Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.6 | ||
Root | \(1.80194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.z.1351.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 1.04892i | 0.396453i | 0.980156 | + | 0.198227i | \(0.0635182\pi\) | ||||
−0.980156 | + | 0.198227i | \(0.936482\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | − 1.35690i | − 0.409119i | −0.978854 | − | 0.204560i | \(-0.934424\pi\) | ||||
0.978854 | − | 0.204560i | \(-0.0655763\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.04892 | −0.280335 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.08815 | 0.263914 | 0.131957 | − | 0.991255i | \(-0.457874\pi\) | ||||
0.131957 | + | 0.991255i | \(0.457874\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 2.93900i | 0.674253i | 0.941459 | + | 0.337127i | \(0.109455\pi\) | ||||
−0.941459 | + | 0.337127i | \(0.890545\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 1.04892i | 0.228893i | ||||||||
\(22\) | 1.35690 | 0.289291 | ||||||||
\(23\) | 0.692021 | 0.144296 | 0.0721482 | − | 0.997394i | \(-0.477015\pi\) | ||||
0.0721482 | + | 0.997394i | \(0.477015\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 1.04892i | − 0.198227i | ||||||||
\(29\) | −2.37867 | −0.441707 | −0.220854 | − | 0.975307i | \(-0.570884\pi\) | ||||
−0.220854 | + | 0.975307i | \(0.570884\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 9.85086i | 1.76927i | 0.466288 | + | 0.884633i | \(0.345591\pi\) | ||||
−0.466288 | + | 0.884633i | \(0.654409\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 1.35690i | − 0.236205i | ||||||||
\(34\) | 1.08815i | 0.186615i | ||||||||
\(35\) | 1.04892 | 0.177299 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 9.26875i | − 1.52377i | −0.647710 | − | 0.761887i | \(-0.724273\pi\) | ||||
0.647710 | − | 0.761887i | \(-0.275727\pi\) | |||||||
\(38\) | −2.93900 | −0.476769 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 2.84117i | 0.443716i | 0.975079 | + | 0.221858i | \(0.0712121\pi\) | ||||
−0.975079 | + | 0.221858i | \(0.928788\pi\) | |||||||
\(42\) | −1.04892 | −0.161851 | ||||||||
\(43\) | 4.45473 | 0.679340 | 0.339670 | − | 0.940545i | \(-0.389685\pi\) | ||||
0.339670 | + | 0.940545i | \(0.389685\pi\) | |||||||
\(44\) | 1.35690i | 0.204560i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | 0.692021i | 0.102033i | ||||||||
\(47\) | 3.31767i | 0.483931i | 0.970285 | + | 0.241966i | \(0.0777922\pi\) | ||||
−0.970285 | + | 0.241966i | \(0.922208\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 5.89977 | 0.842825 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | 1.08815 | 0.152371 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.664874 | 0.0913275 | 0.0456638 | − | 0.998957i | \(-0.485460\pi\) | ||||
0.0456638 | + | 0.998957i | \(0.485460\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −1.35690 | −0.182964 | ||||||||
\(56\) | 1.04892 | 0.140167 | ||||||||
\(57\) | 2.93900i | 0.389280i | ||||||||
\(58\) | − 2.37867i | − 0.312334i | ||||||||
\(59\) | 1.96077i | 0.255271i | 0.991821 | + | 0.127635i | \(0.0407387\pi\) | ||||
−0.991821 | + | 0.127635i | \(0.959261\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 3.24698 | 0.415733 | 0.207867 | − | 0.978157i | \(-0.433348\pi\) | ||||
0.207867 | + | 0.978157i | \(0.433348\pi\) | |||||||
\(62\) | −9.85086 | −1.25106 | ||||||||
\(63\) | 1.04892i | 0.132151i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.35690 | 0.167022 | ||||||||
\(67\) | 6.91185i | 0.844417i | 0.906499 | + | 0.422209i | \(0.138745\pi\) | ||||
−0.906499 | + | 0.422209i | \(0.861255\pi\) | |||||||
\(68\) | −1.08815 | −0.131957 | ||||||||
\(69\) | 0.692021 | 0.0833096 | ||||||||
\(70\) | 1.04892i | 0.125370i | ||||||||
\(71\) | 2.29590i | 0.272473i | 0.990676 | + | 0.136236i | \(0.0435007\pi\) | ||||
−0.990676 | + | 0.136236i | \(0.956499\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 3.36227i | − 0.393524i | −0.980451 | − | 0.196762i | \(-0.936957\pi\) | ||||
0.980451 | − | 0.196762i | \(-0.0630427\pi\) | |||||||
\(74\) | 9.26875 | 1.07747 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | − 2.93900i | − 0.337127i | ||||||||
\(77\) | 1.42327 | 0.162197 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3230 | 1.38645 | 0.693225 | − | 0.720721i | \(-0.256189\pi\) | ||||
0.693225 | + | 0.720721i | \(0.256189\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.84117 | −0.313754 | ||||||||
\(83\) | 2.68664i | 0.294898i | 0.989070 | + | 0.147449i | \(0.0471062\pi\) | ||||
−0.989070 | + | 0.147449i | \(0.952894\pi\) | |||||||
\(84\) | − 1.04892i | − 0.114446i | ||||||||
\(85\) | − 1.08815i | − 0.118026i | ||||||||
\(86\) | 4.45473i | 0.480366i | ||||||||
\(87\) | −2.37867 | −0.255020 | ||||||||
\(88\) | −1.35690 | −0.144646 | ||||||||
\(89\) | − 12.8877i | − 1.36609i | −0.730375 | − | 0.683046i | \(-0.760655\pi\) | ||||
0.730375 | − | 0.683046i | \(-0.239345\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.692021 | −0.0721482 | ||||||||
\(93\) | 9.85086i | 1.02149i | ||||||||
\(94\) | −3.31767 | −0.342191 | ||||||||
\(95\) | 2.93900 | 0.301535 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 1.56704i | 0.159109i | 0.996831 | + | 0.0795544i | \(0.0253497\pi\) | ||||
−0.996831 | + | 0.0795544i | \(0.974650\pi\) | |||||||
\(98\) | 5.89977i | 0.595967i | ||||||||
\(99\) | − 1.35690i | − 0.136373i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −4.71379 | −0.469040 | −0.234520 | − | 0.972111i | \(-0.575352\pi\) | ||||
−0.234520 | + | 0.972111i | \(0.575352\pi\) | |||||||
\(102\) | 1.08815i | 0.107743i | ||||||||
\(103\) | 12.1642 | 1.19858 | 0.599288 | − | 0.800534i | \(-0.295451\pi\) | ||||
0.599288 | + | 0.800534i | \(0.295451\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.04892 | 0.102364 | ||||||||
\(106\) | 0.664874i | 0.0645783i | ||||||||
\(107\) | 1.83877 | 0.177761 | 0.0888805 | − | 0.996042i | \(-0.471671\pi\) | ||||
0.0888805 | + | 0.996042i | \(0.471671\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 16.2403i | 1.55554i | 0.628551 | + | 0.777768i | \(0.283648\pi\) | ||||
−0.628551 | + | 0.777768i | \(0.716352\pi\) | |||||||
\(110\) | − 1.35690i | − 0.129375i | ||||||||
\(111\) | − 9.26875i | − 0.879751i | ||||||||
\(112\) | 1.04892i | 0.0991134i | ||||||||
\(113\) | 16.8267 | 1.58292 | 0.791461 | − | 0.611220i | \(-0.209321\pi\) | ||||
0.791461 | + | 0.611220i | \(0.209321\pi\) | |||||||
\(114\) | −2.93900 | −0.275263 | ||||||||
\(115\) | − 0.692021i | − 0.0645313i | ||||||||
\(116\) | 2.37867 | 0.220854 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.96077 | −0.180504 | ||||||||
\(119\) | 1.14138i | 0.104630i | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 9.15883 | 0.832621 | ||||||||
\(122\) | 3.24698i | 0.293968i | ||||||||
\(123\) | 2.84117i | 0.256179i | ||||||||
\(124\) | − 9.85086i | − 0.884633i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −1.04892 | −0.0934450 | ||||||||
\(127\) | 5.06100 | 0.449091 | 0.224546 | − | 0.974464i | \(-0.427910\pi\) | ||||
0.224546 | + | 0.974464i | \(0.427910\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 4.45473 | 0.392217 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.81940 | 0.333702 | 0.166851 | − | 0.985982i | \(-0.446640\pi\) | ||||
0.166851 | + | 0.985982i | \(0.446640\pi\) | |||||||
\(132\) | 1.35690i | 0.118103i | ||||||||
\(133\) | −3.08277 | −0.267310 | ||||||||
\(134\) | −6.91185 | −0.597093 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | − 1.08815i | − 0.0933077i | ||||||||
\(137\) | 8.59717i | 0.734506i | 0.930121 | + | 0.367253i | \(0.119702\pi\) | ||||
−0.930121 | + | 0.367253i | \(0.880298\pi\) | |||||||
\(138\) | 0.692021i | 0.0589088i | ||||||||
\(139\) | −2.38404 | −0.202212 | −0.101106 | − | 0.994876i | \(-0.532238\pi\) | ||||
−0.101106 | + | 0.994876i | \(0.532238\pi\) | |||||||
\(140\) | −1.04892 | −0.0886497 | ||||||||
\(141\) | 3.31767i | 0.279398i | ||||||||
\(142\) | −2.29590 | −0.192667 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.37867i | 0.197537i | ||||||||
\(146\) | 3.36227 | 0.278264 | ||||||||
\(147\) | 5.89977 | 0.486605 | ||||||||
\(148\) | 9.26875i | 0.761887i | ||||||||
\(149\) | − 8.93900i | − 0.732312i | −0.930554 | − | 0.366156i | \(-0.880674\pi\) | ||||
0.930554 | − | 0.366156i | \(-0.119326\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | 8.45473i | 0.688036i | 0.938963 | + | 0.344018i | \(0.111788\pi\) | ||||
−0.938963 | + | 0.344018i | \(0.888212\pi\) | |||||||
\(152\) | 2.93900 | 0.238384 | ||||||||
\(153\) | 1.08815 | 0.0879714 | ||||||||
\(154\) | 1.42327i | 0.114690i | ||||||||
\(155\) | 9.85086 | 0.791240 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.70410 | −0.215811 | −0.107905 | − | 0.994161i | \(-0.534414\pi\) | ||||
−0.107905 | + | 0.994161i | \(0.534414\pi\) | |||||||
\(158\) | 12.3230i | 0.980369i | ||||||||
\(159\) | 0.664874 | 0.0527280 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 0.725873i | 0.0572068i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 22.5284i | 1.76456i | 0.470724 | + | 0.882280i | \(0.343993\pi\) | ||||
−0.470724 | + | 0.882280i | \(0.656007\pi\) | |||||||
\(164\) | − 2.84117i | − 0.221858i | ||||||||
\(165\) | −1.35690 | −0.105634 | ||||||||
\(166\) | −2.68664 | −0.208524 | ||||||||
\(167\) | − 12.2228i | − 0.945830i | −0.881108 | − | 0.472915i | \(-0.843202\pi\) | ||||
0.881108 | − | 0.472915i | \(-0.156798\pi\) | |||||||
\(168\) | 1.04892 | 0.0809257 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1.08815 | 0.0834570 | ||||||||
\(171\) | 2.93900i | 0.224751i | ||||||||
\(172\) | −4.45473 | −0.339670 | ||||||||
\(173\) | 11.7168 | 0.890810 | 0.445405 | − | 0.895329i | \(-0.353060\pi\) | ||||
0.445405 | + | 0.895329i | \(0.353060\pi\) | |||||||
\(174\) | − 2.37867i | − 0.180326i | ||||||||
\(175\) | − 1.04892i | − 0.0792907i | ||||||||
\(176\) | − 1.35690i | − 0.102280i | ||||||||
\(177\) | 1.96077i | 0.147381i | ||||||||
\(178\) | 12.8877 | 0.965973 | ||||||||
\(179\) | −8.89738 | −0.665021 | −0.332511 | − | 0.943099i | \(-0.607896\pi\) | ||||
−0.332511 | + | 0.943099i | \(0.607896\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | −1.31229 | −0.0975418 | −0.0487709 | − | 0.998810i | \(-0.515530\pi\) | ||||
−0.0487709 | + | 0.998810i | \(0.515530\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.24698 | 0.240024 | ||||||||
\(184\) | − 0.692021i | − 0.0510165i | ||||||||
\(185\) | −9.26875 | −0.681452 | ||||||||
\(186\) | −9.85086 | −0.722300 | ||||||||
\(187\) | − 1.47650i | − 0.107972i | ||||||||
\(188\) | − 3.31767i | − 0.241966i | ||||||||
\(189\) | 1.04892i | 0.0762975i | ||||||||
\(190\) | 2.93900i | 0.213218i | ||||||||
\(191\) | 5.75063 | 0.416101 | 0.208050 | − | 0.978118i | \(-0.433288\pi\) | ||||
0.208050 | + | 0.978118i | \(0.433288\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | − 10.0339i | − 0.722252i | −0.932517 | − | 0.361126i | \(-0.882392\pi\) | ||||
0.932517 | − | 0.361126i | \(-0.117608\pi\) | |||||||
\(194\) | −1.56704 | −0.112507 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.89977 | −0.421412 | ||||||||
\(197\) | 22.9071i | 1.63206i | 0.578009 | + | 0.816031i | \(0.303830\pi\) | ||||
−0.578009 | + | 0.816031i | \(0.696170\pi\) | |||||||
\(198\) | 1.35690 | 0.0964304 | ||||||||
\(199\) | −27.0291 | −1.91604 | −0.958020 | − | 0.286702i | \(-0.907441\pi\) | ||||
−0.958020 | + | 0.286702i | \(0.907441\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 6.91185i | 0.487525i | ||||||||
\(202\) | − 4.71379i | − 0.331661i | ||||||||
\(203\) | − 2.49502i | − 0.175116i | ||||||||
\(204\) | −1.08815 | −0.0761855 | ||||||||
\(205\) | 2.84117 | 0.198436 | ||||||||
\(206\) | 12.1642i | 0.847521i | ||||||||
\(207\) | 0.692021 | 0.0480988 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.98792 | 0.275850 | ||||||||
\(210\) | 1.04892i | 0.0723822i | ||||||||
\(211\) | 10.3720 | 0.714035 | 0.357018 | − | 0.934098i | \(-0.383794\pi\) | ||||
0.357018 | + | 0.934098i | \(0.383794\pi\) | |||||||
\(212\) | −0.664874 | −0.0456638 | ||||||||
\(213\) | 2.29590i | 0.157312i | ||||||||
\(214\) | 1.83877i | 0.125696i | ||||||||
\(215\) | − 4.45473i | − 0.303810i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | −10.3327 | −0.701432 | ||||||||
\(218\) | −16.2403 | −1.09993 | ||||||||
\(219\) | − 3.36227i | − 0.227201i | ||||||||
\(220\) | 1.35690 | 0.0914819 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 9.26875 | 0.622078 | ||||||||
\(223\) | 14.0532i | 0.941074i | 0.882380 | + | 0.470537i | \(0.155940\pi\) | ||||
−0.882380 | + | 0.470537i | \(0.844060\pi\) | |||||||
\(224\) | −1.04892 | −0.0700837 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 16.8267i | 1.11929i | ||||||||
\(227\) | − 1.93362i | − 0.128339i | −0.997939 | − | 0.0641696i | \(-0.979560\pi\) | ||||
0.997939 | − | 0.0641696i | \(-0.0204399\pi\) | |||||||
\(228\) | − 2.93900i | − 0.194640i | ||||||||
\(229\) | 10.9148i | 0.721273i | 0.932706 | + | 0.360636i | \(0.117440\pi\) | ||||
−0.932706 | + | 0.360636i | \(0.882560\pi\) | |||||||
\(230\) | 0.692021 | 0.0456305 | ||||||||
\(231\) | 1.42327 | 0.0936444 | ||||||||
\(232\) | 2.37867i | 0.156167i | ||||||||
\(233\) | 21.6896 | 1.42093 | 0.710467 | − | 0.703730i | \(-0.248484\pi\) | ||||
0.710467 | + | 0.703730i | \(0.248484\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.31767 | 0.216421 | ||||||||
\(236\) | − 1.96077i | − 0.127635i | ||||||||
\(237\) | 12.3230 | 0.800468 | ||||||||
\(238\) | −1.14138 | −0.0739844 | ||||||||
\(239\) | − 27.2349i | − 1.76168i | −0.473415 | − | 0.880840i | \(-0.656979\pi\) | ||||
0.473415 | − | 0.880840i | \(-0.343021\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | − 8.21014i | − 0.528862i | −0.964405 | − | 0.264431i | \(-0.914816\pi\) | ||||
0.964405 | − | 0.264431i | \(-0.0851841\pi\) | |||||||
\(242\) | 9.15883i | 0.588752i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.24698 | −0.207867 | ||||||||
\(245\) | − 5.89977i | − 0.376923i | ||||||||
\(246\) | −2.84117 | −0.181146 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 9.85086 | 0.625530 | ||||||||
\(249\) | 2.68664i | 0.170259i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 6.57002 | 0.414696 | 0.207348 | − | 0.978267i | \(-0.433517\pi\) | ||||
0.207348 | + | 0.978267i | \(0.433517\pi\) | |||||||
\(252\) | − 1.04892i | − 0.0660756i | ||||||||
\(253\) | − 0.939001i | − 0.0590345i | ||||||||
\(254\) | 5.06100i | 0.317555i | ||||||||
\(255\) | − 1.08815i | − 0.0681423i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.7657 | −0.858680 | −0.429340 | − | 0.903143i | \(-0.641254\pi\) | ||||
−0.429340 | + | 0.903143i | \(0.641254\pi\) | |||||||
\(258\) | 4.45473i | 0.277339i | ||||||||
\(259\) | 9.72215 | 0.604105 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.37867 | −0.147236 | ||||||||
\(262\) | 3.81940i | 0.235963i | ||||||||
\(263\) | −9.54288 | −0.588439 | −0.294219 | − | 0.955738i | \(-0.595060\pi\) | ||||
−0.294219 | + | 0.955738i | \(0.595060\pi\) | |||||||
\(264\) | −1.35690 | −0.0835112 | ||||||||
\(265\) | − 0.664874i | − 0.0408429i | ||||||||
\(266\) | − 3.08277i | − 0.189017i | ||||||||
\(267\) | − 12.8877i | − 0.788714i | ||||||||
\(268\) | − 6.91185i | − 0.422209i | ||||||||
\(269\) | 9.07069 | 0.553050 | 0.276525 | − | 0.961007i | \(-0.410817\pi\) | ||||
0.276525 | + | 0.961007i | \(0.410817\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | − 17.5579i | − 1.06657i | −0.845936 | − | 0.533285i | \(-0.820958\pi\) | ||||
0.845936 | − | 0.533285i | \(-0.179042\pi\) | |||||||
\(272\) | 1.08815 | 0.0659785 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.59717 | −0.519374 | ||||||||
\(275\) | 1.35690i | 0.0818239i | ||||||||
\(276\) | −0.692021 | −0.0416548 | ||||||||
\(277\) | −13.7071 | −0.823579 | −0.411790 | − | 0.911279i | \(-0.635096\pi\) | ||||
−0.411790 | + | 0.911279i | \(0.635096\pi\) | |||||||
\(278\) | − 2.38404i | − 0.142985i | ||||||||
\(279\) | 9.85086i | 0.589755i | ||||||||
\(280\) | − 1.04892i | − 0.0626848i | ||||||||
\(281\) | 24.3696i | 1.45377i | 0.686761 | + | 0.726883i | \(0.259032\pi\) | ||||
−0.686761 | + | 0.726883i | \(0.740968\pi\) | |||||||
\(282\) | −3.31767 | −0.197564 | ||||||||
\(283\) | 17.1511 | 1.01952 | 0.509762 | − | 0.860315i | \(-0.329733\pi\) | ||||
0.509762 | + | 0.860315i | \(0.329733\pi\) | |||||||
\(284\) | − 2.29590i | − 0.136236i | ||||||||
\(285\) | 2.93900 | 0.174091 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.98015 | −0.175913 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −15.8159 | −0.930349 | ||||||||
\(290\) | −2.37867 | −0.139680 | ||||||||
\(291\) | 1.56704i | 0.0918615i | ||||||||
\(292\) | 3.36227i | 0.196762i | ||||||||
\(293\) | 24.1172i | 1.40894i | 0.709732 | + | 0.704471i | \(0.248816\pi\) | ||||
−0.709732 | + | 0.704471i | \(0.751184\pi\) | |||||||
\(294\) | 5.89977i | 0.344082i | ||||||||
\(295\) | 1.96077 | 0.114161 | ||||||||
\(296\) | −9.26875 | −0.538735 | ||||||||
\(297\) | − 1.35690i | − 0.0787351i | ||||||||
\(298\) | 8.93900 | 0.517822 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 4.67264i | 0.269327i | ||||||||
\(302\) | −8.45473 | −0.486515 | ||||||||
\(303\) | −4.71379 | −0.270800 | ||||||||
\(304\) | 2.93900i | 0.168563i | ||||||||
\(305\) | − 3.24698i | − 0.185922i | ||||||||
\(306\) | 1.08815i | 0.0622052i | ||||||||
\(307\) | 17.2282i | 0.983265i | 0.870803 | + | 0.491632i | \(0.163600\pi\) | ||||
−0.870803 | + | 0.491632i | \(0.836400\pi\) | |||||||
\(308\) | −1.42327 | −0.0810984 | ||||||||
\(309\) | 12.1642 | 0.691998 | ||||||||
\(310\) | 9.85086i | 0.559491i | ||||||||
\(311\) | 25.9801 | 1.47320 | 0.736600 | − | 0.676329i | \(-0.236430\pi\) | ||||
0.736600 | + | 0.676329i | \(0.236430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.82669 | 0.442391 | 0.221195 | − | 0.975230i | \(-0.429004\pi\) | ||||
0.221195 | + | 0.975230i | \(0.429004\pi\) | |||||||
\(314\) | − 2.70410i | − 0.152601i | ||||||||
\(315\) | 1.04892 | 0.0590998 | ||||||||
\(316\) | −12.3230 | −0.693225 | ||||||||
\(317\) | 0.391813i | 0.0220064i | 0.999939 | + | 0.0110032i | \(0.00350250\pi\) | ||||
−0.999939 | + | 0.0110032i | \(0.996498\pi\) | |||||||
\(318\) | 0.664874i | 0.0372843i | ||||||||
\(319\) | 3.22760i | 0.180711i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 1.83877 | 0.102630 | ||||||||
\(322\) | −0.725873 | −0.0404513 | ||||||||
\(323\) | 3.19806i | 0.177945i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −22.5284 | −1.24773 | ||||||||
\(327\) | 16.2403i | 0.898089i | ||||||||
\(328\) | 2.84117 | 0.156877 | ||||||||
\(329\) | −3.47996 | −0.191856 | ||||||||
\(330\) | − 1.35690i | − 0.0746947i | ||||||||
\(331\) | 26.3424i | 1.44791i | 0.689847 | + | 0.723955i | \(0.257678\pi\) | ||||
−0.689847 | + | 0.723955i | \(0.742322\pi\) | |||||||
\(332\) | − 2.68664i | − 0.147449i | ||||||||
\(333\) | − 9.26875i | − 0.507924i | ||||||||
\(334\) | 12.2228 | 0.668803 | ||||||||
\(335\) | 6.91185 | 0.377635 | ||||||||
\(336\) | 1.04892i | 0.0572231i | ||||||||
\(337\) | −14.8345 | −0.808085 | −0.404042 | − | 0.914740i | \(-0.632395\pi\) | ||||
−0.404042 | + | 0.914740i | \(0.632395\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.8267 | 0.913900 | ||||||||
\(340\) | 1.08815i | 0.0590130i | ||||||||
\(341\) | 13.3666 | 0.723841 | ||||||||
\(342\) | −2.93900 | −0.158923 | ||||||||
\(343\) | 13.5308i | 0.730594i | ||||||||
\(344\) | − 4.45473i | − 0.240183i | ||||||||
\(345\) | − 0.692021i | − 0.0372572i | ||||||||
\(346\) | 11.7168i | 0.629898i | ||||||||
\(347\) | −0.636399 | −0.0341637 | −0.0170819 | − | 0.999854i | \(-0.505438\pi\) | ||||
−0.0170819 | + | 0.999854i | \(0.505438\pi\) | |||||||
\(348\) | 2.37867 | 0.127510 | ||||||||
\(349\) | − 17.2784i | − 0.924894i | −0.886647 | − | 0.462447i | \(-0.846972\pi\) | ||||
0.886647 | − | 0.462447i | \(-0.153028\pi\) | |||||||
\(350\) | 1.04892 | 0.0560670 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.35690 | 0.0723228 | ||||||||
\(353\) | − 21.7614i | − 1.15824i | −0.815242 | − | 0.579121i | \(-0.803396\pi\) | ||||
0.815242 | − | 0.579121i | \(-0.196604\pi\) | |||||||
\(354\) | −1.96077 | −0.104214 | ||||||||
\(355\) | 2.29590 | 0.121854 | ||||||||
\(356\) | 12.8877i | 0.683046i | ||||||||
\(357\) | 1.14138i | 0.0604080i | ||||||||
\(358\) | − 8.89738i | − 0.470241i | ||||||||
\(359\) | 22.8412i | 1.20551i | 0.797926 | + | 0.602755i | \(0.205930\pi\) | ||||
−0.797926 | + | 0.602755i | \(0.794070\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 10.3623 | 0.545383 | ||||||||
\(362\) | − 1.31229i | − 0.0689725i | ||||||||
\(363\) | 9.15883 | 0.480714 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.36227 | −0.175989 | ||||||||
\(366\) | 3.24698i | 0.169722i | ||||||||
\(367\) | −7.78315 | −0.406277 | −0.203139 | − | 0.979150i | \(-0.565114\pi\) | ||||
−0.203139 | + | 0.979150i | \(0.565114\pi\) | |||||||
\(368\) | 0.692021 | 0.0360741 | ||||||||
\(369\) | 2.84117i | 0.147905i | ||||||||
\(370\) | − 9.26875i | − 0.481859i | ||||||||
\(371\) | 0.697398i | 0.0362071i | ||||||||
\(372\) | − 9.85086i | − 0.510743i | ||||||||
\(373\) | −30.5133 | −1.57992 | −0.789960 | − | 0.613158i | \(-0.789899\pi\) | ||||
−0.789960 | + | 0.613158i | \(0.789899\pi\) | |||||||
\(374\) | 1.47650 | 0.0763480 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 3.31767 | 0.171096 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.04892 | −0.0539505 | ||||||||
\(379\) | − 6.41358i | − 0.329444i | −0.986340 | − | 0.164722i | \(-0.947327\pi\) | ||||
0.986340 | − | 0.164722i | \(-0.0526726\pi\) | |||||||
\(380\) | −2.93900 | −0.150768 | ||||||||
\(381\) | 5.06100 | 0.259283 | ||||||||
\(382\) | 5.75063i | 0.294228i | ||||||||
\(383\) | − 2.89440i | − 0.147897i | −0.997262 | − | 0.0739484i | \(-0.976440\pi\) | ||||
0.997262 | − | 0.0739484i | \(-0.0235600\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | − 1.42327i | − 0.0725366i | ||||||||
\(386\) | 10.0339 | 0.510710 | ||||||||
\(387\) | 4.45473 | 0.226447 | ||||||||
\(388\) | − 1.56704i | − 0.0795544i | ||||||||
\(389\) | 17.1250 | 0.868271 | 0.434136 | − | 0.900848i | \(-0.357054\pi\) | ||||
0.434136 | + | 0.900848i | \(0.357054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.753020 | 0.0380819 | ||||||||
\(392\) | − 5.89977i | − 0.297984i | ||||||||
\(393\) | 3.81940 | 0.192663 | ||||||||
\(394\) | −22.9071 | −1.15404 | ||||||||
\(395\) | − 12.3230i | − 0.620040i | ||||||||
\(396\) | 1.35690i | 0.0681866i | ||||||||
\(397\) | 25.0103i | 1.25523i | 0.778524 | + | 0.627615i | \(0.215969\pi\) | ||||
−0.778524 | + | 0.627615i | \(0.784031\pi\) | |||||||
\(398\) | − 27.0291i | − 1.35484i | ||||||||
\(399\) | −3.08277 | −0.154331 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 30.8689i | − 1.54152i | −0.637126 | − | 0.770760i | \(-0.719877\pi\) | ||||
0.637126 | − | 0.770760i | \(-0.280123\pi\) | |||||||
\(402\) | −6.91185 | −0.344732 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 4.71379 | 0.234520 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | 2.49502 | 0.123826 | ||||||||
\(407\) | −12.5767 | −0.623405 | ||||||||
\(408\) | − 1.08815i | − 0.0538713i | ||||||||
\(409\) | − 11.0871i | − 0.548221i | −0.961698 | − | 0.274110i | \(-0.911617\pi\) | ||||
0.961698 | − | 0.274110i | \(-0.0883834\pi\) | |||||||
\(410\) | 2.84117i | 0.140315i | ||||||||
\(411\) | 8.59717i | 0.424067i | ||||||||
\(412\) | −12.1642 | −0.599288 | ||||||||
\(413\) | −2.05669 | −0.101203 | ||||||||
\(414\) | 0.692021i | 0.0340110i | ||||||||
\(415\) | 2.68664 | 0.131882 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.38404 | −0.116747 | ||||||||
\(418\) | 3.98792i | 0.195055i | ||||||||
\(419\) | 17.5080 | 0.855320 | 0.427660 | − | 0.903940i | \(-0.359338\pi\) | ||||
0.427660 | + | 0.903940i | \(0.359338\pi\) | |||||||
\(420\) | −1.04892 | −0.0511819 | ||||||||
\(421\) | 16.1274i | 0.786000i | 0.919538 | + | 0.393000i | \(0.128563\pi\) | ||||
−0.919538 | + | 0.393000i | \(0.871437\pi\) | |||||||
\(422\) | 10.3720i | 0.504899i | ||||||||
\(423\) | 3.31767i | 0.161310i | ||||||||
\(424\) | − 0.664874i | − 0.0322892i | ||||||||
\(425\) | −1.08815 | −0.0527828 | ||||||||
\(426\) | −2.29590 | −0.111237 | ||||||||
\(427\) | 3.40581i | 0.164819i | ||||||||
\(428\) | −1.83877 | −0.0888805 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.45473 | 0.214826 | ||||||||
\(431\) | − 33.2905i | − 1.60355i | −0.597627 | − | 0.801774i | \(-0.703890\pi\) | ||||
0.597627 | − | 0.801774i | \(-0.296110\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 11.1056 | 0.533701 | 0.266851 | − | 0.963738i | \(-0.414017\pi\) | ||||
0.266851 | + | 0.963738i | \(0.414017\pi\) | |||||||
\(434\) | − 10.3327i | − 0.495987i | ||||||||
\(435\) | 2.37867i | 0.114048i | ||||||||
\(436\) | − 16.2403i | − 0.777768i | ||||||||
\(437\) | 2.03385i | 0.0972923i | ||||||||
\(438\) | 3.36227 | 0.160656 | ||||||||
\(439\) | −12.6950 | −0.605900 | −0.302950 | − | 0.953007i | \(-0.597971\pi\) | ||||
−0.302950 | + | 0.953007i | \(0.597971\pi\) | |||||||
\(440\) | 1.35690i | 0.0646875i | ||||||||
\(441\) | 5.89977 | 0.280942 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.90110 | −0.327881 | −0.163941 | − | 0.986470i | \(-0.552421\pi\) | ||||
−0.163941 | + | 0.986470i | \(0.552421\pi\) | |||||||
\(444\) | 9.26875i | 0.439875i | ||||||||
\(445\) | −12.8877 | −0.610935 | ||||||||
\(446\) | −14.0532 | −0.665440 | ||||||||
\(447\) | − 8.93900i | − 0.422800i | ||||||||
\(448\) | − 1.04892i | − 0.0495567i | ||||||||
\(449\) | 3.27652i | 0.154629i | 0.997007 | + | 0.0773143i | \(0.0246345\pi\) | ||||
−0.997007 | + | 0.0773143i | \(0.975366\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | 3.85517 | 0.181533 | ||||||||
\(452\) | −16.8267 | −0.791461 | ||||||||
\(453\) | 8.45473i | 0.397238i | ||||||||
\(454\) | 1.93362 | 0.0907495 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.93900 | 0.137631 | ||||||||
\(457\) | 1.40581i | 0.0657612i | 0.999459 | + | 0.0328806i | \(0.0104681\pi\) | ||||
−0.999459 | + | 0.0328806i | \(0.989532\pi\) | |||||||
\(458\) | −10.9148 | −0.510017 | ||||||||
\(459\) | 1.08815 | 0.0507903 | ||||||||
\(460\) | 0.692021i | 0.0322657i | ||||||||
\(461\) | 12.3773i | 0.576470i | 0.957560 | + | 0.288235i | \(0.0930684\pi\) | ||||
−0.957560 | + | 0.288235i | \(0.906932\pi\) | |||||||
\(462\) | 1.42327i | 0.0662166i | ||||||||
\(463\) | − 31.7797i | − 1.47693i | −0.674293 | − | 0.738464i | \(-0.735552\pi\) | ||||
0.674293 | − | 0.738464i | \(-0.264448\pi\) | |||||||
\(464\) | −2.37867 | −0.110427 | ||||||||
\(465\) | 9.85086 | 0.456822 | ||||||||
\(466\) | 21.6896i | 1.00475i | ||||||||
\(467\) | 36.2790 | 1.67879 | 0.839397 | − | 0.543519i | \(-0.182909\pi\) | ||||
0.839397 | + | 0.543519i | \(0.182909\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.24996 | −0.334772 | ||||||||
\(470\) | 3.31767i | 0.153033i | ||||||||
\(471\) | −2.70410 | −0.124598 | ||||||||
\(472\) | 1.96077 | 0.0902518 | ||||||||
\(473\) | − 6.04461i | − 0.277931i | ||||||||
\(474\) | 12.3230i | 0.566016i | ||||||||
\(475\) | − 2.93900i | − 0.134851i | ||||||||
\(476\) | − 1.14138i | − 0.0523148i | ||||||||
\(477\) | 0.664874 | 0.0304425 | ||||||||
\(478\) | 27.2349 | 1.24570 | ||||||||
\(479\) | 5.87933i | 0.268633i | 0.990938 | + | 0.134317i | \(0.0428840\pi\) | ||||
−0.990938 | + | 0.134317i | \(0.957116\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 8.21014 | 0.373962 | ||||||||
\(483\) | 0.725873i | 0.0330284i | ||||||||
\(484\) | −9.15883 | −0.416311 | ||||||||
\(485\) | 1.56704 | 0.0711556 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 30.6243i | 1.38772i | 0.720110 | + | 0.693860i | \(0.244091\pi\) | ||||
−0.720110 | + | 0.693860i | \(0.755909\pi\) | |||||||
\(488\) | − 3.24698i | − 0.146984i | ||||||||
\(489\) | 22.5284i | 1.01877i | ||||||||
\(490\) | 5.89977 | 0.266525 | ||||||||
\(491\) | −34.4456 | −1.55451 | −0.777255 | − | 0.629186i | \(-0.783388\pi\) | ||||
−0.777255 | + | 0.629186i | \(0.783388\pi\) | |||||||
\(492\) | − 2.84117i | − 0.128090i | ||||||||
\(493\) | −2.58834 | −0.116573 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.35690 | −0.0609879 | ||||||||
\(496\) | 9.85086i | 0.442316i | ||||||||
\(497\) | −2.40821 | −0.108023 | ||||||||
\(498\) | −2.68664 | −0.120391 | ||||||||
\(499\) | − 10.0194i | − 0.448529i | −0.974528 | − | 0.224264i | \(-0.928002\pi\) | ||||
0.974528 | − | 0.224264i | \(-0.0719979\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | − 12.2228i | − 0.546075i | ||||||||
\(502\) | 6.57002i | 0.293235i | ||||||||
\(503\) | 8.27950 | 0.369165 | 0.184582 | − | 0.982817i | \(-0.440907\pi\) | ||||
0.184582 | + | 0.982817i | \(0.440907\pi\) | |||||||
\(504\) | 1.04892 | 0.0467225 | ||||||||
\(505\) | 4.71379i | 0.209761i | ||||||||
\(506\) | 0.939001 | 0.0417437 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.06100 | −0.224546 | ||||||||
\(509\) | − 44.4607i | − 1.97069i | −0.170585 | − | 0.985343i | \(-0.554566\pi\) | ||||
0.170585 | − | 0.985343i | \(-0.445434\pi\) | |||||||
\(510\) | 1.08815 | 0.0481839 | ||||||||
\(511\) | 3.52675 | 0.156014 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 2.93900i | 0.129760i | ||||||||
\(514\) | − 13.7657i | − 0.607179i | ||||||||
\(515\) | − 12.1642i | − 0.536019i | ||||||||
\(516\) | −4.45473 | −0.196109 | ||||||||
\(517\) | 4.50173 | 0.197986 | ||||||||
\(518\) | 9.72215i | 0.427167i | ||||||||
\(519\) | 11.7168 | 0.514309 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.8461 | −1.57044 | −0.785222 | − | 0.619214i | \(-0.787451\pi\) | ||||
−0.785222 | + | 0.619214i | \(0.787451\pi\) | |||||||
\(522\) | − 2.37867i | − 0.104111i | ||||||||
\(523\) | −5.80433 | −0.253806 | −0.126903 | − | 0.991915i | \(-0.540504\pi\) | ||||
−0.126903 | + | 0.991915i | \(0.540504\pi\) | |||||||
\(524\) | −3.81940 | −0.166851 | ||||||||
\(525\) | − 1.04892i | − 0.0457785i | ||||||||
\(526\) | − 9.54288i | − 0.416089i | ||||||||
\(527\) | 10.7192i | 0.466934i | ||||||||
\(528\) | − 1.35690i | − 0.0590513i | ||||||||
\(529\) | −22.5211 | −0.979179 | ||||||||
\(530\) | 0.664874 | 0.0288803 | ||||||||
\(531\) | 1.96077i | 0.0850902i | ||||||||
\(532\) | 3.08277 | 0.133655 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 12.8877 | 0.557705 | ||||||||
\(535\) | − 1.83877i | − 0.0794971i | ||||||||
\(536\) | 6.91185 | 0.298547 | ||||||||
\(537\) | −8.89738 | −0.383950 | ||||||||
\(538\) | 9.07069i | 0.391065i | ||||||||
\(539\) | − 8.00538i | − 0.344816i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 23.2446i | 0.999363i | 0.866209 | + | 0.499681i | \(0.166550\pi\) | ||||
−0.866209 | + | 0.499681i | \(0.833450\pi\) | |||||||
\(542\) | 17.5579 | 0.754178 | ||||||||
\(543\) | −1.31229 | −0.0563158 | ||||||||
\(544\) | 1.08815i | 0.0466539i | ||||||||
\(545\) | 16.2403 | 0.695657 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.1588 | −0.690902 | −0.345451 | − | 0.938437i | \(-0.612274\pi\) | ||||
−0.345451 | + | 0.938437i | \(0.612274\pi\) | |||||||
\(548\) | − 8.59717i | − 0.367253i | ||||||||
\(549\) | 3.24698 | 0.138578 | ||||||||
\(550\) | −1.35690 | −0.0578582 | ||||||||
\(551\) | − 6.99090i | − 0.297822i | ||||||||
\(552\) | − 0.692021i | − 0.0294544i | ||||||||
\(553\) | 12.9259i | 0.549663i | ||||||||
\(554\) | − 13.7071i | − 0.582358i | ||||||||
\(555\) | −9.26875 | −0.393437 | ||||||||
\(556\) | 2.38404 | 0.101106 | ||||||||
\(557\) | − 25.5937i | − 1.08444i | −0.840236 | − | 0.542220i | \(-0.817584\pi\) | ||||
0.840236 | − | 0.542220i | \(-0.182416\pi\) | |||||||
\(558\) | −9.85086 | −0.417020 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.04892 | 0.0443248 | ||||||||
\(561\) | − 1.47650i | − 0.0623379i | ||||||||
\(562\) | −24.3696 | −1.02797 | ||||||||
\(563\) | 40.9232 | 1.72471 | 0.862354 | − | 0.506307i | \(-0.168990\pi\) | ||||
0.862354 | + | 0.506307i | \(0.168990\pi\) | |||||||
\(564\) | − 3.31767i | − 0.139699i | ||||||||
\(565\) | − 16.8267i | − 0.707904i | ||||||||
\(566\) | 17.1511i | 0.720913i | ||||||||
\(567\) | 1.04892i | 0.0440504i | ||||||||
\(568\) | 2.29590 | 0.0963337 | ||||||||
\(569\) | 20.1946 | 0.846602 | 0.423301 | − | 0.905989i | \(-0.360871\pi\) | ||||
0.423301 | + | 0.905989i | \(0.360871\pi\) | |||||||
\(570\) | 2.93900i | 0.123101i | ||||||||
\(571\) | −36.8756 | −1.54320 | −0.771598 | − | 0.636110i | \(-0.780542\pi\) | ||||
−0.771598 | + | 0.636110i | \(0.780542\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.75063 | 0.240236 | ||||||||
\(574\) | − 2.98015i | − 0.124389i | ||||||||
\(575\) | −0.692021 | −0.0288593 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 5.07500i | − 0.211275i | −0.994405 | − | 0.105637i | \(-0.966312\pi\) | ||||
0.994405 | − | 0.105637i | \(-0.0336883\pi\) | |||||||
\(578\) | − 15.8159i | − 0.657856i | ||||||||
\(579\) | − 10.0339i | − 0.416993i | ||||||||
\(580\) | − 2.37867i | − 0.0987687i | ||||||||
\(581\) | −2.81807 | −0.116913 | ||||||||
\(582\) | −1.56704 | −0.0649559 | ||||||||
\(583\) | − 0.902165i | − 0.0373639i | ||||||||
\(584\) | −3.36227 | −0.139132 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.1172 | −0.996273 | ||||||||
\(587\) | − 10.5714i | − 0.436326i | −0.975912 | − | 0.218163i | \(-0.929993\pi\) | ||||
0.975912 | − | 0.218163i | \(-0.0700065\pi\) | |||||||
\(588\) | −5.89977 | −0.243303 | ||||||||
\(589\) | −28.9517 | −1.19293 | ||||||||
\(590\) | 1.96077i | 0.0807237i | ||||||||
\(591\) | 22.9071i | 0.942271i | ||||||||
\(592\) | − 9.26875i | − 0.380943i | ||||||||
\(593\) | − 38.4999i | − 1.58100i | −0.612460 | − | 0.790501i | \(-0.709820\pi\) | ||||
0.612460 | − | 0.790501i | \(-0.290180\pi\) | |||||||
\(594\) | 1.35690 | 0.0556741 | ||||||||
\(595\) | 1.14138 | 0.0467918 | ||||||||
\(596\) | 8.93900i | 0.366156i | ||||||||
\(597\) | −27.0291 | −1.10623 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.332142 | −0.0135709 | −0.00678547 | − | 0.999977i | \(-0.502160\pi\) | ||||
−0.00678547 | + | 0.999977i | \(0.502160\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | −7.04162 | −0.287234 | −0.143617 | − | 0.989633i | \(-0.545873\pi\) | ||||
−0.143617 | + | 0.989633i | \(0.545873\pi\) | |||||||
\(602\) | −4.67264 | −0.190443 | ||||||||
\(603\) | 6.91185i | 0.281472i | ||||||||
\(604\) | − 8.45473i | − 0.344018i | ||||||||
\(605\) | − 9.15883i | − 0.372360i | ||||||||
\(606\) | − 4.71379i | − 0.191485i | ||||||||
\(607\) | −29.4185 | −1.19406 | −0.597030 | − | 0.802219i | \(-0.703653\pi\) | ||||
−0.597030 | + | 0.802219i | \(0.703653\pi\) | |||||||
\(608\) | −2.93900 | −0.119192 | ||||||||
\(609\) | − 2.49502i | − 0.101103i | ||||||||
\(610\) | 3.24698 | 0.131466 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.08815 | −0.0439857 | ||||||||
\(613\) | 34.1987i | 1.38127i | 0.723203 | + | 0.690635i | \(0.242669\pi\) | ||||
−0.723203 | + | 0.690635i | \(0.757331\pi\) | |||||||
\(614\) | −17.2282 | −0.695273 | ||||||||
\(615\) | 2.84117 | 0.114567 | ||||||||
\(616\) | − 1.42327i | − 0.0573452i | ||||||||
\(617\) | − 34.1890i | − 1.37640i | −0.725523 | − | 0.688198i | \(-0.758402\pi\) | ||||
0.725523 | − | 0.688198i | \(-0.241598\pi\) | |||||||
\(618\) | 12.1642i | 0.489316i | ||||||||
\(619\) | − 9.80061i | − 0.393920i | −0.980412 | − | 0.196960i | \(-0.936893\pi\) | ||||
0.980412 | − | 0.196960i | \(-0.0631069\pi\) | |||||||
\(620\) | −9.85086 | −0.395620 | ||||||||
\(621\) | 0.692021 | 0.0277699 | ||||||||
\(622\) | 25.9801i | 1.04171i | ||||||||
\(623\) | 13.5181 | 0.541592 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 7.82669i | 0.312818i | ||||||||
\(627\) | 3.98792 | 0.159262 | ||||||||
\(628\) | 2.70410 | 0.107905 | ||||||||
\(629\) | − 10.0858i | − 0.402145i | ||||||||
\(630\) | 1.04892i | 0.0417899i | ||||||||
\(631\) | − 17.0968i | − 0.680612i | −0.940315 | − | 0.340306i | \(-0.889469\pi\) | ||||
0.940315 | − | 0.340306i | \(-0.110531\pi\) | |||||||
\(632\) | − 12.3230i | − 0.490184i | ||||||||
\(633\) | 10.3720 | 0.412248 | ||||||||
\(634\) | −0.391813 | −0.0155609 | ||||||||
\(635\) | − 5.06100i | − 0.200840i | ||||||||
\(636\) | −0.664874 | −0.0263640 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.22760 | −0.127782 | ||||||||
\(639\) | 2.29590i | 0.0908243i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 14.7030 | 0.580735 | 0.290368 | − | 0.956915i | \(-0.406222\pi\) | ||||
0.290368 | + | 0.956915i | \(0.406222\pi\) | |||||||
\(642\) | 1.83877i | 0.0725706i | ||||||||
\(643\) | 42.7036i | 1.68407i | 0.539425 | + | 0.842033i | \(0.318641\pi\) | ||||
−0.539425 | + | 0.842033i | \(0.681359\pi\) | |||||||
\(644\) | − 0.725873i | − 0.0286034i | ||||||||
\(645\) | − 4.45473i | − 0.175405i | ||||||||
\(646\) | −3.19806 | −0.125826 | ||||||||
\(647\) | −41.7265 | −1.64044 | −0.820218 | − | 0.572051i | \(-0.806148\pi\) | ||||
−0.820218 | + | 0.572051i | \(0.806148\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 2.66056 | 0.104436 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.3327 | −0.404972 | ||||||||
\(652\) | − 22.5284i | − 0.882280i | ||||||||
\(653\) | −28.2306 | −1.10475 | −0.552374 | − | 0.833596i | \(-0.686278\pi\) | ||||
−0.552374 | + | 0.833596i | \(0.686278\pi\) | |||||||
\(654\) | −16.2403 | −0.635045 | ||||||||
\(655\) | − 3.81940i | − 0.149236i | ||||||||
\(656\) | 2.84117i | 0.110929i | ||||||||
\(657\) | − 3.36227i | − 0.131175i | ||||||||
\(658\) | − 3.47996i | − 0.135663i | ||||||||
\(659\) | −38.7885 | −1.51099 | −0.755493 | − | 0.655156i | \(-0.772603\pi\) | ||||
−0.755493 | + | 0.655156i | \(0.772603\pi\) | |||||||
\(660\) | 1.35690 | 0.0528171 | ||||||||
\(661\) | − 31.5733i | − 1.22806i | −0.789284 | − | 0.614029i | \(-0.789548\pi\) | ||||
0.789284 | − | 0.614029i | \(-0.210452\pi\) | |||||||
\(662\) | −26.3424 | −1.02383 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.68664 | 0.104262 | ||||||||
\(665\) | 3.08277i | 0.119545i | ||||||||
\(666\) | 9.26875 | 0.359157 | ||||||||
\(667\) | −1.64609 | −0.0637368 | ||||||||
\(668\) | 12.2228i | 0.472915i | ||||||||
\(669\) | 14.0532i | 0.543329i | ||||||||
\(670\) | 6.91185i | 0.267028i | ||||||||
\(671\) | − 4.40581i | − 0.170085i | ||||||||
\(672\) | −1.04892 | −0.0404629 | ||||||||
\(673\) | 44.1400 | 1.70147 | 0.850737 | − | 0.525592i | \(-0.176156\pi\) | ||||
0.850737 | + | 0.525592i | \(0.176156\pi\) | |||||||
\(674\) | − 14.8345i | − 0.571402i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.8431 | −0.877931 | −0.438966 | − | 0.898504i | \(-0.644655\pi\) | ||||
−0.438966 | + | 0.898504i | \(0.644655\pi\) | |||||||
\(678\) | 16.8267i | 0.646225i | ||||||||
\(679\) | −1.64370 | −0.0630792 | ||||||||
\(680\) | −1.08815 | −0.0417285 | ||||||||
\(681\) | − 1.93362i | − 0.0740966i | ||||||||
\(682\) | 13.3666i | 0.511833i | ||||||||
\(683\) | 13.6866i | 0.523705i | 0.965108 | + | 0.261852i | \(0.0843334\pi\) | ||||
−0.965108 | + | 0.261852i | \(0.915667\pi\) | |||||||
\(684\) | − 2.93900i | − 0.112376i | ||||||||
\(685\) | 8.59717 | 0.328481 | ||||||||
\(686\) | −13.5308 | −0.516608 | ||||||||
\(687\) | 10.9148i | 0.416427i | ||||||||
\(688\) | 4.45473 | 0.169835 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.692021 | 0.0263448 | ||||||||
\(691\) | − 24.0261i | − 0.913995i | −0.889468 | − | 0.456998i | \(-0.848925\pi\) | ||||
0.889468 | − | 0.456998i | \(-0.151075\pi\) | |||||||
\(692\) | −11.7168 | −0.445405 | ||||||||
\(693\) | 1.42327 | 0.0540656 | ||||||||
\(694\) | − 0.636399i | − 0.0241574i | ||||||||
\(695\) | 2.38404i | 0.0904319i | ||||||||
\(696\) | 2.37867i | 0.0901631i | ||||||||
\(697\) | 3.09160i | 0.117103i | ||||||||
\(698\) | 17.2784 | 0.653999 | ||||||||
\(699\) | 21.6896 | 0.820377 | ||||||||
\(700\) | 1.04892i | 0.0396453i | ||||||||
\(701\) | −50.5392 | −1.90884 | −0.954419 | − | 0.298471i | \(-0.903523\pi\) | ||||
−0.954419 | + | 0.298471i | \(0.903523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 27.2409 | 1.02741 | ||||||||
\(704\) | 1.35690i | 0.0511399i | ||||||||
\(705\) | 3.31767 | 0.124951 | ||||||||
\(706\) | 21.7614 | 0.819000 | ||||||||
\(707\) | − 4.94438i | − 0.185952i | ||||||||
\(708\) | − 1.96077i | − 0.0736903i | ||||||||
\(709\) | 12.1847i | 0.457604i | 0.973473 | + | 0.228802i | \(0.0734809\pi\) | ||||
−0.973473 | + | 0.228802i | \(0.926519\pi\) | |||||||
\(710\) | 2.29590i | 0.0861635i | ||||||||
\(711\) | 12.3230 | 0.462150 | ||||||||
\(712\) | −12.8877 | −0.482987 | ||||||||
\(713\) | 6.81700i | 0.255299i | ||||||||
\(714\) | −1.14138 | −0.0427149 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.89738 | 0.332511 | ||||||||
\(717\) | − 27.2349i | − 1.01711i | ||||||||
\(718\) | −22.8412 | −0.852425 | ||||||||
\(719\) | 10.8401 | 0.404268 | 0.202134 | − | 0.979358i | \(-0.435212\pi\) | ||||
0.202134 | + | 0.979358i | \(0.435212\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | 12.7593i | 0.475179i | ||||||||
\(722\) | 10.3623i | 0.385644i | ||||||||
\(723\) | − 8.21014i | − 0.305339i | ||||||||
\(724\) | 1.31229 | 0.0487709 | ||||||||
\(725\) | 2.37867 | 0.0883414 | ||||||||
\(726\) | 9.15883i | 0.339916i | ||||||||
\(727\) | −33.2489 | −1.23313 | −0.616567 | − | 0.787303i | \(-0.711477\pi\) | ||||
−0.616567 | + | 0.787303i | \(0.711477\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − 3.36227i | − 0.124443i | ||||||||
\(731\) | 4.84740 | 0.179287 | ||||||||
\(732\) | −3.24698 | −0.120012 | ||||||||
\(733\) | − 8.59120i | − 0.317323i | −0.987333 | − | 0.158662i | \(-0.949282\pi\) | ||||
0.987333 | − | 0.158662i | \(-0.0507179\pi\) | |||||||
\(734\) | − 7.78315i | − 0.287281i | ||||||||
\(735\) | − 5.89977i | − 0.217616i | ||||||||
\(736\) | 0.692021i | 0.0255082i | ||||||||
\(737\) | 9.37867 | 0.345468 | ||||||||
\(738\) | −2.84117 | −0.104585 | ||||||||
\(739\) | 38.4131i | 1.41305i | 0.707689 | + | 0.706525i | \(0.249738\pi\) | ||||
−0.707689 | + | 0.706525i | \(0.750262\pi\) | |||||||
\(740\) | 9.26875 | 0.340726 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.697398 | −0.0256023 | ||||||||
\(743\) | 21.7904i | 0.799414i | 0.916643 | + | 0.399707i | \(0.130888\pi\) | ||||
−0.916643 | + | 0.399707i | \(0.869112\pi\) | |||||||
\(744\) | 9.85086 | 0.361150 | ||||||||
\(745\) | −8.93900 | −0.327500 | ||||||||
\(746\) | − 30.5133i | − 1.11717i | ||||||||
\(747\) | 2.68664i | 0.0982992i | ||||||||
\(748\) | 1.47650i | 0.0539862i | ||||||||
\(749\) | 1.92872i | 0.0704739i | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −0.715120 | −0.0260951 | −0.0130475 | − | 0.999915i | \(-0.504153\pi\) | ||||
−0.0130475 | + | 0.999915i | \(0.504153\pi\) | |||||||
\(752\) | 3.31767i | 0.120983i | ||||||||
\(753\) | 6.57002 | 0.239425 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.45473 | 0.307699 | ||||||||
\(756\) | − 1.04892i | − 0.0381488i | ||||||||
\(757\) | 29.7894 | 1.08271 | 0.541357 | − | 0.840793i | \(-0.317911\pi\) | ||||
0.541357 | + | 0.840793i | \(0.317911\pi\) | |||||||
\(758\) | 6.41358 | 0.232952 | ||||||||
\(759\) | − 0.939001i | − 0.0340836i | ||||||||
\(760\) | − 2.93900i | − 0.106609i | ||||||||
\(761\) | − 28.4112i | − 1.02990i | −0.857219 | − | 0.514952i | \(-0.827810\pi\) | ||||
0.857219 | − | 0.514952i | \(-0.172190\pi\) | |||||||
\(762\) | 5.06100i | 0.183341i | ||||||||
\(763\) | −17.0347 | −0.616698 | ||||||||
\(764\) | −5.75063 | −0.208050 | ||||||||
\(765\) | − 1.08815i | − 0.0393420i | ||||||||
\(766\) | 2.89440 | 0.104579 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 16.6200i | 0.599333i | 0.954044 | + | 0.299666i | \(0.0968754\pi\) | ||||
−0.954044 | + | 0.299666i | \(0.903125\pi\) | |||||||
\(770\) | 1.42327 | 0.0512911 | ||||||||
\(771\) | −13.7657 | −0.495759 | ||||||||
\(772\) | 10.0339i | 0.361126i | ||||||||
\(773\) | − 10.8388i | − 0.389844i | −0.980819 | − | 0.194922i | \(-0.937555\pi\) | ||||
0.980819 | − | 0.194922i | \(-0.0624453\pi\) | |||||||
\(774\) | 4.45473i | 0.160122i | ||||||||
\(775\) | − 9.85086i | − 0.353853i | ||||||||
\(776\) | 1.56704 | 0.0562534 | ||||||||
\(777\) | 9.72215 | 0.348780 | ||||||||
\(778\) | 17.1250i | 0.613960i | ||||||||
\(779\) | −8.35019 | −0.299177 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.11529 | 0.111474 | ||||||||
\(782\) | 0.753020i | 0.0269280i | ||||||||
\(783\) | −2.37867 | −0.0850066 | ||||||||
\(784\) | 5.89977 | 0.210706 | ||||||||
\(785\) | 2.70410i | 0.0965136i | ||||||||
\(786\) | 3.81940i | 0.136233i | ||||||||
\(787\) | 4.55974i | 0.162537i | 0.996692 | + | 0.0812687i | \(0.0258972\pi\) | ||||
−0.996692 | + | 0.0812687i | \(0.974103\pi\) | |||||||
\(788\) | − 22.9071i | − 0.816031i | ||||||||
\(789\) | −9.54288 | −0.339735 | ||||||||
\(790\) | 12.3230 | 0.438434 | ||||||||
\(791\) | 17.6498i | 0.627555i | ||||||||
\(792\) | −1.35690 | −0.0482152 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −25.0103 | −0.887582 | ||||||||
\(795\) | − 0.664874i | − 0.0235807i | ||||||||
\(796\) | 27.0291 | 0.958020 | ||||||||
\(797\) | 13.6601 | 0.483865 | 0.241933 | − | 0.970293i | \(-0.422219\pi\) | ||||
0.241933 | + | 0.970293i | \(0.422219\pi\) | |||||||
\(798\) | − 3.08277i | − 0.109129i | ||||||||
\(799\) | 3.61011i | 0.127716i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | − 12.8877i | − 0.455364i | ||||||||
\(802\) | 30.8689 | 1.09002 | ||||||||
\(803\) | −4.56225 | −0.160998 | ||||||||
\(804\) | − 6.91185i | − 0.243762i | ||||||||
\(805\) | 0.725873 | 0.0255837 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.07069 | 0.319303 | ||||||||
\(808\) | 4.71379i | 0.165831i | ||||||||
\(809\) | 30.2857 | 1.06479 | 0.532395 | − | 0.846496i | \(-0.321292\pi\) | ||||
0.532395 | + | 0.846496i | \(0.321292\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | − 26.5327i | − 0.931690i | −0.884866 | − | 0.465845i | \(-0.845751\pi\) | ||||
0.884866 | − | 0.465845i | \(-0.154249\pi\) | |||||||
\(812\) | 2.49502i | 0.0875582i | ||||||||
\(813\) | − 17.5579i | − 0.615784i | ||||||||
\(814\) | − 12.5767i | − 0.440814i | ||||||||
\(815\) | 22.5284 | 0.789136 | ||||||||
\(816\) | 1.08815 | 0.0380927 | ||||||||
\(817\) | 13.0925i | 0.458047i | ||||||||
\(818\) | 11.0871 | 0.387651 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.84117 | −0.0992178 | ||||||||
\(821\) | − 48.5370i | − 1.69395i | −0.531630 | − | 0.846977i | \(-0.678420\pi\) | ||||
0.531630 | − | 0.846977i | \(-0.321580\pi\) | |||||||
\(822\) | −8.59717 | −0.299861 | ||||||||
\(823\) | 41.2650 | 1.43841 | 0.719204 | − | 0.694799i | \(-0.244507\pi\) | ||||
0.719204 | + | 0.694799i | \(0.244507\pi\) | |||||||
\(824\) | − 12.1642i | − 0.423760i | ||||||||
\(825\) | 1.35690i | 0.0472411i | ||||||||
\(826\) | − 2.05669i | − 0.0715613i | ||||||||
\(827\) | 22.9004i | 0.796324i | 0.917315 | + | 0.398162i | \(0.130352\pi\) | ||||
−0.917315 | + | 0.398162i | \(0.869648\pi\) | |||||||
\(828\) | −0.692021 | −0.0240494 | ||||||||
\(829\) | −13.9782 | −0.485484 | −0.242742 | − | 0.970091i | \(-0.578047\pi\) | ||||
−0.242742 | + | 0.970091i | \(0.578047\pi\) | |||||||
\(830\) | 2.68664i | 0.0932548i | ||||||||
\(831\) | −13.7071 | −0.475494 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.41981 | 0.222433 | ||||||||
\(834\) | − 2.38404i | − 0.0825527i | ||||||||
\(835\) | −12.2228 | −0.422988 | ||||||||
\(836\) | −3.98792 | −0.137925 | ||||||||
\(837\) | 9.85086i | 0.340495i | ||||||||
\(838\) | 17.5080i | 0.604802i | ||||||||
\(839\) | − 1.35258i | − 0.0466964i | −0.999727 | − | 0.0233482i | \(-0.992567\pi\) | ||||
0.999727 | − | 0.0233482i | \(-0.00743264\pi\) | |||||||
\(840\) | − 1.04892i | − 0.0361911i | ||||||||
\(841\) | −23.3419 | −0.804895 | ||||||||
\(842\) | −16.1274 | −0.555786 | ||||||||
\(843\) | 24.3696i | 0.839333i | ||||||||
\(844\) | −10.3720 | −0.357018 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.31767 | −0.114064 | ||||||||
\(847\) | 9.60686i | 0.330096i | ||||||||
\(848\) | 0.664874 | 0.0228319 | ||||||||
\(849\) | 17.1511 | 0.588623 | ||||||||
\(850\) | − 1.08815i | − 0.0373231i | ||||||||
\(851\) | − 6.41417i | − 0.219875i | ||||||||
\(852\) | − 2.29590i | − 0.0786561i | ||||||||
\(853\) | − 18.0887i | − 0.619347i | −0.950843 | − | 0.309673i | \(-0.899780\pi\) | ||||
0.950843 | − | 0.309673i | \(-0.100220\pi\) | |||||||
\(854\) | −3.40581 | −0.116545 | ||||||||
\(855\) | 2.93900 | 0.100512 | ||||||||
\(856\) | − 1.83877i | − 0.0628480i | ||||||||
\(857\) | 8.47889 | 0.289633 | 0.144817 | − | 0.989458i | \(-0.453741\pi\) | ||||
0.144817 | + | 0.989458i | \(0.453741\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.8968 | 0.678870 | 0.339435 | − | 0.940630i | \(-0.389764\pi\) | ||||
0.339435 | + | 0.940630i | \(0.389764\pi\) | |||||||
\(860\) | 4.45473i | 0.151905i | ||||||||
\(861\) | −2.98015 | −0.101563 | ||||||||
\(862\) | 33.2905 | 1.13388 | ||||||||
\(863\) | − 16.0989i | − 0.548013i | −0.961728 | − | 0.274006i | \(-0.911651\pi\) | ||||
0.961728 | − | 0.274006i | \(-0.0883490\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | − 11.7168i | − 0.398382i | ||||||||
\(866\) | 11.1056i | 0.377384i | ||||||||
\(867\) | −15.8159 | −0.537137 | ||||||||
\(868\) | 10.3327 | 0.350716 | ||||||||
\(869\) | − 16.7211i | − 0.567224i | ||||||||
\(870\) | −2.37867 | −0.0806443 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 16.2403 | 0.549965 | ||||||||
\(873\) | 1.56704i | 0.0530363i | ||||||||
\(874\) | −2.03385 | −0.0687961 | ||||||||
\(875\) | −1.04892 | −0.0354599 | ||||||||
\(876\) | 3.36227i | 0.113601i | ||||||||
\(877\) | 7.14377i | 0.241228i | 0.992699 | + | 0.120614i | \(0.0384863\pi\) | ||||
−0.992699 | + | 0.120614i | \(0.961514\pi\) | |||||||
\(878\) | − 12.6950i | − 0.428436i | ||||||||
\(879\) | 24.1172i | 0.813453i | ||||||||
\(880\) | −1.35690 | −0.0457410 | ||||||||
\(881\) | −42.5786 | −1.43451 | −0.717256 | − | 0.696810i | \(-0.754602\pi\) | ||||
−0.717256 | + | 0.696810i | \(0.754602\pi\) | |||||||
\(882\) | 5.89977i | 0.198656i | ||||||||
\(883\) | 38.3997 | 1.29225 | 0.646126 | − | 0.763230i | \(-0.276388\pi\) | ||||
0.646126 | + | 0.763230i | \(0.276388\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.96077 | 0.0659106 | ||||||||
\(886\) | − 6.90110i | − 0.231847i | ||||||||
\(887\) | 57.1943 | 1.92040 | 0.960199 | − | 0.279317i | \(-0.0901079\pi\) | ||||
0.960199 | + | 0.279317i | \(0.0901079\pi\) | |||||||
\(888\) | −9.26875 | −0.311039 | ||||||||
\(889\) | 5.30857i | 0.178044i | ||||||||
\(890\) | − 12.8877i | − 0.431996i | ||||||||
\(891\) | − 1.35690i | − 0.0454577i | ||||||||
\(892\) | − 14.0532i | − 0.470537i | ||||||||
\(893\) | −9.75063 | −0.326292 | ||||||||
\(894\) | 8.93900 | 0.298965 | ||||||||
\(895\) | 8.89738i | 0.297407i | ||||||||
\(896\) | 1.04892 | 0.0350419 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.27652 | −0.109339 | ||||||||
\(899\) | − 23.4319i | − 0.781497i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 0.723480 | 0.0241026 | ||||||||
\(902\) | 3.85517i | 0.128363i | ||||||||
\(903\) | 4.67264i | 0.155496i | ||||||||
\(904\) | − 16.8267i | − 0.559647i | ||||||||
\(905\) | 1.31229i | 0.0436220i | ||||||||
\(906\) | −8.45473 | −0.280890 | ||||||||
\(907\) | −1.07415 | −0.0356664 | −0.0178332 | − | 0.999841i | \(-0.505677\pi\) | ||||
−0.0178332 | + | 0.999841i | \(0.505677\pi\) | |||||||
\(908\) | 1.93362i | 0.0641696i | ||||||||
\(909\) | −4.71379 | −0.156347 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.9904 | −1.68939 | −0.844694 | − | 0.535249i | \(-0.820218\pi\) | ||||
−0.844694 | + | 0.535249i | \(0.820218\pi\) | |||||||
\(912\) | 2.93900i | 0.0973201i | ||||||||
\(913\) | 3.64550 | 0.120648 | ||||||||
\(914\) | −1.40581 | −0.0465002 | ||||||||
\(915\) | − 3.24698i | − 0.107342i | ||||||||
\(916\) | − 10.9148i | − 0.360636i | ||||||||
\(917\) | 4.00623i | 0.132297i | ||||||||
\(918\) | 1.08815i | 0.0359142i | ||||||||
\(919\) | 7.82344 | 0.258072 | 0.129036 | − | 0.991640i | \(-0.458812\pi\) | ||||
0.129036 | + | 0.991640i | \(0.458812\pi\) | |||||||
\(920\) | −0.692021 | −0.0228153 | ||||||||
\(921\) | 17.2282i | 0.567688i | ||||||||
\(922\) | −12.3773 | −0.407626 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.42327 | −0.0468222 | ||||||||
\(925\) | 9.26875i | 0.304755i | ||||||||
\(926\) | 31.7797 | 1.04435 | ||||||||
\(927\) | 12.1642 | 0.399525 | ||||||||
\(928\) | − 2.37867i | − 0.0780835i | ||||||||
\(929\) | − 19.5007i | − 0.639796i | −0.947452 | − | 0.319898i | \(-0.896351\pi\) | ||||
0.947452 | − | 0.319898i | \(-0.103649\pi\) | |||||||
\(930\) | 9.85086i | 0.323022i | ||||||||
\(931\) | 17.3394i | 0.568277i | ||||||||
\(932\) | −21.6896 | −0.710467 | ||||||||
\(933\) | 25.9801 | 0.850552 | ||||||||
\(934\) | 36.2790i | 1.18709i | ||||||||
\(935\) | −1.47650 | −0.0482867 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.0968 | −1.04856 | −0.524278 | − | 0.851547i | \(-0.675665\pi\) | ||||
−0.524278 | + | 0.851547i | \(0.675665\pi\) | |||||||
\(938\) | − 7.24996i | − 0.236720i | ||||||||
\(939\) | 7.82669 | 0.255414 | ||||||||
\(940\) | −3.31767 | −0.108210 | ||||||||
\(941\) | 35.9181i | 1.17090i | 0.810710 | + | 0.585448i | \(0.199081\pi\) | ||||
−0.810710 | + | 0.585448i | \(0.800919\pi\) | |||||||
\(942\) | − 2.70410i | − 0.0881044i | ||||||||
\(943\) | 1.96615i | 0.0640266i | ||||||||
\(944\) | 1.96077i | 0.0638177i | ||||||||
\(945\) | 1.04892 | 0.0341213 | ||||||||
\(946\) | 6.04461 | 0.196527 | ||||||||
\(947\) | − 20.7700i | − 0.674934i | −0.941337 | − | 0.337467i | \(-0.890430\pi\) | ||||
0.941337 | − | 0.337467i | \(-0.109570\pi\) | |||||||
\(948\) | −12.3230 | −0.400234 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.93900 | 0.0953538 | ||||||||
\(951\) | 0.391813i | 0.0127054i | ||||||||
\(952\) | 1.14138 | 0.0369922 | ||||||||
\(953\) | 11.7855 | 0.381771 | 0.190886 | − | 0.981612i | \(-0.438864\pi\) | ||||
0.190886 | + | 0.981612i | \(0.438864\pi\) | |||||||
\(954\) | 0.664874i | 0.0215261i | ||||||||
\(955\) | − 5.75063i | − 0.186086i | ||||||||
\(956\) | 27.2349i | 0.880840i | ||||||||
\(957\) | 3.22760i | 0.104334i | ||||||||
\(958\) | −5.87933 | −0.189953 | ||||||||
\(959\) | −9.01772 | −0.291197 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | −66.0393 | −2.13030 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.83877 | 0.0592536 | ||||||||
\(964\) | 8.21014i | 0.264431i | ||||||||
\(965\) | −10.0339 | −0.323001 | ||||||||
\(966\) | −0.725873 | −0.0233546 | ||||||||
\(967\) | − 52.0116i | − 1.67258i | −0.548287 | − | 0.836290i | \(-0.684720\pi\) | ||||
0.548287 | − | 0.836290i | \(-0.315280\pi\) | |||||||
\(968\) | − 9.15883i | − 0.294376i | ||||||||
\(969\) | 3.19806i | 0.102737i | ||||||||
\(970\) | 1.56704i | 0.0503146i | ||||||||
\(971\) | −17.7144 | −0.568482 | −0.284241 | − | 0.958753i | \(-0.591742\pi\) | ||||
−0.284241 | + | 0.958753i | \(0.591742\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | − 2.50066i | − 0.0801676i | ||||||||
\(974\) | −30.6243 | −0.981266 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.24698 | 0.103933 | ||||||||
\(977\) | − 8.16959i | − 0.261368i | −0.991424 | − | 0.130684i | \(-0.958283\pi\) | ||||
0.991424 | − | 0.130684i | \(-0.0417174\pi\) | |||||||
\(978\) | −22.5284 | −0.720379 | ||||||||
\(979\) | −17.4873 | −0.558895 | ||||||||
\(980\) | 5.89977i | 0.188461i | ||||||||
\(981\) | 16.2403i | 0.518512i | ||||||||
\(982\) | − 34.4456i | − 1.09920i | ||||||||
\(983\) | − 57.0256i | − 1.81883i | −0.415885 | − | 0.909417i | \(-0.636528\pi\) | ||||
0.415885 | − | 0.909417i | \(-0.363472\pi\) | |||||||
\(984\) | 2.84117 | 0.0905731 | ||||||||
\(985\) | 22.9071 | 0.729880 | ||||||||
\(986\) | − 2.58834i | − 0.0824294i | ||||||||
\(987\) | −3.47996 | −0.110768 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.08277 | 0.0980264 | ||||||||
\(990\) | − 1.35690i | − 0.0431250i | ||||||||
\(991\) | 37.2416 | 1.18302 | 0.591509 | − | 0.806298i | \(-0.298532\pi\) | ||||
0.591509 | + | 0.806298i | \(0.298532\pi\) | |||||||
\(992\) | −9.85086 | −0.312765 | ||||||||
\(993\) | 26.3424i | 0.835951i | ||||||||
\(994\) | − 2.40821i | − 0.0763837i | ||||||||
\(995\) | 27.0291i | 0.856879i | ||||||||
\(996\) | − 2.68664i | − 0.0851296i | ||||||||
\(997\) | −9.00059 | −0.285052 | −0.142526 | − | 0.989791i | \(-0.545522\pi\) | ||||
−0.142526 | + | 0.989791i | \(0.545522\pi\) | |||||||
\(998\) | 10.0194 | 0.317158 | ||||||||
\(999\) | − 9.26875i | − 0.293250i |
(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 | 5070.2.b.z.1351.6 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bw.1.1 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bp.1.3 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.z.1351.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bp.1.3 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.bw.1.1 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.z.1351.1 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.z.1351.6 | 6 | 1.1 | even | 1 | trivial |