | 131313.i | 0.289854 | − | 0.289854i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −278209. | − | 32145.4i | −0.597643 | − | 0.0690541i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 112185. | + | 112185.i | 0.234602 | + | 0.234602i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 107617.i | 0.219142i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 368495.i | − | 0.730884i | −0.930834 | − | 0.365442i | \(-0.880918\pi\) | ||
0.930834 | − | 0.365442i | \(-0.119082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 169450. | + | 169450.i | 0.327453 | + | 0.327453i | 0.851617 | − | 0.524164i | \(-0.175622\pi\) |
−0.524164 | + | 0.851617i | \(0.675622\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −22976.8 | − | 28980.2i | −0.0432717 | − | 0.0545776i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 219866. | − | 219866.i | 0.403638 | − | 0.403638i | −0.475875 | − | 0.879513i | \(-0.657868\pi\) |
0.879513 | + | 0.475875i | \(0.157868\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −672141. | −1.20317 | −0.601586 | − | 0.798808i | \(-0.705464\pi\) | ||||
−0.601586 | + | 0.798808i | \(0.705464\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −465285. | −0.812324 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13569.9 | − | 13569.9i | 0.0231120 | − | 0.0231120i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 378817. | + | 477793.i | 0.629571 | + | 0.794063i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −292573. | − | 292573.i | −0.474579 | − | 0.474579i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 483091.i | 0.765003i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 594402.i | 0.919124i | 0.888146 | + | 0.459562i | \(0.151994\pi\) | ||||
−0.888146 | + | 0.459562i | \(0.848006\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 79396.4 | + | 79396.4i | 0.119909 | + | 0.119909i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −420125. | − | 48542.9i | −0.619844 | − | 0.0716193i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −53085.9 | + | 53085.9i | −0.0765296 | + | 0.0765296i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −762716. | −1.07461 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −54905.8 | −0.0756202 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −422559. | + | 422559.i | −0.569017 | + | 0.569017i | −0.931853 | − | 0.362836i | \(-0.881809\pi\) |
0.362836 | + | 0.931853i | \(0.381809\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −398607. | − | 93359.7i | −0.524914 | − | 0.122943i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −747586. | − | 747586.i | −0.962934 | − | 0.962934i | 0.0364031 | − | 0.999337i | \(-0.488410\pi\) |
−0.999337 | + | 0.0364031i | \(0.988410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 740343.i | 0.932920i | 0.884542 | + | 0.466460i | \(0.154471\pi\) | ||||
−0.884542 | + | 0.466460i | \(0.845529\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 51978.1i | − | 0.0640901i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −427262. | − | 427262.i | −0.515590 | − | 0.515590i | 0.400644 | − | 0.916234i | \(-0.368786\pi\) |
−0.916234 | + | 0.400644i | \(0.868786\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −120502. | + | 1.04291e6i | −0.142339 | + | 1.23190i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −185361. | + | 185361.i | −0.214362 | + | 0.214362i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −508899. | −0.576284 | −0.288142 | − | 0.957588i | \(-0.593038\pi\) | ||||
−0.288142 | + | 0.957588i | \(0.593038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5494.45 | 0.00609370 | 0.00304685 | − | 0.999995i | \(-0.499030\pi\) | ||||
0.00304685 | + | 0.999995i | \(0.499030\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 604871. | − | 604871.i | 0.657124 | − | 0.657124i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 703836. | − | 558034.i | 0.749128 | − | 0.593944i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −118217. | − | 118217.i | −0.123293 | − | 0.123293i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 732308.i | − | 0.748506i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 150381.i | − | 0.150664i | −0.997159 | − | 0.0753321i | \(-0.975998\pi\) | ||
0.997159 | − | 0.0753321i | \(-0.0240017\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 403424. | + | 403424.i | 0.396242 | + | 0.396242i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 407142. | − | 322802.i | 0.392099 | − | 0.310875i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.07319e6 | + | 1.07319e6i | −1.01355 | + | 1.01355i | −0.0136415 | + | 0.999907i | \(0.504342\pi\) |
−0.999907 | + | 0.0136415i | \(0.995658\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 136217. | 0.126177 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −92465.4 | −0.0840191 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.13111e6 | − | 1.13111e6i | 1.00836 | − | 1.00836i | 0.00839852 | − | 0.999965i | \(-0.497327\pi\) |
0.999965 | − | 0.00839852i | \(-0.00267336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 142287. | − | 1.23145e6i | 0.124466 | − | 1.07722i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −195370. | − | 195370.i | −0.167718 | − | 0.167718i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.59558e6i | 1.34443i | 0.740356 | + | 0.672216i | \(0.234657\pi\) | ||||
−0.740356 | + | 0.672216i | \(0.765343\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.05748e6i | 1.70182i | 0.525312 | + | 0.850910i | \(0.323949\pi\) | ||||
−0.525312 | + | 0.850910i | \(0.676051\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12719.6 | + | 12719.6i | 0.0103292 | + | 0.0103292i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 549633. | + | 128732.i | 0.438269 | + | 0.102649i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.50847e6 | − | 1.50847e6i | 1.18123 | − | 1.18123i | 0.201809 | − | 0.979425i | \(-0.435318\pi\) |
0.979425 | − | 0.201809i | \(-0.0646820\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 361727. | 0.278209 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −113566. | −0.0857993 | −0.0428997 | − | 0.999079i | \(-0.513660\pi\) | ||||
−0.0428997 | + | 0.999079i | \(0.513660\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 693960. | − | 693960.i | 0.515072 | − | 0.515072i | −0.401004 | − | 0.916076i | \(-0.631339\pi\) |
0.916076 | + | 0.401004i | \(0.131339\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.57164e6 | + | 181593.i | 1.14615 | + | 0.132430i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −209706. | − | 209706.i | −0.150282 | − | 0.150282i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 648484.i | 0.456725i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 598167.i | 0.414085i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.44248e6 | − | 1.44248e6i | −0.981616 | − | 0.981616i | 0.0182181 | − | 0.999834i | \(-0.494201\pi\) |
−0.999834 | + | 0.0182181i | \(0.994201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.59520e6 | + | 2.01199e6i | 1.06724 | + | 1.34608i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −505569. | + | 505569.i | −0.332575 | + | 0.332575i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −197444. | −0.127722 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 205701. | 0.130864 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.46699e6 | − | 1.46699e6i | 0.917951 | − | 0.917951i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −609439. | − | 768672.i | −0.375129 | − | 0.473142i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 415774. | + | 415774.i | 0.251774 | + | 0.251774i | 0.821698 | − | 0.569924i | \(-0.193027\pi\) |
−0.569924 | + | 0.821698i | \(0.693027\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2.21525e6i | − | 1.31986i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 722906.i | − | 0.423819i | −0.977289 | − | 0.211910i | \(-0.932032\pi\) | ||
0.977289 | − | 0.211910i | \(-0.0679683\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −768778. | − | 768778.i | −0.443547 | − | 0.443547i | 0.449655 | − | 0.893202i | \(-0.351547\pi\) |
−0.893202 | + | 0.449655i | \(0.851547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 197807. | + | 22855.4i | 0.112322 | + | 0.0129781i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 342207. | − | 342207.i | 0.191267 | − | 0.191267i | −0.604976 | − | 0.796244i | \(-0.706817\pi\) |
0.796244 | + | 0.604976i | \(0.206817\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 127499. | 0.0701505 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 607636. | 0.329140 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.66084e6 | − | 1.66084e6i | 0.885769 | − | 0.885769i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −166003. | + | 102999.i | −0.0871781 | + | 0.0540908i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −377239. | − | 377239.i | −0.195096 | − | 0.195096i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 510629.i | − | 0.260085i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 595925.i | 0.298966i | 0.988764 | + | 0.149483i | \(0.0477609\pi\) | ||||
−0.988764 | + | 0.149483i | \(0.952239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −464090. | − | 464090.i | −0.229346 | − | 0.229346i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −282108. | + | 2.44156e6i | −0.137342 | + | 1.18865i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.54112e6 | + | 1.54112e6i | −0.739199 | + | 0.739199i | −0.972423 | − | 0.233224i | \(-0.925072\pi\) |
0.233224 | + | 0.972423i | \(0.425072\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.28891e6 | −1.08175 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −498780. | −0.232286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −632050. | + | 632050.i | −0.290079 | + | 0.290079i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.46410e6 | − | 1.16081e6i | 0.662254 | − | 0.525066i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −334328. | − | 334328.i | −0.149056 | − | 0.149056i | 0.628640 | − | 0.777696i | \(-0.283612\pi\) |
−0.777696 | + | 0.628640i | \(0.783612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.55159e6i | 1.56084i | 0.625254 | + | 0.780422i | \(0.284995\pi\) | ||||
−0.625254 | + | 0.780422i | \(0.715005\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 247436.i | − | 0.107200i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 942189. | + | 942189.i | 0.402440 | + | 0.402440i | 0.879092 | − | 0.476652i | \(-0.158150\pi\) |
−0.476652 | + | 0.879092i | \(0.658150\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 464767. | − | 368489.i | 0.195733 | − | 0.155186i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −178698. | + | 178698.i | −0.0742075 | + | 0.0742075i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.75716e6 | −0.719575 | −0.359787 | − | 0.933034i | \(-0.617151\pi\) | ||||
−0.359787 | + | 0.933034i | \(0.617151\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.67577e6 | 1.88836 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −960977. | + | 960977.i | −0.382777 | + | 0.382777i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −462444. | + | 4.00231e6i | −0.181688 | + | 1.57246i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.33482e6 | − | 2.33482e6i | −0.904876 | − | 0.904876i | 0.0909771 | − | 0.995853i | \(-0.471001\pi\) |
−0.995853 | + | 0.0909771i | \(0.971001\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.42894e6i | 0.546321i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 602943.i | 0.227427i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.44665e6 | − | 2.44665e6i | −0.910542 | − | 0.910542i | 0.0857724 | − | 0.996315i | \(-0.472664\pi\) |
−0.996315 | + | 0.0857724i | \(0.972664\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 625410. | − | 1.73973e6i | 0.229661 | − | 0.638856i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −31200.4 | + | 31200.4i | −0.0113059 | + | 0.0113059i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.21109e6 | −0.790694 | −0.395347 | − | 0.918532i | \(-0.629376\pi\) | ||||
−0.395347 | + | 0.918532i | \(0.629376\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.84529e6 | −1.00418 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.12909e6 | + | 1.12909e6i | −0.393307 | + | 0.393307i | −0.875865 | − | 0.482557i | \(-0.839708\pi\) |
0.482557 | + | 0.875865i | \(0.339708\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −272752. | − | 31514.9i | −0.0937814 | − | 0.0108359i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −700825. | − | 700825.i | −0.237866 | − | 0.237866i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 501579.i | − | 0.168060i | −0.996463 | − | 0.0840302i | \(-0.973221\pi\) | ||
0.996463 | − | 0.0840302i | \(-0.0267792\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.77390e6i | − | 0.917589i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.68501e6 | + | 1.68501e6i | 0.550327 | + | 0.550327i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 860284. | + | 1.08506e6i | 0.277427 | + | 0.349913i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.04060e6 | + | 2.04060e6i | −0.649802 | + | 0.649802i | −0.952945 | − | 0.303143i | \(-0.901964\pi\) |
0.303143 | + | 0.952945i | \(0.401964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −769504. | −0.241980 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.62084e6 | 1.12447 | 0.562236 | − | 0.826977i | \(-0.309941\pi\) | ||||
0.562236 | + | 0.826977i | \(0.309941\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 122057. | − | 122057.i | 0.0374368 | − | 0.0374368i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 349105. | + | 440319.i | 0.105759 | + | 0.133392i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 639926. | + | 639926.i | 0.191489 | + | 0.191489i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.16692e6i | − | 1.23171i | −0.787861 | − | 0.615853i | \(-0.788811\pi\) | ||
0.787861 | − | 0.615853i | \(-0.211189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.79890e6i | 0.525294i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −883076. | − | 883076.i | −0.254755 | − | 0.254755i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.84275e6 | − | 444007.i | −1.09527 | − | 0.126552i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.51683e6 | + | 2.51683e6i | −0.708784 | + | 0.708784i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −256351. | −0.0713346 | −0.0356673 | − | 0.999364i | \(-0.511356\pi\) | ||||
−0.0356673 | + | 0.999364i | \(0.511356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.13509e6 | −1.41203 | −0.706013 | − | 0.708199i | \(-0.749508\pi\) | ||||
−0.706013 | + | 0.708199i | \(0.749508\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.73971e6 | + | 1.73971e6i | −0.472745 | + | 0.472745i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.44703e6 | − | 2.33218e6i | −0.388602 | − | 0.626309i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 337375. | + | 337375.i | 0.0895455 | + | 0.0895455i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 119510.i | 0.0313516i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 541018.i | − | 0.140287i | −0.997537 | − | 0.0701437i | \(-0.977654\pi\) | ||
0.997537 | − | 0.0701437i | \(-0.0223458\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.73118e6 | + | 3.73118e6i | 0.956372 | + | 0.956372i | 0.999087 | − | 0.0427150i | \(-0.0136007\pi\) |
−0.0427150 | + | 0.999087i | \(0.513601\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 47926.8 | − | 414792.i | 0.0121438 | − | 0.105101i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.97245e6 | − | 5.97245e6i | 1.49606 | − | 1.49606i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.37825e6 | 1.08427 | 0.542137 | − | 0.840290i | \(-0.317615\pi\) | ||||
0.542137 | + | 0.840290i | \(0.317615\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.10497e6 | 0.515406 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −880315. | + | 880315.i | −0.213122 | + | 0.213122i | −0.805592 | − | 0.592470i | \(-0.798153\pi\) |
0.592470 | + | 0.805592i | \(0.298153\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.14365e6 | + | 906738.i | −0.273774 | + | 0.217061i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.54409e6 | + | 2.54409e6i | 0.602232 | + | 0.602232i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.14012e6i | 0.266892i | 0.991056 | + | 0.133446i | \(0.0426042\pi\) | ||||
−0.991056 | + | 0.133446i | \(0.957396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.97034e6i | − | 0.456143i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.67644e6 | − | 1.67644e6i | −0.383833 | − | 0.383833i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 74457.3 | − | 59033.3i | 0.0168608 | − | 0.0133681i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.88319e6 | − | 1.88319e6i | 0.421796 | − | 0.421796i | −0.464025 | − | 0.885822i | \(-0.653595\pi\) |
0.885822 | + | 0.464025i | \(0.153595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.47623e6 | 0.770152 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.75143e6 | −0.822138 | −0.411069 | − | 0.911604i | \(-0.634845\pi\) | ||||
−0.411069 | + | 0.911604i | \(0.634845\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.38649e6 | − | 3.38649e6i | 0.734171 | − | 0.734171i | −0.237273 | − | 0.971443i | \(-0.576253\pi\) |
0.971443 | + | 0.237273i | \(0.0762534\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −187491. | + | 1.62268e6i | −0.0402113 | + | 0.348016i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.16438e6 | + | 5.16438e6i | 1.09579 | + | 1.09579i | 0.994898 | + | 0.100888i | \(0.0321685\pi\) |
0.100888 | + | 0.994898i | \(0.467832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.19544e6i | − | 0.250954i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.52700e6i | 0.524872i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 966356. | + | 966356.i | 0.198602 | + | 0.198602i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.90580e6 | − | 8.13698e6i | 0.387564 | − | 1.65474i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.05423e6 | − | 2.05423e6i | 0.413383 | − | 0.413383i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.72951e6 | 1.53926 | 0.769632 | − | 0.638488i | \(-0.220440\pi\) | ||||
0.769632 | + | 0.638488i | \(0.220440\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −313193. | −0.0617234 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −642605. | + | 642605.i | −0.125336 | + | 0.125336i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.13885e6 | + | 362675.i | 0.605921 | + | 0.0700106i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −237457. | − | 237457.i | −0.0453694 | − | 0.0453694i | 0.684058 | − | 0.729428i | \(-0.260213\pi\) |
−0.729428 | + | 0.684058i | \(0.760213\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5.14379e6i | − | 0.972771i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.99956e6i | − | 0.748701i | −0.927287 | − | 0.374350i | \(-0.877866\pi\) | ||
0.927287 | − | 0.374350i | \(-0.122134\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −438334. | − | 438334.i | −0.0812247 | − | 0.0812247i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 821896. | + | 1.03664e6i | 0.150766 | + | 0.190158i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −203989. | + | 203989.i | −0.0370439 | + | 0.0370439i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.58102e6 | 1.18316 | 0.591578 | − | 0.806248i | \(-0.298505\pi\) | ||||
0.591578 | + | 0.806248i | \(0.298505\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.29314e6 | −0.586159 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.79249e6 | + | 4.79249e6i | −0.844582 | + | 0.844582i | −0.989451 | − | 0.144869i | \(-0.953724\pi\) |
0.144869 | + | 0.989451i | \(0.453724\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.80848e6 | − | 8.58738e6i | −1.18801 | − | 1.49842i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.74918e6 | + | 2.74918e6i | 0.474989 | + | 0.474989i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.21148e6i | 0.720511i | 0.932854 | + | 0.360255i | \(0.117310\pi\) | ||||
−0.932854 | + | 0.360255i | \(0.882690\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.95961e6i | − | 0.331984i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.48464e6 | + | 7.48464e6i | 1.25567 | + | 1.25567i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.16244e7 | − | 1.34313e6i | −1.93132 | − | 0.223152i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.39887e6 | − | 2.39887e6i | 0.394711 | − | 0.394711i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.54831e6 | 0.252312 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 884172. | 0.142706 | 0.0713531 | − | 0.997451i | \(-0.477268\pi\) | ||||
0.0713531 | + | 0.997451i | \(0.477268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.86026e6 | + | 3.86026e6i | −0.617109 | + | 0.617109i | −0.944789 | − | 0.327680i | \(-0.893733\pi\) |
0.327680 | + | 0.944789i | \(0.393733\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −205055. | + | 875497.i | −0.0324692 | + | 0.138630i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.71477e6 | + | 1.71477e6i | 0.268955 | + | 0.268955i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 3.53873e6i | − | 0.549804i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.01728e6i | 0.926114i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 482163. | + | 482163.i | 0.0735150 | + | 0.0735150i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 368416. | − | 3.18854e6i | 0.0556486 | − | 0.481623i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.82787e6 | + | 2.82787e6i | −0.423178 | + | 0.423178i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.90251e6 | −0.430330 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.20713e6 | −0.618007 | −0.309003 | − | 0.951061i | \(-0.599995\pi\) | ||||
−0.309003 | + | 0.951061i | \(0.599995\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.36697e6 | + | 4.36697e6i | −0.635595 | + | 0.635595i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.20827e6 | + | 1.75082e6i | −0.318464 | + | 0.252493i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.13449e6 | − | 6.13449e6i | −0.876617 | − | 0.876617i | 0.116566 | − | 0.993183i | \(-0.462811\pi\) |
−0.993183 | + | 0.116566i | \(0.962811\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 2.29888e6i | − | 0.325525i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.88755e6i | − | 0.264861i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −476239. | − | 476239.i | −0.0662235 | − | 0.0662235i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.32242e6 | − | 1.84132e6i | 0.320042 | − | 0.253745i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.02695e6 | − | 3.02695e6i | 0.413397 | − | 0.413397i | −0.469523 | − | 0.882920i | \(-0.655574\pi\) |
0.882920 | + | 0.469523i | \(0.155574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −472955. | −0.0640162 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.67899e6 | −0.225238 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.91311e6 | + | 1.91311e6i | −0.254372 | + | 0.254372i | −0.822760 | − | 0.568388i | \(-0.807567\pi\) |
0.568388 | + | 0.822760i | \(0.307567\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.38779e6 | + | 1.20109e7i | −0.182895 | + | 1.58290i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −193259. | − | 193259.i | −0.0252454 | − | 0.0252454i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 399515.i | − | 0.0517311i | −0.999665 | − | 0.0258656i | \(-0.991766\pi\) | ||
0.999665 | − | 0.0258656i | \(-0.00823418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.17755e7i | − | 1.51143i | −0.654900 | − | 0.755716i | \(-0.727289\pi\) | ||
0.654900 | − | 0.755716i | \(-0.272711\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.75749e6 | + | 2.75749e6i | 0.350855 | + | 0.350855i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.20359e6 | − | 8.38662e6i | −0.656347 | − | 1.05783i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.88705e6 | + | 3.88705e6i | −0.486050 | + | 0.486050i | −0.907057 | − | 0.421007i | \(-0.861677\pi\) |
0.421007 | + | 0.907057i | \(0.361677\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.53603e6 | −0.314383 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.88148e6 | 0.231239 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.83254e6 | + | 2.83254e6i | −0.345148 | + | 0.345148i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −454803. | − | 52549.8i | −0.0549456 | − | 0.00634865i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.87317e6 | + | 4.87317e6i | 0.583735 | + | 0.583735i | 0.935928 | − | 0.352192i | \(-0.114564\pi\) |
−0.352192 | + | 0.935928i | \(0.614564\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.38413e6i | 0.877023i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.29056e6i | 0.387527i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.28474e6 | + | 2.28474e6i | 0.266808 | + | 0.266808i | 0.827813 | − | 0.561004i | \(-0.189585\pi\) |
−0.561004 | + | 0.827813i | \(0.689585\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 829359. | + | 1.04605e6i | 0.0960396 | + | 0.121133i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.02971e6 | − | 5.02971e6i | 0.577573 | − | 0.577573i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.01689e7 | −1.15799 | −0.578997 | − | 0.815330i | \(-0.696556\pi\) | ||||
−0.578997 | + | 0.815330i | \(0.696556\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.61358e6 | −0.182223 | −0.0911117 | − | 0.995841i | \(-0.529042\pi\) | ||||
−0.0911117 | + | 0.995841i | \(0.529042\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.07285e6 | + | 4.07285e6i | −0.456147 | + | 0.456147i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.46002e6 | + | 5.62532e6i | 0.495391 | + | 0.624826i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.14202e6 | − | 1.14202e6i | −0.125806 | − | 0.125806i | 0.641400 | − | 0.767206i | \(-0.278354\pi\) |
−0.767206 | + | 0.641400i | \(0.778354\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 203090.i | 0.0221894i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.17405e6i | 0.127229i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.44148e6 | + | 3.44148e6i | 0.369908 | + | 0.369908i | 0.867444 | − | 0.497536i | \(-0.165762\pi\) |
−0.497536 | + | 0.867444i | \(0.665762\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.41011e6 | − | 740650.i | −0.683404 | − | 0.0789633i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.50497e6 | + | 7.50497e6i | −0.793663 | + | 0.793663i | −0.982088 | − | 0.188425i | \(-0.939662\pi\) |
0.188425 | + | 0.982088i | \(0.439662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.89736e6 | 0.303931 | 0.151966 | − | 0.988386i | \(-0.451440\pi\) | ||||
0.151966 | + | 0.988386i | \(0.451440\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.25007e7 | 1.30078 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 501955. | − | 501955.i | 0.0518137 | − | 0.0518137i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.74992e6 | − | 4.33662e6i | −0.895992 | − | 0.444070i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.61502e6 | − | 3.61502e6i | −0.367234 | − | 0.367234i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.40005e6i | − | 0.443436i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.03301e7i | − | 1.03284i | −0.856336 | − | 0.516420i | \(-0.827264\pi\) | ||
0.856336 | − | 0.516420i | \(-0.172736\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.44798e6 | − | 4.44798e6i | −0.441218 | − | 0.441218i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.72513e6 | + | 1.49305e7i | −0.169780 | + | 1.46940i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 710274. | − | 710274.i | 0.0693549 | − | 0.0693549i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.38998e6 | 0.134666 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.35436e6 | −0.322452 | −0.161226 | − | 0.986918i | \(-0.551545\pi\) | ||||
−0.161226 | + | 0.986918i | \(0.551545\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −126819. | + | 126819.i | −0.0120964 | + | 0.0120964i | −0.713129 | − | 0.701033i | \(-0.752723\pi\) |
0.701033 | + | 0.713129i | \(0.252723\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.50709e6 | − | 2.78059e6i | 0.331931 | − | 0.263171i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.07986e7 | + | 1.07986e7i | 1.01416 | + | 1.01416i | 0.999898 | + | 0.0142641i | \(0.00454055\pi\) |
0.0142641 | + | 0.999898i | \(0.495459\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.29714e6i | − | 0.773244i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 794495.i | − | 0.0734748i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.57502e6 | − | 5.57502e6i | −0.511639 | − | 0.511639i | 0.403390 | − | 0.915028i | \(-0.367832\pi\) |
−0.915028 | + | 0.403390i | \(0.867832\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.86362e6 | − | 7.82034e6i | 0.898324 | − | 0.712234i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.67640e6 | + | 6.67640e6i | −0.603432 | + | 0.603432i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.37611e6 | 0.841026 | 0.420513 | − | 0.907287i | \(-0.361850\pi\) | ||||
0.420513 | + | 0.907287i | \(0.361850\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.43499e6 | −0.127746 | −0.0638729 | − | 0.997958i | \(-0.520345\pi\) | ||||
−0.0638729 | + | 0.997958i | \(0.520345\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 410867. | − | 410867.i | 0.0363009 | − | 0.0363009i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −466559. | + | 4.03793e6i | −0.0409122 | + | 0.354083i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.57627e6 | − | 1.57627e6i | −0.137188 | − | 0.137188i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 6.32411e6i | − | 0.546304i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.16988e6i | 0.271792i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.49219e7 | − | 1.49219e7i | −1.26995 | − | 1.26995i | −0.946114 | − | 0.323834i | \(-0.895028\pi\) |
−0.323834 | − | 0.946114i | \(-0.604972\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.05101e7 | − | 6.52110e6i | 0.887862 | − | 0.550886i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.54101e7 | − | 1.54101e7i | 1.29221 | − | 1.29221i | 0.358791 | − | 0.933418i | \(-0.383189\pi\) |
0.933418 | − | 0.358791i | \(-0.116811\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.53684e6 | −0.127925 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.11885e7 | 0.924497 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.68836e6 | − | 9.68836e6i | 0.794691 | − | 0.794691i | −0.187562 | − | 0.982253i | \(-0.560058\pi\) |
0.982253 | + | 0.187562i | \(0.0600584\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.43962e6 | + | 1.09069e6i | 0.768649 | + | 0.0888129i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.54007e6 | − | 5.54007e6i | −0.447841 | − | 0.447841i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.38630e6i | − | 0.111253i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.49923e7i | 1.19447i | 0.802068 | + | 0.597233i | \(0.203733\pi\) | ||||
−0.802068 | + | 0.597233i | \(0.796267\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −454988. | − | 454988.i | −0.0359887 | − | 0.0359887i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.16810e7 | + | 1.47329e7i | 0.917310 | + | 1.15698i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.77392e6 | + | 6.77392e6i | −0.528151 | + | 0.528151i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.39450e6 | 0.495010 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.06612e6 | −0.312525 | −0.156263 | − | 0.987716i | \(-0.549945\pi\) | ||||
−0.156263 | + | 0.987716i | \(0.549945\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.47372e6 | − | 9.47372e6i | 0.722990 | − | 0.722990i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.90248e6 | − | 8.70594e6i | −0.523037 | − | 0.659695i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.76906e6 | + | 3.76906e6i | 0.283586 | + | 0.283586i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.00306e7i | 0.749395i | 0.927147 | + | 0.374698i | \(0.122254\pi\) | ||||
−0.927147 | + | 0.374698i | \(0.877746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.24509e6i | 0.240743i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.16641e6 | + | 6.16641e6i | 0.454265 | + | 0.454265i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 627120. | + | 72460.0i | 0.0458760 | + | 0.00530070i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.80815e6 | − | 3.80815e6i | 0.276640 | − | 0.276640i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.83635e6 | −0.348895 | −0.174448 | − | 0.984666i | \(-0.555814\pi\) | ||||
−0.174448 | + | 0.984666i | \(0.555814\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.69154e6 | 0.407748 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −41115.6 | + | 41115.6i | −0.00292523 | + | 0.00292523i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.14754e6 | − | 502986.i | −0.151739 | − | 0.0355395i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.30692e6 | − | 2.30692e6i | −0.161881 | − | 0.161881i | 0.621519 | − | 0.783399i | \(-0.286516\pi\) |
−0.783399 | + | 0.621519i | \(0.786516\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.14953e7i | 0.801125i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 6.64454e6i | − | 0.459909i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.94419e6 | + | 5.94419e6i | 0.408632 | + | 0.408632i | 0.881261 | − | 0.472629i | \(-0.156695\pi\) |
−0.472629 | + | 0.881261i | \(0.656695\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.09105e6 | + | 9.44271e6i | −0.0744948 | + | 0.644731i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.61599e6 | − | 5.61599e6i | 0.380853 | − | 0.380853i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.19188e6 | 0.0802829 | 0.0401415 | − | 0.999194i | \(-0.487219\pi\) | ||||
0.0401415 | + | 0.999194i | \(0.487219\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.76927e6 | 0.118372 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.87097e7 | − | 1.87097e7i | 1.24336 | − | 1.24336i | 0.284758 | − | 0.958600i | \(-0.408087\pi\) |
0.958600 | − | 0.284758i | \(-0.0919132\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.48925e7 | − | 1.18075e7i | 0.983052 | − | 0.779410i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.41022e6 | − | 6.41022e6i | −0.420312 | − | 0.420312i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.56117e6i | 0.101682i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.35884e7i | 1.52615i | 0.646308 | + | 0.763076i | \(0.276312\pi\) | ||||
−0.646308 | + | 0.763076i | \(0.723688\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.12532e6 | + | 1.12532e6i | 0.0723251 | + | 0.0723251i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.81346e6 | + | 7.78058e6i | −0.626549 | + | 0.496757i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.08571e7 | + | 2.08571e7i | −1.32286 | + | 1.32286i | −0.411417 | + | 0.911447i | \(0.634966\pi\) |
−0.911447 | + | 0.411417i | \(0.865034\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.03774e6 | −0.380426 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.14245e7 | −0.715114 | −0.357557 | − | 0.933891i | \(-0.616390\pi\) | ||||
−0.357557 | + | 0.933891i | \(0.616390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 969223. | − | 969223.i | 0.0602716 | − | 0.0602716i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 738272. | − | 6.38953e6i | 0.0456103 | − | 0.394744i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.03040e6 | + | 2.03040e6i | 0.124621 | + | 0.124621i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.61255e7i | − | 0.983325i | −0.870786 | − | 0.491663i | \(-0.836389\pi\) | ||
0.870786 | − | 0.491663i | \(-0.163611\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 1.60616e7i | − | 0.973092i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.32344e7 | − | 1.32344e7i | −0.796630 | − | 0.796630i | 0.185933 | − | 0.982563i | \(-0.440469\pi\) |
−0.982563 | + | 0.185933i | \(0.940469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.40123e6 | + | 1.96770e6i | 0.502445 | + | 0.117680i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.01932e6 | + | 1.01932e6i | −0.0605703 | + | 0.0605703i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.91697e7 | −1.72222 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.91663e6 | −0.112437 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.97537e6 | − | 1.97537e6i | 0.115145 | − | 0.115145i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.32603e7 | + | 1.53215e6i | 0.768032 | + | 0.0887415i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.61771e7 | − | 1.61771e7i | −0.931032 | − | 0.931032i | 0.0667386 | − | 0.997770i | \(-0.478741\pi\) |
−0.997770 | + | 0.0667386i | \(0.978741\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.69285e7i | 0.968113i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.88078e6i | − | 0.334190i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −775703. | − | 775703.i | −0.0438039 | − | 0.0438039i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.15034e6 | + | 1.02798e7i | 0.457360 | + | 0.576858i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.99273e6 | + | 2.99273e6i | −0.166887 | + | 0.166887i | −0.785609 | − | 0.618723i | \(-0.787650\pi\) |
0.618723 | + | 0.785609i | \(0.287650\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.64943e7 | −0.914044 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.42032e6 | −0.188359 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.20598e6 | − | 9.20598e6i | 0.503827 | − | 0.503827i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.98242e6 | + | 3.76166e6i | 0.162210 | + | 0.204592i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.19399e7 | − | 1.19399e7i | −0.645383 | − | 0.645383i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.52391e7i | 1.89301i | 0.322683 | + | 0.946507i | \(0.395415\pi\) | ||||
−0.322683 | + | 0.946507i | \(0.604585\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.75053e7i | 1.46847i | 0.678897 | + | 0.734234i | \(0.262458\pi\) | ||||
−0.678897 | + | 0.734234i | \(0.737542\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.53964e7 | − | 1.53964e7i | −0.816945 | − | 0.816945i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.69917e7 | − | 3.11874e6i | −1.42343 | − | 0.164469i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.43063e7 | − | 1.43063e7i | 0.749847 | − | 0.749847i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 222680. | 0.0116004 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.95665e7 | −1.01311 | −0.506554 | − | 0.862208i | \(-0.669081\pi\) | ||||
−0.506554 | + | 0.862208i | \(0.669081\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.15110e7 | + | 1.15110e7i | −0.592399 | + | 0.592399i | −0.938279 | − | 0.345880i | \(-0.887580\pi\) |
0.345880 | + | 0.938279i | \(0.387580\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.07628e6 | + | 3.14965e6i | −0.259663 | + | 0.161112i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.12263e7 | − | 1.12263e7i | −0.570787 | − | 0.570787i | 0.361561 | − | 0.932348i | \(-0.382244\pi\) |
−0.932348 | + | 0.361561i | \(0.882244\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.81335e6i | 0.445405i | 0.974887 | + | 0.222702i | \(0.0714878\pi\) | ||||
−0.974887 | + | 0.222702i | \(0.928512\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.25760e7i | 1.13408i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.97864e6 | + | 9.97864e6i | 0.498263 | + | 0.498263i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.99667e6 | + | 1.72806e7i | −0.0991036 | + | 0.857713i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.72771e6 | + | 7.72771e6i | −0.381274 | + | 0.381274i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.32474e7 | −1.14017 | −0.570086 | − | 0.821585i | \(-0.693090\pi\) | ||||
−0.570086 | + | 0.821585i | \(0.693090\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00130e7 | 0.975712 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 849830. | − | 849830.i | 0.0411873 | − | 0.0411873i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.60930e7 | − | 1.27593e7i | 0.775347 | − | 0.614732i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.46899e6 | − | 2.46899e6i | −0.118253 | − | 0.118253i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.03860e7i | 0.494513i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.58228e7i | − | 0.748962i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.95949e7 | + | 1.95949e7i | 0.922085 | + | 0.922085i | 0.997177 | − | 0.0750917i | \(-0.0239249\pi\) |
−0.0750917 | + | 0.997177i | \(0.523925\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.53468e7 | − | 1.21677e7i | 0.717964 | − | 0.569236i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.52052e7 | + | 1.52052e7i | −0.707197 | + | 0.707197i | −0.965945 | − | 0.258748i | \(-0.916690\pi\) |
0.258748 | + | 0.965945i | \(0.416690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.55233e7 | −0.717795 | −0.358897 | − | 0.933377i | \(-0.616847\pi\) | ||||
−0.358897 | + | 0.933377i | \(0.616847\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.13851e6 | 0.144283 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.63784e7 | − | 1.63784e7i | 0.748590 | − | 0.748590i | −0.225624 | − | 0.974214i | \(-0.572442\pi\) |
0.974214 | + | 0.225624i | \(0.0724421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 938755. | − | 8.12465e6i | 0.0426591 | − | 0.369202i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.85268e6 | − | 4.85268e6i | −0.219247 | − | 0.219247i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.47461e6i | − | 0.201004i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.74858e6i | 0.122762i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.23602e6 | + | 5.23602e6i | 0.232523 | + | 0.232523i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.46980e6 | + | 1.60684e6i | 0.197364 | + | 0.0709499i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.76278e6 | + | 4.76278e6i | −0.209103 | + | 0.209103i | −0.803886 | − | 0.594783i | \(-0.797238\pi\) |
0.594783 | + | 0.803886i | \(0.297238\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.15885e7 | 0.942434 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.98884e6 | 0.433586 | 0.216793 | − | 0.976218i | \(-0.430440\pi\) | ||||
0.216793 | + | 0.976218i | \(0.430440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.37685e7 | − | 1.37685e7i | 0.594272 | − | 0.594272i | −0.344511 | − | 0.938782i | \(-0.611955\pi\) |
0.938782 | + | 0.344511i | \(0.111955\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.69930e7 | − | 3.11889e6i | −1.15849 | − | 0.133857i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.78096e6 | + | 1.78096e6i | 0.0760056 | + | 0.0760056i | 0.744088 | − | 0.668082i | \(-0.232884\pi\) |
−0.668082 | + | 0.744088i | \(0.732884\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.31026e6i | − | 0.310226i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.81581e6i | − | 0.0766258i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.55137e7 | − | 3.55137e7i | −1.49028 | − | 1.49028i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.31245e7 | + | 1.65536e7i | 0.547678 | + | 0.690774i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.47750e6 | − | 1.47750e6i | 0.0613120 | − | 0.0613120i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.94885e6 | 0.0804227 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.94762e7 | 0.799268 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.53929e6 | + | 1.53929e6i | −0.0628203 | + | 0.0628203i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.02677e7 | + | 2.55632e7i | 0.822588 | + | 1.03751i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.51162e7 | + | 1.51162e7i | 0.610134 | + | 0.610134i | 0.942981 | − | 0.332847i | \(-0.108009\pi\) |
−0.332847 | + | 0.942981i | \(0.608009\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.56824e7i | − | 1.03092i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.91576e7i | − | 1.56322i | −0.623767 | − | 0.781611i | \(-0.714398\pi\) | ||
0.623767 | − | 0.781611i | \(-0.285602\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.83895e6 | + | 8.83895e6i | 0.350933 | + | 0.350933i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.03126e7 | + | 1.19156e6i | 0.407206 | + | 0.0470502i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.32921e6 | + | 4.32921e6i | −0.170014 | + | 0.170014i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.39571e7 | 0.935720 | 0.467860 | − | 0.883803i | \(-0.345025\pi\) | ||||
0.467860 | + | 0.883803i | \(0.345025\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.22256e6 | −0.241724 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 469018. | − | 469018.i | 0.0181211 | − | 0.0181211i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.25412e6 | − | 1.33032e7i | −0.317188 | − | 0.511211i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.93911e7 | − | 1.93911e7i | −0.741145 | − | 0.741145i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 2.59769e7i | − | 0.987526i | −0.869597 | − | 0.493763i | \(-0.835621\pi\) | ||
0.869597 | − | 0.493763i | \(-0.164379\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.29699e7i | 1.62476i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.40959e6 | + | 5.40959e6i | 0.203451 | + | 0.203451i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.01799e6 | + | 8.81042e6i | −0.0380816 | + | 0.329585i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.66598e7 | − | 2.66598e7i | 0.991993 | − | 0.991993i | −0.00797527 | − | 0.999968i | \(-0.502539\pi\) |
0.999968 | + | 0.00797527i | \(0.00253863\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.15057e7 | 0.425843 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.69843e7 | −0.625280 | −0.312640 | − | 0.949872i | \(-0.601213\pi\) | ||||
−0.312640 | + | 0.949872i | \(0.601213\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.43594e7 | + | 2.43594e7i | −0.892045 | + | 0.892045i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.71408e6 | + | 3.73754e6i | −0.171719 | + | 0.136147i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.65542e7 | + | 3.65542e7i | 1.32453 | + | 1.32453i | 0.910063 | + | 0.414470i | \(0.136033\pi\) |
0.414470 | + | 0.910063i | \(0.363967\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.50560e6i | 0.162400i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.12155e6i | 0.183633i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.50021e7 | − | 3.50021e7i | −1.24842 | − | 1.24842i | −0.956416 | − | 0.292008i | \(-0.905677\pi\) |
−0.292008 | − | 0.956416i | \(-0.594323\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.61417e7 | − | 1.27979e7i | 0.572717 | − | 0.454077i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −954091. | + | 954091.i | −0.0336752 | + | 0.0336752i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.62183e6 | −0.162281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.10052e7 | 0.733700 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.31891e6 | − | 5.31891e6i | 0.184823 | − | 0.184823i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.53763e6 | + | 1.33077e7i | −0.0531535 | + | 0.460028i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.65238e6 | + | 6.65238e6i | 0.228776 | + | 0.228776i | 0.812181 | − | 0.583405i | \(-0.198280\pi\) |
−0.583405 | + | 0.812181i | \(0.698280\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.48565e7i | 0.850413i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.00433e7i | − | 0.682215i | −0.940024 | − | 0.341108i | \(-0.889198\pi\) | ||
0.940024 | − | 0.341108i | \(-0.110802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.46638e6 | − | 6.46638e6i | −0.218967 | − | 0.218967i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 471468. | − | 2.01297e6i | 0.0158833 | − | 0.0678150i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.48210e7 | − | 3.48210e7i | 1.16709 | − | 1.16709i | 0.184204 | − | 0.982888i | \(-0.441029\pi\) |
0.982888 | − | 0.184204i | \(-0.0589706\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.71623e6 | 0.157267 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.60429e6 | −0.219106 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.26938e7 | − | 2.26938e7i | 0.749073 | − | 0.749073i | −0.225232 | − | 0.974305i | \(-0.572314\pi\) |
0.974305 | + | 0.225232i | \(0.0723140\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.72670e7 | + | 1.99511e6i | 0.567058 | + | 0.0655202i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.82110e6 | + | 3.82110e6i | 0.124852 | + | 0.124852i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.38941e7i | − | 0.776784i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 7.33026e6i | − | 0.237102i | −0.992948 | − | 0.118551i | \(-0.962175\pi\) | ||
0.992948 | − | 0.118551i | \(-0.0378249\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.45938e6 | − | 4.45938e6i | −0.143516 | − | 0.143516i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.33435e7 | − | 2.94427e7i | −0.747496 | − | 0.942800i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.70672e7 | + | 3.70672e7i | −1.18101 | + | 1.18101i | −0.201521 | + | 0.979484i | \(0.564589\pi\) |
−0.979484 | + | 0.201521i | \(0.935411\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.98290e7 | 0.628620 |
(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 | 80.6.n.d.63.4 | yes | 20 | |
4.3 | odd | 2 | inner | 80.6.n.d.63.7 | yes | 20 | |
5.2 | odd | 4 | inner | 80.6.n.d.47.7 | yes | 20 | |
5.3 | odd | 4 | 400.6.n.g.207.4 | 20 | |||
5.4 | even | 2 | 400.6.n.g.143.7 | 20 | |||
20.3 | even | 4 | 400.6.n.g.207.7 | 20 | |||
20.7 | even | 4 | inner | 80.6.n.d.47.4 | ✓ | 20 | |
20.19 | odd | 2 | 400.6.n.g.143.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.n.d.47.4 | ✓ | 20 | 20.7 | even | 4 | inner | |
80.6.n.d.47.7 | yes | 20 | 5.2 | odd | 4 | inner | |
80.6.n.d.63.4 | yes | 20 | 1.1 | even | 1 | trivial | |
80.6.n.d.63.7 | yes | 20 | 4.3 | odd | 2 | inner | |
400.6.n.g.143.4 | 20 | 20.19 | odd | 2 | |||
400.6.n.g.143.7 | 20 | 5.4 | even | 2 | |||
400.6.n.g.207.4 | 20 | 5.3 | odd | 4 | |||
400.6.n.g.207.7 | 20 | 20.3 | even | 4 |