Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,3,Mod(53,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.53");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.d (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: | \(4.41418028264\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 53.4 | ||
Root | \(0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.53 |
Dual form | 162.3.d.c.107.4 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | − | 0.707107i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 5.01910 | + | 2.89778i | 1.00382 | + | 0.579555i | 0.909376 | − | 0.415975i | \(-0.136560\pi\) |
0.0944434 | + | 0.995530i | \(0.469893\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.19615 | + | 7.26795i | 0.599450 | + | 1.03828i | 0.992902 | + | 0.118933i | \(0.0379475\pi\) |
−0.393452 | + | 0.919345i | \(0.628719\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.19615 | 0.819615 | ||||||||
\(11\) | −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 | \(-0.136726\pi\) | |||||||
\(14\) | 10.2784 | + | 5.93426i | 0.734174 | + | 0.423875i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | − | 7.76457i | − | 0.456739i | −0.973574 | − | 0.228370i | \(-0.926660\pi\) | ||
0.973574 | − | 0.228370i | \(-0.0733395\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.3923 | 1.28381 | 0.641903 | − | 0.766786i | \(-0.278145\pi\) | ||||
0.641903 | + | 0.766786i | \(0.278145\pi\) | |||||||
\(20\) | 10.0382 | − | 5.79555i | 0.501910 | − | 0.289778i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.3923 | + | 18.0000i | −0.472377 | + | 0.818182i | ||||
\(23\) | −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 | ||||
\(26\) | − | 29.9759i | − | 1.15292i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.7846 | 0.599450 | ||||||||
\(29\) | −30.7387 | + | 17.7470i | −1.05996 | + | 0.611966i | −0.925420 | − | 0.378942i | \(-0.876288\pi\) |
−0.134536 | + | 0.990909i | \(0.542954\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.129032 | + | 0.223490i | −0.923302 | − | 0.384075i | \(-0.874520\pi\) |
0.794270 | + | 0.607565i | \(0.207854\pi\) | |||||||
\(32\) | −4.89898 | − | 2.82843i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.49038 | − | 9.50962i | −0.161482 | − | 0.279695i | ||||
\(35\) | 48.6381i | 1.38966i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −60.5692 | −1.63701 | −0.818503 | − | 0.574502i | \(-0.805196\pi\) | ||||
−0.818503 | + | 0.574502i | \(0.805196\pi\) | |||||||
\(38\) | 29.8744 | − | 17.2480i | 0.786167 | − | 0.453894i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.19615 | − | 14.1962i | 0.204904 | − | 0.354904i | ||||
\(41\) | −29.1301 | − | 16.8183i | −0.710490 | − | 0.410201i | 0.100753 | − | 0.994912i | \(-0.467875\pi\) |
−0.811242 | + | 0.584710i | \(0.801208\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.58846 | − | 7.94744i | −0.106708 | − | 0.184824i | 0.807727 | − | 0.589557i | \(-0.200698\pi\) |
−0.914435 | + | 0.404733i | \(0.867364\pi\) | |||||||
\(44\) | 29.3939i | 0.668043i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −20.7846 | −0.451839 | ||||||||
\(47\) | 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 | ||||
\(50\) | 10.5187 | + | 6.07296i | 0.210373 | + | 0.121459i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −21.1962 | − | 36.7128i | −0.407618 | − | 0.706016i | ||||
\(53\) | − | 25.7605i | − | 0.486046i | −0.970020 | − | 0.243023i | \(-0.921861\pi\) | ||
0.970020 | − | 0.243023i | \(-0.0781391\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −85.1769 | −1.54867 | ||||||||
\(56\) | 20.5569 | − | 11.8685i | 0.367087 | − | 0.211938i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −25.0981 | + | 43.4711i | −0.432725 | + | 0.749502i | ||||
\(59\) | 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 | \(0.799351\pi\) | |||||||
\(62\) | 11.3137i | 0.182479i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 106.386 | − | 61.4217i | 1.63670 | − | 0.944950i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5885 | + | 18.3397i | −0.158037 | + | 0.273728i | −0.934161 | − | 0.356853i | \(-0.883850\pi\) |
0.776124 | + | 0.630580i | \(0.217183\pi\) | |||||||
\(68\) | −13.4486 | − | 7.76457i | −0.197774 | − | 0.114185i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 34.3923 | + | 59.5692i | 0.491319 | + | 0.850989i | ||||
\(71\) | 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 | \(0.410729\pi\) | |||||||
\(74\) | −74.1818 | + | 42.8289i | −1.00246 | + | 0.578769i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 24.3923 | − | 42.2487i | 0.320951 | − | 0.555904i | ||||
\(77\) | −106.817 | − | 61.6706i | −1.38723 | − | 0.800917i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −49.3731 | − | 85.5167i | −0.624976 | − | 1.08249i | −0.988546 | − | 0.150923i | \(-0.951776\pi\) |
0.363570 | − | 0.931567i | \(-0.381558\pi\) | |||||||
\(80\) | − | 23.1822i | − | 0.289778i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −47.5692 | −0.580112 | ||||||||
\(83\) | −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 | ||||
\(86\) | −11.2394 | − | 6.48906i | −0.130690 | − | 0.0754542i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 20.7846 | + | 36.0000i | 0.236189 | + | 0.409091i | ||||
\(89\) | − | 134.130i | − | 1.50708i | −0.657403 | − | 0.753539i | \(-0.728345\pi\) | ||
0.657403 | − | 0.753539i | \(-0.271655\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 177.885 | 1.95478 | ||||||||
\(92\) | −25.4558 | + | 14.6969i | −0.276694 | + | 0.159749i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.0000 | − | 20.7846i | 0.127660 | − | 0.221113i | ||||
\(95\) | 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 | \(0.706737\pi\) | |||||||
\(98\) | 30.3077i | 0.309262i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 17.1769 | 0.171769 | ||||||||
\(101\) | 25.1920 | − | 14.5446i | 0.249426 | − | 0.144006i | −0.370075 | − | 0.929002i | \(-0.620668\pi\) |
0.619501 | + | 0.784995i | \(0.287335\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −48.3538 | + | 83.7513i | −0.469455 | + | 0.813119i | −0.999390 | − | 0.0349186i | \(-0.988883\pi\) |
0.529936 | + | 0.848038i | \(0.322216\pi\) | |||||||
\(104\) | −51.9198 | − | 29.9759i | −0.499228 | − | 0.288230i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.2154 | − | 31.5500i | −0.171843 | − | 0.297641i | ||||
\(107\) | − | 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 | \(0.408292\pi\) | |||||||
\(110\) | −104.320 | + | 60.2292i | −0.948364 | + | 0.547538i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.7846 | − | 29.0718i | 0.149863 | − | 0.259570i | ||||
\(113\) | 95.0991 | + | 54.9055i | 0.841585 | + | 0.485889i | 0.857803 | − | 0.513979i | \(-0.171829\pi\) |
−0.0162179 | + | 0.999868i | \(0.505163\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −42.5885 | − | 73.7654i | −0.370334 | − | 0.641438i | ||||
\(116\) | 70.9881i | 0.611966i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 87.2154 | 0.739113 | ||||||||
\(119\) | 56.4325 | − | 32.5813i | 0.474223 | − | 0.273793i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 47.5000 | − | 82.2724i | 0.392562 | − | 0.679937i | ||||
\(122\) | 15.9217 | + | 9.19239i | 0.130506 | + | 0.0753474i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.00000 | + | 13.8564i | 0.0645161 | + | 0.111745i | ||||
\(125\) | − | 95.1140i | − | 0.760912i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 141.177 | 1.11163 | 0.555815 | − | 0.831306i | \(-0.312406\pi\) | ||||
0.555815 | + | 0.831306i | \(0.312406\pi\) | |||||||
\(128\) | −9.79796 | + | 5.65685i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 86.8634 | − | 150.452i | 0.668180 | − | 1.15732i | ||||
\(131\) | −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 | ||||
\(134\) | 29.9487i | 0.223498i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −21.9615 | −0.161482 | ||||||||
\(137\) | −1.41555 | + | 0.817267i | −0.0103325 | + | 0.00596545i | −0.505157 | − | 0.863027i | \(-0.668566\pi\) |
0.494825 | + | 0.868993i | \(0.335232\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.60770 | − | 16.6410i | 0.0691201 | − | 0.119720i | −0.829394 | − | 0.558664i | \(-0.811314\pi\) |
0.898514 | + | 0.438944i | \(0.144647\pi\) | |||||||
\(140\) | 84.2436 | + | 48.6381i | 0.601740 | + | 0.347415i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 71.5692 | + | 123.962i | 0.504009 | + | 0.872968i | ||||
\(143\) | 311.519i | 2.17845i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −205.708 | −1.41867 | ||||||||
\(146\) | 49.4938 | − | 28.5753i | 0.338999 | − | 0.195721i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −60.5692 | + | 104.909i | −0.409251 | + | 0.708844i | ||||
\(149\) | 81.6504 | + | 47.1409i | 0.547989 | + | 0.316382i | 0.748311 | − | 0.663348i | \(-0.230865\pi\) |
−0.200321 | + | 0.979730i | \(0.564199\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | − | 27.7128i | −0.105960 | − | 0.183529i | 0.808170 | − | 0.588949i | \(-0.200458\pi\) |
−0.914130 | + | 0.405421i | \(0.867125\pi\) | |||||||
\(152\) | − | 68.9919i | − | 0.453894i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −174.431 | −1.13267 | ||||||||
\(155\) | −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 | \(0.166963\pi\) | |||||||
\(158\) | −120.939 | − | 69.8241i | −0.765436 | − | 0.441924i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.3923 | − | 28.3923i | −0.102452 | − | 0.177452i | ||||
\(161\) | − | 123.341i | − | 0.766094i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 28.7846 | 0.176593 | 0.0882963 | − | 0.996094i | \(-0.471858\pi\) | ||||
0.0882963 | + | 0.996094i | \(0.471858\pi\) | |||||||
\(164\) | −58.2602 | + | 33.6365i | −0.355245 | + | 0.205101i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −73.1769 | + | 126.746i | −0.440825 | + | 0.763531i | ||||
\(167\) | 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 | ||||
\(170\) | − | 63.6396i | − | 0.374351i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −18.3538 | −0.106708 | ||||||||
\(173\) | 191.350 | − | 110.476i | 1.10607 | − | 0.638589i | 0.168260 | − | 0.985743i | \(-0.446185\pi\) |
0.937808 | + | 0.347154i | \(0.112852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −36.0385 | + | 62.4205i | −0.205934 | + | 0.356688i | ||||
\(176\) | 50.9117 | + | 29.3939i | 0.289271 | + | 0.167011i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −94.8442 | − | 164.275i | −0.532833 | − | 0.922893i | ||||
\(179\) | 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 | \(0.644040\pi\) | |||||||
\(182\) | 217.863 | − | 125.783i | 1.19705 | − | 0.691118i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −20.7846 | + | 36.0000i | −0.112960 | + | 0.195652i | ||||
\(185\) | −304.003 | − | 175.516i | −1.64326 | − | 0.948736i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 57.0577 | + | 98.8269i | 0.305121 | + | 0.528486i | ||||
\(188\) | − | 33.9411i | − | 0.180538i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 199.923 | 1.05223 | ||||||||
\(191\) | −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 | \(0.121157\pi\) | |||||||
\(194\) | 92.0254 | + | 53.1309i | 0.474358 | + | 0.273871i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 21.4308 | + | 37.1192i | 0.109341 | + | 0.189384i | ||||
\(197\) | − | 35.7170i | − | 0.181305i | −0.995883 | − | 0.0906524i | \(-0.971105\pi\) | ||
0.995883 | − | 0.0906524i | \(-0.0288952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −375.138 | −1.88512 | −0.942559 | − | 0.334040i | \(-0.891588\pi\) | ||||
−0.942559 | + | 0.334040i | \(0.891588\pi\) | |||||||
\(200\) | 21.0373 | − | 12.1459i | 0.105187 | − | 0.0607296i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 20.5692 | − | 35.6269i | 0.101828 | − | 0.176371i | ||||
\(203\) | −257.969 | − | 148.938i | −1.27078 | − | 0.733687i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −97.4711 | − | 168.825i | −0.475469 | − | 0.823536i | ||||
\(206\) | 136.765i | 0.663909i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −84.7846 | −0.407618 | ||||||||
\(209\) | −310.463 | + | 179.246i | −1.48547 | + | 0.857637i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −153.727 | + | 266.263i | −0.728563 | + | 1.26191i | 0.228927 | + | 0.973444i | \(0.426478\pi\) |
−0.957490 | + | 0.288465i | \(0.906855\pi\) | |||||||
\(212\) | −44.6184 | − | 25.7605i | −0.210464 | − | 0.121512i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −125.569 | − | 217.492i | −0.586772 | − | 1.01632i | ||||
\(215\) | − | 53.1853i | − | 0.247374i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −67.1384 | −0.309394 | ||||||||
\(218\) | 75.8635 | − | 43.7998i | 0.347998 | − | 0.200917i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −85.1769 | + | 147.531i | −0.387168 | + | 0.670594i | ||||
\(221\) | −142.530 | − | 82.2895i | −0.644930 | − | 0.372351i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 169.296 | + | 293.229i | 0.759175 | + | 1.31493i | 0.943272 | + | 0.332022i | \(0.107731\pi\) |
−0.184096 | + | 0.982908i | \(0.558936\pi\) | |||||||
\(224\) | − | 47.4740i | − | 0.211938i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 155.296 | 0.687151 | ||||||||
\(227\) | −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 | \(0.218364\pi\) | |||||||
\(230\) | −104.320 | − | 60.2292i | −0.453565 | − | 0.261866i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 50.1962 | + | 86.9423i | 0.216363 | + | 0.374751i | ||||
\(233\) | 273.223i | 1.17263i | 0.810082 | + | 0.586316i | \(0.199422\pi\) | ||||
−0.810082 | + | 0.586316i | \(0.800578\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 98.3538 | 0.418527 | ||||||||
\(236\) | 106.817 | − | 61.6706i | 0.452613 | − | 0.261316i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 46.0770 | − | 79.8076i | 0.193601 | − | 0.335326i | ||||
\(239\) | 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 | \(0.541350\pi\) | |||||||
\(242\) | − | 134.350i | − | 0.555166i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26.0000 | 0.106557 | ||||||||
\(245\) | −107.563 | + | 62.1016i | −0.439033 | + | 0.253476i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 258.512 | − | 447.755i | 1.04661 | − | 1.81277i | ||||
\(248\) | 19.5959 | + | 11.3137i | 0.0790158 | + | 0.0456198i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −67.2558 | − | 116.490i | −0.269023 | − | 0.465962i | ||||
\(251\) | − | 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 | ||||||||
\(254\) | 172.906 | − | 99.8272i | 0.680731 | − | 0.393020i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 138.398 | + | 79.9044i | 0.538515 | + | 0.310912i | 0.744477 | − | 0.667648i | \(-0.232699\pi\) |
−0.205962 | + | 0.978560i | \(0.566032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −254.158 | − | 440.214i | −0.981304 | − | 1.69967i | ||||
\(260\) | − | 245.687i | − | 0.944950i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −75.2154 | −0.287082 | ||||||||
\(263\) | 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 | ||||
\(266\) | 250.715 | + | 144.750i | 0.942536 | + | 0.544174i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21.1769 | + | 36.6795i | 0.0790183 | + | 0.136864i | ||||
\(269\) | 24.8168i | 0.0922556i | 0.998936 | + | 0.0461278i | \(0.0146881\pi\) | ||||
−0.998936 | + | 0.0461278i | \(0.985312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 98.1154 | 0.362050 | 0.181025 | − | 0.983479i | \(-0.442059\pi\) | ||||
0.181025 | + | 0.983479i | \(0.442059\pi\) | |||||||
\(272\) | −26.8973 | + | 15.5291i | −0.0988870 | + | 0.0570924i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.15579 | + | 2.00189i | −0.00421821 | + | 0.00730616i | ||||
\(275\) | −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 | \(0.832520\pi\) | |||||||
\(278\) | − | 27.1747i | − | 0.0977506i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 137.569 | 0.491319 | ||||||||
\(281\) | −87.2230 | + | 50.3582i | −0.310402 | + | 0.179211i | −0.647106 | − | 0.762400i | \(-0.724021\pi\) |
0.336704 | + | 0.941610i | \(0.390688\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.6462 | − | 40.9564i | 0.0835554 | − | 0.144722i | −0.821219 | − | 0.570613i | \(-0.806706\pi\) |
0.904775 | + | 0.425890i | \(0.140039\pi\) | |||||||
\(284\) | 175.308 | + | 101.214i | 0.617282 | + | 0.356388i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 220.277 | + | 381.531i | 0.770199 | + | 1.33402i | ||||
\(287\) | − | 282.288i | − | 0.983582i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 228.711 | 0.791389 | ||||||||
\(290\) | −251.939 | + | 145.457i | −0.868757 | + | 0.501577i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 40.4115 | − | 69.9948i | 0.138396 | − | 0.239708i | ||||
\(293\) | 288.920 | + | 166.808i | 0.986074 | + | 0.569310i | 0.904098 | − | 0.427324i | \(-0.140544\pi\) |
0.0819755 | + | 0.996634i | \(0.473877\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 178.708 | + | 309.531i | 0.605789 | + | 1.04926i | ||||
\(296\) | 171.316i | 0.578769i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 133.335 | 0.447432 | ||||||||
\(299\) | −269.783 | + | 155.759i | −0.902284 | + | 0.520934i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.5077 | − | 66.6973i | 0.127933 | − | 0.221586i | ||||
\(302\) | −39.1918 | − | 22.6274i | −0.129774 | − | 0.0749252i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −48.7846 | − | 84.4974i | −0.160476 | − | 0.277952i | ||||
\(305\) | 75.3422i | 0.247024i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3538 | 0.0337258 | 0.0168629 | − | 0.999858i | \(-0.494632\pi\) | ||||
0.0168629 | + | 0.999858i | \(0.494632\pi\) | |||||||
\(308\) | −213.633 | + | 123.341i | −0.693614 | + | 0.400458i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −32.7846 | + | 56.7846i | −0.105757 | + | 0.183176i | ||||
\(311\) | 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 | \(0.555767\pi\) | |||||||
\(314\) | 0.413434i | 0.00131667i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −197.492 | −0.624976 | ||||||||
\(317\) | 155.592 | − | 89.8311i | 0.490827 | − | 0.283379i | −0.234091 | − | 0.972215i | \(-0.575211\pi\) |
0.724917 | + | 0.688836i | \(0.241878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 260.827 | − | 451.765i | 0.817639 | − | 1.41619i | ||||
\(320\) | −40.1528 | − | 23.1822i | −0.125477 | − | 0.0724444i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −87.2154 | − | 151.061i | −0.270855 | − | 0.469135i | ||||
\(323\) | − | 189.396i | − | 0.586365i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 182.042 | 0.560130 | ||||||||
\(326\) | 35.2538 | − | 20.3538i | 0.108141 | − | 0.0624349i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −47.5692 | + | 82.3923i | −0.145028 | + | 0.251196i | ||||
\(329\) | 123.341 | + | 71.2111i | 0.374897 | + | 0.216447i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −147.727 | − | 255.870i | −0.446305 | − | 0.773023i | 0.551837 | − | 0.833952i | \(-0.313927\pi\) |
−0.998142 | + | 0.0609292i | \(0.980594\pi\) | |||||||
\(332\) | 206.976i | 0.623420i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 79.2923 | 0.237402 | ||||||||
\(335\) | −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 | \(0.908087\pi\) | |||||||
\(338\) | −343.268 | − | 198.186i | −1.01558 | − | 0.586348i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −45.0000 | − | 77.9423i | −0.132353 | − | 0.229242i | ||||
\(341\) | − | 117.576i | − | 0.344796i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 231.369 | 0.674546 | ||||||||
\(344\) | −22.4788 | + | 12.9781i | −0.0653452 | + | 0.0377271i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 156.237 | − | 270.610i | 0.451551 | − | 0.782109i | ||||
\(347\) | −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 | \(-0.428772\pi\) | |||||||
\(350\) | 101.932i | 0.291235i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 83.1384 | 0.236189 | ||||||||
\(353\) | 508.081 | − | 293.340i | 1.43932 | − | 0.830993i | 0.441519 | − | 0.897252i | \(-0.354440\pi\) |
0.997802 | + | 0.0662588i | \(0.0211063\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −293.296 | + | 508.004i | −0.826186 | + | 1.43100i | ||||
\(356\) | −232.320 | − | 134.130i | −0.652584 | − | 0.376770i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 175.608 | + | 304.161i | 0.490524 | + | 0.849613i | ||||
\(359\) | − | 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 | ||||||||
\(362\) | −193.849 | + | 111.919i | −0.535494 | + | 0.309168i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 177.885 | − | 308.105i | 0.488694 | − | 0.846443i | ||||
\(365\) | 202.829 | + | 117.104i | 0.555697 | + | 0.320832i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.64617 | − | 13.2436i | −0.0208343 | − | 0.0360860i | 0.855420 | − | 0.517934i | \(-0.173299\pi\) |
−0.876255 | + | 0.481848i | \(0.839966\pi\) | |||||||
\(368\) | 58.7878i | 0.159749i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −496.435 | −1.34172 | ||||||||
\(371\) | 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 | \(0.827321\pi\) | |||||||
\(374\) | 139.762 | + | 80.6918i | 0.373696 | + | 0.215753i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.0000 | − | 41.5692i | −0.0638298 | − | 0.110556i | ||||
\(377\) | 752.337i | 1.99559i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −655.215 | −1.72880 | −0.864400 | − | 0.502804i | \(-0.832302\pi\) | ||||
−0.864400 | + | 0.502804i | \(0.832302\pi\) | |||||||
\(380\) | 244.855 | − | 141.367i | 0.644355 | − | 0.372018i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.4308 | + | 42.3154i | −0.0639549 | + | 0.110773i | ||||
\(383\) | 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 | ||||
\(386\) | − | 77.7817i | − | 0.201507i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 150.277 | 0.387312 | ||||||||
\(389\) | −402.319 | + | 232.279i | −1.03424 | + | 0.597119i | −0.918196 | − | 0.396126i | \(-0.870354\pi\) |
−0.116043 | + | 0.993244i | \(0.537021\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −57.0577 | + | 98.8269i | −0.145928 | + | 0.252754i | ||||
\(392\) | 52.4945 | + | 30.3077i | 0.133914 | + | 0.0773156i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −25.2558 | − | 43.7442i | −0.0641009 | − | 0.111026i | ||||
\(395\) | − | 572.289i | − | 1.44883i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −185.708 | −0.467777 | −0.233889 | − | 0.972263i | \(-0.575145\pi\) | ||||
−0.233889 | + | 0.972263i | \(0.575145\pi\) | |||||||
\(398\) | −459.449 | + | 265.263i | −1.15439 | + | 0.666490i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 17.1769 | − | 29.7513i | 0.0429423 | − | 0.0743782i | ||||
\(401\) | 54.4376 | + | 31.4296i | 0.135755 | + | 0.0783780i | 0.566339 | − | 0.824172i | \(-0.308359\pi\) |
−0.430585 | + | 0.902550i | \(0.641693\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 84.7846 | + | 146.851i | 0.210384 | + | 0.364395i | ||||
\(404\) | − | 58.1785i | − | 0.144006i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −421.261 | −1.03759 | ||||||||
\(407\) | 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 | \(0.0356425\pi\) | |||||||
\(410\) | −238.755 | − | 137.845i | −0.582328 | − | 0.336207i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 96.7077 | + | 167.503i | 0.234727 | + | 0.406560i | ||||
\(413\) | 517.558i | 1.25317i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −599.769 | −1.44523 | ||||||||
\(416\) | −103.840 | + | 59.9518i | −0.249614 | + | 0.144115i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −253.492 | + | 439.061i | −0.606441 | + | 1.05039i | ||||
\(419\) | −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 | \(0.834588\pi\) | |||||||
\(422\) | 434.805i | 1.03034i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −72.8616 | −0.171843 | ||||||||
\(425\) | 57.7515 | − | 33.3428i | 0.135886 | − | 0.0784538i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −54.5500 | + | 94.4833i | −0.127752 | + | 0.221272i | ||||
\(428\) | −307.581 | − | 177.582i | −0.718646 | − | 0.414910i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −37.6077 | − | 65.1384i | −0.0874598 | − | 0.151485i | ||||
\(431\) | 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 | \(0.534295\pi\) | |||||||
\(434\) | −82.2275 | + | 47.4740i | −0.189464 | + | 0.109387i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 61.9423 | − | 107.287i | 0.142069 | − | 0.246072i | ||||
\(437\) | −310.463 | − | 179.246i | −0.710442 | − | 0.410174i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 236.000 | + | 408.764i | 0.537585 | + | 0.931125i | 0.999033 | + | 0.0439580i | \(0.0139968\pi\) |
−0.461448 | + | 0.887167i | \(0.652670\pi\) | |||||||
\(440\) | 240.917i | 0.547538i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −232.750 | −0.526584 | ||||||||
\(443\) | 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 | ||||
\(446\) | 414.689 | + | 239.421i | 0.929796 | + | 0.536818i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −33.5692 | − | 58.1436i | −0.0749313 | − | 0.129785i | ||||
\(449\) | − | 559.115i | − | 1.24524i | −0.782523 | − | 0.622622i | \(-0.786067\pi\) | ||
0.782523 | − | 0.622622i | \(-0.213933\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 494.354 | 1.09613 | ||||||||
\(452\) | 190.198 | − | 109.811i | 0.420792 | − | 0.242945i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −87.6462 | + | 151.808i | −0.193053 | + | 0.334378i | ||||
\(455\) | 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 | \(-0.396600\pi\) | |||||||
\(458\) | 104.733i | 0.228676i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −170.354 | −0.370334 | ||||||||
\(461\) | −4.44669 | + | 2.56730i | −0.00964575 | + | 0.00556897i | −0.504815 | − | 0.863227i | \(-0.668439\pi\) |
0.495169 | + | 0.868796i | \(0.335106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 80.7461 | − | 139.856i | 0.174398 | − | 0.302066i | −0.765555 | − | 0.643370i | \(-0.777536\pi\) |
0.939953 | + | 0.341305i | \(0.110869\pi\) | |||||||
\(464\) | 122.955 | + | 70.9881i | 0.264989 | + | 0.152992i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 193.198 | + | 334.629i | 0.414588 | + | 0.718088i | ||||
\(467\) | − | 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 | ||||||||
\(470\) | 120.458 | − | 69.5467i | 0.256294 | − | 0.147972i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 87.2154 | − | 151.061i | 0.184778 | − | 0.320046i | ||||
\(473\) | 116.803 | + | 67.4363i | 0.246941 | + | 0.142571i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 104.746 | + | 181.426i | 0.220518 | + | 0.381949i | ||||
\(476\) | − | 130.325i | − | 0.273793i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 640.477 | 1.33991 | ||||||||
\(479\) | 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 | ||||
\(482\) | 468.696 | + | 270.602i | 0.972398 | + | 0.561414i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −95.0000 | − | 164.545i | −0.196281 | − | 0.339969i | ||||
\(485\) | 435.469i | 0.897874i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.63071 | 0.0177222 | 0.00886110 | − | 0.999961i | \(-0.497179\pi\) | ||||
0.00886110 | + | 0.999961i | \(0.497179\pi\) | |||||||
\(488\) | 31.8434 | − | 18.3848i | 0.0652528 | − | 0.0376737i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −87.8250 | + | 152.117i | −0.179235 | + | 0.310443i | ||||
\(491\) | −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 | ||||
\(494\) | − | 731.181i | − | 1.48012i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0000 | 0.0645161 | ||||||||
\(497\) | −735.619 | + | 424.710i | −1.48012 | + | 0.854547i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 217.296 | − | 376.368i | 0.435463 | − | 0.754244i | −0.561870 | − | 0.827225i | \(-0.689918\pi\) |
0.997333 | + | 0.0729811i | \(0.0232513\pi\) | |||||||
\(500\) | −164.742 | − | 95.1140i | −0.329485 | − | 0.190228i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −52.2769 | − | 90.5462i | −0.104137 | − | 0.180371i | ||||
\(503\) | 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 | ||||||||
\(506\) | 264.545 | − | 152.735i | 0.522816 | − | 0.301848i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 141.177 | − | 244.526i | 0.277907 | − | 0.481350i | ||||
\(509\) | 603.856 | + | 348.636i | 1.18636 | + | 0.684943i | 0.957477 | − | 0.288511i | \(-0.0931602\pi\) |
0.228880 | + | 0.973455i | \(0.426494\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 169.573 | + | 293.709i | 0.331845 | + | 0.574773i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 226.004 | 0.439696 | ||||||||
\(515\) | −485.385 | + | 280.237i | −0.942496 | + | 0.544150i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −124.708 | + | 216.000i | −0.241214 | + | 0.417795i | ||||
\(518\) | −622.557 | − | 359.433i | −1.20185 | − | 0.693887i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −173.727 | − | 300.904i | −0.334090 | − | 0.578661i | ||||
\(521\) | − | 426.962i | − | 0.819504i | −0.912197 | − | 0.409752i | \(-0.865615\pi\) | ||
0.912197 | − | 0.409752i | \(-0.134385\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 179.762 | 0.343712 | 0.171856 | − | 0.985122i | \(-0.445024\pi\) | ||||
0.171856 | + | 0.985122i | \(0.445024\pi\) | |||||||
\(524\) | −92.1197 | + | 53.1853i | −0.175801 | + | 0.101499i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 183.215 | − | 317.338i | 0.348318 | − | 0.603305i | ||||
\(527\) | 53.7945 | + | 31.0583i | 0.102077 | + | 0.0589341i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −156.500 | − | 271.066i | −0.295841 | − | 0.512412i | ||||
\(530\) | − | 211.137i | − | 0.398371i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 409.415 | 0.769578 | ||||||||
\(533\) | −617.446 | + | 356.482i | −1.15843 | + | 0.668822i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 514.592 | − | 891.300i | 0.961855 | − | 1.66598i | ||||
\(536\) | 51.8726 | + | 29.9487i | 0.0967773 | + | 0.0558744i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.5481 | + | 30.3942i | 0.0326173 | + | 0.0564948i | ||||
\(539\) | − | 314.967i | − | 0.584354i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 708.734 | 1.31005 | 0.655023 | − | 0.755609i | \(-0.272659\pi\) | ||||
0.655023 | + | 0.755609i | \(0.272659\pi\) | |||||||
\(542\) | 120.166 | − | 69.3781i | 0.221709 | − | 0.128004i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −21.9615 | + | 38.0385i | −0.0403704 | + | 0.0699237i | ||||
\(545\) | 310.894 | + | 179.495i | 0.570448 | + | 0.329349i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 98.1154 | + | 169.941i | 0.179370 | + | 0.310678i | 0.941665 | − | 0.336552i | \(-0.109261\pi\) |
−0.762295 | + | 0.647230i | \(0.775927\pi\) | |||||||
\(548\) | 3.26907i | 0.00596545i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −178.508 | −0.324560 | ||||||||
\(551\) | −749.789 | + | 432.891i | −1.36078 | + | 0.785646i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 414.354 | − | 717.682i | 0.749284 | − | 1.29780i | ||||
\(554\) | 1.73340 | + | 1.00078i | 0.00312888 | + | 0.00180646i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.2154 | − | 33.2820i | −0.0345601 | − | 0.0598598i | ||||
\(557\) | 353.610i | 0.634848i | 0.948284 | + | 0.317424i | \(0.102818\pi\) | ||||
−0.948284 | + | 0.317424i | \(0.897182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −194.515 | −0.347970 | ||||||||
\(560\) | 168.487 | − | 97.2761i | 0.300870 | − | 0.173707i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −71.2173 | + | 123.352i | −0.126721 | + | 0.219487i | ||||
\(563\) | −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 | ||||
\(566\) | − | 66.8815i | − | 0.118165i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 286.277 | 0.504009 | ||||||||
\(569\) | 52.0634 | − | 30.0588i | 0.0914999 | − | 0.0528275i | −0.453552 | − | 0.891230i | \(-0.649843\pi\) |
0.545052 | + | 0.838402i | \(0.316510\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.1000 | + | 74.6513i | −0.0754815 | + | 0.130738i | −0.901296 | − | 0.433205i | \(-0.857383\pi\) |
0.825814 | + | 0.563943i | \(0.190716\pi\) | |||||||
\(572\) | 539.566 | + | 311.519i | 0.943297 | + | 0.544613i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −199.608 | − | 345.731i | −0.347749 | − | 0.602318i | ||||
\(575\) | − | 126.224i | − | 0.219520i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 709.123 | 1.22898 | 0.614491 | − | 0.788924i | \(-0.289361\pi\) | ||||
0.614491 | + | 0.788924i | \(0.289361\pi\) | |||||||
\(578\) | 280.113 | − | 161.723i | 0.484625 | − | 0.279798i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −205.708 | + | 356.296i | −0.354668 | + | 0.614304i | ||||
\(581\) | −752.144 | − | 434.251i | −1.29457 | − | 0.747419i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 189.300 | + | 327.877i | 0.324700 | + | 0.562396i | ||||
\(584\) | − | 114.301i | − | 0.195721i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 471.804 | 0.805126 | ||||||||
\(587\) | −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 | ||||
\(590\) | 437.743 | + | 252.731i | 0.741937 | + | 0.428357i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 121.138 | + | 209.818i | 0.204626 | + | 0.354422i | ||||
\(593\) | − | 104.350i | − | 0.175969i | −0.996122 | − | 0.0879847i | \(-0.971957\pi\) | ||
0.996122 | − | 0.0879847i | \(-0.0280427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 377.654 | 0.634712 | ||||||||
\(596\) | 163.301 | − | 94.2818i | 0.273995 | − | 0.158191i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −220.277 | + | 381.531i | −0.368356 | + | 0.638011i | ||||
\(599\) | −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 | \(0.758384\pi\) | |||||||
\(602\) | − | 108.916i | − | 0.180924i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −64.0000 | −0.105960 | ||||||||
\(605\) | 476.814 | − | 275.289i | 0.788123 | − | 0.455023i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −368.865 | + | 638.894i | −0.607686 | + | 1.05254i | 0.383935 | + | 0.923360i | \(0.374569\pi\) |
−0.991621 | + | 0.129183i | \(0.958765\pi\) | |||||||
\(608\) | −119.497 | − | 68.9919i | −0.196542 | − | 0.113473i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 53.2750 | + | 92.2750i | 0.0873361 | + | 0.151270i | ||||
\(611\) | − | 359.711i | − | 0.588724i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −679.415 | −1.10834 | −0.554172 | − | 0.832402i | \(-0.686965\pi\) | ||||
−0.554172 | + | 0.832402i | \(0.686965\pi\) | |||||||
\(614\) | 12.6808 | − | 7.32126i | 0.0206528 | − | 0.0119239i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −174.431 | + | 302.123i | −0.283167 | + | 0.490459i | ||||
\(617\) | 409.326 | + | 236.325i | 0.663414 | + | 0.383022i | 0.793576 | − | 0.608471i | \(-0.208217\pi\) |
−0.130163 | + | 0.991493i | \(0.541550\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −443.177 | − | 767.605i | −0.715956 | − | 1.24007i | −0.962590 | − | 0.270964i | \(-0.912658\pi\) |
0.246633 | − | 0.969109i | \(-0.420676\pi\) | |||||||
\(620\) | 92.7289i | 0.149563i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.4923 | 0.0216917 | ||||||||
\(623\) | 974.850 | − | 562.830i | 1.56477 | − | 0.903419i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 382.975 | − | 663.332i | 0.612760 | − | 1.06133i | ||||
\(626\) | 586.992 | + | 338.900i | 0.937687 | + | 0.541374i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.292342 | + | 0.506351i | 0.000465513 | + | 0.000806291i | ||||
\(629\) | 470.294i | 0.747685i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −729.108 | −1.15548 | −0.577740 | − | 0.816221i | \(-0.696065\pi\) | ||||
−0.577740 | + | 0.816221i | \(0.696065\pi\) | |||||||
\(632\) | −241.878 | + | 139.648i | −0.382718 | + | 0.220962i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 127.040 | − | 220.040i | 0.200379 | − | 0.347067i | ||||
\(635\) | 708.581 | + | 409.099i | 1.11588 | + | 0.644251i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 227.125 | + | 393.392i | 0.356554 | + | 0.617570i | ||||
\(638\) | − | 737.730i | − | 1.15632i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −65.5692 | −0.102452 | ||||||||
\(641\) | 753.611 | − | 435.098i | 1.17568 | − | 0.678780i | 0.220669 | − | 0.975349i | \(-0.429176\pi\) |
0.955011 | + | 0.296569i | \(0.0958425\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 309.061 | − | 535.310i | 0.480656 | − | 0.832520i | −0.519098 | − | 0.854715i | \(-0.673732\pi\) |
0.999754 | + | 0.0221949i | \(0.00706543\pi\) | |||||||
\(644\) | −213.633 | − | 123.341i | −0.331729 | − | 0.191524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −133.923 | − | 231.962i | −0.207311 | − | 0.359074i | ||||
\(647\) | 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 | ||||||||
\(650\) | 222.955 | − | 128.723i | 0.343008 | − | 0.198036i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28.7846 | − | 49.8564i | 0.0441482 | − | 0.0764669i | ||||
\(653\) | −163.513 | − | 94.4042i | −0.250403 | − | 0.144570i | 0.369546 | − | 0.929212i | \(-0.379513\pi\) |
−0.619949 | + | 0.784642i | \(0.712847\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −154.119 | − | 266.942i | −0.235296 | − | 0.407545i | ||||
\(656\) | 134.546i | 0.205101i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 201.415 | 0.306102 | ||||||||
\(659\) | −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 | \(0.0194560\pi\) | |||||||
\(662\) | −361.856 | − | 208.917i | −0.546610 | − | 0.315585i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 146.354 | + | 253.492i | 0.220412 | + | 0.381765i | ||||
\(665\) | 1186.39i | 1.78405i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 521.654 | 0.782090 | ||||||||
\(668\) | 97.1129 | − | 56.0682i | 0.145379 | − | 0.0839344i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −86.7846 | + | 150.315i | −0.129529 | + | 0.224351i | ||||
\(671\) | −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 | \(0.739408\pi\) | |||||||
\(674\) | 691.920i | 1.02659i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −560.554 | −0.829222 | ||||||||
\(677\) | −600.728 | + | 346.830i | −0.887338 | + | 0.512305i | −0.873071 | − | 0.487593i | \(-0.837875\pi\) |
−0.0142672 | + | 0.999898i | \(0.504542\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −315.292 | + | 546.102i | −0.464348 | + | 0.804274i | ||||
\(680\) | −110.227 | − | 63.6396i | −0.162099 | − | 0.0935877i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −83.1384 | − | 144.000i | −0.121904 | − | 0.211144i | ||||
\(683\) | 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 | ||||||||
\(686\) | 283.368 | − | 163.603i | 0.413073 | − | 0.238488i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.3538 | + | 31.7898i | −0.0266771 | + | 0.0462061i | ||||
\(689\) | −472.869 | − | 273.011i | −0.686313 | − | 0.396243i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −337.888 | − | 585.240i | −0.488985 | − | 0.846946i | 0.510935 | − | 0.859619i | \(-0.329299\pi\) |
−0.999920 | + | 0.0126731i | \(0.995966\pi\) | |||||||
\(692\) | − | 441.904i | − | 0.638589i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −942.831 | −1.35855 | ||||||||
\(695\) | 96.4439 | − | 55.6819i | 0.138768 | − | 0.0801179i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −130.587 | + | 226.183i | −0.187355 | + | 0.324509i | ||||
\(698\) | −627.031 | − | 362.017i | −0.898326 | − | 0.518649i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 72.0770 | + | 124.841i | 0.102967 | + | 0.178344i | ||||
\(701\) | − | 797.260i | − | 1.13732i | −0.822573 | − | 0.568659i | \(-0.807462\pi\) | ||
0.822573 | − | 0.568659i | \(-0.192538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1477.42 | −2.10160 | ||||||||
\(704\) | 101.823 | − | 58.7878i | 0.144635 | − | 0.0835053i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 414.846 | − | 718.535i | 0.587601 | − | 1.01775i | ||||
\(707\) | 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 | \(0.872379\pi\) | |||||||
\(710\) | 829.567i | 1.16840i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −379.377 | −0.532833 | ||||||||
\(713\) | 101.823 | − | 58.7878i | 0.142810 | − | 0.0824513i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −902.711 | + | 1563.54i | −1.26253 | + | 2.18677i | ||||
\(716\) | 430.149 | + | 248.347i | 0.600767 | + | 0.346853i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −378.000 | − | 654.715i | −0.526462 | − | 0.911860i | ||||
\(719\) | − | 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 | ||||||||
\(722\) | 286.571 | − | 165.452i | 0.396913 | − | 0.229158i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −158.277 | + | 274.144i | −0.218614 | + | 0.378651i | ||||
\(725\) | −263.998 | − | 152.420i | −0.364136 | − | 0.210234i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −355.888 | − | 616.417i | −0.489530 | − | 0.847891i | 0.510397 | − | 0.859939i | \(-0.329498\pi\) |
−0.999927 | + | 0.0120478i | \(0.996165\pi\) | |||||||
\(728\) | − | 503.134i | − | 0.691118i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 331.219 | 0.453725 | ||||||||
\(731\) | −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 | \(0.851058\pi\) | |||||||
\(734\) | −18.7292 | − | 10.8133i | −0.0255166 | − | 0.0147320i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.5692 | + | 72.0000i | 0.0564799 | + | 0.0978261i | ||||
\(737\) | − | 311.236i | − | 0.422301i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 741.892 | 1.00391 | 0.501957 | − | 0.864893i | \(-0.332614\pi\) | ||||
0.501957 | + | 0.864893i | \(0.332614\pi\) | |||||||
\(740\) | −608.006 | + | 351.032i | −0.821629 | + | 0.474368i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 152.869 | − | 264.777i | 0.206023 | − | 0.356842i | ||||
\(743\) | 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 | ||||
\(746\) | 923.460i | 1.23788i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 228.231 | 0.305121 | ||||||||
\(749\) | 1290.65 | − | 745.160i | 1.72317 | − | 0.994873i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 516.665 | − | 894.891i | 0.687970 | − | 1.19160i | −0.284524 | − | 0.958669i | \(-0.591835\pi\) |
0.972494 | − | 0.232930i | \(-0.0748312\pi\) | |||||||
\(752\) | −58.7878 | − | 33.9411i | −0.0781752 | − | 0.0451345i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 531.983 | + | 921.421i | 0.705547 | + | 1.22204i | ||||
\(755\) | − | 185.458i | − | 0.245639i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 473.877 | 0.625993 | 0.312997 | − | 0.949754i | \(-0.398667\pi\) | ||||
0.312997 | + | 0.949754i | \(0.398667\pi\) | |||||||
\(758\) | −802.472 | + | 463.307i | −1.05867 | + | 0.611223i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 199.923 | − | 346.277i | 0.263057 | − | 0.455627i | ||||
\(761\) | −814.458 | − | 470.227i | −1.07025 | − | 0.617907i | −0.141998 | − | 0.989867i | \(-0.545353\pi\) |
−0.928249 | + | 0.371960i | \(0.878686\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 259.919 | + | 450.193i | 0.340654 | + | 0.590031i | ||||
\(764\) | 69.1007i | 0.0904459i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 423.615 | 0.553023 | ||||||||
\(767\) | 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 | \(0.946544\pi\) | |||||||
\(770\) | −875.485 | − | 505.462i | −1.13699 | − | 0.656444i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −55.0000 | − | 95.2628i | −0.0712435 | − | 0.123397i | ||||
\(773\) | − | 1042.20i | − | 1.34825i | −0.738618 | − | 0.674124i | \(-0.764521\pi\) | ||
0.738618 | − | 0.674124i | \(-0.235479\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −68.7077 | −0.0886550 | ||||||||
\(776\) | 184.051 | − | 106.262i | 0.237179 | − | 0.136935i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −328.492 | + | 568.965i | −0.422227 | + | 0.731318i | ||||
\(779\) | −710.550 | − | 410.236i | −0.912131 | − | 0.526619i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −743.769 | − | 1288.25i | −0.952329 | − | 1.64948i | ||||
\(782\) | 161.384i | 0.206373i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 85.7231 | 0.109341 | ||||||||
\(785\) | −1.46729 | + | 0.847142i | −0.00186916 | + | 0.00107916i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 72.3501 | − | 125.314i | 0.0919315 | − | 0.159230i | −0.816392 | − | 0.577498i | \(-0.804029\pi\) |
0.908324 | + | 0.418268i | \(0.137363\pi\) | |||||||
\(788\) | −61.8637 | − | 35.7170i | −0.0785072 | − | 0.0453262i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −404.669 | − | 700.908i | −0.512239 | − | 0.887225i | ||||
\(791\) | 921.567i | 1.16507i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 275.550 | 0.347478 | ||||||||
\(794\) | −227.445 | + | 131.315i | −0.286454 | + | 0.165384i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −375.138 | + | 649.759i | −0.471279 | + | 0.816280i | ||||
\(797\) | 134.866 | + | 77.8647i | 0.169217 | + | 0.0976972i | 0.582216 | − | 0.813034i | \(-0.302186\pi\) |
−0.413000 | + | 0.910731i | \(0.635519\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −65.8846 | − | 114.115i | −0.0824588 | − | 0.142823i | ||||
\(800\) | − | 48.5837i | − | 0.0607296i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 88.8963 | 0.110843 | ||||||||
\(803\) | −514.355 | + | 296.963i | −0.640542 | + | 0.369817i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 357.415 | − | 619.061i | 0.443994 | − | 0.769020i | ||||
\(806\) | 207.679 | + | 119.904i | 0.257666 | + | 0.148764i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −41.1384 | − | 71.2539i | −0.0509139 | − | 0.0881855i | ||||
\(809\) | − | 1216.92i | − | 1.50422i | −0.659035 | − | 0.752112i | \(-0.729035\pi\) | ||
0.659035 | − | 0.752112i | \(-0.270965\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1243.31 | 1.53305 | 0.766527 | − | 0.642212i | \(-0.221983\pi\) | ||||
0.766527 | + | 0.642212i | \(0.221983\pi\) | |||||||
\(812\) | −515.938 | + | 297.877i | −0.635391 | + | 0.366843i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 629.454 | − | 1090.25i | 0.773285 | − | 1.33937i | ||||
\(815\) | 144.473 | + | 83.4114i | 0.177267 | + | 0.102345i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −111.923 | − | 193.856i | −0.136993 | − | 0.237278i | ||||
\(818\) | − | 462.845i | − | 0.565825i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −389.885 | −0.475469 | ||||||||
\(821\) | 11.5055 | − | 6.64270i | 0.0140140 | − | 0.00809098i | −0.492977 | − | 0.870043i | \(-0.664091\pi\) |
0.506991 | + | 0.861952i | \(0.330758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 107.100 | − | 185.503i | 0.130134 | − | 0.225398i | −0.793594 | − | 0.608447i | \(-0.791793\pi\) |
0.923728 | + | 0.383049i | \(0.125126\pi\) | |||||||
\(824\) | 236.884 | + | 136.765i | 0.287481 | + | 0.165977i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 365.969 | + | 633.877i | 0.443062 | + | 0.767406i | ||||
\(827\) | 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 | \(0.569361\pi\) | |||||||
\(830\) | −734.564 | + | 424.101i | −0.885017 | + | 0.510965i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −84.7846 | + | 146.851i | −0.101905 | + | 0.176504i | ||||
\(833\) | 144.107 | + | 83.2004i | 0.172998 | + | 0.0998804i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 162.473 | + | 281.412i | 0.194578 | + | 0.337020i | ||||
\(836\) | 716.984i | 0.857637i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −919.061 | −1.09673 | ||||||||
\(839\) | −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 | ||||
\(842\) | −4.06508 | − | 2.34698i | −0.00482789 | − | 0.00278738i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 307.454 | + | 532.526i | 0.364282 | + | 0.630954i | ||||
\(845\) | − | 1624.36i | − | 1.92232i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 797.269 | 0.941286 | ||||||||
\(848\) | −89.2368 | + | 51.5209i | −0.105232 | + | 0.0607558i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 47.1539 | − | 81.6730i | 0.0554752 | − | 0.0960858i | ||||
\(851\) | 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 | \(0.823474\pi\) | |||||||
\(854\) | 154.291i | 0.180668i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −502.277 | −0.586772 | ||||||||
\(857\) | −1081.16 | + | 624.211i | −1.26157 | + | 0.728367i | −0.973378 | − | 0.229206i | \(-0.926387\pi\) |
−0.288191 | + | 0.957573i | \(0.593054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 223.369 | − | 386.887i | 0.260034 | − | 0.450392i | −0.706217 | − | 0.707996i | \(-0.749600\pi\) |
0.966251 | + | 0.257604i | \(0.0829329\pi\) | |||||||
\(860\) | −92.1197 | − | 53.1853i | −0.107116 | − | 0.0618434i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 568.161 | + | 984.084i | 0.659120 | + | 1.14163i | ||||
\(863\) | 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 | ||||||||
\(866\) | −114.052 | + | 65.8479i | −0.131700 | + | 0.0760368i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −67.1384 | + | 116.287i | −0.0773484 | + | 0.133971i | ||||
\(869\) | 1256.83 | + | 725.633i | 1.44630 | + | 0.835021i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 224.435 | + | 388.732i | 0.257675 | + | 0.446305i | ||||
\(872\) | − | 175.199i | − | 0.200917i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −506.985 | −0.580074 | ||||||||
\(875\) | 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 | \(0.0182141\pi\) | |||||||
\(878\) | 578.080 | + | 333.754i | 0.658405 | + | 0.380130i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 170.354 | + | 295.061i | 0.193584 | + | 0.335297i | ||||
\(881\) | − | 558.506i | − | 0.633945i | −0.948435 | − | 0.316972i | \(-0.897334\pi\) | ||
0.948435 | − | 0.316972i | \(-0.102666\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 313.338 | 0.354857 | 0.177428 | − | 0.984134i | \(-0.443222\pi\) | ||||
0.177428 | + | 0.984134i | \(0.443222\pi\) | |||||||
\(884\) | −285.059 | + | 164.579i | −0.322465 | + | 0.186175i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 402.831 | − | 697.723i | 0.454662 | − | 0.787498i | ||||
\(887\) | 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 | ||||
\(890\) | − | 1099.35i | − | 1.23522i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 677.184 | 0.759175 | ||||||||
\(893\) | 358.492 | − | 206.976i | 0.401447 | − | 0.231776i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −719.654 | + | 1246.48i | −0.804082 | + | 1.39271i | ||||
\(896\) | −82.2275 | − | 47.4740i | −0.0917717 | − | 0.0529844i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −395.354 | − | 684.773i | −0.440260 | − | 0.762553i | ||||
\(899\) | − | 283.952i | − | 0.315854i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −200.019 | −0.221997 | ||||||||
\(902\) | 605.457 | − | 349.561i | 0.671239 | − | 0.387540i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 155.296 | − | 268.981i | 0.171788 | − | 0.297545i | ||||
\(905\) | −794.407 | − | 458.651i | −0.877798 | − | 0.506797i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −543.254 | − | 940.943i | −0.598957 | − | 1.03742i | −0.992975 | − | 0.118321i | \(-0.962249\pi\) |
0.394019 | − | 0.919103i | \(-0.371085\pi\) | |||||||
\(908\) | 247.901i | 0.273019i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1457.97 | 1.60216 | ||||||||
\(911\) | −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 | ||||
\(914\) | −740.109 | − | 427.302i | −0.809747 | − | 0.467508i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 74.0577 | + | 128.272i | 0.0808490 | + | 0.140035i | ||||
\(917\) | − | 446.347i | − | 0.486747i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1540.01 | 1.67574 | 0.837871 | − | 0.545868i | \(-0.183800\pi\) | ||||
0.837871 | + | 0.545868i | \(0.183800\pi\) | |||||||
\(920\) | −208.640 | + | 120.458i | −0.226783 | + | 0.130933i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.63071 | + | 6.28857i | −0.00393786 | + | 0.00682057i | ||||
\(923\) | 1857.93 | + | 1072.68i | 2.01292 | + | 1.16216i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −260.098 | − | 450.503i | −0.281187 | − | 0.487030i | ||||
\(926\) | − | 228.385i | − | 0.246636i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 200.785 | 0.216363 | ||||||||
\(929\) | 1370.57 | − | 791.297i | 1.47531 | − | 0.851773i | 0.475702 | − | 0.879607i | \(-0.342194\pi\) |
0.999613 | + | 0.0278334i | \(0.00886078\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −261.373 | + | 452.711i | −0.280744 | + | 0.486264i | ||||
\(932\) | 473.237 | + | 273.223i | 0.507765 | + | 0.293158i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −355.692 | − | 616.077i | −0.380827 | − | 0.659611i | ||||
\(935\) | 661.362i | 0.707339i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1747.40 | −1.86489 | −0.932444 | − | 0.361315i | \(-0.882328\pi\) | ||||
−0.932444 | + | 0.361315i | \(0.882328\pi\) | |||||||
\(938\) | −217.665 | + | 125.669i | −0.232053 | + | 0.133976i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 98.3538 | − | 170.354i | 0.104632 | − | 0.181227i | ||||
\(941\) | −318.332 | − | 183.789i | −0.338292 | − | 0.195313i | 0.321225 | − | 0.947003i | \(-0.395906\pi\) |
−0.659516 | + | 0.751690i | \(0.729239\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 247.177 | + | 428.123i | 0.262118 | + | 0.454001i | ||||
\(944\) | − | 246.682i | − | 0.261316i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 190.739 | 0.201626 | ||||||||
\(947\) | 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 | ||||
\(950\) | 256.575 | + | 148.133i | 0.270079 | + | 0.155930i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −92.1539 | − | 159.615i | −0.0968003 | − | 0.167663i | ||||
\(953\) | 861.754i | 0.904254i | 0.891954 | + | 0.452127i | \(0.149335\pi\) | ||||
−0.891954 | + | 0.452127i | \(0.850665\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −200.238 | −0.209674 | ||||||||
\(956\) | 784.421 | − | 452.885i | 0.820524 | − | 0.473730i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 151.177 | − | 261.846i | 0.157805 | − | 0.273326i | ||||
\(959\) | −11.8797 | − | 6.85875i | −0.0123876 | − | 0.00715198i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 448.500 | + | 776.825i | 0.466701 | + | 0.808350i | ||||
\(962\) | 1815.62i | 1.88733i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 765.377 | 0.793959 | ||||||||
\(965\) | 276.050 | − | 159.378i | 0.286063 | − | 0.165158i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −637.657 | + | 1104.46i | −0.659418 | + | 1.14215i | 0.321348 | + | 0.946961i | \(0.395864\pi\) |
−0.980766 | + | 0.195185i | \(0.937469\pi\) | |||||||
\(968\) | −232.702 | − | 134.350i | −0.240394 | − | 0.138792i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 307.923 | + | 533.338i | 0.317446 | + | 0.549833i | ||||
\(971\) | − | 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 | ||||||||
\(974\) | 10.5704 | − | 6.10283i | 0.0108526 | − | 0.00626574i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.0000 | − | 45.0333i | 0.0266393 | − | 0.0461407i | ||||
\(977\) | 16.0159 | + | 9.24680i | 0.0163930 | + | 0.00946448i | 0.508174 | − | 0.861254i | \(-0.330321\pi\) |
−0.491781 | + | 0.870719i | \(0.663654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 985.650 | + | 1707.20i | 1.00679 | + | 1.74382i | ||||
\(980\) | 248.407i | 0.253476i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1304.55 | −1.32847 | ||||||||
\(983\) | −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 | ||||
\(986\) | 337.535 | + | 194.876i | 0.342327 | + | 0.197643i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −517.023 | − | 895.510i | −0.523303 | − | 0.906387i | ||||
\(989\) | 134.873i | 0.136373i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 608.484 | 0.614010 | 0.307005 | − | 0.951708i | \(-0.400673\pi\) | ||||
0.307005 | + | 0.951708i | \(0.400673\pi\) | |||||||
\(992\) | 39.1918 | − | 22.6274i | 0.0395079 | − | 0.0228099i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −600.631 | + | 1040.32i | −0.604256 | + | 1.04660i | ||||
\(995\) | −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 | \(0.733154\pi\) | |||||||
\(998\) | − | 614.606i | − | 0.615838i | ||||||
\(999\) | 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 | 162.3.d.c.53.4 | 8 | ||
3.2 | odd | 2 | inner | 162.3.d.c.53.1 | 8 | ||
4.3 | odd | 2 | 1296.3.q.o.1025.4 | 8 | |||
9.2 | odd | 6 | inner | 162.3.d.c.107.4 | 8 | ||
9.4 | even | 3 | 162.3.b.b.161.3 | yes | 4 | ||
9.5 | odd | 6 | 162.3.b.b.161.2 | ✓ | 4 | ||
9.7 | even | 3 | inner | 162.3.d.c.107.1 | 8 | ||
12.11 | even | 2 | 1296.3.q.o.1025.1 | 8 | |||
36.7 | odd | 6 | 1296.3.q.o.593.1 | 8 | |||
36.11 | even | 6 | 1296.3.q.o.593.4 | 8 | |||
36.23 | even | 6 | 1296.3.e.d.161.4 | 4 | |||
36.31 | odd | 6 | 1296.3.e.d.161.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.3.b.b.161.2 | ✓ | 4 | 9.5 | odd | 6 | ||
162.3.b.b.161.3 | yes | 4 | 9.4 | even | 3 | ||
162.3.d.c.53.1 | 8 | 3.2 | odd | 2 | inner | ||
162.3.d.c.53.4 | 8 | 1.1 | even | 1 | trivial | ||
162.3.d.c.107.1 | 8 | 9.7 | even | 3 | inner | ||
162.3.d.c.107.4 | 8 | 9.2 | odd | 6 | inner | ||
1296.3.e.d.161.1 | 4 | 36.31 | odd | 6 | |||
1296.3.e.d.161.4 | 4 | 36.23 | even | 6 | |||
1296.3.q.o.593.1 | 8 | 36.7 | odd | 6 | |||
1296.3.q.o.593.4 | 8 | 36.11 | even | 6 | |||
1296.3.q.o.1025.1 | 8 | 12.11 | even | 2 | |||
1296.3.q.o.1025.4 | 8 | 4.3 | odd | 2 |