Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{1345})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 337x^{2} + 336x + 112896 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(-8.91856 + 15.4474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.289 |
Dual form | 336.4.q.j.193.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.91856 | − | 13.7153i | 0.708258 | − | 1.22674i | −0.257245 | − | 0.966346i | \(-0.582815\pi\) |
0.965503 | − | 0.260392i | \(-0.0838518\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.3371 | − | 2.59808i | −0.990111 | − | 0.140283i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25.9186 | + | 44.8923i | 0.710431 | + | 1.23050i | 0.964696 | + | 0.263368i | \(0.0848333\pi\) |
−0.254265 | + | 0.967135i | \(0.581833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.8371 | 0.828575 | 0.414288 | − | 0.910146i | \(-0.364031\pi\) | ||||
0.414288 | + | 0.910146i | \(0.364031\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 47.5114 | 0.817825 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −13.6742 | − | 23.6845i | −0.195088 | − | 0.337902i | 0.751842 | − | 0.659344i | \(-0.229166\pi\) |
−0.946929 | + | 0.321442i | \(0.895832\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38.2557 | − | 66.2608i | 0.461919 | − | 0.800067i | −0.537138 | − | 0.843494i | \(-0.680495\pi\) |
0.999057 | + | 0.0434278i | \(0.0138279\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −20.7557 | − | 51.5384i | −0.215679 | − | 0.535552i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 73.6742 | − | 127.608i | 0.667919 | − | 1.15687i | −0.310566 | − | 0.950552i | \(-0.600519\pi\) |
0.978485 | − | 0.206318i | \(-0.0661482\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −62.9072 | − | 108.958i | −0.503258 | − | 0.871668i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 240.208 | 1.53812 | 0.769061 | − | 0.639175i | \(-0.220724\pi\) | ||||
0.769061 | + | 0.639175i | \(0.220724\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −148.337 | − | 256.927i | −0.859424 | − | 1.48857i | −0.872480 | − | 0.488651i | \(-0.837489\pi\) |
0.0130559 | − | 0.999915i | \(-0.495844\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −77.7557 | + | 134.677i | −0.410167 | + | 0.710431i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −180.837 | + | 230.927i | −0.873344 | + | 1.11525i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 80.7670 | − | 139.893i | 0.358865 | − | 0.621573i | −0.628906 | − | 0.777481i | \(-0.716497\pi\) |
0.987772 | + | 0.155908i | \(0.0498304\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 58.2557 | + | 100.902i | 0.239189 | + | 0.414288i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −102.977 | −0.392252 | −0.196126 | − | 0.980579i | \(-0.562836\pi\) | ||||
−0.196126 | + | 0.980579i | \(0.562836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 328.557 | 1.16522 | 0.582610 | − | 0.812752i | \(-0.302032\pi\) | ||||
0.582610 | + | 0.812752i | \(0.302032\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 71.2670 | + | 123.438i | 0.236086 | + | 0.408913i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 33.9773 | − | 58.8504i | 0.105449 | − | 0.182643i | −0.808473 | − | 0.588534i | \(-0.799705\pi\) |
0.913921 | + | 0.405891i | \(0.133039\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 329.500 | + | 95.2825i | 0.960641 | + | 0.277791i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 41.0227 | − | 71.0534i | 0.112634 | − | 0.195088i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 33.2443 | + | 57.5808i | 0.0861596 | + | 0.149233i | 0.905885 | − | 0.423524i | \(-0.139207\pi\) |
−0.819725 | + | 0.572757i | \(0.805874\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 820.951 | 2.01267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 229.534 | 0.533378 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −230.964 | − | 400.041i | −0.509643 | − | 0.882728i | −0.999938 | − | 0.0111711i | \(-0.996444\pi\) |
0.490294 | − | 0.871557i | \(-0.336889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −92.6742 | + | 160.516i | −0.194520 | + | 0.336919i | −0.946743 | − | 0.321990i | \(-0.895648\pi\) |
0.752223 | + | 0.658909i | \(0.228982\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 102.767 | − | 131.232i | 0.205515 | − | 0.262440i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 307.534 | − | 532.665i | 0.586845 | − | 1.01644i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 272.604 | + | 472.164i | 0.497073 | + | 0.860956i | 0.999994 | − | 0.00337637i | \(-0.00107474\pi\) |
−0.502921 | + | 0.864332i | \(0.667741\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 442.045 | 0.771247 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 130.742 | 0.218539 | 0.109270 | − | 0.994012i | \(-0.465149\pi\) | ||||
0.109270 | + | 0.994012i | \(0.465149\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −90.6496 | − | 157.010i | −0.145339 | − | 0.251734i | 0.784160 | − | 0.620558i | \(-0.213094\pi\) |
−0.929499 | + | 0.368824i | \(0.879761\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 188.722 | − | 326.875i | 0.290556 | − | 0.503258i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −358.638 | − | 890.533i | −0.530787 | − | 1.31800i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −204.848 | + | 354.808i | −0.291737 | + | 0.505304i | −0.974221 | − | 0.225597i | \(-0.927567\pi\) |
0.682483 | + | 0.730901i | \(0.260900\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −347.928 | −0.460121 | −0.230061 | − | 0.973176i | \(-0.573892\pi\) | ||||
−0.230061 | + | 0.973176i | \(0.573892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −433.121 | −0.552689 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 360.312 | + | 624.080i | 0.444018 | + | 0.769061i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −578.580 | + | 1002.13i | −0.689093 | + | 1.19354i | 0.283038 | + | 0.959109i | \(0.408658\pi\) |
−0.972132 | + | 0.234436i | \(0.924676\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −712.161 | − | 100.902i | −0.820382 | − | 0.116235i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 445.011 | − | 770.782i | 0.496188 | − | 0.859424i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −605.860 | − | 1049.38i | −0.654315 | − | 1.13331i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1618.30 | 1.69395 | 0.846976 | − | 0.531631i | \(-0.178421\pi\) | ||||
0.846976 | + | 0.531631i | \(0.178421\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −466.534 | −0.473621 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −359.371 | − | 622.449i | −0.354047 | − | 0.613228i | 0.632907 | − | 0.774228i | \(-0.281861\pi\) |
−0.986954 | + | 0.161000i | \(0.948528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −805.790 | + | 1395.67i | −0.770843 | + | 1.33514i | 0.166259 | + | 0.986082i | \(0.446831\pi\) |
−0.937102 | + | 0.349057i | \(0.886502\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −871.222 | − | 123.438i | −0.809738 | − | 0.114727i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 467.335 | − | 809.448i | 0.422234 | − | 0.731330i | −0.573924 | − | 0.818909i | \(-0.694580\pi\) |
0.996158 | + | 0.0875784i | \(0.0279128\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 598.509 | + | 1036.65i | 0.525934 | + | 0.910944i | 0.999544 | + | 0.0302095i | \(0.00961746\pi\) |
−0.473610 | + | 0.880735i | \(0.657049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 484.602 | 0.414382 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2384.64 | −1.98521 | −0.992604 | − | 0.121400i | \(-0.961262\pi\) | ||||
−0.992604 | + | 0.121400i | \(0.961262\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1166.79 | − | 2020.94i | −0.946118 | − | 1.63872i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −174.767 | + | 302.705i | −0.138096 | + | 0.239189i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 189.212 | + | 469.832i | 0.145757 | + | 0.361928i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −678.044 | + | 1174.41i | −0.509424 | + | 0.882349i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −154.466 | − | 267.543i | −0.113234 | − | 0.196126i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.8977 | −0.00922883 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2673.92 | 1.86829 | 0.934143 | − | 0.356898i | \(-0.116166\pi\) | ||||
0.934143 | + | 0.356898i | \(0.116166\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 492.835 | + | 853.616i | 0.336370 | + | 0.582610i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.4299 | + | 33.6536i | −0.0129588 | + | 0.0224453i | −0.872432 | − | 0.488735i | \(-0.837458\pi\) |
0.859473 | + | 0.511181i | \(0.170792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −873.650 | + | 1115.64i | −0.569587 | + | 0.727356i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −213.801 | + | 370.314i | −0.136304 | + | 0.236086i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 384.072 | + | 665.232i | 0.239514 | + | 0.414851i | 0.960575 | − | 0.278021i | \(-0.0896784\pi\) |
−0.721061 | + | 0.692872i | \(0.756345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1052.55 | −0.642274 | −0.321137 | − | 0.947033i | \(-0.604065\pi\) | ||||
−0.321137 | + | 0.947033i | \(0.604065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 203.864 | 0.121762 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1006.60 | + | 1743.49i | 0.588646 | + | 1.01956i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1902.10 | − | 3294.54i | 1.08939 | − | 1.88687i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 246.699 | + | 998.990i | 0.138418 | + | 0.560512i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −180.489 | + | 312.615i | −0.0992363 | + | 0.171882i | −0.911369 | − | 0.411591i | \(-0.864973\pi\) |
0.812132 | + | 0.583473i | \(0.198307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 774.195 | + | 1340.95i | 0.417239 | + | 0.722679i | 0.995661 | − | 0.0930587i | \(-0.0296644\pi\) |
−0.578422 | + | 0.815738i | \(0.696331\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 246.136 | 0.130058 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4698.47 | −2.43477 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 483.534 | + | 837.506i | 0.245798 | + | 0.425734i | 0.962356 | − | 0.271794i | \(-0.0876168\pi\) |
−0.716558 | + | 0.697528i | \(0.754283\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −99.7330 | + | 172.743i | −0.0497443 | + | 0.0861596i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1682.51 | + | 2148.54i | −0.823604 | + | 1.05173i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −663.250 | + | 1148.78i | −0.318710 | + | 0.552022i | −0.980219 | − | 0.197915i | \(-0.936583\pi\) |
0.661509 | + | 0.749937i | \(0.269916\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1231.43 | + | 2132.89i | 0.581008 | + | 1.00634i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1416.70 | −0.656451 | −0.328225 | − | 0.944599i | \(-0.606451\pi\) | ||||
−0.328225 | + | 0.944599i | \(0.606451\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −688.678 | −0.313463 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 344.301 | + | 596.347i | 0.153973 | + | 0.266689i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 518.299 | − | 897.721i | 0.227778 | − | 0.394523i | −0.729371 | − | 0.684118i | \(-0.760187\pi\) |
0.957149 | + | 0.289595i | \(0.0935207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 870.454 | + | 2161.42i | 0.376001 | + | 0.933647i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 692.892 | − | 1200.12i | 0.294243 | − | 0.509643i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −383.716 | − | 664.615i | −0.160225 | − | 0.277518i | 0.774724 | − | 0.632299i | \(-0.217889\pi\) |
−0.934949 | + | 0.354781i | \(0.884555\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3957.71 | −1.62527 | −0.812636 | − | 0.582772i | \(-0.801968\pi\) | ||||
−0.812636 | + | 0.582772i | \(0.801968\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −556.045 | −0.224612 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1279.12 | − | 2215.50i | −0.508338 | − | 0.880468i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 708.833 | − | 1227.74i | 0.277193 | − | 0.480112i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 495.102 | + | 70.1481i | 0.190547 | + | 0.0269975i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −902.648 | + | 1563.43i | −0.341954 | + | 0.592282i | −0.984796 | − | 0.173717i | \(-0.944422\pi\) |
0.642841 | + | 0.765999i | \(0.277756\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1685.42 | − | 2919.23i | −0.628597 | − | 1.08876i | −0.987833 | − | 0.155515i | \(-0.950296\pi\) |
0.359237 | − | 0.933247i | \(-0.383037\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1845.20 | 0.677630 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4612.31 | −1.66809 | −0.834044 | − | 0.551697i | \(-0.813980\pi\) | ||||
−0.834044 | + | 0.551697i | \(0.813980\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1114.93 | − | 1931.12i | −0.397163 | − | 0.687906i | 0.596212 | − | 0.802827i | \(-0.296672\pi\) |
−0.993375 | + | 0.114921i | \(0.963339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −817.812 | + | 1416.49i | −0.286985 | + | 0.497073i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4404.73 | − | 624.080i | −1.52291 | − | 0.215772i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −815.432 | + | 1412.37i | −0.277816 | + | 0.481191i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 663.068 | + | 1148.47i | 0.222640 | + | 0.385623i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3966.13 | 1.31265 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −912.614 | −0.297758 | −0.148879 | − | 0.988855i | \(-0.547566\pi\) | ||||
−0.148879 | + | 0.988855i | \(0.547566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 196.114 | + | 339.679i | 0.0630868 | + | 0.109270i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2601.70 | − | 4506.27i | 0.825276 | − | 1.42942i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2052.56 | + | 5096.70i | 0.642105 | + | 1.59441i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 271.949 | − | 471.029i | 0.0839114 | − | 0.145339i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −531.068 | − | 919.837i | −0.161645 | − | 0.279977i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4319.47 | 1.29710 | 0.648549 | − | 0.761173i | \(-0.275376\pi\) | ||||
0.648549 | + | 0.761173i | \(0.275376\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1132.33 | 0.335505 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1030.64 | + | 1785.12i | 0.301349 | + | 0.521951i | 0.976442 | − | 0.215782i | \(-0.0692299\pi\) |
−0.675093 | + | 0.737733i | \(0.735897\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1737.32 | − | 3009.12i | 0.501332 | − | 0.868333i | −0.498667 | − | 0.866794i | \(-0.666177\pi\) |
0.999999 | − | 0.00153905i | \(-0.000489896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1775.72 | − | 2267.57i | 0.505773 | − | 0.645866i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −388.049 | + | 672.121i | −0.109107 | + | 0.188979i | −0.915409 | − | 0.402525i | \(-0.868132\pi\) |
0.806302 | + | 0.591505i | \(0.201466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −538.102 | − | 932.020i | −0.149370 | − | 0.258716i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1229.09 | −0.336869 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2006.80 | −0.543133 | −0.271567 | − | 0.962420i | \(-0.587542\pi\) | ||||
−0.271567 | + | 0.962420i | \(0.587542\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −402.824 | − | 697.711i | −0.107669 | − | 0.186488i | 0.807157 | − | 0.590337i | \(-0.201005\pi\) |
−0.914825 | + | 0.403850i | \(0.867672\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3916.00 | − | 3764.71i | 1.02116 | − | 0.981707i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1485.74 | − | 2573.38i | 0.382734 | − | 0.662915i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −521.892 | − | 903.944i | −0.132826 | − | 0.230061i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1421.78 | −0.357539 | −0.178769 | − | 0.983891i | \(-0.557212\pi\) | ||||
−0.178769 | + | 0.983891i | \(0.557212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7638.12 | 1.89804 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −649.682 | − | 1125.28i | −0.159548 | − | 0.276345i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 732.909 | − | 1269.44i | 0.177890 | − | 0.308114i | −0.763268 | − | 0.646082i | \(-0.776406\pi\) |
0.941157 | + | 0.337968i | \(0.109740\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1844.49 | + | 2355.39i | −0.442513 | + | 0.565084i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1080.94 | + | 1872.24i | −0.256354 | + | 0.444018i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3495.69 | + | 6054.72i | 0.819596 | + | 1.41958i | 0.905980 | + | 0.423320i | \(0.139135\pi\) |
−0.0863847 | + | 0.996262i | \(0.527531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1052.99 | 0.244093 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3471.48 | −0.795696 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −404.479 | − | 700.578i | −0.0916786 | − | 0.158792i | 0.816539 | − | 0.577290i | \(-0.195890\pi\) |
−0.908218 | + | 0.418498i | \(0.862557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3330.88 | − | 5769.26i | 0.746630 | − | 1.29320i | −0.202799 | − | 0.979220i | \(-0.565004\pi\) |
0.949429 | − | 0.313981i | \(-0.101663\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −806.091 | − | 2001.60i | −0.178706 | − | 0.443745i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3260.93 | − | 5648.09i | 0.715059 | − | 1.23852i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3765.73 | + | 6522.44i | 0.816827 | + | 1.41479i | 0.908009 | + | 0.418951i | \(0.137602\pi\) |
−0.0911823 | + | 0.995834i | \(0.529065\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2670.07 | 0.572949 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1690.19 | 0.358819 | 0.179410 | − | 0.983774i | \(-0.442581\pi\) | ||||
0.179410 | + | 0.983774i | \(0.442581\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1589.12 | + | 2752.43i | 0.333792 | + | 0.578145i | 0.983252 | − | 0.182251i | \(-0.0583384\pi\) |
−0.649460 | + | 0.760396i | \(0.725005\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1817.58 | − | 3148.14i | 0.377769 | − | 0.654315i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1888.31 | + | 267.543i | 0.388374 | + | 0.0550263i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2082.53 | − | 3607.05i | 0.423882 | − | 0.734184i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2427.45 | + | 4204.46i | 0.489002 | + | 0.846976i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2176.53 | −0.433974 | −0.216987 | − | 0.976174i | \(-0.569623\pi\) | ||||
−0.216987 | + | 0.976174i | \(0.569623\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7315.61 | −1.44383 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −699.801 | − | 1212.09i | −0.136722 | − | 0.236810i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2861.30 | − | 4955.91i | 0.553421 | − | 0.958554i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6024.79 | − | 853.616i | −1.15370 | − | 0.163460i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1078.11 | − | 1867.35i | 0.204409 | − | 0.354047i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1467.69 | + | 2542.12i | 0.275541 | + | 0.477250i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −623.504 | −0.115913 | −0.0579564 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579564 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4834.74 | −0.890093 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 233.996 | + | 405.293i | 0.0426647 | + | 0.0738973i | 0.886569 | − | 0.462596i | \(-0.153082\pi\) |
−0.843905 | + | 0.536493i | \(0.819749\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1806.41 | + | 3128.79i | −0.326211 | + | 0.565014i | −0.981757 | − | 0.190141i | \(-0.939105\pi\) |
0.655546 | + | 0.755156i | \(0.272439\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −986.131 | − | 2448.66i | −0.176388 | − | 0.437988i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2265.87 | + | 3924.60i | −0.401463 | + | 0.695355i | −0.993903 | − | 0.110260i | \(-0.964832\pi\) |
0.592439 | + | 0.805615i | \(0.298165\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6225.85 | + | 10783.5i | 1.09273 | + | 1.89266i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2804.01 | 0.487553 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2092.47 | −0.360459 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2443.13 | − | 4231.63i | −0.416987 | − | 0.722242i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1795.53 | + | 3109.95i | −0.303648 | + | 0.525934i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −775.943 | + | 990.871i | −0.130028 | + | 0.166044i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −618.528 | + | 1071.32i | −0.102711 | + | 0.177901i | −0.912801 | − | 0.408405i | \(-0.866085\pi\) |
0.810090 | + | 0.586306i | \(0.199418\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 726.903 | + | 1259.03i | 0.119622 | + | 0.207191i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8634.53 | 1.40822 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1867.83 | −0.301921 | −0.150960 | − | 0.988540i | \(-0.548237\pi\) | ||||
−0.150960 | + | 0.988540i | \(0.548237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3576.97 | − | 6195.49i | −0.573080 | − | 0.992604i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7689.37 | − | 13318.4i | 1.22112 | − | 2.11505i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5794.53 | − | 2603.27i | −0.912173 | − | 0.409806i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3500.36 | − | 6062.81i | 0.546241 | − | 0.946118i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −31.6819 | − | 54.8746i | −0.00490136 | − | 0.00848940i | 0.863564 | − | 0.504239i | \(-0.168227\pi\) |
−0.868466 | + | 0.495749i | \(0.834893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1223.79 | 0.187702 | 0.0938508 | − | 0.995586i | \(-0.470082\pi\) | ||||
0.0938508 | + | 0.995586i | \(0.470082\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1048.60 | −0.159459 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2257.81 | + | 3910.64i | 0.340428 | + | 0.589638i | 0.984512 | − | 0.175316i | \(-0.0560949\pi\) |
−0.644085 | + | 0.764954i | \(0.722762\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1035.29 | − | 1793.18i | 0.154782 | − | 0.268090i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −936.841 | + | 1196.34i | −0.138888 | + | 0.177358i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1114.25 | − | 1929.93i | 0.163810 | − | 0.283727i | −0.772422 | − | 0.635109i | \(-0.780955\pi\) |
0.936232 | + | 0.351383i | \(0.114288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 502.506 | + | 870.365i | 0.0732622 | + | 0.126894i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4068.26 | −0.588232 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2871.26 | −0.411749 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −718.670 | − | 1244.77i | −0.102219 | − | 0.177048i | 0.810380 | − | 0.585905i | \(-0.199261\pi\) |
−0.912598 | + | 0.408857i | \(0.865928\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 463.398 | − | 802.628i | 0.0653754 | − | 0.113234i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −460.006 | − | 1142.24i | −0.0643728 | − | 0.159844i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6118.71 | − | 10597.9i | 0.849370 | − | 1.47115i | −0.0324014 | − | 0.999475i | \(-0.510315\pi\) |
0.881771 | − | 0.471677i | \(-0.156351\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −19.3465 | − | 33.5092i | −0.00266413 | − | 0.00461442i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9329.00 | 1.27445 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10647.0 | 1.44301 | 0.721503 | − | 0.692411i | \(-0.243451\pi\) | ||||
0.721503 | + | 0.692411i | \(0.243451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4010.89 | + | 6947.06i | 0.539328 | + | 0.934143i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3357.41 | + | 5815.20i | −0.447925 | + | 0.775829i | −0.998251 | − | 0.0591208i | \(-0.981170\pi\) |
0.550326 | + | 0.834950i | \(0.314504\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15053.9 | − | 2132.89i | −1.99277 | − | 0.282344i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1478.51 | + | 2560.85i | −0.194203 | + | 0.336370i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5326.54 | + | 9225.83i | 0.694258 | + | 1.20249i | 0.970430 | + | 0.241381i | \(0.0776005\pi\) |
−0.276173 | + | 0.961108i | \(0.589066\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4029.76 | −0.521211 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −116.580 | −0.0149635 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3244.21 | + | 5619.14i | 0.413250 | + | 0.715771i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1610.52 | + | 2789.50i | −0.203601 | + | 0.352648i | −0.949686 | − | 0.313203i | \(-0.898598\pi\) |
0.746085 | + | 0.665851i | \(0.231931\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4208.99 | − | 596.347i | −0.528103 | − | 0.0748238i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6242.50 | + | 10812.3i | −0.777395 | + | 1.34649i | 0.156043 | + | 0.987750i | \(0.450126\pi\) |
−0.933438 | + | 0.358738i | \(0.883207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5760.99 | − | 9978.32i | −0.712097 | − | 1.23339i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1282.81 | −0.157391 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8373.46 | 1.01980 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3518.69 | − | 6094.56i | −0.425399 | − | 0.736813i | 0.571059 | − | 0.820909i | \(-0.306533\pi\) |
−0.996458 | + | 0.0840967i | \(0.973200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1152.22 | + | 1995.70i | −0.138284 | + | 0.239514i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3195.88 | + | 7935.67i | 0.380772 | + | 0.945493i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2755.09 | + | 4771.95i | −0.325884 | + | 0.564448i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1578.82 | − | 2734.60i | −0.185408 | − | 0.321137i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1549.66 | 0.180682 | 0.0903410 | − | 0.995911i | \(-0.471204\pi\) | ||||
0.0903410 | + | 0.995911i | \(0.471204\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5531.63 | 0.640369 | 0.320184 | − | 0.947355i | \(-0.396255\pi\) | ||||
0.320184 | + | 0.947355i | \(0.396255\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 305.795 | + | 529.653i | 0.0351496 | + | 0.0608809i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1720.42 | + | 2979.85i | −0.196359 | + | 0.340103i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2116.41 | − | 2702.64i | 0.239860 | − | 0.306299i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3019.81 | + | 5230.46i | −0.339855 | + | 0.588646i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1014.97 | − | 1757.97i | −0.113432 | − | 0.196470i | 0.803720 | − | 0.595008i | \(-0.202851\pi\) |
−0.917152 | + | 0.398538i | \(0.869518\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −327.739 | −0.0363744 | −0.0181872 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181872 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11412.6 | 1.25792 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5636.92 | − | 9763.43i | −0.617049 | − | 1.06876i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3954.34 | − | 6849.12i | 0.429910 | − | 0.744625i | −0.566955 | − | 0.823749i | \(-0.691879\pi\) |
0.996865 | + | 0.0791234i | \(0.0252121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2225.40 | + | 2139.43i | −0.240298 | + | 0.231015i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1460.41 | + | 2529.51i | −0.156628 | + | 0.271288i | −0.933651 | − | 0.358185i | \(-0.883396\pi\) |
0.777023 | + | 0.629473i | \(0.216729\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9163.03 | + | 15870.8i | 0.976111 | + | 1.69067i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1082.93 | −0.114588 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10240.2 | −1.07631 | −0.538156 | − | 0.842845i | \(-0.680879\pi\) | ||||
−0.538156 | + | 0.842845i | \(0.680879\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2669.02 | − | 4622.88i | −0.278668 | − | 0.482668i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2322.59 | + | 4022.84i | −0.240893 | + | 0.417239i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7023.19 | + | 8968.54i | −0.723632 | + | 0.924069i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2946.31 | + | 5103.17i | −0.301582 | + | 0.522355i | −0.976494 | − | 0.215543i | \(-0.930848\pi\) |
0.674913 | + | 0.737897i | \(0.264181\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 369.205 | + | 639.481i | 0.0375446 | + | 0.0650292i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12643.4 | −1.27735 | −0.638677 | − | 0.769475i | \(-0.720518\pi\) | ||||
−0.638677 | + | 0.769475i | \(0.720518\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15093.2 | −1.51499 | −0.757494 | − | 0.652842i | \(-0.773577\pi\) | ||||
−0.757494 | + | 0.652842i | \(0.773577\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7047.70 | − | 12207.0i | −0.702858 | − | 1.21739i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1410.12 | + | 2442.39i | −0.139727 | + | 0.242014i | −0.927393 | − | 0.374088i | \(-0.877956\pi\) |
0.787666 | + | 0.616102i | \(0.211289\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3772.06 | − | 9366.38i | −0.371380 | − | 0.922173i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1450.60 | + | 2512.52i | −0.141911 | + | 0.245798i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8515.72 | + | 14749.7i | 0.827808 | + | 1.43381i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9626.23 | −0.929856 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −598.398 | −0.0574397 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8224.25 | − | 14244.8i | −0.784500 | − | 1.35879i | −0.929297 | − | 0.369332i | \(-0.879586\pi\) |
0.144798 | − | 0.989461i | \(-0.453747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3136.76 | − | 5433.03i | 0.297347 | − | 0.515020i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8105.84 | − | 1148.47i | −0.763620 | − | 0.108193i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12814.6 | − | 22195.5i | 1.19975 | − | 2.07804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3165.53 | + | 5482.87i | 0.294546 | + | 0.510169i | 0.974879 | − | 0.222734i | \(-0.0714982\pi\) |
−0.680333 | + | 0.732903i | \(0.738165\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3979.50 | −0.368015 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9286.90 | 0.853588 | 0.426794 | − | 0.904349i | \(-0.359643\pi\) | ||||
0.426794 | + | 0.904349i | \(0.359643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3284.67 | − | 5689.21i | −0.300069 | − | 0.519735i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3694.28 | + | 6398.68i | −0.335445 | + | 0.581008i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2397.44 | − | 339.679i | −0.216378 | − | 0.0306573i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −121.725 | + | 210.835i | −0.0109202 | + | 0.0189143i | −0.871434 | − | 0.490513i | \(-0.836809\pi\) |
0.860514 | + | 0.509427i | \(0.170143\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2125.05 | − | 3680.69i | −0.189501 | − | 0.328225i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8499.30 | −0.753409 | −0.376705 | − | 0.926333i | \(-0.622943\pi\) | ||||
−0.376705 | + | 0.926333i | \(0.622943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11382.8 | −1.00303 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1033.02 | − | 1789.24i | −0.0904890 | − | 0.156731i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3841.55 | − | 6653.76i | 0.334526 | − | 0.579416i | −0.648868 | − | 0.760901i | \(-0.724757\pi\) |
0.983394 | + | 0.181485i | \(0.0580904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1254.33 | + | 3114.62i | 0.108588 | + | 0.269634i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1032.90 | + | 1789.04i | −0.0888963 | + | 0.153973i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12761.4 | + | 22103.4i | 1.09191 | + | 1.89124i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3522.57 | 0.299656 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3109.80 | 0.263015 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10765.3 | + | 18646.1i | 0.905253 | + | 1.56794i | 0.820578 | + | 0.571535i | \(0.193652\pi\) |
0.0846750 | + | 0.996409i | \(0.473015\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8423.53 | + | 14590.0i | −0.704274 | + | 1.21984i | 0.262679 | + | 0.964883i | \(0.415394\pi\) |
−0.966953 | + | 0.254955i | \(0.917939\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4309.86 | + | 5503.64i | −0.358281 | + | 0.457521i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4056.80 | + | 7026.58i | −0.335326 | + | 0.580802i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4772.29 | − | 8265.84i | −0.392232 | − | 0.679366i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4157.35 | 0.339762 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3999.34 | −0.325011 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7401.24 | − | 12819.3i | −0.598100 | − | 1.03594i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1151.15 | − | 1993.85i | 0.0925059 | − | 0.160225i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4262.72 | + | 17261.6i | 0.340646 | + | 1.37942i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8720.02 | + | 15103.5i | −0.692981 | + | 1.20028i | 0.277875 | + | 0.960617i | \(0.410370\pi\) |
−0.970856 | + | 0.239662i | \(0.922963\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5936.56 | − | 10282.4i | −0.469175 | − | 0.812636i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18957.3 | 1.48999 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11520.7 | −0.900530 | −0.450265 | − | 0.892895i | \(-0.648671\pi\) | ||||
−0.450265 | + | 0.892895i | \(0.648671\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −834.068 | − | 1444.65i | −0.0648400 | − | 0.112306i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9189.33 | − | 15916.4i | 0.710488 | − | 1.23060i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4678.15 | − | 5973.94i | 0.359738 | − | 0.459382i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3837.35 | − | 6646.49i | 0.293489 | − | 0.508338i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5746.51 | − | 9953.25i | −0.437141 | − | 0.757151i | 0.560327 | − | 0.828272i | \(-0.310676\pi\) |
−0.997468 | + | 0.0711212i | \(0.977342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12760.2 | 0.965472 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4253.00 | 0.320075 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9055.65 | + | 15684.8i | 0.677886 | + | 1.17413i | 0.975616 | + | 0.219483i | \(0.0704372\pi\) |
−0.297730 | + | 0.954650i | \(0.596230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18882.9 | + | 32706.2i | −1.40604 | + | 2.43533i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 560.403 | + | 1391.54i | 0.0415075 | + | 0.103067i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2208.81 | + | 3825.77i | −0.162738 | + | 0.281871i | −0.935850 | − | 0.352399i | \(-0.885366\pi\) |
0.773112 | + | 0.634270i | \(0.218699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6609.87 | + | 11448.6i | 0.484439 | + | 0.839073i | 0.999840 | − | 0.0178762i | \(-0.00569048\pi\) |
−0.515401 | + | 0.856949i | \(0.672357\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5415.89 | −0.394855 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18538.6 | −1.34454 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8748.20 | + | 15152.3i | 0.631182 | + | 1.09324i | 0.987310 | + | 0.158803i | \(0.0507634\pi\) |
−0.356128 | + | 0.934437i | \(0.615903\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5056.26 | − | 8757.70i | 0.362921 | − | 0.628597i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6380.00 | + | 903.944i | 0.455571 | + | 0.0645472i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1723.29 | + | 2984.83i | −0.122421 | + | 0.212039i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2767.81 | + | 4793.98i | 0.195615 | + | 0.338815i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4280.53 | 0.300982 | 0.150491 | − | 0.988611i | \(-0.451915\pi\) | ||||
0.150491 | + | 0.988611i | \(0.451915\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22699.0 | −1.58794 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6918.47 | − | 11983.1i | −0.481536 | − | 0.834044i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 795.466 | − | 1377.79i | 0.0550858 | − | 0.0954114i | −0.837168 | − | 0.546946i | \(-0.815790\pi\) |
0.892253 | + | 0.451535i | \(0.149123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7942.20 | + | 1125.28i | 0.547224 | + | 0.0775329i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3344.80 | − | 5793.36i | 0.229302 | − | 0.397163i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6961.42 | − | 12057.5i | −0.474851 | − | 0.822467i | 0.524734 | − | 0.851266i | \(-0.324165\pi\) |
−0.999585 | + | 0.0287997i | \(0.990831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12559.7 | 0.852446 | 0.426223 | − | 0.904618i | \(-0.359844\pi\) | ||||
0.426223 | + | 0.904618i | \(0.359844\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4906.87 | −0.331382 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10738.3 | + | 18599.2i | 0.721607 | + | 1.24986i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3839.19 | − | 6649.66i | 0.256718 | − | 0.444648i | −0.708643 | − | 0.705567i | \(-0.750692\pi\) |
0.965361 | + | 0.260919i | \(0.0840256\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4985.69 | − | 12379.9i | −0.331741 | − | 0.823745i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1319.58 | − | 2285.58i | 0.0873723 | − | 0.151333i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3079.19 | − | 5333.31i | −0.202883 | − | 0.351403i | 0.746573 | − | 0.665303i | \(-0.231698\pi\) |
−0.949456 | + | 0.313900i | \(0.898364\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4892.59 | −0.320794 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8813.12 | 0.575045 | 0.287523 | − | 0.957774i | \(-0.407168\pi\) | ||||
0.287523 | + | 0.957774i | \(0.407168\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11595.0 | + | 20083.1i | 0.752894 | + | 1.30405i | 0.946415 | + | 0.322954i | \(0.104676\pi\) |
−0.193521 | + | 0.981096i | \(0.561991\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1989.20 | + | 3445.40i | −0.128541 | + | 0.222640i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13213.1 | − | 16873.0i | 0.849713 | − | 1.08507i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7761.27 | − | 13442.9i | 0.496721 | − | 0.860346i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5949.19 | + | 10304.3i | 0.378928 | + | 0.656323i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4417.71 | −0.280041 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7936.94 | −0.500736 | −0.250368 | − | 0.968151i | \(-0.580552\pi\) | ||||
−0.250368 | + | 0.968151i | \(0.580552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1368.92 | − | 2371.04i | −0.0859553 | − | 0.148879i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21173.6 | − | 36673.8i | 1.32323 | − | 2.29190i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12796.8 | + | 3700.50i | 0.795964 | + | 0.230171i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −588.341 | + | 1019.04i | −0.0364232 | + | 0.0630868i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16057.3 | − | 27812.1i | −0.989432 | − | 1.71375i | −0.620286 | − | 0.784376i | \(-0.712984\pi\) |
−0.369146 | − | 0.929371i | \(-0.620350\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24786.7 | 1.52021 | 0.760104 | − | 0.649802i | \(-0.225148\pi\) | ||||
0.760104 | + | 0.649802i | \(0.225148\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15610.2 | 0.952946 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3772.80 | + | 6534.67i | 0.229249 | + | 0.397070i | 0.957586 | − | 0.288149i | \(-0.0930398\pi\) |
−0.728337 | + | 0.685219i | \(0.759706\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11972.5 | − | 20737.0i | 0.724133 | − | 1.25423i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10162.8 | + | 12977.8i | −0.611844 | + | 0.781318i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2444.49 | − | 4233.99i | 0.146494 | − | 0.253735i | −0.783435 | − | 0.621473i | \(-0.786534\pi\) |
0.929929 | + | 0.367738i | \(0.119868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 307.714 | + | 532.976i | 0.0183563 | + | 0.0317941i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1631.69 | 0.0968926 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25895.9 | −1.53075 | −0.765374 | − | 0.643586i | \(-0.777446\pi\) | ||||
−0.765374 | + | 0.643586i | \(0.777446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4091.68 | − | 7087.00i | −0.240769 | − | 0.417023i | 0.720165 | − | 0.693803i | \(-0.244066\pi\) |
−0.960933 | + | 0.276780i | \(0.910733\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1593.20 | − | 2759.51i | 0.0933257 | − | 0.161645i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8383.36 | + | 20816.7i | 0.488861 | + | 1.21389i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17697.2 | − | 30652.4i | 1.02734 | − | 1.77941i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6479.20 | + | 11222.3i | 0.374440 | + | 0.648549i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9607.93 | −0.552772 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4635.02 | −0.265478 | −0.132739 | − | 0.991151i | \(-0.542377\pi\) | ||||
−0.132739 | + | 0.991151i | \(0.542377\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1698.49 | + | 2941.88i | 0.0968520 | + | 0.167753i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12192.9 | − | 21118.7i | 0.692187 | − | 1.19890i | −0.278932 | − | 0.960311i | \(-0.589980\pi\) |
0.971120 | − | 0.238593i | \(-0.0766862\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29674.9 | − | 4204.46i | −1.67720 | − | 0.237633i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3091.93 | + | 5355.37i | −0.173984 | + | 0.301349i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9196.71 | − | 15929.2i | −0.515230 | − | 0.892405i | −0.999844 | − | 0.0176767i | \(-0.994373\pi\) |
0.484613 | − | 0.874728i | \(-0.338960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12165.2 | 0.678552 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10423.9 | 0.578889 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1291.11 | + | 2236.27i | 0.0713897 | + | 0.123651i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7449.44 | + | 12902.8i | −0.410116 | + | 0.710341i | −0.994902 | − | 0.100846i | \(-0.967845\pi\) |
0.584786 | + | 0.811187i | \(0.301178\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8554.89 | + | 1212.09i | 0.468937 | + | 0.0664409i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8334.67 | + | 14436.1i | −0.454895 | + | 0.787902i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1408.14 | + | 2438.96i | 0.0765236 | + | 0.132543i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2328.30 | −0.125986 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5725.70 | −0.308497 | −0.154249 | − | 0.988032i | \(-0.549296\pi\) | ||||
−0.154249 | + | 0.988032i | \(0.549296\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6179.60 | − | 10703.4i | −0.331533 | − | 0.574232i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1614.31 | − | 2796.06i | 0.0862387 | − | 0.149370i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4972.66 | + | 12347.6i | 0.264521 | + | 0.656831i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11728.4 | − | 20314.2i | 0.621255 | − | 1.07604i | −0.367998 | − | 0.929827i | \(-0.619957\pi\) |
0.989252 | − | 0.146218i | \(-0.0467101\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1843.64 | − | 3193.27i | −0.0972458 | − | 0.168435i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43714.5 | −2.29610 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31883.4 | 1.66765 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3010.19 | − | 5213.81i | −0.156789 | − | 0.271567i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4229.50 | + | 7325.71i | −0.219379 | + | 0.379976i | −0.954618 | − | 0.297832i | \(-0.903737\pi\) |
0.735239 | + | 0.677808i | \(0.237070\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18401.9 | − | 23499.0i | 0.950518 | − | 1.21380i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1208.47 | − | 2093.13i | 0.0621626 | − | 0.107669i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15110.8 | − | 26172.7i | −0.774072 | − | 1.34073i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11822.2 | 0.603111 | 0.301555 | − | 0.953449i | \(-0.402494\pi\) | ||||
0.301555 | + | 0.953449i | \(0.402494\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4492.77 | − | 7781.70i | −0.227320 | − | 0.393730i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2514.48 | + | 4355.20i | −0.126704 | + | 0.219458i | −0.922398 | − | 0.386241i | \(-0.873773\pi\) |
0.795694 | + | 0.605699i | \(0.207107\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15655.0 | + | 4527.00i | 0.785637 | + | 0.227185i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14131.0 | + | 24475.6i | −0.706272 | + | 1.22330i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8871.95 | − | 15366.7i | −0.441624 | − | 0.764914i | 0.556187 | − | 0.831057i | \(-0.312264\pi\) |
−0.997810 | + | 0.0661431i | \(0.978931\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8914.44 | 0.441944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13202.3 | 0.651877 | 0.325938 | − | 0.945391i | \(-0.394320\pi\) | ||||
0.325938 | + | 0.945391i | \(0.394320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2858.42 | + | 4950.93i | 0.140570 | + | 0.243474i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1565.68 | − | 2711.83i | 0.0766869 | − | 0.132826i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10672.6 | + | 13628.8i | −0.520652 | + | 0.664866i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7800.49 | − | 13510.8i | 0.379020 | − | 0.656482i | −0.611900 | − | 0.790935i | \(-0.709594\pi\) |
0.990920 | + | 0.134453i | \(0.0429278\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2132.68 | − | 3693.90i | −0.103213 | − | 0.178769i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24522.0 | 1.18205 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2948.08 | 0.141545 | 0.0707725 | − | 0.997492i | \(-0.477454\pi\) | ||||
0.0707725 | + | 0.997492i | \(0.477454\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11457.2 | + | 19844.4i | 0.547917 | + | 0.949021i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −848.515 | + | 1469.67i | −0.0404187 | + | 0.0700073i | −0.885527 | − | 0.464588i | \(-0.846203\pi\) |
0.845108 | + | 0.534595i | \(0.179536\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8281.65 | − | 20564.1i | −0.392943 | − | 0.975716i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1949.05 | − | 3375.85i | 0.0921149 | − | 0.159548i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8969.98 | − | 15536.5i | −0.422278 | − | 0.731407i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −96.7799 | −0.00453833 | −0.00226916 | − | 0.999997i | \(-0.500722\pi\) | ||||
−0.00226916 | + | 0.999997i | \(0.500722\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4397.45 | 0.205409 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18163.4 | − | 31459.9i | −0.845138 | − | 1.46382i | −0.885501 | − | 0.464637i | \(-0.846185\pi\) |
0.0403629 | − | 0.999185i | \(-0.487149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18662.9 | + | 32325.2i | −0.865023 | + | 1.49826i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8886.21 | − | 1259.03i | −0.410284 | − | 0.0581307i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3939.47 | + | 6823.35i | −0.181189 | + | 0.313828i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3388.66 | + | 5869.32i | 0.155257 | + | 0.268913i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6485.62 | −0.296012 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15315.6 | 0.696352 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3548.23 | + | 6145.72i | 0.160713 | + | 0.278362i | 0.935124 | − | 0.354319i | \(-0.115287\pi\) |
−0.774412 | + | 0.632682i | \(0.781954\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10487.1 | + | 18164.2i | −0.473194 | + | 0.819596i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43727.5 | + | 6195.49i | 1.96558 | + | 0.278491i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3599.20 | + | 6234.00i | −0.161174 | + | 0.279162i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1579.48 | + | 2735.74i | 0.0704635 | + | 0.122046i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40289.6 | 1.79063 | 0.895314 | − | 0.445436i | \(-0.146951\pi\) | ||||
0.895314 | + | 0.445436i | \(0.146951\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1858.45 | −0.0822871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5207.22 | − | 9019.16i | −0.229698 | − | 0.397848i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4699.02 | − | 8138.93i | 0.206506 | − | 0.357680i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16145.0 | + | 40089.5i | 0.706877 | + | 1.75524i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1213.44 | − | 2101.74i | 0.0529306 | − | 0.0916786i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5782.98 | + | 10016.4i | 0.251321 | + | 0.435301i | 0.963890 | − | 0.266301i | \(-0.0858017\pi\) |
−0.712569 | + | 0.701602i | \(0.752468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18014.2 | −0.779981 | −0.389991 | − | 0.920819i | \(-0.627522\pi\) | ||||
−0.389991 | + | 0.920819i | \(0.627522\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19985.3 | 0.862134 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10504.0 | + | 18193.4i | 0.451458 | + | 0.781948i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12569.2 | − | 21770.4i | 0.538237 | − | 0.932253i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3991.18 | − | 5096.69i | 0.170284 | − | 0.217451i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8396.22 | − | 14542.7i | 0.356918 | − | 0.618201i | −0.630526 | − | 0.776168i | \(-0.717161\pi\) |
0.987444 | + | 0.157967i | \(0.0504941\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4409.52 | − | 7637.50i | −0.186763 | − | 0.323483i | 0.757406 | − | 0.652944i | \(-0.226466\pi\) |
−0.944169 | + | 0.329461i | \(0.893133\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19565.6 | 0.825680 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8250.13 | −0.346898 | −0.173449 | − | 0.984843i | \(-0.555491\pi\) | ||||
−0.173449 | + | 0.984843i | \(0.555491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10775.2 | + | 18663.3i | 0.451435 | + | 0.781909i | 0.998475 | − | 0.0551975i | \(-0.0175789\pi\) |
−0.547040 | + | 0.837106i | \(0.684246\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11297.2 | + | 19567.3i | −0.471595 | + | 0.816827i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2248.95 | − | 9106.95i | −0.0935431 | − | 0.378796i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11218.2 | + | 19430.5i | −0.464936 | + | 0.805293i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4005.10 | + | 6937.04i | 0.165396 | + | 0.286475i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30130.4 | −1.23983 | −0.619916 | − | 0.784669i | \(-0.712833\pi\) | ||||
−0.619916 | + | 0.784669i | \(0.712833\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 33311.0 | 1.36582 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2535.28 | + | 4391.24i | 0.103582 | + | 0.179410i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5453.34 | + | 9445.46i | −0.222012 | + | 0.384537i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15484.6 | − | 19773.6i | 0.628165 | − | 0.802160i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4767.35 | + | 8257.29i | −0.192715 | + | 0.333792i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11900.9 | − | 20613.0i | −0.479386 | − | 0.830321i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40738.6 | −1.63525 | −0.817623 | − | 0.575754i | \(-0.804709\pi\) | ||||
−0.817623 | + | 0.575754i | \(0.804709\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10905.5 | 0.436210 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18254.1 | + | 31617.0i | 0.727594 | + | 1.26023i | 0.957897 | + | 0.287111i | \(0.0926949\pi\) |
−0.230303 | + | 0.973119i | \(0.573972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10990.4 | + | 19036.0i | −0.436541 | + | 0.756110i | −0.997420 | − | 0.0717871i | \(-0.977130\pi\) |
0.560879 | + | 0.827897i | \(0.310463\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2137.36 | + | 5307.28i | 0.0846006 | + | 0.210072i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11713.0 | + | 20287.6i | −0.462012 | + | 0.800228i | −0.999061 | − | 0.0433226i | \(-0.986206\pi\) |
0.537049 | + | 0.843551i | \(0.319539\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8208.37 | − | 14217.3i | −0.322651 | − | 0.558847i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12495.2 | 0.489456 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21237.5 | −0.829037 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10587.2 | + | 18337.5i | 0.411863 | + | 0.713367i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7282.35 | + | 12613.4i | −0.282325 | + | 0.489002i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 236.506 | + | 33.5092i | 0.00913757 | + | 0.00129465i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −153.701 | + | 266.217i | −0.00591802 | + | 0.0102503i | −0.868969 | − | 0.494866i | \(-0.835217\pi\) |
0.863051 | + | 0.505116i | \(0.168550\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3264.80 | − | 5654.80i | −0.125278 | − | 0.216987i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19941.7 | −0.762605 | −0.381302 | − | 0.924450i | \(-0.624524\pi\) | ||||
−0.381302 | + | 0.924450i | \(0.624524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37524.1 | 1.43011 | 0.715056 | − | 0.699068i | \(-0.246401\pi\) | ||||
0.715056 | + | 0.699068i | \(0.246401\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10973.4 | − | 19006.5i | −0.416799 | − | 0.721917i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1440.10 | + | 2494.33i | −0.0545140 | + | 0.0944210i | −0.891995 | − | 0.452046i | \(-0.850694\pi\) |
0.837481 | + | 0.546467i | \(0.184028\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49032.1 | − | 6947.06i | −1.84981 | − | 0.262089i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2099.40 | − | 3636.27i | 0.0789368 | − | 0.136722i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2599.65 | − | 4502.72i | −0.0974176 | − | 0.168732i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12153.9 | −0.453922 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17167.8 | 0.639036 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −35631.8 | − | 61716.1i | −1.32190 | − | 2.28960i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 909.182 | − | 1574.75i | 0.0336174 | − | 0.0582270i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6819.42 | − | 16933.3i | −0.251314 | − | 0.624036i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31339.4 | + | 54281.4i | −1.15111 | + | 1.99378i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9159.62 | + | 15864.9i | 0.335326 | + | 0.580801i | 0.983547 | − | 0.180651i | \(-0.0578204\pi\) |
−0.648222 | + | 0.761452i | \(0.724487\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6468.68 | 0.236031 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46150.7 | −1.67842 | −0.839210 | − | 0.543807i | \(-0.816982\pi\) | ||||
−0.839210 | + | 0.543807i | \(0.816982\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9017.79 | − | 15619.3i | −0.326884 | − | 0.566180i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4403.08 | + | 7626.36i | −0.159083 | + | 0.275541i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 443.723 | − | 566.630i | 0.0159793 | − | 0.0204054i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23632.1 | − | 40932.1i | 0.848261 | − | 1.46923i | −0.0344969 | − | 0.999405i | \(-0.510983\pi\) |
0.882758 | − | 0.469827i | \(-0.155684\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −935.256 | − | 1619.91i | −0.0334612 | − | 0.0579564i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5077.66 | 0.181076 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20323.3 | −0.722407 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7252.11 | − | 12561.0i | −0.256948 | − | 0.445046i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26635.7 | − | 46134.4i | 0.940678 | − | 1.62930i | 0.176496 | − | 0.984301i | \(-0.443524\pi\) |
0.764182 | − | 0.645001i | \(-0.223143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18918.7 | − | 18187.8i | 0.665990 | − | 0.640260i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −701.989 | + | 1215.88i | −0.0246324 | + | 0.0426647i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11225.9 | − | 19443.8i | −0.392648 | − | 0.680086i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17197.8 | 0.599602 | 0.299801 | − | 0.954002i | \(-0.403080\pi\) | ||||
0.299801 | + | 0.954002i | \(0.403080\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10838.4 | −0.376676 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14417.4 | − | 24971.7i | −0.499463 | − | 0.865096i | 0.500537 | − | 0.865715i | \(-0.333136\pi\) |
−1.00000 | 0.000619696i | \(0.999803\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7586.77 | + | 13140.7i | −0.261993 | + | 0.453785i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4882.60 | − | 6235.03i | 0.168075 | − | 0.214630i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25920.6 | + | 44895.8i | −0.889448 | + | 1.54057i | −0.0489180 | + | 0.998803i | \(0.515577\pi\) |
−0.840530 | + | 0.541766i | \(0.817756\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3520.57 | − | 6097.81i | −0.120424 | − | 0.208581i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13595.2 | −0.463570 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5887.31 | −0.200114 | −0.100057 | − | 0.994982i | \(-0.531903\pi\) | ||||
−0.100057 | + | 0.994982i | \(0.531903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14295.3 | + | 24760.3i | 0.484384 | + | 0.838977i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −18677.6 | + | 32350.5i | −0.630888 | + | 1.09273i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5314.45 | − | 13196.3i | −0.178949 | − | 0.444349i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29112.3 | + | 50424.0i | −0.977218 | + | 1.69259i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4206.02 | + | 7285.04i | 0.140745 | + | 0.243777i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −53384.4 | −1.78083 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36620.0 | 1.21781 | 0.608904 | − | 0.793244i | \(-0.291609\pi\) | ||||
0.608904 | + | 0.793244i | \(0.291609\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3138.70 | − | 5436.40i | −0.104055 | − | 0.180229i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21182.4 | + | 36689.1i | −0.700079 | + | 1.21257i | 0.268359 | + | 0.963319i | \(0.413519\pi\) |
−0.968438 | + | 0.249254i | \(0.919815\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19300.7 | + | 2734.60i | 0.635923 | + | 0.0901001i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7329.40 | − | 12694.9i | 0.240747 | − | 0.416987i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2511.16 | − | 4349.46i | −0.0822304 | − | 0.142427i | 0.821977 | − | 0.569520i | \(-0.192871\pi\) |
−0.904208 | + | 0.427093i | \(0.859538\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −59983.8 | −1.95821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10773.2 | −0.350623 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14146.4 | + | 24502.3i | 0.459003 | + | 0.795016i | 0.998909 | − | 0.0467095i | \(-0.0148735\pi\) |
−0.539906 | + | 0.841725i | \(0.681540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36522.9 | + | 63259.4i | −1.18144 | + | 2.04631i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3738.27 | − | 529.653i | −0.120558 | − | 0.0170811i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24206.2 | − | 41926.3i | 0.778273 | − | 1.34801i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18200.5 | + | 31524.2i | 0.583410 | + | 1.01050i | 0.995072 | + | 0.0991586i | \(0.0316151\pi\) |
−0.411662 | + | 0.911337i | \(0.635052\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3711.17 | −0.118601 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −35314.6 | −1.12517 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1178.60 | + | 2041.39i | 0.0374389 | + | 0.0648460i | 0.884138 | − | 0.467226i | \(-0.154747\pi\) |
−0.846699 | + | 0.532072i | \(0.821413\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2180.71 | + | 3777.10i | −0.0690637 | + | 0.119622i |
(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 | 336.4.q.j.289.2 | 4 | ||
4.3 | odd | 2 | 42.4.e.c.37.2 | yes | 4 | ||
7.2 | even | 3 | 2352.4.a.bq.1.1 | 2 | |||
7.4 | even | 3 | inner | 336.4.q.j.193.2 | 4 | ||
7.5 | odd | 6 | 2352.4.a.ca.1.2 | 2 | |||
12.11 | even | 2 | 126.4.g.g.37.1 | 4 | |||
28.3 | even | 6 | 294.4.e.l.67.1 | 4 | |||
28.11 | odd | 6 | 42.4.e.c.25.2 | ✓ | 4 | ||
28.19 | even | 6 | 294.4.a.m.1.2 | 2 | |||
28.23 | odd | 6 | 294.4.a.n.1.1 | 2 | |||
28.27 | even | 2 | 294.4.e.l.79.1 | 4 | |||
84.11 | even | 6 | 126.4.g.g.109.1 | 4 | |||
84.23 | even | 6 | 882.4.a.v.1.2 | 2 | |||
84.47 | odd | 6 | 882.4.a.z.1.1 | 2 | |||
84.59 | odd | 6 | 882.4.g.bf.361.2 | 4 | |||
84.83 | odd | 2 | 882.4.g.bf.667.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.4.e.c.25.2 | ✓ | 4 | 28.11 | odd | 6 | ||
42.4.e.c.37.2 | yes | 4 | 4.3 | odd | 2 | ||
126.4.g.g.37.1 | 4 | 12.11 | even | 2 | |||
126.4.g.g.109.1 | 4 | 84.11 | even | 6 | |||
294.4.a.m.1.2 | 2 | 28.19 | even | 6 | |||
294.4.a.n.1.1 | 2 | 28.23 | odd | 6 | |||
294.4.e.l.67.1 | 4 | 28.3 | even | 6 | |||
294.4.e.l.79.1 | 4 | 28.27 | even | 2 | |||
336.4.q.j.193.2 | 4 | 7.4 | even | 3 | inner | ||
336.4.q.j.289.2 | 4 | 1.1 | even | 1 | trivial | ||
882.4.a.v.1.2 | 2 | 84.23 | even | 6 | |||
882.4.a.z.1.1 | 2 | 84.47 | odd | 6 | |||
882.4.g.bf.361.2 | 4 | 84.59 | odd | 6 | |||
882.4.g.bf.667.2 | 4 | 84.83 | odd | 2 | |||
2352.4.a.bq.1.1 | 2 | 7.2 | even | 3 | |||
2352.4.a.ca.1.2 | 2 | 7.5 | odd | 6 |