Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(569,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.c (of order \(2\), degree \(1\), 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: | \(4.55147291521\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 569.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.569 |
Dual form | 570.2.c.a.569.3 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||
\(3\) | −1.41421 | − | 1.00000i | −0.816497 | − | 0.577350i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.12132 | + | 0.707107i | 0.948683 | + | 0.316228i | ||||
\(6\) | −1.00000 | + | 1.41421i | −0.408248 | + | 0.577350i | ||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 0.707107 | − | 2.12132i | 0.223607 | − | 0.670820i | ||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 1.41421 | + | 1.00000i | 0.408248 | + | 0.288675i | ||||
\(13\) | 4.24264 | 1.17670 | 0.588348 | − | 0.808608i | \(-0.299778\pi\) | ||||
0.588348 | + | 0.808608i | \(0.299778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.29289 | − | 3.12132i | −0.592022 | − | 0.805921i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 2.82843 | − | 1.00000i | 0.666667 | − | 0.235702i | ||||
\(19\) | 1.00000 | + | 4.24264i | 0.229416 | + | 0.973329i | ||||
\(20\) | −2.12132 | − | 0.707107i | −0.474342 | − | 0.158114i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.82843 | 0.603023 | ||||||||
\(23\) | 4.24264 | 0.884652 | 0.442326 | − | 0.896854i | \(-0.354153\pi\) | ||||
0.442326 | + | 0.896854i | \(0.354153\pi\) | |||||||
\(24\) | 1.00000 | − | 1.41421i | 0.204124 | − | 0.288675i | ||||
\(25\) | 4.00000 | + | 3.00000i | 0.800000 | + | 0.600000i | ||||
\(26\) | − | 4.24264i | − | 0.832050i | ||||||
\(27\) | 1.41421 | − | 5.00000i | 0.272166 | − | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | −3.12132 | + | 2.29289i | −0.569873 | + | 0.418623i | ||||
\(31\) | − | 4.24264i | − | 0.762001i | −0.924575 | − | 0.381000i | \(-0.875580\pi\) | ||
0.924575 | − | 0.381000i | \(-0.124420\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 2.82843 | − | 4.00000i | 0.492366 | − | 0.696311i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | − | 2.82843i | −0.166667 | − | 0.471405i | ||||
\(37\) | 4.24264 | 0.697486 | 0.348743 | − | 0.937218i | \(-0.386609\pi\) | ||||
0.348743 | + | 0.937218i | \(0.386609\pi\) | |||||||
\(38\) | 4.24264 | − | 1.00000i | 0.688247 | − | 0.162221i | ||||
\(39\) | −6.00000 | − | 4.24264i | −0.960769 | − | 0.679366i | ||||
\(40\) | −0.707107 | + | 2.12132i | −0.111803 | + | 0.335410i | ||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.0000i | − | 1.82998i | −0.403473 | − | 0.914991i | \(-0.632197\pi\) | ||
0.403473 | − | 0.914991i | \(-0.367803\pi\) | |||||||
\(44\) | − | 2.82843i | − | 0.426401i | ||||||
\(45\) | 0.121320 | + | 6.70711i | 0.0180854 | + | 0.999836i | ||||
\(46\) | − | 4.24264i | − | 0.625543i | ||||||
\(47\) | −12.7279 | −1.85656 | −0.928279 | − | 0.371884i | \(-0.878712\pi\) | ||||
−0.928279 | + | 0.371884i | \(0.878712\pi\) | |||||||
\(48\) | −1.41421 | − | 1.00000i | −0.204124 | − | 0.144338i | ||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 3.00000 | − | 4.00000i | 0.424264 | − | 0.565685i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.24264 | −0.588348 | ||||||||
\(53\) | 6.00000i | 0.824163i | 0.911147 | + | 0.412082i | \(0.135198\pi\) | ||||
−0.911147 | + | 0.412082i | \(0.864802\pi\) | |||||||
\(54\) | −5.00000 | − | 1.41421i | −0.680414 | − | 0.192450i | ||||
\(55\) | −2.00000 | + | 6.00000i | −0.269680 | + | 0.809040i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.82843 | − | 7.00000i | 0.374634 | − | 0.927173i | ||||
\(58\) | 6.00000i | 0.787839i | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 2.29289 | + | 3.12132i | 0.296011 | + | 0.402961i | ||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | −4.24264 | −0.538816 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 9.00000 | + | 3.00000i | 1.11631 | + | 0.372104i | ||||
\(66\) | −4.00000 | − | 2.82843i | −0.492366 | − | 0.348155i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | − | 4.24264i | −0.722315 | − | 0.510754i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | −2.82843 | + | 1.00000i | −0.333333 | + | 0.117851i | ||||
\(73\) | − | 6.00000i | − | 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | − | 4.24264i | − | 0.493197i | ||||||
\(75\) | −2.65685 | − | 8.24264i | −0.306787 | − | 0.951778i | ||||
\(76\) | −1.00000 | − | 4.24264i | −0.114708 | − | 0.486664i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.24264 | + | 6.00000i | −0.480384 | + | 0.679366i | ||||
\(79\) | 12.7279i | 1.43200i | 0.698099 | + | 0.716002i | \(0.254030\pi\) | ||||
−0.698099 | + | 0.716002i | \(0.745970\pi\) | |||||||
\(80\) | 2.12132 | + | 0.707107i | 0.237171 | + | 0.0790569i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | − | 6.00000i | − | 0.662589i | ||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.0000 | −1.29399 | ||||||||
\(87\) | 8.48528 | + | 6.00000i | 0.909718 | + | 0.643268i | ||||
\(88\) | −2.82843 | −0.301511 | ||||||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 6.70711 | − | 0.121320i | 0.706991 | − | 0.0127883i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.24264 | −0.442326 | ||||||||
\(93\) | −4.24264 | + | 6.00000i | −0.439941 | + | 0.622171i | ||||
\(94\) | 12.7279i | 1.31278i | ||||||||
\(95\) | −0.878680 | + | 9.70711i | −0.0901506 | + | 0.995928i | ||||
\(96\) | −1.00000 | + | 1.41421i | −0.102062 | + | 0.144338i | ||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | − | 7.00000i | − | 0.707107i | ||||||
\(99\) | −8.00000 | + | 2.82843i | −0.804030 | + | 0.284268i | ||||
\(100\) | −4.00000 | − | 3.00000i | −0.400000 | − | 0.300000i | ||||
\(101\) | 15.5563i | 1.54791i | 0.633238 | + | 0.773957i | \(0.281726\pi\) | ||||
−0.633238 | + | 0.773957i | \(0.718274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.24264 | −0.418040 | −0.209020 | − | 0.977911i | \(-0.567027\pi\) | ||||
−0.209020 | + | 0.977911i | \(0.567027\pi\) | |||||||
\(104\) | 4.24264i | 0.416025i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | −1.41421 | + | 5.00000i | −0.136083 | + | 0.481125i | ||||
\(109\) | − | 4.24264i | − | 0.406371i | −0.979140 | − | 0.203186i | \(-0.934871\pi\) | ||
0.979140 | − | 0.203186i | \(-0.0651295\pi\) | |||||||
\(110\) | 6.00000 | + | 2.00000i | 0.572078 | + | 0.190693i | ||||
\(111\) | −6.00000 | − | 4.24264i | −0.569495 | − | 0.402694i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | −7.00000 | − | 2.82843i | −0.655610 | − | 0.264906i | ||||
\(115\) | 9.00000 | + | 3.00000i | 0.839254 | + | 0.279751i | ||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 4.24264 | + | 12.0000i | 0.392232 | + | 1.10940i | ||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.12132 | − | 2.29289i | 0.284936 | − | 0.209312i | ||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | − | 10.0000i | − | 0.905357i | ||||||
\(123\) | −8.48528 | − | 6.00000i | −0.765092 | − | 0.541002i | ||||
\(124\) | 4.24264i | 0.381000i | ||||||||
\(125\) | 6.36396 | + | 9.19239i | 0.569210 | + | 0.822192i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.7279 | −1.12942 | −0.564710 | − | 0.825289i | \(-0.691012\pi\) | ||||
−0.564710 | + | 0.825289i | \(0.691012\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −12.0000 | + | 16.9706i | −1.05654 | + | 1.49417i | ||||
\(130\) | 3.00000 | − | 9.00000i | 0.263117 | − | 0.789352i | ||||
\(131\) | − | 11.3137i | − | 0.988483i | −0.869325 | − | 0.494242i | \(-0.835446\pi\) | ||
0.869325 | − | 0.494242i | \(-0.164554\pi\) | |||||||
\(132\) | −2.82843 | + | 4.00000i | −0.246183 | + | 0.348155i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.53553 | − | 9.60660i | 0.562489 | − | 0.826805i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | −4.24264 | + | 6.00000i | −0.361158 | + | 0.510754i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.0000 | + | 12.7279i | 1.51587 | + | 1.07188i | ||||
\(142\) | − | 12.0000i | − | 1.00702i | ||||||
\(143\) | 12.0000i | 1.00349i | ||||||||
\(144\) | 1.00000 | + | 2.82843i | 0.0833333 | + | 0.235702i | ||||
\(145\) | −12.7279 | − | 4.24264i | −1.05700 | − | 0.352332i | ||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | −9.89949 | − | 7.00000i | −0.816497 | − | 0.577350i | ||||
\(148\) | −4.24264 | −0.348743 | ||||||||
\(149\) | − | 1.41421i | − | 0.115857i | −0.998321 | − | 0.0579284i | \(-0.981550\pi\) | ||
0.998321 | − | 0.0579284i | \(-0.0184495\pi\) | |||||||
\(150\) | −8.24264 | + | 2.65685i | −0.673009 | + | 0.216931i | ||||
\(151\) | 4.24264i | 0.345261i | 0.984987 | + | 0.172631i | \(0.0552267\pi\) | ||||
−0.984987 | + | 0.172631i | \(0.944773\pi\) | |||||||
\(152\) | −4.24264 | + | 1.00000i | −0.344124 | + | 0.0811107i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.00000 | − | 9.00000i | 0.240966 | − | 0.722897i | ||||
\(156\) | 6.00000 | + | 4.24264i | 0.480384 | + | 0.339683i | ||||
\(157\) | − | 18.0000i | − | 1.43656i | −0.695756 | − | 0.718278i | \(-0.744931\pi\) | ||
0.695756 | − | 0.718278i | \(-0.255069\pi\) | |||||||
\(158\) | 12.7279 | 1.01258 | ||||||||
\(159\) | 6.00000 | − | 8.48528i | 0.475831 | − | 0.672927i | ||||
\(160\) | 0.707107 | − | 2.12132i | 0.0559017 | − | 0.167705i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 5.65685 | + | 7.00000i | 0.444444 | + | 0.549972i | ||||
\(163\) | 6.00000i | 0.469956i | 0.972001 | + | 0.234978i | \(0.0755019\pi\) | ||||
−0.972001 | + | 0.234978i | \(0.924498\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 8.82843 | − | 6.48528i | 0.687292 | − | 0.504878i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 12.0000i | − | 0.928588i | −0.885681 | − | 0.464294i | \(-0.846308\pi\) | ||
0.885681 | − | 0.464294i | \(-0.153692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.0000 | + | 7.07107i | −0.841191 | + | 0.540738i | ||||
\(172\) | 12.0000i | 0.914991i | ||||||||
\(173\) | − | 6.00000i | − | 0.456172i | −0.973641 | − | 0.228086i | \(-0.926753\pi\) | ||
0.973641 | − | 0.228086i | \(-0.0732467\pi\) | |||||||
\(174\) | 6.00000 | − | 8.48528i | 0.454859 | − | 0.643268i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.82843i | 0.213201i | ||||||||
\(177\) | 8.48528 | + | 6.00000i | 0.637793 | + | 0.450988i | ||||
\(178\) | 12.0000i | 0.899438i | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | −0.121320 | − | 6.70711i | −0.00904268 | − | 0.499918i | ||||
\(181\) | − | 4.24264i | − | 0.315353i | −0.987491 | − | 0.157676i | \(-0.949600\pi\) | ||
0.987491 | − | 0.157676i | \(-0.0504003\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.1421 | − | 10.0000i | −1.04542 | − | 0.739221i | ||||
\(184\) | 4.24264i | 0.312772i | ||||||||
\(185\) | 9.00000 | + | 3.00000i | 0.661693 | + | 0.220564i | ||||
\(186\) | 6.00000 | + | 4.24264i | 0.439941 | + | 0.311086i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.7279 | 0.928279 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.70711 | + | 0.878680i | 0.704228 | + | 0.0637461i | ||||
\(191\) | − | 15.5563i | − | 1.12562i | −0.826587 | − | 0.562809i | \(-0.809721\pi\) | ||
0.826587 | − | 0.562809i | \(-0.190279\pi\) | |||||||
\(192\) | 1.41421 | + | 1.00000i | 0.102062 | + | 0.0721688i | ||||
\(193\) | −16.9706 | −1.22157 | −0.610784 | − | 0.791797i | \(-0.709146\pi\) | ||||
−0.610784 | + | 0.791797i | \(0.709146\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.72792 | − | 13.2426i | −0.696631 | − | 0.948325i | ||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | −12.7279 | −0.906827 | −0.453413 | − | 0.891300i | \(-0.649794\pi\) | ||||
−0.453413 | + | 0.891300i | \(0.649794\pi\) | |||||||
\(198\) | 2.82843 | + | 8.00000i | 0.201008 | + | 0.568535i | ||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | −3.00000 | + | 4.00000i | −0.212132 | + | 0.282843i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.5563 | 1.09454 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.7279 | + | 4.24264i | 0.888957 | + | 0.296319i | ||||
\(206\) | 4.24264i | 0.295599i | ||||||||
\(207\) | 4.24264 | + | 12.0000i | 0.294884 | + | 0.834058i | ||||
\(208\) | 4.24264 | 0.294174 | ||||||||
\(209\) | −12.0000 | + | 2.82843i | −0.830057 | + | 0.195646i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 8.48528i | − | 0.584151i | −0.956395 | − | 0.292075i | \(-0.905654\pi\) | ||
0.956395 | − | 0.292075i | \(-0.0943458\pi\) | |||||||
\(212\) | − | 6.00000i | − | 0.412082i | ||||||
\(213\) | −16.9706 | − | 12.0000i | −1.16280 | − | 0.822226i | ||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | 8.48528 | − | 25.4558i | 0.578691 | − | 1.73607i | ||||
\(216\) | 5.00000 | + | 1.41421i | 0.340207 | + | 0.0962250i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.24264 | −0.287348 | ||||||||
\(219\) | −6.00000 | + | 8.48528i | −0.405442 | + | 0.573382i | ||||
\(220\) | 2.00000 | − | 6.00000i | 0.134840 | − | 0.404520i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.24264 | + | 6.00000i | −0.284747 | + | 0.402694i | ||||
\(223\) | 21.2132 | 1.42054 | 0.710271 | − | 0.703929i | \(-0.248573\pi\) | ||||
0.710271 | + | 0.703929i | \(0.248573\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.48528 | + | 14.3137i | −0.299019 | + | 0.954247i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.0000i | 1.19470i | 0.801980 | + | 0.597351i | \(0.203780\pi\) | ||||
−0.801980 | + | 0.597351i | \(0.796220\pi\) | |||||||
\(228\) | −2.82843 | + | 7.00000i | −0.187317 | + | 0.463586i | ||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 3.00000 | − | 9.00000i | 0.197814 | − | 0.593442i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | −8.48528 | −0.555889 | −0.277945 | − | 0.960597i | \(-0.589653\pi\) | ||||
−0.277945 | + | 0.960597i | \(0.589653\pi\) | |||||||
\(234\) | 12.0000 | − | 4.24264i | 0.784465 | − | 0.277350i | ||||
\(235\) | −27.0000 | − | 9.00000i | −1.76129 | − | 0.587095i | ||||
\(236\) | 6.00000 | 0.390567 | ||||||||
\(237\) | 12.7279 | − | 18.0000i | 0.826767 | − | 1.16923i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 24.0416i | − | 1.55512i | −0.628806 | − | 0.777562i | \(-0.716456\pi\) | ||
0.628806 | − | 0.777562i | \(-0.283544\pi\) | |||||||
\(240\) | −2.29289 | − | 3.12132i | −0.148006 | − | 0.201480i | ||||
\(241\) | − | 8.48528i | − | 0.546585i | −0.961931 | − | 0.273293i | \(-0.911887\pi\) | ||
0.961931 | − | 0.273293i | \(-0.0881127\pi\) | |||||||
\(242\) | − | 3.00000i | − | 0.192847i | ||||||
\(243\) | 15.5563 | − | 1.00000i | 0.997940 | − | 0.0641500i | ||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 14.8492 | + | 4.94975i | 0.948683 | + | 0.316228i | ||||
\(246\) | −6.00000 | + | 8.48528i | −0.382546 | + | 0.541002i | ||||
\(247\) | 4.24264 | + | 18.0000i | 0.269953 | + | 1.14531i | ||||
\(248\) | 4.24264 | 0.269408 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.19239 | − | 6.36396i | 0.581378 | − | 0.402492i | ||||
\(251\) | 5.65685i | 0.357057i | 0.983935 | + | 0.178529i | \(0.0571337\pi\) | ||||
−0.983935 | + | 0.178529i | \(0.942866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000i | 0.754434i | ||||||||
\(254\) | 12.7279i | 0.798621i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 18.0000i | − | 1.12281i | −0.827541 | − | 0.561405i | \(-0.810261\pi\) | ||
0.827541 | − | 0.561405i | \(-0.189739\pi\) | |||||||
\(258\) | 16.9706 | + | 12.0000i | 1.05654 | + | 0.747087i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −9.00000 | − | 3.00000i | −0.558156 | − | 0.186052i | ||||
\(261\) | −6.00000 | − | 16.9706i | −0.371391 | − | 1.05045i | ||||
\(262\) | −11.3137 | −0.698963 | ||||||||
\(263\) | −21.2132 | −1.30806 | −0.654031 | − | 0.756468i | \(-0.726923\pi\) | ||||
−0.654031 | + | 0.756468i | \(0.726923\pi\) | |||||||
\(264\) | 4.00000 | + | 2.82843i | 0.246183 | + | 0.174078i | ||||
\(265\) | −4.24264 | + | 12.7279i | −0.260623 | + | 0.781870i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.9706 | + | 12.0000i | 1.03858 | + | 0.734388i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.00000 | −0.365826 | −0.182913 | − | 0.983129i | \(-0.558553\pi\) | ||||
−0.182913 | + | 0.983129i | \(0.558553\pi\) | |||||||
\(270\) | −9.60660 | − | 6.53553i | −0.584639 | − | 0.397740i | ||||
\(271\) | −20.0000 | −1.21491 | −0.607457 | − | 0.794353i | \(-0.707810\pi\) | ||||
−0.607457 | + | 0.794353i | \(0.707810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.48528 | + | 11.3137i | −0.511682 | + | 0.682242i | ||||
\(276\) | 6.00000 | + | 4.24264i | 0.361158 | + | 0.255377i | ||||
\(277\) | 18.0000i | 1.08152i | 0.841178 | + | 0.540758i | \(0.181862\pi\) | ||||
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(278\) | − | 4.00000i | − | 0.239904i | ||||||
\(279\) | 12.0000 | − | 4.24264i | 0.718421 | − | 0.254000i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 12.7279 | − | 18.0000i | 0.757937 | − | 1.07188i | ||||
\(283\) | 18.0000i | 1.06999i | 0.844856 | + | 0.534994i | \(0.179686\pi\) | ||||
−0.844856 | + | 0.534994i | \(0.820314\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | 10.9497 | − | 12.8492i | 0.648607 | − | 0.761123i | ||||
\(286\) | 12.0000 | 0.709575 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.82843 | − | 1.00000i | 0.166667 | − | 0.0589256i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −4.24264 | + | 12.7279i | −0.249136 | + | 0.747409i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.00000i | 0.351123i | ||||||||
\(293\) | − | 18.0000i | − | 1.05157i | −0.850617 | − | 0.525786i | \(-0.823771\pi\) | ||
0.850617 | − | 0.525786i | \(-0.176229\pi\) | |||||||
\(294\) | −7.00000 | + | 9.89949i | −0.408248 | + | 0.577350i | ||||
\(295\) | −12.7279 | − | 4.24264i | −0.741048 | − | 0.247016i | ||||
\(296\) | 4.24264i | 0.246598i | ||||||||
\(297\) | 14.1421 | + | 4.00000i | 0.820610 | + | 0.232104i | ||||
\(298\) | −1.41421 | −0.0819232 | ||||||||
\(299\) | 18.0000 | 1.04097 | ||||||||
\(300\) | 2.65685 | + | 8.24264i | 0.153394 | + | 0.475889i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.24264 | 0.244137 | ||||||||
\(303\) | 15.5563 | − | 22.0000i | 0.893689 | − | 1.26387i | ||||
\(304\) | 1.00000 | + | 4.24264i | 0.0573539 | + | 0.243332i | ||||
\(305\) | 21.2132 | + | 7.07107i | 1.21466 | + | 0.404888i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 33.9411 | 1.93712 | 0.968561 | − | 0.248776i | \(-0.0800281\pi\) | ||||
0.968561 | + | 0.248776i | \(0.0800281\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000 | + | 4.24264i | 0.341328 | + | 0.241355i | ||||
\(310\) | −9.00000 | − | 3.00000i | −0.511166 | − | 0.170389i | ||||
\(311\) | − | 1.41421i | − | 0.0801927i | −0.999196 | − | 0.0400963i | \(-0.987234\pi\) | ||
0.999196 | − | 0.0400963i | \(-0.0127665\pi\) | |||||||
\(312\) | 4.24264 | − | 6.00000i | 0.240192 | − | 0.339683i | ||||
\(313\) | − | 30.0000i | − | 1.69570i | −0.530236 | − | 0.847850i | \(-0.677897\pi\) | ||
0.530236 | − | 0.847850i | \(-0.322103\pi\) | |||||||
\(314\) | −18.0000 | −1.01580 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 12.7279i | − | 0.716002i | ||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | −8.48528 | − | 6.00000i | −0.475831 | − | 0.336463i | ||||
\(319\) | − | 16.9706i | − | 0.950169i | ||||||
\(320\) | −2.12132 | − | 0.707107i | −0.118585 | − | 0.0395285i | ||||
\(321\) | 12.0000 | − | 16.9706i | 0.669775 | − | 0.947204i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.00000 | − | 5.65685i | 0.388889 | − | 0.314270i | ||||
\(325\) | 16.9706 | + | 12.7279i | 0.941357 | + | 0.706018i | ||||
\(326\) | 6.00000 | 0.332309 | ||||||||
\(327\) | −4.24264 | + | 6.00000i | −0.234619 | + | 0.331801i | ||||
\(328\) | 6.00000i | 0.331295i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.48528 | − | 8.82843i | −0.357003 | − | 0.485989i | ||||
\(331\) | − | 33.9411i | − | 1.86557i | −0.360429 | − | 0.932786i | \(-0.617370\pi\) | ||
0.360429 | − | 0.932786i | \(-0.382630\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.24264 | + | 12.0000i | 0.232495 | + | 0.657596i | ||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.4558 | −1.38667 | −0.693334 | − | 0.720616i | \(-0.743859\pi\) | ||||
−0.693334 | + | 0.720616i | \(0.743859\pi\) | |||||||
\(338\) | − | 5.00000i | − | 0.271964i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 7.07107 | + | 11.0000i | 0.382360 | + | 0.594812i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.0000 | 0.646997 | ||||||||
\(345\) | −9.72792 | − | 13.2426i | −0.523734 | − | 0.712960i | ||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | −8.48528 | −0.455514 | −0.227757 | − | 0.973718i | \(-0.573139\pi\) | ||||
−0.227757 | + | 0.973718i | \(0.573139\pi\) | |||||||
\(348\) | −8.48528 | − | 6.00000i | −0.454859 | − | 0.321634i | ||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.00000 | − | 21.2132i | 0.320256 | − | 1.13228i | ||||
\(352\) | 2.82843 | 0.150756 | ||||||||
\(353\) | 8.48528 | 0.451626 | 0.225813 | − | 0.974171i | \(-0.427496\pi\) | ||||
0.225813 | + | 0.974171i | \(0.427496\pi\) | |||||||
\(354\) | 6.00000 | − | 8.48528i | 0.318896 | − | 0.450988i | ||||
\(355\) | 25.4558 | + | 8.48528i | 1.35106 | + | 0.450352i | ||||
\(356\) | 12.0000 | 0.635999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 12.0000i | − | 0.634220i | ||||||
\(359\) | 7.07107i | 0.373197i | 0.982436 | + | 0.186598i | \(0.0597463\pi\) | ||||
−0.982436 | + | 0.186598i | \(0.940254\pi\) | |||||||
\(360\) | −6.70711 | + | 0.121320i | −0.353496 | + | 0.00639414i | ||||
\(361\) | −17.0000 | + | 8.48528i | −0.894737 | + | 0.446594i | ||||
\(362\) | −4.24264 | −0.222988 | ||||||||
\(363\) | −4.24264 | − | 3.00000i | −0.222681 | − | 0.157459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.24264 | − | 12.7279i | 0.222070 | − | 0.666210i | ||||
\(366\) | −10.0000 | + | 14.1421i | −0.522708 | + | 0.739221i | ||||
\(367\) | 24.0000i | 1.25279i | 0.779506 | + | 0.626395i | \(0.215470\pi\) | ||||
−0.779506 | + | 0.626395i | \(0.784530\pi\) | |||||||
\(368\) | 4.24264 | 0.221163 | ||||||||
\(369\) | 6.00000 | + | 16.9706i | 0.312348 | + | 0.883452i | ||||
\(370\) | 3.00000 | − | 9.00000i | 0.155963 | − | 0.467888i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4.24264 | − | 6.00000i | 0.219971 | − | 0.311086i | ||||
\(373\) | 21.2132 | 1.09838 | 0.549189 | − | 0.835698i | \(-0.314937\pi\) | ||||
0.549189 | + | 0.835698i | \(0.314937\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.192388 | − | 19.3640i | 0.00993488 | − | 0.999951i | ||||
\(376\) | − | 12.7279i | − | 0.656392i | ||||||
\(377\) | −25.4558 | −1.31104 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0.878680 | − | 9.70711i | 0.0450753 | − | 0.497964i | ||||
\(381\) | 18.0000 | + | 12.7279i | 0.922168 | + | 0.652071i | ||||
\(382\) | −15.5563 | −0.795932 | ||||||||
\(383\) | 12.0000i | 0.613171i | 0.951843 | + | 0.306586i | \(0.0991866\pi\) | ||||
−0.951843 | + | 0.306586i | \(0.900813\pi\) | |||||||
\(384\) | 1.00000 | − | 1.41421i | 0.0510310 | − | 0.0721688i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 16.9706i | 0.863779i | ||||||||
\(387\) | 33.9411 | − | 12.0000i | 1.72532 | − | 0.609994i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.89949i | 0.501924i | 0.967997 | + | 0.250962i | \(0.0807470\pi\) | ||||
−0.967997 | + | 0.250962i | \(0.919253\pi\) | |||||||
\(390\) | −13.2426 | + | 9.72792i | −0.670567 | + | 0.492592i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 7.00000i | 0.353553i | ||||||||
\(393\) | −11.3137 | + | 16.0000i | −0.570701 | + | 0.807093i | ||||
\(394\) | 12.7279i | 0.641223i | ||||||||
\(395\) | −9.00000 | + | 27.0000i | −0.452839 | + | 1.35852i | ||||
\(396\) | 8.00000 | − | 2.82843i | 0.402015 | − | 0.142134i | ||||
\(397\) | 30.0000i | 1.50566i | 0.658217 | + | 0.752828i | \(0.271311\pi\) | ||||
−0.658217 | + | 0.752828i | \(0.728689\pi\) | |||||||
\(398\) | 16.0000i | 0.802008i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | + | 3.00000i | 0.200000 | + | 0.150000i | ||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 18.0000i | − | 0.896644i | ||||||
\(404\) | − | 15.5563i | − | 0.773957i | ||||||
\(405\) | −18.8492 | + | 7.05025i | −0.936626 | + | 0.350330i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000i | 0.594818i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.4558i | − | 1.25871i | −0.777118 | − | 0.629355i | \(-0.783319\pi\) | ||
0.777118 | − | 0.629355i | \(-0.216681\pi\) | |||||||
\(410\) | 4.24264 | − | 12.7279i | 0.209529 | − | 0.628587i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.24264 | 0.209020 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.0000 | − | 4.24264i | 0.589768 | − | 0.208514i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 4.24264i | − | 0.208013i | ||||||
\(417\) | −5.65685 | − | 4.00000i | −0.277017 | − | 0.195881i | ||||
\(418\) | 2.82843 | + | 12.0000i | 0.138343 | + | 0.586939i | ||||
\(419\) | 14.1421i | 0.690889i | 0.938439 | + | 0.345444i | \(0.112272\pi\) | ||||
−0.938439 | + | 0.345444i | \(0.887728\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.6985i | 1.44742i | 0.690107 | + | 0.723708i | \(0.257564\pi\) | ||||
−0.690107 | + | 0.723708i | \(0.742436\pi\) | |||||||
\(422\) | −8.48528 | −0.413057 | ||||||||
\(423\) | −12.7279 | − | 36.0000i | −0.618853 | − | 1.75038i | ||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | + | 16.9706i | −0.581402 | + | 0.822226i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | 12.0000 | − | 16.9706i | 0.579365 | − | 0.819346i | ||||
\(430\) | −25.4558 | − | 8.48528i | −1.22759 | − | 0.409197i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 1.41421 | − | 5.00000i | 0.0680414 | − | 0.240563i | ||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.7574 | + | 18.7279i | 0.659615 | + | 0.897935i | ||||
\(436\) | 4.24264i | 0.203186i | ||||||||
\(437\) | 4.24264 | + | 18.0000i | 0.202953 | + | 0.861057i | ||||
\(438\) | 8.48528 | + | 6.00000i | 0.405442 | + | 0.286691i | ||||
\(439\) | 4.24264i | 0.202490i | 0.994862 | + | 0.101245i | \(0.0322826\pi\) | ||||
−0.994862 | + | 0.101245i | \(0.967717\pi\) | |||||||
\(440\) | −6.00000 | − | 2.00000i | −0.286039 | − | 0.0953463i | ||||
\(441\) | 7.00000 | + | 19.7990i | 0.333333 | + | 0.942809i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.48528 | −0.403148 | −0.201574 | − | 0.979473i | \(-0.564606\pi\) | ||||
−0.201574 | + | 0.979473i | \(0.564606\pi\) | |||||||
\(444\) | 6.00000 | + | 4.24264i | 0.284747 | + | 0.201347i | ||||
\(445\) | −25.4558 | − | 8.48528i | −1.20672 | − | 0.402241i | ||||
\(446\) | − | 21.2132i | − | 1.00447i | ||||||
\(447\) | −1.41421 | + | 2.00000i | −0.0668900 | + | 0.0945968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.0000 | 1.13263 | 0.566315 | − | 0.824189i | \(-0.308369\pi\) | ||||
0.566315 | + | 0.824189i | \(0.308369\pi\) | |||||||
\(450\) | 14.3137 | + | 4.48528i | 0.674755 | + | 0.211438i | ||||
\(451\) | 16.9706i | 0.799113i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.24264 | − | 6.00000i | 0.199337 | − | 0.281905i | ||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.00000 | + | 2.82843i | 0.327805 | + | 0.132453i | ||||
\(457\) | − | 12.0000i | − | 0.561336i | −0.959805 | − | 0.280668i | \(-0.909444\pi\) | ||
0.959805 | − | 0.280668i | \(-0.0905560\pi\) | |||||||
\(458\) | 14.0000i | 0.654177i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.00000 | − | 3.00000i | −0.419627 | − | 0.139876i | ||||
\(461\) | − | 15.5563i | − | 0.724531i | −0.932075 | − | 0.362266i | \(-0.882003\pi\) | ||
0.932075 | − | 0.362266i | \(-0.117997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 36.0000i | − | 1.67306i | −0.547920 | − | 0.836531i | \(-0.684580\pi\) | ||
0.547920 | − | 0.836531i | \(-0.315420\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | −13.2426 | + | 9.72792i | −0.614113 | + | 0.451122i | ||||
\(466\) | 8.48528i | 0.393073i | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | −4.24264 | − | 12.0000i | −0.196116 | − | 0.554700i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.00000 | + | 27.0000i | −0.415139 | + | 1.24542i | ||||
\(471\) | −18.0000 | + | 25.4558i | −0.829396 | + | 1.17294i | ||||
\(472\) | − | 6.00000i | − | 0.276172i | ||||||
\(473\) | 33.9411 | 1.56061 | ||||||||
\(474\) | −18.0000 | − | 12.7279i | −0.826767 | − | 0.584613i | ||||
\(475\) | −8.72792 | + | 19.9706i | −0.400465 | + | 0.916312i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.9706 | + | 6.00000i | −0.777029 | + | 0.274721i | ||||
\(478\) | −24.0416 | −1.09964 | ||||||||
\(479\) | − | 9.89949i | − | 0.452319i | −0.974090 | − | 0.226160i | \(-0.927383\pi\) | ||
0.974090 | − | 0.226160i | \(-0.0726171\pi\) | |||||||
\(480\) | −3.12132 | + | 2.29289i | −0.142468 | + | 0.104656i | ||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | −8.48528 | −0.386494 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.00000 | −0.136364 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | − | 15.5563i | −0.0453609 | − | 0.705650i | ||||
\(487\) | −12.7279 | −0.576757 | −0.288379 | − | 0.957516i | \(-0.593116\pi\) | ||||
−0.288379 | + | 0.957516i | \(0.593116\pi\) | |||||||
\(488\) | 10.0000i | 0.452679i | ||||||||
\(489\) | 6.00000 | − | 8.48528i | 0.271329 | − | 0.383718i | ||||
\(490\) | 4.94975 | − | 14.8492i | 0.223607 | − | 0.670820i | ||||
\(491\) | 39.5980i | 1.78703i | 0.449032 | + | 0.893516i | \(0.351769\pi\) | ||||
−0.449032 | + | 0.893516i | \(0.648231\pi\) | |||||||
\(492\) | 8.48528 | + | 6.00000i | 0.382546 | + | 0.270501i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 18.0000 | − | 4.24264i | 0.809858 | − | 0.190885i | ||||
\(495\) | −18.9706 | + | 0.343146i | −0.852663 | + | 0.0154233i | ||||
\(496\) | − | 4.24264i | − | 0.190500i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | −0.626726 | −0.313363 | − | 0.949633i | \(-0.601456\pi\) | ||||
−0.313363 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(500\) | −6.36396 | − | 9.19239i | −0.284605 | − | 0.411096i | ||||
\(501\) | −12.0000 | + | 16.9706i | −0.536120 | + | 0.758189i | ||||
\(502\) | 5.65685 | 0.252478 | ||||||||
\(503\) | −21.2132 | −0.945850 | −0.472925 | − | 0.881103i | \(-0.656802\pi\) | ||||
−0.472925 | + | 0.881103i | \(0.656802\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.0000 | + | 33.0000i | −0.489494 | + | 1.46848i | ||||
\(506\) | 12.0000 | 0.533465 | ||||||||
\(507\) | −7.07107 | − | 5.00000i | −0.314037 | − | 0.222058i | ||||
\(508\) | 12.7279 | 0.564710 | ||||||||
\(509\) | −18.0000 | −0.797836 | −0.398918 | − | 0.916987i | \(-0.630614\pi\) | ||||
−0.398918 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 22.6274 | + | 1.00000i | 0.999025 | + | 0.0441511i | ||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | −9.00000 | − | 3.00000i | −0.396587 | − | 0.132196i | ||||
\(516\) | 12.0000 | − | 16.9706i | 0.528271 | − | 0.747087i | ||||
\(517\) | − | 36.0000i | − | 1.58328i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | + | 8.48528i | −0.263371 | + | 0.372463i | ||||
\(520\) | −3.00000 | + | 9.00000i | −0.131559 | + | 0.394676i | ||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | −16.9706 | + | 6.00000i | −0.742781 | + | 0.262613i | ||||
\(523\) | −16.9706 | −0.742071 | −0.371035 | − | 0.928619i | \(-0.620997\pi\) | ||||
−0.371035 | + | 0.928619i | \(0.620997\pi\) | |||||||
\(524\) | 11.3137i | 0.494242i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.2132i | 0.924940i | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 2.82843 | − | 4.00000i | 0.123091 | − | 0.174078i | ||||
\(529\) | −5.00000 | −0.217391 | ||||||||
\(530\) | 12.7279 | + | 4.24264i | 0.552866 | + | 0.184289i | ||||
\(531\) | −6.00000 | − | 16.9706i | −0.260378 | − | 0.736460i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.4558 | 1.10262 | ||||||||
\(534\) | 12.0000 | − | 16.9706i | 0.519291 | − | 0.734388i | ||||
\(535\) | −8.48528 | + | 25.4558i | −0.366851 | + | 1.10055i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16.9706 | − | 12.0000i | −0.732334 | − | 0.517838i | ||||
\(538\) | 6.00000i | 0.258678i | ||||||||
\(539\) | 19.7990i | 0.852803i | ||||||||
\(540\) | −6.53553 | + | 9.60660i | −0.281245 | + | 0.413402i | ||||
\(541\) | −38.0000 | −1.63375 | −0.816874 | − | 0.576816i | \(-0.804295\pi\) | ||||
−0.816874 | + | 0.576816i | \(0.804295\pi\) | |||||||
\(542\) | 20.0000i | 0.859074i | ||||||||
\(543\) | −4.24264 | + | 6.00000i | −0.182069 | + | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.00000 | − | 9.00000i | 0.128506 | − | 0.385518i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.9411 | −1.45122 | −0.725609 | − | 0.688107i | \(-0.758442\pi\) | ||||
−0.725609 | + | 0.688107i | \(0.758442\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.0000 | + | 28.2843i | 0.426790 | + | 1.20714i | ||||
\(550\) | 11.3137 | + | 8.48528i | 0.482418 | + | 0.361814i | ||||
\(551\) | −6.00000 | − | 25.4558i | −0.255609 | − | 1.08446i | ||||
\(552\) | 4.24264 | − | 6.00000i | 0.180579 | − | 0.255377i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 18.0000 | 0.764747 | ||||||||
\(555\) | −9.72792 | − | 13.2426i | −0.412927 | − | 0.562119i | ||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | −21.2132 | −0.898832 | −0.449416 | − | 0.893323i | \(-0.648368\pi\) | ||||
−0.449416 | + | 0.893323i | \(0.648368\pi\) | |||||||
\(558\) | −4.24264 | − | 12.0000i | −0.179605 | − | 0.508001i | ||||
\(559\) | − | 50.9117i | − | 2.15333i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000i | 0.759284i | ||||||||
\(563\) | 12.0000i | 0.505740i | 0.967500 | + | 0.252870i | \(0.0813744\pi\) | ||||
−0.967500 | + | 0.252870i | \(0.918626\pi\) | |||||||
\(564\) | −18.0000 | − | 12.7279i | −0.757937 | − | 0.535942i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.0000 | 0.756596 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.0000i | 0.503509i | ||||||||
\(569\) | 24.0000 | 1.00613 | 0.503066 | − | 0.864248i | \(-0.332205\pi\) | ||||
0.503066 | + | 0.864248i | \(0.332205\pi\) | |||||||
\(570\) | −12.8492 | − | 10.9497i | −0.538196 | − | 0.458634i | ||||
\(571\) | 22.0000 | 0.920671 | 0.460336 | − | 0.887745i | \(-0.347729\pi\) | ||||
0.460336 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(572\) | − | 12.0000i | − | 0.501745i | ||||||
\(573\) | −15.5563 | + | 22.0000i | −0.649876 | + | 0.919063i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.9706 | + | 12.7279i | 0.707721 | + | 0.530791i | ||||
\(576\) | −1.00000 | − | 2.82843i | −0.0416667 | − | 0.117851i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 17.0000i | 0.707107i | ||||||||
\(579\) | 24.0000 | + | 16.9706i | 0.997406 | + | 0.705273i | ||||
\(580\) | 12.7279 | + | 4.24264i | 0.528498 | + | 0.176166i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.9706 | −0.702849 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0.514719 | + | 28.4558i | 0.0212810 | + | 1.17650i | ||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 42.4264 | 1.75113 | 0.875563 | − | 0.483105i | \(-0.160491\pi\) | ||||
0.875563 | + | 0.483105i | \(0.160491\pi\) | |||||||
\(588\) | 9.89949 | + | 7.00000i | 0.408248 | + | 0.288675i | ||||
\(589\) | 18.0000 | − | 4.24264i | 0.741677 | − | 0.174815i | ||||
\(590\) | −4.24264 | + | 12.7279i | −0.174667 | + | 0.524000i | ||||
\(591\) | 18.0000 | + | 12.7279i | 0.740421 | + | 0.523557i | ||||
\(592\) | 4.24264 | 0.174371 | ||||||||
\(593\) | 8.48528 | 0.348449 | 0.174224 | − | 0.984706i | \(-0.444258\pi\) | ||||
0.174224 | + | 0.984706i | \(0.444258\pi\) | |||||||
\(594\) | 4.00000 | − | 14.1421i | 0.164122 | − | 0.580259i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.41421i | 0.0579284i | ||||||||
\(597\) | 22.6274 | + | 16.0000i | 0.926079 | + | 0.654836i | ||||
\(598\) | − | 18.0000i | − | 0.736075i | ||||||
\(599\) | 48.0000 | 1.96123 | 0.980613 | − | 0.195952i | \(-0.0627798\pi\) | ||||
0.980613 | + | 0.195952i | \(0.0627798\pi\) | |||||||
\(600\) | 8.24264 | − | 2.65685i | 0.336504 | − | 0.108466i | ||||
\(601\) | 16.9706i | 0.692244i | 0.938190 | + | 0.346122i | \(0.112502\pi\) | ||||
−0.938190 | + | 0.346122i | \(0.887498\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 4.24264i | − | 0.172631i | ||||||
\(605\) | 6.36396 | + | 2.12132i | 0.258732 | + | 0.0862439i | ||||
\(606\) | −22.0000 | − | 15.5563i | −0.893689 | − | 0.631933i | ||||
\(607\) | 4.24264 | 0.172203 | 0.0861017 | − | 0.996286i | \(-0.472559\pi\) | ||||
0.0861017 | + | 0.996286i | \(0.472559\pi\) | |||||||
\(608\) | 4.24264 | − | 1.00000i | 0.172062 | − | 0.0405554i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.07107 | − | 21.2132i | 0.286299 | − | 0.858898i | ||||
\(611\) | −54.0000 | −2.18461 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 6.00000i | − | 0.242338i | −0.992632 | − | 0.121169i | \(-0.961336\pi\) | ||
0.992632 | − | 0.121169i | \(-0.0386643\pi\) | |||||||
\(614\) | − | 33.9411i | − | 1.36975i | ||||||
\(615\) | −13.7574 | − | 18.7279i | −0.554750 | − | 0.755183i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −42.4264 | −1.70802 | −0.854011 | − | 0.520254i | \(-0.825837\pi\) | ||||
−0.854011 | + | 0.520254i | \(0.825837\pi\) | |||||||
\(618\) | 4.24264 | − | 6.00000i | 0.170664 | − | 0.241355i | ||||
\(619\) | 10.0000 | 0.401934 | 0.200967 | − | 0.979598i | \(-0.435592\pi\) | ||||
0.200967 | + | 0.979598i | \(0.435592\pi\) | |||||||
\(620\) | −3.00000 | + | 9.00000i | −0.120483 | + | 0.361449i | ||||
\(621\) | 6.00000 | − | 21.2132i | 0.240772 | − | 0.851257i | ||||
\(622\) | −1.41421 | −0.0567048 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | − | 4.24264i | −0.240192 | − | 0.169842i | ||||
\(625\) | 7.00000 | + | 24.0000i | 0.280000 | + | 0.960000i | ||||
\(626\) | −30.0000 | −1.19904 | ||||||||
\(627\) | 19.7990 | + | 8.00000i | 0.790695 | + | 0.319489i | ||||
\(628\) | 18.0000i | 0.718278i | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | −12.7279 | −0.506290 | ||||||||
\(633\) | −8.48528 | + | 12.0000i | −0.337260 | + | 0.476957i | ||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −27.0000 | − | 9.00000i | −1.07146 | − | 0.357154i | ||||
\(636\) | −6.00000 | + | 8.48528i | −0.237915 | + | 0.336463i | ||||
\(637\) | 29.6985 | 1.17670 | ||||||||
\(638\) | −16.9706 | −0.671871 | ||||||||
\(639\) | 12.0000 | + | 33.9411i | 0.474713 | + | 1.34269i | ||||
\(640\) | −0.707107 | + | 2.12132i | −0.0279508 | + | 0.0838525i | ||||
\(641\) | −24.0000 | −0.947943 | −0.473972 | − | 0.880540i | \(-0.657180\pi\) | ||||
−0.473972 | + | 0.880540i | \(0.657180\pi\) | |||||||
\(642\) | −16.9706 | − | 12.0000i | −0.669775 | − | 0.473602i | ||||
\(643\) | − | 6.00000i | − | 0.236617i | −0.992977 | − | 0.118308i | \(-0.962253\pi\) | ||
0.992977 | − | 0.118308i | \(-0.0377472\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37.4558 | + | 27.5147i | −1.47482 | + | 1.08339i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.24264 | 0.166795 | 0.0833977 | − | 0.996516i | \(-0.473423\pi\) | ||||
0.0833977 | + | 0.996516i | \(0.473423\pi\) | |||||||
\(648\) | −5.65685 | − | 7.00000i | −0.222222 | − | 0.274986i | ||||
\(649\) | − | 16.9706i | − | 0.666153i | ||||||
\(650\) | 12.7279 | − | 16.9706i | 0.499230 | − | 0.665640i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 6.00000i | − | 0.234978i | ||||||
\(653\) | −21.2132 | −0.830137 | −0.415068 | − | 0.909790i | \(-0.636242\pi\) | ||||
−0.415068 | + | 0.909790i | \(0.636242\pi\) | |||||||
\(654\) | 6.00000 | + | 4.24264i | 0.234619 | + | 0.165900i | ||||
\(655\) | 8.00000 | − | 24.0000i | 0.312586 | − | 0.937758i | ||||
\(656\) | 6.00000 | 0.234261 | ||||||||
\(657\) | 16.9706 | − | 6.00000i | 0.662085 | − | 0.234082i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | −8.82843 | + | 6.48528i | −0.343646 | + | 0.252439i | ||||
\(661\) | 4.24264i | 0.165020i | 0.996590 | + | 0.0825098i | \(0.0262936\pi\) | ||||
−0.996590 | + | 0.0825098i | \(0.973706\pi\) | |||||||
\(662\) | −33.9411 | −1.31916 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.0000 | − | 4.24264i | 0.464991 | − | 0.164399i | ||||
\(667\) | −25.4558 | −0.985654 | ||||||||
\(668\) | 12.0000i | 0.464294i | ||||||||
\(669\) | −30.0000 | − | 21.2132i | −1.15987 | − | 0.820150i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.2843i | 1.09190i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.9706 | −0.654167 | −0.327084 | − | 0.944995i | \(-0.606066\pi\) | ||||
−0.327084 | + | 0.944995i | \(0.606066\pi\) | |||||||
\(674\) | 25.4558i | 0.980522i | ||||||||
\(675\) | 20.6569 | − | 15.7574i | 0.795083 | − | 0.606501i | ||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | − | 42.0000i | − | 1.61419i | −0.590421 | − | 0.807096i | \(-0.701038\pi\) | ||
0.590421 | − | 0.807096i | \(-0.298962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.0000 | − | 25.4558i | 0.689761 | − | 0.975470i | ||||
\(682\) | − | 12.0000i | − | 0.459504i | ||||||
\(683\) | − | 18.0000i | − | 0.688751i | −0.938832 | − | 0.344375i | \(-0.888091\pi\) | ||
0.938832 | − | 0.344375i | \(-0.111909\pi\) | |||||||
\(684\) | 11.0000 | − | 7.07107i | 0.420596 | − | 0.270369i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.7990 | + | 14.0000i | 0.755379 | + | 0.534133i | ||||
\(688\) | − | 12.0000i | − | 0.457496i | ||||||
\(689\) | 25.4558i | 0.969790i | ||||||||
\(690\) | −13.2426 | + | 9.72792i | −0.504139 | + | 0.370336i | ||||
\(691\) | 46.0000 | 1.74992 | 0.874961 | − | 0.484193i | \(-0.160887\pi\) | ||||
0.874961 | + | 0.484193i | \(0.160887\pi\) | |||||||
\(692\) | 6.00000i | 0.228086i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.48528i | 0.322097i | ||||||||
\(695\) | 8.48528 | + | 2.82843i | 0.321865 | + | 0.107288i | ||||
\(696\) | −6.00000 | + | 8.48528i | −0.227429 | + | 0.321634i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 26.0000i | − | 0.984115i | ||||||
\(699\) | 12.0000 | + | 8.48528i | 0.453882 | + | 0.320943i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 43.8406i | − | 1.65584i | −0.560848 | − | 0.827919i | \(-0.689525\pi\) | ||
0.560848 | − | 0.827919i | \(-0.310475\pi\) | |||||||
\(702\) | −21.2132 | − | 6.00000i | −0.800641 | − | 0.226455i | ||||
\(703\) | 4.24264 | + | 18.0000i | 0.160014 | + | 0.678883i | ||||
\(704\) | − | 2.82843i | − | 0.106600i | ||||||
\(705\) | 29.1838 | + | 39.7279i | 1.09912 | + | 1.49624i | ||||
\(706\) | − | 8.48528i | − | 0.319348i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −8.48528 | − | 6.00000i | −0.318896 | − | 0.225494i | ||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 8.48528 | − | 25.4558i | 0.318447 | − | 0.955341i | ||||
\(711\) | −36.0000 | + | 12.7279i | −1.35011 | + | 0.477334i | ||||
\(712\) | − | 12.0000i | − | 0.449719i | ||||||
\(713\) | − | 18.0000i | − | 0.674105i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.48528 | + | 25.4558i | −0.317332 | + | 0.951995i | ||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | −24.0416 | + | 34.0000i | −0.897851 | + | 1.26975i | ||||
\(718\) | 7.07107 | 0.263890 | ||||||||
\(719\) | − | 18.3848i | − | 0.685636i | −0.939402 | − | 0.342818i | \(-0.888619\pi\) | ||
0.939402 | − | 0.342818i | \(-0.111381\pi\) | |||||||
\(720\) | 0.121320 | + | 6.70711i | 0.00452134 | + | 0.249959i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.48528 | + | 17.0000i | 0.315789 | + | 0.632674i | ||||
\(723\) | −8.48528 | + | 12.0000i | −0.315571 | + | 0.446285i | ||||
\(724\) | 4.24264i | 0.157676i | ||||||||
\(725\) | −24.0000 | − | 18.0000i | −0.891338 | − | 0.668503i | ||||
\(726\) | −3.00000 | + | 4.24264i | −0.111340 | + | 0.157459i | ||||
\(727\) | − | 12.0000i | − | 0.445055i | −0.974926 | − | 0.222528i | \(-0.928569\pi\) | ||
0.974926 | − | 0.222528i | \(-0.0714308\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | −12.7279 | − | 4.24264i | −0.471082 | − | 0.157027i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 14.1421 | + | 10.0000i | 0.522708 | + | 0.369611i | ||||
\(733\) | 42.0000i | 1.55131i | 0.631160 | + | 0.775653i | \(0.282579\pi\) | ||||
−0.631160 | + | 0.775653i | \(0.717421\pi\) | |||||||
\(734\) | 24.0000 | 0.885856 | ||||||||
\(735\) | −16.0503 | − | 21.8492i | −0.592022 | − | 0.805921i | ||||
\(736\) | − | 4.24264i | − | 0.156386i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 16.9706 | − | 6.00000i | 0.624695 | − | 0.220863i | ||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | −9.00000 | − | 3.00000i | −0.330847 | − | 0.110282i | ||||
\(741\) | 12.0000 | − | 29.6985i | 0.440831 | − | 1.09100i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.0000i | 0.880475i | 0.897881 | + | 0.440237i | \(0.145106\pi\) | ||||
−0.897881 | + | 0.440237i | \(0.854894\pi\) | |||||||
\(744\) | −6.00000 | − | 4.24264i | −0.219971 | − | 0.155543i | ||||
\(745\) | 1.00000 | − | 3.00000i | 0.0366372 | − | 0.109911i | ||||
\(746\) | − | 21.2132i | − | 0.776671i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −19.3640 | − | 0.192388i | −0.707072 | − | 0.00702502i | ||||
\(751\) | − | 12.7279i | − | 0.464448i | −0.972662 | − | 0.232224i | \(-0.925400\pi\) | ||
0.972662 | − | 0.232224i | \(-0.0746003\pi\) | |||||||
\(752\) | −12.7279 | −0.464140 | ||||||||
\(753\) | 5.65685 | − | 8.00000i | 0.206147 | − | 0.291536i | ||||
\(754\) | 25.4558i | 0.927047i | ||||||||
\(755\) | −3.00000 | + | 9.00000i | −0.109181 | + | 0.327544i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 42.0000i | − | 1.52652i | −0.646094 | − | 0.763258i | \(-0.723599\pi\) | ||
0.646094 | − | 0.763258i | \(-0.276401\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.0000 | − | 16.9706i | 0.435572 | − | 0.615992i | ||||
\(760\) | −9.70711 | − | 0.878680i | −0.352114 | − | 0.0318731i | ||||
\(761\) | − | 14.1421i | − | 0.512652i | −0.966590 | − | 0.256326i | \(-0.917488\pi\) | ||
0.966590 | − | 0.256326i | \(-0.0825121\pi\) | |||||||
\(762\) | 12.7279 | − | 18.0000i | 0.461084 | − | 0.652071i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15.5563i | 0.562809i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | −25.4558 | −0.919157 | ||||||||
\(768\) | −1.41421 | − | 1.00000i | −0.0510310 | − | 0.0360844i | ||||
\(769\) | 40.0000 | 1.44244 | 0.721218 | − | 0.692708i | \(-0.243582\pi\) | ||||
0.721218 | + | 0.692708i | \(0.243582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.0000 | + | 25.4558i | −0.648254 | + | 0.916770i | ||||
\(772\) | 16.9706 | 0.610784 | ||||||||
\(773\) | − | 6.00000i | − | 0.215805i | −0.994161 | − | 0.107903i | \(-0.965587\pi\) | ||
0.994161 | − | 0.107903i | \(-0.0344134\pi\) | |||||||
\(774\) | −12.0000 | − | 33.9411i | −0.431331 | − | 1.21999i | ||||
\(775\) | 12.7279 | − | 16.9706i | 0.457200 | − | 0.609601i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.89949 | 0.354914 | ||||||||
\(779\) | 6.00000 | + | 25.4558i | 0.214972 | + | 0.912050i | ||||
\(780\) | 9.72792 | + | 13.2426i | 0.348315 | + | 0.474163i | ||||
\(781\) | 33.9411i | 1.21451i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.48528 | + | 30.0000i | −0.303239 | + | 1.07211i | ||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | 12.7279 | − | 38.1838i | 0.454279 | − | 1.36284i | ||||
\(786\) | 16.0000 | + | 11.3137i | 0.570701 | + | 0.403547i | ||||
\(787\) | 25.4558 | 0.907403 | 0.453701 | − | 0.891154i | \(-0.350103\pi\) | ||||
0.453701 | + | 0.891154i | \(0.350103\pi\) | |||||||
\(788\) | 12.7279 | 0.453413 | ||||||||
\(789\) | 30.0000 | + | 21.2132i | 1.06803 | + | 0.755210i | ||||
\(790\) | 27.0000 | + | 9.00000i | 0.960617 | + | 0.320206i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.82843 | − | 8.00000i | −0.100504 | − | 0.284268i | ||||
\(793\) | 42.4264 | 1.50661 | ||||||||
\(794\) | 30.0000 | 1.06466 | ||||||||
\(795\) | 18.7279 | − | 13.7574i | 0.664211 | − | 0.487923i | ||||
\(796\) | 16.0000 | 0.567105 | ||||||||
\(797\) | − | 42.0000i | − | 1.48772i | −0.668338 | − | 0.743858i | \(-0.732994\pi\) | ||
0.668338 | − | 0.743858i | \(-0.267006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 3.00000 | − | 4.00000i | 0.106066 | − | 0.141421i | ||||
\(801\) | −12.0000 | − | 33.9411i | −0.423999 | − | 1.19925i | ||||
\(802\) | 18.0000i | 0.635602i | ||||||||
\(803\) | 16.9706 | 0.598878 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.0000 | −0.634023 | ||||||||
\(807\) | 8.48528 | + | 6.00000i | 0.298696 | + | 0.211210i | ||||
\(808\) | −15.5563 | −0.547270 | ||||||||
\(809\) | − | 19.7990i | − | 0.696095i | −0.937477 | − | 0.348048i | \(-0.886845\pi\) | ||
0.937477 | − | 0.348048i | \(-0.113155\pi\) | |||||||
\(810\) | 7.05025 | + | 18.8492i | 0.247721 | + | 0.662295i | ||||
\(811\) | 33.9411i | 1.19183i | 0.803046 | + | 0.595917i | \(0.203211\pi\) | ||||
−0.803046 | + | 0.595917i | \(0.796789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.2843 | + | 20.0000i | 0.991973 | + | 0.701431i | ||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | −4.24264 | + | 12.7279i | −0.148613 | + | 0.445840i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.9117 | − | 12.0000i | 1.78117 | − | 0.419827i | ||||
\(818\) | −25.4558 | −0.890043 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.7279 | − | 4.24264i | −0.444478 | − | 0.148159i | ||||
\(821\) | 35.3553i | 1.23391i | 0.786998 | + | 0.616955i | \(0.211634\pi\) | ||||
−0.786998 | + | 0.616955i | \(0.788366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 24.0000i | − | 0.836587i | −0.908312 | − | 0.418294i | \(-0.862628\pi\) | ||
0.908312 | − | 0.418294i | \(-0.137372\pi\) | |||||||
\(824\) | − | 4.24264i | − | 0.147799i | ||||||
\(825\) | 23.3137 | − | 7.51472i | 0.811679 | − | 0.261629i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18.0000i | − | 0.625921i | −0.949766 | − | 0.312961i | \(-0.898679\pi\) | ||
0.949766 | − | 0.312961i | \(-0.101321\pi\) | |||||||
\(828\) | −4.24264 | − | 12.0000i | −0.147442 | − | 0.417029i | ||||
\(829\) | − | 46.6690i | − | 1.62088i | −0.585820 | − | 0.810442i | \(-0.699227\pi\) | ||
0.585820 | − | 0.810442i | \(-0.300773\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.0000 | − | 25.4558i | 0.624413 | − | 0.883053i | ||||
\(832\) | −4.24264 | −0.147087 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.00000 | + | 5.65685i | −0.138509 | + | 0.195881i | ||||
\(835\) | 8.48528 | − | 25.4558i | 0.293645 | − | 0.880936i | ||||
\(836\) | 12.0000 | − | 2.82843i | 0.415029 | − | 0.0978232i | ||||
\(837\) | −21.2132 | − | 6.00000i | −0.733236 | − | 0.207390i | ||||
\(838\) | 14.1421 | 0.488532 | ||||||||
\(839\) | −48.0000 | −1.65714 | −0.828572 | − | 0.559883i | \(-0.810846\pi\) | ||||
−0.828572 | + | 0.559883i | \(0.810846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 29.6985 | 1.02348 | ||||||||
\(843\) | 25.4558 | + | 18.0000i | 0.876746 | + | 0.619953i | ||||
\(844\) | 8.48528i | 0.292075i | ||||||||
\(845\) | 10.6066 | + | 3.53553i | 0.364878 | + | 0.121626i | ||||
\(846\) | −36.0000 | + | 12.7279i | −1.23771 | + | 0.437595i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.00000i | 0.206041i | ||||||||
\(849\) | 18.0000 | − | 25.4558i | 0.617758 | − | 0.873642i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0000 | 0.617032 | ||||||||
\(852\) | 16.9706 | + | 12.0000i | 0.581402 | + | 0.411113i | ||||
\(853\) | 30.0000i | 1.02718i | 0.858036 | + | 0.513590i | \(0.171685\pi\) | ||||
−0.858036 | + | 0.513590i | \(0.828315\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −28.3345 | + | 7.22183i | −0.969020 | + | 0.246981i | ||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | − | 30.0000i | − | 1.02478i | −0.858753 | − | 0.512390i | \(-0.828760\pi\) | ||
0.858753 | − | 0.512390i | \(-0.171240\pi\) | |||||||
\(858\) | −16.9706 | − | 12.0000i | −0.579365 | − | 0.409673i | ||||
\(859\) | 50.0000 | 1.70598 | 0.852989 | − | 0.521929i | \(-0.174787\pi\) | ||||
0.852989 | + | 0.521929i | \(0.174787\pi\) | |||||||
\(860\) | −8.48528 | + | 25.4558i | −0.289346 | + | 0.868037i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 12.0000i | − | 0.408722i | ||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | −5.00000 | − | 1.41421i | −0.170103 | − | 0.0481125i | ||||
\(865\) | 4.24264 | − | 12.7279i | 0.144254 | − | 0.432762i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.0416 | + | 17.0000i | 0.816497 | + | 0.577350i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.0000 | −1.22122 | ||||||||
\(870\) | 18.7279 | − | 13.7574i | 0.634936 | − | 0.466418i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.24264 | 0.143674 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.0000 | − | 4.24264i | 0.608859 | − | 0.143509i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.00000 | − | 8.48528i | 0.202721 | − | 0.286691i | ||||
\(877\) | 38.1838 | 1.28937 | 0.644687 | − | 0.764447i | \(-0.276988\pi\) | ||||
0.644687 | + | 0.764447i | \(0.276988\pi\) | |||||||
\(878\) | 4.24264 | 0.143182 | ||||||||
\(879\) | −18.0000 | + | 25.4558i | −0.607125 | + | 0.858604i | ||||
\(880\) | −2.00000 | + | 6.00000i | −0.0674200 | + | 0.202260i | ||||
\(881\) | 45.2548i | 1.52467i | 0.647180 | + | 0.762337i | \(0.275948\pi\) | ||||
−0.647180 | + | 0.762337i | \(0.724052\pi\) | |||||||
\(882\) | 19.7990 | − | 7.00000i | 0.666667 | − | 0.235702i | ||||
\(883\) | 36.0000i | 1.21150i | 0.795656 | + | 0.605748i | \(0.207126\pi\) | ||||
−0.795656 | + | 0.605748i | \(0.792874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.7574 | + | 18.7279i | 0.462449 | + | 0.629532i | ||||
\(886\) | 8.48528i | 0.285069i | ||||||||
\(887\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(888\) | 4.24264 | − | 6.00000i | 0.142374 | − | 0.201347i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.48528 | + | 25.4558i | −0.284427 | + | 0.853282i | ||||
\(891\) | −16.0000 | − | 19.7990i | −0.536020 | − | 0.663291i | ||||
\(892\) | −21.2132 | −0.710271 | ||||||||
\(893\) | −12.7279 | − | 54.0000i | −0.425924 | − | 1.80704i | ||||
\(894\) | 2.00000 | + | 1.41421i | 0.0668900 | + | 0.0472984i | ||||
\(895\) | 25.4558 | + | 8.48528i | 0.850895 | + | 0.283632i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.4558 | − | 18.0000i | −0.849946 | − | 0.601003i | ||||
\(898\) | − | 24.0000i | − | 0.800890i | ||||||
\(899\) | 25.4558i | 0.849000i | ||||||||
\(900\) | 4.48528 | − | 14.3137i | 0.149509 | − | 0.477124i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 16.9706 | 0.565058 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.00000 | − | 9.00000i | 0.0997234 | − | 0.299170i | ||||
\(906\) | −6.00000 | − | 4.24264i | −0.199337 | − | 0.140952i | ||||
\(907\) | −33.9411 | −1.12700 | −0.563498 | − | 0.826117i | \(-0.690545\pi\) | ||||
−0.563498 | + | 0.826117i | \(0.690545\pi\) | |||||||
\(908\) | − | 18.0000i | − | 0.597351i | ||||||
\(909\) | −44.0000 | + | 15.5563i | −1.45939 | + | 0.515972i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 2.82843 | − | 7.00000i | 0.0936586 | − | 0.231793i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −12.0000 | −0.396925 | ||||||||
\(915\) | −22.9289 | − | 31.2132i | −0.758007 | − | 1.03188i | ||||
\(916\) | 14.0000 | 0.462573 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | −3.00000 | + | 9.00000i | −0.0989071 | + | 0.296721i | ||||
\(921\) | −48.0000 | − | 33.9411i | −1.58165 | − | 1.11840i | ||||
\(922\) | −15.5563 | −0.512321 | ||||||||
\(923\) | 50.9117 | 1.67578 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.9706 | + | 12.7279i | 0.557989 | + | 0.418491i | ||||
\(926\) | −36.0000 | −1.18303 | ||||||||
\(927\) | −4.24264 | − | 12.0000i | −0.139347 | − | 0.394132i | ||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | − | 2.82843i | − | 0.0927977i | −0.998923 | − | 0.0463988i | \(-0.985225\pi\) | ||
0.998923 | − | 0.0463988i | \(-0.0147745\pi\) | |||||||
\(930\) | 9.72792 | + | 13.2426i | 0.318991 | + | 0.434243i | ||||
\(931\) | 7.00000 | + | 29.6985i | 0.229416 | + | 0.973329i | ||||
\(932\) | 8.48528 | 0.277945 | ||||||||
\(933\) | −1.41421 | + | 2.00000i | −0.0462993 | + | 0.0654771i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.0000 | + | 4.24264i | −0.392232 | + | 0.138675i | ||||
\(937\) | − | 42.0000i | − | 1.37208i | −0.727564 | − | 0.686040i | \(-0.759347\pi\) | ||
0.727564 | − | 0.686040i | \(-0.240653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.0000 | + | 42.4264i | −0.979013 | + | 1.38453i | ||||
\(940\) | 27.0000 | + | 9.00000i | 0.880643 | + | 0.293548i | ||||
\(941\) | 54.0000 | 1.76035 | 0.880175 | − | 0.474650i | \(-0.157425\pi\) | ||||
0.880175 | + | 0.474650i | \(0.157425\pi\) | |||||||
\(942\) | 25.4558 | + | 18.0000i | 0.829396 | + | 0.586472i | ||||
\(943\) | 25.4558 | 0.828956 | ||||||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 33.9411i | − | 1.10352i | ||||||
\(947\) | 16.9706 | 0.551469 | 0.275735 | − | 0.961234i | \(-0.411079\pi\) | ||||
0.275735 | + | 0.961234i | \(0.411079\pi\) | |||||||
\(948\) | −12.7279 | + | 18.0000i | −0.413384 | + | 0.584613i | ||||
\(949\) | − | 25.4558i | − | 0.826332i | ||||||
\(950\) | 19.9706 | + | 8.72792i | 0.647931 | + | 0.283171i | ||||
\(951\) | −18.0000 | + | 25.4558i | −0.583690 | + | 0.825462i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0000i | 1.16615i | 0.812417 | + | 0.583077i | \(0.198151\pi\) | ||||
−0.812417 | + | 0.583077i | \(0.801849\pi\) | |||||||
\(954\) | 6.00000 | + | 16.9706i | 0.194257 | + | 0.549442i | ||||
\(955\) | 11.0000 | − | 33.0000i | 0.355952 | − | 1.06785i | ||||
\(956\) | 24.0416i | 0.777562i | ||||||||
\(957\) | −16.9706 | + | 24.0000i | −0.548580 | + | 0.775810i | ||||
\(958\) | −9.89949 | −0.319838 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.29289 | + | 3.12132i | 0.0740028 | + | 0.100740i | ||||
\(961\) | 13.0000 | 0.419355 | ||||||||
\(962\) | − | 18.0000i | − | 0.580343i | ||||||
\(963\) | −33.9411 | + | 12.0000i | −1.09374 | + | 0.386695i | ||||
\(964\) | 8.48528i | 0.273293i | ||||||||
\(965\) | −36.0000 | − | 12.0000i | −1.15888 | − | 0.386294i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.0000i | 0.385894i | 0.981209 | + | 0.192947i | \(0.0618045\pi\) | ||||
−0.981209 | + | 0.192947i | \(0.938195\pi\) | |||||||
\(968\) | 3.00000i | 0.0964237i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | −15.5563 | + | 1.00000i | −0.498970 | + | 0.0320750i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12.7279i | 0.407829i | ||||||||
\(975\) | −11.2721 | − | 34.9706i | −0.360995 | − | 1.11995i | ||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 60.0000i | 1.91957i | 0.280736 | + | 0.959785i | \(0.409421\pi\) | ||||
−0.280736 | + | 0.959785i | \(0.590579\pi\) | |||||||
\(978\) | −8.48528 | − | 6.00000i | −0.271329 | − | 0.191859i | ||||
\(979\) | − | 33.9411i | − | 1.08476i | ||||||
\(980\) | −14.8492 | − | 4.94975i | −0.474342 | − | 0.158114i | ||||
\(981\) | 12.0000 | − | 4.24264i | 0.383131 | − | 0.135457i | ||||
\(982\) | 39.5980 | 1.26362 | ||||||||
\(983\) | − | 12.0000i | − | 0.382741i | −0.981518 | − | 0.191370i | \(-0.938707\pi\) | ||
0.981518 | − | 0.191370i | \(-0.0612931\pi\) | |||||||
\(984\) | 6.00000 | − | 8.48528i | 0.191273 | − | 0.270501i | ||||
\(985\) | −27.0000 | − | 9.00000i | −0.860292 | − | 0.286764i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.24264 | − | 18.0000i | −0.134976 | − | 0.572656i | ||||
\(989\) | − | 50.9117i | − | 1.61890i | ||||||
\(990\) | 0.343146 | + | 18.9706i | 0.0109059 | + | 0.602924i | ||||
\(991\) | 4.24264i | 0.134772i | 0.997727 | + | 0.0673860i | \(0.0214659\pi\) | ||||
−0.997727 | + | 0.0673860i | \(0.978534\pi\) | |||||||
\(992\) | −4.24264 | −0.134704 | ||||||||
\(993\) | −33.9411 | + | 48.0000i | −1.07709 | + | 1.52323i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.9411 | − | 11.3137i | −1.07601 | − | 0.358669i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 42.0000i | − | 1.33015i | −0.746775 | − | 0.665077i | \(-0.768399\pi\) | ||
0.746775 | − | 0.665077i | \(-0.231601\pi\) | |||||||
\(998\) | 14.0000i | 0.443162i | ||||||||
\(999\) | 6.00000 | − | 21.2132i | 0.189832 | − | 0.671156i |
(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 | 570.2.c.a.569.1 | ✓ | 4 | |
3.2 | odd | 2 | 570.2.c.b.569.3 | yes | 4 | ||
5.4 | even | 2 | inner | 570.2.c.a.569.4 | yes | 4 | |
15.14 | odd | 2 | 570.2.c.b.569.2 | yes | 4 | ||
19.18 | odd | 2 | 570.2.c.b.569.4 | yes | 4 | ||
57.56 | even | 2 | inner | 570.2.c.a.569.2 | yes | 4 | |
95.94 | odd | 2 | 570.2.c.b.569.1 | yes | 4 | ||
285.284 | even | 2 | inner | 570.2.c.a.569.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.c.a.569.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
570.2.c.a.569.2 | yes | 4 | 57.56 | even | 2 | inner | |
570.2.c.a.569.3 | yes | 4 | 285.284 | even | 2 | inner | |
570.2.c.a.569.4 | yes | 4 | 5.4 | even | 2 | inner | |
570.2.c.b.569.1 | yes | 4 | 95.94 | odd | 2 | ||
570.2.c.b.569.2 | yes | 4 | 15.14 | odd | 2 | ||
570.2.c.b.569.3 | yes | 4 | 3.2 | odd | 2 | ||
570.2.c.b.569.4 | yes | 4 | 19.18 | odd | 2 |