Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 12x^{10} + 112x^{8} - 368x^{6} + 928x^{4} - 256x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.6 | ||
Root | \(2.48442 - 1.43438i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.4.b.a.107.5 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.889241 | + | 2.68500i | −0.314394 | + | 0.949293i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.41850 | − | 4.77523i | −0.802313 | − | 0.596904i | ||||
\(5\) | − | 14.9230i | − | 1.33475i | −0.744720 | − | 0.667377i | \(-0.767417\pi\) | ||
0.744720 | − | 0.667377i | \(-0.232583\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.0528i | 1.62270i | 0.584563 | + | 0.811348i | \(0.301266\pi\) | ||||
−0.584563 | + | 0.811348i | \(0.698734\pi\) | |||||||
\(8\) | 18.5291 | − | 12.9874i | 0.818879 | − | 0.573966i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 40.0683 | + | 13.2701i | 1.26707 | + | 0.419639i | ||||
\(11\) | 55.9380 | 1.53327 | 0.766634 | − | 0.642085i | \(-0.221930\pi\) | ||||
0.766634 | + | 0.642085i | \(0.221930\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 57.4627 | 1.22594 | 0.612972 | − | 0.790105i | \(-0.289974\pi\) | ||||
0.612972 | + | 0.790105i | \(0.289974\pi\) | |||||||
\(14\) | −80.6918 | − | 26.7241i | −1.54041 | − | 0.510166i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 18.3943 | + | 61.2997i | 0.287411 | + | 0.957807i | ||||
\(17\) | 29.2840i | 0.417789i | 0.977938 | + | 0.208895i | \(0.0669865\pi\) | ||||
−0.977938 | + | 0.208895i | \(0.933013\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.709738i | − | 0.00856974i | −0.999991 | − | 0.00428487i | \(-0.998636\pi\) | ||
0.999991 | − | 0.00428487i | \(-0.00136392\pi\) | |||||||
\(20\) | −71.2608 | + | 95.7833i | −0.796720 | + | 1.07089i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −49.7423 | + | 150.194i | −0.482050 | + | 1.45552i | ||||
\(23\) | 48.0368 | 0.435494 | 0.217747 | − | 0.976005i | \(-0.430129\pi\) | ||||
0.217747 | + | 0.976005i | \(0.430129\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −97.6960 | −0.781568 | ||||||||
\(26\) | −51.0981 | + | 154.288i | −0.385430 | + | 1.16378i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 143.509 | − | 192.894i | 0.968594 | − | 1.30191i | ||||
\(29\) | − | 172.964i | − | 1.10754i | −0.832670 | − | 0.553770i | \(-0.813189\pi\) | ||
0.832670 | − | 0.553770i | \(-0.186811\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 45.2268i | 0.262031i | 0.991380 | + | 0.131016i | \(0.0418238\pi\) | ||||
−0.991380 | + | 0.131016i | \(0.958176\pi\) | |||||||
\(32\) | −180.947 | − | 5.12130i | −0.999600 | − | 0.0282914i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −78.6277 | − | 26.0405i | −0.396604 | − | 0.131350i | ||||
\(35\) | 448.477 | 2.16590 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 248.625 | 1.10470 | 0.552348 | − | 0.833613i | \(-0.313732\pi\) | ||||
0.552348 | + | 0.833613i | \(0.313732\pi\) | |||||||
\(38\) | 1.90565 | + | 0.631128i | 0.00813519 | + | 0.00269427i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −193.811 | − | 276.510i | −0.766104 | − | 1.09300i | ||||
\(41\) | 51.3323i | 0.195531i | 0.995209 | + | 0.0977653i | \(0.0311695\pi\) | ||||
−0.995209 | + | 0.0977653i | \(0.968831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19.9660i | 0.0708090i | 0.999373 | + | 0.0354045i | \(0.0112720\pi\) | ||||
−0.999373 | + | 0.0354045i | \(0.988728\pi\) | |||||||
\(44\) | −359.038 | − | 267.117i | −1.23016 | − | 0.915213i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −42.7163 | + | 128.979i | −0.136917 | + | 0.413411i | ||||
\(47\) | −10.8215 | −0.0335845 | −0.0167923 | − | 0.999859i | \(-0.505345\pi\) | ||||
−0.0167923 | + | 0.999859i | \(0.505345\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −560.168 | −1.63314 | ||||||||
\(50\) | 86.8753 | − | 262.314i | 0.245720 | − | 0.741937i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −368.824 | − | 274.398i | −0.983591 | − | 0.731771i | ||||
\(53\) | − | 37.0817i | − | 0.0961051i | −0.998845 | − | 0.0480525i | \(-0.984699\pi\) | ||
0.998845 | − | 0.0480525i | \(-0.0153015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 834.763i | − | 2.04653i | ||||||
\(56\) | 390.306 | + | 556.851i | 0.931373 | + | 1.32879i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 464.410 | + | 153.807i | 1.05138 | + | 0.348204i | ||||
\(59\) | 411.262 | 0.907487 | 0.453744 | − | 0.891132i | \(-0.350088\pi\) | ||||
0.453744 | + | 0.891132i | \(0.350088\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −308.855 | −0.648275 | −0.324138 | − | 0.946010i | \(-0.605074\pi\) | ||||
−0.324138 | + | 0.946010i | \(0.605074\pi\) | |||||||
\(62\) | −121.434 | − | 40.2175i | −0.248744 | − | 0.0823811i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 174.656 | − | 481.289i | 0.341125 | − | 0.940018i | ||||
\(65\) | − | 857.516i | − | 1.63633i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 113.616i | 0.207170i | 0.994621 | + | 0.103585i | \(0.0330314\pi\) | ||||
−0.994621 | + | 0.103585i | \(0.966969\pi\) | |||||||
\(68\) | 139.838 | − | 187.959i | 0.249380 | − | 0.335197i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −398.804 | + | 1204.16i | −0.680946 | + | 2.05607i | ||||
\(71\) | −1134.56 | −1.89645 | −0.948224 | − | 0.317603i | \(-0.897122\pi\) | ||||
−0.948224 | + | 0.317603i | \(0.897122\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 728.560 | 1.16810 | 0.584051 | − | 0.811717i | \(-0.301467\pi\) | ||||
0.584051 | + | 0.811717i | \(0.301467\pi\) | |||||||
\(74\) | −221.088 | + | 667.560i | −0.347310 | + | 1.04868i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.38916 | + | 4.55545i | −0.00511531 | + | 0.00687561i | ||||
\(77\) | 1681.09i | 2.48803i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 487.025i | 0.693602i | 0.937939 | + | 0.346801i | \(0.112732\pi\) | ||||
−0.937939 | + | 0.346801i | \(0.887268\pi\) | |||||||
\(80\) | 914.775 | − | 274.499i | 1.27844 | − | 0.383623i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −137.827 | − | 45.6468i | −0.185616 | − | 0.0614737i | ||||
\(83\) | −1165.71 | −1.54161 | −0.770803 | − | 0.637074i | \(-0.780145\pi\) | ||||
−0.770803 | + | 0.637074i | \(0.780145\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 437.005 | 0.557646 | ||||||||
\(86\) | −53.6088 | − | 17.7546i | −0.0672184 | − | 0.0222619i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1036.48 | − | 726.488i | 1.25556 | − | 0.880044i | ||||
\(89\) | 1198.68i | 1.42764i | 0.700332 | + | 0.713818i | \(0.253035\pi\) | ||||
−0.700332 | + | 0.713818i | \(0.746965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1726.91i | 1.98934i | ||||||||
\(92\) | −308.324 | − | 229.387i | −0.349402 | − | 0.259948i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.62289 | − | 29.0557i | 0.0105588 | − | 0.0318815i | ||||
\(95\) | −10.5914 | −0.0114385 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 624.472 | 0.653665 | 0.326833 | − | 0.945082i | \(-0.394019\pi\) | ||||
0.326833 | + | 0.945082i | \(0.394019\pi\) | |||||||
\(98\) | 498.124 | − | 1504.05i | 0.513450 | − | 1.55033i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 627.062 | + | 466.521i | 0.627062 | + | 0.466521i | ||||
\(101\) | − | 1757.10i | − | 1.73107i | −0.500849 | − | 0.865535i | \(-0.666979\pi\) | ||
0.500849 | − | 0.865535i | \(-0.333021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.90175i | 0.00373254i | 0.999998 | + | 0.00186627i | \(0.000594052\pi\) | ||||
−0.999998 | + | 0.00186627i | \(0.999406\pi\) | |||||||
\(104\) | 1064.73 | − | 746.289i | 1.00390 | − | 0.703651i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 99.5646 | + | 32.9746i | 0.0912318 | + | 0.0302149i | ||||
\(107\) | −77.3509 | −0.0698859 | −0.0349429 | − | 0.999389i | \(-0.511125\pi\) | ||||
−0.0349429 | + | 0.999389i | \(0.511125\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1660.75 | −1.45937 | −0.729683 | − | 0.683785i | \(-0.760333\pi\) | ||||
−0.729683 | + | 0.683785i | \(0.760333\pi\) | |||||||
\(110\) | 2241.34 | + | 742.305i | 1.94276 | + | 0.643418i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1842.22 | + | 552.800i | −1.55423 | + | 0.466381i | ||||
\(113\) | − | 253.390i | − | 0.210946i | −0.994422 | − | 0.105473i | \(-0.966364\pi\) | ||
0.994422 | − | 0.105473i | \(-0.0336357\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 716.853i | − | 0.581277i | ||||||
\(116\) | −825.945 | + | 1110.17i | −0.661095 | + | 0.888594i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −365.711 | + | 1104.24i | −0.285309 | + | 0.861471i | ||||
\(119\) | −880.065 | −0.677945 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1798.06 | 1.35091 | ||||||||
\(122\) | 274.646 | − | 829.276i | 0.203814 | − | 0.615403i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 215.968 | − | 290.288i | 0.156408 | − | 0.210231i | ||||
\(125\) | − | 407.457i | − | 0.291553i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1429.82i | − | 0.999022i | −0.866307 | − | 0.499511i | \(-0.833513\pi\) | ||
0.866307 | − | 0.499511i | \(-0.166487\pi\) | |||||||
\(128\) | 1136.95 | + | 896.934i | 0.785104 | + | 0.619364i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2302.43 | + | 762.538i | 1.55336 | + | 0.514454i | ||||
\(131\) | −2037.82 | −1.35912 | −0.679560 | − | 0.733620i | \(-0.737829\pi\) | ||||
−0.679560 | + | 0.733620i | \(0.737829\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.3296 | 0.0139061 | ||||||||
\(134\) | −305.059 | − | 101.032i | −0.196665 | − | 0.0651330i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 380.322 | + | 542.607i | 0.239797 | + | 0.342119i | ||||
\(137\) | 804.869i | 0.501931i | 0.967996 | + | 0.250966i | \(0.0807481\pi\) | ||||
−0.967996 | + | 0.250966i | \(0.919252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 413.813i | − | 0.252512i | −0.991998 | − | 0.126256i | \(-0.959704\pi\) | ||
0.991998 | − | 0.126256i | \(-0.0402961\pi\) | |||||||
\(140\) | −2878.55 | − | 2141.58i | −1.73773 | − | 1.29283i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1008.90 | − | 3046.31i | 0.596232 | − | 1.80028i | ||||
\(143\) | 3214.35 | 1.87970 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2581.15 | −1.47829 | ||||||||
\(146\) | −647.865 | + | 1956.19i | −0.367245 | + | 1.10887i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1595.80 | − | 1187.24i | −0.886312 | − | 0.659398i | ||||
\(149\) | 1459.08i | 0.802233i | 0.916027 | + | 0.401116i | \(0.131378\pi\) | ||||
−0.916027 | + | 0.401116i | \(0.868622\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1668.38i | − | 0.899144i | −0.893244 | − | 0.449572i | \(-0.851576\pi\) | ||
0.893244 | − | 0.449572i | \(-0.148424\pi\) | |||||||
\(152\) | −9.21763 | − | 13.1508i | −0.00491874 | − | 0.00701757i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4513.74 | − | 1494.89i | −2.36187 | − | 0.782221i | ||||
\(155\) | 674.920 | 0.349747 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1773.81 | −0.901691 | −0.450846 | − | 0.892602i | \(-0.648877\pi\) | ||||
−0.450846 | + | 0.892602i | \(0.648877\pi\) | |||||||
\(158\) | −1307.66 | − | 433.082i | −0.658431 | − | 0.218064i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −76.4251 | + | 2700.27i | −0.0377621 | + | 1.33422i | ||||
\(161\) | 1443.64i | 0.706674i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3549.13i | 1.70546i | 0.522356 | + | 0.852728i | \(0.325053\pi\) | ||||
−0.522356 | + | 0.852728i | \(0.674947\pi\) | |||||||
\(164\) | 245.124 | − | 329.476i | 0.116713 | − | 0.156877i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1036.60 | − | 3129.94i | 0.484672 | − | 1.46343i | ||||
\(167\) | 1888.67 | 0.875146 | 0.437573 | − | 0.899183i | \(-0.355838\pi\) | ||||
0.437573 | + | 0.899183i | \(0.355838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1104.96 | 0.502939 | ||||||||
\(170\) | −388.603 | + | 1173.36i | −0.175320 | + | 0.529369i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 95.3422 | − | 128.152i | 0.0422661 | − | 0.0568109i | ||||
\(173\) | − | 2104.10i | − | 0.924694i | −0.886699 | − | 0.462347i | \(-0.847008\pi\) | ||
0.886699 | − | 0.462347i | \(-0.152992\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2936.03i | − | 1.26825i | ||||||
\(176\) | 1028.94 | + | 3428.98i | 0.440678 | + | 1.46857i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3218.45 | − | 1065.91i | −1.35524 | − | 0.448840i | ||||
\(179\) | −1830.10 | −0.764178 | −0.382089 | − | 0.924126i | \(-0.624795\pi\) | ||||
−0.382089 | + | 0.924126i | \(0.624795\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3333.54 | 1.36895 | 0.684475 | − | 0.729036i | \(-0.260032\pi\) | ||||
0.684475 | + | 0.729036i | \(0.260032\pi\) | |||||||
\(182\) | −4636.77 | − | 1535.64i | −1.88846 | − | 0.625435i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 890.079 | − | 623.872i | 0.356617 | − | 0.249959i | ||||
\(185\) | − | 3710.24i | − | 1.47450i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1638.09i | 0.640582i | ||||||||
\(188\) | 69.4576 | + | 51.6750i | 0.0269453 | + | 0.0200467i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.41832 | − | 28.4380i | 0.00359619 | − | 0.0108585i | ||||
\(191\) | 3622.23 | 1.37223 | 0.686114 | − | 0.727494i | \(-0.259315\pi\) | ||||
0.686114 | + | 0.727494i | \(0.259315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2588.68 | −0.965479 | −0.482740 | − | 0.875764i | \(-0.660358\pi\) | ||||
−0.482740 | + | 0.875764i | \(0.660358\pi\) | |||||||
\(194\) | −555.306 | + | 1676.71i | −0.205508 | + | 0.620520i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3595.44 | + | 2674.93i | 1.31029 | + | 0.974829i | ||||
\(197\) | − | 1752.24i | − | 0.633717i | −0.948473 | − | 0.316858i | \(-0.897372\pi\) | ||
0.948473 | − | 0.316858i | \(-0.102628\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3316.58i | − | 1.18144i | −0.806877 | − | 0.590719i | \(-0.798844\pi\) | ||
0.806877 | − | 0.590719i | \(-0.201156\pi\) | |||||||
\(200\) | −1810.22 | + | 1268.82i | −0.640010 | + | 0.448594i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4717.82 | + | 1562.49i | 1.64329 | + | 0.544238i | ||||
\(203\) | 5198.05 | 1.79720 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 766.032 | 0.260985 | ||||||||
\(206\) | −10.4762 | − | 3.46960i | −0.00354327 | − | 0.00117349i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1056.99 | + | 3522.44i | 0.352350 | + | 1.17422i | ||||
\(209\) | − | 39.7013i | − | 0.0131397i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5960.10i | 1.94460i | 0.233738 | + | 0.972300i | \(0.424904\pi\) | ||||
−0.233738 | + | 0.972300i | \(0.575096\pi\) | |||||||
\(212\) | −177.074 | + | 238.009i | −0.0573655 | + | 0.0771063i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 68.7836 | − | 207.687i | 0.0219717 | − | 0.0663422i | ||||
\(215\) | 297.953 | 0.0945125 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1359.19 | −0.425197 | ||||||||
\(218\) | 1476.81 | − | 4459.12i | 0.458816 | − | 1.38537i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3986.19 | + | 5357.93i | −1.22158 | + | 1.64196i | ||||
\(221\) | 1682.74i | 0.512186i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1995.23i | − | 0.599150i | −0.954073 | − | 0.299575i | \(-0.903155\pi\) | ||
0.954073 | − | 0.299575i | \(-0.0968449\pi\) | |||||||
\(224\) | 153.909 | − | 5437.95i | 0.0459084 | − | 1.62205i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 680.354 | + | 225.325i | 0.200250 | + | 0.0663203i | ||||
\(227\) | 2280.12 | 0.666682 | 0.333341 | − | 0.942806i | \(-0.391824\pi\) | ||||
0.333341 | + | 0.942806i | \(0.391824\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4647.94 | 1.34124 | 0.670621 | − | 0.741800i | \(-0.266028\pi\) | ||||
0.670621 | + | 0.741800i | \(0.266028\pi\) | |||||||
\(230\) | 1924.75 | + | 637.455i | 0.551802 | + | 0.182750i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2246.35 | − | 3204.88i | −0.635691 | − | 0.906941i | ||||
\(233\) | − | 2824.81i | − | 0.794247i | −0.917765 | − | 0.397124i | \(-0.870008\pi\) | ||
0.917765 | − | 0.397124i | \(-0.129992\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 161.489i | 0.0448271i | ||||||||
\(236\) | −2639.69 | − | 1963.87i | −0.728089 | − | 0.541683i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 782.590 | − | 2362.98i | 0.213142 | − | 0.643568i | ||||
\(239\) | −2405.85 | −0.651136 | −0.325568 | − | 0.945519i | \(-0.605555\pi\) | ||||
−0.325568 | + | 0.945519i | \(0.605555\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −226.108 | −0.0604352 | −0.0302176 | − | 0.999543i | \(-0.509620\pi\) | ||||
−0.0302176 | + | 0.999543i | \(0.509620\pi\) | |||||||
\(242\) | −1598.91 | + | 4827.80i | −0.424718 | + | 1.28241i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1982.38 | + | 1474.85i | 0.520120 | + | 0.386958i | ||||
\(245\) | 8359.39i | 2.17984i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 40.7834i | − | 0.0105060i | ||||||
\(248\) | 587.377 | + | 838.012i | 0.150397 | + | 0.214572i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1094.02 | + | 362.328i | 0.276769 | + | 0.0916624i | ||||
\(251\) | −1071.12 | −0.269357 | −0.134679 | − | 0.990889i | \(-0.543000\pi\) | ||||
−0.134679 | + | 0.990889i | \(0.543000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2687.08 | 0.667729 | ||||||||
\(254\) | 3839.07 | + | 1271.45i | 0.948365 | + | 0.314087i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3419.30 | + | 2255.13i | −0.834789 | + | 0.550569i | ||||
\(257\) | − | 1844.28i | − | 0.447638i | −0.974631 | − | 0.223819i | \(-0.928148\pi\) | ||
0.974631 | − | 0.223819i | \(-0.0718525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7471.88i | 1.79259i | ||||||||
\(260\) | −4094.84 | + | 5503.96i | −0.976734 | + | 1.31285i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1812.11 | − | 5471.54i | 0.427299 | − | 1.29020i | ||||
\(263\) | −7502.45 | −1.75901 | −0.879507 | − | 0.475886i | \(-0.842128\pi\) | ||||
−0.879507 | + | 0.475886i | \(0.842128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −553.371 | −0.128277 | ||||||||
\(266\) | −18.9671 | + | 57.2700i | −0.00437199 | + | 0.0132009i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 542.542 | − | 729.243i | 0.123661 | − | 0.166215i | ||||
\(269\) | − | 3465.21i | − | 0.785418i | −0.919663 | − | 0.392709i | \(-0.871538\pi\) | ||
0.919663 | − | 0.392709i | \(-0.128462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2922.27i | 0.655038i | 0.944845 | + | 0.327519i | \(0.106212\pi\) | ||||
−0.944845 | + | 0.327519i | \(0.893788\pi\) | |||||||
\(272\) | −1795.10 | + | 538.660i | −0.400161 | + | 0.120077i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2161.08 | − | 715.722i | −0.476480 | − | 0.157804i | ||||
\(275\) | −5464.92 | −1.19835 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6644.62 | −1.44129 | −0.720643 | − | 0.693306i | \(-0.756153\pi\) | ||||
−0.720643 | + | 0.693306i | \(0.756153\pi\) | |||||||
\(278\) | 1111.09 | + | 367.980i | 0.239708 | + | 0.0793883i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8309.89 | − | 5824.54i | 1.77361 | − | 1.24315i | ||||
\(281\) | 6612.13i | 1.40373i | 0.712312 | + | 0.701863i | \(0.247648\pi\) | ||||
−0.712312 | + | 0.701863i | \(0.752352\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2658.33i | − | 0.558379i | −0.960236 | − | 0.279190i | \(-0.909934\pi\) | ||
0.960236 | − | 0.279190i | \(-0.0900658\pi\) | |||||||
\(284\) | 7282.19 | + | 5417.80i | 1.52154 | + | 1.13200i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2858.33 | + | 8630.53i | −0.590967 | + | 1.78439i | ||||
\(287\) | −1542.68 | −0.317287 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4055.45 | 0.825452 | ||||||||
\(290\) | 2295.26 | − | 6930.39i | 0.464767 | − | 1.40333i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4676.26 | − | 3479.04i | −0.937184 | − | 0.697245i | ||||
\(293\) | − | 5553.60i | − | 1.10732i | −0.832743 | − | 0.553660i | \(-0.813231\pi\) | ||
0.832743 | − | 0.553660i | \(-0.186769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 6137.26i | − | 1.21127i | ||||||
\(296\) | 4606.81 | − | 3228.99i | 0.904613 | − | 0.634059i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3917.64 | − | 1297.48i | −0.761554 | − | 0.252217i | ||||
\(299\) | 2760.32 | 0.533891 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −600.033 | −0.114901 | ||||||||
\(302\) | 4479.61 | + | 1483.59i | 0.853551 | + | 0.282686i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 43.5067 | − | 13.0551i | 0.00820815 | − | 0.00246304i | ||||
\(305\) | 4609.04i | 0.865288i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8694.95i | − | 1.61644i | −0.588880 | − | 0.808220i | \(-0.700431\pi\) | ||
0.588880 | − | 0.808220i | \(-0.299569\pi\) | |||||||
\(308\) | 8027.60 | − | 10790.1i | 1.48511 | − | 1.99618i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −600.166 | + | 1812.16i | −0.109959 | + | 0.332013i | ||||
\(311\) | −6717.09 | −1.22473 | −0.612365 | − | 0.790575i | \(-0.709782\pi\) | ||||
−0.612365 | + | 0.790575i | \(0.709782\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1389.06 | −0.250844 | −0.125422 | − | 0.992103i | \(-0.540028\pi\) | ||||
−0.125422 | + | 0.992103i | \(0.540028\pi\) | |||||||
\(314\) | 1577.34 | − | 4762.69i | 0.283486 | − | 0.855969i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2325.66 | − | 3125.97i | 0.414014 | − | 0.556486i | ||||
\(317\) | 1457.63i | 0.258260i | 0.991628 | + | 0.129130i | \(0.0412185\pi\) | ||||
−0.991628 | + | 0.129130i | \(0.958782\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9675.28i | − | 1.69816i | ||||||
\(320\) | −7182.28 | − | 2606.39i | −1.25469 | − | 0.455318i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3876.17 | − | 1283.74i | −0.670841 | − | 0.222174i | ||||
\(323\) | 20.7840 | 0.00358034 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5613.87 | −0.958159 | ||||||||
\(326\) | −9529.43 | − | 3156.03i | −1.61898 | − | 0.536185i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 666.672 | + | 951.142i | 0.112228 | + | 0.160116i | ||||
\(329\) | − | 325.215i | − | 0.0544975i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4966.82i | 0.824776i | 0.911008 | + | 0.412388i | \(0.135305\pi\) | ||||
−0.911008 | + | 0.412388i | \(0.864695\pi\) | |||||||
\(332\) | 7482.11 | + | 5566.53i | 1.23685 | + | 0.920190i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1679.48 | + | 5071.08i | −0.275141 | + | 0.830769i | ||||
\(335\) | 1695.49 | 0.276521 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4892.90 | −0.790899 | −0.395450 | − | 0.918488i | \(-0.629411\pi\) | ||||
−0.395450 | + | 0.918488i | \(0.629411\pi\) | |||||||
\(338\) | −982.574 | + | 2966.82i | −0.158121 | + | 0.477437i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2804.92 | − | 2086.80i | −0.447406 | − | 0.332861i | ||||
\(341\) | 2529.90i | 0.401764i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6526.50i | − | 1.02740i | ||||||
\(344\) | 259.306 | + | 369.952i | 0.0406420 | + | 0.0579840i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5649.53 | + | 1871.05i | 0.877805 | + | 0.290718i | ||||
\(347\) | 253.981 | 0.0392923 | 0.0196461 | − | 0.999807i | \(-0.493746\pi\) | ||||
0.0196461 | + | 0.999807i | \(0.493746\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6464.21 | −0.991465 | −0.495732 | − | 0.868475i | \(-0.665100\pi\) | ||||
−0.495732 | + | 0.868475i | \(0.665100\pi\) | |||||||
\(350\) | 7883.27 | + | 2610.84i | 1.20394 | + | 0.398730i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10121.8 | − | 286.475i | −1.53265 | − | 0.0433783i | ||||
\(353\) | 4033.67i | 0.608188i | 0.952642 | + | 0.304094i | \(0.0983537\pi\) | ||||
−0.952642 | + | 0.304094i | \(0.901646\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16931.1i | 2.53129i | ||||||||
\(356\) | 5723.96 | − | 7693.71i | 0.852161 | − | 1.14541i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1627.40 | − | 4913.82i | 0.240253 | − | 0.725428i | ||||
\(359\) | −10670.4 | −1.56870 | −0.784350 | − | 0.620319i | \(-0.787003\pi\) | ||||
−0.784350 | + | 0.620319i | \(0.787003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6858.50 | 0.999927 | ||||||||
\(362\) | −2964.32 | + | 8950.56i | −0.430390 | + | 1.29953i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8246.40 | − | 11084.2i | 1.18744 | − | 1.59607i | ||||
\(365\) | − | 10872.3i | − | 1.55913i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2559.84i | − | 0.364094i | −0.983290 | − | 0.182047i | \(-0.941728\pi\) | ||
0.983290 | − | 0.182047i | \(-0.0582724\pi\) | |||||||
\(368\) | 883.604 | + | 2944.64i | 0.125166 | + | 0.417119i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 9962.01 | + | 3299.29i | 1.39973 | + | 0.463573i | ||||
\(371\) | 1114.41 | 0.155949 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1935.92 | 0.268735 | 0.134368 | − | 0.990932i | \(-0.457100\pi\) | ||||
0.134368 | + | 0.990932i | \(0.457100\pi\) | |||||||
\(374\) | −4398.28 | − | 1456.65i | −0.608100 | − | 0.201395i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −200.512 | + | 140.542i | −0.0275017 | + | 0.0192764i | ||||
\(377\) | − | 9938.99i | − | 1.35778i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5944.90i | 0.805722i | 0.915261 | + | 0.402861i | \(0.131984\pi\) | ||||
−0.915261 | + | 0.402861i | \(0.868016\pi\) | |||||||
\(380\) | 67.9810 | + | 50.5765i | 0.00917724 | + | 0.00682768i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3221.03 | + | 9725.71i | −0.431420 | + | 1.30264i | ||||
\(383\) | −1696.80 | −0.226378 | −0.113189 | − | 0.993573i | \(-0.536107\pi\) | ||||
−0.113189 | + | 0.993573i | \(0.536107\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25086.9 | 3.32090 | ||||||||
\(386\) | 2301.96 | − | 6950.63i | 0.303541 | − | 0.916522i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4008.17 | − | 2982.00i | −0.524444 | − | 0.390175i | ||||
\(389\) | 3913.71i | 0.510111i | 0.966926 | + | 0.255055i | \(0.0820937\pi\) | ||||
−0.966926 | + | 0.255055i | \(0.917906\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1406.71i | 0.181945i | ||||||||
\(392\) | −10379.4 | + | 7275.11i | −1.33735 | + | 0.937369i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4704.78 | + | 1558.17i | 0.601583 | + | 0.199237i | ||||
\(395\) | 7267.87 | 0.925788 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5079.98 | 0.642208 | 0.321104 | − | 0.947044i | \(-0.395946\pi\) | ||||
0.321104 | + | 0.947044i | \(0.395946\pi\) | |||||||
\(398\) | 8905.04 | + | 2949.24i | 1.12153 | + | 0.371437i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1797.05 | − | 5988.73i | −0.224632 | − | 0.748592i | ||||
\(401\) | 9374.44i | 1.16742i | 0.811961 | + | 0.583712i | \(0.198400\pi\) | ||||
−0.811961 | + | 0.583712i | \(0.801600\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2598.85i | 0.321236i | ||||||||
\(404\) | −8390.56 | + | 11278.0i | −1.03328 | + | 1.38886i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4622.32 | + | 13956.8i | −0.565029 | + | 1.70607i | ||||
\(407\) | 13907.6 | 1.69379 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12392.7 | −1.49824 | −0.749120 | − | 0.662434i | \(-0.769523\pi\) | ||||
−0.749120 | + | 0.662434i | \(0.769523\pi\) | |||||||
\(410\) | −681.187 | + | 2056.80i | −0.0820522 | + | 0.247751i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 18.6318 | − | 25.0434i | 0.00222797 | − | 0.00299466i | ||||
\(413\) | 12359.6i | 1.47258i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17395.9i | 2.05766i | ||||||||
\(416\) | −10397.7 | − | 294.283i | −1.22545 | − | 0.0346837i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 106.598 | + | 35.3040i | 0.0124734 | + | 0.00413104i | ||||
\(419\) | −266.866 | −0.0311151 | −0.0155576 | − | 0.999879i | \(-0.504952\pi\) | ||||
−0.0155576 | + | 0.999879i | \(0.504952\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9952.62 | −1.15216 | −0.576082 | − | 0.817392i | \(-0.695419\pi\) | ||||
−0.576082 | + | 0.817392i | \(0.695419\pi\) | |||||||
\(422\) | −16002.9 | − | 5299.97i | −1.84599 | − | 0.611371i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −481.595 | − | 687.092i | −0.0551611 | − | 0.0786984i | ||||
\(425\) | − | 2860.93i | − | 0.326531i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 9281.94i | − | 1.05195i | ||||||
\(428\) | 496.477 | + | 369.368i | 0.0560703 | + | 0.0417152i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −264.952 | + | 800.004i | −0.0297142 | + | 0.0897200i | ||||
\(431\) | 6583.33 | 0.735749 | 0.367875 | − | 0.929875i | \(-0.380086\pi\) | ||||
0.367875 | + | 0.929875i | \(0.380086\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13747.0 | −1.52572 | −0.762860 | − | 0.646564i | \(-0.776205\pi\) | ||||
−0.762860 | + | 0.646564i | \(0.776205\pi\) | |||||||
\(434\) | 1208.65 | − | 3649.43i | 0.133679 | − | 0.403637i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10659.5 | + | 7930.46i | 1.17087 | + | 0.871102i | ||||
\(437\) | − | 34.0935i | − | 0.00373207i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13380.0i | − | 1.45466i | −0.686290 | − | 0.727328i | \(-0.740762\pi\) | ||
0.686290 | − | 0.727328i | \(-0.259238\pi\) | |||||||
\(440\) | −10841.4 | − | 15467.4i | −1.17464 | − | 1.67586i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4518.16 | − | 1496.36i | −0.486214 | − | 0.161028i | ||||
\(443\) | −16108.1 | −1.72758 | −0.863791 | − | 0.503851i | \(-0.831916\pi\) | ||||
−0.863791 | + | 0.503851i | \(0.831916\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17887.9 | 1.90554 | ||||||||
\(446\) | 5357.20 | + | 1774.24i | 0.568769 | + | 0.188369i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14464.1 | + | 5248.90i | 1.52536 | + | 0.553542i | ||||
\(449\) | − | 11283.5i | − | 1.18597i | −0.805214 | − | 0.592984i | \(-0.797950\pi\) | ||
0.805214 | − | 0.592984i | \(-0.202050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2871.42i | 0.299801i | ||||||||
\(452\) | −1210.00 | + | 1626.39i | −0.125915 | + | 0.169245i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2027.57 | + | 6122.13i | −0.209601 | + | 0.632876i | ||||
\(455\) | 25770.7 | 2.65527 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1984.72 | 0.203154 | 0.101577 | − | 0.994828i | \(-0.467611\pi\) | ||||
0.101577 | + | 0.994828i | \(0.467611\pi\) | |||||||
\(458\) | −4133.14 | + | 12479.7i | −0.421679 | + | 1.27323i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3423.14 | + | 4601.12i | −0.346967 | + | 0.466366i | ||||
\(461\) | − | 9634.41i | − | 0.973360i | −0.873580 | − | 0.486680i | \(-0.838208\pi\) | ||
0.873580 | − | 0.486680i | \(-0.161792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1392.38i | − | 0.139762i | −0.997555 | − | 0.0698808i | \(-0.977738\pi\) | ||
0.997555 | − | 0.0698808i | \(-0.0222619\pi\) | |||||||
\(464\) | 10602.7 | − | 3181.56i | 1.06081 | − | 0.318320i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7584.64 | + | 2511.94i | 0.753973 | + | 0.249707i | ||||
\(467\) | 15161.4 | 1.50232 | 0.751161 | − | 0.660119i | \(-0.229494\pi\) | ||||
0.751161 | + | 0.660119i | \(0.229494\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3414.47 | −0.336174 | ||||||||
\(470\) | −433.598 | − | 143.602i | −0.0425540 | − | 0.0140934i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7620.32 | − | 5341.22i | 0.743122 | − | 0.520867i | ||||
\(473\) | 1116.86i | 0.108569i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 69.3385i | 0.00669783i | ||||||||
\(476\) | 5648.70 | + | 4202.51i | 0.543924 | + | 0.404668i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2139.38 | − | 6459.72i | 0.204713 | − | 0.618118i | ||||
\(479\) | −273.224 | −0.0260625 | −0.0130312 | − | 0.999915i | \(-0.504148\pi\) | ||||
−0.0130312 | + | 0.999915i | \(0.504148\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14286.7 | 1.35430 | ||||||||
\(482\) | 201.064 | − | 607.100i | 0.0190005 | − | 0.0573707i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11540.8 | − | 8586.15i | −1.08385 | − | 0.806362i | ||||
\(485\) | − | 9319.00i | − | 0.872482i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8706.60i | − | 0.810131i | −0.914288 | − | 0.405065i | \(-0.867249\pi\) | ||
0.914288 | − | 0.405065i | \(-0.132751\pi\) | |||||||
\(488\) | −5722.80 | + | 4011.21i | −0.530859 | + | 0.372088i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −22445.0 | − | 7433.51i | −2.06931 | − | 0.685330i | ||||
\(491\) | 4442.47 | 0.408321 | 0.204161 | − | 0.978937i | \(-0.434554\pi\) | ||||
0.204161 | + | 0.978937i | \(0.434554\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5065.09 | 0.462718 | ||||||||
\(494\) | 109.504 | + | 36.2663i | 0.00997328 | + | 0.00330303i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2772.39 | + | 831.916i | −0.250975 | + | 0.0753108i | ||||
\(497\) | − | 34096.7i | − | 3.07736i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4920.29i | − | 0.441408i | −0.975341 | − | 0.220704i | \(-0.929165\pi\) | ||
0.975341 | − | 0.220704i | \(-0.0708355\pi\) | |||||||
\(500\) | −1945.70 | + | 2615.27i | −0.174029 | + | 0.233916i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 952.486 | − | 2875.97i | 0.0846843 | − | 0.255699i | ||||
\(503\) | 5575.54 | 0.494237 | 0.247118 | − | 0.968985i | \(-0.420516\pi\) | ||||
0.247118 | + | 0.968985i | \(0.420516\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26221.2 | −2.31055 | ||||||||
\(506\) | −2389.46 | + | 7214.83i | −0.209930 | + | 0.633870i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6827.71 | + | 9177.29i | −0.596320 | + | 0.801528i | ||||
\(509\) | 17508.5i | 1.52466i | 0.647190 | + | 0.762328i | \(0.275944\pi\) | ||||
−0.647190 | + | 0.762328i | \(0.724056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21895.2i | 1.89548i | ||||||||
\(512\) | −3014.46 | − | 11186.2i | −0.260199 | − | 0.965555i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4951.90 | + | 1640.01i | 0.424940 | + | 0.140735i | ||||
\(515\) | 58.2259 | 0.00498202 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −605.331 | −0.0514941 | ||||||||
\(518\) | −20062.0 | − | 6644.30i | −1.70169 | − | 0.563579i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −11136.9 | − | 15889.0i | −0.939201 | − | 1.33996i | ||||
\(521\) | 12662.1i | 1.06475i | 0.846507 | + | 0.532377i | \(0.178701\pi\) | ||||
−0.846507 | + | 0.532377i | \(0.821299\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2988.40i | − | 0.249854i | −0.992166 | − | 0.124927i | \(-0.960130\pi\) | ||
0.992166 | − | 0.124927i | \(-0.0398697\pi\) | |||||||
\(524\) | 13079.7 | + | 9731.04i | 1.09044 | + | 0.811264i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6671.48 | − | 20144.1i | 0.553024 | − | 1.66982i | ||||
\(527\) | −1324.42 | −0.109474 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9859.47 | −0.810345 | ||||||||
\(530\) | 492.080 | − | 1485.80i | 0.0403294 | − | 0.121772i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −136.904 | − | 101.854i | −0.0111570 | − | 0.00830059i | ||||
\(533\) | 2949.69i | 0.239710i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1154.31i | 0.0932805i | ||||||||
\(536\) | 1475.57 | + | 2105.20i | 0.118909 | + | 0.169647i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9304.10 | + | 3081.40i | 0.745591 | + | 0.246931i | ||||
\(539\) | −31334.7 | −2.50404 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9079.39 | 0.721541 | 0.360770 | − | 0.932655i | \(-0.382514\pi\) | ||||
0.360770 | + | 0.932655i | \(0.382514\pi\) | |||||||
\(542\) | −7846.31 | − | 2598.60i | −0.621822 | − | 0.205940i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 149.972 | − | 5298.85i | 0.0118199 | − | 0.417622i | ||||
\(545\) | 24783.4i | 1.94790i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21690.2i | − | 1.69544i | −0.530444 | − | 0.847720i | \(-0.677975\pi\) | ||
0.530444 | − | 0.847720i | \(-0.322025\pi\) | |||||||
\(548\) | 3843.43 | − | 5166.05i | 0.299605 | − | 0.402706i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4859.63 | − | 14673.3i | 0.376755 | − | 1.13759i | ||||
\(551\) | −122.759 | −0.00949133 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14636.4 | −1.12551 | ||||||||
\(554\) | 5908.66 | − | 17840.8i | 0.453132 | − | 1.36820i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1976.05 | + | 2656.06i | −0.150725 | + | 0.202594i | ||||
\(557\) | 18129.0i | 1.37908i | 0.724247 | + | 0.689541i | \(0.242188\pi\) | ||||
−0.724247 | + | 0.689541i | \(0.757812\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1147.30i | 0.0868078i | ||||||||
\(560\) | 8249.44 | + | 27491.5i | 0.622504 | + | 2.07451i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17753.6 | − | 5879.78i | −1.33255 | − | 0.441323i | ||||
\(563\) | −4922.54 | −0.368491 | −0.184245 | − | 0.982880i | \(-0.558984\pi\) | ||||
−0.184245 | + | 0.982880i | \(0.558984\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3781.34 | −0.281562 | ||||||||
\(566\) | 7137.63 | + | 2363.90i | 0.530065 | + | 0.175551i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21022.4 | + | 14735.0i | −1.55296 | + | 1.08850i | ||||
\(569\) | 17731.7i | 1.30641i | 0.757179 | + | 0.653207i | \(0.226577\pi\) | ||||
−0.757179 | + | 0.653207i | \(0.773423\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17237.0i | − | 1.26330i | −0.775254 | − | 0.631650i | \(-0.782378\pi\) | ||
0.775254 | − | 0.631650i | \(-0.217622\pi\) | |||||||
\(572\) | −20631.3 | − | 15349.2i | −1.50811 | − | 1.12200i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1371.81 | − | 4142.09i | 0.0997531 | − | 0.301198i | ||||
\(575\) | −4693.00 | −0.340368 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6166.73 | 0.444929 | 0.222465 | − | 0.974941i | \(-0.428590\pi\) | ||||
0.222465 | + | 0.974941i | \(0.428590\pi\) | |||||||
\(578\) | −3606.27 | + | 10888.9i | −0.259517 | + | 0.783596i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16567.1 | + | 12325.6i | 1.18605 | + | 0.882399i | ||||
\(581\) | − | 35032.8i | − | 2.50156i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2074.28i | − | 0.147355i | ||||||
\(584\) | 13499.6 | − | 9462.09i | 0.956535 | − | 0.670452i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14911.5 | + | 4938.49i | 1.05117 | + | 0.348135i | ||||
\(587\) | 11268.2 | 0.792311 | 0.396155 | − | 0.918183i | \(-0.370344\pi\) | ||||
0.396155 | + | 0.918183i | \(0.370344\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.0992 | 0.00224554 | ||||||||
\(590\) | 16478.6 | + | 5457.51i | 1.14985 | + | 0.380817i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4573.30 | + | 15240.7i | 0.317502 | + | 1.05809i | ||||
\(593\) | 4766.20i | 0.330058i | 0.986289 | + | 0.165029i | \(0.0527718\pi\) | ||||
−0.986289 | + | 0.165029i | \(0.947228\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13133.2i | 0.904889i | ||||||||
\(596\) | 6967.46 | − | 9365.12i | 0.478856 | − | 0.643642i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2454.59 | + | 7411.48i | −0.167852 | + | 0.506819i | ||||
\(599\) | −11994.7 | −0.818177 | −0.409089 | − | 0.912495i | \(-0.634153\pi\) | ||||
−0.409089 | + | 0.912495i | \(0.634153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23975.3 | 1.62724 | 0.813622 | − | 0.581394i | \(-0.197493\pi\) | ||||
0.813622 | + | 0.581394i | \(0.197493\pi\) | |||||||
\(602\) | 533.574 | − | 1611.09i | 0.0361243 | − | 0.109075i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7966.90 | + | 10708.5i | −0.536703 | + | 0.721395i | ||||
\(605\) | − | 26832.4i | − | 1.80313i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18629.0i | 1.24568i | 0.782349 | + | 0.622840i | \(0.214021\pi\) | ||||
−0.782349 | + | 0.622840i | \(0.785979\pi\) | |||||||
\(608\) | −3.63478 | + | 128.425i | −0.000242450 | + | 0.00856630i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12375.3 | − | 4098.55i | −0.821412 | − | 0.272041i | ||||
\(611\) | −621.830 | −0.0411728 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18552.5 | 1.22240 | 0.611198 | − | 0.791478i | \(-0.290688\pi\) | ||||
0.611198 | + | 0.791478i | \(0.290688\pi\) | |||||||
\(614\) | 23346.0 | + | 7731.91i | 1.53447 | + | 0.508199i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21833.0 | + | 31149.1i | 1.42804 | + | 2.03739i | ||||
\(617\) | 7836.95i | 0.511351i | 0.966763 | + | 0.255676i | \(0.0822979\pi\) | ||||
−0.966763 | + | 0.255676i | \(0.917702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16023.6i | − | 1.04045i | −0.854028 | − | 0.520227i | \(-0.825847\pi\) | ||
0.854028 | − | 0.520227i | \(-0.174153\pi\) | |||||||
\(620\) | −4331.97 | − | 3222.90i | −0.280607 | − | 0.208766i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5973.11 | − | 18035.4i | 0.385048 | − | 1.16263i | ||||
\(623\) | −36023.6 | −2.31662 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18292.5 | −1.17072 | ||||||||
\(626\) | 1235.21 | − | 3729.62i | 0.0788638 | − | 0.238124i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11385.2 | + | 8470.36i | 0.723438 | + | 0.538223i | ||||
\(629\) | 7280.75i | 0.461530i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18451.1i | − | 1.16407i | −0.813164 | − | 0.582035i | \(-0.802257\pi\) | ||
0.813164 | − | 0.582035i | \(-0.197743\pi\) | |||||||
\(632\) | 6325.18 | + | 9024.14i | 0.398104 | + | 0.567976i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3913.73 | − | 1296.18i | −0.245164 | − | 0.0811955i | ||||
\(635\) | −21337.2 | −1.33345 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32188.7 | −2.00214 | ||||||||
\(638\) | 25978.2 | + | 8603.65i | 1.61205 | + | 0.533890i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 13385.0 | − | 16966.7i | 0.826698 | − | 1.04792i | ||||
\(641\) | − | 20544.4i | − | 1.26592i | −0.774185 | − | 0.632960i | \(-0.781840\pi\) | ||
0.774185 | − | 0.632960i | \(-0.218160\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27413.8i | 1.68133i | 0.541555 | + | 0.840665i | \(0.317836\pi\) | ||||
−0.541555 | + | 0.840665i | \(0.682164\pi\) | |||||||
\(644\) | 6893.70 | − | 9265.99i | 0.421817 | − | 0.566974i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.4819 | + | 55.8050i | −0.00112564 | + | 0.00339879i | ||||
\(647\) | 23051.0 | 1.40066 | 0.700332 | − | 0.713817i | \(-0.253035\pi\) | ||||
0.700332 | + | 0.713817i | \(0.253035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23005.2 | 1.39142 | ||||||||
\(650\) | 4992.09 | − | 15073.3i | 0.301240 | − | 0.909573i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16947.9 | − | 22780.1i | 1.01799 | − | 1.36831i | ||||
\(653\) | 27762.7i | 1.66376i | 0.554953 | + | 0.831882i | \(0.312736\pi\) | ||||
−0.554953 | + | 0.831882i | \(0.687264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30410.3i | 1.81409i | ||||||||
\(656\) | −3146.65 | + | 944.223i | −0.187281 | + | 0.0561977i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 873.203 | + | 289.194i | 0.0517341 | + | 0.0171337i | ||||
\(659\) | −9857.22 | −0.582675 | −0.291338 | − | 0.956620i | \(-0.594100\pi\) | ||||
−0.291338 | + | 0.956620i | \(0.594100\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3542.53 | 0.208454 | 0.104227 | − | 0.994554i | \(-0.466763\pi\) | ||||
0.104227 | + | 0.994554i | \(0.466763\pi\) | |||||||
\(662\) | −13335.9 | − | 4416.70i | −0.782954 | − | 0.259305i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −21599.6 | + | 15139.5i | −1.26239 | + | 0.884830i | ||||
\(665\) | − | 318.301i | − | 0.0185612i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8308.65i | − | 0.482327i | ||||||
\(668\) | −12122.4 | − | 9018.82i | −0.702141 | − | 0.522378i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1507.70 | + | 4552.40i | −0.0869365 | + | 0.262499i | ||||
\(671\) | −17276.7 | −0.993979 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19216.6 | 1.10066 | 0.550330 | − | 0.834947i | \(-0.314502\pi\) | ||||
0.550330 | + | 0.834947i | \(0.314502\pi\) | |||||||
\(674\) | 4350.96 | − | 13137.5i | 0.248654 | − | 0.750795i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7092.17 | − | 5276.43i | −0.403515 | − | 0.300206i | ||||
\(677\) | 15731.9i | 0.893093i | 0.894760 | + | 0.446547i | \(0.147346\pi\) | ||||
−0.894760 | + | 0.446547i | \(0.852654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18767.1i | 1.06070i | ||||||||
\(680\) | 8097.32 | − | 5675.55i | 0.456644 | − | 0.320070i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6792.78 | − | 2249.69i | −0.381392 | − | 0.126312i | ||||
\(683\) | 16870.5 | 0.945142 | 0.472571 | − | 0.881293i | \(-0.343326\pi\) | ||||
0.472571 | + | 0.881293i | \(0.343326\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12011.1 | 0.669955 | ||||||||
\(686\) | 17523.7 | + | 5803.63i | 0.975302 | + | 0.323008i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1223.91 | + | 367.261i | −0.0678213 | + | 0.0203513i | ||||
\(689\) | − | 2130.82i | − | 0.117819i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29234.5i | 1.60945i | 0.593645 | + | 0.804727i | \(0.297688\pi\) | ||||
−0.593645 | + | 0.804727i | \(0.702312\pi\) | |||||||
\(692\) | −10047.6 | + | 13505.2i | −0.551953 | + | 0.741894i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −225.850 | + | 681.941i | −0.0123533 | + | 0.0372999i | ||||
\(695\) | −6175.33 | −0.337041 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1503.21 | −0.0816905 | ||||||||
\(698\) | 5748.24 | − | 17356.4i | 0.311711 | − | 0.941190i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −14020.2 | + | 18844.9i | −0.757022 | + | 1.01753i | ||||
\(701\) | − | 14904.4i | − | 0.803041i | −0.915850 | − | 0.401520i | \(-0.868482\pi\) | ||
0.915850 | − | 0.401520i | \(-0.131518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 176.459i | − | 0.00946696i | ||||||
\(704\) | 9769.91 | − | 26922.3i | 0.523036 | − | 1.44130i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10830.4 | − | 3586.90i | −0.577348 | − | 0.191211i | ||||
\(707\) | 52805.7 | 2.80900 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17930.1 | −0.949758 | −0.474879 | − | 0.880051i | \(-0.657508\pi\) | ||||
−0.474879 | + | 0.880051i | \(0.657508\pi\) | |||||||
\(710\) | −45460.0 | − | 15055.8i | −2.40294 | − | 0.795823i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15567.7 | + | 22210.4i | 0.819415 | + | 1.16906i | ||||
\(713\) | 2172.55i | 0.114113i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 47967.7i | − | 2.50894i | ||||||
\(716\) | 11746.5 | + | 8739.13i | 0.613109 | + | 0.456141i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9488.57 | − | 28650.1i | 0.493190 | − | 1.48915i | ||||
\(719\) | −19033.4 | −0.987238 | −0.493619 | − | 0.869678i | \(-0.664326\pi\) | ||||
−0.493619 | + | 0.869678i | \(0.664326\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −117.258 | −0.00605677 | ||||||||
\(722\) | −6098.85 | + | 18415.1i | −0.314371 | + | 0.949223i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21396.3 | − | 15918.4i | −1.09833 | − | 0.817131i | ||||
\(725\) | 16897.9i | 0.865618i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19643.0i | 1.00209i | 0.865422 | + | 0.501043i | \(0.167050\pi\) | ||||
−0.865422 | + | 0.501043i | \(0.832950\pi\) | |||||||
\(728\) | 22428.0 | + | 31998.1i | 1.14181 | + | 1.62902i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 29192.2 | + | 9668.10i | 1.48007 | + | 0.490181i | ||||
\(731\) | −584.684 | −0.0295832 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8335.12 | 0.420006 | 0.210003 | − | 0.977701i | \(-0.432653\pi\) | ||||
0.210003 | + | 0.977701i | \(0.432653\pi\) | |||||||
\(734\) | 6873.19 | + | 2276.32i | 0.345632 | + | 0.114469i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8692.10 | − | 246.011i | −0.435320 | − | 0.0123208i | ||||
\(737\) | 6355.44i | 0.317647i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 12308.0i | − | 0.612661i | −0.951925 | − | 0.306331i | \(-0.900899\pi\) | ||
0.951925 | − | 0.306331i | \(-0.0991013\pi\) | |||||||
\(740\) | −17717.2 | + | 23814.2i | −0.880134 | + | 1.18301i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −990.977 | + | 2992.19i | −0.0490295 | + | 0.148042i | ||||
\(743\) | −26227.7 | −1.29502 | −0.647511 | − | 0.762056i | \(-0.724190\pi\) | ||||
−0.647511 | + | 0.762056i | \(0.724190\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21773.9 | 1.07078 | ||||||||
\(746\) | −1721.50 | + | 5197.96i | −0.0844887 | + | 0.255108i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7822.25 | − | 10514.1i | 0.382366 | − | 0.513947i | ||||
\(749\) | − | 2324.61i | − | 0.113404i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2741.63i | 0.133214i | 0.997779 | + | 0.0666068i | \(0.0212173\pi\) | ||||
−0.997779 | + | 0.0666068i | \(0.978783\pi\) | |||||||
\(752\) | −199.054 | − | 663.352i | −0.00965258 | − | 0.0321675i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26686.2 | + | 8838.16i | 1.28893 | + | 0.426879i | ||||
\(755\) | −24897.2 | −1.20014 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17816.8 | −0.855434 | −0.427717 | − | 0.903913i | \(-0.640682\pi\) | ||||
−0.427717 | + | 0.903913i | \(0.640682\pi\) | |||||||
\(758\) | −15962.1 | − | 5286.44i | −0.764866 | − | 0.253314i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −196.250 | + | 137.555i | −0.00936674 | + | 0.00656531i | ||||
\(761\) | − | 32228.2i | − | 1.53518i | −0.640940 | − | 0.767591i | \(-0.721455\pi\) | ||
0.640940 | − | 0.767591i | \(-0.278545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 49910.1i | − | 2.36811i | ||||||
\(764\) | −23249.3 | − | 17297.0i | −1.10096 | − | 0.819088i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1508.87 | − | 4555.93i | 0.0711718 | − | 0.214899i | ||||
\(767\) | 23632.2 | 1.11253 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4236.60 | −0.198668 | −0.0993340 | − | 0.995054i | \(-0.531671\pi\) | ||||
−0.0993340 | + | 0.995054i | \(0.531671\pi\) | |||||||
\(770\) | −22308.3 | + | 67358.5i | −1.04407 | + | 3.15251i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16615.5 | + | 12361.6i | 0.774616 | + | 0.576298i | ||||
\(773\) | 1754.64i | 0.0816431i | 0.999166 | + | 0.0408215i | \(0.0129975\pi\) | ||||
−0.999166 | + | 0.0408215i | \(0.987002\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4418.48i | − | 0.204795i | ||||||
\(776\) | 11570.9 | − | 8110.25i | 0.535273 | − | 0.375182i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10508.3 | − | 3480.23i | −0.484244 | − | 0.160376i | ||||
\(779\) | 36.4324 | 0.00167565 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −63465.1 | −2.90776 | ||||||||
\(782\) | −3777.02 | − | 1250.90i | −0.172719 | − | 0.0572023i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10303.9 | − | 34338.1i | −0.469384 | − | 1.56424i | ||||
\(785\) | 26470.6i | 1.20354i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 11896.9i | − | 0.538857i | −0.963020 | − | 0.269428i | \(-0.913165\pi\) | ||
0.963020 | − | 0.269428i | \(-0.0868347\pi\) | |||||||
\(788\) | −8367.37 | + | 11246.8i | −0.378268 | + | 0.508439i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6462.89 | + | 19514.3i | −0.291062 | + | 0.878844i | ||||
\(791\) | 7615.07 | 0.342302 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17747.6 | −0.794749 | ||||||||
\(794\) | −4517.32 | + | 13639.8i | −0.201906 | + | 0.609644i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15837.4 | + | 21287.5i | −0.705205 | + | 0.947883i | ||||
\(797\) | − | 16762.4i | − | 0.744986i | −0.928035 | − | 0.372493i | \(-0.878503\pi\) | ||
0.928035 | − | 0.372493i | \(-0.121497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 316.896i | − | 0.0140313i | ||||||
\(800\) | 17677.8 | + | 500.330i | 0.781255 | + | 0.0221117i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −25170.4 | − | 8336.13i | −1.10823 | − | 0.367031i | ||||
\(803\) | 40754.2 | 1.79101 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21543.4 | 0.943236 | ||||||||
\(806\) | −6977.93 | − | 2311.00i | −0.304947 | − | 0.100995i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −22820.1 | − | 32557.5i | −0.993576 | − | 1.41754i | ||||
\(809\) | − | 28039.3i | − | 1.21855i | −0.792957 | − | 0.609277i | \(-0.791460\pi\) | ||
0.792957 | − | 0.609277i | \(-0.208540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 14131.8i | − | 0.611882i | −0.952051 | − | 0.305941i | \(-0.901029\pi\) | ||
0.952051 | − | 0.305941i | \(-0.0989710\pi\) | |||||||
\(812\) | −33363.7 | − | 24821.9i | −1.44192 | − | 1.07276i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12367.2 | + | 37342.0i | −0.532519 | + | 1.60791i | ||||
\(815\) | 52963.7 | 2.27636 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.1706 | 0.000606814 | ||||||||
\(818\) | 11020.1 | − | 33274.5i | 0.471038 | − | 1.42227i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4916.78 | − | 3657.98i | −0.209392 | − | 0.155783i | ||||
\(821\) | 8233.70i | 0.350010i | 0.984568 | + | 0.175005i | \(0.0559942\pi\) | ||||
−0.984568 | + | 0.175005i | \(0.944006\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5824.72i | 0.246704i | 0.992363 | + | 0.123352i | \(0.0393644\pi\) | ||||
−0.992363 | + | 0.123352i | \(0.960636\pi\) | |||||||
\(824\) | 50.6736 | + | 72.2961i | 0.00214235 | + | 0.00305650i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −33185.5 | − | 10990.6i | −1.39791 | − | 0.462969i | ||||
\(827\) | 20581.6 | 0.865406 | 0.432703 | − | 0.901536i | \(-0.357560\pi\) | ||||
0.432703 | + | 0.901536i | \(0.357560\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2844.67 | 0.119179 | 0.0595896 | − | 0.998223i | \(-0.481021\pi\) | ||||
0.0595896 | + | 0.998223i | \(0.481021\pi\) | |||||||
\(830\) | −46708.0 | − | 15469.1i | −1.95332 | − | 0.646917i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10036.2 | − | 27656.2i | 0.418200 | − | 1.15241i | ||||
\(833\) | − | 16404.0i | − | 0.682309i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 28184.6i | − | 1.16810i | ||||||
\(836\) | −189.583 | + | 254.823i | −0.00784313 | + | 0.0105421i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 237.308 | − | 716.535i | 0.00978241 | − | 0.0295374i | ||||
\(839\) | 12881.0 | 0.530037 | 0.265019 | − | 0.964243i | \(-0.414622\pi\) | ||||
0.265019 | + | 0.964243i | \(0.414622\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5527.65 | −0.226645 | ||||||||
\(842\) | 8850.28 | − | 26722.8i | 0.362234 | − | 1.09374i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 28460.9 | − | 38254.9i | 1.16074 | − | 1.56018i | ||||
\(845\) | − | 16489.3i | − | 0.671300i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 54036.6i | 2.19211i | ||||||||
\(848\) | 2273.10 | − | 682.094i | 0.0920501 | − | 0.0276217i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7681.61 | + | 2544.06i | 0.309973 | + | 0.102659i | ||||
\(851\) | 11943.2 | 0.481089 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43159.3 | 1.73241 | 0.866205 | − | 0.499689i | \(-0.166552\pi\) | ||||
0.866205 | + | 0.499689i | \(0.166552\pi\) | |||||||
\(854\) | 24922.0 | + | 8253.87i | 0.998612 | + | 0.330728i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1433.24 | + | 1004.59i | −0.0572281 | + | 0.0401122i | ||||
\(857\) | 236.518i | 0.00942741i | 0.999989 | + | 0.00471371i | \(0.00150042\pi\) | ||||
−0.999989 | + | 0.00471371i | \(0.998500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1103.24i | 0.0438210i | 0.999760 | + | 0.0219105i | \(0.00697488\pi\) | ||||
−0.999760 | + | 0.0219105i | \(0.993025\pi\) | |||||||
\(860\) | −1912.41 | − | 1422.79i | −0.0758286 | − | 0.0564149i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5854.17 | + | 17676.3i | −0.231315 | + | 0.698441i | ||||
\(863\) | −22297.9 | −0.879522 | −0.439761 | − | 0.898115i | \(-0.644937\pi\) | ||||
−0.439761 | + | 0.898115i | \(0.644937\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31399.5 | −1.23424 | ||||||||
\(866\) | 12224.4 | − | 36910.7i | 0.479677 | − | 1.44835i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8723.96 | + | 6490.44i | 0.341141 | + | 0.253802i | ||||
\(869\) | 27243.2i | 1.06348i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6528.67i | 0.253979i | ||||||||
\(872\) | −30772.2 | + | 21568.8i | −1.19504 | + | 0.837627i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 91.5412 | + | 30.3173i | 0.00354282 | + | 0.00117334i | ||||
\(875\) | 12245.2 | 0.473101 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29308.0 | 1.12846 | 0.564231 | − | 0.825617i | \(-0.309173\pi\) | ||||
0.564231 | + | 0.825617i | \(0.309173\pi\) | |||||||
\(878\) | 35925.4 | + | 11898.1i | 1.38089 | + | 0.457335i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 51170.7 | − | 15354.9i | 1.96019 | − | 0.588197i | ||||
\(881\) | 25857.5i | 0.988831i | 0.869226 | + | 0.494415i | \(0.164618\pi\) | ||||
−0.869226 | + | 0.494415i | \(0.835382\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15147.3i | 0.577290i | 0.957436 | + | 0.288645i | \(0.0932047\pi\) | ||||
−0.957436 | + | 0.288645i | \(0.906795\pi\) | |||||||
\(884\) | 8035.46 | − | 10800.6i | 0.305726 | − | 0.410933i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14324.0 | − | 43250.3i | 0.543141 | − | 1.63998i | ||||
\(887\) | 18719.8 | 0.708624 | 0.354312 | − | 0.935127i | \(-0.384715\pi\) | ||||
0.354312 | + | 0.935127i | \(0.384715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42970.0 | 1.62111 | ||||||||
\(890\) | −15906.6 | + | 48029.0i | −0.599091 | + | 1.80892i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9527.68 | + | 12806.4i | −0.357635 | + | 0.480706i | ||||
\(893\) | 7.68040i | 0.000287811i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27310.5i | 1.01999i | ||||||||
\(896\) | −26955.3 | + | 34168.6i | −1.00504 | + | 1.27399i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30296.2 | + | 10033.7i | 1.12583 | + | 0.372861i | ||||
\(899\) | 7822.62 | 0.290210 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1085.90 | 0.0401516 | ||||||||
\(902\) | −7709.79 | − | 2553.39i | −0.284599 | − | 0.0942556i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3290.87 | − | 4695.09i | −0.121076 | − | 0.172740i | ||||
\(905\) | − | 49746.4i | − | 1.82721i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10374.7i | 0.379807i | 0.981803 | + | 0.189904i | \(0.0608175\pi\) | ||||
−0.981803 | + | 0.189904i | \(0.939182\pi\) | |||||||
\(908\) | −14634.9 | − | 10888.1i | −0.534887 | − | 0.397945i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −22916.4 | + | 69194.5i | −0.834802 | + | 2.52063i | ||||
\(911\) | −10860.1 | −0.394962 | −0.197481 | − | 0.980307i | \(-0.563276\pi\) | ||||
−0.197481 | + | 0.980307i | \(0.563276\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −65207.4 | −2.36369 | ||||||||
\(914\) | −1764.90 | + | 5328.99i | −0.0638704 | + | 0.192853i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29832.8 | − | 22195.0i | −1.07610 | − | 0.800593i | ||||
\(917\) | − | 61242.0i | − | 2.20544i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5743.96i | 0.206176i | 0.994672 | + | 0.103088i | \(0.0328723\pi\) | ||||
−0.994672 | + | 0.103088i | \(0.967128\pi\) | |||||||
\(920\) | −9310.04 | − | 13282.6i | −0.333634 | − | 0.475996i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25868.4 | + | 8567.31i | 0.924004 | + | 0.306019i | ||||
\(923\) | −65195.0 | −2.32494 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24289.7 | −0.863396 | ||||||||
\(926\) | 3738.56 | + | 1238.17i | 0.132675 | + | 0.0439402i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −885.802 | + | 31297.4i | −0.0313339 | + | 1.10710i | ||||
\(929\) | 28379.7i | 1.00227i | 0.865369 | + | 0.501135i | \(0.167084\pi\) | ||||
−0.865369 | + | 0.501135i | \(0.832916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 397.572i | 0.0139956i | ||||||||
\(932\) | −13489.1 | + | 18131.1i | −0.474089 | + | 0.637235i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13482.1 | + | 40708.4i | −0.472321 | + | 1.42614i | ||||
\(935\) | 24445.2 | 0.855020 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24896.7 | 0.868025 | 0.434013 | − | 0.900907i | \(-0.357097\pi\) | ||||
0.434013 | + | 0.900907i | \(0.357097\pi\) | |||||||
\(938\) | 3036.29 | − | 9167.87i | 0.105691 | − | 0.319127i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 771.146 | − | 1036.52i | 0.0267575 | − | 0.0359653i | ||||
\(941\) | − | 601.120i | − | 0.0208246i | −0.999946 | − | 0.0104123i | \(-0.996686\pi\) | ||
0.999946 | − | 0.0104123i | \(-0.00331440\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2465.84i | 0.0851524i | ||||||||
\(944\) | 7564.89 | + | 25210.2i | 0.260822 | + | 0.869198i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2998.77 | − | 993.155i | −0.103064 | − | 0.0341335i | ||||
\(947\) | −25774.5 | −0.884432 | −0.442216 | − | 0.896908i | \(-0.645808\pi\) | ||||
−0.442216 | + | 0.896908i | \(0.645808\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 41865.0 | 1.43203 | ||||||||
\(950\) | −186.174 | − | 61.6587i | −0.00635820 | − | 0.00210576i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −16306.8 | + | 11429.7i | −0.555155 | + | 0.389118i | ||||
\(953\) | 40615.9i | 1.38056i | 0.723541 | + | 0.690282i | \(0.242513\pi\) | ||||
−0.723541 | + | 0.690282i | \(0.757487\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 54054.6i | − | 1.83159i | ||||||
\(956\) | 15441.9 | + | 11488.5i | 0.522415 | + | 0.388666i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 242.962 | − | 733.608i | 0.00819389 | − | 0.0247409i | ||||
\(959\) | −24188.5 | −0.814482 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27745.5 | 0.931340 | ||||||||
\(962\) | −12704.3 | + | 38359.8i | −0.425783 | + | 1.28562i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1451.27 | + | 1079.72i | 0.0484879 | + | 0.0360740i | ||||
\(965\) | 38630.9i | 1.28868i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52148.0i | − | 1.73420i | −0.498138 | − | 0.867098i | \(-0.665983\pi\) | ||
0.498138 | − | 0.867098i | \(-0.334017\pi\) | |||||||
\(968\) | 33316.4 | − | 23352.1i | 1.10623 | − | 0.775376i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25021.6 | + | 8286.83i | 0.828241 | + | 0.274303i | ||||
\(971\) | 29877.8 | 0.987461 | 0.493731 | − | 0.869615i | \(-0.335633\pi\) | ||||
0.493731 | + | 0.869615i | \(0.335633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12436.2 | 0.409750 | ||||||||
\(974\) | 23377.3 | + | 7742.26i | 0.769051 | + | 0.254700i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5681.18 | − | 18932.7i | −0.186322 | − | 0.620923i | ||||
\(977\) | − | 10385.8i | − | 0.340094i | −0.985436 | − | 0.170047i | \(-0.945608\pi\) | ||
0.985436 | − | 0.170047i | \(-0.0543920\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 67051.6i | 2.18895i | ||||||||
\(980\) | 39918.0 | − | 53654.8i | 1.30116 | − | 1.74892i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3950.42 | + | 11928.0i | −0.128374 | + | 0.387616i | ||||
\(983\) | 14316.7 | 0.464530 | 0.232265 | − | 0.972652i | \(-0.425386\pi\) | ||||
0.232265 | + | 0.972652i | \(0.425386\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26148.7 | −0.845856 | ||||||||
\(986\) | −4504.08 | + | 13599.8i | −0.145476 | + | 0.439255i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −194.750 | + | 261.768i | −0.00627108 | + | 0.00842911i | ||||
\(989\) | 959.102i | 0.0308369i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30199.0i | 0.968013i | 0.875064 | + | 0.484007i | \(0.160819\pi\) | ||||
−0.875064 | + | 0.484007i | \(0.839181\pi\) | |||||||
\(992\) | 231.620 | − | 8183.65i | 0.00741324 | − | 0.261926i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 91549.9 | + | 30320.2i | 2.92131 | + | 0.967503i | ||||
\(995\) | −49493.3 | −1.57693 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17508.8 | 0.556178 | 0.278089 | − | 0.960555i | \(-0.410299\pi\) | ||||
0.278089 | + | 0.960555i | \(0.410299\pi\) | |||||||
\(998\) | 13211.0 | + | 4375.32i | 0.419025 | + | 0.138776i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.4.b.a.107.6 | yes | 12 | |
3.2 | odd | 2 | inner | 108.4.b.a.107.7 | yes | 12 | |
4.3 | odd | 2 | inner | 108.4.b.a.107.8 | yes | 12 | |
8.3 | odd | 2 | 1728.4.c.i.1727.11 | 12 | |||
8.5 | even | 2 | 1728.4.c.i.1727.12 | 12 | |||
12.11 | even | 2 | inner | 108.4.b.a.107.5 | ✓ | 12 | |
24.5 | odd | 2 | 1728.4.c.i.1727.2 | 12 | |||
24.11 | even | 2 | 1728.4.c.i.1727.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.b.a.107.5 | ✓ | 12 | 12.11 | even | 2 | inner | |
108.4.b.a.107.6 | yes | 12 | 1.1 | even | 1 | trivial | |
108.4.b.a.107.7 | yes | 12 | 3.2 | odd | 2 | inner | |
108.4.b.a.107.8 | yes | 12 | 4.3 | odd | 2 | inner | |
1728.4.c.i.1727.1 | 12 | 24.11 | even | 2 | |||
1728.4.c.i.1727.2 | 12 | 24.5 | odd | 2 | |||
1728.4.c.i.1727.11 | 12 | 8.3 | odd | 2 | |||
1728.4.c.i.1727.12 | 12 | 8.5 | even | 2 |