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: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.q.1351.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(7\) | − 2.82843i | − 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 5.65685i | 1.70561i | 0.522233 | + | 0.852803i | \(0.325099\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.82843 | −0.755929 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.828427 | −0.200923 | −0.100462 | − | 0.994941i | \(-0.532032\pi\) | ||||
−0.100462 | + | 0.994941i | \(0.532032\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | − 2.82843i | − 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | − 2.82843i | − 0.617213i | ||||||||
\(22\) | 5.65685 | 1.20605 | ||||||||
\(23\) | 8.48528 | 1.76930 | 0.884652 | − | 0.466252i | \(-0.154396\pi\) | ||||
0.884652 | + | 0.466252i | \(0.154396\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.82843i | 0.534522i | ||||||||
\(29\) | −8.82843 | −1.63940 | −0.819699 | − | 0.572795i | \(-0.805859\pi\) | ||||
−0.819699 | + | 0.572795i | \(0.805859\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − 4.00000i | − 0.718421i | −0.933257 | − | 0.359211i | \(-0.883046\pi\) | ||||
0.933257 | − | 0.359211i | \(-0.116954\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 5.65685i | 0.984732i | ||||||||
\(34\) | 0.828427i | 0.142074i | ||||||||
\(35\) | −2.82843 | −0.478091 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 11.6569i | − 1.91638i | −0.286141 | − | 0.958188i | \(-0.592373\pi\) | ||||
0.286141 | − | 0.958188i | \(-0.407627\pi\) | |||||||
\(38\) | −2.82843 | −0.458831 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 7.65685i | 1.19580i | 0.801571 | + | 0.597900i | \(0.203998\pi\) | ||||
−0.801571 | + | 0.597900i | \(0.796002\pi\) | |||||||
\(42\) | −2.82843 | −0.436436 | ||||||||
\(43\) | −9.65685 | −1.47266 | −0.736328 | − | 0.676625i | \(-0.763442\pi\) | ||||
−0.736328 | + | 0.676625i | \(0.763442\pi\) | |||||||
\(44\) | − 5.65685i | − 0.852803i | ||||||||
\(45\) | − 1.00000i | − 0.149071i | ||||||||
\(46\) | − 8.48528i | − 1.25109i | ||||||||
\(47\) | − 8.00000i | − 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −0.828427 | −0.116003 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3137 | 1.82878 | 0.914389 | − | 0.404836i | \(-0.132671\pi\) | ||||
0.914389 | + | 0.404836i | \(0.132671\pi\) | |||||||
\(54\) | − 1.00000i | − 0.136083i | ||||||||
\(55\) | 5.65685 | 0.762770 | ||||||||
\(56\) | 2.82843 | 0.377964 | ||||||||
\(57\) | − 2.82843i | − 0.374634i | ||||||||
\(58\) | 8.82843i | 1.15923i | ||||||||
\(59\) | − 2.34315i | − 0.305052i | −0.988299 | − | 0.152526i | \(-0.951259\pi\) | ||||
0.988299 | − | 0.152526i | \(-0.0487407\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | − 2.82843i | − 0.356348i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.65685 | 0.696311 | ||||||||
\(67\) | − 5.65685i | − 0.691095i | −0.938401 | − | 0.345547i | \(-0.887693\pi\) | ||||
0.938401 | − | 0.345547i | \(-0.112307\pi\) | |||||||
\(68\) | 0.828427 | 0.100462 | ||||||||
\(69\) | 8.48528 | 1.02151 | ||||||||
\(70\) | 2.82843i | 0.338062i | ||||||||
\(71\) | 5.65685i | 0.671345i | 0.941979 | + | 0.335673i | \(0.108964\pi\) | ||||
−0.941979 | + | 0.335673i | \(0.891036\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | − 14.4853i | − 1.69537i | −0.530497 | − | 0.847687i | \(-0.677995\pi\) | ||||
0.530497 | − | 0.847687i | \(-0.322005\pi\) | |||||||
\(74\) | −11.6569 | −1.35508 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.82843i | 0.324443i | ||||||||
\(77\) | 16.0000 | 1.82337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.34315 | 0.263624 | 0.131812 | − | 0.991275i | \(-0.457920\pi\) | ||||
0.131812 | + | 0.991275i | \(0.457920\pi\) | |||||||
\(80\) | − 1.00000i | − 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.65685 | 0.845558 | ||||||||
\(83\) | − 6.34315i | − 0.696251i | −0.937448 | − | 0.348125i | \(-0.886818\pi\) | ||||
0.937448 | − | 0.348125i | \(-0.113182\pi\) | |||||||
\(84\) | 2.82843i | 0.308607i | ||||||||
\(85\) | 0.828427i | 0.0898555i | ||||||||
\(86\) | 9.65685i | 1.04133i | ||||||||
\(87\) | −8.82843 | −0.946507 | ||||||||
\(88\) | −5.65685 | −0.603023 | ||||||||
\(89\) | − 15.6569i | − 1.65962i | −0.558044 | − | 0.829812i | \(-0.688448\pi\) | ||||
0.558044 | − | 0.829812i | \(-0.311552\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.48528 | −0.884652 | ||||||||
\(93\) | − 4.00000i | − 0.414781i | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | − 1.00000i | − 0.102062i | ||||||||
\(97\) | 3.17157i | 0.322024i | 0.986952 | + | 0.161012i | \(0.0514759\pi\) | ||||
−0.986952 | + | 0.161012i | \(0.948524\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | 5.65685i | 0.568535i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −16.1421 | −1.60620 | −0.803101 | − | 0.595843i | \(-0.796818\pi\) | ||||
−0.803101 | + | 0.595843i | \(0.796818\pi\) | |||||||
\(102\) | 0.828427i | 0.0820265i | ||||||||
\(103\) | 1.65685 | 0.163255 | 0.0816274 | − | 0.996663i | \(-0.473988\pi\) | ||||
0.0816274 | + | 0.996663i | \(0.473988\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.82843 | −0.276026 | ||||||||
\(106\) | − 13.3137i | − 1.29314i | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | − 8.82843i | − 0.845610i | −0.906221 | − | 0.422805i | \(-0.861046\pi\) | ||||
0.906221 | − | 0.422805i | \(-0.138954\pi\) | |||||||
\(110\) | − 5.65685i | − 0.539360i | ||||||||
\(111\) | − 11.6569i | − 1.10642i | ||||||||
\(112\) | − 2.82843i | − 0.267261i | ||||||||
\(113\) | 6.48528 | 0.610084 | 0.305042 | − | 0.952339i | \(-0.401330\pi\) | ||||
0.305042 | + | 0.952339i | \(0.401330\pi\) | |||||||
\(114\) | −2.82843 | −0.264906 | ||||||||
\(115\) | − 8.48528i | − 0.791257i | ||||||||
\(116\) | 8.82843 | 0.819699 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.34315 | −0.215704 | ||||||||
\(119\) | 2.34315i | 0.214796i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −21.0000 | −1.90909 | ||||||||
\(122\) | − 6.00000i | − 0.543214i | ||||||||
\(123\) | 7.65685i | 0.690395i | ||||||||
\(124\) | 4.00000i | 0.359211i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −2.82843 | −0.251976 | ||||||||
\(127\) | −9.65685 | −0.856907 | −0.428454 | − | 0.903564i | \(-0.640941\pi\) | ||||
−0.428454 | + | 0.903564i | \(0.640941\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −9.65685 | −0.850239 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.14214 | −0.536641 | −0.268320 | − | 0.963330i | \(-0.586469\pi\) | ||||
−0.268320 | + | 0.963330i | \(0.586469\pi\) | |||||||
\(132\) | − 5.65685i | − 0.492366i | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | −5.65685 | −0.488678 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | − 0.828427i | − 0.0710370i | ||||||||
\(137\) | − 17.3137i | − 1.47921i | −0.673041 | − | 0.739605i | \(-0.735012\pi\) | ||||
0.673041 | − | 0.739605i | \(-0.264988\pi\) | |||||||
\(138\) | − 8.48528i | − 0.722315i | ||||||||
\(139\) | 6.34315 | 0.538019 | 0.269009 | − | 0.963138i | \(-0.413304\pi\) | ||||
0.269009 | + | 0.963138i | \(0.413304\pi\) | |||||||
\(140\) | 2.82843 | 0.239046 | ||||||||
\(141\) | − 8.00000i | − 0.673722i | ||||||||
\(142\) | 5.65685 | 0.474713 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 8.82843i | 0.733161i | ||||||||
\(146\) | −14.4853 | −1.19881 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 11.6569i | 0.958188i | ||||||||
\(149\) | − 3.65685i | − 0.299581i | −0.988718 | − | 0.149791i | \(-0.952140\pi\) | ||||
0.988718 | − | 0.149791i | \(-0.0478599\pi\) | |||||||
\(150\) | 1.00000i | 0.0816497i | ||||||||
\(151\) | 12.0000i | 0.976546i | 0.872691 | + | 0.488273i | \(0.162373\pi\) | ||||
−0.872691 | + | 0.488273i | \(0.837627\pi\) | |||||||
\(152\) | 2.82843 | 0.229416 | ||||||||
\(153\) | −0.828427 | −0.0669744 | ||||||||
\(154\) | − 16.0000i | − 1.28932i | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.31371 | 0.424080 | 0.212040 | − | 0.977261i | \(-0.431989\pi\) | ||||
0.212040 | + | 0.977261i | \(0.431989\pi\) | |||||||
\(158\) | − 2.34315i | − 0.186411i | ||||||||
\(159\) | 13.3137 | 1.05585 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | − 24.0000i | − 1.89146i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 11.3137i | 0.886158i | 0.896483 | + | 0.443079i | \(0.146114\pi\) | ||||
−0.896483 | + | 0.443079i | \(0.853886\pi\) | |||||||
\(164\) | − 7.65685i | − 0.597900i | ||||||||
\(165\) | 5.65685 | 0.440386 | ||||||||
\(166\) | −6.34315 | −0.492324 | ||||||||
\(167\) | 8.97056i | 0.694163i | 0.937835 | + | 0.347081i | \(0.112827\pi\) | ||||
−0.937835 | + | 0.347081i | \(0.887173\pi\) | |||||||
\(168\) | 2.82843 | 0.218218 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.828427 | 0.0635375 | ||||||||
\(171\) | − 2.82843i | − 0.216295i | ||||||||
\(172\) | 9.65685 | 0.736328 | ||||||||
\(173\) | 9.31371 | 0.708108 | 0.354054 | − | 0.935225i | \(-0.384803\pi\) | ||||
0.354054 | + | 0.935225i | \(0.384803\pi\) | |||||||
\(174\) | 8.82843i | 0.669281i | ||||||||
\(175\) | 2.82843i | 0.213809i | ||||||||
\(176\) | 5.65685i | 0.426401i | ||||||||
\(177\) | − 2.34315i | − 0.176122i | ||||||||
\(178\) | −15.6569 | −1.17353 | ||||||||
\(179\) | −7.51472 | −0.561676 | −0.280838 | − | 0.959755i | \(-0.590612\pi\) | ||||
−0.280838 | + | 0.959755i | \(0.590612\pi\) | |||||||
\(180\) | 1.00000i | 0.0745356i | ||||||||
\(181\) | 7.65685 | 0.569129 | 0.284565 | − | 0.958657i | \(-0.408151\pi\) | ||||
0.284565 | + | 0.958657i | \(0.408151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | 8.48528i | 0.625543i | ||||||||
\(185\) | −11.6569 | −0.857029 | ||||||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | − 4.68629i | − 0.342696i | ||||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | − 2.82843i | − 0.205738i | ||||||||
\(190\) | 2.82843i | 0.205196i | ||||||||
\(191\) | 11.3137 | 0.818631 | 0.409316 | − | 0.912393i | \(-0.365768\pi\) | ||||
0.409316 | + | 0.912393i | \(0.365768\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 2.48528i | 0.178894i | 0.995992 | + | 0.0894472i | \(0.0285100\pi\) | ||||
−0.995992 | + | 0.0894472i | \(0.971490\pi\) | |||||||
\(194\) | 3.17157 | 0.227706 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 13.3137i | 0.948562i | 0.880373 | + | 0.474281i | \(0.157292\pi\) | ||||
−0.880373 | + | 0.474281i | \(0.842708\pi\) | |||||||
\(198\) | 5.65685 | 0.402015 | ||||||||
\(199\) | −10.3431 | −0.733206 | −0.366603 | − | 0.930377i | \(-0.619479\pi\) | ||||
−0.366603 | + | 0.930377i | \(0.619479\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | − 5.65685i | − 0.399004i | ||||||||
\(202\) | 16.1421i | 1.13576i | ||||||||
\(203\) | 24.9706i | 1.75259i | ||||||||
\(204\) | 0.828427 | 0.0580015 | ||||||||
\(205\) | 7.65685 | 0.534778 | ||||||||
\(206\) | − 1.65685i | − 0.115439i | ||||||||
\(207\) | 8.48528 | 0.589768 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 2.82843i | 0.195180i | ||||||||
\(211\) | 0.686292 | 0.0472463 | 0.0236231 | − | 0.999721i | \(-0.492480\pi\) | ||||
0.0236231 | + | 0.999721i | \(0.492480\pi\) | |||||||
\(212\) | −13.3137 | −0.914389 | ||||||||
\(213\) | 5.65685i | 0.387601i | ||||||||
\(214\) | 4.00000i | 0.273434i | ||||||||
\(215\) | 9.65685i | 0.658592i | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −11.3137 | −0.768025 | ||||||||
\(218\) | −8.82843 | −0.597937 | ||||||||
\(219\) | − 14.4853i | − 0.978825i | ||||||||
\(220\) | −5.65685 | −0.381385 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −11.6569 | −0.782357 | ||||||||
\(223\) | − 10.8284i | − 0.725125i | −0.931959 | − | 0.362563i | \(-0.881902\pi\) | ||||
0.931959 | − | 0.362563i | \(-0.118098\pi\) | |||||||
\(224\) | −2.82843 | −0.188982 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 6.48528i | − 0.431394i | ||||||||
\(227\) | − 4.00000i | − 0.265489i | −0.991150 | − | 0.132745i | \(-0.957621\pi\) | ||||
0.991150 | − | 0.132745i | \(-0.0423790\pi\) | |||||||
\(228\) | 2.82843i | 0.187317i | ||||||||
\(229\) | 4.14214i | 0.273720i | 0.990590 | + | 0.136860i | \(0.0437011\pi\) | ||||
−0.990590 | + | 0.136860i | \(0.956299\pi\) | |||||||
\(230\) | −8.48528 | −0.559503 | ||||||||
\(231\) | 16.0000 | 1.05272 | ||||||||
\(232\) | − 8.82843i | − 0.579615i | ||||||||
\(233\) | −5.51472 | −0.361281 | −0.180641 | − | 0.983549i | \(-0.557817\pi\) | ||||
−0.180641 | + | 0.983549i | \(0.557817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 2.34315i | 0.152526i | ||||||||
\(237\) | 2.34315 | 0.152204 | ||||||||
\(238\) | 2.34315 | 0.151884 | ||||||||
\(239\) | − 16.0000i | − 1.03495i | −0.855697 | − | 0.517477i | \(-0.826871\pi\) | ||||
0.855697 | − | 0.517477i | \(-0.173129\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | 5.31371i | 0.342286i | 0.985246 | + | 0.171143i | \(0.0547460\pi\) | ||||
−0.985246 | + | 0.171143i | \(0.945254\pi\) | |||||||
\(242\) | 21.0000i | 1.34993i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | 7.65685 | 0.488183 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | − 6.34315i | − 0.401981i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −10.8284 | −0.683484 | −0.341742 | − | 0.939794i | \(-0.611017\pi\) | ||||
−0.341742 | + | 0.939794i | \(0.611017\pi\) | |||||||
\(252\) | 2.82843i | 0.178174i | ||||||||
\(253\) | 48.0000i | 3.01773i | ||||||||
\(254\) | 9.65685i | 0.605925i | ||||||||
\(255\) | 0.828427i | 0.0518781i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.82843 | 0.301189 | 0.150595 | − | 0.988596i | \(-0.451881\pi\) | ||||
0.150595 | + | 0.988596i | \(0.451881\pi\) | |||||||
\(258\) | 9.65685i | 0.601209i | ||||||||
\(259\) | −32.9706 | −2.04869 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.82843 | −0.546466 | ||||||||
\(262\) | 6.14214i | 0.379462i | ||||||||
\(263\) | 16.4853 | 1.01653 | 0.508263 | − | 0.861202i | \(-0.330288\pi\) | ||||
0.508263 | + | 0.861202i | \(0.330288\pi\) | |||||||
\(264\) | −5.65685 | −0.348155 | ||||||||
\(265\) | − 13.3137i | − 0.817855i | ||||||||
\(266\) | 8.00000i | 0.490511i | ||||||||
\(267\) | − 15.6569i | − 0.958184i | ||||||||
\(268\) | 5.65685i | 0.345547i | ||||||||
\(269\) | −14.4853 | −0.883183 | −0.441592 | − | 0.897216i | \(-0.645586\pi\) | ||||
−0.441592 | + | 0.897216i | \(0.645586\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 7.31371i | 0.444276i | 0.975015 | + | 0.222138i | \(0.0713036\pi\) | ||||
−0.975015 | + | 0.222138i | \(0.928696\pi\) | |||||||
\(272\) | −0.828427 | −0.0502308 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.3137 | −1.04596 | ||||||||
\(275\) | − 5.65685i | − 0.341121i | ||||||||
\(276\) | −8.48528 | −0.510754 | ||||||||
\(277\) | −26.0000 | −1.56219 | −0.781094 | − | 0.624413i | \(-0.785338\pi\) | ||||
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | − 6.34315i | − 0.380437i | ||||||||
\(279\) | − 4.00000i | − 0.239474i | ||||||||
\(280\) | − 2.82843i | − 0.169031i | ||||||||
\(281\) | 8.34315i | 0.497710i | 0.968541 | + | 0.248855i | \(0.0800543\pi\) | ||||
−0.968541 | + | 0.248855i | \(0.919946\pi\) | |||||||
\(282\) | −8.00000 | −0.476393 | ||||||||
\(283\) | 17.6569 | 1.04959 | 0.524796 | − | 0.851228i | \(-0.324142\pi\) | ||||
0.524796 | + | 0.851228i | \(0.324142\pi\) | |||||||
\(284\) | − 5.65685i | − 0.335673i | ||||||||
\(285\) | −2.82843 | −0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.6569 | 1.27836 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −16.3137 | −0.959630 | ||||||||
\(290\) | 8.82843 | 0.518423 | ||||||||
\(291\) | 3.17157i | 0.185921i | ||||||||
\(292\) | 14.4853i | 0.847687i | ||||||||
\(293\) | − 16.6274i | − 0.971384i | −0.874130 | − | 0.485692i | \(-0.838568\pi\) | ||||
0.874130 | − | 0.485692i | \(-0.161432\pi\) | |||||||
\(294\) | 1.00000i | 0.0583212i | ||||||||
\(295\) | −2.34315 | −0.136423 | ||||||||
\(296\) | 11.6569 | 0.677541 | ||||||||
\(297\) | 5.65685i | 0.328244i | ||||||||
\(298\) | −3.65685 | −0.211836 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 27.3137i | 1.57434i | ||||||||
\(302\) | 12.0000 | 0.690522 | ||||||||
\(303\) | −16.1421 | −0.927341 | ||||||||
\(304\) | − 2.82843i | − 0.162221i | ||||||||
\(305\) | − 6.00000i | − 0.343559i | ||||||||
\(306\) | 0.828427i | 0.0473580i | ||||||||
\(307\) | − 21.6569i | − 1.23602i | −0.786169 | − | 0.618011i | \(-0.787939\pi\) | ||||
0.786169 | − | 0.618011i | \(-0.212061\pi\) | |||||||
\(308\) | −16.0000 | −0.911685 | ||||||||
\(309\) | 1.65685 | 0.0942551 | ||||||||
\(310\) | 4.00000i | 0.227185i | ||||||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.9706 | −1.75056 | −0.875280 | − | 0.483617i | \(-0.839323\pi\) | ||||
−0.875280 | + | 0.483617i | \(0.839323\pi\) | |||||||
\(314\) | − 5.31371i | − 0.299870i | ||||||||
\(315\) | −2.82843 | −0.159364 | ||||||||
\(316\) | −2.34315 | −0.131812 | ||||||||
\(317\) | − 25.3137i | − 1.42176i | −0.703314 | − | 0.710880i | \(-0.748297\pi\) | ||||
0.703314 | − | 0.710880i | \(-0.251703\pi\) | |||||||
\(318\) | − 13.3137i | − 0.746596i | ||||||||
\(319\) | − 49.9411i | − 2.79617i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | −24.0000 | −1.33747 | ||||||||
\(323\) | 2.34315i | 0.130376i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.3137 | 0.626608 | ||||||||
\(327\) | − 8.82843i | − 0.488213i | ||||||||
\(328\) | −7.65685 | −0.422779 | ||||||||
\(329\) | −22.6274 | −1.24749 | ||||||||
\(330\) | − 5.65685i | − 0.311400i | ||||||||
\(331\) | 8.48528i | 0.466393i | 0.972430 | + | 0.233197i | \(0.0749186\pi\) | ||||
−0.972430 | + | 0.233197i | \(0.925081\pi\) | |||||||
\(332\) | 6.34315i | 0.348125i | ||||||||
\(333\) | − 11.6569i | − 0.638792i | ||||||||
\(334\) | 8.97056 | 0.490847 | ||||||||
\(335\) | −5.65685 | −0.309067 | ||||||||
\(336\) | − 2.82843i | − 0.154303i | ||||||||
\(337\) | −10.9706 | −0.597605 | −0.298802 | − | 0.954315i | \(-0.596587\pi\) | ||||
−0.298802 | + | 0.954315i | \(0.596587\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.48528 | 0.352232 | ||||||||
\(340\) | − 0.828427i | − 0.0449278i | ||||||||
\(341\) | 22.6274 | 1.22534 | ||||||||
\(342\) | −2.82843 | −0.152944 | ||||||||
\(343\) | − 16.9706i | − 0.916324i | ||||||||
\(344\) | − 9.65685i | − 0.520663i | ||||||||
\(345\) | − 8.48528i | − 0.456832i | ||||||||
\(346\) | − 9.31371i | − 0.500708i | ||||||||
\(347\) | −9.65685 | −0.518407 | −0.259204 | − | 0.965823i | \(-0.583460\pi\) | ||||
−0.259204 | + | 0.965823i | \(0.583460\pi\) | |||||||
\(348\) | 8.82843 | 0.473253 | ||||||||
\(349\) | 12.1421i | 0.649954i | 0.945722 | + | 0.324977i | \(0.105356\pi\) | ||||
−0.945722 | + | 0.324977i | \(0.894644\pi\) | |||||||
\(350\) | 2.82843 | 0.151186 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.65685 | 0.301511 | ||||||||
\(353\) | − 5.31371i | − 0.282820i | −0.989951 | − | 0.141410i | \(-0.954836\pi\) | ||||
0.989951 | − | 0.141410i | \(-0.0451636\pi\) | |||||||
\(354\) | −2.34315 | −0.124537 | ||||||||
\(355\) | 5.65685 | 0.300235 | ||||||||
\(356\) | 15.6569i | 0.829812i | ||||||||
\(357\) | 2.34315i | 0.124012i | ||||||||
\(358\) | 7.51472i | 0.397165i | ||||||||
\(359\) | − 28.2843i | − 1.49279i | −0.665505 | − | 0.746393i | \(-0.731784\pi\) | ||||
0.665505 | − | 0.746393i | \(-0.268216\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | − 7.65685i | − 0.402435i | ||||||||
\(363\) | −21.0000 | −1.10221 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.4853 | −0.758194 | ||||||||
\(366\) | − 6.00000i | − 0.313625i | ||||||||
\(367\) | 25.6569 | 1.33928 | 0.669638 | − | 0.742687i | \(-0.266449\pi\) | ||||
0.669638 | + | 0.742687i | \(0.266449\pi\) | |||||||
\(368\) | 8.48528 | 0.442326 | ||||||||
\(369\) | 7.65685i | 0.398600i | ||||||||
\(370\) | 11.6569i | 0.606011i | ||||||||
\(371\) | − 37.6569i | − 1.95505i | ||||||||
\(372\) | 4.00000i | 0.207390i | ||||||||
\(373\) | −2.68629 | −0.139091 | −0.0695455 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695455 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(374\) | −4.68629 | −0.242322 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 8.00000 | 0.412568 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.82843 | −0.145479 | ||||||||
\(379\) | 7.51472i | 0.386005i | 0.981198 | + | 0.193003i | \(0.0618226\pi\) | ||||
−0.981198 | + | 0.193003i | \(0.938177\pi\) | |||||||
\(380\) | 2.82843 | 0.145095 | ||||||||
\(381\) | −9.65685 | −0.494736 | ||||||||
\(382\) | − 11.3137i | − 0.578860i | ||||||||
\(383\) | 29.6569i | 1.51539i | 0.652606 | + | 0.757697i | \(0.273676\pi\) | ||||
−0.652606 | + | 0.757697i | \(0.726324\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | − 16.0000i | − 0.815436i | ||||||||
\(386\) | 2.48528 | 0.126497 | ||||||||
\(387\) | −9.65685 | −0.490885 | ||||||||
\(388\) | − 3.17157i | − 0.161012i | ||||||||
\(389\) | 6.48528 | 0.328817 | 0.164408 | − | 0.986392i | \(-0.447429\pi\) | ||||
0.164408 | + | 0.986392i | \(0.447429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.02944 | −0.355494 | ||||||||
\(392\) | − 1.00000i | − 0.0505076i | ||||||||
\(393\) | −6.14214 | −0.309830 | ||||||||
\(394\) | 13.3137 | 0.670735 | ||||||||
\(395\) | − 2.34315i | − 0.117896i | ||||||||
\(396\) | − 5.65685i | − 0.284268i | ||||||||
\(397\) | 30.2843i | 1.51992i | 0.649968 | + | 0.759962i | \(0.274782\pi\) | ||||
−0.649968 | + | 0.759962i | \(0.725218\pi\) | |||||||
\(398\) | 10.3431i | 0.518455i | ||||||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | − 26.9706i | − 1.34685i | −0.739258 | − | 0.673423i | \(-0.764823\pi\) | ||||
0.739258 | − | 0.673423i | \(-0.235177\pi\) | |||||||
\(402\) | −5.65685 | −0.282138 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 16.1421 | 0.803101 | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | 24.9706 | 1.23927 | ||||||||
\(407\) | 65.9411 | 3.26858 | ||||||||
\(408\) | − 0.828427i | − 0.0410133i | ||||||||
\(409\) | 3.65685i | 0.180820i | 0.995905 | + | 0.0904099i | \(0.0288177\pi\) | ||||
−0.995905 | + | 0.0904099i | \(0.971182\pi\) | |||||||
\(410\) | − 7.65685i | − 0.378145i | ||||||||
\(411\) | − 17.3137i | − 0.854022i | ||||||||
\(412\) | −1.65685 | −0.0816274 | ||||||||
\(413\) | −6.62742 | −0.326114 | ||||||||
\(414\) | − 8.48528i | − 0.417029i | ||||||||
\(415\) | −6.34315 | −0.311373 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.34315 | 0.310625 | ||||||||
\(418\) | − 16.0000i | − 0.782586i | ||||||||
\(419\) | −10.8284 | −0.529003 | −0.264502 | − | 0.964385i | \(-0.585207\pi\) | ||||
−0.264502 | + | 0.964385i | \(0.585207\pi\) | |||||||
\(420\) | 2.82843 | 0.138013 | ||||||||
\(421\) | 24.1421i | 1.17662i | 0.808637 | + | 0.588308i | \(0.200206\pi\) | ||||
−0.808637 | + | 0.588308i | \(0.799794\pi\) | |||||||
\(422\) | − 0.686292i | − 0.0334081i | ||||||||
\(423\) | − 8.00000i | − 0.388973i | ||||||||
\(424\) | 13.3137i | 0.646571i | ||||||||
\(425\) | 0.828427 | 0.0401846 | ||||||||
\(426\) | 5.65685 | 0.274075 | ||||||||
\(427\) | − 16.9706i | − 0.821263i | ||||||||
\(428\) | 4.00000 | 0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.65685 | 0.465695 | ||||||||
\(431\) | 16.0000i | 0.770693i | 0.922772 | + | 0.385346i | \(0.125918\pi\) | ||||
−0.922772 | + | 0.385346i | \(0.874082\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 22.9706 | 1.10389 | 0.551947 | − | 0.833879i | \(-0.313885\pi\) | ||||
0.551947 | + | 0.833879i | \(0.313885\pi\) | |||||||
\(434\) | 11.3137i | 0.543075i | ||||||||
\(435\) | 8.82843i | 0.423291i | ||||||||
\(436\) | 8.82843i | 0.422805i | ||||||||
\(437\) | − 24.0000i | − 1.14808i | ||||||||
\(438\) | −14.4853 | −0.692134 | ||||||||
\(439\) | −22.6274 | −1.07995 | −0.539974 | − | 0.841682i | \(-0.681566\pi\) | ||||
−0.539974 | + | 0.841682i | \(0.681566\pi\) | |||||||
\(440\) | 5.65685i | 0.269680i | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.3431 | 1.44165 | 0.720823 | − | 0.693119i | \(-0.243764\pi\) | ||||
0.720823 | + | 0.693119i | \(0.243764\pi\) | |||||||
\(444\) | 11.6569i | 0.553210i | ||||||||
\(445\) | −15.6569 | −0.742206 | ||||||||
\(446\) | −10.8284 | −0.512741 | ||||||||
\(447\) | − 3.65685i | − 0.172963i | ||||||||
\(448\) | 2.82843i | 0.133631i | ||||||||
\(449\) | 26.2843i | 1.24043i | 0.784431 | + | 0.620216i | \(0.212955\pi\) | ||||
−0.784431 | + | 0.620216i | \(0.787045\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | −43.3137 | −2.03956 | ||||||||
\(452\) | −6.48528 | −0.305042 | ||||||||
\(453\) | 12.0000i | 0.563809i | ||||||||
\(454\) | −4.00000 | −0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.82843 | 0.132453 | ||||||||
\(457\) | − 20.8284i | − 0.974313i | −0.873315 | − | 0.487156i | \(-0.838034\pi\) | ||||
0.873315 | − | 0.487156i | \(-0.161966\pi\) | |||||||
\(458\) | 4.14214 | 0.193549 | ||||||||
\(459\) | −0.828427 | −0.0386677 | ||||||||
\(460\) | 8.48528i | 0.395628i | ||||||||
\(461\) | − 14.0000i | − 0.652045i | −0.945362 | − | 0.326023i | \(-0.894291\pi\) | ||||
0.945362 | − | 0.326023i | \(-0.105709\pi\) | |||||||
\(462\) | − 16.0000i | − 0.744387i | ||||||||
\(463\) | − 3.79899i | − 0.176554i | −0.996096 | − | 0.0882770i | \(-0.971864\pi\) | ||||
0.996096 | − | 0.0882770i | \(-0.0281361\pi\) | |||||||
\(464\) | −8.82843 | −0.409849 | ||||||||
\(465\) | −4.00000 | −0.185496 | ||||||||
\(466\) | 5.51472i | 0.255464i | ||||||||
\(467\) | −7.31371 | −0.338438 | −0.169219 | − | 0.985578i | \(-0.554125\pi\) | ||||
−0.169219 | + | 0.985578i | \(0.554125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 8.00000i | 0.369012i | ||||||||
\(471\) | 5.31371 | 0.244843 | ||||||||
\(472\) | 2.34315 | 0.107852 | ||||||||
\(473\) | − 54.6274i | − 2.51177i | ||||||||
\(474\) | − 2.34315i | − 0.107624i | ||||||||
\(475\) | 2.82843i | 0.129777i | ||||||||
\(476\) | − 2.34315i | − 0.107398i | ||||||||
\(477\) | 13.3137 | 0.609593 | ||||||||
\(478\) | −16.0000 | −0.731823 | ||||||||
\(479\) | − 11.3137i | − 0.516937i | −0.966020 | − | 0.258468i | \(-0.916782\pi\) | ||||
0.966020 | − | 0.258468i | \(-0.0832177\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5.31371 | 0.242033 | ||||||||
\(483\) | − 24.0000i | − 1.09204i | ||||||||
\(484\) | 21.0000 | 0.954545 | ||||||||
\(485\) | 3.17157 | 0.144014 | ||||||||
\(486\) | − 1.00000i | − 0.0453609i | ||||||||
\(487\) | − 16.4853i | − 0.747019i | −0.927626 | − | 0.373510i | \(-0.878154\pi\) | ||||
0.927626 | − | 0.373510i | \(-0.121846\pi\) | |||||||
\(488\) | 6.00000i | 0.271607i | ||||||||
\(489\) | 11.3137i | 0.511624i | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 38.1421 | 1.72133 | 0.860665 | − | 0.509171i | \(-0.170048\pi\) | ||||
0.860665 | + | 0.509171i | \(0.170048\pi\) | |||||||
\(492\) | − 7.65685i | − 0.345198i | ||||||||
\(493\) | 7.31371 | 0.329393 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.65685 | 0.254257 | ||||||||
\(496\) | − 4.00000i | − 0.179605i | ||||||||
\(497\) | 16.0000 | 0.717698 | ||||||||
\(498\) | −6.34315 | −0.284243 | ||||||||
\(499\) | − 0.485281i | − 0.0217242i | −0.999941 | − | 0.0108621i | \(-0.996542\pi\) | ||||
0.999941 | − | 0.0108621i | \(-0.00345758\pi\) | |||||||
\(500\) | − 1.00000i | − 0.0447214i | ||||||||
\(501\) | 8.97056i | 0.400775i | ||||||||
\(502\) | 10.8284i | 0.483296i | ||||||||
\(503\) | −23.5147 | −1.04847 | −0.524235 | − | 0.851574i | \(-0.675649\pi\) | ||||
−0.524235 | + | 0.851574i | \(0.675649\pi\) | |||||||
\(504\) | 2.82843 | 0.125988 | ||||||||
\(505\) | 16.1421i | 0.718316i | ||||||||
\(506\) | 48.0000 | 2.13386 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.65685 | 0.428454 | ||||||||
\(509\) | 37.3137i | 1.65390i | 0.562275 | + | 0.826951i | \(0.309926\pi\) | ||||
−0.562275 | + | 0.826951i | \(0.690074\pi\) | |||||||
\(510\) | 0.828427 | 0.0366834 | ||||||||
\(511\) | −40.9706 | −1.81243 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 2.82843i | − 0.124878i | ||||||||
\(514\) | − 4.82843i | − 0.212973i | ||||||||
\(515\) | − 1.65685i | − 0.0730097i | ||||||||
\(516\) | 9.65685 | 0.425119 | ||||||||
\(517\) | 45.2548 | 1.99031 | ||||||||
\(518\) | 32.9706i | 1.44864i | ||||||||
\(519\) | 9.31371 | 0.408826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9706 | 1.18160 | 0.590801 | − | 0.806817i | \(-0.298812\pi\) | ||||
0.590801 | + | 0.806817i | \(0.298812\pi\) | |||||||
\(522\) | 8.82843i | 0.386410i | ||||||||
\(523\) | −10.6274 | −0.464704 | −0.232352 | − | 0.972632i | \(-0.574642\pi\) | ||||
−0.232352 | + | 0.972632i | \(0.574642\pi\) | |||||||
\(524\) | 6.14214 | 0.268320 | ||||||||
\(525\) | 2.82843i | 0.123443i | ||||||||
\(526\) | − 16.4853i | − 0.718792i | ||||||||
\(527\) | 3.31371i | 0.144347i | ||||||||
\(528\) | 5.65685i | 0.246183i | ||||||||
\(529\) | 49.0000 | 2.13043 | ||||||||
\(530\) | −13.3137 | −0.578311 | ||||||||
\(531\) | − 2.34315i | − 0.101684i | ||||||||
\(532\) | 8.00000 | 0.346844 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −15.6569 | −0.677538 | ||||||||
\(535\) | 4.00000i | 0.172935i | ||||||||
\(536\) | 5.65685 | 0.244339 | ||||||||
\(537\) | −7.51472 | −0.324284 | ||||||||
\(538\) | 14.4853i | 0.624505i | ||||||||
\(539\) | − 5.65685i | − 0.243658i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 14.4853i | 0.622771i | 0.950284 | + | 0.311385i | \(0.100793\pi\) | ||||
−0.950284 | + | 0.311385i | \(0.899207\pi\) | |||||||
\(542\) | 7.31371 | 0.314151 | ||||||||
\(543\) | 7.65685 | 0.328587 | ||||||||
\(544\) | 0.828427i | 0.0355185i | ||||||||
\(545\) | −8.82843 | −0.378168 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.686292 | 0.0293437 | 0.0146719 | − | 0.999892i | \(-0.495330\pi\) | ||||
0.0146719 | + | 0.999892i | \(0.495330\pi\) | |||||||
\(548\) | 17.3137i | 0.739605i | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | −5.65685 | −0.241209 | ||||||||
\(551\) | 24.9706i | 1.06378i | ||||||||
\(552\) | 8.48528i | 0.361158i | ||||||||
\(553\) | − 6.62742i | − 0.281826i | ||||||||
\(554\) | 26.0000i | 1.10463i | ||||||||
\(555\) | −11.6569 | −0.494806 | ||||||||
\(556\) | −6.34315 | −0.269009 | ||||||||
\(557\) | 10.6863i | 0.452793i | 0.974035 | + | 0.226396i | \(0.0726945\pi\) | ||||
−0.974035 | + | 0.226396i | \(0.927306\pi\) | |||||||
\(558\) | −4.00000 | −0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.82843 | −0.119523 | ||||||||
\(561\) | − 4.68629i | − 0.197855i | ||||||||
\(562\) | 8.34315 | 0.351934 | ||||||||
\(563\) | 30.3431 | 1.27881 | 0.639406 | − | 0.768870i | \(-0.279181\pi\) | ||||
0.639406 | + | 0.768870i | \(0.279181\pi\) | |||||||
\(564\) | 8.00000i | 0.336861i | ||||||||
\(565\) | − 6.48528i | − 0.272838i | ||||||||
\(566\) | − 17.6569i | − 0.742173i | ||||||||
\(567\) | − 2.82843i | − 0.118783i | ||||||||
\(568\) | −5.65685 | −0.237356 | ||||||||
\(569\) | −31.6569 | −1.32712 | −0.663562 | − | 0.748121i | \(-0.730956\pi\) | ||||
−0.663562 | + | 0.748121i | \(0.730956\pi\) | |||||||
\(570\) | 2.82843i | 0.118470i | ||||||||
\(571\) | −20.9706 | −0.877591 | −0.438795 | − | 0.898587i | \(-0.644595\pi\) | ||||
−0.438795 | + | 0.898587i | \(0.644595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.3137 | 0.472637 | ||||||||
\(574\) | − 21.6569i | − 0.903940i | ||||||||
\(575\) | −8.48528 | −0.353861 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 23.4558i | 0.976480i | 0.872710 | + | 0.488240i | \(0.162361\pi\) | ||||
−0.872710 | + | 0.488240i | \(0.837639\pi\) | |||||||
\(578\) | 16.3137i | 0.678561i | ||||||||
\(579\) | 2.48528i | 0.103285i | ||||||||
\(580\) | − 8.82843i | − 0.366580i | ||||||||
\(581\) | −17.9411 | −0.744323 | ||||||||
\(582\) | 3.17157 | 0.131466 | ||||||||
\(583\) | 75.3137i | 3.11918i | ||||||||
\(584\) | 14.4853 | 0.599405 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.6274 | −0.686872 | ||||||||
\(587\) | − 2.62742i | − 0.108445i | −0.998529 | − | 0.0542226i | \(-0.982732\pi\) | ||||
0.998529 | − | 0.0542226i | \(-0.0172680\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | −11.3137 | −0.466173 | ||||||||
\(590\) | 2.34315i | 0.0964658i | ||||||||
\(591\) | 13.3137i | 0.547653i | ||||||||
\(592\) | − 11.6569i | − 0.479094i | ||||||||
\(593\) | − 0.343146i | − 0.0140913i | −0.999975 | − | 0.00704565i | \(-0.997757\pi\) | ||||
0.999975 | − | 0.00704565i | \(-0.00224272\pi\) | |||||||
\(594\) | 5.65685 | 0.232104 | ||||||||
\(595\) | 2.34315 | 0.0960596 | ||||||||
\(596\) | 3.65685i | 0.149791i | ||||||||
\(597\) | −10.3431 | −0.423317 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.0000 | 1.63436 | 0.817178 | − | 0.576386i | \(-0.195537\pi\) | ||||
0.817178 | + | 0.576386i | \(0.195537\pi\) | |||||||
\(600\) | − 1.00000i | − 0.0408248i | ||||||||
\(601\) | 29.3137 | 1.19573 | 0.597866 | − | 0.801596i | \(-0.296016\pi\) | ||||
0.597866 | + | 0.801596i | \(0.296016\pi\) | |||||||
\(602\) | 27.3137 | 1.11322 | ||||||||
\(603\) | − 5.65685i | − 0.230365i | ||||||||
\(604\) | − 12.0000i | − 0.488273i | ||||||||
\(605\) | 21.0000i | 0.853771i | ||||||||
\(606\) | 16.1421i | 0.655729i | ||||||||
\(607\) | 28.9706 | 1.17588 | 0.587939 | − | 0.808905i | \(-0.299939\pi\) | ||||
0.587939 | + | 0.808905i | \(0.299939\pi\) | |||||||
\(608\) | −2.82843 | −0.114708 | ||||||||
\(609\) | 24.9706i | 1.01186i | ||||||||
\(610\) | −6.00000 | −0.242933 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.828427 | 0.0334872 | ||||||||
\(613\) | − 22.2843i | − 0.900053i | −0.893015 | − | 0.450027i | \(-0.851414\pi\) | ||||
0.893015 | − | 0.450027i | \(-0.148586\pi\) | |||||||
\(614\) | −21.6569 | −0.874000 | ||||||||
\(615\) | 7.65685 | 0.308754 | ||||||||
\(616\) | 16.0000i | 0.644658i | ||||||||
\(617\) | − 2.00000i | − 0.0805170i | −0.999189 | − | 0.0402585i | \(-0.987182\pi\) | ||||
0.999189 | − | 0.0402585i | \(-0.0128181\pi\) | |||||||
\(618\) | − 1.65685i | − 0.0666485i | ||||||||
\(619\) | − 34.8284i | − 1.39987i | −0.714205 | − | 0.699936i | \(-0.753212\pi\) | ||||
0.714205 | − | 0.699936i | \(-0.246788\pi\) | |||||||
\(620\) | 4.00000 | 0.160644 | ||||||||
\(621\) | 8.48528 | 0.340503 | ||||||||
\(622\) | − 24.0000i | − 0.962312i | ||||||||
\(623\) | −44.2843 | −1.77421 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 30.9706i | 1.23783i | ||||||||
\(627\) | 16.0000 | 0.638978 | ||||||||
\(628\) | −5.31371 | −0.212040 | ||||||||
\(629\) | 9.65685i | 0.385044i | ||||||||
\(630\) | 2.82843i | 0.112687i | ||||||||
\(631\) | − 33.6569i | − 1.33986i | −0.742425 | − | 0.669929i | \(-0.766324\pi\) | ||||
0.742425 | − | 0.669929i | \(-0.233676\pi\) | |||||||
\(632\) | 2.34315i | 0.0932053i | ||||||||
\(633\) | 0.686292 | 0.0272776 | ||||||||
\(634\) | −25.3137 | −1.00534 | ||||||||
\(635\) | 9.65685i | 0.383221i | ||||||||
\(636\) | −13.3137 | −0.527923 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −49.9411 | −1.97719 | ||||||||
\(639\) | 5.65685i | 0.223782i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 4.62742 | 0.182772 | 0.0913860 | − | 0.995816i | \(-0.470870\pi\) | ||||
0.0913860 | + | 0.995816i | \(0.470870\pi\) | |||||||
\(642\) | 4.00000i | 0.157867i | ||||||||
\(643\) | − 39.5980i | − 1.56159i | −0.624786 | − | 0.780796i | \(-0.714814\pi\) | ||||
0.624786 | − | 0.780796i | \(-0.285186\pi\) | |||||||
\(644\) | 24.0000i | 0.945732i | ||||||||
\(645\) | 9.65685i | 0.380238i | ||||||||
\(646\) | 2.34315 | 0.0921898 | ||||||||
\(647\) | −8.48528 | −0.333591 | −0.166795 | − | 0.985992i | \(-0.553342\pi\) | ||||
−0.166795 | + | 0.985992i | \(0.553342\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 13.2548 | 0.520298 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.3137 | −0.443419 | ||||||||
\(652\) | − 11.3137i | − 0.443079i | ||||||||
\(653\) | −42.2843 | −1.65471 | −0.827356 | − | 0.561678i | \(-0.810156\pi\) | ||||
−0.827356 | + | 0.561678i | \(0.810156\pi\) | |||||||
\(654\) | −8.82843 | −0.345219 | ||||||||
\(655\) | 6.14214i | 0.239993i | ||||||||
\(656\) | 7.65685i | 0.298950i | ||||||||
\(657\) | − 14.4853i | − 0.565125i | ||||||||
\(658\) | 22.6274i | 0.882109i | ||||||||
\(659\) | −7.51472 | −0.292732 | −0.146366 | − | 0.989231i | \(-0.546758\pi\) | ||||
−0.146366 | + | 0.989231i | \(0.546758\pi\) | |||||||
\(660\) | −5.65685 | −0.220193 | ||||||||
\(661\) | − 8.14214i | − 0.316692i | −0.987384 | − | 0.158346i | \(-0.949384\pi\) | ||||
0.987384 | − | 0.158346i | \(-0.0506162\pi\) | |||||||
\(662\) | 8.48528 | 0.329790 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.34315 | 0.246162 | ||||||||
\(665\) | 8.00000i | 0.310227i | ||||||||
\(666\) | −11.6569 | −0.451694 | ||||||||
\(667\) | −74.9117 | −2.90059 | ||||||||
\(668\) | − 8.97056i | − 0.347081i | ||||||||
\(669\) | − 10.8284i | − 0.418651i | ||||||||
\(670\) | 5.65685i | 0.218543i | ||||||||
\(671\) | 33.9411i | 1.31028i | ||||||||
\(672\) | −2.82843 | −0.109109 | ||||||||
\(673\) | −32.6274 | −1.25769 | −0.628847 | − | 0.777529i | \(-0.716473\pi\) | ||||
−0.628847 | + | 0.777529i | \(0.716473\pi\) | |||||||
\(674\) | 10.9706i | 0.422570i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.3431 | 0.474386 | 0.237193 | − | 0.971463i | \(-0.423773\pi\) | ||||
0.237193 | + | 0.971463i | \(0.423773\pi\) | |||||||
\(678\) | − 6.48528i | − 0.249066i | ||||||||
\(679\) | 8.97056 | 0.344259 | ||||||||
\(680\) | −0.828427 | −0.0317687 | ||||||||
\(681\) | − 4.00000i | − 0.153280i | ||||||||
\(682\) | − 22.6274i | − 0.866449i | ||||||||
\(683\) | 33.6569i | 1.28784i | 0.765091 | + | 0.643922i | \(0.222694\pi\) | ||||
−0.765091 | + | 0.643922i | \(0.777306\pi\) | |||||||
\(684\) | 2.82843i | 0.108148i | ||||||||
\(685\) | −17.3137 | −0.661523 | ||||||||
\(686\) | −16.9706 | −0.647939 | ||||||||
\(687\) | 4.14214i | 0.158032i | ||||||||
\(688\) | −9.65685 | −0.368164 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.48528 | −0.323029 | ||||||||
\(691\) | 27.7990i | 1.05752i | 0.848770 | + | 0.528762i | \(0.177343\pi\) | ||||
−0.848770 | + | 0.528762i | \(0.822657\pi\) | |||||||
\(692\) | −9.31371 | −0.354054 | ||||||||
\(693\) | 16.0000 | 0.607790 | ||||||||
\(694\) | 9.65685i | 0.366569i | ||||||||
\(695\) | − 6.34315i | − 0.240609i | ||||||||
\(696\) | − 8.82843i | − 0.334641i | ||||||||
\(697\) | − 6.34315i | − 0.240264i | ||||||||
\(698\) | 12.1421 | 0.459587 | ||||||||
\(699\) | −5.51472 | −0.208586 | ||||||||
\(700\) | − 2.82843i | − 0.106904i | ||||||||
\(701\) | −0.142136 | −0.00536839 | −0.00268419 | − | 0.999996i | \(-0.500854\pi\) | ||||
−0.00268419 | + | 0.999996i | \(0.500854\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.9706 | −1.24351 | ||||||||
\(704\) | − 5.65685i | − 0.213201i | ||||||||
\(705\) | −8.00000 | −0.301297 | ||||||||
\(706\) | −5.31371 | −0.199984 | ||||||||
\(707\) | 45.6569i | 1.71710i | ||||||||
\(708\) | 2.34315i | 0.0880608i | ||||||||
\(709\) | − 7.17157i | − 0.269334i | −0.990891 | − | 0.134667i | \(-0.957004\pi\) | ||||
0.990891 | − | 0.134667i | \(-0.0429965\pi\) | |||||||
\(710\) | − 5.65685i | − 0.212298i | ||||||||
\(711\) | 2.34315 | 0.0878748 | ||||||||
\(712\) | 15.6569 | 0.586765 | ||||||||
\(713\) | − 33.9411i | − 1.27111i | ||||||||
\(714\) | 2.34315 | 0.0876900 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.51472 | 0.280838 | ||||||||
\(717\) | − 16.0000i | − 0.597531i | ||||||||
\(718\) | −28.2843 | −1.05556 | ||||||||
\(719\) | 29.6569 | 1.10601 | 0.553007 | − | 0.833177i | \(-0.313480\pi\) | ||||
0.553007 | + | 0.833177i | \(0.313480\pi\) | |||||||
\(720\) | − 1.00000i | − 0.0372678i | ||||||||
\(721\) | − 4.68629i | − 0.174527i | ||||||||
\(722\) | − 11.0000i | − 0.409378i | ||||||||
\(723\) | 5.31371i | 0.197619i | ||||||||
\(724\) | −7.65685 | −0.284565 | ||||||||
\(725\) | 8.82843 | 0.327880 | ||||||||
\(726\) | 21.0000i | 0.779383i | ||||||||
\(727\) | 45.9411 | 1.70386 | 0.851931 | − | 0.523654i | \(-0.175432\pi\) | ||||
0.851931 | + | 0.523654i | \(0.175432\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.4853i | 0.536124i | ||||||||
\(731\) | 8.00000 | 0.295891 | ||||||||
\(732\) | −6.00000 | −0.221766 | ||||||||
\(733\) | 0.343146i | 0.0126744i | 0.999980 | + | 0.00633719i | \(0.00201720\pi\) | ||||
−0.999980 | + | 0.00633719i | \(0.997983\pi\) | |||||||
\(734\) | − 25.6569i | − 0.947012i | ||||||||
\(735\) | 1.00000i | 0.0368856i | ||||||||
\(736\) | − 8.48528i | − 0.312772i | ||||||||
\(737\) | 32.0000 | 1.17874 | ||||||||
\(738\) | 7.65685 | 0.281853 | ||||||||
\(739\) | − 14.1421i | − 0.520227i | −0.965578 | − | 0.260113i | \(-0.916240\pi\) | ||||
0.965578 | − | 0.260113i | \(-0.0837600\pi\) | |||||||
\(740\) | 11.6569 | 0.428514 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −37.6569 | −1.38243 | ||||||||
\(743\) | 36.2843i | 1.33114i | 0.746335 | + | 0.665570i | \(0.231812\pi\) | ||||
−0.746335 | + | 0.665570i | \(0.768188\pi\) | |||||||
\(744\) | 4.00000 | 0.146647 | ||||||||
\(745\) | −3.65685 | −0.133977 | ||||||||
\(746\) | 2.68629i | 0.0983521i | ||||||||
\(747\) | − 6.34315i | − 0.232084i | ||||||||
\(748\) | 4.68629i | 0.171348i | ||||||||
\(749\) | 11.3137i | 0.413394i | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −11.3137 | −0.412843 | −0.206422 | − | 0.978463i | \(-0.566182\pi\) | ||||
−0.206422 | + | 0.978463i | \(0.566182\pi\) | |||||||
\(752\) | − 8.00000i | − 0.291730i | ||||||||
\(753\) | −10.8284 | −0.394610 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 2.82843i | 0.102869i | ||||||||
\(757\) | 19.9411 | 0.724773 | 0.362386 | − | 0.932028i | \(-0.381962\pi\) | ||||
0.362386 | + | 0.932028i | \(0.381962\pi\) | |||||||
\(758\) | 7.51472 | 0.272947 | ||||||||
\(759\) | 48.0000i | 1.74229i | ||||||||
\(760\) | − 2.82843i | − 0.102598i | ||||||||
\(761\) | 27.6569i | 1.00256i | 0.865285 | + | 0.501280i | \(0.167137\pi\) | ||||
−0.865285 | + | 0.501280i | \(0.832863\pi\) | |||||||
\(762\) | 9.65685i | 0.349831i | ||||||||
\(763\) | −24.9706 | −0.903995 | ||||||||
\(764\) | −11.3137 | −0.409316 | ||||||||
\(765\) | 0.828427i | 0.0299518i | ||||||||
\(766\) | 29.6569 | 1.07155 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 14.0000i | 0.504853i | 0.967616 | + | 0.252426i | \(0.0812286\pi\) | ||||
−0.967616 | + | 0.252426i | \(0.918771\pi\) | |||||||
\(770\) | −16.0000 | −0.576600 | ||||||||
\(771\) | 4.82843 | 0.173892 | ||||||||
\(772\) | − 2.48528i | − 0.0894472i | ||||||||
\(773\) | 53.3137i | 1.91756i | 0.284148 | + | 0.958780i | \(0.408289\pi\) | ||||
−0.284148 | + | 0.958780i | \(0.591711\pi\) | |||||||
\(774\) | 9.65685i | 0.347108i | ||||||||
\(775\) | 4.00000i | 0.143684i | ||||||||
\(776\) | −3.17157 | −0.113853 | ||||||||
\(777\) | −32.9706 | −1.18281 | ||||||||
\(778\) | − 6.48528i | − 0.232509i | ||||||||
\(779\) | 21.6569 | 0.775937 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.0000 | −1.14505 | ||||||||
\(782\) | 7.02944i | 0.251372i | ||||||||
\(783\) | −8.82843 | −0.315502 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | − 5.31371i | − 0.189654i | ||||||||
\(786\) | 6.14214i | 0.219083i | ||||||||
\(787\) | − 24.0000i | − 0.855508i | −0.903895 | − | 0.427754i | \(-0.859305\pi\) | ||||
0.903895 | − | 0.427754i | \(-0.140695\pi\) | |||||||
\(788\) | − 13.3137i | − 0.474281i | ||||||||
\(789\) | 16.4853 | 0.586892 | ||||||||
\(790\) | −2.34315 | −0.0833654 | ||||||||
\(791\) | − 18.3431i | − 0.652207i | ||||||||
\(792\) | −5.65685 | −0.201008 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 30.2843 | 1.07475 | ||||||||
\(795\) | − 13.3137i | − 0.472189i | ||||||||
\(796\) | 10.3431 | 0.366603 | ||||||||
\(797\) | −16.6274 | −0.588973 | −0.294487 | − | 0.955656i | \(-0.595149\pi\) | ||||
−0.294487 | + | 0.955656i | \(0.595149\pi\) | |||||||
\(798\) | 8.00000i | 0.283197i | ||||||||
\(799\) | 6.62742i | 0.234461i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | − 15.6569i | − 0.553208i | ||||||||
\(802\) | −26.9706 | −0.952364 | ||||||||
\(803\) | 81.9411 | 2.89164 | ||||||||
\(804\) | 5.65685i | 0.199502i | ||||||||
\(805\) | −24.0000 | −0.845889 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −14.4853 | −0.509906 | ||||||||
\(808\) | − 16.1421i | − 0.567878i | ||||||||
\(809\) | 13.3137 | 0.468085 | 0.234043 | − | 0.972226i | \(-0.424804\pi\) | ||||
0.234043 | + | 0.972226i | \(0.424804\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 1.85786i | 0.0652384i | 0.999468 | + | 0.0326192i | \(0.0103849\pi\) | ||||
−0.999468 | + | 0.0326192i | \(0.989615\pi\) | |||||||
\(812\) | − 24.9706i | − 0.876295i | ||||||||
\(813\) | 7.31371i | 0.256503i | ||||||||
\(814\) | − 65.9411i | − 2.31124i | ||||||||
\(815\) | 11.3137 | 0.396302 | ||||||||
\(816\) | −0.828427 | −0.0290008 | ||||||||
\(817\) | 27.3137i | 0.955586i | ||||||||
\(818\) | 3.65685 | 0.127859 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.65685 | −0.267389 | ||||||||
\(821\) | − 34.2843i | − 1.19653i | −0.801299 | − | 0.598265i | \(-0.795857\pi\) | ||||
0.801299 | − | 0.598265i | \(-0.204143\pi\) | |||||||
\(822\) | −17.3137 | −0.603885 | ||||||||
\(823\) | 52.9706 | 1.84644 | 0.923219 | − | 0.384275i | \(-0.125548\pi\) | ||||
0.923219 | + | 0.384275i | \(0.125548\pi\) | |||||||
\(824\) | 1.65685i | 0.0577193i | ||||||||
\(825\) | − 5.65685i | − 0.196946i | ||||||||
\(826\) | 6.62742i | 0.230597i | ||||||||
\(827\) | 9.65685i | 0.335802i | 0.985804 | + | 0.167901i | \(0.0536989\pi\) | ||||
−0.985804 | + | 0.167901i | \(0.946301\pi\) | |||||||
\(828\) | −8.48528 | −0.294884 | ||||||||
\(829\) | 53.3137 | 1.85166 | 0.925831 | − | 0.377938i | \(-0.123367\pi\) | ||||
0.925831 | + | 0.377938i | \(0.123367\pi\) | |||||||
\(830\) | 6.34315i | 0.220174i | ||||||||
\(831\) | −26.0000 | −0.901930 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.828427 | 0.0287033 | ||||||||
\(834\) | − 6.34315i | − 0.219645i | ||||||||
\(835\) | 8.97056 | 0.310439 | ||||||||
\(836\) | −16.0000 | −0.553372 | ||||||||
\(837\) | − 4.00000i | − 0.138260i | ||||||||
\(838\) | 10.8284i | 0.374062i | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | − 2.82843i | − 0.0975900i | ||||||||
\(841\) | 48.9411 | 1.68763 | ||||||||
\(842\) | 24.1421 | 0.831993 | ||||||||
\(843\) | 8.34315i | 0.287353i | ||||||||
\(844\) | −0.686292 | −0.0236231 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | 59.3970i | 2.04090i | ||||||||
\(848\) | 13.3137 | 0.457195 | ||||||||
\(849\) | 17.6569 | 0.605982 | ||||||||
\(850\) | − 0.828427i | − 0.0284148i | ||||||||
\(851\) | − 98.9117i | − 3.39065i | ||||||||
\(852\) | − 5.65685i | − 0.193801i | ||||||||
\(853\) | 38.2843i | 1.31083i | 0.755270 | + | 0.655414i | \(0.227506\pi\) | ||||
−0.755270 | + | 0.655414i | \(0.772494\pi\) | |||||||
\(854\) | −16.9706 | −0.580721 | ||||||||
\(855\) | −2.82843 | −0.0967302 | ||||||||
\(856\) | − 4.00000i | − 0.136717i | ||||||||
\(857\) | 20.8284 | 0.711486 | 0.355743 | − | 0.934584i | \(-0.384228\pi\) | ||||
0.355743 | + | 0.934584i | \(0.384228\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.9411 | 1.29453 | 0.647267 | − | 0.762263i | \(-0.275912\pi\) | ||||
0.647267 | + | 0.762263i | \(0.275912\pi\) | |||||||
\(860\) | − 9.65685i | − 0.329296i | ||||||||
\(861\) | 21.6569 | 0.738064 | ||||||||
\(862\) | 16.0000 | 0.544962 | ||||||||
\(863\) | 28.2843i | 0.962808i | 0.876499 | + | 0.481404i | \(0.159873\pi\) | ||||
−0.876499 | + | 0.481404i | \(0.840127\pi\) | |||||||
\(864\) | − 1.00000i | − 0.0340207i | ||||||||
\(865\) | − 9.31371i | − 0.316676i | ||||||||
\(866\) | − 22.9706i | − 0.780571i | ||||||||
\(867\) | −16.3137 | −0.554043 | ||||||||
\(868\) | 11.3137 | 0.384012 | ||||||||
\(869\) | 13.2548i | 0.449639i | ||||||||
\(870\) | 8.82843 | 0.299312 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.82843 | 0.298968 | ||||||||
\(873\) | 3.17157i | 0.107341i | ||||||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | 2.82843 | 0.0956183 | ||||||||
\(876\) | 14.4853i | 0.489412i | ||||||||
\(877\) | 51.2548i | 1.73075i | 0.501122 | + | 0.865376i | \(0.332921\pi\) | ||||
−0.501122 | + | 0.865376i | \(0.667079\pi\) | |||||||
\(878\) | 22.6274i | 0.763638i | ||||||||
\(879\) | − 16.6274i | − 0.560829i | ||||||||
\(880\) | 5.65685 | 0.190693 | ||||||||
\(881\) | 10.2843 | 0.346486 | 0.173243 | − | 0.984879i | \(-0.444575\pi\) | ||||
0.173243 | + | 0.984879i | \(0.444575\pi\) | |||||||
\(882\) | 1.00000i | 0.0336718i | ||||||||
\(883\) | −31.3137 | −1.05379 | −0.526895 | − | 0.849930i | \(-0.676644\pi\) | ||||
−0.526895 | + | 0.849930i | \(0.676644\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.34315 | −0.0787640 | ||||||||
\(886\) | − 30.3431i | − 1.01940i | ||||||||
\(887\) | −40.4853 | −1.35936 | −0.679681 | − | 0.733508i | \(-0.737882\pi\) | ||||
−0.679681 | + | 0.733508i | \(0.737882\pi\) | |||||||
\(888\) | 11.6569 | 0.391178 | ||||||||
\(889\) | 27.3137i | 0.916072i | ||||||||
\(890\) | 15.6569i | 0.524819i | ||||||||
\(891\) | 5.65685i | 0.189512i | ||||||||
\(892\) | 10.8284i | 0.362563i | ||||||||
\(893\) | −22.6274 | −0.757198 | ||||||||
\(894\) | −3.65685 | −0.122304 | ||||||||
\(895\) | 7.51472i | 0.251189i | ||||||||
\(896\) | 2.82843 | 0.0944911 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.2843 | 0.877117 | ||||||||
\(899\) | 35.3137i | 1.17778i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −11.0294 | −0.367444 | ||||||||
\(902\) | 43.3137i | 1.44219i | ||||||||
\(903\) | 27.3137i | 0.908943i | ||||||||
\(904\) | 6.48528i | 0.215697i | ||||||||
\(905\) | − 7.65685i | − 0.254522i | ||||||||
\(906\) | 12.0000 | 0.398673 | ||||||||
\(907\) | −8.28427 | −0.275075 | −0.137537 | − | 0.990497i | \(-0.543919\pi\) | ||||
−0.137537 | + | 0.990497i | \(0.543919\pi\) | |||||||
\(908\) | 4.00000i | 0.132745i | ||||||||
\(909\) | −16.1421 | −0.535401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9706 | 0.827312 | 0.413656 | − | 0.910433i | \(-0.364252\pi\) | ||||
0.413656 | + | 0.910433i | \(0.364252\pi\) | |||||||
\(912\) | − 2.82843i | − 0.0936586i | ||||||||
\(913\) | 35.8823 | 1.18753 | ||||||||
\(914\) | −20.8284 | −0.688943 | ||||||||
\(915\) | − 6.00000i | − 0.198354i | ||||||||
\(916\) | − 4.14214i | − 0.136860i | ||||||||
\(917\) | 17.3726i | 0.573693i | ||||||||
\(918\) | 0.828427i | 0.0273422i | ||||||||
\(919\) | 41.9411 | 1.38351 | 0.691755 | − | 0.722132i | \(-0.256838\pi\) | ||||
0.691755 | + | 0.722132i | \(0.256838\pi\) | |||||||
\(920\) | 8.48528 | 0.279751 | ||||||||
\(921\) | − 21.6569i | − 0.713618i | ||||||||
\(922\) | −14.0000 | −0.461065 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −16.0000 | −0.526361 | ||||||||
\(925\) | 11.6569i | 0.383275i | ||||||||
\(926\) | −3.79899 | −0.124843 | ||||||||
\(927\) | 1.65685 | 0.0544182 | ||||||||
\(928\) | 8.82843i | 0.289807i | ||||||||
\(929\) | 33.5980i | 1.10231i | 0.834402 | + | 0.551157i | \(0.185813\pi\) | ||||
−0.834402 | + | 0.551157i | \(0.814187\pi\) | |||||||
\(930\) | 4.00000i | 0.131165i | ||||||||
\(931\) | 2.82843i | 0.0926980i | ||||||||
\(932\) | 5.51472 | 0.180641 | ||||||||
\(933\) | 24.0000 | 0.785725 | ||||||||
\(934\) | 7.31371i | 0.239312i | ||||||||
\(935\) | −4.68629 | −0.153258 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6274 | 0.543194 | 0.271597 | − | 0.962411i | \(-0.412448\pi\) | ||||
0.271597 | + | 0.962411i | \(0.412448\pi\) | |||||||
\(938\) | 16.0000i | 0.522419i | ||||||||
\(939\) | −30.9706 | −1.01069 | ||||||||
\(940\) | 8.00000 | 0.260931 | ||||||||
\(941\) | − 54.9706i | − 1.79199i | −0.444065 | − | 0.895995i | \(-0.646464\pi\) | ||||
0.444065 | − | 0.895995i | \(-0.353536\pi\) | |||||||
\(942\) | − 5.31371i | − 0.173130i | ||||||||
\(943\) | 64.9706i | 2.11573i | ||||||||
\(944\) | − 2.34315i | − 0.0762629i | ||||||||
\(945\) | −2.82843 | −0.0920087 | ||||||||
\(946\) | −54.6274 | −1.77609 | ||||||||
\(947\) | 30.3431i | 0.986020i | 0.870024 | + | 0.493010i | \(0.164103\pi\) | ||||
−0.870024 | + | 0.493010i | \(0.835897\pi\) | |||||||
\(948\) | −2.34315 | −0.0761018 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.82843 | 0.0917663 | ||||||||
\(951\) | − 25.3137i | − 0.820853i | ||||||||
\(952\) | −2.34315 | −0.0759418 | ||||||||
\(953\) | 27.8579 | 0.902405 | 0.451202 | − | 0.892422i | \(-0.350995\pi\) | ||||
0.451202 | + | 0.892422i | \(0.350995\pi\) | |||||||
\(954\) | − 13.3137i | − 0.431047i | ||||||||
\(955\) | − 11.3137i | − 0.366103i | ||||||||
\(956\) | 16.0000i | 0.517477i | ||||||||
\(957\) | − 49.9411i | − 1.61437i | ||||||||
\(958\) | −11.3137 | −0.365529 | ||||||||
\(959\) | −48.9706 | −1.58134 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | − 5.31371i | − 0.171143i | ||||||||
\(965\) | 2.48528 | 0.0800040 | ||||||||
\(966\) | −24.0000 | −0.772187 | ||||||||
\(967\) | 7.51472i | 0.241657i | 0.992673 | + | 0.120829i | \(0.0385551\pi\) | ||||
−0.992673 | + | 0.120829i | \(0.961445\pi\) | |||||||
\(968\) | − 21.0000i | − 0.674966i | ||||||||
\(969\) | 2.34315i | 0.0752727i | ||||||||
\(970\) | − 3.17157i | − 0.101833i | ||||||||
\(971\) | 15.5147 | 0.497891 | 0.248946 | − | 0.968517i | \(-0.419916\pi\) | ||||
0.248946 | + | 0.968517i | \(0.419916\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | − 17.9411i | − 0.575166i | ||||||||
\(974\) | −16.4853 | −0.528222 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | 8.34315i | 0.266921i | 0.991054 | + | 0.133460i | \(0.0426089\pi\) | ||||
−0.991054 | + | 0.133460i | \(0.957391\pi\) | |||||||
\(978\) | 11.3137 | 0.361773 | ||||||||
\(979\) | 88.5685 | 2.83066 | ||||||||
\(980\) | − 1.00000i | − 0.0319438i | ||||||||
\(981\) | − 8.82843i | − 0.281870i | ||||||||
\(982\) | − 38.1421i | − 1.21716i | ||||||||
\(983\) | − 2.34315i | − 0.0747347i | −0.999302 | − | 0.0373674i | \(-0.988103\pi\) | ||||
0.999302 | − | 0.0373674i | \(-0.0118972\pi\) | |||||||
\(984\) | −7.65685 | −0.244092 | ||||||||
\(985\) | 13.3137 | 0.424210 | ||||||||
\(986\) | − 7.31371i | − 0.232916i | ||||||||
\(987\) | −22.6274 | −0.720239 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −81.9411 | −2.60558 | ||||||||
\(990\) | − 5.65685i | − 0.179787i | ||||||||
\(991\) | −42.9117 | −1.36313 | −0.681567 | − | 0.731755i | \(-0.738701\pi\) | ||||
−0.681567 | + | 0.731755i | \(0.738701\pi\) | |||||||
\(992\) | −4.00000 | −0.127000 | ||||||||
\(993\) | 8.48528i | 0.269272i | ||||||||
\(994\) | − 16.0000i | − 0.507489i | ||||||||
\(995\) | 10.3431i | 0.327900i | ||||||||
\(996\) | 6.34315i | 0.200990i | ||||||||
\(997\) | 61.3137 | 1.94182 | 0.970912 | − | 0.239435i | \(-0.0769623\pi\) | ||||
0.970912 | + | 0.239435i | \(0.0769623\pi\) | |||||||
\(998\) | −0.485281 | −0.0153613 | ||||||||
\(999\) | − 11.6569i | − 0.368807i |
(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.q.1351.1 | 4 | ||
13.5 | odd | 4 | 5070.2.a.bc.1.2 | 2 | |||
13.8 | odd | 4 | 390.2.a.h.1.1 | ✓ | 2 | ||
13.12 | even | 2 | inner | 5070.2.b.q.1351.4 | 4 | ||
39.8 | even | 4 | 1170.2.a.o.1.1 | 2 | |||
52.47 | even | 4 | 3120.2.a.bc.1.2 | 2 | |||
65.8 | even | 4 | 1950.2.e.o.1249.2 | 4 | |||
65.34 | odd | 4 | 1950.2.a.bd.1.2 | 2 | |||
65.47 | even | 4 | 1950.2.e.o.1249.3 | 4 | |||
156.47 | odd | 4 | 9360.2.a.ch.1.2 | 2 | |||
195.8 | odd | 4 | 5850.2.e.bk.5149.4 | 4 | |||
195.47 | odd | 4 | 5850.2.e.bk.5149.1 | 4 | |||
195.164 | even | 4 | 5850.2.a.cl.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.a.h.1.1 | ✓ | 2 | 13.8 | odd | 4 | ||
1170.2.a.o.1.1 | 2 | 39.8 | even | 4 | |||
1950.2.a.bd.1.2 | 2 | 65.34 | odd | 4 | |||
1950.2.e.o.1249.2 | 4 | 65.8 | even | 4 | |||
1950.2.e.o.1249.3 | 4 | 65.47 | even | 4 | |||
3120.2.a.bc.1.2 | 2 | 52.47 | even | 4 | |||
5070.2.a.bc.1.2 | 2 | 13.5 | odd | 4 | |||
5070.2.b.q.1351.1 | 4 | 1.1 | even | 1 | trivial | ||
5070.2.b.q.1351.4 | 4 | 13.12 | even | 2 | inner | ||
5850.2.a.cl.1.2 | 2 | 195.164 | even | 4 | |||
5850.2.e.bk.5149.1 | 4 | 195.47 | odd | 4 | |||
5850.2.e.bk.5149.4 | 4 | 195.8 | odd | 4 | |||
9360.2.a.ch.1.2 | 2 | 156.47 | odd | 4 |