Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,4,Mod(5,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.95616044048\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 14 x^{10} - 32 x^{9} + 70 x^{8} + 224 x^{7} - 50 x^{6} + 2016 x^{5} + 5670 x^{4} - 23328 x^{3} - 91854 x^{2} + 531441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.4 | ||
Root | \(-1.67777 + 2.48698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.5 |
Dual form | 84.4.k.c.17.4 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.362863 | − | 5.18347i | −0.0698330 | − | 0.997559i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.41560 | − | 12.8442i | 0.663272 | − | 1.14882i | −0.316479 | − | 0.948600i | \(-0.602501\pi\) |
0.979751 | − | 0.200221i | \(-0.0641660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −16.6528 | + | 8.10467i | −0.899164 | + | 0.437611i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.7367 | + | 3.76177i | −0.990247 | + | 0.139325i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.589052 | + | 0.340089i | −0.0161460 | + | 0.00932189i | −0.508051 | − | 0.861327i | \(-0.669634\pi\) |
0.491905 | + | 0.870649i | \(0.336301\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 52.4373i | − | 1.11873i | −0.828921 | − | 0.559365i | \(-0.811045\pi\) | ||
0.828921 | − | 0.559365i | \(-0.188955\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −69.2683 | − | 33.7779i | −1.19233 | − | 0.581427i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −51.6784 | − | 89.5096i | −0.737286 | − | 1.27702i | −0.953713 | − | 0.300717i | \(-0.902774\pi\) |
0.216428 | − | 0.976299i | \(-0.430559\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 86.7417 | + | 50.0804i | 1.04736 | + | 0.604696i | 0.921910 | − | 0.387404i | \(-0.126628\pi\) |
0.125454 | + | 0.992099i | \(0.459961\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 48.0530 | + | 83.3781i | 0.499334 | + | 0.866410i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.63771 | + | 2.10024i | 0.0329790 | + | 0.0190404i | 0.516399 | − | 0.856348i | \(-0.327272\pi\) |
−0.483420 | + | 0.875389i | \(0.660606\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −47.4824 | − | 82.2418i | −0.379859 | − | 0.657935i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.2008 | + | 137.224i | 0.208137 | + | 0.978100i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 53.5367i | 0.342811i | 0.985201 | + | 0.171406i | \(0.0548308\pi\) | ||||
−0.985201 | + | 0.171406i | \(0.945169\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 235.952 | − | 136.227i | 1.36704 | − | 0.789261i | 0.376492 | − | 0.926420i | \(-0.377130\pi\) |
0.990549 | + | 0.137158i | \(0.0437969\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.97659 | + | 2.92992i | 0.0104266 | + | 0.0154556i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −19.3922 | + | 273.992i | −0.0936537 | + | 1.32323i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.2855 | − | 43.7957i | 0.112349 | − | 0.194594i | −0.804368 | − | 0.594131i | \(-0.797496\pi\) |
0.916717 | + | 0.399538i | \(0.130829\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −271.807 | + | 19.0276i | −1.11600 | + | 0.0781243i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 318.804 | 1.21436 | 0.607181 | − | 0.794563i | \(-0.292300\pi\) | ||||
0.607181 | + | 0.794563i | \(0.292300\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 168.515 | 0.597634 | 0.298817 | − | 0.954310i | \(-0.403408\pi\) | ||||
0.298817 | + | 0.954310i | \(0.403408\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −149.951 | + | 371.307i | −0.496743 | + | 1.23003i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −313.988 | + | 543.844i | −0.974467 | + | 1.68783i | −0.292782 | + | 0.956179i | \(0.594581\pi\) |
−0.681684 | + | 0.731647i | \(0.738752\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 211.629 | − | 269.930i | 0.616993 | − | 0.786969i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −445.218 | + | 300.353i | −1.22241 | + | 0.824663i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 625.481 | − | 361.121i | 1.62106 | − | 0.935922i | 0.634427 | − | 0.772982i | \(-0.281236\pi\) |
0.986636 | − | 0.162939i | \(-0.0520974\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0879i | 0.0247318i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 228.115 | − | 467.795i | 0.530079 | − | 1.08703i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −263.093 | − | 455.691i | −0.580539 | − | 1.00552i | −0.995415 | − | 0.0956456i | \(-0.969508\pi\) |
0.414876 | − | 0.909878i | \(-0.363825\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 205.162 | + | 118.450i | 0.430627 | + | 0.248623i | 0.699614 | − | 0.714521i | \(-0.253355\pi\) |
−0.268987 | + | 0.963144i | \(0.586689\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 414.751 | − | 279.336i | 0.829424 | − | 0.558619i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −673.515 | − | 388.854i | −1.28522 | − | 0.742022i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −149.359 | − | 258.697i | −0.272344 | − | 0.471714i | 0.697117 | − | 0.716957i | \(-0.254466\pi\) |
−0.969462 | + | 0.245243i | \(0.921132\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.56651 | − | 19.6181i | 0.0166909 | − | 0.0342281i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 379.893i | − | 0.634999i | −0.948258 | − | 0.317500i | \(-0.897157\pi\) | ||
0.948258 | − | 0.317500i | \(-0.102843\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −559.469 | + | 323.010i | −0.896999 | + | 0.517882i | −0.876225 | − | 0.481902i | \(-0.839946\pi\) |
−0.0207735 | + | 0.999784i | \(0.506613\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −409.068 | + | 275.966i | −0.629802 | + | 0.424877i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.05302 | − | 10.4375i | 0.0104385 | − | 0.0154476i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −211.386 | + | 366.132i | −0.301048 | + | 0.521431i | −0.976374 | − | 0.216089i | \(-0.930670\pi\) |
0.675325 | + | 0.737520i | \(0.264003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 700.698 | − | 201.155i | 0.961177 | − | 0.275932i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −391.295 | −0.517472 | −0.258736 | − | 0.965948i | \(-0.583306\pi\) | ||||
−0.258736 | + | 0.965948i | \(0.583306\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1532.91 | −1.95608 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 277.506 | − | 19.4265i | 0.341974 | − | 0.0239395i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −316.431 | + | 548.075i | −0.376872 | + | 0.652762i | −0.990605 | − | 0.136752i | \(-0.956334\pi\) |
0.613733 | + | 0.789513i | \(0.289667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 424.987 | + | 873.226i | 0.489569 | + | 1.00592i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −791.747 | − | 1173.62i | −0.882799 | − | 1.30859i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1286.48 | − | 742.752i | 1.38937 | − | 0.802155i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1432.13i | − | 1.49908i | −0.661959 | − | 0.749540i | \(-0.730275\pi\) | ||
0.661959 | − | 0.749540i | \(-0.269725\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.4699 | − | 11.3087i | 0.0146897 | − | 0.0114805i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 445.537 | + | 771.692i | 0.438936 | + | 0.760260i | 0.997608 | − | 0.0691294i | \(-0.0220221\pi\) |
−0.558672 | + | 0.829389i | \(0.688689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1067.48 | + | 616.313i | 1.02119 | + | 0.589583i | 0.914448 | − | 0.404704i | \(-0.132625\pi\) |
0.106740 | + | 0.994287i | \(0.465959\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1427.27 | + | 1.09716i | 1.32654 | + | 0.00101973i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −585.738 | − | 338.176i | −0.529209 | − | 0.305539i | 0.211485 | − | 0.977381i | \(-0.432170\pi\) |
−0.740694 | + | 0.671842i | \(0.765503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 497.209 | + | 861.191i | 0.436917 | + | 0.756762i | 0.997450 | − | 0.0713697i | \(-0.0227370\pi\) |
−0.560533 | + | 0.828132i | \(0.689404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −236.189 | − | 115.175i | −0.201964 | − | 0.0984854i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 707.915i | 0.589337i | 0.955600 | + | 0.294668i | \(0.0952091\pi\) | ||||
−0.955600 | + | 0.294668i | \(0.904791\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 53.9517 | − | 31.1490i | 0.0437480 | − | 0.0252579i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 197.257 | + | 1402.00i | 0.155867 | + | 1.10782i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1586.03 | + | 1071.75i | 1.22178 | + | 0.825603i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −665.269 | + | 1152.28i | −0.499826 | + | 0.865724i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −115.682 | − | 1652.51i | −0.0848026 | − | 1.21140i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 445.460 | 0.318745 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −885.551 | −0.618740 | −0.309370 | − | 0.950942i | \(-0.600118\pi\) | ||||
−0.309370 | + | 0.950942i | \(0.600118\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −61.1477 | − | 873.490i | −0.0417345 | − | 0.596175i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −844.911 | + | 1463.43i | −0.563513 | + | 0.976034i | 0.433673 | + | 0.901070i | \(0.357217\pi\) |
−0.997186 | + | 0.0749634i | \(0.976116\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1850.37 | − | 130.963i | −1.20637 | − | 0.0853828i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1979.07 | + | 642.535i | 1.26171 | + | 0.409634i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1670.17 | + | 964.276i | −1.04155 | + | 0.601340i | −0.920273 | − | 0.391278i | \(-0.872033\pi\) |
−0.121280 | + | 0.992618i | \(0.538700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 402.721i | − | 0.245744i | −0.992423 | − | 0.122872i | \(-0.960790\pi\) | ||
0.992423 | − | 0.122872i | \(-0.0392104\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2932.93 | + | 1430.21i | 1.75176 | + | 0.854222i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.8334 | + | 30.8883i | 0.0104287 | + | 0.0180630i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 687.637 | + | 397.007i | 0.393828 | + | 0.227377i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1475.97 | − | 999.022i | −0.828134 | − | 0.560530i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1392.62 | − | 804.032i | −0.765692 | − | 0.442073i | 0.0656434 | − | 0.997843i | \(-0.479090\pi\) |
−0.831336 | + | 0.555770i | \(0.812423\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −183.275 | − | 317.442i | −0.0987731 | − | 0.171080i | 0.812404 | − | 0.583095i | \(-0.198158\pi\) |
−0.911177 | + | 0.412015i | \(0.864825\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1718.42 | + | 2198.79i | 0.908015 | + | 1.16184i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 4040.82i | − | 2.09398i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 370.608 | − | 213.970i | 0.188393 | − | 0.108769i | −0.402837 | − | 0.915272i | \(-0.631976\pi\) |
0.591230 | + | 0.806503i | \(0.298643\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2098.82 | − | 3111.12i | −1.04684 | − | 1.55175i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −77.5997 | − | 5.49223i | −0.0379858 | − | 0.00268850i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 116.502 | − | 201.787i | 0.0559823 | − | 0.0969643i | −0.836676 | − | 0.547698i | \(-0.815504\pi\) |
0.892658 | + | 0.450734i | \(0.148838\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 52.2901 | − | 3.66051i | 0.0246714 | − | 0.00172709i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1013.86 | 0.469791 | 0.234896 | − | 0.972021i | \(-0.424525\pi\) | ||||
0.234896 | + | 0.972021i | \(0.424525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −552.672 | −0.251558 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2507.57 | − | 1012.68i | −1.12140 | − | 0.452874i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1657.13 | − | 2870.23i | 0.728262 | − | 1.26139i | −0.229356 | − | 0.973343i | \(-0.573662\pi\) |
0.957617 | − | 0.288044i | \(-0.0930048\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1457.26 | + | 984.725i | 0.629475 | + | 0.425361i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2266.59 | + | 1529.09i | −0.962528 | + | 0.649341i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1196.04 | + | 690.531i | −0.499418 | + | 0.288339i | −0.728473 | − | 0.685074i | \(-0.759770\pi\) |
0.229055 | + | 0.973413i | \(0.426436\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1558.38i | 0.639963i | 0.947424 | + | 0.319981i | \(0.103677\pi\) | ||||
−0.947424 | + | 0.319981i | \(0.896323\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 539.537 | − | 1106.43i | 0.217944 | − | 0.446938i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −375.014 | − | 649.543i | −0.149035 | − | 0.258137i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 60.8825 | + | 35.1505i | 0.0238084 | + | 0.0137458i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1598.43 | − | 2048.49i | −0.615176 | − | 0.788389i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1884.48 | + | 1088.00i | 0.713905 | + | 0.412173i | 0.812505 | − | 0.582954i | \(-0.198103\pi\) |
−0.0986002 | + | 0.995127i | \(0.531436\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1749.63 | − | 3030.45i | −0.652546 | − | 1.13024i | −0.982503 | − | 0.186247i | \(-0.940368\pi\) |
0.329957 | − | 0.943996i | \(-0.392966\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1771.22 | + | 3632.25i | −0.650460 | + | 1.33390i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1297.91i | 0.469401i | 0.972068 | + | 0.234700i | \(0.0754109\pi\) | ||||
−0.972068 | + | 0.234700i | \(0.924589\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3062.79 | − | 1768.30i | 1.09103 | − | 0.629908i | 0.157182 | − | 0.987570i | \(-0.449759\pi\) |
0.933851 | + | 0.357661i | \(0.116426\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1286.75 | + | 868.067i | −0.451544 | + | 0.304621i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −433.898 | − | 891.534i | −0.150018 | − | 0.308244i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2364.13 | − | 4094.79i | 0.805452 | − | 1.39508i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −105.161 | − | 42.4690i | −0.0353101 | − | 0.0142599i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −68.1271 | −0.0225476 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2131.02 | −0.695286 | −0.347643 | − | 0.937627i | \(-0.613018\pi\) | ||||
−0.347643 | + | 0.937627i | \(0.613018\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1969.16 | + | 137.849i | −0.633449 | + | 0.0443439i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1249.64 | − | 2164.44i | 0.396394 | − | 0.686574i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2825.18 | + | 4180.87i | −0.883805 | + | 1.30791i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1877.32 | + | 2782.78i | 0.579258 | + | 0.858644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4693.64 | + | 2709.88i | −1.42864 | + | 0.824824i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6147.95i | − | 1.84617i | −0.384590 | − | 0.923087i | \(-0.625657\pi\) | ||
0.384590 | − | 0.923087i | \(-0.374343\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1578.89 | + | 2020.25i | 0.467821 | + | 0.598594i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1484.97 | + | 2572.05i | 0.434190 | + | 0.752039i | 0.997229 | − | 0.0743914i | \(-0.0237014\pi\) |
−0.563039 | + | 0.826430i | \(0.690368\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2479.18 | + | 1431.35i | 0.715409 | + | 0.413042i | 0.813061 | − | 0.582179i | \(-0.197800\pi\) |
−0.0976515 | + | 0.995221i | \(0.531133\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −56.6617 | − | 32.7717i | −0.0161388 | − | 0.00933429i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5177.16 | + | 2989.03i | 1.45565 | + | 0.840421i | 0.998793 | − | 0.0491180i | \(-0.0156410\pi\) |
0.456859 | + | 0.889539i | \(0.348974\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4656.83 | + | 8065.86i | 1.29267 | + | 2.23897i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1974.54 | + | 962.858i | 0.541181 | + | 0.263900i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5571.82i | 1.50800i | 0.656876 | + | 0.753998i | \(0.271877\pi\) | ||||
−0.656876 | + | 0.753998i | \(0.728123\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3591.11 | − | 2073.33i | 0.959851 | − | 0.554170i | 0.0637236 | − | 0.997968i | \(-0.479702\pi\) |
0.896127 | + | 0.443798i | \(0.146369\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1296.94 | − | 3559.05i | −0.342380 | − | 0.939561i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1897.68 | − | 4719.90i | −0.494852 | − | 1.23079i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2626.08 | − | 4548.50i | 0.676492 | − | 1.17172i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 141.986 | + | 2028.27i | 0.0361366 | + | 0.516209i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7611.35 | −1.91404 | −0.957021 | − | 0.290020i | \(-0.906338\pi\) | ||||
−0.957021 | + | 0.290020i | \(0.906338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.85707 | −0.000709970 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 556.235 | + | 7945.77i | 0.136599 | + | 1.95131i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1174.76 | − | 2034.74i | 0.285134 | − | 0.493867i | −0.687507 | − | 0.726177i | \(-0.741295\pi\) |
0.972642 | + | 0.232310i | \(0.0746284\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −66.1228 | + | 934.249i | −0.0158636 | + | 0.224137i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −201.393 | − | 1431.39i | −0.0477622 | − | 0.339468i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4441.42 | − | 2564.25i | 1.04133 | − | 0.601211i | 0.121119 | − | 0.992638i | \(-0.461352\pi\) |
0.920209 | + | 0.391426i | \(0.128018\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10711.7i | − | 2.48308i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2955.75 | + | 1441.33i | 0.677486 | + | 0.330368i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.2532 | − | 35.0795i | −0.00459055 | − | 0.00795107i | 0.863721 | − | 0.503970i | \(-0.168128\pi\) |
−0.868312 | + | 0.496019i | \(0.834795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2807.84 | + | 1621.11i | 0.629389 | + | 0.363378i | 0.780515 | − | 0.625137i | \(-0.214957\pi\) |
−0.151127 | + | 0.988514i | \(0.548290\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4372.13 | − | 2519.77i | 0.969279 | − | 0.558620i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 55.9391 | + | 32.2965i | 0.0122664 | + | 0.00708200i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1107.85 | + | 1918.85i | 0.240304 | + | 0.416219i | 0.960801 | − | 0.277239i | \(-0.0894195\pi\) |
−0.720497 | + | 0.693458i | \(0.756086\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5796.12 | + | 4529.86i | −1.24374 | + | 0.972027i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5882.33i | 1.24879i | 0.781108 | + | 0.624395i | \(0.214655\pi\) | ||||
−0.781108 | + | 0.624395i | \(0.785345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1323.79 | + | 764.290i | −0.278060 | + | 0.160538i | −0.632545 | − | 0.774524i | \(-0.717990\pi\) |
0.354485 | + | 0.935062i | \(0.384656\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4316.85 | − | 6398.93i | −0.897221 | − | 1.32996i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5308.97 | + | 2583.80i | −1.09191 | + | 0.531419i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2884.82 | + | 4996.65i | −0.587180 | + | 1.01703i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7423.40 | + | 519.667i | −1.49542 | + | 0.104685i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6038.37 | 1.20398 | 0.601989 | − | 0.798505i | \(-0.294375\pi\) | ||||
0.601989 | + | 0.798505i | \(0.294375\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7803.98 | −1.54022 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −63.8690 | − | 70.9009i | −0.0124783 | − | 0.0138522i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 110.131 | − | 190.752i | 0.0213011 | − | 0.0368946i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2806.23 | + | 1365.76i | −0.537371 | + | 0.261531i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3838.37 | − | 2589.44i | 0.727751 | − | 0.490956i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3042.79 | − | 1756.76i | 0.571246 | − | 0.329809i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7231.98i | 1.34447i | 0.740340 | + | 0.672233i | \(0.234665\pi\) | ||||
−0.740340 | + | 0.672233i | \(0.765335\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2807.29 | − | 5756.91i | 0.516831 | − | 1.05987i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −859.000 | − | 1487.83i | −0.156622 | − | 0.271277i | 0.777027 | − | 0.629468i | \(-0.216727\pi\) |
−0.933648 | + | 0.358191i | \(0.883394\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4787.88 | − | 2764.28i | −0.864622 | − | 0.499190i | 0.000935213 | − | 1.00000i | \(-0.499702\pi\) |
−0.865557 | + | 0.500810i | \(0.833036\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −512.215 | − | 7398.59i | −0.0916192 | − | 1.32338i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1541.66 | + | 890.076i | 0.273149 | + | 0.157702i | 0.630318 | − | 0.776337i | \(-0.282925\pi\) |
−0.357169 | + | 0.934040i | \(0.616258\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.2073 | − | 31.5359i | −0.00319565 | − | 0.00553502i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1540.38 | + | 3158.86i | −0.267837 | + | 0.549254i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10352.3i | − | 1.78333i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4312.54 | + | 2489.85i | −0.736052 | + | 0.424960i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4283.53 | − | 2889.76i | 0.724404 | − | 0.488697i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 821.097 | − | 11601.3i | 0.137594 | − | 1.94407i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3219.65 | − | 5576.59i | 0.534646 | − | 0.926034i | −0.464534 | − | 0.885555i | \(-0.653778\pi\) |
0.999180 | − | 0.0404789i | \(-0.0128884\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −511.299 | + | 1266.07i | −0.0841412 | + | 0.208349i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4430.34 | −0.722553 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2095.32 | 0.338692 | 0.169346 | − | 0.985557i | \(-0.445834\pi\) | ||||
0.169346 | + | 0.985557i | \(0.445834\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3669.45 | − | 256.876i | 0.587898 | − | 0.0411551i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −92.6587 | + | 160.490i | −0.0147148 | + | 0.0254868i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1336.50 | + | 6210.26i | −0.210392 | + | 0.977617i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −181.037 | − | 268.354i | −0.0282513 | − | 0.0418774i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2115.84 | + | 1221.58i | −0.327332 | + | 0.188985i | −0.654656 | − | 0.755927i | \(-0.727186\pi\) |
0.327324 | + | 0.944912i | \(0.393853\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1583.72i | 0.242907i | 0.992597 | + | 0.121453i | \(0.0387555\pi\) | ||||
−0.992597 | + | 0.121453i | \(0.961244\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7195.64 | − | 1531.21i | 1.09423 | − | 0.232849i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4032.35 | − | 6984.23i | −0.607989 | − | 1.05307i | −0.991571 | − | 0.129561i | \(-0.958643\pi\) |
0.383583 | − | 0.923507i | \(-0.374690\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4879.42 | − | 2817.13i | −0.729500 | − | 0.421177i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4979.84 | − | 8610.05i | 0.738267 | − | 1.27645i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5312.56 | + | 3067.21i | 0.781020 | + | 0.450922i | 0.836792 | − | 0.547522i | \(-0.184429\pi\) |
−0.0557719 | + | 0.998444i | \(0.517762\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1586.58 | + | 2748.04i | 0.231314 | + | 0.400648i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6214.20 | + | 3030.28i | 0.898515 | + | 0.438150i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9581.25i | 1.37399i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3351.77 | + | 1935.14i | −0.476733 | + | 0.275242i | −0.719054 | − | 0.694954i | \(-0.755425\pi\) |
0.242321 | + | 0.970196i | \(0.422091\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8523.76 | + | 1199.27i | −1.20252 | + | 0.169191i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7489.21 | + | 11083.0i | −1.04803 | + | 1.55094i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3644.06 | + | 6311.70i | −0.505851 | + | 0.876160i | 0.494126 | + | 0.869390i | \(0.335488\pi\) |
−0.999977 | + | 0.00676929i | \(0.997845\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −161.641 | − | 2309.03i | −0.0222589 | − | 0.317967i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2807.32 | 0.383513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3203.69 | −0.434201 | −0.217101 | − | 0.976149i | \(-0.569660\pi\) | ||||
−0.217101 | + | 0.976149i | \(0.569660\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 321.334 | + | 4590.23i | 0.0432085 | + | 0.617229i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2096.49 | − | 3631.22i | 0.279701 | − | 0.484456i | −0.691610 | − | 0.722272i | \(-0.743098\pi\) |
0.971310 | + | 0.237816i | \(0.0764314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −81.7588 | − | 167.991i | −0.0108229 | − | 0.0222379i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4505.52 | + | 633.914i | −0.591805 | + | 0.0832653i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5025.75 | + | 2901.62i | −0.655053 | + | 0.378195i | −0.790390 | − | 0.612605i | \(-0.790122\pi\) |
0.135336 | + | 0.990800i | \(0.456788\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 434.147i | − | 0.0561529i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7892.22 | + | 3848.55i | 1.01300 | + | 0.493978i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3135.11 | + | 5430.18i | 0.399354 | + | 0.691701i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13668.1 | + | 7891.30i | 1.72792 | + | 0.997614i | 0.898478 | + | 0.439018i | \(0.144673\pi\) |
0.829440 | + | 0.558596i | \(0.188660\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.40953 | + | 9638.87i | −0.000929675 | + | 1.20939i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6782.69 | − | 3915.99i | −0.844667 | − | 0.487669i | 0.0141808 | − | 0.999899i | \(-0.495486\pi\) |
−0.858848 | + | 0.512231i | \(0.828819\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7143.38 | − | 12372.7i | −0.882971 | − | 1.52935i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2612.43 | − | 10491.6i | 0.320525 | − | 1.28724i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 34.3972i | 0.00418921i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11913.3 | − | 6878.12i | 1.44028 | − | 0.831543i | 0.442408 | − | 0.896814i | \(-0.354124\pi\) |
0.997868 | + | 0.0652706i | \(0.0207911\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5604.34 | + | 8307.39i | 0.672607 | + | 0.997016i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8074.45 | + | 5456.22i | 0.962028 | + | 0.650080i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2901.69 | + | 5025.87i | −0.343225 | + | 0.594483i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2087.49 | + | 146.133i | −0.245144 | + | 0.0171610i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9478.94 | 1.10519 | 0.552597 | − | 0.833448i | \(-0.313637\pi\) | ||||
0.552597 | + | 0.833448i | \(0.313637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7360.46 | −0.852082 | −0.426041 | − | 0.904704i | \(-0.640092\pi\) | ||||
−0.426041 | + | 0.904704i | \(0.640092\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6349.19 | − | 15721.7i | 0.729806 | − | 1.80713i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4907.62 | + | 8500.26i | −0.560129 | + | 0.970172i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4376.51 | − | 309.753i | −0.496005 | − | 0.0351054i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 153.637 | − | 103.647i | 0.0172906 | − | 0.0116646i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −76.0396 | + | 43.9015i | −0.00849814 | + | 0.00490641i | −0.504243 | − | 0.863562i | \(-0.668228\pi\) |
0.495745 | + | 0.868468i | \(0.334895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1782.09i | − | 0.197787i | −0.995098 | − | 0.0988936i | \(-0.968470\pi\) | ||
0.995098 | − | 0.0988936i | \(-0.0315303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1808.36 | − | 3708.40i | 0.199320 | − | 0.408745i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 210.361 | + | 364.356i | 0.0230273 | + | 0.0398845i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8035.74 | + | 4639.44i | 0.873634 | + | 0.504393i | 0.868554 | − | 0.495595i | \(-0.165050\pi\) |
0.00507951 | + | 0.999987i | \(0.498383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4642.83 | + | 8013.13i | −0.501331 | + | 0.865256i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4831.09 | + | 2789.23i | 0.518131 | + | 0.299143i | 0.736170 | − | 0.676797i | \(-0.236633\pi\) |
−0.218039 | + | 0.975940i | \(0.569966\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4693.05 | + | 8128.61i | 0.499937 | + | 0.865917i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3662.34 | + | 7510.37i | −0.387523 | + | 0.794694i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5410.98i | − | 0.568730i | −0.958716 | − | 0.284365i | \(-0.908217\pi\) | ||
0.958716 | − | 0.284365i | \(-0.0917827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −187.792 | + | 108.422i | −0.0196071 | + | 0.0113201i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1578.95 | + | 1065.19i | −0.163765 | + | 0.110479i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14367.4 | + | 1016.87i | 1.48034 | + | 0.104773i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3971.67 | − | 6879.13i | 0.406536 | − | 0.704140i | −0.587963 | − | 0.808888i | \(-0.700070\pi\) |
0.994499 | + | 0.104747i | \(0.0334034\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10773.8 | − | 9705.25i | 1.09559 | − | 0.986933i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2715.21 | −0.274317 | −0.137159 | − | 0.990549i | \(-0.543797\pi\) | ||||
−0.137159 | + | 0.990549i | \(0.543797\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11587.7 | −1.16313 | −0.581563 | − | 0.813502i | \(-0.697558\pi\) | ||||
−0.581563 | + | 0.813502i | \(0.697558\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20945.5 | + | 1466.26i | −2.08887 | + | 0.146229i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1879.76 | − | 3255.83i | 0.186263 | − | 0.322617i | −0.757738 | − | 0.652558i | \(-0.773696\pi\) |
0.944001 | + | 0.329942i | \(0.107029\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4583.88 | + | 3097.51i | 0.451309 | + | 0.304968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1243.59 | − | 1843.39i | −0.121659 | − | 0.180337i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −99.2639 | + | 57.3100i | −0.00964938 | + | 0.00557107i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 9511.73i | − | 0.918796i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15364.8 | + | 12008.1i | −1.47486 | + | 1.15265i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2666.10 | − | 4617.82i | −0.254316 | − | 0.440488i | 0.710394 | − | 0.703804i | \(-0.248517\pi\) |
−0.964709 | + | 0.263317i | \(0.915184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2296.53 | − | 1325.90i | −0.217698 | − | 0.125688i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.310736 | + | 404.228i | −2.92732e−5 | + | 0.0380808i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18394.6 | − | 10620.1i | −1.72217 | − | 0.994297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −521.790 | − | 903.766i | −0.0485514 | − | 0.0840935i | 0.840728 | − | 0.541457i | \(-0.182127\pi\) |
−0.889280 | + | 0.457364i | \(0.848794\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1088.23 | − | 530.662i | −0.100637 | − | 0.0490744i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13213.2i | − | 1.21446i | −0.794525 | − | 0.607232i | \(-0.792280\pi\) | ||
0.794525 | − | 0.607232i | \(-0.207720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4792.05 | − | 2766.69i | 0.437775 | − | 0.252750i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −37.9483 | − | 269.716i | −0.00344575 | − | 0.0244906i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3078.90 | + | 6326.26i | 0.277883 | + | 0.570969i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 874.489 | − | 1514.66i | 0.0784519 | − | 0.135883i | −0.824130 | − | 0.566400i | \(-0.808336\pi\) |
0.902582 | + | 0.430518i | \(0.141669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −367.893 | − | 5255.33i | −0.0328069 | − | 0.468644i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12215.5 | −1.08283 | −0.541414 | − | 0.840756i | \(-0.682111\pi\) | ||||
−0.541414 | + | 0.840756i | \(0.682111\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13215.7 | 1.16454 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 200.544 | + | 2864.76i | 0.0175670 | + | 0.250943i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8483.69 | + | 14694.2i | −0.738768 | + | 1.27958i | 0.214282 | + | 0.976772i | \(0.431259\pi\) |
−0.953050 | + | 0.302812i | \(0.902074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6698.82 | − | 9913.31i | 0.579918 | − | 0.858198i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4339.28 | + | 13365.4i | −0.373458 | + | 1.15029i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15832.1 | − | 9140.66i | 1.35465 | − | 0.782108i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 427.136i | − | 0.0363355i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15479.1 | − | 7548.18i | −1.30916 | − | 0.638397i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2103.60 | + | 3643.55i | 0.176892 | + | 0.306385i | 0.940814 | − | 0.338922i | \(-0.110062\pi\) |
−0.763923 | + | 0.645308i | \(0.776729\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5104.44 | − | 2947.05i | −0.426772 | − | 0.246397i | 0.271199 | − | 0.962523i | \(-0.412580\pi\) |
−0.697970 | + | 0.716127i | \(0.745913\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4575.50 | − | 7910.95i | 0.380364 | − | 0.657643i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24387.3 | − | 14080.0i | −2.01580 | − | 1.16382i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6074.68 | − | 10521.7i | −0.499275 | − | 0.864770i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8748.44 | + | 11194.0i | 0.714972 | + | 0.914833i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 16717.2i | − | 1.35854i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8687.20 | + | 5015.56i | −0.702019 | + | 0.405311i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4013.34 | + | 5949.04i | 0.322511 | + | 0.478064i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −32.8598 | + | 230.975i | −0.00262592 | + | 0.0184579i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8059.86 | + | 13960.1i | −0.640518 | + | 1.10941i | 0.344799 | + | 0.938677i | \(0.387947\pi\) |
−0.985317 | + | 0.170734i | \(0.945386\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8077.79 | − | 565.477i | 0.638400 | − | 0.0446905i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14748.4 | 1.15918 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14061.3 | 1.09912 | 0.549558 | − | 0.835456i | \(-0.314796\pi\) | ||||
0.549558 | + | 0.835456i | \(0.314796\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5930.92 | − | 2395.19i | −0.461066 | − | 0.186201i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2681.14 | + | 4643.87i | −0.207296 | + | 0.359048i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 552.786 | − | 7810.32i | 0.0425079 | − | 0.600594i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3230.81 | + | 2179.57i | −0.247099 | + | 0.166698i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7010.50 | − | 4047.52i | 0.533294 | − | 0.307897i | −0.209063 | − | 0.977902i | \(-0.567041\pi\) |
0.742357 | + | 0.670005i | \(0.233708\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8836.46i | − | 0.668591i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 160.110 | − | 328.337i | 0.0120496 | − | 0.0247102i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5149.34 | + | 8918.92i | 0.385469 | + | 0.667651i | 0.991834 | − | 0.127535i | \(-0.0407065\pi\) |
−0.606366 | + | 0.795186i | \(0.707373\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9092.60 | + | 5249.62i | 0.677042 | + | 0.390890i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10038.3 | + | 9028.71i | −0.743505 | + | 0.668730i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2507.30 | − | 1447.59i | −0.184730 | − | 0.106654i | 0.404783 | − | 0.914413i | \(-0.367347\pi\) |
−0.589513 | + | 0.807759i | \(0.700680\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 310.198 | + | 537.278i | 0.0227345 | + | 0.0393772i | 0.877169 | − | 0.480182i | \(-0.159429\pi\) |
−0.854434 | + | 0.519559i | \(0.826096\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4955.82 | − | 10162.9i | 0.361313 | − | 0.740946i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 398.897i | − | 0.0289307i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8241.62 | + | 4758.30i | −0.594633 | + | 0.343312i | −0.766927 | − | 0.641734i | \(-0.778215\pi\) |
0.172294 | + | 0.985046i | \(0.444882\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15073.4 | + | 10168.8i | −1.08191 | + | 0.729881i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6516.14 | − | 3171.32i | 0.465293 | − | 0.226452i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −245.627 | + | 425.438i | −0.0174491 | + | 0.0302227i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19470.3 | + | 7863.05i | 1.37607 | + | 0.555722i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1093.47 | −0.0768861 | −0.0384431 | − | 0.999261i | \(-0.512240\pi\) | ||||
−0.0384431 | + | 0.999261i | \(0.512240\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27289.2 | 1.90905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6727.65 | − | 470.962i | 0.468255 | − | 0.0327796i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4882.36 | + | 8456.49i | −0.338102 | + | 0.585610i | −0.984076 | − | 0.177750i | \(-0.943118\pi\) |
0.645974 | + | 0.763360i | \(0.276451\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25527.1 | − | 12423.7i | 1.75884 | − | 0.856004i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10277.3 | − | 15234.2i | −0.704561 | − | 1.04438i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12740.2 | + | 7355.53i | −0.869029 | + | 0.501734i | −0.867026 | − | 0.498264i | \(-0.833971\pi\) |
−0.00200376 | + | 0.999998i | \(0.500638\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14047.5i | 0.953425i | 0.879059 | + | 0.476713i | \(0.158172\pi\) | ||||
−0.879059 | + | 0.476713i | \(0.841828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4966.51 | + | 6354.83i | 0.335409 | + | 0.429169i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9866.74 | + | 17089.7i | 0.663041 | + | 1.14842i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14931.5 | − | 8620.73i | −0.998439 | − | 0.576449i | −0.0906530 | − | 0.995883i | \(-0.528895\pi\) |
−0.907786 | + | 0.419434i | \(0.862229\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4463.79 | + | 2572.60i | −0.297015 | + | 0.171177i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28517.7 | + | 16464.7i | 1.88822 | + | 1.09017i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3608.26 | − | 6249.69i | −0.237742 | − | 0.411782i | 0.722324 | − | 0.691555i | \(-0.243074\pi\) |
−0.960066 | + | 0.279773i | \(0.909741\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22083.0 | − | 10768.5i | −1.44793 | − | 0.706063i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25662.2i | 1.67443i | 0.546877 | + | 0.837213i | \(0.315817\pi\) | ||||
−0.546877 | + | 0.837213i | \(0.684183\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10818.3 | + | 6245.96i | −0.702464 | + | 0.405568i | −0.808265 | − | 0.588820i | \(-0.799593\pi\) |
0.105800 | + | 0.994387i | \(0.466260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −181.978 | + | 560.509i | −0.0117593 | + | 0.0362197i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 827.484 | − | 11691.5i | 0.0532142 | − | 0.751863i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9238.65 | − | 16001.8i | 0.591273 | − | 1.02412i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.7208 | + | 353.135i | 0.00157457 | + | 0.0224926i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5226.85 | −0.331332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11952.7 | −0.754091 | −0.377046 | − | 0.926195i | \(-0.623060\pi\) | ||||
−0.377046 | + | 0.926195i | \(0.623060\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 773.267 | + | 11046.1i | 0.0485539 | + | 0.693588i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6566.90 | + | 11374.2i | −0.410393 | + | 0.710821i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14154.4 | − | 11097.2i | −0.880406 | − | 0.690249i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1429.07 | + | 10157.1i | 0.0884713 | + | 0.628806i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12156.4 | − | 7018.51i | 0.749063 | − | 0.432472i | −0.0762922 | − | 0.997086i | \(-0.524308\pi\) |
0.825355 | + | 0.564614i | \(0.190975\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12089.9i | 0.741493i | 0.928734 | + | 0.370747i | \(0.120898\pi\) | ||||
−0.928734 | + | 0.370747i | \(0.879102\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11672.7 | − | 5692.06i | −0.712579 | − | 0.347480i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2411.27 | − | 4176.44i | −0.146517 | − | 0.253775i | 0.783421 | − | 0.621492i | \(-0.213473\pi\) |
−0.929938 | + | 0.367716i | \(0.880140\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 309.951 | + | 178.950i | 0.0187467 | + | 0.0108234i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22696.6 | + | 13127.1i | 1.36643 | + | 0.790312i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2592.48 | − | 1496.77i | −0.155362 | − | 0.0896983i | 0.420303 | − | 0.907384i | \(-0.361924\pi\) |
−0.575666 | + | 0.817685i | \(0.695257\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12531.1 | + | 21704.4i | 0.747525 | + | 1.29475i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13743.2 | − | 10740.8i | 0.816096 | − | 0.637806i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4336.79i | 0.256354i | 0.991751 | + | 0.128177i | \(0.0409125\pi\) | ||||
−0.991751 | + | 0.128177i | \(0.959087\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16220.2 | − | 9364.73i | 0.954451 | − | 0.551053i | 0.0599904 | − | 0.998199i | \(-0.480893\pi\) |
0.894461 | + | 0.447146i | \(0.147560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15749.7 | + | 23346.0i | 0.922576 | + | 1.36755i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15403.7 | + | 22795.4i | −0.898243 | + | 1.32927i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −112.440 | + | 194.751i | −0.00652726 | + | 0.0113056i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31867.7 | + | 2230.86i | −1.84167 | + | 0.128924i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −161.134 | −0.00927053 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19919.4 | −1.14092 | −0.570459 | − | 0.821326i | \(-0.693235\pi\) | ||||
−0.570459 | + | 0.821326i | \(0.693235\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9899.00 | − | 8917.22i | 0.564463 | − | 0.508480i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15019.2 | − | 26014.1i | 0.852638 | − | 1.47681i | −0.0261815 | − | 0.999657i | \(-0.508335\pi\) |
0.878819 | − | 0.477155i | \(-0.158332\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11606.9 | + | 23848.9i | 0.656014 | + | 1.34792i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12793.3 | − | 8630.60i | 0.719882 | − | 0.485647i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3348.00 | + | 1932.97i | −0.187566 | + | 0.108291i | −0.590843 | − | 0.806787i | \(-0.701205\pi\) |
0.403277 | + | 0.915078i | \(0.367871\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28602.7i | 1.59541i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6519.78 | − | 13370.1i | 0.362074 | − | 0.742507i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18936.2 | − | 32798.5i | −1.04704 | − | 1.81353i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5762.10 | − | 3326.75i | −0.317222 | − | 0.183148i | 0.332931 | − | 0.942951i | \(-0.391962\pi\) |
−0.650154 | + | 0.759803i | \(0.725296\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −149.311 | + | 305.596i | −0.00818449 | + | 0.0167513i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5172.64 | − | 2986.42i | −0.282315 | − | 0.162995i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16475.3 | − | 28536.1i | −0.895332 | − | 1.55076i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13615.0 | − | 27920.2i | 0.736717 | − | 1.51079i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21100.3i | − | 1.13687i | −0.822728 | − | 0.568435i | \(-0.807549\pi\) | ||
0.822728 | − | 0.568435i | \(-0.192451\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4386.61 | − | 2532.61i | 0.235340 | − | 0.135874i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40119.3 | − | 27065.3i | 2.14324 | − | 1.44587i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13673.7 | − | 9239.87i | −0.727374 | − | 0.491515i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11715.1 | + | 20291.1i | −0.620548 | + | 1.07482i | 0.368836 | + | 0.929494i | \(0.379756\pi\) |
−0.989384 | + | 0.145326i | \(0.953577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4274.46 | − | 10584.3i | 0.225464 | − | 0.558289i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1144.44 | 0.0601114 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 528.981 | 0.0276682 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28881.4 | − | 2021.81i | 1.50432 | − | 0.105308i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4247.60 | − | 7357.06i | 0.220318 | − | 0.381603i | −0.734586 | − | 0.678515i | \(-0.762624\pi\) |
0.954905 | + | 0.296913i | \(0.0959571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22771.6 | − | 1611.69i | −1.17622 | − | 0.0832489i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12050.1 | − | 17862.1i | −0.619846 | − | 0.918808i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4402.96 | − | 2542.05i | 0.225547 | − | 0.130220i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2662.18i | 0.135811i | 0.997692 | + | 0.0679057i | \(0.0216317\pi\) | ||||
−0.997692 | + | 0.0679057i | \(0.978368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17977.6 | + | 8014.07i | −0.913358 | + | 0.407157i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8708.57 | − | 15083.7i | −0.440627 | − | 0.763188i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17425.1 | − | 10060.4i | −0.878052 | − | 0.506943i | −0.00803608 | − | 0.999968i | \(-0.502558\pi\) |
−0.870015 | + | 0.493024i | \(0.835891\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −23776.8 | + | 11549.3i | −1.19323 | + | 0.579593i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 175.960 | + | 101.590i | 0.00879453 | + | 0.00507752i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4889.49 | + | 8468.84i | 0.243387 | + | 0.421558i | 0.961677 | − | 0.274186i | \(-0.0884083\pi\) |
−0.718290 | + | 0.695744i | \(0.755075\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24529.9 | − | 11961.7i | −1.21610 | − | 0.593015i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35045.8i | 1.73043i | 0.501404 | + | 0.865213i | \(0.332817\pi\) | ||||
−0.501404 | + | 0.865213i | \(0.667183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20654.3 | + | 11924.8i | −1.01572 | + | 0.586429i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10461.9 | − | 1471.96i | 0.512425 | − | 0.0720969i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12495.0 | + | 884.348i | 0.609554 | + | 0.0431420i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10043.6 | + | 17396.0i | −0.488011 | + | 0.845260i | −0.999905 | − | 0.0137887i | \(-0.995611\pi\) |
0.511894 | + | 0.859049i | \(0.328944\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2761.88 | + | 39453.2i | 0.133663 | + | 1.90937i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5436.39 | −0.262054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2813.68 | −0.135092 | −0.0675462 | − | 0.997716i | \(-0.521517\pi\) | ||||
−0.0675462 | + | 0.997716i | \(0.521517\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.03672 | + | 14.8095i | 4.95793e−5 | + | 0.000708237i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10857.5 | − | 18805.7i | 0.517191 | − | 0.895801i | −0.482610 | − | 0.875836i | \(-0.660311\pi\) |
0.999801 | − | 0.0199656i | \(-0.00635567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15259.6 | − | 10311.5i | −0.724028 | − | 0.489254i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 40984.8 | − | 5766.45i | 1.93700 | − | 0.272531i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23895.2 | + | 13795.9i | −1.12491 | + | 0.649467i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15956.6i | 0.748257i | 0.927377 | + | 0.374128i | \(0.122058\pi\) | ||||
−0.927377 | + | 0.374128i | \(0.877942\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10973.3 | − | 5351.00i | −0.512573 | − | 0.249950i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3910.77 | − | 6773.65i | −0.181967 | − | 0.315176i | 0.760583 | − | 0.649240i | \(-0.224913\pi\) |
−0.942550 | + | 0.334064i | \(0.891580\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22407.1 | − | 12936.8i | −1.03857 | − | 0.599616i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4866.64 | + | 3.74105i | 0.224697 | + | 0.000172728i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27653.6 | + | 15965.8i | 1.27188 | + | 0.734320i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 129.197 | + | 223.776i | 0.00591939 | + | 0.0102527i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7346.50 | + | 1563.31i | −0.335304 | + | 0.0713516i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6346.88i | − | 0.288573i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21587.3 | + | 12463.4i | −0.977767 | + | 0.564514i | −0.901595 | − | 0.432581i | \(-0.857603\pi\) |
−0.0761716 | + | 0.997095i | \(0.524270\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14903.3 | − | 22091.5i | −0.672463 | − | 0.996802i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5737.42 | − | 11788.7i | −0.257900 | − | 0.529910i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6211.21 | − | 10758.1i | 0.278142 | − | 0.481756i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −55523.9 | + | 3886.89i | −2.47702 | + | 0.173401i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16452.6 | 0.731217 | 0.365609 | − | 0.930769i | \(-0.380861\pi\) | ||||
0.365609 | + | 0.930769i | \(0.380861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 64905.7 | 2.87384 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6398.58 | − | 15844.0i | 0.282250 | − | 0.698903i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 219.704 | − | 380.539i | 0.00965528 | − | 0.0167234i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −645.992 | + | 955.978i | −0.0282835 | + | 0.0418557i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −174.485 | + | 117.711i | −0.00761109 | + | 0.00513459i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8105.17 | − | 4679.52i | 0.352240 | − | 0.203366i | −0.313431 | − | 0.949611i | \(-0.601479\pi\) |
0.665672 | + | 0.746245i | \(0.268145\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6805.42i | − | 0.294662i | −0.989087 | − | 0.147331i | \(-0.952932\pi\) | ||
0.989087 | − | 0.147331i | \(-0.0470682\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7384.10 | − | 15142.6i | 0.318539 | − | 0.653228i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1727.86 | − | 2992.74i | −0.0742630 | − | 0.128627i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14617.3 | + | 8439.27i | 0.625940 | + | 0.361387i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14647.6 | − | 21748.4i | −0.624944 | − | 0.927902i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23251.5 | + | 13424.3i | 0.988407 | + | 0.570657i | 0.904798 | − | 0.425841i | \(-0.140022\pi\) |
0.0836095 | + | 0.996499i | \(0.473355\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7846.13 | + | 13589.9i | 0.332319 | + | 0.575594i | 0.982966 | − | 0.183786i | \(-0.0588355\pi\) |
−0.650647 | + | 0.759381i | \(0.725502\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 147.109 | − | 301.678i | 0.00620811 | − | 0.0127310i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17201.9i | 0.723301i | 0.932314 | + | 0.361650i | \(0.117787\pi\) | ||||
−0.932314 | + | 0.361650i | \(0.882213\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16605.1 | − | 9586.94i | 0.695679 | − | 0.401650i | −0.110057 | − | 0.993925i | \(-0.535103\pi\) |
0.805736 | + | 0.592275i | \(0.201770\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9544.31 | − | 6438.78i | 0.398422 | − | 0.268783i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −35098.0 | − | 4993.23i | −1.45987 | − | 0.207689i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7518.41 | − | 13022.3i | 0.311599 | − | 0.539706i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 25583.6 | + | 28400.3i | 1.05651 | + | 1.17283i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10848.7 | 0.446410 | 0.223205 | − | 0.974771i | \(-0.428348\pi\) | ||||
0.223205 | + | 0.974771i | \(0.428348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21522.8 | 0.882481 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30490.8 | − | 2134.48i | 1.24574 | − | 0.0872068i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4098.40 | + | 7098.63i | −0.166851 | + | 0.288994i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1739.71 | − | 24580.4i | 0.0705753 | − | 0.997158i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4442.02 | + | 6584.48i | 0.179564 | + | 0.266171i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 183.963 | − | 106.211i | 0.00741029 | − | 0.00427833i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42970.3i | 1.72482i | 0.506207 | + | 0.862412i | \(0.331047\pi\) | ||||
−0.506207 | + | 0.862412i | \(0.668953\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −31602.2 | + | 24698.2i | −1.26406 | + | 0.987906i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18302.7 | + | 31701.2i | 0.729532 | + | 1.26359i | 0.957081 | + | 0.289820i | \(0.0935955\pi\) |
−0.227549 | + | 0.973767i | \(0.573071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8607.79 | − | 4969.71i | −0.341902 | − | 0.197397i | 0.319211 | − | 0.947684i | \(-0.396582\pi\) |
−0.661113 | + | 0.750286i | \(0.729916\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15319.5 | + | 26581.3i | 0.606373 | + | 1.05214i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11425.0 | + | 6596.25i | 0.450652 | + | 0.260184i | 0.708106 | − | 0.706106i | \(-0.249550\pi\) |
−0.257453 | + | 0.966291i | \(0.582883\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24577.2 | − | 42569.0i | −0.966071 | − | 1.67328i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26946.7 | + | 13140.2i | 1.05555 | + | 0.514725i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 287.561i | − | 0.0112254i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13565.4 | + | 7831.97i | −0.527721 | + | 0.304680i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5387.35 | + | 38290.4i | 0.208859 | + | 1.48446i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7418.13 | + | 3610.30i | −0.286604 | + | 0.139486i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4666.37 | + | 8082.39i | −0.179672 | + | 0.311201i | −0.941768 | − | 0.336263i | \(-0.890837\pi\) |
0.762096 | + | 0.647464i | \(0.224170\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2191.10 | − | 31299.7i | −0.0840773 | − | 1.20104i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22655.3 | −0.866376 | −0.433188 | − | 0.901304i | \(-0.642611\pi\) | ||||
−0.433188 | + | 0.901304i | \(0.642611\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32700.9 | 1.24629 | 0.623145 | − | 0.782107i | \(-0.285855\pi\) | ||||
0.623145 | + | 0.782107i | \(0.285855\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2831.77 | + | 40451.7i | 0.107558 | + | 1.53646i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12678.9 | − | 21960.5i | 0.479950 | − | 0.831299i | −0.519785 | − | 0.854297i | \(-0.673988\pi\) |
0.999735 | + | 0.0229985i | \(0.00732131\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14746.9 | − | 7177.10i | 0.556349 | − | 0.270768i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −344.337 | + | 356.790i | −0.0129469 | + | 0.0134152i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −54471.8 | + | 31449.3i | −2.04124 | + | 1.17851i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20482.8i | 0.764989i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1028.72 | − | 501.642i | −0.0382920 | − | 0.0186726i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7293.15 | + | 12632.1i | 0.270568 | + | 0.468637i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64647.7 | − | 37324.4i | −2.39037 | − | 1.38008i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8097.63 | + | 14050.4i | 0.298419 | + | 0.517796i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20016.1 | + | 11556.3i | 0.735202 | + | 0.424469i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22286.5 | + | 38601.3i | 0.815888 | + | 1.41316i | 0.908688 | + | 0.417475i | \(0.137085\pi\) |
−0.0928000 | + | 0.995685i | \(0.529582\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14815.1 | − | 18956.5i | −0.540578 | − | 0.691690i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 581.992i | 0.0211660i | 0.999944 | + | 0.0105830i | \(0.00336874\pi\) | ||||
−0.999944 | + | 0.0105830i | \(0.996631\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 230.493 | − | 133.075i | 0.00835510 | − | 0.00482382i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10210.2 | − | 15134.8i | −0.368895 | − | 0.546819i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2209.49 | − | 31217.9i | 0.0795679 | − | 1.12421i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20983.4 | − | 36344.4i | 0.753188 | − | 1.30456i | −0.193082 | − | 0.981183i | \(-0.561848\pi\) |
0.946270 | − | 0.323377i | \(-0.104818\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 37486.7 | − | 2624.22i | 1.34118 | − | 0.0938880i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −19920.5 | −0.710393 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4802.45 | −0.170707 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30859.4 | − | 12462.5i | −1.09337 | − | 0.441556i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.0320 | − | 60.6772i | 0.00123720 | − | 0.00214290i | −0.865406 | − | 0.501071i | \(-0.832940\pi\) |
0.866643 | + | 0.498928i | \(0.166273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31875.2 | − | 12815.8i | 1.12209 | − | 0.451149i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7400.43 | + | 4992.48i | −0.259677 | + | 0.175184i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 902.961 | − | 521.325i | 0.0315829 | − | 0.0182344i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26725.4i | − | 0.931783i | −0.884842 | − | 0.465892i | \(-0.845734\pi\) | ||
0.884842 | − | 0.465892i | \(-0.154266\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12591.2 | + | 25820.9i | −0.437592 | + | 0.897371i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19532.8 | + | 33831.7i | 0.676673 | + | 1.17203i | 0.975977 | + | 0.217875i | \(0.0699124\pi\) |
−0.299303 | + | 0.954158i | \(0.596754\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1159.72 | + | 669.564i | 0.0400484 | + | 0.0231220i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −38164.5 | + | 5339.72i | −1.31375 | + | 0.183811i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25718.0 | − | 14848.3i | −0.882495 | − | 0.509509i | −0.0110151 | − | 0.999939i | \(-0.503506\pi\) |
−0.871480 | + | 0.490430i | \(0.836840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16937.8 | + | 29337.1i | 0.579371 | + | 1.00350i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4054.27 | − | 8314.11i | 0.138243 | − | 0.283495i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29039.6i | 0.987079i | 0.869723 | + | 0.493539i | \(0.164297\pi\) | ||||
−0.869723 | + | 0.493539i | \(0.835703\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27949.0 | − | 16136.4i | 0.947026 | − | 0.546766i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −156.859 | + | 105.820i | −0.00529835 | + | 0.00357437i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19997.9 | − | 29594.1i | 0.673373 | − | 0.996499i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22220.1 | − | 38486.4i | 0.745867 | − | 1.29188i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16932.8 | + | 6838.28i | 0.566617 | + | 0.228827i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −51898.3 | −1.73126 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10669.9 | −0.354831 | −0.177416 | − | 0.984136i | \(-0.556774\pi\) | ||||
−0.177416 | + | 0.984136i | \(0.556774\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −53660.8 | + | 3756.46i | −1.77898 | + | 0.124536i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20680.1 | − | 35819.0i | 0.683478 | − | 1.18382i | −0.290435 | − | 0.956895i | \(-0.593800\pi\) |
0.973913 | − | 0.226923i | \(-0.0728667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3263.92 | + | 6706.42i | 0.107540 | + | 0.220964i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14470.9 | + | 21450.4i | 0.475323 | + | 0.704578i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31547.9 | − | 18214.2i | 1.03307 | − | 0.596443i | 0.115207 | − | 0.993342i | \(-0.463247\pi\) |
0.917862 | + | 0.396899i | \(0.129914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 430.459i | − | 0.0140526i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16533.3 | − | 21155.0i | −0.538092 | − | 0.688508i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 362.416 | + | 627.723i | 0.0117592 | + | 0.0203675i | 0.871845 | − | 0.489782i | \(-0.162924\pi\) |
−0.860086 | + | 0.510149i | \(0.829590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16670.6 | + | 9624.75i | 0.539257 | + | 0.311340i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −60432.8 | − | 46.4555i | −1.94893 | − | 0.00149817i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 613.008 | + | 353.921i | 0.0197093 | + | 0.0113792i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14449.0 | − | 25026.5i | −0.463157 | − | 0.802212i | 0.535959 | − | 0.844244i | \(-0.319950\pi\) |
−0.999116 | + | 0.0420324i | \(0.986617\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −30074.4 | − | 14665.4i | −0.961109 | − | 0.468673i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 52452.2i | − | 1.67120i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8836.00 | + | 5101.46i | −0.280681 | + | 0.162051i | −0.633732 | − | 0.773553i | \(-0.718478\pi\) |
0.353051 | + | 0.935604i | \(0.385144\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6748.16 | + | 2190.89i | 0.213716 | + | 0.0693862i |
(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 | 84.4.k.c.5.4 | ✓ | 12 | |
3.2 | odd | 2 | inner | 84.4.k.c.5.6 | yes | 12 | |
4.3 | odd | 2 | 336.4.bc.c.257.3 | 12 | |||
7.2 | even | 3 | 588.4.f.c.293.10 | 12 | |||
7.3 | odd | 6 | inner | 84.4.k.c.17.6 | yes | 12 | |
7.4 | even | 3 | 588.4.k.c.521.1 | 12 | |||
7.5 | odd | 6 | 588.4.f.c.293.3 | 12 | |||
7.6 | odd | 2 | 588.4.k.c.509.3 | 12 | |||
12.11 | even | 2 | 336.4.bc.c.257.1 | 12 | |||
21.2 | odd | 6 | 588.4.f.c.293.4 | 12 | |||
21.5 | even | 6 | 588.4.f.c.293.9 | 12 | |||
21.11 | odd | 6 | 588.4.k.c.521.3 | 12 | |||
21.17 | even | 6 | inner | 84.4.k.c.17.4 | yes | 12 | |
21.20 | even | 2 | 588.4.k.c.509.1 | 12 | |||
28.3 | even | 6 | 336.4.bc.c.17.1 | 12 | |||
84.59 | odd | 6 | 336.4.bc.c.17.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.k.c.5.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
84.4.k.c.5.6 | yes | 12 | 3.2 | odd | 2 | inner | |
84.4.k.c.17.4 | yes | 12 | 21.17 | even | 6 | inner | |
84.4.k.c.17.6 | yes | 12 | 7.3 | odd | 6 | inner | |
336.4.bc.c.17.1 | 12 | 28.3 | even | 6 | |||
336.4.bc.c.17.3 | 12 | 84.59 | odd | 6 | |||
336.4.bc.c.257.1 | 12 | 12.11 | even | 2 | |||
336.4.bc.c.257.3 | 12 | 4.3 | odd | 2 | |||
588.4.f.c.293.3 | 12 | 7.5 | odd | 6 | |||
588.4.f.c.293.4 | 12 | 21.2 | odd | 6 | |||
588.4.f.c.293.9 | 12 | 21.5 | even | 6 | |||
588.4.f.c.293.10 | 12 | 7.2 | even | 3 | |||
588.4.k.c.509.1 | 12 | 21.20 | even | 2 | |||
588.4.k.c.509.3 | 12 | 7.6 | odd | 2 | |||
588.4.k.c.521.1 | 12 | 7.4 | even | 3 | |||
588.4.k.c.521.3 | 12 | 21.11 | odd | 6 |