Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,2,Mod(113,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("114.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.b (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: | \(0.910294583043\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.1 | ||
Root | \(-1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.113 |
Dual form | 114.2.b.d.113.2 |
$q$-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 \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | − | 1.41421i | 0.577350 | − | 0.816497i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.41421i | 0.632456i | 0.948683 | + | 0.316228i | \(0.102416\pi\) | ||||
−0.948683 | + | 0.316228i | \(0.897584\pi\) | |||||||
\(6\) | 1.00000 | − | 1.41421i | 0.408248 | − | 0.577350i | ||||
\(7\) | −4.00000 | −1.51186 | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | 1.41421i | 0.447214i | ||||||||
\(11\) | 5.65685i | 1.70561i | 0.522233 | + | 0.852803i | \(0.325099\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 1.00000 | − | 1.41421i | 0.288675 | − | 0.408248i | ||||
\(13\) | − | 4.24264i | − | 1.17670i | −0.808608 | − | 0.588348i | \(-0.799778\pi\) | ||
0.808608 | − | 0.588348i | \(-0.200222\pi\) | |||||||
\(14\) | −4.00000 | −1.06904 | ||||||||
\(15\) | 2.00000 | + | 1.41421i | 0.516398 | + | 0.365148i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.82843i | − | 0.685994i | −0.939336 | − | 0.342997i | \(-0.888558\pi\) | ||
0.939336 | − | 0.342997i | \(-0.111442\pi\) | |||||||
\(18\) | −1.00000 | − | 2.82843i | −0.235702 | − | 0.666667i | ||||
\(19\) | 1.00000 | + | 4.24264i | 0.229416 | + | 0.973329i | ||||
\(20\) | 1.41421i | 0.316228i | ||||||||
\(21\) | −4.00000 | + | 5.65685i | −0.872872 | + | 1.23443i | ||||
\(22\) | 5.65685i | 1.20605i | ||||||||
\(23\) | 1.41421i | 0.294884i | 0.989071 | + | 0.147442i | \(0.0471040\pi\) | ||||
−0.989071 | + | 0.147442i | \(0.952896\pi\) | |||||||
\(24\) | 1.00000 | − | 1.41421i | 0.204124 | − | 0.288675i | ||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | − | 4.24264i | − | 0.832050i | ||||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | −4.00000 | −0.755929 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 2.00000 | + | 1.41421i | 0.365148 | + | 0.258199i | ||||
\(31\) | − | 4.24264i | − | 0.762001i | −0.924575 | − | 0.381000i | \(-0.875580\pi\) | ||
0.924575 | − | 0.381000i | \(-0.124420\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 8.00000 | + | 5.65685i | 1.39262 | + | 0.984732i | ||||
\(34\) | − | 2.82843i | − | 0.485071i | ||||||
\(35\) | − | 5.65685i | − | 0.956183i | ||||||
\(36\) | −1.00000 | − | 2.82843i | −0.166667 | − | 0.471405i | ||||
\(37\) | − | 4.24264i | − | 0.697486i | −0.937218 | − | 0.348743i | \(-0.886609\pi\) | ||
0.937218 | − | 0.348743i | \(-0.113391\pi\) | |||||||
\(38\) | 1.00000 | + | 4.24264i | 0.162221 | + | 0.688247i | ||||
\(39\) | −6.00000 | − | 4.24264i | −0.960769 | − | 0.679366i | ||||
\(40\) | 1.41421i | 0.223607i | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | −4.00000 | + | 5.65685i | −0.617213 | + | 0.872872i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 5.65685i | 0.852803i | ||||||||
\(45\) | 4.00000 | − | 1.41421i | 0.596285 | − | 0.210819i | ||||
\(46\) | 1.41421i | 0.208514i | ||||||||
\(47\) | 1.41421i | 0.206284i | 0.994667 | + | 0.103142i | \(0.0328896\pi\) | ||||
−0.994667 | + | 0.103142i | \(0.967110\pi\) | |||||||
\(48\) | 1.00000 | − | 1.41421i | 0.144338 | − | 0.204124i | ||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | −4.00000 | − | 2.82843i | −0.560112 | − | 0.396059i | ||||
\(52\) | − | 4.24264i | − | 0.588348i | ||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −5.00000 | − | 1.41421i | −0.680414 | − | 0.192450i | ||||
\(55\) | −8.00000 | −1.07872 | ||||||||
\(56\) | −4.00000 | −0.534522 | ||||||||
\(57\) | 7.00000 | + | 2.82843i | 0.927173 | + | 0.374634i | ||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 2.00000 | + | 1.41421i | 0.258199 | + | 0.182574i | ||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | − | 4.24264i | − | 0.538816i | ||||||
\(63\) | 4.00000 | + | 11.3137i | 0.503953 | + | 1.42539i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 8.00000 | + | 5.65685i | 0.984732 | + | 0.696311i | ||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | − | 2.82843i | − | 0.342997i | ||||||
\(69\) | 2.00000 | + | 1.41421i | 0.240772 | + | 0.170251i | ||||
\(70\) | − | 5.65685i | − | 0.676123i | ||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | −1.00000 | − | 2.82843i | −0.117851 | − | 0.333333i | ||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | − | 4.24264i | − | 0.493197i | ||||||
\(75\) | 3.00000 | − | 4.24264i | 0.346410 | − | 0.489898i | ||||
\(76\) | 1.00000 | + | 4.24264i | 0.114708 | + | 0.486664i | ||||
\(77\) | − | 22.6274i | − | 2.57863i | ||||||
\(78\) | −6.00000 | − | 4.24264i | −0.679366 | − | 0.480384i | ||||
\(79\) | − | 4.24264i | − | 0.477334i | −0.971101 | − | 0.238667i | \(-0.923290\pi\) | ||
0.971101 | − | 0.238667i | \(-0.0767105\pi\) | |||||||
\(80\) | 1.41421i | 0.158114i | ||||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.82843i | − | 0.310460i | −0.987878 | − | 0.155230i | \(-0.950388\pi\) | ||
0.987878 | − | 0.155230i | \(-0.0496119\pi\) | |||||||
\(84\) | −4.00000 | + | 5.65685i | −0.436436 | + | 0.617213i | ||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | −6.00000 | + | 8.48528i | −0.643268 | + | 0.909718i | ||||
\(88\) | 5.65685i | 0.603023i | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 4.00000 | − | 1.41421i | 0.421637 | − | 0.149071i | ||||
\(91\) | 16.9706i | 1.77900i | ||||||||
\(92\) | 1.41421i | 0.147442i | ||||||||
\(93\) | −6.00000 | − | 4.24264i | −0.622171 | − | 0.439941i | ||||
\(94\) | 1.41421i | 0.145865i | ||||||||
\(95\) | −6.00000 | + | 1.41421i | −0.615587 | + | 0.145095i | ||||
\(96\) | 1.00000 | − | 1.41421i | 0.102062 | − | 0.144338i | ||||
\(97\) | 8.48528i | 0.861550i | 0.902459 | + | 0.430775i | \(0.141760\pi\) | ||||
−0.902459 | + | 0.430775i | \(0.858240\pi\) | |||||||
\(98\) | 9.00000 | 0.909137 | ||||||||
\(99\) | 16.0000 | − | 5.65685i | 1.60806 | − | 0.568535i | ||||
\(100\) | 3.00000 | 0.300000 | ||||||||
\(101\) | 9.89949i | 0.985037i | 0.870302 | + | 0.492518i | \(0.163924\pi\) | ||||
−0.870302 | + | 0.492518i | \(0.836076\pi\) | |||||||
\(102\) | −4.00000 | − | 2.82843i | −0.396059 | − | 0.280056i | ||||
\(103\) | − | 12.7279i | − | 1.25412i | −0.778971 | − | 0.627060i | \(-0.784258\pi\) | ||
0.778971 | − | 0.627060i | \(-0.215742\pi\) | |||||||
\(104\) | − | 4.24264i | − | 0.416025i | ||||||
\(105\) | −8.00000 | − | 5.65685i | −0.780720 | − | 0.552052i | ||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | −5.00000 | − | 1.41421i | −0.481125 | − | 0.136083i | ||||
\(109\) | 4.24264i | 0.406371i | 0.979140 | + | 0.203186i | \(0.0651295\pi\) | ||||
−0.979140 | + | 0.203186i | \(0.934871\pi\) | |||||||
\(110\) | −8.00000 | −0.762770 | ||||||||
\(111\) | −6.00000 | − | 4.24264i | −0.569495 | − | 0.402694i | ||||
\(112\) | −4.00000 | −0.377964 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 7.00000 | + | 2.82843i | 0.655610 | + | 0.264906i | ||||
\(115\) | −2.00000 | −0.186501 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | −12.0000 | + | 4.24264i | −1.10940 | + | 0.392232i | ||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 11.3137i | 1.03713i | ||||||||
\(120\) | 2.00000 | + | 1.41421i | 0.182574 | + | 0.129099i | ||||
\(121\) | −21.0000 | −1.90909 | ||||||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4.24264i | − | 0.381000i | ||||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | 4.00000 | + | 11.3137i | 0.356348 | + | 1.00791i | ||||
\(127\) | 21.2132i | 1.88237i | 0.337895 | + | 0.941184i | \(0.390285\pi\) | ||||
−0.337895 | + | 0.941184i | \(0.609715\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.00000 | − | 2.82843i | 0.176090 | − | 0.249029i | ||||
\(130\) | 6.00000 | 0.526235 | ||||||||
\(131\) | − | 19.7990i | − | 1.72985i | −0.501905 | − | 0.864923i | \(-0.667367\pi\) | ||
0.501905 | − | 0.864923i | \(-0.332633\pi\) | |||||||
\(132\) | 8.00000 | + | 5.65685i | 0.696311 | + | 0.492366i | ||||
\(133\) | −4.00000 | − | 16.9706i | −0.346844 | − | 1.47153i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.00000 | − | 7.07107i | 0.172133 | − | 0.608581i | ||||
\(136\) | − | 2.82843i | − | 0.242536i | ||||||
\(137\) | 14.1421i | 1.20824i | 0.796892 | + | 0.604122i | \(0.206476\pi\) | ||||
−0.796892 | + | 0.604122i | \(0.793524\pi\) | |||||||
\(138\) | 2.00000 | + | 1.41421i | 0.170251 | + | 0.120386i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | − | 5.65685i | − | 0.478091i | ||||||
\(141\) | 2.00000 | + | 1.41421i | 0.168430 | + | 0.119098i | ||||
\(142\) | −12.0000 | −1.00702 | ||||||||
\(143\) | 24.0000 | 2.00698 | ||||||||
\(144\) | −1.00000 | − | 2.82843i | −0.0833333 | − | 0.235702i | ||||
\(145\) | − | 8.48528i | − | 0.704664i | ||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 9.00000 | − | 12.7279i | 0.742307 | − | 1.04978i | ||||
\(148\) | − | 4.24264i | − | 0.348743i | ||||||
\(149\) | 9.89949i | 0.810998i | 0.914095 | + | 0.405499i | \(0.132902\pi\) | ||||
−0.914095 | + | 0.405499i | \(0.867098\pi\) | |||||||
\(150\) | 3.00000 | − | 4.24264i | 0.244949 | − | 0.346410i | ||||
\(151\) | 12.7279i | 1.03578i | 0.855446 | + | 0.517892i | \(0.173283\pi\) | ||||
−0.855446 | + | 0.517892i | \(0.826717\pi\) | |||||||
\(152\) | 1.00000 | + | 4.24264i | 0.0811107 | + | 0.344124i | ||||
\(153\) | −8.00000 | + | 2.82843i | −0.646762 | + | 0.228665i | ||||
\(154\) | − | 22.6274i | − | 1.82337i | ||||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | −6.00000 | − | 4.24264i | −0.480384 | − | 0.339683i | ||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | − | 4.24264i | − | 0.337526i | ||||||
\(159\) | 6.00000 | − | 8.48528i | 0.475831 | − | 0.672927i | ||||
\(160\) | 1.41421i | 0.111803i | ||||||||
\(161\) | − | 5.65685i | − | 0.445823i | ||||||
\(162\) | −7.00000 | + | 5.65685i | −0.549972 | + | 0.444444i | ||||
\(163\) | 20.0000 | 1.56652 | 0.783260 | − | 0.621694i | \(-0.213555\pi\) | ||||
0.783260 | + | 0.621694i | \(0.213555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00000 | + | 11.3137i | −0.622799 | + | 0.880771i | ||||
\(166\) | − | 2.82843i | − | 0.219529i | ||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | −4.00000 | + | 5.65685i | −0.308607 | + | 0.436436i | ||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 11.0000 | − | 7.07107i | 0.841191 | − | 0.540738i | ||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | −6.00000 | + | 8.48528i | −0.454859 | + | 0.643268i | ||||
\(175\) | −12.0000 | −0.907115 | ||||||||
\(176\) | 5.65685i | 0.426401i | ||||||||
\(177\) | 12.0000 | − | 16.9706i | 0.901975 | − | 1.27559i | ||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | −18.0000 | −1.34538 | −0.672692 | − | 0.739923i | \(-0.734862\pi\) | ||||
−0.672692 | + | 0.739923i | \(0.734862\pi\) | |||||||
\(180\) | 4.00000 | − | 1.41421i | 0.298142 | − | 0.105409i | ||||
\(181\) | − | 12.7279i | − | 0.946059i | −0.881047 | − | 0.473029i | \(-0.843160\pi\) | ||
0.881047 | − | 0.473029i | \(-0.156840\pi\) | |||||||
\(182\) | 16.9706i | 1.25794i | ||||||||
\(183\) | 2.00000 | − | 2.82843i | 0.147844 | − | 0.209083i | ||||
\(184\) | 1.41421i | 0.104257i | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | −6.00000 | − | 4.24264i | −0.439941 | − | 0.311086i | ||||
\(187\) | 16.0000 | 1.17004 | ||||||||
\(188\) | 1.41421i | 0.103142i | ||||||||
\(189\) | 20.0000 | + | 5.65685i | 1.45479 | + | 0.411476i | ||||
\(190\) | −6.00000 | + | 1.41421i | −0.435286 | + | 0.102598i | ||||
\(191\) | 18.3848i | 1.33028i | 0.746721 | + | 0.665138i | \(0.231627\pi\) | ||||
−0.746721 | + | 0.665138i | \(0.768373\pi\) | |||||||
\(192\) | 1.00000 | − | 1.41421i | 0.0721688 | − | 0.102062i | ||||
\(193\) | − | 8.48528i | − | 0.610784i | −0.952227 | − | 0.305392i | \(-0.901213\pi\) | ||
0.952227 | − | 0.305392i | \(-0.0987875\pi\) | |||||||
\(194\) | 8.48528i | 0.609208i | ||||||||
\(195\) | 6.00000 | − | 8.48528i | 0.429669 | − | 0.607644i | ||||
\(196\) | 9.00000 | 0.642857 | ||||||||
\(197\) | − | 7.07107i | − | 0.503793i | −0.967754 | − | 0.251896i | \(-0.918946\pi\) | ||
0.967754 | − | 0.251896i | \(-0.0810542\pi\) | |||||||
\(198\) | 16.0000 | − | 5.65685i | 1.13707 | − | 0.402015i | ||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 3.00000 | 0.212132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.89949i | 0.696526i | ||||||||
\(203\) | 24.0000 | 1.68447 | ||||||||
\(204\) | −4.00000 | − | 2.82843i | −0.280056 | − | 0.198030i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 12.7279i | − | 0.886796i | ||||||
\(207\) | 4.00000 | − | 1.41421i | 0.278019 | − | 0.0982946i | ||||
\(208\) | − | 4.24264i | − | 0.294174i | ||||||
\(209\) | −24.0000 | + | 5.65685i | −1.66011 | + | 0.391293i | ||||
\(210\) | −8.00000 | − | 5.65685i | −0.552052 | − | 0.390360i | ||||
\(211\) | 8.48528i | 0.584151i | 0.956395 | + | 0.292075i | \(0.0943458\pi\) | ||||
−0.956395 | + | 0.292075i | \(0.905654\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | −12.0000 | + | 16.9706i | −0.822226 | + | 1.16280i | ||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | 2.82843i | 0.192897i | ||||||||
\(216\) | −5.00000 | − | 1.41421i | −0.340207 | − | 0.0962250i | ||||
\(217\) | 16.9706i | 1.15204i | ||||||||
\(218\) | 4.24264i | 0.287348i | ||||||||
\(219\) | −4.00000 | + | 5.65685i | −0.270295 | + | 0.382255i | ||||
\(220\) | −8.00000 | −0.539360 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | −6.00000 | − | 4.24264i | −0.402694 | − | 0.284747i | ||||
\(223\) | 4.24264i | 0.284108i | 0.989859 | + | 0.142054i | \(0.0453707\pi\) | ||||
−0.989859 | + | 0.142054i | \(0.954629\pi\) | |||||||
\(224\) | −4.00000 | −0.267261 | ||||||||
\(225\) | −3.00000 | − | 8.48528i | −0.200000 | − | 0.565685i | ||||
\(226\) | −12.0000 | −0.798228 | ||||||||
\(227\) | −18.0000 | −1.19470 | −0.597351 | − | 0.801980i | \(-0.703780\pi\) | ||||
−0.597351 | + | 0.801980i | \(0.703780\pi\) | |||||||
\(228\) | 7.00000 | + | 2.82843i | 0.463586 | + | 0.187317i | ||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | −2.00000 | −0.131876 | ||||||||
\(231\) | −32.0000 | − | 22.6274i | −2.10545 | − | 1.48877i | ||||
\(232\) | −6.00000 | −0.393919 | ||||||||
\(233\) | − | 11.3137i | − | 0.741186i | −0.928795 | − | 0.370593i | \(-0.879155\pi\) | ||
0.928795 | − | 0.370593i | \(-0.120845\pi\) | |||||||
\(234\) | −12.0000 | + | 4.24264i | −0.784465 | + | 0.277350i | ||||
\(235\) | −2.00000 | −0.130466 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | −6.00000 | − | 4.24264i | −0.389742 | − | 0.275589i | ||||
\(238\) | 11.3137i | 0.733359i | ||||||||
\(239\) | − | 15.5563i | − | 1.00626i | −0.864212 | − | 0.503128i | \(-0.832182\pi\) | ||
0.864212 | − | 0.503128i | \(-0.167818\pi\) | |||||||
\(240\) | 2.00000 | + | 1.41421i | 0.129099 | + | 0.0912871i | ||||
\(241\) | − | 8.48528i | − | 0.546585i | −0.961931 | − | 0.273293i | \(-0.911887\pi\) | ||
0.961931 | − | 0.273293i | \(-0.0881127\pi\) | |||||||
\(242\) | −21.0000 | −1.34993 | ||||||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 12.7279i | 0.813157i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.0000 | − | 4.24264i | 1.14531 | − | 0.269953i | ||||
\(248\) | − | 4.24264i | − | 0.269408i | ||||||
\(249\) | −4.00000 | − | 2.82843i | −0.253490 | − | 0.179244i | ||||
\(250\) | 11.3137i | 0.715542i | ||||||||
\(251\) | − | 19.7990i | − | 1.24970i | −0.780744 | − | 0.624851i | \(-0.785160\pi\) | ||
0.780744 | − | 0.624851i | \(-0.214840\pi\) | |||||||
\(252\) | 4.00000 | + | 11.3137i | 0.251976 | + | 0.712697i | ||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 21.2132i | 1.33103i | ||||||||
\(255\) | 4.00000 | − | 5.65685i | 0.250490 | − | 0.354246i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 2.00000 | − | 2.82843i | 0.124515 | − | 0.176090i | ||||
\(259\) | 16.9706i | 1.05450i | ||||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 6.00000 | + | 16.9706i | 0.371391 | + | 1.05045i | ||||
\(262\) | − | 19.7990i | − | 1.22319i | ||||||
\(263\) | − | 15.5563i | − | 0.959246i | −0.877475 | − | 0.479623i | \(-0.840774\pi\) | ||
0.877475 | − | 0.479623i | \(-0.159226\pi\) | |||||||
\(264\) | 8.00000 | + | 5.65685i | 0.492366 | + | 0.348155i | ||||
\(265\) | 8.48528i | 0.521247i | ||||||||
\(266\) | −4.00000 | − | 16.9706i | −0.245256 | − | 1.04053i | ||||
\(267\) | 6.00000 | − | 8.48528i | 0.367194 | − | 0.519291i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.0000 | 1.09748 | 0.548740 | − | 0.835993i | \(-0.315108\pi\) | ||||
0.548740 | + | 0.835993i | \(0.315108\pi\) | |||||||
\(270\) | 2.00000 | − | 7.07107i | 0.121716 | − | 0.430331i | ||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | − | 2.82843i | − | 0.171499i | ||||||
\(273\) | 24.0000 | + | 16.9706i | 1.45255 | + | 1.02711i | ||||
\(274\) | 14.1421i | 0.854358i | ||||||||
\(275\) | 16.9706i | 1.02336i | ||||||||
\(276\) | 2.00000 | + | 1.41421i | 0.120386 | + | 0.0851257i | ||||
\(277\) | −22.0000 | −1.32185 | −0.660926 | − | 0.750451i | \(-0.729836\pi\) | ||||
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | −12.0000 | + | 4.24264i | −0.718421 | + | 0.254000i | ||||
\(280\) | − | 5.65685i | − | 0.338062i | ||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 2.00000 | + | 1.41421i | 0.119098 | + | 0.0842152i | ||||
\(283\) | 20.0000 | 1.18888 | 0.594438 | − | 0.804141i | \(-0.297374\pi\) | ||||
0.594438 | + | 0.804141i | \(0.297374\pi\) | |||||||
\(284\) | −12.0000 | −0.712069 | ||||||||
\(285\) | −4.00000 | + | 9.89949i | −0.236940 | + | 0.586395i | ||||
\(286\) | 24.0000 | 1.41915 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | − | 2.82843i | −0.0589256 | − | 0.166667i | ||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | − | 8.48528i | − | 0.498273i | ||||||
\(291\) | 12.0000 | + | 8.48528i | 0.703452 | + | 0.497416i | ||||
\(292\) | −4.00000 | −0.234082 | ||||||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 9.00000 | − | 12.7279i | 0.524891 | − | 0.742307i | ||||
\(295\) | 16.9706i | 0.988064i | ||||||||
\(296\) | − | 4.24264i | − | 0.246598i | ||||||
\(297\) | 8.00000 | − | 28.2843i | 0.464207 | − | 1.64122i | ||||
\(298\) | 9.89949i | 0.573462i | ||||||||
\(299\) | 6.00000 | 0.346989 | ||||||||
\(300\) | 3.00000 | − | 4.24264i | 0.173205 | − | 0.244949i | ||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 12.7279i | 0.732410i | ||||||||
\(303\) | 14.0000 | + | 9.89949i | 0.804279 | + | 0.568711i | ||||
\(304\) | 1.00000 | + | 4.24264i | 0.0573539 | + | 0.243332i | ||||
\(305\) | 2.82843i | 0.161955i | ||||||||
\(306\) | −8.00000 | + | 2.82843i | −0.457330 | + | 0.161690i | ||||
\(307\) | − | 16.9706i | − | 0.968561i | −0.874913 | − | 0.484281i | \(-0.839081\pi\) | ||
0.874913 | − | 0.484281i | \(-0.160919\pi\) | |||||||
\(308\) | − | 22.6274i | − | 1.28932i | ||||||
\(309\) | −18.0000 | − | 12.7279i | −1.02398 | − | 0.724066i | ||||
\(310\) | 6.00000 | 0.340777 | ||||||||
\(311\) | 1.41421i | 0.0801927i | 0.999196 | + | 0.0400963i | \(0.0127665\pi\) | ||||
−0.999196 | + | 0.0400963i | \(0.987234\pi\) | |||||||
\(312\) | −6.00000 | − | 4.24264i | −0.339683 | − | 0.240192i | ||||
\(313\) | 8.00000 | 0.452187 | 0.226093 | − | 0.974106i | \(-0.427405\pi\) | ||||
0.226093 | + | 0.974106i | \(0.427405\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | −16.0000 | + | 5.65685i | −0.901498 | + | 0.318728i | ||||
\(316\) | − | 4.24264i | − | 0.238667i | ||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 6.00000 | − | 8.48528i | 0.336463 | − | 0.475831i | ||||
\(319\) | − | 33.9411i | − | 1.90034i | ||||||
\(320\) | 1.41421i | 0.0790569i | ||||||||
\(321\) | −12.0000 | + | 16.9706i | −0.669775 | + | 0.947204i | ||||
\(322\) | − | 5.65685i | − | 0.315244i | ||||||
\(323\) | 12.0000 | − | 2.82843i | 0.667698 | − | 0.157378i | ||||
\(324\) | −7.00000 | + | 5.65685i | −0.388889 | + | 0.314270i | ||||
\(325\) | − | 12.7279i | − | 0.706018i | ||||||
\(326\) | 20.0000 | 1.10770 | ||||||||
\(327\) | 6.00000 | + | 4.24264i | 0.331801 | + | 0.234619i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 5.65685i | − | 0.311872i | ||||||
\(330\) | −8.00000 | + | 11.3137i | −0.440386 | + | 0.622799i | ||||
\(331\) | − | 16.9706i | − | 0.932786i | −0.884577 | − | 0.466393i | \(-0.845553\pi\) | ||
0.884577 | − | 0.466393i | \(-0.154447\pi\) | |||||||
\(332\) | − | 2.82843i | − | 0.155230i | ||||||
\(333\) | −12.0000 | + | 4.24264i | −0.657596 | + | 0.232495i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.00000 | + | 5.65685i | −0.218218 | + | 0.308607i | ||||
\(337\) | 16.9706i | 0.924445i | 0.886764 | + | 0.462223i | \(0.152948\pi\) | ||||
−0.886764 | + | 0.462223i | \(0.847052\pi\) | |||||||
\(338\) | −5.00000 | −0.271964 | ||||||||
\(339\) | −12.0000 | + | 16.9706i | −0.651751 | + | 0.921714i | ||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | 11.0000 | − | 7.07107i | 0.594812 | − | 0.382360i | ||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | −2.00000 | + | 2.82843i | −0.107676 | + | 0.152277i | ||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | − | 11.3137i | − | 0.607352i | −0.952775 | − | 0.303676i | \(-0.901786\pi\) | ||
0.952775 | − | 0.303676i | \(-0.0982140\pi\) | |||||||
\(348\) | −6.00000 | + | 8.48528i | −0.321634 | + | 0.454859i | ||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | −12.0000 | −0.641427 | ||||||||
\(351\) | −6.00000 | + | 21.2132i | −0.320256 | + | 1.13228i | ||||
\(352\) | 5.65685i | 0.301511i | ||||||||
\(353\) | − | 28.2843i | − | 1.50542i | −0.658352 | − | 0.752710i | \(-0.728746\pi\) | ||
0.658352 | − | 0.752710i | \(-0.271254\pi\) | |||||||
\(354\) | 12.0000 | − | 16.9706i | 0.637793 | − | 0.901975i | ||||
\(355\) | − | 16.9706i | − | 0.900704i | ||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 16.0000 | + | 11.3137i | 0.846810 | + | 0.598785i | ||||
\(358\) | −18.0000 | −0.951330 | ||||||||
\(359\) | 18.3848i | 0.970311i | 0.874428 | + | 0.485156i | \(0.161237\pi\) | ||||
−0.874428 | + | 0.485156i | \(0.838763\pi\) | |||||||
\(360\) | 4.00000 | − | 1.41421i | 0.210819 | − | 0.0745356i | ||||
\(361\) | −17.0000 | + | 8.48528i | −0.894737 | + | 0.446594i | ||||
\(362\) | − | 12.7279i | − | 0.668965i | ||||||
\(363\) | −21.0000 | + | 29.6985i | −1.10221 | + | 1.55877i | ||||
\(364\) | 16.9706i | 0.889499i | ||||||||
\(365\) | − | 5.65685i | − | 0.296093i | ||||||
\(366\) | 2.00000 | − | 2.82843i | 0.104542 | − | 0.147844i | ||||
\(367\) | −28.0000 | −1.46159 | −0.730794 | − | 0.682598i | \(-0.760850\pi\) | ||||
−0.730794 | + | 0.682598i | \(0.760850\pi\) | |||||||
\(368\) | 1.41421i | 0.0737210i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | −24.0000 | −1.24602 | ||||||||
\(372\) | −6.00000 | − | 4.24264i | −0.311086 | − | 0.219971i | ||||
\(373\) | − | 29.6985i | − | 1.53773i | −0.639412 | − | 0.768865i | \(-0.720822\pi\) | ||
0.639412 | − | 0.768865i | \(-0.279178\pi\) | |||||||
\(374\) | 16.0000 | 0.827340 | ||||||||
\(375\) | 16.0000 | + | 11.3137i | 0.826236 | + | 0.584237i | ||||
\(376\) | 1.41421i | 0.0729325i | ||||||||
\(377\) | 25.4558i | 1.31104i | ||||||||
\(378\) | 20.0000 | + | 5.65685i | 1.02869 | + | 0.290957i | ||||
\(379\) | − | 33.9411i | − | 1.74344i | −0.490006 | − | 0.871719i | \(-0.663005\pi\) | ||
0.490006 | − | 0.871719i | \(-0.336995\pi\) | |||||||
\(380\) | −6.00000 | + | 1.41421i | −0.307794 | + | 0.0725476i | ||||
\(381\) | 30.0000 | + | 21.2132i | 1.53695 | + | 1.08679i | ||||
\(382\) | 18.3848i | 0.940647i | ||||||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | 1.00000 | − | 1.41421i | 0.0510310 | − | 0.0721688i | ||||
\(385\) | 32.0000 | 1.63087 | ||||||||
\(386\) | − | 8.48528i | − | 0.431889i | ||||||
\(387\) | −2.00000 | − | 5.65685i | −0.101666 | − | 0.287554i | ||||
\(388\) | 8.48528i | 0.430775i | ||||||||
\(389\) | − | 15.5563i | − | 0.788738i | −0.918952 | − | 0.394369i | \(-0.870963\pi\) | ||
0.918952 | − | 0.394369i | \(-0.129037\pi\) | |||||||
\(390\) | 6.00000 | − | 8.48528i | 0.303822 | − | 0.429669i | ||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | 9.00000 | 0.454569 | ||||||||
\(393\) | −28.0000 | − | 19.7990i | −1.41241 | − | 0.998727i | ||||
\(394\) | − | 7.07107i | − | 0.356235i | ||||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | 16.0000 | − | 5.65685i | 0.804030 | − | 0.284268i | ||||
\(397\) | 38.0000 | 1.90717 | 0.953583 | − | 0.301131i | \(-0.0973643\pi\) | ||||
0.953583 | + | 0.301131i | \(0.0973643\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | −28.0000 | − | 11.3137i | −1.40175 | − | 0.566394i | ||||
\(400\) | 3.00000 | 0.150000 | ||||||||
\(401\) | 24.0000 | 1.19850 | 0.599251 | − | 0.800561i | \(-0.295465\pi\) | ||||
0.599251 | + | 0.800561i | \(0.295465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.0000 | −0.896644 | ||||||||
\(404\) | 9.89949i | 0.492518i | ||||||||
\(405\) | −8.00000 | − | 9.89949i | −0.397523 | − | 0.491910i | ||||
\(406\) | 24.0000 | 1.19110 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | −4.00000 | − | 2.82843i | −0.198030 | − | 0.140028i | ||||
\(409\) | 8.48528i | 0.419570i | 0.977748 | + | 0.209785i | \(0.0672764\pi\) | ||||
−0.977748 | + | 0.209785i | \(0.932724\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.0000 | + | 14.1421i | 0.986527 | + | 0.697580i | ||||
\(412\) | − | 12.7279i | − | 0.627060i | ||||||
\(413\) | −48.0000 | −2.36193 | ||||||||
\(414\) | 4.00000 | − | 1.41421i | 0.196589 | − | 0.0695048i | ||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | − | 4.24264i | − | 0.208013i | ||||||
\(417\) | −4.00000 | + | 5.65685i | −0.195881 | + | 0.277017i | ||||
\(418\) | −24.0000 | + | 5.65685i | −1.17388 | + | 0.276686i | ||||
\(419\) | 39.5980i | 1.93449i | 0.253849 | + | 0.967244i | \(0.418303\pi\) | ||||
−0.253849 | + | 0.967244i | \(0.581697\pi\) | |||||||
\(420\) | −8.00000 | − | 5.65685i | −0.390360 | − | 0.276026i | ||||
\(421\) | 12.7279i | 0.620321i | 0.950684 | + | 0.310160i | \(0.100383\pi\) | ||||
−0.950684 | + | 0.310160i | \(0.899617\pi\) | |||||||
\(422\) | 8.48528i | 0.413057i | ||||||||
\(423\) | 4.00000 | − | 1.41421i | 0.194487 | − | 0.0687614i | ||||
\(424\) | 6.00000 | 0.291386 | ||||||||
\(425\) | − | 8.48528i | − | 0.411597i | ||||||
\(426\) | −12.0000 | + | 16.9706i | −0.581402 | + | 0.822226i | ||||
\(427\) | −8.00000 | −0.387147 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 24.0000 | − | 33.9411i | 1.15873 | − | 1.63869i | ||||
\(430\) | 2.82843i | 0.136399i | ||||||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | −5.00000 | − | 1.41421i | −0.240563 | − | 0.0680414i | ||||
\(433\) | 25.4558i | 1.22333i | 0.791117 | + | 0.611665i | \(0.209500\pi\) | ||||
−0.791117 | + | 0.611665i | \(0.790500\pi\) | |||||||
\(434\) | 16.9706i | 0.814613i | ||||||||
\(435\) | −12.0000 | − | 8.48528i | −0.575356 | − | 0.406838i | ||||
\(436\) | 4.24264i | 0.203186i | ||||||||
\(437\) | −6.00000 | + | 1.41421i | −0.287019 | + | 0.0676510i | ||||
\(438\) | −4.00000 | + | 5.65685i | −0.191127 | + | 0.270295i | ||||
\(439\) | 12.7279i | 0.607471i | 0.952756 | + | 0.303735i | \(0.0982338\pi\) | ||||
−0.952756 | + | 0.303735i | \(0.901766\pi\) | |||||||
\(440\) | −8.00000 | −0.381385 | ||||||||
\(441\) | −9.00000 | − | 25.4558i | −0.428571 | − | 1.21218i | ||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | − | 28.2843i | − | 1.34383i | −0.740630 | − | 0.671913i | \(-0.765473\pi\) | ||
0.740630 | − | 0.671913i | \(-0.234527\pi\) | |||||||
\(444\) | −6.00000 | − | 4.24264i | −0.284747 | − | 0.201347i | ||||
\(445\) | 8.48528i | 0.402241i | ||||||||
\(446\) | 4.24264i | 0.200895i | ||||||||
\(447\) | 14.0000 | + | 9.89949i | 0.662177 | + | 0.468230i | ||||
\(448\) | −4.00000 | −0.188982 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | −3.00000 | − | 8.48528i | −0.141421 | − | 0.400000i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −12.0000 | −0.564433 | ||||||||
\(453\) | 18.0000 | + | 12.7279i | 0.845714 | + | 0.598010i | ||||
\(454\) | −18.0000 | −0.844782 | ||||||||
\(455\) | −24.0000 | −1.12514 | ||||||||
\(456\) | 7.00000 | + | 2.82843i | 0.327805 | + | 0.132453i | ||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 2.00000 | 0.0934539 | ||||||||
\(459\) | −4.00000 | + | 14.1421i | −0.186704 | + | 0.660098i | ||||
\(460\) | −2.00000 | −0.0932505 | ||||||||
\(461\) | 1.41421i | 0.0658665i | 0.999458 | + | 0.0329332i | \(0.0104849\pi\) | ||||
−0.999458 | + | 0.0329332i | \(0.989515\pi\) | |||||||
\(462\) | −32.0000 | − | 22.6274i | −1.48877 | − | 1.05272i | ||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 6.00000 | − | 8.48528i | 0.278243 | − | 0.393496i | ||||
\(466\) | − | 11.3137i | − | 0.524097i | ||||||
\(467\) | − | 2.82843i | − | 0.130884i | −0.997856 | − | 0.0654420i | \(-0.979154\pi\) | ||
0.997856 | − | 0.0654420i | \(-0.0208457\pi\) | |||||||
\(468\) | −12.0000 | + | 4.24264i | −0.554700 | + | 0.196116i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.00000 | −0.0922531 | ||||||||
\(471\) | 14.0000 | − | 19.7990i | 0.645086 | − | 0.912289i | ||||
\(472\) | 12.0000 | 0.552345 | ||||||||
\(473\) | 11.3137i | 0.520205i | ||||||||
\(474\) | −6.00000 | − | 4.24264i | −0.275589 | − | 0.194871i | ||||
\(475\) | 3.00000 | + | 12.7279i | 0.137649 | + | 0.583997i | ||||
\(476\) | 11.3137i | 0.518563i | ||||||||
\(477\) | −6.00000 | − | 16.9706i | −0.274721 | − | 0.777029i | ||||
\(478\) | − | 15.5563i | − | 0.711531i | ||||||
\(479\) | 9.89949i | 0.452319i | 0.974090 | + | 0.226160i | \(0.0726171\pi\) | ||||
−0.974090 | + | 0.226160i | \(0.927383\pi\) | |||||||
\(480\) | 2.00000 | + | 1.41421i | 0.0912871 | + | 0.0645497i | ||||
\(481\) | −18.0000 | −0.820729 | ||||||||
\(482\) | − | 8.48528i | − | 0.386494i | ||||||
\(483\) | −8.00000 | − | 5.65685i | −0.364013 | − | 0.257396i | ||||
\(484\) | −21.0000 | −0.954545 | ||||||||
\(485\) | −12.0000 | −0.544892 | ||||||||
\(486\) | 1.00000 | + | 15.5563i | 0.0453609 | + | 0.705650i | ||||
\(487\) | 12.7279i | 0.576757i | 0.957516 | + | 0.288379i | \(0.0931162\pi\) | ||||
−0.957516 | + | 0.288379i | \(0.906884\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | 20.0000 | − | 28.2843i | 0.904431 | − | 1.27906i | ||||
\(490\) | 12.7279i | 0.574989i | ||||||||
\(491\) | 14.1421i | 0.638226i | 0.947717 | + | 0.319113i | \(0.103385\pi\) | ||||
−0.947717 | + | 0.319113i | \(0.896615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.9706i | 0.764316i | ||||||||
\(494\) | 18.0000 | − | 4.24264i | 0.809858 | − | 0.190885i | ||||
\(495\) | 8.00000 | + | 22.6274i | 0.359573 | + | 1.01703i | ||||
\(496\) | − | 4.24264i | − | 0.190500i | ||||||
\(497\) | 48.0000 | 2.15309 | ||||||||
\(498\) | −4.00000 | − | 2.82843i | −0.179244 | − | 0.126745i | ||||
\(499\) | −10.0000 | −0.447661 | −0.223831 | − | 0.974628i | \(-0.571856\pi\) | ||||
−0.223831 | + | 0.974628i | \(0.571856\pi\) | |||||||
\(500\) | 11.3137i | 0.505964i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 19.7990i | − | 0.883672i | ||||||
\(503\) | − | 7.07107i | − | 0.315283i | −0.987496 | − | 0.157642i | \(-0.949611\pi\) | ||
0.987496 | − | 0.157642i | \(-0.0503891\pi\) | |||||||
\(504\) | 4.00000 | + | 11.3137i | 0.178174 | + | 0.503953i | ||||
\(505\) | −14.0000 | −0.622992 | ||||||||
\(506\) | −8.00000 | −0.355643 | ||||||||
\(507\) | −5.00000 | + | 7.07107i | −0.222058 | + | 0.314037i | ||||
\(508\) | 21.2132i | 0.941184i | ||||||||
\(509\) | 6.00000 | 0.265945 | 0.132973 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132973 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(510\) | 4.00000 | − | 5.65685i | 0.177123 | − | 0.250490i | ||||
\(511\) | 16.0000 | 0.707798 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | − | 22.6274i | 0.0441511 | − | 0.999025i | ||||
\(514\) | 6.00000 | 0.264649 | ||||||||
\(515\) | 18.0000 | 0.793175 | ||||||||
\(516\) | 2.00000 | − | 2.82843i | 0.0880451 | − | 0.124515i | ||||
\(517\) | −8.00000 | −0.351840 | ||||||||
\(518\) | 16.9706i | 0.745644i | ||||||||
\(519\) | 6.00000 | − | 8.48528i | 0.263371 | − | 0.372463i | ||||
\(520\) | 6.00000 | 0.263117 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 6.00000 | + | 16.9706i | 0.262613 | + | 0.742781i | ||||
\(523\) | − | 16.9706i | − | 0.742071i | −0.928619 | − | 0.371035i | \(-0.879003\pi\) | ||
0.928619 | − | 0.371035i | \(-0.120997\pi\) | |||||||
\(524\) | − | 19.7990i | − | 0.864923i | ||||||
\(525\) | −12.0000 | + | 16.9706i | −0.523723 | + | 0.740656i | ||||
\(526\) | − | 15.5563i | − | 0.678289i | ||||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | 8.00000 | + | 5.65685i | 0.348155 | + | 0.246183i | ||||
\(529\) | 21.0000 | 0.913043 | ||||||||
\(530\) | 8.48528i | 0.368577i | ||||||||
\(531\) | −12.0000 | − | 33.9411i | −0.520756 | − | 1.47292i | ||||
\(532\) | −4.00000 | − | 16.9706i | −0.173422 | − | 0.735767i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.00000 | − | 8.48528i | 0.259645 | − | 0.367194i | ||||
\(535\) | − | 16.9706i | − | 0.733701i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.0000 | + | 25.4558i | −0.776757 | + | 1.09850i | ||||
\(538\) | 18.0000 | 0.776035 | ||||||||
\(539\) | 50.9117i | 2.19292i | ||||||||
\(540\) | 2.00000 | − | 7.07107i | 0.0860663 | − | 0.304290i | ||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | −16.0000 | −0.687259 | ||||||||
\(543\) | −18.0000 | − | 12.7279i | −0.772454 | − | 0.546207i | ||||
\(544\) | − | 2.82843i | − | 0.121268i | ||||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 24.0000 | + | 16.9706i | 1.02711 | + | 0.726273i | ||||
\(547\) | 16.9706i | 0.725609i | 0.931865 | + | 0.362804i | \(0.118181\pi\) | ||||
−0.931865 | + | 0.362804i | \(0.881819\pi\) | |||||||
\(548\) | 14.1421i | 0.604122i | ||||||||
\(549\) | −2.00000 | − | 5.65685i | −0.0853579 | − | 0.241429i | ||||
\(550\) | 16.9706i | 0.723627i | ||||||||
\(551\) | −6.00000 | − | 25.4558i | −0.255609 | − | 1.08446i | ||||
\(552\) | 2.00000 | + | 1.41421i | 0.0851257 | + | 0.0601929i | ||||
\(553\) | 16.9706i | 0.721662i | ||||||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 6.00000 | − | 8.48528i | 0.254686 | − | 0.360180i | ||||
\(556\) | −4.00000 | −0.169638 | ||||||||
\(557\) | − | 24.0416i | − | 1.01868i | −0.860566 | − | 0.509338i | \(-0.829890\pi\) | ||
0.860566 | − | 0.509338i | \(-0.170110\pi\) | |||||||
\(558\) | −12.0000 | + | 4.24264i | −0.508001 | + | 0.179605i | ||||
\(559\) | − | 8.48528i | − | 0.358889i | ||||||
\(560\) | − | 5.65685i | − | 0.239046i | ||||||
\(561\) | 16.0000 | − | 22.6274i | 0.675521 | − | 0.955330i | ||||
\(562\) | −12.0000 | −0.506189 | ||||||||
\(563\) | 36.0000 | 1.51722 | 0.758610 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(564\) | 2.00000 | + | 1.41421i | 0.0842152 | + | 0.0595491i | ||||
\(565\) | − | 16.9706i | − | 0.713957i | ||||||
\(566\) | 20.0000 | 0.840663 | ||||||||
\(567\) | 28.0000 | − | 22.6274i | 1.17589 | − | 0.950262i | ||||
\(568\) | −12.0000 | −0.503509 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | −4.00000 | + | 9.89949i | −0.167542 | + | 0.414644i | ||||
\(571\) | 14.0000 | 0.585882 | 0.292941 | − | 0.956131i | \(-0.405366\pi\) | ||||
0.292941 | + | 0.956131i | \(0.405366\pi\) | |||||||
\(572\) | 24.0000 | 1.00349 | ||||||||
\(573\) | 26.0000 | + | 18.3848i | 1.08617 | + | 0.768035i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.24264i | 0.176930i | ||||||||
\(576\) | −1.00000 | − | 2.82843i | −0.0416667 | − | 0.117851i | ||||
\(577\) | −10.0000 | −0.416305 | −0.208153 | − | 0.978096i | \(-0.566745\pi\) | ||||
−0.208153 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(578\) | 9.00000 | 0.374351 | ||||||||
\(579\) | −12.0000 | − | 8.48528i | −0.498703 | − | 0.352636i | ||||
\(580\) | − | 8.48528i | − | 0.352332i | ||||||
\(581\) | 11.3137i | 0.469372i | ||||||||
\(582\) | 12.0000 | + | 8.48528i | 0.497416 | + | 0.351726i | ||||
\(583\) | 33.9411i | 1.40570i | ||||||||
\(584\) | −4.00000 | −0.165521 | ||||||||
\(585\) | −6.00000 | − | 16.9706i | −0.248069 | − | 0.701646i | ||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 22.6274i | 0.933933i | 0.884275 | + | 0.466967i | \(0.154653\pi\) | ||||
−0.884275 | + | 0.466967i | \(0.845347\pi\) | |||||||
\(588\) | 9.00000 | − | 12.7279i | 0.371154 | − | 0.524891i | ||||
\(589\) | 18.0000 | − | 4.24264i | 0.741677 | − | 0.174815i | ||||
\(590\) | 16.9706i | 0.698667i | ||||||||
\(591\) | −10.0000 | − | 7.07107i | −0.411345 | − | 0.290865i | ||||
\(592\) | − | 4.24264i | − | 0.174371i | ||||||
\(593\) | 5.65685i | 0.232299i | 0.993232 | + | 0.116150i | \(0.0370552\pi\) | ||||
−0.993232 | + | 0.116150i | \(0.962945\pi\) | |||||||
\(594\) | 8.00000 | − | 28.2843i | 0.328244 | − | 1.16052i | ||||
\(595\) | −16.0000 | −0.655936 | ||||||||
\(596\) | 9.89949i | 0.405499i | ||||||||
\(597\) | −4.00000 | + | 5.65685i | −0.163709 | + | 0.231520i | ||||
\(598\) | 6.00000 | 0.245358 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 3.00000 | − | 4.24264i | 0.122474 | − | 0.173205i | ||||
\(601\) | − | 16.9706i | − | 0.692244i | −0.938190 | − | 0.346122i | \(-0.887498\pi\) | ||
0.938190 | − | 0.346122i | \(-0.112502\pi\) | |||||||
\(602\) | −8.00000 | −0.326056 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.7279i | 0.517892i | ||||||||
\(605\) | − | 29.6985i | − | 1.20742i | ||||||
\(606\) | 14.0000 | + | 9.89949i | 0.568711 | + | 0.402139i | ||||
\(607\) | − | 38.1838i | − | 1.54983i | −0.632065 | − | 0.774916i | \(-0.717792\pi\) | ||
0.632065 | − | 0.774916i | \(-0.282208\pi\) | |||||||
\(608\) | 1.00000 | + | 4.24264i | 0.0405554 | + | 0.172062i | ||||
\(609\) | 24.0000 | − | 33.9411i | 0.972529 | − | 1.37536i | ||||
\(610\) | 2.82843i | 0.114520i | ||||||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | −8.00000 | + | 2.82843i | −0.323381 | + | 0.114332i | ||||
\(613\) | −22.0000 | −0.888572 | −0.444286 | − | 0.895885i | \(-0.646543\pi\) | ||||
−0.444286 | + | 0.895885i | \(0.646543\pi\) | |||||||
\(614\) | − | 16.9706i | − | 0.684876i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 22.6274i | − | 0.911685i | ||||||
\(617\) | 22.6274i | 0.910946i | 0.890250 | + | 0.455473i | \(0.150530\pi\) | ||||
−0.890250 | + | 0.455473i | \(0.849470\pi\) | |||||||
\(618\) | −18.0000 | − | 12.7279i | −0.724066 | − | 0.511992i | ||||
\(619\) | −46.0000 | −1.84890 | −0.924448 | − | 0.381308i | \(-0.875474\pi\) | ||||
−0.924448 | + | 0.381308i | \(0.875474\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | 2.00000 | − | 7.07107i | 0.0802572 | − | 0.283752i | ||||
\(622\) | 1.41421i | 0.0567048i | ||||||||
\(623\) | −24.0000 | −0.961540 | ||||||||
\(624\) | −6.00000 | − | 4.24264i | −0.240192 | − | 0.169842i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 8.00000 | 0.319744 | ||||||||
\(627\) | −16.0000 | + | 39.5980i | −0.638978 | + | 1.58139i | ||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | −16.0000 | + | 5.65685i | −0.637455 | + | 0.225374i | ||||
\(631\) | −4.00000 | −0.159237 | −0.0796187 | − | 0.996825i | \(-0.525370\pi\) | ||||
−0.0796187 | + | 0.996825i | \(0.525370\pi\) | |||||||
\(632\) | − | 4.24264i | − | 0.168763i | ||||||
\(633\) | 12.0000 | + | 8.48528i | 0.476957 | + | 0.337260i | ||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | −30.0000 | −1.19051 | ||||||||
\(636\) | 6.00000 | − | 8.48528i | 0.237915 | − | 0.336463i | ||||
\(637\) | − | 38.1838i | − | 1.51290i | ||||||
\(638\) | − | 33.9411i | − | 1.34374i | ||||||
\(639\) | 12.0000 | + | 33.9411i | 0.474713 | + | 1.34269i | ||||
\(640\) | 1.41421i | 0.0559017i | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | −12.0000 | + | 16.9706i | −0.473602 | + | 0.669775i | ||||
\(643\) | −28.0000 | −1.10421 | −0.552106 | − | 0.833774i | \(-0.686176\pi\) | ||||
−0.552106 | + | 0.833774i | \(0.686176\pi\) | |||||||
\(644\) | − | 5.65685i | − | 0.222911i | ||||||
\(645\) | 4.00000 | + | 2.82843i | 0.157500 | + | 0.111369i | ||||
\(646\) | 12.0000 | − | 2.82843i | 0.472134 | − | 0.111283i | ||||
\(647\) | − | 24.0416i | − | 0.945174i | −0.881284 | − | 0.472587i | \(-0.843320\pi\) | ||
0.881284 | − | 0.472587i | \(-0.156680\pi\) | |||||||
\(648\) | −7.00000 | + | 5.65685i | −0.274986 | + | 0.222222i | ||||
\(649\) | 67.8823i | 2.66461i | ||||||||
\(650\) | − | 12.7279i | − | 0.499230i | ||||||
\(651\) | 24.0000 | + | 16.9706i | 0.940634 | + | 0.665129i | ||||
\(652\) | 20.0000 | 0.783260 | ||||||||
\(653\) | 35.3553i | 1.38356i | 0.722108 | + | 0.691781i | \(0.243173\pi\) | ||||
−0.722108 | + | 0.691781i | \(0.756827\pi\) | |||||||
\(654\) | 6.00000 | + | 4.24264i | 0.234619 | + | 0.165900i | ||||
\(655\) | 28.0000 | 1.09405 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | + | 11.3137i | 0.156055 | + | 0.441390i | ||||
\(658\) | − | 5.65685i | − | 0.220527i | ||||||
\(659\) | −18.0000 | −0.701180 | −0.350590 | − | 0.936529i | \(-0.614019\pi\) | ||||
−0.350590 | + | 0.936529i | \(0.614019\pi\) | |||||||
\(660\) | −8.00000 | + | 11.3137i | −0.311400 | + | 0.440386i | ||||
\(661\) | 29.6985i | 1.15514i | 0.816342 | + | 0.577569i | \(0.195998\pi\) | ||||
−0.816342 | + | 0.577569i | \(0.804002\pi\) | |||||||
\(662\) | − | 16.9706i | − | 0.659580i | ||||||
\(663\) | −12.0000 | + | 16.9706i | −0.466041 | + | 0.659082i | ||||
\(664\) | − | 2.82843i | − | 0.109764i | ||||||
\(665\) | 24.0000 | − | 5.65685i | 0.930680 | − | 0.219363i | ||||
\(666\) | −12.0000 | + | 4.24264i | −0.464991 | + | 0.164399i | ||||
\(667\) | − | 8.48528i | − | 0.328551i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.00000 | + | 4.24264i | 0.231973 | + | 0.164030i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.3137i | 0.436761i | ||||||||
\(672\) | −4.00000 | + | 5.65685i | −0.154303 | + | 0.218218i | ||||
\(673\) | 8.48528i | 0.327084i | 0.986536 | + | 0.163542i | \(0.0522919\pi\) | ||||
−0.986536 | + | 0.163542i | \(0.947708\pi\) | |||||||
\(674\) | 16.9706i | 0.653682i | ||||||||
\(675\) | −15.0000 | − | 4.24264i | −0.577350 | − | 0.163299i | ||||
\(676\) | −5.00000 | −0.192308 | ||||||||
\(677\) | −30.0000 | −1.15299 | −0.576497 | − | 0.817099i | \(-0.695581\pi\) | ||||
−0.576497 | + | 0.817099i | \(0.695581\pi\) | |||||||
\(678\) | −12.0000 | + | 16.9706i | −0.460857 | + | 0.651751i | ||||
\(679\) | − | 33.9411i | − | 1.30254i | ||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | −18.0000 | + | 25.4558i | −0.689761 | + | 0.975470i | ||||
\(682\) | 24.0000 | 0.919007 | ||||||||
\(683\) | −18.0000 | −0.688751 | −0.344375 | − | 0.938832i | \(-0.611909\pi\) | ||||
−0.344375 | + | 0.938832i | \(0.611909\pi\) | |||||||
\(684\) | 11.0000 | − | 7.07107i | 0.420596 | − | 0.270369i | ||||
\(685\) | −20.0000 | −0.764161 | ||||||||
\(686\) | −8.00000 | −0.305441 | ||||||||
\(687\) | 2.00000 | − | 2.82843i | 0.0763048 | − | 0.107911i | ||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | − | 25.4558i | − | 0.969790i | ||||||
\(690\) | −2.00000 | + | 2.82843i | −0.0761387 | + | 0.107676i | ||||
\(691\) | −10.0000 | −0.380418 | −0.190209 | − | 0.981744i | \(-0.560917\pi\) | ||||
−0.190209 | + | 0.981744i | \(0.560917\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | −64.0000 | + | 22.6274i | −2.43116 | + | 0.859544i | ||||
\(694\) | − | 11.3137i | − | 0.429463i | ||||||
\(695\) | − | 5.65685i | − | 0.214577i | ||||||
\(696\) | −6.00000 | + | 8.48528i | −0.227429 | + | 0.321634i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.00000 | 0.0757011 | ||||||||
\(699\) | −16.0000 | − | 11.3137i | −0.605176 | − | 0.427924i | ||||
\(700\) | −12.0000 | −0.453557 | ||||||||
\(701\) | − | 7.07107i | − | 0.267071i | −0.991044 | − | 0.133535i | \(-0.957367\pi\) | ||
0.991044 | − | 0.133535i | \(-0.0426329\pi\) | |||||||
\(702\) | −6.00000 | + | 21.2132i | −0.226455 | + | 0.800641i | ||||
\(703\) | 18.0000 | − | 4.24264i | 0.678883 | − | 0.160014i | ||||
\(704\) | 5.65685i | 0.213201i | ||||||||
\(705\) | −2.00000 | + | 2.82843i | −0.0753244 | + | 0.106525i | ||||
\(706\) | − | 28.2843i | − | 1.06449i | ||||||
\(707\) | − | 39.5980i | − | 1.48924i | ||||||
\(708\) | 12.0000 | − | 16.9706i | 0.450988 | − | 0.637793i | ||||
\(709\) | 26.0000 | 0.976450 | 0.488225 | − | 0.872718i | \(-0.337644\pi\) | ||||
0.488225 | + | 0.872718i | \(0.337644\pi\) | |||||||
\(710\) | − | 16.9706i | − | 0.636894i | ||||||
\(711\) | −12.0000 | + | 4.24264i | −0.450035 | + | 0.159111i | ||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | 16.0000 | + | 11.3137i | 0.598785 | + | 0.423405i | ||||
\(715\) | 33.9411i | 1.26933i | ||||||||
\(716\) | −18.0000 | −0.672692 | ||||||||
\(717\) | −22.0000 | − | 15.5563i | −0.821605 | − | 0.580963i | ||||
\(718\) | 18.3848i | 0.686114i | ||||||||
\(719\) | − | 7.07107i | − | 0.263706i | −0.991269 | − | 0.131853i | \(-0.957907\pi\) | ||
0.991269 | − | 0.131853i | \(-0.0420927\pi\) | |||||||
\(720\) | 4.00000 | − | 1.41421i | 0.149071 | − | 0.0527046i | ||||
\(721\) | 50.9117i | 1.89605i | ||||||||
\(722\) | −17.0000 | + | 8.48528i | −0.632674 | + | 0.315789i | ||||
\(723\) | −12.0000 | − | 8.48528i | −0.446285 | − | 0.315571i | ||||
\(724\) | − | 12.7279i | − | 0.473029i | ||||||
\(725\) | −18.0000 | −0.668503 | ||||||||
\(726\) | −21.0000 | + | 29.6985i | −0.779383 | + | 1.10221i | ||||
\(727\) | 8.00000 | 0.296704 | 0.148352 | − | 0.988935i | \(-0.452603\pi\) | ||||
0.148352 | + | 0.988935i | \(0.452603\pi\) | |||||||
\(728\) | 16.9706i | 0.628971i | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | − | 5.65685i | − | 0.209370i | ||||||
\(731\) | − | 5.65685i | − | 0.209226i | ||||||
\(732\) | 2.00000 | − | 2.82843i | 0.0739221 | − | 0.104542i | ||||
\(733\) | −22.0000 | −0.812589 | −0.406294 | − | 0.913742i | \(-0.633179\pi\) | ||||
−0.406294 | + | 0.913742i | \(0.633179\pi\) | |||||||
\(734\) | −28.0000 | −1.03350 | ||||||||
\(735\) | 18.0000 | + | 12.7279i | 0.663940 | + | 0.469476i | ||||
\(736\) | 1.41421i | 0.0521286i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 6.00000 | 0.220564 | ||||||||
\(741\) | 12.0000 | − | 29.6985i | 0.440831 | − | 1.09100i | ||||
\(742\) | −24.0000 | −0.881068 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | −6.00000 | − | 4.24264i | −0.219971 | − | 0.155543i | ||||
\(745\) | −14.0000 | −0.512920 | ||||||||
\(746\) | − | 29.6985i | − | 1.08734i | ||||||
\(747\) | −8.00000 | + | 2.82843i | −0.292705 | + | 0.103487i | ||||
\(748\) | 16.0000 | 0.585018 | ||||||||
\(749\) | 48.0000 | 1.75388 | ||||||||
\(750\) | 16.0000 | + | 11.3137i | 0.584237 | + | 0.413118i | ||||
\(751\) | 38.1838i | 1.39335i | 0.717389 | + | 0.696673i | \(0.245337\pi\) | ||||
−0.717389 | + | 0.696673i | \(0.754663\pi\) | |||||||
\(752\) | 1.41421i | 0.0515711i | ||||||||
\(753\) | −28.0000 | − | 19.7990i | −1.02038 | − | 0.721515i | ||||
\(754\) | 25.4558i | 0.927047i | ||||||||
\(755\) | −18.0000 | −0.655087 | ||||||||
\(756\) | 20.0000 | + | 5.65685i | 0.727393 | + | 0.205738i | ||||
\(757\) | −34.0000 | −1.23575 | −0.617876 | − | 0.786276i | \(-0.712006\pi\) | ||||
−0.617876 | + | 0.786276i | \(0.712006\pi\) | |||||||
\(758\) | − | 33.9411i | − | 1.23280i | ||||||
\(759\) | −8.00000 | + | 11.3137i | −0.290382 | + | 0.410662i | ||||
\(760\) | −6.00000 | + | 1.41421i | −0.217643 | + | 0.0512989i | ||||
\(761\) | 14.1421i | 0.512652i | 0.966590 | + | 0.256326i | \(0.0825121\pi\) | ||||
−0.966590 | + | 0.256326i | \(0.917488\pi\) | |||||||
\(762\) | 30.0000 | + | 21.2132i | 1.08679 | + | 0.768473i | ||||
\(763\) | − | 16.9706i | − | 0.614376i | ||||||
\(764\) | 18.3848i | 0.665138i | ||||||||
\(765\) | −4.00000 | − | 11.3137i | −0.144620 | − | 0.409048i | ||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | − | 50.9117i | − | 1.83831i | ||||||
\(768\) | 1.00000 | − | 1.41421i | 0.0360844 | − | 0.0510310i | ||||
\(769\) | −16.0000 | −0.576975 | −0.288487 | − | 0.957484i | \(-0.593152\pi\) | ||||
−0.288487 | + | 0.957484i | \(0.593152\pi\) | |||||||
\(770\) | 32.0000 | 1.15320 | ||||||||
\(771\) | 6.00000 | − | 8.48528i | 0.216085 | − | 0.305590i | ||||
\(772\) | − | 8.48528i | − | 0.305392i | ||||||
\(773\) | −18.0000 | −0.647415 | −0.323708 | − | 0.946157i | \(-0.604929\pi\) | ||||
−0.323708 | + | 0.946157i | \(0.604929\pi\) | |||||||
\(774\) | −2.00000 | − | 5.65685i | −0.0718885 | − | 0.203331i | ||||
\(775\) | − | 12.7279i | − | 0.457200i | ||||||
\(776\) | 8.48528i | 0.304604i | ||||||||
\(777\) | 24.0000 | + | 16.9706i | 0.860995 | + | 0.608816i | ||||
\(778\) | − | 15.5563i | − | 0.557722i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 6.00000 | − | 8.48528i | 0.214834 | − | 0.303822i | ||||
\(781\) | − | 67.8823i | − | 2.42902i | ||||||
\(782\) | 4.00000 | 0.143040 | ||||||||
\(783\) | 30.0000 | + | 8.48528i | 1.07211 | + | 0.303239i | ||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | 19.7990i | 0.706656i | ||||||||
\(786\) | −28.0000 | − | 19.7990i | −0.998727 | − | 0.706207i | ||||
\(787\) | 8.48528i | 0.302468i | 0.988498 | + | 0.151234i | \(0.0483246\pi\) | ||||
−0.988498 | + | 0.151234i | \(0.951675\pi\) | |||||||
\(788\) | − | 7.07107i | − | 0.251896i | ||||||
\(789\) | −22.0000 | − | 15.5563i | −0.783221 | − | 0.553821i | ||||
\(790\) | 6.00000 | 0.213470 | ||||||||
\(791\) | 48.0000 | 1.70668 | ||||||||
\(792\) | 16.0000 | − | 5.65685i | 0.568535 | − | 0.201008i | ||||
\(793\) | − | 8.48528i | − | 0.301321i | ||||||
\(794\) | 38.0000 | 1.34857 | ||||||||
\(795\) | 12.0000 | + | 8.48528i | 0.425596 | + | 0.300942i | ||||
\(796\) | −4.00000 | −0.141776 | ||||||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | −28.0000 | − | 11.3137i | −0.991189 | − | 0.400501i | ||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | 3.00000 | 0.106066 | ||||||||
\(801\) | −6.00000 | − | 16.9706i | −0.212000 | − | 0.599625i | ||||
\(802\) | 24.0000 | 0.847469 | ||||||||
\(803\) | − | 22.6274i | − | 0.798504i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | 0.281963 | ||||||||
\(806\) | −18.0000 | −0.634023 | ||||||||
\(807\) | 18.0000 | − | 25.4558i | 0.633630 | − | 0.896088i | ||||
\(808\) | 9.89949i | 0.348263i | ||||||||
\(809\) | 31.1127i | 1.09386i | 0.837177 | + | 0.546932i | \(0.184204\pi\) | ||||
−0.837177 | + | 0.546932i | \(0.815796\pi\) | |||||||
\(810\) | −8.00000 | − | 9.89949i | −0.281091 | − | 0.347833i | ||||
\(811\) | − | 33.9411i | − | 1.19183i | −0.803046 | − | 0.595917i | \(-0.796789\pi\) | ||
0.803046 | − | 0.595917i | \(-0.203211\pi\) | |||||||
\(812\) | 24.0000 | 0.842235 | ||||||||
\(813\) | −16.0000 | + | 22.6274i | −0.561144 | + | 0.793578i | ||||
\(814\) | 24.0000 | 0.841200 | ||||||||
\(815\) | 28.2843i | 0.990755i | ||||||||
\(816\) | −4.00000 | − | 2.82843i | −0.140028 | − | 0.0990148i | ||||
\(817\) | 2.00000 | + | 8.48528i | 0.0699711 | + | 0.296862i | ||||
\(818\) | 8.48528i | 0.296681i | ||||||||
\(819\) | 48.0000 | − | 16.9706i | 1.67726 | − | 0.592999i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 7.07107i | − | 0.246782i | −0.992358 | − | 0.123391i | \(-0.960623\pi\) | ||
0.992358 | − | 0.123391i | \(-0.0393769\pi\) | |||||||
\(822\) | 20.0000 | + | 14.1421i | 0.697580 | + | 0.493264i | ||||
\(823\) | 32.0000 | 1.11545 | 0.557725 | − | 0.830026i | \(-0.311674\pi\) | ||||
0.557725 | + | 0.830026i | \(0.311674\pi\) | |||||||
\(824\) | − | 12.7279i | − | 0.443398i | ||||||
\(825\) | 24.0000 | + | 16.9706i | 0.835573 | + | 0.590839i | ||||
\(826\) | −48.0000 | −1.67013 | ||||||||
\(827\) | 42.0000 | 1.46048 | 0.730242 | − | 0.683189i | \(-0.239408\pi\) | ||||
0.730242 | + | 0.683189i | \(0.239408\pi\) | |||||||
\(828\) | 4.00000 | − | 1.41421i | 0.139010 | − | 0.0491473i | ||||
\(829\) | 46.6690i | 1.62088i | 0.585820 | + | 0.810442i | \(0.300773\pi\) | ||||
−0.585820 | + | 0.810442i | \(0.699227\pi\) | |||||||
\(830\) | 4.00000 | 0.138842 | ||||||||
\(831\) | −22.0000 | + | 31.1127i | −0.763172 | + | 1.07929i | ||||
\(832\) | − | 4.24264i | − | 0.147087i | ||||||
\(833\) | − | 25.4558i | − | 0.881993i | ||||||
\(834\) | −4.00000 | + | 5.65685i | −0.138509 | + | 0.195881i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −24.0000 | + | 5.65685i | −0.830057 | + | 0.195646i | ||||
\(837\) | −6.00000 | + | 21.2132i | −0.207390 | + | 0.733236i | ||||
\(838\) | 39.5980i | 1.36789i | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | −8.00000 | − | 5.65685i | −0.276026 | − | 0.195180i | ||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 12.7279i | 0.438633i | ||||||||
\(843\) | −12.0000 | + | 16.9706i | −0.413302 | + | 0.584497i | ||||
\(844\) | 8.48528i | 0.292075i | ||||||||
\(845\) | − | 7.07107i | − | 0.243252i | ||||||
\(846\) | 4.00000 | − | 1.41421i | 0.137523 | − | 0.0486217i | ||||
\(847\) | 84.0000 | 2.88627 | ||||||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | 20.0000 | − | 28.2843i | 0.686398 | − | 0.970714i | ||||
\(850\) | − | 8.48528i | − | 0.291043i | ||||||
\(851\) | 6.00000 | 0.205677 | ||||||||
\(852\) | −12.0000 | + | 16.9706i | −0.411113 | + | 0.581402i | ||||
\(853\) | −46.0000 | −1.57501 | −0.787505 | − | 0.616308i | \(-0.788628\pi\) | ||||
−0.787505 | + | 0.616308i | \(0.788628\pi\) | |||||||
\(854\) | −8.00000 | −0.273754 | ||||||||
\(855\) | 10.0000 | + | 15.5563i | 0.341993 | + | 0.532016i | ||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | −54.0000 | −1.84460 | −0.922302 | − | 0.386469i | \(-0.873695\pi\) | ||||
−0.922302 | + | 0.386469i | \(0.873695\pi\) | |||||||
\(858\) | 24.0000 | − | 33.9411i | 0.819346 | − | 1.15873i | ||||
\(859\) | −10.0000 | −0.341196 | −0.170598 | − | 0.985341i | \(-0.554570\pi\) | ||||
−0.170598 | + | 0.985341i | \(0.554570\pi\) | |||||||
\(860\) | 2.82843i | 0.0964486i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | −5.00000 | − | 1.41421i | −0.170103 | − | 0.0481125i | ||||
\(865\) | 8.48528i | 0.288508i | ||||||||
\(866\) | 25.4558i | 0.865025i | ||||||||
\(867\) | 9.00000 | − | 12.7279i | 0.305656 | − | 0.432263i | ||||
\(868\) | 16.9706i | 0.576018i | ||||||||
\(869\) | 24.0000 | 0.814144 | ||||||||
\(870\) | −12.0000 | − | 8.48528i | −0.406838 | − | 0.287678i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.24264i | 0.143674i | ||||||||
\(873\) | 24.0000 | − | 8.48528i | 0.812277 | − | 0.287183i | ||||
\(874\) | −6.00000 | + | 1.41421i | −0.202953 | + | 0.0478365i | ||||
\(875\) | − | 45.2548i | − | 1.52989i | ||||||
\(876\) | −4.00000 | + | 5.65685i | −0.135147 | + | 0.191127i | ||||
\(877\) | 38.1838i | 1.28937i | 0.764447 | + | 0.644687i | \(0.223012\pi\) | ||||
−0.764447 | + | 0.644687i | \(0.776988\pi\) | |||||||
\(878\) | 12.7279i | 0.429547i | ||||||||
\(879\) | −6.00000 | + | 8.48528i | −0.202375 | + | 0.286201i | ||||
\(880\) | −8.00000 | −0.269680 | ||||||||
\(881\) | − | 28.2843i | − | 0.952921i | −0.879196 | − | 0.476461i | \(-0.841919\pi\) | ||
0.879196 | − | 0.476461i | \(-0.158081\pi\) | |||||||
\(882\) | −9.00000 | − | 25.4558i | −0.303046 | − | 0.857143i | ||||
\(883\) | 26.0000 | 0.874970 | 0.437485 | − | 0.899226i | \(-0.355869\pi\) | ||||
0.437485 | + | 0.899226i | \(0.355869\pi\) | |||||||
\(884\) | −12.0000 | −0.403604 | ||||||||
\(885\) | 24.0000 | + | 16.9706i | 0.806751 | + | 0.570459i | ||||
\(886\) | − | 28.2843i | − | 0.950229i | ||||||
\(887\) | 24.0000 | 0.805841 | 0.402921 | − | 0.915235i | \(-0.367995\pi\) | ||||
0.402921 | + | 0.915235i | \(0.367995\pi\) | |||||||
\(888\) | −6.00000 | − | 4.24264i | −0.201347 | − | 0.142374i | ||||
\(889\) | − | 84.8528i | − | 2.84587i | ||||||
\(890\) | 8.48528i | 0.284427i | ||||||||
\(891\) | −32.0000 | − | 39.5980i | −1.07204 | − | 1.32658i | ||||
\(892\) | 4.24264i | 0.142054i | ||||||||
\(893\) | −6.00000 | + | 1.41421i | −0.200782 | + | 0.0473249i | ||||
\(894\) | 14.0000 | + | 9.89949i | 0.468230 | + | 0.331089i | ||||
\(895\) | − | 25.4558i | − | 0.850895i | ||||||
\(896\) | −4.00000 | −0.133631 | ||||||||
\(897\) | 6.00000 | − | 8.48528i | 0.200334 | − | 0.283315i | ||||
\(898\) | −30.0000 | −1.00111 | ||||||||
\(899\) | 25.4558i | 0.849000i | ||||||||
\(900\) | −3.00000 | − | 8.48528i | −0.100000 | − | 0.282843i | ||||
\(901\) | − | 16.9706i | − | 0.565371i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.00000 | + | 11.3137i | −0.266223 | + | 0.376497i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | 18.0000 | 0.598340 | ||||||||
\(906\) | 18.0000 | + | 12.7279i | 0.598010 | + | 0.422857i | ||||
\(907\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(908\) | −18.0000 | −0.597351 | ||||||||
\(909\) | 28.0000 | − | 9.89949i | 0.928701 | − | 0.328346i | ||||
\(910\) | −24.0000 | −0.795592 | ||||||||
\(911\) | 60.0000 | 1.98789 | 0.993944 | − | 0.109885i | \(-0.0350482\pi\) | ||||
0.993944 | + | 0.109885i | \(0.0350482\pi\) | |||||||
\(912\) | 7.00000 | + | 2.82843i | 0.231793 | + | 0.0936586i | ||||
\(913\) | 16.0000 | 0.529523 | ||||||||
\(914\) | −10.0000 | −0.330771 | ||||||||
\(915\) | 4.00000 | + | 2.82843i | 0.132236 | + | 0.0935049i | ||||
\(916\) | 2.00000 | 0.0660819 | ||||||||
\(917\) | 79.1960i | 2.61528i | ||||||||
\(918\) | −4.00000 | + | 14.1421i | −0.132020 | + | 0.466760i | ||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | −2.00000 | −0.0659380 | ||||||||
\(921\) | −24.0000 | − | 16.9706i | −0.790827 | − | 0.559199i | ||||
\(922\) | 1.41421i | 0.0465746i | ||||||||
\(923\) | 50.9117i | 1.67578i | ||||||||
\(924\) | −32.0000 | − | 22.6274i | −1.05272 | − | 0.744387i | ||||
\(925\) | − | 12.7279i | − | 0.418491i | ||||||
\(926\) | 20.0000 | 0.657241 | ||||||||
\(927\) | −36.0000 | + | 12.7279i | −1.18240 | + | 0.418040i | ||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | − | 53.7401i | − | 1.76316i | −0.472038 | − | 0.881578i | \(-0.656482\pi\) | ||
0.472038 | − | 0.881578i | \(-0.343518\pi\) | |||||||
\(930\) | 6.00000 | − | 8.48528i | 0.196748 | − | 0.278243i | ||||
\(931\) | 9.00000 | + | 38.1838i | 0.294963 | + | 1.25142i | ||||
\(932\) | − | 11.3137i | − | 0.370593i | ||||||
\(933\) | 2.00000 | + | 1.41421i | 0.0654771 | + | 0.0462993i | ||||
\(934\) | − | 2.82843i | − | 0.0925490i | ||||||
\(935\) | 22.6274i | 0.739996i | ||||||||
\(936\) | −12.0000 | + | 4.24264i | −0.392232 | + | 0.138675i | ||||
\(937\) | −52.0000 | −1.69877 | −0.849383 | − | 0.527777i | \(-0.823026\pi\) | ||||
−0.849383 | + | 0.527777i | \(0.823026\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.00000 | − | 11.3137i | 0.261070 | − | 0.369209i | ||||
\(940\) | −2.00000 | −0.0652328 | ||||||||
\(941\) | −6.00000 | −0.195594 | −0.0977972 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977972 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(942\) | 14.0000 | − | 19.7990i | 0.456145 | − | 0.645086i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | −8.00000 | + | 28.2843i | −0.260240 | + | 0.920087i | ||||
\(946\) | 11.3137i | 0.367840i | ||||||||
\(947\) | 48.0833i | 1.56250i | 0.624221 | + | 0.781248i | \(0.285417\pi\) | ||||
−0.624221 | + | 0.781248i | \(0.714583\pi\) | |||||||
\(948\) | −6.00000 | − | 4.24264i | −0.194871 | − | 0.137795i | ||||
\(949\) | 16.9706i | 0.550888i | ||||||||
\(950\) | 3.00000 | + | 12.7279i | 0.0973329 | + | 0.412948i | ||||
\(951\) | 18.0000 | − | 25.4558i | 0.583690 | − | 0.825462i | ||||
\(952\) | 11.3137i | 0.366679i | ||||||||
\(953\) | −24.0000 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(954\) | −6.00000 | − | 16.9706i | −0.194257 | − | 0.549442i | ||||
\(955\) | −26.0000 | −0.841340 | ||||||||
\(956\) | − | 15.5563i | − | 0.503128i | ||||||
\(957\) | −48.0000 | − | 33.9411i | −1.55162 | − | 1.09716i | ||||
\(958\) | 9.89949i | 0.319838i | ||||||||
\(959\) | − | 56.5685i | − | 1.82669i | ||||||
\(960\) | 2.00000 | + | 1.41421i | 0.0645497 | + | 0.0456435i | ||||
\(961\) | 13.0000 | 0.419355 | ||||||||
\(962\) | −18.0000 | −0.580343 | ||||||||
\(963\) | 12.0000 | + | 33.9411i | 0.386695 | + | 1.09374i | ||||
\(964\) | − | 8.48528i | − | 0.273293i | ||||||
\(965\) | 12.0000 | 0.386294 | ||||||||
\(966\) | −8.00000 | − | 5.65685i | −0.257396 | − | 0.182006i | ||||
\(967\) | −4.00000 | −0.128631 | −0.0643157 | − | 0.997930i | \(-0.520486\pi\) | ||||
−0.0643157 | + | 0.997930i | \(0.520486\pi\) | |||||||
\(968\) | −21.0000 | −0.674966 | ||||||||
\(969\) | 8.00000 | − | 19.7990i | 0.256997 | − | 0.636035i | ||||
\(970\) | −12.0000 | −0.385297 | ||||||||
\(971\) | −42.0000 | −1.34784 | −0.673922 | − | 0.738802i | \(-0.735392\pi\) | ||||
−0.673922 | + | 0.738802i | \(0.735392\pi\) | |||||||
\(972\) | 1.00000 | + | 15.5563i | 0.0320750 | + | 0.498970i | ||||
\(973\) | 16.0000 | 0.512936 | ||||||||
\(974\) | 12.7279i | 0.407829i | ||||||||
\(975\) | −18.0000 | − | 12.7279i | −0.576461 | − | 0.407620i | ||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 20.0000 | − | 28.2843i | 0.639529 | − | 0.904431i | ||||
\(979\) | 33.9411i | 1.08476i | ||||||||
\(980\) | 12.7279i | 0.406579i | ||||||||
\(981\) | 12.0000 | − | 4.24264i | 0.383131 | − | 0.135457i | ||||
\(982\) | 14.1421i | 0.451294i | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0000 | 0.318626 | ||||||||
\(986\) | 16.9706i | 0.540453i | ||||||||
\(987\) | −8.00000 | − | 5.65685i | −0.254643 | − | 0.180060i | ||||
\(988\) | 18.0000 | − | 4.24264i | 0.572656 | − | 0.134976i | ||||
\(989\) | 2.82843i | 0.0899388i | ||||||||
\(990\) | 8.00000 | + | 22.6274i | 0.254257 | + | 0.719147i | ||||
\(991\) | − | 29.6985i | − | 0.943403i | −0.881758 | − | 0.471702i | \(-0.843640\pi\) | ||
0.881758 | − | 0.471702i | \(-0.156360\pi\) | |||||||
\(992\) | − | 4.24264i | − | 0.134704i | ||||||
\(993\) | −24.0000 | − | 16.9706i | −0.761617 | − | 0.538545i | ||||
\(994\) | 48.0000 | 1.52247 | ||||||||
\(995\) | − | 5.65685i | − | 0.179334i | ||||||
\(996\) | −4.00000 | − | 2.82843i | −0.126745 | − | 0.0896221i | ||||
\(997\) | 62.0000 | 1.96356 | 0.981780 | − | 0.190022i | \(-0.0608559\pi\) | ||||
0.981780 | + | 0.190022i | \(0.0608559\pi\) | |||||||
\(998\) | −10.0000 | −0.316544 | ||||||||
\(999\) | −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 | 114.2.b.d.113.1 | yes | 2 | |
3.2 | odd | 2 | 114.2.b.a.113.1 | ✓ | 2 | ||
4.3 | odd | 2 | 912.2.f.b.113.2 | 2 | |||
12.11 | even | 2 | 912.2.f.d.113.2 | 2 | |||
19.18 | odd | 2 | 114.2.b.a.113.2 | yes | 2 | ||
57.56 | even | 2 | inner | 114.2.b.d.113.2 | yes | 2 | |
76.75 | even | 2 | 912.2.f.d.113.1 | 2 | |||
228.227 | odd | 2 | 912.2.f.b.113.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.b.a.113.1 | ✓ | 2 | 3.2 | odd | 2 | ||
114.2.b.a.113.2 | yes | 2 | 19.18 | odd | 2 | ||
114.2.b.d.113.1 | yes | 2 | 1.1 | even | 1 | trivial | |
114.2.b.d.113.2 | yes | 2 | 57.56 | even | 2 | inner | |
912.2.f.b.113.1 | 2 | 228.227 | odd | 2 | |||
912.2.f.b.113.2 | 2 | 4.3 | odd | 2 | |||
912.2.f.d.113.1 | 2 | 76.75 | even | 2 | |||
912.2.f.d.113.2 | 2 | 12.11 | even | 2 |