Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 147) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.u.361.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20711 | − | 2.09077i | 0.426777 | − | 0.739199i | −0.569808 | − | 0.821778i | \(-0.692982\pi\) |
0.996585 | + | 0.0825791i | \(0.0263157\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.08579 | + | 1.88064i | 0.135723 | + | 0.235080i | ||||
\(5\) | −9.94975 | + | 17.2335i | −0.889932 | + | 1.54141i | −0.0499787 | + | 0.998750i | \(0.515915\pi\) |
−0.839954 | + | 0.542658i | \(0.817418\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.5563 | 1.08525 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 24.0208 | + | 41.6053i | 0.759605 | + | 1.31567i | ||||
\(11\) | 11.9706 | + | 20.7336i | 0.328115 | + | 0.568311i | 0.982138 | − | 0.188163i | \(-0.0602535\pi\) |
−0.654023 | + | 0.756475i | \(0.726920\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −87.3553 | −1.86369 | −0.931847 | − | 0.362852i | \(-0.881803\pi\) | ||||
−0.931847 | + | 0.362852i | \(0.881803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 20.9558 | − | 36.2966i | 0.327435 | − | 0.567134i | ||||
\(17\) | 2.81981 | + | 4.88405i | 0.0402296 | + | 0.0696797i | 0.885439 | − | 0.464755i | \(-0.153858\pi\) |
−0.845210 | + | 0.534435i | \(0.820524\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.4437 | − | 56.1941i | 0.391741 | − | 0.678516i | −0.600938 | − | 0.799296i | \(-0.705206\pi\) |
0.992679 | + | 0.120780i | \(0.0385395\pi\) | |||||||
\(20\) | −43.2132 | −0.483138 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 57.7990 | 0.560127 | ||||||||
\(23\) | −12.7990 | + | 22.1685i | −0.116034 | + | 0.200976i | −0.918192 | − | 0.396135i | \(-0.870351\pi\) |
0.802159 | + | 0.597111i | \(0.203685\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −135.495 | − | 234.684i | −1.08396 | − | 1.87747i | ||||
\(26\) | −105.447 | + | 182.640i | −0.795381 | + | 1.37764i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −60.3188 | −0.386238 | −0.193119 | − | 0.981175i | \(-0.561860\pi\) | ||||
−0.193119 | + | 0.981175i | \(0.561860\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −61.3553 | − | 106.271i | −0.355476 | − | 0.615702i | 0.631724 | − | 0.775194i | \(-0.282348\pi\) |
−0.987199 | + | 0.159492i | \(0.949014\pi\) | |||||||
\(32\) | 47.6335 | + | 82.5037i | 0.263140 | + | 0.455773i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.6152 | 0.0686762 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 28.0589 | − | 48.5994i | 0.124672 | − | 0.215938i | −0.796933 | − | 0.604068i | \(-0.793546\pi\) |
0.921605 | + | 0.388130i | \(0.126879\pi\) | |||||||
\(38\) | −78.3259 | − | 135.664i | −0.334372 | − | 0.579149i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −244.329 | + | 423.191i | −0.965797 | + | 1.67281i | ||||
\(41\) | −299.713 | −1.14164 | −0.570820 | − | 0.821075i | \(-0.693375\pi\) | ||||
−0.570820 | + | 0.821075i | \(0.693375\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −501.421 | −1.77828 | −0.889140 | − | 0.457635i | \(-0.848697\pi\) | ||||
−0.889140 | + | 0.457635i | \(0.848697\pi\) | |||||||
\(44\) | −25.9949 | + | 45.0246i | −0.0890656 | + | 0.154266i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 30.8995 | + | 53.5195i | 0.0990409 | + | 0.171544i | ||||
\(47\) | −152.777 | + | 264.617i | −0.474144 | + | 0.821242i | −0.999562 | − | 0.0296028i | \(-0.990576\pi\) |
0.525418 | + | 0.850844i | \(0.323909\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −654.227 | −1.85043 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −94.8492 | − | 164.284i | −0.252947 | − | 0.438116i | ||||
\(53\) | −187.558 | − | 324.861i | −0.486097 | − | 0.841944i | 0.513775 | − | 0.857925i | \(-0.328246\pi\) |
−0.999872 | + | 0.0159802i | \(0.994913\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −476.416 | −1.16800 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −72.8112 | + | 126.113i | −0.164838 | + | 0.285507i | ||||
\(59\) | 313.806 | + | 543.528i | 0.692442 | + | 1.19934i | 0.971035 | + | 0.238936i | \(0.0767985\pi\) |
−0.278593 | + | 0.960409i | \(0.589868\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.87868 | − | 3.25397i | 0.00394328 | − | 0.00682997i | −0.864047 | − | 0.503411i | \(-0.832078\pi\) |
0.867990 | + | 0.496581i | \(0.165411\pi\) | |||||||
\(62\) | −296.250 | −0.606835 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 565.288 | 1.10408 | ||||||||
\(65\) | 869.164 | − | 1505.44i | 1.65856 | − | 2.87271i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 406.524 | + | 704.120i | 0.741266 | + | 1.28391i | 0.951919 | + | 0.306349i | \(0.0991075\pi\) |
−0.210653 | + | 0.977561i | \(0.567559\pi\) | |||||||
\(68\) | −6.12341 | + | 10.6061i | −0.0109202 | + | 0.0189143i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −165.902 | −0.277310 | −0.138655 | − | 0.990341i | \(-0.544278\pi\) | ||||
−0.138655 | + | 0.990341i | \(0.544278\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 309.550 | + | 536.156i | 0.496302 | + | 0.859621i | 0.999991 | − | 0.00426452i | \(-0.00135744\pi\) |
−0.503689 | + | 0.863885i | \(0.668024\pi\) | |||||||
\(74\) | −67.7401 | − | 117.329i | −0.106414 | − | 0.184314i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 140.908 | 0.212674 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 69.1228 | − | 119.724i | 0.0984421 | − | 0.170507i | −0.812598 | − | 0.582825i | \(-0.801947\pi\) |
0.911040 | + | 0.412318i | \(0.135281\pi\) | |||||||
\(80\) | 417.011 | + | 722.284i | 0.582790 | + | 1.00942i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −361.785 | + | 626.631i | −0.487226 | + | 0.843900i | ||||
\(83\) | 621.137 | 0.821430 | 0.410715 | − | 0.911764i | \(-0.365279\pi\) | ||||
0.410715 | + | 0.911764i | \(0.365279\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −112.225 | −0.143207 | ||||||||
\(86\) | −605.269 | + | 1048.36i | −0.758928 | + | 1.31450i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 293.953 | + | 509.142i | 0.356086 | + | 0.616758i | ||||
\(89\) | −142.709 | + | 247.180i | −0.169968 | + | 0.294393i | −0.938408 | − | 0.345528i | \(-0.887700\pi\) |
0.768440 | + | 0.639921i | \(0.221033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −55.5879 | −0.0629939 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 368.836 | + | 638.842i | 0.404707 | + | 0.700974i | ||||
\(95\) | 645.612 | + | 1118.23i | 0.697247 | + | 1.20767i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 603.114 | 0.631309 | 0.315654 | − | 0.948874i | \(-0.397776\pi\) | ||||
0.315654 | + | 0.948874i | \(0.397776\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 294.237 | − | 509.634i | 0.294237 | − | 0.509634i | ||||
\(101\) | −228.605 | − | 395.955i | −0.225218 | − | 0.390089i | 0.731167 | − | 0.682199i | \(-0.238976\pi\) |
−0.956385 | + | 0.292110i | \(0.905643\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 393.022 | − | 680.735i | 0.375977 | − | 0.651211i | −0.614496 | − | 0.788920i | \(-0.710640\pi\) |
0.990473 | + | 0.137709i | \(0.0439738\pi\) | |||||||
\(104\) | −2145.13 | −2.02257 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −905.612 | −0.829819 | ||||||||
\(107\) | −98.2304 | + | 170.140i | −0.0887504 | + | 0.153720i | −0.906983 | − | 0.421167i | \(-0.861621\pi\) |
0.818233 | + | 0.574887i | \(0.194954\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 153.172 | + | 265.301i | 0.134598 | + | 0.233130i | 0.925444 | − | 0.378885i | \(-0.123692\pi\) |
−0.790846 | + | 0.612015i | \(0.790359\pi\) | |||||||
\(110\) | −575.085 | + | 996.077i | −0.498475 | + | 0.863384i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1997.63 | −1.66302 | −0.831508 | − | 0.555512i | \(-0.812522\pi\) | ||||
−0.831508 | + | 0.555512i | \(0.812522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −254.693 | − | 441.142i | −0.206524 | − | 0.357710i | ||||
\(116\) | −65.4933 | − | 113.438i | −0.0524215 | − | 0.0907968i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1515.19 | 1.18207 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 378.911 | − | 656.294i | 0.284682 | − | 0.493083i | ||||
\(122\) | −4.53553 | − | 7.85578i | −0.00336580 | − | 0.00582974i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 133.238 | − | 230.774i | 0.0964927 | − | 0.167130i | ||||
\(125\) | 2905.13 | 2.07874 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2311.40 | −1.61499 | −0.807494 | − | 0.589875i | \(-0.799177\pi\) | ||||
−0.807494 | + | 0.589875i | \(0.799177\pi\) | |||||||
\(128\) | 301.295 | − | 521.859i | 0.208055 | − | 0.360361i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2098.35 | − | 3634.44i | −1.41567 | − | 2.45201i | ||||
\(131\) | 77.5088 | − | 134.249i | 0.0516945 | − | 0.0895374i | −0.839020 | − | 0.544100i | \(-0.816871\pi\) |
0.890715 | + | 0.454563i | \(0.150204\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1962.87 | 1.26542 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 69.2441 | + | 119.934i | 0.0436591 | + | 0.0756197i | ||||
\(137\) | 258.468 | + | 447.680i | 0.161186 | + | 0.279181i | 0.935294 | − | 0.353871i | \(-0.115135\pi\) |
−0.774109 | + | 0.633053i | \(0.781802\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −958.067 | −0.584620 | −0.292310 | − | 0.956324i | \(-0.594424\pi\) | ||||
−0.292310 | + | 0.956324i | \(0.594424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −200.262 | + | 346.864i | −0.118349 | + | 0.204987i | ||||
\(143\) | −1045.69 | − | 1811.19i | −0.611505 | − | 1.05916i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 600.156 | − | 1039.50i | 0.343726 | − | 0.595351i | ||||
\(146\) | 1494.64 | 0.847241 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 121.864 | 0.0676834 | ||||||||
\(149\) | −885.313 | + | 1533.41i | −0.486763 | + | 0.843098i | −0.999884 | − | 0.0152182i | \(-0.995156\pi\) |
0.513121 | + | 0.858316i | \(0.328489\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1270.12 | + | 2199.91i | 0.684508 | + | 1.18560i | 0.973591 | + | 0.228299i | \(0.0733163\pi\) |
−0.289083 | + | 0.957304i | \(0.593350\pi\) | |||||||
\(152\) | 796.698 | − | 1379.92i | 0.425136 | − | 0.736358i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2441.88 | 1.26540 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −541.672 | − | 938.203i | −0.275351 | − | 0.476922i | 0.694873 | − | 0.719133i | \(-0.255461\pi\) |
−0.970224 | + | 0.242211i | \(0.922127\pi\) | |||||||
\(158\) | −166.877 | − | 289.040i | −0.0840256 | − | 0.145537i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1895.77 | −0.936709 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1484.36 | + | 2570.99i | −0.713277 | + | 1.23543i | 0.250343 | + | 0.968157i | \(0.419457\pi\) |
−0.963620 | + | 0.267275i | \(0.913877\pi\) | |||||||
\(164\) | −325.424 | − | 563.651i | −0.154947 | − | 0.268377i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 749.779 | − | 1298.65i | 0.350567 | − | 0.607200i | ||||
\(167\) | −2091.53 | −0.969149 | −0.484574 | − | 0.874750i | \(-0.661025\pi\) | ||||
−0.484574 | + | 0.874750i | \(0.661025\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5433.96 | 2.47335 | ||||||||
\(170\) | −135.468 | + | 234.638i | −0.0611172 | + | 0.105858i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −544.437 | − | 942.992i | −0.241354 | − | 0.418037i | ||||
\(173\) | 235.074 | − | 407.160i | 0.103308 | − | 0.178935i | −0.809738 | − | 0.586792i | \(-0.800391\pi\) |
0.913046 | + | 0.407857i | \(0.133724\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1003.41 | 0.429745 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 344.530 | + | 596.744i | 0.145077 | + | 0.251280i | ||||
\(179\) | 528.230 | + | 914.922i | 0.220569 | + | 0.382036i | 0.954981 | − | 0.296668i | \(-0.0958753\pi\) |
−0.734412 | + | 0.678704i | \(0.762542\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 406.470 | 0.166921 | 0.0834605 | − | 0.996511i | \(-0.473403\pi\) | ||||
0.0834605 | + | 0.996511i | \(0.473403\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −314.296 | + | 544.377i | −0.125925 | + | 0.218109i | ||||
\(185\) | 558.357 | + | 967.103i | 0.221899 | + | 0.384340i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −67.5093 | + | 116.930i | −0.0263998 | + | 0.0457259i | ||||
\(188\) | −663.531 | −0.257410 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3117.29 | 1.19027 | ||||||||
\(191\) | 89.7048 | − | 155.373i | 0.0339833 | − | 0.0588608i | −0.848534 | − | 0.529142i | \(-0.822514\pi\) |
0.882517 | + | 0.470281i | \(0.155847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1194.18 | + | 2068.39i | 0.445385 | + | 0.771429i | 0.998079 | − | 0.0619551i | \(-0.0197336\pi\) |
−0.552694 | + | 0.833384i | \(0.686400\pi\) | |||||||
\(194\) | 728.023 | − | 1260.97i | 0.269428 | − | 0.466663i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2665.35 | 0.963952 | 0.481976 | − | 0.876184i | \(-0.339919\pi\) | ||||
0.481976 | + | 0.876184i | \(0.339919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −671.153 | − | 1162.47i | −0.239079 | − | 0.414098i | 0.721371 | − | 0.692549i | \(-0.243512\pi\) |
−0.960450 | + | 0.278451i | \(0.910179\pi\) | |||||||
\(200\) | −3327.26 | − | 5762.99i | −1.17636 | − | 2.03752i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1103.80 | −0.384471 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2982.07 | − | 5165.09i | 1.01598 | − | 1.75973i | ||||
\(206\) | −948.840 | − | 1643.44i | −0.320916 | − | 0.555844i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1830.60 | + | 3170.70i | −0.610239 | + | 1.05696i | ||||
\(209\) | 1553.48 | 0.514144 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 628.442 | 0.205042 | 0.102521 | − | 0.994731i | \(-0.467309\pi\) | ||||
0.102521 | + | 0.994731i | \(0.467309\pi\) | |||||||
\(212\) | 407.297 | − | 705.459i | 0.131949 | − | 0.228543i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 237.149 | + | 410.755i | 0.0757532 | + | 0.131208i | ||||
\(215\) | 4989.02 | − | 8641.23i | 1.58255 | − | 2.74106i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 739.578 | 0.229773 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −517.286 | − | 895.966i | −0.158525 | − | 0.274573i | ||||
\(221\) | −246.325 | − | 426.647i | −0.0749756 | − | 0.129862i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 969.970 | 0.291273 | 0.145637 | − | 0.989338i | \(-0.453477\pi\) | ||||
0.145637 | + | 0.989338i | \(0.453477\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2411.35 | + | 4176.58i | −0.709737 | + | 1.22930i | ||||
\(227\) | 2374.32 | + | 4112.44i | 0.694225 | + | 1.20243i | 0.970441 | + | 0.241338i | \(0.0775862\pi\) |
−0.276216 | + | 0.961096i | \(0.589080\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2401.00 | + | 4158.65i | −0.692848 | + | 1.20005i | 0.278052 | + | 0.960566i | \(0.410311\pi\) |
−0.970901 | + | 0.239482i | \(0.923022\pi\) | |||||||
\(230\) | −1229.77 | −0.352559 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1481.21 | −0.419164 | ||||||||
\(233\) | −1577.64 | + | 2732.56i | −0.443583 | + | 0.768309i | −0.997952 | − | 0.0639623i | \(-0.979626\pi\) |
0.554369 | + | 0.832271i | \(0.312960\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3040.18 | − | 5265.74i | −0.843912 | − | 1.46170i | ||||
\(236\) | −681.453 | + | 1180.31i | −0.187961 | + | 0.325558i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4241.93 | −1.14806 | −0.574032 | − | 0.818833i | \(-0.694622\pi\) | ||||
−0.574032 | + | 0.818833i | \(0.694622\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2171.49 | − | 3761.14i | −0.580407 | − | 1.00530i | −0.995431 | − | 0.0954844i | \(-0.969560\pi\) |
0.415024 | − | 0.909811i | \(-0.363773\pi\) | |||||||
\(242\) | −914.773 | − | 1584.43i | −0.242991 | − | 0.420873i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.15938 | 0.00214078 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2834.13 | + | 4908.85i | −0.730086 | + | 1.26455i | ||||
\(248\) | −1506.66 | − | 2609.62i | −0.385779 | − | 0.668189i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3506.80 | − | 6073.95i | 0.887157 | − | 1.53660i | ||||
\(251\) | 3003.01 | 0.755172 | 0.377586 | − | 0.925974i | \(-0.376754\pi\) | ||||
0.377586 | + | 0.925974i | \(0.376754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −612.844 | −0.152289 | ||||||||
\(254\) | −2790.11 | + | 4832.61i | −0.689239 | + | 1.19380i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1533.76 | + | 2656.55i | 0.374454 | + | 0.648573i | ||||
\(257\) | −2234.42 | + | 3870.13i | −0.542332 | + | 0.939347i | 0.456437 | + | 0.889756i | \(0.349125\pi\) |
−0.998770 | + | 0.0495916i | \(0.984208\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3774.90 | 0.900422 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −187.123 | − | 324.106i | −0.0441240 | − | 0.0764250i | ||||
\(263\) | 3080.07 | + | 5334.83i | 0.722148 | + | 1.25080i | 0.960137 | + | 0.279530i | \(0.0901786\pi\) |
−0.237989 | + | 0.971268i | \(0.576488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7464.64 | 1.73037 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −882.796 | + | 1529.05i | −0.201214 | + | 0.348513i | ||||
\(269\) | −2494.45 | − | 4320.52i | −0.565388 | − | 0.979281i | −0.997013 | − | 0.0772281i | \(-0.975393\pi\) |
0.431625 | − | 0.902053i | \(-0.357940\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2216.86 | − | 3839.72i | 0.496918 | − | 0.860688i | −0.503075 | − | 0.864243i | \(-0.667798\pi\) |
0.999994 | + | 0.00355459i | \(0.00113146\pi\) | |||||||
\(272\) | 236.366 | 0.0526903 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1247.99 | 0.275161 | ||||||||
\(275\) | 3243.90 | − | 5618.60i | 0.711326 | − | 1.23205i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −556.184 | − | 963.339i | −0.120642 | − | 0.208958i | 0.799379 | − | 0.600827i | \(-0.205162\pi\) |
−0.920021 | + | 0.391869i | \(0.871829\pi\) | |||||||
\(278\) | −1156.49 | + | 2003.10i | −0.249502 | + | 0.432151i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2813.22 | −0.597233 | −0.298616 | − | 0.954373i | \(-0.596525\pi\) | ||||
−0.298616 | + | 0.954373i | \(0.596525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1573.77 | + | 2725.85i | 0.330569 | + | 0.572562i | 0.982623 | − | 0.185610i | \(-0.0594262\pi\) |
−0.652055 | + | 0.758172i | \(0.726093\pi\) | |||||||
\(284\) | −180.135 | − | 312.002i | −0.0376374 | − | 0.0651899i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5049.05 | −1.04390 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2440.60 | − | 4227.24i | 0.496763 | − | 0.860419i | ||||
\(290\) | −1448.91 | − | 2509.58i | −0.293389 | − | 0.508164i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −672.210 | + | 1164.30i | −0.134720 | + | 0.233341i | ||||
\(293\) | 9143.04 | 1.82301 | 0.911505 | − | 0.411289i | \(-0.134921\pi\) | ||||
0.911505 | + | 0.411289i | \(0.134921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12489.2 | −2.46491 | ||||||||
\(296\) | 689.024 | − | 1193.42i | 0.135300 | − | 0.234346i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2137.33 | + | 3701.97i | 0.415478 | + | 0.719629i | ||||
\(299\) | 1118.06 | − | 1936.54i | 0.216251 | − | 0.374558i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6132.67 | 1.16853 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1359.77 | − | 2355.19i | −0.256540 | − | 0.444340i | ||||
\(305\) | 37.3848 | + | 64.7523i | 0.00701851 | + | 0.0121564i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4648.90 | 0.864257 | 0.432129 | − | 0.901812i | \(-0.357763\pi\) | ||||
0.432129 | + | 0.901812i | \(0.357763\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2947.61 | − | 5105.41i | 0.540042 | − | 0.935380i | ||||
\(311\) | 3208.59 | + | 5557.44i | 0.585024 | + | 1.01329i | 0.994872 | + | 0.101138i | \(0.0322482\pi\) |
−0.409849 | + | 0.912154i | \(0.634418\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2934.11 | − | 5082.02i | 0.529858 | − | 0.917741i | −0.469535 | − | 0.882914i | \(-0.655578\pi\) |
0.999393 | − | 0.0348275i | \(-0.0110882\pi\) | |||||||
\(314\) | −2615.42 | −0.470054 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 300.210 | 0.0534435 | ||||||||
\(317\) | −1987.26 | + | 3442.04i | −0.352100 | + | 0.609855i | −0.986617 | − | 0.163054i | \(-0.947866\pi\) |
0.634517 | + | 0.772909i | \(0.281199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −722.049 | − | 1250.63i | −0.126730 | − | 0.219504i | ||||
\(320\) | −5624.48 | + | 9741.88i | −0.982556 | + | 1.70184i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 365.939 | 0.0630384 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11836.2 | + | 20500.9i | 2.02017 | + | 3.49903i | ||||
\(326\) | 3583.57 | + | 6206.92i | 0.608820 | + | 1.05451i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7359.85 | −1.23896 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4456.41 | − | 7718.73i | 0.740020 | − | 1.28175i | −0.212466 | − | 0.977168i | \(-0.568149\pi\) |
0.952486 | − | 0.304583i | \(-0.0985172\pi\) | |||||||
\(332\) | 674.422 | + | 1168.13i | 0.111487 | + | 0.193101i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2524.71 | + | 4372.92i | −0.413610 | + | 0.716394i | ||||
\(335\) | −16179.2 | −2.63871 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3977.06 | 0.642862 | 0.321431 | − | 0.946933i | \(-0.395836\pi\) | ||||
0.321431 | + | 0.946933i | \(0.395836\pi\) | |||||||
\(338\) | 6559.36 | − | 11361.2i | 1.05557 | − | 1.82830i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −121.853 | − | 211.055i | −0.0194365 | − | 0.0336649i | ||||
\(341\) | 1468.92 | − | 2544.24i | 0.233273 | − | 0.404042i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12313.1 | −1.92987 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −567.518 | − | 982.971i | −0.0881791 | − | 0.152731i | ||||
\(347\) | 3413.21 | + | 5911.86i | 0.528043 | + | 0.914597i | 0.999466 | + | 0.0326898i | \(0.0104073\pi\) |
−0.471423 | + | 0.881907i | \(0.656259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 807.342 | 0.123828 | 0.0619141 | − | 0.998081i | \(-0.480280\pi\) | ||||
0.0619141 | + | 0.998081i | \(0.480280\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1140.40 | + | 1975.23i | −0.172680 | + | 0.299091i | ||||
\(353\) | 3959.60 | + | 6858.23i | 0.597020 | + | 1.03407i | 0.993258 | + | 0.115922i | \(0.0369822\pi\) |
−0.396238 | + | 0.918148i | \(0.629684\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1650.69 | − | 2859.07i | 0.246787 | − | 0.427448i | ||||
\(356\) | −619.807 | −0.0922744 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2550.52 | 0.376534 | ||||||||
\(359\) | −4409.61 | + | 7637.66i | −0.648273 | + | 1.12284i | 0.335262 | + | 0.942125i | \(0.391175\pi\) |
−0.983535 | + | 0.180717i | \(0.942158\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1324.32 | + | 2293.79i | 0.193078 | + | 0.334420i | ||||
\(362\) | 490.653 | − | 849.836i | 0.0712380 | − | 0.123388i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12319.8 | −1.76670 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5580.89 | − | 9666.39i | −0.793788 | − | 1.37488i | −0.923606 | − | 0.383344i | \(-0.874772\pi\) |
0.129817 | − | 0.991538i | \(-0.458561\pi\) | |||||||
\(368\) | 536.427 | + | 929.119i | 0.0759870 | + | 0.131613i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2695.99 | 0.378805 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1363.93 | + | 2362.39i | −0.189334 | + | 0.327936i | −0.945028 | − | 0.326988i | \(-0.893966\pi\) |
0.755694 | + | 0.654924i | \(0.227300\pi\) | |||||||
\(374\) | 162.982 | + | 282.293i | 0.0225337 | + | 0.0390295i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3751.64 | + | 6498.03i | −0.514564 | + | 0.891250i | ||||
\(377\) | 5269.17 | 0.719830 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4086.49 | 0.553849 | 0.276924 | − | 0.960892i | \(-0.410685\pi\) | ||||
0.276924 | + | 0.960892i | \(0.410685\pi\) | |||||||
\(380\) | −1401.99 | + | 2428.32i | −0.189265 | + | 0.327817i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −216.566 | − | 375.104i | −0.0290066 | − | 0.0502408i | ||||
\(383\) | −6516.47 | + | 11286.9i | −0.869389 | + | 1.50583i | −0.00676631 | + | 0.999977i | \(0.502154\pi\) |
−0.862622 | + | 0.505848i | \(0.831180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5766.03 | 0.760319 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 654.853 | + | 1134.24i | 0.0856833 | + | 0.148408i | ||||
\(389\) | −97.4957 | − | 168.868i | −0.0127075 | − | 0.0220101i | 0.859602 | − | 0.510965i | \(-0.170712\pi\) |
−0.872309 | + | 0.488955i | \(0.837378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −144.363 | −0.0186719 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3217.37 | − | 5572.64i | 0.411392 | − | 0.712553i | ||||
\(395\) | 1375.51 | + | 2382.45i | 0.175214 | + | 0.303479i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7091.48 | + | 12282.8i | −0.896501 | + | 1.55279i | −0.0645653 | + | 0.997913i | \(0.520566\pi\) |
−0.831936 | + | 0.554872i | \(0.812767\pi\) | |||||||
\(398\) | −3240.61 | −0.408134 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −11357.6 | −1.41971 | ||||||||
\(401\) | 5002.52 | − | 8664.63i | 0.622978 | − | 1.07903i | −0.365950 | − | 0.930634i | \(-0.619256\pi\) |
0.988928 | − | 0.148395i | \(-0.0474107\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5359.72 | + | 9283.30i | 0.662498 | + | 1.14748i | ||||
\(404\) | 496.431 | − | 859.844i | 0.0611346 | − | 0.105888i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1343.52 | 0.163626 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2317.47 | + | 4013.97i | 0.280174 | + | 0.485276i | 0.971428 | − | 0.237336i | \(-0.0762744\pi\) |
−0.691253 | + | 0.722613i | \(0.742941\pi\) | |||||||
\(410\) | −7199.35 | − | 12469.6i | −0.867196 | − | 1.50203i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1706.95 | 0.204115 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6180.16 | + | 10704.3i | −0.731017 | + | 1.26616i | ||||
\(416\) | −4161.04 | − | 7207.14i | −0.490413 | − | 0.849420i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1875.21 | − | 3247.96i | 0.219425 | − | 0.380055i | ||||
\(419\) | 4998.31 | 0.582777 | 0.291388 | − | 0.956605i | \(-0.405883\pi\) | ||||
0.291388 | + | 0.956605i | \(0.405883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −704.160 | −0.0815170 | −0.0407585 | − | 0.999169i | \(-0.512977\pi\) | ||||
−0.0407585 | + | 0.999169i | \(0.512977\pi\) | |||||||
\(422\) | 758.597 | − | 1313.93i | 0.0875069 | − | 0.151566i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4605.75 | − | 7977.39i | −0.527535 | − | 0.913718i | ||||
\(425\) | 764.139 | − | 1323.53i | 0.0872145 | − | 0.151060i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −426.629 | −0.0481820 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12044.5 | − | 20861.8i | −1.35079 | − | 2.33964i | ||||
\(431\) | −5166.39 | − | 8948.45i | −0.577393 | − | 1.00007i | −0.995777 | − | 0.0918037i | \(-0.970737\pi\) |
0.418384 | − | 0.908270i | \(-0.362597\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11106.8 | −1.23270 | −0.616348 | − | 0.787474i | \(-0.711389\pi\) | ||||
−0.616348 | + | 0.787474i | \(0.711389\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −332.623 | + | 576.120i | −0.0365362 | + | 0.0632825i | ||||
\(437\) | 830.492 | + | 1438.45i | 0.0909103 | + | 0.157461i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3649.64 | + | 6321.36i | −0.396783 | + | 0.687249i | −0.993327 | − | 0.115332i | \(-0.963207\pi\) |
0.596544 | + | 0.802581i | \(0.296540\pi\) | |||||||
\(440\) | −11699.0 | −1.26757 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1189.36 | −0.127991 | ||||||||
\(443\) | 8044.83 | − | 13934.1i | 0.862802 | − | 1.49442i | −0.00641088 | − | 0.999979i | \(-0.502041\pi\) |
0.869213 | − | 0.494438i | \(-0.164626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2839.84 | − | 4918.75i | −0.302520 | − | 0.523980i | ||||
\(446\) | 1170.86 | − | 2027.98i | 0.124309 | − | 0.215309i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13561.7 | −1.42543 | −0.712715 | − | 0.701454i | \(-0.752534\pi\) | ||||
−0.712715 | + | 0.701454i | \(0.752534\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3587.73 | − | 6214.13i | −0.374589 | − | 0.648807i | ||||
\(452\) | −2169.00 | − | 3756.81i | −0.225710 | − | 0.390941i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11464.2 | 1.18512 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5424.28 | + | 9395.14i | −0.555224 | + | 0.961676i | 0.442662 | + | 0.896688i | \(0.354034\pi\) |
−0.997886 | + | 0.0649876i | \(0.979299\pi\) | |||||||
\(458\) | 5796.52 | + | 10039.9i | 0.591383 | + | 1.02431i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 553.085 | − | 957.972i | 0.0560603 | − | 0.0970993i | ||||
\(461\) | −1758.69 | −0.177679 | −0.0888397 | − | 0.996046i | \(-0.528316\pi\) | ||||
−0.0888397 | + | 0.996046i | \(0.528316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5411.95 | −0.543228 | −0.271614 | − | 0.962406i | \(-0.587557\pi\) | ||||
−0.271614 | + | 0.962406i | \(0.587557\pi\) | |||||||
\(464\) | −1264.03 | + | 2189.37i | −0.126468 | + | 0.219049i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3808.77 | + | 6596.98i | 0.378622 | + | 0.655792i | ||||
\(467\) | −4055.67 | + | 7024.63i | −0.401872 | + | 0.696062i | −0.993952 | − | 0.109817i | \(-0.964974\pi\) |
0.592080 | + | 0.805879i | \(0.298307\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −14679.3 | −1.44065 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7705.93 | + | 13347.1i | 0.751471 | + | 1.30159i | ||||
\(473\) | −6002.30 | − | 10396.3i | −0.583480 | − | 1.01062i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17583.8 | −1.69853 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5120.46 | + | 8868.90i | −0.489967 | + | 0.848648i | ||||
\(479\) | −1047.88 | − | 1814.98i | −0.0999559 | − | 0.173129i | 0.811710 | − | 0.584060i | \(-0.198537\pi\) |
−0.911666 | + | 0.410932i | \(0.865203\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2451.09 | + | 4245.42i | −0.232350 | + | 0.402441i | ||||
\(482\) | −10484.9 | −0.990817 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1645.67 | 0.154552 | ||||||||
\(485\) | −6000.83 | + | 10393.7i | −0.561822 | + | 0.973104i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4805.04 | − | 8322.57i | −0.447099 | − | 0.774398i | 0.551097 | − | 0.834441i | \(-0.314209\pi\) |
−0.998196 | + | 0.0600435i | \(0.980876\pi\) | |||||||
\(488\) | 46.1335 | − | 79.9056i | 0.00427944 | − | 0.00741221i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11717.3 | 1.07698 | 0.538488 | − | 0.842633i | \(-0.318996\pi\) | ||||
0.538488 | + | 0.842633i | \(0.318996\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −170.087 | − | 294.600i | −0.0155382 | − | 0.0269130i | ||||
\(494\) | 6842.19 | + | 11851.0i | 0.623167 | + | 1.07936i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5143.01 | −0.465581 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4597.59 | − | 7963.26i | 0.412458 | − | 0.714398i | −0.582700 | − | 0.812687i | \(-0.698004\pi\) |
0.995158 | + | 0.0982893i | \(0.0313370\pi\) | |||||||
\(500\) | 3154.35 | + | 5463.49i | 0.282133 | + | 0.488669i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3624.95 | − | 6278.60i | 0.322290 | − | 0.558222i | ||||
\(503\) | 16118.8 | 1.42883 | 0.714414 | − | 0.699724i | \(-0.246693\pi\) | ||||
0.714414 | + | 0.699724i | \(0.246693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9098.23 | 0.801715 | ||||||||
\(506\) | −739.769 | + | 1281.32i | −0.0649935 | + | 0.112572i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2509.69 | − | 4346.90i | −0.219192 | − | 0.379651i | ||||
\(509\) | −2459.39 | + | 4259.79i | −0.214166 | + | 0.370947i | −0.953014 | − | 0.302925i | \(-0.902037\pi\) |
0.738848 | + | 0.673872i | \(0.235370\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 12226.4 | 1.05534 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5394.37 | + | 9343.33i | 0.462910 | + | 0.801783i | ||||
\(515\) | 7820.95 | + | 13546.3i | 0.669188 | + | 1.15907i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7315.29 | −0.622294 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21343.5 | − | 36968.0i | 1.79995 | − | 3.11760i | ||||
\(521\) | −6981.69 | − | 12092.6i | −0.587089 | − | 1.01687i | −0.994611 | − | 0.103673i | \(-0.966940\pi\) |
0.407522 | − | 0.913195i | \(-0.366393\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6877.63 | + | 11912.4i | −0.575024 | + | 0.995972i | 0.421015 | + | 0.907054i | \(0.361674\pi\) |
−0.996039 | + | 0.0889177i | \(0.971659\pi\) | |||||||
\(524\) | 336.632 | 0.0280646 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14871.9 | 1.23278 | ||||||||
\(527\) | 346.020 | − | 599.325i | 0.0286013 | − | 0.0495389i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5755.87 | + | 9969.46i | 0.473072 | + | 0.819385i | ||||
\(530\) | 9010.61 | − | 15606.8i | 0.738483 | − | 1.27909i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 26181.5 | 2.12767 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1954.74 | − | 3385.70i | −0.157964 | − | 0.273601i | ||||
\(536\) | 9982.74 | + | 17290.6i | 0.804457 | + | 1.39336i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12044.3 | −0.965178 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7231.34 | + | 12525.1i | −0.574676 | + | 0.995368i | 0.421401 | + | 0.906875i | \(0.361539\pi\) |
−0.996077 | + | 0.0884937i | \(0.971795\pi\) | |||||||
\(542\) | −5351.98 | − | 9269.91i | −0.424146 | − | 0.734643i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −268.634 | + | 465.289i | −0.0211721 | + | 0.0366711i | ||||
\(545\) | −6096.07 | −0.479132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13682.5 | 1.06951 | 0.534755 | − | 0.845007i | \(-0.320404\pi\) | ||||
0.534755 | + | 0.845007i | \(0.320404\pi\) | |||||||
\(548\) | −561.282 | + | 972.169i | −0.0437533 | + | 0.0757829i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7831.47 | − | 13564.5i | −0.607155 | − | 1.05162i | ||||
\(551\) | −1956.96 | + | 3389.56i | −0.151306 | + | 0.262069i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2685.49 | −0.205949 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1040.26 | − | 1801.78i | −0.0793466 | − | 0.137432i | ||||
\(557\) | −3831.56 | − | 6636.46i | −0.291470 | − | 0.504840i | 0.682688 | − | 0.730710i | \(-0.260811\pi\) |
−0.974157 | + | 0.225870i | \(0.927478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43801.8 | 3.31417 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3395.85 | + | 5881.79i | −0.254885 | + | 0.441474i | ||||
\(563\) | −8735.24 | − | 15129.9i | −0.653902 | − | 1.13259i | −0.982168 | − | 0.188006i | \(-0.939798\pi\) |
0.328266 | − | 0.944585i | \(-0.393536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19875.9 | − | 34426.0i | 1.47997 | − | 2.56339i | ||||
\(566\) | 7598.83 | 0.564316 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4073.96 | −0.300950 | ||||||||
\(569\) | −6936.96 | + | 12015.2i | −0.511094 | + | 0.885240i | 0.488824 | + | 0.872383i | \(0.337426\pi\) |
−0.999917 | + | 0.0128577i | \(0.995907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1888.76 | + | 3271.43i | 0.138428 | + | 0.239764i | 0.926902 | − | 0.375305i | \(-0.122462\pi\) |
−0.788474 | + | 0.615068i | \(0.789129\pi\) | |||||||
\(572\) | 2270.80 | − | 3933.14i | 0.165991 | − | 0.287505i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6936.79 | 0.503103 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6940.23 | + | 12020.8i | 0.500738 | + | 0.867303i | 1.00000 | 0.000852075i | \(0.000271224\pi\) | |
−0.499262 | + | 0.866451i | \(0.666395\pi\) | |||||||
\(578\) | −5892.12 | − | 10205.5i | −0.424014 | − | 0.734414i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2606.57 | 0.186607 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4490.36 | − | 7777.53i | 0.318991 | − | 0.552509i | ||||
\(584\) | 7601.41 | + | 13166.0i | 0.538611 | + | 0.932901i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11036.6 | − | 19116.0i | 0.778018 | − | 1.34757i | ||||
\(587\) | −2395.61 | −0.168445 | −0.0842227 | − | 0.996447i | \(-0.526841\pi\) | ||||
−0.0842227 | + | 0.996447i | \(0.526841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7962.36 | −0.557018 | ||||||||
\(590\) | −15075.8 | + | 26112.0i | −1.05196 | + | 1.82206i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1175.99 | − | 2036.88i | −0.0816437 | − | 0.141411i | ||||
\(593\) | −3301.75 | + | 5718.80i | −0.228645 | + | 0.396025i | −0.957407 | − | 0.288742i | \(-0.906763\pi\) |
0.728762 | + | 0.684767i | \(0.240096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3845.04 | −0.264260 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2699.24 | − | 4675.21i | −0.184582 | − | 0.319705i | ||||
\(599\) | 8626.05 | + | 14940.8i | 0.588399 | + | 1.01914i | 0.994442 | + | 0.105283i | \(0.0335747\pi\) |
−0.406044 | + | 0.913854i | \(0.633092\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12833.1 | −0.871005 | −0.435503 | − | 0.900187i | \(-0.643429\pi\) | ||||
−0.435503 | + | 0.900187i | \(0.643429\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2758.15 | + | 4777.26i | −0.185807 | + | 0.321828i | ||||
\(605\) | 7540.14 | + | 13059.9i | 0.506695 | + | 0.877621i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4310.08 | − | 7465.28i | 0.288206 | − | 0.499187i | −0.685176 | − | 0.728378i | \(-0.740275\pi\) |
0.973381 | + | 0.229191i | \(0.0736080\pi\) | |||||||
\(608\) | 6181.62 | 0.412332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 180.510 | 0.0119813 | ||||||||
\(611\) | 13345.9 | − | 23115.7i | 0.883659 | − | 1.53054i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2568.37 | − | 4448.54i | −0.169226 | − | 0.293107i | 0.768922 | − | 0.639342i | \(-0.220793\pi\) |
−0.938148 | + | 0.346235i | \(0.887460\pi\) | |||||||
\(614\) | 5611.72 | − | 9719.79i | 0.368845 | − | 0.638858i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1759.82 | 0.114826 | 0.0574131 | − | 0.998351i | \(-0.481715\pi\) | ||||
0.0574131 | + | 0.998351i | \(0.481715\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1780.12 | − | 3083.26i | −0.115588 | − | 0.200205i | 0.802427 | − | 0.596751i | \(-0.203542\pi\) |
−0.918015 | + | 0.396546i | \(0.870209\pi\) | |||||||
\(620\) | 2651.36 | + | 4592.29i | 0.171744 | + | 0.297469i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15492.4 | 0.998698 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11968.4 | + | 20729.9i | −0.765977 | + | 1.32671i | ||||
\(626\) | −7083.56 | − | 12269.1i | −0.452262 | − | 0.783341i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1176.28 | − | 2037.38i | 0.0747431 | − | 0.129459i | ||||
\(629\) | 316.482 | 0.0200620 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27321.4 | −1.72369 | −0.861845 | − | 0.507172i | \(-0.830691\pi\) | ||||
−0.861845 | + | 0.507172i | \(0.830691\pi\) | |||||||
\(632\) | 1697.40 | − | 2939.99i | 0.106834 | − | 0.185042i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4797.67 | + | 8309.81i | 0.300536 | + | 0.520544i | ||||
\(635\) | 22997.8 | − | 39833.4i | 1.43723 | − | 2.48936i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3486.36 | −0.216342 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5995.63 | + | 10384.7i | 0.370309 | + | 0.641395i | ||||
\(641\) | −10963.5 | − | 18989.4i | −0.675558 | − | 1.17010i | −0.976306 | − | 0.216397i | \(-0.930570\pi\) |
0.300748 | − | 0.953704i | \(-0.402764\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5826.04 | 0.357320 | 0.178660 | − | 0.983911i | \(-0.442824\pi\) | ||||
0.178660 | + | 0.983911i | \(0.442824\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 441.728 | − | 765.095i | 0.0269033 | − | 0.0465979i | ||||
\(647\) | −12105.4 | − | 20967.1i | −0.735565 | − | 1.27404i | −0.954475 | − | 0.298291i | \(-0.903583\pi\) |
0.218910 | − | 0.975745i | \(-0.429750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7512.87 | + | 13012.7i | −0.454401 | + | 0.787045i | ||||
\(650\) | 57150.3 | 3.44864 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6446.80 | −0.387233 | ||||||||
\(653\) | −12811.7 | + | 22190.4i | −0.767778 | + | 1.32983i | 0.170988 | + | 0.985273i | \(0.445304\pi\) |
−0.938765 | + | 0.344557i | \(0.888029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1542.39 | + | 2671.49i | 0.0920092 | + | 0.159365i | ||||
\(656\) | −6280.73 | + | 10878.6i | −0.373813 | + | 0.647463i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23273.7 | 1.37574 | 0.687871 | − | 0.725833i | \(-0.258545\pi\) | ||||
0.687871 | + | 0.725833i | \(0.258545\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10018.2 | − | 17352.1i | −0.589508 | − | 1.02106i | −0.994297 | − | 0.106647i | \(-0.965988\pi\) |
0.404789 | − | 0.914410i | \(-0.367345\pi\) | |||||||
\(662\) | −10758.7 | − | 18634.7i | −0.631646 | − | 1.09404i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15252.9 | 0.891454 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 772.019 | − | 1337.18i | 0.0448166 | − | 0.0776247i | ||||
\(668\) | −2270.96 | − | 3933.42i | −0.131536 | − | 0.227827i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19530.1 | + | 33827.1i | −1.12614 | + | 1.95053i | ||||
\(671\) | 89.9554 | 0.00517540 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18127.8 | −1.03830 | −0.519149 | − | 0.854684i | \(-0.673751\pi\) | ||||
−0.519149 | + | 0.854684i | \(0.673751\pi\) | |||||||
\(674\) | 4800.74 | − | 8315.12i | 0.274358 | − | 0.475203i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5900.11 | + | 10219.3i | 0.335692 | + | 0.581435i | ||||
\(677\) | −6907.73 | + | 11964.5i | −0.392150 | + | 0.679224i | −0.992733 | − | 0.120339i | \(-0.961602\pi\) |
0.600583 | + | 0.799563i | \(0.294935\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2755.85 | −0.155415 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3546.28 | − | 6142.33i | −0.199111 | − | 0.344871i | ||||
\(683\) | −2302.11 | − | 3987.38i | −0.128972 | − | 0.223386i | 0.794306 | − | 0.607517i | \(-0.207834\pi\) |
−0.923279 | + | 0.384131i | \(0.874501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10286.8 | −0.573777 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10507.7 | + | 18199.9i | −0.582271 | + | 1.00852i | ||||
\(689\) | 16384.2 | + | 28378.3i | 0.905935 | + | 1.56913i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8956.83 | − | 15513.7i | 0.493103 | − | 0.854079i | −0.506866 | − | 0.862025i | \(-0.669196\pi\) |
0.999968 | + | 0.00794632i | \(0.00252942\pi\) | |||||||
\(692\) | 1020.96 | 0.0560854 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16480.5 | 0.901426 | ||||||||
\(695\) | 9532.53 | − | 16510.8i | 0.520272 | − | 0.901138i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −845.132 | − | 1463.81i | −0.0459278 | − | 0.0795492i | ||||
\(698\) | 974.548 | − | 1687.97i | 0.0528470 | − | 0.0915336i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11303.7 | −0.609035 | −0.304518 | − | 0.952507i | \(-0.598495\pi\) | ||||
−0.304518 | + | 0.952507i | \(0.598495\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1820.66 | − | 3153.48i | −0.0976780 | − | 0.169183i | ||||
\(704\) | 6766.82 | + | 11720.5i | 0.362264 | + | 0.627460i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19118.6 | 1.01918 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8023.15 | − | 13896.5i | 0.424987 | − | 0.736099i | −0.571432 | − | 0.820649i | \(-0.693612\pi\) |
0.996419 | + | 0.0845505i | \(0.0269454\pi\) | |||||||
\(710\) | −3985.11 | − | 6902.42i | −0.210646 | − | 0.364849i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3504.42 | + | 6069.83i | −0.184457 | + | 0.319489i | ||||
\(713\) | 3141.15 | 0.164989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41617.5 | 2.17679 | ||||||||
\(716\) | −1147.09 | + | 1986.82i | −0.0598726 | + | 0.103702i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10645.7 | + | 18438.9i | 0.553336 | + | 0.958406i | ||||
\(719\) | 12595.2 | − | 21815.6i | 0.653300 | − | 1.13155i | −0.329017 | − | 0.944324i | \(-0.606717\pi\) |
0.982317 | − | 0.187225i | \(-0.0599493\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6394.38 | 0.329604 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 441.340 | + | 764.424i | 0.0226551 | + | 0.0392397i | ||||
\(725\) | 8172.89 | + | 14155.9i | 0.418667 | + | 0.725152i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11277.2 | −0.575307 | −0.287653 | − | 0.957735i | \(-0.592875\pi\) | ||||
−0.287653 | + | 0.957735i | \(0.592875\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14871.3 | + | 25757.8i | −0.753987 | + | 1.30594i | ||||
\(731\) | −1413.91 | − | 2448.96i | −0.0715395 | − | 0.123910i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11860.0 | − | 20542.2i | 0.597626 | − | 1.03512i | −0.395544 | − | 0.918447i | \(-0.629444\pi\) |
0.993171 | − | 0.116672i | \(-0.0372226\pi\) | |||||||
\(734\) | −26946.9 | −1.35508 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2438.64 | −0.122133 | ||||||||
\(737\) | −9732.64 | + | 16857.4i | −0.486440 | + | 0.842539i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4062.36 | − | 7036.21i | −0.202214 | − | 0.350245i | 0.747027 | − | 0.664793i | \(-0.231480\pi\) |
−0.949242 | + | 0.314548i | \(0.898147\pi\) | |||||||
\(740\) | −1212.51 | + | 2100.14i | −0.0602336 | + | 0.104328i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20955.3 | −1.03469 | −0.517346 | − | 0.855777i | \(-0.673080\pi\) | ||||
−0.517346 | + | 0.855777i | \(0.673080\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17617.3 | − | 30514.0i | −0.866372 | − | 1.50060i | ||||
\(746\) | 3292.81 | + | 5703.32i | 0.161607 | + | 0.279911i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −293.203 | −0.0143323 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19104.0 | − | 33089.2i | 0.928251 | − | 1.60778i | 0.142004 | − | 0.989866i | \(-0.454645\pi\) |
0.786247 | − | 0.617912i | \(-0.212021\pi\) | |||||||
\(752\) | 6403.13 | + | 11090.5i | 0.310503 | + | 0.537807i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6360.45 | − | 11016.6i | 0.307207 | − | 0.532097i | ||||
\(755\) | −50549.4 | −2.43666 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30958.1 | 1.48638 | 0.743191 | − | 0.669079i | \(-0.233311\pi\) | ||||
0.743191 | + | 0.669079i | \(0.233311\pi\) | |||||||
\(758\) | 4932.82 | − | 8543.90i | 0.236370 | − | 0.409404i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 15853.9 | + | 27459.7i | 0.756685 | + | 1.31062i | ||||
\(761\) | 20024.7 | − | 34683.8i | 0.953871 | − | 1.65215i | 0.216939 | − | 0.976185i | \(-0.430393\pi\) |
0.736932 | − | 0.675967i | \(-0.236274\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 389.601 | 0.0184493 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15732.1 | + | 27248.9i | 0.742070 | + | 1.28530i | ||||
\(767\) | −27412.6 | − | 47480.1i | −1.29050 | − | 2.23521i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8002.01 | 0.375240 | 0.187620 | − | 0.982242i | \(-0.439923\pi\) | ||||
0.187620 | + | 0.982242i | \(0.439923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2593.26 | + | 4491.65i | −0.120898 | + | 0.209402i | ||||
\(773\) | 6966.68 | + | 12066.6i | 0.324158 | + | 0.561458i | 0.981342 | − | 0.192273i | \(-0.0615858\pi\) |
−0.657184 | + | 0.753730i | \(0.728252\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16626.7 | + | 28798.2i | −0.770642 | + | 1.33479i | ||||
\(776\) | 14810.3 | 0.685126 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −470.751 | −0.0216931 | ||||||||
\(779\) | −9723.78 | + | 16842.1i | −0.447228 | + | 0.774621i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1985.95 | − | 3439.76i | −0.0909894 | − | 0.157598i | ||||
\(782\) | −174.261 | + | 301.829i | −0.00796875 | + | 0.0138023i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21558.0 | 0.980175 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18790.9 | + | 32546.7i | 0.851108 | + | 1.47416i | 0.880209 | + | 0.474586i | \(0.157402\pi\) |
−0.0291013 | + | 0.999576i | \(0.509265\pi\) | |||||||
\(788\) | 2894.01 | + | 5012.56i | 0.130831 | + | 0.226606i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6641.54 | 0.299108 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −164.113 | + | 284.252i | −0.00734907 | + | 0.0127290i | ||||
\(794\) | 17120.3 | + | 29653.3i | 0.765212 | + | 1.32539i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1457.46 | − | 2524.39i | 0.0648973 | − | 0.112405i | ||||
\(797\) | −9458.78 | −0.420385 | −0.210193 | − | 0.977660i | \(-0.567409\pi\) | ||||
−0.210193 | + | 0.977660i | \(0.567409\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1723.20 | −0.0762985 | ||||||||
\(800\) | 12908.2 | − | 22357.7i | 0.570467 | − | 0.988078i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −12077.2 | − | 20918.3i | −0.531745 | − | 0.921009i | ||||
\(803\) | −7410.97 | + | 12836.2i | −0.325688 | + | 0.564108i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 25879.0 | 1.13095 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5613.69 | − | 9723.20i | −0.244417 | − | 0.423343i | ||||
\(809\) | −954.968 | − | 1654.05i | −0.0415017 | − | 0.0718831i | 0.844528 | − | 0.535511i | \(-0.179881\pi\) |
−0.886030 | + | 0.463628i | \(0.846548\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43110.6 | −1.86661 | −0.933303 | − | 0.359091i | \(-0.883087\pi\) | ||||
−0.933303 | + | 0.359091i | \(0.883087\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1621.77 | − | 2809.00i | 0.0698319 | − | 0.120952i | ||||
\(815\) | −29538.0 | − | 51161.4i | −1.26954 | − | 2.19890i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16267.9 | + | 28176.9i | −0.696626 | + | 1.20659i | ||||
\(818\) | 11189.7 | 0.478287 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12951.5 | 0.551570 | ||||||||
\(821\) | 2013.28 | − | 3487.10i | 0.0855834 | − | 0.148235i | −0.820056 | − | 0.572283i | \(-0.806058\pi\) |
0.905640 | + | 0.424048i | \(0.139391\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19834.0 | − | 34353.5i | −0.840062 | − | 1.45503i | −0.889842 | − | 0.456269i | \(-0.849185\pi\) |
0.0497799 | − | 0.998760i | \(-0.484148\pi\) | |||||||
\(824\) | 9651.19 | − | 16716.4i | 0.408028 | − | 0.706726i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30137.7 | −1.26722 | −0.633611 | − | 0.773652i | \(-0.718428\pi\) | ||||
−0.633611 | + | 0.773652i | \(0.718428\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11639.0 | + | 20159.3i | 0.487622 | + | 0.844587i | 0.999899 | − | 0.0142341i | \(-0.00453100\pi\) |
−0.512276 | + | 0.858821i | \(0.671198\pi\) | |||||||
\(830\) | 14920.2 | + | 25842.6i | 0.623962 | + | 1.08073i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −49381.0 | −2.05766 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20810.2 | − | 36044.4i | 0.862477 | − | 1.49385i | ||||
\(836\) | 1686.74 | + | 2921.52i | 0.0697813 | + | 0.120865i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6033.49 | − | 10450.3i | 0.248716 | − | 0.430788i | ||||
\(839\) | −9494.43 | −0.390684 | −0.195342 | − | 0.980735i | \(-0.562582\pi\) | ||||
−0.195342 | + | 0.980735i | \(0.562582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20750.6 | −0.850820 | ||||||||
\(842\) | −849.996 | + | 1472.24i | −0.0347896 | + | 0.0602573i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 682.354 | + | 1181.87i | 0.0278289 | + | 0.0482011i | ||||
\(845\) | −54066.5 | + | 93645.9i | −2.20112 | + | 3.81245i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −15721.8 | −0.636661 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1844.79 | − | 3195.28i | −0.0744423 | − | 0.128938i | ||||
\(851\) | 718.251 | + | 1244.05i | 0.0289322 | + | 0.0501121i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12692.4 | 0.509471 | 0.254736 | − | 0.967011i | \(-0.418012\pi\) | ||||
0.254736 | + | 0.967011i | \(0.418012\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2412.18 | + | 4178.02i | −0.0963162 | + | 0.166825i | ||||
\(857\) | −11103.0 | − | 19231.0i | −0.442557 | − | 0.766531i | 0.555322 | − | 0.831636i | \(-0.312595\pi\) |
−0.997878 | + | 0.0651047i | \(0.979262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9910.24 | − | 17165.0i | 0.393636 | − | 0.681797i | −0.599290 | − | 0.800532i | \(-0.704550\pi\) |
0.992926 | + | 0.118735i | \(0.0378838\pi\) | |||||||
\(860\) | 21668.0 | 0.859155 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24945.5 | −0.985671 | ||||||||
\(863\) | 18206.9 | − | 31535.3i | 0.718157 | − | 1.24389i | −0.243572 | − | 0.969883i | \(-0.578319\pi\) |
0.961729 | − | 0.274002i | \(-0.0883476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4677.85 | + | 8102.27i | 0.183875 | + | 0.318480i | ||||
\(866\) | −13407.1 | + | 23221.7i | −0.526086 | + | 0.911208i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3309.76 | 0.129201 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35512.0 | − | 61508.7i | −1.38149 | − | 2.39281i | ||||
\(872\) | 3761.33 | + | 6514.82i | 0.146072 | + | 0.253004i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4009.97 | 0.155194 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9721.31 | + | 16837.8i | −0.374305 | + | 0.648315i | −0.990223 | − | 0.139496i | \(-0.955452\pi\) |
0.615918 | + | 0.787810i | \(0.288785\pi\) | |||||||
\(878\) | 8811.01 | + | 15261.1i | 0.338676 | + | 0.586603i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9983.71 | + | 17292.3i | −0.382444 | + | 0.662412i | ||||
\(881\) | −25184.2 | −0.963082 | −0.481541 | − | 0.876423i | \(-0.659923\pi\) | ||||
−0.481541 | + | 0.876423i | \(0.659923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4050.03 | −0.154354 | −0.0771769 | − | 0.997017i | \(-0.524591\pi\) | ||||
−0.0771769 | + | 0.997017i | \(0.524591\pi\) | |||||||
\(884\) | 534.913 | − | 926.496i | 0.0203519 | − | 0.0352505i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19421.9 | − | 33639.8i | −0.736448 | − | 1.27556i | ||||
\(887\) | −20802.1 | + | 36030.3i | −0.787447 | + | 1.36390i | 0.140080 | + | 0.990140i | \(0.455264\pi\) |
−0.927526 | + | 0.373758i | \(0.878069\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −13712.0 | −0.516434 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1053.18 | + | 1824.16i | 0.0395326 | + | 0.0684725i | ||||
\(893\) | 9913.27 | + | 17170.3i | 0.371484 | + | 0.643428i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21023.0 | −0.785165 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16370.5 | + | 28354.5i | −0.608340 | + | 1.05368i | ||||
\(899\) | 3700.88 | + | 6410.11i | 0.137298 | + | 0.237808i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1057.76 | − | 1832.09i | 0.0391110 | − | 0.0677422i | ||||
\(902\) | −17323.1 | −0.639463 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −49054.4 | −1.80478 | ||||||||
\(905\) | −4044.28 | + | 7004.90i | −0.148548 | + | 0.257294i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1786.30 | + | 3093.96i | 0.0653949 | + | 0.113267i | 0.896869 | − | 0.442296i | \(-0.145836\pi\) |
−0.831474 | + | 0.555563i | \(0.812503\pi\) | |||||||
\(908\) | −5156.01 | + | 8930.47i | −0.188445 | + | 0.326397i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29457.7 | −1.07133 | −0.535663 | − | 0.844432i | \(-0.679938\pi\) | ||||
−0.535663 | + | 0.844432i | \(0.679938\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7435.36 | + | 12878.4i | 0.269523 | + | 0.466828i | ||||
\(914\) | 13095.4 | + | 22681.9i | 0.473913 | + | 0.820842i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10427.9 | −0.376143 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1655.32 | − | 2867.10i | 0.0594168 | − | 0.102913i | −0.834787 | − | 0.550573i | \(-0.814409\pi\) |
0.894204 | + | 0.447660i | \(0.147743\pi\) | |||||||
\(920\) | −6254.34 | − | 10832.8i | −0.224130 | − | 0.388204i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2122.92 | + | 3677.01i | −0.0758295 | + | 0.131340i | ||||
\(923\) | 14492.5 | 0.516820 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15207.3 | −0.540556 | ||||||||
\(926\) | −6532.80 | + | 11315.1i | −0.231837 | + | 0.401554i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2873.19 | − | 4976.52i | −0.101635 | − | 0.176037i | ||||
\(929\) | 15733.8 | − | 27251.7i | 0.555660 | − | 0.962431i | −0.442192 | − | 0.896920i | \(-0.645799\pi\) |
0.997852 | − | 0.0655103i | \(-0.0208675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6851.94 | −0.240818 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 9791.26 | + | 16959.0i | 0.343019 | + | 0.594126i | ||||
\(935\) | −1343.40 | − | 2326.84i | −0.0469881 | − | 0.0813859i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17363.4 | 0.605375 | 0.302688 | − | 0.953090i | \(-0.402116\pi\) | ||||
0.302688 | + | 0.953090i | \(0.402116\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6601.97 | − | 11434.9i | 0.229077 | − | 0.396773i | ||||
\(941\) | 2773.89 | + | 4804.51i | 0.0960958 | + | 0.166443i | 0.910065 | − | 0.414465i | \(-0.136031\pi\) |
−0.813970 | + | 0.580907i | \(0.802698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3836.02 | − | 6644.18i | 0.132469 | − | 0.229443i | ||||
\(944\) | 26304.3 | 0.906919 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28981.6 | −0.996062 | ||||||||
\(947\) | −18980.1 | + | 32874.6i | −0.651290 | + | 1.12807i | 0.331520 | + | 0.943448i | \(0.392438\pi\) |
−0.982810 | + | 0.184619i | \(0.940895\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27040.8 | − | 46836.1i | −0.924955 | − | 1.60207i | ||||
\(950\) | −21225.5 | + | 36763.7i | −0.724892 | + | 1.25555i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10019.3 | 0.340563 | 0.170282 | − | 0.985395i | \(-0.445532\pi\) | ||||
0.170282 | + | 0.985395i | \(0.445532\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1785.08 | + | 3091.85i | 0.0604857 | + | 0.104764i | ||||
\(956\) | −4605.83 | − | 7977.53i | −0.155819 | − | 0.269887i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5059.61 | −0.170635 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7366.54 | − | 12759.2i | 0.247274 | − | 0.428291i | ||||
\(962\) | 5917.46 | + | 10249.3i | 0.198323 | + | 0.343505i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4715.56 | − | 8167.58i | 0.157550 | − | 0.272884i | ||||
\(965\) | −47527.3 | −1.58545 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27834.4 | 0.925641 | 0.462820 | − | 0.886452i | \(-0.346837\pi\) | ||||
0.462820 | + | 0.886452i | \(0.346837\pi\) | |||||||
\(968\) | 9304.68 | − | 16116.2i | 0.308950 | − | 0.535117i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14487.3 | + | 25092.7i | 0.479545 | + | 0.830597i | ||||
\(971\) | 9137.67 | − | 15826.9i | 0.302000 | − | 0.523079i | −0.674589 | − | 0.738193i | \(-0.735679\pi\) |
0.976589 | + | 0.215115i | \(0.0690125\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −23200.8 | −0.763245 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −78.7386 | − | 136.379i | −0.00258234 | − | 0.00447274i | ||||
\(977\) | −21514.5 | − | 37264.2i | −0.704513 | − | 1.22025i | −0.966867 | − | 0.255280i | \(-0.917832\pi\) |
0.262354 | − | 0.964972i | \(-0.415501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6833.24 | −0.223076 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14144.0 | − | 24498.2i | 0.459628 | − | 0.796099i | ||||
\(983\) | −15279.6 | − | 26465.1i | −0.495772 | − | 0.858702i | 0.504216 | − | 0.863577i | \(-0.331781\pi\) |
−0.999988 | + | 0.00487535i | \(0.998448\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26519.6 | + | 45933.3i | −0.857853 | + | 1.48584i | ||||
\(986\) | −821.253 | −0.0265254 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12309.0 | −0.396358 | ||||||||
\(989\) | 6417.69 | − | 11115.8i | 0.206340 | − | 0.357392i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22473.0 | + | 38924.3i | 0.720360 | + | 1.24770i | 0.960855 | + | 0.277050i | \(0.0893569\pi\) |
−0.240495 | + | 0.970650i | \(0.577310\pi\) | |||||||
\(992\) | 5845.14 | − | 10124.1i | 0.187080 | − | 0.324032i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 26711.2 | 0.851058 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14503.1 | + | 25120.0i | 0.460698 | + | 0.797953i | 0.998996 | − | 0.0448018i | \(-0.0142656\pi\) |
−0.538297 | + | 0.842755i | \(0.680932\pi\) | |||||||
\(998\) | −11099.6 | − | 19225.0i | −0.352055 | − | 0.609777i | ||||
\(999\) | 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 | 441.4.e.u.226.2 | 4 | ||
3.2 | odd | 2 | 147.4.e.j.79.1 | 4 | |||
7.2 | even | 3 | 441.4.a.o.1.1 | 2 | |||
7.3 | odd | 6 | 441.4.e.v.361.2 | 4 | |||
7.4 | even | 3 | inner | 441.4.e.u.361.2 | 4 | ||
7.5 | odd | 6 | 441.4.a.n.1.1 | 2 | |||
7.6 | odd | 2 | 441.4.e.v.226.2 | 4 | |||
21.2 | odd | 6 | 147.4.a.k.1.2 | yes | 2 | ||
21.5 | even | 6 | 147.4.a.j.1.2 | ✓ | 2 | ||
21.11 | odd | 6 | 147.4.e.j.67.1 | 4 | |||
21.17 | even | 6 | 147.4.e.k.67.1 | 4 | |||
21.20 | even | 2 | 147.4.e.k.79.1 | 4 | |||
84.23 | even | 6 | 2352.4.a.bl.1.1 | 2 | |||
84.47 | odd | 6 | 2352.4.a.cf.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.a.j.1.2 | ✓ | 2 | 21.5 | even | 6 | ||
147.4.a.k.1.2 | yes | 2 | 21.2 | odd | 6 | ||
147.4.e.j.67.1 | 4 | 21.11 | odd | 6 | |||
147.4.e.j.79.1 | 4 | 3.2 | odd | 2 | |||
147.4.e.k.67.1 | 4 | 21.17 | even | 6 | |||
147.4.e.k.79.1 | 4 | 21.20 | even | 2 | |||
441.4.a.n.1.1 | 2 | 7.5 | odd | 6 | |||
441.4.a.o.1.1 | 2 | 7.2 | even | 3 | |||
441.4.e.u.226.2 | 4 | 1.1 | even | 1 | trivial | ||
441.4.e.u.361.2 | 4 | 7.4 | even | 3 | inner | ||
441.4.e.v.226.2 | 4 | 7.6 | odd | 2 | |||
441.4.e.v.361.2 | 4 | 7.3 | odd | 6 | |||
2352.4.a.bl.1.1 | 2 | 84.23 | even | 6 | |||
2352.4.a.cf.1.2 | 2 | 84.47 | odd | 6 |