Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,3,Mod(593,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.593");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(35.3134422611\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{8} \) |
Twist minimal: | no (minimal twist has level 162) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1025.1 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.1025 |
Dual form | 1296.3.q.o.593.1 |
$q$-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 \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.01910 | − | 2.89778i | −1.00382 | − | 0.579555i | −0.0944434 | − | 0.995530i | \(-0.530107\pi\) |
−0.909376 | + | 0.415975i | \(0.863440\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.19615 | − | 7.26795i | −0.599450 | − | 1.03828i | −0.992902 | − | 0.118933i | \(-0.962053\pi\) |
0.393452 | − | 0.919345i | \(-0.371281\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.7279 | + | 7.34847i | −1.15708 | + | 0.668043i | −0.950603 | − | 0.310408i | \(-0.899534\pi\) |
−0.206480 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 10.5981 | − | 18.3564i | 0.815237 | − | 1.41203i | −0.0939212 | − | 0.995580i | \(-0.529940\pi\) |
0.909158 | − | 0.416452i | \(-0.136726\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.76457i | 0.456739i | 0.973574 | + | 0.228370i | \(0.0733395\pi\) | ||||
−0.973574 | + | 0.228370i | \(0.926660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −24.3923 | −1.28381 | −0.641903 | − | 0.766786i | \(-0.721855\pi\) | ||||
−0.641903 | + | 0.766786i | \(0.721855\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −12.7279 | − | 7.34847i | −0.553388 | − | 0.319499i | 0.197099 | − | 0.980384i | \(-0.436848\pi\) |
−0.750487 | + | 0.660885i | \(0.770181\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.29423 | + | 7.43782i | 0.171769 | + | 0.297513i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 30.7387 | − | 17.7470i | 1.05996 | − | 0.611966i | 0.134536 | − | 0.990909i | \(-0.457046\pi\) |
0.925420 | + | 0.378942i | \(0.123712\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | − | 6.92820i | 0.129032 | − | 0.223490i | −0.794270 | − | 0.607565i | \(-0.792146\pi\) |
0.923302 | + | 0.384075i | \(0.125480\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 48.6381i | 1.38966i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −60.5692 | −1.63701 | −0.818503 | − | 0.574502i | \(-0.805196\pi\) | ||||
−0.818503 | + | 0.574502i | \(0.805196\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 29.1301 | + | 16.8183i | 0.710490 | + | 0.410201i | 0.811242 | − | 0.584710i | \(-0.198792\pi\) |
−0.100753 | + | 0.994912i | \(0.532125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.58846 | + | 7.94744i | 0.106708 | + | 0.184824i | 0.914435 | − | 0.404733i | \(-0.132636\pi\) |
−0.807727 | + | 0.589557i | \(0.799302\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14.6969 | − | 8.48528i | 0.312701 | − | 0.180538i | −0.335434 | − | 0.942064i | \(-0.608883\pi\) |
0.648134 | + | 0.761526i | \(0.275549\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.7154 | + | 18.5596i | −0.218681 | + | 0.378767i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25.7605i | 0.486046i | 0.970020 | + | 0.243023i | \(0.0781391\pi\) | ||||
−0.970020 | + | 0.243023i | \(0.921861\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 85.1769 | 1.54867 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 53.4083 | + | 30.8353i | 0.905225 | + | 0.522632i | 0.878892 | − | 0.477021i | \(-0.158283\pi\) |
0.0263336 | + | 0.999653i | \(0.491617\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.106557 | + | 0.184563i | 0.914373 | − | 0.404872i | \(-0.132684\pi\) |
−0.807816 | + | 0.589435i | \(0.799351\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −106.386 | + | 61.4217i | −1.63670 | + | 0.944950i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5885 | − | 18.3397i | 0.158037 | − | 0.273728i | −0.776124 | − | 0.630580i | \(-0.782817\pi\) |
0.934161 | + | 0.356853i | \(0.116150\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 101.214i | 1.42555i | 0.701392 | + | 0.712776i | \(0.252562\pi\) | ||||
−0.701392 | + | 0.712776i | \(0.747438\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.4115 | 0.553583 | 0.276791 | − | 0.960930i | \(-0.410729\pi\) | ||||
0.276791 | + | 0.960930i | \(0.410729\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 106.817 | + | 61.6706i | 1.38723 | + | 0.800917i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 49.3731 | + | 85.5167i | 0.624976 | + | 1.08249i | 0.988546 | + | 0.150923i | \(0.0482244\pi\) |
−0.363570 | + | 0.931567i | \(0.618442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −89.6231 | + | 51.7439i | −1.07980 | + | 0.623420i | −0.930841 | − | 0.365424i | \(-0.880924\pi\) |
−0.148954 | + | 0.988844i | \(0.547591\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.5000 | − | 38.9711i | 0.264706 | − | 0.458484i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 134.130i | 1.50708i | 0.657403 | + | 0.753539i | \(0.271655\pi\) | ||||
−0.657403 | + | 0.753539i | \(0.728345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −177.885 | −1.95478 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 122.427 | + | 70.6835i | 1.28871 | + | 0.744037i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 37.5692 | + | 65.0718i | 0.387312 | + | 0.670843i | 0.992087 | − | 0.125553i | \(-0.0400705\pi\) |
−0.604775 | + | 0.796396i | \(0.706737\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −25.1920 | + | 14.5446i | −0.249426 | + | 0.144006i | −0.619501 | − | 0.784995i | \(-0.712665\pi\) |
0.370075 | + | 0.929002i | \(0.379332\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 48.3538 | − | 83.7513i | 0.469455 | − | 0.813119i | −0.529936 | − | 0.848038i | \(-0.677784\pi\) |
0.999390 | + | 0.0349186i | \(0.0111172\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 177.582i | − | 1.65964i | −0.558030 | − | 0.829821i | \(-0.688442\pi\) | ||
0.558030 | − | 0.829821i | \(-0.311558\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 61.9423 | 0.568278 | 0.284139 | − | 0.958783i | \(-0.408292\pi\) | ||||
0.284139 | + | 0.958783i | \(0.408292\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −95.0991 | − | 54.9055i | −0.841585 | − | 0.485889i | 0.0162179 | − | 0.999868i | \(-0.494837\pi\) |
−0.857803 | + | 0.513979i | \(0.828171\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 42.5885 | + | 73.7654i | 0.370334 | + | 0.641438i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 56.4325 | − | 32.5813i | 0.474223 | − | 0.273793i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 47.5000 | − | 82.2724i | 0.392562 | − | 0.679937i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 95.1140i | 0.760912i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −141.177 | −1.11163 | −0.555815 | − | 0.831306i | \(-0.687594\pi\) | ||||
−0.555815 | + | 0.831306i | \(0.687594\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −46.0598 | − | 26.5927i | −0.351602 | − | 0.202997i | 0.313789 | − | 0.949493i | \(-0.398402\pi\) |
−0.665391 | + | 0.746495i | \(0.731735\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 102.354 | + | 177.282i | 0.769578 | + | 1.33295i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.41555 | − | 0.817267i | 0.0103325 | − | 0.00596545i | −0.494825 | − | 0.868993i | \(-0.664768\pi\) |
0.505157 | + | 0.863027i | \(0.331434\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.60770 | + | 16.6410i | −0.0691201 | + | 0.119720i | −0.898514 | − | 0.438944i | \(-0.855353\pi\) |
0.829394 | + | 0.558664i | \(0.188686\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 311.519i | 2.17845i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −205.708 | −1.41867 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −81.6504 | − | 47.1409i | −0.547989 | − | 0.316382i | 0.200321 | − | 0.979730i | \(-0.435801\pi\) |
−0.748311 | + | 0.663348i | \(0.769135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0000 | + | 27.7128i | 0.105960 | + | 0.183529i | 0.914130 | − | 0.405421i | \(-0.132875\pi\) |
−0.808170 | + | 0.588949i | \(0.799542\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −40.1528 | + | 23.1822i | −0.259050 | + | 0.149563i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.146171 | + | 0.253175i | −0.000931025 | + | 0.00161258i | −0.866491 | − | 0.499193i | \(-0.833630\pi\) |
0.865560 | + | 0.500806i | \(0.166963\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 123.341i | 0.766094i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −28.7846 | −0.176593 | −0.0882963 | − | 0.996094i | \(-0.528142\pi\) | ||||
−0.0882963 | + | 0.996094i | \(0.528142\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 48.5564 | + | 28.0341i | 0.290757 | + | 0.167869i | 0.638283 | − | 0.769802i | \(-0.279645\pi\) |
−0.347526 | + | 0.937670i | \(0.612978\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −140.138 | − | 242.727i | −0.829222 | − | 1.43625i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −191.350 | + | 110.476i | −1.10607 | + | 0.638589i | −0.937808 | − | 0.347154i | \(-0.887148\pi\) |
−0.168260 | + | 0.985743i | \(0.553815\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 36.0385 | − | 62.4205i | 0.205934 | − | 0.356688i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 248.347i | 1.38741i | 0.720258 | + | 0.693706i | \(0.244023\pi\) | ||||
−0.720258 | + | 0.693706i | \(0.755977\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −158.277 | −0.874458 | −0.437229 | − | 0.899350i | \(-0.644040\pi\) | ||||
−0.437229 | + | 0.899350i | \(0.644040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 304.003 | + | 175.516i | 1.64326 | + | 0.948736i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −57.0577 | − | 98.8269i | −0.305121 | − | 0.528486i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −29.9215 | + | 17.2752i | −0.156657 | + | 0.0904459i | −0.576279 | − | 0.817253i | \(-0.695496\pi\) |
0.419622 | + | 0.907699i | \(0.362163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.5000 | − | 47.6314i | 0.142487 | − | 0.246795i | −0.785946 | − | 0.618296i | \(-0.787823\pi\) |
0.928433 | + | 0.371501i | \(0.121157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 35.7170i | 0.181305i | 0.995883 | + | 0.0906524i | \(0.0288952\pi\) | ||||
−0.995883 | + | 0.0906524i | \(0.971105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 375.138 | 1.88512 | 0.942559 | − | 0.334040i | \(-0.108412\pi\) | ||||
0.942559 | + | 0.334040i | \(0.108412\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −257.969 | − | 148.938i | −1.27078 | − | 0.733687i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −97.4711 | − | 168.825i | −0.475469 | − | 0.823536i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 310.463 | − | 179.246i | 1.48547 | − | 0.857637i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 153.727 | − | 266.263i | 0.728563 | − | 1.26191i | −0.228927 | − | 0.973444i | \(-0.573522\pi\) |
0.957490 | − | 0.288465i | \(-0.0931450\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 53.1853i | − | 0.247374i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −67.1384 | −0.309394 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 142.530 | + | 82.2895i | 0.644930 | + | 0.372351i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −169.296 | − | 293.229i | −0.759175 | − | 1.31493i | −0.943272 | − | 0.332022i | \(-0.892269\pi\) |
0.184096 | − | 0.982908i | \(-0.441064\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −107.344 | + | 61.9752i | −0.472882 | + | 0.273019i | −0.717445 | − | 0.696615i | \(-0.754689\pi\) |
0.244563 | + | 0.969633i | \(0.421355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −37.0289 | + | 64.1359i | −0.161698 | + | 0.280069i | −0.935478 | − | 0.353386i | \(-0.885030\pi\) |
0.773780 | + | 0.633455i | \(0.218364\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 273.223i | − | 1.17263i | −0.810082 | − | 0.586316i | \(-0.800578\pi\) | ||
0.810082 | − | 0.586316i | \(-0.199422\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −98.3538 | −0.418527 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 392.210 | + | 226.443i | 1.64105 | + | 0.947459i | 0.980462 | + | 0.196708i | \(0.0630252\pi\) |
0.660585 | + | 0.750751i | \(0.270308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 191.344 | + | 331.418i | 0.793959 | + | 1.37518i | 0.923498 | + | 0.383604i | \(0.125317\pi\) |
−0.129538 | + | 0.991574i | \(0.541350\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 107.563 | − | 62.1016i | 0.439033 | − | 0.253476i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −258.512 | + | 447.755i | −1.04661 | + | 1.81277i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 73.9307i | − | 0.294544i | −0.989096 | − | 0.147272i | \(-0.952951\pi\) | ||
0.989096 | − | 0.147272i | \(-0.0470493\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 216.000 | 0.853755 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −138.398 | − | 79.9044i | −0.538515 | − | 0.310912i | 0.205962 | − | 0.978560i | \(-0.433968\pi\) |
−0.744477 | + | 0.667648i | \(0.767301\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 254.158 | + | 440.214i | 0.981304 | + | 1.69967i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 224.392 | − | 129.553i | 0.853202 | − | 0.492596i | −0.00852798 | − | 0.999964i | \(-0.502715\pi\) |
0.861730 | + | 0.507367i | \(0.169381\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 74.6481 | − | 129.294i | 0.281691 | − | 0.487903i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 24.8168i | − | 0.0922556i | −0.998936 | − | 0.0461278i | \(-0.985312\pi\) | ||
0.998936 | − | 0.0461278i | \(-0.0146881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −98.1154 | −0.362050 | −0.181025 | − | 0.983479i | \(-0.557941\pi\) | ||||
−0.181025 | + | 0.983479i | \(0.557941\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −109.313 | − | 63.1120i | −0.397503 | − | 0.229498i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.707658 | + | 1.22570i | 0.00255472 | + | 0.00442491i | 0.867300 | − | 0.497786i | \(-0.165853\pi\) |
−0.864745 | + | 0.502211i | \(0.832520\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 87.2230 | − | 50.3582i | 0.310402 | − | 0.179211i | −0.336704 | − | 0.941610i | \(-0.609312\pi\) |
0.647106 | + | 0.762400i | \(0.275979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.6462 | + | 40.9564i | −0.0835554 | + | 0.144722i | −0.904775 | − | 0.425890i | \(-0.859961\pi\) |
0.821219 | + | 0.570613i | \(0.193294\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 282.288i | − | 0.983582i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 228.711 | 0.791389 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −288.920 | − | 166.808i | −0.986074 | − | 0.569310i | −0.0819755 | − | 0.996634i | \(-0.526123\pi\) |
−0.904098 | + | 0.427324i | \(0.859456\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −178.708 | − | 309.531i | −0.605789 | − | 1.04926i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −269.783 | + | 155.759i | −0.902284 | + | 0.520934i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.5077 | − | 66.6973i | 0.127933 | − | 0.221586i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 75.3422i | − | 0.247024i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.3538 | −0.0337258 | −0.0168629 | − | 0.999858i | \(-0.505368\pi\) | ||||
−0.0168629 | + | 0.999858i | \(0.505368\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.26229 | + | 4.77024i | 0.0265669 | + | 0.0153384i | 0.513225 | − | 0.858254i | \(-0.328451\pi\) |
−0.486658 | + | 0.873593i | \(0.661784\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 239.638 | + | 415.066i | 0.765618 | + | 1.32609i | 0.939919 | + | 0.341397i | \(0.110900\pi\) |
−0.174301 | + | 0.984692i | \(0.555767\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −155.592 | + | 89.8311i | −0.490827 | + | 0.283379i | −0.724917 | − | 0.688836i | \(-0.758122\pi\) |
0.234091 | + | 0.972215i | \(0.424789\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −260.827 | + | 451.765i | −0.817639 | + | 1.41619i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 189.396i | − | 0.586365i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 182.042 | 0.560130 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −123.341 | − | 71.2111i | −0.374897 | − | 0.216447i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 147.727 | + | 255.870i | 0.446305 | + | 0.773023i | 0.998142 | − | 0.0609292i | \(-0.0194064\pi\) |
−0.551837 | + | 0.833952i | \(0.686073\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −106.289 | + | 61.3660i | −0.317281 | + | 0.183182i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −244.631 | + | 423.713i | −0.725907 | + | 1.25731i | 0.232692 | + | 0.972550i | \(0.425246\pi\) |
−0.958600 | + | 0.284758i | \(0.908087\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 117.576i | 0.344796i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −231.369 | −0.674546 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −577.363 | − | 333.341i | −1.66387 | − | 0.960637i | −0.970840 | − | 0.239730i | \(-0.922941\pi\) |
−0.693032 | − | 0.720907i | \(-0.743726\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −255.985 | − | 443.378i | −0.733480 | − | 1.27042i | −0.955387 | − | 0.295357i | \(-0.904561\pi\) |
0.221907 | − | 0.975068i | \(-0.428772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −508.081 | + | 293.340i | −1.43932 | + | 0.830993i | −0.997802 | − | 0.0662588i | \(-0.978894\pi\) |
−0.441519 | + | 0.897252i | \(0.645560\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 293.296 | − | 508.004i | 0.826186 | − | 1.43100i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 534.573i | − | 1.48906i | −0.667589 | − | 0.744530i | \(-0.732674\pi\) | ||
0.667589 | − | 0.744530i | \(-0.267326\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 233.985 | 0.648157 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −202.829 | − | 117.104i | −0.555697 | − | 0.320832i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.64617 | + | 13.2436i | 0.0208343 | + | 0.0360860i | 0.876255 | − | 0.481848i | \(-0.160034\pi\) |
−0.855420 | + | 0.517934i | \(0.826701\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 187.226 | − | 108.095i | 0.504651 | − | 0.291361i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −326.492 | + | 565.501i | −0.875314 | + | 1.51609i | −0.0188869 | + | 0.999822i | \(0.506012\pi\) |
−0.856427 | + | 0.516267i | \(0.827321\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 752.337i | − | 1.99559i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 655.215 | 1.72880 | 0.864400 | − | 0.502804i | \(-0.167698\pi\) | ||||
0.864400 | + | 0.502804i | \(0.167698\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 259.410 | + | 149.771i | 0.677311 | + | 0.391046i | 0.798841 | − | 0.601542i | \(-0.205447\pi\) |
−0.121530 | + | 0.992588i | \(0.538780\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −357.415 | − | 619.061i | −0.928351 | − | 1.60795i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 402.319 | − | 232.279i | 1.03424 | − | 0.597119i | 0.116043 | − | 0.993244i | \(-0.462979\pi\) |
0.918196 | + | 0.396126i | \(0.129646\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 57.0577 | − | 98.8269i | 0.145928 | − | 0.252754i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 572.289i | − | 1.44883i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −185.708 | −0.467777 | −0.233889 | − | 0.972263i | \(-0.575145\pi\) | ||||
−0.233889 | + | 0.972263i | \(0.575145\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −54.4376 | − | 31.4296i | −0.135755 | − | 0.0783780i | 0.430585 | − | 0.902550i | \(-0.358307\pi\) |
−0.566339 | + | 0.824172i | \(0.691641\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −84.7846 | − | 146.851i | −0.210384 | − | 0.364395i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 770.920 | − | 445.091i | 1.89415 | − | 1.09359i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 163.640 | − | 283.433i | 0.400099 | − | 0.692991i | −0.593639 | − | 0.804732i | \(-0.702309\pi\) |
0.993737 | + | 0.111741i | \(0.0356425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 517.558i | − | 1.25317i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 599.769 | 1.44523 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −562.808 | − | 324.937i | −1.34322 | − | 0.775507i | −0.355939 | − | 0.934509i | \(-0.615839\pi\) |
−0.987278 | + | 0.159003i | \(0.949172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.65956 | − | 2.87445i | −0.00394196 | − | 0.00682767i | 0.864048 | − | 0.503410i | \(-0.167921\pi\) |
−0.867990 | + | 0.496582i | \(0.834588\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −57.7515 | + | 33.3428i | −0.135886 | + | 0.0784538i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 54.5500 | − | 94.4833i | 0.127752 | − | 0.221272i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 803.502i | 1.86427i | 0.362107 | + | 0.932136i | \(0.382057\pi\) | ||||
−0.362107 | + | 0.932136i | \(0.617943\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −93.1230 | −0.215065 | −0.107532 | − | 0.994202i | \(-0.534295\pi\) | ||||
−0.107532 | + | 0.994202i | \(0.534295\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 310.463 | + | 179.246i | 0.710442 | + | 0.410174i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −236.000 | − | 408.764i | −0.537585 | − | 0.931125i | −0.999033 | − | 0.0439580i | \(-0.986003\pi\) |
0.461448 | − | 0.887167i | \(-0.347330\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 493.365 | − | 284.844i | 1.11369 | − | 0.642989i | 0.173908 | − | 0.984762i | \(-0.444361\pi\) |
0.939783 | + | 0.341773i | \(0.111027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 388.679 | − | 673.211i | 0.873436 | − | 1.51283i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 559.115i | 1.24524i | 0.782523 | + | 0.622622i | \(0.213933\pi\) | ||||
−0.782523 | + | 0.622622i | \(0.786067\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −494.354 | −1.09613 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 892.820 | + | 515.470i | 1.96224 | + | 1.13290i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −302.148 | − | 523.336i | −0.661155 | − | 1.14515i | −0.980312 | − | 0.197453i | \(-0.936733\pi\) |
0.319157 | − | 0.947702i | \(-0.396600\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.44669 | − | 2.56730i | 0.00964575 | − | 0.00556897i | −0.495169 | − | 0.868796i | \(-0.664894\pi\) |
0.504815 | + | 0.863227i | \(0.331561\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −80.7461 | + | 139.856i | −0.174398 | + | 0.302066i | −0.939953 | − | 0.341305i | \(-0.889131\pi\) |
0.765555 | + | 0.643370i | \(0.222464\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 503.025i | − | 1.07714i | −0.842581 | − | 0.538570i | \(-0.818965\pi\) | ||
0.842581 | − | 0.538570i | \(-0.181035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −177.723 | −0.378941 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −116.803 | − | 67.4363i | −0.246941 | − | 0.142571i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −104.746 | − | 181.426i | −0.220518 | − | 0.381949i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 185.153 | − | 106.898i | 0.386541 | − | 0.223170i | −0.294119 | − | 0.955769i | \(-0.595026\pi\) |
0.680660 | + | 0.732599i | \(0.261693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −641.917 | + | 1111.83i | −1.33455 | + | 2.31150i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 435.469i | − | 0.897874i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.63071 | −0.0177222 | −0.00886110 | − | 0.999961i | \(-0.502821\pi\) | ||||
−0.00886110 | + | 0.999961i | \(0.502821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −798.873 | − | 461.229i | −1.62703 | − | 0.939367i | −0.984972 | − | 0.172713i | \(-0.944747\pi\) |
−0.642060 | − | 0.766654i | \(-0.721920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 137.798 | + | 238.673i | 0.279509 | + | 0.484124i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 735.619 | − | 424.710i | 1.48012 | − | 0.854547i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −217.296 | + | 376.368i | −0.435463 | + | 0.754244i | −0.997333 | − | 0.0729811i | \(-0.976749\pi\) |
0.561870 | + | 0.827225i | \(0.310082\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 144.087i | 0.286454i | 0.989690 | + | 0.143227i | \(0.0457480\pi\) | ||||
−0.989690 | + | 0.143227i | \(0.954252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 168.588 | 0.333839 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −603.856 | − | 348.636i | −1.18636 | − | 0.684943i | −0.228880 | − | 0.973455i | \(-0.573506\pi\) |
−0.957477 | + | 0.288511i | \(0.906840\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −169.573 | − | 293.709i | −0.331845 | − | 0.574773i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −485.385 | + | 280.237i | −0.942496 | + | 0.544150i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −124.708 | + | 216.000i | −0.241214 | + | 0.417795i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 426.962i | 0.819504i | 0.912197 | + | 0.409752i | \(0.134385\pi\) | ||||
−0.912197 | + | 0.409752i | \(0.865615\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −179.762 | −0.343712 | −0.171856 | − | 0.985122i | \(-0.554976\pi\) | ||||
−0.171856 | + | 0.985122i | \(0.554976\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53.7945 | + | 31.0583i | 0.102077 | + | 0.0589341i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −156.500 | − | 271.066i | −0.295841 | − | 0.512412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 617.446 | − | 356.482i | 1.15843 | − | 0.668822i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −514.592 | + | 891.300i | −0.961855 | + | 1.66598i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 314.967i | − | 0.584354i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 708.734 | 1.31005 | 0.655023 | − | 0.755609i | \(-0.272659\pi\) | ||||
0.655023 | + | 0.755609i | \(0.272659\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −310.894 | − | 179.495i | −0.570448 | − | 0.329349i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −98.1154 | − | 169.941i | −0.179370 | − | 0.310678i | 0.762295 | − | 0.647230i | \(-0.224073\pi\) |
−0.941665 | + | 0.336552i | \(0.890739\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −749.789 | + | 432.891i | −1.36078 | + | 0.785646i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 414.354 | − | 717.682i | 0.749284 | − | 1.29780i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 353.610i | − | 0.634848i | −0.948284 | − | 0.317424i | \(-0.897182\pi\) | ||
0.948284 | − | 0.317424i | \(-0.102818\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 194.515 | 0.347970 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −323.050 | − | 186.513i | −0.573801 | − | 0.331284i | 0.184865 | − | 0.982764i | \(-0.440815\pi\) |
−0.758666 | + | 0.651480i | \(0.774149\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 318.208 | + | 551.152i | 0.563199 | + | 0.975490i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −52.0634 | + | 30.0588i | −0.0914999 | + | 0.0528275i | −0.545052 | − | 0.838402i | \(-0.683490\pi\) |
0.453552 | + | 0.891230i | \(0.350157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.1000 | − | 74.6513i | 0.0754815 | − | 0.130738i | −0.825814 | − | 0.563943i | \(-0.809284\pi\) |
0.901296 | + | 0.433205i | \(0.142617\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 126.224i | − | 0.219520i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 709.123 | 1.22898 | 0.614491 | − | 0.788924i | \(-0.289361\pi\) | ||||
0.614491 | + | 0.788924i | \(0.289361\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 752.144 | + | 434.251i | 1.29457 | + | 0.747419i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −189.300 | − | 327.877i | −0.324700 | − | 0.562396i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −833.363 | + | 481.143i | −1.41970 | + | 0.819664i | −0.996272 | − | 0.0862666i | \(-0.972506\pi\) |
−0.423427 | + | 0.905930i | \(0.639173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −97.5692 | + | 168.995i | −0.165652 | + | 0.286918i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 104.350i | 0.175969i | 0.996122 | + | 0.0879847i | \(0.0280427\pi\) | ||||
−0.996122 | + | 0.0879847i | \(0.971957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −377.654 | −0.634712 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −247.738 | − | 143.031i | −0.413585 | − | 0.238784i | 0.278744 | − | 0.960366i | \(-0.410082\pi\) |
−0.692329 | + | 0.721582i | \(0.743415\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 140.208 | + | 242.847i | 0.233291 | + | 0.404071i | 0.958775 | − | 0.284168i | \(-0.0917173\pi\) |
−0.725484 | + | 0.688239i | \(0.758384\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −476.814 | + | 275.289i | −0.788123 | + | 0.455023i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 368.865 | − | 638.894i | 0.607686 | − | 1.05254i | −0.383935 | − | 0.923360i | \(-0.625431\pi\) |
0.991621 | − | 0.129183i | \(-0.0412354\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 359.711i | − | 0.588724i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −679.415 | −1.10834 | −0.554172 | − | 0.832402i | \(-0.686965\pi\) | ||||
−0.554172 | + | 0.832402i | \(0.686965\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −409.326 | − | 236.325i | −0.663414 | − | 0.383022i | 0.130163 | − | 0.991493i | \(-0.458450\pi\) |
−0.793576 | + | 0.608471i | \(0.791783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 443.177 | + | 767.605i | 0.715956 | + | 1.24007i | 0.962590 | + | 0.270964i | \(0.0873423\pi\) |
−0.246633 | + | 0.969109i | \(0.579324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 974.850 | − | 562.830i | 1.56477 | − | 0.903419i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 382.975 | − | 663.332i | 0.612760 | − | 1.06133i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 470.294i | − | 0.747685i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 729.108 | 1.15548 | 0.577740 | − | 0.816221i | \(-0.303935\pi\) | ||||
0.577740 | + | 0.816221i | \(0.303935\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 708.581 | + | 409.099i | 1.11588 | + | 0.644251i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 227.125 | + | 393.392i | 0.356554 | + | 0.617570i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −753.611 | + | 435.098i | −1.17568 | + | 0.678780i | −0.955011 | − | 0.296569i | \(-0.904157\pi\) |
−0.220669 | + | 0.975349i | \(0.570824\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −309.061 | + | 535.310i | −0.480656 | + | 0.832520i | −0.999754 | − | 0.0221949i | \(-0.992935\pi\) |
0.519098 | + | 0.854715i | \(0.326268\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 425.439i | 0.657556i | 0.944407 | + | 0.328778i | \(0.106637\pi\) | ||||
−0.944407 | + | 0.328778i | \(0.893363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −906.369 | −1.39656 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 163.513 | + | 94.4042i | 0.250403 | + | 0.144570i | 0.619949 | − | 0.784642i | \(-0.287153\pi\) |
−0.369546 | + | 0.929212i | \(0.620487\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 154.119 | + | 266.942i | 0.235296 | + | 0.407545i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −571.984 | + | 330.235i | −0.867958 | + | 0.501116i | −0.866669 | − | 0.498884i | \(-0.833744\pi\) |
−0.00128859 | + | 0.999999i | \(0.500410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 294.915 | − | 510.808i | 0.446165 | − | 0.772781i | −0.551967 | − | 0.833866i | \(-0.686123\pi\) |
0.998133 | + | 0.0610847i | \(0.0194560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1186.39i | − | 1.78405i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −521.654 | −0.782090 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −165.463 | − | 95.5301i | −0.246592 | − | 0.142370i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 195.715 | + | 338.989i | 0.290810 | + | 0.503698i | 0.974002 | − | 0.226541i | \(-0.0727418\pi\) |
−0.683191 | + | 0.730240i | \(0.739408\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 600.728 | − | 346.830i | 0.887338 | − | 0.512305i | 0.0142672 | − | 0.999898i | \(-0.495458\pi\) |
0.873071 | + | 0.487593i | \(0.162125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 315.292 | − | 546.102i | 0.464348 | − | 0.804274i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 678.170i | 0.992928i | 0.868057 | + | 0.496464i | \(0.165368\pi\) | ||||
−0.868057 | + | 0.496464i | \(0.834632\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.47303 | −0.0138292 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 472.869 | + | 273.011i | 0.686313 | + | 0.396243i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 337.888 | + | 585.240i | 0.488985 | + | 0.846946i | 0.999920 | − | 0.0126731i | \(-0.00403409\pi\) |
−0.510935 | + | 0.859619i | \(0.670701\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 96.4439 | − | 55.6819i | 0.138768 | − | 0.0801179i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −130.587 | + | 226.183i | −0.187355 | + | 0.324509i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 797.260i | 1.13732i | 0.822573 | + | 0.568659i | \(0.192538\pi\) | ||||
−0.822573 | + | 0.568659i | \(0.807462\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1477.42 | 2.10160 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 211.419 | + | 122.063i | 0.299037 | + | 0.172649i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −86.7520 | − | 150.259i | −0.122358 | − | 0.211931i | 0.798339 | − | 0.602208i | \(-0.205712\pi\) |
−0.920697 | + | 0.390278i | \(0.872379\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −101.823 | + | 58.7878i | −0.142810 | + | 0.0824513i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 902.711 | − | 1563.54i | 1.26253 | − | 2.18677i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 188.177i | − | 0.261721i | −0.991401 | − | 0.130860i | \(-0.958226\pi\) | ||
0.991401 | − | 0.130860i | \(-0.0417740\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −811.600 | −1.12566 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 263.998 | + | 152.420i | 0.364136 | + | 0.210234i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 355.888 | + | 616.417i | 0.489530 | + | 0.847891i | 0.999927 | − | 0.0120478i | \(-0.00383501\pi\) |
−0.510397 | + | 0.859939i | \(0.670502\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −61.7085 | + | 35.6274i | −0.0844165 | + | 0.0487379i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −613.415 | + | 1062.47i | −0.836856 | + | 1.44948i | 0.0556546 | + | 0.998450i | \(0.482275\pi\) |
−0.892510 | + | 0.451027i | \(0.851058\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 311.236i | 0.422301i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −741.892 | −1.00391 | −0.501957 | − | 0.864893i | \(-0.667386\pi\) | ||||
−0.501957 | + | 0.864893i | \(0.667386\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 677.218 | + | 390.992i | 0.911464 | + | 0.526234i | 0.880902 | − | 0.473299i | \(-0.156937\pi\) |
0.0305622 | + | 0.999533i | \(0.490270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 273.208 | + | 473.210i | 0.366722 | + | 0.635181i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1290.65 | + | 745.160i | −1.72317 | + | 0.994873i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −516.665 | + | 894.891i | −0.687970 | + | 1.19160i | 0.284524 | + | 0.958669i | \(0.408165\pi\) |
−0.972494 | + | 0.232930i | \(0.925169\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 185.458i | − | 0.245639i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 473.877 | 0.625993 | 0.312997 | − | 0.949754i | \(-0.398667\pi\) | ||||
0.312997 | + | 0.949754i | \(0.398667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 814.458 | + | 470.227i | 1.07025 | + | 0.617907i | 0.928249 | − | 0.371960i | \(-0.121314\pi\) |
0.141998 | + | 0.989867i | \(0.454647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −259.919 | − | 450.193i | −0.340654 | − | 0.590031i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1132.05 | − | 653.590i | 1.47595 | − | 0.852138i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −490.408 | + | 849.411i | −0.637721 | + | 1.10457i | 0.348210 | + | 0.937416i | \(0.386789\pi\) |
−0.985932 | + | 0.167149i | \(0.946544\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1042.20i | 1.34825i | 0.738618 | + | 0.674124i | \(0.235479\pi\) | ||||
−0.738618 | + | 0.674124i | \(0.764521\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 68.7077 | 0.0886550 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −710.550 | − | 410.236i | −0.912131 | − | 0.526619i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −743.769 | − | 1288.25i | −0.952329 | − | 1.64948i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.46729 | − | 0.847142i | 0.00186916 | − | 0.00107916i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −72.3501 | + | 125.314i | −0.0919315 | + | 0.159230i | −0.908324 | − | 0.418268i | \(-0.862637\pi\) |
0.816392 | + | 0.577498i | \(0.195971\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 921.567i | 1.16507i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 275.550 | 0.347478 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −134.866 | − | 77.8647i | −0.169217 | − | 0.0976972i | 0.413000 | − | 0.910731i | \(-0.364481\pi\) |
−0.582216 | + | 0.813034i | \(0.697814\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 65.8846 | + | 114.115i | 0.0824588 | + | 0.142823i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −514.355 | + | 296.963i | −0.640542 | + | 0.369817i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 357.415 | − | 619.061i | 0.443994 | − | 0.769020i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1216.92i | 1.50422i | 0.659035 | + | 0.752112i | \(0.270965\pi\) | ||||
−0.659035 | + | 0.752112i | \(0.729035\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1243.31 | −1.53305 | −0.766527 | − | 0.642212i | \(-0.778017\pi\) | ||||
−0.766527 | + | 0.642212i | \(0.778017\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 144.473 | + | 83.4114i | 0.177267 | + | 0.102345i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −111.923 | − | 193.856i | −0.136993 | − | 0.237278i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.5055 | + | 6.64270i | −0.0140140 | + | 0.00809098i | −0.506991 | − | 0.861952i | \(-0.669242\pi\) |
0.492977 | + | 0.870043i | \(0.335909\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −107.100 | + | 185.503i | −0.130134 | + | 0.225398i | −0.923728 | − | 0.383049i | \(-0.874874\pi\) |
0.793594 | + | 0.608447i | \(0.208207\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1221.27i | 1.47675i | 0.674391 | + | 0.738374i | \(0.264406\pi\) | ||||
−0.674391 | + | 0.738374i | \(0.735594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −358.431 | −0.432365 | −0.216183 | − | 0.976353i | \(-0.569361\pi\) | ||||
−0.216183 | + | 0.976353i | \(0.569361\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −144.107 | − | 83.2004i | −0.172998 | − | 0.0998804i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −162.473 | − | 281.412i | −0.194578 | − | 0.337020i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −283.707 | + | 163.799i | −0.338150 | + | 0.195231i | −0.659453 | − | 0.751745i | \(-0.729212\pi\) |
0.321304 | + | 0.946976i | \(0.395879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 209.413 | − | 362.715i | 0.249005 | − | 0.431290i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1624.36i | 1.92232i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −797.269 | −0.941286 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 770.920 | + | 445.091i | 0.905899 | + | 0.523021i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.4153 | + | 45.7527i | 0.0309675 | + | 0.0536374i | 0.881094 | − | 0.472942i | \(-0.156808\pi\) |
−0.850126 | + | 0.526579i | \(0.823474\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1081.16 | − | 624.211i | 1.26157 | − | 0.728367i | 0.288191 | − | 0.957573i | \(-0.406946\pi\) |
0.973378 | + | 0.229206i | \(0.0736128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −223.369 | + | 386.887i | −0.260034 | + | 0.450392i | −0.966251 | − | 0.257604i | \(-0.917067\pi\) |
0.706217 | + | 0.707996i | \(0.250400\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 635.297i | 0.736150i | 0.929796 | + | 0.368075i | \(0.119983\pi\) | ||||
−0.929796 | + | 0.368075i | \(0.880017\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1280.54 | 1.48039 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1256.83 | − | 725.633i | −1.44630 | − | 0.835021i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −224.435 | − | 388.732i | −0.257675 | − | 0.446305i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 691.284 | − | 399.113i | 0.790039 | − | 0.456129i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 394.346 | − | 683.027i | 0.449653 | − | 0.778823i | −0.548710 | − | 0.836013i | \(-0.684881\pi\) |
0.998363 | + | 0.0571902i | \(0.0182141\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 558.506i | 0.633945i | 0.948435 | + | 0.316972i | \(0.102666\pi\) | ||||
−0.948435 | + | 0.316972i | \(0.897334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −313.338 | −0.354857 | −0.177428 | − | 0.984134i | \(-0.556778\pi\) | ||||
−0.177428 | + | 0.984134i | \(0.556778\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 517.624 | + | 298.850i | 0.583567 | + | 0.336923i | 0.762550 | − | 0.646930i | \(-0.223947\pi\) |
−0.178983 | + | 0.983852i | \(0.557281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 592.400 | + | 1026.07i | 0.666367 | + | 1.15418i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −358.492 | + | 206.976i | −0.401447 | + | 0.231776i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 719.654 | − | 1246.48i | 0.804082 | − | 1.39271i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 283.952i | − | 0.315854i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −200.019 | −0.221997 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 794.407 | + | 458.651i | 0.877798 | + | 0.506797i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 543.254 | + | 940.943i | 0.598957 | + | 1.03742i | 0.992975 | + | 0.118321i | \(0.0377512\pi\) |
−0.394019 | + | 0.919103i | \(0.628915\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −615.123 | + | 355.142i | −0.675218 | + | 0.389837i | −0.798051 | − | 0.602590i | \(-0.794135\pi\) |
0.122833 | + | 0.992427i | \(0.460802\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 760.477 | − | 1317.18i | 0.832943 | − | 1.44270i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 446.347i | 0.486747i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1540.01 | −1.67574 | −0.837871 | − | 0.545868i | \(-0.816200\pi\) | ||||
−0.837871 | + | 0.545868i | \(0.816200\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1857.93 | + | 1072.68i | 2.01292 | + | 1.16216i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −260.098 | − | 450.503i | −0.281187 | − | 0.487030i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1370.57 | + | 791.297i | −1.47531 | + | 0.851773i | −0.999613 | − | 0.0278334i | \(-0.991139\pi\) |
−0.475702 | + | 0.879607i | \(0.657806\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 261.373 | − | 452.711i | 0.280744 | − | 0.486264i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 661.362i | 0.707339i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1747.40 | −1.86489 | −0.932444 | − | 0.361315i | \(-0.882328\pi\) | ||||
−0.932444 | + | 0.361315i | \(0.882328\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 318.332 | + | 183.789i | 0.338292 | + | 0.195313i | 0.659516 | − | 0.751690i | \(-0.270761\pi\) |
−0.321225 | + | 0.947003i | \(0.604094\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −247.177 | − | 428.123i | −0.262118 | − | 0.454001i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 164.691 | − | 95.0841i | 0.173908 | − | 0.100406i | −0.410519 | − | 0.911852i | \(-0.634653\pi\) |
0.584427 | + | 0.811446i | \(0.301319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 428.285 | − | 741.811i | 0.451301 | − | 0.781676i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 861.754i | − | 0.904254i | −0.891954 | − | 0.452127i | \(-0.850665\pi\) | ||
0.891954 | − | 0.452127i | \(-0.149335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 200.238 | 0.209674 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.8797 | − | 6.85875i | −0.0123876 | − | 0.00715198i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 448.500 | + | 776.825i | 0.466701 | + | 0.808350i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −276.050 | + | 159.378i | −0.286063 | + | 0.165158i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 637.657 | − | 1104.46i | 0.659418 | − | 1.14215i | −0.321348 | − | 0.946961i | \(-0.604136\pi\) |
0.980766 | − | 0.195185i | \(-0.0625307\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1238.69i | − | 1.27568i | −0.770168 | − | 0.637841i | \(-0.779828\pi\) | ||
0.770168 | − | 0.637841i | \(-0.220172\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 161.261 | 0.165736 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.0159 | − | 9.24680i | −0.0163930 | − | 0.00946448i | 0.491781 | − | 0.870719i | \(-0.336346\pi\) |
−0.508174 | + | 0.861254i | \(0.669679\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −985.650 | − | 1707.20i | −1.00679 | − | 1.74382i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −570.401 | + | 329.321i | −0.580266 | + | 0.335017i | −0.761239 | − | 0.648471i | \(-0.775409\pi\) |
0.180973 | + | 0.983488i | \(0.442075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 103.500 | − | 179.267i | 0.105076 | − | 0.181997i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 134.873i | − | 0.136373i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −608.484 | −0.614010 | −0.307005 | − | 0.951708i | \(-0.599327\pi\) | ||||
−0.307005 | + | 0.951708i | \(0.599327\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1882.86 | − | 1087.07i | −1.89232 | − | 1.09253i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 308.623 | + | 534.551i | 0.309552 | + | 0.536159i | 0.978264 | − | 0.207362i | \(-0.0664877\pi\) |
−0.668713 | + | 0.743521i | \(0.733154\pi\) | |||||||
\(998\) | 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 | 1296.3.q.o.1025.1 | 8 | ||
3.2 | odd | 2 | inner | 1296.3.q.o.1025.4 | 8 | ||
4.3 | odd | 2 | 162.3.d.c.53.1 | 8 | |||
9.2 | odd | 6 | inner | 1296.3.q.o.593.1 | 8 | ||
9.4 | even | 3 | 1296.3.e.d.161.4 | 4 | |||
9.5 | odd | 6 | 1296.3.e.d.161.1 | 4 | |||
9.7 | even | 3 | inner | 1296.3.q.o.593.4 | 8 | ||
12.11 | even | 2 | 162.3.d.c.53.4 | 8 | |||
36.7 | odd | 6 | 162.3.d.c.107.4 | 8 | |||
36.11 | even | 6 | 162.3.d.c.107.1 | 8 | |||
36.23 | even | 6 | 162.3.b.b.161.3 | yes | 4 | ||
36.31 | odd | 6 | 162.3.b.b.161.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.3.b.b.161.2 | ✓ | 4 | 36.31 | odd | 6 | ||
162.3.b.b.161.3 | yes | 4 | 36.23 | even | 6 | ||
162.3.d.c.53.1 | 8 | 4.3 | odd | 2 | |||
162.3.d.c.53.4 | 8 | 12.11 | even | 2 | |||
162.3.d.c.107.1 | 8 | 36.11 | even | 6 | |||
162.3.d.c.107.4 | 8 | 36.7 | odd | 6 | |||
1296.3.e.d.161.1 | 4 | 9.5 | odd | 6 | |||
1296.3.e.d.161.4 | 4 | 9.4 | even | 3 | |||
1296.3.q.o.593.1 | 8 | 9.2 | odd | 6 | inner | ||
1296.3.q.o.593.4 | 8 | 9.7 | even | 3 | inner | ||
1296.3.q.o.1025.1 | 8 | 1.1 | even | 1 | trivial | ||
1296.3.q.o.1025.4 | 8 | 3.2 | odd | 2 | inner |