Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [208,4,Mod(17,208)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(208, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("208.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 208 = 2^{4} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 208.w (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: | \(12.2723972812\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 208.17 |
Dual form | 208.4.w.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/208\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.50000 | + | 6.06218i | −0.673575 | + | 1.16667i | 0.303308 | + | 0.952893i | \(0.401909\pi\) |
−0.976883 | + | 0.213774i | \(0.931424\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.8564i | 1.23935i | 0.784857 | + | 0.619677i | \(0.212737\pi\) | ||||
−0.784857 | + | 0.619677i | \(0.787263\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −19.5000 | + | 11.2583i | −1.05290 | + | 0.607893i | −0.923460 | − | 0.383694i | \(-0.874652\pi\) |
−0.129441 | + | 0.991587i | \(0.541318\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −11.0000 | − | 19.0526i | −0.407407 | − | 0.705650i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.5000 | + | 11.2583i | 0.534497 | + | 0.308592i | 0.742846 | − | 0.669462i | \(-0.233475\pi\) |
−0.208349 | + | 0.978055i | \(0.566809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | + | 45.0333i | −0.277350 | + | 0.960769i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −84.0000 | − | 48.4974i | −1.44591 | − | 0.834799i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.5000 | − | 23.3827i | −0.192602 | − | 0.333596i | 0.753510 | − | 0.657437i | \(-0.228359\pi\) |
−0.946112 | + | 0.323840i | \(0.895026\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 76.5000 | − | 44.1673i | 0.923700 | − | 0.533299i | 0.0388865 | − | 0.999244i | \(-0.487619\pi\) |
0.884814 | + | 0.465945i | \(0.154286\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 157.617i | − | 1.63785i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 28.5000 | − | 49.3634i | 0.258377 | − | 0.447521i | −0.707431 | − | 0.706783i | \(-0.750146\pi\) |
0.965807 | + | 0.259261i | \(0.0834791\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −67.0000 | −0.536000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −35.0000 | −0.249472 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 34.5000 | − | 59.7558i | 0.220913 | − | 0.382633i | −0.734172 | − | 0.678963i | \(-0.762430\pi\) |
0.955086 | + | 0.296330i | \(0.0957628\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 72.7461i | 0.421471i | 0.977543 | + | 0.210735i | \(0.0675858\pi\) | ||||
−0.977543 | + | 0.210735i | \(0.932414\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −136.500 | + | 78.8083i | −0.720048 | + | 0.415720i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −156.000 | − | 270.200i | −0.753395 | − | 1.30492i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −34.5000 | − | 19.9186i | −0.153291 | − | 0.0885026i | 0.421393 | − | 0.906878i | \(-0.361541\pi\) |
−0.574683 | + | 0.818376i | \(0.694875\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −227.500 | − | 236.425i | −0.934081 | − | 0.970725i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −340.500 | − | 196.588i | −1.29700 | − | 0.748826i | −0.317118 | − | 0.948386i | \(-0.602715\pi\) |
−0.979886 | + | 0.199560i | \(0.936049\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −42.5000 | − | 73.6122i | −0.150725 | − | 0.261064i | 0.780769 | − | 0.624820i | \(-0.214828\pi\) |
−0.931494 | + | 0.363756i | \(0.881494\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 264.000 | − | 152.420i | 0.874551 | − | 0.504922i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 342.946i | 1.06434i | 0.846639 | + | 0.532168i | \(0.178623\pi\) | ||||
−0.846639 | + | 0.532168i | \(0.821377\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 82.0000 | − | 142.028i | 0.239067 | − | 0.414076i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 189.000 | 0.518927 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 426.000 | 1.10407 | 0.552034 | − | 0.833822i | \(-0.313852\pi\) | ||||
0.552034 | + | 0.833822i | \(0.313852\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −156.000 | + | 270.200i | −0.382455 | + | 0.662432i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 618.342i | 1.43687i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16.5000 | − | 9.52628i | 0.0364088 | − | 0.0210206i | −0.481685 | − | 0.876344i | \(-0.659975\pi\) |
0.518094 | + | 0.855324i | \(0.326642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.50000 | + | 14.7224i | 0.0178412 | + | 0.0309019i | 0.874808 | − | 0.484469i | \(-0.160987\pi\) |
−0.856967 | + | 0.515371i | \(0.827654\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 429.000 | + | 247.683i | 0.857919 | + | 0.495320i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −624.000 | − | 180.133i | −1.19073 | − | 0.343735i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −142.500 | − | 82.2724i | −0.259838 | − | 0.150018i | 0.364423 | − | 0.931234i | \(-0.381266\pi\) |
−0.624261 | + | 0.781216i | \(0.714600\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 199.500 | + | 345.544i | 0.348072 | + | 0.602879i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −505.500 | + | 291.851i | −0.844955 | + | 0.487835i | −0.858945 | − | 0.512067i | \(-0.828880\pi\) |
0.0139904 | + | 0.999902i | \(0.495547\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1004.59i | 1.61066i | 0.592826 | + | 0.805331i | \(0.298012\pi\) | ||||
−0.592826 | + | 0.805331i | \(0.701988\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 234.500 | − | 406.166i | 0.361036 | − | 0.625333i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −507.000 | −0.750364 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1244.00 | 1.77166 | 0.885829 | − | 0.464012i | \(-0.153591\pi\) | ||||
0.885829 | + | 0.464012i | \(0.153591\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 419.500 | − | 726.595i | 0.575446 | − | 0.996701i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 426.084i | 0.563480i | 0.959491 | + | 0.281740i | \(0.0909116\pi\) | ||||
−0.959491 | + | 0.281740i | \(0.909088\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 324.000 | − | 187.061i | 0.413444 | − | 0.238702i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 241.500 | + | 418.290i | 0.297604 | + | 0.515465i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 265.500 | + | 153.286i | 0.316213 | + | 0.182566i | 0.649703 | − | 0.760188i | \(-0.274893\pi\) |
−0.333490 | + | 0.942753i | \(0.608226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −253.500 | − | 1024.51i | −0.292022 | − | 1.18019i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −441.000 | − | 254.611i | −0.491716 | − | 0.283892i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 612.000 | + | 1060.02i | 0.660946 | + | 1.14479i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1069.50 | − | 617.476i | 1.11950 | − | 0.646342i | 0.178225 | − | 0.983990i | \(-0.442965\pi\) |
0.941273 | + | 0.337647i | \(0.109631\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 495.367i | − | 0.502891i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −979.500 | + | 1696.54i | −0.964989 | + | 1.67141i | −0.255345 | + | 0.966850i | \(0.582189\pi\) |
−0.709645 | + | 0.704560i | \(0.751144\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1856.00 | −1.77551 | −0.887753 | − | 0.460320i | \(-0.847735\pi\) | ||||
−0.887753 | + | 0.460320i | \(0.847735\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2184.00 | 2.02987 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −127.500 | + | 220.836i | −0.115195 | + | 0.199524i | −0.917858 | − | 0.396909i | \(-0.870083\pi\) |
0.802663 | + | 0.596433i | \(0.203416\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 609.682i | − | 0.535752i | −0.963453 | − | 0.267876i | \(-0.913678\pi\) | ||
0.963453 | − | 0.267876i | \(-0.0863217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 241.500 | − | 139.430i | 0.206506 | − | 0.119226i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −205.500 | − | 355.936i | −0.171078 | − | 0.296316i | 0.767719 | − | 0.640787i | \(-0.221392\pi\) |
−0.938797 | + | 0.344471i | \(0.888058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 684.000 | + | 394.908i | 0.554638 | + | 0.320220i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1001.00 | − | 247.683i | 0.790961 | − | 0.195712i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 526.500 | + | 303.975i | 0.405581 | + | 0.234162i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −412.000 | − | 713.605i | −0.309542 | − | 0.536142i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2383.50 | − | 1376.11i | 1.74726 | − | 1.00878i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 803.672i | 0.575061i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1121.50 | + | 1942.49i | −0.783599 | + | 1.35723i | 0.146234 | + | 0.989250i | \(0.453285\pi\) |
−0.929833 | + | 0.367983i | \(0.880049\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 595.000 | 0.406099 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 372.000 | 0.248105 | 0.124053 | − | 0.992276i | \(-0.460411\pi\) | ||||
0.124053 | + | 0.992276i | \(0.460411\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −994.500 | + | 1722.52i | −0.648377 | + | 1.12302i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 484.974i | − | 0.309185i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1030.50 | + | 594.959i | −0.642639 | + | 0.371028i | −0.785630 | − | 0.618696i | \(-0.787661\pi\) |
0.142991 | + | 0.989724i | \(0.454328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1272.50 | − | 2204.03i | −0.776490 | − | 1.34492i | −0.933953 | − | 0.357395i | \(-0.883665\pi\) |
0.157464 | − | 0.987525i | \(-0.449668\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2079.00 | − | 1200.31i | −1.24173 | − | 0.716911i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −760.500 | + | 731.791i | −0.444729 | + | 0.427940i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 828.000 | + | 478.046i | 0.474218 | + | 0.273790i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 574.000 | + | 994.197i | 0.322059 | + | 0.557823i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1129.50 | − | 652.117i | 0.621022 | − | 0.358547i | −0.156245 | − | 0.987718i | \(-0.549939\pi\) |
0.777267 | + | 0.629171i | \(0.216606\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 86.6025i | 0.0466729i | 0.999728 | + | 0.0233365i | \(0.00742890\pi\) | ||||
−0.999728 | + | 0.0233365i | \(0.992571\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −297.000 | + | 514.419i | −0.156935 | + | 0.271819i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1008.00 | −0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1534.00 | −0.779787 | −0.389893 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389893 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1491.00 | + | 2582.49i | −0.743673 | + | 1.28808i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1283.45i | 0.628261i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1414.50 | − | 816.662i | 0.679707 | − | 0.392429i | −0.120038 | − | 0.992769i | \(-0.538302\pi\) |
0.799745 | + | 0.600340i | \(0.204968\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1092.00 | − | 1891.40i | −0.515225 | − | 0.892395i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1408.50 | − | 813.198i | −0.652653 | − | 0.376809i | 0.136819 | − | 0.990596i | \(-0.456312\pi\) |
−0.789472 | + | 0.613787i | \(0.789645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1859.00 | − | 1170.87i | −0.846154 | − | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1683.00 | − | 971.681i | −0.752645 | − | 0.434540i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 436.500 | + | 756.040i | 0.191829 | + | 0.332258i | 0.945857 | − | 0.324585i | \(-0.105225\pi\) |
−0.754027 | + | 0.656843i | \(0.771891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1306.50 | − | 754.308i | 0.564355 | − | 0.325830i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 133.368i | 0.0566359i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −643.500 | + | 1114.57i | −0.268701 | + | 0.465403i | −0.968527 | − | 0.248910i | \(-0.919928\pi\) |
0.699826 | + | 0.714314i | \(0.253261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.000821319 | 0.000410660 | − | 1.00000i | \(-0.499869\pi\) | ||||
0.000410660 | 1.00000i | \(0.499869\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −119.000 | −0.0480696 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 276.000 | − | 478.046i | 0.109686 | − | 0.189982i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 607.950i | − | 0.237742i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 682.500 | − | 394.042i | 0.262670 | − | 0.151652i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1420.50 | − | 2460.38i | −0.538135 | − | 0.932077i | −0.999005 | − | 0.0446092i | \(-0.985796\pi\) |
0.460870 | − | 0.887468i | \(-0.347538\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3676.50 | − | 2122.63i | −1.37119 | − | 0.791659i | −0.380115 | − | 0.924939i | \(-0.624115\pi\) |
−0.991078 | + | 0.133281i | \(0.957449\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3276.00 | − | 3152.33i | 1.20307 | − | 1.15766i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2383.50 | + | 1376.11i | 0.862017 | + | 0.497686i | 0.864687 | − | 0.502311i | \(-0.167517\pi\) |
−0.00267023 | + | 0.999996i | \(0.500850\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −842.500 | − | 1459.25i | −0.300117 | − | 0.519818i | 0.676045 | − | 0.736860i | \(-0.263692\pi\) |
−0.976162 | + | 0.217042i | \(0.930359\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 997.500 | − | 575.907i | 0.350041 | − | 0.202096i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1553.65i | 0.537167i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2724.00 | − | 4718.11i | 0.928061 | − | 1.60745i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1254.00 | −0.421058 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1989.00 | 0.658287 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 840.500 | − | 1455.79i | 0.274229 | − | 0.474979i | −0.695711 | − | 0.718322i | \(-0.744911\pi\) |
0.969940 | + | 0.243343i | \(0.0782439\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 4085.91i | − | 1.31437i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1020.00 | − | 588.897i | 0.323551 | − | 0.186802i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −819.000 | − | 1418.55i | −0.256209 | − | 0.443767i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6090.00 | − | 3516.06i | −1.87911 | − | 1.08490i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1228.50 | − | 303.975i | 0.373927 | − | 0.0925229i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3547.50 | + | 2048.15i | 1.06528 | + | 0.615042i | 0.926889 | − | 0.375336i | \(-0.122473\pi\) |
0.138394 | + | 0.990377i | \(0.455806\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 737.000 | + | 1276.52i | 0.218370 | + | 0.378229i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −379.500 | + | 219.104i | −0.110962 | + | 0.0640638i | −0.554454 | − | 0.832215i | \(-0.687073\pi\) |
0.443492 | + | 0.896278i | \(0.353739\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 180.133i | 0.0519805i | 0.999662 | + | 0.0259903i | \(0.00827389\pi\) | ||||
−0.999662 | + | 0.0259903i | \(0.991726\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1774.50 | − | 3073.52i | 0.505427 | − | 0.875424i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5778.00 | −1.62459 | −0.812295 | − | 0.583247i | \(-0.801782\pi\) | ||||
−0.812295 | + | 0.583247i | \(0.801782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4752.00 | −1.31909 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4354.00 | + | 7541.35i | −1.19334 | + | 2.06693i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1860.22i | 0.503464i | 0.967797 | + | 0.251732i | \(0.0810001\pi\) | ||||
−0.967797 | + | 0.251732i | \(0.919000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1783.50 | − | 1029.70i | 0.476703 | − | 0.275224i | −0.242339 | − | 0.970192i | \(-0.577915\pi\) |
0.719041 | + | 0.694967i | \(0.244581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2464.00 | + | 4267.77i | 0.650476 | + | 1.12666i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1968.00 | + | 1136.23i | 0.513187 | + | 0.296289i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 994.500 | + | 4019.22i | 0.256188 | + | 1.03537i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2583.00 | − | 1491.30i | −0.657393 | − | 0.379546i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2245.50 | + | 3889.32i | 0.564680 | + | 0.978055i | 0.997079 | + | 0.0763724i | \(0.0243338\pi\) |
−0.432399 | + | 0.901682i | \(0.642333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1111.50 | − | 641.725i | 0.276203 | − | 0.159466i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2618.86i | 0.643135i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2725.50 | + | 4720.70i | −0.661525 | + | 1.14580i | 0.318690 | + | 0.947859i | \(0.396757\pi\) |
−0.980215 | + | 0.197936i | \(0.936576\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 897.000 | 0.215200 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1518.00 | −0.360007 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −391.500 | + | 678.098i | −0.0917906 | + | 0.158986i | −0.908265 | − | 0.418396i | \(-0.862592\pi\) |
0.816474 | + | 0.577382i | \(0.195926\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5902.83i | 1.36833i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1858.50 | + | 1073.01i | −0.425986 | + | 0.245943i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2542.50 | + | 4403.74i | 0.576279 | + | 0.998144i | 0.995901 | + | 0.0904453i | \(0.0288290\pi\) |
−0.419623 | + | 0.907699i | \(0.637838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1147.50 | + | 662.509i | 0.257216 | + | 0.148504i | 0.623064 | − | 0.782171i | \(-0.285888\pi\) |
−0.365848 | + | 0.930675i | \(0.619221\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7098.00 | + | 2049.02i | 1.57359 | + | 0.454257i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1306.50 | − | 754.308i | −0.286491 | − | 0.165405i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1710.50 | + | 2962.67i | 0.371025 | + | 0.642635i | 0.989724 | − | 0.142994i | \(-0.0456730\pi\) |
−0.618698 | + | 0.785629i | \(0.712340\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1386.00 | − | 800.207i | 0.297411 | − | 0.171710i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 810.600i | 0.172087i | 0.996291 | + | 0.0860433i | \(0.0274223\pi\) | ||||
−0.996291 | + | 0.0860433i | \(0.972578\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3588.50 | − | 6215.46i | 0.753760 | − | 1.30555i | −0.192228 | − | 0.981350i | \(-0.561571\pi\) |
0.945988 | − | 0.324201i | \(-0.105095\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8568.00 | −1.78079 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8853.00 | 1.82082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2092.00 | − | 3623.45i | 0.425809 | − | 0.737523i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8644.67i | 1.74144i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8065.50 | − | 4656.62i | 1.60816 | − | 0.928473i | 0.618381 | − | 0.785878i | \(-0.287789\pi\) |
0.989781 | − | 0.142595i | \(-0.0455445\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 132.000 | + | 228.631i | 0.0260520 | + | 0.0451234i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −682.500 | − | 394.042i | −0.133342 | − | 0.0769852i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1852.50 | + | 1925.17i | 0.358304 | + | 0.372360i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1657.50 | + | 956.958i | 0.317398 | + | 0.183250i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6856.50 | − | 11875.8i | −1.29999 | − | 2.25164i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −204.000 | + | 117.779i | −0.0382984 | + | 0.0221116i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4777.00i | 0.888070i | 0.896009 | + | 0.444035i | \(0.146453\pi\) | ||||
−0.896009 | + | 0.444035i | \(0.853547\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6496.00 | − | 11251.4i | 1.19594 | − | 2.07142i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6192.00 | −1.12899 | −0.564495 | − | 0.825436i | \(-0.690929\pi\) | ||||
−0.564495 | + | 0.825436i | \(0.690929\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −770.000 | −0.139051 | −0.0695255 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695255 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3432.00 | + | 5944.40i | −0.613877 | + | 1.06327i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8057.50i | 1.42762i | 0.700341 | + | 0.713808i | \(0.253031\pi\) | ||||
−0.700341 | + | 0.713808i | \(0.746969\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1345.50 | − | 776.825i | 0.236155 | − | 0.136344i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −892.500 | − | 1545.86i | −0.155185 | − | 0.268789i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2065.50 | − | 1192.52i | −0.355813 | − | 0.205429i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 871.000 | − | 3017.23i | 0.148660 | − | 0.514972i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3696.00 | + | 2133.89i | 0.625044 | + | 0.360869i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3861.00 | − | 6687.45i | −0.647002 | − | 1.12064i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4570.50 | − | 2638.78i | 0.758965 | − | 0.438189i | −0.0699590 | − | 0.997550i | \(-0.522287\pi\) |
0.828924 | + | 0.559361i | \(0.188954\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 876.418i | 0.144226i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1140.00 | − | 1974.54i | 0.185925 | − | 0.322031i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8278.00 | 1.33808 | 0.669038 | − | 0.743228i | \(-0.266706\pi\) | ||||
0.669038 | + | 0.743228i | \(0.266706\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2877.00 | 0.460936 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −819.000 | + | 1418.55i | −0.130063 | + | 0.225275i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4030.48i | − | 0.634477i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4788.00 | + | 2764.35i | −0.747180 | + | 0.431385i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3433.50 | + | 5947.00i | 0.531181 | + | 0.920033i | 0.999338 | + | 0.0363875i | \(0.0115851\pi\) |
−0.468156 | + | 0.883646i | \(0.655082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10525.5 | + | 6076.90i | 1.61438 | + | 0.932060i | 0.988340 | + | 0.152266i | \(0.0486571\pi\) |
0.626036 | + | 0.779794i | \(0.284676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 455.000 | − | 1576.17i | 0.0691912 | − | 0.239685i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5029.50 | + | 2903.78i | 0.758338 | + | 0.437827i | 0.828699 | − | 0.559695i | \(-0.189082\pi\) |
−0.0703608 | + | 0.997522i | \(0.522415\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4044.00 | − | 7004.41i | −0.604601 | − | 1.04720i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3685.50 | + | 2127.82i | −0.546379 | + | 0.315452i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1340.61i | − | 0.197088i | −0.995133 | − | 0.0985439i | \(-0.968581\pi\) | ||
0.995133 | − | 0.0985439i | \(-0.0314185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 472.000 | − | 817.528i | 0.0688147 | − | 0.119191i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5768.00 | 0.833999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13920.0 | −1.99618 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1832.50 | − | 3173.98i | 0.260642 | − | 0.451446i | −0.705770 | − | 0.708441i | \(-0.749399\pi\) |
0.966413 | + | 0.256995i | \(0.0827324\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8649.86i | 1.22031i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8307.00 | + | 4796.05i | −1.16247 | + | 0.671155i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2685.50 | − | 4651.42i | −0.372788 | − | 0.645688i | 0.617205 | − | 0.786802i | \(-0.288265\pi\) |
−0.989993 | + | 0.141114i | \(0.954931\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4872.00 | − | 2812.85i | −0.670904 | − | 0.387347i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2242.50 | + | 2330.47i | 0.306352 | + | 0.318370i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9967.50 | + | 5754.74i | 1.35091 | + | 0.779950i | 0.988377 | − | 0.152020i | \(-0.0485778\pi\) |
0.362536 | + | 0.931970i | \(0.381911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7850.50 | − | 13597.5i | −1.05563 | − | 1.82840i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2095.50 | + | 1209.84i | −0.279569 | + | 0.161409i | −0.633228 | − | 0.773965i | \(-0.718271\pi\) |
0.353659 | + | 0.935374i | \(0.384937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 7025.20i | − | 0.929967i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −935.000 | + | 1619.47i | −0.122813 | + | 0.212719i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9858.00 | −1.28489 | −0.642443 | − | 0.766334i | \(-0.722079\pi\) | ||||
−0.642443 | + | 0.766334i | \(0.722079\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1539.00 | −0.199055 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1302.00 | + | 2255.13i | −0.167118 | + | 0.289456i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 17237.4i | 2.19571i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7552.50 | + | 4360.44i | −0.954784 | + | 0.551245i | −0.894564 | − | 0.446941i | \(-0.852514\pi\) |
−0.0602200 | + | 0.998185i | \(0.519180\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6961.50 | − | 12057.7i | −0.873461 | − | 1.51288i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6568.50 | − | 3792.33i | −0.817993 | − | 0.472269i | 0.0317308 | − | 0.999496i | \(-0.489898\pi\) |
−0.849724 | + | 0.527228i | \(0.823231\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3276.00 | − | 945.700i | −0.404936 | − | 0.116895i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10068.0 | + | 5812.76i | 1.23527 | + | 0.713181i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −448.500 | − | 776.825i | −0.0546224 | − | 0.0946088i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3727.50 | − | 2152.07i | 0.450643 | − | 0.260179i | −0.257459 | − | 0.966289i | \(-0.582885\pi\) |
0.708102 | + | 0.706110i | \(0.249552\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 8329.43i | − | 0.999661i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −214.500 | + | 371.525i | −0.0255565 | + | 0.0442652i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5904.00 | −0.698352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17815.0 | 2.09210 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2698.50 | − | 4673.94i | 0.314631 | − | 0.544957i | −0.664728 | − | 0.747085i | \(-0.731453\pi\) |
0.979359 | + | 0.202129i | \(0.0647859\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7260.76i | 0.840541i | 0.907399 | + | 0.420270i | \(0.138065\pi\) | ||||
−0.907399 | + | 0.420270i | \(0.861935\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6534.00 | − | 3772.41i | 0.751050 | − | 0.433619i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 904.500 | + | 1566.64i | 0.103235 | + | 0.178808i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −331.500 | − | 191.392i | −0.0375700 | − | 0.0216911i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1774.50 | − | 7171.56i | −0.199706 | − | 0.807100i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 421.500 | + | 243.353i | 0.0471066 | + | 0.0271970i | 0.523368 | − | 0.852107i | \(-0.324675\pi\) |
−0.476262 | + | 0.879304i | \(0.658009\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6069.50 | − | 10512.7i | −0.673629 | − | 1.16676i | −0.976867 | − | 0.213846i | \(-0.931401\pi\) |
0.303238 | − | 0.952915i | \(-0.401932\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5796.00 | + | 3346.32i | −0.638844 | + | 0.368836i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5035.07i | − | 0.551167i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 230.500 | − | 399.238i | 0.0250596 | − | 0.0434045i | −0.853224 | − | 0.521545i | \(-0.825356\pi\) |
0.878283 | + | 0.478141i | \(0.158689\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3608.00 | −0.389591 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12156.0 | −1.30372 | −0.651861 | − | 0.758338i | \(-0.726012\pi\) | ||||
−0.651861 | + | 0.758338i | \(0.726012\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2124.00 | + | 3678.88i | −0.226263 | + | 0.391900i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9129.64i | 0.966034i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −256.500 | + | 148.090i | −0.0269599 | + | 0.0155653i | −0.513419 | − | 0.858138i | \(-0.671621\pi\) |
0.486459 | + | 0.873703i | \(0.338288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4426.50 | − | 7666.92i | −0.462164 | − | 0.800491i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −525.000 | − | 303.109i | −0.0544518 | − | 0.0314377i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14196.0 | − | 3512.60i | 1.46268 | − | 0.361919i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 529.500 | + | 305.707i | 0.0541990 | + | 0.0312918i | 0.526855 | − | 0.849955i | \(-0.323371\pi\) |
−0.472656 | + | 0.881247i | \(0.656705\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 472.500 | + | 818.394i | 0.0480488 | + | 0.0832230i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11368.5 | + | 6563.61i | −1.14855 | + | 0.663119i | −0.948535 | − | 0.316673i | \(-0.897434\pi\) |
−0.200020 | + | 0.979792i | \(0.564101\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 834.848i | 0.0837985i | 0.999122 | + | 0.0418992i | \(0.0133408\pi\) | ||||
−0.999122 | + | 0.0418992i | \(0.986659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3528.00 | − | 6110.68i | 0.351843 | − | 0.609410i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14496.0 | −1.43639 | −0.718196 | − | 0.695841i | \(-0.755032\pi\) | ||||
−0.718196 | + | 0.695841i | \(0.755032\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3705.00 | 0.364778 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5369.00 | − | 9299.38i | 0.525245 | − | 0.909751i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1913.92i | − | 0.186051i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5125.50 | + | 2959.21i | −0.495103 | + | 0.285848i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4686.00 | − | 8116.39i | −0.449805 | − | 0.779086i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7705.50 | + | 4448.77i | 0.735017 | + | 0.424362i | 0.820255 | − | 0.571998i | \(-0.193832\pi\) |
−0.0852376 | + | 0.996361i | \(0.527165\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1345.50 | − | 1294.71i | 0.127546 | − | 0.122731i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7780.50 | − | 4492.07i | −0.732971 | − | 0.423181i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8556.00 | + | 14819.4i | 0.801047 | + | 1.38745i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4117.50 | + | 2377.24i | −0.383125 | + | 0.221197i | −0.679177 | − | 0.733975i | \(-0.737663\pi\) |
0.296052 | + | 0.955172i | \(0.404330\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11433.3i | 1.05732i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −817.500 | + | 1415.95i | −0.0751390 | + | 0.130145i | −0.901147 | − | 0.433514i | \(-0.857273\pi\) |
0.826008 | + | 0.563659i | \(0.190607\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1863.00 | −0.170193 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6864.00 | 0.623260 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6571.50 | − | 11382.2i | 0.593103 | − | 1.02728i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14434.9i | 1.29498i | 0.762074 | + | 0.647490i | \(0.224181\pi\) | ||||
−0.762074 | + | 0.647490i | \(0.775819\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9859.50 | − | 5692.38i | 0.879222 | − | 0.507619i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6343.50 | + | 10987.3i | 0.562312 | + | 0.973952i | 0.997294 | + | 0.0735133i | \(0.0234211\pi\) |
−0.434983 | + | 0.900439i | \(0.643246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23508.0 | − | 13572.4i | −2.07147 | − | 1.19596i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13604.5 | − | 7171.56i | 1.19171 | − | 0.628205i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4978.50 | − | 2874.34i | −0.433533 | − | 0.250300i | 0.267318 | − | 0.963608i | \(-0.413863\pi\) |
−0.700850 | + | 0.713308i | \(0.747196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11310.0 | − | 19589.5i | −0.979109 | − | 1.69587i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2677.50 | + | 1545.86i | −0.230438 | + | 0.133043i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 25717.5i | − | 2.20048i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3861.00 | + | 6687.45i | −0.328446 | + | 0.568885i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6111.00 | −0.516846 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6054.00 | 0.509080 | 0.254540 | − | 0.967062i | \(-0.418076\pi\) | ||||
0.254540 | + | 0.967062i | \(0.418076\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7401.50 | + | 12819.8i | −0.618824 | + | 1.07183i | 0.370877 | + | 0.928682i | \(0.379057\pi\) |
−0.989701 | + | 0.143153i | \(0.954276\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10560.3i | 0.877885i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1701.00 | − | 982.073i | 0.140601 | − | 0.0811760i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4459.00 | + | 7723.21i | 0.366483 | + | 0.634767i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −363.000 | − | 209.578i | −0.0296664 | − | 0.0171279i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13279.5 | − | 12778.2i | 1.07917 | − | 1.03843i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3060.00 | − | 1766.69i | −0.247281 | − | 0.142768i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4504.50 | − | 7802.02i | −0.361980 | − | 0.626969i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3198.00 | − | 1846.37i | 0.255561 | − | 0.147548i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 21470.5i | − | 1.70626i | −0.521695 | − | 0.853132i | \(-0.674700\pi\) | ||
0.521695 | − | 0.853132i | \(-0.325300\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.00000 | + | 12.1244i | −0.000553221 | + | 0.000958206i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8448.00 | 0.663986 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13516.0 | 1.05649 | 0.528247 | − | 0.849091i | \(-0.322849\pi\) | ||||
0.528247 | + | 0.849091i | \(0.322849\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 187.000 | − | 323.894i | 0.0145373 | − | 0.0251793i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6095.09i | − | 0.471251i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24258.0 | + | 14005.4i | −1.86538 | + | 1.07698i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1932.00 | + | 3346.32i | 0.147764 | + | 0.255934i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2503.50 | + | 1445.40i | 0.190443 | + | 0.109952i | 0.592190 | − | 0.805798i | \(-0.298264\pi\) |
−0.401747 | + | 0.915751i | \(0.631597\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3867.50 | − | 956.958i | 0.292626 | − | 0.0724061i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3685.50 | + | 2127.82i | 0.277365 | + | 0.160137i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5791.50 | + | 10031.2i | 0.433539 | + | 0.750912i | 0.997175 | − | 0.0751113i | \(-0.0239312\pi\) |
−0.563636 | + | 0.826023i | \(0.690598\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4932.00 | − | 2847.49i | 0.367240 | − | 0.212026i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18891.5i | 1.39924i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6439.50 | + | 11153.5i | −0.474443 | + | 0.821759i | −0.999572 | − | 0.0292638i | \(-0.990684\pi\) |
0.525129 | + | 0.851023i | \(0.324017\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11636.0 | 0.852805 | 0.426402 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426402 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19887.0 | 1.44990 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1909.50 | + | 3307.35i | −0.138490 | + | 0.239871i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12311.4i | 0.888269i | 0.895960 | + | 0.444134i | \(0.146489\pi\) | ||||
−0.895960 | + | 0.444134i | \(0.853511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25735.5 | − | 14858.4i | 1.84720 | − | 1.06648i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4797.00 | − | 8308.65i | −0.342535 | − | 0.593289i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8307.00 | + | 4796.05i | 0.590121 | + | 0.340707i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3432.00 | + | 13870.3i | 0.242557 | + | 0.980282i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13549.5 | + | 7822.81i | 0.952722 | + | 0.550054i | 0.893925 | − | 0.448216i | \(-0.147940\pi\) |
0.0587964 | + | 0.998270i | \(0.481274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3213.00 | + | 5565.08i | 0.224770 | + | 0.389313i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16684.5 | + | 9632.80i | −1.16127 | + | 0.670458i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25821.4i | 1.78813i | 0.447942 | + | 0.894063i | \(0.352157\pi\) | ||||
−0.447942 | + | 0.894063i | \(0.647843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4212.00 | + | 7295.40i | −0.290210 | + | 0.502659i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11795.0 | 0.808605 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1668.00 | −0.113777 | −0.0568887 | − | 0.998381i | \(-0.518118\pi\) | ||||
−0.0568887 | + | 0.998381i | \(0.518118\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6849.50 | + | 11863.7i | −0.464887 | + | 0.805207i | −0.999196 | − | 0.0400813i | \(-0.987238\pi\) |
0.534310 | + | 0.845289i | \(0.320572\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3619.99i | 0.244473i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9888.00 | − | 5708.84i | 0.664470 | − | 0.383632i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11586.5 | − | 20068.4i | −0.774764 | − | 1.34193i | −0.934927 | − | 0.354839i | \(-0.884536\pi\) |
0.160164 | − | 0.987090i | \(-0.448798\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9418.50 | − | 5437.77i | −0.626694 | − | 0.361822i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15444.0 | − | 4458.30i | −1.02258 | − | 0.295194i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14389.5 | + | 8307.78i | 0.948102 | + | 0.547387i | 0.892491 | − | 0.451066i | \(-0.148956\pi\) |
0.0556111 | + | 0.998453i | \(0.482289\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19068.0 | + | 33026.7i | 1.25024 | + | 2.16547i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24589.5 | − | 14196.8i | 1.60443 | − | 0.926321i | 0.613849 | − | 0.789423i | \(-0.289620\pi\) |
0.990585 | − | 0.136897i | \(-0.0437130\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6245.78i | 0.405556i | 0.979225 | + | 0.202778i | \(0.0649969\pi\) | ||||
−0.979225 | + | 0.202778i | \(0.935003\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −997.500 | + | 1727.72i | −0.0644578 | + | 0.111644i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6903.00 | −0.443921 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19511.0 | −1.24870 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6961.50 | + | 12057.7i | −0.443406 | + | 0.768002i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1075.60i | 0.0681830i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19381.5 | + | 11189.9i | −1.22277 | + | 0.705964i | −0.965507 | − | 0.260378i | \(-0.916153\pi\) |
−0.257259 | + | 0.966342i | \(0.582819\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5883.50 | + | 10190.5i | 0.369428 | + | 0.639869i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26916.0 | − | 15540.0i | −1.68209 | − | 0.971157i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5330.00 | + | 5539.10i | 0.331526 | + | 0.344532i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11121.0 | + | 6420.71i | 0.688482 | + | 0.397495i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9913.50 | − | 17170.7i | −0.610858 | − | 1.05804i | −0.991096 | − | 0.133148i | \(-0.957491\pi\) |
0.380239 | − | 0.924888i | \(-0.375842\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7318.50 | − | 4225.34i | 0.448855 | − | 0.259146i | −0.258492 | − | 0.966013i | \(-0.583225\pi\) |
0.707346 | + | 0.706867i | \(0.249892\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8244.56i | 0.503301i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1474.50 | − | 2553.91i | 0.0895959 | − | 0.155185i | −0.817744 | − | 0.575581i | \(-0.804776\pi\) |
0.907340 | + | 0.420397i | \(0.138109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 429.000 | 0.0259472 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11466.0 | 0.690304 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6019.50 | + | 10426.1i | −0.360737 | + | 0.624815i | −0.988082 | − | 0.153926i | \(-0.950808\pi\) |
0.627345 | + | 0.778741i | \(0.284141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5154.58i | 0.307490i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19140.0 | − | 11050.5i | 1.13656 | − | 0.656196i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1681.50 | + | 2912.44i | 0.0993960 | + | 0.172159i | 0.911435 | − | 0.411445i | \(-0.134976\pi\) |
−0.812039 | + | 0.583603i | \(0.801642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8797.50 | + | 5079.24i | 0.517675 | + | 0.298880i | 0.735983 | − | 0.677000i | \(-0.236720\pi\) |
−0.218308 | + | 0.975880i | \(0.570054\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2457.00 | + | 8511.30i | −0.143925 | + | 0.498569i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23868.0 | − | 13780.2i | −1.39182 | − | 0.803569i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1966.50 | − | 3406.08i | −0.114158 | − | 0.197727i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24832.5 | + | 14337.1i | −1.43510 | + | 0.828554i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 382.783i | 0.0220226i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9084.50 | − | 15734.8i | 0.520329 | − | 0.901237i | −0.479391 | − | 0.877601i | \(-0.659142\pi\) |
0.999721 | − | 0.0236358i | \(-0.00752419\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2345.00 | 0.133717 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9042.00 | 0.513312 | 0.256656 | − | 0.966503i | \(-0.417379\pi\) | ||||
0.256656 | + | 0.966503i | \(0.417379\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13903.5 | + | 24081.6i | −0.785813 | + | 1.36107i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 3067.46i | − | 0.172607i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10792.5 | − | 6231.05i | 0.604632 | − | 0.349084i | −0.166230 | − | 0.986087i | \(-0.553159\pi\) |
0.770862 | + | 0.637003i | \(0.219826\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8244.00 | − | 14279.0i | −0.459835 | − | 0.796458i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1092.00 | − | 630.466i | −0.0606440 | − | 0.0350128i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5538.00 | + | 19184.2i | −0.306213 | + | 1.06075i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3739.50 | + | 2159.00i | 0.205872 | + | 0.118860i | 0.599391 | − | 0.800456i | \(-0.295409\pi\) |
−0.393520 | + | 0.919316i | \(0.628743\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5577.00 | + | 9659.65i | 0.305704 | + | 0.529494i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 30540.0 | − | 17632.3i | 1.66683 | − | 0.962346i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10615.7i | 0.576901i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20223.0 | − | 35027.3i | 1.09428 | − | 1.89535i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18270.0 | −0.984377 | −0.492189 | − | 0.870489i | \(-0.663803\pi\) | ||||
−0.492189 | + | 0.870489i | \(0.663803\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3519.00 | −0.188793 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16632.0 | − | 28807.5i | 0.888507 | − | 1.53894i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 44110.1i | − | 2.34644i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1411.50 | − | 814.930i | 0.0747673 | − | 0.0431669i | −0.462150 | − | 0.886802i | \(-0.652922\pi\) |
0.536918 | + | 0.843635i | \(0.319589\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13684.0 | − | 23701.4i | −0.721786 | − | 1.25017i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3591.00 | + | 2073.26i | 0.188617 | + | 0.108898i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10140.0 | − | 10537.8i | −0.530370 | − | 0.551177i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11277.0 | − | 6510.78i | −0.587374 | − | 0.339121i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4915.50 | + | 8513.90i | 0.254961 | + | 0.441606i | 0.964885 | − | 0.262673i | \(-0.0846039\pi\) |
−0.709924 | + | 0.704279i | \(0.751271\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36192.0 | − | 20895.5i | 1.86943 | − | 1.07932i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14415.9i | 0.741537i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2311.50 | + | 4003.64i | −0.118410 | + | 0.205091i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15464.0 | 0.788897 | 0.394448 | − | 0.918918i | \(-0.370936\pi\) | ||||
0.394448 | + | 0.918918i | \(0.370936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1147.50 | + | 1987.53i | −0.0580599 | + | 0.100563i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12616.3i | − | 0.635733i | −0.948136 | − | 0.317866i | \(-0.897034\pi\) | ||
0.948136 | − | 0.317866i | \(-0.102966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13776.0 | + | 7953.58i | −0.691341 | + | 0.399146i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1852.50 | − | 3208.62i | −0.0925885 | − | 0.160368i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14101.5 | + | 8141.50i | 0.701938 | + | 0.405264i | 0.808069 | − | 0.589088i | \(-0.200513\pi\) |
−0.106131 | + | 0.994352i | \(0.533846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27846.0 | − | 8038.45i | −1.38050 | − | 0.398515i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9358.50 | − | 5403.13i | −0.462086 | − | 0.266786i | 0.250835 | − | 0.968030i | \(-0.419295\pi\) |
−0.712921 | + | 0.701244i | \(0.752628\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9036.00 | + | 15650.8i | 0.444367 | + | 0.769666i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8118.00 | − | 4686.93i | 0.397620 | − | 0.229566i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 5741.75i | − | 0.280105i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6807.50 | + | 11790.9i | −0.330771 | + | 0.572913i | −0.982663 | − | 0.185399i | \(-0.940642\pi\) |
0.651892 | + | 0.758312i | \(0.273976\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31437.0 | −1.52142 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1200.00 | −0.0578443 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2775.50 | + | 4807.31i | −0.133259 | + | 0.230812i | −0.924931 | − | 0.380135i | \(-0.875878\pi\) |
0.791672 | + | 0.610947i | \(0.209211\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8984.15i | 0.429649i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8731.50 | − | 5041.13i | 0.415922 | − | 0.240133i | −0.277409 | − | 0.960752i | \(-0.589476\pi\) |
0.693331 | + | 0.720619i | \(0.256142\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6864.00 | + | 11888.8i | 0.325680 | + | 0.564093i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7128.00 | − | 4115.35i | −0.336880 | − | 0.194498i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 214.500 | + | 866.891i | 0.0100980 | + | 0.0408105i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25771.5 | + | 14879.2i | 1.20851 | + | 0.697733i | 0.962434 | − | 0.271517i | \(-0.0875253\pi\) |
0.246076 | + | 0.969250i | \(0.420859\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19078.5 | − | 33044.9i | −0.891174 | − | 1.54356i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24019.5 | − | 13867.7i | 1.11762 | − | 0.645259i | 0.176829 | − | 0.984242i | \(-0.443416\pi\) |
0.940793 | + | 0.338983i | \(0.110083\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4873.99i | − | 0.225908i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3139.50 | + | 5437.77i | −0.144954 | + | 0.251067i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −34731.0 | −1.59739 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13143.0 | −0.602168 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1207.50 | + | 2091.45i | −0.0551118 | + | 0.0954564i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 21255.7i | − | 0.966432i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27322.5 | − | 15774.7i | 1.23754 | − | 0.714493i | 0.268947 | − | 0.963155i | \(-0.413324\pi\) |
0.968590 | + | 0.248662i | \(0.0799910\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2740.50 | − | 4746.69i | −0.123656 | − | 0.214178i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8014.50 | + | 4627.17i | 0.360256 | + | 0.207994i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −773.500 | + | 191.392i | −0.0346378 | + | 0.00857064i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −35784.0 | − | 20659.9i | −1.59639 | − | 0.921674i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −727.500 | − | 1260.07i | −0.0323330 | − | 0.0560023i | 0.849406 | − | 0.527740i | \(-0.176960\pi\) |
−0.881739 | + | 0.471737i | \(0.843627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8019.00 | − | 4629.77i | 0.355059 | − | 0.204993i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 6744.61i | − | 0.297514i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11310.0 | + | 19589.5i | −0.497038 | + | 0.860894i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17784.0 | −0.778638 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35595.0 | −1.55267 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −829.500 | + | 1436.74i | −0.0360490 | + | 0.0624388i | −0.883487 | − | 0.468456i | \(-0.844811\pi\) |
0.847438 | + | 0.530894i | \(0.178144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4402.87i | − | 0.190636i | −0.995447 | − | 0.0953180i | \(-0.969613\pi\) | ||
0.995447 | − | 0.0953180i | \(-0.0303868\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8032.50 | + | 4637.57i | −0.346509 | + | 0.200057i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11316.0 | + | 19599.9i | 0.486359 | + | 0.842398i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6502.50 | − | 3754.22i | −0.278450 | − | 0.160763i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16731.0 | + | 16099.4i | −0.713832 | + | 0.686885i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24856.5 | − | 14350.9i | −1.05664 | − | 0.610049i | −0.132136 | − | 0.991232i | \(-0.542184\pi\) |
−0.924500 | + | 0.381183i | \(0.875517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7889.50 | + | 13665.0i | 0.334156 | + | 0.578776i | 0.983322 | − | 0.181871i | \(-0.0582153\pi\) |
−0.649166 | + | 0.760647i | \(0.724882\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9145.50 | − | 5280.16i | 0.385946 | − | 0.222826i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7354.29i | 0.309231i | 0.987975 | + | 0.154615i | \(0.0494138\pi\) | ||||
−0.987975 | + | 0.154615i | \(0.950586\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8685.50 | + | 15043.7i | −0.363884 | + | 0.630266i | −0.988596 | − | 0.150589i | \(-0.951883\pi\) |
0.624712 | + | 0.780855i | \(0.285216\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23947.0 | −0.999654 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4428.00 | −0.184179 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11268.0 | − | 19516.7i | 0.467000 | − | 0.808868i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 2546.11i | − | 0.105145i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25525.5 | + | 14737.2i | −1.05034 | + | 0.606416i | −0.922745 | − | 0.385410i | \(-0.874060\pi\) |
−0.127598 | + | 0.991826i | \(0.540727\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9814.00 | + | 16998.3i | 0.402395 | + | 0.696968i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4914.00 | − | 2837.10i | −0.200768 | − | 0.115913i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16224.0 | − | 25759.1i | 0.660500 | − | 1.04868i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16068.0 | + | 9276.86i | 0.651834 | + | 0.376336i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25119.5 | + | 43508.3i | 1.01543 | + | 1.75877i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1966.50 | + | 1135.36i | −0.0792136 | + | 0.0457340i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2909.85i | 0.116801i | 0.998293 | + | 0.0584005i | \(0.0186000\pi\) | ||||
−0.998293 | + | 0.0584005i | \(0.981400\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 13464.0 | − | 23320.3i | 0.538549 | − | 0.932794i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5346.00 | −0.213087 | −0.106544 | − | 0.994308i | \(-0.533978\pi\) | ||||
−0.106544 | + | 0.994308i | \(0.533978\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24244.0 | −0.962974 | −0.481487 | − | 0.876453i | \(-0.659903\pi\) | ||||
−0.481487 | + | 0.876453i | \(0.659903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30985.5 | + | 53668.5i | −1.22646 | + | 2.12429i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 32780.8i | − | 1.29301i | −0.762908 | − | 0.646507i | \(-0.776229\pi\) | ||
0.762908 | − | 0.646507i | \(-0.223771\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10476.0 | + | 6048.32i | −0.411786 | + | 0.237745i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14644.0 | + | 25364.2i | 0.573629 | + | 0.993555i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24258.0 | + | 14005.4i | 0.946946 | + | 0.546720i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5557.50 | − | 5347.71i | 0.216198 | − | 0.208037i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −23529.0 | − | 13584.5i | −0.912183 | − | 0.526649i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9048.00 | − | 15671.6i | −0.349575 | − | 0.605482i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3934.50 | + | 2271.58i | −0.151492 | + | 0.0874640i | −0.573830 | − | 0.818974i | \(-0.694543\pi\) |
0.422338 | + | 0.906439i | \(0.361210\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 65192.7i | 2.50159i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10258.5 | − | 17768.2i | 0.392302 | − | 0.679486i | −0.600451 | − | 0.799661i | \(-0.705012\pi\) |
0.992753 | + | 0.120175i | \(0.0383456\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23852.0 | 0.909042 | 0.454521 | − | 0.890736i | \(-0.349811\pi\) | ||||
0.454521 | + | 0.890736i | \(0.349811\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1848.00 | −0.0701919 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19378.5 | − | 33564.5i | 0.733558 | − | 1.27056i | −0.221794 | − | 0.975093i | \(-0.571191\pi\) |
0.955353 | − | 0.295467i | \(-0.0954753\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 50504.9i | − | 1.90538i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16360.5 | − | 9445.74i | 0.615149 | − | 0.355156i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15147.0 | + | 26235.4i | 0.567609 | + | 0.983128i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15444.0 | − | 8916.60i | −0.576800 | − | 0.333016i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18154.5 | + | 4492.07i | −0.675765 | + | 0.167208i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4347.00 | + | 2509.74i | 0.161269 | + | 0.0931085i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5751.00 | − | 9961.02i | −0.212645 | − | 0.368313i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11602.5 | + | 6698.71i | −0.427583 | + | 0.246865i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.7128i | 0.00101791i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19535.5 | + | 33836.5i | −0.715177 | + | 1.23872i | 0.247714 | + | 0.968833i | \(0.420321\pi\) |
−0.962891 | + | 0.269890i | \(0.913013\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 43098.0 | 1.57257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53040.0 | 1.92897 | 0.964486 | − | 0.264134i | \(-0.0850860\pi\) | ||||
0.964486 | + | 0.264134i | \(0.0850860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4797.00 | + | 8308.65i | −0.173886 | + | 0.301179i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1648.91i | − | 0.0595753i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7254.00 | + | 4188.10i | −0.261230 | + | 0.150821i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 183.500 | + | 317.831i | 0.00658662 | + | 0.0114084i | 0.869300 | − | 0.494285i | \(-0.164570\pi\) |
−0.862713 | + | 0.505693i | \(0.831237\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28959.0 | − | 16719.5i | −1.03608 | − | 0.598182i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6571.50 | − | 26558.4i | −0.234348 | − | 0.947108i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2311.50 | + | 1334.55i | 0.0821639 | + | 0.0474374i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20416.0 | + | 35361.5i | 0.723354 | + | 1.25289i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25924.5 | + | 14967.5i | −0.915560 | + | 0.528599i | −0.882216 | − | 0.470845i | \(-0.843949\pi\) |
−0.0333441 | + | 0.999444i | \(0.510616\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 14486.9i | − | 0.509976i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21672.0 | − | 37537.0i | 0.760460 | − | 1.31716i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8424.00 | 0.294646 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42166.0 | 1.47012 | 0.735060 | − | 0.678002i | \(-0.237154\pi\) | ||||
0.735060 | + | 0.678002i | \(0.237154\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2695.00 | − | 4667.88i | 0.0936613 | − | 0.162226i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 35022.1i | − | 1.21327i | −0.794981 | − | 0.606635i | \(-0.792519\pi\) | ||
0.794981 | − | 0.606635i | \(-0.207481\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19408.5 | + | 11205.5i | −0.670231 | + | 0.386958i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5460.00 | + | 9457.00i | 0.187951 | + | 0.325541i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2251.50 | + | 1299.90i | 0.0772586 | + | 0.0446053i | 0.538132 | − | 0.842861i | \(-0.319130\pi\) |
−0.460873 | + | 0.887466i | \(0.652464\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45240.0 | − | 13059.7i | −1.54747 | − | 0.446717i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −48846.0 | − | 28201.3i | −1.66555 | − | 0.961607i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5311.50 | − | 9199.79i | −0.180542 | − | 0.312708i | 0.761523 | − | 0.648137i | \(-0.224452\pi\) |
−0.942065 | + | 0.335430i | \(0.891118\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34092.0 | − | 19683.0i | 1.15517 | − | 0.666940i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10875.5i | 0.367353i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13396.5 | − | 23203.4i | 0.451090 | − | 0.781311i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24499.0 | 0.822362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5610.00 | 0.187726 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29412.0 | − | 50943.1i | 0.981146 | − | 1.69939i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 20199.2i | − | 0.671729i | −0.941910 | − | 0.335864i | \(-0.890972\pi\) | ||
0.941910 | − | 0.335864i | \(-0.109028\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14458.5 | − | 8347.62i | 0.479333 | − | 0.276743i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1162.50 | − | 2013.51i | −0.0384206 | − | 0.0665464i | 0.846176 | − | 0.532904i | \(-0.178899\pi\) |
−0.884596 | + | 0.466358i | \(0.845566\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49627.5 | + | 28652.5i | 1.63513 | + | 0.944045i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15242.5 | + | 15840.5i | 0.500667 | + | 0.520309i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28525.5 | + | 16469.2i | 0.934096 | + | 0.539300i | 0.888105 | − | 0.459641i | \(-0.152022\pi\) |
0.0459912 | + | 0.998942i | \(0.485355\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3451.50 | + | 5978.17i | 0.112677 | + | 0.195162i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11616.0 | + | 6706.50i | −0.378053 | + | 0.218269i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 42702.0i | − | 1.38554i | −0.721161 | − | 0.692768i | \(-0.756391\pi\) | ||
0.721161 | − | 0.692768i | \(-0.243609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19068.0 | + | 33026.7i | −0.616809 | + | 1.06834i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 54054.0 | 1.74322 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4845.00 | −0.155776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2421.50 | + | 4194.16i | −0.0776201 | + | 0.134442i | −0.902223 | − | 0.431271i | \(-0.858065\pi\) |
0.824603 | + | 0.565712i | \(0.191399\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 36942.9i | 1.18061i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20220.0 | − | 11674.0i | 0.644238 | − | 0.371951i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5471.50 | − | 9476.92i | −0.173806 | − | 0.301040i | 0.765942 | − | 0.642910i | \(-0.222273\pi\) |
−0.939747 | + | 0.341870i | \(0.888940\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1207.50 | + | 697.150i | 0.0382419 | + | 0.0220789i |
(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 | 208.4.w.a.17.1 | 2 | ||
4.3 | odd | 2 | 13.4.e.a.4.1 | ✓ | 2 | ||
12.11 | even | 2 | 117.4.q.c.82.1 | 2 | |||
13.10 | even | 6 | inner | 208.4.w.a.49.1 | 2 | ||
52.3 | odd | 6 | 169.4.e.b.23.1 | 2 | |||
52.7 | even | 12 | 169.4.a.h.1.1 | 2 | |||
52.11 | even | 12 | 169.4.c.i.146.2 | 4 | |||
52.15 | even | 12 | 169.4.c.i.146.1 | 4 | |||
52.19 | even | 12 | 169.4.a.h.1.2 | 2 | |||
52.23 | odd | 6 | 13.4.e.a.10.1 | yes | 2 | ||
52.31 | even | 4 | 169.4.c.i.22.1 | 4 | |||
52.35 | odd | 6 | 169.4.b.b.168.2 | 2 | |||
52.43 | odd | 6 | 169.4.b.b.168.1 | 2 | |||
52.47 | even | 4 | 169.4.c.i.22.2 | 4 | |||
52.51 | odd | 2 | 169.4.e.b.147.1 | 2 | |||
156.23 | even | 6 | 117.4.q.c.10.1 | 2 | |||
156.59 | odd | 12 | 1521.4.a.q.1.2 | 2 | |||
156.71 | odd | 12 | 1521.4.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.e.a.4.1 | ✓ | 2 | 4.3 | odd | 2 | ||
13.4.e.a.10.1 | yes | 2 | 52.23 | odd | 6 | ||
117.4.q.c.10.1 | 2 | 156.23 | even | 6 | |||
117.4.q.c.82.1 | 2 | 12.11 | even | 2 | |||
169.4.a.h.1.1 | 2 | 52.7 | even | 12 | |||
169.4.a.h.1.2 | 2 | 52.19 | even | 12 | |||
169.4.b.b.168.1 | 2 | 52.43 | odd | 6 | |||
169.4.b.b.168.2 | 2 | 52.35 | odd | 6 | |||
169.4.c.i.22.1 | 4 | 52.31 | even | 4 | |||
169.4.c.i.22.2 | 4 | 52.47 | even | 4 | |||
169.4.c.i.146.1 | 4 | 52.15 | even | 12 | |||
169.4.c.i.146.2 | 4 | 52.11 | even | 12 | |||
169.4.e.b.23.1 | 2 | 52.3 | odd | 6 | |||
169.4.e.b.147.1 | 2 | 52.51 | odd | 2 | |||
208.4.w.a.17.1 | 2 | 1.1 | even | 1 | trivial | ||
208.4.w.a.49.1 | 2 | 13.10 | even | 6 | inner | ||
1521.4.a.q.1.1 | 2 | 156.71 | odd | 12 | |||
1521.4.a.q.1.2 | 2 | 156.59 | odd | 12 |