Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1225,2,Mod(99,1225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1225.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1225.b (of order \(2\), degree \(1\), 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: | \(9.78167424761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1225.99 |
Dual form | 1225.2.b.h.99.4 |
$q$-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 \(\left(\mathbb{Z}/1225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.41421i | − 1.70711i | −0.521005 | − | 0.853553i | \(-0.674443\pi\) | ||||
0.521005 | − | 0.853553i | \(-0.325557\pi\) | |||||||
\(3\) | 0.414214i | 0.239146i | 0.992825 | + | 0.119573i | \(0.0381526\pi\) | ||||
−0.992825 | + | 0.119573i | \(0.961847\pi\) | |||||||
\(4\) | −3.82843 | −1.91421 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.41421i | 1.56066i | ||||||||
\(9\) | 2.82843 | 0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.828427 | −0.249780 | −0.124890 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124890 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(12\) | − 1.58579i | − 0.457777i | ||||||||
\(13\) | 4.82843i | 1.33916i | 0.742738 | + | 0.669582i | \(0.233527\pi\) | ||||
−0.742738 | + | 0.669582i | \(0.766473\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 4.82843i | 1.17107i | 0.810649 | + | 0.585533i | \(0.199115\pi\) | ||||
−0.810649 | + | 0.585533i | \(0.800885\pi\) | |||||||
\(18\) | − 6.82843i | − 1.60948i | ||||||||
\(19\) | 2.82843 | 0.648886 | 0.324443 | − | 0.945905i | \(-0.394823\pi\) | ||||
0.324443 | + | 0.945905i | \(0.394823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000i | 0.426401i | ||||||||
\(23\) | 0.414214i | 0.0863695i | 0.999067 | + | 0.0431847i | \(0.0137504\pi\) | ||||
−0.999067 | + | 0.0431847i | \(0.986250\pi\) | |||||||
\(24\) | −1.82843 | −0.373226 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 11.6569 | 2.28610 | ||||||||
\(27\) | 2.41421i | 0.464616i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.58579i | 0.280330i | ||||||||
\(33\) | − 0.343146i | − 0.0597340i | ||||||||
\(34\) | 11.6569 | 1.99913 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.8284 | −1.80474 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | − 6.82843i | − 1.10772i | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.82843 | 1.22259 | 0.611297 | − | 0.791401i | \(-0.290648\pi\) | ||||
0.611297 | + | 0.791401i | \(0.290648\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.58579i | 0.546827i | 0.961897 | + | 0.273414i | \(0.0881528\pi\) | ||||
−0.961897 | + | 0.273414i | \(0.911847\pi\) | |||||||
\(44\) | 3.17157 | 0.478133 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.00000i | 0.291730i | 0.989305 | + | 0.145865i | \(0.0465965\pi\) | ||||
−0.989305 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(48\) | 1.24264i | 0.179360i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | − 18.4853i | − 2.56345i | ||||||||
\(53\) | − 1.17157i | − 0.160928i | −0.996758 | − | 0.0804640i | \(-0.974360\pi\) | ||||
0.996758 | − | 0.0804640i | \(-0.0256402\pi\) | |||||||
\(54\) | 5.82843 | 0.793148 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17157i | 0.155179i | ||||||||
\(58\) | − 2.41421i | − 0.317002i | ||||||||
\(59\) | 4.48528 | 0.583934 | 0.291967 | − | 0.956428i | \(-0.405690\pi\) | ||||
0.291967 | + | 0.956428i | \(0.405690\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.48528 | −0.702318 | −0.351159 | − | 0.936316i | \(-0.614212\pi\) | ||||
−0.351159 | + | 0.936316i | \(0.614212\pi\) | |||||||
\(62\) | − 14.4853i | − 1.83963i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 9.82843 | 1.22855 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.828427 | −0.101972 | ||||||||
\(67\) | − 9.58579i | − 1.17109i | −0.810640 | − | 0.585545i | \(-0.800881\pi\) | ||||
0.810640 | − | 0.585545i | \(-0.199119\pi\) | |||||||
\(68\) | − 18.4853i | − 2.24167i | ||||||||
\(69\) | −0.171573 | −0.0206549 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.48528 | 0.532305 | 0.266152 | − | 0.963931i | \(-0.414248\pi\) | ||||
0.266152 | + | 0.963931i | \(0.414248\pi\) | |||||||
\(72\) | 12.4853i | 1.47140i | ||||||||
\(73\) | 0.828427i | 0.0969601i | 0.998824 | + | 0.0484800i | \(0.0154377\pi\) | ||||
−0.998824 | + | 0.0484800i | \(0.984562\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.8284 | −1.24211 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.82843i | 0.546712i | ||||||||
\(79\) | −14.8284 | −1.66833 | −0.834164 | − | 0.551516i | \(-0.814049\pi\) | ||||
−0.834164 | + | 0.551516i | \(0.814049\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | − 18.8995i | − 2.08710i | ||||||||
\(83\) | − 13.7279i | − 1.50684i | −0.657542 | − | 0.753418i | \(-0.728404\pi\) | ||||
0.657542 | − | 0.753418i | \(-0.271596\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.65685 | 0.933493 | ||||||||
\(87\) | 0.414214i | 0.0444084i | ||||||||
\(88\) | − 3.65685i | − 0.389822i | ||||||||
\(89\) | −8.65685 | −0.917625 | −0.458812 | − | 0.888533i | \(-0.651725\pi\) | ||||
−0.458812 | + | 0.888533i | \(0.651725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 1.58579i | − 0.165330i | ||||||||
\(93\) | 2.48528i | 0.257712i | ||||||||
\(94\) | 4.82843 | 0.498014 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.656854 | −0.0670399 | ||||||||
\(97\) | 11.6569i | 1.18357i | 0.806094 | + | 0.591787i | \(0.201577\pi\) | ||||
−0.806094 | + | 0.591787i | \(0.798423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.34315 | −0.235495 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3137 | 1.02625 | 0.513126 | − | 0.858313i | \(-0.328487\pi\) | ||||
0.513126 | + | 0.858313i | \(0.328487\pi\) | |||||||
\(102\) | 4.82843i | 0.478086i | ||||||||
\(103\) | 2.41421i | 0.237880i | 0.992901 | + | 0.118940i | \(0.0379495\pi\) | ||||
−0.992901 | + | 0.118940i | \(0.962050\pi\) | |||||||
\(104\) | −21.3137 | −2.08998 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.82843 | −0.274721 | ||||||||
\(107\) | − 11.2426i | − 1.08687i | −0.839452 | − | 0.543434i | \(-0.817124\pi\) | ||||
0.839452 | − | 0.543434i | \(-0.182876\pi\) | |||||||
\(108\) | − 9.24264i | − 0.889374i | ||||||||
\(109\) | 13.4853 | 1.29166 | 0.645828 | − | 0.763483i | \(-0.276512\pi\) | ||||
0.645828 | + | 0.763483i | \(0.276512\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 4.48528i | − 0.421940i | −0.977493 | − | 0.210970i | \(-0.932338\pi\) | ||||
0.977493 | − | 0.210970i | \(-0.0676622\pi\) | |||||||
\(114\) | 2.82843 | 0.264906 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.82843 | −0.355461 | ||||||||
\(117\) | 13.6569i | 1.26258i | ||||||||
\(118\) | − 10.8284i | − 0.996838i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 13.2426i | 1.19893i | ||||||||
\(123\) | 3.24264i | 0.292379i | ||||||||
\(124\) | −22.9706 | −2.06282 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.31371i | 0.826458i | 0.910627 | + | 0.413229i | \(0.135599\pi\) | ||||
−0.910627 | + | 0.413229i | \(0.864401\pi\) | |||||||
\(128\) | − 20.5563i | − 1.81694i | ||||||||
\(129\) | −1.48528 | −0.130772 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.3137 | 1.68745 | 0.843723 | − | 0.536778i | \(-0.180359\pi\) | ||||
0.843723 | + | 0.536778i | \(0.180359\pi\) | |||||||
\(132\) | 1.31371i | 0.114344i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −23.1421 | −1.99918 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −21.3137 | −1.82764 | ||||||||
\(137\) | 9.65685i | 0.825041i | 0.910948 | + | 0.412520i | \(0.135351\pi\) | ||||
−0.910948 | + | 0.412520i | \(0.864649\pi\) | |||||||
\(138\) | 0.414214i | 0.0352602i | ||||||||
\(139\) | −16.1421 | −1.36916 | −0.684579 | − | 0.728939i | \(-0.740014\pi\) | ||||
−0.684579 | + | 0.728939i | \(0.740014\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.828427 | −0.0697661 | ||||||||
\(142\) | − 10.8284i | − 0.908701i | ||||||||
\(143\) | − 4.00000i | − 0.334497i | ||||||||
\(144\) | 8.48528 | 0.707107 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.00000 | 0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.17157 | 0.177902 | 0.0889511 | − | 0.996036i | \(-0.471649\pi\) | ||||
0.0889511 | + | 0.996036i | \(0.471649\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.6569 | 0.948621 | 0.474311 | − | 0.880358i | \(-0.342697\pi\) | ||||
0.474311 | + | 0.880358i | \(0.342697\pi\) | |||||||
\(152\) | 12.4853i | 1.01269i | ||||||||
\(153\) | 13.6569i | 1.10409i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.65685 | 0.613039 | ||||||||
\(157\) | 17.3137i | 1.38178i | 0.722958 | + | 0.690892i | \(0.242782\pi\) | ||||
−0.722958 | + | 0.690892i | \(0.757218\pi\) | |||||||
\(158\) | 35.7990i | 2.84801i | ||||||||
\(159\) | 0.485281 | 0.0384853 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − 18.0711i | − 1.41980i | ||||||||
\(163\) | 12.3431i | 0.966790i | 0.875402 | + | 0.483395i | \(0.160596\pi\) | ||||
−0.875402 | + | 0.483395i | \(0.839404\pi\) | |||||||
\(164\) | −29.9706 | −2.34031 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −33.1421 | −2.57233 | ||||||||
\(167\) | 22.4142i | 1.73446i | 0.497904 | + | 0.867232i | \(0.334103\pi\) | ||||
−0.497904 | + | 0.867232i | \(0.665897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.3137 | −0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.00000 | 0.611775 | ||||||||
\(172\) | − 13.7279i | − 1.04674i | ||||||||
\(173\) | − 3.31371i | − 0.251937i | −0.992034 | − | 0.125968i | \(-0.959796\pi\) | ||||
0.992034 | − | 0.125968i | \(-0.0402038\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.48528 | −0.187335 | ||||||||
\(177\) | 1.85786i | 0.139646i | ||||||||
\(178\) | 20.8995i | 1.56648i | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.65685 | −0.197482 | −0.0987412 | − | 0.995113i | \(-0.531482\pi\) | ||||
−0.0987412 | + | 0.995113i | \(0.531482\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 2.27208i | − 0.167957i | ||||||||
\(184\) | −1.82843 | −0.134793 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | − 4.00000i | − 0.292509i | ||||||||
\(188\) | − 7.65685i | − 0.558433i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.8284 | −0.928232 | −0.464116 | − | 0.885774i | \(-0.653628\pi\) | ||||
−0.464116 | + | 0.885774i | \(0.653628\pi\) | |||||||
\(192\) | 4.07107i | 0.293804i | ||||||||
\(193\) | − 2.00000i | − 0.143963i | −0.997406 | − | 0.0719816i | \(-0.977068\pi\) | ||||
0.997406 | − | 0.0719816i | \(-0.0229323\pi\) | |||||||
\(194\) | 28.1421 | 2.02049 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3431i | 0.879413i | 0.898142 | + | 0.439706i | \(0.144917\pi\) | ||||
−0.898142 | + | 0.439706i | \(0.855083\pi\) | |||||||
\(198\) | 5.65685i | 0.402015i | ||||||||
\(199\) | −9.65685 | −0.684556 | −0.342278 | − | 0.939599i | \(-0.611199\pi\) | ||||
−0.342278 | + | 0.939599i | \(0.611199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.97056 | 0.280062 | ||||||||
\(202\) | − 24.8995i | − 1.75192i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.65685 | 0.536087 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.82843 | 0.406086 | ||||||||
\(207\) | 1.17157i | 0.0814299i | ||||||||
\(208\) | 14.4853i | 1.00437i | ||||||||
\(209\) | −2.34315 | −0.162079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.4853 | 1.41026 | 0.705132 | − | 0.709076i | \(-0.250888\pi\) | ||||
0.705132 | + | 0.709076i | \(0.250888\pi\) | |||||||
\(212\) | 4.48528i | 0.308050i | ||||||||
\(213\) | 1.85786i | 0.127299i | ||||||||
\(214\) | −27.1421 | −1.85540 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.6569 | −0.725107 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 32.5563i | − 2.20499i | ||||||||
\(219\) | −0.343146 | −0.0231876 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.3137 | −1.56825 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 0.343146i | − 0.0229787i | −0.999934 | − | 0.0114894i | \(-0.996343\pi\) | ||||
0.999934 | − | 0.0114894i | \(-0.00365726\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.8284 | −0.720296 | ||||||||
\(227\) | − 6.97056i | − 0.462652i | −0.972876 | − | 0.231326i | \(-0.925694\pi\) | ||||
0.972876 | − | 0.231326i | \(-0.0743065\pi\) | |||||||
\(228\) | − 4.48528i | − 0.297045i | ||||||||
\(229\) | −11.6569 | −0.770307 | −0.385153 | − | 0.922853i | \(-0.625851\pi\) | ||||
−0.385153 | + | 0.922853i | \(0.625851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.41421i | 0.289807i | ||||||||
\(233\) | − 16.8284i | − 1.10247i | −0.834351 | − | 0.551233i | \(-0.814157\pi\) | ||||
0.834351 | − | 0.551233i | \(-0.185843\pi\) | |||||||
\(234\) | 32.9706 | 2.15535 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −17.1716 | −1.11777 | ||||||||
\(237\) | − 6.14214i | − 0.398975i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3137 | 1.37867 | 0.689335 | − | 0.724443i | \(-0.257903\pi\) | ||||
0.689335 | + | 0.724443i | \(0.257903\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.6569 | −1.78153 | −0.890767 | − | 0.454460i | \(-0.849832\pi\) | ||||
−0.890767 | + | 0.454460i | \(0.849832\pi\) | |||||||
\(242\) | 24.8995i | 1.60060i | ||||||||
\(243\) | 10.3431i | 0.663513i | ||||||||
\(244\) | 21.0000 | 1.34439 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.82843 | 0.499122 | ||||||||
\(247\) | 13.6569i | 0.868965i | ||||||||
\(248\) | 26.4853i | 1.68182i | ||||||||
\(249\) | 5.68629 | 0.360354 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.31371 | 0.587876 | 0.293938 | − | 0.955824i | \(-0.405034\pi\) | ||||
0.293938 | + | 0.955824i | \(0.405034\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 0.343146i | − 0.0215734i | ||||||||
\(254\) | 22.4853 | 1.41085 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.9706 | −1.87316 | ||||||||
\(257\) | 6.34315i | 0.395675i | 0.980235 | + | 0.197837i | \(0.0633918\pi\) | ||||
−0.980235 | + | 0.197837i | \(0.936608\pi\) | |||||||
\(258\) | 3.58579i | 0.223241i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.82843 | 0.175075 | ||||||||
\(262\) | − 46.6274i | − 2.88065i | ||||||||
\(263\) | − 29.0416i | − 1.79078i | −0.445279 | − | 0.895392i | \(-0.646896\pi\) | ||||
0.445279 | − | 0.895392i | \(-0.353104\pi\) | |||||||
\(264\) | 1.51472 | 0.0932245 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3.58579i | − 0.219447i | ||||||||
\(268\) | 36.6985i | 2.24172i | ||||||||
\(269\) | 20.4558 | 1.24721 | 0.623607 | − | 0.781738i | \(-0.285666\pi\) | ||||
0.623607 | + | 0.781738i | \(0.285666\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.4853 | −1.00141 | −0.500705 | − | 0.865618i | \(-0.666926\pi\) | ||||
−0.500705 | + | 0.865618i | \(0.666926\pi\) | |||||||
\(272\) | 14.4853i | 0.878299i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 23.3137 | 1.40843 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.656854 | 0.0395380 | ||||||||
\(277\) | − 16.1421i | − 0.969887i | −0.874546 | − | 0.484943i | \(-0.838840\pi\) | ||||
0.874546 | − | 0.484943i | \(-0.161160\pi\) | |||||||
\(278\) | 38.9706i | 2.33730i | ||||||||
\(279\) | 16.9706 | 1.01600 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.2843 | −1.80661 | −0.903304 | − | 0.429001i | \(-0.858866\pi\) | ||||
−0.903304 | + | 0.429001i | \(0.858866\pi\) | |||||||
\(282\) | 2.00000i | 0.119098i | ||||||||
\(283\) | − 14.0000i | − 0.832214i | −0.909316 | − | 0.416107i | \(-0.863394\pi\) | ||||
0.909316 | − | 0.416107i | \(-0.136606\pi\) | |||||||
\(284\) | −17.1716 | −1.01895 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.65685 | −0.571022 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.48528i | 0.264298i | ||||||||
\(289\) | −6.31371 | −0.371395 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.82843 | −0.283047 | ||||||||
\(292\) | − 3.17157i | − 0.185602i | ||||||||
\(293\) | 16.0000i | 0.934730i | 0.884064 | + | 0.467365i | \(0.154797\pi\) | ||||
−0.884064 | + | 0.467365i | \(0.845203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.00000i | − 0.116052i | ||||||||
\(298\) | − 5.24264i | − 0.303698i | ||||||||
\(299\) | −2.00000 | −0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 28.1421i | − 1.61940i | ||||||||
\(303\) | 4.27208i | 0.245424i | ||||||||
\(304\) | 8.48528 | 0.486664 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 32.9706 | 1.88480 | ||||||||
\(307\) | − 4.75736i | − 0.271517i | −0.990742 | − | 0.135758i | \(-0.956653\pi\) | ||||
0.990742 | − | 0.135758i | \(-0.0433471\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1716 | 0.746891 | 0.373446 | − | 0.927652i | \(-0.378176\pi\) | ||||
0.373446 | + | 0.927652i | \(0.378176\pi\) | |||||||
\(312\) | − 8.82843i | − 0.499811i | ||||||||
\(313\) | 6.34315i | 0.358536i | 0.983800 | + | 0.179268i | \(0.0573729\pi\) | ||||
−0.983800 | + | 0.179268i | \(0.942627\pi\) | |||||||
\(314\) | 41.7990 | 2.35885 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 56.7696 | 3.19354 | ||||||||
\(317\) | 13.7990i | 0.775028i | 0.921864 | + | 0.387514i | \(0.126666\pi\) | ||||
−0.921864 | + | 0.387514i | \(0.873334\pi\) | |||||||
\(318\) | − 1.17157i | − 0.0656985i | ||||||||
\(319\) | −0.828427 | −0.0463830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.65685 | 0.259920 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.6569i | 0.759888i | ||||||||
\(324\) | −28.6569 | −1.59205 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.7990 | 1.65041 | ||||||||
\(327\) | 5.58579i | 0.308895i | ||||||||
\(328\) | 34.5563i | 1.90806i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.9706 | 1.26258 | 0.631288 | − | 0.775548i | \(-0.282527\pi\) | ||||
0.631288 | + | 0.775548i | \(0.282527\pi\) | |||||||
\(332\) | 52.5563i | 2.88440i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 54.1127 | 2.96092 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 9.17157i | − 0.499607i | −0.968296 | − | 0.249804i | \(-0.919634\pi\) | ||||
0.968296 | − | 0.249804i | \(-0.0803661\pi\) | |||||||
\(338\) | 24.8995i | 1.35435i | ||||||||
\(339\) | 1.85786 | 0.100905 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.97056 | −0.269171 | ||||||||
\(342\) | − 19.3137i | − 1.04437i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −15.8284 | −0.853412 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.00000 | −0.430083 | ||||||||
\(347\) | − 7.92893i | − 0.425647i | −0.977091 | − | 0.212824i | \(-0.931734\pi\) | ||||
0.977091 | − | 0.212824i | \(-0.0682660\pi\) | |||||||
\(348\) | − 1.58579i | − 0.0850071i | ||||||||
\(349\) | −15.3431 | −0.821300 | −0.410650 | − | 0.911793i | \(-0.634698\pi\) | ||||
−0.410650 | + | 0.911793i | \(0.634698\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6569 | −0.622197 | ||||||||
\(352\) | − 1.31371i | − 0.0700209i | ||||||||
\(353\) | 26.8284i | 1.42793i | 0.700180 | + | 0.713967i | \(0.253103\pi\) | ||||
−0.700180 | + | 0.713967i | \(0.746897\pi\) | |||||||
\(354\) | 4.48528 | 0.238390 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 33.1421 | 1.75653 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 24.1421i | − 1.27595i | ||||||||
\(359\) | 10.0000 | 0.527780 | 0.263890 | − | 0.964553i | \(-0.414994\pi\) | ||||
0.263890 | + | 0.964553i | \(0.414994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0000 | −0.578947 | ||||||||
\(362\) | 6.41421i | 0.337124i | ||||||||
\(363\) | − 4.27208i | − 0.224226i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.48528 | −0.286720 | ||||||||
\(367\) | − 2.75736i | − 0.143933i | −0.997407 | − | 0.0719665i | \(-0.977073\pi\) | ||||
0.997407 | − | 0.0719665i | \(-0.0229275\pi\) | |||||||
\(368\) | 1.24264i | 0.0647771i | ||||||||
\(369\) | 22.1421 | 1.15267 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − 9.51472i | − 0.493315i | ||||||||
\(373\) | − 20.9706i | − 1.08581i | −0.839793 | − | 0.542907i | \(-0.817323\pi\) | ||||
0.839793 | − | 0.542907i | \(-0.182677\pi\) | |||||||
\(374\) | −9.65685 | −0.499344 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.82843 | −0.455291 | ||||||||
\(377\) | 4.82843i | 0.248677i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.8284 | −1.37808 | −0.689042 | − | 0.724722i | \(-0.741968\pi\) | ||||
−0.689042 | + | 0.724722i | \(0.741968\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.85786 | −0.197644 | ||||||||
\(382\) | 30.9706i | 1.58459i | ||||||||
\(383\) | 2.89949i | 0.148157i | 0.997252 | + | 0.0740786i | \(0.0236016\pi\) | ||||
−0.997252 | + | 0.0740786i | \(0.976398\pi\) | |||||||
\(384\) | 8.51472 | 0.434515 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.82843 | −0.245760 | ||||||||
\(387\) | 10.1421i | 0.515554i | ||||||||
\(388\) | − 44.6274i | − 2.26561i | ||||||||
\(389\) | −23.6569 | −1.19945 | −0.599725 | − | 0.800206i | \(-0.704723\pi\) | ||||
−0.599725 | + | 0.800206i | \(0.704723\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.00000 | −0.101144 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.00000i | 0.403547i | ||||||||
\(394\) | 29.7990 | 1.50125 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.97056 | 0.450788 | ||||||||
\(397\) | − 16.6274i | − 0.834506i | −0.908790 | − | 0.417253i | \(-0.862993\pi\) | ||||
0.908790 | − | 0.417253i | \(-0.137007\pi\) | |||||||
\(398\) | 23.3137i | 1.16861i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.3137 | 1.51379 | 0.756897 | − | 0.653534i | \(-0.226714\pi\) | ||||
0.756897 | + | 0.653534i | \(0.226714\pi\) | |||||||
\(402\) | − 9.58579i | − 0.478096i | ||||||||
\(403\) | 28.9706i | 1.44313i | ||||||||
\(404\) | −39.4853 | −1.96447 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − 8.82843i | − 0.437072i | ||||||||
\(409\) | −14.7990 | −0.731763 | −0.365881 | − | 0.930661i | \(-0.619232\pi\) | ||||
−0.365881 | + | 0.930661i | \(0.619232\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.00000 | −0.197305 | ||||||||
\(412\) | − 9.24264i | − 0.455352i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.82843 | 0.139010 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.65685 | −0.375408 | ||||||||
\(417\) | − 6.68629i | − 0.327429i | ||||||||
\(418\) | 5.65685i | 0.276686i | ||||||||
\(419\) | −0.686292 | −0.0335275 | −0.0167638 | − | 0.999859i | \(-0.505336\pi\) | ||||
−0.0167638 | + | 0.999859i | \(0.505336\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.4853 | 0.657232 | 0.328616 | − | 0.944464i | \(-0.393418\pi\) | ||||
0.328616 | + | 0.944464i | \(0.393418\pi\) | |||||||
\(422\) | − 49.4558i | − 2.40747i | ||||||||
\(423\) | 5.65685i | 0.275046i | ||||||||
\(424\) | 5.17157 | 0.251154 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.48528 | 0.217313 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 43.0416i | 2.08050i | ||||||||
\(429\) | 1.65685 | 0.0799937 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7990 | 0.857347 | 0.428674 | − | 0.903459i | \(-0.358981\pi\) | ||||
0.428674 | + | 0.903459i | \(0.358981\pi\) | |||||||
\(432\) | 7.24264i | 0.348462i | ||||||||
\(433\) | − 7.79899i | − 0.374796i | −0.982284 | − | 0.187398i | \(-0.939995\pi\) | ||||
0.982284 | − | 0.187398i | \(-0.0600053\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −51.6274 | −2.47250 | ||||||||
\(437\) | 1.17157i | 0.0560439i | ||||||||
\(438\) | 0.828427i | 0.0395838i | ||||||||
\(439\) | −33.9411 | −1.61992 | −0.809961 | − | 0.586484i | \(-0.800512\pi\) | ||||
−0.809961 | + | 0.586484i | \(0.800512\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 56.2843i | 2.67717i | ||||||||
\(443\) | 30.2132i | 1.43547i | 0.696315 | + | 0.717736i | \(0.254822\pi\) | ||||
−0.696315 | + | 0.717736i | \(0.745178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.828427 | −0.0392272 | ||||||||
\(447\) | 0.899495i | 0.0425447i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.82843 | −0.180675 | −0.0903373 | − | 0.995911i | \(-0.528795\pi\) | ||||
−0.0903373 | + | 0.995911i | \(0.528795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.48528 | −0.305380 | ||||||||
\(452\) | 17.1716i | 0.807683i | ||||||||
\(453\) | 4.82843i | 0.226859i | ||||||||
\(454\) | −16.8284 | −0.789797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.17157 | −0.242181 | ||||||||
\(457\) | − 24.2843i | − 1.13597i | −0.823039 | − | 0.567985i | \(-0.807723\pi\) | ||||
0.823039 | − | 0.567985i | \(-0.192277\pi\) | |||||||
\(458\) | 28.1421i | 1.31500i | ||||||||
\(459\) | −11.6569 | −0.544095 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −41.3137 | −1.92417 | −0.962086 | − | 0.272748i | \(-0.912068\pi\) | ||||
−0.962086 | + | 0.272748i | \(0.912068\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 37.0416i | − 1.72147i | −0.509053 | − | 0.860735i | \(-0.670004\pi\) | ||||
0.509053 | − | 0.860735i | \(-0.329996\pi\) | |||||||
\(464\) | 3.00000 | 0.139272 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −40.6274 | −1.88203 | ||||||||
\(467\) | − 3.10051i | − 0.143474i | −0.997424 | − | 0.0717371i | \(-0.977146\pi\) | ||||
0.997424 | − | 0.0717371i | \(-0.0228543\pi\) | |||||||
\(468\) | − 52.2843i | − 2.41684i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.17157 | −0.330449 | ||||||||
\(472\) | 19.7990i | 0.911322i | ||||||||
\(473\) | − 2.97056i | − 0.136587i | ||||||||
\(474\) | −14.8284 | −0.681092 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.31371i | − 0.151724i | ||||||||
\(478\) | − 51.4558i | − 2.35354i | ||||||||
\(479\) | −35.6569 | −1.62920 | −0.814602 | − | 0.580021i | \(-0.803044\pi\) | ||||
−0.814602 | + | 0.580021i | \(0.803044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 66.7696i | 3.04127i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39.4853 | 1.79479 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 24.9706 | 1.13269 | ||||||||
\(487\) | − 4.34315i | − 0.196807i | −0.995147 | − | 0.0984034i | \(-0.968626\pi\) | ||||
0.995147 | − | 0.0984034i | \(-0.0313735\pi\) | |||||||
\(488\) | − 24.2132i | − 1.09608i | ||||||||
\(489\) | −5.11270 | −0.231204 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.31371 | 0.420322 | 0.210161 | − | 0.977667i | \(-0.432601\pi\) | ||||
0.210161 | + | 0.977667i | \(0.432601\pi\) | |||||||
\(492\) | − 12.4142i | − 0.559676i | ||||||||
\(493\) | 4.82843i | 0.217461i | ||||||||
\(494\) | 32.9706 | 1.48342 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.0000 | 0.808224 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − 13.7279i | − 0.615163i | ||||||||
\(499\) | 0.828427 | 0.0370855 | 0.0185427 | − | 0.999828i | \(-0.494097\pi\) | ||||
0.0185427 | + | 0.999828i | \(0.494097\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.28427 | −0.414791 | ||||||||
\(502\) | − 22.4853i | − 1.00357i | ||||||||
\(503\) | 15.8701i | 0.707611i | 0.935319 | + | 0.353805i | \(0.115113\pi\) | ||||
−0.935319 | + | 0.353805i | \(0.884887\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.828427 | −0.0368281 | ||||||||
\(507\) | − 4.27208i | − 0.189730i | ||||||||
\(508\) | − 35.6569i | − 1.58202i | ||||||||
\(509\) | 13.3431 | 0.591425 | 0.295712 | − | 0.955277i | \(-0.404443\pi\) | ||||
0.295712 | + | 0.955277i | \(0.404443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 31.2426i | 1.38074i | ||||||||
\(513\) | 6.82843i | 0.301482i | ||||||||
\(514\) | 15.3137 | 0.675459 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.68629 | 0.250325 | ||||||||
\(517\) | − 1.65685i | − 0.0728684i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.37258 | 0.0602497 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.9706 | −0.655872 | −0.327936 | − | 0.944700i | \(-0.606353\pi\) | ||||
−0.327936 | + | 0.944700i | \(0.606353\pi\) | |||||||
\(522\) | − 6.82843i | − 0.298872i | ||||||||
\(523\) | − 35.6569i | − 1.55917i | −0.626299 | − | 0.779583i | \(-0.715431\pi\) | ||||
0.626299 | − | 0.779583i | \(-0.284569\pi\) | |||||||
\(524\) | −73.9411 | −3.23013 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −70.1127 | −3.05706 | ||||||||
\(527\) | 28.9706i | 1.26198i | ||||||||
\(528\) | − 1.02944i | − 0.0448005i | ||||||||
\(529\) | 22.8284 | 0.992540 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.6863 | 0.550538 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.7990i | 1.63726i | ||||||||
\(534\) | −8.65685 | −0.374619 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 42.3137 | 1.82767 | ||||||||
\(537\) | 4.14214i | 0.178746i | ||||||||
\(538\) | − 49.3848i | − 2.12913i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.34315 | 0.315706 | 0.157853 | − | 0.987463i | \(-0.449543\pi\) | ||||
0.157853 | + | 0.987463i | \(0.449543\pi\) | |||||||
\(542\) | 39.7990i | 1.70951i | ||||||||
\(543\) | − 1.10051i | − 0.0472272i | ||||||||
\(544\) | −7.65685 | −0.328285 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 24.8995i | − 1.06463i | −0.846548 | − | 0.532313i | \(-0.821323\pi\) | ||||
0.846548 | − | 0.532313i | \(-0.178677\pi\) | |||||||
\(548\) | − 36.9706i | − 1.57930i | ||||||||
\(549\) | −15.5147 | −0.662152 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.82843 | 0.120495 | ||||||||
\(552\) | − 0.757359i | − 0.0322354i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −38.9706 | −1.65570 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 61.7990 | 2.62086 | ||||||||
\(557\) | − 22.2843i | − 0.944215i | −0.881541 | − | 0.472107i | \(-0.843493\pi\) | ||||
0.881541 | − | 0.472107i | \(-0.156507\pi\) | |||||||
\(558\) | − 40.9706i | − 1.73442i | ||||||||
\(559\) | −17.3137 | −0.732292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.65685 | 0.0699524 | ||||||||
\(562\) | 73.1127i | 3.08407i | ||||||||
\(563\) | − 41.7279i | − 1.75862i | −0.476248 | − | 0.879311i | \(-0.658003\pi\) | ||||
0.476248 | − | 0.879311i | \(-0.341997\pi\) | |||||||
\(564\) | 3.17157 | 0.133547 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −33.7990 | −1.42068 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 19.7990i | 0.830747i | ||||||||
\(569\) | −7.65685 | −0.320992 | −0.160496 | − | 0.987036i | \(-0.551309\pi\) | ||||
−0.160496 | + | 0.987036i | \(0.551309\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.17157 | 0.383818 | 0.191909 | − | 0.981413i | \(-0.438532\pi\) | ||||
0.191909 | + | 0.981413i | \(0.438532\pi\) | |||||||
\(572\) | 15.3137i | 0.640298i | ||||||||
\(573\) | − 5.31371i | − 0.221983i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 27.7990 | 1.15829 | ||||||||
\(577\) | − 43.9411i | − 1.82929i | −0.404255 | − | 0.914646i | \(-0.632469\pi\) | ||||
0.404255 | − | 0.914646i | \(-0.367531\pi\) | |||||||
\(578\) | 15.2426i | 0.634010i | ||||||||
\(579\) | 0.828427 | 0.0344283 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 11.6569i | 0.483192i | ||||||||
\(583\) | 0.970563i | 0.0401966i | ||||||||
\(584\) | −3.65685 | −0.151322 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 38.6274 | 1.59568 | ||||||||
\(587\) | − 34.2843i | − 1.41506i | −0.706682 | − | 0.707532i | \(-0.749809\pi\) | ||||
0.706682 | − | 0.707532i | \(-0.250191\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9706 | 0.699260 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.11270 | −0.210308 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 4.20101i | − 0.172515i | −0.996273 | − | 0.0862574i | \(-0.972509\pi\) | ||||
0.996273 | − | 0.0862574i | \(-0.0274907\pi\) | |||||||
\(594\) | −4.82843 | −0.198113 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.31371 | −0.340543 | ||||||||
\(597\) | − 4.00000i | − 0.163709i | ||||||||
\(598\) | 4.82843i | 0.197449i | ||||||||
\(599\) | −6.34315 | −0.259174 | −0.129587 | − | 0.991568i | \(-0.541365\pi\) | ||||
−0.129587 | + | 0.991568i | \(0.541365\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6569 | −0.801820 | −0.400910 | − | 0.916117i | \(-0.631306\pi\) | ||||
−0.400910 | + | 0.916117i | \(0.631306\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 27.1127i | − 1.10411i | ||||||||
\(604\) | −44.6274 | −1.81586 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.3137 | 0.418966 | ||||||||
\(607\) | 38.2132i | 1.55103i | 0.631332 | + | 0.775513i | \(0.282509\pi\) | ||||
−0.631332 | + | 0.775513i | \(0.717491\pi\) | |||||||
\(608\) | 4.48528i | 0.181902i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.65685 | −0.390675 | ||||||||
\(612\) | − 52.2843i | − 2.11347i | ||||||||
\(613\) | 35.4558i | 1.43205i | 0.698076 | + | 0.716024i | \(0.254040\pi\) | ||||
−0.698076 | + | 0.716024i | \(0.745960\pi\) | |||||||
\(614\) | −11.4853 | −0.463508 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 11.3137i | − 0.455473i | −0.973723 | − | 0.227736i | \(-0.926868\pi\) | ||||
0.973723 | − | 0.227736i | \(-0.0731324\pi\) | |||||||
\(618\) | 2.41421i | 0.0971139i | ||||||||
\(619\) | 25.5147 | 1.02552 | 0.512762 | − | 0.858531i | \(-0.328622\pi\) | ||||
0.512762 | + | 0.858531i | \(0.328622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | − 31.7990i | − 1.27502i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.3137 | 0.612059 | ||||||||
\(627\) | − 0.970563i | − 0.0387605i | ||||||||
\(628\) | − 66.2843i | − 2.64503i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.1421 | −0.801846 | −0.400923 | − | 0.916112i | \(-0.631310\pi\) | ||||
−0.400923 | + | 0.916112i | \(0.631310\pi\) | |||||||
\(632\) | − 65.4558i | − 2.60369i | ||||||||
\(633\) | 8.48528i | 0.337260i | ||||||||
\(634\) | 33.3137 | 1.32306 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.85786 | −0.0736691 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.00000i | 0.0791808i | ||||||||
\(639\) | 12.6863 | 0.501862 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.4853 | 1.24359 | 0.621797 | − | 0.783179i | \(-0.286403\pi\) | ||||
0.621797 | + | 0.783179i | \(0.286403\pi\) | |||||||
\(642\) | − 11.2426i | − 0.443712i | ||||||||
\(643\) | − 26.2843i | − 1.03655i | −0.855214 | − | 0.518275i | \(-0.826574\pi\) | ||||
0.855214 | − | 0.518275i | \(-0.173426\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 32.9706 | 1.29721 | ||||||||
\(647\) | − 31.0416i | − 1.22037i | −0.792258 | − | 0.610186i | \(-0.791095\pi\) | ||||
0.792258 | − | 0.610186i | \(-0.208905\pi\) | |||||||
\(648\) | 33.0416i | 1.29800i | ||||||||
\(649\) | −3.71573 | −0.145855 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 47.2548i | − 1.85064i | ||||||||
\(653\) | − 19.1716i | − 0.750242i | −0.926976 | − | 0.375121i | \(-0.877601\pi\) | ||||
0.926976 | − | 0.375121i | \(-0.122399\pi\) | |||||||
\(654\) | 13.4853 | 0.527316 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 23.4853 | 0.916946 | ||||||||
\(657\) | 2.34315i | 0.0914148i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.1716 | −0.824727 | −0.412364 | − | 0.911019i | \(-0.635297\pi\) | ||||
−0.412364 | + | 0.911019i | \(0.635297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.8284 | −1.23798 | −0.618991 | − | 0.785398i | \(-0.712458\pi\) | ||||
−0.618991 | + | 0.785398i | \(0.712458\pi\) | |||||||
\(662\) | − 55.4558i | − 2.15535i | ||||||||
\(663\) | − 9.65685i | − 0.375041i | ||||||||
\(664\) | 60.5980 | 2.35166 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.414214i | 0.0160384i | ||||||||
\(668\) | − 85.8112i | − 3.32013i | ||||||||
\(669\) | 0.142136 | 0.00549528 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.54416 | 0.175425 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.6569i | 1.14319i | 0.820537 | + | 0.571594i | \(0.193675\pi\) | ||||
−0.820537 | + | 0.571594i | \(0.806325\pi\) | |||||||
\(674\) | −22.1421 | −0.852883 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 39.4853 | 1.51866 | ||||||||
\(677\) | − 28.1421i | − 1.08159i | −0.841154 | − | 0.540795i | \(-0.818123\pi\) | ||||
0.841154 | − | 0.540795i | \(-0.181877\pi\) | |||||||
\(678\) | − 4.48528i | − 0.172256i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.88730 | 0.110642 | ||||||||
\(682\) | 12.0000i | 0.459504i | ||||||||
\(683\) | − 34.7574i | − 1.32995i | −0.746864 | − | 0.664977i | \(-0.768441\pi\) | ||||
0.746864 | − | 0.664977i | \(-0.231559\pi\) | |||||||
\(684\) | −30.6274 | −1.17107 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 4.82843i | − 0.184216i | ||||||||
\(688\) | 10.7574i | 0.410120i | ||||||||
\(689\) | 5.65685 | 0.215509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.828427 | −0.0315149 | −0.0157574 | − | 0.999876i | \(-0.505016\pi\) | ||||
−0.0157574 | + | 0.999876i | \(0.505016\pi\) | |||||||
\(692\) | 12.6863i | 0.482260i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.1421 | −0.726626 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.82843 | −0.0693064 | ||||||||
\(697\) | 37.7990i | 1.43174i | ||||||||
\(698\) | 37.0416i | 1.40205i | ||||||||
\(699\) | 6.97056 | 0.263651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.20101 | −0.120900 | −0.0604502 | − | 0.998171i | \(-0.519254\pi\) | ||||
−0.0604502 | + | 0.998171i | \(0.519254\pi\) | |||||||
\(702\) | 28.1421i | 1.06216i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −8.14214 | −0.306868 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 64.7696 | 2.43763 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − 7.11270i | − 0.267312i | ||||||||
\(709\) | −15.6863 | −0.589111 | −0.294556 | − | 0.955634i | \(-0.595172\pi\) | ||||
−0.294556 | + | 0.955634i | \(0.595172\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −41.9411 | −1.57292 | ||||||||
\(712\) | − 38.2132i | − 1.43210i | ||||||||
\(713\) | 2.48528i | 0.0930745i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −38.2843 | −1.43075 | ||||||||
\(717\) | 8.82843i | 0.329704i | ||||||||
\(718\) | − 24.1421i | − 0.900976i | ||||||||
\(719\) | 21.1127 | 0.787371 | 0.393685 | − | 0.919245i | \(-0.371200\pi\) | ||||
0.393685 | + | 0.919245i | \(0.371200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26.5563i | 0.988325i | ||||||||
\(723\) | − 11.4558i | − 0.426047i | ||||||||
\(724\) | 10.1716 | 0.378024 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −10.3137 | −0.382778 | ||||||||
\(727\) | − 37.5858i | − 1.39398i | −0.717081 | − | 0.696990i | \(-0.754522\pi\) | ||||
0.717081 | − | 0.696990i | \(-0.245478\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18.1716 | 0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.3137 | −0.640371 | ||||||||
\(732\) | 8.69848i | 0.321505i | ||||||||
\(733\) | 22.0000i | 0.812589i | 0.913742 | + | 0.406294i | \(0.133179\pi\) | ||||
−0.913742 | + | 0.406294i | \(0.866821\pi\) | |||||||
\(734\) | −6.65685 | −0.245709 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.656854 | −0.0242120 | ||||||||
\(737\) | 7.94113i | 0.292515i | ||||||||
\(738\) | − 53.4558i | − 1.96774i | ||||||||
\(739\) | 21.1127 | 0.776643 | 0.388322 | − | 0.921524i | \(-0.373055\pi\) | ||||
0.388322 | + | 0.921524i | \(0.373055\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.65685 | −0.207810 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 16.0711i | − 0.589590i | −0.955560 | − | 0.294795i | \(-0.904749\pi\) | ||||
0.955560 | − | 0.294795i | \(-0.0952514\pi\) | |||||||
\(744\) | −10.9706 | −0.402200 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −50.6274 | −1.85360 | ||||||||
\(747\) | − 38.8284i | − 1.42066i | ||||||||
\(748\) | 15.3137i | 0.559925i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.3431 | −1.10724 | −0.553619 | − | 0.832770i | \(-0.686753\pi\) | ||||
−0.553619 | + | 0.832770i | \(0.686753\pi\) | |||||||
\(752\) | 6.00000i | 0.218797i | ||||||||
\(753\) | 3.85786i | 0.140588i | ||||||||
\(754\) | 11.6569 | 0.424518 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.4558i | 1.14328i | 0.820504 | + | 0.571641i | \(0.193693\pi\) | ||||
−0.820504 | + | 0.571641i | \(0.806307\pi\) | |||||||
\(758\) | 64.7696i | 2.35254i | ||||||||
\(759\) | 0.142136 | 0.00515920 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.31371 | −0.337622 | −0.168811 | − | 0.985648i | \(-0.553993\pi\) | ||||
−0.168811 | + | 0.985648i | \(0.553993\pi\) | |||||||
\(762\) | 9.31371i | 0.337400i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 49.1127 | 1.77684 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.00000 | 0.252920 | ||||||||
\(767\) | 21.6569i | 0.781984i | ||||||||
\(768\) | − 12.4142i | − 0.447959i | ||||||||
\(769\) | −0.627417 | −0.0226252 | −0.0113126 | − | 0.999936i | \(-0.503601\pi\) | ||||
−0.0113126 | + | 0.999936i | \(0.503601\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.62742 | −0.0946241 | ||||||||
\(772\) | 7.65685i | 0.275576i | ||||||||
\(773\) | 37.1127i | 1.33485i | 0.744677 | + | 0.667425i | \(0.232604\pi\) | ||||
−0.744677 | + | 0.667425i | \(0.767396\pi\) | |||||||
\(774\) | 24.4853 | 0.880105 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −51.4558 | −1.84716 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 57.1127i | 2.04759i | ||||||||
\(779\) | 22.1421 | 0.793324 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.71573 | −0.132959 | ||||||||
\(782\) | 4.82843i | 0.172664i | ||||||||
\(783\) | 2.41421i | 0.0862770i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.3137 | 0.688897 | ||||||||
\(787\) | 2.55635i | 0.0911240i | 0.998962 | + | 0.0455620i | \(0.0145079\pi\) | ||||
−0.998962 | + | 0.0455620i | \(0.985492\pi\) | |||||||
\(788\) | − 47.2548i | − 1.68338i | ||||||||
\(789\) | 12.0294 | 0.428259 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − 10.3431i | − 0.367528i | ||||||||
\(793\) | − 26.4853i | − 0.940520i | ||||||||
\(794\) | −40.1421 | −1.42459 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 36.9706 | 1.31039 | ||||||||
\(797\) | − 8.00000i | − 0.283375i | −0.989911 | − | 0.141687i | \(-0.954747\pi\) | ||||
0.989911 | − | 0.141687i | \(-0.0452527\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.65685 | −0.341635 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −24.4853 | −0.865145 | ||||||||
\(802\) | − 73.1838i | − 2.58421i | ||||||||
\(803\) | − 0.686292i | − 0.0242187i | ||||||||
\(804\) | −15.2010 | −0.536098 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 69.9411 | 2.46357 | ||||||||
\(807\) | 8.47309i | 0.298267i | ||||||||
\(808\) | 45.5269i | 1.60163i | ||||||||
\(809\) | −35.6274 | −1.25259 | −0.626297 | − | 0.779585i | \(-0.715430\pi\) | ||||
−0.626297 | + | 0.779585i | \(0.715430\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.6274 | 0.724327 | 0.362163 | − | 0.932115i | \(-0.382038\pi\) | ||||
0.362163 | + | 0.932115i | \(0.382038\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 6.82843i | − 0.239483i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.00000 | −0.210042 | ||||||||
\(817\) | 10.1421i | 0.354828i | ||||||||
\(818\) | 35.7279i | 1.24920i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 47.9411 | 1.67316 | 0.836578 | − | 0.547847i | \(-0.184552\pi\) | ||||
0.836578 | + | 0.547847i | \(0.184552\pi\) | |||||||
\(822\) | 9.65685i | 0.336821i | ||||||||
\(823\) | 2.07107i | 0.0721929i | 0.999348 | + | 0.0360964i | \(0.0114924\pi\) | ||||
−0.999348 | + | 0.0360964i | \(0.988508\pi\) | |||||||
\(824\) | −10.6569 | −0.371249 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.2132i | 0.911522i | 0.890102 | + | 0.455761i | \(0.150633\pi\) | ||||
−0.890102 | + | 0.455761i | \(0.849367\pi\) | |||||||
\(828\) | − 4.48528i | − 0.155874i | ||||||||
\(829\) | 29.3137 | 1.01811 | 0.509054 | − | 0.860735i | \(-0.329995\pi\) | ||||
0.509054 | + | 0.860735i | \(0.329995\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.68629 | 0.231945 | ||||||||
\(832\) | 47.4558i | 1.64524i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.1421 | −0.558956 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.97056 | 0.310253 | ||||||||
\(837\) | 14.4853i | 0.500685i | ||||||||
\(838\) | 1.65685i | 0.0572351i | ||||||||
\(839\) | 15.1716 | 0.523781 | 0.261890 | − | 0.965098i | \(-0.415654\pi\) | ||||
0.261890 | + | 0.965098i | \(0.415654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | − 32.5563i | − 1.12197i | ||||||||
\(843\) | − 12.5442i | − 0.432044i | ||||||||
\(844\) | −78.4264 | −2.69955 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.6569 | 0.469532 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 3.51472i | − 0.120696i | ||||||||
\(849\) | 5.79899 | 0.199021 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | − 7.11270i | − 0.243677i | ||||||||
\(853\) | − 2.54416i | − 0.0871102i | −0.999051 | − | 0.0435551i | \(-0.986132\pi\) | ||||
0.999051 | − | 0.0435551i | \(-0.0138684\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 49.6274 | 1.69623 | ||||||||
\(857\) | 34.2843i | 1.17113i | 0.810626 | + | 0.585564i | \(0.199127\pi\) | ||||
−0.810626 | + | 0.585564i | \(0.800873\pi\) | |||||||
\(858\) | − 4.00000i | − 0.136558i | ||||||||
\(859\) | 1.37258 | 0.0468319 | 0.0234160 | − | 0.999726i | \(-0.492546\pi\) | ||||
0.0234160 | + | 0.999726i | \(0.492546\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 42.9706i | − 1.46358i | ||||||||
\(863\) | 14.5563i | 0.495504i | 0.968823 | + | 0.247752i | \(0.0796918\pi\) | ||||
−0.968823 | + | 0.247752i | \(0.920308\pi\) | |||||||
\(864\) | −3.82843 | −0.130246 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −18.8284 | −0.639816 | ||||||||
\(867\) | − 2.61522i | − 0.0888177i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.2843 | 0.416715 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.2843 | 1.56828 | ||||||||
\(872\) | 59.5269i | 2.01584i | ||||||||
\(873\) | 32.9706i | 1.11588i | ||||||||
\(874\) | 2.82843 | 0.0956730 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.31371 | 0.0443861 | ||||||||
\(877\) | − 25.1716i | − 0.849984i | −0.905197 | − | 0.424992i | \(-0.860277\pi\) | ||||
0.905197 | − | 0.424992i | \(-0.139723\pi\) | |||||||
\(878\) | 81.9411i | 2.76538i | ||||||||
\(879\) | −6.62742 | −0.223537 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.82843 | −0.0616013 | −0.0308006 | − | 0.999526i | \(-0.509806\pi\) | ||||
−0.0308006 | + | 0.999526i | \(0.509806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.2843i | 0.615315i | 0.951497 | + | 0.307657i | \(0.0995450\pi\) | ||||
−0.951497 | + | 0.307657i | \(0.900455\pi\) | |||||||
\(884\) | 89.2548 | 3.00196 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 72.9411 | 2.45051 | ||||||||
\(887\) | 29.9289i | 1.00492i | 0.864602 | + | 0.502458i | \(0.167571\pi\) | ||||
−0.864602 | + | 0.502458i | \(0.832429\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.20101 | −0.207742 | ||||||||
\(892\) | 1.31371i | 0.0439862i | ||||||||
\(893\) | 5.65685i | 0.189299i | ||||||||
\(894\) | 2.17157 | 0.0726283 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 0.828427i | − 0.0276604i | ||||||||
\(898\) | 9.24264i | 0.308431i | ||||||||
\(899\) | 6.00000 | 0.200111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.65685 | 0.188457 | ||||||||
\(902\) | 15.6569i | 0.521316i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.7990 | 0.658505 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.6569 | 0.387273 | ||||||||
\(907\) | 14.2132i | 0.471942i | 0.971760 | + | 0.235971i | \(0.0758270\pi\) | ||||
−0.971760 | + | 0.235971i | \(0.924173\pi\) | |||||||
\(908\) | 26.6863i | 0.885616i | ||||||||
\(909\) | 29.1716 | 0.967560 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.2010 | −0.337975 | −0.168987 | − | 0.985618i | \(-0.554050\pi\) | ||||
−0.168987 | + | 0.985618i | \(0.554050\pi\) | |||||||
\(912\) | 3.51472i | 0.116384i | ||||||||
\(913\) | 11.3726i | 0.376378i | ||||||||
\(914\) | −58.6274 | −1.93922 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 44.6274 | 1.47453 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 28.1421i | 0.928829i | ||||||||
\(919\) | 43.1127 | 1.42216 | 0.711078 | − | 0.703113i | \(-0.248207\pi\) | ||||
0.711078 | + | 0.703113i | \(0.248207\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.97056 | 0.0649323 | ||||||||
\(922\) | 99.7401i | 3.28477i | ||||||||
\(923\) | 21.6569i | 0.712844i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −89.4264 | −2.93873 | ||||||||
\(927\) | 6.82843i | 0.224275i | ||||||||
\(928\) | 1.58579i | 0.0520560i | ||||||||
\(929\) | 5.48528 | 0.179966 | 0.0899831 | − | 0.995943i | \(-0.471319\pi\) | ||||
0.0899831 | + | 0.995943i | \(0.471319\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 64.4264i | 2.11036i | ||||||||
\(933\) | 5.45584i | 0.178616i | ||||||||
\(934\) | −7.48528 | −0.244926 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −60.2843 | −1.97045 | ||||||||
\(937\) | 34.6274i | 1.13123i | 0.824670 | + | 0.565614i | \(0.191361\pi\) | ||||
−0.824670 | + | 0.565614i | \(0.808639\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.62742 | −0.0857425 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.2843 | 1.50882 | 0.754412 | − | 0.656401i | \(-0.227922\pi\) | ||||
0.754412 | + | 0.656401i | \(0.227922\pi\) | |||||||
\(942\) | 17.3137i | 0.564111i | ||||||||
\(943\) | 3.24264i | 0.105595i | ||||||||
\(944\) | 13.4558 | 0.437950 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.17157 | −0.233168 | ||||||||
\(947\) | − 33.1838i | − 1.07833i | −0.842201 | − | 0.539164i | \(-0.818740\pi\) | ||||
0.842201 | − | 0.539164i | \(-0.181260\pi\) | |||||||
\(948\) | 23.5147i | 0.763723i | ||||||||
\(949\) | −4.00000 | −0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.71573 | −0.185345 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 13.6569i | − 0.442389i | −0.975230 | − | 0.221194i | \(-0.929004\pi\) | ||||
0.975230 | − | 0.221194i | \(-0.0709955\pi\) | |||||||
\(954\) | −8.00000 | −0.259010 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −81.5980 | −2.63907 | ||||||||
\(957\) | − 0.343146i | − 0.0110923i | ||||||||
\(958\) | 86.0833i | 2.78122i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 31.7990i | − 1.02471i | ||||||||
\(964\) | 105.882 | 3.41024 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 37.5269i | − 1.20678i | −0.797445 | − | 0.603392i | \(-0.793815\pi\) | ||||
0.797445 | − | 0.603392i | \(-0.206185\pi\) | |||||||
\(968\) | − 45.5269i | − 1.46329i | ||||||||
\(969\) | −5.65685 | −0.181724 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0000 | 0.770197 | 0.385098 | − | 0.922876i | \(-0.374168\pi\) | ||||
0.385098 | + | 0.922876i | \(0.374168\pi\) | |||||||
\(972\) | − 39.5980i | − 1.27011i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −10.4853 | −0.335970 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16.4558 | −0.526739 | ||||||||
\(977\) | 1.31371i | 0.0420293i | 0.999779 | + | 0.0210146i | \(0.00668966\pi\) | ||||
−0.999779 | + | 0.0210146i | \(0.993310\pi\) | |||||||
\(978\) | 12.3431i | 0.394690i | ||||||||
\(979\) | 7.17157 | 0.229204 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 38.1421 | 1.21778 | ||||||||
\(982\) | − 22.4853i | − 0.717534i | ||||||||
\(983\) | − 28.2132i | − 0.899861i | −0.893063 | − | 0.449931i | \(-0.851449\pi\) | ||||
0.893063 | − | 0.449931i | \(-0.148551\pi\) | |||||||
\(984\) | −14.3137 | −0.456304 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.6569 | 0.371230 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − 52.2843i | − 1.66338i | ||||||||
\(989\) | −1.48528 | −0.0472292 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.34315 | −0.137965 | −0.0689823 | − | 0.997618i | \(-0.521975\pi\) | ||||
−0.0689823 | + | 0.997618i | \(0.521975\pi\) | |||||||
\(992\) | 9.51472i | 0.302093i | ||||||||
\(993\) | 9.51472i | 0.301940i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.7696 | −0.689795 | ||||||||
\(997\) | 33.4558i | 1.05956i | 0.848136 | + | 0.529779i | \(0.177725\pi\) | ||||
−0.848136 | + | 0.529779i | \(0.822275\pi\) | |||||||
\(998\) | − 2.00000i | − 0.0633089i | ||||||||
\(999\) | 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 | 1225.2.b.h.99.1 | 4 | ||
5.2 | odd | 4 | 245.2.a.g.1.2 | 2 | |||
5.3 | odd | 4 | 1225.2.a.m.1.1 | 2 | |||
5.4 | even | 2 | inner | 1225.2.b.h.99.4 | 4 | ||
7.3 | odd | 6 | 175.2.k.a.149.4 | 8 | |||
7.5 | odd | 6 | 175.2.k.a.74.1 | 8 | |||
7.6 | odd | 2 | 1225.2.b.g.99.1 | 4 | |||
15.2 | even | 4 | 2205.2.a.q.1.1 | 2 | |||
20.7 | even | 4 | 3920.2.a.bv.1.1 | 2 | |||
35.2 | odd | 12 | 245.2.e.e.116.1 | 4 | |||
35.3 | even | 12 | 175.2.e.c.51.2 | 4 | |||
35.12 | even | 12 | 35.2.e.a.11.1 | ✓ | 4 | ||
35.13 | even | 4 | 1225.2.a.k.1.1 | 2 | |||
35.17 | even | 12 | 35.2.e.a.16.1 | yes | 4 | ||
35.19 | odd | 6 | 175.2.k.a.74.4 | 8 | |||
35.24 | odd | 6 | 175.2.k.a.149.1 | 8 | |||
35.27 | even | 4 | 245.2.a.h.1.2 | 2 | |||
35.32 | odd | 12 | 245.2.e.e.226.1 | 4 | |||
35.33 | even | 12 | 175.2.e.c.151.2 | 4 | |||
35.34 | odd | 2 | 1225.2.b.g.99.4 | 4 | |||
105.17 | odd | 12 | 315.2.j.e.226.2 | 4 | |||
105.47 | odd | 12 | 315.2.j.e.46.2 | 4 | |||
105.62 | odd | 4 | 2205.2.a.n.1.1 | 2 | |||
140.27 | odd | 4 | 3920.2.a.bq.1.2 | 2 | |||
140.47 | odd | 12 | 560.2.q.k.81.1 | 4 | |||
140.87 | odd | 12 | 560.2.q.k.401.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.e.a.11.1 | ✓ | 4 | 35.12 | even | 12 | ||
35.2.e.a.16.1 | yes | 4 | 35.17 | even | 12 | ||
175.2.e.c.51.2 | 4 | 35.3 | even | 12 | |||
175.2.e.c.151.2 | 4 | 35.33 | even | 12 | |||
175.2.k.a.74.1 | 8 | 7.5 | odd | 6 | |||
175.2.k.a.74.4 | 8 | 35.19 | odd | 6 | |||
175.2.k.a.149.1 | 8 | 35.24 | odd | 6 | |||
175.2.k.a.149.4 | 8 | 7.3 | odd | 6 | |||
245.2.a.g.1.2 | 2 | 5.2 | odd | 4 | |||
245.2.a.h.1.2 | 2 | 35.27 | even | 4 | |||
245.2.e.e.116.1 | 4 | 35.2 | odd | 12 | |||
245.2.e.e.226.1 | 4 | 35.32 | odd | 12 | |||
315.2.j.e.46.2 | 4 | 105.47 | odd | 12 | |||
315.2.j.e.226.2 | 4 | 105.17 | odd | 12 | |||
560.2.q.k.81.1 | 4 | 140.47 | odd | 12 | |||
560.2.q.k.401.1 | 4 | 140.87 | odd | 12 | |||
1225.2.a.k.1.1 | 2 | 35.13 | even | 4 | |||
1225.2.a.m.1.1 | 2 | 5.3 | odd | 4 | |||
1225.2.b.g.99.1 | 4 | 7.6 | odd | 2 | |||
1225.2.b.g.99.4 | 4 | 35.34 | odd | 2 | |||
1225.2.b.h.99.1 | 4 | 1.1 | even | 1 | trivial | ||
1225.2.b.h.99.4 | 4 | 5.4 | even | 2 | inner | ||
2205.2.a.n.1.1 | 2 | 105.62 | odd | 4 | |||
2205.2.a.q.1.1 | 2 | 15.2 | even | 4 | |||
3920.2.a.bq.1.2 | 2 | 140.27 | odd | 4 | |||
3920.2.a.bv.1.1 | 2 | 20.7 | even | 4 |