Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(107,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.f (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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.11007531417600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.1 | ||
Root | \(0.596975 + 0.159959i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.143 |
Dual form | 225.4.f.d.107.1 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.80252 | − | 2.80252i | −0.990839 | − | 0.990839i | 0.00911901 | − | 0.999958i | \(-0.497097\pi\) |
−0.999958 | + | 0.00911901i | \(0.997097\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.70820i | 0.963525i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −25.0049 | + | 25.0049i | −1.35014 | + | 1.35014i | −0.464635 | + | 0.885502i | \(0.653814\pi\) |
−0.885502 | + | 0.464635i | \(0.846186\pi\) | |||||||
\(8\) | −0.817763 | + | 0.817763i | −0.0361404 | + | 0.0361404i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 42.1900i | − | 1.15643i | −0.815884 | − | 0.578216i | \(-0.803749\pi\) | ||
0.815884 | − | 0.578216i | \(-0.196251\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −25.7196 | − | 25.7196i | −0.548719 | − | 0.548719i | 0.377351 | − | 0.926070i | \(-0.376835\pi\) |
−0.926070 | + | 0.377351i | \(0.876835\pi\) | |||||||
\(14\) | 140.153 | 2.67554 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 66.2492 | 1.03514 | ||||||||
\(17\) | 42.0974 | + | 42.0974i | 0.600595 | + | 0.600595i | 0.940471 | − | 0.339875i | \(-0.110385\pi\) |
−0.339875 | + | 0.940471i | \(0.610385\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 58.9149i | 0.711368i | 0.934606 | + | 0.355684i | \(0.115752\pi\) | ||||
−0.934606 | + | 0.355684i | \(0.884248\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −118.238 | + | 118.238i | −1.14584 | + | 1.14584i | ||||
\(23\) | 141.932 | − | 141.932i | 1.28673 | − | 1.28673i | 0.349969 | − | 0.936761i | \(-0.386192\pi\) |
0.936761 | − | 0.349969i | \(-0.113808\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 144.159i | 1.08738i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −192.743 | − | 192.743i | −1.30089 | − | 1.30089i | ||||
\(29\) | 79.0799 | 0.506372 | 0.253186 | − | 0.967418i | \(-0.418522\pi\) | ||||
0.253186 | + | 0.967418i | \(0.418522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 184.915 | 1.07134 | 0.535672 | − | 0.844426i | \(-0.320058\pi\) | ||||
0.535672 | + | 0.844426i | \(0.320058\pi\) | |||||||
\(32\) | −179.122 | − | 179.122i | −0.989521 | − | 0.989521i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 235.957i | − | 1.19019i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 81.4436 | − | 81.4436i | 0.361872 | − | 0.361872i | −0.502630 | − | 0.864502i | \(-0.667634\pi\) |
0.864502 | + | 0.502630i | \(0.167634\pi\) | |||||||
\(38\) | 165.110 | − | 165.110i | 0.704852 | − | 0.704852i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 14.0217i | − | 0.0534104i | −0.999643 | − | 0.0267052i | \(-0.991498\pi\) | ||
0.999643 | − | 0.0267052i | \(-0.00850154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 152.170 | + | 152.170i | 0.539667 | + | 0.539667i | 0.923431 | − | 0.383764i | \(-0.125372\pi\) |
−0.383764 | + | 0.923431i | \(0.625372\pi\) | |||||||
\(44\) | 325.209 | 1.11425 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −795.532 | −2.54989 | ||||||||
\(47\) | −199.038 | − | 199.038i | −0.617718 | − | 0.617718i | 0.327228 | − | 0.944945i | \(-0.393886\pi\) |
−0.944945 | + | 0.327228i | \(0.893886\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 907.489i | − | 2.64574i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 198.252 | − | 198.252i | 0.528705 | − | 0.528705i | ||||
\(53\) | 84.5353 | − | 84.5353i | 0.219091 | − | 0.219091i | −0.589024 | − | 0.808115i | \(-0.700488\pi\) |
0.808115 | + | 0.589024i | \(0.200488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 40.8962i | − | 0.0975889i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −221.623 | − | 221.623i | −0.501733 | − | 0.501733i | ||||
\(59\) | −665.733 | −1.46900 | −0.734501 | − | 0.678608i | \(-0.762584\pi\) | ||||
−0.734501 | + | 0.678608i | \(0.762584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 600.830 | 1.26112 | 0.630560 | − | 0.776140i | \(-0.282825\pi\) | ||||
0.630560 | + | 0.776140i | \(0.282825\pi\) | |||||||
\(62\) | −518.227 | − | 518.227i | −1.06153 | − | 1.06153i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 473.994i | 0.925769i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.22801 | − | 6.22801i | 0.0113563 | − | 0.0113563i | −0.701406 | − | 0.712762i | \(-0.747444\pi\) |
0.712762 | + | 0.701406i | \(0.247444\pi\) | |||||||
\(68\) | −324.495 | + | 324.495i | −0.578689 | + | 0.578689i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 750.823i | 1.25502i | 0.778609 | + | 0.627509i | \(0.215925\pi\) | ||||
−0.778609 | + | 0.627509i | \(0.784075\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 418.654 | + | 418.654i | 0.671230 | + | 0.671230i | 0.958000 | − | 0.286770i | \(-0.0925815\pi\) |
−0.286770 | + | 0.958000i | \(0.592581\pi\) | |||||||
\(74\) | −456.494 | −0.717113 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −454.128 | −0.685421 | ||||||||
\(77\) | 1054.96 | + | 1054.96i | 1.56134 | + | 1.56134i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 825.830i | 1.17612i | 0.808819 | + | 0.588058i | \(0.200107\pi\) | ||||
−0.808819 | + | 0.588058i | \(0.799893\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −39.2961 | + | 39.2961i | −0.0529211 | + | 0.0529211i | ||||
\(83\) | 463.072 | − | 463.072i | 0.612394 | − | 0.612394i | −0.331175 | − | 0.943569i | \(-0.607445\pi\) |
0.943569 | + | 0.331175i | \(0.107445\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 852.917i | − | 1.06945i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 34.5014 | + | 34.5014i | 0.0417939 | + | 0.0417939i | ||||
\(89\) | 646.747 | 0.770281 | 0.385140 | − | 0.922858i | \(-0.374153\pi\) | ||||
0.385140 | + | 0.922858i | \(0.374153\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1286.23 | 1.48169 | ||||||||
\(92\) | 1094.04 | + | 1094.04i | 1.23980 | + | 1.23980i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1115.62i | 1.22412i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 371.515 | − | 371.515i | 0.388883 | − | 0.388883i | −0.485406 | − | 0.874289i | \(-0.661328\pi\) |
0.874289 | + | 0.485406i | \(0.161328\pi\) | |||||||
\(98\) | −2543.25 | + | 2543.25i | −2.62150 | + | 2.62150i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1579.77i | − | 1.55636i | −0.628040 | − | 0.778181i | \(-0.716142\pi\) | ||
0.628040 | − | 0.778181i | \(-0.283858\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −31.4262 | − | 31.4262i | −0.0300633 | − | 0.0300633i | 0.691915 | − | 0.721979i | \(-0.256767\pi\) |
−0.721979 | + | 0.691915i | \(0.756767\pi\) | |||||||
\(104\) | 42.0652 | 0.0396618 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −473.823 | −0.434168 | ||||||||
\(107\) | 669.877 | + | 669.877i | 0.605229 | + | 0.605229i | 0.941695 | − | 0.336467i | \(-0.109232\pi\) |
−0.336467 | + | 0.941695i | \(0.609232\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1174.82i | 1.03236i | 0.856479 | + | 0.516182i | \(0.172647\pi\) | ||||
−0.856479 | + | 0.516182i | \(0.827353\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1656.55 | + | 1656.55i | −1.39759 | + | 1.39759i | ||||
\(113\) | 594.951 | − | 594.951i | 0.495295 | − | 0.495295i | −0.414675 | − | 0.909970i | \(-0.636105\pi\) |
0.909970 | + | 0.414675i | \(0.136105\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 609.564i | 0.487902i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1865.73 | + | 1865.73i | 1.45554 | + | 1.45554i | ||||
\(119\) | −2105.28 | −1.62177 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −448.994 | −0.337336 | ||||||||
\(122\) | −1683.84 | − | 1683.84i | −1.24957 | − | 1.24957i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1425.36i | 1.03227i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 137.380 | − | 137.380i | 0.0959882 | − | 0.0959882i | −0.657482 | − | 0.753470i | \(-0.728378\pi\) |
0.753470 | + | 0.657482i | \(0.228378\pi\) | |||||||
\(128\) | −104.604 | + | 104.604i | −0.0722327 | + | 0.0722327i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 492.508i | 0.328478i | 0.986421 | + | 0.164239i | \(0.0525168\pi\) | ||||
−0.986421 | + | 0.164239i | \(0.947483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1473.16 | − | 1473.16i | −0.960445 | − | 0.960445i | ||||
\(134\) | −34.9082 | −0.0225045 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −68.8514 | −0.0434115 | ||||||||
\(137\) | 176.482 | + | 176.482i | 0.110057 | + | 0.110057i | 0.759991 | − | 0.649934i | \(-0.225203\pi\) |
−0.649934 | + | 0.759991i | \(0.725203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1224.98i | − | 0.747491i | −0.927531 | − | 0.373746i | \(-0.878073\pi\) | ||
0.927531 | − | 0.373746i | \(-0.121927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2104.19 | − | 2104.19i | 1.24352 | − | 1.24352i | ||||
\(143\) | −1085.11 | + | 1085.11i | −0.634556 | + | 0.634556i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 2346.57i | − | 1.33016i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 627.784 | + | 627.784i | 0.348673 | + | 0.348673i | ||||
\(149\) | −41.9404 | −0.0230597 | −0.0115298 | − | 0.999934i | \(-0.503670\pi\) | ||||
−0.0115298 | + | 0.999934i | \(0.503670\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −47.2182 | −0.0254474 | −0.0127237 | − | 0.999919i | \(-0.504050\pi\) | ||||
−0.0127237 | + | 0.999919i | \(0.504050\pi\) | |||||||
\(152\) | −48.1784 | − | 48.1784i | −0.0257091 | − | 0.0257091i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 5913.06i | − | 3.09408i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1856.06 | − | 1856.06i | 0.943502 | − | 0.943502i | −0.0549853 | − | 0.998487i | \(-0.517511\pi\) |
0.998487 | + | 0.0549853i | \(0.0175112\pi\) | |||||||
\(158\) | 2314.40 | − | 2314.40i | 1.16534 | − | 1.16534i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7097.97i | 3.47452i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −295.059 | − | 295.059i | −0.141784 | − | 0.141784i | 0.632652 | − | 0.774436i | \(-0.281966\pi\) |
−0.774436 | + | 0.632652i | \(0.781966\pi\) | |||||||
\(164\) | 108.082 | 0.0514623 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2595.53 | −1.21357 | ||||||||
\(167\) | 1081.41 | + | 1081.41i | 0.501092 | + | 0.501092i | 0.911777 | − | 0.410685i | \(-0.134711\pi\) |
−0.410685 | + | 0.911777i | \(0.634711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 874.000i | − | 0.397815i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1172.96 | + | 1172.96i | −0.519983 | + | 0.519983i | ||||
\(173\) | 2369.97 | − | 2369.97i | 1.04154 | − | 1.04154i | 0.0424371 | − | 0.999099i | \(-0.486488\pi\) |
0.999099 | − | 0.0424371i | \(-0.0135122\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2795.05i | − | 1.19707i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1812.52 | − | 1812.52i | −0.763225 | − | 0.763225i | ||||
\(179\) | 2631.01 | 1.09861 | 0.549304 | − | 0.835623i | \(-0.314893\pi\) | ||||
0.549304 | + | 0.835623i | \(0.314893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −492.319 | −0.202176 | −0.101088 | − | 0.994878i | \(-0.532232\pi\) | ||||
−0.101088 | + | 0.994878i | \(0.532232\pi\) | |||||||
\(182\) | −3604.69 | − | 3604.69i | −1.46812 | − | 1.46812i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 232.133i | 0.0930058i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1776.09 | − | 1776.09i | 0.694548 | − | 0.694548i | ||||
\(188\) | 1534.23 | − | 1534.23i | 0.595187 | − | 0.595187i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1285.52i | 0.487000i | 0.969901 | + | 0.243500i | \(0.0782956\pi\) | ||||
−0.969901 | + | 0.243500i | \(0.921704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 49.9908 | + | 49.9908i | 0.0186446 | + | 0.0186446i | 0.716368 | − | 0.697723i | \(-0.245803\pi\) |
−0.697723 | + | 0.716368i | \(0.745803\pi\) | |||||||
\(194\) | −2082.35 | −0.770640 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6995.11 | 2.54924 | ||||||||
\(197\) | −3313.77 | − | 3313.77i | −1.19846 | − | 1.19846i | −0.974628 | − | 0.223829i | \(-0.928144\pi\) |
−0.223829 | − | 0.974628i | \(-0.571856\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1653.72i | 0.589092i | 0.955637 | + | 0.294546i | \(0.0951684\pi\) | ||||
−0.955637 | + | 0.294546i | \(0.904832\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4427.32 | + | 4427.32i | −1.54211 | + | 1.54211i | ||||
\(203\) | −1977.39 | + | 1977.39i | −0.683671 | + | 0.683671i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 176.145i | 0.0595758i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1703.91 | − | 1703.91i | −0.568003 | − | 0.568003i | ||||
\(209\) | 2485.62 | 0.822649 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3436.40 | −1.12119 | −0.560597 | − | 0.828089i | \(-0.689428\pi\) | ||||
−0.560597 | + | 0.828089i | \(0.689428\pi\) | |||||||
\(212\) | 651.616 | + | 651.616i | 0.211100 | + | 0.211100i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 3754.69i | − | 1.19937i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4623.78 | + | 4623.78i | −1.44646 | + | 1.44646i | ||||
\(218\) | 3292.46 | − | 3292.46i | 1.02291 | − | 1.02291i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2165.46i | − | 0.659116i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2589.81 | − | 2589.81i | −0.777699 | − | 0.777699i | 0.201740 | − | 0.979439i | \(-0.435340\pi\) |
−0.979439 | + | 0.201740i | \(0.935340\pi\) | |||||||
\(224\) | 8957.88 | 2.67198 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3334.72 | −0.981515 | ||||||||
\(227\) | 3944.75 | + | 3944.75i | 1.15340 | + | 1.15340i | 0.985866 | + | 0.167536i | \(0.0535812\pi\) |
0.167536 | + | 0.985866i | \(0.446419\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2269.08i | 0.654783i | 0.944889 | + | 0.327391i | \(0.106170\pi\) | ||||
−0.944889 | + | 0.327391i | \(0.893830\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −64.6687 | + | 64.6687i | −0.0183005 | + | 0.0183005i | ||||
\(233\) | −1757.84 | + | 1757.84i | −0.494247 | + | 0.494247i | −0.909642 | − | 0.415394i | \(-0.863644\pi\) |
0.415394 | + | 0.909642i | \(0.363644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 5131.61i | − | 1.41542i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5900.09 | + | 5900.09i | 1.60692 | + | 1.60692i | ||||
\(239\) | 3570.92 | 0.966458 | 0.483229 | − | 0.875494i | \(-0.339464\pi\) | ||||
0.483229 | + | 0.875494i | \(0.339464\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6036.32 | 1.61342 | 0.806708 | − | 0.590950i | \(-0.201247\pi\) | ||||
0.806708 | + | 0.590950i | \(0.201247\pi\) | |||||||
\(242\) | 1258.31 | + | 1258.31i | 0.334245 | + | 0.334245i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4631.32i | 1.21512i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1515.27 | − | 1515.27i | 0.390341 | − | 0.390341i | ||||
\(248\) | −151.217 | + | 151.217i | −0.0387188 | + | 0.0387188i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3085.33i | − | 0.775874i | −0.921686 | − | 0.387937i | \(-0.873188\pi\) | ||
0.921686 | − | 0.387937i | \(-0.126812\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5988.09 | − | 5988.09i | −1.48802 | − | 1.48802i | ||||
\(254\) | −770.020 | −0.190218 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4378.26 | 1.06891 | ||||||||
\(257\) | −490.380 | − | 490.380i | −0.119023 | − | 0.119023i | 0.645086 | − | 0.764110i | \(-0.276821\pi\) |
−0.764110 | + | 0.645086i | \(0.776821\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4072.98i | 0.977153i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1380.26 | − | 1380.26i | 0.325469 | − | 0.325469i | ||||
\(263\) | 157.421 | − | 157.421i | 0.0369087 | − | 0.0369087i | −0.688412 | − | 0.725320i | \(-0.741692\pi\) |
0.725320 | + | 0.688412i | \(0.241692\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8257.11i | 1.90329i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 48.0067 | + | 48.0067i | 0.0109421 | + | 0.0109421i | ||||
\(269\) | −6197.83 | −1.40479 | −0.702395 | − | 0.711787i | \(-0.747886\pi\) | ||||
−0.702395 | + | 0.711787i | \(0.747886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4561.66 | −1.02251 | −0.511257 | − | 0.859428i | \(-0.670820\pi\) | ||||
−0.511257 | + | 0.859428i | \(0.670820\pi\) | |||||||
\(272\) | 2788.92 | + | 2788.92i | 0.621703 | + | 0.621703i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 989.185i | − | 0.218098i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −900.134 | + | 900.134i | −0.195248 | + | 0.195248i | −0.797960 | − | 0.602711i | \(-0.794087\pi\) |
0.602711 | + | 0.797960i | \(0.294087\pi\) | |||||||
\(278\) | −3433.02 | + | 3433.02i | −0.740644 | + | 0.740644i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4485.95i | 0.952346i | 0.879352 | + | 0.476173i | \(0.157976\pi\) | ||||
−0.879352 | + | 0.476173i | \(0.842024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4735.98 | + | 4735.98i | 0.994788 | + | 0.994788i | 0.999986 | − | 0.00519838i | \(-0.00165470\pi\) |
−0.00519838 | + | 0.999986i | \(0.501655\pi\) | |||||||
\(284\) | −5787.49 | −1.20924 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6082.08 | 1.25749 | ||||||||
\(287\) | 350.612 | + | 350.612i | 0.0721113 | + | 0.0721113i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1368.62i | − | 0.278570i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3227.07 | + | 3227.07i | −0.646747 | + | 0.646747i | ||||
\(293\) | 4617.95 | − | 4617.95i | 0.920763 | − | 0.920763i | −0.0763199 | − | 0.997083i | \(-0.524317\pi\) |
0.997083 | + | 0.0763199i | \(0.0243170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 133.203i | 0.0261564i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 117.539 | + | 117.539i | 0.0228484 | + | 0.0228484i | ||||
\(299\) | −7300.86 | −1.41211 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7609.98 | −1.45725 | ||||||||
\(302\) | 132.330 | + | 132.330i | 0.0252143 | + | 0.0252143i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3903.06i | 0.736369i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5000.27 | − | 5000.27i | 0.929578 | − | 0.929578i | −0.0681008 | − | 0.997678i | \(-0.521694\pi\) |
0.997678 | + | 0.0681008i | \(0.0216940\pi\) | |||||||
\(308\) | −8131.81 | + | 8131.81i | −1.50439 | + | 1.50439i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6874.37i | − | 1.25341i | −0.779257 | − | 0.626704i | \(-0.784404\pi\) | ||
0.779257 | − | 0.626704i | \(-0.215596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3422.07 | + | 3422.07i | 0.617976 | + | 0.617976i | 0.945012 | − | 0.327036i | \(-0.106050\pi\) |
−0.327036 | + | 0.945012i | \(0.606050\pi\) | |||||||
\(314\) | −10403.3 | −1.86972 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6365.66 | −1.13322 | ||||||||
\(317\) | −4689.86 | − | 4689.86i | −0.830943 | − | 0.830943i | 0.156703 | − | 0.987646i | \(-0.449914\pi\) |
−0.987646 | + | 0.156703i | \(0.949914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3336.38i | − | 0.585584i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 19892.2 | − | 19892.2i | 3.44270 | − | 3.44270i | ||||
\(323\) | −2480.16 | + | 2480.16i | −0.427244 | + | 0.427244i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1653.82i | 0.280971i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 11.4665 | + | 11.4665i | 0.00193027 | + | 0.00193027i | ||||
\(329\) | 9953.87 | 1.66801 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 952.081 | 0.158100 | 0.0790500 | − | 0.996871i | \(-0.474811\pi\) | ||||
0.0790500 | + | 0.996871i | \(0.474811\pi\) | |||||||
\(332\) | 3569.45 | + | 3569.45i | 0.590057 | + | 0.590057i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6061.36i | − | 0.993003i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4007.99 | + | 4007.99i | −0.647860 | + | 0.647860i | −0.952476 | − | 0.304615i | \(-0.901472\pi\) |
0.304615 | + | 0.952476i | \(0.401472\pi\) | |||||||
\(338\) | −2449.40 | + | 2449.40i | −0.394171 | + | 0.394171i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7801.55i | − | 1.23894i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14115.0 | + | 14115.0i | 2.22198 | + | 2.22198i | ||||
\(344\) | −248.878 | −0.0390075 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13283.8 | −2.06399 | ||||||||
\(347\) | −1873.29 | − | 1873.29i | −0.289809 | − | 0.289809i | 0.547196 | − | 0.837005i | \(-0.315695\pi\) |
−0.837005 | + | 0.547196i | \(0.815695\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10642.2i | − | 1.63228i | −0.577857 | − | 0.816138i | \(-0.696111\pi\) | ||
0.577857 | − | 0.816138i | \(-0.303889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7557.17 | + | 7557.17i | −1.14431 | + | 1.14431i | ||||
\(353\) | −5699.37 | + | 5699.37i | −0.859339 | + | 0.859339i | −0.991260 | − | 0.131921i | \(-0.957885\pi\) |
0.131921 | + | 0.991260i | \(0.457885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4985.25i | 0.742185i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7373.45 | − | 7373.45i | −1.08854 | − | 1.08854i | ||||
\(359\) | −12273.5 | −1.80437 | −0.902186 | − | 0.431347i | \(-0.858038\pi\) | ||||
−0.902186 | + | 0.431347i | \(0.858038\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3388.04 | 0.493955 | ||||||||
\(362\) | 1379.73 | + | 1379.73i | 0.200323 | + | 0.200323i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9914.55i | 1.42765i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2865.51 | + | 2865.51i | −0.407571 | + | 0.407571i | −0.880891 | − | 0.473320i | \(-0.843055\pi\) |
0.473320 | + | 0.880891i | \(0.343055\pi\) | |||||||
\(368\) | 9402.86 | − | 9402.86i | 1.33195 | − | 1.33195i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4227.59i | 0.591606i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3859.53 | − | 3859.53i | −0.535762 | − | 0.535762i | 0.386519 | − | 0.922281i | \(-0.373677\pi\) |
−0.922281 | + | 0.386519i | \(0.873677\pi\) | |||||||
\(374\) | −9955.04 | −1.37637 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 325.533 | 0.0446491 | ||||||||
\(377\) | −2033.91 | − | 2033.91i | −0.277856 | − | 0.277856i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2981.39i | 0.404073i | 0.979378 | + | 0.202036i | \(0.0647560\pi\) | ||||
−0.979378 | + | 0.202036i | \(0.935244\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3602.69 | − | 3602.69i | 0.482539 | − | 0.482539i | ||||
\(383\) | −10252.4 | + | 10252.4i | −1.36782 | + | 1.36782i | −0.504280 | + | 0.863540i | \(0.668242\pi\) |
−0.863540 | + | 0.504280i | \(0.831758\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 280.200i | − | 0.0369477i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2863.71 | + | 2863.71i | 0.374698 | + | 0.374698i | ||||
\(389\) | 6840.61 | 0.891601 | 0.445801 | − | 0.895132i | \(-0.352919\pi\) | ||||
0.445801 | + | 0.895132i | \(0.352919\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11949.9 | 1.54561 | ||||||||
\(392\) | 742.111 | + | 742.111i | 0.0956181 | + | 0.0956181i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18573.8i | 2.37496i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 288.543 | − | 288.543i | 0.0364774 | − | 0.0364774i | −0.688633 | − | 0.725110i | \(-0.741789\pi\) |
0.725110 | + | 0.688633i | \(0.241789\pi\) | |||||||
\(398\) | 4634.59 | − | 4634.59i | 0.583696 | − | 0.583696i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 4765.08i | − | 0.593409i | −0.954969 | − | 0.296704i | \(-0.904112\pi\) | ||
0.954969 | − | 0.296704i | \(-0.0958876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4755.94 | − | 4755.94i | −0.587867 | − | 0.587867i | ||||
\(404\) | 12177.2 | 1.49959 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11083.3 | 1.35482 | ||||||||
\(407\) | −3436.10 | − | 3436.10i | −0.418480 | − | 0.418480i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8132.87i | − | 0.983239i | −0.870810 | − | 0.491619i | \(-0.836405\pi\) | ||
0.870810 | − | 0.491619i | \(-0.163595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 242.240 | − | 242.240i | 0.0289668 | − | 0.0289668i | ||||
\(413\) | 16646.6 | − | 16646.6i | 1.98335 | − | 1.98335i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9213.93i | 1.08594i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6965.98 | − | 6965.98i | −0.815113 | − | 0.815113i | ||||
\(419\) | −222.003 | −0.0258844 | −0.0129422 | − | 0.999916i | \(-0.504120\pi\) | ||||
−0.0129422 | + | 0.999916i | \(0.504120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4412.17 | 0.510774 | 0.255387 | − | 0.966839i | \(-0.417797\pi\) | ||||
0.255387 | + | 0.966839i | \(0.417797\pi\) | |||||||
\(422\) | 9630.58 | + | 9630.58i | 1.11092 | + | 1.11092i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 138.260i | 0.0158361i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15023.7 | + | 15023.7i | −1.70269 | + | 1.70269i | ||||
\(428\) | −5163.55 | + | 5163.55i | −0.583153 | + | 0.583153i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10285.6i | − | 1.14952i | −0.818323 | − | 0.574758i | \(-0.805096\pi\) | ||
0.818323 | − | 0.574758i | \(-0.194904\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6616.98 | + | 6616.98i | 0.734392 | + | 0.734392i | 0.971487 | − | 0.237094i | \(-0.0761951\pi\) |
−0.237094 | + | 0.971487i | \(0.576195\pi\) | |||||||
\(434\) | 25916.4 | 2.86642 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9055.78 | −0.994709 | ||||||||
\(437\) | 8361.88 | + | 8361.88i | 0.915339 | + | 0.915339i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11483.9i | 1.24852i | 0.781219 | + | 0.624258i | \(0.214598\pi\) | ||||
−0.781219 | + | 0.624258i | \(0.785402\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6068.74 | + | 6068.74i | −0.653078 | + | 0.653078i | ||||
\(443\) | −3420.37 | + | 3420.37i | −0.366832 | + | 0.366832i | −0.866320 | − | 0.499489i | \(-0.833521\pi\) |
0.499489 | + | 0.866320i | \(0.333521\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14516.0i | 1.54115i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11852.2 | − | 11852.2i | −1.24992 | − | 1.24992i | ||||
\(449\) | 11995.6 | 1.26082 | 0.630410 | − | 0.776262i | \(-0.282887\pi\) | ||||
0.630410 | + | 0.776262i | \(0.282887\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −591.576 | −0.0617655 | ||||||||
\(452\) | 4586.01 | + | 4586.01i | 0.477229 | + | 0.477229i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 22110.5i | − | 2.28567i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3243.45 | − | 3243.45i | 0.331996 | − | 0.331996i | −0.521348 | − | 0.853344i | \(-0.674571\pi\) |
0.853344 | + | 0.521348i | \(0.174571\pi\) | |||||||
\(458\) | 6359.14 | − | 6359.14i | 0.648785 | − | 0.648785i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 15008.4i | − | 1.51629i | −0.652087 | − | 0.758144i | \(-0.726106\pi\) | ||
0.652087 | − | 0.758144i | \(-0.273894\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1250.28 | + | 1250.28i | 0.125498 | + | 0.125498i | 0.767066 | − | 0.641568i | \(-0.221716\pi\) |
−0.641568 | + | 0.767066i | \(0.721716\pi\) | |||||||
\(464\) | 5238.98 | 0.524168 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9852.73 | 0.979440 | ||||||||
\(467\) | −4274.49 | − | 4274.49i | −0.423554 | − | 0.423554i | 0.462871 | − | 0.886426i | \(-0.346819\pi\) |
−0.886426 | + | 0.462871i | \(0.846819\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 311.461i | 0.0306651i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 544.412 | − | 544.412i | 0.0530903 | − | 0.0530903i | ||||
\(473\) | 6420.04 | − | 6420.04i | 0.624088 | − | 0.624088i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 16227.9i | − | 1.56262i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10007.6 | − | 10007.6i | −0.957605 | − | 0.957605i | ||||
\(479\) | −7189.29 | −0.685776 | −0.342888 | − | 0.939376i | \(-0.611405\pi\) | ||||
−0.342888 | + | 0.939376i | \(0.611405\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4189.40 | −0.397132 | ||||||||
\(482\) | −16916.9 | − | 16916.9i | −1.59864 | − | 1.59864i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 3460.94i | − | 0.325032i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −923.729 | + | 923.729i | −0.0859510 | + | 0.0859510i | −0.748775 | − | 0.662824i | \(-0.769358\pi\) |
0.662824 | + | 0.748775i | \(0.269358\pi\) | |||||||
\(488\) | −491.337 | + | 491.337i | −0.0455774 | + | 0.0455774i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 434.588i | − | 0.0399444i | −0.999801 | − | 0.0199722i | \(-0.993642\pi\) | ||
0.999801 | − | 0.0199722i | \(-0.00635777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3329.06 | + | 3329.06i | 0.304124 | + | 0.304124i | ||||
\(494\) | −8493.13 | −0.773531 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12250.5 | 1.10900 | ||||||||
\(497\) | −18774.2 | − | 18774.2i | −1.69445 | − | 1.69445i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7228.02i | 0.648438i | 0.945982 | + | 0.324219i | \(0.105101\pi\) | ||||
−0.945982 | + | 0.324219i | \(0.894899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8646.70 | + | 8646.70i | −0.768767 | + | 0.768767i | ||||
\(503\) | 1240.98 | − | 1240.98i | 0.110005 | − | 0.110005i | −0.649962 | − | 0.759967i | \(-0.725215\pi\) |
0.759967 | + | 0.649962i | \(0.225215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 33563.5i | 2.94877i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1058.95 | + | 1058.95i | 0.0924871 | + | 0.0924871i | ||||
\(509\) | 20683.3 | 1.80112 | 0.900561 | − | 0.434730i | \(-0.143156\pi\) | ||||
0.900561 | + | 0.434730i | \(0.143156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20936.8 | −1.81250 | ||||||||
\(512\) | −11433.3 | − | 11433.3i | −0.986887 | − | 0.986887i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2748.59i | 0.235866i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8397.42 | + | 8397.42i | −0.714349 | + | 0.714349i | ||||
\(518\) | 11414.6 | − | 11414.6i | 0.968201 | − | 0.968201i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1904.89i | 0.160182i | 0.996788 | + | 0.0800908i | \(0.0255210\pi\) | ||||
−0.996788 | + | 0.0800908i | \(0.974479\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1799.72 | + | 1799.72i | 0.150471 | + | 0.150471i | 0.778329 | − | 0.627857i | \(-0.216068\pi\) |
−0.627857 | + | 0.778329i | \(0.716068\pi\) | |||||||
\(524\) | −3796.35 | −0.316497 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −882.349 | −0.0731411 | ||||||||
\(527\) | 7784.44 | + | 7784.44i | 0.643445 | + | 0.643445i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 28122.2i | − | 2.31135i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11355.4 | − | 11355.4i | 0.925413 | − | 0.925413i | ||||
\(533\) | −360.634 | + | 360.634i | −0.0293073 | + | 0.0293073i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 10.1861i | 0.000820842i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17369.5 | + | 17369.5i | 1.39192 | + | 1.39192i | ||||
\(539\) | −38286.9 | −3.05962 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19472.7 | −1.54749 | −0.773747 | − | 0.633494i | \(-0.781620\pi\) | ||||
−0.773747 | + | 0.633494i | \(0.781620\pi\) | |||||||
\(542\) | 12784.1 | + | 12784.1i | 1.01315 | + | 1.01315i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 15081.2i | − | 1.18860i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15899.0 | − | 15899.0i | 1.24277 | − | 1.24277i | 0.283916 | − | 0.958849i | \(-0.408366\pi\) |
0.958849 | − | 0.283916i | \(-0.0916336\pi\) | |||||||
\(548\) | −1360.36 | + | 1360.36i | −0.106043 | + | 0.106043i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4658.98i | 0.360217i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20649.8 | − | 20649.8i | −1.58792 | − | 1.58792i | ||||
\(554\) | 5045.28 | 0.386920 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9442.38 | 0.720227 | ||||||||
\(557\) | −2403.47 | − | 2403.47i | −0.182834 | − | 0.182834i | 0.609756 | − | 0.792589i | \(-0.291268\pi\) |
−0.792589 | + | 0.609756i | \(0.791268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7827.51i | − | 0.592251i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12571.9 | − | 12571.9i | 0.943622 | − | 0.943622i | ||||
\(563\) | −7264.48 | + | 7264.48i | −0.543803 | + | 0.543803i | −0.924642 | − | 0.380838i | \(-0.875635\pi\) |
0.380838 | + | 0.924642i | \(0.375635\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 26545.4i | − | 1.97135i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −613.995 | − | 613.995i | −0.0453568 | − | 0.0453568i | ||||
\(569\) | 5273.08 | 0.388505 | 0.194252 | − | 0.980952i | \(-0.437772\pi\) | ||||
0.194252 | + | 0.980952i | \(0.437772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14061.0 | 1.03053 | 0.515267 | − | 0.857030i | \(-0.327693\pi\) | ||||
0.515267 | + | 0.857030i | \(0.327693\pi\) | |||||||
\(572\) | −8364.26 | − | 8364.26i | −0.611411 | − | 0.611411i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1965.19i | − | 0.142901i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10570.7 | − | 10570.7i | 0.762673 | − | 0.762673i | −0.214131 | − | 0.976805i | \(-0.568692\pi\) |
0.976805 | + | 0.214131i | \(0.0686921\pi\) | |||||||
\(578\) | −3835.57 | + | 3835.57i | −0.276018 | + | 0.276018i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23158.1i | 1.65363i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3566.54 | − | 3566.54i | −0.253364 | − | 0.253364i | ||||
\(584\) | −684.720 | −0.0485170 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −25883.8 | −1.82466 | ||||||||
\(587\) | 7292.50 | + | 7292.50i | 0.512766 | + | 0.512766i | 0.915373 | − | 0.402607i | \(-0.131896\pi\) |
−0.402607 | + | 0.915373i | \(0.631896\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10894.2i | 0.762121i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5395.58 | − | 5395.58i | 0.374589 | − | 0.374589i | ||||
\(593\) | −454.363 | + | 454.363i | −0.0314645 | + | 0.0314645i | −0.722664 | − | 0.691199i | \(-0.757083\pi\) |
0.691199 | + | 0.722664i | \(0.257083\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 323.285i | − | 0.0222186i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20460.8 | + | 20460.8i | 1.39917 | + | 1.39917i | ||||
\(599\) | 7281.47 | 0.496683 | 0.248341 | − | 0.968673i | \(-0.420115\pi\) | ||||
0.248341 | + | 0.968673i | \(0.420115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14273.8 | 0.968786 | 0.484393 | − | 0.874850i | \(-0.339040\pi\) | ||||
0.484393 | + | 0.874850i | \(0.339040\pi\) | |||||||
\(602\) | 21327.1 | + | 21327.1i | 1.44390 | + | 1.44390i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 363.967i | − | 0.0245192i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7824.40 | − | 7824.40i | 0.523200 | − | 0.523200i | −0.395336 | − | 0.918536i | \(-0.629372\pi\) |
0.918536 | + | 0.395336i | \(0.129372\pi\) | |||||||
\(608\) | 10553.0 | − | 10553.0i | 0.703914 | − | 0.703914i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10238.4i | 0.677907i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2893.58 | − | 2893.58i | −0.190653 | − | 0.190653i | 0.605325 | − | 0.795978i | \(-0.293043\pi\) |
−0.795978 | + | 0.605325i | \(0.793043\pi\) | |||||||
\(614\) | −28026.7 | −1.84212 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1725.41 | −0.112855 | ||||||||
\(617\) | 2847.70 | + | 2847.70i | 0.185809 | + | 0.185809i | 0.793881 | − | 0.608073i | \(-0.208057\pi\) |
−0.608073 | + | 0.793881i | \(0.708057\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16644.3i | 1.08076i | 0.841421 | + | 0.540380i | \(0.181719\pi\) | ||||
−0.841421 | + | 0.540380i | \(0.818281\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19265.5 | + | 19265.5i | −1.24193 | + | 1.24193i | ||||
\(623\) | −16171.8 | + | 16171.8i | −1.03998 | + | 1.03998i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 19180.8i | − | 1.22463i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14306.9 | + | 14306.9i | 0.909088 | + | 0.909088i | ||||
\(629\) | 6857.13 | 0.434677 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5327.30 | −0.336096 | −0.168048 | − | 0.985779i | \(-0.553746\pi\) | ||||
−0.168048 | + | 0.985779i | \(0.553746\pi\) | |||||||
\(632\) | −675.333 | − | 675.333i | −0.0425053 | − | 0.0425053i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26286.8i | 1.64666i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23340.3 | + | 23340.3i | −1.45177 | + | 1.45177i | ||||
\(638\) | −9350.26 | + | 9350.26i | −0.580220 | + | 0.580220i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16450.6i | 1.01367i | 0.862044 | + | 0.506834i | \(0.169184\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21894.3 | + | 21894.3i | 1.34281 | + | 1.34281i | 0.893252 | + | 0.449555i | \(0.148418\pi\) |
0.449555 | + | 0.893252i | \(0.351582\pi\) | |||||||
\(644\) | −54712.6 | −3.34779 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13901.4 | 0.846661 | ||||||||
\(647\) | −7768.11 | − | 7768.11i | −0.472018 | − | 0.472018i | 0.430549 | − | 0.902567i | \(-0.358320\pi\) |
−0.902567 | + | 0.430549i | \(0.858320\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 28087.3i | 1.69880i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2274.38 | − | 2274.38i | 0.136613 | − | 0.136613i | ||||
\(653\) | −14364.4 | + | 14364.4i | −0.860831 | + | 0.860831i | −0.991435 | − | 0.130603i | \(-0.958309\pi\) |
0.130603 | + | 0.991435i | \(0.458309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 928.928i | − | 0.0552874i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −27895.9 | − | 27895.9i | −1.65273 | − | 1.65273i | ||||
\(659\) | 18185.5 | 1.07497 | 0.537486 | − | 0.843272i | \(-0.319374\pi\) | ||||
0.537486 | + | 0.843272i | \(0.319374\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8833.96 | 0.519820 | 0.259910 | − | 0.965633i | \(-0.416307\pi\) | ||||
0.259910 | + | 0.965633i | \(0.416307\pi\) | |||||||
\(662\) | −2668.22 | − | 2668.22i | −0.156652 | − | 0.156652i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 757.366i | 0.0442643i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11223.9 | − | 11223.9i | 0.651564 | − | 0.651564i | ||||
\(668\) | −8335.76 | + | 8335.76i | −0.482815 | + | 0.482815i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 25349.0i | − | 1.45840i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12769.6 | − | 12769.6i | −0.731398 | − | 0.731398i | 0.239499 | − | 0.970897i | \(-0.423017\pi\) |
−0.970897 | + | 0.239499i | \(0.923017\pi\) | |||||||
\(674\) | 22464.9 | 1.28385 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6736.97 | 0.383305 | ||||||||
\(677\) | −1478.18 | − | 1478.18i | −0.0839157 | − | 0.0839157i | 0.663903 | − | 0.747819i | \(-0.268899\pi\) |
−0.747819 | + | 0.663903i | \(0.768899\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18579.4i | 1.05009i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21864.0 | + | 21864.0i | −1.22759 | + | 1.22759i | ||||
\(683\) | −2681.69 | + | 2681.69i | −0.150237 | + | 0.150237i | −0.778224 | − | 0.627987i | \(-0.783879\pi\) |
0.627987 | + | 0.778224i | \(0.283879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 79115.0i | − | 4.40324i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10081.1 | + | 10081.1i | 0.558633 | + | 0.558633i | ||||
\(689\) | −4348.44 | −0.240439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23210.5 | −1.27782 | −0.638908 | − | 0.769283i | \(-0.720614\pi\) | ||||
−0.638908 | + | 0.769283i | \(0.720614\pi\) | |||||||
\(692\) | 18268.2 | + | 18268.2i | 1.00355 | + | 1.00355i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10499.9i | 0.574308i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 590.278 | − | 590.278i | 0.0320780 | − | 0.0320780i | ||||
\(698\) | −29825.0 | + | 29825.0i | −1.61732 | + | 1.61732i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26169.3i | 1.40999i | 0.709213 | + | 0.704995i | \(0.249051\pi\) | ||||
−0.709213 | + | 0.704995i | \(0.750949\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4798.24 | + | 4798.24i | 0.257424 | + | 0.257424i | ||||
\(704\) | 19997.8 | 1.07059 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31945.1 | 1.70293 | ||||||||
\(707\) | 39501.9 | + | 39501.9i | 2.10130 | + | 2.10130i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 13604.6i | − | 0.720636i | −0.932830 | − | 0.360318i | \(-0.882668\pi\) | ||
0.932830 | − | 0.360318i | \(-0.117332\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −528.886 | + | 528.886i | −0.0278382 | + | 0.0278382i | ||||
\(713\) | 26245.3 | − | 26245.3i | 1.37853 | − | 1.37853i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20280.4i | 1.05854i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 34396.6 | + | 34396.6i | 1.78784 | + | 1.78784i | ||||
\(719\) | 15020.4 | 0.779088 | 0.389544 | − | 0.921008i | \(-0.372633\pi\) | ||||
0.389544 | + | 0.921008i | \(0.372633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1571.62 | 0.0811792 | ||||||||
\(722\) | −9495.04 | − | 9495.04i | −0.489430 | − | 0.489430i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 3794.89i | − | 0.194801i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1195.38 | + | 1195.38i | −0.0609824 | + | 0.0609824i | −0.736940 | − | 0.675958i | \(-0.763730\pi\) |
0.675958 | + | 0.736940i | \(0.263730\pi\) | |||||||
\(728\) | −1051.83 | + | 1051.83i | −0.0535489 | + | 0.0535489i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12811.9i | 0.648243i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14097.2 | − | 14097.2i | −0.710359 | − | 0.710359i | 0.256251 | − | 0.966610i | \(-0.417513\pi\) |
−0.966610 | + | 0.256251i | \(0.917513\pi\) | |||||||
\(734\) | 16061.3 | 0.807674 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −50846.3 | −2.54649 | ||||||||
\(737\) | −262.759 | − | 262.759i | −0.0131328 | − | 0.0131328i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8052.39i | 0.400828i | 0.979711 | + | 0.200414i | \(0.0642287\pi\) | ||||
−0.979711 | + | 0.200414i | \(0.935771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11847.9 | − | 11847.9i | 0.586186 | − | 0.586186i | ||||
\(743\) | −6706.82 | + | 6706.82i | −0.331156 | + | 0.331156i | −0.853026 | − | 0.521869i | \(-0.825235\pi\) |
0.521869 | + | 0.853026i | \(0.325235\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21632.8i | 1.06171i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13690.5 | + | 13690.5i | 0.669215 | + | 0.669215i | ||||
\(749\) | −33500.4 | −1.63428 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17782.1 | −0.864018 | −0.432009 | − | 0.901869i | \(-0.642195\pi\) | ||||
−0.432009 | + | 0.901869i | \(0.642195\pi\) | |||||||
\(752\) | −13186.1 | − | 13186.1i | −0.639427 | − | 0.639427i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11400.1i | 0.550621i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3547.92 | − | 3547.92i | 0.170345 | − | 0.170345i | −0.616786 | − | 0.787131i | \(-0.711566\pi\) |
0.787131 | + | 0.616786i | \(0.211566\pi\) | |||||||
\(758\) | 8355.39 | − | 8355.39i | 0.400371 | − | 0.400371i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 29802.3i | − | 1.41962i | −0.704392 | − | 0.709811i | \(-0.748780\pi\) | ||
0.704392 | − | 0.709811i | \(-0.251220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29376.3 | − | 29376.3i | −1.39383 | − | 1.39383i | ||||
\(764\) | −9909.05 | −0.469237 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 57465.3 | 2.71058 | ||||||||
\(767\) | 17122.4 | + | 17122.4i | 0.806069 | + | 0.806069i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1720.92i | 0.0806994i | 0.999186 | + | 0.0403497i | \(0.0128472\pi\) | ||||
−0.999186 | + | 0.0403497i | \(0.987153\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −385.339 | + | 385.339i | −0.0179646 | + | 0.0179646i | ||||
\(773\) | 8247.02 | − | 8247.02i | 0.383732 | − | 0.383732i | −0.488713 | − | 0.872445i | \(-0.662533\pi\) |
0.872445 | + | 0.488713i | \(0.162533\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 607.622i | 0.0281087i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19170.9 | − | 19170.9i | −0.883434 | − | 0.883434i | ||||
\(779\) | 826.088 | 0.0379944 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31677.2 | 1.45134 | ||||||||
\(782\) | −33489.8 | − | 33489.8i | −1.53145 | − | 1.53145i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 60120.5i | − | 2.73872i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24948.6 | − | 24948.6i | 1.13001 | − | 1.13001i | 0.139840 | − | 0.990174i | \(-0.455341\pi\) |
0.990174 | − | 0.139840i | \(-0.0446590\pi\) | |||||||
\(788\) | 25543.2 | − | 25543.2i | 1.15474 | − | 1.15474i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29753.4i | 1.33743i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15453.1 | − | 15453.1i | −0.692001 | − | 0.692001i | ||||
\(794\) | −1617.29 | −0.0722866 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12747.2 | −0.567605 | ||||||||
\(797\) | −13046.4 | − | 13046.4i | −0.579832 | − | 0.579832i | 0.355025 | − | 0.934857i | \(-0.384472\pi\) |
−0.934857 | + | 0.355025i | \(0.884472\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 16758.0i | − | 0.741997i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13354.2 | + | 13354.2i | −0.587973 | + | 0.587973i | ||||
\(803\) | 17663.0 | − | 17663.0i | 0.776232 | − | 0.776232i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26657.2i | 1.16496i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1291.88 | + | 1291.88i | 0.0562475 | + | 0.0562475i | ||||
\(809\) | −23979.2 | −1.04211 | −0.521053 | − | 0.853524i | \(-0.674461\pi\) | ||||
−0.521053 | + | 0.853524i | \(0.674461\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32204.9 | 1.39441 | 0.697205 | − | 0.716871i | \(-0.254427\pi\) | ||||
0.697205 | + | 0.716871i | \(0.254427\pi\) | |||||||
\(812\) | −15242.1 | − | 15242.1i | −0.658735 | − | 0.658735i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 19259.5i | 0.829293i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8965.06 | + | 8965.06i | −0.383902 | + | 0.383902i | ||||
\(818\) | −22792.5 | + | 22792.5i | −0.974232 | + | 0.974232i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30723.2i | 1.30603i | 0.757346 | + | 0.653014i | \(0.226496\pi\) | ||||
−0.757346 | + | 0.653014i | \(0.773504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11028.6 | + | 11028.6i | 0.467112 | + | 0.467112i | 0.900978 | − | 0.433866i | \(-0.142851\pi\) |
−0.433866 | + | 0.900978i | \(0.642851\pi\) | |||||||
\(824\) | 51.3985 | 0.00217300 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −93304.7 | −3.93037 | ||||||||
\(827\) | −6174.37 | − | 6174.37i | −0.259618 | − | 0.259618i | 0.565281 | − | 0.824898i | \(-0.308768\pi\) |
−0.824898 | + | 0.565281i | \(0.808768\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 25346.8i | − | 1.06192i | −0.847398 | − | 0.530959i | \(-0.821832\pi\) | ||
0.847398 | − | 0.530959i | \(-0.178168\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12191.0 | − | 12191.0i | 0.507987 | − | 0.507987i | ||||
\(833\) | 38202.9 | − | 38202.9i | 1.58902 | − | 1.58902i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 19159.6i | 0.792643i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 622.168 | + | 622.168i | 0.0256473 | + | 0.0256473i | ||||
\(839\) | −31583.9 | −1.29964 | −0.649820 | − | 0.760088i | \(-0.725156\pi\) | ||||
−0.649820 | + | 0.760088i | \(0.725156\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18135.4 | −0.743588 | ||||||||
\(842\) | −12365.2 | − | 12365.2i | −0.506095 | − | 0.506095i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 26488.5i | − | 1.08030i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11227.0 | − | 11227.0i | 0.455449 | − | 0.455449i | ||||
\(848\) | 5600.40 | − | 5600.40i | 0.226791 | − | 0.226791i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 23118.9i | − | 0.931262i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28855.5 | + | 28855.5i | 1.15826 | + | 1.15826i | 0.984850 | + | 0.173408i | \(0.0554780\pi\) |
0.173408 | + | 0.984850i | \(0.444522\pi\) | |||||||
\(854\) | 84208.2 | 3.37418 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1095.60 | −0.0437464 | ||||||||
\(857\) | −423.601 | − | 423.601i | −0.0168844 | − | 0.0168844i | 0.698614 | − | 0.715499i | \(-0.253800\pi\) |
−0.715499 | + | 0.698614i | \(0.753800\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 37170.9i | − | 1.47643i | −0.674565 | − | 0.738216i | \(-0.735669\pi\) | ||
0.674565 | − | 0.738216i | \(-0.264331\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −28825.7 | + | 28825.7i | −1.13899 | + | 1.13899i | ||||
\(863\) | −24808.1 | + | 24808.1i | −0.978538 | + | 0.978538i | −0.999774 | − | 0.0212362i | \(-0.993240\pi\) |
0.0212362 | + | 0.999774i | \(0.493240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 37088.4i | − | 1.45533i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −35641.0 | − | 35641.0i | −1.39370 | − | 1.39370i | ||||
\(869\) | 34841.7 | 1.36010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −320.364 | −0.0124628 | ||||||||
\(872\) | −960.728 | − | 960.728i | −0.0373100 | − | 0.0373100i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 46868.6i | − | 1.81391i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33936.8 | − | 33936.8i | 1.30669 | − | 1.30669i | 0.382896 | − | 0.923792i | \(-0.374927\pi\) |
0.923792 | − | 0.382896i | \(-0.125073\pi\) | |||||||
\(878\) | 32183.9 | − | 32183.9i | 1.23708 | − | 1.23708i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6463.97i | − | 0.247193i | −0.992333 | − | 0.123596i | \(-0.960557\pi\) | ||
0.992333 | − | 0.123596i | \(-0.0394428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27976.2 | + | 27976.2i | 1.06622 | + | 1.06622i | 0.997646 | + | 0.0685762i | \(0.0218456\pi\) |
0.0685762 | + | 0.997646i | \(0.478154\pi\) | |||||||
\(884\) | 16691.8 | 0.635075 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19171.3 | 0.726943 | ||||||||
\(887\) | −18609.3 | − | 18609.3i | −0.704441 | − | 0.704441i | 0.260920 | − | 0.965360i | \(-0.415974\pi\) |
−0.965360 | + | 0.260920i | \(0.915974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6870.34i | 0.259195i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19962.8 | − | 19962.8i | 0.749332 | − | 0.749332i | ||||
\(893\) | 11726.3 | − | 11726.3i | 0.439425 | − | 0.439425i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 5231.23i | − | 0.195048i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33617.9 | − | 33617.9i | −1.24927 | − | 1.24927i | ||||
\(899\) | 14623.1 | 0.542499 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7117.44 | 0.263170 | ||||||||
\(902\) | 1657.90 | + | 1657.90i | 0.0611997 | + | 0.0611997i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 973.059i | 0.0358003i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22007.2 | + | 22007.2i | −0.805663 | + | 0.805663i | −0.983974 | − | 0.178311i | \(-0.942937\pi\) |
0.178311 | + | 0.983974i | \(0.442937\pi\) | |||||||
\(908\) | −30406.9 | + | 30406.9i | −1.11133 | + | 1.11133i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 27845.6i | − | 1.01269i | −0.862330 | − | 0.506347i | \(-0.830995\pi\) | ||
0.862330 | − | 0.506347i | \(-0.169005\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19537.0 | − | 19537.0i | −0.708192 | − | 0.708192i | ||||
\(914\) | −18179.6 | −0.657910 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17490.6 | −0.630900 | ||||||||
\(917\) | −12315.1 | − | 12315.1i | −0.443490 | − | 0.443490i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40017.1i | 1.43639i | 0.695841 | + | 0.718196i | \(0.255032\pi\) | ||||
−0.695841 | + | 0.718196i | \(0.744968\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −42061.2 | + | 42061.2i | −1.50240 | + | 1.50240i | ||||
\(923\) | 19310.9 | − | 19310.9i | 0.688652 | − | 0.688652i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 7007.88i | − | 0.248697i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14165.0 | − | 14165.0i | −0.501065 | − | 0.501065i | ||||
\(929\) | 22680.8 | 0.801003 | 0.400502 | − | 0.916296i | \(-0.368836\pi\) | ||||
0.400502 | + | 0.916296i | \(0.368836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 53464.6 | 1.88210 | ||||||||
\(932\) | −13549.8 | − | 13549.8i | −0.476220 | − | 0.476220i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 23958.7i | 0.839349i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17387.5 | + | 17387.5i | −0.606216 | + | 0.606216i | −0.941955 | − | 0.335739i | \(-0.891014\pi\) |
0.335739 | + | 0.941955i | \(0.391014\pi\) | |||||||
\(938\) | 872.875 | − | 872.875i | 0.0303842 | − | 0.0303842i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26573.5i | 0.920587i | 0.887767 | + | 0.460293i | \(0.152256\pi\) | ||||
−0.887767 | + | 0.460293i | \(0.847744\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1990.13 | − | 1990.13i | −0.0687247 | − | 0.0687247i | ||||
\(944\) | −44104.3 | −1.52063 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35984.5 | −1.23674 | ||||||||
\(947\) | 34605.4 | + | 34605.4i | 1.18746 | + | 1.18746i | 0.977767 | + | 0.209694i | \(0.0672469\pi\) |
0.209694 | + | 0.977767i | \(0.432753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 21535.3i | − | 0.736633i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1721.62 | − | 1721.62i | 0.0586115 | − | 0.0586115i | ||||
\(953\) | −15334.3 | + | 15334.3i | −0.521225 | + | 0.521225i | −0.917941 | − | 0.396717i | \(-0.870150\pi\) |
0.396717 | + | 0.917941i | \(0.370150\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 27525.4i | 0.931207i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20148.1 | + | 20148.1i | 0.679494 | + | 0.679494i | ||||
\(959\) | −8825.80 | −0.297185 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4402.50 | 0.147780 | ||||||||
\(962\) | 11740.9 | + | 11740.9i | 0.393494 | + | 0.393494i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 46529.2i | 1.55457i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37027.3 | + | 37027.3i | −1.23135 | + | 1.23135i | −0.267908 | + | 0.963444i | \(0.586332\pi\) |
−0.963444 | + | 0.267908i | \(0.913668\pi\) | |||||||
\(968\) | 367.171 | − | 367.171i | 0.0121914 | − | 0.0121914i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 49325.9i | 1.63022i | 0.579306 | + | 0.815110i | \(0.303324\pi\) | ||||
−0.579306 | + | 0.815110i | \(0.696676\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30630.4 | + | 30630.4i | 1.00922 | + | 1.00922i | ||||
\(974\) | 5177.53 | 0.170327 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39804.5 | 1.30544 | ||||||||
\(977\) | 34615.8 | + | 34615.8i | 1.13353 | + | 1.13353i | 0.989586 | + | 0.143945i | \(0.0459787\pi\) |
0.143945 | + | 0.989586i | \(0.454021\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 27286.2i | − | 0.890778i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1217.94 | + | 1217.94i | −0.0395785 | + | 0.0395785i | ||||
\(983\) | 18512.8 | − | 18512.8i | 0.600679 | − | 0.600679i | −0.339813 | − | 0.940493i | \(-0.610364\pi\) |
0.940493 | + | 0.339813i | \(0.110364\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 18659.5i | − | 0.602677i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11680.0 | + | 11680.0i | 0.376104 | + | 0.376104i | ||||
\(989\) | 43195.4 | 1.38881 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49717.5 | 1.59367 | 0.796837 | − | 0.604195i | \(-0.206505\pi\) | ||||
0.796837 | + | 0.604195i | \(0.206505\pi\) | |||||||
\(992\) | −33122.4 | − | 33122.4i | −1.06012 | − | 1.06012i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 105230.i | 3.35785i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12494.0 | + | 12494.0i | −0.396880 | + | 0.396880i | −0.877131 | − | 0.480251i | \(-0.840546\pi\) |
0.480251 | + | 0.877131i | \(0.340546\pi\) | |||||||
\(998\) | 20256.6 | − | 20256.6i | 0.642498 | − | 0.642498i | ||||
\(999\) | 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 | 225.4.f.d.143.1 | yes | 16 | |
3.2 | odd | 2 | inner | 225.4.f.d.143.7 | yes | 16 | |
5.2 | odd | 4 | inner | 225.4.f.d.107.7 | yes | 16 | |
5.3 | odd | 4 | inner | 225.4.f.d.107.2 | yes | 16 | |
5.4 | even | 2 | inner | 225.4.f.d.143.8 | yes | 16 | |
15.2 | even | 4 | inner | 225.4.f.d.107.1 | ✓ | 16 | |
15.8 | even | 4 | inner | 225.4.f.d.107.8 | yes | 16 | |
15.14 | odd | 2 | inner | 225.4.f.d.143.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.f.d.107.1 | ✓ | 16 | 15.2 | even | 4 | inner | |
225.4.f.d.107.2 | yes | 16 | 5.3 | odd | 4 | inner | |
225.4.f.d.107.7 | yes | 16 | 5.2 | odd | 4 | inner | |
225.4.f.d.107.8 | yes | 16 | 15.8 | even | 4 | inner | |
225.4.f.d.143.1 | yes | 16 | 1.1 | even | 1 | trivial | |
225.4.f.d.143.2 | yes | 16 | 15.14 | odd | 2 | inner | |
225.4.f.d.143.7 | yes | 16 | 3.2 | odd | 2 | inner | |
225.4.f.d.143.8 | yes | 16 | 5.4 | even | 2 | inner |