Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.66064384.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 9x^{4} + 13x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.285442\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.906968 | 0.641323 | 0.320661 | − | 0.947194i | \(-0.396095\pi\) | ||||
0.320661 | + | 0.947194i | \(0.396095\pi\) | |||||||
\(3\) | −3.21789 | −1.85785 | −0.928925 | − | 0.370268i | \(-0.879266\pi\) | ||||
−0.928925 | + | 0.370268i | \(0.879266\pi\) | |||||||
\(4\) | −1.17741 | −0.588705 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.91852 | −1.19148 | ||||||||
\(7\) | 2.59637 | 0.981334 | 0.490667 | − | 0.871347i | \(-0.336753\pi\) | ||||
0.490667 | + | 0.871347i | \(0.336753\pi\) | |||||||
\(8\) | −2.88181 | −1.01887 | ||||||||
\(9\) | 7.35482 | 2.45161 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.741113 | 0.223454 | 0.111727 | − | 0.993739i | \(-0.464362\pi\) | ||||
0.111727 | + | 0.993739i | \(0.464362\pi\) | |||||||
\(12\) | 3.78878 | 1.09373 | ||||||||
\(13\) | 3.78878 | 1.05082 | 0.525409 | − | 0.850850i | \(-0.323912\pi\) | ||||
0.525409 | + | 0.850850i | \(0.323912\pi\) | |||||||
\(14\) | 2.35482 | 0.629352 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.258887 | −0.0647218 | ||||||||
\(17\) | −3.16725 | −0.768171 | −0.384086 | − | 0.923298i | \(-0.625483\pi\) | ||||
−0.384086 | + | 0.923298i | \(0.625483\pi\) | |||||||
\(18\) | 6.67058 | 1.57227 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −8.35482 | −1.82317 | ||||||||
\(22\) | 0.672165 | 0.143306 | ||||||||
\(23\) | 0.570885 | 0.119038 | 0.0595189 | − | 0.998227i | \(-0.481043\pi\) | ||||
0.0595189 | + | 0.998227i | \(0.481043\pi\) | |||||||
\(24\) | 9.27334 | 1.89291 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.43630 | 0.673913 | ||||||||
\(27\) | −14.0133 | −2.69687 | ||||||||
\(28\) | −3.05699 | −0.577716 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.83705 | −1.04836 | −0.524182 | − | 0.851606i | \(-0.675629\pi\) | ||||
−0.524182 | + | 0.851606i | \(0.675629\pi\) | |||||||
\(32\) | 5.52881 | 0.977365 | ||||||||
\(33\) | −2.38482 | −0.415144 | ||||||||
\(34\) | −2.87259 | −0.492646 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.65964 | −1.44327 | ||||||||
\(37\) | 1.40396 | 0.230809 | 0.115404 | − | 0.993319i | \(-0.463184\pi\) | ||||
0.115404 | + | 0.993319i | \(0.463184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.1919 | −1.95226 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.83705 | 0.599246 | 0.299623 | − | 0.954058i | \(-0.403139\pi\) | ||||
0.299623 | + | 0.954058i | \(0.403139\pi\) | |||||||
\(42\) | −7.57755 | −1.16924 | ||||||||
\(43\) | −2.59637 | −0.395942 | −0.197971 | − | 0.980208i | \(-0.563435\pi\) | ||||
−0.197971 | + | 0.980208i | \(0.563435\pi\) | |||||||
\(44\) | −0.872594 | −0.131548 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.517774 | 0.0763416 | ||||||||
\(47\) | 5.08247 | 0.741354 | 0.370677 | − | 0.928762i | \(-0.379126\pi\) | ||||
0.370677 | + | 0.928762i | \(0.379126\pi\) | |||||||
\(48\) | 0.833070 | 0.120243 | ||||||||
\(49\) | −0.258887 | −0.0369839 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.1919 | 1.42715 | ||||||||
\(52\) | −4.46094 | −0.618621 | ||||||||
\(53\) | 0.160905 | 0.0221020 | 0.0110510 | − | 0.999939i | \(-0.496482\pi\) | ||||
0.0110510 | + | 0.999939i | \(0.496482\pi\) | |||||||
\(54\) | −12.7096 | −1.72956 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.48223 | −0.999854 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.44181 | −0.714544 | ||||||||
\(59\) | −8.35482 | −1.08770 | −0.543852 | − | 0.839181i | \(-0.683035\pi\) | ||||
−0.543852 | + | 0.839181i | \(0.683035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.57816 | −1.09832 | −0.549160 | − | 0.835717i | \(-0.685052\pi\) | ||||
−0.549160 | + | 0.835717i | \(0.685052\pi\) | |||||||
\(62\) | −5.29401 | −0.672340 | ||||||||
\(63\) | 19.0958 | 2.40584 | ||||||||
\(64\) | 5.53223 | 0.691529 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.16295 | −0.266241 | ||||||||
\(67\) | 14.8464 | 1.81378 | 0.906888 | − | 0.421371i | \(-0.138451\pi\) | ||||
0.906888 | + | 0.421371i | \(0.138451\pi\) | |||||||
\(68\) | 3.72915 | 0.452226 | ||||||||
\(69\) | −1.83705 | −0.221154 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.64518 | −0.432603 | −0.216302 | − | 0.976327i | \(-0.569399\pi\) | ||||
−0.216302 | + | 0.976327i | \(0.569399\pi\) | |||||||
\(72\) | −21.1952 | −2.49788 | ||||||||
\(73\) | −10.8461 | −1.26944 | −0.634719 | − | 0.772743i | \(-0.718884\pi\) | ||||
−0.634719 | + | 0.772743i | \(0.718884\pi\) | |||||||
\(74\) | 1.27334 | 0.148023 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.92420 | 0.219283 | ||||||||
\(78\) | −11.0576 | −1.25203 | ||||||||
\(79\) | −1.83705 | −0.206684 | −0.103342 | − | 0.994646i | \(-0.532954\pi\) | ||||
−0.103342 | + | 0.994646i | \(0.532954\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.0289 | 2.55877 | ||||||||
\(82\) | 3.48008 | 0.384310 | ||||||||
\(83\) | −4.19876 | −0.460873 | −0.230437 | − | 0.973087i | \(-0.574015\pi\) | ||||
−0.230437 | + | 0.973087i | \(0.574015\pi\) | |||||||
\(84\) | 9.83705 | 1.07331 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.35482 | −0.253927 | ||||||||
\(87\) | 19.3073 | 2.06996 | ||||||||
\(88\) | −2.13574 | −0.227671 | ||||||||
\(89\) | 16.9015 | 1.79156 | 0.895778 | − | 0.444502i | \(-0.146619\pi\) | ||||
0.895778 | + | 0.444502i | \(0.146619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.83705 | 1.03120 | ||||||||
\(92\) | −0.672165 | −0.0700781 | ||||||||
\(93\) | 18.7830 | 1.94770 | ||||||||
\(94\) | 4.60963 | 0.475447 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −17.7911 | −1.81580 | ||||||||
\(97\) | 3.78878 | 0.384692 | 0.192346 | − | 0.981327i | \(-0.438390\pi\) | ||||
0.192346 | + | 0.981327i | \(0.438390\pi\) | |||||||
\(98\) | −0.234802 | −0.0237186 | ||||||||
\(99\) | 5.45075 | 0.547821 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.35482 | 0.831336 | 0.415668 | − | 0.909517i | \(-0.363548\pi\) | ||||
0.415668 | + | 0.909517i | \(0.363548\pi\) | |||||||
\(102\) | 9.24369 | 0.915262 | ||||||||
\(103\) | −2.07612 | −0.204566 | −0.102283 | − | 0.994755i | \(-0.532615\pi\) | ||||
−0.102283 | + | 0.994755i | \(0.532615\pi\) | |||||||
\(104\) | −10.9185 | −1.07065 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.145935 | 0.0141745 | ||||||||
\(107\) | 5.70399 | 0.551426 | 0.275713 | − | 0.961240i | \(-0.411086\pi\) | ||||
0.275713 | + | 0.961240i | \(0.411086\pi\) | |||||||
\(108\) | 16.4994 | 1.58766 | ||||||||
\(109\) | −1.64518 | −0.157580 | −0.0787899 | − | 0.996891i | \(-0.525106\pi\) | ||||
−0.0787899 | + | 0.996891i | \(0.525106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.51777 | −0.428808 | ||||||||
\(112\) | −0.672165 | −0.0635137 | ||||||||
\(113\) | 3.89006 | 0.365946 | 0.182973 | − | 0.983118i | \(-0.441428\pi\) | ||||
0.182973 | + | 0.983118i | \(0.441428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.06446 | 0.655918 | ||||||||
\(117\) | 27.8658 | 2.57619 | ||||||||
\(118\) | −7.57755 | −0.697570 | ||||||||
\(119\) | −8.22334 | −0.753832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4508 | −0.950068 | ||||||||
\(122\) | −7.78011 | −0.704378 | ||||||||
\(123\) | −12.3472 | −1.11331 | ||||||||
\(124\) | 6.87259 | 0.617177 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 17.3193 | 1.54292 | ||||||||
\(127\) | 14.4233 | 1.27986 | 0.639931 | − | 0.768432i | \(-0.278963\pi\) | ||||
0.639931 | + | 0.768432i | \(0.278963\pi\) | |||||||
\(128\) | −6.04007 | −0.533872 | ||||||||
\(129\) | 8.35482 | 0.735601 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.96853 | 0.870954 | 0.435477 | − | 0.900200i | \(-0.356580\pi\) | ||||
0.435477 | + | 0.900200i | \(0.356580\pi\) | |||||||
\(132\) | 2.80791 | 0.244397 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.4652 | 1.16322 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.12741 | 0.782669 | ||||||||
\(137\) | −9.70431 | −0.829095 | −0.414548 | − | 0.910028i | \(-0.636060\pi\) | ||||
−0.414548 | + | 0.910028i | \(0.636060\pi\) | |||||||
\(138\) | −1.66614 | −0.141831 | ||||||||
\(139\) | −13.4508 | −1.14088 | −0.570439 | − | 0.821340i | \(-0.693227\pi\) | ||||
−0.570439 | + | 0.821340i | \(0.693227\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.3548 | −1.37732 | ||||||||
\(142\) | −3.30606 | −0.277438 | ||||||||
\(143\) | 2.80791 | 0.234809 | ||||||||
\(144\) | −1.90407 | −0.158672 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.83705 | −0.814120 | ||||||||
\(147\) | 0.833070 | 0.0687105 | ||||||||
\(148\) | −1.65303 | −0.135878 | ||||||||
\(149\) | 15.0959 | 1.23671 | 0.618353 | − | 0.785900i | \(-0.287800\pi\) | ||||
0.618353 | + | 0.785900i | \(0.287800\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1919 | −1.15492 | −0.577459 | − | 0.816420i | \(-0.695956\pi\) | ||||
−0.577459 | + | 0.816420i | \(0.695956\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −23.2946 | −1.88325 | ||||||||
\(154\) | 1.74519 | 0.140631 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 14.3548 | 1.14931 | ||||||||
\(157\) | −7.57755 | −0.604754 | −0.302377 | − | 0.953188i | \(-0.597780\pi\) | ||||
−0.302377 | + | 0.953188i | \(0.597780\pi\) | |||||||
\(158\) | −1.66614 | −0.132551 | ||||||||
\(159\) | −0.517774 | −0.0410622 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.48223 | 0.116816 | ||||||||
\(162\) | 20.8865 | 1.64100 | ||||||||
\(163\) | 19.6757 | 1.54112 | 0.770559 | − | 0.637369i | \(-0.219977\pi\) | ||||
0.770559 | + | 0.637369i | \(0.219977\pi\) | |||||||
\(164\) | −4.51777 | −0.352779 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.80814 | −0.295569 | ||||||||
\(167\) | −10.7954 | −0.835376 | −0.417688 | − | 0.908590i | \(-0.637160\pi\) | ||||
−0.417688 | + | 0.908590i | \(0.637160\pi\) | |||||||
\(168\) | 24.0770 | 1.85758 | ||||||||
\(169\) | 1.35482 | 0.104217 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.05699 | 0.233093 | ||||||||
\(173\) | 20.3895 | 1.55018 | 0.775092 | − | 0.631848i | \(-0.217703\pi\) | ||||
0.775092 | + | 0.631848i | \(0.217703\pi\) | |||||||
\(174\) | 17.5111 | 1.32752 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.191865 | −0.0144623 | ||||||||
\(177\) | 26.8849 | 2.02079 | ||||||||
\(178\) | 15.3291 | 1.14897 | ||||||||
\(179\) | −25.0645 | −1.87341 | −0.936703 | − | 0.350126i | \(-0.886139\pi\) | ||||
−0.936703 | + | 0.350126i | \(0.886139\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.4193 | 1.44342 | 0.721712 | − | 0.692194i | \(-0.243356\pi\) | ||||
0.721712 | + | 0.692194i | \(0.243356\pi\) | |||||||
\(182\) | 8.92188 | 0.661334 | ||||||||
\(183\) | 27.6036 | 2.04051 | ||||||||
\(184\) | −1.64518 | −0.121284 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 17.0355 | 1.24911 | ||||||||
\(187\) | −2.34729 | −0.171651 | ||||||||
\(188\) | −5.98414 | −0.436439 | ||||||||
\(189\) | −36.3837 | −2.64653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.4508 | 0.828547 | 0.414274 | − | 0.910152i | \(-0.364036\pi\) | ||||
0.414274 | + | 0.910152i | \(0.364036\pi\) | |||||||
\(192\) | −17.8021 | −1.28476 | ||||||||
\(193\) | 3.78878 | 0.272722 | 0.136361 | − | 0.990659i | \(-0.456459\pi\) | ||||
0.136361 | + | 0.990659i | \(0.456459\pi\) | |||||||
\(194\) | 3.43630 | 0.246712 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.304816 | 0.0217726 | ||||||||
\(197\) | −2.28354 | −0.162695 | −0.0813477 | − | 0.996686i | \(-0.525922\pi\) | ||||
−0.0813477 | + | 0.996686i | \(0.525922\pi\) | |||||||
\(198\) | 4.94366 | 0.351330 | ||||||||
\(199\) | −19.4508 | −1.37883 | −0.689414 | − | 0.724368i | \(-0.742132\pi\) | ||||
−0.689414 | + | 0.724368i | \(0.742132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −47.7741 | −3.36972 | ||||||||
\(202\) | 7.57755 | 0.533155 | ||||||||
\(203\) | −15.5782 | −1.09337 | ||||||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.88297 | −0.131193 | ||||||||
\(207\) | 4.19876 | 0.291834 | ||||||||
\(208\) | −0.980865 | −0.0680108 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.2274 | −0.772927 | −0.386463 | − | 0.922305i | \(-0.626303\pi\) | ||||
−0.386463 | + | 0.922305i | \(0.626303\pi\) | |||||||
\(212\) | −0.189451 | −0.0130115 | ||||||||
\(213\) | 11.7298 | 0.803712 | ||||||||
\(214\) | 5.17334 | 0.353642 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 40.3837 | 2.74776 | ||||||||
\(217\) | −15.1551 | −1.02880 | ||||||||
\(218\) | −1.49213 | −0.101059 | ||||||||
\(219\) | 34.9015 | 2.35843 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | −4.09748 | −0.275005 | ||||||||
\(223\) | −4.03785 | −0.270394 | −0.135197 | − | 0.990819i | \(-0.543167\pi\) | ||||
−0.135197 | + | 0.990819i | \(0.543167\pi\) | |||||||
\(224\) | 14.3548 | 0.959122 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.52815 | 0.234689 | ||||||||
\(227\) | −11.2185 | −0.744600 | −0.372300 | − | 0.928112i | \(-0.621431\pi\) | ||||
−0.372300 | + | 0.928112i | \(0.621431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.1315 | 1.06600 | 0.532999 | − | 0.846116i | \(-0.321065\pi\) | ||||
0.532999 | + | 0.846116i | \(0.321065\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.19186 | −0.407395 | ||||||||
\(232\) | 17.2908 | 1.13520 | ||||||||
\(233\) | 2.12676 | 0.139329 | 0.0696644 | − | 0.997570i | \(-0.477807\pi\) | ||||
0.0696644 | + | 0.997570i | \(0.477807\pi\) | |||||||
\(234\) | 25.2733 | 1.65217 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.83705 | 0.640337 | ||||||||
\(237\) | 5.91141 | 0.383987 | ||||||||
\(238\) | −7.45830 | −0.483450 | ||||||||
\(239\) | −14.4152 | −0.932442 | −0.466221 | − | 0.884668i | \(-0.654385\pi\) | ||||
−0.466221 | + | 0.884668i | \(0.654385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.162955 | 0.0104968 | 0.00524842 | − | 0.999986i | \(-0.498329\pi\) | ||||
0.00524842 | + | 0.999986i | \(0.498329\pi\) | |||||||
\(242\) | −9.47849 | −0.609301 | ||||||||
\(243\) | −32.0645 | −2.05694 | ||||||||
\(244\) | 10.1000 | 0.646587 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.1985 | −0.713990 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 16.8212 | 1.06815 | ||||||||
\(249\) | 13.5111 | 0.856233 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.9330 | 0.816322 | 0.408161 | − | 0.912910i | \(-0.366170\pi\) | ||||
0.408161 | + | 0.912910i | \(0.366170\pi\) | |||||||
\(252\) | −22.4836 | −1.41633 | ||||||||
\(253\) | 0.423090 | 0.0265995 | ||||||||
\(254\) | 13.0815 | 0.820805 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.5426 | −1.03391 | ||||||||
\(257\) | −11.0445 | −0.688938 | −0.344469 | − | 0.938798i | \(-0.611941\pi\) | ||||
−0.344469 | + | 0.938798i | \(0.611941\pi\) | |||||||
\(258\) | 7.57755 | 0.471758 | ||||||||
\(259\) | 3.64518 | 0.226501 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −44.1289 | −2.73151 | ||||||||
\(262\) | 9.04113 | 0.558563 | ||||||||
\(263\) | −17.8527 | −1.10085 | −0.550424 | − | 0.834885i | \(-0.685534\pi\) | ||||
−0.550424 | + | 0.834885i | \(0.685534\pi\) | |||||||
\(264\) | 6.87259 | 0.422979 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −54.3872 | −3.32844 | ||||||||
\(268\) | −17.4803 | −1.06778 | ||||||||
\(269\) | −24.9934 | −1.52387 | −0.761936 | − | 0.647652i | \(-0.775751\pi\) | ||||
−0.761936 | + | 0.647652i | \(0.775751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.8660 | −1.44975 | −0.724877 | − | 0.688879i | \(-0.758103\pi\) | ||||
−0.724877 | + | 0.688879i | \(0.758103\pi\) | |||||||
\(272\) | 0.819960 | 0.0497174 | ||||||||
\(273\) | −31.6545 | −1.91582 | ||||||||
\(274\) | −8.80150 | −0.531718 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.16295 | 0.130195 | ||||||||
\(277\) | 21.2315 | 1.27568 | 0.637840 | − | 0.770169i | \(-0.279828\pi\) | ||||
0.637840 | + | 0.770169i | \(0.279828\pi\) | |||||||
\(278\) | −12.1994 | −0.731671 | ||||||||
\(279\) | −42.9304 | −2.57018 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.83705 | −0.228899 | −0.114449 | − | 0.993429i | \(-0.536510\pi\) | ||||
−0.114449 | + | 0.993429i | \(0.536510\pi\) | |||||||
\(282\) | −14.8333 | −0.883310 | ||||||||
\(283\) | −0.211545 | −0.0125751 | −0.00628753 | − | 0.999980i | \(-0.502001\pi\) | ||||
−0.00628753 | + | 0.999980i | \(0.502001\pi\) | |||||||
\(284\) | 4.29187 | 0.254676 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.54668 | 0.150589 | ||||||||
\(287\) | 9.96237 | 0.588060 | ||||||||
\(288\) | 40.6634 | 2.39612 | ||||||||
\(289\) | −6.96853 | −0.409913 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.1919 | −0.714700 | ||||||||
\(292\) | 12.7703 | 0.747324 | ||||||||
\(293\) | −14.9942 | −0.875970 | −0.437985 | − | 0.898982i | \(-0.644308\pi\) | ||||
−0.437985 | + | 0.898982i | \(0.644308\pi\) | |||||||
\(294\) | 0.755568 | 0.0440656 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.04593 | −0.235165 | ||||||||
\(297\) | −10.3855 | −0.602626 | ||||||||
\(298\) | 13.6915 | 0.793129 | ||||||||
\(299\) | 2.16295 | 0.125087 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.74111 | −0.388551 | ||||||||
\(302\) | −12.8716 | −0.740675 | ||||||||
\(303\) | −26.8849 | −1.54450 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.1274 | −1.20777 | ||||||||
\(307\) | 1.65303 | 0.0943434 | 0.0471717 | − | 0.998887i | \(-0.484979\pi\) | ||||
0.0471717 | + | 0.998887i | \(0.484979\pi\) | |||||||
\(308\) | −2.26557 | −0.129093 | ||||||||
\(309\) | 6.68073 | 0.380053 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.741113 | −0.0420247 | −0.0210123 | − | 0.999779i | \(-0.506689\pi\) | ||||
−0.0210123 | + | 0.999779i | \(0.506689\pi\) | |||||||
\(312\) | 35.1346 | 1.98911 | ||||||||
\(313\) | 26.8849 | 1.51962 | 0.759812 | − | 0.650143i | \(-0.225291\pi\) | ||||
0.759812 | + | 0.650143i | \(0.225291\pi\) | |||||||
\(314\) | −6.87259 | −0.387843 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.16295 | 0.121676 | ||||||||
\(317\) | −8.16155 | −0.458398 | −0.229199 | − | 0.973380i | \(-0.573611\pi\) | ||||
−0.229199 | + | 0.973380i | \(0.573611\pi\) | |||||||
\(318\) | −0.469604 | −0.0263341 | ||||||||
\(319\) | −4.44668 | −0.248966 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.3548 | −1.02447 | ||||||||
\(322\) | 1.34433 | 0.0749166 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −27.1145 | −1.50636 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.8452 | 0.988354 | ||||||||
\(327\) | 5.29401 | 0.292759 | ||||||||
\(328\) | −11.0576 | −0.610555 | ||||||||
\(329\) | 13.1959 | 0.727516 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 4.94366 | 0.271318 | ||||||||
\(333\) | 10.3258 | 0.565852 | ||||||||
\(334\) | −9.79112 | −0.535746 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.16295 | 0.117999 | ||||||||
\(337\) | −9.90275 | −0.539437 | −0.269718 | − | 0.962939i | \(-0.586931\pi\) | ||||
−0.269718 | + | 0.962939i | \(0.586931\pi\) | |||||||
\(338\) | 1.22878 | 0.0668367 | ||||||||
\(339\) | −12.5178 | −0.679872 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.32591 | −0.234261 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.8467 | −1.01763 | ||||||||
\(344\) | 7.48223 | 0.403415 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.4926 | 0.994169 | ||||||||
\(347\) | 21.2781 | 1.14227 | 0.571133 | − | 0.820858i | \(-0.306504\pi\) | ||||
0.571133 | + | 0.820858i | \(0.306504\pi\) | |||||||
\(348\) | −22.7327 | −1.21860 | ||||||||
\(349\) | −16.4152 | −0.878686 | −0.439343 | − | 0.898319i | \(-0.644789\pi\) | ||||
−0.439343 | + | 0.898319i | \(0.644789\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −53.0934 | −2.83391 | ||||||||
\(352\) | 4.09748 | 0.218396 | ||||||||
\(353\) | −23.8744 | −1.27071 | −0.635354 | − | 0.772221i | \(-0.719146\pi\) | ||||
−0.635354 | + | 0.772221i | \(0.719146\pi\) | |||||||
\(354\) | 24.3837 | 1.29598 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −19.9000 | −1.05470 | ||||||||
\(357\) | 26.4618 | 1.40051 | ||||||||
\(358\) | −22.7327 | −1.20146 | ||||||||
\(359\) | 2.22334 | 0.117343 | 0.0586717 | − | 0.998277i | \(-0.481313\pi\) | ||||
0.0586717 | + | 0.998277i | \(0.481313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 17.6127 | 0.925701 | ||||||||
\(363\) | 33.6294 | 1.76508 | ||||||||
\(364\) | −11.5822 | −0.607074 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 25.0355 | 1.30863 | ||||||||
\(367\) | 4.52057 | 0.235972 | 0.117986 | − | 0.993015i | \(-0.462356\pi\) | ||||
0.117986 | + | 0.993015i | \(0.462356\pi\) | |||||||
\(368\) | −0.147795 | −0.00770433 | ||||||||
\(369\) | 28.2208 | 1.46911 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.417768 | 0.0216894 | ||||||||
\(372\) | −22.1153 | −1.14662 | ||||||||
\(373\) | 15.5186 | 0.803521 | 0.401760 | − | 0.915745i | \(-0.368398\pi\) | ||||
0.401760 | + | 0.915745i | \(0.368398\pi\) | |||||||
\(374\) | −2.12892 | −0.110084 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −14.6467 | −0.755345 | ||||||||
\(377\) | −22.7327 | −1.17079 | ||||||||
\(378\) | −32.9989 | −1.69728 | ||||||||
\(379\) | 18.9015 | 0.970905 | 0.485453 | − | 0.874263i | \(-0.338655\pi\) | ||||
0.485453 | + | 0.874263i | \(0.338655\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −46.4126 | −2.37779 | ||||||||
\(382\) | 10.3855 | 0.531366 | ||||||||
\(383\) | −13.7046 | −0.700274 | −0.350137 | − | 0.936699i | \(-0.613865\pi\) | ||||
−0.350137 | + | 0.936699i | \(0.613865\pi\) | |||||||
\(384\) | 19.4363 | 0.991854 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.43630 | 0.174903 | ||||||||
\(387\) | −19.0958 | −0.970694 | ||||||||
\(388\) | −4.46094 | −0.226470 | ||||||||
\(389\) | 12.7411 | 0.646000 | 0.323000 | − | 0.946399i | \(-0.395309\pi\) | ||||
0.323000 | + | 0.946399i | \(0.395309\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.80814 | −0.0914413 | ||||||||
\(392\) | 0.746063 | 0.0376819 | ||||||||
\(393\) | −32.0776 | −1.61810 | ||||||||
\(394\) | −2.07110 | −0.104340 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.41777 | −0.322505 | ||||||||
\(397\) | 38.6522 | 1.93990 | 0.969950 | − | 0.243306i | \(-0.0782319\pi\) | ||||
0.969950 | + | 0.243306i | \(0.0782319\pi\) | |||||||
\(398\) | −17.6412 | −0.884274 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.8660 | −1.59131 | −0.795655 | − | 0.605750i | \(-0.792873\pi\) | ||||
−0.795655 | + | 0.605750i | \(0.792873\pi\) | |||||||
\(402\) | −43.3296 | −2.16108 | ||||||||
\(403\) | −22.1153 | −1.10164 | ||||||||
\(404\) | −9.83705 | −0.489411 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −14.1289 | −0.701206 | ||||||||
\(407\) | 1.04049 | 0.0515751 | ||||||||
\(408\) | −29.3710 | −1.45408 | ||||||||
\(409\) | −11.0645 | −0.547102 | −0.273551 | − | 0.961857i | \(-0.588198\pi\) | ||||
−0.273551 | + | 0.961857i | \(0.588198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.2274 | 1.54033 | ||||||||
\(412\) | 2.44444 | 0.120429 | ||||||||
\(413\) | −21.6922 | −1.06740 | ||||||||
\(414\) | 3.80814 | 0.187160 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 20.9474 | 1.02703 | ||||||||
\(417\) | 43.2830 | 2.11958 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.7452 | −1.25773 | −0.628867 | − | 0.777513i | \(-0.716481\pi\) | ||||
−0.628867 | + | 0.777513i | \(0.716481\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.4482 | −1.33774 | −0.668871 | − | 0.743378i | \(-0.733222\pi\) | ||||
−0.668871 | + | 0.743378i | \(0.733222\pi\) | |||||||
\(422\) | −10.1829 | −0.495696 | ||||||||
\(423\) | 37.3806 | 1.81751 | ||||||||
\(424\) | −0.463697 | −0.0225191 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.6385 | 0.515439 | ||||||||
\(427\) | −22.2720 | −1.07782 | ||||||||
\(428\) | −6.71593 | −0.324627 | ||||||||
\(429\) | −9.03555 | −0.436240 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.74519 | −0.0840627 | −0.0420314 | − | 0.999116i | \(-0.513383\pi\) | ||||
−0.0420314 | + | 0.999116i | \(0.513383\pi\) | |||||||
\(432\) | 3.62787 | 0.174546 | ||||||||
\(433\) | −18.5208 | −0.890052 | −0.445026 | − | 0.895518i | \(-0.646806\pi\) | ||||
−0.445026 | + | 0.895518i | \(0.646806\pi\) | |||||||
\(434\) | −13.7452 | −0.659790 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.93705 | 0.0927679 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 31.6545 | 1.51251 | ||||||||
\(439\) | −29.4482 | −1.40549 | −0.702743 | − | 0.711444i | \(-0.748041\pi\) | ||||
−0.702743 | + | 0.711444i | \(0.748041\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.90407 | −0.0906699 | ||||||||
\(442\) | −10.8836 | −0.517681 | ||||||||
\(443\) | −11.7388 | −0.557726 | −0.278863 | − | 0.960331i | \(-0.589958\pi\) | ||||
−0.278863 | + | 0.960331i | \(0.589958\pi\) | |||||||
\(444\) | 5.31927 | 0.252441 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.66220 | −0.173410 | ||||||||
\(447\) | −48.5771 | −2.29762 | ||||||||
\(448\) | 14.3637 | 0.678620 | ||||||||
\(449\) | 7.06446 | 0.333392 | 0.166696 | − | 0.986008i | \(-0.446690\pi\) | ||||
0.166696 | + | 0.986008i | \(0.446690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.84368 | 0.133904 | ||||||||
\(452\) | −4.58019 | −0.215434 | ||||||||
\(453\) | 45.6679 | 2.14566 | ||||||||
\(454\) | −10.1748 | −0.477529 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.5000 | 1.61384 | 0.806920 | − | 0.590660i | \(-0.201133\pi\) | ||||
0.806920 | + | 0.590660i | \(0.201133\pi\) | |||||||
\(458\) | 14.6307 | 0.683649 | ||||||||
\(459\) | 44.3837 | 2.07166 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.03147 | 0.374063 | 0.187032 | − | 0.982354i | \(-0.440113\pi\) | ||||
0.187032 | + | 0.982354i | \(0.440113\pi\) | |||||||
\(462\) | −5.61582 | −0.261272 | ||||||||
\(463\) | 25.3290 | 1.17714 | 0.588570 | − | 0.808447i | \(-0.299691\pi\) | ||||
0.588570 | + | 0.808447i | \(0.299691\pi\) | |||||||
\(464\) | 1.55332 | 0.0721112 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.92890 | 0.0893547 | ||||||||
\(467\) | −26.8759 | −1.24367 | −0.621834 | − | 0.783149i | \(-0.713612\pi\) | ||||
−0.621834 | + | 0.783149i | \(0.713612\pi\) | |||||||
\(468\) | −32.8094 | −1.51662 | ||||||||
\(469\) | 38.5467 | 1.77992 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.3837 | 1.12354 | ||||||||
\(472\) | 24.0770 | 1.10823 | ||||||||
\(473\) | −1.92420 | −0.0884748 | ||||||||
\(474\) | 5.36146 | 0.246260 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.68224 | 0.443785 | ||||||||
\(477\) | 1.18343 | 0.0541854 | ||||||||
\(478\) | −13.0741 | −0.597996 | ||||||||
\(479\) | −28.9015 | −1.32054 | −0.660272 | − | 0.751027i | \(-0.729559\pi\) | ||||
−0.660272 | + | 0.751027i | \(0.729559\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.31927 | 0.242538 | ||||||||
\(482\) | 0.147795 | 0.00673187 | ||||||||
\(483\) | −4.76964 | −0.217026 | ||||||||
\(484\) | 12.3048 | 0.559310 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −29.0815 | −1.31916 | ||||||||
\(487\) | −17.7294 | −0.803395 | −0.401697 | − | 0.915773i | \(-0.631580\pi\) | ||||
−0.401697 | + | 0.915773i | \(0.631580\pi\) | |||||||
\(488\) | 24.7206 | 1.11905 | ||||||||
\(489\) | −63.3141 | −2.86316 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −35.1645 | −1.58695 | −0.793475 | − | 0.608603i | \(-0.791730\pi\) | ||||
−0.793475 | + | 0.608603i | \(0.791730\pi\) | |||||||
\(492\) | 14.5377 | 0.655410 | ||||||||
\(493\) | 19.0035 | 0.855875 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.51114 | 0.0678520 | ||||||||
\(497\) | −9.46422 | −0.424528 | ||||||||
\(498\) | 12.2542 | 0.549122 | ||||||||
\(499\) | 21.4508 | 0.960268 | 0.480134 | − | 0.877195i | \(-0.340588\pi\) | ||||
0.480134 | + | 0.877195i | \(0.340588\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 34.7385 | 1.55200 | ||||||||
\(502\) | 11.7298 | 0.523526 | ||||||||
\(503\) | 5.34053 | 0.238122 | 0.119061 | − | 0.992887i | \(-0.462012\pi\) | ||||
0.119061 | + | 0.992887i | \(0.462012\pi\) | |||||||
\(504\) | −55.0304 | −2.45125 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.383729 | 0.0170588 | ||||||||
\(507\) | −4.35966 | −0.193619 | ||||||||
\(508\) | −16.9821 | −0.753461 | ||||||||
\(509\) | −36.1919 | −1.60418 | −0.802088 | − | 0.597206i | \(-0.796278\pi\) | ||||
−0.802088 | + | 0.597206i | \(0.796278\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −28.1604 | −1.24574 | ||||||||
\(512\) | −2.92346 | −0.129200 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.0170 | −0.441832 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.83705 | −0.433052 | ||||||||
\(517\) | 3.76668 | 0.165658 | ||||||||
\(518\) | 3.30606 | 0.145260 | ||||||||
\(519\) | −65.6111 | −2.88001 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.77259 | 0.121469 | 0.0607346 | − | 0.998154i | \(-0.480656\pi\) | ||||
0.0607346 | + | 0.998154i | \(0.480656\pi\) | |||||||
\(522\) | −40.0235 | −1.75178 | ||||||||
\(523\) | −20.5373 | −0.898033 | −0.449016 | − | 0.893524i | \(-0.648226\pi\) | ||||
−0.449016 | + | 0.893524i | \(0.648226\pi\) | |||||||
\(524\) | −11.7370 | −0.512735 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.1919 | −0.705999 | ||||||||
\(527\) | 18.4874 | 0.805323 | ||||||||
\(528\) | 0.617399 | 0.0268688 | ||||||||
\(529\) | −22.6741 | −0.985830 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −61.4482 | −2.66662 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.5377 | 0.629698 | ||||||||
\(534\) | −49.3274 | −2.13461 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −42.7845 | −1.84801 | ||||||||
\(537\) | 80.6547 | 3.48051 | ||||||||
\(538\) | −22.6682 | −0.977294 | ||||||||
\(539\) | −0.191865 | −0.00826419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.4797 | 1.52539 | 0.762695 | − | 0.646758i | \(-0.223876\pi\) | ||||
0.762695 | + | 0.646758i | \(0.223876\pi\) | |||||||
\(542\) | −21.6456 | −0.929760 | ||||||||
\(543\) | −62.4891 | −2.68166 | ||||||||
\(544\) | −17.5111 | −0.750784 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −28.7096 | −1.22866 | ||||||||
\(547\) | 43.0756 | 1.84178 | 0.920890 | − | 0.389822i | \(-0.127463\pi\) | ||||
0.920890 | + | 0.389822i | \(0.127463\pi\) | |||||||
\(548\) | 11.4260 | 0.488092 | ||||||||
\(549\) | −63.0908 | −2.69265 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 5.29401 | 0.225328 | ||||||||
\(553\) | −4.76964 | −0.202826 | ||||||||
\(554\) | 19.2563 | 0.818123 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.8370 | 0.671640 | ||||||||
\(557\) | −40.4376 | −1.71340 | −0.856698 | − | 0.515818i | \(-0.827488\pi\) | ||||
−0.856698 | + | 0.515818i | \(0.827488\pi\) | |||||||
\(558\) | −38.9365 | −1.64831 | ||||||||
\(559\) | −9.83705 | −0.416063 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.55332 | 0.318902 | ||||||||
\(562\) | −3.48008 | −0.146798 | ||||||||
\(563\) | 19.7173 | 0.830986 | 0.415493 | − | 0.909596i | \(-0.363609\pi\) | ||||
0.415493 | + | 0.909596i | \(0.363609\pi\) | |||||||
\(564\) | 19.2563 | 0.810837 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.191865 | −0.00806467 | ||||||||
\(567\) | 59.7915 | 2.51101 | ||||||||
\(568\) | 10.5047 | 0.440768 | ||||||||
\(569\) | −18.6807 | −0.783137 | −0.391568 | − | 0.920149i | \(-0.628067\pi\) | ||||
−0.391568 | + | 0.920149i | \(0.628067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.9371 | −1.25283 | −0.626413 | − | 0.779491i | \(-0.715478\pi\) | ||||
−0.626413 | + | 0.779491i | \(0.715478\pi\) | |||||||
\(572\) | −3.30606 | −0.138233 | ||||||||
\(573\) | −36.8473 | −1.53932 | ||||||||
\(574\) | 9.03555 | 0.377137 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 40.6885 | 1.69536 | ||||||||
\(577\) | 0.156779 | 0.00652679 | 0.00326339 | − | 0.999995i | \(-0.498961\pi\) | ||||
0.00326339 | + | 0.999995i | \(0.498961\pi\) | |||||||
\(578\) | −6.32023 | −0.262887 | ||||||||
\(579\) | −12.1919 | −0.506677 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.9015 | −0.452271 | ||||||||
\(582\) | −11.0576 | −0.458353 | ||||||||
\(583\) | 0.119249 | 0.00493877 | ||||||||
\(584\) | 31.2563 | 1.29340 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.5993 | −0.561780 | ||||||||
\(587\) | −31.1474 | −1.28559 | −0.642795 | − | 0.766038i | \(-0.722225\pi\) | ||||
−0.642795 | + | 0.766038i | \(0.722225\pi\) | |||||||
\(588\) | −0.980865 | −0.0404502 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.34818 | 0.302264 | ||||||||
\(592\) | −0.363466 | −0.0149384 | ||||||||
\(593\) | −28.8728 | −1.18567 | −0.592833 | − | 0.805326i | \(-0.701991\pi\) | ||||
−0.592833 | + | 0.805326i | \(0.701991\pi\) | |||||||
\(594\) | −9.41928 | −0.386478 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.7741 | −0.728055 | ||||||||
\(597\) | 62.5904 | 2.56165 | ||||||||
\(598\) | 1.96173 | 0.0802211 | ||||||||
\(599\) | −25.3274 | −1.03485 | −0.517425 | − | 0.855728i | \(-0.673109\pi\) | ||||
−0.517425 | + | 0.855728i | \(0.673109\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.8370 | 0.809170 | 0.404585 | − | 0.914500i | \(-0.367416\pi\) | ||||
0.404585 | + | 0.914500i | \(0.367416\pi\) | |||||||
\(602\) | −6.11397 | −0.249187 | ||||||||
\(603\) | 109.193 | 4.44667 | ||||||||
\(604\) | 16.7096 | 0.679906 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −24.3837 | −0.990521 | ||||||||
\(607\) | −2.49921 | −0.101440 | −0.0507199 | − | 0.998713i | \(-0.516152\pi\) | ||||
−0.0507199 | + | 0.998713i | \(0.516152\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 50.1289 | 2.03133 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.2563 | 0.779027 | ||||||||
\(612\) | 27.4272 | 1.10868 | ||||||||
\(613\) | 0.883711 | 0.0356927 | 0.0178464 | − | 0.999841i | \(-0.494319\pi\) | ||||
0.0178464 | + | 0.999841i | \(0.494319\pi\) | |||||||
\(614\) | 1.49925 | 0.0605046 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.54517 | −0.223421 | ||||||||
\(617\) | 29.4085 | 1.18394 | 0.591971 | − | 0.805959i | \(-0.298350\pi\) | ||||
0.591971 | + | 0.805959i | \(0.298350\pi\) | |||||||
\(618\) | 6.05921 | 0.243737 | ||||||||
\(619\) | 30.3208 | 1.21870 | 0.609348 | − | 0.792903i | \(-0.291431\pi\) | ||||
0.609348 | + | 0.792903i | \(0.291431\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.00000 | −0.321029 | ||||||||
\(622\) | −0.672165 | −0.0269514 | ||||||||
\(623\) | 43.8825 | 1.75811 | ||||||||
\(624\) | 3.15632 | 0.126354 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 24.3837 | 0.974570 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.92188 | 0.356022 | ||||||||
\(629\) | −4.44668 | −0.177301 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.7767 | 0.707678 | 0.353839 | − | 0.935306i | \(-0.384876\pi\) | ||||
0.353839 | + | 0.935306i | \(0.384876\pi\) | |||||||
\(632\) | 5.29401 | 0.210584 | ||||||||
\(633\) | 36.1286 | 1.43598 | ||||||||
\(634\) | −7.40226 | −0.293981 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.609632 | 0.0241735 | ||||||||
\(637\) | −0.980865 | −0.0388633 | ||||||||
\(638\) | −4.03299 | −0.159668 | ||||||||
\(639\) | −26.8096 | −1.06057 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.6675 | 1.29029 | 0.645143 | − | 0.764062i | \(-0.276798\pi\) | ||||
0.645143 | + | 0.764062i | \(0.276798\pi\) | |||||||
\(642\) | −16.6472 | −0.657014 | ||||||||
\(643\) | −31.8661 | −1.25668 | −0.628338 | − | 0.777941i | \(-0.716264\pi\) | ||||
−0.628338 | + | 0.777941i | \(0.716264\pi\) | |||||||
\(644\) | −1.74519 | −0.0687700 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.2601 | −0.835820 | −0.417910 | − | 0.908488i | \(-0.637237\pi\) | ||||
−0.417910 | + | 0.908488i | \(0.637237\pi\) | |||||||
\(648\) | −66.3649 | −2.60706 | ||||||||
\(649\) | −6.19186 | −0.243052 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 48.7675 | 1.91135 | ||||||||
\(652\) | −23.1663 | −0.907263 | ||||||||
\(653\) | −12.8340 | −0.502234 | −0.251117 | − | 0.967957i | \(-0.580798\pi\) | ||||
−0.251117 | + | 0.967957i | \(0.580798\pi\) | |||||||
\(654\) | 4.80150 | 0.187753 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.993361 | −0.0387842 | ||||||||
\(657\) | −79.7710 | −3.11216 | ||||||||
\(658\) | 11.9683 | 0.466573 | ||||||||
\(659\) | −20.3548 | −0.792911 | −0.396456 | − | 0.918054i | \(-0.629760\pi\) | ||||
−0.396456 | + | 0.918054i | \(0.629760\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7385 | 1.19559 | 0.597795 | − | 0.801649i | \(-0.296043\pi\) | ||||
0.597795 | + | 0.801649i | \(0.296043\pi\) | |||||||
\(662\) | −7.25574 | −0.282002 | ||||||||
\(663\) | 38.6147 | 1.49967 | ||||||||
\(664\) | 12.1000 | 0.469571 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.36520 | 0.362894 | ||||||||
\(667\) | −3.42531 | −0.132629 | ||||||||
\(668\) | 12.7107 | 0.491790 | ||||||||
\(669\) | 12.9934 | 0.502352 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.35738 | −0.245424 | ||||||||
\(672\) | −46.1922 | −1.78190 | ||||||||
\(673\) | 21.2094 | 0.817564 | 0.408782 | − | 0.912632i | \(-0.365954\pi\) | ||||
0.408782 | + | 0.912632i | \(0.365954\pi\) | |||||||
\(674\) | −8.98147 | −0.345953 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.59518 | −0.0613530 | ||||||||
\(677\) | 11.2650 | 0.432951 | 0.216475 | − | 0.976288i | \(-0.430544\pi\) | ||||
0.216475 | + | 0.976288i | \(0.430544\pi\) | |||||||
\(678\) | −11.3532 | −0.436018 | ||||||||
\(679\) | 9.83705 | 0.377511 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 36.1000 | 1.38336 | ||||||||
\(682\) | −3.92346 | −0.150237 | ||||||||
\(683\) | −12.3603 | −0.472954 | −0.236477 | − | 0.971637i | \(-0.575993\pi\) | ||||
−0.236477 | + | 0.971637i | \(0.575993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −17.0934 | −0.652628 | ||||||||
\(687\) | −51.9093 | −1.98046 | ||||||||
\(688\) | 0.672165 | 0.0256261 | ||||||||
\(689\) | 0.609632 | 0.0232251 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.7493 | 0.865423 | 0.432711 | − | 0.901533i | \(-0.357557\pi\) | ||||
0.432711 | + | 0.901533i | \(0.357557\pi\) | |||||||
\(692\) | −24.0068 | −0.912601 | ||||||||
\(693\) | 14.1521 | 0.537595 | ||||||||
\(694\) | 19.2985 | 0.732561 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −55.6401 | −2.10903 | ||||||||
\(697\) | −12.1529 | −0.460323 | ||||||||
\(698\) | −14.8881 | −0.563521 | ||||||||
\(699\) | −6.84368 | −0.258852 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.0289 | −0.605404 | −0.302702 | − | 0.953085i | \(-0.597889\pi\) | ||||
−0.302702 | + | 0.953085i | \(0.597889\pi\) | |||||||
\(702\) | −48.1540 | −1.81745 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.10001 | 0.154525 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.6533 | −0.814934 | ||||||||
\(707\) | 21.6922 | 0.815818 | ||||||||
\(708\) | −31.6545 | −1.18965 | ||||||||
\(709\) | 31.4193 | 1.17998 | 0.589988 | − | 0.807412i | \(-0.299133\pi\) | ||||
0.589988 | + | 0.807412i | \(0.299133\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.5111 | −0.506707 | ||||||||
\(712\) | −48.7069 | −1.82537 | ||||||||
\(713\) | −3.33228 | −0.124795 | ||||||||
\(714\) | 24.0000 | 0.898177 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.5111 | 1.10288 | ||||||||
\(717\) | 46.3865 | 1.73234 | ||||||||
\(718\) | 2.01650 | 0.0752550 | ||||||||
\(719\) | 11.2589 | 0.419886 | 0.209943 | − | 0.977714i | \(-0.432672\pi\) | ||||
0.209943 | + | 0.977714i | \(0.432672\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.39037 | −0.200748 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.524371 | −0.0195016 | ||||||||
\(724\) | −22.8644 | −0.849750 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 30.5008 | 1.13199 | ||||||||
\(727\) | −48.9829 | −1.81668 | −0.908338 | − | 0.418237i | \(-0.862648\pi\) | ||||
−0.908338 | + | 0.418237i | \(0.862648\pi\) | |||||||
\(728\) | −28.3485 | −1.05066 | ||||||||
\(729\) | 34.0934 | 1.26272 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.22334 | 0.304151 | ||||||||
\(732\) | −32.5007 | −1.20126 | ||||||||
\(733\) | 35.9260 | 1.32696 | 0.663479 | − | 0.748195i | \(-0.269079\pi\) | ||||
0.663479 | + | 0.748195i | \(0.269079\pi\) | |||||||
\(734\) | 4.10001 | 0.151334 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.15632 | 0.116343 | ||||||||
\(737\) | 11.0029 | 0.405296 | ||||||||
\(738\) | 25.5953 | 0.942177 | ||||||||
\(739\) | 14.3523 | 0.527956 | 0.263978 | − | 0.964529i | \(-0.414965\pi\) | ||||
0.263978 | + | 0.964529i | \(0.414965\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.378902 | 0.0139099 | ||||||||
\(743\) | 12.5629 | 0.460887 | 0.230443 | − | 0.973086i | \(-0.425982\pi\) | ||||
0.230443 | + | 0.973086i | \(0.425982\pi\) | |||||||
\(744\) | −54.1289 | −1.98446 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14.0748 | 0.515316 | ||||||||
\(747\) | −30.8811 | −1.12988 | ||||||||
\(748\) | 2.76372 | 0.101052 | ||||||||
\(749\) | 14.8096 | 0.541133 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.4548 | −0.965350 | −0.482675 | − | 0.875799i | \(-0.660335\pi\) | ||||
−0.482675 | + | 0.875799i | \(0.660335\pi\) | |||||||
\(752\) | −1.31578 | −0.0479817 | ||||||||
\(753\) | −41.6169 | −1.51660 | ||||||||
\(754\) | −20.6178 | −0.750855 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 42.8386 | 1.55802 | ||||||||
\(757\) | 15.7350 | 0.571897 | 0.285949 | − | 0.958245i | \(-0.407691\pi\) | ||||
0.285949 | + | 0.958245i | \(0.407691\pi\) | |||||||
\(758\) | 17.1431 | 0.622664 | ||||||||
\(759\) | −1.36146 | −0.0494178 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.9619 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(762\) | −42.0948 | −1.52493 | ||||||||
\(763\) | −4.27149 | −0.154638 | ||||||||
\(764\) | −13.4822 | −0.487770 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.4297 | −0.449102 | ||||||||
\(767\) | −31.6545 | −1.14298 | ||||||||
\(768\) | 53.2323 | 1.92086 | ||||||||
\(769\) | 41.9974 | 1.51447 | 0.757233 | − | 0.653145i | \(-0.226551\pi\) | ||||
0.757233 | + | 0.653145i | \(0.226551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.5400 | 1.27994 | ||||||||
\(772\) | −4.46094 | −0.160553 | ||||||||
\(773\) | −40.9579 | −1.47315 | −0.736576 | − | 0.676355i | \(-0.763559\pi\) | ||||
−0.736576 | + | 0.676355i | \(0.763559\pi\) | |||||||
\(774\) | −17.3193 | −0.622528 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.9185 | −0.391952 | ||||||||
\(777\) | −11.7298 | −0.420804 | ||||||||
\(778\) | 11.5558 | 0.414295 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.70149 | −0.0966669 | ||||||||
\(782\) | −1.63992 | −0.0586434 | ||||||||
\(783\) | 84.0800 | 3.00477 | ||||||||
\(784\) | 0.0670225 | 0.00239366 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −29.0934 | −1.03773 | ||||||||
\(787\) | −28.5379 | −1.01727 | −0.508634 | − | 0.860983i | \(-0.669849\pi\) | ||||
−0.508634 | + | 0.860983i | \(0.669849\pi\) | |||||||
\(788\) | 2.68866 | 0.0957796 | ||||||||
\(789\) | 57.4482 | 2.04521 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.1000 | 0.359115 | ||||||||
\(792\) | −15.7080 | −0.558160 | ||||||||
\(793\) | −32.5007 | −1.15413 | ||||||||
\(794\) | 35.0563 | 1.24410 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.9015 | 0.811722 | ||||||||
\(797\) | −33.2790 | −1.17880 | −0.589402 | − | 0.807840i | \(-0.700636\pi\) | ||||
−0.589402 | + | 0.807840i | \(0.700636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0974 | −0.569487 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 124.308 | 4.39219 | ||||||||
\(802\) | −28.9014 | −1.02054 | ||||||||
\(803\) | −8.03817 | −0.283661 | ||||||||
\(804\) | 56.2497 | 1.98377 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.0578 | −0.706507 | ||||||||
\(807\) | 80.4259 | 2.83113 | ||||||||
\(808\) | −24.0770 | −0.847025 | ||||||||
\(809\) | −34.4234 | −1.21026 | −0.605130 | − | 0.796126i | \(-0.706879\pi\) | ||||
−0.605130 | + | 0.796126i | \(0.706879\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.2563 | 0.395263 | 0.197631 | − | 0.980276i | \(-0.436675\pi\) | ||||
0.197631 | + | 0.980276i | \(0.436675\pi\) | |||||||
\(812\) | 18.3419 | 0.643675 | ||||||||
\(813\) | 76.7980 | 2.69342 | ||||||||
\(814\) | 0.943690 | 0.0330763 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.63854 | −0.0923674 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −10.0351 | −0.350869 | ||||||||
\(819\) | 72.3497 | 2.52810 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.3167 | −1.09296 | −0.546480 | − | 0.837472i | \(-0.684033\pi\) | ||||
−0.546480 | + | 0.837472i | \(0.684033\pi\) | |||||||
\(822\) | 28.3223 | 0.987852 | ||||||||
\(823\) | −13.4800 | −0.469882 | −0.234941 | − | 0.972010i | \(-0.575490\pi\) | ||||
−0.234941 | + | 0.972010i | \(0.575490\pi\) | |||||||
\(824\) | 5.98298 | 0.208427 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19.6741 | −0.684549 | ||||||||
\(827\) | −15.9882 | −0.555963 | −0.277982 | − | 0.960586i | \(-0.589665\pi\) | ||||
−0.277982 | + | 0.960586i | \(0.589665\pi\) | |||||||
\(828\) | −4.94366 | −0.171804 | ||||||||
\(829\) | 48.4837 | 1.68391 | 0.841955 | − | 0.539548i | \(-0.181405\pi\) | ||||
0.841955 | + | 0.539548i | \(0.181405\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −68.3208 | −2.37002 | ||||||||
\(832\) | 20.9604 | 0.726670 | ||||||||
\(833\) | 0.819960 | 0.0284099 | ||||||||
\(834\) | 39.2563 | 1.35934 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 81.7965 | 2.82730 | ||||||||
\(838\) | −23.3501 | −0.806614 | ||||||||
\(839\) | 18.9934 | 0.655724 | 0.327862 | − | 0.944726i | \(-0.393672\pi\) | ||||
0.327862 | + | 0.944726i | \(0.393672\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −24.8946 | −0.857925 | ||||||||
\(843\) | 12.3472 | 0.425260 | ||||||||
\(844\) | 13.2193 | 0.455026 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 33.9030 | 1.16561 | ||||||||
\(847\) | −27.1340 | −0.932334 | ||||||||
\(848\) | −0.0416562 | −0.00143048 | ||||||||
\(849\) | 0.680729 | 0.0233626 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.801497 | 0.0274750 | ||||||||
\(852\) | −13.8108 | −0.473149 | ||||||||
\(853\) | −44.1210 | −1.51067 | −0.755337 | − | 0.655337i | \(-0.772527\pi\) | ||||
−0.755337 | + | 0.655337i | \(0.772527\pi\) | |||||||
\(854\) | −20.2000 | −0.691230 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.4378 | −0.561833 | ||||||||
\(857\) | 32.4149 | 1.10727 | 0.553635 | − | 0.832759i | \(-0.313240\pi\) | ||||
0.553635 | + | 0.832759i | \(0.313240\pi\) | |||||||
\(858\) | −8.19495 | −0.279771 | ||||||||
\(859\) | 6.29444 | 0.214763 | 0.107382 | − | 0.994218i | \(-0.465753\pi\) | ||||
0.107382 | + | 0.994218i | \(0.465753\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −32.0578 | −1.09253 | ||||||||
\(862\) | −1.58283 | −0.0539113 | ||||||||
\(863\) | −17.4338 | −0.593453 | −0.296726 | − | 0.954963i | \(-0.595895\pi\) | ||||
−0.296726 | + | 0.954963i | \(0.595895\pi\) | |||||||
\(864\) | −77.4771 | −2.63582 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16.7978 | −0.570811 | ||||||||
\(867\) | 22.4240 | 0.761557 | ||||||||
\(868\) | 17.8438 | 0.605657 | ||||||||
\(869\) | −1.36146 | −0.0461843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.2497 | 1.90595 | ||||||||
\(872\) | 4.74109 | 0.160554 | ||||||||
\(873\) | 27.8658 | 0.943113 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −41.0934 | −1.38842 | ||||||||
\(877\) | 23.2904 | 0.786462 | 0.393231 | − | 0.919440i | \(-0.371357\pi\) | ||||
0.393231 | + | 0.919440i | \(0.371357\pi\) | |||||||
\(878\) | −26.7086 | −0.901370 | ||||||||
\(879\) | 48.2497 | 1.62742 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.9619 | 0.975751 | 0.487875 | − | 0.872913i | \(-0.337772\pi\) | ||||
0.487875 | + | 0.872913i | \(0.337772\pi\) | |||||||
\(882\) | −1.72693 | −0.0581487 | ||||||||
\(883\) | 37.3627 | 1.25735 | 0.628677 | − | 0.777667i | \(-0.283597\pi\) | ||||
0.628677 | + | 0.777667i | \(0.283597\pi\) | |||||||
\(884\) | 14.1289 | 0.475207 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.6467 | −0.357683 | ||||||||
\(887\) | −23.0234 | −0.773050 | −0.386525 | − | 0.922279i | \(-0.626325\pi\) | ||||
−0.386525 | + | 0.922279i | \(0.626325\pi\) | |||||||
\(888\) | 13.0194 | 0.436901 | ||||||||
\(889\) | 37.4482 | 1.25597 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.0670 | 0.571767 | ||||||||
\(892\) | 4.75420 | 0.159183 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −44.0578 | −1.47351 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −15.6822 | −0.523907 | ||||||||
\(897\) | −6.96015 | −0.232393 | ||||||||
\(898\) | 6.40723 | 0.213812 | ||||||||
\(899\) | 35.0223 | 1.16806 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.509626 | −0.0169781 | ||||||||
\(902\) | 2.57913 | 0.0858756 | ||||||||
\(903\) | 21.6922 | 0.721870 | ||||||||
\(904\) | −11.2104 | −0.372852 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 41.4193 | 1.37606 | ||||||||
\(907\) | −35.2693 | −1.17110 | −0.585549 | − | 0.810637i | \(-0.699121\pi\) | ||||
−0.585549 | + | 0.810637i | \(0.699121\pi\) | |||||||
\(908\) | 13.2088 | 0.438350 | ||||||||
\(909\) | 61.4482 | 2.03811 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.97260 | 0.164750 | 0.0823748 | − | 0.996601i | \(-0.473750\pi\) | ||||
0.0823748 | + | 0.996601i | \(0.473750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.11175 | −0.102984 | ||||||||
\(914\) | 31.2904 | 1.03499 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.9934 | −0.627558 | ||||||||
\(917\) | 25.8819 | 0.854697 | ||||||||
\(918\) | 40.2546 | 1.32860 | ||||||||
\(919\) | −48.7096 | −1.60678 | −0.803391 | − | 0.595451i | \(-0.796973\pi\) | ||||
−0.803391 | + | 0.595451i | \(0.796973\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.31927 | −0.175276 | ||||||||
\(922\) | 7.28429 | 0.239895 | ||||||||
\(923\) | −13.8108 | −0.454587 | ||||||||
\(924\) | 7.29036 | 0.239835 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.9726 | 0.754926 | ||||||||
\(927\) | −15.2695 | −0.501516 | ||||||||
\(928\) | −33.1729 | −1.08895 | ||||||||
\(929\) | 32.5126 | 1.06671 | 0.533353 | − | 0.845893i | \(-0.320932\pi\) | ||||
0.533353 | + | 0.845893i | \(0.320932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.50407 | −0.0820235 | ||||||||
\(933\) | 2.38482 | 0.0780755 | ||||||||
\(934\) | −24.3756 | −0.797593 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −80.3038 | −2.62481 | ||||||||
\(937\) | 0.385560 | 0.0125957 | 0.00629785 | − | 0.999980i | \(-0.497995\pi\) | ||||
0.00629785 | + | 0.999980i | \(0.497995\pi\) | |||||||
\(938\) | 34.9606 | 1.14150 | ||||||||
\(939\) | −86.5126 | −2.82323 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.3482 | −1.47831 | −0.739154 | − | 0.673536i | \(-0.764775\pi\) | ||||
−0.739154 | + | 0.673536i | \(0.764775\pi\) | |||||||
\(942\) | 22.1153 | 0.720554 | ||||||||
\(943\) | 2.19051 | 0.0713329 | ||||||||
\(944\) | 2.16295 | 0.0703982 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.74519 | −0.0567409 | ||||||||
\(947\) | −9.61202 | −0.312349 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(948\) | −6.96015 | −0.226055 | ||||||||
\(949\) | −41.0934 | −1.33395 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.2630 | 0.851635 | ||||||||
\(952\) | 23.6981 | 0.768059 | ||||||||
\(953\) | −59.8421 | −1.93848 | −0.969238 | − | 0.246126i | \(-0.920842\pi\) | ||||
−0.969238 | + | 0.246126i | \(0.920842\pi\) | |||||||
\(954\) | 1.07333 | 0.0347503 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16.9726 | 0.548933 | ||||||||
\(957\) | 14.3089 | 0.462542 | ||||||||
\(958\) | −26.2127 | −0.846895 | ||||||||
\(959\) | −25.1959 | −0.813619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.07110 | 0.0990676 | ||||||||
\(962\) | 4.82441 | 0.155545 | ||||||||
\(963\) | 41.9518 | 1.35188 | ||||||||
\(964\) | −0.191865 | −0.00617954 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.32591 | −0.139184 | ||||||||
\(967\) | 0.368324 | 0.0118445 | 0.00592225 | − | 0.999982i | \(-0.498115\pi\) | ||||
0.00592225 | + | 0.999982i | \(0.498115\pi\) | |||||||
\(968\) | 30.1171 | 0.967999 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.8370 | 1.47098 | 0.735490 | − | 0.677535i | \(-0.236952\pi\) | ||||
0.735490 | + | 0.677535i | \(0.236952\pi\) | |||||||
\(972\) | 37.7531 | 1.21093 | ||||||||
\(973\) | −34.9231 | −1.11958 | ||||||||
\(974\) | −16.0800 | −0.515235 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.22077 | 0.0710853 | ||||||||
\(977\) | 29.0337 | 0.928872 | 0.464436 | − | 0.885607i | \(-0.346257\pi\) | ||||
0.464436 | + | 0.885607i | \(0.346257\pi\) | |||||||
\(978\) | −57.4239 | −1.83621 | ||||||||
\(979\) | 12.5259 | 0.400330 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.1000 | −0.386323 | ||||||||
\(982\) | −31.8930 | −1.01775 | ||||||||
\(983\) | −11.0160 | −0.351355 | −0.175677 | − | 0.984448i | \(-0.556212\pi\) | ||||
−0.175677 | + | 0.984448i | \(0.556212\pi\) | |||||||
\(984\) | 35.5822 | 1.13432 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17.2356 | 0.548892 | ||||||||
\(987\) | −42.4631 | −1.35161 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.48223 | −0.0471320 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.6822 | 0.815823 | 0.407912 | − | 0.913021i | \(-0.366257\pi\) | ||||
0.407912 | + | 0.913021i | \(0.366257\pi\) | |||||||
\(992\) | −32.2719 | −1.02463 | ||||||||
\(993\) | 25.7431 | 0.816933 | ||||||||
\(994\) | −8.58374 | −0.272260 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −15.9081 | −0.504069 | ||||||||
\(997\) | −20.3854 | −0.645611 | −0.322805 | − | 0.946465i | \(-0.604626\pi\) | ||||
−0.322805 | + | 0.946465i | \(0.604626\pi\) | |||||||
\(998\) | 19.4551 | 0.615842 | ||||||||
\(999\) | −19.6741 | −0.622461 |
(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 | 9025.2.a.bx.1.4 | 6 | ||
5.2 | odd | 4 | 1805.2.b.e.1084.4 | 6 | |||
5.3 | odd | 4 | 1805.2.b.e.1084.3 | 6 | |||
5.4 | even | 2 | inner | 9025.2.a.bx.1.3 | 6 | ||
19.18 | odd | 2 | 475.2.a.j.1.3 | 6 | |||
57.56 | even | 2 | 4275.2.a.br.1.4 | 6 | |||
76.75 | even | 2 | 7600.2.a.ck.1.1 | 6 | |||
95.18 | even | 4 | 95.2.b.b.39.4 | yes | 6 | ||
95.37 | even | 4 | 95.2.b.b.39.3 | ✓ | 6 | ||
95.94 | odd | 2 | 475.2.a.j.1.4 | 6 | |||
285.113 | odd | 4 | 855.2.c.d.514.3 | 6 | |||
285.227 | odd | 4 | 855.2.c.d.514.4 | 6 | |||
285.284 | even | 2 | 4275.2.a.br.1.3 | 6 | |||
380.227 | odd | 4 | 1520.2.d.h.609.6 | 6 | |||
380.303 | odd | 4 | 1520.2.d.h.609.1 | 6 | |||
380.379 | even | 2 | 7600.2.a.ck.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.b.b.39.3 | ✓ | 6 | 95.37 | even | 4 | ||
95.2.b.b.39.4 | yes | 6 | 95.18 | even | 4 | ||
475.2.a.j.1.3 | 6 | 19.18 | odd | 2 | |||
475.2.a.j.1.4 | 6 | 95.94 | odd | 2 | |||
855.2.c.d.514.3 | 6 | 285.113 | odd | 4 | |||
855.2.c.d.514.4 | 6 | 285.227 | odd | 4 | |||
1520.2.d.h.609.1 | 6 | 380.303 | odd | 4 | |||
1520.2.d.h.609.6 | 6 | 380.227 | odd | 4 | |||
1805.2.b.e.1084.3 | 6 | 5.3 | odd | 4 | |||
1805.2.b.e.1084.4 | 6 | 5.2 | odd | 4 | |||
4275.2.a.br.1.3 | 6 | 285.284 | even | 2 | |||
4275.2.a.br.1.4 | 6 | 57.56 | even | 2 | |||
7600.2.a.ck.1.1 | 6 | 76.75 | even | 2 | |||
7600.2.a.ck.1.6 | 6 | 380.379 | even | 2 | |||
9025.2.a.bx.1.3 | 6 | 5.4 | even | 2 | inner | ||
9025.2.a.bx.1.4 | 6 | 1.1 | even | 1 | trivial |