Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,4,Mod(64,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.64");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.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: | \(18.5856016518\) |
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: | \( x^{20} + 144 x^{18} + 8518 x^{16} + 269932 x^{14} + 5002289 x^{12} + 55478700 x^{10} + 361614704 x^{8} + \cdots + 603979776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{26}\cdot 5^{2}\cdot 7^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.13 | ||
Root | \(-3.18874i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.64 |
Dual form | 315.4.d.d.64.7 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.18874i | 0.773838i | 0.922114 | + | 0.386919i | \(0.126461\pi\) | ||||
−0.922114 | + | 0.386919i | \(0.873539\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.20940 | 0.401175 | ||||||||
\(5\) | −10.6651 | − | 3.35486i | −0.953918 | − | 0.300068i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.00000i | − | 0.377964i | ||||||
\(8\) | 24.5345i | 1.08428i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.34293 | − | 23.3432i | 0.232204 | − | 0.738178i | ||||
\(11\) | 38.2891 | 1.04951 | 0.524755 | − | 0.851253i | \(-0.324157\pi\) | ||||
0.524755 | + | 0.851253i | \(0.324157\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 30.6983i | − | 0.654937i | −0.944862 | − | 0.327468i | \(-0.893804\pi\) | ||
0.944862 | − | 0.327468i | \(-0.106196\pi\) | |||||||
\(14\) | 15.3212 | 0.292483 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −28.0246 | −0.437884 | ||||||||
\(17\) | 36.2007i | 0.516468i | 0.966082 | + | 0.258234i | \(0.0831405\pi\) | ||||
−0.966082 | + | 0.258234i | \(0.916860\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 63.7569 | 0.769833 | 0.384917 | − | 0.922951i | \(-0.374230\pi\) | ||||
0.384917 | + | 0.922951i | \(0.374230\pi\) | |||||||
\(20\) | −34.2286 | − | 10.7671i | −0.382688 | − | 0.120380i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 83.8051i | 0.812150i | ||||||||
\(23\) | 139.745i | 1.26691i | 0.773780 | + | 0.633454i | \(0.218363\pi\) | ||||
−0.773780 | + | 0.633454i | \(0.781637\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 102.490 | + | 71.5600i | 0.819919 | + | 0.572480i | ||||
\(26\) | 67.1908 | 0.506815 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 22.4658i | − | 0.151630i | ||||||
\(29\) | 17.9911 | 0.115202 | 0.0576011 | − | 0.998340i | \(-0.481655\pi\) | ||||
0.0576011 | + | 0.998340i | \(0.481655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 318.751 | 1.84675 | 0.923376 | − | 0.383898i | \(-0.125419\pi\) | ||||
0.923376 | + | 0.383898i | \(0.125419\pi\) | |||||||
\(32\) | 134.937i | 0.745431i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −79.2340 | −0.399662 | ||||||||
\(35\) | −23.4840 | + | 74.6559i | −0.113415 | + | 0.360547i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 144.735i | − | 0.643090i | −0.946894 | − | 0.321545i | \(-0.895798\pi\) | ||
0.946894 | − | 0.321545i | \(-0.104202\pi\) | |||||||
\(38\) | 139.548i | 0.595726i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 82.3098 | − | 261.664i | 0.325358 | − | 1.03432i | ||||
\(41\) | 96.6420 | 0.368121 | 0.184060 | − | 0.982915i | \(-0.441076\pi\) | ||||
0.184060 | + | 0.982915i | \(0.441076\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 306.949i | 1.08859i | 0.838895 | + | 0.544294i | \(0.183202\pi\) | ||||
−0.838895 | + | 0.544294i | \(0.816798\pi\) | |||||||
\(44\) | 122.885 | 0.421037 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −305.867 | −0.980382 | ||||||||
\(47\) | 105.633i | 0.327833i | 0.986474 | + | 0.163916i | \(0.0524127\pi\) | ||||
−0.986474 | + | 0.163916i | \(0.947587\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | −156.627 | + | 224.324i | −0.443007 | + | 0.634484i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 98.5231i | − | 0.262744i | ||||||
\(53\) | 188.729i | 0.489131i | 0.969633 | + | 0.244566i | \(0.0786454\pi\) | ||||
−0.969633 | + | 0.244566i | \(0.921355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −408.358 | − | 128.455i | −1.00115 | − | 0.314924i | ||||
\(56\) | 171.742 | 0.409820 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 39.3779i | 0.0891478i | ||||||||
\(59\) | 405.962 | 0.895793 | 0.447897 | − | 0.894085i | \(-0.352173\pi\) | ||||
0.447897 | + | 0.894085i | \(0.352173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −217.786 | −0.457126 | −0.228563 | − | 0.973529i | \(-0.573403\pi\) | ||||
−0.228563 | + | 0.973529i | \(0.573403\pi\) | |||||||
\(62\) | 697.663i | 1.42909i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −519.540 | −1.01473 | ||||||||
\(65\) | −102.989 | + | 327.401i | −0.196525 | + | 0.624756i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 729.073i | 1.32941i | 0.747106 | + | 0.664705i | \(0.231443\pi\) | ||||
−0.747106 | + | 0.664705i | \(0.768557\pi\) | |||||||
\(68\) | 116.182i | 0.207194i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −163.403 | − | 51.4005i | −0.279005 | − | 0.0877648i | ||||
\(71\) | −328.630 | −0.549312 | −0.274656 | − | 0.961543i | \(-0.588564\pi\) | ||||
−0.274656 | + | 0.961543i | \(0.588564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 546.064i | − | 0.875506i | −0.899095 | − | 0.437753i | \(-0.855774\pi\) | ||
0.899095 | − | 0.437753i | \(-0.144226\pi\) | |||||||
\(74\) | 316.788 | 0.497647 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 204.621 | 0.308838 | ||||||||
\(77\) | − | 268.024i | − | 0.396677i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 648.965 | 0.924231 | 0.462115 | − | 0.886820i | \(-0.347091\pi\) | ||||
0.462115 | + | 0.886820i | \(0.347091\pi\) | |||||||
\(80\) | 298.886 | + | 94.0186i | 0.417706 | + | 0.131395i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 211.525i | 0.284866i | ||||||||
\(83\) | − | 429.083i | − | 0.567445i | −0.958906 | − | 0.283723i | \(-0.908430\pi\) | ||
0.958906 | − | 0.283723i | \(-0.0915695\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 121.448 | − | 386.085i | 0.154975 | − | 0.492668i | ||||
\(86\) | −671.833 | −0.842390 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 939.405i | 1.13796i | ||||||||
\(89\) | 1108.25 | 1.31993 | 0.659967 | − | 0.751295i | \(-0.270570\pi\) | ||||
0.659967 | + | 0.751295i | \(0.270570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −214.888 | −0.247543 | ||||||||
\(92\) | 448.498i | 0.508251i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −231.203 | −0.253689 | ||||||||
\(95\) | −679.975 | − | 213.895i | −0.734358 | − | 0.231002i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 916.936i | − | 0.959801i | −0.877323 | − | 0.479901i | \(-0.840673\pi\) | ||
0.877323 | − | 0.479901i | \(-0.159327\pi\) | |||||||
\(98\) | − | 107.248i | − | 0.110548i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 328.931 | + | 229.665i | 0.328931 | + | 0.229665i | ||||
\(101\) | −1812.80 | −1.78594 | −0.892970 | − | 0.450115i | \(-0.851383\pi\) | ||||
−0.892970 | + | 0.450115i | \(0.851383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1681.12i | 1.60821i | 0.594490 | + | 0.804103i | \(0.297354\pi\) | ||||
−0.594490 | + | 0.804103i | \(0.702646\pi\) | |||||||
\(104\) | 753.168 | 0.710136 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −413.080 | −0.378508 | ||||||||
\(107\) | − | 1371.58i | − | 1.23921i | −0.784915 | − | 0.619604i | \(-0.787293\pi\) | ||
0.784915 | − | 0.619604i | \(-0.212707\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −56.5255 | −0.0496712 | −0.0248356 | − | 0.999692i | \(-0.507906\pi\) | ||||
−0.0248356 | + | 0.999692i | \(0.507906\pi\) | |||||||
\(110\) | 281.154 | − | 893.792i | 0.243700 | − | 0.774725i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 196.172i | 0.165505i | ||||||||
\(113\) | − | 250.725i | − | 0.208728i | −0.994539 | − | 0.104364i | \(-0.966719\pi\) | ||
0.994539 | − | 0.104364i | \(-0.0332806\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 468.826 | − | 1490.40i | 0.380158 | − | 1.20853i | ||||
\(116\) | 57.7406 | 0.0462162 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 888.548i | 0.693199i | ||||||||
\(119\) | 253.405 | 0.195206 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 135.057 | 0.101470 | ||||||||
\(122\) | − | 476.679i | − | 0.353742i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1023.00 | 0.740870 | ||||||||
\(125\) | −852.993 | − | 1107.04i | −0.610352 | − | 0.792130i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2133.33i | − | 1.49057i | −0.666744 | − | 0.745287i | \(-0.732313\pi\) | ||
0.666744 | − | 0.745287i | \(-0.267687\pi\) | |||||||
\(128\) | − | 57.6415i | − | 0.0398034i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −716.598 | − | 225.416i | −0.483460 | − | 0.152079i | ||||
\(131\) | 236.901 | 0.158001 | 0.0790005 | − | 0.996875i | \(-0.474827\pi\) | ||||
0.0790005 | + | 0.996875i | \(0.474827\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 446.298i | − | 0.290970i | ||||||
\(134\) | −1595.76 | −1.02875 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −888.165 | −0.559997 | ||||||||
\(137\) | − | 2607.45i | − | 1.62606i | −0.582225 | − | 0.813028i | \(-0.697818\pi\) | ||
0.582225 | − | 0.813028i | \(-0.302182\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 368.116 | 0.224627 | 0.112314 | − | 0.993673i | \(-0.464174\pi\) | ||||
0.112314 | + | 0.993673i | \(0.464174\pi\) | |||||||
\(140\) | −75.3696 | + | 239.600i | −0.0454992 | + | 0.144642i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 719.286i | − | 0.425078i | ||||||
\(143\) | − | 1175.41i | − | 0.687363i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −191.877 | − | 60.3576i | −0.109893 | − | 0.0345685i | ||||
\(146\) | 1195.19 | 0.677500 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 464.513i | − | 0.257991i | ||||||
\(149\) | 1458.55 | 0.801937 | 0.400969 | − | 0.916092i | \(-0.368674\pi\) | ||||
0.400969 | + | 0.916092i | \(0.368674\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3516.33 | 1.89506 | 0.947532 | − | 0.319662i | \(-0.103569\pi\) | ||||
0.947532 | + | 0.319662i | \(0.103569\pi\) | |||||||
\(152\) | 1564.24i | 0.834717i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 586.636 | 0.306964 | ||||||||
\(155\) | −3399.51 | − | 1069.36i | −1.76165 | − | 0.554151i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1339.74i | − | 0.681039i | −0.940237 | − | 0.340519i | \(-0.889397\pi\) | ||
0.940237 | − | 0.340519i | \(-0.110603\pi\) | |||||||
\(158\) | 1420.42i | 0.715205i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 452.696 | − | 1439.12i | 0.223680 | − | 0.711080i | ||||
\(161\) | 978.216 | 0.478846 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3850.14i | 1.85010i | 0.379843 | + | 0.925051i | \(0.375978\pi\) | ||||
−0.379843 | + | 0.925051i | \(0.624022\pi\) | |||||||
\(164\) | 310.163 | 0.147681 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 939.153 | 0.439111 | ||||||||
\(167\) | − | 2326.18i | − | 1.07788i | −0.842345 | − | 0.538939i | \(-0.818825\pi\) | ||
0.842345 | − | 0.538939i | \(-0.181175\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1254.61 | 0.571058 | ||||||||
\(170\) | 845.040 | + | 265.819i | 0.381245 | + | 0.119926i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 985.121i | 0.436714i | ||||||||
\(173\) | − | 3954.46i | − | 1.73787i | −0.494924 | − | 0.868936i | \(-0.664804\pi\) | ||
0.494924 | − | 0.868936i | \(-0.335196\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 500.920 | − | 717.429i | 0.216377 | − | 0.309900i | ||||
\(176\) | −1073.04 | −0.459564 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2425.67i | 1.02141i | ||||||||
\(179\) | −1784.17 | −0.744999 | −0.372500 | − | 0.928032i | \(-0.621499\pi\) | ||||
−0.372500 | + | 0.928032i | \(0.621499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1949.69 | −0.800658 | −0.400329 | − | 0.916372i | \(-0.631104\pi\) | ||||
−0.400329 | + | 0.916372i | \(0.631104\pi\) | |||||||
\(182\) | − | 470.335i | − | 0.191558i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3428.58 | −1.37369 | ||||||||
\(185\) | −485.566 | + | 1543.62i | −0.192971 | + | 0.613455i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1386.09i | 0.542038i | ||||||||
\(188\) | 339.018i | 0.131518i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 468.163 | − | 1488.29i | 0.178758 | − | 0.568274i | ||||
\(191\) | 1007.85 | 0.381810 | 0.190905 | − | 0.981609i | \(-0.438858\pi\) | ||||
0.190905 | + | 0.981609i | \(0.438858\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5188.46i | 1.93510i | 0.252686 | + | 0.967548i | \(0.418686\pi\) | ||||
−0.252686 | + | 0.967548i | \(0.581314\pi\) | |||||||
\(194\) | 2006.94 | 0.742731 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −157.260 | −0.0573107 | ||||||||
\(197\) | 3394.75i | 1.22774i | 0.789405 | + | 0.613872i | \(0.210389\pi\) | ||||
−0.789405 | + | 0.613872i | \(0.789611\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2916.06 | −1.03876 | −0.519381 | − | 0.854543i | \(-0.673837\pi\) | ||||
−0.519381 | + | 0.854543i | \(0.673837\pi\) | |||||||
\(200\) | −1755.69 | + | 2514.54i | −0.620730 | + | 0.889023i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3967.75i | − | 1.38203i | ||||||
\(203\) | − | 125.938i | − | 0.0435423i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1030.70 | − | 324.220i | −0.351157 | − | 0.110461i | ||||
\(206\) | −3679.53 | −1.24449 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 860.307i | 0.286786i | ||||||||
\(209\) | 2441.20 | 0.807948 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1129.68 | −0.368581 | −0.184290 | − | 0.982872i | \(-0.558999\pi\) | ||||
−0.184290 | + | 0.982872i | \(0.558999\pi\) | |||||||
\(212\) | 605.707i | 0.196227i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3002.03 | 0.958946 | ||||||||
\(215\) | 1029.77 | − | 3273.65i | 0.326650 | − | 1.03842i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2231.25i | − | 0.698006i | ||||||
\(218\) | − | 123.720i | − | 0.0384374i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1310.58 | − | 412.262i | −0.401634 | − | 0.126340i | ||||
\(221\) | 1111.30 | 0.338254 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 787.987i | − | 0.236626i | −0.992976 | − | 0.118313i | \(-0.962251\pi\) | ||
0.992976 | − | 0.118313i | \(-0.0377486\pi\) | |||||||
\(224\) | 944.562 | 0.281746 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 548.773 | 0.161521 | ||||||||
\(227\) | − | 879.537i | − | 0.257167i | −0.991699 | − | 0.128584i | \(-0.958957\pi\) | ||
0.991699 | − | 0.128584i | \(-0.0410430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4014.49 | −1.15845 | −0.579224 | − | 0.815168i | \(-0.696644\pi\) | ||||
−0.579224 | + | 0.815168i | \(0.696644\pi\) | |||||||
\(230\) | 3262.10 | + | 1026.14i | 0.935204 | + | 0.294181i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 441.403i | 0.124912i | ||||||||
\(233\) | − | 3092.44i | − | 0.869497i | −0.900552 | − | 0.434748i | \(-0.856837\pi\) | ||
0.900552 | − | 0.434748i | \(-0.143163\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 354.384 | − | 1126.59i | 0.0983721 | − | 0.312726i | ||||
\(236\) | 1302.89 | 0.359370 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 554.638i | 0.151058i | ||||||||
\(239\) | −6416.47 | −1.73660 | −0.868299 | − | 0.496042i | \(-0.834786\pi\) | ||||
−0.868299 | + | 0.496042i | \(0.834786\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −620.723 | −0.165910 | −0.0829550 | − | 0.996553i | \(-0.526436\pi\) | ||||
−0.0829550 | + | 0.996553i | \(0.526436\pi\) | |||||||
\(242\) | 295.606i | 0.0785217i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −698.963 | −0.183387 | ||||||||
\(245\) | 522.591 | + | 164.388i | 0.136274 | + | 0.0428668i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1957.23i | − | 0.504192i | ||||||
\(248\) | 7820.39i | 2.00240i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2423.02 | − | 1866.98i | 0.612981 | − | 0.472314i | ||||
\(251\) | 4672.65 | 1.17504 | 0.587520 | − | 0.809210i | \(-0.300104\pi\) | ||||
0.587520 | + | 0.809210i | \(0.300104\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5350.72i | 1.32963i | ||||||||
\(254\) | 4669.32 | 1.15346 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4030.16 | −0.983925 | ||||||||
\(257\) | 6778.08i | 1.64516i | 0.568653 | + | 0.822578i | \(0.307465\pi\) | ||||
−0.568653 | + | 0.822578i | \(0.692535\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1013.15 | −0.243065 | ||||||||
\(260\) | −330.531 | + | 1050.76i | −0.0788411 | + | 0.250636i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 518.515i | 0.122267i | ||||||||
\(263\) | 2624.42i | 0.615318i | 0.951497 | + | 0.307659i | \(0.0995456\pi\) | ||||
−0.951497 | + | 0.307659i | \(0.900454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 633.160 | − | 2012.82i | 0.146773 | − | 0.466591i | ||||
\(266\) | 976.833 | 0.225163 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2339.89i | 0.533326i | ||||||||
\(269\) | −6906.55 | −1.56543 | −0.782713 | − | 0.622383i | \(-0.786165\pi\) | ||||
−0.782713 | + | 0.622383i | \(0.786165\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3131.68 | −0.701978 | −0.350989 | − | 0.936380i | \(-0.614155\pi\) | ||||
−0.350989 | + | 0.936380i | \(0.614155\pi\) | |||||||
\(272\) | − | 1014.51i | − | 0.226153i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5707.04 | 1.25830 | ||||||||
\(275\) | 3924.25 | + | 2739.97i | 0.860512 | + | 0.600823i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2579.62i | − | 0.559547i | −0.960066 | − | 0.279774i | \(-0.909741\pi\) | ||
0.960066 | − | 0.279774i | \(-0.0902594\pi\) | |||||||
\(278\) | 805.712i | 0.173825i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1831.65 | − | 576.169i | −0.390935 | − | 0.122974i | ||||
\(281\) | −7511.13 | −1.59458 | −0.797289 | − | 0.603598i | \(-0.793733\pi\) | ||||
−0.797289 | + | 0.603598i | \(0.793733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3545.52i | 0.744732i | 0.928086 | + | 0.372366i | \(0.121453\pi\) | ||||
−0.928086 | + | 0.372366i | \(0.878547\pi\) | |||||||
\(284\) | −1054.70 | −0.220370 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2572.68 | 0.531907 | ||||||||
\(287\) | − | 676.494i | − | 0.139137i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3602.51 | 0.733261 | ||||||||
\(290\) | 132.107 | − | 419.970i | 0.0267504 | − | 0.0850397i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 1752.54i | − | 0.351231i | ||||||
\(293\) | 7116.99i | 1.41904i | 0.704685 | + | 0.709520i | \(0.251088\pi\) | ||||
−0.704685 | + | 0.709520i | \(0.748912\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4329.64 | − | 1361.95i | −0.854513 | − | 0.268799i | ||||
\(296\) | 3551.01 | 0.697291 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3192.38i | 0.620570i | ||||||||
\(299\) | 4289.94 | 0.829745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2148.64 | 0.411447 | ||||||||
\(302\) | 7696.34i | 1.46647i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1786.76 | −0.337098 | ||||||||
\(305\) | 2322.72 | + | 730.643i | 0.436061 | + | 0.137169i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3726.77i | 0.692827i | 0.938082 | + | 0.346414i | \(0.112601\pi\) | ||||
−0.938082 | + | 0.346414i | \(0.887399\pi\) | |||||||
\(308\) | − | 860.195i | − | 0.159137i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2340.56 | − | 7440.67i | 0.428823 | − | 1.36323i | ||||
\(311\) | −1064.23 | −0.194041 | −0.0970204 | − | 0.995282i | \(-0.530931\pi\) | ||||
−0.0970204 | + | 0.995282i | \(0.530931\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3090.63i | 0.558124i | 0.960273 | + | 0.279062i | \(0.0900235\pi\) | ||||
−0.960273 | + | 0.279062i | \(0.909976\pi\) | |||||||
\(314\) | 2932.35 | 0.527014 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2082.79 | 0.370778 | ||||||||
\(317\) | − | 2811.07i | − | 0.498061i | −0.968496 | − | 0.249031i | \(-0.919888\pi\) | ||
0.968496 | − | 0.249031i | \(-0.0801120\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 688.863 | 0.120906 | ||||||||
\(320\) | 5540.96 | + | 1742.98i | 0.967966 | + | 0.304487i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2141.07i | 0.370549i | ||||||||
\(323\) | 2308.04i | 0.397594i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2196.77 | − | 3146.26i | 0.374938 | − | 0.536995i | ||||
\(326\) | −8426.98 | −1.43168 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2371.06i | 0.399147i | ||||||||
\(329\) | 739.430 | 0.123909 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4666.48 | 0.774904 | 0.387452 | − | 0.921890i | \(-0.373355\pi\) | ||||
0.387452 | + | 0.921890i | \(0.373355\pi\) | |||||||
\(332\) | − | 1377.10i | − | 0.227645i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5091.42 | 0.834102 | ||||||||
\(335\) | 2445.94 | − | 7775.66i | 0.398913 | − | 1.26815i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 424.171i | − | 0.0685641i | −0.999412 | − | 0.0342820i | \(-0.989086\pi\) | ||
0.999412 | − | 0.0342820i | \(-0.0109144\pi\) | |||||||
\(338\) | 2746.03i | 0.441906i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 389.775 | − | 1239.10i | 0.0621722 | − | 0.197646i | ||||
\(341\) | 12204.7 | 1.93818 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | −7530.84 | −1.18034 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8655.30 | 1.34483 | ||||||||
\(347\) | 148.130i | 0.0229166i | 0.999934 | + | 0.0114583i | \(0.00364737\pi\) | ||||
−0.999934 | + | 0.0114583i | \(0.996353\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2551.08 | 0.391278 | 0.195639 | − | 0.980676i | \(-0.437322\pi\) | ||||
0.195639 | + | 0.980676i | \(0.437322\pi\) | |||||||
\(350\) | 1570.27 | + | 1096.39i | 0.239812 | + | 0.167441i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5166.63i | 0.782337i | ||||||||
\(353\) | 103.057i | 0.0155388i | 0.999970 | + | 0.00776938i | \(0.00247309\pi\) | ||||
−0.999970 | + | 0.00776938i | \(0.997527\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3504.88 | + | 1102.51i | 0.523998 | + | 0.164831i | ||||
\(356\) | 3556.81 | 0.529524 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3905.08i | − | 0.576509i | ||||||
\(359\) | −5888.89 | −0.865749 | −0.432874 | − | 0.901454i | \(-0.642501\pi\) | ||||
−0.432874 | + | 0.901454i | \(0.642501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2794.06 | −0.407357 | ||||||||
\(362\) | − | 4267.37i | − | 0.619580i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −689.662 | −0.0993079 | ||||||||
\(365\) | −1831.97 | + | 5823.84i | −0.262711 | + | 0.835161i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 7923.29i | − | 1.12696i | −0.826131 | − | 0.563478i | \(-0.809463\pi\) | ||
0.826131 | − | 0.563478i | \(-0.190537\pi\) | |||||||
\(368\) | − | 3916.30i | − | 0.554759i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3378.59 | − | 1062.78i | −0.474715 | − | 0.149328i | ||||
\(371\) | 1321.10 | 0.184874 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2276.35i | − | 0.315992i | −0.987440 | − | 0.157996i | \(-0.949497\pi\) | ||
0.987440 | − | 0.157996i | \(-0.0505034\pi\) | |||||||
\(374\) | −3033.80 | −0.419449 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2591.65 | −0.355463 | ||||||||
\(377\) | − | 552.296i | − | 0.0754501i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5754.55 | −0.779925 | −0.389963 | − | 0.920831i | \(-0.627512\pi\) | ||||
−0.389963 | + | 0.920831i | \(0.627512\pi\) | |||||||
\(380\) | −2182.31 | − | 686.476i | −0.294606 | − | 0.0926723i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2205.93i | 0.295459i | ||||||||
\(383\) | − | 7706.66i | − | 1.02818i | −0.857737 | − | 0.514089i | \(-0.828130\pi\) | ||
0.857737 | − | 0.514089i | \(-0.171870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −899.183 | + | 2858.51i | −0.119030 | + | 0.378398i | ||||
\(386\) | −11356.2 | −1.49745 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 2942.81i | − | 0.385048i | ||||||
\(389\) | −7109.10 | −0.926596 | −0.463298 | − | 0.886203i | \(-0.653334\pi\) | ||||
−0.463298 | + | 0.886203i | \(0.653334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5058.87 | −0.654317 | ||||||||
\(392\) | − | 1202.19i | − | 0.154897i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7430.23 | −0.950076 | ||||||||
\(395\) | −6921.29 | − | 2177.19i | −0.881640 | − | 0.277332i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10541.5i | − | 1.33266i | −0.745659 | − | 0.666328i | \(-0.767865\pi\) | ||
0.745659 | − | 0.666328i | \(-0.232135\pi\) | |||||||
\(398\) | − | 6382.50i | − | 0.803834i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2872.23 | − | 2005.44i | −0.359029 | − | 0.250680i | ||||
\(401\) | 12793.4 | 1.59320 | 0.796599 | − | 0.604509i | \(-0.206631\pi\) | ||||
0.796599 | + | 0.604509i | \(0.206631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 9785.10i | − | 1.20951i | ||||||
\(404\) | −5817.99 | −0.716474 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 275.645 | 0.0336947 | ||||||||
\(407\) | − | 5541.79i | − | 0.674929i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4187.96 | 0.506311 | 0.253156 | − | 0.967426i | \(-0.418531\pi\) | ||||
0.253156 | + | 0.967426i | \(0.418531\pi\) | |||||||
\(410\) | 709.636 | − | 2255.94i | 0.0854790 | − | 0.271739i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5395.37i | 0.645172i | ||||||||
\(413\) | − | 2841.74i | − | 0.338578i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1439.51 | + | 4576.22i | −0.170272 | + | 0.541296i | ||||
\(416\) | 4142.35 | 0.488210 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5343.15i | 0.625221i | ||||||||
\(419\) | 1165.65 | 0.135909 | 0.0679546 | − | 0.997688i | \(-0.478353\pi\) | ||||
0.0679546 | + | 0.997688i | \(0.478353\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9835.71 | −1.13863 | −0.569315 | − | 0.822120i | \(-0.692791\pi\) | ||||
−0.569315 | + | 0.822120i | \(0.692791\pi\) | |||||||
\(422\) | − | 2472.59i | − | 0.285222i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4630.38 | −0.530356 | ||||||||
\(425\) | −2590.52 | + | 3710.20i | −0.295667 | + | 0.423461i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1524.50i | 0.172777i | ||||||||
\(428\) | − | 4401.93i | − | 0.497139i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7165.18 | + | 2253.90i | 0.803571 | + | 0.252774i | ||||
\(431\) | 5897.82 | 0.659137 | 0.329568 | − | 0.944132i | \(-0.393097\pi\) | ||||
0.329568 | + | 0.944132i | \(0.393097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15493.7i | 1.71958i | 0.510649 | + | 0.859790i | \(0.329405\pi\) | ||||
−0.510649 | + | 0.859790i | \(0.670595\pi\) | |||||||
\(434\) | 4883.64 | 0.540144 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −181.413 | −0.0199268 | ||||||||
\(437\) | 8909.72i | 0.975308i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1649.59 | 0.179341 | 0.0896705 | − | 0.995971i | \(-0.471419\pi\) | ||||
0.0896705 | + | 0.995971i | \(0.471419\pi\) | |||||||
\(440\) | 3151.57 | − | 10018.9i | 0.341467 | − | 1.08552i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2432.35i | 0.261754i | ||||||||
\(443\) | − | 14931.4i | − | 1.60138i | −0.599078 | − | 0.800691i | \(-0.704466\pi\) | ||
0.599078 | − | 0.800691i | \(-0.295534\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11819.6 | − | 3718.02i | −1.25911 | − | 0.396070i | ||||
\(446\) | 1724.70 | 0.183110 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3636.78i | 0.383531i | ||||||||
\(449\) | −11883.4 | −1.24903 | −0.624514 | − | 0.781014i | \(-0.714703\pi\) | ||||
−0.624514 | + | 0.781014i | \(0.714703\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3700.34 | 0.386346 | ||||||||
\(452\) | − | 804.676i | − | 0.0837363i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1925.08 | 0.199006 | ||||||||
\(455\) | 2291.81 | + | 720.920i | 0.236136 | + | 0.0742797i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4953.25i | 0.507010i | 0.967334 | + | 0.253505i | \(0.0815834\pi\) | ||||
−0.967334 | + | 0.253505i | \(0.918417\pi\) | |||||||
\(458\) | − | 8786.68i | − | 0.896451i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1504.65 | − | 4783.29i | 0.152510 | − | 0.484830i | ||||
\(461\) | 793.410 | 0.0801579 | 0.0400789 | − | 0.999197i | \(-0.487239\pi\) | ||||
0.0400789 | + | 0.999197i | \(0.487239\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10841.0i | 1.08817i | 0.839029 | + | 0.544087i | \(0.183124\pi\) | ||||
−0.839029 | + | 0.544087i | \(0.816876\pi\) | |||||||
\(464\) | −504.193 | −0.0504452 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6768.57 | 0.672849 | ||||||||
\(467\) | − | 16996.8i | − | 1.68420i | −0.539323 | − | 0.842099i | \(-0.681320\pi\) | ||
0.539323 | − | 0.842099i | \(-0.318680\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5103.51 | 0.502470 | ||||||||
\(470\) | 2465.81 | + | 775.655i | 0.241999 | + | 0.0761241i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9960.09i | 0.971293i | ||||||||
\(473\) | 11752.8i | 1.14248i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6534.43 | + | 4562.44i | 0.631201 | + | 0.440714i | ||||
\(476\) | 813.276 | 0.0783119 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 14044.0i | − | 1.34385i | ||||||
\(479\) | −12747.3 | −1.21595 | −0.607975 | − | 0.793956i | \(-0.708018\pi\) | ||||
−0.607975 | + | 0.793956i | \(0.708018\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4443.13 | −0.421183 | ||||||||
\(482\) | − | 1358.60i | − | 0.128387i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 433.452 | 0.0407074 | ||||||||
\(485\) | −3076.19 | + | 9779.24i | −0.288006 | + | 0.915572i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 18646.9i | − | 1.73505i | −0.497389 | − | 0.867527i | \(-0.665708\pi\) | ||
0.497389 | − | 0.867527i | \(-0.334292\pi\) | |||||||
\(488\) | − | 5343.28i | − | 0.495654i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −359.804 | + | 1143.82i | −0.0331720 | + | 0.105454i | ||||
\(491\) | −14156.9 | −1.30120 | −0.650601 | − | 0.759420i | \(-0.725483\pi\) | ||||
−0.650601 | + | 0.759420i | \(0.725483\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 651.289i | 0.0594982i | ||||||||
\(494\) | 4283.87 | 0.390163 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8932.85 | −0.808663 | ||||||||
\(497\) | 2300.41i | 0.207620i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4907.11 | −0.440225 | −0.220112 | − | 0.975475i | \(-0.570642\pi\) | ||||
−0.220112 | + | 0.975475i | \(0.570642\pi\) | |||||||
\(500\) | −2737.59 | − | 3552.92i | −0.244858 | − | 0.317783i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10227.2i | 0.909290i | ||||||||
\(503\) | 18597.4i | 1.64854i | 0.566193 | + | 0.824272i | \(0.308416\pi\) | ||||
−0.566193 | + | 0.824272i | \(0.691584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19333.7 | + | 6081.68i | 1.70364 | + | 0.535903i | ||||
\(506\) | −11711.4 | −1.02892 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 6846.72i | − | 0.597980i | ||||||
\(509\) | 17426.9 | 1.51755 | 0.758776 | − | 0.651351i | \(-0.225797\pi\) | ||||
0.758776 | + | 0.651351i | \(0.225797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3822.45 | −0.330910 | ||||||||
\(512\) | − | 9282.12i | − | 0.801202i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14835.5 | −1.27308 | ||||||||
\(515\) | 5639.91 | − | 17929.3i | 0.482571 | − | 1.53410i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4044.59i | 0.344064i | ||||||||
\(518\) | − | 2217.52i | − | 0.188093i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8032.63 | − | 2526.77i | −0.677412 | − | 0.213089i | ||||
\(521\) | 10927.3 | 0.918871 | 0.459435 | − | 0.888211i | \(-0.348052\pi\) | ||||
0.459435 | + | 0.888211i | \(0.348052\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18458.9i | − | 1.54331i | −0.636041 | − | 0.771656i | \(-0.719429\pi\) | ||
0.636041 | − | 0.771656i | \(-0.280571\pi\) | |||||||
\(524\) | 760.309 | 0.0633860 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5744.18 | −0.476156 | ||||||||
\(527\) | 11539.0i | 0.953787i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7361.72 | −0.605056 | ||||||||
\(530\) | 4405.55 | + | 1385.83i | 0.361066 | + | 0.113578i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 1432.35i | − | 0.116730i | ||||||
\(533\) | − | 2966.75i | − | 0.241096i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4601.44 | + | 14628.0i | −0.371846 | + | 1.18210i | ||||
\(536\) | −17887.5 | −1.44146 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 15116.7i | − | 1.21139i | ||||||
\(539\) | −1876.17 | −0.149930 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13142.8 | 1.04446 | 0.522228 | − | 0.852806i | \(-0.325101\pi\) | ||||
0.522228 | + | 0.852806i | \(0.325101\pi\) | |||||||
\(542\) | − | 6854.45i | − | 0.543217i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4884.82 | −0.384991 | ||||||||
\(545\) | 602.851 | + | 189.635i | 0.0473822 | + | 0.0149047i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6339.05i | 0.495500i | 0.968824 | + | 0.247750i | \(0.0796911\pi\) | ||||
−0.968824 | + | 0.247750i | \(0.920309\pi\) | |||||||
\(548\) | − | 8368.35i | − | 0.652332i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5997.10 | + | 8589.17i | −0.464940 | + | 0.665897i | ||||
\(551\) | 1147.06 | 0.0886864 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4542.75i | − | 0.349326i | ||||||
\(554\) | 5646.14 | 0.432999 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1181.43 | 0.0901148 | ||||||||
\(557\) | 4748.24i | 0.361202i | 0.983556 | + | 0.180601i | \(0.0578042\pi\) | ||||
−0.983556 | + | 0.180601i | \(0.942196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9422.81 | 0.712956 | ||||||||
\(560\) | 658.130 | − | 2092.20i | 0.0496626 | − | 0.157878i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 16439.9i | − | 1.23395i | ||||||
\(563\) | 13228.5i | 0.990257i | 0.868820 | + | 0.495129i | \(0.164879\pi\) | ||||
−0.868820 | + | 0.495129i | \(0.835121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −841.147 | + | 2674.01i | −0.0626325 | + | 0.199109i | ||||
\(566\) | −7760.23 | −0.576302 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 8062.76i | − | 0.595609i | ||||||
\(569\) | 6807.04 | 0.501522 | 0.250761 | − | 0.968049i | \(-0.419319\pi\) | ||||
0.250761 | + | 0.968049i | \(0.419319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18517.5 | 1.35715 | 0.678575 | − | 0.734531i | \(-0.262598\pi\) | ||||
0.678575 | + | 0.734531i | \(0.262598\pi\) | |||||||
\(572\) | − | 3772.36i | − | 0.275752i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1480.67 | 0.107669 | ||||||||
\(575\) | −10000.2 | + | 14322.5i | −0.725280 | + | 1.03876i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3712.63i | 0.267867i | 0.990990 | + | 0.133933i | \(0.0427608\pi\) | ||||
−0.990990 | + | 0.133933i | \(0.957239\pi\) | |||||||
\(578\) | 7884.98i | 0.567425i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −615.810 | − | 193.712i | −0.0440864 | − | 0.0138680i | ||||
\(581\) | −3003.58 | −0.214474 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7226.28i | 0.513348i | ||||||||
\(584\) | 13397.4 | 0.949296 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15577.3 | −1.09811 | ||||||||
\(587\) | − | 17691.3i | − | 1.24395i | −0.783038 | − | 0.621974i | \(-0.786331\pi\) | ||
0.783038 | − | 0.621974i | \(-0.213669\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20322.5 | 1.42169 | ||||||||
\(590\) | 2980.95 | − | 9476.48i | 0.208007 | − | 0.661255i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4056.14i | 0.281599i | ||||||||
\(593\) | 12475.0i | 0.863891i | 0.901900 | + | 0.431945i | \(0.142173\pi\) | ||||
−0.901900 | + | 0.431945i | \(0.857827\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2702.59 | − | 850.137i | −0.186211 | − | 0.0585752i | ||||
\(596\) | 4681.05 | 0.321717 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9389.58i | 0.642088i | ||||||||
\(599\) | 13912.8 | 0.949019 | 0.474510 | − | 0.880250i | \(-0.342625\pi\) | ||||
0.474510 | + | 0.880250i | \(0.342625\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14295.7 | 0.970274 | 0.485137 | − | 0.874438i | \(-0.338770\pi\) | ||||
0.485137 | + | 0.874438i | \(0.338770\pi\) | |||||||
\(602\) | 4702.83i | 0.318394i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11285.3 | 0.760252 | ||||||||
\(605\) | −1440.40 | − | 453.098i | −0.0967944 | − | 0.0304480i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 16170.6i | − | 1.08129i | −0.841251 | − | 0.540645i | \(-0.818180\pi\) | ||
0.841251 | − | 0.540645i | \(-0.181820\pi\) | |||||||
\(608\) | 8603.19i | 0.573858i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1599.19 | + | 5083.84i | −0.106146 | + | 0.337440i | ||||
\(611\) | 3242.75 | 0.214710 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 15820.7i | − | 1.04240i | −0.853435 | − | 0.521199i | \(-0.825485\pi\) | ||
0.853435 | − | 0.521199i | \(-0.174515\pi\) | |||||||
\(614\) | −8156.95 | −0.536136 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6575.83 | 0.430110 | ||||||||
\(617\) | 23613.4i | 1.54074i | 0.637594 | + | 0.770372i | \(0.279930\pi\) | ||||
−0.637594 | + | 0.770372i | \(0.720070\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7803.97 | −0.506734 | −0.253367 | − | 0.967370i | \(-0.581538\pi\) | ||||
−0.253367 | + | 0.967370i | \(0.581538\pi\) | |||||||
\(620\) | −10910.4 | − | 3432.01i | −0.706729 | − | 0.222311i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 2329.32i | − | 0.150156i | ||||||
\(623\) | − | 7757.74i | − | 0.498888i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5383.33 | + | 14668.3i | 0.344533 | + | 0.938774i | ||||
\(626\) | −6764.61 | −0.431898 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 4299.77i | − | 0.273216i | ||||||
\(629\) | 5239.51 | 0.332135 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11637.0 | 0.734170 | 0.367085 | − | 0.930187i | \(-0.380356\pi\) | ||||
0.367085 | + | 0.930187i | \(0.380356\pi\) | |||||||
\(632\) | 15922.0i | 1.00213i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6152.71 | 0.385419 | ||||||||
\(635\) | −7157.04 | + | 22752.3i | −0.447273 | + | 1.42188i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1504.22i | 0.0935624i | ||||||||
\(638\) | 1507.75i | 0.0935615i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −193.379 | + | 614.754i | −0.0119437 | + | 0.0379692i | ||||
\(641\) | 12956.9 | 0.798388 | 0.399194 | − | 0.916867i | \(-0.369290\pi\) | ||||
0.399194 | + | 0.916867i | \(0.369290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 18828.6i | − | 1.15478i | −0.816467 | − | 0.577392i | \(-0.804071\pi\) | ||
0.816467 | − | 0.577392i | \(-0.195929\pi\) | |||||||
\(644\) | 3139.48 | 0.192101 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5051.71 | −0.307673 | ||||||||
\(647\) | 9779.98i | 0.594267i | 0.954836 | + | 0.297133i | \(0.0960306\pi\) | ||||
−0.954836 | + | 0.297133i | \(0.903969\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15543.9 | 0.940144 | ||||||||
\(650\) | 6886.37 | + | 4808.17i | 0.415547 | + | 0.290142i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12356.6i | 0.742214i | ||||||||
\(653\) | − | 113.220i | − | 0.00678508i | −0.999994 | − | 0.00339254i | \(-0.998920\pi\) | ||
0.999994 | − | 0.00339254i | \(-0.00107988\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2526.58 | − | 794.769i | −0.150720 | − | 0.0474110i | ||||
\(656\) | −2708.35 | −0.161194 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1618.42i | 0.0958856i | ||||||||
\(659\) | 21374.6 | 1.26349 | 0.631743 | − | 0.775178i | \(-0.282340\pi\) | ||||
0.631743 | + | 0.775178i | \(0.282340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2246.72 | −0.132204 | −0.0661022 | − | 0.997813i | \(-0.521056\pi\) | ||||
−0.0661022 | + | 0.997813i | \(0.521056\pi\) | |||||||
\(662\) | 10213.7i | 0.599650i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10527.3 | 0.615271 | ||||||||
\(665\) | −1497.27 | + | 4759.83i | −0.0873106 | + | 0.277561i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2514.17i | 0.145951i | ||||||||
\(668\) | − | 7465.65i | − | 0.432417i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17018.9 | + | 5353.54i | 0.981341 | + | 0.308694i | ||||
\(671\) | −8338.85 | −0.479758 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15724.1i | − | 0.900624i | −0.892871 | − | 0.450312i | \(-0.851313\pi\) | ||
0.892871 | − | 0.450312i | \(-0.148687\pi\) | |||||||
\(674\) | 928.403 | 0.0530575 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4026.55 | 0.229094 | ||||||||
\(677\) | 14211.8i | 0.806799i | 0.915024 | + | 0.403400i | \(0.132172\pi\) | ||||
−0.915024 | + | 0.403400i | \(0.867828\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6418.55 | −0.362771 | ||||||||
\(680\) | 9472.39 | + | 2979.67i | 0.534191 | + | 0.168037i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26712.9i | 1.49984i | ||||||||
\(683\) | − | 1053.56i | − | 0.0590239i | −0.999564 | − | 0.0295119i | \(-0.990605\pi\) | ||
0.999564 | − | 0.0295119i | \(-0.00939531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8747.63 | + | 27808.8i | −0.487927 | + | 1.55112i | ||||
\(686\) | −750.739 | −0.0417833 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 8602.11i | − | 0.476675i | ||||||
\(689\) | 5793.67 | 0.320350 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36212.8 | −1.99363 | −0.996815 | − | 0.0797508i | \(-0.974588\pi\) | ||||
−0.996815 | + | 0.0797508i | \(0.974588\pi\) | |||||||
\(692\) | − | 12691.4i | − | 0.697191i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −324.219 | −0.0177337 | ||||||||
\(695\) | −3926.00 | − | 1234.98i | −0.214276 | − | 0.0674034i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3498.50i | 0.190122i | ||||||||
\(698\) | 5583.66i | 0.302786i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1607.65 | − | 2302.51i | 0.0868050 | − | 0.124324i | ||||
\(701\) | 27675.0 | 1.49111 | 0.745556 | − | 0.666443i | \(-0.232184\pi\) | ||||
0.745556 | + | 0.666443i | \(0.232184\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9227.87i | − | 0.495072i | ||||||
\(704\) | −19892.7 | −1.06497 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −225.566 | −0.0120245 | ||||||||
\(707\) | 12689.6i | 0.675022i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28861.6 | −1.52880 | −0.764401 | − | 0.644741i | \(-0.776965\pi\) | ||||
−0.764401 | + | 0.644741i | \(0.776965\pi\) | |||||||
\(710\) | −2413.10 | + | 7671.28i | −0.127552 | + | 0.405490i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27190.3i | 1.43118i | ||||||||
\(713\) | 44543.8i | 2.33966i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3943.34 | + | 12535.9i | −0.206255 | + | 0.655687i | ||||
\(716\) | −5726.10 | −0.298875 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 12889.3i | − | 0.669949i | ||||||
\(719\) | 13406.8 | 0.695395 | 0.347698 | − | 0.937607i | \(-0.386964\pi\) | ||||
0.347698 | + | 0.937607i | \(0.386964\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11767.8 | 0.607845 | ||||||||
\(722\) | − | 6115.48i | − | 0.315228i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6257.32 | −0.321204 | ||||||||
\(725\) | 1843.90 | + | 1287.44i | 0.0944564 | + | 0.0659509i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2052.02i | − | 0.104684i | −0.998629 | − | 0.0523419i | \(-0.983331\pi\) | ||
0.998629 | − | 0.0523419i | \(-0.0166686\pi\) | |||||||
\(728\) | − | 5272.18i | − | 0.268406i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12746.9 | − | 4009.71i | −0.646279 | − | 0.203296i | ||||
\(731\) | −11111.7 | −0.562220 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 22230.3i | − | 1.12019i | −0.828430 | − | 0.560093i | \(-0.810765\pi\) | ||
0.828430 | − | 0.560093i | \(-0.189235\pi\) | |||||||
\(734\) | 17342.1 | 0.872081 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18856.9 | −0.944392 | ||||||||
\(737\) | 27915.6i | 1.39523i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1568.17 | 0.0780597 | 0.0390299 | − | 0.999238i | \(-0.487573\pi\) | ||||
0.0390299 | + | 0.999238i | \(0.487573\pi\) | |||||||
\(740\) | −1558.38 | + | 4954.09i | −0.0774149 | + | 0.246103i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2891.56i | 0.143063i | ||||||||
\(743\) | − | 36436.6i | − | 1.79910i | −0.436820 | − | 0.899549i | \(-0.643895\pi\) | ||
0.436820 | − | 0.899549i | \(-0.356105\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15555.6 | − | 4893.22i | −0.764982 | − | 0.240636i | ||||
\(746\) | 4982.36 | 0.244527 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4448.52i | 0.217452i | ||||||||
\(749\) | −9601.03 | −0.468376 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6257.06 | −0.304026 | −0.152013 | − | 0.988379i | \(-0.548575\pi\) | ||||
−0.152013 | + | 0.988379i | \(0.548575\pi\) | |||||||
\(752\) | − | 2960.32i | − | 0.143553i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1208.84 | 0.0583862 | ||||||||
\(755\) | −37502.1 | − | 11796.8i | −1.80773 | − | 0.568648i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34671.7i | − | 1.66468i | −0.554264 | − | 0.832341i | \(-0.687000\pi\) | ||
0.554264 | − | 0.832341i | \(-0.313000\pi\) | |||||||
\(758\) | − | 12595.2i | − | 0.603536i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5247.82 | − | 16682.9i | 0.250472 | − | 0.796251i | ||||
\(761\) | −20451.1 | −0.974183 | −0.487091 | − | 0.873351i | \(-0.661942\pi\) | ||||
−0.487091 | + | 0.873351i | \(0.661942\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 395.678i | 0.0187739i | ||||||||
\(764\) | 3234.60 | 0.153172 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16867.9 | 0.795643 | ||||||||
\(767\) | − | 12462.4i | − | 0.586688i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25022.7 | −1.17340 | −0.586698 | − | 0.809806i | \(-0.699572\pi\) | ||||
−0.586698 | + | 0.809806i | \(0.699572\pi\) | |||||||
\(770\) | −6256.54 | − | 1968.08i | −0.292818 | − | 0.0921100i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16651.8i | 0.776312i | ||||||||
\(773\) | 21135.6i | 0.983435i | 0.870755 | + | 0.491717i | \(0.163631\pi\) | ||||
−0.870755 | + | 0.491717i | \(0.836369\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32668.7 | + | 22809.8i | 1.51419 | + | 1.05723i | ||||
\(776\) | 22496.6 | 1.04070 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 15560.0i | − | 0.717035i | ||||||
\(779\) | 6161.59 | 0.283392 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12582.9 | −0.576508 | ||||||||
\(782\) | − | 11072.6i | − | 0.506335i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1373.20 | 0.0625549 | ||||||||
\(785\) | −4494.65 | + | 14288.5i | −0.204358 | + | 0.649655i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 19827.1i | − | 0.898044i | −0.893521 | − | 0.449022i | \(-0.851773\pi\) | ||
0.893521 | − | 0.449022i | \(-0.148227\pi\) | |||||||
\(788\) | 10895.1i | 0.492540i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4765.30 | − | 15148.9i | 0.214610 | − | 0.682247i | ||||
\(791\) | −1755.08 | −0.0788916 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6685.67i | 0.299389i | ||||||||
\(794\) | 23072.7 | 1.03126 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9358.78 | −0.416725 | ||||||||
\(797\) | − | 9818.26i | − | 0.436362i | −0.975908 | − | 0.218181i | \(-0.929988\pi\) | ||
0.975908 | − | 0.218181i | \(-0.0700124\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3823.98 | −0.169315 | ||||||||
\(800\) | −9656.12 | + | 13829.7i | −0.426744 | + | 0.611193i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28001.5i | 1.23288i | ||||||||
\(803\) | − | 20908.3i | − | 0.918852i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10432.8 | − | 3281.78i | −0.456780 | − | 0.143686i | ||||
\(806\) | 21417.1 | 0.935961 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 44476.1i | − | 1.93646i | ||||||
\(809\) | 33454.5 | 1.45389 | 0.726946 | − | 0.686695i | \(-0.240939\pi\) | ||||
0.726946 | + | 0.686695i | \(0.240939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8664.82 | −0.375170 | −0.187585 | − | 0.982248i | \(-0.560066\pi\) | ||||
−0.187585 | + | 0.982248i | \(0.560066\pi\) | |||||||
\(812\) | − | 404.184i | − | 0.0174681i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12129.6 | 0.522286 | ||||||||
\(815\) | 12916.7 | − | 41062.3i | 0.555156 | − | 1.76485i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19570.1i | 0.838031i | ||||||||
\(818\) | 9166.38i | 0.391803i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3307.92 | − | 1040.55i | −0.140875 | − | 0.0443142i | ||||
\(821\) | −1035.20 | −0.0440058 | −0.0220029 | − | 0.999758i | \(-0.507004\pi\) | ||||
−0.0220029 | + | 0.999758i | \(0.507004\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24721.7i | 1.04708i | 0.852002 | + | 0.523538i | \(0.175388\pi\) | ||||
−0.852002 | + | 0.523538i | \(0.824612\pi\) | |||||||
\(824\) | −41245.3 | −1.74375 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6219.84 | 0.262005 | ||||||||
\(827\) | − | 19994.5i | − | 0.840722i | −0.907357 | − | 0.420361i | \(-0.861904\pi\) | ||
0.907357 | − | 0.420361i | \(-0.138096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6458.16 | 0.270568 | 0.135284 | − | 0.990807i | \(-0.456805\pi\) | ||||
0.135284 | + | 0.990807i | \(0.456805\pi\) | |||||||
\(830\) | −10016.2 | − | 3150.73i | −0.418876 | − | 0.131763i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15949.0i | 0.664582i | ||||||||
\(833\) | − | 1773.83i | − | 0.0737811i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7804.02 | + | 24809.0i | −0.323436 | + | 1.02821i | ||||
\(836\) | 7834.77 | 0.324128 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2551.32i | 0.105172i | ||||||||
\(839\) | −47308.6 | −1.94669 | −0.973346 | − | 0.229341i | \(-0.926343\pi\) | ||||
−0.973346 | + | 0.229341i | \(0.926343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24065.3 | −0.986728 | ||||||||
\(842\) | − | 21527.9i | − | 0.881115i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3625.60 | −0.147865 | ||||||||
\(845\) | −13380.6 | − | 4209.05i | −0.544742 | − | 0.171356i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 945.400i | − | 0.0383522i | ||||||
\(848\) | − | 5289.06i | − | 0.214183i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8120.68 | − | 5669.99i | −0.327691 | − | 0.228799i | ||||
\(851\) | 20226.1 | 0.814736 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 634.531i | 0.0254700i | 0.999919 | + | 0.0127350i | \(0.00405379\pi\) | ||||
−0.999919 | + | 0.0127350i | \(0.995946\pi\) | |||||||
\(854\) | −3336.75 | −0.133702 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33650.9 | 1.34365 | ||||||||
\(857\) | − | 8778.84i | − | 0.349918i | −0.984576 | − | 0.174959i | \(-0.944021\pi\) | ||
0.984576 | − | 0.174959i | \(-0.0559792\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15693.4 | 0.623344 | 0.311672 | − | 0.950190i | \(-0.399111\pi\) | ||||
0.311672 | + | 0.950190i | \(0.399111\pi\) | |||||||
\(860\) | 3304.94 | − | 10506.4i | 0.131044 | − | 0.416589i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12908.8i | 0.510065i | ||||||||
\(863\) | − | 36190.2i | − | 1.42749i | −0.700404 | − | 0.713747i | \(-0.746997\pi\) | ||
0.700404 | − | 0.713747i | \(-0.253003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13266.7 | + | 42174.8i | −0.521480 | + | 1.65779i | ||||
\(866\) | −33911.7 | −1.33068 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 7160.98i | − | 0.280022i | ||||||
\(869\) | 24848.3 | 0.969989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22381.3 | 0.870680 | ||||||||
\(872\) | − | 1386.82i | − | 0.0538576i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −19501.1 | −0.754731 | ||||||||
\(875\) | −7749.25 | + | 5970.95i | −0.299397 | + | 0.230691i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1674.50i | − | 0.0644740i | −0.999480 | − | 0.0322370i | \(-0.989737\pi\) | ||
0.999480 | − | 0.0322370i | \(-0.0102631\pi\) | |||||||
\(878\) | 3610.53i | 0.138781i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11444.1 | + | 3599.89i | 0.438386 | + | 0.137900i | ||||
\(881\) | −31999.1 | −1.22370 | −0.611848 | − | 0.790975i | \(-0.709574\pi\) | ||||
−0.611848 | + | 0.790975i | \(0.709574\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 11627.5i | − | 0.443145i | −0.975144 | − | 0.221572i | \(-0.928881\pi\) | ||
0.975144 | − | 0.221572i | \(-0.0711189\pi\) | |||||||
\(884\) | 3566.60 | 0.135699 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32681.0 | 1.23921 | ||||||||
\(887\) | − | 17494.7i | − | 0.662250i | −0.943587 | − | 0.331125i | \(-0.892572\pi\) | ||
0.943587 | − | 0.331125i | \(-0.107428\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14933.3 | −0.563384 | ||||||||
\(890\) | 8137.79 | − | 25870.1i | 0.306494 | − | 0.974346i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 2528.96i | − | 0.0949282i | ||||||
\(893\) | 6734.83i | 0.252377i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19028.4 | + | 5985.63i | 0.710668 | + | 0.223550i | ||||
\(896\) | −403.491 | −0.0150443 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 26009.8i | − | 0.966545i | ||||||
\(899\) | 5734.67 | 0.212750 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6832.12 | −0.252620 | ||||||||
\(902\) | 8099.09i | 0.298969i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6151.41 | 0.226320 | ||||||||
\(905\) | 20793.7 | + | 6540.93i | 0.763762 | + | 0.240252i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14261.9i | 0.522116i | 0.965323 | + | 0.261058i | \(0.0840713\pi\) | ||||
−0.965323 | + | 0.261058i | \(0.915929\pi\) | |||||||
\(908\) | − | 2822.78i | − | 0.103169i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1577.91 | + | 5016.19i | −0.0574804 | + | 0.182731i | ||||
\(911\) | 15247.4 | 0.554521 | 0.277260 | − | 0.960795i | \(-0.410574\pi\) | ||||
0.277260 | + | 0.960795i | \(0.410574\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 16429.2i | − | 0.595539i | ||||||
\(914\) | −10841.4 | −0.392343 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12884.1 | −0.464740 | ||||||||
\(917\) | − | 1658.31i | − | 0.0597187i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2406.86 | −0.0863928 | −0.0431964 | − | 0.999067i | \(-0.513754\pi\) | ||||
−0.0431964 | + | 0.999067i | \(0.513754\pi\) | |||||||
\(920\) | 36566.2 | + | 11502.4i | 1.31038 | + | 0.412199i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1736.57i | 0.0620292i | ||||||||
\(923\) | 10088.4i | 0.359765i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10357.3 | − | 14833.9i | 0.368156 | − | 0.527281i | ||||
\(926\) | −23728.2 | −0.842071 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2427.67i | 0.0858752i | ||||||||
\(929\) | −11356.2 | −0.401061 | −0.200530 | − | 0.979687i | \(-0.564267\pi\) | ||||
−0.200530 | + | 0.979687i | \(0.564267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3124.09 | −0.109976 | ||||||||
\(932\) | − | 9924.88i | − | 0.348820i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37201.8 | 1.30330 | ||||||||
\(935\) | 4650.14 | − | 14782.8i | 0.162648 | − | 0.517059i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 40140.9i | − | 1.39951i | −0.714381 | − | 0.699757i | \(-0.753292\pi\) | ||
0.714381 | − | 0.699757i | \(-0.246708\pi\) | |||||||
\(938\) | 11170.3i | 0.388830i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1137.36 | − | 3615.67i | 0.0394644 | − | 0.125458i | ||||
\(941\) | −44475.8 | −1.54078 | −0.770388 | − | 0.637576i | \(-0.779937\pi\) | ||||
−0.770388 | + | 0.637576i | \(0.779937\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13505.3i | 0.466375i | ||||||||
\(944\) | −11376.9 | −0.392254 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25723.9 | −0.884097 | ||||||||
\(947\) | − | 7280.66i | − | 0.249831i | −0.992167 | − | 0.124915i | \(-0.960134\pi\) | ||
0.992167 | − | 0.124915i | \(-0.0398660\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16763.2 | −0.573401 | ||||||||
\(950\) | −9986.03 | + | 14302.2i | −0.341042 | + | 0.488447i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6217.16i | 0.211659i | ||||||||
\(953\) | − | 22114.1i | − | 0.751674i | −0.926686 | − | 0.375837i | \(-0.877355\pi\) | ||
0.926686 | − | 0.375837i | \(-0.122645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10748.9 | − | 3381.21i | −0.364215 | − | 0.114569i | ||||
\(956\) | −20593.0 | −0.696679 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 27900.6i | − | 0.940948i | ||||||
\(959\) | −18252.2 | −0.614591 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71810.9 | 2.41049 | ||||||||
\(962\) | − | 9724.87i | − | 0.325928i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1992.15 | −0.0665589 | ||||||||
\(965\) | 17406.6 | − | 55335.6i | 0.580660 | − | 1.84592i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34353.8i | 1.14245i | 0.820795 | + | 0.571223i | \(0.193531\pi\) | ||||
−0.820795 | + | 0.571223i | \(0.806469\pi\) | |||||||
\(968\) | 3313.56i | 0.110023i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21404.3 | − | 6733.00i | −0.708504 | − | 0.222870i | ||||
\(971\) | 7495.37 | 0.247722 | 0.123861 | − | 0.992300i | \(-0.460472\pi\) | ||||
0.123861 | + | 0.992300i | \(0.460472\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2576.81i | − | 0.0849011i | ||||||
\(974\) | 40813.3 | 1.34265 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6103.37 | 0.200168 | ||||||||
\(977\) | − | 31269.3i | − | 1.02394i | −0.859002 | − | 0.511972i | \(-0.828915\pi\) | ||
0.859002 | − | 0.511972i | \(-0.171085\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 42433.9 | 1.38528 | ||||||||
\(980\) | 1677.20 | + | 527.587i | 0.0546697 | + | 0.0171971i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 30985.8i | − | 1.00692i | ||||||
\(983\) | − | 25055.2i | − | 0.812958i | −0.913660 | − | 0.406479i | \(-0.866756\pi\) | ||
0.913660 | − | 0.406479i | \(-0.133244\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11388.9 | − | 36205.4i | 0.368407 | − | 1.17117i | ||||
\(986\) | −1425.51 | −0.0460419 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 6281.53i | − | 0.202269i | ||||||
\(989\) | −42894.6 | −1.37914 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35098.7 | 1.12507 | 0.562536 | − | 0.826773i | \(-0.309826\pi\) | ||||
0.562536 | + | 0.826773i | \(0.309826\pi\) | |||||||
\(992\) | 43011.4i | 1.37663i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5035.00 | −0.160665 | ||||||||
\(995\) | 31100.1 | + | 9782.96i | 0.990894 | + | 0.311699i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 30175.1i | − | 0.958530i | −0.877670 | − | 0.479265i | \(-0.840903\pi\) | ||
0.877670 | − | 0.479265i | \(-0.159097\pi\) | |||||||
\(998\) | − | 10740.4i | − | 0.340663i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.4.d.d.64.13 | yes | 20 | |
3.2 | odd | 2 | inner | 315.4.d.d.64.8 | yes | 20 | |
5.2 | odd | 4 | 1575.4.a.bu.1.4 | 10 | |||
5.3 | odd | 4 | 1575.4.a.bt.1.7 | 10 | |||
5.4 | even | 2 | inner | 315.4.d.d.64.7 | ✓ | 20 | |
15.2 | even | 4 | 1575.4.a.bu.1.7 | 10 | |||
15.8 | even | 4 | 1575.4.a.bt.1.4 | 10 | |||
15.14 | odd | 2 | inner | 315.4.d.d.64.14 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.4.d.d.64.7 | ✓ | 20 | 5.4 | even | 2 | inner | |
315.4.d.d.64.8 | yes | 20 | 3.2 | odd | 2 | inner | |
315.4.d.d.64.13 | yes | 20 | 1.1 | even | 1 | trivial | |
315.4.d.d.64.14 | yes | 20 | 15.14 | odd | 2 | inner | |
1575.4.a.bt.1.4 | 10 | 15.8 | even | 4 | |||
1575.4.a.bt.1.7 | 10 | 5.3 | odd | 4 | |||
1575.4.a.bu.1.4 | 10 | 5.2 | odd | 4 | |||
1575.4.a.bu.1.7 | 10 | 15.2 | even | 4 |