Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,5,Mod(145,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.145");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.y (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(70.7050547493\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 2358 x^{12} + 15572 x^{11} + 4050518 x^{10} + 21628620 x^{9} + 2974230644 x^{8} + 5952397856 x^{7} + 1565987836020 x^{6} + \cdots + 96\!\cdots\!24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(-15.2075 + 26.3401i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.145 |
Dual form | 684.5.y.e.217.1 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −13.2075 | − | 22.8760i | −0.528299 | − | 0.915041i | −0.999456 | − | 0.0329913i | \(-0.989497\pi\) |
0.471157 | − | 0.882050i | \(-0.343837\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.95127 | 0.0806382 | 0.0403191 | − | 0.999187i | \(-0.487163\pi\) | ||||
0.0403191 | + | 0.999187i | \(0.487163\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 66.0544 | 0.545904 | 0.272952 | − | 0.962028i | \(-0.412000\pi\) | ||||
0.272952 | + | 0.962028i | \(0.412000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 251.823 | + | 145.390i | 1.49007 | + | 0.860295i | 0.999936 | − | 0.0113498i | \(-0.00361285\pi\) |
0.490139 | + | 0.871645i | \(0.336946\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −203.993 | − | 353.326i | −0.705857 | − | 1.22258i | −0.966381 | − | 0.257113i | \(-0.917229\pi\) |
0.260524 | − | 0.965467i | \(-0.416105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −248.401 | − | 261.951i | −0.688090 | − | 0.725625i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −62.6209 | + | 108.463i | −0.118376 | + | 0.205033i | −0.919124 | − | 0.393968i | \(-0.871102\pi\) |
0.800748 | + | 0.599001i | \(0.204435\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −36.3749 | + | 63.0032i | −0.0581999 | + | 0.100805i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1371.33 | + | 791.736i | 1.63059 | + | 0.941422i | 0.983911 | + | 0.178661i | \(0.0571766\pi\) |
0.646681 | + | 0.762761i | \(0.276157\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 457.962i | 0.476548i | 0.971198 | + | 0.238274i | \(0.0765816\pi\) | ||||
−0.971198 | + | 0.238274i | \(0.923418\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −52.1863 | − | 90.3894i | −0.0426011 | − | 0.0737872i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2191.32i | 1.60068i | 0.599550 | + | 0.800338i | \(0.295346\pi\) | ||||
−0.599550 | + | 0.800338i | \(0.704654\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1957.61 | − | 1130.22i | 1.16455 | − | 0.672352i | 0.212159 | − | 0.977235i | \(-0.431951\pi\) |
0.952390 | + | 0.304883i | \(0.0986173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1261.53 | + | 2185.04i | 0.682278 | + | 1.18174i | 0.974284 | + | 0.225324i | \(0.0723441\pi\) |
−0.292006 | + | 0.956417i | \(0.594323\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1323.10 | − | 2291.68i | 0.598960 | − | 1.03743i | −0.394015 | − | 0.919104i | \(-0.628914\pi\) |
0.992975 | − | 0.118325i | \(-0.0377526\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2385.39 | −0.993497 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3853.60 | − | 2224.88i | −1.37188 | − | 0.792053i | −0.380712 | − | 0.924694i | \(-0.624321\pi\) |
−0.991164 | + | 0.132640i | \(0.957654\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −872.412 | − | 1511.06i | −0.288401 | − | 0.499525i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3689.16 | − | 2129.93i | 1.05980 | − | 0.611874i | 0.134421 | − | 0.990924i | \(-0.457082\pi\) |
0.925376 | + | 0.379050i | \(0.123749\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 123.741 | − | 214.326i | 0.0332548 | − | 0.0575989i | −0.848919 | − | 0.528523i | \(-0.822746\pi\) |
0.882174 | + | 0.470924i | \(0.156079\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7680.93i | − | 1.81797i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6640.45 | − | 3833.86i | −1.47927 | − | 0.854057i | −0.479546 | − | 0.877517i | \(-0.659199\pi\) |
−0.999725 | + | 0.0234595i | \(0.992532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2609.52 | + | 1506.61i | −0.517660 | + | 0.298871i | −0.735977 | − | 0.677007i | \(-0.763277\pi\) |
0.218317 | + | 0.975878i | \(0.429943\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1797.57 | − | 3113.47i | −0.337318 | − | 0.584251i | 0.646610 | − | 0.762821i | \(-0.276186\pi\) |
−0.983927 | + | 0.178570i | \(0.942853\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 260.999 | 0.0440207 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6435.38 | − | 3715.47i | 1.03115 | − | 0.595332i | 0.113833 | − | 0.993500i | \(-0.463687\pi\) |
0.917312 | + | 0.398168i | \(0.130354\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1653.76 | 0.240059 | 0.120029 | − | 0.992770i | \(-0.461701\pi\) | ||||
0.120029 | + | 0.992770i | \(0.461701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5388.46 | + | 9333.08i | −0.745807 | + | 1.29178i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1852.60 | + | 1069.60i | 0.233884 | + | 0.135033i | 0.612363 | − | 0.790577i | \(-0.290219\pi\) |
−0.378478 | + | 0.925610i | \(0.623553\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 995.019 | + | 574.474i | 0.120157 | + | 0.0693726i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2711.65 | + | 9142.12i | −0.300459 | + | 1.01298i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12756.3 | − | 7364.84i | 1.35575 | − | 0.782744i | 0.366704 | − | 0.930338i | \(-0.380486\pi\) |
0.989048 | + | 0.147594i | \(0.0471529\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −190.130 | + | 329.315i | −0.0186384 | + | 0.0322826i | −0.875194 | − | 0.483772i | \(-0.839266\pi\) |
0.856556 | + | 0.516054i | \(0.172600\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15522.1i | − | 1.46310i | −0.681787 | − | 0.731551i | \(-0.738797\pi\) | ||
0.681787 | − | 0.731551i | \(-0.261203\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 19304.7i | − | 1.68615i | −0.537796 | − | 0.843075i | \(-0.680743\pi\) | ||
0.537796 | − | 0.843075i | \(-0.319257\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5069.64 | + | 2926.96i | −0.426701 | + | 0.246356i | −0.697940 | − | 0.716156i | \(-0.745900\pi\) |
0.271239 | + | 0.962512i | \(0.412567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 20207.0i | − | 1.58251i | −0.611488 | − | 0.791254i | \(-0.709429\pi\) | ||
0.611488 | − | 0.791254i | \(-0.290571\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3308.25 | 0.250152 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −806.030 | − | 1396.09i | −0.0569190 | − | 0.0985867i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10277.8 | −0.701989 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −14587.7 | −0.933610 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13379.6 | + | 7724.74i | 0.829539 | + | 0.478935i | 0.853695 | − | 0.520773i | \(-0.174356\pi\) |
−0.0241556 | + | 0.999708i | \(0.507690\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1431.61 | − | 2479.63i | −0.0834225 | − | 0.144492i | 0.821295 | − | 0.570503i | \(-0.193252\pi\) |
−0.904718 | + | 0.426011i | \(0.859918\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −981.498 | − | 1035.04i | −0.0554863 | − | 0.0585131i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1152.70 | + | 1996.53i | −0.0614149 | + | 0.106374i | −0.895098 | − | 0.445869i | \(-0.852895\pi\) |
0.833683 | + | 0.552243i | \(0.186228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16171.7 | − | 28010.3i | 0.837003 | − | 1.44973i | −0.0553863 | − | 0.998465i | \(-0.517639\pi\) |
0.892389 | − | 0.451267i | \(-0.149028\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 16634.0 | + | 9603.64i | 0.813438 | + | 0.469638i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 41827.3i | − | 1.98941i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6161.61 | − | 10672.2i | −0.277538 | − | 0.480709i | 0.693235 | − | 0.720712i | \(-0.256185\pi\) |
−0.970772 | + | 0.240003i | \(0.922852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 26041.0i | − | 1.14210i | −0.820916 | − | 0.571050i | \(-0.806536\pi\) | ||
0.820916 | − | 0.571050i | \(-0.193464\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10476.4 | − | 6048.53i | 0.436061 | − | 0.251760i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9055.18 | + | 15684.0i | 0.367365 | + | 0.636295i | 0.989153 | − | 0.146891i | \(-0.0469267\pi\) |
−0.621788 | + | 0.783186i | \(0.713593\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −247.432 | + | 428.565i | −0.00954562 | + | 0.0165335i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1816.65 | 0.0683748 | 0.0341874 | − | 0.999415i | \(-0.489116\pi\) | ||||
0.0341874 | + | 0.999415i | \(0.489116\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 26066.6 | + | 15049.5i | 0.934655 | + | 0.539623i | 0.888281 | − | 0.459301i | \(-0.151900\pi\) |
0.0463740 | + | 0.998924i | \(0.485233\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27995.9 | + | 48490.3i | 0.980214 | + | 1.69778i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −27606.0 | + | 15938.3i | −0.922383 | + | 0.532538i | −0.884395 | − | 0.466740i | \(-0.845428\pi\) |
−0.0379886 | + | 0.999278i | \(0.512095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −143.727 | + | 248.943i | −0.00469313 | + | 0.00812874i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 25052.3i | − | 0.781884i | −0.920415 | − | 0.390942i | \(-0.872149\pi\) | ||
0.920415 | − | 0.390942i | \(-0.127851\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 30483.9 | + | 17599.9i | 0.930494 | + | 0.537221i | 0.886968 | − | 0.461831i | \(-0.152807\pi\) |
0.0435262 | + | 0.999052i | \(0.486141\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 50128.8 | − | 28941.9i | 1.46468 | − | 0.845635i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13474.6 | − | 23338.7i | −0.385330 | − | 0.667412i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −69403.7 | −1.90246 | −0.951231 | − | 0.308479i | \(-0.900180\pi\) | ||||
−0.951231 | + | 0.308479i | \(0.900180\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 572.006 | − | 330.248i | 0.0153563 | − | 0.00886595i | −0.492302 | − | 0.870424i | \(-0.663845\pi\) |
0.507658 | + | 0.861558i | \(0.330511\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8731.63 | −0.224990 | −0.112495 | − | 0.993652i | \(-0.535884\pi\) | ||||
−0.112495 | + | 0.993652i | \(0.535884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18442.2 | − | 31942.8i | 0.465700 | − | 0.806616i | −0.533533 | − | 0.845779i | \(-0.679136\pi\) |
0.999233 | + | 0.0391632i | \(0.0124692\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5418.48 | + | 3128.36i | 0.131488 | + | 0.0759146i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −51710.1 | − | 29854.8i | −1.23046 | − | 0.710406i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16407.9 | − | 17303.0i | −0.375631 | − | 0.396122i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28075.1 | + | 16209.2i | −0.630604 | + | 0.364079i | −0.780986 | − | 0.624549i | \(-0.785283\pi\) |
0.150382 | + | 0.988628i | \(0.451950\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 33323.3 | − | 57717.7i | 0.720894 | − | 1.24863i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1809.53i | 0.0384279i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 118634.i | − | 2.42898i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −73819.4 | + | 42619.7i | −1.48443 | + | 0.857039i | −0.999843 | − | 0.0177024i | \(-0.994365\pi\) |
−0.484591 | + | 0.874741i | \(0.661032\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 27523.0i | − | 0.534126i | −0.963679 | − | 0.267063i | \(-0.913947\pi\) | ||
0.963679 | − | 0.267063i | \(-0.0860532\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 53550.6 | 1.02116 | 0.510580 | − | 0.859830i | \(-0.329431\pi\) | ||||
0.510580 | + | 0.859830i | \(0.329431\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20198.3 | − | 34984.4i | −0.372051 | − | 0.644411i | 0.617830 | − | 0.786312i | \(-0.288012\pi\) |
−0.989881 | + | 0.141901i | \(0.954679\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −69899.4 | −1.26572 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 54594.4 | 0.955768 | 0.477884 | − | 0.878423i | \(-0.341404\pi\) | ||||
0.477884 | + | 0.878423i | \(0.341404\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −41863.1 | − | 24169.7i | −0.720771 | − | 0.416137i | 0.0942654 | − | 0.995547i | \(-0.469950\pi\) |
−0.815036 | + | 0.579410i | \(0.803283\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 31505.0 | + | 54568.2i | 0.524864 | + | 0.909091i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24467.9 | − | 102080.i | −0.401054 | − | 1.67320i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −37943.6 | + | 65720.3i | −0.602270 | + | 1.04316i | 0.390206 | + | 0.920728i | \(0.372404\pi\) |
−0.992476 | + | 0.122435i | \(0.960930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4136.38 | + | 7164.43i | −0.0646219 | + | 0.111928i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 107798. | + | 62237.0i | 1.63209 | + | 0.942286i | 0.983448 | + | 0.181189i | \(0.0579947\pi\) |
0.648639 | + | 0.761096i | \(0.275339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8658.52i | 0.129076i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −34739.9 | − | 60171.2i | −0.502246 | − | 0.869916i | −0.999997 | − | 0.00259575i | \(-0.999174\pi\) |
0.497750 | − | 0.867320i | \(-0.334160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 117540.i | 1.67376i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 54316.7 | − | 31359.8i | 0.750635 | − | 0.433379i | −0.0752883 | − | 0.997162i | \(-0.523988\pi\) |
0.825923 | + | 0.563782i | \(0.190654\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24492.5 | + | 42422.3i | 0.333499 | + | 0.577638i | 0.983195 | − | 0.182556i | \(-0.0584372\pi\) |
−0.649696 | + | 0.760194i | \(0.725104\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2402.72 | + | 4161.64i | −0.0317716 | + | 0.0550299i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 83714.4 | 1.09104 | 0.545520 | − | 0.838098i | \(-0.316332\pi\) | ||||
0.545520 | + | 0.838098i | \(0.316332\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32897.2 | − | 18993.2i | −0.416626 | − | 0.240539i | 0.277007 | − | 0.960868i | \(-0.410658\pi\) |
−0.693633 | + | 0.720329i | \(0.743991\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 35732.7 | + | 61890.8i | 0.446162 | + | 0.772775i | 0.998132 | − | 0.0610884i | \(-0.0194571\pi\) |
−0.551970 | + | 0.833864i | \(0.686124\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7735.03 | − | 4465.82i | 0.0939071 | − | 0.0542173i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −41465.6 | + | 71820.4i | −0.496469 | + | 0.859909i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8987.73i | − | 0.104692i | −0.998629 | − | 0.0523461i | \(-0.983330\pi\) | ||
0.998629 | − | 0.0523461i | \(-0.0166699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −97448.9 | − | 56262.1i | −1.11978 | − | 0.646505i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −31538.7 | + | 18208.9i | −0.352778 | + | 0.203676i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4984.66 | + | 8633.68i | 0.0550177 | + | 0.0952934i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6537.22 | −0.0702738 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7608.34 | − | 4392.68i | 0.0807260 | − | 0.0466072i | −0.459094 | − | 0.888388i | \(-0.651826\pi\) |
0.539820 | + | 0.841781i | \(0.318492\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −59943.3 | −0.619755 | −0.309878 | − | 0.950776i | \(-0.600288\pi\) | ||||
−0.309878 | + | 0.950776i | \(0.600288\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20206.9 | − | 34999.3i | 0.206258 | − | 0.357249i | −0.744275 | − | 0.667873i | \(-0.767205\pi\) |
0.950533 | + | 0.310624i | \(0.100538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 43676.0 | + | 25216.4i | 0.434635 | + | 0.250937i | 0.701319 | − | 0.712847i | \(-0.252595\pi\) |
−0.266684 | + | 0.963784i | \(0.585928\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 90582.2 | + | 52297.7i | 0.890147 | + | 0.513926i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −41882.0 | + | 141202.i | −0.401442 | + | 1.35343i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18320.0 | + | 10577.1i | −0.173444 | + | 0.100138i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5227.94 | − | 9055.05i | 0.0482991 | − | 0.0836564i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27515.7i | 0.251145i | 0.992084 | + | 0.125573i | \(0.0400768\pi\) | ||||
−0.992084 | + | 0.125573i | \(0.959923\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 202543.i | 1.80479i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 108897. | − | 62872.0i | 0.958866 | − | 0.553602i | 0.0630421 | − | 0.998011i | \(-0.479920\pi\) |
0.895824 | + | 0.444409i | \(0.146586\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30250.4i | 0.260149i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18912.3 | −0.160752 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7145.75 | + | 12376.8i | 0.0593457 | + | 0.102790i | 0.894172 | − | 0.447724i | \(-0.147765\pi\) |
−0.834826 | + | 0.550514i | \(0.814432\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 66467.6 | 0.545706 | 0.272853 | − | 0.962056i | \(-0.412033\pi\) | ||||
0.272853 | + | 0.962056i | \(0.412033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −107847. | −0.865487 | −0.432743 | − | 0.901517i | \(-0.642454\pi\) | ||||
−0.432743 | + | 0.901517i | \(0.642454\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 68930.4 | + | 39797.0i | 0.546959 | + | 0.315787i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32192.7 | − | 55759.4i | −0.249786 | − | 0.432643i | 0.713680 | − | 0.700472i | \(-0.247027\pi\) |
−0.963466 | + | 0.267829i | \(0.913694\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6915.34 | + | 130137.i | −0.0530639 | + | 0.998591i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −47482.6 | + | 82242.3i | −0.356409 | + | 0.617319i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8645.43 | + | 14974.3i | −0.0641881 | + | 0.111177i | −0.896334 | − | 0.443380i | \(-0.853779\pi\) |
0.832145 | + | 0.554557i | \(0.187112\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15226.6 | − | 8791.09i | −0.110626 | − | 0.0638697i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 83855.1i | − | 0.602715i | −0.953511 | − | 0.301358i | \(-0.902560\pi\) | ||
0.953511 | − | 0.301358i | \(-0.0974398\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 230221. | + | 398754.i | 1.61980 | + | 2.80558i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 237159.i | − | 1.65105i | −0.564363 | − | 0.825526i | \(-0.690878\pi\) | ||
0.564363 | − | 0.825526i | \(-0.309122\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −647.503 | + | 373.836i | −0.00441412 | + | 0.00254849i | −0.502205 | − | 0.864748i | \(-0.667478\pi\) |
0.497791 | + | 0.867297i | \(0.334145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3447.14 | − | 5970.61i | −0.0232561 | − | 0.0402808i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25400.9 | + | 43995.7i | −0.167861 | + | 0.290744i | −0.937668 | − | 0.347533i | \(-0.887019\pi\) |
0.769806 | + | 0.638277i | \(0.220353\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 51096.8 | 0.334226 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −169990. | − | 98143.9i | −1.08951 | − | 0.629027i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 58870.5 | + | 101967.i | 0.373522 | + | 0.646959i | 0.990105 | − | 0.140331i | \(-0.0448167\pi\) |
−0.616582 | + | 0.787290i | \(0.711483\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −143708. | + | 82970.0i | −0.893702 | + | 0.515979i | −0.875152 | − | 0.483849i | \(-0.839238\pi\) |
−0.0185504 | + | 0.999828i | \(0.505905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −66583.0 | + | 115325.i | −0.409971 | + | 0.710091i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 144747.i | 0.873815i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −184594. | − | 106575.i | −1.10349 | − | 0.637103i | −0.166358 | − | 0.986066i | \(-0.553201\pi\) |
−0.937137 | + | 0.348963i | \(0.886534\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14576.9 | − | 8415.95i | 0.0854601 | − | 0.0493404i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −21842.1 | − | 37831.6i | −0.126823 | − | 0.219664i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −59218.3 | −0.337309 | −0.168654 | − | 0.985675i | \(-0.553942\pi\) | ||||
−0.168654 | + | 0.985675i | \(0.553942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 57179.4 | − | 33012.5i | 0.322608 | − | 0.186258i | −0.329946 | − | 0.944000i | \(-0.607031\pi\) |
0.652555 | + | 0.757742i | \(0.273697\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29680.9 | 0.164323 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 488.934 | − | 846.859i | 0.00268160 | − | 0.00464467i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 101448. | + | 58570.8i | 0.546119 | + | 0.315302i | 0.747555 | − | 0.664200i | \(-0.231228\pi\) |
−0.201436 | + | 0.979502i | \(0.564561\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 185685. | + | 107205.i | 0.990379 | + | 0.571796i | 0.905388 | − | 0.424586i | \(-0.139580\pi\) |
0.0849918 | + | 0.996382i | \(0.472914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 43966.9 | − | 10538.6i | 0.230230 | − | 0.0551847i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −228113. | + | 131701.i | −1.18364 | + | 0.683376i | −0.956854 | − | 0.290568i | \(-0.906156\pi\) |
−0.226788 | + | 0.973944i | \(0.572822\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25906.1 | − | 44870.8i | 0.132006 | − | 0.228642i | −0.792443 | − | 0.609945i | \(-0.791191\pi\) |
0.924450 | + | 0.381303i | \(0.124525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 56506.8i | − | 0.285352i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 300762.i | 1.49187i | 0.666019 | + | 0.745935i | \(0.267997\pi\) | ||||
−0.666019 | + | 0.745935i | \(0.732003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 129308. | − | 74656.3i | 0.635732 | − | 0.367040i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 30349.4i | − | 0.146598i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 143035. | 0.684872 | 0.342436 | − | 0.939541i | \(-0.388748\pi\) | ||||
0.342436 | + | 0.939541i | \(0.388748\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 62369.0 | + | 108026.i | 0.293472 | + | 0.508309i | 0.974628 | − | 0.223830i | \(-0.0718559\pi\) |
−0.681156 | + | 0.732138i | \(0.738523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −303815. | −1.41725 | −0.708626 | − | 0.705585i | \(-0.750684\pi\) | ||||
−0.708626 | + | 0.705585i | \(0.750684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −407608. | −1.86900 | −0.934499 | − | 0.355966i | \(-0.884152\pi\) | ||||
−0.934499 | + | 0.355966i | \(0.884152\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −26238.2 | − | 15148.6i | −0.119286 | − | 0.0688696i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 83329.8 | + | 144331.i | 0.372459 | + | 0.645117i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25539.3 | − | 6121.60i | 0.113194 | − | 0.0271317i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 91751.1 | − | 158918.i | 0.399890 | − | 0.692630i | −0.593822 | − | 0.804596i | \(-0.702382\pi\) |
0.993712 | + | 0.111967i | \(0.0357150\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −318596. | + | 551825.i | −1.37705 | + | 2.38512i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −336956. | − | 194542.i | −1.43248 | − | 0.827046i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 74156.9i | 0.312676i | 0.987704 | + | 0.156338i | \(0.0499688\pi\) | ||||
−0.987704 | + | 0.156338i | \(0.950031\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −62825.2 | − | 108816.i | −0.260598 | − | 0.451369i | 0.705803 | − | 0.708408i | \(-0.250586\pi\) |
−0.966401 | + | 0.257039i | \(0.917253\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 646034.i | − | 2.65804i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10310.9 | + | 5953.02i | −0.0417432 | + | 0.0241004i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −51694.7 | − | 89537.8i | −0.207608 | − | 0.359588i | 0.743352 | − | 0.668900i | \(-0.233235\pi\) |
−0.950961 | + | 0.309312i | \(0.899901\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 147700. | − | 255825.i | 0.583775 | − | 1.01113i | −0.411252 | − | 0.911522i | \(-0.634908\pi\) |
0.995027 | − | 0.0996066i | \(-0.0317584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10044.6 | 0.0393866 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 311158. | + | 179647.i | 1.20101 | + | 0.693401i | 0.960779 | − | 0.277316i | \(-0.0894448\pi\) |
0.240227 | + | 0.970717i | \(0.422778\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7102.67 | − | 12302.2i | −0.0272007 | − | 0.0471129i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −355083. | + | 205007.i | −1.33880 | + | 0.772956i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 87396.8 | − | 151376.i | 0.326975 | − | 0.566337i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 195107.i | 0.718782i | 0.933187 | + | 0.359391i | \(0.117016\pi\) | ||||
−0.933187 | + | 0.359391i | \(0.882984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 259323. | + | 149720.i | 0.948063 | + | 0.547364i | 0.892479 | − | 0.451090i | \(-0.148965\pi\) |
0.0555841 | + | 0.998454i | \(0.482298\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 161810. | − | 93421.0i | 0.582618 | − | 0.336375i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 132078. | + | 228765.i | 0.471974 | + | 0.817483i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 657292. | 2.31368 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −441616. | + | 254967.i | −1.54290 | + | 0.890792i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −157565. | −0.542354 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 83074.6 | − | 143889.i | 0.283840 | − | 0.491625i | −0.688487 | − | 0.725249i | \(-0.741725\pi\) |
0.972327 | + | 0.233623i | \(0.0750582\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 133914. | + | 77315.4i | 0.450852 | + | 0.260299i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 345204. | + | 199304.i | 1.15372 | + | 0.666102i | 0.949792 | − | 0.312883i | \(-0.101295\pi\) |
0.203931 | + | 0.978985i | \(0.434628\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −133243. | − | 555888.i | −0.438874 | − | 1.83098i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25427.9 | − | 14680.8i | 0.0831497 | − | 0.0480065i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 157159. | − | 272208.i | 0.506558 | − | 0.877384i | −0.493413 | − | 0.869795i | \(-0.664251\pi\) |
0.999971 | − | 0.00758920i | \(-0.00241574\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 733656.i | 2.34784i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39467.4i | 0.124515i | 0.998060 | + | 0.0622574i | \(0.0198300\pi\) | ||||
−0.998060 | + | 0.0622574i | \(0.980170\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −462257. | + | 266884.i | −1.44806 | + | 0.836037i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 376002.i | 1.16136i | 0.814133 | + | 0.580679i | \(0.197213\pi\) | ||||
−0.814133 | + | 0.580679i | \(0.802787\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 452184. | 1.38689 | 0.693446 | − | 0.720508i | \(-0.256091\pi\) | ||||
0.693446 | + | 0.720508i | \(0.256091\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4555.66 | − | 7890.63i | −0.0137789 | − | 0.0238658i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −394141. | −1.18386 | −0.591929 | − | 0.805990i | \(-0.701633\pi\) | ||||
−0.591929 | + | 0.805990i | \(0.701633\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6534.47 | 0.0193579 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −254547. | − | 146963.i | −0.748913 | − | 0.432385i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −248196. | − | 429888.i | −0.720308 | − | 1.24761i | −0.960876 | − | 0.276978i | \(-0.910667\pi\) |
0.240568 | − | 0.970632i | \(-0.422666\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 119964. | − | 113758.i | 0.345795 | − | 0.327908i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 89679.7 | − | 155330.i | 0.255026 | − | 0.441718i | −0.709876 | − | 0.704326i | \(-0.751249\pi\) |
0.964903 | + | 0.262608i | \(0.0845826\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21291.3 | + | 36877.5i | −0.0601405 | + | 0.104166i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −57674.8 | − | 33298.5i | −0.160743 | − | 0.0928050i | 0.417471 | − | 0.908690i | \(-0.362917\pi\) |
−0.578214 | + | 0.815885i | \(0.696250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 117101.i | − | 0.324200i | −0.986774 | − | 0.162100i | \(-0.948173\pi\) | ||
0.986774 | − | 0.162100i | \(-0.0518267\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 135744. | + | 235116.i | 0.370860 | + | 0.642348i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 480656.i | − | 1.30454i | −0.757988 | − | 0.652269i | \(-0.773817\pi\) | ||
0.757988 | − | 0.652269i | \(-0.226183\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 666374. | − | 384731.i | 1.78499 | − | 1.03056i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 274075. | + | 474712.i | 0.729372 | + | 1.26331i | 0.957149 | + | 0.289596i | \(0.0935209\pi\) |
−0.227777 | + | 0.973713i | \(0.573146\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −346802. | + | 600678.i | −0.910985 | + | 1.57787i | −0.0983085 | + | 0.995156i | \(0.531343\pi\) |
−0.812676 | + | 0.582716i | \(0.801990\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −89967.6 | −0.234804 | −0.117402 | − | 0.993084i | \(-0.537457\pi\) | ||||
−0.117402 | + | 0.993084i | \(0.537457\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7320.11 | + | 4226.27i | 0.0188600 | + | 0.0108888i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 215401. | + | 373085.i | 0.551425 | + | 0.955097i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 774251. | − | 447014.i | 1.95695 | − | 1.12985i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 266143. | − | 460974.i | 0.668431 | − | 1.15776i | −0.309912 | − | 0.950765i | \(-0.600299\pi\) |
0.978343 | − | 0.206991i | \(-0.0663672\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 408097.i | − | 1.01208i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −600694. | − | 346811.i | −1.48038 | − | 0.854701i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 346114. | − | 199829.i | 0.842371 | − | 0.486343i | −0.0156986 | − | 0.999877i | \(-0.504997\pi\) |
0.858069 | + | 0.513534i | \(0.171664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 59063.7 | + | 102301.i | 0.142856 | + | 0.247434i | 0.928571 | − | 0.371155i | \(-0.121038\pi\) |
−0.785715 | + | 0.618589i | \(0.787705\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −343903. | −0.821538 | −0.410769 | − | 0.911740i | \(-0.634740\pi\) | ||||
−0.410769 | + | 0.911740i | \(0.634740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 243685. | − | 140692.i | 0.578548 | − | 0.334025i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −327275. | −0.767515 | −0.383757 | − | 0.923434i | \(-0.625370\pi\) | ||||
−0.383757 | + | 0.923434i | \(0.625370\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37816.0 | + | 65499.3i | −0.0881441 | + | 0.152670i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −112125. | − | 64735.4i | −0.258185 | − | 0.149063i | 0.365321 | − | 0.930882i | \(-0.380959\pi\) |
−0.623506 | + | 0.781818i | \(0.714292\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 121616. | + | 70215.1i | 0.278348 | + | 0.160704i | 0.632675 | − | 0.774417i | \(-0.281957\pi\) |
−0.354327 | + | 0.935121i | \(0.615290\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10714.4 | + | 36123.0i | −0.0242285 | + | 0.0816847i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −171747. | + | 99158.4i | −0.386045 | + | 0.222883i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8173.64 | − | 14157.2i | 0.0181539 | − | 0.0314435i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 245792.i | − | 0.542673i | −0.962485 | − | 0.271336i | \(-0.912534\pi\) | ||
0.962485 | − | 0.271336i | \(-0.0874656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 429443.i | 0.936974i | 0.883470 | + | 0.468487i | \(0.155201\pi\) | ||||
−0.883470 | + | 0.468487i | \(0.844799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50403.5 | − | 29100.5i | 0.109325 | − | 0.0631190i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 110387.i | − | 0.236634i | −0.992976 | − | 0.118317i | \(-0.962250\pi\) | ||
0.992976 | − | 0.118317i | \(-0.0377499\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 60896.8 | 0.129782 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −646949. | − | 1.12055e6i | −1.36280 | − | 2.36044i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 202528. | 0.424159 | 0.212080 | − | 0.977252i | \(-0.431976\pi\) | ||||
0.212080 | + | 0.977252i | \(0.431976\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −854351. | −1.76875 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −798675. | − | 461115.i | −1.64401 | − | 0.949169i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 121102. | + | 209755.i | 0.246443 | + | 0.426851i | 0.962536 | − | 0.271153i | \(-0.0874050\pi\) |
−0.716094 | + | 0.698004i | \(0.754072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 574019. | − | 544326.i | 1.16149 | − | 1.10141i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −751.256 | + | 1301.21i | −0.00150297 | + | 0.00260321i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 187900. | − | 325452.i | 0.373795 | − | 0.647432i | −0.616351 | − | 0.787472i | \(-0.711390\pi\) |
0.990146 | + | 0.140040i | \(0.0447230\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −49671.7 | − | 28678.0i | −0.0977080 | − | 0.0564118i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 507359.i | − | 0.992438i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 408662. | + | 707823.i | 0.790508 | + | 1.36920i | 0.925653 | + | 0.378374i | \(0.123517\pi\) |
−0.135144 | + | 0.990826i | \(0.543150\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 61331.8i | − | 0.117982i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −99763.8 | + | 57598.7i | −0.189800 | + | 0.109581i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −423400. | − | 733351.i | −0.801092 | − | 1.38753i | −0.918898 | − | 0.394495i | \(-0.870920\pi\) |
0.117806 | − | 0.993037i | \(-0.462414\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 514687. | − | 891464.i | 0.963182 | − | 1.66828i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 562446. | 1.04682 | 0.523411 | − | 0.852080i | \(-0.324659\pi\) | ||||
0.523411 | + | 0.852080i | \(0.324659\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −438631. | − | 253244.i | −0.807540 | − | 0.466233i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −138927. | − | 240628.i | −0.254388 | − | 0.440613i | 0.710341 | − | 0.703858i | \(-0.248541\pi\) |
−0.964729 | + | 0.263245i | \(0.915207\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −220105. | + | 127078.i | −0.398705 | + | 0.230193i | −0.685925 | − | 0.727672i | \(-0.740602\pi\) |
0.287220 | + | 0.957865i | \(0.407269\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −162759. | + | 281906.i | −0.293246 | + | 0.507917i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 76278.2i | − | 0.135968i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 671263. | + | 387554.i | 1.19018 | + | 0.687151i | 0.958347 | − | 0.285605i | \(-0.0921945\pi\) |
0.231833 | + | 0.972756i | \(0.425528\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −595715. | + | 343936.i | −1.04507 | + | 0.603370i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 82777.3 | + | 143374.i | 0.144451 | + | 0.250196i | 0.929168 | − | 0.369658i | \(-0.120525\pi\) |
−0.784717 | + | 0.619854i | \(0.787192\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −88512.4 | −0.152839 | −0.0764196 | − | 0.997076i | \(-0.524349\pi\) | ||||
−0.0764196 | + | 0.997076i | \(0.524349\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20031.5 | + | 11565.2i | −0.0344084 | + | 0.0198657i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.23868e6 | 2.10557 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 266238. | − | 461138.i | 0.450212 | − | 0.779790i | −0.548187 | − | 0.836356i | \(-0.684682\pi\) |
0.998399 | + | 0.0565656i | \(0.0180150\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −372719. | − | 215189.i | −0.623767 | − | 0.360132i | 0.154567 | − | 0.987982i | \(-0.450602\pi\) |
−0.778334 | + | 0.627850i | \(0.783935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28853.1 | − | 16658.3i | −0.0480384 | − | 0.0277350i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −782333. | − | 232048.i | −1.28919 | − | 0.382387i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −172371. | + | 99518.2i | −0.282593 | + | 0.163155i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 239192. | − | 414293.i | 0.388157 | − | 0.672308i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 399690.i | − | 0.645318i | −0.946515 | − | 0.322659i | \(-0.895423\pi\) | ||
0.946515 | − | 0.322659i | \(-0.104577\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 79843.5i | − | 0.127610i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 62321.5 | − | 35981.3i | 0.0991041 | − | 0.0572178i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 993609.i | 1.56422i | 0.623138 | + | 0.782112i | \(0.285858\pi\) | ||||
−0.623138 | + | 0.782112i | \(0.714142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.07961e6 | −1.69112 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −118737. | − | 205659.i | −0.184143 | − | 0.318945i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13071.8 | 0.0201718 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −162243. | −0.247896 | −0.123948 | − | 0.992289i | \(-0.539556\pi\) | ||||
−0.123948 | + | 0.992289i | \(0.539556\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 208547. | + | 120405.i | 0.317075 | + | 0.183064i | 0.650088 | − | 0.759859i | \(-0.274732\pi\) |
−0.333013 | + | 0.942922i | \(0.608065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23993.4 | − | 41557.7i | −0.0361224 | − | 0.0625658i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 259007. | − | 873224.i | 0.388032 | − | 1.30822i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −148698. | + | 257553.i | −0.220607 | + | 0.382102i | −0.954992 | − | 0.296630i | \(-0.904137\pi\) |
0.734386 | + | 0.678733i | \(0.237470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −168468. | + | 291795.i | −0.248724 | + | 0.430803i | −0.963172 | − | 0.268886i | \(-0.913345\pi\) |
0.714448 | + | 0.699689i | \(0.246678\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −346639. | − | 200132.i | −0.506835 | − | 0.292621i | 0.224697 | − | 0.974429i | \(-0.427861\pi\) |
−0.731532 | + | 0.681807i | \(0.761194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 450567.i | − | 0.655617i | −0.944744 | − | 0.327808i | \(-0.893690\pi\) | ||
0.944744 | − | 0.327808i | \(-0.106310\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 486602. | + | 842819.i | 0.701267 | + | 1.21463i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 795066.i | − | 1.14033i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 373845. | − | 215840.i | 0.531089 | − | 0.306625i | −0.210371 | − | 0.977622i | \(-0.567467\pi\) |
0.741460 | + | 0.670997i | \(0.234134\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 900052. | + | 1.55894e6i | 1.27255 | + | 2.20412i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 739510. | − | 1.28087e6i | 1.03569 | − | 1.79387i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40610.4 | −0.0566071 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −237677. | − | 137223.i | −0.328191 | − | 0.189481i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 190271. | + | 329558.i | 0.261501 | + | 0.452933i | 0.966641 | − | 0.256135i | \(-0.0824492\pi\) |
−0.705140 | + | 0.709068i | \(0.749116\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 943560. | − | 544765.i | 1.28472 | − | 0.741732i | 0.307011 | − | 0.951706i | \(-0.400671\pi\) |
0.977707 | + | 0.209973i | \(0.0673378\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 65215.6 | − | 112957.i | 0.0883823 | − | 0.153083i | −0.818445 | − | 0.574585i | \(-0.805164\pi\) |
0.906827 | + | 0.421502i | \(0.138497\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 253989.i | − | 0.341031i | −0.985355 | − | 0.170515i | \(-0.945457\pi\) | ||
0.985355 | − | 0.170515i | \(-0.0545432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 729211. | + | 421010.i | 0.974588 | + | 0.562679i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 425085. | − | 245423.i | 0.562906 | − | 0.324994i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.11481e6 | − | 1.93091e6i | −1.46948 | − | 2.54522i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −57639.8 | −0.0752846 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 759687. | − | 438606.i | 0.987724 | − | 0.570263i | 0.0831309 | − | 0.996539i | \(-0.473508\pi\) |
0.904593 | + | 0.426276i | \(0.140175\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 143314. | 0.184645 | 0.0923223 | − | 0.995729i | \(-0.470571\pi\) | ||||
0.0923223 | + | 0.995729i | \(0.470571\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −140425. | + | 243224.i | −0.180104 | + | 0.311950i | −0.941916 | − | 0.335849i | \(-0.890977\pi\) |
0.761812 | + | 0.647799i | \(0.224310\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 214235. | + | 123689.i | 0.272297 | + | 0.157211i | 0.629931 | − | 0.776651i | \(-0.283083\pi\) |
−0.357634 | + | 0.933862i | \(0.616416\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 52866.6 | + | 30522.5i | 0.0668925 | + | 0.0386204i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −928967. | + | 222667.i | −1.16492 | + | 0.279224i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −573098. | + | 330878.i | −0.715456 | + | 0.413069i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −362585. | + | 628016.i | −0.448632 | + | 0.777054i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.81544e6i | 2.23631i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 929801.i | − | 1.13525i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −967269. | + | 558453.i | −1.17580 | + | 0.678847i | −0.955039 | − | 0.296481i | \(-0.904187\pi\) |
−0.220759 | + | 0.975328i | \(0.570853\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.08226e6i | − | 1.30405i | −0.758198 | − | 0.652025i | \(-0.773920\pi\) | ||
0.758198 | − | 0.652025i | \(-0.226080\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 109238. | 0.131049 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5656.69 | − | 9797.68i | −0.00672704 | − | 0.0116516i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −920659. | −1.09010 | −0.545052 | − | 0.838402i | \(-0.683490\pi\) | ||||
−0.545052 | + | 0.838402i | \(0.683490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −876182. | −1.02847 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −138060. | − | 79709.2i | −0.161356 | − | 0.0931591i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 282674. | + | 489605.i | 0.327532 | + | 0.567302i | 0.982022 | − | 0.188769i | \(-0.0604497\pi\) |
−0.654489 | + | 0.756071i | \(0.727116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 592532. | + | 624854.i | 0.683616 | + | 0.720907i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −355931. | + | 616491.i | −0.407139 | + | 0.705186i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 140444. | − | 243257.i | 0.159965 | − | 0.277068i | −0.774891 | − | 0.632095i | \(-0.782195\pi\) |
0.934856 | + | 0.355027i | \(0.115528\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.21593e6 | + | 702015.i | 1.37318 | + | 0.792807i | 0.991327 | − | 0.131416i | \(-0.0419523\pi\) |
0.381854 | + | 0.924223i | \(0.375286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 283102.i | 0.318361i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 458463. | + | 794081.i | 0.511215 | + | 0.885451i | 0.999916 | + | 0.0129993i | \(0.00413793\pi\) |
−0.488700 | + | 0.872452i | \(0.662529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.04539e6i | − | 1.16077i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.31224e6 | − | 757621.i | 1.44486 | − | 0.834192i | 0.446694 | − | 0.894687i | \(-0.352601\pi\) |
0.998169 | + | 0.0604947i | \(0.0192678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 916648. | + | 1.58768e6i | 1.00507 | + | 1.74083i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4554.61 | + | 7888.82i | −0.00495238 | + | 0.00857778i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 713792. | 0.772902 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15109.5 | − | 8723.48i | −0.0162254 | − | 0.00936775i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 660547. | + | 1.14410e6i | 0.706400 | + | 1.22352i | 0.966184 | + | 0.257854i | \(0.0830155\pi\) |
−0.259784 | + | 0.965667i | \(0.583651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −902679. | + | 521162.i | −0.957403 | + | 0.552757i | −0.895373 | − | 0.445317i | \(-0.853091\pi\) |
−0.0620301 | + | 0.998074i | \(0.519757\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 63898.9 | − | 110676.i | 0.0674944 | − | 0.116904i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.19511e6i | − | 1.25204i | −0.779808 | − | 0.626019i | \(-0.784683\pi\) | ||
0.779808 | − | 0.626019i | \(-0.215317\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 122372. | + | 70651.6i | 0.127678 | + | 0.0737152i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 904865. | − | 522424.i | 0.936433 | − | 0.540650i | 0.0475925 | − | 0.998867i | \(-0.484845\pi\) |
0.888840 | + | 0.458217i | \(0.151512\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 115323. | + | 199745.i | 0.118862 | + | 0.205875i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −315993. | −0.323061 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.06594e6 | + | 615421.i | −1.08539 | + | 0.626650i | −0.932345 | − | 0.361569i | \(-0.882241\pi\) |
−0.153045 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −974299. | −0.984116 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −729969. | + | 1.26434e6i | −0.734369 | + | 1.27196i | 0.220631 | + | 0.975357i | \(0.429188\pi\) |
−0.955000 | + | 0.296607i | \(0.904145\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.5.y.e.145.1 | 14 | ||
3.2 | odd | 2 | 228.5.l.a.145.7 | ✓ | 14 | ||
19.8 | odd | 6 | inner | 684.5.y.e.217.1 | 14 | ||
57.8 | even | 6 | 228.5.l.a.217.7 | yes | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.5.l.a.145.7 | ✓ | 14 | 3.2 | odd | 2 | ||
228.5.l.a.217.7 | yes | 14 | 57.8 | even | 6 | ||
684.5.y.e.145.1 | 14 | 1.1 | even | 1 | trivial | ||
684.5.y.e.217.1 | 14 | 19.8 | odd | 6 | inner |