Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(1.28078 - 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.361 |
Dual form | 1960.2.q.u.961.2 |
$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.28078 | − | 2.21837i | 0.739457 | − | 1.28078i | −0.213284 | − | 0.976990i | \(-0.568416\pi\) |
0.952740 | − | 0.303786i | \(-0.0982508\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.78078 | − | 3.08440i | −0.593592 | − | 1.02813i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.28078 | − | 2.21837i | 0.386169 | − | 0.668864i | −0.605762 | − | 0.795646i | \(-0.707132\pi\) |
0.991931 | + | 0.126782i | \(0.0404650\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.68466 | 1.57664 | 0.788320 | − | 0.615265i | \(-0.210951\pi\) | ||||
0.788320 | + | 0.615265i | \(0.210951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.56155 | 0.661390 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.71922 | − | 2.97778i | 0.416973 | − | 0.722218i | −0.578660 | − | 0.815569i | \(-0.696424\pi\) |
0.995633 | + | 0.0933503i | \(0.0297576\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.561553 | + | 0.972638i | 0.128829 | + | 0.223138i | 0.923223 | − | 0.384264i | \(-0.125545\pi\) |
−0.794394 | + | 0.607403i | \(0.792211\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.56155 | + | 4.43674i | 0.534121 | + | 0.925124i | 0.999205 | + | 0.0398580i | \(0.0126905\pi\) |
−0.465085 | + | 0.885266i | \(0.653976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.56155 | 0.847059 | 0.423530 | − | 0.905882i | \(-0.360791\pi\) | ||||
0.423530 | + | 0.905882i | \(0.360791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12311 | + | 8.87348i | −0.920137 | + | 1.59372i | −0.120936 | + | 0.992660i | \(0.538589\pi\) |
−0.799201 | + | 0.601064i | \(0.794744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.28078 | − | 5.68247i | −0.571110 | − | 0.989191i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.12311 | − | 7.14143i | −0.677834 | − | 1.17404i | −0.975632 | − | 0.219414i | \(-0.929585\pi\) |
0.297797 | − | 0.954629i | \(-0.403748\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.28078 | − | 12.6107i | 1.16586 | − | 2.01932i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.12311 | −1.11244 | −0.556221 | − | 0.831034i | \(-0.687749\pi\) | ||||
−0.556221 | + | 0.831034i | \(0.687749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.12311 | 0.171272 | 0.0856360 | − | 0.996326i | \(-0.472708\pi\) | ||||
0.0856360 | + | 0.996326i | \(0.472708\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.78078 | − | 3.08440i | 0.265462 | − | 0.459794i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.28078 | + | 5.68247i | 0.478550 | + | 0.828874i | 0.999698 | − | 0.0245932i | \(-0.00782905\pi\) |
−0.521147 | + | 0.853467i | \(0.674496\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.40388 | − | 7.62775i | −0.616667 | − | 1.06810i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.43845 | − | 4.22351i | 0.334946 | − | 0.580144i | −0.648528 | − | 0.761191i | \(-0.724615\pi\) |
0.983475 | + | 0.181046i | \(0.0579484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.56155 | 0.345400 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.87689 | 0.381054 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.56155 | − | 13.0970i | −0.968158 | − | 1.67690i | −0.700881 | − | 0.713278i | \(-0.747210\pi\) |
−0.267277 | − | 0.963620i | \(-0.586124\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.84233 | + | 4.92306i | 0.352548 | + | 0.610630i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.12311 | − | 12.3376i | 0.870226 | − | 1.50728i | 0.00846293 | − | 0.999964i | \(-0.497306\pi\) |
0.861763 | − | 0.507311i | \(-0.169361\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.1231 | 1.57984 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.12311 | − | 10.6055i | 0.716655 | − | 1.24128i | −0.245662 | − | 0.969355i | \(-0.579005\pi\) |
0.962318 | − | 0.271928i | \(-0.0876612\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.28078 | + | 2.21837i | 0.147891 | + | 0.256155i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.84233 | + | 10.1192i | 0.657313 | + | 1.13850i | 0.981308 | + | 0.192441i | \(0.0616405\pi\) |
−0.323995 | + | 0.946059i | \(0.605026\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.50000 | − | 6.06218i | 0.388889 | − | 0.673575i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.43845 | 0.372952 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.84233 | − | 10.1192i | 0.626363 | − | 1.08489i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.56155 | − | 2.70469i | −0.165524 | − | 0.286696i | 0.771317 | − | 0.636451i | \(-0.219598\pi\) |
−0.936841 | + | 0.349755i | \(0.886265\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.1231 | + | 22.7299i | 1.36080 | + | 2.35698i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.561553 | + | 0.972638i | −0.0576141 | + | 0.0997906i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.6847 | −1.38947 | −0.694733 | − | 0.719267i | \(-0.744478\pi\) | ||||
−0.694733 | + | 0.719267i | \(0.744478\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.12311 | −0.916907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.40388 | + | 7.62775i | 0.433927 | + | 0.751584i | 0.997207 | − | 0.0746818i | \(-0.0237941\pi\) |
−0.563280 | + | 0.826266i | \(0.690461\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.43845 | − | 5.95557i | −0.332407 | − | 0.575746i | 0.650576 | − | 0.759441i | \(-0.274528\pi\) |
−0.982983 | + | 0.183695i | \(0.941194\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.28078 | − | 7.41452i | 0.410024 | − | 0.710182i | −0.584868 | − | 0.811129i | \(-0.698854\pi\) |
0.994892 | + | 0.100946i | \(0.0321870\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.1231 | −2.00492 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.24621 | −0.775738 | −0.387869 | − | 0.921714i | \(-0.626789\pi\) | ||||
−0.387869 | + | 0.921714i | \(0.626789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.56155 | + | 4.43674i | −0.238866 | + | 0.413728i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.1231 | − | 17.5337i | −0.935881 | − | 1.62099i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.21922 | + | 3.84381i | 0.201748 | + | 0.349437i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.12311 | + | 15.8017i | −0.822603 | + | 1.42479i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2462 | 0.909204 | 0.454602 | − | 0.890695i | \(-0.349781\pi\) | ||||
0.454602 | + | 0.890695i | \(0.349781\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.43845 | − | 2.49146i | 0.126648 | − | 0.219361i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.43845 | + | 5.95557i | 0.300419 | + | 0.520340i | 0.976231 | − | 0.216734i | \(-0.0695403\pi\) |
−0.675812 | + | 0.737074i | \(0.736207\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.719224 | − | 1.24573i | −0.0619009 | − | 0.107216i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.68466 | + | 15.0423i | −0.741980 | + | 1.28515i | 0.209612 | + | 0.977785i | \(0.432780\pi\) |
−0.951592 | + | 0.307363i | \(0.900553\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.36932 | −0.285782 | −0.142891 | − | 0.989738i | \(-0.545640\pi\) | ||||
−0.142891 | + | 0.989738i | \(0.545640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.8078 | 1.41547 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.28078 | − | 12.6107i | 0.608849 | − | 1.05456i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.28078 | + | 3.95042i | 0.189408 | + | 0.328065i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.12311 | − | 14.0696i | −0.665471 | − | 1.15263i | −0.979157 | − | 0.203103i | \(-0.934898\pi\) |
0.313687 | − | 0.949527i | \(-0.398436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.403882 | + | 0.699544i | −0.0328675 | + | 0.0569281i | −0.881991 | − | 0.471266i | \(-0.843797\pi\) |
0.849124 | + | 0.528194i | \(0.177131\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.2462 | −0.990048 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2462 | −0.822995 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.12311 | + | 10.6055i | −0.488677 | + | 0.846413i | −0.999915 | − | 0.0130257i | \(-0.995854\pi\) |
0.511238 | + | 0.859439i | \(0.329187\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.24621 | − | 10.8188i | −0.495357 | − | 0.857983i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8078 | + | 18.7196i | 0.846529 | + | 1.46623i | 0.884286 | + | 0.466945i | \(0.154645\pi\) |
−0.0377569 | + | 0.999287i | \(0.512021\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.28078 | − | 5.68247i | 0.255408 | − | 0.442380i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.8078 | −1.91968 | −0.959841 | − | 0.280544i | \(-0.909485\pi\) | ||||
−0.959841 | + | 0.280544i | \(0.909485\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.3153 | 1.48580 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.00000 | − | 3.46410i | 0.152944 | − | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0885 | + | 19.2059i | 0.843046 | + | 1.46020i | 0.887307 | + | 0.461179i | \(0.152573\pi\) |
−0.0442611 | + | 0.999020i | \(0.514093\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.12311 | + | 8.87348i | 0.385076 | + | 0.666972i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000 | − | 3.46410i | 0.149487 | − | 0.258919i | −0.781551 | − | 0.623841i | \(-0.785571\pi\) |
0.931038 | + | 0.364922i | \(0.118904\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.12311 | −0.232139 | −0.116069 | − | 0.993241i | \(-0.537029\pi\) | ||||
−0.116069 | + | 0.993241i | \(0.537029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −38.7386 | −2.86364 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.12311 | − | 7.14143i | 0.303137 | − | 0.525048i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.40388 | − | 7.62775i | −0.322044 | − | 0.557796i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.84233 | − | 10.1192i | −0.422736 | − | 0.732200i | 0.573470 | − | 0.819227i | \(-0.305597\pi\) |
−0.996206 | + | 0.0870262i | \(0.972264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.43845 | + | 4.22351i | −0.175523 | + | 0.304015i | −0.940342 | − | 0.340230i | \(-0.889495\pi\) |
0.764819 | + | 0.644245i | \(0.222828\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.5616 | 1.04277 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.87689 | −0.347464 | −0.173732 | − | 0.984793i | \(-0.555583\pi\) | ||||
−0.173732 | + | 0.984793i | \(0.555583\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.12311 | − | 1.94528i | 0.0796148 | − | 0.137897i | −0.823469 | − | 0.567361i | \(-0.807964\pi\) |
0.903084 | + | 0.429464i | \(0.141298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.2462 | − | 31.6034i | −1.28699 | − | 2.22913i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.56155 | − | 6.16879i | −0.248750 | − | 0.430847i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.12311 | − | 15.8017i | 0.634100 | − | 1.09829i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.87689 | 0.198999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4384 | −0.925141 | −0.462570 | − | 0.886583i | \(-0.653073\pi\) | ||||
−0.462570 | + | 0.886583i | \(0.653073\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.561553 | + | 0.972638i | 0.0382976 | + | 0.0663334i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.6847 | − | 27.1666i | −1.05987 | − | 1.83575i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.77320 | − | 16.9277i | 0.657417 | − | 1.13868i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.3153 | −0.824696 | −0.412348 | − | 0.911026i | \(-0.635291\pi\) | ||||
−0.412348 | + | 0.911026i | \(0.635291\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.56155 | 0.237437 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.8423 | + | 20.5115i | −0.786003 | + | 1.36140i | 0.142395 | + | 0.989810i | \(0.454520\pi\) |
−0.928398 | + | 0.371587i | \(0.878814\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.68466 | + | 11.5782i | 0.441735 | + | 0.765107i | 0.997818 | − | 0.0660194i | \(-0.0210299\pi\) |
−0.556084 | + | 0.831126i | \(0.687697\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.56155 | + | 16.5611i | 0.626398 | + | 1.08495i | 0.988269 | + | 0.152725i | \(0.0488049\pi\) |
−0.361871 | + | 0.932228i | \(0.617862\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.28078 | + | 5.68247i | −0.214014 | + | 0.370684i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 29.9309 | 1.94422 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.0540 | 1.23250 | 0.616250 | − | 0.787551i | \(-0.288651\pi\) | ||||
0.616250 | + | 0.787551i | \(0.288651\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | − | 1.73205i | 0.0644157 | − | 0.111571i | −0.832019 | − | 0.554747i | \(-0.812815\pi\) |
0.896435 | + | 0.443176i | \(0.146148\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.1231 | − | 19.2658i | −0.713548 | − | 1.23590i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.19224 | + | 5.52911i | 0.203117 | + | 0.351809i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.3693 | + | 26.6204i | −0.973991 | + | 1.68700i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.3693 | 0.717625 | 0.358812 | − | 0.933410i | \(-0.383182\pi\) | ||||
0.358812 | + | 0.933410i | \(0.383182\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.1231 | 0.825043 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.40388 | − | 7.62775i | 0.275782 | − | 0.477668i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.24621 | + | 12.5508i | 0.452006 | + | 0.782898i | 0.998511 | − | 0.0545585i | \(-0.0173751\pi\) |
−0.546504 | + | 0.837456i | \(0.684042\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.12311 | − | 14.0696i | −0.502808 | − | 0.870888i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.68466 | − | 13.3102i | 0.473856 | − | 0.820743i | −0.525696 | − | 0.850673i | \(-0.676195\pi\) |
0.999552 | + | 0.0299295i | \(0.00952826\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.87689 | 0.299585 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.00000 | −0.489592 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.12311 | + | 10.6055i | −0.373332 | + | 0.646631i | −0.990076 | − | 0.140534i | \(-0.955118\pi\) |
0.616744 | + | 0.787164i | \(0.288452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.12311 | + | 8.87348i | 0.311207 | + | 0.539025i | 0.978624 | − | 0.205658i | \(-0.0659336\pi\) |
−0.667417 | + | 0.744684i | \(0.732600\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.28078 | + | 2.21837i | 0.0772337 | + | 0.133773i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.12311 | + | 7.14143i | −0.247733 | + | 0.429087i | −0.962897 | − | 0.269871i | \(-0.913019\pi\) |
0.715163 | + | 0.698958i | \(0.246352\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 36.4924 | 2.18474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.4384 | −0.920981 | −0.460490 | − | 0.887665i | \(-0.652326\pi\) | ||||
−0.460490 | + | 0.887665i | \(0.652326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.84233 | − | 6.65511i | 0.228403 | − | 0.395605i | −0.728932 | − | 0.684586i | \(-0.759983\pi\) |
0.957335 | + | 0.288981i | \(0.0933164\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.43845 | + | 2.49146i | 0.0852063 | + | 0.147582i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.58854 | + | 4.48348i | 0.152267 | + | 0.263734i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.5270 | + | 30.3576i | −1.02745 | + | 1.77960i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.05398 | 0.295256 | 0.147628 | − | 0.989043i | \(-0.452836\pi\) | ||||
0.147628 | + | 0.989043i | \(0.452836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.84233 | + | 3.19101i | −0.106903 | + | 0.185161i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.5616 | + | 25.2213i | 0.842116 | + | 1.45859i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.68466 | − | 13.3102i | −0.441472 | − | 0.764652i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.56155 | − | 13.0970i | 0.432973 | − | 0.749932i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.3153 | 0.931166 | 0.465583 | − | 0.885004i | \(-0.345845\pi\) | ||||
0.465583 | + | 0.885004i | \(0.345845\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.5616 | 1.28348 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5616 | + | 18.2931i | −0.598891 | + | 1.03731i | 0.394094 | + | 0.919070i | \(0.371058\pi\) |
−0.992985 | + | 0.118239i | \(0.962275\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.15767 | + | 12.3974i | 0.404575 | + | 0.700745i | 0.994272 | − | 0.106880i | \(-0.0340860\pi\) |
−0.589696 | + | 0.807625i | \(0.700753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.00000 | + | 8.66025i | 0.280828 | + | 0.486408i | 0.971589 | − | 0.236675i | \(-0.0760576\pi\) |
−0.690761 | + | 0.723083i | \(0.742724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.84233 | − | 10.1192i | 0.327108 | − | 0.566567i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.6155 | −0.983203 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.86174 | 0.214873 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.84233 | + | 4.92306i | −0.157664 | + | 0.273082i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.9654 | − | 18.9927i | −0.606390 | − | 1.05030i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.00000 | + | 10.3923i | 0.329790 | + | 0.571213i | 0.982470 | − | 0.186421i | \(-0.0596888\pi\) |
−0.652680 | + | 0.757634i | \(0.726355\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.6847 | + | 25.4346i | −0.804714 | + | 1.39381i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.2462 | 0.778354 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.5616 | + | 18.2931i | −0.573625 | + | 0.993547i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.1231 | + | 22.7299i | 0.710656 | + | 1.23089i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.56155 | + | 11.3649i | 0.353262 | + | 0.611868i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.43845 | + | 5.95557i | −0.184586 | + | 0.319711i | −0.943437 | − | 0.331552i | \(-0.892428\pi\) |
0.758851 | + | 0.651264i | \(0.225761\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.2462 | 1.51199 | 0.755993 | − | 0.654580i | \(-0.227155\pi\) | ||||
0.755993 | + | 0.654580i | \(0.227155\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.17708 | −0.436460 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.4039 | + | 19.7521i | −0.606967 | + | 1.05130i | 0.384770 | + | 0.923013i | \(0.374281\pi\) |
−0.991737 | + | 0.128286i | \(0.959053\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.0000 | − | 27.7128i | −0.844448 | − | 1.46263i | −0.886100 | − | 0.463494i | \(-0.846596\pi\) |
0.0416523 | − | 0.999132i | \(-0.486738\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.86932 | − | 15.3621i | 0.466806 | − | 0.808532i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.3693 | 0.596734 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.2462 | 0.640996 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.96543 | + | 12.0645i | −0.363593 | + | 0.629761i | −0.988549 | − | 0.150898i | \(-0.951783\pi\) |
0.624957 | + | 0.780660i | \(0.285117\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.6847 | + | 21.9705i | 0.660337 | + | 1.14374i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.68466 | + | 8.11407i | 0.242562 | + | 0.420130i | 0.961443 | − | 0.275003i | \(-0.0886787\pi\) |
−0.718881 | + | 0.695133i | \(0.755345\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.28078 | + | 2.21837i | −0.0661390 | + | 0.114556i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.9309 | 1.33551 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.492423 | −0.0252940 | −0.0126470 | − | 0.999920i | \(-0.504026\pi\) | ||||
−0.0126470 | + | 0.999920i | \(0.504026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.1231 | − | 22.7299i | 0.672317 | − | 1.16449i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.1231 | − | 22.7299i | −0.670559 | − | 1.16144i | −0.977746 | − | 0.209794i | \(-0.932721\pi\) |
0.307186 | − | 0.951649i | \(-0.400613\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.00000 | − | 3.46410i | −0.101666 | − | 0.176090i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.6501 | − | 27.1068i | 0.793491 | − | 1.37437i | −0.130302 | − | 0.991474i | \(-0.541595\pi\) |
0.923793 | − | 0.382893i | \(-0.125072\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.6155 | 0.890856 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.6155 | 0.888586 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.84233 | + | 10.1192i | −0.293959 | + | 0.509153i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.0885 | + | 19.2059i | 0.556518 | + | 0.963917i | 0.997784 | + | 0.0665408i | \(0.0211963\pi\) |
−0.441266 | + | 0.897376i | \(0.645470\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.96543 | − | 13.7965i | −0.397775 | − | 0.688966i | 0.595676 | − | 0.803225i | \(-0.296884\pi\) |
−0.993451 | + | 0.114258i | \(0.963551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.1231 | + | 50.4427i | −1.45073 | + | 2.51273i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000 | 0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1231 | −1.04703 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.24621 | − | 12.5508i | 0.358302 | − | 0.620597i | −0.629375 | − | 0.777102i | \(-0.716689\pi\) |
0.987677 | + | 0.156504i | \(0.0500225\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.2462 | + | 38.5316i | 1.09732 | + | 1.90062i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.00000 | − | 10.3923i | −0.294528 | − | 0.510138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.31534 | + | 7.47439i | −0.211323 | + | 0.366022i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.75379 | 0.0856782 | 0.0428391 | − | 0.999082i | \(-0.486360\pi\) | ||||
0.0428391 | + | 0.999082i | \(0.486360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.561553 | −0.0273684 | −0.0136842 | − | 0.999906i | \(-0.504356\pi\) | ||||
−0.0136842 | + | 0.999906i | \(0.504356\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.6847 | − | 20.2384i | 0.568128 | − | 0.984026i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.71922 | + | 2.97778i | 0.0833946 | + | 0.144444i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.6501 | − | 32.3029i | −0.900435 | − | 1.55960i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.96543 | + | 5.13628i | −0.142840 | + | 0.247406i | −0.928565 | − | 0.371170i | \(-0.878957\pi\) |
0.785725 | + | 0.618576i | \(0.212290\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.2462 | −1.74188 | −0.870941 | − | 0.491388i | \(-0.836490\pi\) | ||||
−0.870941 | + | 0.491388i | \(0.836490\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.6847 | 0.560236 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.87689 | + | 4.98293i | −0.137621 | + | 0.238366i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.43845 | + | 9.41967i | 0.259563 | + | 0.449576i | 0.966125 | − | 0.258075i | \(-0.0830882\pi\) |
−0.706562 | + | 0.707651i | \(0.749755\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8078 | − | 18.7196i | −0.513492 | − | 0.889395i | −0.999878 | − | 0.0156504i | \(-0.995018\pi\) |
0.486385 | − | 0.873745i | \(-0.338315\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.56155 | − | 2.70469i | 0.0740247 | − | 0.128215i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −41.6155 | −1.96835 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.6847 | −1.58968 | −0.794839 | − | 0.606821i | \(-0.792445\pi\) | ||||
−0.794839 | + | 0.606821i | \(0.792445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.12311 | + | 15.8017i | −0.429590 | + | 0.744072i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.03457 | + | 1.79192i | 0.0486081 | + | 0.0841917i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.6847 | − | 28.8987i | −0.780475 | − | 1.35182i | −0.931665 | − | 0.363318i | \(-0.881644\pi\) |
0.151190 | − | 0.988505i | \(-0.451690\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.47301 | + | 4.28338i | −0.115430 | + | 0.199931i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.1231 | −1.26325 | −0.631624 | − | 0.775274i | \(-0.717612\pi\) | ||||
−0.631624 | + | 0.775274i | \(0.717612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2462 | 0.476182 | 0.238091 | − | 0.971243i | \(-0.423478\pi\) | ||||
0.238091 | + | 0.971243i | \(0.423478\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.1231 | + | 22.7299i | −0.608569 | + | 1.05407i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.7192 | + | 18.5662i | 0.496027 | + | 0.859143i | 0.999990 | − | 0.00458213i | \(-0.00145854\pi\) |
−0.503963 | + | 0.863725i | \(0.668125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.6847 | + | 27.1666i | 0.722711 | + | 1.25177i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.43845 | − | 2.49146i | 0.0661399 | − | 0.114558i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.12311 | −0.0515316 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.3693 | −0.795286 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.68466 | + | 6.38202i | −0.168356 | + | 0.291602i | −0.937842 | − | 0.347062i | \(-0.887179\pi\) |
0.769486 | + | 0.638664i | \(0.220513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.4384 | − | 40.5966i | −1.06870 | − | 1.85104i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.84233 | − | 11.8513i | −0.310694 | − | 0.538138i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.56155 | − | 4.43674i | 0.116075 | − | 0.201048i | −0.802134 | − | 0.597144i | \(-0.796302\pi\) |
0.918209 | + | 0.396096i | \(0.129635\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 55.3693 | 2.50389 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6847 | −0.707839 | −0.353919 | − | 0.935276i | \(-0.615151\pi\) | ||||
−0.353919 | + | 0.935276i | \(0.615151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.84233 | − | 13.5833i | 0.353201 | − | 0.611762i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.56155 | − | 7.90084i | −0.205027 | − | 0.355116i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.4039 | + | 18.0201i | 0.465742 | + | 0.806688i | 0.999235 | − | 0.0391162i | \(-0.0124542\pi\) |
−0.533493 | + | 0.845805i | \(0.679121\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −31.7732 | + | 55.0328i | −1.41952 | + | 2.45868i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.1771 | −0.721300 | −0.360650 | − | 0.932701i | \(-0.617445\pi\) | ||||
−0.360650 | + | 0.932701i | \(0.617445\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.7386 | − | 42.8486i | 1.09868 | − | 1.90297i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.36932 | − | 14.4961i | −0.370963 | − | 0.642528i | 0.618751 | − | 0.785588i | \(-0.287639\pi\) |
−0.989714 | + | 0.143060i | \(0.954306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.807764 | − | 1.39909i | −0.0356637 | − | 0.0617713i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.40388 | + | 7.62775i | −0.194058 | + | 0.336119i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.8078 | 0.739205 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 56.8078 | 2.49358 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.12311 | − | 3.67733i | 0.0930149 | − | 0.161107i | −0.815763 | − | 0.578386i | \(-0.803683\pi\) |
0.908778 | + | 0.417279i | \(0.137016\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.00000 | − | 10.3923i | −0.262362 | − | 0.454424i | 0.704507 | − | 0.709697i | \(-0.251168\pi\) |
−0.966869 | + | 0.255273i | \(0.917835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.6155 | + | 30.5110i | 0.767344 | + | 1.32908i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.62311 | + | 2.81130i | −0.0705698 | + | 0.122230i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.2462 | 0.618233 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −40.4924 | −1.75392 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.43845 | − | 5.95557i | 0.148657 | − | 0.257482i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.12311 | − | 8.87348i | −0.221078 | − | 0.382919i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.2116 | + | 17.6871i | 0.439033 | + | 0.760427i | 0.997615 | − | 0.0690218i | \(-0.0219878\pi\) |
−0.558582 | + | 0.829449i | \(0.688654\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.00000 | + | 6.92820i | −0.171656 | + | 0.297318i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.56155 | 0.366737 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000 | 0.513083 | 0.256541 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256541 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −26.9309 | + | 46.6456i | −1.14938 | + | 1.99079i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.56155 | + | 4.43674i | 0.109126 | + | 0.189011i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.5616 | − | 18.2931i | −0.448313 | − | 0.776501i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.8078 | + | 20.4516i | −0.500311 | + | 0.866564i | 0.499689 | + | 0.866205i | \(0.333448\pi\) |
−1.00000 | 0.000359173i | \(0.999886\pi\) | ||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.38447 | 0.270034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5616 | −0.952550 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.2462 | + | 35.0675i | −0.853276 | + | 1.47792i | 0.0249591 | + | 0.999688i | \(0.492054\pi\) |
−0.878235 | + | 0.478229i | \(0.841279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.12311 | − | 7.14143i | −0.173460 | − | 0.300442i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.4924 | + | 40.6901i | 0.984854 | + | 1.70582i | 0.642585 | + | 0.766214i | \(0.277862\pi\) |
0.342268 | + | 0.939602i | \(0.388805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.9309 | −1.25038 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.12311 | −0.213648 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.280776 | − | 0.486319i | 0.0116889 | − | 0.0202457i | −0.860122 | − | 0.510089i | \(-0.829613\pi\) |
0.871811 | + | 0.489843i | \(0.162946\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.24621 | + | 10.8188i | 0.259584 | + | 0.449612i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.24621 | − | 10.8188i | −0.258692 | − | 0.448067i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.1231 | − | 17.5337i | 0.418539 | − | 0.724931i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.24621 | 0.257809 | 0.128904 | − | 0.991657i | \(-0.458854\pi\) | ||||
0.128904 | + | 0.991657i | \(0.458854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.5076 | −0.474161 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.24621 | + | 10.8188i | −0.256935 | + | 0.445024i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.2116 | − | 21.1512i | −0.501472 | − | 0.868575i | −0.999999 | − | 0.00170079i | \(-0.999459\pi\) |
0.498526 | − | 0.866875i | \(-0.333875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.87689 | − | 4.98293i | −0.117743 | − | 0.203938i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.03457 | − | 15.6483i | 0.369142 | − | 0.639373i | −0.620289 | − | 0.784373i | \(-0.712985\pi\) |
0.989432 | + | 0.145000i | \(0.0463182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −50.7386 | −2.06624 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.21922 | + | 3.84381i | −0.0902243 | + | 0.156273i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.84233 | + | 3.19101i | 0.0747778 | + | 0.129519i | 0.900990 | − | 0.433841i | \(-0.142842\pi\) |
−0.826212 | + | 0.563360i | \(0.809509\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.6501 | + | 32.3029i | 0.754502 | + | 1.30684i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.3693 | − | 28.3525i | 0.661150 | − | 1.14515i | −0.319163 | − | 0.947700i | \(-0.603402\pi\) |
0.980314 | − | 0.197446i | \(-0.0632649\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.2462 | −0.735758 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −32.2462 | −1.29818 | −0.649092 | − | 0.760710i | \(-0.724851\pi\) | ||||
−0.649092 | + | 0.760710i | \(0.724851\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.6847 | − | 30.6307i | 0.710806 | − | 1.23115i | −0.253748 | − | 0.967270i | \(-0.581664\pi\) |
0.964555 | − | 0.263883i | \(-0.0850032\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.68466 | − | 6.38202i | −0.147860 | − | 0.256101i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.68466 | − | 6.38202i | 0.147151 | − | 0.254873i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −28.3542 | −1.13055 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.4233 | 1.37037 | 0.685185 | − | 0.728369i | \(-0.259721\pi\) | ||||
0.685185 | + | 0.728369i | \(0.259721\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.2116 | + | 29.8114i | −0.684102 | + | 1.18490i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.12311 | + | 8.87348i | 0.203304 | + | 0.352133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.4924 | + | 37.2260i | −0.848900 | + | 1.47034i | 0.0332914 | + | 0.999446i | \(0.489401\pi\) |
−0.882191 | + | 0.470892i | \(0.843932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.05398 | −0.278182 | −0.139091 | − | 0.990280i | \(-0.544418\pi\) | ||||
−0.139091 | + | 0.990280i | \(0.544418\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.87689 | 0.113278 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.00000 | − | 6.92820i | 0.157256 | − | 0.272376i | −0.776622 | − | 0.629967i | \(-0.783068\pi\) |
0.933878 | + | 0.357591i | \(0.116402\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.12311 | + | 8.87348i | 0.201099 | + | 0.348315i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.75379 | + | 4.76970i | 0.107764 | + | 0.186653i | 0.914864 | − | 0.403762i | \(-0.132298\pi\) |
−0.807100 | + | 0.590415i | \(0.798964\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.43845 | + | 5.95557i | −0.134351 | + | 0.232703i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −43.6155 | −1.70160 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.8078 | −0.810555 | −0.405278 | − | 0.914194i | \(-0.632825\pi\) | ||||
−0.405278 | + | 0.914194i | \(0.632825\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.8078 | − | 20.4516i | 0.459269 | − | 0.795477i | −0.539654 | − | 0.841887i | \(-0.681445\pi\) |
0.998922 | + | 0.0464102i | \(0.0147781\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −25.0346 | − | 43.3611i | −0.972262 | − | 1.68401i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.6847 | + | 20.2384i | 0.452432 | + | 0.783635i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15.7732 | + | 27.3200i | −0.609827 | + | 1.05625i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.7386 | −1.49549 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.384472 | 0.0148203 | 0.00741015 | − | 0.999973i | \(-0.497641\pi\) | ||||
0.00741015 | + | 0.999973i | \(0.497641\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.719224 | − | 1.24573i | 0.0276829 | − | 0.0479482i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.84233 | − | 11.8513i | −0.262972 | − | 0.455481i | 0.704058 | − | 0.710142i | \(-0.251369\pi\) |
−0.967030 | + | 0.254661i | \(0.918036\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30.3348 | + | 52.5413i | 1.16243 | + | 2.01339i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.4924 | − | 18.1734i | 0.401481 | − | 0.695386i | −0.592424 | − | 0.805627i | \(-0.701829\pi\) |
0.993905 | + | 0.110241i | \(0.0351621\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.3693 | −0.663647 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.2462 | 1.30657 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.8617 | − | 24.0092i | 0.528090 | − | 0.914679i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.24621 | − | 14.2829i | −0.313701 | − | 0.543345i | 0.665460 | − | 0.746434i | \(-0.268236\pi\) |
−0.979160 | + | 0.203088i | \(0.934902\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.68466 | − | 2.91791i | −0.0639027 | − | 0.110683i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.2462 | + | 21.2111i | −0.463858 | + | 0.803426i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.9848 | 1.85278 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.6847 | −0.819018 | −0.409509 | − | 0.912306i | \(-0.634300\pi\) | ||||
−0.409509 | + | 0.912306i | \(0.634300\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.63068 | − | 8.02058i | 0.174650 | − | 0.302502i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.40388 | + | 14.5560i | 0.316509 | + | 0.548209i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.5270 | − | 28.6256i | −0.620684 | − | 1.07506i | −0.989359 | − | 0.145498i | \(-0.953522\pi\) |
0.368675 | − | 0.929559i | \(-0.379812\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 20.8078 | − | 36.0401i | 0.780352 | − | 1.35161i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −52.4924 | −1.96586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.5616 | 0.544571 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.4039 | − | 42.2688i | 0.911380 | − | 1.57856i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.80776 | + | 15.2555i | 0.328474 | + | 0.568934i | 0.982209 | − | 0.187789i | \(-0.0601323\pi\) |
−0.653735 | + | 0.756723i | \(0.726799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.56155 | − | 4.43674i | −0.0952652 | − | 0.165004i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.28078 | + | 3.95042i | −0.0847059 | + | 0.146715i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9848 | 0.629933 | 0.314967 | − | 0.949103i | \(-0.398007\pi\) | ||||
0.314967 | + | 0.949103i | \(0.398007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.93087 | − | 3.34436i | 0.0714158 | − | 0.123696i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.2808 | + | 17.8068i | 0.379729 | + | 0.657710i | 0.991023 | − | 0.133694i | \(-0.0426839\pi\) |
−0.611294 | + | 0.791404i | \(0.709351\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.2462 | − | 31.6034i | −0.672108 | − | 1.16412i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.28078 | − | 9.14657i | 0.194257 | − | 0.336462i | −0.752400 | − | 0.658706i | \(-0.771104\pi\) |
0.946657 | + | 0.322244i | \(0.104437\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.3542 | 0.600785 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.12311 | − | 14.0696i | 0.297608 | − | 0.515471i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.3693 | + | 37.0127i | 0.781862 | + | 1.35423i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8423 | + | 37.8320i | 0.797038 | + | 1.38051i | 0.921537 | + | 0.388290i | \(0.126934\pi\) |
−0.124499 | + | 0.992220i | \(0.539732\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14.5616 | − | 25.2213i | 0.530652 | − | 0.919117i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.807764 | −0.0293975 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.36932 | −0.340534 | −0.170267 | − | 0.985398i | \(-0.554463\pi\) | ||||
−0.170267 | + | 0.985398i | \(0.554463\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.8078 | − | 29.1119i | 0.610083 | − | 1.05670i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.0000 | + | 22.5167i | 0.471250 | + | 0.816228i | 0.999459 | − | 0.0328858i | \(-0.0104698\pi\) |
−0.528209 | + | 0.849114i | \(0.677136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.12311 | − | 10.6055i | −0.221381 | − | 0.383444i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.3693 | + | 19.6922i | −0.410522 | + | 0.711045i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.9848 | 0.828855 | 0.414427 | − | 0.910082i | \(-0.363982\pi\) | ||||
0.414427 | + | 0.910082i | \(0.363982\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.1231 | 1.33696 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.59612 | + | 7.96071i | −0.165311 | + | 0.286327i | −0.936766 | − | 0.349957i | \(-0.886196\pi\) |
0.771455 | + | 0.636284i | \(0.219529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.12311 | − | 8.87348i | −0.184027 | − | 0.318745i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.00000 | − | 6.92820i | −0.143315 | − | 0.248229i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.56155 | −0.234491 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.2462 | −0.437086 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.08854 | + | 10.5457i | −0.217033 | + | 0.375912i | −0.953900 | − | 0.300126i | \(-0.902971\pi\) |
0.736867 | + | 0.676038i | \(0.236305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.6847 | − | 34.0948i | −0.700792 | − | 1.21381i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.9848 | − | 74.4519i | −1.52644 | − | 2.64387i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.24621 | − | 10.8188i | 0.221530 | − | 0.383702i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.80776 | 0.0994561 | 0.0497281 | − | 0.998763i | \(-0.484165\pi\) | ||||
0.0497281 | + | 0.998763i | \(0.484165\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.5616 | 0.798170 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.56155 | + | 9.63289i | −0.196508 | + | 0.340362i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.6847 | − | 27.1666i | −0.553500 | − | 0.958689i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.6847 | + | 27.1666i | 0.552126 | + | 0.956311i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.5270 | − | 28.6256i | 0.581058 | − | 1.00642i | −0.414296 | − | 0.910142i | \(-0.635972\pi\) |
0.995354 | − | 0.0962798i | \(-0.0306944\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6155 | −0.478106 | −0.239053 | − | 0.971007i | \(-0.576837\pi\) | ||||
−0.239053 | + | 0.971007i | \(0.576837\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.2462 | 0.920495 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.8078 | + | 18.7196i | −0.378579 | + | 0.655719i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.630683 | + | 1.09238i | 0.0220648 | + | 0.0382174i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.349907 | − | 0.606056i | −0.0122118 | − | 0.0211515i | 0.859855 | − | 0.510538i | \(-0.170554\pi\) |
−0.872067 | + | 0.489387i | \(0.837221\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.1231 | − | 29.6581i | 0.596874 | − | 1.03382i | −0.396406 | − | 0.918076i | \(-0.629743\pi\) |
0.993279 | − | 0.115740i | \(-0.0369241\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.56155 | 0.228444 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.1231 | 1.15180 | 0.575902 | − | 0.817519i | \(-0.304651\pi\) | ||||
0.575902 | + | 0.817519i | \(0.304651\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.8078 | + | 30.8440i | −0.618489 | + | 1.07125i | 0.371272 | + | 0.928524i | \(0.378922\pi\) |
−0.989762 | + | 0.142731i | \(0.954412\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5616 | + | 18.2931i | 0.366376 | + | 0.634582i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.4039 | − | 21.4842i | −0.429254 | − | 0.743490i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.36932 | − | 12.7640i | 0.254721 | − | 0.441189i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.8769 | −0.375512 | −0.187756 | − | 0.982216i | \(-0.560121\pi\) | ||||
−0.187756 | + | 0.982216i | \(0.560121\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.19224 | −0.282491 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.7732 | + | 34.2482i | −0.681025 | + | 1.17957i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.65767 | + | 16.7276i | 0.332234 | + | 0.575446i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.84233 | − | 17.0474i | −0.337788 | − | 0.585066i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.1231 | − | 36.5863i | 0.724091 | − | 1.25416i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.2462 | −1.10409 | −0.552045 | − | 0.833815i | \(-0.686152\pi\) | ||||
−0.552045 | + | 0.833815i | \(0.686152\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.63068 | − | 2.82443i | 0.0557031 | − | 0.0964806i | −0.836829 | − | 0.547464i | \(-0.815593\pi\) |
0.892532 | + | 0.450983i | \(0.148927\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.4924 | − | 25.1016i | −0.494475 | − | 0.856456i | 0.505505 | − | 0.862824i | \(-0.331306\pi\) |
−0.999980 | + | 0.00636793i | \(0.997973\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.24621 | + | 3.89055i | 0.0764619 | + | 0.132436i | 0.901721 | − | 0.432318i | \(-0.142304\pi\) |
−0.825259 | + | 0.564754i | \(0.808971\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0885 | + | 19.2059i | −0.377022 | + | 0.653021i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.2614 | 0.450380 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.9309 | 1.01534 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.4924 | − | 70.1349i | 1.37203 | − | 2.37643i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.3693 | + | 42.2089i | 0.824776 | + | 1.42855i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.2462 | + | 40.2636i | 0.784969 | + | 1.35961i | 0.929018 | + | 0.370035i | \(0.120654\pi\) |
−0.144049 | + | 0.989571i | \(0.546012\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.47301 | − | 11.2116i | 0.218329 | − | 0.378157i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.1080 | 0.677454 | 0.338727 | − | 0.940885i | \(-0.390004\pi\) | ||||
0.338727 | + | 0.940885i | \(0.390004\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.2462 | 1.28709 | 0.643544 | − | 0.765409i | \(-0.277463\pi\) | ||||
0.643544 | + | 0.765409i | \(0.277463\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.12311 | + | 8.87348i | −0.172211 | + | 0.298279i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.75379 | − | 3.03765i | −0.0588865 | − | 0.101994i | 0.835079 | − | 0.550130i | \(-0.185422\pi\) |
−0.893966 | + | 0.448135i | \(0.852088\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.96543 | − | 15.5286i | −0.300353 | − | 0.520227i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.68466 | + | 6.38202i | −0.123302 | + | 0.213566i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.00000 | 0.133705 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 74.6004 | 2.49083 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.3693 | + | 40.4768i | −0.779410 | + | 1.34998i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.38447 | − | 14.5223i | −0.279327 | − | 0.483809i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.56155 | − | 2.70469i | −0.0519078 | − | 0.0899069i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.0540 | + | 22.6101i | −0.433450 | + | 0.750758i | −0.997168 | − | 0.0752099i | \(-0.976037\pi\) |
0.563718 | + | 0.825968i | \(0.309371\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −21.3693 | −0.708776 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.3693 | + | 26.6204i | −0.508650 | + | 0.881008i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −19.3693 | − | 33.5486i | −0.640330 | − | 1.10908i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.28078 | − | 5.68247i | −0.108223 | − | 0.187447i | 0.806828 | − | 0.590787i | \(-0.201183\pi\) |
−0.915050 | + | 0.403340i | \(0.867849\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.8963 | − | 36.1935i | 0.688557 | − | 1.19262i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.24621 | 0.271134 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.6847 | − | 27.1666i | 0.515152 | − | 0.892269i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.56155 | − | 9.63289i | −0.182469 | − | 0.316045i | 0.760252 | − | 0.649628i | \(-0.225075\pi\) |
−0.942721 | + | 0.333583i | \(0.891742\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27.0540 | + | 46.8589i | 0.885707 | + | 1.53409i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.40388 | − | 7.62775i | 0.144022 | − | 0.249454i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.1922 | −0.561646 | −0.280823 | − | 0.959760i | \(-0.590607\pi\) | ||||
−0.280823 | + | 0.959760i | \(0.590607\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36.6695 | 1.19666 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.6847 | − | 46.2192i | 0.869895 | − | 1.50670i | 0.00779178 | − | 0.999970i | \(-0.497520\pi\) |
0.862103 | − | 0.506733i | \(-0.169147\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.2462 | − | 31.6034i | −0.594178 | − | 1.02915i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.6155 | − | 40.9033i | −0.767402 | − | 1.32918i | −0.938968 | − | 0.344006i | \(-0.888216\pi\) |
0.171566 | − | 0.985173i | \(-0.445117\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.8078 | − | 60.2888i | 1.12991 | − | 1.95706i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.6155 | 0.830640 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.86174 | 0.189880 | 0.0949402 | − | 0.995483i | \(-0.469734\pi\) | ||||
0.0949402 | + | 0.995483i | \(0.469734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.84233 | − | 10.1192i | 0.189053 | − | 0.327450i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.9654 | − | 25.9209i | −0.483764 | − | 0.837903i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36.9924 | − | 64.0728i | −1.19330 | − | 2.06686i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.2462 | + | 21.2111i | −0.394629 | + | 0.683517i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.87689 | −0.156993 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.1080 | −0.968206 | −0.484103 | − | 0.875011i | \(-0.660854\pi\) | ||||
−0.484103 | + | 0.875011i | \(0.660854\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.94602 | − | 8.56677i | 0.158889 | − | 0.275204i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.3693 | + | 23.1563i | 0.429042 | + | 0.743122i | 0.996788 | − | 0.0800812i | \(-0.0255180\pi\) |
−0.567747 | + | 0.823203i | \(0.692185\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.28078 | + | 12.6107i | 0.233171 | + | 0.403865i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.4924 | − | 47.6183i | 0.879561 | − | 1.52344i | 0.0277366 | − | 0.999615i | \(-0.491170\pi\) |
0.851824 | − | 0.523828i | \(-0.175497\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.4924 | −0.973548 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.08854 | − | 14.0098i | 0.257984 | − | 0.446842i | −0.707717 | − | 0.706496i | \(-0.750275\pi\) |
0.965702 | + | 0.259654i | \(0.0836084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.43845 | − | 4.22351i | −0.0776954 | − | 0.134572i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.87689 | + | 4.98293i | 0.0914799 | + | 0.158448i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.24621 | + | 10.8188i | −0.198417 | + | 0.343669i | −0.948015 | − | 0.318224i | \(-0.896914\pi\) |
0.749598 | + | 0.661893i | \(0.230247\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.7386 | 0.975461 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.24621 | 0.0712097 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.0346 | + | 24.3086i | −0.444479 | + | 0.769860i | −0.998016 | − | 0.0629644i | \(-0.979945\pi\) |
0.553537 | + | 0.832825i | \(0.313278\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.93087 | + | 10.2726i | 0.187644 | + | 0.325010i |
(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 | 1960.2.q.u.361.2 | 4 | ||
7.2 | even | 3 | inner | 1960.2.q.u.961.2 | 4 | ||
7.3 | odd | 6 | 280.2.a.d.1.2 | ✓ | 2 | ||
7.4 | even | 3 | 1960.2.a.r.1.1 | 2 | |||
7.5 | odd | 6 | 1960.2.q.s.961.1 | 4 | |||
7.6 | odd | 2 | 1960.2.q.s.361.1 | 4 | |||
21.17 | even | 6 | 2520.2.a.w.1.2 | 2 | |||
28.3 | even | 6 | 560.2.a.g.1.1 | 2 | |||
28.11 | odd | 6 | 3920.2.a.bu.1.2 | 2 | |||
35.3 | even | 12 | 1400.2.g.k.449.4 | 4 | |||
35.4 | even | 6 | 9800.2.a.by.1.2 | 2 | |||
35.17 | even | 12 | 1400.2.g.k.449.1 | 4 | |||
35.24 | odd | 6 | 1400.2.a.p.1.1 | 2 | |||
56.3 | even | 6 | 2240.2.a.bi.1.2 | 2 | |||
56.45 | odd | 6 | 2240.2.a.be.1.1 | 2 | |||
84.59 | odd | 6 | 5040.2.a.bq.1.1 | 2 | |||
140.3 | odd | 12 | 2800.2.g.u.449.1 | 4 | |||
140.59 | even | 6 | 2800.2.a.bn.1.2 | 2 | |||
140.87 | odd | 12 | 2800.2.g.u.449.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.a.d.1.2 | ✓ | 2 | 7.3 | odd | 6 | ||
560.2.a.g.1.1 | 2 | 28.3 | even | 6 | |||
1400.2.a.p.1.1 | 2 | 35.24 | odd | 6 | |||
1400.2.g.k.449.1 | 4 | 35.17 | even | 12 | |||
1400.2.g.k.449.4 | 4 | 35.3 | even | 12 | |||
1960.2.a.r.1.1 | 2 | 7.4 | even | 3 | |||
1960.2.q.s.361.1 | 4 | 7.6 | odd | 2 | |||
1960.2.q.s.961.1 | 4 | 7.5 | odd | 6 | |||
1960.2.q.u.361.2 | 4 | 1.1 | even | 1 | trivial | ||
1960.2.q.u.961.2 | 4 | 7.2 | even | 3 | inner | ||
2240.2.a.be.1.1 | 2 | 56.45 | odd | 6 | |||
2240.2.a.bi.1.2 | 2 | 56.3 | even | 6 | |||
2520.2.a.w.1.2 | 2 | 21.17 | even | 6 | |||
2800.2.a.bn.1.2 | 2 | 140.59 | even | 6 | |||
2800.2.g.u.449.1 | 4 | 140.3 | odd | 12 | |||
2800.2.g.u.449.4 | 4 | 140.87 | odd | 12 | |||
3920.2.a.bu.1.2 | 2 | 28.11 | odd | 6 | |||
5040.2.a.bq.1.1 | 2 | 84.59 | odd | 6 | |||
9800.2.a.by.1.2 | 2 | 35.4 | even | 6 |