Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,4,Mod(253,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.253");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.7369626429\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} - 2 x^{19} - 5 x^{18} - 26 x^{17} + 122 x^{16} + 124 x^{15} - 276 x^{14} - 1376 x^{13} + \cdots + 1073741824 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{31}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 253.13 | ||
Root | \(2.78865 + 0.472666i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.253 |
Dual form | 504.4.c.e.253.14 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.472666 | − | 2.78865i | 0.167113 | − | 0.985938i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.55317 | − | 2.63620i | −0.944147 | − | 0.329525i | ||||
\(5\) | 8.98099i | 0.803284i | 0.915797 | + | 0.401642i | \(0.131560\pi\) | ||||
−0.915797 | + | 0.401642i | \(0.868440\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | −10.9216 | + | 19.8171i | −0.482670 | + | 0.875802i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 25.0449 | + | 4.24501i | 0.791988 | + | 0.134239i | ||||
\(11\) | − | 58.9468i | − | 1.61574i | −0.589362 | − | 0.807869i | \(-0.700621\pi\) | ||
0.589362 | − | 0.807869i | \(-0.299379\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54.8428i | 1.17005i | 0.811015 | + | 0.585025i | \(0.198915\pi\) | ||||
−0.811015 | + | 0.585025i | \(0.801085\pi\) | |||||||
\(14\) | −3.30866 | + | 19.5206i | −0.0631626 | + | 0.372649i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 50.1009 | + | 39.8234i | 0.782826 | + | 0.622240i | ||||
\(17\) | 111.971 | 1.59747 | 0.798734 | − | 0.601684i | \(-0.205503\pi\) | ||||
0.798734 | + | 0.601684i | \(0.205503\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38.6067i | 0.466157i | 0.972458 | + | 0.233078i | \(0.0748798\pi\) | ||||
−0.972458 | + | 0.233078i | \(0.925120\pi\) | |||||||
\(20\) | 23.6757 | − | 67.8350i | 0.264703 | − | 0.758418i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −164.382 | − | 27.8621i | −1.59302 | − | 0.270010i | ||||
\(23\) | −112.146 | −1.01670 | −0.508350 | − | 0.861151i | \(-0.669744\pi\) | ||||
−0.508350 | + | 0.861151i | \(0.669744\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.3418 | 0.354734 | ||||||||
\(26\) | 152.937 | + | 25.9223i | 1.15360 | + | 0.195530i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 52.8722 | + | 18.4534i | 0.356854 | + | 0.124549i | ||||
\(29\) | − | 234.402i | − | 1.50094i | −0.660902 | − | 0.750472i | \(-0.729826\pi\) | ||
0.660902 | − | 0.750472i | \(-0.270174\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −180.033 | −1.04306 | −0.521529 | − | 0.853234i | \(-0.674638\pi\) | ||||
−0.521529 | + | 0.853234i | \(0.674638\pi\) | |||||||
\(32\) | 134.735 | − | 120.891i | 0.744311 | − | 0.667834i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 52.9249 | − | 312.248i | 0.266957 | − | 1.57500i | ||||
\(35\) | − | 62.8669i | − | 0.303613i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 131.345i | − | 0.583594i | −0.956480 | − | 0.291797i | \(-0.905747\pi\) | ||
0.956480 | − | 0.291797i | \(-0.0942532\pi\) | |||||||
\(38\) | 107.661 | + | 18.2480i | 0.459601 | + | 0.0779006i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −177.978 | − | 98.0866i | −0.703518 | − | 0.387721i | ||||
\(41\) | 500.500 | 1.90646 | 0.953231 | − | 0.302242i | \(-0.0977350\pi\) | ||||
0.953231 | + | 0.302242i | \(0.0977350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 495.083i | − | 1.75580i | −0.478844 | − | 0.877900i | \(-0.658944\pi\) | ||
0.478844 | − | 0.877900i | \(-0.341056\pi\) | |||||||
\(44\) | −155.396 | + | 445.235i | −0.532426 | + | 1.52549i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −53.0077 | + | 312.737i | −0.169903 | + | 1.00240i | ||||
\(47\) | −111.705 | −0.346677 | −0.173338 | − | 0.984862i | \(-0.555455\pi\) | ||||
−0.173338 | + | 0.984862i | \(0.555455\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 20.9588 | − | 123.654i | 0.0592806 | − | 0.349746i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 144.577 | − | 414.237i | 0.385561 | − | 1.10470i | ||||
\(53\) | − | 696.410i | − | 1.80489i | −0.430804 | − | 0.902445i | \(-0.641770\pi\) | ||
0.430804 | − | 0.902445i | \(-0.358230\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 529.400 | 1.29790 | ||||||||
\(56\) | 76.4511 | − | 138.720i | 0.182432 | − | 0.331022i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −653.666 | − | 110.794i | −1.47984 | − | 0.250827i | ||||
\(59\) | − | 407.787i | − | 0.899819i | −0.893074 | − | 0.449909i | \(-0.851456\pi\) | ||
0.893074 | − | 0.449909i | \(-0.148544\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 124.411i | 0.261134i | 0.991440 | + | 0.130567i | \(0.0416797\pi\) | ||||
−0.991440 | + | 0.130567i | \(0.958320\pi\) | |||||||
\(62\) | −85.0952 | + | 502.048i | −0.174308 | + | 1.02839i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −273.438 | − | 432.869i | −0.534059 | − | 0.845447i | ||||
\(65\) | −492.542 | −0.939882 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 143.848i | 0.262296i | 0.991363 | + | 0.131148i | \(0.0418663\pi\) | ||||
−0.991363 | + | 0.131148i | \(0.958134\pi\) | |||||||
\(68\) | −845.736 | − | 295.178i | −1.50824 | − | 0.526406i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −175.314 | − | 29.7151i | −0.299343 | − | 0.0507376i | ||||
\(71\) | −251.341 | −0.420122 | −0.210061 | − | 0.977688i | \(-0.567366\pi\) | ||||
−0.210061 | + | 0.977688i | \(0.567366\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −709.691 | −1.13785 | −0.568925 | − | 0.822390i | \(-0.692640\pi\) | ||||
−0.568925 | + | 0.822390i | \(0.692640\pi\) | |||||||
\(74\) | −366.276 | − | 62.0823i | −0.575387 | − | 0.0975259i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 101.775 | − | 291.603i | 0.153610 | − | 0.440120i | ||||
\(77\) | 412.627i | 0.610691i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 865.909 | 1.23319 | 0.616597 | − | 0.787279i | \(-0.288511\pi\) | ||||
0.616597 | + | 0.787279i | \(0.288511\pi\) | |||||||
\(80\) | −357.654 | + | 449.956i | −0.499836 | + | 0.628832i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 236.569 | − | 1395.72i | 0.318594 | − | 1.87965i | ||||
\(83\) | 57.3886i | 0.0758942i | 0.999280 | + | 0.0379471i | \(0.0120818\pi\) | ||||
−0.999280 | + | 0.0379471i | \(0.987918\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1005.61i | 1.28322i | ||||||||
\(86\) | −1380.61 | − | 234.009i | −1.73111 | − | 0.293416i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1168.16 | + | 643.792i | 1.41507 | + | 0.779869i | ||||
\(89\) | 765.447 | 0.911654 | 0.455827 | − | 0.890068i | \(-0.349344\pi\) | ||||
0.455827 | + | 0.890068i | \(0.349344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 383.899i | − | 0.442237i | ||||||
\(92\) | 847.060 | + | 295.640i | 0.959914 | + | 0.335028i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −52.7990 | + | 311.506i | −0.0579340 | + | 0.341802i | ||||
\(95\) | −346.726 | −0.374456 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 370.748 | 0.388080 | 0.194040 | − | 0.980994i | \(-0.437841\pi\) | ||||
0.194040 | + | 0.980994i | \(0.437841\pi\) | |||||||
\(98\) | 23.1606 | − | 136.644i | 0.0238732 | − | 0.140848i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −334.921 | − | 116.894i | −0.334921 | − | 0.116894i | ||||
\(101\) | 621.424i | 0.612218i | 0.951997 | + | 0.306109i | \(0.0990272\pi\) | ||||
−0.951997 | + | 0.306109i | \(0.900973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 433.871 | 0.415054 | 0.207527 | − | 0.978229i | \(-0.433458\pi\) | ||||
0.207527 | + | 0.978229i | \(0.433458\pi\) | |||||||
\(104\) | −1086.83 | − | 598.970i | −1.02473 | − | 0.564748i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1942.04 | − | 329.169i | −1.77951 | − | 0.301620i | ||||
\(107\) | − | 926.967i | − | 0.837508i | −0.908100 | − | 0.418754i | \(-0.862467\pi\) | ||
0.908100 | − | 0.418754i | \(-0.137533\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1423.90i | − | 1.25123i | −0.780131 | − | 0.625617i | \(-0.784847\pi\) | ||
0.780131 | − | 0.625617i | \(-0.215153\pi\) | |||||||
\(110\) | 250.229 | − | 1476.31i | 0.216895 | − | 1.27965i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −350.706 | − | 278.764i | −0.295880 | − | 0.235185i | ||||
\(113\) | 2027.39 | 1.68779 | 0.843897 | − | 0.536505i | \(-0.180256\pi\) | ||||
0.843897 | + | 0.536505i | \(0.180256\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1007.18i | − | 0.816699i | ||||||
\(116\) | −617.931 | + | 1770.48i | −0.494599 | + | 1.41711i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1137.18 | − | 192.747i | −0.887165 | − | 0.150371i | ||||
\(119\) | −783.797 | −0.603786 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2143.72 | −1.61061 | ||||||||
\(122\) | 346.938 | + | 58.8047i | 0.257461 | + | 0.0436387i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1359.82 | + | 474.602i | 0.984800 | + | 0.343714i | ||||
\(125\) | 1520.86i | 1.08824i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −482.735 | −0.337290 | −0.168645 | − | 0.985677i | \(-0.553939\pi\) | ||||
−0.168645 | + | 0.985677i | \(0.553939\pi\) | |||||||
\(128\) | −1336.37 | + | 557.922i | −0.922806 | + | 0.385264i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −232.808 | + | 1373.53i | −0.157066 | + | 0.926666i | ||||
\(131\) | 1448.68i | 0.966193i | 0.875567 | + | 0.483097i | \(0.160488\pi\) | ||||
−0.875567 | + | 0.483097i | \(0.839512\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 270.247i | − | 0.176191i | ||||||
\(134\) | 401.142 | + | 67.9920i | 0.258608 | + | 0.0438330i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1222.90 | + | 2218.94i | −0.771050 | + | 1.39907i | ||||
\(137\) | 1043.62 | 0.650823 | 0.325412 | − | 0.945572i | \(-0.394497\pi\) | ||||
0.325412 | + | 0.945572i | \(0.394497\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 630.925i | 0.384995i | 0.981297 | + | 0.192498i | \(0.0616588\pi\) | ||||
−0.981297 | + | 0.192498i | \(0.938341\pi\) | |||||||
\(140\) | −165.730 | + | 474.845i | −0.100048 | + | 0.286655i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −118.800 | + | 700.903i | −0.0702077 | + | 0.414214i | ||||
\(143\) | 3232.80 | 1.89049 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2105.16 | 1.20568 | ||||||||
\(146\) | −335.447 | + | 1979.08i | −0.190149 | + | 1.12185i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −346.252 | + | 992.071i | −0.192309 | + | 0.550998i | ||||
\(149\) | − | 562.011i | − | 0.309005i | −0.987992 | − | 0.154502i | \(-0.950623\pi\) | ||
0.987992 | − | 0.154502i | \(-0.0493775\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −466.027 | −0.251157 | −0.125579 | − | 0.992084i | \(-0.540079\pi\) | ||||
−0.125579 | + | 0.992084i | \(0.540079\pi\) | |||||||
\(152\) | −765.074 | − | 421.646i | −0.408261 | − | 0.225000i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1150.67 | + | 195.035i | 0.602104 | + | 0.102054i | ||||
\(155\) | − | 1616.87i | − | 0.837872i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 314.250i | − | 0.159745i | −0.996805 | − | 0.0798723i | \(-0.974549\pi\) | ||
0.996805 | − | 0.0798723i | \(-0.0254513\pi\) | |||||||
\(158\) | 409.285 | − | 2414.72i | 0.206082 | − | 1.21585i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1085.72 | + | 1210.05i | 0.536460 | + | 0.597893i | ||||
\(161\) | 785.023 | 0.384276 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1926.67i | − | 0.925820i | −0.886405 | − | 0.462910i | \(-0.846805\pi\) | ||
0.886405 | − | 0.462910i | \(-0.153195\pi\) | |||||||
\(164\) | −3780.36 | − | 1319.42i | −1.79998 | − | 0.628228i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 160.037 | + | 27.1256i | 0.0748270 | + | 0.0126829i | ||||
\(167\) | −1454.39 | −0.673917 | −0.336958 | − | 0.941520i | \(-0.609398\pi\) | ||||
−0.336958 | + | 0.941520i | \(0.609398\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −810.727 | −0.369016 | ||||||||
\(170\) | 2804.30 | + | 475.318i | 1.26518 | + | 0.214442i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1305.14 | + | 3739.45i | −0.578581 | + | 1.65773i | ||||
\(173\) | − | 3142.64i | − | 1.38110i | −0.723284 | − | 0.690550i | \(-0.757368\pi\) | ||
0.723284 | − | 0.690550i | \(-0.242632\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −310.392 | −0.134077 | ||||||||
\(176\) | 2347.46 | − | 2953.28i | 1.00538 | − | 1.26484i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 361.801 | − | 2134.57i | 0.152349 | − | 0.898834i | ||||
\(179\) | 608.194i | 0.253958i | 0.991905 | + | 0.126979i | \(0.0405281\pi\) | ||||
−0.991905 | + | 0.126979i | \(0.959472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3075.47i | 1.26297i | 0.775387 | + | 0.631486i | \(0.217555\pi\) | ||||
−0.775387 | + | 0.631486i | \(0.782445\pi\) | |||||||
\(182\) | −1070.56 | − | 181.456i | −0.436018 | − | 0.0739034i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1224.81 | − | 2222.42i | 0.490731 | − | 0.890428i | ||||
\(185\) | 1179.61 | 0.468792 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6600.33i | − | 2.58109i | ||||||
\(188\) | 843.725 | + | 294.476i | 0.327314 | + | 0.114239i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −163.886 | + | 966.899i | −0.0625764 | + | 0.369191i | ||||
\(191\) | 222.395 | 0.0842509 | 0.0421255 | − | 0.999112i | \(-0.486587\pi\) | ||||
0.0421255 | + | 0.999112i | \(0.486587\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2275.04 | 0.848502 | 0.424251 | − | 0.905545i | \(-0.360537\pi\) | ||||
0.424251 | + | 0.905545i | \(0.360537\pi\) | |||||||
\(194\) | 175.240 | − | 1033.89i | 0.0648531 | − | 0.382623i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −370.106 | − | 129.174i | −0.134878 | − | 0.0470750i | ||||
\(197\) | − | 140.119i | − | 0.0506754i | −0.999679 | − | 0.0253377i | \(-0.991934\pi\) | ||
0.999679 | − | 0.0253377i | \(-0.00806610\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1003.14 | 0.357342 | 0.178671 | − | 0.983909i | \(-0.442820\pi\) | ||||
0.178671 | + | 0.983909i | \(0.442820\pi\) | |||||||
\(200\) | −484.282 | + | 878.727i | −0.171220 | + | 0.310677i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1732.94 | + | 293.726i | 0.603609 | + | 0.102309i | ||||
\(203\) | 1640.81i | 0.567303i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4494.99i | 1.53143i | ||||||||
\(206\) | 205.076 | − | 1209.92i | 0.0693608 | − | 0.409218i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2184.02 | + | 2747.67i | −0.728052 | + | 0.915945i | ||||
\(209\) | 2275.74 | 0.753187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2462.02i | 0.803283i | 0.915797 | + | 0.401641i | \(0.131560\pi\) | ||||
−0.915797 | + | 0.401641i | \(0.868440\pi\) | |||||||
\(212\) | −1835.88 | + | 5260.10i | −0.594757 | + | 1.70408i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2584.99 | − | 438.146i | −0.825730 | − | 0.139958i | ||||
\(215\) | 4446.33 | 1.41041 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1260.23 | 0.394239 | ||||||||
\(218\) | −3970.75 | − | 673.027i | −1.23364 | − | 0.209097i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3998.65 | − | 1395.61i | −1.22541 | − | 0.427690i | ||||
\(221\) | 6140.80i | 1.86912i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6458.67 | 1.93948 | 0.969741 | − | 0.244138i | \(-0.0785050\pi\) | ||||
0.969741 | + | 0.244138i | \(0.0785050\pi\) | |||||||
\(224\) | −943.142 | + | 846.236i | −0.281323 | + | 0.252417i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 958.278 | − | 5653.69i | 0.282052 | − | 1.66406i | ||||
\(227\) | − | 1776.16i | − | 0.519329i | −0.965699 | − | 0.259664i | \(-0.916388\pi\) | ||
0.965699 | − | 0.259664i | \(-0.0836120\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2046.20i | − | 0.590466i | −0.955425 | − | 0.295233i | \(-0.904603\pi\) | ||
0.955425 | − | 0.295233i | \(-0.0953972\pi\) | |||||||
\(230\) | −2808.69 | − | 476.062i | −0.805215 | − | 0.136481i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4645.18 | + | 2560.04i | 1.31453 | + | 0.724461i | ||||
\(233\) | −5827.32 | −1.63846 | −0.819229 | − | 0.573467i | \(-0.805598\pi\) | ||||
−0.819229 | + | 0.573467i | \(0.805598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1003.22i | − | 0.278480i | ||||||
\(236\) | −1075.01 | + | 3080.08i | −0.296513 | + | 0.849561i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −370.474 | + | 2185.74i | −0.100900 | + | 0.595296i | ||||
\(239\) | 5894.12 | 1.59523 | 0.797613 | − | 0.603169i | \(-0.206096\pi\) | ||||
0.797613 | + | 0.603169i | \(0.206096\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2057.48 | −0.549934 | −0.274967 | − | 0.961454i | \(-0.588667\pi\) | ||||
−0.274967 | + | 0.961454i | \(0.588667\pi\) | |||||||
\(242\) | −1013.26 | + | 5978.09i | −0.269153 | + | 1.58796i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 327.972 | − | 939.695i | 0.0860501 | − | 0.246548i | ||||
\(245\) | 440.069i | 0.114755i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2117.30 | −0.545426 | ||||||||
\(248\) | 1966.24 | − | 3567.73i | 0.503453 | − | 0.913512i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4241.14 | + | 718.857i | 1.07293 | + | 0.181858i | ||||
\(251\) | − | 5593.16i | − | 1.40652i | −0.710932 | − | 0.703261i | \(-0.751727\pi\) | ||
0.710932 | − | 0.703261i | \(-0.248273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6610.65i | 1.64272i | ||||||||
\(254\) | −228.172 | + | 1346.18i | −0.0563654 | + | 0.332547i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 924.195 | + | 3990.37i | 0.225634 | + | 0.974212i | ||||
\(257\) | −1528.67 | −0.371035 | −0.185517 | − | 0.982641i | \(-0.559396\pi\) | ||||
−0.185517 | + | 0.982641i | \(0.559396\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 919.415i | 0.220578i | ||||||||
\(260\) | 3720.26 | + | 1298.44i | 0.887387 | + | 0.309715i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4039.85 | + | 684.739i | 0.952607 | + | 0.161463i | ||||
\(263\) | 2983.60 | 0.699530 | 0.349765 | − | 0.936837i | \(-0.386261\pi\) | ||||
0.349765 | + | 0.936837i | \(0.386261\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6254.45 | 1.44984 | ||||||||
\(266\) | −753.624 | − | 127.736i | −0.173713 | − | 0.0294437i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 379.212 | − | 1086.51i | 0.0864332 | − | 0.247646i | ||||
\(269\) | 5552.68i | 1.25856i | 0.777178 | + | 0.629281i | \(0.216650\pi\) | ||||
−0.777178 | + | 0.629281i | \(0.783350\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4238.12 | −0.949990 | −0.474995 | − | 0.879988i | \(-0.657550\pi\) | ||||
−0.474995 | + | 0.879988i | \(0.657550\pi\) | |||||||
\(272\) | 5609.84 | + | 4459.06i | 1.25054 | + | 0.994009i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 493.285 | − | 2910.30i | 0.108761 | − | 0.641671i | ||||
\(275\) | − | 2613.80i | − | 0.573157i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3761.88i | 0.815990i | 0.912984 | + | 0.407995i | \(0.133772\pi\) | ||||
−0.912984 | + | 0.407995i | \(0.866228\pi\) | |||||||
\(278\) | 1759.43 | + | 298.217i | 0.379582 | + | 0.0643376i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1245.84 | + | 686.606i | 0.265905 | + | 0.146545i | ||||
\(281\) | −1343.51 | −0.285221 | −0.142610 | − | 0.989779i | \(-0.545550\pi\) | ||||
−0.142610 | + | 0.989779i | \(0.545550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2863.45i | − | 0.601463i | −0.953709 | − | 0.300732i | \(-0.902769\pi\) | ||
0.953709 | − | 0.300732i | \(-0.0972309\pi\) | |||||||
\(284\) | 1898.42 | + | 662.586i | 0.396657 | + | 0.138441i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1528.04 | − | 9015.16i | 0.315925 | − | 1.86391i | ||||
\(287\) | −3503.50 | −0.720575 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7624.50 | 1.55190 | ||||||||
\(290\) | 995.039 | − | 5870.57i | 0.201485 | − | 1.18873i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5360.42 | + | 1870.89i | 1.07430 | + | 0.374950i | ||||
\(293\) | − | 3539.23i | − | 0.705680i | −0.935684 | − | 0.352840i | \(-0.885216\pi\) | ||
0.935684 | − | 0.352840i | \(-0.114784\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3662.33 | 0.722810 | ||||||||
\(296\) | 2602.88 | + | 1434.49i | 0.511113 | + | 0.281683i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1567.25 | − | 265.643i | −0.304660 | − | 0.0516386i | ||||
\(299\) | − | 6150.41i | − | 1.18959i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3465.58i | 0.663630i | ||||||||
\(302\) | −220.275 | + | 1299.59i | −0.0419716 | + | 0.247626i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1537.45 | + | 1934.23i | −0.290061 | + | 0.364920i | ||||
\(305\) | −1117.33 | −0.209765 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3008.84i | 0.559360i | 0.960093 | + | 0.279680i | \(0.0902283\pi\) | ||||
−0.960093 | + | 0.279680i | \(0.909772\pi\) | |||||||
\(308\) | 1087.77 | − | 3116.65i | 0.201238 | − | 0.576582i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4508.89 | − | 764.240i | −0.826090 | − | 0.140019i | ||||
\(311\) | −3951.63 | −0.720503 | −0.360252 | − | 0.932855i | \(-0.617309\pi\) | ||||
−0.360252 | + | 0.932855i | \(0.617309\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −262.745 | −0.0474479 | −0.0237240 | − | 0.999719i | \(-0.507552\pi\) | ||||
−0.0237240 | + | 0.999719i | \(0.507552\pi\) | |||||||
\(314\) | −876.336 | − | 148.535i | −0.157498 | − | 0.0266954i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6540.36 | − | 2282.71i | −1.16432 | − | 0.406369i | ||||
\(317\) | − | 5155.26i | − | 0.913401i | −0.889621 | − | 0.456700i | \(-0.849031\pi\) | ||
0.889621 | − | 0.456700i | \(-0.150969\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13817.2 | −2.42513 | ||||||||
\(320\) | 3887.59 | − | 2455.75i | 0.679135 | − | 0.429001i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 371.054 | − | 2189.16i | 0.0642174 | − | 0.378873i | ||||
\(323\) | 4322.83i | 0.744670i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2431.83i | 0.415057i | ||||||||
\(326\) | −5372.82 | − | 910.673i | −0.912801 | − | 0.154716i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5466.25 | + | 9918.48i | −0.920193 | + | 1.66968i | ||||
\(329\) | 781.933 | 0.131031 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6802.50i | 1.12961i | 0.825226 | + | 0.564803i | \(0.191048\pi\) | ||||
−0.825226 | + | 0.564803i | \(0.808952\pi\) | |||||||
\(332\) | 151.288 | − | 433.466i | 0.0250091 | − | 0.0716553i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −687.440 | + | 4055.79i | −0.112620 | + | 0.664440i | ||||
\(335\) | −1291.90 | −0.210698 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 433.772 | 0.0701159 | 0.0350580 | − | 0.999385i | \(-0.488838\pi\) | ||||
0.0350580 | + | 0.999385i | \(0.488838\pi\) | |||||||
\(338\) | −383.203 | + | 2260.84i | −0.0616672 | + | 0.363826i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2650.99 | − | 7595.55i | 0.422854 | − | 1.21155i | ||||
\(341\) | 10612.3i | 1.68531i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 9811.12 | + | 5407.09i | 1.53773 | + | 0.847473i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8763.73 | − | 1485.42i | −1.36168 | − | 0.230799i | ||||
\(347\) | − | 4388.13i | − | 0.678867i | −0.940630 | − | 0.339434i | \(-0.889765\pi\) | ||
0.940630 | − | 0.339434i | \(-0.110235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1270.81i | − | 0.194914i | −0.995240 | − | 0.0974571i | \(-0.968929\pi\) | ||
0.995240 | − | 0.0974571i | \(-0.0310709\pi\) | |||||||
\(350\) | −146.712 | + | 865.577i | −0.0224059 | + | 0.132192i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7126.12 | − | 7942.17i | −1.07904 | − | 1.20261i | ||||
\(353\) | −12777.9 | −1.92663 | −0.963315 | − | 0.268375i | \(-0.913514\pi\) | ||||
−0.963315 | + | 0.268375i | \(0.913514\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 2257.29i | − | 0.337478i | ||||||
\(356\) | −5781.55 | − | 2017.87i | −0.860735 | − | 0.300413i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1696.04 | + | 287.472i | 0.250387 | + | 0.0424396i | ||||
\(359\) | −6124.58 | −0.900399 | −0.450199 | − | 0.892928i | \(-0.648647\pi\) | ||||
−0.450199 | + | 0.892928i | \(0.648647\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5368.53 | 0.782698 | ||||||||
\(362\) | 8576.43 | + | 1453.67i | 1.24521 | + | 0.211059i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1012.04 | + | 2899.66i | −0.145728 | + | 0.417537i | ||||
\(365\) | − | 6373.73i | − | 0.914017i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3190.01 | −0.453725 | −0.226863 | − | 0.973927i | \(-0.572847\pi\) | ||||
−0.226863 | + | 0.973927i | \(0.572847\pi\) | |||||||
\(368\) | −5618.62 | − | 4466.04i | −0.795899 | − | 0.632632i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 557.560 | − | 3289.52i | 0.0783410 | − | 0.462200i | ||||
\(371\) | 4874.87i | 0.682185i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8037.61i | 1.11574i | 0.829928 | + | 0.557871i | \(0.188382\pi\) | ||||
−0.829928 | + | 0.557871i | \(0.811618\pi\) | |||||||
\(374\) | −18406.0 | − | 3119.75i | −2.54479 | − | 0.431333i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1219.99 | − | 2213.67i | 0.167331 | − | 0.303620i | ||||
\(377\) | 12855.3 | 1.75618 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3762.31i | − | 0.509913i | −0.966953 | − | 0.254956i | \(-0.917939\pi\) | ||
0.966953 | − | 0.254956i | \(-0.0820611\pi\) | |||||||
\(380\) | 2618.88 | + | 914.040i | 0.353542 | + | 0.123393i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 105.118 | − | 620.182i | 0.0140794 | − | 0.0830662i | ||||
\(383\) | −9479.32 | −1.26468 | −0.632338 | − | 0.774693i | \(-0.717904\pi\) | ||||
−0.632338 | + | 0.774693i | \(0.717904\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3705.80 | −0.490559 | ||||||||
\(386\) | 1075.33 | − | 6344.30i | 0.141795 | − | 0.836571i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2800.33 | − | 977.367i | −0.366405 | − | 0.127882i | ||||
\(389\) | 6672.27i | 0.869660i | 0.900513 | + | 0.434830i | \(0.143192\pi\) | ||||
−0.900513 | + | 0.434830i | \(0.856808\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12557.1 | −1.62415 | ||||||||
\(392\) | −535.158 | + | 971.040i | −0.0689529 | + | 0.125115i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −390.743 | − | 66.2294i | −0.0499628 | − | 0.00846850i | ||||
\(395\) | 7776.72i | 0.990606i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13824.8i | − | 1.74772i | −0.486178 | − | 0.873860i | \(-0.661609\pi\) | ||
0.486178 | − | 0.873860i | \(-0.338391\pi\) | |||||||
\(398\) | 474.152 | − | 2797.42i | 0.0597163 | − | 0.352317i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2221.56 | + | 1765.84i | 0.277695 | + | 0.220730i | ||||
\(401\) | 137.695 | 0.0171475 | 0.00857377 | − | 0.999963i | \(-0.497271\pi\) | ||||
0.00857377 | + | 0.999963i | \(0.497271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 9873.48i | − | 1.22043i | ||||||
\(404\) | 1638.20 | − | 4693.72i | 0.201741 | − | 0.578023i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4575.66 | + | 775.557i | 0.559326 | + | 0.0948036i | ||||
\(407\) | −7742.36 | −0.942935 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12325.1 | −1.49007 | −0.745034 | − | 0.667027i | \(-0.767567\pi\) | ||||
−0.745034 | + | 0.667027i | \(0.767567\pi\) | |||||||
\(410\) | 12535.0 | + | 2124.63i | 1.50990 | + | 0.255922i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3277.10 | − | 1143.77i | −0.391872 | − | 0.136771i | ||||
\(413\) | 2854.51i | 0.340100i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −515.407 | −0.0609646 | ||||||||
\(416\) | 6629.98 | + | 7389.22i | 0.781398 | + | 0.870880i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1075.66 | − | 6346.24i | 0.125867 | − | 0.742595i | ||||
\(419\) | − | 3339.25i | − | 0.389339i | −0.980869 | − | 0.194670i | \(-0.937637\pi\) | ||
0.980869 | − | 0.194670i | \(-0.0623635\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3287.17i | 0.380539i | 0.981732 | + | 0.190270i | \(0.0609362\pi\) | ||||
−0.981732 | + | 0.190270i | \(0.939064\pi\) | |||||||
\(422\) | 6865.73 | + | 1163.71i | 0.791987 | + | 0.134239i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13800.8 | + | 7605.89i | 1.58073 | + | 0.871167i | ||||
\(425\) | 4964.99 | 0.566677 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 870.874i | − | 0.0986992i | ||||||
\(428\) | −2443.67 | + | 7001.55i | −0.275980 | + | 0.790730i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2101.63 | − | 12399.3i | 0.235697 | − | 1.39057i | ||||
\(431\) | 12701.9 | 1.41955 | 0.709776 | − | 0.704427i | \(-0.248796\pi\) | ||||
0.709776 | + | 0.704427i | \(0.248796\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11643.1 | −1.29222 | −0.646108 | − | 0.763246i | \(-0.723604\pi\) | ||||
−0.646108 | + | 0.763246i | \(0.723604\pi\) | |||||||
\(434\) | 595.667 | − | 3514.34i | 0.0658823 | − | 0.388695i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3753.68 | + | 10754.9i | −0.412313 | + | 1.18135i | ||||
\(437\) | − | 4329.59i | − | 0.473941i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11073.2 | −1.20386 | −0.601930 | − | 0.798549i | \(-0.705601\pi\) | ||||
−0.601930 | + | 0.798549i | \(0.705601\pi\) | |||||||
\(440\) | −5781.89 | + | 10491.2i | −0.626456 | + | 1.13670i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 17124.6 | + | 2902.55i | 1.84283 | + | 0.312353i | ||||
\(443\) | − | 7274.35i | − | 0.780168i | −0.920779 | − | 0.390084i | \(-0.872446\pi\) | ||
0.920779 | − | 0.390084i | \(-0.127554\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6874.47i | 0.732318i | ||||||||
\(446\) | 3052.79 | − | 18011.0i | 0.324112 | − | 1.91221i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1914.07 | + | 3030.08i | 0.201855 | + | 0.319549i | ||||
\(449\) | −9735.36 | −1.02325 | −0.511626 | − | 0.859208i | \(-0.670957\pi\) | ||||
−0.511626 | + | 0.859208i | \(0.670957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 29502.8i | − | 3.08034i | ||||||
\(452\) | −15313.2 | − | 5344.61i | −1.59353 | − | 0.556171i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4953.09 | − | 839.529i | −0.512026 | − | 0.0867864i | ||||
\(455\) | 3447.80 | 0.355242 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2155.33 | 0.220617 | 0.110309 | − | 0.993897i | \(-0.464816\pi\) | ||||
0.110309 | + | 0.993897i | \(0.464816\pi\) | |||||||
\(458\) | −5706.14 | − | 967.168i | −0.582162 | − | 0.0986742i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2655.14 | + | 7607.44i | −0.269123 | + | 0.771084i | ||||
\(461\) | − | 3606.81i | − | 0.364395i | −0.983262 | − | 0.182197i | \(-0.941679\pi\) | ||
0.983262 | − | 0.182197i | \(-0.0583209\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8719.74 | 0.875250 | 0.437625 | − | 0.899158i | \(-0.355820\pi\) | ||||
0.437625 | + | 0.899158i | \(0.355820\pi\) | |||||||
\(464\) | 9334.68 | − | 11743.7i | 0.933948 | − | 1.17498i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2754.38 | + | 16250.4i | −0.273807 | + | 1.61542i | ||||
\(467\) | 9661.28i | 0.957325i | 0.877999 | + | 0.478662i | \(0.158878\pi\) | ||||
−0.877999 | + | 0.478662i | \(0.841122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1006.94i | − | 0.0991386i | ||||||
\(470\) | −2797.63 | − | 474.187i | −0.274564 | − | 0.0465375i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8081.17 | + | 4453.68i | 0.788063 | + | 0.434316i | ||||
\(473\) | −29183.5 | −2.83691 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1711.89i | 0.165362i | ||||||||
\(476\) | 5920.15 | + | 2066.25i | 0.570063 | + | 0.198963i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2785.95 | − | 16436.7i | 0.266582 | − | 1.57279i | ||||
\(479\) | −7341.60 | −0.700306 | −0.350153 | − | 0.936693i | \(-0.613870\pi\) | ||||
−0.350153 | + | 0.936693i | \(0.613870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7203.32 | 0.682834 | ||||||||
\(482\) | −972.502 | + | 5737.61i | −0.0919010 | + | 0.542201i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16191.9 | + | 5651.28i | 1.52065 | + | 0.530736i | ||||
\(485\) | 3329.69i | 0.311739i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14785.8 | 1.37579 | 0.687894 | − | 0.725811i | \(-0.258535\pi\) | ||||
0.687894 | + | 0.725811i | \(0.258535\pi\) | |||||||
\(488\) | −2465.46 | − | 1358.76i | −0.228701 | − | 0.126041i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1227.20 | + | 208.005i | 0.113141 | + | 0.0191770i | ||||
\(491\) | − | 7352.33i | − | 0.675776i | −0.941186 | − | 0.337888i | \(-0.890288\pi\) | ||
0.941186 | − | 0.337888i | \(-0.109712\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 26246.2i | − | 2.39771i | ||||||
\(494\) | −1000.77 | + | 5904.40i | −0.0911476 | + | 0.537756i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9019.79 | − | 7169.51i | −0.816533 | − | 0.649033i | ||||
\(497\) | 1759.39 | 0.158791 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16803.9i | − | 1.50751i | −0.657157 | − | 0.753754i | \(-0.728241\pi\) | ||
0.657157 | − | 0.753754i | \(-0.271759\pi\) | |||||||
\(500\) | 4009.29 | − | 11487.3i | 0.358602 | − | 1.02746i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −15597.4 | − | 2643.69i | −1.38674 | − | 0.235047i | ||||
\(503\) | −3372.87 | −0.298984 | −0.149492 | − | 0.988763i | \(-0.547764\pi\) | ||||
−0.149492 | + | 0.988763i | \(0.547764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5581.00 | −0.491785 | ||||||||
\(506\) | 18434.8 | + | 3124.63i | 1.61962 | + | 0.274519i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3646.18 | + | 1272.59i | 0.318451 | + | 0.111146i | ||||
\(509\) | − | 1413.69i | − | 0.123106i | −0.998104 | − | 0.0615530i | \(-0.980395\pi\) | ||
0.998104 | − | 0.0615530i | \(-0.0196053\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4967.83 | 0.430067 | ||||||||
\(512\) | 11564.6 | − | 691.147i | 0.998219 | − | 0.0596575i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −722.551 | + | 4262.93i | −0.0620046 | + | 0.365817i | ||||
\(515\) | 3896.59i | 0.333407i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6584.63i | 0.560139i | ||||||||
\(518\) | 2563.93 | + | 434.576i | 0.217476 | + | 0.0368613i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5379.34 | − | 9760.78i | 0.453653 | − | 0.823151i | ||||
\(521\) | 20868.7 | 1.75484 | 0.877422 | − | 0.479720i | \(-0.159262\pi\) | ||||
0.877422 | + | 0.479720i | \(0.159262\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17290.7i | 1.44564i | 0.691035 | + | 0.722821i | \(0.257155\pi\) | ||||
−0.691035 | + | 0.722821i | \(0.742845\pi\) | |||||||
\(524\) | 3819.00 | − | 10942.1i | 0.318385 | − | 0.912228i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1410.24 | − | 8320.21i | 0.116900 | − | 0.689693i | ||||
\(527\) | −20158.4 | −1.66625 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 409.770 | 0.0336788 | ||||||||
\(530\) | 2956.26 | − | 17441.5i | 0.242287 | − | 1.42945i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −712.425 | + | 2041.22i | −0.0580593 | + | 0.166350i | ||||
\(533\) | 27448.8i | 2.23066i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8325.09 | 0.672757 | ||||||||
\(536\) | −2850.66 | − | 1571.05i | −0.229719 | − | 0.126602i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15484.5 | + | 2624.56i | 1.24086 | + | 0.210321i | ||||
\(539\) | − | 2888.39i | − | 0.230820i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4714.93i | 0.374696i | 0.982294 | + | 0.187348i | \(0.0599892\pi\) | ||||
−0.982294 | + | 0.187348i | \(0.940011\pi\) | |||||||
\(542\) | −2003.21 | + | 11818.6i | −0.158755 | + | 0.936631i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15086.4 | − | 13536.3i | 1.18901 | − | 1.06684i | ||||
\(545\) | 12788.0 | 1.00510 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11384.3i | 0.889868i | 0.895563 | + | 0.444934i | \(0.146773\pi\) | ||||
−0.895563 | + | 0.444934i | \(0.853227\pi\) | |||||||
\(548\) | −7882.67 | − | 2751.20i | −0.614473 | − | 0.214463i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7288.99 | − | 1235.46i | −0.565098 | − | 0.0957818i | ||||
\(551\) | 9049.48 | 0.699675 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6061.36 | −0.466104 | ||||||||
\(554\) | 10490.6 | + | 1778.11i | 0.804515 | + | 0.136362i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1663.25 | − | 4765.49i | 0.126866 | − | 0.363492i | ||||
\(557\) | 1616.13i | 0.122940i | 0.998109 | + | 0.0614699i | \(0.0195788\pi\) | ||||
−0.998109 | + | 0.0614699i | \(0.980421\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27151.7 | 2.05437 | ||||||||
\(560\) | 2503.57 | − | 3149.69i | 0.188920 | − | 0.237676i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −635.031 | + | 3746.58i | −0.0476640 | + | 0.281210i | ||||
\(563\) | 2529.62i | 0.189362i | 0.995508 | + | 0.0946811i | \(0.0301831\pi\) | ||||
−0.995508 | + | 0.0946811i | \(0.969817\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18208.0i | 1.35578i | ||||||||
\(566\) | −7985.16 | − | 1353.45i | −0.593006 | − | 0.100512i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2745.04 | − | 4980.86i | 0.202781 | − | 0.367944i | ||||
\(569\) | −5697.25 | −0.419756 | −0.209878 | − | 0.977728i | \(-0.567307\pi\) | ||||
−0.209878 | + | 0.977728i | \(0.567307\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15930.1i | 1.16752i | 0.811926 | + | 0.583760i | \(0.198419\pi\) | ||||
−0.811926 | + | 0.583760i | \(0.801581\pi\) | |||||||
\(572\) | −24417.9 | − | 8522.32i | −1.78490 | − | 0.622965i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1655.98 | + | 9770.05i | −0.120417 | + | 0.710442i | ||||
\(575\) | −4972.76 | −0.360658 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9446.91 | −0.681595 | −0.340797 | − | 0.940137i | \(-0.610697\pi\) | ||||
−0.340797 | + | 0.940137i | \(0.610697\pi\) | |||||||
\(578\) | 3603.84 | − | 21262.1i | 0.259343 | − | 1.53008i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −15900.7 | − | 5549.64i | −1.13834 | − | 0.397304i | ||||
\(581\) | − | 401.720i | − | 0.0286853i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −41051.1 | −2.91623 | ||||||||
\(584\) | 7750.94 | − | 14064.0i | 0.549206 | − | 0.996531i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9869.69 | − | 1672.87i | −0.695756 | − | 0.117928i | ||||
\(587\) | 17574.2i | 1.23571i | 0.786290 | + | 0.617857i | \(0.211999\pi\) | ||||
−0.786290 | + | 0.617857i | \(0.788001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6950.45i | − | 0.486228i | ||||||
\(590\) | 1731.06 | − | 10213.0i | 0.120791 | − | 0.712646i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5230.60 | − | 6580.50i | 0.363136 | − | 0.456853i | ||||
\(593\) | −6137.13 | −0.424995 | −0.212497 | − | 0.977162i | \(-0.568160\pi\) | ||||
−0.212497 | + | 0.977162i | \(0.568160\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 7039.27i | − | 0.485012i | ||||||
\(596\) | −1481.57 | + | 4244.97i | −0.101825 | + | 0.291746i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17151.3 | − | 2907.09i | −1.17286 | − | 0.198795i | ||||
\(599\) | 26532.1 | 1.80980 | 0.904901 | − | 0.425622i | \(-0.139945\pi\) | ||||
0.904901 | + | 0.425622i | \(0.139945\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6237.94 | −0.423379 | −0.211690 | − | 0.977337i | \(-0.567897\pi\) | ||||
−0.211690 | + | 0.977337i | \(0.567897\pi\) | |||||||
\(602\) | 9664.30 | + | 1638.06i | 0.654298 | + | 0.110901i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3519.99 | + | 1228.54i | 0.237130 | + | 0.0827627i | ||||
\(605\) | − | 19252.7i | − | 1.29378i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2650.63 | 0.177242 | 0.0886209 | − | 0.996065i | \(-0.471754\pi\) | ||||
0.0886209 | + | 0.996065i | \(0.471754\pi\) | |||||||
\(608\) | 4667.19 | + | 5201.65i | 0.311315 | + | 0.346965i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −528.124 | + | 3115.85i | −0.0350543 | + | 0.206815i | ||||
\(611\) | − | 6126.19i | − | 0.405629i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2531.31i | 0.166784i | 0.996517 | + | 0.0833921i | \(0.0265754\pi\) | ||||
−0.996517 | + | 0.0833921i | \(0.973425\pi\) | |||||||
\(614\) | 8390.60 | + | 1422.17i | 0.551494 | + | 0.0934760i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8177.09 | − | 4506.54i | −0.534845 | − | 0.294763i | ||||
\(617\) | −22390.8 | −1.46097 | −0.730485 | − | 0.682928i | \(-0.760706\pi\) | ||||
−0.730485 | + | 0.682928i | \(0.760706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 4854.99i | − | 0.315248i | −0.987499 | − | 0.157624i | \(-0.949617\pi\) | ||
0.987499 | − | 0.157624i | \(-0.0503834\pi\) | |||||||
\(620\) | −4262.40 | + | 12212.5i | −0.276100 | + | 0.791074i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1867.80 | + | 11019.7i | −0.120405 | + | 0.710371i | ||||
\(623\) | −5358.13 | −0.344573 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8116.08 | −0.519429 | ||||||||
\(626\) | −124.190 | + | 732.704i | −0.00792915 | + | 0.0467807i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −828.428 | + | 2373.59i | −0.0526399 | + | 0.150822i | ||||
\(629\) | − | 14706.8i | − | 0.932273i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23946.3 | 1.51076 | 0.755379 | − | 0.655289i | \(-0.227453\pi\) | ||||
0.755379 | + | 0.655289i | \(0.227453\pi\) | |||||||
\(632\) | −9457.09 | + | 17159.8i | −0.595226 | + | 1.08003i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14376.2 | − | 2436.71i | −0.900556 | − | 0.152641i | ||||
\(635\) | − | 4335.44i | − | 0.270940i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2687.29i | 0.167150i | ||||||||
\(638\) | −6530.94 | + | 38531.5i | −0.405270 | + | 2.39103i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5010.69 | − | 12001.9i | −0.309476 | − | 0.741276i | ||||
\(641\) | 17358.0 | 1.06958 | 0.534790 | − | 0.844985i | \(-0.320391\pi\) | ||||
0.534790 | + | 0.844985i | \(0.320391\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 11744.3i | − | 0.720293i | −0.932896 | − | 0.360146i | \(-0.882727\pi\) | ||
0.932896 | − | 0.360146i | \(-0.117273\pi\) | |||||||
\(644\) | −5929.42 | − | 2069.48i | −0.362813 | − | 0.126629i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12054.9 | + | 2043.25i | 0.734199 | + | 0.124444i | ||||
\(647\) | −23793.4 | −1.44577 | −0.722887 | − | 0.690967i | \(-0.757185\pi\) | ||||
−0.722887 | + | 0.690967i | \(0.757185\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24037.7 | −1.45387 | ||||||||
\(650\) | 6781.52 | + | 1149.44i | 0.409220 | + | 0.0693612i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5079.10 | + | 14552.5i | −0.305081 | + | 0.874110i | ||||
\(653\) | − | 7027.81i | − | 0.421163i | −0.977576 | − | 0.210582i | \(-0.932464\pi\) | ||
0.977576 | − | 0.210582i | \(-0.0675358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13010.5 | −0.776128 | ||||||||
\(656\) | 25075.5 | + | 19931.6i | 1.49243 | + | 1.18628i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 369.593 | − | 2180.54i | 0.0218970 | − | 0.129189i | ||||
\(659\) | 16588.1i | 0.980547i | 0.871569 | + | 0.490273i | \(0.163103\pi\) | ||||
−0.871569 | + | 0.490273i | \(0.836897\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5341.60i | 0.314318i | 0.987573 | + | 0.157159i | \(0.0502335\pi\) | ||||
−0.987573 | + | 0.157159i | \(0.949766\pi\) | |||||||
\(662\) | 18969.8 | + | 3215.31i | 1.11372 | + | 0.188771i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1137.28 | − | 626.774i | −0.0664683 | − | 0.0366319i | ||||
\(665\) | 2427.08 | 0.141531 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26287.3i | 1.52601i | ||||||||
\(668\) | 10985.3 | + | 3834.07i | 0.636276 | + | 0.222073i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −610.636 | + | 3602.66i | −0.0352103 | + | 0.207735i | ||||
\(671\) | 7333.60 | 0.421923 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10396.5 | −0.595477 | −0.297738 | − | 0.954648i | \(-0.596232\pi\) | ||||
−0.297738 | + | 0.954648i | \(0.596232\pi\) | |||||||
\(674\) | 205.029 | − | 1209.64i | 0.0117173 | − | 0.0691300i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6123.56 | + | 2137.24i | 0.348405 | + | 0.121600i | ||||
\(677\) | − | 7689.12i | − | 0.436510i | −0.975892 | − | 0.218255i | \(-0.929964\pi\) | ||
0.975892 | − | 0.218255i | \(-0.0700364\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2595.24 | −0.146681 | ||||||||
\(680\) | −19928.3 | − | 10982.9i | −1.12385 | − | 0.619373i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 29594.1 | + | 5016.09i | 1.66161 | + | 0.281636i | ||||
\(683\) | − | 1703.19i | − | 0.0954182i | −0.998861 | − | 0.0477091i | \(-0.984808\pi\) | ||
0.998861 | − | 0.0477091i | \(-0.0151920\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9372.78i | 0.522796i | ||||||||
\(686\) | −162.124 | + | 956.508i | −0.00902323 | + | 0.0532356i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 19715.9 | − | 24804.1i | 1.09253 | − | 1.37449i | ||||
\(689\) | 38193.0 | 2.11181 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19314.7i | 1.06334i | 0.846952 | + | 0.531669i | \(0.178435\pi\) | ||||
−0.846952 | + | 0.531669i | \(0.821565\pi\) | |||||||
\(692\) | −8284.63 | + | 23736.9i | −0.455108 | + | 1.30396i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12237.0 | − | 2074.12i | −0.669321 | − | 0.113447i | ||||
\(695\) | −5666.33 | −0.309261 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 56041.5 | 3.04551 | ||||||||
\(698\) | −3543.86 | − | 600.670i | −0.192173 | − | 0.0325726i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2344.45 | + | 818.257i | 0.126588 | + | 0.0441817i | ||||
\(701\) | 8776.10i | 0.472851i | 0.971650 | + | 0.236426i | \(0.0759760\pi\) | ||||
−0.971650 | + | 0.236426i | \(0.924024\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5070.79 | 0.272046 | ||||||||
\(704\) | −25516.2 | + | 16118.3i | −1.36602 | + | 0.862899i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6039.69 | + | 35633.2i | −0.321964 | + | 1.89954i | ||||
\(707\) | − | 4349.97i | − | 0.231397i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 15446.1i | − | 0.818180i | −0.912494 | − | 0.409090i | \(-0.865846\pi\) | ||
0.912494 | − | 0.409090i | \(-0.134154\pi\) | |||||||
\(710\) | −6294.80 | − | 1066.94i | −0.332732 | − | 0.0563968i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8359.89 | + | 15169.0i | −0.440028 | + | 0.798429i | ||||
\(713\) | 20190.0 | 1.06048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29033.8i | 1.51860i | ||||||||
\(716\) | 1603.32 | − | 4593.79i | 0.0836857 | − | 0.239774i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2894.88 | + | 17079.3i | −0.150468 | + | 0.887737i | ||||
\(719\) | −1510.03 | −0.0783237 | −0.0391618 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391618 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3037.10 | −0.156876 | ||||||||
\(722\) | 2537.52 | − | 14971.0i | 0.130799 | − | 0.771692i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8107.57 | − | 23229.6i | 0.416181 | − | 1.19243i | ||||
\(725\) | − | 10393.8i | − | 0.532436i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32352.4 | 1.65046 | 0.825231 | − | 0.564795i | \(-0.191045\pi\) | ||||
0.825231 | + | 0.564795i | \(0.191045\pi\) | |||||||
\(728\) | 7607.79 | + | 4192.79i | 0.387312 | + | 0.213455i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17774.1 | − | 3012.64i | −0.901164 | − | 0.152744i | ||||
\(731\) | − | 55434.9i | − | 2.80483i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11397.7i | − | 0.574327i | −0.957882 | − | 0.287164i | \(-0.907288\pi\) | ||
0.957882 | − | 0.287164i | \(-0.0927123\pi\) | |||||||
\(734\) | −1507.81 | + | 8895.84i | −0.0758232 | + | 0.447345i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15110.0 | + | 13557.4i | −0.756740 | + | 0.678986i | ||||
\(737\) | 8479.37 | 0.423802 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5146.85i | − | 0.256198i | −0.991761 | − | 0.128099i | \(-0.959113\pi\) | ||
0.991761 | − | 0.128099i | \(-0.0408875\pi\) | |||||||
\(740\) | −8909.78 | − | 3109.69i | −0.442608 | − | 0.154479i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13594.3 | + | 2304.18i | 0.672592 | + | 0.114002i | ||||
\(743\) | −22350.2 | −1.10357 | −0.551783 | − | 0.833988i | \(-0.686052\pi\) | ||||
−0.551783 | + | 0.833988i | \(0.686052\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5047.42 | 0.248219 | ||||||||
\(746\) | 22414.1 | + | 3799.11i | 1.10005 | + | 0.186455i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17399.8 | + | 49853.4i | −0.850534 | + | 2.43693i | ||||
\(749\) | 6488.77i | 0.316548i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12773.8 | 0.620670 | 0.310335 | − | 0.950627i | \(-0.399559\pi\) | ||||
0.310335 | + | 0.950627i | \(0.399559\pi\) | |||||||
\(752\) | −5596.50 | − | 4448.46i | −0.271388 | − | 0.215716i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6076.24 | − | 35848.8i | 0.293480 | − | 1.73148i | ||||
\(755\) | − | 4185.39i | − | 0.201751i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1662.37i | 0.0798149i | 0.999203 | + | 0.0399075i | \(0.0127063\pi\) | ||||
−0.999203 | + | 0.0399075i | \(0.987294\pi\) | |||||||
\(758\) | −10491.8 | − | 1778.32i | −0.502742 | − | 0.0852129i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3786.80 | − | 6871.12i | 0.180739 | − | 0.327950i | ||||
\(761\) | −36358.5 | −1.73192 | −0.865962 | − | 0.500109i | \(-0.833293\pi\) | ||||
−0.865962 | + | 0.500109i | \(0.833293\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9967.27i | 0.472922i | ||||||||
\(764\) | −1679.79 | − | 586.278i | −0.0795452 | − | 0.0277628i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4480.55 | + | 26434.5i | −0.211343 | + | 1.24689i | ||||
\(767\) | 22364.1 | 1.05283 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17531.9 | 0.822127 | 0.411063 | − | 0.911607i | \(-0.365158\pi\) | ||||
0.411063 | + | 0.911607i | \(0.365158\pi\) | |||||||
\(770\) | −1751.61 | + | 10334.2i | −0.0819786 | + | 0.483661i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17183.8 | − | 5997.47i | −0.801111 | − | 0.279603i | ||||
\(773\) | 17860.7i | 0.831054i | 0.909581 | + | 0.415527i | \(0.136403\pi\) | ||||
−0.909581 | + | 0.415527i | \(0.863597\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7982.96 | −0.370008 | ||||||||
\(776\) | −4049.16 | + | 7347.17i | −0.187315 | + | 0.339882i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18606.7 | + | 3153.76i | 0.857431 | + | 0.145331i | ||||
\(779\) | 19322.6i | 0.888710i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14815.7i | 0.678807i | ||||||||
\(782\) | −5935.32 | + | 35017.5i | −0.271415 | + | 1.60131i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2454.94 | + | 1951.35i | 0.111832 | + | 0.0888915i | ||||
\(785\) | 2822.28 | 0.128320 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11778.6i | 0.533496i | 0.963766 | + | 0.266748i | \(0.0859492\pi\) | ||||
−0.963766 | + | 0.266748i | \(0.914051\pi\) | |||||||
\(788\) | −369.382 | + | 1058.34i | −0.0166988 | + | 0.0478450i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21686.6 | + | 3675.79i | 0.976675 | + | 0.165543i | ||||
\(791\) | −14191.7 | −0.637926 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6823.02 | −0.305539 | ||||||||
\(794\) | −38552.5 | − | 6534.49i | −1.72314 | − | 0.292066i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7576.93 | − | 2644.49i | −0.337383 | − | 0.117753i | ||||
\(797\) | − | 9149.34i | − | 0.406633i | −0.979113 | − | 0.203316i | \(-0.934828\pi\) | ||
0.979113 | − | 0.203316i | \(-0.0651720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12507.7 | −0.553805 | ||||||||
\(800\) | 5974.37 | − | 5360.51i | 0.264032 | − | 0.236903i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 65.0838 | − | 383.984i | 0.00286557 | − | 0.0169064i | ||||
\(803\) | 41834.0i | 1.83847i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7050.29i | 0.308683i | ||||||||
\(806\) | −27533.7 | − | 4666.86i | −1.20327 | − | 0.203949i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12314.8 | − | 6786.93i | −0.536182 | − | 0.295499i | ||||
\(809\) | −11885.2 | −0.516514 | −0.258257 | − | 0.966076i | \(-0.583148\pi\) | ||||
−0.258257 | + | 0.966076i | \(0.583148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22554.1i | 0.976549i | 0.872690 | + | 0.488274i | \(0.162374\pi\) | ||||
−0.872690 | + | 0.488274i | \(0.837626\pi\) | |||||||
\(812\) | 4325.52 | − | 12393.4i | 0.186941 | − | 0.535618i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3659.55 | + | 21590.8i | −0.157576 | + | 0.929675i | ||||
\(815\) | 17303.4 | 0.743697 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19113.5 | 0.818478 | ||||||||
\(818\) | −5825.66 | + | 34370.5i | −0.249009 | + | 1.46911i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11849.7 | − | 33951.4i | 0.504645 | − | 1.44590i | ||||
\(821\) | 9016.04i | 0.383267i | 0.981467 | + | 0.191633i | \(0.0613784\pi\) | ||||
−0.981467 | + | 0.191633i | \(0.938622\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8909.42 | 0.377355 | 0.188677 | − | 0.982039i | \(-0.439580\pi\) | ||||
0.188677 | + | 0.982039i | \(0.439580\pi\) | |||||||
\(824\) | −4738.56 | + | 8598.08i | −0.200334 | + | 0.363505i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7960.23 | + | 1349.23i | 0.335317 | + | 0.0568349i | ||||
\(827\) | 24206.8i | 1.01784i | 0.860814 | + | 0.508920i | \(0.169955\pi\) | ||||
−0.860814 | + | 0.508920i | \(0.830045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 498.801i | − | 0.0208976i | −0.999945 | − | 0.0104488i | \(-0.996674\pi\) | ||
0.999945 | − | 0.0104488i | \(-0.00332601\pi\) | |||||||
\(830\) | −243.615 | + | 1437.29i | −0.0101880 | + | 0.0601073i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 23739.7 | − | 14996.1i | 0.989215 | − | 0.624875i | ||||
\(833\) | 5486.58 | 0.228210 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 13061.9i | − | 0.541347i | ||||||
\(836\) | −17189.0 | − | 5999.30i | −0.711119 | − | 0.248194i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9312.02 | − | 1578.35i | −0.383864 | − | 0.0650635i | ||||
\(839\) | 23273.2 | 0.957666 | 0.478833 | − | 0.877906i | \(-0.341060\pi\) | ||||
0.478833 | + | 0.877906i | \(0.341060\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30555.3 | −1.25283 | ||||||||
\(842\) | 9166.79 | + | 1553.74i | 0.375188 | + | 0.0635929i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6490.39 | − | 18596.1i | 0.264702 | − | 0.758417i | ||||
\(845\) | − | 7281.14i | − | 0.296424i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15006.0 | 0.608753 | ||||||||
\(848\) | 27733.4 | − | 34890.7i | 1.12308 | − | 1.41292i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2346.78 | − | 13845.6i | 0.0946988 | − | 0.558708i | ||||
\(851\) | 14729.8i | 0.593340i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 17701.4i | − | 0.710531i | −0.934765 | − | 0.355266i | \(-0.884390\pi\) | ||
0.934765 | − | 0.355266i | \(-0.115610\pi\) | |||||||
\(854\) | −2428.57 | − | 411.633i | −0.0973113 | − | 0.0164939i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18369.8 | + | 10123.9i | 0.733491 | + | 0.404240i | ||||
\(857\) | −13312.4 | −0.530620 | −0.265310 | − | 0.964163i | \(-0.585474\pi\) | ||||
−0.265310 | + | 0.964163i | \(0.585474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6535.20i | 0.259579i | 0.991542 | + | 0.129789i | \(0.0414301\pi\) | ||||
−0.991542 | + | 0.129789i | \(0.958570\pi\) | |||||||
\(860\) | −33583.9 | − | 11721.4i | −1.33163 | − | 0.464765i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6003.74 | − | 35421.1i | 0.237225 | − | 1.39959i | ||||
\(863\) | 32795.4 | 1.29359 | 0.646795 | − | 0.762664i | \(-0.276109\pi\) | ||||
0.646795 | + | 0.762664i | \(0.276109\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28224.0 | 1.10942 | ||||||||
\(866\) | −5503.28 | + | 32468.4i | −0.215946 | + | 1.27404i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9518.72 | − | 3322.22i | −0.372219 | − | 0.129912i | ||||
\(869\) | − | 51042.5i | − | 1.99252i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7889.02 | −0.306899 | ||||||||
\(872\) | 28217.5 | + | 15551.2i | 1.09583 | + | 0.603933i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12073.7 | − | 2046.45i | −0.467277 | − | 0.0792016i | ||||
\(875\) | − | 10646.0i | − | 0.411315i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 47714.2i | − | 1.83716i | −0.395231 | − | 0.918582i | \(-0.629335\pi\) | ||
0.395231 | − | 0.918582i | \(-0.370665\pi\) | |||||||
\(878\) | −5233.92 | + | 30879.3i | −0.201180 | + | 1.18693i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 26523.4 | + | 21082.5i | 1.01603 | + | 0.807604i | ||||
\(881\) | 26128.4 | 0.999191 | 0.499595 | − | 0.866259i | \(-0.333482\pi\) | ||||
0.499595 | + | 0.866259i | \(0.333482\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26426.3i | − | 1.00715i | −0.863950 | − | 0.503577i | \(-0.832017\pi\) | ||
0.863950 | − | 0.503577i | \(-0.167983\pi\) | |||||||
\(884\) | 16188.4 | − | 46382.5i | 0.615921 | − | 1.76472i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20285.6 | − | 3438.34i | −0.769198 | − | 0.130376i | ||||
\(887\) | −11595.6 | −0.438944 | −0.219472 | − | 0.975619i | \(-0.570433\pi\) | ||||
−0.219472 | + | 0.975619i | \(0.570433\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3379.15 | 0.127484 | ||||||||
\(890\) | 19170.5 | + | 3249.33i | 0.722020 | + | 0.122379i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −48783.4 | − | 17026.4i | −1.83115 | − | 0.639108i | ||||
\(893\) | − | 4312.55i | − | 0.161606i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5462.18 | −0.204001 | ||||||||
\(896\) | 9354.57 | − | 3905.45i | 0.348788 | − | 0.145616i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4601.57 | + | 27148.5i | −0.170998 | + | 1.00886i | ||||
\(899\) | 42200.0i | 1.56557i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 77977.7i | − | 2.88326i | ||||||
\(902\) | −82273.2 | − | 13945.0i | −3.03703 | − | 0.514764i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22142.3 | + | 40177.1i | −0.814648 | + | 1.47817i | ||||
\(905\) | −27620.8 | −1.01453 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42382.2i | 1.55158i | 0.630994 | + | 0.775788i | \(0.282647\pi\) | ||||
−0.630994 | + | 0.775788i | \(0.717353\pi\) | |||||||
\(908\) | −4682.31 | + | 13415.6i | −0.171132 | + | 0.490323i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1629.66 | − | 9614.71i | 0.0593654 | − | 0.350247i | ||||
\(911\) | 8454.22 | 0.307465 | 0.153733 | − | 0.988112i | \(-0.450871\pi\) | ||||
0.153733 | + | 0.988112i | \(0.450871\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3382.87 | 0.122625 | ||||||||
\(914\) | 1018.75 | − | 6010.47i | 0.0368680 | − | 0.217515i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5394.19 | + | 15455.3i | −0.194573 | + | 0.557486i | ||||
\(917\) | − | 10140.7i | − | 0.365187i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36015.8 | 1.29277 | 0.646383 | − | 0.763014i | \(-0.276281\pi\) | ||||
0.646383 | + | 0.763014i | \(0.276281\pi\) | |||||||
\(920\) | 19959.5 | + | 11000.0i | 0.715267 | + | 0.394196i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10058.1 | − | 1704.82i | −0.359270 | − | 0.0608949i | ||||
\(923\) | − | 13784.2i | − | 0.491564i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 5824.07i | − | 0.207021i | ||||||
\(926\) | 4121.53 | − | 24316.3i | 0.146265 | − | 0.862942i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −28337.1 | − | 31582.1i | −1.00238 | − | 1.11717i | ||||
\(929\) | −19664.5 | −0.694481 | −0.347240 | − | 0.937776i | \(-0.612881\pi\) | ||||
−0.347240 | + | 0.937776i | \(0.612881\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1891.73i | 0.0665938i | ||||||||
\(932\) | 44014.8 | + | 15362.0i | 1.54694 | + | 0.539913i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 26942.0 | + | 4566.56i | 0.943863 | + | 0.159981i | ||||
\(935\) | 59277.5 | 2.07335 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20967.0 | 0.731017 | 0.365509 | − | 0.930808i | \(-0.380895\pi\) | ||||
0.365509 | + | 0.930808i | \(0.380895\pi\) | |||||||
\(938\) | −2808.00 | − | 475.944i | −0.0977445 | − | 0.0165673i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2644.69 | + | 7577.49i | −0.0917662 | + | 0.262926i | ||||
\(941\) | − | 37124.0i | − | 1.28609i | −0.765829 | − | 0.643044i | \(-0.777671\pi\) | ||
0.765829 | − | 0.643044i | \(-0.222329\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56129.2 | −1.93830 | ||||||||
\(944\) | 16239.5 | − | 20430.5i | 0.559904 | − | 0.704402i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13794.1 | + | 81382.7i | −0.474084 | + | 2.79702i | ||||
\(947\) | − | 28450.0i | − | 0.976240i | −0.872776 | − | 0.488120i | \(-0.837683\pi\) | ||
0.872776 | − | 0.488120i | \(-0.162317\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 38921.4i | − | 1.33134i | ||||||
\(950\) | 4773.86 | + | 809.151i | 0.163036 | + | 0.0276340i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8560.30 | − | 15532.6i | 0.291430 | − | 0.528797i | ||||
\(953\) | 36489.4 | 1.24030 | 0.620151 | − | 0.784483i | \(-0.287071\pi\) | ||||
0.620151 | + | 0.784483i | \(0.287071\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1997.33i | 0.0676774i | ||||||||
\(956\) | −44519.3 | − | 15538.1i | −1.50613 | − | 0.525667i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3470.13 | + | 20473.2i | −0.117030 | + | 0.690458i | ||||
\(959\) | −7305.37 | −0.245988 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2620.72 | 0.0879700 | ||||||||
\(962\) | 3404.76 | − | 20087.6i | 0.114110 | − | 0.673232i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15540.5 | + | 5423.94i | 0.519219 | + | 0.181217i | ||||
\(965\) | 20432.1i | 0.681589i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39597.5 | −1.31682 | −0.658412 | − | 0.752658i | \(-0.728772\pi\) | ||||
−0.658412 | + | 0.752658i | \(0.728772\pi\) | |||||||
\(968\) | 23412.8 | − | 42482.4i | 0.777393 | − | 1.41057i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9285.34 | + | 1573.83i | 0.307355 | + | 0.0520955i | ||||
\(971\) | − | 6633.40i | − | 0.219234i | −0.993974 | − | 0.109617i | \(-0.965038\pi\) | ||
0.993974 | − | 0.109617i | \(-0.0349624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 4416.48i | − | 0.145515i | ||||||
\(974\) | 6988.75 | − | 41232.5i | 0.229912 | − | 1.35644i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4954.45 | + | 6233.08i | −0.162488 | + | 0.204422i | ||||
\(977\) | 24844.2 | 0.813549 | 0.406774 | − | 0.913529i | \(-0.366654\pi\) | ||||
0.406774 | + | 0.913529i | \(0.366654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 45120.6i | − | 1.47299i | ||||||
\(980\) | 1160.11 | − | 3323.91i | 0.0378146 | − | 0.108345i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20503.1 | − | 3475.19i | −0.666273 | − | 0.112931i | ||||
\(983\) | 7133.71 | 0.231465 | 0.115732 | − | 0.993280i | \(-0.463078\pi\) | ||||
0.115732 | + | 0.993280i | \(0.463078\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1258.41 | 0.0407068 | ||||||||
\(986\) | −73191.6 | − | 12405.7i | −2.36399 | − | 0.400688i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15992.3 | + | 5581.62i | 0.514962 | + | 0.179732i | ||||
\(989\) | 55521.6i | 1.78512i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56431.1 | −1.80887 | −0.904436 | − | 0.426609i | \(-0.859708\pi\) | ||||
−0.904436 | + | 0.426609i | \(0.859708\pi\) | |||||||
\(992\) | −24256.6 | + | 21764.3i | −0.776359 | + | 0.696589i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 831.602 | − | 4906.32i | 0.0265360 | − | 0.156558i | ||||
\(995\) | 9009.23i | 0.287047i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55825.3i | 1.77333i | 0.462417 | + | 0.886663i | \(0.346982\pi\) | ||||
−0.462417 | + | 0.886663i | \(0.653018\pi\) | |||||||
\(998\) | −46860.3 | − | 7942.63i | −1.48631 | − | 0.251923i | ||||
\(999\) | 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 | 504.4.c.e.253.13 | 20 | ||
3.2 | odd | 2 | 168.4.c.b.85.8 | yes | 20 | ||
4.3 | odd | 2 | 2016.4.c.f.1009.15 | 20 | |||
8.3 | odd | 2 | 2016.4.c.f.1009.6 | 20 | |||
8.5 | even | 2 | inner | 504.4.c.e.253.14 | 20 | ||
12.11 | even | 2 | 672.4.c.b.337.14 | 20 | |||
24.5 | odd | 2 | 168.4.c.b.85.7 | ✓ | 20 | ||
24.11 | even | 2 | 672.4.c.b.337.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.c.b.85.7 | ✓ | 20 | 24.5 | odd | 2 | ||
168.4.c.b.85.8 | yes | 20 | 3.2 | odd | 2 | ||
504.4.c.e.253.13 | 20 | 1.1 | even | 1 | trivial | ||
504.4.c.e.253.14 | 20 | 8.5 | even | 2 | inner | ||
672.4.c.b.337.7 | 20 | 24.11 | even | 2 | |||
672.4.c.b.337.14 | 20 | 12.11 | even | 2 | |||
2016.4.c.f.1009.6 | 20 | 8.3 | odd | 2 | |||
2016.4.c.f.1009.15 | 20 | 4.3 | odd | 2 |