Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(127,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.127");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.121550625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 4x^{6} - 9x^{5} + 23x^{4} + 18x^{3} - 16x^{2} + 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1279.3 | ||
Root | \(-1.44918 - 1.77086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1279 |
Dual form | 1728.3.o.d.127.3 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.81174 | − | 3.13802i | 0.362348 | − | 0.627604i | −0.625999 | − | 0.779824i | \(-0.715309\pi\) |
0.988347 | + | 0.152219i | \(0.0486420\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.59422 | + | 0.920424i | −0.227746 | + | 0.131489i | −0.609532 | − | 0.792762i | \(-0.708643\pi\) |
0.381786 | + | 0.924251i | \(0.375309\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.0623 | − | 5.80948i | 0.914755 | − | 0.528134i | 0.0327970 | − | 0.999462i | \(-0.489559\pi\) |
0.881958 | + | 0.471328i | \(0.156225\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.43521 | + | 11.1461i | −0.495016 | + | 0.857394i | −0.999983 | − | 0.00574505i | \(-0.998171\pi\) |
0.504967 | + | 0.863139i | \(0.331505\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.6235 | −0.742557 | −0.371279 | − | 0.928521i | \(-0.621081\pi\) | ||||
−0.371279 | + | 0.928521i | \(0.621081\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.6526i | 1.35014i | 0.737755 | + | 0.675069i | \(0.235886\pi\) | ||||
−0.737755 | + | 0.675069i | \(0.764114\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −25.9012 | − | 14.9541i | −1.12614 | − | 0.650178i | −0.183179 | − | 0.983080i | \(-0.558639\pi\) |
−0.942961 | + | 0.332902i | \(0.891972\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.93521 | + | 10.2801i | 0.237409 | + | 0.411204i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.8117 | − | 18.7265i | −0.372819 | − | 0.645741i | 0.617179 | − | 0.786822i | \(-0.288275\pi\) |
−0.989998 | + | 0.141082i | \(0.954942\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −52.4027 | − | 30.2547i | −1.69041 | − | 0.975959i | −0.954182 | − | 0.299226i | \(-0.903272\pi\) |
−0.736228 | − | 0.676733i | \(-0.763395\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.67027i | 0.190579i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.7409 | 0.695699 | 0.347849 | − | 0.937550i | \(-0.386912\pi\) | ||||
0.347849 | + | 0.937550i | \(0.386912\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.3704 | − | 57.7993i | 0.813913 | − | 1.40974i | −0.0961931 | − | 0.995363i | \(-0.530667\pi\) |
0.910106 | − | 0.414376i | \(-0.136000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14.2447 | + | 8.22418i | −0.331272 | + | 0.191260i | −0.656406 | − | 0.754408i | \(-0.727924\pi\) |
0.325134 | + | 0.945668i | \(0.394591\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −66.1505 | + | 38.1920i | −1.40746 | + | 0.812595i | −0.995142 | − | 0.0984463i | \(-0.968613\pi\) |
−0.412314 | + | 0.911042i | \(0.635279\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −22.8056 | + | 39.5005i | −0.465421 | + | 0.806133i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14.2591 | 0.269041 | 0.134520 | − | 0.990911i | \(-0.457051\pi\) | ||||
0.134520 | + | 0.990911i | \(0.457051\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 42.1010i | − | 0.765472i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 50.3115 | + | 29.0474i | 0.852738 | + | 0.492328i | 0.861574 | − | 0.507633i | \(-0.169479\pi\) |
−0.00883587 | + | 0.999961i | \(0.502813\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.43521 | + | 16.3423i | 0.154676 | + | 0.267906i | 0.932941 | − | 0.360030i | \(-0.117233\pi\) |
−0.778265 | + | 0.627936i | \(0.783900\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.3178 | + | 40.3877i | 0.358736 | + | 0.621349i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −20.6216 | − | 11.9059i | −0.307785 | − | 0.177700i | 0.338150 | − | 0.941092i | \(-0.390199\pi\) |
−0.645935 | + | 0.763393i | \(0.723532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 46.4758i | 0.654589i | 0.944922 | + | 0.327294i | \(0.106137\pi\) | ||||
−0.944922 | + | 0.327294i | \(0.893863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 49.3521 | 0.676057 | 0.338028 | − | 0.941136i | \(-0.390240\pi\) | ||||
0.338028 | + | 0.941136i | \(0.390240\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.6944 | + | 18.5232i | −0.138888 | + | 0.240561i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −52.4027 | + | 30.2547i | −0.663326 | + | 0.382971i | −0.793543 | − | 0.608514i | \(-0.791766\pi\) |
0.130217 | + | 0.991485i | \(0.458433\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −86.2751 | + | 49.8109i | −1.03946 | + | 0.600132i | −0.919680 | − | 0.392669i | \(-0.871552\pi\) |
−0.119779 | + | 0.992801i | \(0.538219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.8704 | + | 39.6127i | −0.269064 | + | 0.466032i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −154.988 | −1.74144 | −0.870718 | − | 0.491783i | \(-0.836345\pi\) | ||||
−0.870718 | + | 0.491783i | \(0.836345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 23.6925i | − | 0.260357i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 80.4984 | + | 46.4758i | 0.847352 | + | 0.489219i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −21.1113 | − | 36.5658i | −0.217642 | − | 0.376967i | 0.736445 | − | 0.676498i | \(-0.236503\pi\) |
−0.954087 | + | 0.299531i | \(0.903170\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −63.1761 | − | 109.424i | −0.625506 | − | 1.08341i | −0.988443 | − | 0.151594i | \(-0.951559\pi\) |
0.362937 | − | 0.931814i | \(-0.381774\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 23.9133 | + | 13.8064i | 0.232168 | + | 0.134042i | 0.611572 | − | 0.791189i | \(-0.290538\pi\) |
−0.379404 | + | 0.925231i | \(0.623871\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 121.138i | 1.13213i | 0.824360 | + | 0.566066i | \(0.191535\pi\) | ||||
−0.824360 | + | 0.566066i | \(0.808465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −61.7409 | −0.566430 | −0.283215 | − | 0.959056i | \(-0.591401\pi\) | ||||
−0.283215 | + | 0.959056i | \(0.591401\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 43.0709 | − | 74.6010i | 0.381158 | − | 0.660186i | −0.610070 | − | 0.792348i | \(-0.708859\pi\) |
0.991228 | + | 0.132162i | \(0.0421920\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −93.8525 | + | 54.1858i | −0.816109 | + | 0.471180i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.1246 | − | 11.6190i | 0.169114 | − | 0.0976382i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | − | 12.1244i | 0.0578512 | − | 0.100201i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 133.599 | 1.06879 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 183.369i | 1.44385i | 0.691970 | + | 0.721926i | \(0.256743\pi\) | ||||
−0.691970 | + | 0.721926i | \(0.743257\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −149.631 | − | 86.3894i | −1.14222 | − | 0.659461i | −0.195240 | − | 0.980755i | \(-0.562549\pi\) |
−0.946979 | + | 0.321295i | \(0.895882\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.6113 | − | 40.8959i | −0.177528 | − | 0.307488i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 80.1235 | + | 138.778i | 0.584843 | + | 1.01298i | 0.994895 | + | 0.100915i | \(0.0321772\pi\) |
−0.410052 | + | 0.912062i | \(0.634489\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −191.971 | − | 110.835i | −1.38109 | − | 0.797371i | −0.388799 | − | 0.921322i | \(-0.627110\pi\) |
−0.992288 | + | 0.123951i | \(0.960443\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 149.541i | 1.04574i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −78.3521 | −0.540360 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −94.0343 | + | 162.872i | −0.631103 | + | 1.09310i | 0.356224 | + | 0.934401i | \(0.384064\pi\) |
−0.987327 | + | 0.158701i | \(0.949269\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −96.8344 | + | 55.9073i | −0.641287 | + | 0.370247i | −0.785110 | − | 0.619356i | \(-0.787394\pi\) |
0.143823 | + | 0.989603i | \(0.454060\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −189.880 | + | 109.627i | −1.22503 | + | 0.707273i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 51.4352 | − | 89.0884i | 0.327613 | − | 0.567442i | −0.654425 | − | 0.756127i | \(-0.727089\pi\) |
0.982038 | + | 0.188685i | \(0.0604225\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 55.0564 | 0.341965 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 205.221i | − | 1.25902i | −0.776991 | − | 0.629512i | \(-0.783255\pi\) | ||
0.776991 | − | 0.629512i | \(-0.216745\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 46.0258 | + | 26.5730i | 0.275604 | + | 0.159120i | 0.631432 | − | 0.775432i | \(-0.282468\pi\) |
−0.355828 | + | 0.934552i | \(0.615801\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.67607 | + | 2.90303i | 0.00991755 | + | 0.0171777i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 94.1517 | + | 163.075i | 0.544229 | + | 0.942633i | 0.998655 | + | 0.0518482i | \(0.0165112\pi\) |
−0.454426 | + | 0.890785i | \(0.650155\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.9241 | − | 10.9258i | −0.108138 | − | 0.0624333i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 92.9516i | 0.519283i | 0.965705 | + | 0.259641i | \(0.0836043\pi\) | ||||
−0.965705 | + | 0.259641i | \(0.916396\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 240.445 | 1.32843 | 0.664213 | − | 0.747543i | \(-0.268767\pi\) | ||||
0.664213 | + | 0.747543i | \(0.268767\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 46.6357 | − | 80.7754i | 0.252085 | − | 0.436624i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −127.021 | + | 73.3358i | −0.679258 | + | 0.392170i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −49.0077 | + | 28.2946i | −0.256585 | + | 0.148139i | −0.622776 | − | 0.782400i | \(-0.713995\pi\) |
0.366191 | + | 0.930540i | \(0.380662\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 50.3704 | − | 87.2441i | 0.260987 | − | 0.452042i | −0.705518 | − | 0.708692i | \(-0.749285\pi\) |
0.966504 | + | 0.256650i | \(0.0826188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −115.247 | −0.585010 | −0.292505 | − | 0.956264i | \(-0.594489\pi\) | ||||
−0.292505 | + | 0.956264i | \(0.594489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 190.733i | − | 0.958455i | −0.877691 | − | 0.479228i | \(-0.840917\pi\) | ||
0.877691 | − | 0.479228i | \(-0.159083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 34.4726 | + | 19.9028i | 0.169816 | + | 0.0980432i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −120.917 | − | 209.434i | −0.589839 | − | 1.02163i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 149.028 | + | 258.124i | 0.713054 | + | 1.23505i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −68.3449 | − | 39.4590i | −0.323910 | − | 0.187009i | 0.329224 | − | 0.944252i | \(-0.393213\pi\) |
−0.653134 | + | 0.757242i | \(0.726546\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 59.6003i | 0.277211i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 111.389 | 0.513312 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 81.2348 | − | 140.703i | 0.367578 | − | 0.636664i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −192.074 | + | 110.894i | −0.861321 | + | 0.497284i | −0.864454 | − | 0.502711i | \(-0.832336\pi\) |
0.00313373 | + | 0.999995i | \(0.499003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.0623 | − | 5.80948i | 0.0443273 | − | 0.0255924i | −0.477673 | − | 0.878538i | \(-0.658519\pi\) |
0.522000 | + | 0.852946i | \(0.325186\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.4352 | + | 42.3230i | −0.106704 | + | 0.184817i | −0.914433 | − | 0.404737i | \(-0.867363\pi\) |
0.807729 | + | 0.589554i | \(0.200696\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −384.785 | −1.65144 | −0.825719 | − | 0.564082i | \(-0.809230\pi\) | ||||
−0.825719 | + | 0.564082i | \(0.809230\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 276.775i | 1.17777i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −169.755 | − | 98.0083i | −0.710274 | − | 0.410077i | 0.100889 | − | 0.994898i | \(-0.467831\pi\) |
−0.811162 | + | 0.584821i | \(0.801165\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −130.593 | − | 226.194i | −0.541880 | − | 0.938563i | −0.998796 | − | 0.0490534i | \(-0.984380\pi\) |
0.456917 | − | 0.889510i | \(-0.348954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 82.6357 | + | 143.129i | 0.337288 | + | 0.584201i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −285.927 | − | 165.080i | −1.15760 | − | 0.668340i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 137.922i | 0.549490i | 0.961517 | + | 0.274745i | \(0.0885934\pi\) | ||||
−0.961517 | + | 0.274745i | \(0.911407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −347.502 | −1.37352 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.7348 | − | 23.7893i | 0.0534426 | − | 0.0925653i | −0.838066 | − | 0.545568i | \(-0.816314\pi\) |
0.891509 | + | 0.453003i | \(0.149647\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −41.0366 | + | 23.6925i | −0.158443 | + | 0.0914768i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −250.254 | + | 144.484i | −0.951535 | + | 0.549369i | −0.893558 | − | 0.448949i | \(-0.851799\pi\) |
−0.0579779 | + | 0.998318i | \(0.518465\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.8338 | − | 44.7455i | 0.0974862 | − | 0.168851i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −180.235 | −0.670018 | −0.335009 | − | 0.942215i | \(-0.608739\pi\) | ||||
−0.335009 | + | 0.942215i | \(0.608739\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 28.9765i | − | 0.106924i | −0.998570 | − | 0.0534622i | \(-0.982974\pi\) | ||
0.998570 | − | 0.0534622i | \(-0.0170257\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 119.444 | + | 68.9609i | 0.434341 | + | 0.250767i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 146.528 | + | 253.794i | 0.528983 | + | 0.916225i | 0.999429 | + | 0.0337961i | \(0.0107597\pi\) |
−0.470446 | + | 0.882429i | \(0.655907\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.6700 | − | 25.4091i | −0.0522063 | − | 0.0904239i | 0.838741 | − | 0.544530i | \(-0.183292\pi\) |
−0.890948 | + | 0.454106i | \(0.849959\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 179.527 | + | 103.650i | 0.634372 | + | 0.366255i | 0.782443 | − | 0.622722i | \(-0.213973\pi\) |
−0.148071 | + | 0.988977i | \(0.547307\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 122.860i | 0.428083i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −129.648 | −0.448609 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 248.905 | − | 431.116i | 0.849504 | − | 1.47138i | −0.0321473 | − | 0.999483i | \(-0.510235\pi\) |
0.881651 | − | 0.471901i | \(-0.156432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 182.303 | − | 105.252i | 0.617975 | − | 0.356788i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 333.360 | − | 192.465i | 1.11492 | − | 0.643697i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.1395 | − | 26.2223i | 0.0502973 | − | 0.0871174i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 68.3765 | 0.224185 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.7775i | 0.106767i | 0.998574 | + | 0.0533835i | \(0.0170006\pi\) | ||||
−0.998574 | + | 0.0533835i | \(0.982999\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −330.752 | − | 190.960i | −1.06351 | − | 0.614019i | −0.137110 | − | 0.990556i | \(-0.543782\pi\) |
−0.926402 | + | 0.376537i | \(0.877115\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 247.593 | + | 428.844i | 0.791032 | + | 1.37011i | 0.925329 | + | 0.379166i | \(0.123789\pi\) |
−0.134297 | + | 0.990941i | \(0.542878\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 140.200 | + | 242.834i | 0.442273 | + | 0.766039i | 0.997858 | − | 0.0654209i | \(-0.0208390\pi\) |
−0.555585 | + | 0.831460i | \(0.687506\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −217.582 | − | 125.621i | −0.682075 | − | 0.393796i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 323.825i | − | 1.00255i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −152.777 | −0.470084 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 70.3056 | − | 121.773i | 0.213695 | − | 0.370131i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.57609 | + | 2.64201i | −0.0138251 | + | 0.00798190i | −0.506897 | − | 0.862007i | \(-0.669207\pi\) |
0.493072 | + | 0.869989i | \(0.335874\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −74.7218 | + | 43.1407i | −0.223050 | + | 0.128778i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −121.945 | + | 211.215i | −0.361855 | + | 0.626751i | −0.988266 | − | 0.152742i | \(-0.951190\pi\) |
0.626411 | + | 0.779493i | \(0.284523\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −703.056 | −2.06175 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 174.165i | − | 0.507770i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 168.452 | + | 97.2556i | 0.485451 | + | 0.280275i | 0.722685 | − | 0.691177i | \(-0.242908\pi\) |
−0.237234 | + | 0.971452i | \(0.576241\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 202.139 | + | 350.116i | 0.579196 | + | 1.00320i | 0.995572 | + | 0.0940045i | \(0.0299668\pi\) |
−0.416376 | + | 0.909193i | \(0.636700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −145.463 | − | 251.950i | −0.412078 | − | 0.713739i | 0.583039 | − | 0.812444i | \(-0.301863\pi\) |
−0.995117 | + | 0.0987047i | \(0.968530\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 145.842 | + | 84.2020i | 0.410823 | + | 0.237189i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 554.699i | − | 1.54512i | −0.634941 | − | 0.772561i | \(-0.718976\pi\) | ||
0.634941 | − | 0.772561i | \(-0.281024\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −297.056 | −0.822871 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 89.4131 | − | 154.868i | 0.244967 | − | 0.424296i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.3661 | − | 6.56223i | 0.0309703 | − | 0.0178807i | −0.484435 | − | 0.874827i | \(-0.660975\pi\) |
0.515405 | + | 0.856947i | \(0.327641\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.7322 | + | 13.1245i | −0.0612729 | + | 0.0353759i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 209.306 | − | 362.528i | 0.561141 | − | 0.971925i | −0.436256 | − | 0.899823i | \(-0.643696\pi\) |
0.997397 | − | 0.0721024i | \(-0.0229708\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 278.303 | 0.738205 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 546.545i | 1.44207i | 0.692898 | + | 0.721036i | \(0.256334\pi\) | ||||
−0.692898 | + | 0.721036i | \(0.743666\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 511.874 | + | 295.530i | 1.33649 | + | 0.771620i | 0.986284 | − | 0.165055i | \(-0.0527801\pi\) |
0.350201 | + | 0.936675i | \(0.386113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 38.7508 | + | 67.1183i | 0.100651 | + | 0.174333i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 172.694 | + | 299.115i | 0.443944 | + | 0.768934i | 0.997978 | − | 0.0635601i | \(-0.0202454\pi\) |
−0.554034 | + | 0.832494i | \(0.686912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 326.964 | + | 188.773i | 0.836224 | + | 0.482794i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 219.255i | 0.555075i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 385.741 | 0.971639 | 0.485820 | − | 0.874059i | \(-0.338521\pi\) | ||||
0.485820 | + | 0.874059i | \(0.338521\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 59.0869 | − | 102.341i | 0.147349 | − | 0.255216i | −0.782898 | − | 0.622150i | \(-0.786259\pi\) |
0.930247 | + | 0.366934i | \(0.119593\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 674.445 | − | 389.391i | 1.67356 | − | 0.966231i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 259.012 | − | 149.541i | 0.636394 | − | 0.367422i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 167.852 | − | 290.728i | 0.410396 | − | 0.710827i | −0.584537 | − | 0.811367i | \(-0.698724\pi\) |
0.994933 | + | 0.100540i | \(0.0320570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −106.944 | −0.258943 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 360.977i | 0.869825i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.8831 | − | 16.6757i | −0.0689334 | − | 0.0397987i | 0.465137 | − | 0.885239i | \(-0.346005\pi\) |
−0.534071 | + | 0.845440i | \(0.679338\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −138.824 | − | 240.450i | −0.329748 | − | 0.571140i | 0.652714 | − | 0.757605i | \(-0.273630\pi\) |
−0.982462 | + | 0.186464i | \(0.940297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −74.9230 | − | 129.770i | −0.176289 | − | 0.305342i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.0836 | − | 17.3688i | −0.0704535 | − | 0.0406763i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 368.795i | 0.855674i | 0.903856 | + | 0.427837i | \(0.140724\pi\) | ||||
−0.903856 | + | 0.427837i | \(0.859276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 585.093 | 1.35125 | 0.675627 | − | 0.737244i | \(-0.263873\pi\) | ||||
0.675627 | + | 0.737244i | \(0.263873\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 383.611 | − | 664.434i | 0.877829 | − | 1.52044i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 569.640 | − | 328.882i | 1.29759 | − | 0.749161i | 0.317599 | − | 0.948225i | \(-0.397123\pi\) |
0.979987 | + | 0.199064i | \(0.0637901\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −96.1502 | + | 55.5124i | −0.217043 | + | 0.125310i | −0.604581 | − | 0.796544i | \(-0.706659\pi\) |
0.387537 | + | 0.921854i | \(0.373326\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −280.797 | + | 486.355i | −0.631005 | + | 1.09293i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −136.056 | −0.303021 | −0.151510 | − | 0.988456i | \(-0.548414\pi\) | ||||
−0.151510 | + | 0.988456i | \(0.548414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 775.459i | − | 1.71942i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −74.3476 | − | 42.9246i | −0.163401 | − | 0.0943398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.0747 | + | 50.3588i | 0.0636208 | + | 0.110194i | 0.896081 | − | 0.443890i | \(-0.146402\pi\) |
−0.832461 | + | 0.554084i | \(0.813069\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −51.4916 | − | 89.1861i | −0.111695 | − | 0.193462i | 0.804759 | − | 0.593602i | \(-0.202295\pi\) |
−0.916454 | + | 0.400140i | \(0.868961\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 672.083 | + | 388.027i | 1.45158 | + | 0.838072i | 0.998571 | − | 0.0534320i | \(-0.0170160\pi\) |
0.453012 | + | 0.891504i | \(0.350349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 692.620i | − | 1.48313i | −0.670882 | − | 0.741564i | \(-0.734085\pi\) | ||
0.670882 | − | 0.741564i | \(-0.265915\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 43.8338 | 0.0934623 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −95.5564 | + | 165.509i | −0.202022 | + | 0.349912i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −263.711 | + | 152.254i | −0.555181 | + | 0.320534i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 630.014 | − | 363.739i | 1.31527 | − | 0.759371i | 0.332305 | − | 0.943172i | \(-0.392174\pi\) |
0.982963 | + | 0.183801i | \(0.0588402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −165.648 | + | 286.911i | −0.344382 | + | 0.596488i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −152.992 | −0.315448 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 285.503i | 0.586248i | 0.956074 | + | 0.293124i | \(0.0946948\pi\) | ||||
−0.956074 | + | 0.293124i | \(0.905305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −188.576 | − | 108.875i | −0.384066 | − | 0.221740i | 0.295520 | − | 0.955337i | \(-0.404507\pi\) |
−0.679586 | + | 0.733596i | \(0.737840\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 136.482 | + | 236.393i | 0.276839 | + | 0.479499i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −42.7774 | − | 74.0927i | −0.0860713 | − | 0.149080i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.1869 | + | 17.4284i | 0.0604948 | + | 0.0349267i | 0.529942 | − | 0.848034i | \(-0.322214\pi\) |
−0.469448 | + | 0.882960i | \(0.655547\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 345.125i | − | 0.686134i | −0.939311 | − | 0.343067i | \(-0.888534\pi\) | ||
0.939311 | − | 0.343067i | \(-0.111466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −457.834 | −0.906602 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 189.528 | − | 328.272i | 0.372354 | − | 0.644936i | −0.617573 | − | 0.786513i | \(-0.711884\pi\) |
0.989927 | + | 0.141577i | \(0.0452174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −78.6782 | + | 45.4249i | −0.153969 | + | 0.0888941i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 86.6493 | − | 50.0270i | 0.168251 | − | 0.0971398i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −443.751 | + | 768.599i | −0.858319 | + | 1.48665i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.2028 | −0.0771646 | −0.0385823 | − | 0.999255i | \(-0.512284\pi\) | ||||
−0.0385823 | + | 0.999255i | \(0.512284\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 623.980i | − | 1.19308i | −0.802584 | − | 0.596539i | \(-0.796542\pi\) | ||
0.802584 | − | 0.596539i | \(-0.203458\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 661.505 | + | 381.920i | 1.25523 | + | 0.724706i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 182.749 | + | 316.531i | 0.345462 | + | 0.598357i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 429.492 | + | 743.901i | 0.805800 | + | 1.39569i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 380.134 | + | 219.471i | 0.710531 | + | 0.410225i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 529.955i | 0.983219i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −529.741 | −0.979188 | −0.489594 | − | 0.871950i | \(-0.662855\pi\) | ||||
−0.489594 | + | 0.871950i | \(0.662855\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −111.858 | + | 193.744i | −0.205244 | + | 0.355494i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 512.558 | − | 295.925i | 0.937035 | − | 0.540997i | 0.0480051 | − | 0.998847i | \(-0.484714\pi\) |
0.889029 | + | 0.457850i | \(0.151380\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 480.383 | − | 277.349i | 0.871839 | − | 0.503356i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 55.6944 | − | 96.4655i | 0.100713 | − | 0.174440i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −682.841 | −1.22593 | −0.612964 | − | 0.790111i | \(-0.710023\pi\) | ||||
−0.612964 | + | 0.790111i | \(0.710023\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 211.698i | − | 0.378708i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −889.956 | − | 513.816i | −1.58074 | − | 0.912640i | −0.994752 | − | 0.102319i | \(-0.967374\pi\) |
−0.585987 | − | 0.810321i | \(-0.699293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −156.066 | − | 270.315i | −0.276224 | − | 0.478433i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 165.913 | + | 287.370i | 0.291587 | + | 0.505044i | 0.974185 | − | 0.225750i | \(-0.0724833\pi\) |
−0.682598 | + | 0.730794i | \(0.739150\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 289.987 | + | 167.424i | 0.507858 | + | 0.293212i | 0.731953 | − | 0.681356i | \(-0.238609\pi\) |
−0.224095 | + | 0.974567i | \(0.571943\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 355.023i | − | 0.617431i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −87.6845 | −0.151966 | −0.0759831 | − | 0.997109i | \(-0.524209\pi\) | ||||
−0.0759831 | + | 0.997109i | \(0.524209\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 91.6944 | − | 158.819i | 0.157822 | − | 0.273355i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 143.480 | − | 82.8382i | 0.246106 | − | 0.142089i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 116.275 | − | 67.1313i | 0.198083 | − | 0.114363i | −0.397678 | − | 0.917525i | \(-0.630184\pi\) |
0.595761 | + | 0.803162i | \(0.296851\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 776.113 | − | 1344.27i | 1.31768 | − | 2.28229i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −256.915 | −0.433246 | −0.216623 | − | 0.976255i | \(-0.569504\pi\) | ||||
−0.216623 | + | 0.976255i | \(0.569504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 84.2020i | − | 0.141516i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −851.385 | − | 491.547i | −1.42134 | − | 0.820613i | −0.424929 | − | 0.905227i | \(-0.639701\pi\) |
−0.996414 | + | 0.0846136i | \(0.973034\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −558.909 | − | 968.058i | −0.929964 | − | 1.61075i | −0.783376 | − | 0.621548i | \(-0.786504\pi\) |
−0.146588 | − | 0.989198i | \(-0.546829\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.3643 | − | 43.9323i | −0.0419245 | − | 0.0726154i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 259.238 | + | 149.671i | 0.427081 | + | 0.246575i | 0.698102 | − | 0.715998i | \(-0.254028\pi\) |
−0.271021 | + | 0.962573i | \(0.587361\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 983.094i | − | 1.60899i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 468.332 | 0.764001 | 0.382000 | − | 0.924162i | \(-0.375235\pi\) | ||||
0.382000 | + | 0.924162i | \(0.375235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 396.884 | − | 687.423i | 0.643248 | − | 1.11414i | −0.341455 | − | 0.939898i | \(-0.610920\pi\) |
0.984703 | − | 0.174240i | \(-0.0557470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −782.130 | + | 451.563i | −1.26354 | + | 0.729504i | −0.973757 | − | 0.227590i | \(-0.926915\pi\) |
−0.289780 | + | 0.957093i | \(0.593582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 247.085 | − | 142.654i | 0.396605 | − | 0.228980i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 93.6662 | − | 162.235i | 0.149866 | − | 0.259575i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −324.939 | −0.516596 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 484.076i | − | 0.767156i | −0.923508 | − | 0.383578i | \(-0.874692\pi\) | ||
0.923508 | − | 0.383578i | \(-0.125308\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 575.417 | + | 332.217i | 0.906168 | + | 0.523176i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −293.518 | − | 508.389i | −0.460782 | − | 0.798098i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 173.864 | + | 301.142i | 0.271239 | + | 0.469800i | 0.969179 | − | 0.246356i | \(-0.0792332\pi\) |
−0.697940 | + | 0.716156i | \(0.745900\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 162.862 | + | 94.0285i | 0.253285 | + | 0.146234i | 0.621267 | − | 0.783599i | \(-0.286618\pi\) |
−0.367983 | + | 0.929833i | \(0.619951\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 853.348i | − | 1.31893i | −0.751735 | − | 0.659465i | \(-0.770783\pi\) | ||
0.751735 | − | 0.659465i | \(-0.229217\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 675.000 | 1.04006 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −599.678 | + | 1038.67i | −0.918342 | + | 1.59062i | −0.116410 | + | 0.993201i | \(0.537139\pi\) |
−0.801933 | + | 0.597414i | \(0.796195\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −542.183 | + | 313.030i | −0.827761 | + | 0.477908i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 534.606 | − | 308.655i | 0.811238 | − | 0.468369i | −0.0361474 | − | 0.999346i | \(-0.511509\pi\) |
0.847386 | + | 0.530978i | \(0.178175\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 109.880 | − | 190.318i | 0.166233 | − | 0.287925i | −0.770859 | − | 0.637006i | \(-0.780173\pi\) |
0.937093 | + | 0.349081i | \(0.113506\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −171.110 | −0.257308 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 646.719i | 0.969593i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 189.880 | + | 109.627i | 0.282981 | + | 0.163379i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −289.492 | − | 501.414i | −0.430151 | − | 0.745043i | 0.566735 | − | 0.823900i | \(-0.308206\pi\) |
−0.996886 | + | 0.0788568i | \(0.974873\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 351.528 | + | 608.865i | 0.519244 | + | 0.899357i | 0.999750 | + | 0.0223655i | \(0.00711975\pi\) |
−0.480506 | + | 0.876992i | \(0.659547\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 67.3121 | + | 38.8627i | 0.0991342 | + | 0.0572351i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 881.535i | − | 1.29068i | −0.763895 | − | 0.645340i | \(-0.776716\pi\) | ||
0.763895 | − | 0.645340i | \(-0.223284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 580.651 | 0.847666 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −91.7607 | + | 158.934i | −0.133179 | + | 0.230674i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 890.846 | − | 514.330i | 1.28921 | − | 0.744328i | 0.310699 | − | 0.950508i | \(-0.399437\pi\) |
0.978514 | + | 0.206181i | \(0.0661034\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −695.603 | + | 401.607i | −1.00087 | + | 0.577851i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −421.251 | + | 729.628i | −0.604377 | + | 1.04681i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 813.287 | 1.16018 | 0.580090 | − | 0.814552i | \(-0.303017\pi\) | ||||
0.580090 | + | 0.814552i | \(0.303017\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 660.320i | 0.939289i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 201.433 | + | 116.298i | 0.284913 | + | 0.164494i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −82.4916 | − | 142.880i | −0.116349 | − | 0.201523i | 0.801969 | − | 0.597366i | \(-0.203786\pi\) |
−0.918318 | + | 0.395843i | \(0.870453\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 904.864 | + | 1567.27i | 1.26909 | + | 2.19813i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 469.262 | + | 270.929i | 0.656311 | + | 0.378921i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 179.881i | − | 0.250182i | −0.992145 | − | 0.125091i | \(-0.960078\pi\) | ||
0.992145 | − | 0.125091i | \(-0.0399223\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.8308 | −0.0705004 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 128.340 | − | 222.291i | 0.177021 | − | 0.306609i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 664.674 | − | 383.749i | 0.914269 | − | 0.527853i | 0.0324668 | − | 0.999473i | \(-0.489664\pi\) |
0.881802 | + | 0.471619i | \(0.156330\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 179.818 | − | 103.818i | 0.245989 | − | 0.142022i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −505.139 | + | 874.927i | −0.689140 | + | 1.19363i | 0.282977 | + | 0.959127i | \(0.408678\pi\) |
−0.972117 | + | 0.234498i | \(0.924655\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −276.668 | −0.375397 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 941.306i | 1.27376i | 0.770964 | + | 0.636878i | \(0.219775\pi\) | ||||
−0.770964 | + | 0.636878i | \(0.780225\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 94.8464 | + | 54.7596i | 0.127653 | + | 0.0737007i | 0.562467 | − | 0.826820i | \(-0.309852\pi\) |
−0.434814 | + | 0.900521i | \(0.643186\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 340.731 | + | 590.163i | 0.457357 | + | 0.792166i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −111.498 | − | 193.121i | −0.148863 | − | 0.257839i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −706.330 | − | 407.800i | −0.940519 | − | 0.543009i | −0.0503961 | − | 0.998729i | \(-0.516048\pi\) |
−0.890123 | + | 0.455720i | \(0.849382\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 405.158i | 0.536633i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1253.34 | −1.65566 | −0.827830 | − | 0.560978i | \(-0.810425\pi\) | ||||
−0.827830 | + | 0.560978i | \(0.810425\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 183.095 | − | 317.130i | 0.240598 | − | 0.416728i | −0.720287 | − | 0.693677i | \(-0.755990\pi\) |
0.960885 | + | 0.276948i | \(0.0893230\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 98.4286 | − | 56.8278i | 0.129002 | − | 0.0744794i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −647.531 | + | 373.852i | −0.844238 | + | 0.487421i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 539.066 | − | 933.690i | 0.700996 | − | 1.21416i | −0.267121 | − | 0.963663i | \(-0.586072\pi\) |
0.968117 | − | 0.250498i | \(-0.0805945\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 283.085 | 0.366217 | 0.183108 | − | 0.983093i | \(-0.441384\pi\) | ||||
0.183108 | + | 0.983093i | \(0.441384\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 718.273i | − | 0.926804i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1482.70 | + | 856.039i | 1.90334 | + | 1.09889i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 270.000 | + | 467.654i | 0.345711 | + | 0.598788i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −186.374 | − | 322.810i | −0.237419 | − | 0.411222i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 255.224 | + | 147.353i | 0.324299 | + | 0.187234i | 0.653307 | − | 0.757093i | \(-0.273381\pi\) |
−0.329008 | + | 0.944327i | \(0.606714\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 158.574i | 0.200473i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −242.870 | −0.306268 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 396.653 | − | 687.023i | 0.497683 | − | 0.862012i | −0.502314 | − | 0.864685i | \(-0.667518\pi\) |
0.999996 | + | 0.00267363i | \(0.000851044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 835.049 | − | 482.116i | 1.04512 | − | 0.603399i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 496.596 | − | 286.710i | 0.618426 | − | 0.357049i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 99.7477 | − | 172.768i | 0.123910 | − | 0.214619i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1215.12 | −1.50200 | −0.751000 | − | 0.660303i | \(-0.770428\pi\) | ||||
−0.751000 | + | 0.660303i | \(0.770428\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 429.447i | 0.529527i | 0.964313 | + | 0.264764i | \(0.0852939\pi\) | ||||
−0.964313 | + | 0.264764i | \(0.914706\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −643.988 | − | 371.806i | −0.790169 | − | 0.456204i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −210.972 | − | 365.414i | −0.258227 | − | 0.447263i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.68216 | + | 6.37769i | 0.00448497 | + | 0.00776820i | 0.868259 | − | 0.496111i | \(-0.165239\pi\) |
−0.863774 | + | 0.503879i | \(0.831906\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1169.36 | − | 675.132i | −1.42085 | − | 0.820331i | −0.424483 | − | 0.905436i | \(-0.639544\pi\) |
−0.996372 | + | 0.0851049i | \(0.972877\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 571.482i | 0.691031i | 0.938413 | + | 0.345515i | \(0.112296\pi\) | ||||
−0.938413 | + | 0.345515i | \(0.887704\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 888.445 | 1.07171 | 0.535854 | − | 0.844311i | \(-0.319990\pi\) | ||||
0.535854 | + | 0.844311i | \(0.319990\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 287.886 | − | 498.634i | 0.345602 | − | 0.598600i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 166.774 | − | 96.2867i | 0.199729 | − | 0.115313i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 506.659 | − | 292.519i | 0.603884 | − | 0.348652i | −0.166684 | − | 0.986010i | \(-0.553306\pi\) |
0.770568 | + | 0.637358i | \(0.219973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 186.713 | − | 323.396i | 0.222013 | − | 0.384537i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.1464 | 0.0143744 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.7719i | 0.0304272i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −666.720 | − | 384.931i | −0.783455 | − | 0.452328i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −437.917 | − | 758.494i | −0.513384 | − | 0.889208i | −0.999879 | − | 0.0155246i | \(-0.995058\pi\) |
0.486495 | − | 0.873683i | \(-0.338275\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 186.836 | + | 323.610i | 0.218012 | + | 0.377608i | 0.954200 | − | 0.299169i | \(-0.0967095\pi\) |
−0.736188 | + | 0.676777i | \(0.763376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 253.378 | + | 146.288i | 0.294968 | + | 0.170300i | 0.640180 | − | 0.768225i | \(-0.278860\pi\) |
−0.345212 | + | 0.938525i | \(0.612193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1461.41i | 1.69341i | 0.532066 | + | 0.846703i | \(0.321416\pi\) | ||||
−0.532066 | + | 0.846703i | \(0.678584\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 682.313 | 0.788801 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −351.528 | + | 608.865i | −0.404520 | + | 0.700650i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 265.409 | − | 153.234i | 0.304717 | − | 0.175929i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −212.986 | + | 122.968i | −0.243413 | + | 0.140535i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.5648 | + | 66.7962i | −0.0439735 | + | 0.0761644i | −0.887174 | − | 0.461434i | \(-0.847335\pi\) |
0.843201 | + | 0.537599i | \(0.180668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −371.927 | −0.422164 | −0.211082 | − | 0.977468i | \(-0.567699\pi\) | ||||
−0.211082 | + | 0.977468i | \(0.567699\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 875.990i | − | 0.992061i | −0.868305 | − | 0.496030i | \(-0.834790\pi\) | ||
0.868305 | − | 0.496030i | \(-0.165210\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −247.646 | − | 142.979i | −0.279195 | − | 0.161193i | 0.353864 | − | 0.935297i | \(-0.384868\pi\) |
−0.633059 | + | 0.774104i | \(0.718201\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −168.777 | − | 292.331i | −0.189851 | − | 0.328831i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −979.724 | − | 1696.93i | −1.09712 | − | 1.90026i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 291.684 | + | 168.404i | 0.325904 | + | 0.188161i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1308.42i | 1.45542i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −180.000 | −0.199778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 435.623 | − | 754.522i | 0.481352 | − | 0.833726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 615.208 | − | 355.190i | 0.678289 | − | 0.391610i | −0.120921 | − | 0.992662i | \(-0.538585\pi\) |
0.799210 | + | 0.601052i | \(0.205252\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −167.148 | + | 96.5028i | −0.183477 | + | 0.105931i | −0.588925 | − | 0.808187i | \(-0.700449\pi\) |
0.405448 | + | 0.914118i | \(0.367115\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −578.751 | + | 1002.43i | −0.633900 | + | 1.09795i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 318.059 | 0.346848 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1106.39i | − | 1.20390i | −0.798533 | − | 0.601951i | \(-0.794390\pi\) | ||
0.798533 | − | 0.601951i | \(-0.205610\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −518.025 | − | 299.082i | −0.561240 | − | 0.324032i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 152.777 | + | 264.618i | 0.165165 | + | 0.286074i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54.4108 | − | 94.2423i | −0.0585692 | − | 0.101445i | 0.835254 | − | 0.549864i | \(-0.185321\pi\) |
−0.893823 | + | 0.448419i | \(0.851987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1013.29 | − | 585.024i | −1.08839 | − | 0.628383i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 531.461i | 0.568407i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1530.74 | −1.63366 | −0.816832 | − | 0.576875i | \(-0.804272\pi\) | ||||
−0.816832 | + | 0.576875i | \(0.804272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −730.350 | + | 1265.00i | −0.776142 | + | 1.34432i | 0.158008 | + | 0.987438i | \(0.449493\pi\) |
−0.934150 | + | 0.356880i | \(0.883841\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1728.67 | + | 998.048i | −1.83316 | + | 1.05838i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −292.181 | + | 168.691i | −0.308533 | + | 0.178132i | −0.646270 | − | 0.763109i | \(-0.723672\pi\) |
0.337737 | + | 0.941241i | \(0.390339\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −317.591 | + | 550.085i | −0.334659 | + | 0.579647i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.6997 | 0.0122767 | 0.00613834 | − | 0.999981i | \(-0.498046\pi\) | ||||
0.00613834 | + | 0.999981i | \(0.498046\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 205.050i | 0.214712i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −255.469 | − | 147.495i | −0.266391 | − | 0.153801i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1350.20 | + | 2338.61i | 1.40499 | + | 2.43352i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −182.516 | − | 316.127i | −0.189136 | − | 0.327593i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1072.38 | + | 619.139i | 1.10898 | + | 0.640268i | 0.938564 | − | 0.345104i | \(-0.112156\pi\) |
0.170413 | + | 0.985373i | \(0.445490\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.4978i | 0.0540658i | 0.999635 | + | 0.0270329i | \(0.00860588\pi\) | ||||
−0.999635 | + | 0.0270329i | \(0.991394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 408.059 | 0.419383 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 52.7789 | − | 91.4158i | 0.0540214 | − | 0.0935679i | −0.837750 | − | 0.546054i | \(-0.816129\pi\) |
0.891772 | + | 0.452486i | \(0.149463\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1559.53 | + | 900.398i | −1.59299 | + | 0.919712i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.77662 | − | 3.33513i | 0.00587652 | − | 0.00339281i | −0.497059 | − | 0.867717i | \(-0.665587\pi\) |
0.502935 | + | 0.864324i | \(0.332253\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −208.797 | + | 361.647i | −0.211977 | + | 0.367155i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 491.941 | 0.497412 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1394.27i | 1.40694i | 0.710727 | + | 0.703468i | \(0.248366\pi\) | ||||
−0.710727 | + | 0.703468i | \(0.751634\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −598.523 | − | 345.557i | −0.601531 | − | 0.347294i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 634.771 | + | 1099.45i | 0.636681 | + | 1.10276i | 0.986156 | + | 0.165818i | \(0.0530263\pi\) |
−0.349476 | + | 0.936945i | \(0.613640\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1728.3.o.d.1279.3 | 8 | ||
3.2 | odd | 2 | 576.3.o.e.319.4 | 8 | |||
4.3 | odd | 2 | inner | 1728.3.o.d.1279.4 | 8 | ||
8.3 | odd | 2 | 432.3.o.c.415.2 | 8 | |||
8.5 | even | 2 | 432.3.o.c.415.1 | 8 | |||
9.2 | odd | 6 | 576.3.o.e.511.1 | 8 | |||
9.7 | even | 3 | inner | 1728.3.o.d.127.4 | 8 | ||
12.11 | even | 2 | 576.3.o.e.319.1 | 8 | |||
24.5 | odd | 2 | 144.3.o.b.31.1 | ✓ | 8 | ||
24.11 | even | 2 | 144.3.o.b.31.4 | yes | 8 | ||
36.7 | odd | 6 | inner | 1728.3.o.d.127.3 | 8 | ||
36.11 | even | 6 | 576.3.o.e.511.4 | 8 | |||
72.5 | odd | 6 | 1296.3.g.h.1135.1 | 4 | |||
72.11 | even | 6 | 144.3.o.b.79.1 | yes | 8 | ||
72.13 | even | 6 | 1296.3.g.d.1135.3 | 4 | |||
72.29 | odd | 6 | 144.3.o.b.79.4 | yes | 8 | ||
72.43 | odd | 6 | 432.3.o.c.127.1 | 8 | |||
72.59 | even | 6 | 1296.3.g.h.1135.2 | 4 | |||
72.61 | even | 6 | 432.3.o.c.127.2 | 8 | |||
72.67 | odd | 6 | 1296.3.g.d.1135.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.o.b.31.1 | ✓ | 8 | 24.5 | odd | 2 | ||
144.3.o.b.31.4 | yes | 8 | 24.11 | even | 2 | ||
144.3.o.b.79.1 | yes | 8 | 72.11 | even | 6 | ||
144.3.o.b.79.4 | yes | 8 | 72.29 | odd | 6 | ||
432.3.o.c.127.1 | 8 | 72.43 | odd | 6 | |||
432.3.o.c.127.2 | 8 | 72.61 | even | 6 | |||
432.3.o.c.415.1 | 8 | 8.5 | even | 2 | |||
432.3.o.c.415.2 | 8 | 8.3 | odd | 2 | |||
576.3.o.e.319.1 | 8 | 12.11 | even | 2 | |||
576.3.o.e.319.4 | 8 | 3.2 | odd | 2 | |||
576.3.o.e.511.1 | 8 | 9.2 | odd | 6 | |||
576.3.o.e.511.4 | 8 | 36.11 | even | 6 | |||
1296.3.g.d.1135.3 | 4 | 72.13 | even | 6 | |||
1296.3.g.d.1135.4 | 4 | 72.67 | odd | 6 | |||
1296.3.g.h.1135.1 | 4 | 72.5 | odd | 6 | |||
1296.3.g.h.1135.2 | 4 | 72.59 | even | 6 | |||
1728.3.o.d.127.3 | 8 | 36.7 | odd | 6 | inner | ||
1728.3.o.d.127.4 | 8 | 9.7 | even | 3 | inner | ||
1728.3.o.d.1279.3 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.o.d.1279.4 | 8 | 4.3 | odd | 2 | inner |