Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(81,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.81");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.k (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: | \(8.02425976078\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 119x^{12} + 5319x^{10} + 112122x^{8} + 1120191x^{6} + 4382607x^{4} + 1699337x^{2} + 2704 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{15}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 89.6 | ||
Root | \(3.80701i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.89 |
Dual form | 136.4.k.b.81.6 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.80701 | − | 3.80701i | 0.732659 | − | 0.732659i | −0.238487 | − | 0.971146i | \(-0.576651\pi\) |
0.971146 | + | 0.238487i | \(0.0766515\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.78003 | − | 2.78003i | 0.248654 | − | 0.248654i | −0.571764 | − | 0.820418i | \(-0.693741\pi\) |
0.820418 | + | 0.571764i | \(0.193741\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 25.7370 | + | 25.7370i | 1.38967 | + | 1.38967i | 0.826007 | + | 0.563660i | \(0.190607\pi\) |
0.563660 | + | 0.826007i | \(0.309393\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.98658i | − | 0.0735772i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.1786 | − | 17.1786i | −0.470867 | − | 0.470867i | 0.431328 | − | 0.902195i | \(-0.358045\pi\) |
−0.902195 | + | 0.431328i | \(0.858045\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 71.6546 | 1.52872 | 0.764362 | − | 0.644787i | \(-0.223054\pi\) | ||||
0.764362 | + | 0.644787i | \(0.223054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 21.1672i | − | 0.364357i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −34.3358 | − | 61.1069i | −0.489862 | − | 0.871800i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 72.2853i | − | 0.872810i | −0.899750 | − | 0.436405i | \(-0.856251\pi\) | ||
0.899750 | − | 0.436405i | \(-0.143749\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 195.962 | 2.03630 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −90.8809 | − | 90.8809i | −0.823912 | − | 0.823912i | 0.162755 | − | 0.986667i | \(-0.447962\pi\) |
−0.986667 | + | 0.162755i | \(0.947962\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 109.543i | 0.876343i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 95.2262 | + | 95.2262i | 0.678752 | + | 0.678752i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −82.0612 | + | 82.0612i | −0.525461 | + | 0.525461i | −0.919216 | − | 0.393754i | \(-0.871176\pi\) |
0.393754 | + | 0.919216i | \(0.371176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 35.2724 | − | 35.2724i | 0.204358 | − | 0.204358i | −0.597506 | − | 0.801864i | \(-0.703842\pi\) |
0.801864 | + | 0.597506i | \(0.203842\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −130.798 | −0.689969 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 143.099 | 0.691092 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 69.5253 | − | 69.5253i | 0.308916 | − | 0.308916i | −0.535573 | − | 0.844489i | \(-0.679904\pi\) |
0.844489 | + | 0.535573i | \(0.179904\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 272.789 | − | 272.789i | 1.12003 | − | 1.12003i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 196.536 | + | 196.536i | 0.748628 | + | 0.748628i | 0.974221 | − | 0.225594i | \(-0.0724322\pi\) |
−0.225594 | + | 0.974221i | \(0.572432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 344.162i | − | 1.22056i | −0.792185 | − | 0.610281i | \(-0.791057\pi\) | ||
0.792185 | − | 0.610281i | \(-0.208943\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.52277 | − | 5.52277i | −0.0182953 | − | 0.0182953i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −626.172 | −1.94333 | −0.971665 | − | 0.236362i | \(-0.924045\pi\) | ||||
−0.971665 | + | 0.236362i | \(0.924045\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 981.785i | 2.86235i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −363.351 | − | 101.918i | −0.997633 | − | 0.279830i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 145.329i | 0.376651i | 0.982107 | + | 0.188326i | \(0.0603060\pi\) | ||||
−0.982107 | + | 0.188326i | \(0.939694\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −95.5140 | −0.234166 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −275.191 | − | 275.191i | −0.639472 | − | 0.639472i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 454.009i | 1.00181i | 0.865502 | + | 0.500906i | \(0.167000\pi\) | ||||
−0.865502 | + | 0.500906i | \(0.833000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −179.197 | − | 179.197i | −0.376129 | − | 0.376129i | 0.493575 | − | 0.869703i | \(-0.335690\pi\) |
−0.869703 | + | 0.493575i | \(0.835690\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 51.1287 | − | 51.1287i | 0.102248 | − | 0.102248i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 199.202 | − | 199.202i | 0.380123 | − | 0.380123i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −874.562 | −1.59470 | −0.797349 | − | 0.603518i | \(-0.793765\pi\) | ||||
−0.797349 | + | 0.603518i | \(0.793765\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −691.968 | −1.20729 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 58.6994 | − | 58.6994i | 0.0981174 | − | 0.0981174i | −0.656344 | − | 0.754462i | \(-0.727898\pi\) |
0.754462 | + | 0.656344i | \(0.227898\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −275.870 | + | 275.870i | −0.442303 | + | 0.442303i | −0.892785 | − | 0.450482i | \(-0.851252\pi\) |
0.450482 | + | 0.892785i | \(0.351252\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 417.030 | + | 417.030i | 0.642060 | + | 0.642060i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 884.249i | − | 1.30870i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −464.841 | − | 464.841i | −0.662009 | − | 0.662009i | 0.293844 | − | 0.955853i | \(-0.405065\pi\) |
−0.955853 | + | 0.293844i | \(0.905065\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 778.691 | 1.06816 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 163.049i | − | 0.215626i | −0.994171 | − | 0.107813i | \(-0.965615\pi\) | ||
0.994171 | − | 0.107813i | \(-0.0343848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −265.334 | − | 74.4246i | −0.338582 | − | 0.0949703i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 624.815i | 0.769968i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −418.761 | −0.498748 | −0.249374 | − | 0.968407i | \(-0.580225\pi\) | ||||
−0.249374 | + | 0.968407i | \(0.580225\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1844.17 | + | 1844.17i | 2.12442 | + | 2.12442i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 268.564i | − | 0.299450i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −200.956 | − | 200.956i | −0.217028 | − | 0.217028i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 162.634 | − | 162.634i | 0.170237 | − | 0.170237i | −0.616846 | − | 0.787084i | \(-0.711590\pi\) |
0.787084 | + | 0.616846i | \(0.211590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −34.1267 | + | 34.1267i | −0.0346451 | + | 0.0346451i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1060.55 | 1.04484 | 0.522420 | − | 0.852689i | \(-0.325029\pi\) | ||||
0.522420 | + | 0.852689i | \(0.325029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 671.076 | 0.641972 | 0.320986 | − | 0.947084i | \(-0.395986\pi\) | ||||
0.320986 | + | 0.947084i | \(0.395986\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 544.780 | − | 544.780i | 0.506334 | − | 0.506334i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −175.136 | + | 175.136i | −0.158234 | + | 0.158234i | −0.781784 | − | 0.623550i | \(-0.785690\pi\) |
0.623550 | + | 0.781784i | \(0.285690\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 509.552 | + | 509.552i | 0.447764 | + | 0.447764i | 0.894611 | − | 0.446847i | \(-0.147453\pi\) |
−0.446847 | + | 0.894611i | \(0.647453\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 529.366i | − | 0.452660i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −208.993 | − | 208.993i | −0.173986 | − | 0.173986i | 0.614742 | − | 0.788728i | \(-0.289260\pi\) |
−0.788728 | + | 0.614742i | \(0.789260\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −505.304 | −0.409738 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 142.348i | − | 0.112479i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 689.008 | − | 2456.41i | 0.530767 | − | 1.89226i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 740.793i | − | 0.556569i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1496.43 | 1.09698 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 652.037 | + | 652.037i | 0.466560 | + | 0.466560i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 450.551i | 0.314803i | 0.987535 | + | 0.157401i | \(0.0503117\pi\) | ||||
−0.987535 | + | 0.157401i | \(0.949688\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1310.22 | − | 1310.22i | −0.894255 | − | 0.894255i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 562.452 | − | 562.452i | 0.375127 | − | 0.375127i | −0.494213 | − | 0.869341i | \(-0.664544\pi\) |
0.869341 | + | 0.494213i | \(0.164544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1860.41 | − | 1860.41i | 1.21292 | − | 1.21292i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 529.464 | 0.337548 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1480.25 | −0.923109 | −0.461555 | − | 0.887112i | \(-0.652708\pi\) | ||||
−0.461555 | + | 0.887112i | \(0.652708\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2213.66 | + | 2213.66i | −1.35079 | + | 1.35079i | −0.466017 | + | 0.884776i | \(0.654311\pi\) |
−0.884776 | + | 0.466017i | \(0.845689\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2383.84 | + | 2383.84i | −1.42380 | + | 1.42380i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1230.92 | − | 1230.92i | −0.719825 | − | 0.719825i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 456.266i | 0.261316i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3737.66 | + | 3737.66i | 2.09712 | + | 2.09712i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2885.80 | −1.58667 | −0.793336 | − | 0.608784i | \(-0.791658\pi\) | ||||
−0.793336 | + | 0.608784i | \(0.791658\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1037.68i | − | 0.559239i | −0.960111 | − | 0.279619i | \(-0.909792\pi\) | ||
0.960111 | − | 0.279619i | \(-0.0902083\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −121.394 | + | 68.2110i | −0.0641446 | + | 0.0360427i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 196.117i | − | 0.101629i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3420.64 | 1.73883 | 0.869415 | − | 0.494082i | \(-0.164496\pi\) | ||||
0.869415 | + | 0.494082i | \(0.164496\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 553.269 | + | 553.269i | 0.275957 | + | 0.275957i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4678.00i | − | 2.28993i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −57.4644 | − | 57.4644i | −0.0276132 | − | 0.0276132i | 0.693165 | − | 0.720779i | \(-0.256216\pi\) |
−0.720779 | + | 0.693165i | \(0.756216\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −363.622 | + | 363.622i | −0.171563 | + | 0.171563i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 857.266 | − | 857.266i | 0.397229 | − | 0.397229i | −0.480025 | − | 0.877255i | \(-0.659373\pi\) |
0.877255 | + | 0.480025i | \(0.159373\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2937.38 | 1.33700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −143.601 | −0.0642189 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1010.59 | + | 1010.59i | −0.444127 | + | 0.444127i | −0.893396 | − | 0.449269i | \(-0.851684\pi\) |
0.449269 | + | 0.893396i | \(0.351684\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2819.30 | + | 2819.30i | −1.21782 | + | 1.21782i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1728.41 | + | 1728.41i | 0.733986 | + | 0.733986i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1950.92i | − | 0.814629i | −0.913288 | − | 0.407315i | \(-0.866465\pi\) | ||
0.913288 | − | 0.407315i | \(-0.133535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1850.30 | − | 1850.30i | −0.759844 | − | 0.759844i | 0.216449 | − | 0.976294i | \(-0.430552\pi\) |
−0.976294 | + | 0.216449i | \(0.930552\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1364.41 | −0.551148 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 386.565i | − | 0.153626i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −459.889 | + | 1639.57i | −0.179842 | + | 0.641161i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4901.67i | 1.88648i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2192.73 | −0.830683 | −0.415342 | − | 0.909665i | \(-0.636338\pi\) | ||||
−0.415342 | + | 0.909665i | \(0.636338\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 70.8011 | + | 70.8011i | 0.0264061 | + | 0.0264061i | 0.720187 | − | 0.693780i | \(-0.244056\pi\) |
−0.693780 | + | 0.720187i | \(0.744056\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 1516.73i | − | 0.557001i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −566.472 | − | 566.472i | −0.204870 | − | 0.204870i | 0.597213 | − | 0.802083i | \(-0.296275\pi\) |
−0.802083 | + | 0.597213i | \(0.796275\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −790.293 | + | 790.293i | −0.281519 | + | 0.281519i | −0.833715 | − | 0.552195i | \(-0.813790\pi\) |
0.552195 | + | 0.833715i | \(0.313790\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3329.46 | + | 3329.46i | −1.16837 | + | 1.16837i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4224.02 | −1.46043 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1092.75 | 0.372298 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −180.543 | + | 180.543i | −0.0606211 | + | 0.0606211i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1241.76 | + | 1241.76i | −0.410977 | + | 0.410977i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 399.006 | + | 399.006i | 0.130183 | + | 0.130183i | 0.769196 | − | 0.639013i | \(-0.220657\pi\) |
−0.639013 | + | 0.769196i | \(0.720657\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 446.938i | − | 0.143773i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −956.781 | − | 956.781i | −0.303497 | − | 0.303497i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1815.61 | 0.567980 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2100.48i | 0.648114i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2460.32 | − | 4378.59i | −0.748864 | − | 1.33274i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5051.79i | − | 1.51701i | −0.651667 | − | 0.758505i | \(-0.725930\pi\) | ||
0.651667 | − | 0.758505i | \(-0.274070\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 217.616 | 0.0644788 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 202.315 | + | 202.315i | 0.0591547 | + | 0.0591547i | 0.736065 | − | 0.676911i | \(-0.236682\pi\) |
−0.676911 | + | 0.736065i | \(0.736682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2265.18i | 0.653657i | 0.945084 | + | 0.326828i | \(0.105980\pi\) | ||||
−0.945084 | + | 0.326828i | \(0.894020\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3366.34 | − | 3366.34i | −0.958827 | − | 0.958827i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3776.51 | − | 3776.51i | 1.06184 | − | 1.06184i | 0.0638776 | − | 0.997958i | \(-0.479653\pi\) |
0.997958 | − | 0.0638776i | \(-0.0203467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1740.78 | + | 1740.78i | −0.483216 | + | 0.483216i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3539.31 | −0.970053 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7017.70 | 1.89932 | 0.949660 | − | 0.313284i | \(-0.101429\pi\) | ||||
0.949660 | + | 0.313284i | \(0.101429\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3368.64 | + | 3368.64i | −0.900386 | + | 0.900386i | −0.995469 | − | 0.0950830i | \(-0.969688\pi\) |
0.0950830 | + | 0.995469i | \(0.469688\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 393.374 | − | 393.374i | 0.103848 | − | 0.103848i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2729.40 | + | 2729.40i | 0.711734 | + | 0.711734i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5179.58i | − | 1.33429i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −620.729 | − | 620.729i | −0.157980 | − | 0.157980i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6592.92 | 1.65793 | 0.828967 | − | 0.559298i | \(-0.188929\pi\) | ||||
0.828967 | + | 0.559298i | \(0.188929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3122.41i | 0.775905i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1293.46 | + | 726.793i | −0.317646 | + | 0.178484i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6128.40i | 1.48747i | 0.668476 | + | 0.743734i | \(0.266947\pi\) | ||||
−0.668476 | + | 0.743734i | \(0.733053\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3578.74 | 0.858580 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 163.022 | + | 163.022i | 0.0386620 | + | 0.0386620i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 6142.19i | − | 1.44009i | −0.693927 | − | 0.720045i | \(-0.744121\pi\) | ||
0.693927 | − | 0.720045i | \(-0.255879\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 404.020 | + | 404.020i | 0.0936557 | + | 0.0936557i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1594.22 | + | 1594.22i | −0.365412 | + | 0.365412i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 831.758 | − | 831.758i | 0.188525 | − | 0.188525i | −0.606533 | − | 0.795058i | \(-0.707440\pi\) |
0.795058 | + | 0.606533i | \(0.207440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2498.30 | −0.560004 | −0.280002 | − | 0.959999i | \(-0.590335\pi\) | ||||
−0.280002 | + | 0.959999i | \(0.590335\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 14041.6 | 3.11294 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1881.79 | − | 1881.79i | 0.412641 | − | 0.412641i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3640.10 | − | 3640.10i | 0.789576 | − | 0.789576i | −0.191848 | − | 0.981425i | \(-0.561448\pi\) |
0.981425 | + | 0.191848i | \(0.0614482\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −70.0716 | − | 70.0716i | −0.0150361 | − | 0.0150361i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3355.18i | 0.712290i | 0.934431 | + | 0.356145i | \(0.115909\pi\) | ||||
−0.934431 | + | 0.356145i | \(0.884091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1847.55 | − | 1847.55i | −0.388076 | − | 0.388076i | 0.485925 | − | 0.874001i | \(-0.338483\pi\) |
−0.874001 | + | 0.485925i | \(0.838483\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1530.08 | −0.318014 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10116.5i | 2.08069i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2555.11 | + | 4196.31i | −0.520070 | + | 0.854123i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1238.30i | − | 0.249452i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1683.63 | −0.335695 | −0.167848 | − | 0.985813i | \(-0.553682\pi\) | ||||
−0.167848 | + | 0.985813i | \(0.553682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1262.16 | + | 1262.16i | 0.249104 | + | 0.249104i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3271.70i | − | 0.639203i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6512.03 | − | 6512.03i | −1.25953 | − | 1.25953i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8857.68 | − | 8857.68i | 1.69617 | − | 1.69617i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4037.52 | − | 4037.52i | 0.765511 | − | 0.765511i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −996.348 | −0.187052 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5864.67 | 1.09028 | 0.545138 | − | 0.838346i | \(-0.316477\pi\) | ||||
0.545138 | + | 0.838346i | \(0.316477\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2554.79 | − | 2554.79i | 0.470346 | − | 0.470346i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4507.41 | − | 4507.41i | 0.821838 | − | 0.821838i | −0.164534 | − | 0.986371i | \(-0.552612\pi\) |
0.986371 | + | 0.164534i | \(0.0526119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2339.52 | − | 2339.52i | −0.422484 | − | 0.422484i | 0.463574 | − | 0.886058i | \(-0.346567\pi\) |
−0.886058 | + | 0.463574i | \(0.846567\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 284.279i | − | 0.0508486i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5257.60 | + | 5257.60i | 0.931534 | + | 0.931534i | 0.997802 | − | 0.0662682i | \(-0.0211093\pi\) |
−0.0662682 | + | 0.997802i | \(0.521109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2819.39 | 0.494845 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1333.49i | 0.231863i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4417.13 | + | 2481.97i | −0.760916 | + | 0.427556i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7849.25i | 1.33969i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3879.74 | 0.656116 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16115.8 | − | 16115.8i | −2.70058 | − | 2.70058i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 953.626i | − | 0.158356i | −0.996860 | − | 0.0791782i | \(-0.974770\pi\) | ||
0.996860 | − | 0.0791782i | \(-0.0252296\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −138.118 | − | 138.118i | −0.0227292 | − | 0.0227292i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2431.31 | + | 2431.31i | −0.396528 | + | 0.396528i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6649.51 | + | 6649.51i | −1.07484 | + | 1.07484i | −0.0778798 | + | 0.996963i | \(0.524815\pi\) |
−0.996963 | + | 0.0778798i | \(0.975185\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1591.27 | −0.254944 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1211.86 | −0.192451 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16440.4 | + | 16440.4i | −2.58804 | + | 2.58804i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1923.69 | + | 1923.69i | −0.300198 | + | 0.300198i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7319.13 | + | 7319.13i | 1.13231 | + | 1.13231i | 0.989792 | + | 0.142518i | \(0.0455200\pi\) |
0.142518 | + | 0.989792i | \(0.454480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9266.42i | − | 1.42126i | −0.703566 | − | 0.710630i | \(-0.748410\pi\) | ||
0.703566 | − | 0.710630i | \(-0.251590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6823.40 | + | 6823.40i | 1.03762 | + | 1.03762i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3315.92 | 0.499968 | 0.249984 | − | 0.968250i | \(-0.419575\pi\) | ||||
0.249984 | + | 0.968250i | \(0.419575\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 326.373i | − | 0.0487945i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6728.50 | − | 11974.6i | −0.997507 | − | 1.77525i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5654.75i | − | 0.831327i | −0.909518 | − | 0.415664i | \(-0.863549\pi\) | ||
0.909518 | − | 0.415664i | \(-0.136451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1633.83 | 0.238203 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2820.21 | − | 2820.21i | −0.407775 | − | 0.407775i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1533.85i | 0.219961i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.03278 | − | 9.03278i | −0.00128476 | − | 0.00128476i | 0.706464 | − | 0.707749i | \(-0.250289\pi\) |
−0.707749 | + | 0.706464i | \(0.750289\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 390.435 | − | 390.435i | 0.0550820 | − | 0.0550820i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3740.34 | + | 3740.34i | −0.523419 | + | 0.523419i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2955.39 | 0.410252 | 0.205126 | − | 0.978736i | \(-0.434240\pi\) | ||||
0.205126 | + | 0.978736i | \(0.434240\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4964.62 | 0.683658 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5880.06 | + | 5880.06i | −0.803286 | + | 0.803286i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3054.12 | + | 3054.12i | −0.413931 | + | 0.413931i | −0.883105 | − | 0.469175i | \(-0.844552\pi\) |
0.469175 | + | 0.883105i | \(0.344552\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1715.25 | + | 1715.25i | 0.230643 | + | 0.230643i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5788.94i | 0.772326i | 0.922431 | + | 0.386163i | \(0.126200\pi\) | ||||
−0.922431 | + | 0.386163i | \(0.873800\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2458.24 | − | 2458.24i | −0.325412 | − | 0.325412i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −683.706 | −0.0898055 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 10329.9i | − | 1.34640i | −0.739462 | − | 0.673198i | \(-0.764920\pi\) | ||
0.739462 | − | 0.673198i | \(-0.235080\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2432.98 | + | 8673.92i | −0.314683 | + | 1.12189i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4282.51i | − | 0.549680i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2584.55 | −0.329222 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7727.58 | + | 7727.58i | 0.976917 | + | 0.976917i | 0.999740 | − | 0.0228226i | \(-0.00726530\pi\) |
−0.0228226 | + | 0.999740i | \(0.507265\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 14165.2i | − | 1.77731i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4285.93 | − | 4285.93i | −0.533739 | − | 0.533739i | 0.387944 | − | 0.921683i | \(-0.373185\pi\) |
−0.921683 | + | 0.387944i | \(0.873185\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2527.43 | − | 2527.43i | 0.312407 | − | 0.312407i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2164.79 | − | 2164.79i | 0.265603 | − | 0.265603i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2388.69 | −0.290916 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12598.8 | 1.52316 | 0.761580 | − | 0.648071i | \(-0.224424\pi\) | ||||
0.761580 | + | 0.648071i | \(0.224424\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5635.31 | + | 5635.31i | −0.676324 | + | 0.676324i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11684.8 | + | 11684.8i | −1.39219 | + | 1.39219i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −453.282 | − | 453.282i | −0.0536162 | − | 0.0536162i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16854.8i | 1.97934i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1462.63 | + | 1462.63i | 0.170536 | + | 0.170536i | 0.787215 | − | 0.616679i | \(-0.211522\pi\) |
−0.616679 | + | 0.787215i | \(0.711522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7194.58 | −0.832880 | −0.416440 | − | 0.909163i | \(-0.636722\pi\) | ||||
−0.416440 | + | 0.909163i | \(0.636722\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1243.94i | 0.142985i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6693.82 | − | 3761.24i | 0.763995 | − | 0.429287i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9223.99i | − | 1.04539i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9372.27 | −1.05477 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9683.60 | + | 9683.60i | 1.08223 | + | 1.08223i | 0.996301 | + | 0.0859325i | \(0.0273869\pi\) |
0.0859325 | + | 0.996301i | \(0.472613\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12504.4i | − | 1.38782i | −0.720063 | − | 0.693909i | \(-0.755887\pi\) | ||
0.720063 | − | 0.693909i | \(-0.244113\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1737.01 | + | 1737.01i | 0.191455 | + | 0.191455i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6569.35 | + | 6569.35i | −0.719119 | + | 0.719119i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9878.38 | + | 9878.38i | −1.07396 | + | 1.07396i | −0.0769257 | + | 0.997037i | \(0.524510\pi\) |
−0.997037 | + | 0.0769257i | \(0.975490\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1950.40 | 0.210604 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 829.809 | 0.0889964 | 0.0444982 | − | 0.999009i | \(-0.485831\pi\) | ||||
0.0444982 | + | 0.999009i | \(0.485831\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1164.17 | + | 1164.17i | −0.124016 | + | 0.124016i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10986.3 | + | 10986.3i | −1.16249 | + | 1.16249i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5937.37 | + | 5937.37i | 0.624057 | + | 0.624057i | 0.946566 | − | 0.322509i | \(-0.104526\pi\) |
−0.322509 | + | 0.946566i | \(0.604526\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6752.41i | − | 0.705008i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3950.45 | − | 3950.45i | −0.409731 | − | 0.409731i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10253.7 | 1.05649 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 4013.92i | − | 0.410861i | −0.978672 | − | 0.205430i | \(-0.934141\pi\) | ||
0.978672 | − | 0.205430i | \(-0.0658594\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2549.31 | − | 9088.65i | 0.259241 | − | 0.924230i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9576.45i | 0.967505i | 0.875205 | + | 0.483753i | \(0.160727\pi\) | ||||
−0.875205 | + | 0.483753i | \(0.839273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8366.78 | 0.839822 | 0.419911 | − | 0.907565i | \(-0.362061\pi\) | ||||
0.419911 | + | 0.907565i | \(0.362061\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −746.618 | − | 746.618i | −0.0744593 | − | 0.0744593i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 8324.94i | − | 0.824909i | −0.910978 | − | 0.412454i | \(-0.864672\pi\) | ||
0.910978 | − | 0.412454i | \(-0.135328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22508.6 | − | 22508.6i | −2.21610 | − | 2.21610i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13022.4 | − | 13022.4i | 1.27397 | − | 1.27397i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5912.20 | + | 5912.20i | −0.574722 | + | 0.574722i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7918.34 | 0.764881 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 288.709 | 0.0277129 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −619.058 | + | 619.058i | −0.0590511 | + | 0.0590511i | −0.736016 | − | 0.676965i | \(-0.763295\pi\) |
0.676965 | + | 0.736016i | \(0.263295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4981.81 | − | 4981.81i | 0.472247 | − | 0.472247i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17809.2 | − | 17809.2i | −1.67773 | − | 1.67773i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 904.258i | − | 0.0846603i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2801.50 | + | 2801.50i | 0.260674 | + | 0.260674i | 0.825328 | − | 0.564654i | \(-0.190990\pi\) |
−0.564654 | + | 0.825328i | \(0.690990\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −437.534 | −0.0404621 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5348.65i | 0.491611i | 0.969319 | + | 0.245806i | \(0.0790525\pi\) | ||||
−0.969319 | + | 0.245806i | \(0.920947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7832.14 | + | 2196.87i | 0.715501 | + | 0.200694i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 189.747i | 0.0172293i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3021.49 | 0.272701 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2291.68 | − | 2291.68i | −0.205591 | − | 0.205591i | 0.596800 | − | 0.802390i | \(-0.296439\pi\) |
−0.802390 | + | 0.596800i | \(0.796439\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 6527.23i | − | 0.582067i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12161.4 | + | 12161.4i | 1.07803 | + | 1.07803i | 0.996686 | + | 0.0813446i | \(0.0259214\pi\) |
0.0813446 | + | 0.996686i | \(0.474079\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2948.37 | − | 2948.37i | 0.259803 | − | 0.259803i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11182.6 | − | 11182.6i | 0.979562 | − | 0.979562i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19542.7 | 1.70179 | 0.850897 | − | 0.525333i | \(-0.176059\pi\) | ||||
0.850897 | + | 0.525333i | \(0.176059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14200.1 | −1.22931 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6883.46 | − | 6883.46i | 0.592421 | − | 0.592421i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1865.61 | − | 1865.61i | 0.159629 | − | 0.159629i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10756.7 | + | 10756.7i | 0.915049 | + | 0.915049i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7694.67i | 0.650787i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13819.8 | + | 13819.8i | 1.16211 | + | 1.16211i | 0.984014 | + | 0.178093i | \(0.0569926\pi\) |
0.178093 | + | 0.984014i | \(0.443007\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13396.9 | −1.12009 | −0.560044 | − | 0.828463i | \(-0.689216\pi\) | ||||
−0.560044 | + | 0.828463i | \(0.689216\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 21466.2i | 1.78450i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3366.49 | − | 944.281i | −0.278267 | − | 0.0780522i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4351.67i | 0.357662i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 901.927 | 0.0737106 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14082.7 | + | 14082.7i | 1.14445 | + | 1.14445i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 973.770i | 0.0786911i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7427.16 | − | 7427.16i | −0.596845 | − | 0.596845i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16865.7 | − | 16865.7i | 1.34778 | − | 1.34778i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7739.88 | − | 7739.88i | 0.615090 | − | 0.615090i | −0.329178 | − | 0.944268i | \(-0.606772\pi\) |
0.944268 | + | 0.329178i | \(0.106772\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14088.2 | −1.11341 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2833.15 | 0.222676 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8933.89 | + | 8933.89i | −0.698328 | + | 0.698328i | −0.964050 | − | 0.265722i | \(-0.914390\pi\) |
0.265722 | + | 0.964050i | \(0.414390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −355.990 | + | 355.990i | −0.0276745 | + | 0.0276745i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5931.82 | + | 5931.82i | 0.458628 | + | 0.458628i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 23927.2i | − | 1.83994i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1471.66 | − | 1471.66i | −0.112556 | − | 0.112556i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3440.59 | 0.261728 | 0.130864 | − | 0.991400i | \(-0.458225\pi\) | ||||
0.130864 | + | 0.991400i | \(0.458225\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 24660.8i | − | 1.86590i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4491.05 | + | 7992.65i | 0.337990 | + | 0.601515i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11973.1i | 0.896278i | 0.893964 | + | 0.448139i | \(0.147913\pi\) | ||||
−0.893964 | + | 0.448139i | \(0.852087\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1162.01 | −0.0865243 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20041.2 | + | 20041.2i | 1.48439 | + | 1.48439i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 12536.9i | − | 0.923680i | −0.886963 | − | 0.461840i | \(-0.847189\pi\) | ||
0.886963 | − | 0.461840i | \(-0.152811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2485.78 | + | 2485.78i | 0.182183 | + | 0.182183i | 0.792306 | − | 0.610123i | \(-0.208880\pi\) |
−0.610123 | + | 0.792306i | \(0.708880\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8347.74 | + | 8347.74i | −0.608607 | + | 0.608607i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9955.35 | − | 9955.35i | 0.722029 | − | 0.722029i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15196.0 | 1.09639 | 0.548195 | − | 0.836350i | \(-0.315315\pi\) | ||||
0.548195 | + | 0.836350i | \(0.315315\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 539.080 | 0.0386933 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4196.39 | − | 4196.39i | 0.299648 | − | 0.299648i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2496.55 | − | 2496.55i | 0.177352 | − | 0.177352i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −395.732 | − | 395.732i | −0.0279684 | − | 0.0279684i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 11409.2i | − | 0.802230i | −0.916028 | − | 0.401115i | \(-0.868623\pi\) | ||
0.916028 | − | 0.401115i | \(-0.131377\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2549.68 | − | 2549.68i | −0.178366 | − | 0.178366i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4313.12 | −0.300200 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3295.58i | 0.228218i | 0.993468 | + | 0.114109i | \(0.0364013\pi\) | ||||
−0.993468 | + | 0.114109i | \(0.963599\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4913.43 | − | 8744.36i | −0.338540 | − | 0.602494i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6017.30i | 0.412515i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1426.99 | −0.0973378 | −0.0486689 | − | 0.998815i | \(-0.515498\pi\) | ||||
−0.0486689 | + | 0.998815i | \(0.515498\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20369.5 | − | 20369.5i | −1.38251 | − | 1.38251i | −0.840136 | − | 0.542376i | \(-0.817525\pi\) |
−0.542376 | − | 0.840136i | \(-0.682475\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1737.39i | 0.117333i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2059.43 | − | 2059.43i | −0.138393 | − | 0.138393i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2322.12 | + | 2322.12i | −0.155275 | + | 0.155275i | −0.780469 | − | 0.625194i | \(-0.785020\pi\) |
0.625194 | + | 0.780469i | \(0.285020\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16080.9 | + | 16080.9i | −1.07000 | + | 1.07000i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −44868.1 | −2.97082 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15397.0 | 1.01449 | 0.507244 | − | 0.861803i | \(-0.330664\pi\) | ||||
0.507244 | + | 0.861803i | \(0.330664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4160.12 | − | 4160.12i | 0.272768 | − | 0.272768i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20796.5 | + | 20796.5i | −1.35695 | + | 1.35695i | −0.479293 | + | 0.877655i | \(0.659107\pi\) |
−0.877655 | + | 0.479293i | \(0.840893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1841.95 | − | 1841.95i | −0.119603 | − | 0.119603i | 0.644772 | − | 0.764375i | \(-0.276952\pi\) |
−0.764375 | + | 0.644772i | \(0.776952\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 17308.5i | − | 1.11846i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10777.6 | − | 10777.6i | −0.693093 | − | 0.693093i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10067.5 | −0.644319 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9454.76i | 0.602212i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6635.68 | − | 1861.27i | −0.420639 | − | 0.117987i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6384.47i | 0.402792i | 0.979510 | + | 0.201396i | \(0.0645478\pi\) | ||||
−0.979510 | + | 0.201396i | \(0.935452\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3038.03 | 0.190760 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1252.55 | + | 1252.55i | 0.0782769 | + | 0.0782769i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 70349.4i | 4.37574i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −116.611 | − | 116.611i | −0.00721920 | − | 0.00721920i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21042.7 | + | 21042.7i | −1.29663 | + | 1.29663i | −0.366021 | + | 0.930607i | \(0.619280\pi\) |
−0.930607 | + | 0.366021i | \(0.880720\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11224.9 | − | 11224.9i | 0.688442 | − | 0.688442i | −0.273445 | − | 0.961888i | \(-0.588163\pi\) |
0.961888 | + | 0.273445i | \(0.0881632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7284.94 | −0.444720 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19644.7 | −1.19368 | −0.596842 | − | 0.802359i | \(-0.703578\pi\) | ||||
−0.596842 | + | 0.802359i | \(0.703578\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7799.22 | − | 7799.22i | 0.471720 | − | 0.471720i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6912.04 | − | 6912.04i | 0.416135 | − | 0.416135i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3999.32 | − | 3999.32i | −0.239672 | − | 0.239672i | 0.577043 | − | 0.816714i | \(-0.304207\pi\) |
−0.816714 | + | 0.577043i | \(0.804207\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 3127.27i | − | 0.186554i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 548.039 | + | 548.039i | 0.0325434 | + | 0.0325434i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22818.1 | 1.34881 | 0.674407 | − | 0.738360i | \(-0.264400\pi\) | ||||
0.674407 | + | 0.738360i | \(0.264400\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 5851.00i | − | 0.344293i | −0.985071 | − | 0.172146i | \(-0.944930\pi\) | ||
0.985071 | − | 0.172146i | \(-0.0550702\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26035.8 | − | 7302.88i | −1.52511 | − | 0.427783i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 10344.0i | − | 0.603192i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14915.6 | 0.865868 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19232.2 | − | 19232.2i | −1.11145 | − | 1.11145i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6156.70i | 0.354213i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8905.21 | + | 8905.21i | 0.510060 | + | 0.510060i | 0.914545 | − | 0.404484i | \(-0.132549\pi\) |
−0.404484 | + | 0.914545i | \(0.632549\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10431.3 | + | 10431.3i | −0.594819 | + | 0.594819i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17965.5 | − | 17965.5i | 1.01990 | − | 1.01990i | 0.0200980 | − | 0.999798i | \(-0.493602\pi\) |
0.999798 | − | 0.0200980i | \(-0.00639784\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8371.43 | 0.473146 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1540.43 | 0.0866804 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14089.4 | + | 14089.4i | −0.789338 | + | 0.789338i | −0.981386 | − | 0.192048i | \(-0.938487\pi\) |
0.192048 | + | 0.981386i | \(0.438487\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4115.13 | + | 4115.13i | −0.229535 | + | 0.229535i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8623.56 | + | 8623.56i | 0.478907 | + | 0.478907i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10413.5i | 0.575795i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18417.0 | − | 18417.0i | −1.01391 | − | 1.01391i | −0.999902 | − | 0.0140112i | \(-0.995540\pi\) |
−0.0140112 | − | 0.999902i | \(-0.504460\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1756.64 | −0.0962902 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12308.1i | 0.671759i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5261.48 | − | 18757.9i | 0.285929 | − | 1.01938i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 28754.4i | − | 1.55593i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8521.04 | 0.459109 | 0.229554 | − | 0.973296i | \(-0.426273\pi\) | ||||
0.229554 | + | 0.973296i | \(0.426273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5025.66 | − | 5025.66i | −0.269625 | − | 0.269625i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13254.3i | 0.708065i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27295.4 | + | 27295.4i | 1.45198 | + | 1.45198i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19634.5 | + | 19634.5i | −1.04004 | + | 1.04004i | −0.0408774 | + | 0.999164i | \(0.513015\pi\) |
−0.999164 | + | 0.0408774i | \(0.986985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −923.446 | + | 923.446i | −0.0487088 | + | 0.0487088i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6411.17 | −0.336746 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6844.02 | −0.357975 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26716.4 | − | 26716.4i | 1.39155 | − | 1.39155i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20219.0 | − | 20219.0i | 1.04874 | − | 1.04874i | 0.0499880 | − | 0.998750i | \(-0.484082\pi\) |
0.998750 | − | 0.0499880i | \(-0.0159183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17271.5 | + | 17271.5i | 0.892127 | + | 0.892127i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 25648.9i | 1.31935i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8989.22 | − | 8989.22i | −0.460484 | − | 0.460484i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22672.4 | −1.15663 | −0.578317 | − | 0.815812i | \(-0.696290\pi\) | ||||
−0.578317 | + | 0.815812i | \(0.696290\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18029.5i | 0.915994i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21030.6 | + | 11817.1i | −1.06409 | + | 0.597907i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3241.83i | 0.163356i | 0.996659 | + | 0.0816779i | \(0.0260279\pi\) | ||||
−0.996659 | + | 0.0816779i | \(0.973972\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20781.7 | 1.04292 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15023.7 | + | 15023.7i | 0.750890 | + | 0.750890i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 8977.81i | − | 0.446893i | −0.974716 | − | 0.223447i | \(-0.928269\pi\) | ||
0.974716 | − | 0.223447i | \(-0.0717309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19718.7 | − | 19718.7i | −0.977576 | − | 0.977576i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3759.91 | + | 3759.91i | −0.185650 | + | 0.185650i | −0.793812 | − | 0.608163i | \(-0.791907\pi\) |
0.608163 | + | 0.793812i | \(0.291907\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8022.63 | + | 8022.63i | −0.394532 | + | 0.394532i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −323.911 | −0.0158652 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9014.96 | −0.439786 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13408.0 | − | 13408.0i | 0.651485 | − | 0.651485i | −0.301865 | − | 0.953351i | \(-0.597609\pi\) |
0.953351 | + | 0.301865i | \(0.0976093\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25099.3 | − | 25099.3i | 1.21470 | − | 1.21470i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2884.78 | − | 2884.78i | −0.139057 | − | 0.139057i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 28601.5i | − | 1.37324i | −0.727018 | − | 0.686619i | \(-0.759094\pi\) | ||
0.727018 | − | 0.686619i | \(-0.240906\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11887.0 | + | 11887.0i | 0.568474 | + | 0.568474i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23710.9 | −1.12946 | −0.564730 | − | 0.825276i | \(-0.691020\pi\) | ||||
−0.564730 | + | 0.825276i | \(0.691020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26228.7i | 1.24449i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −147.851 | + | 527.108i | −0.00698765 | + | 0.0249120i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32531.8i | 1.53149i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3392.20 | −0.159071 | −0.0795357 | − | 0.996832i | \(-0.525344\pi\) | ||||
−0.0795357 | + | 0.996832i | \(0.525344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23330.9 | + | 23330.9i | 1.08981 | + | 1.08981i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 10444.4i | − | 0.485977i | −0.970029 | − | 0.242988i | \(-0.921872\pi\) | ||
0.970029 | − | 0.242988i | \(-0.0781277\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3863.84 | + | 3863.84i | 0.179088 | + | 0.179088i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13624.3 | − | 13624.3i | 0.629046 | − | 0.629046i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14206.7 | − | 14206.7i | 0.653410 | − | 0.653410i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2016.74 | −0.0924004 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15628.8 | −0.713316 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9509.48 | − | 9509.48i | 0.432367 | − | 0.432367i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8973.36 | + | 8973.36i | −0.406437 | + | 0.406437i | −0.880494 | − | 0.474057i | \(-0.842789\pi\) |
0.474057 | + | 0.880494i | \(0.342789\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −23383.4 | − | 23383.4i | −1.05509 | − | 1.05509i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 10757.7i | − | 0.483564i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12840.3 | − | 12840.3i | −0.574997 | − | 0.574997i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3076.21 | 0.137235 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 31949.2i | − | 1.41995i | −0.704228 | − | 0.709974i | \(-0.748707\pi\) | ||
0.704228 | − | 0.709974i | \(-0.251293\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21500.1 | + | 38263.4i | 0.951964 | + | 1.69420i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 831.904i | 0.0366965i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9478.10 | 0.416531 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13005.0 | − | 13005.0i | −0.569399 | − | 0.569399i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6333.02i | − | 0.276249i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13072.2 | + | 13072.2i | 0.568101 | + | 0.568101i | 0.931596 | − | 0.363495i | \(-0.118417\pi\) |
−0.363495 | + | 0.931596i | \(0.618417\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15766.6 | − | 15766.6i | 0.682665 | − | 0.682665i | −0.277935 | − | 0.960600i | \(-0.589650\pi\) |
0.960600 | + | 0.277935i | \(0.0896500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9511.05 | + | 9511.05i | −0.410292 | + | 0.410292i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −319.506 | −0.0137323 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24877.8 | −1.06532 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3663.61 | − | 3663.61i | 0.156309 | − | 0.156309i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13357.5 | − | 13357.5i | 0.567818 | − | 0.567818i | −0.363699 | − | 0.931517i | \(-0.618486\pi\) |
0.931517 | + | 0.363699i | \(0.118486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5642.25 | + | 5642.25i | 0.238975 | + | 0.238975i | 0.816426 | − | 0.577451i | \(-0.195952\pi\) |
−0.577451 | + | 0.816426i | \(0.695952\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 14328.0i | − | 0.604649i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3153.39 | − | 3153.39i | −0.132593 | − | 0.132593i | 0.637696 | − | 0.770288i | \(-0.279888\pi\) |
−0.770288 | + | 0.637696i | \(0.779888\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19686.3 | 0.824769 | 0.412384 | − | 0.911010i | \(-0.364696\pi\) | ||||
0.412384 | + | 0.911010i | \(0.364696\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 27715.8i | − | 1.15698i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 59993.8 | − | 33710.4i | 2.49539 | − | 1.40216i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4766.46i | − | 0.197545i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6717.71 | 0.277417 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20299.7 | − | 20299.7i | −0.835307 | − | 0.835307i | 0.152930 | − | 0.988237i | \(-0.451129\pi\) |
−0.988237 | + | 0.152930i | \(0.951129\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10920.9i | 0.447780i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12773.2 | + | 12773.2i | 0.521865 | + | 0.521865i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8166.02 | − | 8166.02i | 0.332449 | − | 0.332449i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19065.8 | − | 19065.8i | 0.773446 | − | 0.773446i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14067.3 | −0.568654 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12637.0 | −0.509039 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5307.45 | − | 5307.45i | 0.213040 | − | 0.213040i | −0.592517 | − | 0.805558i | \(-0.701866\pi\) |
0.805558 | + | 0.592517i | \(0.201866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −399.215 | + | 399.215i | −0.0159683 | + | 0.0159683i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −55.7082 | − | 55.7082i | −0.00222048 | − | 0.00222048i | 0.705996 | − | 0.708216i | \(-0.250500\pi\) |
−0.708216 | + | 0.705996i | \(0.750500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5441.53i | 0.216138i | 0.994143 | + | 0.108069i | \(0.0344668\pi\) | ||||
−0.994143 | + | 0.108069i | \(0.965533\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 38513.5 | + | 38513.5i | 1.52443 | + | 1.52443i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7156.86 | 0.282297 | 0.141148 | − | 0.989988i | \(-0.454921\pi\) | ||||
0.141148 | + | 0.989988i | \(0.454921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5618.97i | 0.220868i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6248.06 | + | 25702.7i | 0.244747 | + | 1.00681i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15970.6i | 0.623436i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −62666.4 | −2.43785 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −323.087 | − | 323.087i | −0.0125256 | − | 0.0125256i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33562.9i | 1.29673i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10284.2 | + | 10284.2i | 0.395979 | + | 0.395979i | 0.876812 | − | 0.480833i | \(-0.159666\pi\) |
−0.480833 | + | 0.876812i | \(0.659666\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6409.59 | + | 6409.59i | −0.245950 | + | 0.245950i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15872.5 | + | 15872.5i | −0.606990 | + | 0.606990i | −0.942158 | − | 0.335168i | \(-0.891207\pi\) |
0.335168 | + | 0.942158i | \(0.391207\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34760.2 | 1.32477 | 0.662385 | − | 0.749163i | \(-0.269544\pi\) | ||||
0.662385 | + | 0.749163i | \(0.269544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9610.10 | 0.365017 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4228.29 | − | 4228.29i | 0.160059 | − | 0.160059i | −0.622534 | − | 0.782593i | \(-0.713897\pi\) |
0.782593 | + | 0.622534i | \(0.213897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11595.8 | + | 11595.8i | −0.437471 | + | 0.437471i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13376.8 | − | 13376.8i | −0.502963 | − | 0.502963i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45263.0i | 1.69616i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5423.62 | − | 5423.62i | −0.202561 | − | 0.202561i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −49582.7 | −1.84562 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5788.99i | 0.214765i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8880.62 | − | 4989.99i | 0.328364 | − | 0.184507i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 67442.5i | − | 2.48543i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10287.8 | −0.377876 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26461.5 | + | 26461.5i | 0.968731 | + | 0.968731i | 0.999526 | − | 0.0307949i | \(-0.00980387\pi\) |
−0.0307949 | + | 0.999526i | \(0.509804\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2106.87i | − | 0.0768764i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.0094 | − | 18.0094i | −0.000654970 | − | 0.000654970i | 0.706779 | − | 0.707434i | \(-0.250147\pi\) |
−0.707434 | + | 0.706779i | \(0.750147\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2800.95 | + | 2800.95i | −0.101531 | + | 0.101531i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3793.10 | + | 3793.10i | −0.137045 | + | 0.137045i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28951.6 | 1.04260 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11502.6 | −0.412878 | −0.206439 | − | 0.978459i | \(-0.566188\pi\) | ||||
−0.206439 | + | 0.978459i | \(0.566188\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22326.8 | − | 22326.8i | 0.798800 | − | 0.798800i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4206.08 | − | 4206.08i | 0.149994 | − | 0.149994i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7616.00 | + | 7616.00i | 0.270716 | + | 0.270716i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1333.15i | − | 0.0472345i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26325.7 | − | 26325.7i | −0.929729 | − | 0.929729i | 0.0679592 | − | 0.997688i | \(-0.478351\pi\) |
−0.997688 | + | 0.0679592i | \(0.978351\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 70968.7 | 2.49829 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 34319.4i | − | 1.20425i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3279.55 | + | 5836.57i | 0.114709 | + | 0.204146i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 72.1695i | − | 0.00251619i | −0.999999 | − | 0.00125810i | \(-0.999600\pi\) | ||
0.999999 | − | 0.00125810i | \(-0.000400465\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17813.1 | −0.619072 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6951.94 | + | 6951.94i | 0.240836 | + | 0.240836i | 0.817196 | − | 0.576360i | \(-0.195527\pi\) |
−0.576360 | + | 0.817196i | \(0.695527\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 35722.7i | − | 1.23361i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13626.8 | + | 13626.8i | 0.469080 | + | 0.469080i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14532.5 | + | 14532.5i | −0.498671 | + | 0.498671i | −0.911024 | − | 0.412353i | \(-0.864707\pi\) |
0.412353 | + | 0.911024i | \(0.364707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19767.3 | + | 19767.3i | −0.676159 | + | 0.676159i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40031.4 | 1.36499 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2360.48 | −0.0802345 | −0.0401172 | − | 0.999195i | \(-0.512773\pi\) | ||||
−0.0401172 | + | 0.999195i | \(0.512773\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6095.87 | + | 6095.87i | −0.206553 | + | 0.206553i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10733.4 | − | 10733.4i | 0.362552 | − | 0.362552i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38097.1 | − | 38097.1i | −1.28281 | − | 1.28281i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27302.7i | 0.916475i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 347.923 | + | 347.923i | 0.0116424 | + | 0.0116424i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 393.659 | 0.0131319 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 9395.70i | − | 0.312456i | −0.987721 | − | 0.156228i | \(-0.950066\pi\) | ||
0.987721 | − | 0.156228i | \(-0.0499335\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7367.16 | + | 26264.9i | −0.244239 | + | 0.870744i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 24081.5i | − | 0.795893i | −0.917409 | − | 0.397947i | \(-0.869723\pi\) | ||
0.917409 | − | 0.397947i | \(-0.130277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −113946. | −3.75430 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 29882.1 | + | 29882.1i | 0.981532 | + | 0.981532i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7503.29i | 0.245703i | 0.992425 | + | 0.122851i | \(0.0392038\pi\) | ||||
−0.992425 | + | 0.122851i | \(0.960796\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7193.71 | + | 7193.71i | 0.234844 | + | 0.234844i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1012.27 | − | 1012.27i | 0.0329452 | − | 0.0329452i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9334.52 | + | 9334.52i | −0.302874 | + | 0.302874i | −0.842137 | − | 0.539263i | \(-0.818703\pi\) |
0.539263 | + | 0.842137i | \(0.318703\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3149.62 | −0.101884 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −122706. | −3.95721 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −31277.7 | + | 31277.7i | −1.00564 | + | 1.00564i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27451.4 | + | 27451.4i | −0.879940 | + | 0.879940i | −0.993528 | − | 0.113588i | \(-0.963766\pi\) |
0.113588 | + | 0.993528i | \(0.463766\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3630.46 | − | 3630.46i | −0.116021 | − | 0.116021i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4394.08i | 0.140002i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14656.5 | + | 14656.5i | 0.465573 | + | 0.465573i | 0.900477 | − | 0.434904i | \(-0.143218\pi\) |
−0.434904 | + | 0.900477i | \(0.643218\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13241.3 | 0.419354 |
(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 | 136.4.k.b.89.6 | yes | 14 | |
4.3 | odd | 2 | 272.4.o.f.225.2 | 14 | |||
17.8 | even | 8 | 2312.4.a.l.1.4 | 14 | |||
17.9 | even | 8 | 2312.4.a.l.1.11 | 14 | |||
17.13 | even | 4 | inner | 136.4.k.b.81.6 | ✓ | 14 | |
68.47 | odd | 4 | 272.4.o.f.81.2 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.k.b.81.6 | ✓ | 14 | 17.13 | even | 4 | inner | |
136.4.k.b.89.6 | yes | 14 | 1.1 | even | 1 | trivial | |
272.4.o.f.81.2 | 14 | 68.47 | odd | 4 | |||
272.4.o.f.225.2 | 14 | 4.3 | odd | 2 | |||
2312.4.a.l.1.4 | 14 | 17.8 | even | 8 | |||
2312.4.a.l.1.11 | 14 | 17.9 | even | 8 |