Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7497,2,Mod(1,7497)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7497, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7497.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7497 = 3^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7497.a (trivial) |
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: | yes |
Analytic conductor: | \(59.8638463954\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.17314349056.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 12x^{6} + 40x^{4} - 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.03016\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7497.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.03016 | −1.43554 | −0.717769 | − | 0.696281i | \(-0.754837\pi\) | ||||
−0.717769 | + | 0.696281i | \(0.754837\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.12154 | 1.06077 | ||||||||
\(5\) | 1.29601 | 0.579594 | 0.289797 | − | 0.957088i | \(-0.406412\pi\) | ||||
0.289797 | + | 0.957088i | \(0.406412\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.246742 | −0.0872364 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.63111 | −0.832029 | ||||||||
\(11\) | 0.899205 | 0.271120 | 0.135560 | − | 0.990769i | \(-0.456717\pi\) | ||||
0.135560 | + | 0.990769i | \(0.456717\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.69747 | −0.470795 | −0.235397 | − | 0.971899i | \(-0.575639\pi\) | ||||
−0.235397 | + | 0.971899i | \(0.575639\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.74215 | −0.935538 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.59063 | 1.74141 | 0.870704 | − | 0.491807i | \(-0.163663\pi\) | ||||
0.870704 | + | 0.491807i | \(0.163663\pi\) | |||||||
\(20\) | 2.74954 | 0.614815 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.82553 | −0.389204 | ||||||||
\(23\) | −2.48530 | −0.518221 | −0.259110 | − | 0.965848i | \(-0.583429\pi\) | ||||
−0.259110 | + | 0.965848i | \(0.583429\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.32035 | −0.664071 | ||||||||
\(26\) | 3.44614 | 0.675844 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.813264 | −0.151019 | −0.0755097 | − | 0.997145i | \(-0.524058\pi\) | ||||
−0.0755097 | + | 0.997145i | \(0.524058\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.78144 | 1.57719 | 0.788597 | − | 0.614910i | \(-0.210808\pi\) | ||||
0.788597 | + | 0.614910i | \(0.210808\pi\) | |||||||
\(32\) | 8.09064 | 1.43024 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.03016 | 0.348169 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.15970 | −1.34145 | −0.670723 | − | 0.741708i | \(-0.734016\pi\) | ||||
−0.670723 | + | 0.741708i | \(0.734016\pi\) | |||||||
\(38\) | −15.4102 | −2.49986 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.319780 | −0.0505617 | ||||||||
\(41\) | −9.01696 | −1.40821 | −0.704106 | − | 0.710095i | \(-0.748652\pi\) | ||||
−0.704106 | + | 0.710095i | \(0.748652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.64367 | −0.555654 | −0.277827 | − | 0.960631i | \(-0.589614\pi\) | ||||
−0.277827 | + | 0.960631i | \(0.589614\pi\) | |||||||
\(44\) | 1.90770 | 0.287596 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.04555 | 0.743926 | ||||||||
\(47\) | −4.49040 | −0.654992 | −0.327496 | − | 0.944853i | \(-0.606205\pi\) | ||||
−0.327496 | + | 0.944853i | \(0.606205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6.74084 | 0.953299 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.60126 | −0.499405 | ||||||||
\(53\) | −7.53911 | −1.03558 | −0.517788 | − | 0.855509i | \(-0.673245\pi\) | ||||
−0.517788 | + | 0.855509i | \(0.673245\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.16538 | 0.157140 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.65105 | 0.216794 | ||||||||
\(59\) | 9.75911 | 1.27053 | 0.635264 | − | 0.772295i | \(-0.280891\pi\) | ||||
0.635264 | + | 0.772295i | \(0.280891\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.44437 | −0.441006 | −0.220503 | − | 0.975386i | \(-0.570770\pi\) | ||||
−0.220503 | + | 0.975386i | \(0.570770\pi\) | |||||||
\(62\) | −17.8277 | −2.26412 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.94097 | −1.11762 | ||||||||
\(65\) | −2.19995 | −0.272870 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.0138 | 1.58989 | 0.794946 | − | 0.606681i | \(-0.207499\pi\) | ||||
0.794946 | + | 0.606681i | \(0.207499\pi\) | |||||||
\(68\) | −2.12154 | −0.257274 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.41924 | 0.761824 | 0.380912 | − | 0.924611i | \(-0.375610\pi\) | ||||
0.380912 | + | 0.924611i | \(0.375610\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.68053 | −0.313732 | −0.156866 | − | 0.987620i | \(-0.550139\pi\) | ||||
−0.156866 | + | 0.987620i | \(0.550139\pi\) | |||||||
\(74\) | 16.5655 | 1.92570 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.1038 | 1.84723 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.62671 | 0.295528 | 0.147764 | − | 0.989023i | \(-0.452792\pi\) | ||||
0.147764 | + | 0.989023i | \(0.452792\pi\) | |||||||
\(80\) | −4.84987 | −0.542232 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 18.3058 | 2.02154 | ||||||||
\(83\) | −4.84987 | −0.532342 | −0.266171 | − | 0.963926i | \(-0.585759\pi\) | ||||
−0.266171 | + | 0.963926i | \(0.585759\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.29601 | −0.140572 | ||||||||
\(86\) | 7.39722 | 0.797663 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.221872 | −0.0236516 | ||||||||
\(89\) | −16.0551 | −1.70184 | −0.850920 | − | 0.525296i | \(-0.823955\pi\) | ||||
−0.850920 | + | 0.525296i | \(0.823955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −5.27266 | −0.549713 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.11622 | 0.940266 | ||||||||
\(95\) | 9.83754 | 1.00931 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.30493 | 0.132495 | 0.0662476 | − | 0.997803i | \(-0.478897\pi\) | ||||
0.0662476 | + | 0.997803i | \(0.478897\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.04426 | −0.704426 | ||||||||
\(101\) | −6.12283 | −0.609244 | −0.304622 | − | 0.952473i | \(-0.598530\pi\) | ||||
−0.304622 | + | 0.952473i | \(0.598530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.85009 | 0.379361 | 0.189680 | − | 0.981846i | \(-0.439255\pi\) | ||||
0.189680 | + | 0.981846i | \(0.439255\pi\) | |||||||
\(104\) | 0.418838 | 0.0410705 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.3056 | 1.48661 | ||||||||
\(107\) | −7.31844 | −0.707501 | −0.353750 | − | 0.935340i | \(-0.615094\pi\) | ||||
−0.353750 | + | 0.935340i | \(0.615094\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.4388 | 1.19142 | 0.595708 | − | 0.803201i | \(-0.296871\pi\) | ||||
0.595708 | + | 0.803201i | \(0.296871\pi\) | |||||||
\(110\) | −2.36590 | −0.225580 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.7970 | −1.95642 | −0.978210 | − | 0.207616i | \(-0.933429\pi\) | ||||
−0.978210 | + | 0.207616i | \(0.933429\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.22098 | −0.300358 | ||||||||
\(116\) | −1.72537 | −0.160197 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −19.8125 | −1.82389 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1914 | −0.926494 | ||||||||
\(122\) | 6.99261 | 0.633082 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.6302 | 1.67304 | ||||||||
\(125\) | −10.7833 | −0.964485 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.208209 | −0.0184755 | −0.00923777 | − | 0.999957i | \(-0.502941\pi\) | ||||
−0.00923777 | + | 0.999957i | \(0.502941\pi\) | |||||||
\(128\) | 1.97029 | 0.174151 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.46624 | 0.391715 | ||||||||
\(131\) | −9.05293 | −0.790959 | −0.395479 | − | 0.918475i | \(-0.629421\pi\) | ||||
−0.395479 | + | 0.918475i | \(0.629421\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −26.4201 | −2.28235 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.246742 | 0.0211579 | ||||||||
\(137\) | −15.9495 | −1.36266 | −0.681330 | − | 0.731976i | \(-0.738598\pi\) | ||||
−0.681330 | + | 0.731976i | \(0.738598\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.27707 | −0.362776 | −0.181388 | − | 0.983412i | \(-0.558059\pi\) | ||||
−0.181388 | + | 0.983412i | \(0.558059\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.0321 | −1.09363 | ||||||||
\(143\) | −1.52638 | −0.127642 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.05400 | −0.0875299 | ||||||||
\(146\) | 5.44189 | 0.450374 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −17.3111 | −1.42297 | ||||||||
\(149\) | −12.6726 | −1.03818 | −0.519090 | − | 0.854720i | \(-0.673729\pi\) | ||||
−0.519090 | + | 0.854720i | \(0.673729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8047 | 1.36754 | 0.683772 | − | 0.729696i | \(-0.260338\pi\) | ||||
0.683772 | + | 0.729696i | \(0.260338\pi\) | |||||||
\(152\) | −1.87293 | −0.151914 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.3809 | 0.914132 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.12654 | 0.169717 | 0.0848583 | − | 0.996393i | \(-0.472956\pi\) | ||||
0.0848583 | + | 0.996393i | \(0.472956\pi\) | |||||||
\(158\) | −5.33264 | −0.424242 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.4856 | 0.828956 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.0507 | −1.02221 | −0.511105 | − | 0.859519i | \(-0.670764\pi\) | ||||
−0.511105 | + | 0.859519i | \(0.670764\pi\) | |||||||
\(164\) | −19.1298 | −1.49379 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.84600 | 0.764198 | ||||||||
\(167\) | −0.212299 | −0.0164282 | −0.00821411 | − | 0.999966i | \(-0.502615\pi\) | ||||
−0.00821411 | + | 0.999966i | \(0.502615\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.1186 | −0.778352 | ||||||||
\(170\) | 2.63111 | 0.201797 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.73018 | −0.589421 | ||||||||
\(173\) | 4.55201 | 0.346083 | 0.173041 | − | 0.984915i | \(-0.444641\pi\) | ||||
0.173041 | + | 0.984915i | \(0.444641\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.36496 | −0.253643 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 32.5944 | 2.44306 | ||||||||
\(179\) | 18.9427 | 1.41584 | 0.707921 | − | 0.706292i | \(-0.249633\pi\) | ||||
0.707921 | + | 0.706292i | \(0.249633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.7424 | 1.61610 | 0.808049 | − | 0.589115i | \(-0.200523\pi\) | ||||
0.808049 | + | 0.589115i | \(0.200523\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.613228 | 0.0452077 | ||||||||
\(185\) | −10.5751 | −0.777494 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.899205 | −0.0657564 | ||||||||
\(188\) | −9.52656 | −0.694796 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −19.9717 | −1.44890 | ||||||||
\(191\) | 15.6956 | 1.13570 | 0.567848 | − | 0.823134i | \(-0.307776\pi\) | ||||
0.567848 | + | 0.823134i | \(0.307776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.12372 | 0.584758 | 0.292379 | − | 0.956302i | \(-0.405553\pi\) | ||||
0.292379 | + | 0.956302i | \(0.405553\pi\) | |||||||
\(194\) | −2.64920 | −0.190202 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.29856 | −0.235013 | −0.117506 | − | 0.993072i | \(-0.537490\pi\) | ||||
−0.117506 | + | 0.993072i | \(0.537490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.07062 | −0.217670 | −0.108835 | − | 0.994060i | \(-0.534712\pi\) | ||||
−0.108835 | + | 0.994060i | \(0.534712\pi\) | |||||||
\(200\) | 0.819271 | 0.0579312 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.4303 | 0.874593 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.6861 | −0.816191 | ||||||||
\(206\) | −7.81629 | −0.544587 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.35221 | 0.440446 | ||||||||
\(209\) | 6.82553 | 0.472132 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5299 | −0.862591 | −0.431295 | − | 0.902211i | \(-0.641943\pi\) | ||||
−0.431295 | + | 0.902211i | \(0.641943\pi\) | |||||||
\(212\) | −15.9945 | −1.09851 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.8576 | 1.01564 | ||||||||
\(215\) | −4.72224 | −0.322054 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −25.2526 | −1.71032 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.47240 | 0.166689 | ||||||||
\(221\) | 1.69747 | 0.114185 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.5532 | −1.24242 | −0.621208 | − | 0.783646i | \(-0.713358\pi\) | ||||
−0.621208 | + | 0.783646i | \(0.713358\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 42.2213 | 2.80852 | ||||||||
\(227\) | −19.3659 | −1.28536 | −0.642680 | − | 0.766135i | \(-0.722178\pi\) | ||||
−0.642680 | + | 0.766135i | \(0.722178\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00665 | 0.463013 | 0.231506 | − | 0.972833i | \(-0.425635\pi\) | ||||
0.231506 | + | 0.972833i | \(0.425635\pi\) | |||||||
\(230\) | 6.53909 | 0.431175 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.200666 | 0.0131744 | ||||||||
\(233\) | 17.8084 | 1.16667 | 0.583335 | − | 0.812232i | \(-0.301747\pi\) | ||||
0.583335 | + | 0.812232i | \(0.301747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.81961 | −0.379629 | ||||||||
\(236\) | 20.7043 | 1.34774 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.49362 | 0.0966145 | 0.0483072 | − | 0.998833i | \(-0.484617\pi\) | ||||
0.0483072 | + | 0.998833i | \(0.484617\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.59112 | 0.424571 | 0.212286 | − | 0.977208i | \(-0.431909\pi\) | ||||
0.212286 | + | 0.977208i | \(0.431909\pi\) | |||||||
\(242\) | 20.6902 | 1.33002 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.30736 | −0.467806 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.8849 | −0.819846 | ||||||||
\(248\) | −2.16675 | −0.137589 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 21.8917 | 1.38456 | ||||||||
\(251\) | −11.8585 | −0.748505 | −0.374252 | − | 0.927327i | \(-0.622101\pi\) | ||||
−0.374252 | + | 0.927327i | \(0.622101\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.23479 | −0.140500 | ||||||||
\(254\) | 0.422697 | 0.0265223 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.8819 | 0.867621 | ||||||||
\(257\) | 9.46528 | 0.590428 | 0.295214 | − | 0.955431i | \(-0.404609\pi\) | ||||
0.295214 | + | 0.955431i | \(0.404609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.66727 | −0.289452 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.3789 | 1.13545 | ||||||||
\(263\) | −6.73902 | −0.415546 | −0.207773 | − | 0.978177i | \(-0.566621\pi\) | ||||
−0.207773 | + | 0.978177i | \(0.566621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.77077 | −0.600214 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 27.6093 | 1.68651 | ||||||||
\(269\) | −11.6263 | −0.708870 | −0.354435 | − | 0.935081i | \(-0.615327\pi\) | ||||
−0.354435 | + | 0.935081i | \(0.615327\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.35905 | −0.568522 | −0.284261 | − | 0.958747i | \(-0.591748\pi\) | ||||
−0.284261 | + | 0.958747i | \(0.591748\pi\) | |||||||
\(272\) | 3.74215 | 0.226901 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 32.3801 | 1.95615 | ||||||||
\(275\) | −2.98568 | −0.180043 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.65363 | 0.219525 | 0.109763 | − | 0.993958i | \(-0.464991\pi\) | ||||
0.109763 | + | 0.993958i | \(0.464991\pi\) | |||||||
\(278\) | 8.68312 | 0.520779 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.32795 | −0.258184 | −0.129092 | − | 0.991633i | \(-0.541206\pi\) | ||||
−0.129092 | + | 0.991633i | \(0.541206\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.272181 | 0.0161795 | 0.00808975 | − | 0.999967i | \(-0.497425\pi\) | ||||
0.00808975 | + | 0.999967i | \(0.497425\pi\) | |||||||
\(284\) | 13.6187 | 0.808119 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.09879 | 0.183235 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 2.13978 | 0.125652 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.68684 | −0.332797 | ||||||||
\(293\) | −6.57339 | −0.384022 | −0.192011 | − | 0.981393i | \(-0.561501\pi\) | ||||
−0.192011 | + | 0.981393i | \(0.561501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.6479 | 0.736390 | ||||||||
\(296\) | 2.01334 | 0.117023 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.7274 | 1.49035 | ||||||||
\(299\) | 4.21873 | 0.243976 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −34.1161 | −1.96316 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −28.4053 | −1.62915 | ||||||||
\(305\) | −4.46394 | −0.255605 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.9092 | −0.965061 | −0.482531 | − | 0.875879i | \(-0.660282\pi\) | ||||
−0.482531 | + | 0.875879i | \(0.660282\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −23.1049 | −1.31227 | ||||||||
\(311\) | 0.228305 | 0.0129460 | 0.00647300 | − | 0.999979i | \(-0.497940\pi\) | ||||
0.00647300 | + | 0.999979i | \(0.497940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.69139 | −0.321697 | −0.160848 | − | 0.986979i | \(-0.551423\pi\) | ||||
−0.160848 | + | 0.986979i | \(0.551423\pi\) | |||||||
\(314\) | −4.31722 | −0.243635 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.57267 | 0.313487 | ||||||||
\(317\) | 15.9750 | 0.897244 | 0.448622 | − | 0.893722i | \(-0.351915\pi\) | ||||
0.448622 | + | 0.893722i | \(0.351915\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.731291 | −0.0409444 | ||||||||
\(320\) | −11.5876 | −0.647766 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.59063 | −0.422354 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.63622 | 0.312641 | ||||||||
\(326\) | 26.4950 | 1.46742 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.22486 | 0.122847 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.5025 | −1.34678 | −0.673391 | − | 0.739287i | \(-0.735163\pi\) | ||||
−0.673391 | + | 0.739287i | \(0.735163\pi\) | |||||||
\(332\) | −10.2892 | −0.564692 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.431001 | 0.0235833 | ||||||||
\(335\) | 16.8661 | 0.921491 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.3059 | 1.75982 | 0.879908 | − | 0.475144i | \(-0.157604\pi\) | ||||
0.879908 | + | 0.475144i | \(0.157604\pi\) | |||||||
\(338\) | 20.5423 | 1.11735 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.74954 | −0.149115 | ||||||||
\(341\) | 7.89632 | 0.427610 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.899046 | 0.0484733 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.24130 | −0.496815 | ||||||||
\(347\) | 13.0894 | 0.702676 | 0.351338 | − | 0.936249i | \(-0.385727\pi\) | ||||
0.351338 | + | 0.936249i | \(0.385727\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.14639 | −0.275480 | −0.137740 | − | 0.990468i | \(-0.543984\pi\) | ||||
−0.137740 | + | 0.990468i | \(0.543984\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.27514 | 0.387766 | ||||||||
\(353\) | 15.2434 | 0.811325 | 0.405663 | − | 0.914023i | \(-0.367041\pi\) | ||||
0.405663 | + | 0.914023i | \(0.367041\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.31941 | 0.441548 | ||||||||
\(356\) | −34.0616 | −1.80526 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.4566 | −2.03250 | ||||||||
\(359\) | 28.5952 | 1.50920 | 0.754600 | − | 0.656186i | \(-0.227831\pi\) | ||||
0.754600 | + | 0.656186i | \(0.227831\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.6176 | 2.03251 | ||||||||
\(362\) | −44.1405 | −2.31997 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.47399 | −0.181837 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.6481 | 1.59982 | 0.799909 | − | 0.600121i | \(-0.204881\pi\) | ||||
0.799909 | + | 0.600121i | \(0.204881\pi\) | |||||||
\(368\) | 9.30037 | 0.484815 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 21.4690 | 1.11612 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.20821 | −0.373227 | −0.186613 | − | 0.982433i | \(-0.559751\pi\) | ||||
−0.186613 | + | 0.982433i | \(0.559751\pi\) | |||||||
\(374\) | 1.82553 | 0.0943958 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.10797 | 0.0571392 | ||||||||
\(377\) | 1.38050 | 0.0710991 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.3257 | −1.04406 | −0.522030 | − | 0.852927i | \(-0.674825\pi\) | ||||
−0.522030 | + | 0.852927i | \(0.674825\pi\) | |||||||
\(380\) | 20.8707 | 1.07064 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −31.8646 | −1.63033 | ||||||||
\(383\) | 18.7674 | 0.958969 | 0.479484 | − | 0.877550i | \(-0.340824\pi\) | ||||
0.479484 | + | 0.877550i | \(0.340824\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.4924 | −0.839443 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.76845 | 0.140547 | ||||||||
\(389\) | −27.3544 | −1.38692 | −0.693461 | − | 0.720494i | \(-0.743915\pi\) | ||||
−0.693461 | + | 0.720494i | \(0.743915\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.48530 | 0.125687 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.69660 | 0.337370 | ||||||||
\(395\) | 3.40425 | 0.171286 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.2555 | −1.76942 | −0.884712 | − | 0.466138i | \(-0.845645\pi\) | ||||
−0.884712 | + | 0.466138i | \(0.845645\pi\) | |||||||
\(398\) | 6.23384 | 0.312474 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.4253 | 0.621264 | ||||||||
\(401\) | 18.2693 | 0.912326 | 0.456163 | − | 0.889896i | \(-0.349223\pi\) | ||||
0.456163 | + | 0.889896i | \(0.349223\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.9063 | −0.742535 | ||||||||
\(404\) | −12.9898 | −0.646267 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.33724 | −0.363694 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.25352 | 0.0619827 | 0.0309914 | − | 0.999520i | \(-0.490134\pi\) | ||||
0.0309914 | + | 0.999520i | \(0.490134\pi\) | |||||||
\(410\) | 23.7246 | 1.17167 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.16812 | 0.402414 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.28549 | −0.308542 | ||||||||
\(416\) | −13.7337 | −0.673348 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.8569 | −0.677763 | ||||||||
\(419\) | 27.2209 | 1.32983 | 0.664914 | − | 0.746920i | \(-0.268468\pi\) | ||||
0.664914 | + | 0.746920i | \(0.268468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.8065 | −0.819099 | −0.409550 | − | 0.912288i | \(-0.634314\pi\) | ||||
−0.409550 | + | 0.912288i | \(0.634314\pi\) | |||||||
\(422\) | 25.4376 | 1.23828 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.86022 | 0.0903400 | ||||||||
\(425\) | 3.32035 | 0.161061 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −15.5264 | −0.750495 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.58688 | 0.462320 | ||||||||
\(431\) | −29.4400 | −1.41807 | −0.709036 | − | 0.705172i | \(-0.750870\pi\) | ||||
−0.709036 | + | 0.705172i | \(0.750870\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.2507 | −0.877072 | −0.438536 | − | 0.898714i | \(-0.644503\pi\) | ||||
−0.438536 | + | 0.898714i | \(0.644503\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.3893 | 1.26382 | ||||||||
\(437\) | −18.8650 | −0.902434 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.8955 | −0.520011 | −0.260006 | − | 0.965607i | \(-0.583724\pi\) | ||||
−0.260006 | + | 0.965607i | \(0.583724\pi\) | |||||||
\(440\) | −0.287548 | −0.0137083 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.44614 | −0.163916 | ||||||||
\(443\) | 22.7204 | 1.07948 | 0.539739 | − | 0.841833i | \(-0.318523\pi\) | ||||
0.539739 | + | 0.841833i | \(0.318523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.8076 | −0.986376 | ||||||||
\(446\) | 37.6660 | 1.78353 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.5993 | −0.500211 | −0.250106 | − | 0.968219i | \(-0.580465\pi\) | ||||
−0.250106 | + | 0.968219i | \(0.580465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.10809 | −0.381795 | ||||||||
\(452\) | −44.1217 | −2.07531 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 39.3158 | 1.84518 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.49079 | −0.443961 | −0.221980 | − | 0.975051i | \(-0.571252\pi\) | ||||
−0.221980 | + | 0.975051i | \(0.571252\pi\) | |||||||
\(458\) | −14.2246 | −0.664672 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.83342 | −0.318610 | ||||||||
\(461\) | 0.940577 | 0.0438071 | 0.0219035 | − | 0.999760i | \(-0.493027\pi\) | ||||
0.0219035 | + | 0.999760i | \(0.493027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.2466 | 0.662093 | 0.331047 | − | 0.943614i | \(-0.392598\pi\) | ||||
0.331047 | + | 0.943614i | \(0.392598\pi\) | |||||||
\(464\) | 3.04336 | 0.141284 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −36.1539 | −1.67480 | ||||||||
\(467\) | −20.1097 | −0.930567 | −0.465284 | − | 0.885162i | \(-0.654048\pi\) | ||||
−0.465284 | + | 0.885162i | \(0.654048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 11.8147 | 0.544973 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.40798 | −0.110836 | ||||||||
\(473\) | −3.27640 | −0.150649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.2036 | −1.15642 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.03229 | −0.138694 | ||||||||
\(479\) | −42.3684 | −1.93586 | −0.967931 | − | 0.251215i | \(-0.919170\pi\) | ||||
−0.967931 | + | 0.251215i | \(0.919170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.8509 | 0.631546 | ||||||||
\(482\) | −13.3810 | −0.609488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.6215 | −0.982796 | ||||||||
\(485\) | 1.69120 | 0.0767934 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0442 | 1.45206 | 0.726031 | − | 0.687662i | \(-0.241363\pi\) | ||||
0.726031 | + | 0.687662i | \(0.241363\pi\) | |||||||
\(488\) | 0.849871 | 0.0384718 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.0163 | 1.12897 | 0.564486 | − | 0.825443i | \(-0.309075\pi\) | ||||
0.564486 | + | 0.825443i | \(0.309075\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.813264 | 0.0366276 | ||||||||
\(494\) | 26.1584 | 1.17692 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −32.8615 | −1.47552 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.2718 | 0.817960 | 0.408980 | − | 0.912543i | \(-0.365885\pi\) | ||||
0.408980 | + | 0.912543i | \(0.365885\pi\) | |||||||
\(500\) | −22.8771 | −1.02310 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.0747 | 1.07451 | ||||||||
\(503\) | −26.0511 | −1.16156 | −0.580780 | − | 0.814060i | \(-0.697252\pi\) | ||||
−0.580780 | + | 0.814060i | \(0.697252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.93525 | −0.353114 | ||||||||
\(506\) | 4.53698 | 0.201693 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.441723 | −0.0195983 | ||||||||
\(509\) | 31.2265 | 1.38409 | 0.692044 | − | 0.721855i | \(-0.256710\pi\) | ||||
0.692044 | + | 0.721855i | \(0.256710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −32.1231 | −1.41965 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.2160 | −0.847582 | ||||||||
\(515\) | 4.98976 | 0.219875 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.03779 | −0.177582 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.542819 | 0.0238042 | ||||||||
\(521\) | 40.5471 | 1.77640 | 0.888201 | − | 0.459454i | \(-0.151955\pi\) | ||||
0.888201 | + | 0.459454i | \(0.151955\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.72888 | 0.425414 | 0.212707 | − | 0.977116i | \(-0.431772\pi\) | ||||
0.212707 | + | 0.977116i | \(0.431772\pi\) | |||||||
\(524\) | −19.2061 | −0.839024 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.6813 | 0.596532 | ||||||||
\(527\) | −8.78144 | −0.382526 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8233 | −0.731447 | ||||||||
\(530\) | 19.8362 | 0.861630 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.3061 | 0.662979 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.48479 | −0.410063 | ||||||||
\(536\) | −3.21106 | −0.138696 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 23.6033 | 1.01761 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.32331 | 0.400841 | 0.200420 | − | 0.979710i | \(-0.435769\pi\) | ||||
0.200420 | + | 0.979710i | \(0.435769\pi\) | |||||||
\(542\) | 19.0003 | 0.816134 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.09064 | −0.346883 | ||||||||
\(545\) | 16.1208 | 0.690538 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.7711 | 1.10189 | 0.550946 | − | 0.834541i | \(-0.314267\pi\) | ||||
0.550946 | + | 0.834541i | \(0.314267\pi\) | |||||||
\(548\) | −33.8375 | −1.44547 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.06140 | 0.258459 | ||||||||
\(551\) | −6.17318 | −0.262986 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7.41745 | −0.315137 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.07396 | −0.384822 | ||||||||
\(557\) | 7.68283 | 0.325532 | 0.162766 | − | 0.986665i | \(-0.447958\pi\) | ||||
0.162766 | + | 0.986665i | \(0.447958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.18503 | 0.261599 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.78641 | 0.370632 | ||||||||
\(563\) | −12.7339 | −0.536669 | −0.268334 | − | 0.963326i | \(-0.586473\pi\) | ||||
−0.268334 | + | 0.963326i | \(0.586473\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.9532 | −1.13393 | ||||||||
\(566\) | −0.552571 | −0.0232263 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.58390 | −0.0664588 | ||||||||
\(569\) | 15.1722 | 0.636050 | 0.318025 | − | 0.948082i | \(-0.396980\pi\) | ||||
0.318025 | + | 0.948082i | \(0.396980\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.7696 | −1.53876 | −0.769380 | − | 0.638792i | \(-0.779434\pi\) | ||||
−0.769380 | + | 0.638792i | \(0.779434\pi\) | |||||||
\(572\) | −3.23827 | −0.135399 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.25208 | 0.344135 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.4329 | −0.517587 | −0.258794 | − | 0.965933i | \(-0.583325\pi\) | ||||
−0.258794 | + | 0.965933i | \(0.583325\pi\) | |||||||
\(578\) | −2.03016 | −0.0844434 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.23610 | −0.0928490 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.77921 | −0.280766 | ||||||||
\(584\) | 0.661399 | 0.0273689 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.3450 | 0.551278 | ||||||||
\(587\) | −11.4461 | −0.472433 | −0.236216 | − | 0.971700i | \(-0.575907\pi\) | ||||
−0.236216 | + | 0.971700i | \(0.575907\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 66.6567 | 2.74654 | ||||||||
\(590\) | −25.6773 | −1.05712 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 30.5348 | 1.25497 | ||||||||
\(593\) | −40.1779 | −1.64991 | −0.824955 | − | 0.565198i | \(-0.808800\pi\) | ||||
−0.824955 | + | 0.565198i | \(0.808800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −26.8854 | −1.10127 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.56469 | −0.350236 | ||||||||
\(599\) | −10.7621 | −0.439726 | −0.219863 | − | 0.975531i | \(-0.570561\pi\) | ||||
−0.219863 | + | 0.975531i | \(0.570561\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.5429 | −0.511634 | −0.255817 | − | 0.966725i | \(-0.582345\pi\) | ||||
−0.255817 | + | 0.966725i | \(0.582345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 35.6517 | 1.45065 | ||||||||
\(605\) | −13.2082 | −0.536990 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.9466 | −1.25609 | −0.628043 | − | 0.778179i | \(-0.716144\pi\) | ||||
−0.628043 | + | 0.778179i | \(0.716144\pi\) | |||||||
\(608\) | 61.4130 | 2.49063 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.06251 | 0.366930 | ||||||||
\(611\) | 7.62234 | 0.308367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.7550 | −1.08063 | −0.540313 | − | 0.841464i | \(-0.681694\pi\) | ||||
−0.540313 | + | 0.841464i | \(0.681694\pi\) | |||||||
\(614\) | 34.3284 | 1.38538 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.6228 | −1.87696 | −0.938482 | − | 0.345328i | \(-0.887768\pi\) | ||||
−0.938482 | + | 0.345328i | \(0.887768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.466775 | 0.0187613 | 0.00938064 | − | 0.999956i | \(-0.497014\pi\) | ||||
0.00938064 | + | 0.999956i | \(0.497014\pi\) | |||||||
\(620\) | 24.1449 | 0.969683 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.463495 | −0.0185845 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.62653 | 0.105061 | ||||||||
\(626\) | 11.5544 | 0.461808 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.51154 | 0.180030 | ||||||||
\(629\) | 8.15970 | 0.325349 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.7761 | −0.588226 | −0.294113 | − | 0.955771i | \(-0.595024\pi\) | ||||
−0.294113 | + | 0.955771i | \(0.595024\pi\) | |||||||
\(632\) | −0.648120 | −0.0257808 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −32.4317 | −1.28803 | ||||||||
\(635\) | −0.269841 | −0.0107083 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.48464 | 0.0587773 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.55352 | 0.100937 | ||||||||
\(641\) | −28.9547 | −1.14364 | −0.571821 | − | 0.820378i | \(-0.693763\pi\) | ||||
−0.571821 | + | 0.820378i | \(0.693763\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.2971 | 1.39198 | 0.695991 | − | 0.718050i | \(-0.254965\pi\) | ||||
0.695991 | + | 0.718050i | \(0.254965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 15.4102 | 0.606305 | ||||||||
\(647\) | −26.4163 | −1.03853 | −0.519265 | − | 0.854613i | \(-0.673794\pi\) | ||||
−0.519265 | + | 0.854613i | \(0.673794\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.77544 | 0.344466 | ||||||||
\(650\) | −11.4424 | −0.448808 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −27.6875 | −1.08433 | ||||||||
\(653\) | −20.4355 | −0.799702 | −0.399851 | − | 0.916580i | \(-0.630938\pi\) | ||||
−0.399851 | + | 0.916580i | \(0.630938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.7327 | −0.458435 | ||||||||
\(656\) | 33.7428 | 1.31744 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.39750 | −0.366075 | −0.183037 | − | 0.983106i | \(-0.558593\pi\) | ||||
−0.183037 | + | 0.983106i | \(0.558593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.12525 | −0.160454 | −0.0802269 | − | 0.996777i | \(-0.525564\pi\) | ||||
−0.0802269 | + | 0.996777i | \(0.525564\pi\) | |||||||
\(662\) | 49.7440 | 1.93336 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.19667 | 0.0464397 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.02121 | 0.0782614 | ||||||||
\(668\) | −0.450401 | −0.0174266 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −34.2407 | −1.32284 | ||||||||
\(671\) | −3.09719 | −0.119566 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.6984 | 1.56881 | 0.784404 | − | 0.620250i | \(-0.212969\pi\) | ||||
0.784404 | + | 0.620250i | \(0.212969\pi\) | |||||||
\(674\) | −65.5861 | −2.52628 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.4670 | −0.825652 | ||||||||
\(677\) | −23.5916 | −0.906700 | −0.453350 | − | 0.891333i | \(-0.649771\pi\) | ||||
−0.453350 | + | 0.891333i | \(0.649771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.319780 | 0.0122630 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.0308 | −0.613850 | ||||||||
\(683\) | −13.2252 | −0.506049 | −0.253024 | − | 0.967460i | \(-0.581425\pi\) | ||||
−0.253024 | + | 0.967460i | \(0.581425\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.6708 | −0.789790 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.6352 | 0.519836 | ||||||||
\(689\) | 12.7975 | 0.487544 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.1181 | −1.48812 | −0.744062 | − | 0.668110i | \(-0.767103\pi\) | ||||
−0.744062 | + | 0.668110i | \(0.767103\pi\) | |||||||
\(692\) | 9.65726 | 0.367114 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −26.5736 | −1.00872 | ||||||||
\(695\) | −5.54313 | −0.210263 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.01696 | 0.341542 | ||||||||
\(698\) | 10.4480 | 0.395462 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.3043 | 1.74889 | 0.874445 | − | 0.485125i | \(-0.161226\pi\) | ||||
0.874445 | + | 0.485125i | \(0.161226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −61.9372 | −2.33601 | ||||||||
\(704\) | −8.03976 | −0.303010 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.9465 | −1.16469 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.5985 | −1.44960 | −0.724798 | − | 0.688962i | \(-0.758067\pi\) | ||||
−0.724798 | + | 0.688962i | \(0.758067\pi\) | |||||||
\(710\) | −16.8897 | −0.633859 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.96147 | 0.148462 | ||||||||
\(713\) | −21.8245 | −0.817335 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.97820 | −0.0739806 | ||||||||
\(716\) | 40.1876 | 1.50188 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −58.0528 | −2.16651 | ||||||||
\(719\) | −37.7065 | −1.40622 | −0.703108 | − | 0.711083i | \(-0.748205\pi\) | ||||
−0.703108 | + | 0.711083i | \(0.748205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −78.3998 | −2.91774 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 46.1273 | 1.71431 | ||||||||
\(725\) | 2.70033 | 0.100288 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.8847 | −1.21963 | −0.609813 | − | 0.792546i | \(-0.708755\pi\) | ||||
−0.609813 | + | 0.792546i | \(0.708755\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.05275 | 0.261034 | ||||||||
\(731\) | 3.64367 | 0.134766 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.7674 | 0.656253 | 0.328126 | − | 0.944634i | \(-0.393583\pi\) | ||||
0.328126 | + | 0.944634i | \(0.393583\pi\) | |||||||
\(734\) | −62.2205 | −2.29660 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.1077 | −0.741178 | ||||||||
\(737\) | 11.7021 | 0.431052 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.7705 | −1.46298 | −0.731490 | − | 0.681852i | \(-0.761175\pi\) | ||||
−0.731490 | + | 0.681852i | \(0.761175\pi\) | |||||||
\(740\) | −22.4354 | −0.824742 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.6666 | −1.67534 | −0.837672 | − | 0.546173i | \(-0.816084\pi\) | ||||
−0.837672 | + | 0.546173i | \(0.816084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.4238 | −0.601723 | ||||||||
\(746\) | 14.6338 | 0.535781 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.90770 | −0.0697523 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.8133 | −1.30685 | −0.653424 | − | 0.756993i | \(-0.726668\pi\) | ||||
−0.653424 | + | 0.756993i | \(0.726668\pi\) | |||||||
\(752\) | 16.8038 | 0.612770 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.80262 | −0.102065 | ||||||||
\(755\) | 21.7790 | 0.792620 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.5236 | −0.527869 | −0.263935 | − | 0.964541i | \(-0.585020\pi\) | ||||
−0.263935 | + | 0.964541i | \(0.585020\pi\) | |||||||
\(758\) | 41.2643 | 1.49879 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.42733 | −0.0880486 | ||||||||
\(761\) | −46.2796 | −1.67763 | −0.838817 | − | 0.544414i | \(-0.816752\pi\) | ||||
−0.838817 | + | 0.544414i | \(0.816752\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 33.2989 | 1.20471 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38.1008 | −1.37664 | ||||||||
\(767\) | −16.5658 | −0.598158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.6526 | 0.672630 | 0.336315 | − | 0.941750i | \(-0.390819\pi\) | ||||
0.336315 | + | 0.941750i | \(0.390819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.2348 | 0.620294 | ||||||||
\(773\) | −22.1689 | −0.797361 | −0.398681 | − | 0.917090i | \(-0.630532\pi\) | ||||
−0.398681 | + | 0.917090i | \(0.630532\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.1575 | −1.04737 | ||||||||
\(776\) | −0.321980 | −0.0115584 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 55.5337 | 1.99098 | ||||||||
\(779\) | −68.4444 | −2.45227 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.77221 | 0.206546 | ||||||||
\(782\) | −5.04555 | −0.180428 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.75602 | 0.0983667 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.3764 | 0.833278 | 0.416639 | − | 0.909072i | \(-0.363208\pi\) | ||||
0.416639 | + | 0.909072i | \(0.363208\pi\) | |||||||
\(788\) | −6.99803 | −0.249294 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.91116 | −0.245888 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.84673 | 0.207624 | ||||||||
\(794\) | 71.5742 | 2.54007 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.51444 | −0.230898 | ||||||||
\(797\) | 9.66634 | 0.342399 | 0.171200 | − | 0.985236i | \(-0.445236\pi\) | ||||
0.171200 | + | 0.985236i | \(0.445236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.49040 | 0.158859 | ||||||||
\(800\) | −26.8638 | −0.949779 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −37.0896 | −1.30968 | ||||||||
\(803\) | −2.41034 | −0.0850592 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 30.2621 | 1.06594 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.51076 | 0.0531483 | ||||||||
\(809\) | 53.8682 | 1.89391 | 0.946953 | − | 0.321372i | \(-0.104144\pi\) | ||||
0.946953 | + | 0.321372i | \(0.104144\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.24730 | −0.149143 | −0.0745714 | − | 0.997216i | \(-0.523759\pi\) | ||||
−0.0745714 | + | 0.997216i | \(0.523759\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.8958 | 0.522096 | ||||||||
\(815\) | −16.9138 | −0.592466 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.6577 | −0.967621 | ||||||||
\(818\) | −2.54485 | −0.0889785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.7925 | −0.865790 | ||||||||
\(821\) | −17.2732 | −0.602838 | −0.301419 | − | 0.953492i | \(-0.597460\pi\) | ||||
−0.301419 | + | 0.953492i | \(0.597460\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 54.4791 | 1.89902 | 0.949511 | − | 0.313733i | \(-0.101580\pi\) | ||||
0.949511 | + | 0.313733i | \(0.101580\pi\) | |||||||
\(824\) | −0.949979 | −0.0330941 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.6045 | 1.23809 | 0.619046 | − | 0.785355i | \(-0.287520\pi\) | ||||
0.619046 | + | 0.785355i | \(0.287520\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −52.3490 | −1.81816 | −0.909078 | − | 0.416626i | \(-0.863213\pi\) | ||||
−0.909078 | + | 0.416626i | \(0.863213\pi\) | |||||||
\(830\) | 12.7605 | 0.442924 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.1771 | 0.526170 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.275143 | −0.00952170 | ||||||||
\(836\) | 14.4806 | 0.500823 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −55.2627 | −1.90902 | ||||||||
\(839\) | −21.5916 | −0.745426 | −0.372713 | − | 0.927947i | \(-0.621572\pi\) | ||||
−0.372713 | + | 0.927947i | \(0.621572\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3386 | −0.977193 | ||||||||
\(842\) | 34.1199 | 1.17585 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −26.5826 | −0.915010 | ||||||||
\(845\) | −13.1138 | −0.451128 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 28.2125 | 0.968821 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.74084 | −0.231209 | ||||||||
\(851\) | 20.2793 | 0.695166 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.6350 | 0.603812 | 0.301906 | − | 0.953338i | \(-0.402377\pi\) | ||||
0.301906 | + | 0.953338i | \(0.402377\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.80577 | 0.0617199 | ||||||||
\(857\) | −1.07818 | −0.0368298 | −0.0184149 | − | 0.999830i | \(-0.505862\pi\) | ||||
−0.0184149 | + | 0.999830i | \(0.505862\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.66631 | −0.261571 | −0.130786 | − | 0.991411i | \(-0.541750\pi\) | ||||
−0.130786 | + | 0.991411i | \(0.541750\pi\) | |||||||
\(860\) | −10.0184 | −0.341625 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 59.7677 | 2.03570 | ||||||||
\(863\) | 5.57191 | 0.189670 | 0.0948351 | − | 0.995493i | \(-0.469768\pi\) | ||||
0.0948351 | + | 0.995493i | \(0.469768\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.89946 | 0.200588 | ||||||||
\(866\) | 37.0518 | 1.25907 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.36195 | 0.0801237 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.0906 | −0.748512 | ||||||||
\(872\) | −3.06916 | −0.103935 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 38.2989 | 1.29548 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.3182 | 0.517258 | 0.258629 | − | 0.965977i | \(-0.416729\pi\) | ||||
0.258629 | + | 0.965977i | \(0.416729\pi\) | |||||||
\(878\) | 22.1195 | 0.746496 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.36103 | −0.147010 | ||||||||
\(881\) | 48.8420 | 1.64553 | 0.822765 | − | 0.568381i | \(-0.192430\pi\) | ||||
0.822765 | + | 0.568381i | \(0.192430\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.46902 | −0.0830890 | −0.0415445 | − | 0.999137i | \(-0.513228\pi\) | ||||
−0.0415445 | + | 0.999137i | \(0.513228\pi\) | |||||||
\(884\) | 3.60126 | 0.121123 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −46.1259 | −1.54963 | ||||||||
\(887\) | −54.9820 | −1.84612 | −0.923058 | − | 0.384661i | \(-0.874318\pi\) | ||||
−0.923058 | + | 0.384661i | \(0.874318\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 42.2427 | 1.41598 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −39.3614 | −1.31792 | ||||||||
\(893\) | −34.0850 | −1.14061 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.5499 | 0.820613 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.5182 | 0.718072 | ||||||||
\(899\) | −7.14163 | −0.238187 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.53911 | 0.251164 | ||||||||
\(902\) | 16.4607 | 0.548081 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.13150 | 0.170671 | ||||||||
\(905\) | 28.1784 | 0.936681 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.7779 | 0.357875 | 0.178937 | − | 0.983860i | \(-0.442734\pi\) | ||||
0.178937 | + | 0.983860i | \(0.442734\pi\) | |||||||
\(908\) | −41.0855 | −1.36347 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.6354 | 1.44571 | 0.722853 | − | 0.691002i | \(-0.242830\pi\) | ||||
0.722853 | + | 0.691002i | \(0.242830\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.36103 | −0.144329 | ||||||||
\(914\) | 19.2678 | 0.637322 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.8649 | 0.491149 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.4463 | 0.377579 | 0.188790 | − | 0.982018i | \(-0.439544\pi\) | ||||
0.188790 | + | 0.982018i | \(0.439544\pi\) | |||||||
\(920\) | 0.794750 | 0.0262021 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.90952 | −0.0628867 | ||||||||
\(923\) | −10.8965 | −0.358663 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.0931 | 0.890816 | ||||||||
\(926\) | −28.9227 | −0.950460 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.57983 | −0.215993 | ||||||||
\(929\) | −22.5540 | −0.739971 | −0.369986 | − | 0.929037i | \(-0.620637\pi\) | ||||
−0.369986 | + | 0.929037i | \(0.620637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 37.7813 | 1.23757 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 40.8259 | 1.33586 | ||||||||
\(935\) | −1.16538 | −0.0381120 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.4643 | −1.19124 | −0.595619 | − | 0.803267i | \(-0.703093\pi\) | ||||
−0.595619 | + | 0.803267i | \(0.703093\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.3465 | −0.402699 | ||||||||
\(941\) | 24.2685 | 0.791130 | 0.395565 | − | 0.918438i | \(-0.370549\pi\) | ||||
0.395565 | + | 0.918438i | \(0.370549\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.4098 | 0.729765 | ||||||||
\(944\) | −36.5201 | −1.18863 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.65162 | 0.216263 | ||||||||
\(947\) | −8.01869 | −0.260573 | −0.130286 | − | 0.991476i | \(-0.541590\pi\) | ||||
−0.130286 | + | 0.991476i | \(0.541590\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.55013 | 0.147703 | ||||||||
\(950\) | 51.1672 | 1.66008 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.0907 | 1.03952 | 0.519760 | − | 0.854313i | \(-0.326022\pi\) | ||||
0.519760 | + | 0.854313i | \(0.326022\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.3417 | 0.658242 | ||||||||
\(956\) | 3.16878 | 0.102486 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 86.0146 | 2.77900 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.1138 | 1.48754 | ||||||||
\(962\) | −28.1195 | −0.906608 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.9833 | 0.450372 | ||||||||
\(965\) | 10.5284 | 0.338922 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.7898 | 1.44034 | 0.720172 | − | 0.693796i | \(-0.244063\pi\) | ||||
0.720172 | + | 0.693796i | \(0.244063\pi\) | |||||||
\(968\) | 2.51465 | 0.0808240 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.43340 | −0.110240 | ||||||||
\(971\) | 13.2205 | 0.424267 | 0.212134 | − | 0.977241i | \(-0.431959\pi\) | ||||
0.212134 | + | 0.977241i | \(0.431959\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −65.0548 | −2.08449 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.8894 | 0.412578 | ||||||||
\(977\) | 4.54724 | 0.145479 | 0.0727395 | − | 0.997351i | \(-0.476826\pi\) | ||||
0.0727395 | + | 0.997351i | \(0.476826\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.4368 | −0.461403 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −50.7871 | −1.62068 | ||||||||
\(983\) | 1.59073 | 0.0507365 | 0.0253683 | − | 0.999678i | \(-0.491924\pi\) | ||||
0.0253683 | + | 0.999678i | \(0.491924\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.27498 | −0.136212 | ||||||||
\(986\) | −1.65105 | −0.0525803 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.3358 | −0.869668 | ||||||||
\(989\) | 9.05561 | 0.287952 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.3044 | −1.31208 | −0.656039 | − | 0.754727i | \(-0.727769\pi\) | ||||
−0.656039 | + | 0.754727i | \(0.727769\pi\) | |||||||
\(992\) | 71.0475 | 2.25576 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.97956 | −0.126160 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.1037 | −1.80849 | −0.904245 | − | 0.427013i | \(-0.859566\pi\) | ||||
−0.904245 | + | 0.427013i | \(0.859566\pi\) | |||||||
\(998\) | −37.0947 | −1.17421 | ||||||||
\(999\) | 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 | 7497.2.a.cd.1.2 | ✓ | 8 | |
3.2 | odd | 2 | 7497.2.a.ce.1.7 | yes | 8 | ||
7.6 | odd | 2 | 7497.2.a.ce.1.2 | yes | 8 | ||
21.20 | even | 2 | inner | 7497.2.a.cd.1.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7497.2.a.cd.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
7497.2.a.cd.1.7 | yes | 8 | 21.20 | even | 2 | inner | |
7497.2.a.ce.1.2 | yes | 8 | 7.6 | odd | 2 | ||
7497.2.a.ce.1.7 | yes | 8 | 3.2 | odd | 2 |